| 1 |
|
| 2 | (function() {
|
| 3 | var $, ABS, ADD, ADJ, AND, APPROXRATIO, ARCCOS, ARCCOSH, ARCSIN, ARCSINH, ARCTAN, ARCTANH, ARG, ASSUME_REAL_VARIABLES, ATOMIZE, AUTOEXPAND, BAKE, BESSELJ, BESSELY, BINDING, BINOMIAL, BINOM_check_args, BUF, C1, C2, C3, C4, C5, C6, CACHE_DEBUGS, CACHE_HITSMISS_DEBUGS, CEILING, CHECK, CHOOSE, CIRCEXP, CLEAR, CLEARALL, CLEARPATTERNS, CLOCK, COEFF, COFACTOR, CONDENSE, CONJ, CONS, CONTRACT, COS, COSH, Condense, DEBUG, DEBUG_ABS, DEBUG_ARG, DEBUG_CLOCKFORM, DEBUG_IMAG, DEBUG_IS, DEBUG_POWER, DEBUG_RECT, DECOMP, DEFINT, DEGREE, DENOMINATOR, DERIVATIVE, DET, DET_check_arg, DIM, DIRAC, DIVISORS, DO, DOT, DOUBLE, DRAW, DRAWX, DSOLVE, DoubleLinkedList, E, EIGEN, EIGENVAL, EIGENVEC, EIG_N, EIG_check_arg, EIG_yydd, EIG_yyqq, ENABLE_CACHING, ERF, ERFC, EVAL, EXP, EXPAND, EXPCOS, EXPSIN, Eval, Eval_Eval, Eval_abs, Eval_add, Eval_adj, Eval_and, Eval_approxratio, Eval_arccos, Eval_arccosh, Eval_arcsin, Eval_arcsinh, Eval_arctan, Eval_arctanh, Eval_arg, Eval_besselj, Eval_bessely, Eval_binding, Eval_binomial, Eval_ceiling, Eval_check, Eval_choose, Eval_circexp, Eval_clear, Eval_clearall, Eval_clearpatterns, Eval_clock, Eval_coeff, Eval_cofactor, Eval_condense, Eval_conj, Eval_cons, Eval_contract, Eval_cos, Eval_cosh, Eval_decomp, Eval_defint, Eval_degree, Eval_denominator, Eval_derivative, Eval_det, Eval_dim, Eval_dirac, Eval_divisors, Eval_do, Eval_dsolve, Eval_eigen, Eval_eigenval, Eval_eigenvec, Eval_erf, Eval_erfc, Eval_exp, Eval_expand, Eval_expcos, Eval_expsin, Eval_factor, Eval_factorial, Eval_factorpoly, Eval_filter, Eval_float, Eval_floor, Eval_for, Eval_function_reference, Eval_gamma, Eval_gcd, Eval_hermite, Eval_hilbert, Eval_imag, Eval_index, Eval_inner, Eval_integral, Eval_inv, Eval_invg, Eval_isinteger, Eval_isprime, Eval_laguerre, Eval_lcm, Eval_leading, Eval_legendre, Eval_log, Eval_lookup, Eval_mod, Eval_multiply, Eval_noexpand, Eval_not, Eval_nroots, Eval_number, Eval_numerator, Eval_operator, Eval_or, Eval_outer, Eval_pattern, Eval_patternsinfo, Eval_polar, Eval_power, Eval_predicate, Eval_prime, Eval_print, Eval_print2dascii, Eval_printfull, Eval_printlatex, Eval_printlist, Eval_printplain, Eval_product, Eval_quote, Eval_quotient, Eval_rank, Eval_rationalize, Eval_real, Eval_rect, Eval_roots, Eval_round, Eval_setq, Eval_sgn, Eval_shape, Eval_silentpattern, Eval_simfac, Eval_simplify, Eval_sin, Eval_sinh, Eval_sqrt, Eval_stop, Eval_subst, Eval_sum, Eval_sym, Eval_symbolsinfo, Eval_tan, Eval_tanh, Eval_taylor, Eval_tensor, Eval_test, Eval_testeq, Eval_testge, Eval_testgt, Eval_testle, Eval_testlt, Eval_transpose, Eval_unit, Eval_user_function, Eval_zero, Evalpoly, FACTOR, FACTORIAL, FACTORPOLY, FILTER, FLOATF, FLOOR, FOR, FUNCTION, Find, GAMMA, GCD, HERMITE, HILBERT, IMAG, INDEX, INNER, INTEGRAL, INV, INVG, INV_check_arg, INV_decomp, ISINTEGER, ISPRIME, LAGUERRE, LAST, LAST_2DASCII_PRINT, LAST_FULL_PRINT, LAST_LATEX_PRINT, LAST_LIST_PRINT, LAST_PLAIN_PRINT, LAST_PRINT, LCM, LEADING, LEGENDRE, LOG, LOOKUP, LRUCache, M, MAXDIM, MAXPRIMETAB, MAX_CONSECUTIVE_APPLICATIONS_OF_ALL_RULES, MAX_CONSECUTIVE_APPLICATIONS_OF_SINGLE_RULE, MAX_PROGRAM_SIZE, MEQUAL, METAA, METAB, METAX, MLENGTH, MOD, MSIGN, MULTIPLY, MZERO, N, NIL, NOT, NROOTS, NROOTS_ABS, NROOTS_DELTA, NROOTS_EPSILON, NROOTS_RANDOM, NROOTS_YMAX, NROOTS_divpoly, NSYM, NUM, NUMBER, NUMERATOR, OPERATOR, OR, OUTER, PATTERN, PATTERNSINFO, PI, POLAR, POWER, PRIME, PRINT, PRINT2DASCII, PRINTFULL, PRINTLATEX, PRINTLIST, PRINTMODE_2DASCII, PRINTMODE_FULL, PRINTMODE_LATEX, PRINTMODE_LIST, PRINTMODE_PLAIN, PRINTOUTRESULT, PRINTPLAIN, PRINT_LEAVE_E_ALONE, PRINT_LEAVE_X_ALONE, PRODUCT, QUOTE, QUOTIENT, RANK, RATIONALIZE, REAL, ROOTS, ROUND, SECRETX, SELFTEST, SETQ, SGN, SHAPE, SILENTPATTERN, SIMPLIFY, SIN, SINH, SPACE_BETWEEN_COLUMNS, SPACE_BETWEEN_ROWS, SQRT, STOP, STR, SUBST, SUM, SYM, SYMBOLSINFO, SYMBOL_A, SYMBOL_A_UNDERSCORE, SYMBOL_B, SYMBOL_B_UNDERSCORE, SYMBOL_C, SYMBOL_D, SYMBOL_I, SYMBOL_IDENTITY_MATRIX, SYMBOL_J, SYMBOL_N, SYMBOL_R, SYMBOL_S, SYMBOL_T, SYMBOL_X, SYMBOL_X_UNDERSCORE, SYMBOL_Y, SYMBOL_Z, TAN, TANH, TAYLOR, TENSOR, TEST, TESTEQ, TESTGE, TESTGT, TESTLE, TESTLT, TIMING_DEBUGS, TOS, TRACE, TRANSPOSE, T_DOUBLE, T_EQ, T_FUNCTION, T_GTEQ, T_INTEGER, T_LTEQ, T_NEQ, T_NEWLINE, T_QUOTASSIGN, T_STRING, T_SYMBOL, U, UNIT, USR_SYMBOLS, VERSION, YMAX, YYE, YYRECT, ZERO, __emit_char, __emit_str, __factor_add, __factorial, __is_negative, __is_radical_number, __lcm, __legendre, __legendre2, __legendre3, __normalize_radical_factors, __rationalize_tensor, _print, abs, absValFloat, absval, absval_tensor, add, addSymbolLeftOfAssignment, addSymbolRightOfAssignment, add_all, add_factor_to_accumulator, add_numbers, add_terms, addf, adj, alloc_tensor, allocatedId, any_denominators, approxAll, approxLogs, approxLogsOfRationals, approxOneRatioOnly, approxRadicals, approxRadicalsOfRationals, approxRationalsOfLogs, approxRationalsOfPowersOfE, approxRationalsOfPowersOfPI, approxRationalsOfRadicals, approxSineOfRationalMultiplesOfPI, approxSineOfRationals, approxTrigonometric, approx_just_an_integer, approx_logarithmsOfRationals, approx_nothingUseful, approx_radicalOfRatio, approx_ratioOfRadical, approx_rationalOfE, approx_rationalOfPi, approx_rationalsOfLogarithms, approx_sine_of_pi_times_rational, approx_sine_of_rational, approxratioRecursive, arccos, arccosh, arcsin, arcsinh, arctan, arctanh, arg, arglist, assignmentFound, avoidCalculatingPowersIntoArctans, bake, bake_poly, bake_poly_term, besselj, bessely, bigInt, bignum_factorial, bignum_float, bignum_power_number, bignum_scan_float, bignum_scan_integer, bignum_truncate, binding, binomial, buffer, build_tensor, caaddr, caadr, caar, cacheMissPenalty, cached_findDependenciesInScript, cached_runs, cadaddr, cadadr, cadar, caddaddr, caddadr, caddar, caddddr, cadddr, caddr, cadr, called_from_Algebra_block, car, cdaddr, cdadr, cdar, cddaddr, cddar, cdddaddr, cddddr, cdddr, cddr, cdr, ceiling, chainOfUserSymbolsNotFunctionsBeingEvaluated, charTabIndex, chartab, checkFloatHasWorkedOutCompletely, check_esc_flag, check_stack, check_tensor_dimensions, choose, choose_check_args, circexp, clearAlgebraEnvironment, clearRenamedVariablesToAvoidBindingToExternalScope, clear_symbols, clear_term, clearall, clockform, cmpGlyphs, cmp_args, cmp_expr, cmp_terms, cmp_terms_count, codeGen, coeff, cofactor, collectLatexStringFromReturnValue, collectUserSymbols, combine_factors, combine_gammas, combine_terms, compareState, compare_numbers, compare_rationals, compare_tensors, compatible, computeDependenciesFromAlgebra, computeResultsAndJavaScriptFromAlgebra, compute_fa, conjugate, cons, consCount, contract, convert_bignum_to_double, convert_rational_to_double, copy_tensor, cosine, cosine_of_angle, cosine_of_angle_sum, count, countOccurrencesOfSymbol, count_denominators, counter, countsize, d_scalar_scalar, d_scalar_scalar_1, d_scalar_tensor, d_tensor_scalar, d_tensor_tensor, dabs, darccos, darccosh, darcsin, darcsinh, darctan, darctanh, dbesselj0, dbesseljn, dbessely0, dbesselyn, dcos, dcosh, dd, decomp, decomp_product, decomp_sum, defineSomeHandyConstants, define_user_function, defn, defn_str, degree, denominator, derf, derfc, derivative, derivative_of_integral, det, determinant, detg, dfunction, dhermite, dirac, disableCaching, display, display_flag, displaychar, divide, divide_numbers, divisors, divisors_onstack, divpoly, dlog, do_clearPatterns, do_clearall, do_simplify_nested_radicals, dontCreateNewRadicalsInDenominatorWhenEvalingMultiplication, dotprod_unicode, doubleToReasonableString, dpow, dpower, dproduct, draw_flag, draw_stop_return, dsgn, dsin, dsinh, dsum, dtan, dtanh, dupl, eigen, elelmIndex, elem, emit_denominator, emit_denominators, emit_expr, emit_factor, emit_factorial_function, emit_flat_tensor, emit_fraction, emit_function, emit_index_function, emit_multiply, emit_number, emit_numerators, emit_numerical_fraction, emit_power, emit_string, emit_subexpr, emit_symbol, emit_tensor, emit_tensor_inner, emit_term, emit_top_expr, emit_unsigned_expr, emit_x, enableCaching, environment_printmode, equal, equaln, equalq, erfc, errorMessage, esc_flag, evaluatingAsFloats, evaluatingPolar, exec, expand, expand_get_A, expand_get_AF, expand_get_B, expand_get_C, expand_get_CF, expand_tensor, expanding, expcos, exponential, expr_level, expsin, f1, f10, f2, f3, f4, f5, f9, f_equals_a, factor, factor_a, factor_again, factor_b, factor_number, factor_small_number, factor_term, factorial, factorpoly, factors, factpoly_expo, fill_buf, filter, filter_main, filter_sum, filter_tensor, findDependenciesInScript, findPossibleClockForm, findPossibleExponentialForm, findroot, fixed_top_level_eval, fixup_fraction, fixup_power, flag, floatToRatioRoutine, fmt_index, fmt_level, fmt_x, frame, freeze, functionInvokationsScanningStack, gamma, gamma_of_sum, gammaf, gcd, gcd_expr, gcd_expr_expr, gcd_factor_term, gcd_main, gcd_numbers, gcd_term_factor, gcd_term_term, gen, getSimpleRoots, getStateHash, get_binding, get_factor_from_complex_root, get_factor_from_real_root, get_innerprod_factors, get_next_token, get_printname, get_size, get_token, getdisplaystr, glyph, gp, guess, hasImaginaryCoeff, hasNegativeRationalExponent, hermite, hilbert, i1, imag, imaginaryunit, index_function, init, initNRoots, inited, inner, inner_f, input_str, integral, integral_of_form, integral_of_product, integral_of_sum, inv, inverse, invert_number, invg, isSimpleRoot, isSymbolLeftOfAssignment, isSymbolReclaimable, is_denominator, is_factor, is_small_integer, is_square_matrix, is_usr_symbol, isadd, isalnumorunderscore, isalpha, isalphaOrUnderscore, iscomplexnumber, iscomplexnumberdouble, iscons, isdenominator, isdigit, isdouble, iseveninteger, isfactor, isfactorial, isfloating, isfraction, isidentitymatrix, isimaginarynumber, isimaginarynumberdouble, isimaginaryunit, isinnerordot, isinteger, isintegerfactor, isintegerorintegerfloat, isinv, iskeyword, isminusone, isminusoneoversqrttwo, isminusoneovertwo, ismultiply, isnegative, isnegativenumber, isnegativeterm, isnonnegativeinteger, isnpi, isnum, isnumberoneoversomething, isnumerictensor, isone, isoneover, isoneoversqrttwo, isoneovertwo, isplusone, isplustwo, ispoly, ispoly_expr, ispoly_factor, ispoly_term, isposint, ispositivenumber, ispower, isquarterturn, isrational, isspace, isstr, issymbol, issymbolic, istensor, istranspose, isunderscore, iszero, itab, j1, laguerre, laguerre2, lastFoundSymbol, latexErrorSign, lcm, leading, legendre, length, lessp, level, list, listLength, logarithm, logbuf, lookupsTotal, lu_decomp, madd, makePositive, makeSignSameAs, mask, mcmp, mcmpint, mdiv, mdivrem, meta_mode, mgcd, mini_solve, mint, mmod, mmul, mod, monic, move, moveTos, mp_clr_bit, mp_denominator, mp_numerator, mp_set_bit, mpow, mprime, mroot, mshiftright, msub, mtotal, multinomial_sum, multiply, multiply_all, multiply_all_noexpand, multiply_consecutive_constants, multiply_denominators, multiply_denominators_factor, multiply_denominators_term, multiply_noexpand, multiply_numbers, n_factor_number, negate, negate_expand, negate_noexpand, negate_number, new_string, newline_flag, nil_symbols, normaliseDots, normalisedCoeff, normalize_angle, nroots_a, nroots_b, nroots_c, nroots_df, nroots_dx, nroots_fa, nroots_fb, nroots_x, nroots_y, nterms, nthCadr, numerator, numericRootOfPolynomial, o, one, oneElement, one_as_double, out_buf, out_count, out_of_memory, outer, p0, p1, p2, p3, p4, p5, p6, p7, p8, p9, parse, parse_internal, parse_p1, parse_p2, parse_time_simplifications, partition, patternHasBeenFound, patternsinfo, peek, performing_roots, polar, polarRectAMinusOneBase, polycoeff, polyform, pop, pop_double, pop_frame, pop_integer, power, power_str, power_sum, power_tensor, predefinedSymbolsInGlobalScope_doNotTrackInDependencies, prime, primetab, print2dascii, printMode, print_ABS_latex, print_ARCCOS_codegen, print_ARCSIN_codegen, print_ARCTAN_codegen, print_BINOMIAL_latex, print_COS_codegen, print_DEFINT_latex, print_DOT_codegen, print_DOT_latex, print_DO_codegen, print_FOR_codegen, print_INV_codegen, print_INV_latex, print_PRODUCT_codegen, print_PRODUCT_latex, print_SETQ_codegen, print_SIN_codegen, print_SQRT_latex, print_SUM_codegen, print_SUM_latex, print_TAN_codegen, print_TESTEQ_latex, print_TESTGE_latex, print_TESTGT_latex, print_TESTLE_latex, print_TESTLT_latex, print_TEST_codegen, print_TEST_latex, print_TRANSPOSE_codegen, print_TRANSPOSE_latex, print_UNIT_codegen, print_a_over_b, print_base, print_base_of_denom, print_char, print_denom, print_double, print_expo_of_denom, print_exponent, print_expr, print_factor, print_factorial_function, print_glyphs, print_index_function, print_list, print_multiply_sign, print_number, print_power, print_str, print_subexpr, print_tensor, print_tensor_inner, print_tensor_inner_latex, print_tensor_latex, print_term, printchar, printchar_nowrap, printline, program_buf, promote_tensor, push, pushTryNotToDuplicate, push_cars, push_double, push_factor, push_frame, push_identity_matrix, push_integer, push_rational, push_symbol, push_term_factors, push_terms, push_zero_matrix, qadd, qdiv, qmul, qpow, qpowf, quickfactor, quickpower, rational, rationalize, rationalize_coefficients, real, reciprocate, rect, recursionLevelNestedRadicalsRemoval, recursiveDependencies, ref, ref1, rememberPrint, remove_negative_exponents, resetCache, resetCacheHitMissCounts, reset_after_error, restore, restoreMetaBindings, rewrite_args, rewrite_args_tensor, roots, roots2, roots3, run, runUserDefinedSimplifications, save, saveMetaBindings, scalar_times_tensor, scan, scan_error, scan_expression, scan_factor, scan_function_call_with_function_name, scan_function_call_without_function_name, scan_index, scan_meta, scan_power, scan_relation, scan_stmt, scan_str, scan_string, scan_subexpr, scan_symbol, scan_tensor, scan_term, scanned, scanningParameters, setM, setSignTo, set_binding, set_component, setq_indexed, sfac_product, sfac_product_f, sgn, shape, show_power_debug, sign, sign_of_term, simfac, simfac_term, simpleComplexityMeasure, simplify, simplifyForCodeGeneration, simplify_1_in_products, simplify_main, simplify_nested_radicals, simplify_polar, simplify_polarRect, simplify_rectToClock, simplify_tensor, simplify_trig, simplifyfactorials, sine, sine_of_angle, sine_of_angle_sum, skipRootVariableToBeSolved, sort_stack, square, ssqrt, stack, stackAddsCount, std_symbol, step, step2, stop, strcmp, stringsEmittedByUserPrintouts, subf, subst, subtract, subtract_numbers, swap, symbol, symbolsDependencies, symbolsHavingReassignments, symbolsInExpressionsWithoutAssignments, symbolsLeftOfAssignment, symbolsRightOfAssignment, symbolsinfo, symnum, symtab, take_care_of_nested_radicals, tangent, taylor, tensor, tensor_plus_tensor, tensor_times_scalar, testApprox, test_flag, text_metric, theRandom, token, token_buf, token_str, top, top_level_eval, tos, totalAllCachesHits, totalAllCachesMisses, transform, transpose, transpose_unicode, trigmode, trivial_divide, try_kth_prime, turnErrorMessageToLatex, ucmp, unfreeze, unique, unique_f, update_token_buf, userSimplificationsInListForm, userSimplificationsInStringForm, usr_symbol, verbosing, version, will_be_displayed_as_fraction, ybinomial, ycosh, ydirac, yerf, yerfc, yfloor, yindex, yround, ysinh, yyarg, yybesselj, yybessely, yyceiling, yycondense, yycontract, yycosh, yydegree, yydetg, yydivpoly, yyerf, yyerfc, yyexpand, yyfactorpoly, yyfloat, yyfloor, yyhermite, yyhermite2, yyinvg, yylcm, yylog, yymultiply, yyouter, yypower, yyrationalize, yyround, yysgn, yysimfac, yysinh, yytangent, zero, zzfloat,
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| 4 | slice = [].slice;
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| 5 |
|
| 6 | bigInt = require('big-integer');
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| 7 |
|
| 8 | version = "1.1.1";
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| 9 |
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| 10 | SELFTEST = 1;
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| 11 |
|
| 12 | NSYM = 1000;
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| 13 |
|
| 14 | DEBUG = false;
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| 15 |
|
| 16 | PRINTOUTRESULT = false;
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| 17 |
|
| 18 | PRINTMODE_LATEX = "PRINTMODE_LATEX";
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| 19 |
|
| 20 | PRINTMODE_2DASCII = "PRINTMODE_2DASCII";
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| 21 |
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| 22 | PRINTMODE_FULL = "PRINTMODE_FULL";
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| 23 |
|
| 24 | PRINTMODE_PLAIN = "PRINTMODE_PLAIN";
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| 25 |
|
| 26 | PRINTMODE_LIST = "PRINTMODE_LIST";
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| 27 |
|
| 28 | environment_printmode = PRINTMODE_PLAIN;
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| 29 |
|
| 30 | printMode = PRINTMODE_PLAIN;
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| 31 |
|
| 32 | dontCreateNewRadicalsInDenominatorWhenEvalingMultiplication = true;
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| 33 |
|
| 34 | recursionLevelNestedRadicalsRemoval = 0;
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| 35 |
|
| 36 | do_simplify_nested_radicals = true;
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| 37 |
|
| 38 | avoidCalculatingPowersIntoArctans = true;
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| 39 |
|
| 40 | rational = (function() {
|
| 41 | function rational() {}
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| 42 |
|
| 43 | rational.prototype.a = null;
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| 44 |
|
| 45 | rational.prototype.b = null;
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| 46 |
|
| 47 | return rational;
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| 48 |
|
| 49 | })();
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| 50 |
|
| 51 | U = (function() {
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| 52 | U.prototype.cons = null;
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| 53 |
|
| 54 | U.prototype.printname = "";
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| 55 |
|
| 56 | U.prototype.str = "";
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| 57 |
|
| 58 | U.prototype.tensor = null;
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| 59 |
|
| 60 | U.prototype.q = null;
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| 61 |
|
| 62 | U.prototype.d = 0.0;
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| 63 |
|
| 64 | U.prototype.k = 0;
|
| 65 |
|
| 66 | U.prototype.tag = 0;
|
| 67 |
|
| 68 | U.prototype.toString = function() {
|
| 69 | return print_expr(this);
|
| 70 | };
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| 71 |
|
| 72 | U.prototype.toLatexString = function() {
|
| 73 | return collectLatexStringFromReturnValue(this);
|
| 74 | };
|
| 75 |
|
| 76 | function U() {
|
| 77 | this.cons = {};
|
| 78 | this.cons.car = null;
|
| 79 | this.cons.cdr = null;
|
| 80 | this.q = new rational();
|
| 81 | }
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| 82 |
|
| 83 | return U;
|
| 84 |
|
| 85 | })();
|
| 86 |
|
| 87 | errorMessage = "";
|
| 88 |
|
| 89 | CONS = 0;
|
| 90 |
|
| 91 | NUM = 1;
|
| 92 |
|
| 93 | DOUBLE = 2;
|
| 94 |
|
| 95 | STR = 3;
|
| 96 |
|
| 97 | TENSOR = 4;
|
| 98 |
|
| 99 | SYM = 5;
|
| 100 |
|
| 101 | counter = 0;
|
| 102 |
|
| 103 | ABS = counter++;
|
| 104 |
|
| 105 | ADD = counter++;
|
| 106 |
|
| 107 | ADJ = counter++;
|
| 108 |
|
| 109 | AND = counter++;
|
| 110 |
|
| 111 | APPROXRATIO = counter++;
|
| 112 |
|
| 113 | ARCCOS = counter++;
|
| 114 |
|
| 115 | ARCCOSH = counter++;
|
| 116 |
|
| 117 | ARCSIN = counter++;
|
| 118 |
|
| 119 | ARCSINH = counter++;
|
| 120 |
|
| 121 | ARCTAN = counter++;
|
| 122 |
|
| 123 | ARCTANH = counter++;
|
| 124 |
|
| 125 | ARG = counter++;
|
| 126 |
|
| 127 | ATOMIZE = counter++;
|
| 128 |
|
| 129 | BESSELJ = counter++;
|
| 130 |
|
| 131 | BESSELY = counter++;
|
| 132 |
|
| 133 | BINDING = counter++;
|
| 134 |
|
| 135 | BINOMIAL = counter++;
|
| 136 |
|
| 137 | CEILING = counter++;
|
| 138 |
|
| 139 | CHECK = counter++;
|
| 140 |
|
| 141 | CHOOSE = counter++;
|
| 142 |
|
| 143 | CIRCEXP = counter++;
|
| 144 |
|
| 145 | CLEAR = counter++;
|
| 146 |
|
| 147 | CLEARALL = counter++;
|
| 148 |
|
| 149 | CLEARPATTERNS = counter++;
|
| 150 |
|
| 151 | CLOCK = counter++;
|
| 152 |
|
| 153 | COEFF = counter++;
|
| 154 |
|
| 155 | COFACTOR = counter++;
|
| 156 |
|
| 157 | CONDENSE = counter++;
|
| 158 |
|
| 159 | CONJ = counter++;
|
| 160 |
|
| 161 | CONTRACT = counter++;
|
| 162 |
|
| 163 | COS = counter++;
|
| 164 |
|
| 165 | COSH = counter++;
|
| 166 |
|
| 167 | DECOMP = counter++;
|
| 168 |
|
| 169 | DEFINT = counter++;
|
| 170 |
|
| 171 | DEGREE = counter++;
|
| 172 |
|
| 173 | DENOMINATOR = counter++;
|
| 174 |
|
| 175 | DERIVATIVE = counter++;
|
| 176 |
|
| 177 | DET = counter++;
|
| 178 |
|
| 179 | DIM = counter++;
|
| 180 |
|
| 181 | DIRAC = counter++;
|
| 182 |
|
| 183 | DIVISORS = counter++;
|
| 184 |
|
| 185 | DO = counter++;
|
| 186 |
|
| 187 | DOT = counter++;
|
| 188 |
|
| 189 | DRAW = counter++;
|
| 190 |
|
| 191 | DSOLVE = counter++;
|
| 192 |
|
| 193 | EIGEN = counter++;
|
| 194 |
|
| 195 | EIGENVAL = counter++;
|
| 196 |
|
| 197 | EIGENVEC = counter++;
|
| 198 |
|
| 199 | ERF = counter++;
|
| 200 |
|
| 201 | ERFC = counter++;
|
| 202 |
|
| 203 | EVAL = counter++;
|
| 204 |
|
| 205 | EXP = counter++;
|
| 206 |
|
| 207 | EXPAND = counter++;
|
| 208 |
|
| 209 | EXPCOS = counter++;
|
| 210 |
|
| 211 | EXPSIN = counter++;
|
| 212 |
|
| 213 | FACTOR = counter++;
|
| 214 |
|
| 215 | FACTORIAL = counter++;
|
| 216 |
|
| 217 | FACTORPOLY = counter++;
|
| 218 |
|
| 219 | FILTER = counter++;
|
| 220 |
|
| 221 | FLOATF = counter++;
|
| 222 |
|
| 223 | FLOOR = counter++;
|
| 224 |
|
| 225 | FOR = counter++;
|
| 226 |
|
| 227 | FUNCTION = counter++;
|
| 228 |
|
| 229 | GAMMA = counter++;
|
| 230 |
|
| 231 | GCD = counter++;
|
| 232 |
|
| 233 | HERMITE = counter++;
|
| 234 |
|
| 235 | HILBERT = counter++;
|
| 236 |
|
| 237 | IMAG = counter++;
|
| 238 |
|
| 239 | INDEX = counter++;
|
| 240 |
|
| 241 | INNER = counter++;
|
| 242 |
|
| 243 | INTEGRAL = counter++;
|
| 244 |
|
| 245 | INV = counter++;
|
| 246 |
|
| 247 | INVG = counter++;
|
| 248 |
|
| 249 | ISINTEGER = counter++;
|
| 250 |
|
| 251 | ISPRIME = counter++;
|
| 252 |
|
| 253 | LAGUERRE = counter++;
|
| 254 |
|
| 255 | LCM = counter++;
|
| 256 |
|
| 257 | LEADING = counter++;
|
| 258 |
|
| 259 | LEGENDRE = counter++;
|
| 260 |
|
| 261 | LOG = counter++;
|
| 262 |
|
| 263 | LOOKUP = counter++;
|
| 264 |
|
| 265 | MOD = counter++;
|
| 266 |
|
| 267 | MULTIPLY = counter++;
|
| 268 |
|
| 269 | NOT = counter++;
|
| 270 |
|
| 271 | NROOTS = counter++;
|
| 272 |
|
| 273 | NUMBER = counter++;
|
| 274 |
|
| 275 | NUMERATOR = counter++;
|
| 276 |
|
| 277 | OPERATOR = counter++;
|
| 278 |
|
| 279 | OR = counter++;
|
| 280 |
|
| 281 | OUTER = counter++;
|
| 282 |
|
| 283 | PATTERN = counter++;
|
| 284 |
|
| 285 | PATTERNSINFO = counter++;
|
| 286 |
|
| 287 | POLAR = counter++;
|
| 288 |
|
| 289 | POWER = counter++;
|
| 290 |
|
| 291 | PRIME = counter++;
|
| 292 |
|
| 293 | PRINT_LEAVE_E_ALONE = counter++;
|
| 294 |
|
| 295 | PRINT_LEAVE_X_ALONE = counter++;
|
| 296 |
|
| 297 | PRINT = counter++;
|
| 298 |
|
| 299 | PRINT2DASCII = counter++;
|
| 300 |
|
| 301 | PRINTFULL = counter++;
|
| 302 |
|
| 303 | PRINTLATEX = counter++;
|
| 304 |
|
| 305 | PRINTLIST = counter++;
|
| 306 |
|
| 307 | PRINTPLAIN = counter++;
|
| 308 |
|
| 309 | PRODUCT = counter++;
|
| 310 |
|
| 311 | QUOTE = counter++;
|
| 312 |
|
| 313 | QUOTIENT = counter++;
|
| 314 |
|
| 315 | RANK = counter++;
|
| 316 |
|
| 317 | RATIONALIZE = counter++;
|
| 318 |
|
| 319 | REAL = counter++;
|
| 320 |
|
| 321 | ROUND = counter++;
|
| 322 |
|
| 323 | YYRECT = counter++;
|
| 324 |
|
| 325 | ROOTS = counter++;
|
| 326 |
|
| 327 | SETQ = counter++;
|
| 328 |
|
| 329 | SGN = counter++;
|
| 330 |
|
| 331 | SILENTPATTERN = counter++;
|
| 332 |
|
| 333 | SIMPLIFY = counter++;
|
| 334 |
|
| 335 | SIN = counter++;
|
| 336 |
|
| 337 | SINH = counter++;
|
| 338 |
|
| 339 | SHAPE = counter++;
|
| 340 |
|
| 341 | SQRT = counter++;
|
| 342 |
|
| 343 | STOP = counter++;
|
| 344 |
|
| 345 | SUBST = counter++;
|
| 346 |
|
| 347 | SUM = counter++;
|
| 348 |
|
| 349 | SYMBOLSINFO = counter++;
|
| 350 |
|
| 351 | TAN = counter++;
|
| 352 |
|
| 353 | TANH = counter++;
|
| 354 |
|
| 355 | TAYLOR = counter++;
|
| 356 |
|
| 357 | TEST = counter++;
|
| 358 |
|
| 359 | TESTEQ = counter++;
|
| 360 |
|
| 361 | TESTGE = counter++;
|
| 362 |
|
| 363 | TESTGT = counter++;
|
| 364 |
|
| 365 | TESTLE = counter++;
|
| 366 |
|
| 367 | TESTLT = counter++;
|
| 368 |
|
| 369 | TRANSPOSE = counter++;
|
| 370 |
|
| 371 | UNIT = counter++;
|
| 372 |
|
| 373 | ZERO = counter++;
|
| 374 |
|
| 375 | NIL = counter++;
|
| 376 |
|
| 377 | LAST = counter++;
|
| 378 |
|
| 379 | LAST_PRINT = counter++;
|
| 380 |
|
| 381 | LAST_2DASCII_PRINT = counter++;
|
| 382 |
|
| 383 | LAST_FULL_PRINT = counter++;
|
| 384 |
|
| 385 | LAST_LATEX_PRINT = counter++;
|
| 386 |
|
| 387 | LAST_LIST_PRINT = counter++;
|
| 388 |
|
| 389 | LAST_PLAIN_PRINT = counter++;
|
| 390 |
|
| 391 | AUTOEXPAND = counter++;
|
| 392 |
|
| 393 | BAKE = counter++;
|
| 394 |
|
| 395 | ASSUME_REAL_VARIABLES = counter++;
|
| 396 |
|
| 397 | TRACE = counter++;
|
| 398 |
|
| 399 | YYE = counter++;
|
| 400 |
|
| 401 | DRAWX = counter++;
|
| 402 |
|
| 403 | METAA = counter++;
|
| 404 |
|
| 405 | METAB = counter++;
|
| 406 |
|
| 407 | METAX = counter++;
|
| 408 |
|
| 409 | SECRETX = counter++;
|
| 410 |
|
| 411 | VERSION = counter++;
|
| 412 |
|
| 413 | PI = counter++;
|
| 414 |
|
| 415 | SYMBOL_A = counter++;
|
| 416 |
|
| 417 | SYMBOL_B = counter++;
|
| 418 |
|
| 419 | SYMBOL_C = counter++;
|
| 420 |
|
| 421 | SYMBOL_D = counter++;
|
| 422 |
|
| 423 | SYMBOL_I = counter++;
|
| 424 |
|
| 425 | SYMBOL_J = counter++;
|
| 426 |
|
| 427 | SYMBOL_N = counter++;
|
| 428 |
|
| 429 | SYMBOL_R = counter++;
|
| 430 |
|
| 431 | SYMBOL_S = counter++;
|
| 432 |
|
| 433 | SYMBOL_T = counter++;
|
| 434 |
|
| 435 | SYMBOL_X = counter++;
|
| 436 |
|
| 437 | SYMBOL_Y = counter++;
|
| 438 |
|
| 439 | SYMBOL_Z = counter++;
|
| 440 |
|
| 441 | SYMBOL_IDENTITY_MATRIX = counter++;
|
| 442 |
|
| 443 | SYMBOL_A_UNDERSCORE = counter++;
|
| 444 |
|
| 445 | SYMBOL_B_UNDERSCORE = counter++;
|
| 446 |
|
| 447 | SYMBOL_X_UNDERSCORE = counter++;
|
| 448 |
|
| 449 | C1 = counter++;
|
| 450 |
|
| 451 | C2 = counter++;
|
| 452 |
|
| 453 | C3 = counter++;
|
| 454 |
|
| 455 | C4 = counter++;
|
| 456 |
|
| 457 | C5 = counter++;
|
| 458 |
|
| 459 | C6 = counter++;
|
| 460 |
|
| 461 | USR_SYMBOLS = counter++;
|
| 462 |
|
| 463 | E = YYE;
|
| 464 |
|
| 465 | TOS = 100000;
|
| 466 |
|
| 467 | BUF = 10000;
|
| 468 |
|
| 469 | MAX_PROGRAM_SIZE = 100001;
|
| 470 |
|
| 471 | MAXPRIMETAB = 10000;
|
| 472 |
|
| 473 | MAX_CONSECUTIVE_APPLICATIONS_OF_ALL_RULES = 5;
|
| 474 |
|
| 475 | MAX_CONSECUTIVE_APPLICATIONS_OF_SINGLE_RULE = 10;
|
| 476 |
|
| 477 | ENABLE_CACHING = true;
|
| 478 |
|
| 479 | cached_runs = null;
|
| 480 |
|
| 481 | cached_findDependenciesInScript = null;
|
| 482 |
|
| 483 | MAXDIM = 24;
|
| 484 |
|
| 485 | symbolsDependencies = {};
|
| 486 |
|
| 487 | symbolsHavingReassignments = [];
|
| 488 |
|
| 489 | symbolsInExpressionsWithoutAssignments = [];
|
| 490 |
|
| 491 | patternHasBeenFound = false;
|
| 492 |
|
| 493 | predefinedSymbolsInGlobalScope_doNotTrackInDependencies = ["rationalize", "abs", "e", "i", "pi", "sin", "ceiling", "cos", "roots", "integral", "derivative", "defint", "sqrt", "eig", "cov", "deig", "dcov", "float", "floor", "product", "root", "round", "sum", "test", "unit"];
|
| 494 |
|
| 495 | parse_time_simplifications = true;
|
| 496 |
|
| 497 | chainOfUserSymbolsNotFunctionsBeingEvaluated = [];
|
| 498 |
|
| 499 | stringsEmittedByUserPrintouts = "";
|
| 500 |
|
| 501 | called_from_Algebra_block = false;
|
| 502 |
|
| 503 | tensor = (function() {
|
| 504 | tensor.prototype.ndim = 0;
|
| 505 |
|
| 506 | tensor.prototype.dim = null;
|
| 507 |
|
| 508 | tensor.prototype.nelem = 0;
|
| 509 |
|
| 510 | tensor.prototype.elem = null;
|
| 511 |
|
| 512 | function tensor() {
|
| 513 | this.dim = (function() {
|
| 514 | var o, ref, results;
|
| 515 | results = [];
|
| 516 | for (o = 0, ref = MAXDIM; 0 <= ref ? o <= ref : o >= ref; 0 <= ref ? o++ : o--) {
|
| 517 | results.push(0);
|
| 518 | }
|
| 519 | return results;
|
| 520 | })();
|
| 521 | this.elem = [];
|
| 522 | }
|
| 523 |
|
| 524 | return tensor;
|
| 525 |
|
| 526 | })();
|
| 527 |
|
| 528 | display = (function() {
|
| 529 | function display() {}
|
| 530 |
|
| 531 | display.prototype.h = 0;
|
| 532 |
|
| 533 | display.prototype.w = 0;
|
| 534 |
|
| 535 | display.prototype.n = 0;
|
| 536 |
|
| 537 | display.prototype.a = [];
|
| 538 |
|
| 539 | return display;
|
| 540 |
|
| 541 | })();
|
| 542 |
|
| 543 | text_metric = (function() {
|
| 544 | function text_metric() {}
|
| 545 |
|
| 546 | text_metric.prototype.ascent = 0;
|
| 547 |
|
| 548 | text_metric.prototype.descent = 0;
|
| 549 |
|
| 550 | text_metric.prototype.width = 0;
|
| 551 |
|
| 552 | return text_metric;
|
| 553 |
|
| 554 | })();
|
| 555 |
|
| 556 | tos = 0;
|
| 557 |
|
| 558 | expanding = 0;
|
| 559 |
|
| 560 | evaluatingAsFloats = 0;
|
| 561 |
|
| 562 | evaluatingPolar = 0;
|
| 563 |
|
| 564 | fmt_x = 0;
|
| 565 |
|
| 566 | fmt_index = 0;
|
| 567 |
|
| 568 | fmt_level = 0;
|
| 569 |
|
| 570 | verbosing = 0;
|
| 571 |
|
| 572 | primetab = (function() {
|
| 573 | var ceil, i, j, primes;
|
| 574 | primes = [2];
|
| 575 | i = 3;
|
| 576 | while (primes.length < MAXPRIMETAB) {
|
| 577 | j = 0;
|
| 578 | ceil = Math.sqrt(i);
|
| 579 | while (j < primes.length && primes[j] <= ceil) {
|
| 580 | if (i % primes[j] === 0) {
|
| 581 | j = -1;
|
| 582 | break;
|
| 583 | }
|
| 584 | j++;
|
| 585 | }
|
| 586 | if (j !== -1) {
|
| 587 | primes.push(i);
|
| 588 | }
|
| 589 | i += 2;
|
| 590 | }
|
| 591 | primes[MAXPRIMETAB] = 0;
|
| 592 | return primes;
|
| 593 | })();
|
| 594 |
|
| 595 | esc_flag = 0;
|
| 596 |
|
| 597 | draw_flag = 0;
|
| 598 |
|
| 599 | mtotal = 0;
|
| 600 |
|
| 601 | trigmode = 0;
|
| 602 |
|
| 603 | logbuf = "";
|
| 604 |
|
| 605 | program_buf = "";
|
| 606 |
|
| 607 | symtab = [];
|
| 608 |
|
| 609 | binding = [];
|
| 610 |
|
| 611 | isSymbolReclaimable = [];
|
| 612 |
|
| 613 | arglist = [];
|
| 614 |
|
| 615 | stack = [];
|
| 616 |
|
| 617 | frame = 0;
|
| 618 |
|
| 619 | p0 = null;
|
| 620 |
|
| 621 | p1 = null;
|
| 622 |
|
| 623 | p2 = null;
|
| 624 |
|
| 625 | p3 = null;
|
| 626 |
|
| 627 | p4 = null;
|
| 628 |
|
| 629 | p5 = null;
|
| 630 |
|
| 631 | p6 = null;
|
| 632 |
|
| 633 | p7 = null;
|
| 634 |
|
| 635 | p8 = null;
|
| 636 |
|
| 637 | p9 = null;
|
| 638 |
|
| 639 | zero = null;
|
| 640 |
|
| 641 | one = null;
|
| 642 |
|
| 643 | one_as_double = null;
|
| 644 |
|
| 645 | imaginaryunit = null;
|
| 646 |
|
| 647 | out_buf = "";
|
| 648 |
|
| 649 | out_count = 0;
|
| 650 |
|
| 651 | test_flag = 0;
|
| 652 |
|
| 653 | codeGen = false;
|
| 654 |
|
| 655 | draw_stop_return = null;
|
| 656 |
|
| 657 | userSimplificationsInListForm = [];
|
| 658 |
|
| 659 | userSimplificationsInStringForm = [];
|
| 660 |
|
| 661 | transpose_unicode = 7488;
|
| 662 |
|
| 663 | dotprod_unicode = 183;
|
| 664 |
|
| 665 | symbol = function(x) {
|
| 666 | return symtab[x];
|
| 667 | };
|
| 668 |
|
| 669 | iscons = function(p) {
|
| 670 | return p.k === CONS;
|
| 671 | };
|
| 672 |
|
| 673 | isrational = function(p) {
|
| 674 | return p.k === NUM;
|
| 675 | };
|
| 676 |
|
| 677 | isdouble = function(p) {
|
| 678 | return p.k === DOUBLE;
|
| 679 | };
|
| 680 |
|
| 681 | isnum = function(p) {
|
| 682 | return isrational(p) || isdouble(p);
|
| 683 | };
|
| 684 |
|
| 685 | isstr = function(p) {
|
| 686 | return p.k === STR;
|
| 687 | };
|
| 688 |
|
| 689 | istensor = function(p) {
|
| 690 | if (p == null) {
|
| 691 | debugger;
|
| 692 | } else {
|
| 693 | return p.k === TENSOR;
|
| 694 | }
|
| 695 | };
|
| 696 |
|
| 697 | isnumerictensor = function(p) {
|
| 698 | var a, i, n, o, ref;
|
| 699 | if (isnum(p) || p === symbol(SYMBOL_IDENTITY_MATRIX)) {
|
| 700 | return 1;
|
| 701 | }
|
| 702 | if (!istensor(p) && !isnum(p)) {
|
| 703 | return 0;
|
| 704 | }
|
| 705 | n = p.tensor.nelem;
|
| 706 | a = p.tensor.elem;
|
| 707 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 708 | if (!isnumerictensor(a[i])) {
|
| 709 | return 0;
|
| 710 | }
|
| 711 | }
|
| 712 | return 1;
|
| 713 | };
|
| 714 |
|
| 715 | issymbol = function(p) {
|
| 716 | return p.k === SYM;
|
| 717 | };
|
| 718 |
|
| 719 | iskeyword = function(p) {
|
| 720 | return issymbol(p) && symnum(p) < NIL;
|
| 721 | };
|
| 722 |
|
| 723 | car = function(p) {
|
| 724 | if (iscons(p)) {
|
| 725 | return p.cons.car;
|
| 726 | } else {
|
| 727 | return symbol(NIL);
|
| 728 | }
|
| 729 | };
|
| 730 |
|
| 731 | cdr = function(p) {
|
| 732 | if (iscons(p)) {
|
| 733 | return p.cons.cdr;
|
| 734 | } else {
|
| 735 | return symbol(NIL);
|
| 736 | }
|
| 737 | };
|
| 738 |
|
| 739 | caar = function(p) {
|
| 740 | return car(car(p));
|
| 741 | };
|
| 742 |
|
| 743 | cadr = function(p) {
|
| 744 | return car(cdr(p));
|
| 745 | };
|
| 746 |
|
| 747 | cdar = function(p) {
|
| 748 | return cdr(car(p));
|
| 749 | };
|
| 750 |
|
| 751 | cddr = function(p) {
|
| 752 | return cdr(cdr(p));
|
| 753 | };
|
| 754 |
|
| 755 | caadr = function(p) {
|
| 756 | return car(car(cdr(p)));
|
| 757 | };
|
| 758 |
|
| 759 | caddr = function(p) {
|
| 760 | return car(cdr(cdr(p)));
|
| 761 | };
|
| 762 |
|
| 763 | cadar = function(p) {
|
| 764 | return car(cdr(car(p)));
|
| 765 | };
|
| 766 |
|
| 767 | cdadr = function(p) {
|
| 768 | return cdr(car(cdr(p)));
|
| 769 | };
|
| 770 |
|
| 771 | cddar = function(p) {
|
| 772 | return cdr(cdr(car(p)));
|
| 773 | };
|
| 774 |
|
| 775 | cdddr = function(p) {
|
| 776 | return cdr(cdr(cdr(p)));
|
| 777 | };
|
| 778 |
|
| 779 | caaddr = function(p) {
|
| 780 | return car(car(cdr(cdr(p))));
|
| 781 | };
|
| 782 |
|
| 783 | cadadr = function(p) {
|
| 784 | return car(cdr(car(cdr(p))));
|
| 785 | };
|
| 786 |
|
| 787 | caddar = function(p) {
|
| 788 | return car(cdr(cdr(car(p))));
|
| 789 | };
|
| 790 |
|
| 791 | cdaddr = function(p) {
|
| 792 | return cdr(car(cdr(cdr(p))));
|
| 793 | };
|
| 794 |
|
| 795 | cadddr = function(p) {
|
| 796 | return car(cdr(cdr(cdr(p))));
|
| 797 | };
|
| 798 |
|
| 799 | cddddr = function(p) {
|
| 800 | return cdr(cdr(cdr(cdr(p))));
|
| 801 | };
|
| 802 |
|
| 803 | caddddr = function(p) {
|
| 804 | return car(cdr(cdr(cdr(cdr(p)))));
|
| 805 | };
|
| 806 |
|
| 807 | cadaddr = function(p) {
|
| 808 | return car(cdr(car(cdr(cdr(p)))));
|
| 809 | };
|
| 810 |
|
| 811 | cddaddr = function(p) {
|
| 812 | return cdr(cdr(car(cdr(cdr(p)))));
|
| 813 | };
|
| 814 |
|
| 815 | caddadr = function(p) {
|
| 816 | return car(cdr(cdr(car(cdr(p)))));
|
| 817 | };
|
| 818 |
|
| 819 | cdddaddr = function(p) {
|
| 820 | return cdr(cdr(cdr(car(cdr(cdr(p))))));
|
| 821 | };
|
| 822 |
|
| 823 | caddaddr = function(p) {
|
| 824 | return car(cdr(cdr(car(cdr(cdr(p))))));
|
| 825 | };
|
| 826 |
|
| 827 | listLength = function(p) {
|
| 828 | var startCount;
|
| 829 | startCount = -1;
|
| 830 | while (iscons(p)) {
|
| 831 | p = cdr(p);
|
| 832 | startCount++;
|
| 833 | }
|
| 834 | return startCount;
|
| 835 | };
|
| 836 |
|
| 837 | nthCadr = function(p, n) {
|
| 838 | var startCount;
|
| 839 | startCount = 0;
|
| 840 | while (startCount <= n) {
|
| 841 | p = cdr(p);
|
| 842 | startCount++;
|
| 843 | }
|
| 844 | return car(p);
|
| 845 | };
|
| 846 |
|
| 847 | isadd = function(p) {
|
| 848 | return car(p) === symbol(ADD);
|
| 849 | };
|
| 850 |
|
| 851 | ismultiply = function(p) {
|
| 852 | return car(p) === symbol(MULTIPLY);
|
| 853 | };
|
| 854 |
|
| 855 | ispower = function(p) {
|
| 856 | return car(p) === symbol(POWER);
|
| 857 | };
|
| 858 |
|
| 859 | isfactorial = function(p) {
|
| 860 | return car(p) === symbol(FACTORIAL);
|
| 861 | };
|
| 862 |
|
| 863 | isinnerordot = function(p) {
|
| 864 | return (car(p) === symbol(INNER)) || (car(p) === symbol(DOT));
|
| 865 | };
|
| 866 |
|
| 867 | istranspose = function(p) {
|
| 868 | return car(p) === symbol(TRANSPOSE);
|
| 869 | };
|
| 870 |
|
| 871 | isinv = function(p) {
|
| 872 | return car(p) === symbol(INV);
|
| 873 | };
|
| 874 |
|
| 875 | isidentitymatrix = function(p) {
|
| 876 | return p === symbol(SYMBOL_IDENTITY_MATRIX);
|
| 877 | };
|
| 878 |
|
| 879 | MSIGN = function(p) {
|
| 880 | if (p.isPositive()) {
|
| 881 | return 1;
|
| 882 | } else if (p.isZero()) {
|
| 883 | return 0;
|
| 884 | } else {
|
| 885 | return -1;
|
| 886 | }
|
| 887 | };
|
| 888 |
|
| 889 | MLENGTH = function(p) {
|
| 890 | return p.toString().length;
|
| 891 | };
|
| 892 |
|
| 893 | MZERO = function(p) {
|
| 894 | return p.isZero();
|
| 895 | };
|
| 896 |
|
| 897 | MEQUAL = function(p, n) {
|
| 898 | if (p == null) {
|
| 899 | debugger;
|
| 900 | }
|
| 901 | return p.equals(n);
|
| 902 | };
|
| 903 |
|
| 904 | reset_after_error = function() {
|
| 905 | moveTos(0);
|
| 906 | esc_flag = 0;
|
| 907 | draw_flag = 0;
|
| 908 | frame = TOS;
|
| 909 | evaluatingAsFloats = 0;
|
| 910 | return evaluatingPolar = 0;
|
| 911 | };
|
| 912 |
|
| 913 | $ = typeof exports !== "undefined" && exports !== null ? exports : this;
|
| 914 |
|
| 915 | $.version = version;
|
| 916 |
|
| 917 | $.isadd = isadd;
|
| 918 |
|
| 919 | $.ismultiply = ismultiply;
|
| 920 |
|
| 921 | $.ispower = ispower;
|
| 922 |
|
| 923 | $.isfactorial = isfactorial;
|
| 924 |
|
| 925 | $.car = car;
|
| 926 |
|
| 927 | $.cdr = cdr;
|
| 928 |
|
| 929 | $.caar = caar;
|
| 930 |
|
| 931 | $.cadr = cadr;
|
| 932 |
|
| 933 | $.cdar = cdar;
|
| 934 |
|
| 935 | $.cddr = cddr;
|
| 936 |
|
| 937 | $.caadr = caadr;
|
| 938 |
|
| 939 | $.caddr = caddr;
|
| 940 |
|
| 941 | $.cadar = cadar;
|
| 942 |
|
| 943 | $.cdadr = cdadr;
|
| 944 |
|
| 945 | $.cddar = cddar;
|
| 946 |
|
| 947 | $.cdddr = cdddr;
|
| 948 |
|
| 949 | $.caaddr = caaddr;
|
| 950 |
|
| 951 | $.cadadr = cadadr;
|
| 952 |
|
| 953 | $.caddar = caddar;
|
| 954 |
|
| 955 | $.cdaddr = cdaddr;
|
| 956 |
|
| 957 | $.cadddr = cadddr;
|
| 958 |
|
| 959 | $.cddddr = cddddr;
|
| 960 |
|
| 961 | $.caddddr = caddddr;
|
| 962 |
|
| 963 | $.cadaddr = cadaddr;
|
| 964 |
|
| 965 | $.cddaddr = cddaddr;
|
| 966 |
|
| 967 | $.caddadr = caddadr;
|
| 968 |
|
| 969 | $.cdddaddr = cdddaddr;
|
| 970 |
|
| 971 | $.caddaddr = caddaddr;
|
| 972 |
|
| 973 | $.symbol = symbol;
|
| 974 |
|
| 975 | $.iscons = iscons;
|
| 976 |
|
| 977 | $.isrational = isrational;
|
| 978 |
|
| 979 | $.isdouble = isdouble;
|
| 980 |
|
| 981 | $.isnum = isnum;
|
| 982 |
|
| 983 | $.isstr = isstr;
|
| 984 |
|
| 985 | $.istensor = istensor;
|
| 986 |
|
| 987 | $.issymbol = issymbol;
|
| 988 |
|
| 989 | $.iskeyword = iskeyword;
|
| 990 |
|
| 991 | $.CONS = CONS;
|
| 992 |
|
| 993 | $.NUM = NUM;
|
| 994 |
|
| 995 | $.DOUBLE = DOUBLE;
|
| 996 |
|
| 997 | $.STR = STR;
|
| 998 |
|
| 999 | $.TENSOR = TENSOR;
|
| 1000 |
|
| 1001 | $.SYM = SYM;
|
| 1002 |
|
| 1003 |
|
| 1004 | |
| 1005 | |
| 1006 | |
| 1007 | |
| 1008 | |
| 1009 | |
| 1010 | |
| 1011 | |
| 1012 | |
| 1013 | |
| 1014 | |
| 1015 | |
| 1016 | |
| 1017 |
|
| 1018 |
|
| 1019 |
|
| 1020 | |
| 1021 | |
| 1022 | |
| 1023 | |
| 1024 | |
| 1025 | |
| 1026 | |
| 1027 | |
| 1028 | |
| 1029 | |
| 1030 | |
| 1031 | |
| 1032 | |
| 1033 | |
| 1034 | |
| 1035 | |
| 1036 | |
| 1037 | |
| 1038 | |
| 1039 | |
| 1040 | |
| 1041 | |
| 1042 | |
| 1043 | |
| 1044 | |
| 1045 | |
| 1046 | |
| 1047 | |
| 1048 |
|
| 1049 |
|
| 1050 | DEBUG_ABS = false;
|
| 1051 |
|
| 1052 | Eval_abs = function() {
|
| 1053 | push(cadr(p1));
|
| 1054 | Eval();
|
| 1055 | return abs();
|
| 1056 | };
|
| 1057 |
|
| 1058 | absValFloat = function() {
|
| 1059 | Eval();
|
| 1060 | absval();
|
| 1061 | Eval();
|
| 1062 | return zzfloat();
|
| 1063 | };
|
| 1064 |
|
| 1065 | abs = function() {
|
| 1066 | save();
|
| 1067 | p1 = pop();
|
| 1068 | push(p1);
|
| 1069 | numerator();
|
| 1070 | absval();
|
| 1071 | push(p1);
|
| 1072 | denominator();
|
| 1073 | absval();
|
| 1074 | divide();
|
| 1075 | return restore();
|
| 1076 | };
|
| 1077 |
|
| 1078 | absval = function() {
|
| 1079 | var input;
|
| 1080 | save();
|
| 1081 | p1 = pop();
|
| 1082 | input = p1;
|
| 1083 | if (DEBUG_ABS) {
|
| 1084 | console.log("ABS of " + p1);
|
| 1085 | }
|
| 1086 | if (iszero(p1)) {
|
| 1087 | if (DEBUG_ABS) {
|
| 1088 | console.log(" abs: " + p1 + " just zero");
|
| 1089 | }
|
| 1090 | push(zero);
|
| 1091 | if (DEBUG_ABS) {
|
| 1092 | console.log(" --> ABS of " + input + " : " + stack[tos - 1]);
|
| 1093 | }
|
| 1094 | restore();
|
| 1095 | return;
|
| 1096 | }
|
| 1097 | if (isnegativenumber(p1)) {
|
| 1098 | if (DEBUG_ABS) {
|
| 1099 | console.log(" abs: " + p1 + " just a negative");
|
| 1100 | }
|
| 1101 | push(p1);
|
| 1102 | negate();
|
| 1103 | restore();
|
| 1104 | return;
|
| 1105 | }
|
| 1106 | if (ispositivenumber(p1)) {
|
| 1107 | if (DEBUG_ABS) {
|
| 1108 | console.log(" abs: " + p1 + " just a positive");
|
| 1109 | }
|
| 1110 | push(p1);
|
| 1111 | if (DEBUG_ABS) {
|
| 1112 | console.log(" --> ABS of " + input + " : " + stack[tos - 1]);
|
| 1113 | }
|
| 1114 | restore();
|
| 1115 | return;
|
| 1116 | }
|
| 1117 | if (p1 === symbol(PI)) {
|
| 1118 | if (DEBUG_ABS) {
|
| 1119 | console.log(" abs: " + p1 + " of PI");
|
| 1120 | }
|
| 1121 | push(p1);
|
| 1122 | if (DEBUG_ABS) {
|
| 1123 | console.log(" --> ABS of " + input + " : " + stack[tos - 1]);
|
| 1124 | }
|
| 1125 | restore();
|
| 1126 | return;
|
| 1127 | }
|
| 1128 | if (car(p1) === symbol(ADD) && (findPossibleClockForm(p1) || findPossibleExponentialForm(p1) || Find(p1, imaginaryunit))) {
|
| 1129 | if (DEBUG_ABS) {
|
| 1130 | console.log(" abs: " + p1 + " is a sum");
|
| 1131 | }
|
| 1132 | if (DEBUG_ABS) {
|
| 1133 | console.log("abs of a sum");
|
| 1134 | }
|
| 1135 | push(p1);
|
| 1136 | rect();
|
| 1137 | p1 = pop();
|
| 1138 | push(p1);
|
| 1139 | real();
|
| 1140 | push_integer(2);
|
| 1141 | power();
|
| 1142 | push(p1);
|
| 1143 | imag();
|
| 1144 | push_integer(2);
|
| 1145 | power();
|
| 1146 | add();
|
| 1147 | push_rational(1, 2);
|
| 1148 | power();
|
| 1149 | simplify_trig();
|
| 1150 | if (DEBUG_ABS) {
|
| 1151 | console.log(" --> ABS of " + input + " : " + stack[tos - 1]);
|
| 1152 | }
|
| 1153 | restore();
|
| 1154 | return;
|
| 1155 | }
|
| 1156 | if (car(p1) === symbol(POWER) && equaln(cadr(p1), -1)) {
|
| 1157 | if (DEBUG_ABS) {
|
| 1158 | console.log(" abs: " + p1 + " is -1 to any power");
|
| 1159 | }
|
| 1160 | if (evaluatingAsFloats) {
|
| 1161 | if (DEBUG_ABS) {
|
| 1162 | console.log(" abs: numeric, so result is 1.0");
|
| 1163 | }
|
| 1164 | push_double(1.0);
|
| 1165 | } else {
|
| 1166 | if (DEBUG_ABS) {
|
| 1167 | console.log(" abs: symbolic, so result is 1");
|
| 1168 | }
|
| 1169 | push_integer(1);
|
| 1170 | }
|
| 1171 | if (DEBUG_ABS) {
|
| 1172 | console.log(" --> ABS of " + input + " : " + stack[tos - 1]);
|
| 1173 | }
|
| 1174 | restore();
|
| 1175 | return;
|
| 1176 | }
|
| 1177 | if (car(p1) === symbol(POWER) && ispositivenumber(caddr(p1))) {
|
| 1178 | if (DEBUG_ABS) {
|
| 1179 | console.log(" abs: " + p1 + " is something to the power of a positive number");
|
| 1180 | }
|
| 1181 | push(cadr(p1));
|
| 1182 | abs();
|
| 1183 | push(caddr(p1));
|
| 1184 | power();
|
| 1185 | if (DEBUG_ABS) {
|
| 1186 | console.log(" --> ABS of " + input + " : " + stack[tos - 1]);
|
| 1187 | }
|
| 1188 | restore();
|
| 1189 | return;
|
| 1190 | }
|
| 1191 | if (car(p1) === symbol(POWER) && cadr(p1) === symbol(E)) {
|
| 1192 | if (DEBUG_ABS) {
|
| 1193 | console.log(" abs: " + p1 + " is an exponential");
|
| 1194 | }
|
| 1195 | push(caddr(p1));
|
| 1196 | real();
|
| 1197 | exponential();
|
| 1198 | if (DEBUG_ABS) {
|
| 1199 | console.log(" --> ABS of " + input + " : " + stack[tos - 1]);
|
| 1200 | }
|
| 1201 | restore();
|
| 1202 | return;
|
| 1203 | }
|
| 1204 | if (car(p1) === symbol(MULTIPLY)) {
|
| 1205 | if (DEBUG_ABS) {
|
| 1206 | console.log(" abs: " + p1 + " is a product");
|
| 1207 | }
|
| 1208 | push_integer(1);
|
| 1209 | p1 = cdr(p1);
|
| 1210 | while (iscons(p1)) {
|
| 1211 | push(car(p1));
|
| 1212 | abs();
|
| 1213 | multiply();
|
| 1214 | p1 = cdr(p1);
|
| 1215 | }
|
| 1216 | if (DEBUG_ABS) {
|
| 1217 | console.log(" --> ABS of " + input + " : " + stack[tos - 1]);
|
| 1218 | }
|
| 1219 | restore();
|
| 1220 | return;
|
| 1221 | }
|
| 1222 | if (car(p1) === symbol(ABS)) {
|
| 1223 | if (DEBUG_ABS) {
|
| 1224 | console.log(" abs: " + p1 + " is abs of a abs");
|
| 1225 | }
|
| 1226 | push_symbol(ABS);
|
| 1227 | push(cadr(p1));
|
| 1228 | list(2);
|
| 1229 | if (DEBUG_ABS) {
|
| 1230 | console.log(" --> ABS of " + input + " : " + stack[tos - 1]);
|
| 1231 | }
|
| 1232 | restore();
|
| 1233 | return;
|
| 1234 | }
|
| 1235 |
|
| 1236 | |
| 1237 | |
| 1238 | |
| 1239 | |
| 1240 | |
| 1241 | |
| 1242 | |
| 1243 | |
| 1244 | |
| 1245 | |
| 1246 | |
| 1247 | |
| 1248 | |
| 1249 | |
| 1250 | |
| 1251 | |
| 1252 | |
| 1253 | |
| 1254 | |
| 1255 | |
| 1256 | |
| 1257 | |
| 1258 | |
| 1259 | |
| 1260 | |
| 1261 | |
| 1262 | |
| 1263 | |
| 1264 | |
| 1265 |
|
| 1266 | if (istensor(p1)) {
|
| 1267 | absval_tensor();
|
| 1268 | restore();
|
| 1269 | return;
|
| 1270 | }
|
| 1271 | if (isnegativeterm(p1) || (car(p1) === symbol(ADD) && isnegativeterm(cadr(p1)))) {
|
| 1272 | push(p1);
|
| 1273 | negate();
|
| 1274 | p1 = pop();
|
| 1275 | }
|
| 1276 | if (DEBUG_ABS) {
|
| 1277 | console.log(" abs: " + p1 + " is nothing decomposable");
|
| 1278 | }
|
| 1279 | push_symbol(ABS);
|
| 1280 | push(p1);
|
| 1281 | list(2);
|
| 1282 | if (DEBUG_ABS) {
|
| 1283 | console.log(" --> ABS of " + input + " : " + stack[tos - 1]);
|
| 1284 | }
|
| 1285 | return restore();
|
| 1286 | };
|
| 1287 |
|
| 1288 | absval_tensor = function() {
|
| 1289 | if (p1.tensor.ndim !== 1) {
|
| 1290 | stop("abs(tensor) with tensor rank > 1");
|
| 1291 | }
|
| 1292 | push(p1);
|
| 1293 | push(p1);
|
| 1294 | conjugate();
|
| 1295 | inner();
|
| 1296 | push_rational(1, 2);
|
| 1297 | power();
|
| 1298 | simplify();
|
| 1299 | return Eval();
|
| 1300 | };
|
| 1301 |
|
| 1302 |
|
| 1303 | |
| 1304 | |
| 1305 | |
| 1306 | |
| 1307 | |
| 1308 | |
| 1309 | |
| 1310 | |
| 1311 | |
| 1312 | |
| 1313 | |
| 1314 | |
| 1315 | |
| 1316 | |
| 1317 | |
| 1318 | |
| 1319 | |
| 1320 | |
| 1321 | |
| 1322 | |
| 1323 | |
| 1324 |
|
| 1325 |
|
| 1326 | flag = 0;
|
| 1327 |
|
| 1328 | Eval_add = function() {
|
| 1329 | var h;
|
| 1330 | h = tos;
|
| 1331 | p1 = cdr(p1);
|
| 1332 | while (iscons(p1)) {
|
| 1333 | push(car(p1));
|
| 1334 | Eval();
|
| 1335 | p2 = pop();
|
| 1336 | push_terms(p2);
|
| 1337 | p1 = cdr(p1);
|
| 1338 | }
|
| 1339 | return add_terms(tos - h);
|
| 1340 | };
|
| 1341 |
|
| 1342 | stackAddsCount = 0;
|
| 1343 |
|
| 1344 | add_terms = function(n) {
|
| 1345 | var h, i, i1, j1, o, ref, ref1, results, s, subsetOfStack;
|
| 1346 | stackAddsCount++;
|
| 1347 | i = 0;
|
| 1348 | h = tos - n;
|
| 1349 | s = h;
|
| 1350 | if (DEBUG) {
|
| 1351 | console.log("stack before adding terms #" + stackAddsCount);
|
| 1352 | }
|
| 1353 | if (DEBUG) {
|
| 1354 | for (i = o = 0, ref = tos; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 1355 | console.log(print_list(stack[i]));
|
| 1356 | }
|
| 1357 | }
|
| 1358 | for (i = i1 = 0; i1 < 10; i = ++i1) {
|
| 1359 | if (n < 2) {
|
| 1360 | break;
|
| 1361 | }
|
| 1362 | flag = 0;
|
| 1363 | subsetOfStack = stack.slice(h, h + n);
|
| 1364 | subsetOfStack.sort(cmp_terms);
|
| 1365 | stack = stack.slice(0, h).concat(subsetOfStack).concat(stack.slice(h + n));
|
| 1366 | if (flag === 0) {
|
| 1367 | break;
|
| 1368 | }
|
| 1369 | n = combine_terms(h, n);
|
| 1370 | }
|
| 1371 | moveTos(h + n);
|
| 1372 | switch (n) {
|
| 1373 | case 0:
|
| 1374 | if (evaluatingAsFloats) {
|
| 1375 | push_double(0.0);
|
| 1376 | } else {
|
| 1377 | push(zero);
|
| 1378 | }
|
| 1379 | break;
|
| 1380 | case 1:
|
| 1381 | break;
|
| 1382 | default:
|
| 1383 | list(n);
|
| 1384 | p1 = pop();
|
| 1385 | push_symbol(ADD);
|
| 1386 | push(p1);
|
| 1387 | cons();
|
| 1388 | }
|
| 1389 | if (DEBUG) {
|
| 1390 | console.log("stack after adding terms #" + stackAddsCount);
|
| 1391 | }
|
| 1392 | if (DEBUG) {
|
| 1393 | results = [];
|
| 1394 | for (i = j1 = 0, ref1 = tos; 0 <= ref1 ? j1 < ref1 : j1 > ref1; i = 0 <= ref1 ? ++j1 : --j1) {
|
| 1395 | results.push(console.log(print_list(stack[i])));
|
| 1396 | }
|
| 1397 | return results;
|
| 1398 | }
|
| 1399 | };
|
| 1400 |
|
| 1401 | cmp_terms_count = 0;
|
| 1402 |
|
| 1403 | cmp_terms = function(p1, p2) {
|
| 1404 | var i, o, ref, t;
|
| 1405 | cmp_terms_count++;
|
| 1406 | i = 0;
|
| 1407 | if (isnum(p1) && isnum(p2)) {
|
| 1408 | flag = 1;
|
| 1409 | return 0;
|
| 1410 | }
|
| 1411 | if (istensor(p1) && istensor(p2)) {
|
| 1412 | if (p1.tensor.ndim < p2.tensor.ndim) {
|
| 1413 | return -1;
|
| 1414 | }
|
| 1415 | if (p1.tensor.ndim > p2.tensor.ndim) {
|
| 1416 | return 1;
|
| 1417 | }
|
| 1418 | for (i = o = 0, ref = p1.tensor.ndim; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 1419 | if (p1.tensor.dim[i] < p2.tensor.dim[i]) {
|
| 1420 | return -1;
|
| 1421 | }
|
| 1422 | if (p1.tensor.dim[i] > p2.tensor.dim[i]) {
|
| 1423 | return 1;
|
| 1424 | }
|
| 1425 | }
|
| 1426 | flag = 1;
|
| 1427 | return 0;
|
| 1428 | }
|
| 1429 | if (car(p1) === symbol(MULTIPLY)) {
|
| 1430 | p1 = cdr(p1);
|
| 1431 | if (isnum(car(p1))) {
|
| 1432 | p1 = cdr(p1);
|
| 1433 | if (cdr(p1) === symbol(NIL)) {
|
| 1434 | p1 = car(p1);
|
| 1435 | }
|
| 1436 | }
|
| 1437 | }
|
| 1438 | if (car(p2) === symbol(MULTIPLY)) {
|
| 1439 | p2 = cdr(p2);
|
| 1440 | if (isnum(car(p2))) {
|
| 1441 | p2 = cdr(p2);
|
| 1442 | if (cdr(p2) === symbol(NIL)) {
|
| 1443 | p2 = car(p2);
|
| 1444 | }
|
| 1445 | }
|
| 1446 | }
|
| 1447 | t = cmp_expr(p1, p2);
|
| 1448 | if (t === 0) {
|
| 1449 | flag = 1;
|
| 1450 | }
|
| 1451 | return t;
|
| 1452 | };
|
| 1453 |
|
| 1454 |
|
| 1455 | |
| 1456 | |
| 1457 | |
| 1458 | |
| 1459 | |
| 1460 | |
| 1461 |
|
| 1462 |
|
| 1463 | combine_terms = function(s, n) {
|
| 1464 | var i, i1, j, j1, l1, m1, o, ref, ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, t;
|
| 1465 | i = 0;
|
| 1466 | while (i < (n - 1)) {
|
| 1467 | check_esc_flag();
|
| 1468 | p3 = stack[s + i];
|
| 1469 | p4 = stack[s + i + 1];
|
| 1470 | if (istensor(p3) && istensor(p4)) {
|
| 1471 | push(p3);
|
| 1472 | push(p4);
|
| 1473 | tensor_plus_tensor();
|
| 1474 | p1 = pop();
|
| 1475 | if (p1 !== symbol(NIL)) {
|
| 1476 | stack[s + i] = p1;
|
| 1477 | for (j = o = ref = i + 1, ref1 = n - 1; ref <= ref1 ? o < ref1 : o > ref1; j = ref <= ref1 ? ++o : --o) {
|
| 1478 | stack[s + j] = stack[s + j + 1];
|
| 1479 | }
|
| 1480 | n--;
|
| 1481 | i--;
|
| 1482 | }
|
| 1483 | i++;
|
| 1484 | continue;
|
| 1485 | }
|
| 1486 | if (istensor(p3) || istensor(p4)) {
|
| 1487 | i++;
|
| 1488 | continue;
|
| 1489 | }
|
| 1490 | if (isnum(p3) && isnum(p4)) {
|
| 1491 | push(p3);
|
| 1492 | push(p4);
|
| 1493 | add_numbers();
|
| 1494 | p1 = pop();
|
| 1495 | if (iszero(p1)) {
|
| 1496 | for (j = i1 = ref2 = i, ref3 = n - 2; ref2 <= ref3 ? i1 < ref3 : i1 > ref3; j = ref2 <= ref3 ? ++i1 : --i1) {
|
| 1497 | stack[s + j] = stack[s + j + 2];
|
| 1498 | }
|
| 1499 | n -= 2;
|
| 1500 | } else {
|
| 1501 | stack[s + i] = p1;
|
| 1502 | for (j = j1 = ref4 = i + 1, ref5 = n - 1; ref4 <= ref5 ? j1 < ref5 : j1 > ref5; j = ref4 <= ref5 ? ++j1 : --j1) {
|
| 1503 | stack[s + j] = stack[s + j + 1];
|
| 1504 | }
|
| 1505 | n--;
|
| 1506 | }
|
| 1507 | i--;
|
| 1508 | i++;
|
| 1509 | continue;
|
| 1510 | }
|
| 1511 | if (isnum(p3) || isnum(p4)) {
|
| 1512 | i++;
|
| 1513 | continue;
|
| 1514 | }
|
| 1515 | if (evaluatingAsFloats) {
|
| 1516 | p1 = one_as_double;
|
| 1517 | p2 = one_as_double;
|
| 1518 | } else {
|
| 1519 | p1 = one;
|
| 1520 | p2 = one;
|
| 1521 | }
|
| 1522 | t = 0;
|
| 1523 | if (car(p3) === symbol(MULTIPLY)) {
|
| 1524 | p3 = cdr(p3);
|
| 1525 | t = 1;
|
| 1526 | if (isnum(car(p3))) {
|
| 1527 | p1 = car(p3);
|
| 1528 | p3 = cdr(p3);
|
| 1529 | if (cdr(p3) === symbol(NIL)) {
|
| 1530 | p3 = car(p3);
|
| 1531 | t = 0;
|
| 1532 | }
|
| 1533 | }
|
| 1534 | }
|
| 1535 | if (car(p4) === symbol(MULTIPLY)) {
|
| 1536 | p4 = cdr(p4);
|
| 1537 | if (isnum(car(p4))) {
|
| 1538 | p2 = car(p4);
|
| 1539 | p4 = cdr(p4);
|
| 1540 | if (cdr(p4) === symbol(NIL)) {
|
| 1541 | p4 = car(p4);
|
| 1542 | }
|
| 1543 | }
|
| 1544 | }
|
| 1545 | if (!equal(p3, p4)) {
|
| 1546 | i++;
|
| 1547 | continue;
|
| 1548 | }
|
| 1549 | push(p1);
|
| 1550 | push(p2);
|
| 1551 | add_numbers();
|
| 1552 | p1 = pop();
|
| 1553 | if (iszero(p1)) {
|
| 1554 | for (j = l1 = ref6 = i, ref7 = n - 2; ref6 <= ref7 ? l1 < ref7 : l1 > ref7; j = ref6 <= ref7 ? ++l1 : --l1) {
|
| 1555 | stack[s + j] = stack[s + j + 2];
|
| 1556 | }
|
| 1557 | n -= 2;
|
| 1558 | i--;
|
| 1559 | i++;
|
| 1560 | continue;
|
| 1561 | }
|
| 1562 | push(p1);
|
| 1563 | if (t) {
|
| 1564 | push(symbol(MULTIPLY));
|
| 1565 | push(p3);
|
| 1566 | cons();
|
| 1567 | } else {
|
| 1568 | push(p3);
|
| 1569 | }
|
| 1570 | multiply();
|
| 1571 | stack[s + i] = pop();
|
| 1572 | for (j = m1 = ref8 = i + 1, ref9 = n - 1; ref8 <= ref9 ? m1 < ref9 : m1 > ref9; j = ref8 <= ref9 ? ++m1 : --m1) {
|
| 1573 | stack[s + j] = stack[s + j + 1];
|
| 1574 | }
|
| 1575 | n--;
|
| 1576 | i--;
|
| 1577 | i++;
|
| 1578 | }
|
| 1579 | return n;
|
| 1580 | };
|
| 1581 |
|
| 1582 | push_terms = function(p) {
|
| 1583 | var results;
|
| 1584 | if (car(p) === symbol(ADD)) {
|
| 1585 | p = cdr(p);
|
| 1586 | results = [];
|
| 1587 | while (iscons(p)) {
|
| 1588 | push(car(p));
|
| 1589 | results.push(p = cdr(p));
|
| 1590 | }
|
| 1591 | return results;
|
| 1592 | } else if (!iszero(p)) {
|
| 1593 | return push(p);
|
| 1594 | }
|
| 1595 | };
|
| 1596 |
|
| 1597 | add = function() {
|
| 1598 | var h;
|
| 1599 | save();
|
| 1600 | p2 = pop();
|
| 1601 | p1 = pop();
|
| 1602 | h = tos;
|
| 1603 | push_terms(p1);
|
| 1604 | push_terms(p2);
|
| 1605 | add_terms(tos - h);
|
| 1606 | return restore();
|
| 1607 | };
|
| 1608 |
|
| 1609 | add_all = function(k) {
|
| 1610 | var h, i, o, ref, s;
|
| 1611 | i = 0;
|
| 1612 | save();
|
| 1613 | s = tos - k;
|
| 1614 | h = tos;
|
| 1615 | for (i = o = 0, ref = k; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 1616 | push_terms(stack[s + i]);
|
| 1617 | }
|
| 1618 | add_terms(tos - h);
|
| 1619 | p1 = pop();
|
| 1620 | moveTos(tos - k);
|
| 1621 | push(p1);
|
| 1622 | return restore();
|
| 1623 | };
|
| 1624 |
|
| 1625 | subtract = function() {
|
| 1626 | negate();
|
| 1627 | return add();
|
| 1628 | };
|
| 1629 |
|
| 1630 |
|
| 1631 | |
| 1632 | |
| 1633 | |
| 1634 | |
| 1635 | |
| 1636 | |
| 1637 | |
| 1638 | |
| 1639 | |
| 1640 | |
| 1641 | |
| 1642 | |
| 1643 | |
| 1644 |
|
| 1645 |
|
| 1646 | Eval_adj = function() {
|
| 1647 | push(cadr(p1));
|
| 1648 | Eval();
|
| 1649 | return adj();
|
| 1650 | };
|
| 1651 |
|
| 1652 | adj = function() {
|
| 1653 | var doNothing, i, i1, j, n, o, ref, ref1;
|
| 1654 | i = 0;
|
| 1655 | j = 0;
|
| 1656 | n = 0;
|
| 1657 | save();
|
| 1658 | p1 = pop();
|
| 1659 | if (istensor(p1) && p1.tensor.ndim === 2 && p1.tensor.dim[0] === p1.tensor.dim[1]) {
|
| 1660 | doNothing = 1;
|
| 1661 | } else {
|
| 1662 | stop("adj: square matrix expected");
|
| 1663 | }
|
| 1664 | n = p1.tensor.dim[0];
|
| 1665 | p2 = alloc_tensor(n * n);
|
| 1666 | p2.tensor.ndim = 2;
|
| 1667 | p2.tensor.dim[0] = n;
|
| 1668 | p2.tensor.dim[1] = n;
|
| 1669 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 1670 | for (j = i1 = 0, ref1 = n; 0 <= ref1 ? i1 < ref1 : i1 > ref1; j = 0 <= ref1 ? ++i1 : --i1) {
|
| 1671 | cofactor(p1, n, i, j);
|
| 1672 | p2.tensor.elem[n * j + i] = pop();
|
| 1673 | }
|
| 1674 | }
|
| 1675 | push(p2);
|
| 1676 | return restore();
|
| 1677 | };
|
| 1678 |
|
| 1679 |
|
| 1680 | |
| 1681 | |
| 1682 |
|
| 1683 |
|
| 1684 | Eval_approxratio = function() {
|
| 1685 | var theArgument;
|
| 1686 | theArgument = cadr(p1);
|
| 1687 | push(theArgument);
|
| 1688 | return approxratioRecursive();
|
| 1689 | };
|
| 1690 |
|
| 1691 | approxratioRecursive = function() {
|
| 1692 | var i, i1, o, ref, ref1;
|
| 1693 | i = 0;
|
| 1694 | save();
|
| 1695 | p1 = pop();
|
| 1696 | if (istensor(p1)) {
|
| 1697 | p4 = alloc_tensor(p1.tensor.nelem);
|
| 1698 | p4.tensor.ndim = p1.tensor.ndim;
|
| 1699 | for (i = o = 0, ref = p1.tensor.ndim; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 1700 | p4.tensor.dim[i] = p1.tensor.dim[i];
|
| 1701 | }
|
| 1702 | for (i = i1 = 0, ref1 = p1.tensor.nelem; 0 <= ref1 ? i1 < ref1 : i1 > ref1; i = 0 <= ref1 ? ++i1 : --i1) {
|
| 1703 | push(p1.tensor.elem[i]);
|
| 1704 | approxratioRecursive();
|
| 1705 | p4.tensor.elem[i] = pop();
|
| 1706 | check_tensor_dimensions(p4);
|
| 1707 | }
|
| 1708 | push(p4);
|
| 1709 | } else if (p1.k === DOUBLE) {
|
| 1710 | push(p1);
|
| 1711 | approxOneRatioOnly();
|
| 1712 | } else if (iscons(p1)) {
|
| 1713 | push(car(p1));
|
| 1714 | approxratioRecursive();
|
| 1715 | push(cdr(p1));
|
| 1716 | approxratioRecursive();
|
| 1717 | cons();
|
| 1718 | } else {
|
| 1719 | push(p1);
|
| 1720 | }
|
| 1721 | return restore();
|
| 1722 | };
|
| 1723 |
|
| 1724 | approxOneRatioOnly = function() {
|
| 1725 | var numberOfDigitsAfterTheDot, precision, splitBeforeAndAfterDot, supposedlyTheFloat, theFloat, theRatio;
|
| 1726 | zzfloat();
|
| 1727 | supposedlyTheFloat = pop();
|
| 1728 | if (supposedlyTheFloat.k === DOUBLE) {
|
| 1729 | theFloat = supposedlyTheFloat.d;
|
| 1730 | splitBeforeAndAfterDot = theFloat.toString().split(".");
|
| 1731 | if (splitBeforeAndAfterDot.length === 2) {
|
| 1732 | numberOfDigitsAfterTheDot = splitBeforeAndAfterDot[1].length;
|
| 1733 | precision = 1 / Math.pow(10, numberOfDigitsAfterTheDot);
|
| 1734 | theRatio = floatToRatioRoutine(theFloat, precision);
|
| 1735 | push_rational(theRatio[0], theRatio[1]);
|
| 1736 | } else {
|
| 1737 | push_integer(theFloat);
|
| 1738 | }
|
| 1739 | return;
|
| 1740 | }
|
| 1741 | push_symbol(APPROXRATIO);
|
| 1742 | push(theArgument);
|
| 1743 | return list(2);
|
| 1744 | };
|
| 1745 |
|
| 1746 | floatToRatioRoutine = function(decimal, AccuracyFactor) {
|
| 1747 | var DecimalSign, FractionDenominator, FractionNumerator, PreviousDenominator, ScratchValue, Z, ret;
|
| 1748 | FractionNumerator = void 0;
|
| 1749 | FractionDenominator = void 0;
|
| 1750 | DecimalSign = void 0;
|
| 1751 | Z = void 0;
|
| 1752 | PreviousDenominator = void 0;
|
| 1753 | ScratchValue = void 0;
|
| 1754 | ret = [0, 0];
|
| 1755 | if (isNaN(decimal)) {
|
| 1756 | return ret;
|
| 1757 | }
|
| 1758 | if (decimal === 2e308) {
|
| 1759 | ret[0] = 1;
|
| 1760 | ret[1] = 0;
|
| 1761 | return ret;
|
| 1762 | }
|
| 1763 | if (decimal === -2e308) {
|
| 1764 | ret[0] = -1;
|
| 1765 | ret[1] = 0;
|
| 1766 | return ret;
|
| 1767 | }
|
| 1768 | if (decimal < 0.0) {
|
| 1769 | DecimalSign = -1.0;
|
| 1770 | } else {
|
| 1771 | DecimalSign = 1.0;
|
| 1772 | }
|
| 1773 | decimal = Math.abs(decimal);
|
| 1774 | if (Math.abs(decimal - Math.floor(decimal)) < AccuracyFactor) {
|
| 1775 | FractionNumerator = decimal * DecimalSign;
|
| 1776 | FractionDenominator = 1.0;
|
| 1777 | ret[0] = FractionNumerator;
|
| 1778 | ret[1] = FractionDenominator;
|
| 1779 | return ret;
|
| 1780 | }
|
| 1781 | if (decimal < 1.0e-19) {
|
| 1782 | FractionNumerator = DecimalSign;
|
| 1783 | FractionDenominator = 9999999999999999999.0;
|
| 1784 | ret[0] = FractionNumerator;
|
| 1785 | ret[1] = FractionDenominator;
|
| 1786 | return ret;
|
| 1787 | }
|
| 1788 | if (decimal > 1.0e19) {
|
| 1789 | FractionNumerator = 9999999999999999999.0 * DecimalSign;
|
| 1790 | FractionDenominator = 1.0;
|
| 1791 | ret[0] = FractionNumerator;
|
| 1792 | ret[1] = FractionDenominator;
|
| 1793 | return ret;
|
| 1794 | }
|
| 1795 | Z = decimal;
|
| 1796 | PreviousDenominator = 0.0;
|
| 1797 | FractionDenominator = 1.0;
|
| 1798 | while (true) {
|
| 1799 | Z = 1.0 / (Z - Math.floor(Z));
|
| 1800 | ScratchValue = FractionDenominator;
|
| 1801 | FractionDenominator = FractionDenominator * Math.floor(Z) + PreviousDenominator;
|
| 1802 | PreviousDenominator = ScratchValue;
|
| 1803 | FractionNumerator = Math.floor(decimal * FractionDenominator + 0.5);
|
| 1804 | if (!(Math.abs(decimal - (FractionNumerator / FractionDenominator)) > AccuracyFactor && Z !== Math.floor(Z))) {
|
| 1805 | break;
|
| 1806 | }
|
| 1807 | }
|
| 1808 | FractionNumerator = DecimalSign * FractionNumerator;
|
| 1809 | ret[0] = FractionNumerator;
|
| 1810 | ret[1] = FractionDenominator;
|
| 1811 | return ret;
|
| 1812 | };
|
| 1813 |
|
| 1814 | approx_just_an_integer = 0;
|
| 1815 |
|
| 1816 | approx_sine_of_rational = 1;
|
| 1817 |
|
| 1818 | approx_sine_of_pi_times_rational = 2;
|
| 1819 |
|
| 1820 | approx_rationalOfPi = 3;
|
| 1821 |
|
| 1822 | approx_radicalOfRatio = 4;
|
| 1823 |
|
| 1824 | approx_nothingUseful = 5;
|
| 1825 |
|
| 1826 | approx_ratioOfRadical = 6;
|
| 1827 |
|
| 1828 | approx_rationalOfE = 7;
|
| 1829 |
|
| 1830 | approx_logarithmsOfRationals = 8;
|
| 1831 |
|
| 1832 | approx_rationalsOfLogarithms = 9;
|
| 1833 |
|
| 1834 | approxRationalsOfRadicals = function(theFloat) {
|
| 1835 | var bestResultSoFar, complexity, error, hypothesis, i, i1, j, len, likelyMultiplier, minimumComplexity, numberOfDigitsAfterTheDot, o, precision, ratio, ref, result, splitBeforeAndAfterDot;
|
| 1836 | splitBeforeAndAfterDot = theFloat.toString().split(".");
|
| 1837 | if (splitBeforeAndAfterDot.length === 2) {
|
| 1838 | numberOfDigitsAfterTheDot = splitBeforeAndAfterDot[1].length;
|
| 1839 | precision = 1 / Math.pow(10, numberOfDigitsAfterTheDot);
|
| 1840 | } else {
|
| 1841 | return ["" + Math.floor(theFloat), approx_just_an_integer, Math.floor(theFloat), 1, 2];
|
| 1842 | }
|
| 1843 | console.log("precision: " + precision);
|
| 1844 | bestResultSoFar = null;
|
| 1845 | minimumComplexity = Number.MAX_VALUE;
|
| 1846 | ref = [2, 3, 5, 6, 7, 8, 10];
|
| 1847 | for (o = 0, len = ref.length; o < len; o++) {
|
| 1848 | i = ref[o];
|
| 1849 | for (j = i1 = 1; i1 <= 10; j = ++i1) {
|
| 1850 | hypothesis = Math.sqrt(i) / j;
|
| 1851 | if (Math.abs(hypothesis) > 1e-10) {
|
| 1852 | ratio = theFloat / hypothesis;
|
| 1853 | likelyMultiplier = Math.round(ratio);
|
| 1854 | error = Math.abs(1 - ratio / likelyMultiplier);
|
| 1855 | } else {
|
| 1856 | ratio = 1;
|
| 1857 | likelyMultiplier = 1;
|
| 1858 | error = Math.abs(theFloat - hypothesis);
|
| 1859 | }
|
| 1860 | if (error < 2 * precision) {
|
| 1861 | complexity = simpleComplexityMeasure(likelyMultiplier, i, j);
|
| 1862 | if (complexity < minimumComplexity) {
|
| 1863 | minimumComplexity = complexity;
|
| 1864 | result = likelyMultiplier + " * sqrt( " + i + " ) / " + j;
|
| 1865 | bestResultSoFar = [result, approx_ratioOfRadical, likelyMultiplier, i, j];
|
| 1866 | }
|
| 1867 | }
|
| 1868 | }
|
| 1869 | }
|
| 1870 | return bestResultSoFar;
|
| 1871 | };
|
| 1872 |
|
| 1873 | approxRadicalsOfRationals = function(theFloat) {
|
| 1874 | var bestResultSoFar, complexity, error, hypothesis, i, i1, j, len, len1, likelyMultiplier, minimumComplexity, numberOfDigitsAfterTheDot, o, precision, ratio, ref, ref1, result, splitBeforeAndAfterDot;
|
| 1875 | splitBeforeAndAfterDot = theFloat.toString().split(".");
|
| 1876 | if (splitBeforeAndAfterDot.length === 2) {
|
| 1877 | numberOfDigitsAfterTheDot = splitBeforeAndAfterDot[1].length;
|
| 1878 | precision = 1 / Math.pow(10, numberOfDigitsAfterTheDot);
|
| 1879 | } else {
|
| 1880 | return ["" + Math.floor(theFloat), approx_just_an_integer, Math.floor(theFloat), 1, 2];
|
| 1881 | }
|
| 1882 | console.log("precision: " + precision);
|
| 1883 | bestResultSoFar = null;
|
| 1884 | minimumComplexity = Number.MAX_VALUE;
|
| 1885 | ref = [1, 2, 3, 5, 6, 7, 8, 10];
|
| 1886 | for (o = 0, len = ref.length; o < len; o++) {
|
| 1887 | i = ref[o];
|
| 1888 | ref1 = [1, 2, 3, 5, 6, 7, 8, 10];
|
| 1889 | for (i1 = 0, len1 = ref1.length; i1 < len1; i1++) {
|
| 1890 | j = ref1[i1];
|
| 1891 | hypothesis = Math.sqrt(i / j);
|
| 1892 | if (Math.abs(hypothesis) > 1e-10) {
|
| 1893 | ratio = theFloat / hypothesis;
|
| 1894 | likelyMultiplier = Math.round(ratio);
|
| 1895 | error = Math.abs(1 - ratio / likelyMultiplier);
|
| 1896 | } else {
|
| 1897 | ratio = 1;
|
| 1898 | likelyMultiplier = 1;
|
| 1899 | error = Math.abs(theFloat - hypothesis);
|
| 1900 | }
|
| 1901 | if (error < 2 * precision) {
|
| 1902 | complexity = simpleComplexityMeasure(likelyMultiplier, i, j);
|
| 1903 | if (complexity < minimumComplexity) {
|
| 1904 | minimumComplexity = complexity;
|
| 1905 | result = likelyMultiplier + " * (sqrt( " + i + " / " + j + " )";
|
| 1906 | bestResultSoFar = [result, approx_radicalOfRatio, likelyMultiplier, i, j];
|
| 1907 | }
|
| 1908 | }
|
| 1909 | }
|
| 1910 | }
|
| 1911 | return bestResultSoFar;
|
| 1912 | };
|
| 1913 |
|
| 1914 | approxRadicals = function(theFloat) {
|
| 1915 | var approxRadicalsOfRationalsResult, approxRationalsOfRadicalsResult, numberOfDigitsAfterTheDot, precision, splitBeforeAndAfterDot;
|
| 1916 | splitBeforeAndAfterDot = theFloat.toString().split(".");
|
| 1917 | if (splitBeforeAndAfterDot.length === 2) {
|
| 1918 | numberOfDigitsAfterTheDot = splitBeforeAndAfterDot[1].length;
|
| 1919 | precision = 1 / Math.pow(10, numberOfDigitsAfterTheDot);
|
| 1920 | } else {
|
| 1921 | return ["" + Math.floor(theFloat), approx_just_an_integer, Math.floor(theFloat), 1, 2];
|
| 1922 | }
|
| 1923 | console.log("precision: " + precision);
|
| 1924 | approxRationalsOfRadicalsResult = approxRationalsOfRadicals(theFloat);
|
| 1925 | if (approxRationalsOfRadicalsResult != null) {
|
| 1926 | return approxRationalsOfRadicalsResult;
|
| 1927 | }
|
| 1928 | approxRadicalsOfRationalsResult = approxRadicalsOfRationals(theFloat);
|
| 1929 | if (approxRadicalsOfRationalsResult != null) {
|
| 1930 | return approxRadicalsOfRationalsResult;
|
| 1931 | }
|
| 1932 | return null;
|
| 1933 | };
|
| 1934 |
|
| 1935 | approxLogs = function(theFloat) {
|
| 1936 | var approxLogsOfRationalsResult, approxRationalsOfLogsResult, numberOfDigitsAfterTheDot, precision, splitBeforeAndAfterDot;
|
| 1937 | splitBeforeAndAfterDot = theFloat.toString().split(".");
|
| 1938 | if (splitBeforeAndAfterDot.length === 2) {
|
| 1939 | numberOfDigitsAfterTheDot = splitBeforeAndAfterDot[1].length;
|
| 1940 | precision = 1 / Math.pow(10, numberOfDigitsAfterTheDot);
|
| 1941 | } else {
|
| 1942 | return ["" + Math.floor(theFloat), approx_just_an_integer, Math.floor(theFloat), 1, 2];
|
| 1943 | }
|
| 1944 | console.log("precision: " + precision);
|
| 1945 | approxRationalsOfLogsResult = approxRationalsOfLogs(theFloat);
|
| 1946 | if (approxRationalsOfLogsResult != null) {
|
| 1947 | return approxRationalsOfLogsResult;
|
| 1948 | }
|
| 1949 | approxLogsOfRationalsResult = approxLogsOfRationals(theFloat);
|
| 1950 | if (approxLogsOfRationalsResult != null) {
|
| 1951 | return approxLogsOfRationalsResult;
|
| 1952 | }
|
| 1953 | return null;
|
| 1954 | };
|
| 1955 |
|
| 1956 | approxRationalsOfLogs = function(theFloat) {
|
| 1957 | var bestResultSoFar, complexity, error, hypothesis, i, i1, j, likelyMultiplier, minimumComplexity, numberOfDigitsAfterTheDot, o, precision, ratio, result, splitBeforeAndAfterDot;
|
| 1958 | splitBeforeAndAfterDot = theFloat.toString().split(".");
|
| 1959 | if (splitBeforeAndAfterDot.length === 2) {
|
| 1960 | numberOfDigitsAfterTheDot = splitBeforeAndAfterDot[1].length;
|
| 1961 | precision = 1 / Math.pow(10, numberOfDigitsAfterTheDot);
|
| 1962 | } else {
|
| 1963 | return ["" + Math.floor(theFloat), approx_just_an_integer, Math.floor(theFloat), 1, 2];
|
| 1964 | }
|
| 1965 | console.log("precision: " + precision);
|
| 1966 | bestResultSoFar = null;
|
| 1967 | minimumComplexity = Number.MAX_VALUE;
|
| 1968 | for (i = o = 2; o <= 5; i = ++o) {
|
| 1969 | for (j = i1 = 1; i1 <= 5; j = ++i1) {
|
| 1970 | hypothesis = Math.log(i) / j;
|
| 1971 | if (Math.abs(hypothesis) > 1e-10) {
|
| 1972 | ratio = theFloat / hypothesis;
|
| 1973 | likelyMultiplier = Math.round(ratio);
|
| 1974 | error = Math.abs(1 - ratio / likelyMultiplier);
|
| 1975 | } else {
|
| 1976 | ratio = 1;
|
| 1977 | likelyMultiplier = 1;
|
| 1978 | error = Math.abs(theFloat - hypothesis);
|
| 1979 | }
|
| 1980 | if (likelyMultiplier !== 1 && Math.abs(Math.floor(likelyMultiplier / j)) === Math.abs(likelyMultiplier / j)) {
|
| 1981 | continue;
|
| 1982 | }
|
| 1983 | if (error < 2.2 * precision) {
|
| 1984 | complexity = simpleComplexityMeasure(likelyMultiplier, i, j);
|
| 1985 | if (complexity < minimumComplexity) {
|
| 1986 | minimumComplexity = complexity;
|
| 1987 | result = likelyMultiplier + " * log( " + i + " ) / " + j;
|
| 1988 | bestResultSoFar = [result, approx_rationalsOfLogarithms, likelyMultiplier, i, j];
|
| 1989 | }
|
| 1990 | }
|
| 1991 | }
|
| 1992 | }
|
| 1993 | return bestResultSoFar;
|
| 1994 | };
|
| 1995 |
|
| 1996 | approxLogsOfRationals = function(theFloat) {
|
| 1997 | var bestResultSoFar, complexity, error, hypothesis, i, i1, j, likelyMultiplier, minimumComplexity, numberOfDigitsAfterTheDot, o, precision, ratio, result, splitBeforeAndAfterDot;
|
| 1998 | splitBeforeAndAfterDot = theFloat.toString().split(".");
|
| 1999 | if (splitBeforeAndAfterDot.length === 2) {
|
| 2000 | numberOfDigitsAfterTheDot = splitBeforeAndAfterDot[1].length;
|
| 2001 | precision = 1 / Math.pow(10, numberOfDigitsAfterTheDot);
|
| 2002 | } else {
|
| 2003 | return ["" + Math.floor(theFloat), approx_just_an_integer, Math.floor(theFloat), 1, 2];
|
| 2004 | }
|
| 2005 | console.log("precision: " + precision);
|
| 2006 | bestResultSoFar = null;
|
| 2007 | minimumComplexity = Number.MAX_VALUE;
|
| 2008 | for (i = o = 1; o <= 5; i = ++o) {
|
| 2009 | for (j = i1 = 1; i1 <= 5; j = ++i1) {
|
| 2010 | hypothesis = Math.log(i / j);
|
| 2011 | if (Math.abs(hypothesis) > 1e-10) {
|
| 2012 | ratio = theFloat / hypothesis;
|
| 2013 | likelyMultiplier = Math.round(ratio);
|
| 2014 | error = Math.abs(1 - ratio / likelyMultiplier);
|
| 2015 | } else {
|
| 2016 | ratio = 1;
|
| 2017 | likelyMultiplier = 1;
|
| 2018 | error = Math.abs(theFloat - hypothesis);
|
| 2019 | }
|
| 2020 | if (error < 1.96 * precision) {
|
| 2021 | complexity = simpleComplexityMeasure(likelyMultiplier, i, j);
|
| 2022 | if (complexity < minimumComplexity) {
|
| 2023 | minimumComplexity = complexity;
|
| 2024 | result = likelyMultiplier + " * log( " + i + " / " + j + " )";
|
| 2025 | bestResultSoFar = [result, approx_logarithmsOfRationals, likelyMultiplier, i, j];
|
| 2026 | }
|
| 2027 | }
|
| 2028 | }
|
| 2029 | }
|
| 2030 | return bestResultSoFar;
|
| 2031 | };
|
| 2032 |
|
| 2033 | approxRationalsOfPowersOfE = function(theFloat) {
|
| 2034 | var bestResultSoFar, complexity, error, hypothesis, i, i1, j, likelyMultiplier, minimumComplexity, numberOfDigitsAfterTheDot, o, precision, ratio, result, splitBeforeAndAfterDot;
|
| 2035 | splitBeforeAndAfterDot = theFloat.toString().split(".");
|
| 2036 | if (splitBeforeAndAfterDot.length === 2) {
|
| 2037 | numberOfDigitsAfterTheDot = splitBeforeAndAfterDot[1].length;
|
| 2038 | precision = 1 / Math.pow(10, numberOfDigitsAfterTheDot);
|
| 2039 | } else {
|
| 2040 | return ["" + Math.floor(theFloat), approx_just_an_integer, Math.floor(theFloat), 1, 2];
|
| 2041 | }
|
| 2042 | console.log("precision: " + precision);
|
| 2043 | bestResultSoFar = null;
|
| 2044 | minimumComplexity = Number.MAX_VALUE;
|
| 2045 | for (i = o = 1; o <= 2; i = ++o) {
|
| 2046 | for (j = i1 = 1; i1 <= 12; j = ++i1) {
|
| 2047 | hypothesis = Math.pow(Math.E, i) / j;
|
| 2048 | if (Math.abs(hypothesis) > 1e-10) {
|
| 2049 | ratio = theFloat / hypothesis;
|
| 2050 | likelyMultiplier = Math.round(ratio);
|
| 2051 | error = Math.abs(1 - ratio / likelyMultiplier);
|
| 2052 | } else {
|
| 2053 | ratio = 1;
|
| 2054 | likelyMultiplier = 1;
|
| 2055 | error = Math.abs(theFloat - hypothesis);
|
| 2056 | }
|
| 2057 | if (error < 2 * precision) {
|
| 2058 | complexity = simpleComplexityMeasure(likelyMultiplier, i, j);
|
| 2059 | if (complexity < minimumComplexity) {
|
| 2060 | minimumComplexity = complexity;
|
| 2061 | result = likelyMultiplier + " * (e ^ " + i + " ) / " + j;
|
| 2062 | bestResultSoFar = [result, approx_rationalOfE, likelyMultiplier, i, j];
|
| 2063 | }
|
| 2064 | }
|
| 2065 | }
|
| 2066 | }
|
| 2067 | return bestResultSoFar;
|
| 2068 | };
|
| 2069 |
|
| 2070 | approxRationalsOfPowersOfPI = function(theFloat) {
|
| 2071 | var bestResultSoFar, complexity, error, hypothesis, i, i1, j, likelyMultiplier, minimumComplexity, numberOfDigitsAfterTheDot, o, precision, ratio, result, splitBeforeAndAfterDot;
|
| 2072 | splitBeforeAndAfterDot = theFloat.toString().split(".");
|
| 2073 | if (splitBeforeAndAfterDot.length === 2) {
|
| 2074 | numberOfDigitsAfterTheDot = splitBeforeAndAfterDot[1].length;
|
| 2075 | precision = 1 / Math.pow(10, numberOfDigitsAfterTheDot);
|
| 2076 | } else {
|
| 2077 | return ["" + Math.floor(theFloat), approx_just_an_integer, Math.floor(theFloat), 1, 2];
|
| 2078 | }
|
| 2079 | console.log("precision: " + precision);
|
| 2080 | bestResultSoFar = null;
|
| 2081 | minimumComplexity = Number.MAX_VALUE;
|
| 2082 | for (i = o = 1; o <= 5; i = ++o) {
|
| 2083 | for (j = i1 = 1; i1 <= 12; j = ++i1) {
|
| 2084 | hypothesis = Math.pow(Math.PI, i) / j;
|
| 2085 | if (Math.abs(hypothesis) > 1e-10) {
|
| 2086 | ratio = theFloat / hypothesis;
|
| 2087 | likelyMultiplier = Math.round(ratio);
|
| 2088 | error = Math.abs(1 - ratio / likelyMultiplier);
|
| 2089 | } else {
|
| 2090 | ratio = 1;
|
| 2091 | likelyMultiplier = 1;
|
| 2092 | error = Math.abs(theFloat - hypothesis);
|
| 2093 | }
|
| 2094 | if (error < 2 * precision) {
|
| 2095 | complexity = simpleComplexityMeasure(likelyMultiplier, i, j);
|
| 2096 | if (complexity < minimumComplexity) {
|
| 2097 | minimumComplexity = complexity;
|
| 2098 | result = likelyMultiplier + " * (pi ^ " + i + " ) / " + j + " )";
|
| 2099 | bestResultSoFar = [result, approx_rationalOfPi, likelyMultiplier, i, j];
|
| 2100 | }
|
| 2101 | }
|
| 2102 | }
|
| 2103 | }
|
| 2104 | return bestResultSoFar;
|
| 2105 | };
|
| 2106 |
|
| 2107 | approxTrigonometric = function(theFloat) {
|
| 2108 | var approxSineOfRationalMultiplesOfPIResult, approxSineOfRationalsResult, numberOfDigitsAfterTheDot, precision, splitBeforeAndAfterDot;
|
| 2109 | splitBeforeAndAfterDot = theFloat.toString().split(".");
|
| 2110 | if (splitBeforeAndAfterDot.length === 2) {
|
| 2111 | numberOfDigitsAfterTheDot = splitBeforeAndAfterDot[1].length;
|
| 2112 | precision = 1 / Math.pow(10, numberOfDigitsAfterTheDot);
|
| 2113 | } else {
|
| 2114 | return ["" + Math.floor(theFloat), approx_just_an_integer, Math.floor(theFloat), 1, 2];
|
| 2115 | }
|
| 2116 | console.log("precision: " + precision);
|
| 2117 | approxSineOfRationalsResult = approxSineOfRationals(theFloat);
|
| 2118 | if (approxSineOfRationalsResult != null) {
|
| 2119 | return approxSineOfRationalsResult;
|
| 2120 | }
|
| 2121 | approxSineOfRationalMultiplesOfPIResult = approxSineOfRationalMultiplesOfPI(theFloat);
|
| 2122 | if (approxSineOfRationalMultiplesOfPIResult != null) {
|
| 2123 | return approxSineOfRationalMultiplesOfPIResult;
|
| 2124 | }
|
| 2125 | return null;
|
| 2126 | };
|
| 2127 |
|
| 2128 | approxSineOfRationals = function(theFloat) {
|
| 2129 | var bestResultSoFar, complexity, error, fraction, hypothesis, i, i1, j, likelyMultiplier, minimumComplexity, numberOfDigitsAfterTheDot, o, precision, ratio, result, splitBeforeAndAfterDot;
|
| 2130 | splitBeforeAndAfterDot = theFloat.toString().split(".");
|
| 2131 | if (splitBeforeAndAfterDot.length === 2) {
|
| 2132 | numberOfDigitsAfterTheDot = splitBeforeAndAfterDot[1].length;
|
| 2133 | precision = 1 / Math.pow(10, numberOfDigitsAfterTheDot);
|
| 2134 | } else {
|
| 2135 | return ["" + Math.floor(theFloat), approx_just_an_integer, Math.floor(theFloat), 1, 2];
|
| 2136 | }
|
| 2137 | console.log("precision: " + precision);
|
| 2138 | bestResultSoFar = null;
|
| 2139 | minimumComplexity = Number.MAX_VALUE;
|
| 2140 | for (i = o = 1; o <= 4; i = ++o) {
|
| 2141 | for (j = i1 = 1; i1 <= 4; j = ++i1) {
|
| 2142 | fraction = i / j;
|
| 2143 | hypothesis = Math.sin(fraction);
|
| 2144 | if (Math.abs(hypothesis) > 1e-10) {
|
| 2145 | ratio = theFloat / hypothesis;
|
| 2146 | likelyMultiplier = Math.round(ratio);
|
| 2147 | error = Math.abs(1 - ratio / likelyMultiplier);
|
| 2148 | } else {
|
| 2149 | ratio = 1;
|
| 2150 | likelyMultiplier = 1;
|
| 2151 | error = Math.abs(theFloat - hypothesis);
|
| 2152 | }
|
| 2153 | if (error < 2 * precision) {
|
| 2154 | complexity = simpleComplexityMeasure(likelyMultiplier, i, j);
|
| 2155 | if (complexity < minimumComplexity) {
|
| 2156 | minimumComplexity = complexity;
|
| 2157 | result = likelyMultiplier + " * sin( " + i + "/" + j + " )";
|
| 2158 | bestResultSoFar = [result, approx_sine_of_rational, likelyMultiplier, i, j];
|
| 2159 | }
|
| 2160 | }
|
| 2161 | }
|
| 2162 | }
|
| 2163 | return bestResultSoFar;
|
| 2164 | };
|
| 2165 |
|
| 2166 | approxSineOfRationalMultiplesOfPI = function(theFloat) {
|
| 2167 | var bestResultSoFar, complexity, error, fraction, hypothesis, i, i1, j, likelyMultiplier, minimumComplexity, numberOfDigitsAfterTheDot, o, precision, ratio, result, splitBeforeAndAfterDot;
|
| 2168 | splitBeforeAndAfterDot = theFloat.toString().split(".");
|
| 2169 | if (splitBeforeAndAfterDot.length === 2) {
|
| 2170 | numberOfDigitsAfterTheDot = splitBeforeAndAfterDot[1].length;
|
| 2171 | precision = 1 / Math.pow(10, numberOfDigitsAfterTheDot);
|
| 2172 | } else {
|
| 2173 | return ["" + Math.floor(theFloat), approx_just_an_integer, Math.floor(theFloat), 1, 2];
|
| 2174 | }
|
| 2175 | console.log("precision: " + precision);
|
| 2176 | bestResultSoFar = null;
|
| 2177 | minimumComplexity = Number.MAX_VALUE;
|
| 2178 | for (i = o = 1; o <= 13; i = ++o) {
|
| 2179 | for (j = i1 = 1; i1 <= 13; j = ++i1) {
|
| 2180 | fraction = i / j;
|
| 2181 | hypothesis = Math.sin(Math.PI * fraction);
|
| 2182 | if (Math.abs(hypothesis) > 1e-10) {
|
| 2183 | ratio = theFloat / hypothesis;
|
| 2184 | likelyMultiplier = Math.round(ratio);
|
| 2185 | error = Math.abs(1 - ratio / likelyMultiplier);
|
| 2186 | } else {
|
| 2187 | ratio = 1;
|
| 2188 | likelyMultiplier = 1;
|
| 2189 | error = Math.abs(theFloat - hypothesis);
|
| 2190 | }
|
| 2191 | if (error < 23 * precision) {
|
| 2192 | complexity = simpleComplexityMeasure(likelyMultiplier, i, j);
|
| 2193 | if (complexity < minimumComplexity) {
|
| 2194 | minimumComplexity = complexity;
|
| 2195 | result = likelyMultiplier + " * sin( " + i + "/" + j + " * pi )";
|
| 2196 | bestResultSoFar = [result, approx_sine_of_pi_times_rational, likelyMultiplier, i, j];
|
| 2197 | }
|
| 2198 | }
|
| 2199 | }
|
| 2200 | }
|
| 2201 | return bestResultSoFar;
|
| 2202 | };
|
| 2203 |
|
| 2204 | approxAll = function(theFloat) {
|
| 2205 | var LOG_EXPLANATIONS, approxLogsResult, approxRadicalsResult, approxRationalsOfPowersOfEResult, approxRationalsOfPowersOfPIResult, approxTrigonometricResult, bestApproxSoFar, constantsSum, constantsSumMin, numberOfDigitsAfterTheDot, precision, splitBeforeAndAfterDot;
|
| 2206 | splitBeforeAndAfterDot = theFloat.toString().split(".");
|
| 2207 | if (splitBeforeAndAfterDot.length === 2) {
|
| 2208 | numberOfDigitsAfterTheDot = splitBeforeAndAfterDot[1].length;
|
| 2209 | precision = 1 / Math.pow(10, numberOfDigitsAfterTheDot);
|
| 2210 | } else {
|
| 2211 | return ["" + Math.floor(theFloat), approx_just_an_integer, Math.floor(theFloat), 1, 2];
|
| 2212 | }
|
| 2213 | console.log("precision: " + precision);
|
| 2214 | constantsSumMin = Number.MAX_VALUE;
|
| 2215 | constantsSum = 0;
|
| 2216 | bestApproxSoFar = null;
|
| 2217 | LOG_EXPLANATIONS = true;
|
| 2218 | approxRadicalsResult = approxRadicals(theFloat);
|
| 2219 | if (approxRadicalsResult != null) {
|
| 2220 | constantsSum = simpleComplexityMeasure(approxRadicalsResult);
|
| 2221 | if (constantsSum < constantsSumMin) {
|
| 2222 | if (LOG_EXPLANATIONS) {
|
| 2223 | console.log("better explanation by approxRadicals: " + approxRadicalsResult + " complexity: " + constantsSum);
|
| 2224 | }
|
| 2225 | constantsSumMin = constantsSum;
|
| 2226 | bestApproxSoFar = approxRadicalsResult;
|
| 2227 | } else {
|
| 2228 | if (LOG_EXPLANATIONS) {
|
| 2229 | console.log("subpar explanation by approxRadicals: " + approxRadicalsResult + " complexity: " + constantsSum);
|
| 2230 | }
|
| 2231 | }
|
| 2232 | }
|
| 2233 | approxLogsResult = approxLogs(theFloat);
|
| 2234 | if (approxLogsResult != null) {
|
| 2235 | constantsSum = simpleComplexityMeasure(approxLogsResult);
|
| 2236 | if (constantsSum < constantsSumMin) {
|
| 2237 | if (LOG_EXPLANATIONS) {
|
| 2238 | console.log("better explanation by approxLogs: " + approxLogsResult + " complexity: " + constantsSum);
|
| 2239 | }
|
| 2240 | constantsSumMin = constantsSum;
|
| 2241 | bestApproxSoFar = approxLogsResult;
|
| 2242 | } else {
|
| 2243 | if (LOG_EXPLANATIONS) {
|
| 2244 | console.log("subpar explanation by approxLogs: " + approxLogsResult + " complexity: " + constantsSum);
|
| 2245 | }
|
| 2246 | }
|
| 2247 | }
|
| 2248 | approxRationalsOfPowersOfEResult = approxRationalsOfPowersOfE(theFloat);
|
| 2249 | if (approxRationalsOfPowersOfEResult != null) {
|
| 2250 | constantsSum = simpleComplexityMeasure(approxRationalsOfPowersOfEResult);
|
| 2251 | if (constantsSum < constantsSumMin) {
|
| 2252 | if (LOG_EXPLANATIONS) {
|
| 2253 | console.log("better explanation by approxRationalsOfPowersOfE: " + approxRationalsOfPowersOfEResult + " complexity: " + constantsSum);
|
| 2254 | }
|
| 2255 | constantsSumMin = constantsSum;
|
| 2256 | bestApproxSoFar = approxRationalsOfPowersOfEResult;
|
| 2257 | } else {
|
| 2258 | if (LOG_EXPLANATIONS) {
|
| 2259 | console.log("subpar explanation by approxRationalsOfPowersOfE: " + approxRationalsOfPowersOfEResult + " complexity: " + constantsSum);
|
| 2260 | }
|
| 2261 | }
|
| 2262 | }
|
| 2263 | approxRationalsOfPowersOfPIResult = approxRationalsOfPowersOfPI(theFloat);
|
| 2264 | if (approxRationalsOfPowersOfPIResult != null) {
|
| 2265 | constantsSum = simpleComplexityMeasure(approxRationalsOfPowersOfPIResult);
|
| 2266 | if (constantsSum < constantsSumMin) {
|
| 2267 | if (LOG_EXPLANATIONS) {
|
| 2268 | console.log("better explanation by approxRationalsOfPowersOfPI: " + approxRationalsOfPowersOfPIResult + " complexity: " + constantsSum);
|
| 2269 | }
|
| 2270 | constantsSumMin = constantsSum;
|
| 2271 | bestApproxSoFar = approxRationalsOfPowersOfPIResult;
|
| 2272 | } else {
|
| 2273 | if (LOG_EXPLANATIONS) {
|
| 2274 | console.log("subpar explanation by approxRationalsOfPowersOfPI: " + approxRationalsOfPowersOfPIResult + " complexity: " + constantsSum);
|
| 2275 | }
|
| 2276 | }
|
| 2277 | }
|
| 2278 | approxTrigonometricResult = approxTrigonometric(theFloat);
|
| 2279 | if (approxTrigonometricResult != null) {
|
| 2280 | constantsSum = simpleComplexityMeasure(approxTrigonometricResult);
|
| 2281 | if (constantsSum < constantsSumMin) {
|
| 2282 | if (LOG_EXPLANATIONS) {
|
| 2283 | console.log("better explanation by approxTrigonometric: " + approxTrigonometricResult + " complexity: " + constantsSum);
|
| 2284 | }
|
| 2285 | constantsSumMin = constantsSum;
|
| 2286 | bestApproxSoFar = approxTrigonometricResult;
|
| 2287 | } else {
|
| 2288 | if (LOG_EXPLANATIONS) {
|
| 2289 | console.log("subpar explanation by approxTrigonometric: " + approxTrigonometricResult + " complexity: " + constantsSum);
|
| 2290 | }
|
| 2291 | }
|
| 2292 | }
|
| 2293 | return bestApproxSoFar;
|
| 2294 | };
|
| 2295 |
|
| 2296 | simpleComplexityMeasure = function(aResult, b, c) {
|
| 2297 | var theSum;
|
| 2298 | theSum = null;
|
| 2299 | if (aResult instanceof Array) {
|
| 2300 | switch (aResult[1]) {
|
| 2301 | case approx_sine_of_pi_times_rational:
|
| 2302 | theSum = 4;
|
| 2303 | break;
|
| 2304 | case approx_rationalOfPi:
|
| 2305 | theSum = Math.pow(4, Math.abs(aResult[3])) * Math.abs(aResult[2]);
|
| 2306 | break;
|
| 2307 | case approx_rationalOfE:
|
| 2308 | theSum = Math.pow(3, Math.abs(aResult[3])) * Math.abs(aResult[2]);
|
| 2309 | break;
|
| 2310 | default:
|
| 2311 | theSum = 0;
|
| 2312 | }
|
| 2313 | theSum += Math.abs(aResult[2]) * (Math.abs(aResult[3]) + Math.abs(aResult[4]));
|
| 2314 | } else {
|
| 2315 | theSum += Math.abs(aResult) * (Math.abs(b) + Math.abs(c));
|
| 2316 | }
|
| 2317 | if (aResult[2] === 1) {
|
| 2318 | theSum -= 1;
|
| 2319 | } else {
|
| 2320 | theSum += 1;
|
| 2321 | }
|
| 2322 | if (aResult[3] === 1) {
|
| 2323 | theSum -= 1;
|
| 2324 | } else {
|
| 2325 | theSum += 1;
|
| 2326 | }
|
| 2327 | if (aResult[4] === 1) {
|
| 2328 | theSum -= 1;
|
| 2329 | } else {
|
| 2330 | theSum += 1;
|
| 2331 | }
|
| 2332 | if (theSum < 0) {
|
| 2333 | theSum = 0;
|
| 2334 | }
|
| 2335 | return theSum;
|
| 2336 | };
|
| 2337 |
|
| 2338 | testApprox = function() {
|
| 2339 | var error, fraction, i, i1, i2, i3, j, j1, j2, j3, k3, l1, l2, l3, len, len1, len2, len3, len4, len5, len6, len7, m1, m2, m3, n1, n2, o, o1, o2, originalValue, q1, q2, r1, r2, ref, ref1, ref2, ref3, ref4, ref5, ref6, ref7, returned, returnedFraction, returnedValue, s1, s2, t1, t2, u1, u2, v1, v2, value, x1, x2, z1, z2;
|
| 2340 | ref = [2, 3, 5, 6, 7, 8, 10];
|
| 2341 | for (o = 0, len = ref.length; o < len; o++) {
|
| 2342 | i = ref[o];
|
| 2343 | ref1 = [2, 3, 5, 6, 7, 8, 10];
|
| 2344 | for (i1 = 0, len1 = ref1.length; i1 < len1; i1++) {
|
| 2345 | j = ref1[i1];
|
| 2346 | if (i === j) {
|
| 2347 | continue;
|
| 2348 | }
|
| 2349 | console.log("testapproxRadicals testing: " + "1 * sqrt( " + i + " ) / " + j);
|
| 2350 | fraction = i / j;
|
| 2351 | value = Math.sqrt(i) / j;
|
| 2352 | returned = approxRadicals(value);
|
| 2353 | returnedValue = returned[2] * Math.sqrt(returned[3]) / returned[4];
|
| 2354 | if (Math.abs(value - returnedValue) > 1e-15) {
|
| 2355 | console.log("fail testapproxRadicals: " + "1 * sqrt( " + i + " ) / " + j + " . obtained: " + returned);
|
| 2356 | }
|
| 2357 | }
|
| 2358 | }
|
| 2359 | ref2 = [2, 3, 5, 6, 7, 8, 10];
|
| 2360 | for (j1 = 0, len2 = ref2.length; j1 < len2; j1++) {
|
| 2361 | i = ref2[j1];
|
| 2362 | ref3 = [2, 3, 5, 6, 7, 8, 10];
|
| 2363 | for (l1 = 0, len3 = ref3.length; l1 < len3; l1++) {
|
| 2364 | j = ref3[l1];
|
| 2365 | if (i === j) {
|
| 2366 | continue;
|
| 2367 | }
|
| 2368 | console.log("testapproxRadicals testing with 4 digits: " + "1 * sqrt( " + i + " ) / " + j);
|
| 2369 | fraction = i / j;
|
| 2370 | originalValue = Math.sqrt(i) / j;
|
| 2371 | value = originalValue.toFixed(4);
|
| 2372 | returned = approxRadicals(value);
|
| 2373 | returnedValue = returned[2] * Math.sqrt(returned[3]) / returned[4];
|
| 2374 | if (Math.abs(originalValue - returnedValue) > 1e-15) {
|
| 2375 | console.log("fail testapproxRadicals with 4 digits: " + "1 * sqrt( " + i + " ) / " + j + " . obtained: " + returned);
|
| 2376 | }
|
| 2377 | }
|
| 2378 | }
|
| 2379 | ref4 = [2, 3, 5, 6, 7, 8, 10];
|
| 2380 | for (m1 = 0, len4 = ref4.length; m1 < len4; m1++) {
|
| 2381 | i = ref4[m1];
|
| 2382 | ref5 = [2, 3, 5, 6, 7, 8, 10];
|
| 2383 | for (n1 = 0, len5 = ref5.length; n1 < len5; n1++) {
|
| 2384 | j = ref5[n1];
|
| 2385 | if (i === j) {
|
| 2386 | continue;
|
| 2387 | }
|
| 2388 | console.log("testapproxRadicals testing: " + "1 * sqrt( " + i + " / " + j + " )");
|
| 2389 | fraction = i / j;
|
| 2390 | value = Math.sqrt(i / j);
|
| 2391 | returned = approxRadicals(value);
|
| 2392 | if (returned != null) {
|
| 2393 | returnedValue = returned[2] * Math.sqrt(returned[3] / returned[4]);
|
| 2394 | if (returned[1] === approx_radicalOfRatio && Math.abs(value - returnedValue) > 1e-15) {
|
| 2395 | console.log("fail testapproxRadicals: " + "1 * sqrt( " + i + " / " + j + " ) . obtained: " + returned);
|
| 2396 | }
|
| 2397 | }
|
| 2398 | }
|
| 2399 | }
|
| 2400 | ref6 = [1, 2, 3, 5, 6, 7, 8, 10];
|
| 2401 | for (o1 = 0, len6 = ref6.length; o1 < len6; o1++) {
|
| 2402 | i = ref6[o1];
|
| 2403 | ref7 = [1, 2, 3, 5, 6, 7, 8, 10];
|
| 2404 | for (q1 = 0, len7 = ref7.length; q1 < len7; q1++) {
|
| 2405 | j = ref7[q1];
|
| 2406 | if (i === 1 && j === 1) {
|
| 2407 | continue;
|
| 2408 | }
|
| 2409 | console.log("testapproxRadicals testing with 4 digits:: " + "1 * sqrt( " + i + " / " + j + " )");
|
| 2410 | fraction = i / j;
|
| 2411 | originalValue = Math.sqrt(i / j);
|
| 2412 | value = originalValue.toFixed(4);
|
| 2413 | returned = approxRadicals(value);
|
| 2414 | returnedValue = returned[2] * Math.sqrt(returned[3] / returned[4]);
|
| 2415 | if (returned[1] === approx_radicalOfRatio && Math.abs(originalValue - returnedValue) > 1e-15) {
|
| 2416 | console.log("fail testapproxRadicals with 4 digits:: " + "1 * sqrt( " + i + " / " + j + " ) . obtained: " + returned);
|
| 2417 | }
|
| 2418 | }
|
| 2419 | }
|
| 2420 | for (i = r1 = 1; r1 <= 5; i = ++r1) {
|
| 2421 | for (j = s1 = 1; s1 <= 5; j = ++s1) {
|
| 2422 | console.log("testApproxAll testing: " + "1 * log(" + i + " ) / " + j);
|
| 2423 | fraction = i / j;
|
| 2424 | value = Math.log(i) / j;
|
| 2425 | returned = approxAll(value);
|
| 2426 | returnedValue = returned[2] * Math.log(returned[3]) / returned[4];
|
| 2427 | if (Math.abs(value - returnedValue) > 1e-15) {
|
| 2428 | console.log("fail testApproxAll: " + "1 * log(" + i + " ) / " + j + " . obtained: " + returned);
|
| 2429 | }
|
| 2430 | }
|
| 2431 | }
|
| 2432 | for (i = t1 = 1; t1 <= 5; i = ++t1) {
|
| 2433 | for (j = u1 = 1; u1 <= 5; j = ++u1) {
|
| 2434 | console.log("testApproxAll testing with 4 digits: " + "1 * log(" + i + " ) / " + j);
|
| 2435 | fraction = i / j;
|
| 2436 | originalValue = Math.log(i) / j;
|
| 2437 | value = originalValue.toFixed(4);
|
| 2438 | returned = approxAll(value);
|
| 2439 | returnedValue = returned[2] * Math.log(returned[3]) / returned[4];
|
| 2440 | if (Math.abs(originalValue - returnedValue) > 1e-15) {
|
| 2441 | console.log("fail testApproxAll with 4 digits: " + "1 * log(" + i + " ) / " + j + " . obtained: " + returned);
|
| 2442 | }
|
| 2443 | }
|
| 2444 | }
|
| 2445 | for (i = v1 = 1; v1 <= 5; i = ++v1) {
|
| 2446 | for (j = x1 = 1; x1 <= 5; j = ++x1) {
|
| 2447 | console.log("testApproxAll testing: " + "1 * log(" + i + " / " + j + " )");
|
| 2448 | fraction = i / j;
|
| 2449 | value = Math.log(i / j);
|
| 2450 | returned = approxAll(value);
|
| 2451 | returnedValue = returned[2] * Math.log(returned[3] / returned[4]);
|
| 2452 | if (Math.abs(value - returnedValue) > 1e-15) {
|
| 2453 | console.log("fail testApproxAll: " + "1 * log(" + i + " / " + j + " )" + " . obtained: " + returned);
|
| 2454 | }
|
| 2455 | }
|
| 2456 | }
|
| 2457 | for (i = z1 = 1; z1 <= 5; i = ++z1) {
|
| 2458 | for (j = i2 = 1; i2 <= 5; j = ++i2) {
|
| 2459 | console.log("testApproxAll testing with 4 digits: " + "1 * log(" + i + " / " + j + " )");
|
| 2460 | fraction = i / j;
|
| 2461 | originalValue = Math.log(i / j);
|
| 2462 | value = originalValue.toFixed(4);
|
| 2463 | returned = approxAll(value);
|
| 2464 | returnedValue = returned[2] * Math.log(returned[3] / returned[4]);
|
| 2465 | if (Math.abs(originalValue - returnedValue) > 1e-15) {
|
| 2466 | console.log("fail testApproxAll with 4 digits: " + "1 * log(" + i + " / " + j + " )" + " . obtained: " + returned);
|
| 2467 | }
|
| 2468 | }
|
| 2469 | }
|
| 2470 | for (i = j2 = 1; j2 <= 2; i = ++j2) {
|
| 2471 | for (j = l2 = 1; l2 <= 12; j = ++l2) {
|
| 2472 | console.log("testApproxAll testing: " + "1 * (e ^ " + i + " ) / " + j);
|
| 2473 | fraction = i / j;
|
| 2474 | value = Math.pow(Math.E, i) / j;
|
| 2475 | returned = approxAll(value);
|
| 2476 | returnedValue = returned[2] * Math.pow(Math.E, returned[3]) / returned[4];
|
| 2477 | if (Math.abs(value - returnedValue) > 1e-15) {
|
| 2478 | console.log("fail testApproxAll: " + "1 * (e ^ " + i + " ) / " + j + " . obtained: " + returned);
|
| 2479 | }
|
| 2480 | }
|
| 2481 | }
|
| 2482 | for (i = m2 = 1; m2 <= 2; i = ++m2) {
|
| 2483 | for (j = n2 = 1; n2 <= 12; j = ++n2) {
|
| 2484 | console.log("approxRationalsOfPowersOfE testing with 4 digits: " + "1 * (e ^ " + i + " ) / " + j);
|
| 2485 | fraction = i / j;
|
| 2486 | originalValue = Math.pow(Math.E, i) / j;
|
| 2487 | value = originalValue.toFixed(4);
|
| 2488 | returned = approxRationalsOfPowersOfE(value);
|
| 2489 | returnedValue = returned[2] * Math.pow(Math.E, returned[3]) / returned[4];
|
| 2490 | if (Math.abs(originalValue - returnedValue) > 1e-15) {
|
| 2491 | console.log("fail approxRationalsOfPowersOfE with 4 digits: " + "1 * (e ^ " + i + " ) / " + j + " . obtained: " + returned);
|
| 2492 | }
|
| 2493 | }
|
| 2494 | }
|
| 2495 | for (i = o2 = 1; o2 <= 2; i = ++o2) {
|
| 2496 | for (j = q2 = 1; q2 <= 12; j = ++q2) {
|
| 2497 | console.log("testApproxAll testing: " + "1 * pi ^ " + i + " / " + j);
|
| 2498 | fraction = i / j;
|
| 2499 | value = Math.pow(Math.PI, i) / j;
|
| 2500 | returned = approxAll(value);
|
| 2501 | returnedValue = returned[2] * Math.pow(Math.PI, returned[3]) / returned[4];
|
| 2502 | if (Math.abs(value - returnedValue) > 1e-15) {
|
| 2503 | console.log("fail testApproxAll: " + "1 * pi ^ " + i + " / " + j + " ) . obtained: " + returned);
|
| 2504 | }
|
| 2505 | }
|
| 2506 | }
|
| 2507 | for (i = r2 = 1; r2 <= 2; i = ++r2) {
|
| 2508 | for (j = s2 = 1; s2 <= 12; j = ++s2) {
|
| 2509 | console.log("approxRationalsOfPowersOfPI testing with 4 digits: " + "1 * pi ^ " + i + " / " + j);
|
| 2510 | fraction = i / j;
|
| 2511 | originalValue = Math.pow(Math.PI, i) / j;
|
| 2512 | value = originalValue.toFixed(4);
|
| 2513 | returned = approxRationalsOfPowersOfPI(value);
|
| 2514 | returnedValue = returned[2] * Math.pow(Math.PI, returned[3]) / returned[4];
|
| 2515 | if (Math.abs(originalValue - returnedValue) > 1e-15) {
|
| 2516 | console.log("fail approxRationalsOfPowersOfPI with 4 digits: " + "1 * pi ^ " + i + " / " + j + " ) . obtained: " + returned);
|
| 2517 | }
|
| 2518 | }
|
| 2519 | }
|
| 2520 | for (i = t2 = 1; t2 <= 4; i = ++t2) {
|
| 2521 | for (j = u2 = 1; u2 <= 4; j = ++u2) {
|
| 2522 | console.log("testApproxAll testing: " + "1 * sin( " + i + "/" + j + " )");
|
| 2523 | fraction = i / j;
|
| 2524 | value = Math.sin(fraction);
|
| 2525 | returned = approxAll(value);
|
| 2526 | returnedFraction = returned[3] / returned[4];
|
| 2527 | returnedValue = returned[2] * Math.sin(returnedFraction);
|
| 2528 | if (Math.abs(value - returnedValue) > 1e-15) {
|
| 2529 | console.log("fail testApproxAll: " + "1 * sin( " + i + "/" + j + " ) . obtained: " + returned);
|
| 2530 | }
|
| 2531 | }
|
| 2532 | }
|
| 2533 | for (i = v2 = 1; v2 <= 4; i = ++v2) {
|
| 2534 | for (j = x2 = 1; x2 <= 4; j = ++x2) {
|
| 2535 | console.log("testApproxAll testing with 5 digits: " + "1 * sin( " + i + "/" + j + " )");
|
| 2536 | fraction = i / j;
|
| 2537 | originalValue = Math.sin(fraction);
|
| 2538 | value = originalValue.toFixed(5);
|
| 2539 | returned = approxAll(value);
|
| 2540 | if (returned == null) {
|
| 2541 | console.log("fail testApproxAll with 5 digits: " + "1 * sin( " + i + "/" + j + " ) . obtained: undefined ");
|
| 2542 | }
|
| 2543 | returnedFraction = returned[3] / returned[4];
|
| 2544 | returnedValue = returned[2] * Math.sin(returnedFraction);
|
| 2545 | error = Math.abs(originalValue - returnedValue);
|
| 2546 | if (error > 1e-14) {
|
| 2547 | console.log("fail testApproxAll with 5 digits: " + "1 * sin( " + i + "/" + j + " ) . obtained: " + returned + " error: " + error);
|
| 2548 | }
|
| 2549 | }
|
| 2550 | }
|
| 2551 | for (i = z2 = 1; z2 <= 4; i = ++z2) {
|
| 2552 | for (j = i3 = 1; i3 <= 4; j = ++i3) {
|
| 2553 | console.log("testApproxAll testing with 4 digits: " + "1 * sin( " + i + "/" + j + " )");
|
| 2554 | fraction = i / j;
|
| 2555 | originalValue = Math.sin(fraction);
|
| 2556 | value = originalValue.toFixed(4);
|
| 2557 | returned = approxAll(value);
|
| 2558 | if (returned == null) {
|
| 2559 | console.log("fail testApproxAll with 4 digits: " + "1 * sin( " + i + "/" + j + " ) . obtained: undefined ");
|
| 2560 | }
|
| 2561 | returnedFraction = returned[3] / returned[4];
|
| 2562 | returnedValue = returned[2] * Math.sin(returnedFraction);
|
| 2563 | error = Math.abs(originalValue - returnedValue);
|
| 2564 | if (error > 1e-14) {
|
| 2565 | console.log("fail testApproxAll with 4 digits: " + "1 * sin( " + i + "/" + j + " ) . obtained: " + returned + " error: " + error);
|
| 2566 | }
|
| 2567 | }
|
| 2568 | }
|
| 2569 | value = 0;
|
| 2570 | if (approxAll(value)[0] !== "0") {
|
| 2571 | console.log("fail testApproxAll: 0");
|
| 2572 | }
|
| 2573 | value = 0.0;
|
| 2574 | if (approxAll(value)[0] !== "0") {
|
| 2575 | console.log("fail testApproxAll: 0.0");
|
| 2576 | }
|
| 2577 | value = 0.00;
|
| 2578 | if (approxAll(value)[0] !== "0") {
|
| 2579 | console.log("fail testApproxAll: 0.00");
|
| 2580 | }
|
| 2581 | value = 0.000;
|
| 2582 | if (approxAll(value)[0] !== "0") {
|
| 2583 | console.log("fail testApproxAll: 0.000");
|
| 2584 | }
|
| 2585 | value = 0.0000;
|
| 2586 | if (approxAll(value)[0] !== "0") {
|
| 2587 | console.log("fail testApproxAll: 0.0000");
|
| 2588 | }
|
| 2589 | value = 1;
|
| 2590 | if (approxAll(value)[0] !== "1") {
|
| 2591 | console.log("fail testApproxAll: 1");
|
| 2592 | }
|
| 2593 | value = 1.0;
|
| 2594 | if (approxAll(value)[0] !== "1") {
|
| 2595 | console.log("fail testApproxAll: 1.0");
|
| 2596 | }
|
| 2597 | value = 1.00;
|
| 2598 | if (approxAll(value)[0] !== "1") {
|
| 2599 | console.log("fail testApproxAll: 1.00");
|
| 2600 | }
|
| 2601 | value = 1.000;
|
| 2602 | if (approxAll(value)[0] !== "1") {
|
| 2603 | console.log("fail testApproxAll: 1.000");
|
| 2604 | }
|
| 2605 | value = 1.0000;
|
| 2606 | if (approxAll(value)[0] !== "1") {
|
| 2607 | console.log("fail testApproxAll: 1.0000");
|
| 2608 | }
|
| 2609 | value = 1.00000;
|
| 2610 | if (approxAll(value)[0] !== "1") {
|
| 2611 | console.log("fail testApproxAll: 1.00000");
|
| 2612 | }
|
| 2613 | value = Math.sqrt(2);
|
| 2614 | if (approxAll(value)[0] !== "1 * sqrt( 2 ) / 1") {
|
| 2615 | console.log("fail testApproxAll: Math.sqrt(2)");
|
| 2616 | }
|
| 2617 | value = 1.41;
|
| 2618 | if (approxAll(value)[0] !== "1 * sqrt( 2 ) / 1") {
|
| 2619 | console.log("fail testApproxAll: 1.41");
|
| 2620 | }
|
| 2621 | value = 1.4;
|
| 2622 | if (approxRadicals(value)[0] !== "1 * sqrt( 2 ) / 1") {
|
| 2623 | console.log("fail approxRadicals: 1.4");
|
| 2624 | }
|
| 2625 | value = 0.6;
|
| 2626 | if (approxLogs(value)[0] !== "1 * log( 2 ) / 1") {
|
| 2627 | console.log("fail approxLogs: 0.6");
|
| 2628 | }
|
| 2629 | value = 0.69;
|
| 2630 | if (approxLogs(value)[0] !== "1 * log( 2 ) / 1") {
|
| 2631 | console.log("fail approxLogs: 0.69");
|
| 2632 | }
|
| 2633 | value = 0.7;
|
| 2634 | if (approxLogs(value)[0] !== "1 * log( 2 ) / 1") {
|
| 2635 | console.log("fail approxLogs: 0.7");
|
| 2636 | }
|
| 2637 | value = 1.09;
|
| 2638 | if (approxLogs(value)[0] !== "1 * log( 3 ) / 1") {
|
| 2639 | console.log("fail approxLogs: 1.09");
|
| 2640 | }
|
| 2641 | value = 1.09;
|
| 2642 | if (approxAll(value)[0] !== "1 * log( 3 ) / 1") {
|
| 2643 | console.log("fail approxAll: 1.09");
|
| 2644 | }
|
| 2645 | value = 1.098;
|
| 2646 | if (approxAll(value)[0] !== "1 * log( 3 ) / 1") {
|
| 2647 | console.log("fail approxAll: 1.098");
|
| 2648 | }
|
| 2649 | value = 1.1;
|
| 2650 | if (approxAll(value)[0] !== "1 * log( 3 ) / 1") {
|
| 2651 | console.log("fail approxAll: 1.1");
|
| 2652 | }
|
| 2653 | value = 1.11;
|
| 2654 | if (approxAll(value)[0] !== "1 * log( 3 ) / 1") {
|
| 2655 | console.log("fail approxAll: 1.11");
|
| 2656 | }
|
| 2657 | value = Math.sqrt(3);
|
| 2658 | if (approxAll(value)[0] !== "1 * sqrt( 3 ) / 1") {
|
| 2659 | console.log("fail testApproxAll: Math.sqrt(3)");
|
| 2660 | }
|
| 2661 | value = 1.0000;
|
| 2662 | if (approxAll(value)[0] !== "1") {
|
| 2663 | console.log("fail testApproxAll: 1.0000");
|
| 2664 | }
|
| 2665 | value = 3.141592;
|
| 2666 | if (approxAll(value)[0] !== "1 * (pi ^ 1 ) / 1 )") {
|
| 2667 | console.log("fail testApproxAll: 3.141592");
|
| 2668 | }
|
| 2669 | value = 31.41592;
|
| 2670 | if (approxAll(value)[0] !== "10 * (pi ^ 1 ) / 1 )") {
|
| 2671 | console.log("fail testApproxAll: 31.41592");
|
| 2672 | }
|
| 2673 | value = 314.1592;
|
| 2674 | if (approxAll(value)[0] !== "100 * (pi ^ 1 ) / 1 )") {
|
| 2675 | console.log("fail testApproxAll: 314.1592");
|
| 2676 | }
|
| 2677 | value = 31415926.53589793;
|
| 2678 | if (approxAll(value)[0] !== "10000000 * (pi ^ 1 ) / 1 )") {
|
| 2679 | console.log("fail testApproxAll: 31415926.53589793");
|
| 2680 | }
|
| 2681 | value = Math.sqrt(2);
|
| 2682 | if (approxTrigonometric(value)[0] !== "2 * sin( 1/4 * pi )") {
|
| 2683 | console.log("fail approxTrigonometric: Math.sqrt(2)");
|
| 2684 | }
|
| 2685 | value = Math.sqrt(3);
|
| 2686 | if (approxTrigonometric(value)[0] !== "2 * sin( 1/3 * pi )") {
|
| 2687 | console.log("fail approxTrigonometric: Math.sqrt(3)");
|
| 2688 | }
|
| 2689 | value = (Math.sqrt(6) - Math.sqrt(2)) / 4;
|
| 2690 | if (approxAll(value)[0] !== "1 * sin( 1/12 * pi )") {
|
| 2691 | console.log("fail testApproxAll: (Math.sqrt(6) - Math.sqrt(2))/4");
|
| 2692 | }
|
| 2693 | value = Math.sqrt(2 - Math.sqrt(2)) / 2;
|
| 2694 | if (approxAll(value)[0] !== "1 * sin( 1/8 * pi )") {
|
| 2695 | console.log("fail testApproxAll: Math.sqrt(2 - Math.sqrt(2))/2");
|
| 2696 | }
|
| 2697 | value = (Math.sqrt(6) + Math.sqrt(2)) / 4;
|
| 2698 | if (approxAll(value)[0] !== "1 * sin( 5/12 * pi )") {
|
| 2699 | console.log("fail testApproxAll: (Math.sqrt(6) + Math.sqrt(2))/4");
|
| 2700 | }
|
| 2701 | value = Math.sqrt(2 + Math.sqrt(3)) / 2;
|
| 2702 | if (approxAll(value)[0] !== "1 * sin( 5/12 * pi )") {
|
| 2703 | console.log("fail testApproxAll: Math.sqrt(2 + Math.sqrt(3))/2");
|
| 2704 | }
|
| 2705 | value = (Math.sqrt(5) - 1) / 4;
|
| 2706 | if (approxAll(value)[0] !== "1 * sin( 1/10 * pi )") {
|
| 2707 | console.log("fail testApproxAll: (Math.sqrt(5) - 1)/4");
|
| 2708 | }
|
| 2709 | value = Math.sqrt(10 - 2 * Math.sqrt(5)) / 4;
|
| 2710 | if (approxAll(value)[0] !== "1 * sin( 1/5 * pi )") {
|
| 2711 | console.log("fail testApproxAll: Math.sqrt(10 - 2*Math.sqrt(5))/4");
|
| 2712 | }
|
| 2713 | value = Math.sin(Math.PI / 7);
|
| 2714 | if (approxAll(value)[0] !== "1 * sin( 1/7 * pi )") {
|
| 2715 | console.log("fail testApproxAll: Math.sin(Math.PI/7)");
|
| 2716 | }
|
| 2717 | value = Math.sin(Math.PI / 9);
|
| 2718 | if (approxAll(value)[0] !== "1 * sin( 1/9 * pi )") {
|
| 2719 | console.log("fail testApproxAll: Math.sin(Math.PI/9)");
|
| 2720 | }
|
| 2721 | value = 1836.15267;
|
| 2722 | if (approxRationalsOfPowersOfPI(value)[0] !== "6 * (pi ^ 5 ) / 1 )") {
|
| 2723 | console.log("fail approxRationalsOfPowersOfPI: 1836.15267");
|
| 2724 | }
|
| 2725 | for (i = j3 = 1; j3 <= 13; i = ++j3) {
|
| 2726 | for (j = k3 = 1; k3 <= 13; j = ++k3) {
|
| 2727 | console.log("approxTrigonometric testing: " + "1 * sin( " + i + "/" + j + " * pi )");
|
| 2728 | fraction = i / j;
|
| 2729 | value = Math.sin(Math.PI * fraction);
|
| 2730 | returned = approxTrigonometric(value);
|
| 2731 | returnedFraction = returned[3] / returned[4];
|
| 2732 | returnedValue = returned[2] * Math.sin(Math.PI * returnedFraction);
|
| 2733 | if (Math.abs(value - returnedValue) > 1e-15) {
|
| 2734 | console.log("fail approxTrigonometric: " + "1 * sin( " + i + "/" + j + " * pi ) . obtained: " + returned);
|
| 2735 | }
|
| 2736 | }
|
| 2737 | }
|
| 2738 | for (i = l3 = 1; l3 <= 13; i = ++l3) {
|
| 2739 | for (j = m3 = 1; m3 <= 13; j = ++m3) {
|
| 2740 | if (i === 5 && j === 11 || i === 6 && j === 11) {
|
| 2741 | continue;
|
| 2742 | }
|
| 2743 | console.log("approxTrigonometric testing with 4 digits: " + "1 * sin( " + i + "/" + j + " * pi )");
|
| 2744 | fraction = i / j;
|
| 2745 | originalValue = Math.sin(Math.PI * fraction);
|
| 2746 | value = originalValue.toFixed(4);
|
| 2747 | returned = approxTrigonometric(value);
|
| 2748 | returnedFraction = returned[3] / returned[4];
|
| 2749 | returnedValue = returned[2] * Math.sin(Math.PI * returnedFraction);
|
| 2750 | error = Math.abs(originalValue - returnedValue);
|
| 2751 | if (error > 1e-14) {
|
| 2752 | console.log("fail approxTrigonometric with 4 digits: " + "1 * sin( " + i + "/" + j + " * pi ) . obtained: " + returned + " error: " + error);
|
| 2753 | }
|
| 2754 | }
|
| 2755 | }
|
| 2756 | return console.log("testApprox done");
|
| 2757 | };
|
| 2758 |
|
| 2759 | $.approxRadicals = approxRadicals;
|
| 2760 |
|
| 2761 | $.approxRationalsOfLogs = approxRationalsOfLogs;
|
| 2762 |
|
| 2763 | $.approxAll = approxAll;
|
| 2764 |
|
| 2765 | $.testApprox = testApprox;
|
| 2766 |
|
| 2767 |
|
| 2768 | |
| 2769 | |
| 2770 | |
| 2771 | |
| 2772 | |
| 2773 | |
| 2774 | |
| 2775 | |
| 2776 | |
| 2777 | |
| 2778 | |
| 2779 | |
| 2780 | |
| 2781 |
|
| 2782 |
|
| 2783 | Eval_arccos = function() {
|
| 2784 | push(cadr(p1));
|
| 2785 | Eval();
|
| 2786 | return arccos();
|
| 2787 | };
|
| 2788 |
|
| 2789 | arccos = function() {
|
| 2790 | var d, errno, n;
|
| 2791 | n = 0;
|
| 2792 | d = 0.0;
|
| 2793 | save();
|
| 2794 | p1 = pop();
|
| 2795 | if (car(p1) === symbol(COS)) {
|
| 2796 | push(cadr(p1));
|
| 2797 | restore();
|
| 2798 | return;
|
| 2799 | }
|
| 2800 | if (isdouble(p1)) {
|
| 2801 | errno = 0;
|
| 2802 | d = Math.acos(p1.d);
|
| 2803 | if (errno) {
|
| 2804 | stop("arccos function argument is not in the interval [-1,1]");
|
| 2805 | }
|
| 2806 | push_double(d);
|
| 2807 | restore();
|
| 2808 | return;
|
| 2809 | }
|
| 2810 | if ((isoneoversqrttwo(p1)) || (car(p1) === symbol(MULTIPLY) && equalq(car(cdr(p1)), 1, 2) && car(car(cdr(cdr(p1)))) === symbol(POWER) && equaln(car(cdr(car(cdr(cdr(p1))))), 2) && equalq(car(cdr(cdr(car(cdr(cdr(p1)))))), 1, 2))) {
|
| 2811 | if (evaluatingAsFloats) {
|
| 2812 | push_double(Math.PI / 4.0);
|
| 2813 | } else {
|
| 2814 | push_rational(1, 4);
|
| 2815 | push_symbol(PI);
|
| 2816 | multiply();
|
| 2817 | }
|
| 2818 | restore();
|
| 2819 | return;
|
| 2820 | }
|
| 2821 | if ((isminusoneoversqrttwo(p1)) || (car(p1) === symbol(MULTIPLY) && equalq(car(cdr(p1)), -1, 2) && car(car(cdr(cdr(p1)))) === symbol(POWER) && equaln(car(cdr(car(cdr(cdr(p1))))), 2) && equalq(car(cdr(cdr(car(cdr(cdr(p1)))))), 1, 2))) {
|
| 2822 | if (evaluatingAsFloats) {
|
| 2823 | push_double(Math.PI * 3.0 / 4.0);
|
| 2824 | } else {
|
| 2825 | push_rational(3, 4);
|
| 2826 | push_symbol(PI);
|
| 2827 | multiply();
|
| 2828 | }
|
| 2829 | restore();
|
| 2830 | return;
|
| 2831 | }
|
| 2832 | if (!isrational(p1)) {
|
| 2833 | push_symbol(ARCCOS);
|
| 2834 | push(p1);
|
| 2835 | list(2);
|
| 2836 | restore();
|
| 2837 | return;
|
| 2838 | }
|
| 2839 | push(p1);
|
| 2840 | push_integer(2);
|
| 2841 | multiply();
|
| 2842 | n = pop_integer();
|
| 2843 | switch (n) {
|
| 2844 | case -2:
|
| 2845 | if (evaluatingAsFloats) {
|
| 2846 | push_double(Math.PI);
|
| 2847 | } else {
|
| 2848 | push_symbol(PI);
|
| 2849 | }
|
| 2850 | break;
|
| 2851 | case -1:
|
| 2852 | if (evaluatingAsFloats) {
|
| 2853 | push_double(Math.PI * 2.0 / 3.0);
|
| 2854 | } else {
|
| 2855 | push_rational(2, 3);
|
| 2856 | push_symbol(PI);
|
| 2857 | multiply();
|
| 2858 | }
|
| 2859 | break;
|
| 2860 | case 0:
|
| 2861 | if (evaluatingAsFloats) {
|
| 2862 | push_double(Math.PI / 2.0);
|
| 2863 | } else {
|
| 2864 | push_rational(1, 2);
|
| 2865 | push_symbol(PI);
|
| 2866 | multiply();
|
| 2867 | }
|
| 2868 | break;
|
| 2869 | case 1:
|
| 2870 | if (evaluatingAsFloats) {
|
| 2871 | push_double(Math.PI / 3.0);
|
| 2872 | } else {
|
| 2873 | push_rational(1, 3);
|
| 2874 | push_symbol(PI);
|
| 2875 | multiply();
|
| 2876 | }
|
| 2877 | break;
|
| 2878 | case 2:
|
| 2879 | if (evaluatingAsFloats) {
|
| 2880 | push_double(0.0);
|
| 2881 | } else {
|
| 2882 | push(zero);
|
| 2883 | }
|
| 2884 | break;
|
| 2885 | default:
|
| 2886 | push_symbol(ARCCOS);
|
| 2887 | push(p1);
|
| 2888 | list(2);
|
| 2889 | }
|
| 2890 | return restore();
|
| 2891 | };
|
| 2892 |
|
| 2893 |
|
| 2894 | |
| 2895 | |
| 2896 | |
| 2897 | |
| 2898 | |
| 2899 | |
| 2900 | |
| 2901 | |
| 2902 | |
| 2903 | |
| 2904 | |
| 2905 | |
| 2906 | |
| 2907 |
|
| 2908 |
|
| 2909 | Eval_arccosh = function() {
|
| 2910 | push(cadr(p1));
|
| 2911 | Eval();
|
| 2912 | return arccosh();
|
| 2913 | };
|
| 2914 |
|
| 2915 | arccosh = function() {
|
| 2916 | var d;
|
| 2917 | d = 0.0;
|
| 2918 | save();
|
| 2919 | p1 = pop();
|
| 2920 | if (car(p1) === symbol(COSH)) {
|
| 2921 | push(cadr(p1));
|
| 2922 | restore();
|
| 2923 | return;
|
| 2924 | }
|
| 2925 | if (isdouble(p1)) {
|
| 2926 | d = p1.d;
|
| 2927 | if (d < 1.0) {
|
| 2928 | stop("arccosh function argument is less than 1.0");
|
| 2929 | }
|
| 2930 | d = Math.log(d + Math.sqrt(d * d - 1.0));
|
| 2931 | push_double(d);
|
| 2932 | restore();
|
| 2933 | return;
|
| 2934 | }
|
| 2935 | if (isplusone(p1)) {
|
| 2936 | push(zero);
|
| 2937 | restore();
|
| 2938 | return;
|
| 2939 | }
|
| 2940 | push_symbol(ARCCOSH);
|
| 2941 | push(p1);
|
| 2942 | list(2);
|
| 2943 | return restore();
|
| 2944 | };
|
| 2945 |
|
| 2946 |
|
| 2947 | |
| 2948 | |
| 2949 | |
| 2950 | |
| 2951 | |
| 2952 | |
| 2953 | |
| 2954 | |
| 2955 | |
| 2956 | |
| 2957 | |
| 2958 | |
| 2959 | |
| 2960 |
|
| 2961 |
|
| 2962 | Eval_arcsin = function() {
|
| 2963 | push(cadr(p1));
|
| 2964 | Eval();
|
| 2965 | return arcsin();
|
| 2966 | };
|
| 2967 |
|
| 2968 | arcsin = function() {
|
| 2969 | var d, errno, n;
|
| 2970 | n = 0;
|
| 2971 | d = 0;
|
| 2972 | save();
|
| 2973 | p1 = pop();
|
| 2974 | if (car(p1) === symbol(SIN)) {
|
| 2975 | push(cadr(p1));
|
| 2976 | restore();
|
| 2977 | return;
|
| 2978 | }
|
| 2979 | if (isdouble(p1)) {
|
| 2980 | errno = 0;
|
| 2981 | d = Math.asin(p1.d);
|
| 2982 | if (errno) {
|
| 2983 | stop("arcsin function argument is not in the interval [-1,1]");
|
| 2984 | }
|
| 2985 | push_double(d);
|
| 2986 | restore();
|
| 2987 | return;
|
| 2988 | }
|
| 2989 | if ((isoneoversqrttwo(p1)) || (car(p1) === symbol(MULTIPLY) && equalq(car(cdr(p1)), 1, 2) && car(car(cdr(cdr(p1)))) === symbol(POWER) && equaln(car(cdr(car(cdr(cdr(p1))))), 2) && equalq(car(cdr(cdr(car(cdr(cdr(p1)))))), 1, 2))) {
|
| 2990 | push_rational(1, 4);
|
| 2991 | push_symbol(PI);
|
| 2992 | multiply();
|
| 2993 | restore();
|
| 2994 | return;
|
| 2995 | }
|
| 2996 | if ((isminusoneoversqrttwo(p1)) || (car(p1) === symbol(MULTIPLY) && equalq(car(cdr(p1)), -1, 2) && car(car(cdr(cdr(p1)))) === symbol(POWER) && equaln(car(cdr(car(cdr(cdr(p1))))), 2) && equalq(car(cdr(cdr(car(cdr(cdr(p1)))))), 1, 2))) {
|
| 2997 | if (evaluatingAsFloats) {
|
| 2998 | push_double(-Math.PI / 4.0);
|
| 2999 | } else {
|
| 3000 | push_rational(-1, 4);
|
| 3001 | push_symbol(PI);
|
| 3002 | multiply();
|
| 3003 | }
|
| 3004 | restore();
|
| 3005 | return;
|
| 3006 | }
|
| 3007 | if (!isrational(p1)) {
|
| 3008 | push_symbol(ARCSIN);
|
| 3009 | push(p1);
|
| 3010 | list(2);
|
| 3011 | restore();
|
| 3012 | return;
|
| 3013 | }
|
| 3014 | push(p1);
|
| 3015 | push_integer(2);
|
| 3016 | multiply();
|
| 3017 | n = pop_integer();
|
| 3018 | switch (n) {
|
| 3019 | case -2:
|
| 3020 | if (evaluatingAsFloats) {
|
| 3021 | push_double(-Math.PI / 2.0);
|
| 3022 | } else {
|
| 3023 | push_rational(-1, 2);
|
| 3024 | push_symbol(PI);
|
| 3025 | multiply();
|
| 3026 | }
|
| 3027 | break;
|
| 3028 | case -1:
|
| 3029 | if (evaluatingAsFloats) {
|
| 3030 | push_double(-Math.PI / 6.0);
|
| 3031 | } else {
|
| 3032 | push_rational(-1, 6);
|
| 3033 | push_symbol(PI);
|
| 3034 | multiply();
|
| 3035 | }
|
| 3036 | break;
|
| 3037 | case 0:
|
| 3038 | if (evaluatingAsFloats) {
|
| 3039 | push_double(0.0);
|
| 3040 | } else {
|
| 3041 | push(zero);
|
| 3042 | }
|
| 3043 | break;
|
| 3044 | case 1:
|
| 3045 | if (evaluatingAsFloats) {
|
| 3046 | push_double(Math.PI / 6.0);
|
| 3047 | } else {
|
| 3048 | push_rational(1, 6);
|
| 3049 | push_symbol(PI);
|
| 3050 | multiply();
|
| 3051 | }
|
| 3052 | break;
|
| 3053 | case 2:
|
| 3054 | if (evaluatingAsFloats) {
|
| 3055 | push_double(Math.PI / 2.0);
|
| 3056 | } else {
|
| 3057 | push_rational(1, 2);
|
| 3058 | push_symbol(PI);
|
| 3059 | multiply();
|
| 3060 | }
|
| 3061 | break;
|
| 3062 | default:
|
| 3063 | push_symbol(ARCSIN);
|
| 3064 | push(p1);
|
| 3065 | list(2);
|
| 3066 | }
|
| 3067 | return restore();
|
| 3068 | };
|
| 3069 |
|
| 3070 |
|
| 3071 | |
| 3072 | |
| 3073 | |
| 3074 | |
| 3075 | |
| 3076 | |
| 3077 | |
| 3078 | |
| 3079 | |
| 3080 | |
| 3081 | |
| 3082 | |
| 3083 | |
| 3084 |
|
| 3085 |
|
| 3086 | Eval_arcsinh = function() {
|
| 3087 | push(cadr(p1));
|
| 3088 | Eval();
|
| 3089 | return arcsinh();
|
| 3090 | };
|
| 3091 |
|
| 3092 | arcsinh = function() {
|
| 3093 | var d;
|
| 3094 | d = 0.0;
|
| 3095 | save();
|
| 3096 | p1 = pop();
|
| 3097 | if (car(p1) === symbol(SINH)) {
|
| 3098 | push(cadr(p1));
|
| 3099 | restore();
|
| 3100 | return;
|
| 3101 | }
|
| 3102 | if (isdouble(p1)) {
|
| 3103 | d = p1.d;
|
| 3104 | d = Math.log(d + Math.sqrt(d * d + 1.0));
|
| 3105 | push_double(d);
|
| 3106 | restore();
|
| 3107 | return;
|
| 3108 | }
|
| 3109 | if (iszero(p1)) {
|
| 3110 | push(zero);
|
| 3111 | restore();
|
| 3112 | return;
|
| 3113 | }
|
| 3114 | push_symbol(ARCSINH);
|
| 3115 | push(p1);
|
| 3116 | list(2);
|
| 3117 | return restore();
|
| 3118 | };
|
| 3119 |
|
| 3120 |
|
| 3121 | |
| 3122 | |
| 3123 | |
| 3124 | |
| 3125 | |
| 3126 | |
| 3127 | |
| 3128 | |
| 3129 | |
| 3130 | |
| 3131 | |
| 3132 | |
| 3133 | |
| 3134 |
|
| 3135 |
|
| 3136 | Eval_arctan = function() {
|
| 3137 | push(cadr(p1));
|
| 3138 | Eval();
|
| 3139 | return arctan();
|
| 3140 | };
|
| 3141 |
|
| 3142 | arctan = function() {
|
| 3143 | var d, errno;
|
| 3144 | d = 0;
|
| 3145 | save();
|
| 3146 | p1 = pop();
|
| 3147 | if (car(p1) === symbol(TAN)) {
|
| 3148 | push(cadr(p1));
|
| 3149 | restore();
|
| 3150 | return;
|
| 3151 | }
|
| 3152 | if (isdouble(p1)) {
|
| 3153 | errno = 0;
|
| 3154 | d = Math.atan(p1.d);
|
| 3155 | if (errno) {
|
| 3156 | stop("arctan function error");
|
| 3157 | }
|
| 3158 | push_double(d);
|
| 3159 | restore();
|
| 3160 | return;
|
| 3161 | }
|
| 3162 | if (iszero(p1)) {
|
| 3163 | push(zero);
|
| 3164 | restore();
|
| 3165 | return;
|
| 3166 | }
|
| 3167 | if (isnegative(p1)) {
|
| 3168 | push(p1);
|
| 3169 | negate();
|
| 3170 | arctan();
|
| 3171 | negate();
|
| 3172 | restore();
|
| 3173 | return;
|
| 3174 | }
|
| 3175 | if (Find(p1, symbol(SIN)) && Find(p1, symbol(COS))) {
|
| 3176 | push(p1);
|
| 3177 | numerator();
|
| 3178 | p2 = pop();
|
| 3179 | push(p1);
|
| 3180 | denominator();
|
| 3181 | p3 = pop();
|
| 3182 | if (car(p2) === symbol(SIN) && car(p3) === symbol(COS) && equal(cadr(p2), cadr(p3))) {
|
| 3183 | push(cadr(p2));
|
| 3184 | restore();
|
| 3185 | return;
|
| 3186 | }
|
| 3187 | }
|
| 3188 | if ((car(p1) === symbol(POWER) && equaln(cadr(p1), 3) && equalq(caddr(p1), -1, 2)) || (car(p1) === symbol(MULTIPLY) && equalq(car(cdr(p1)), 1, 3) && car(car(cdr(cdr(p1)))) === symbol(POWER) && equaln(car(cdr(car(cdr(cdr(p1))))), 3) && equalq(car(cdr(cdr(car(cdr(cdr(p1)))))), 1, 2))) {
|
| 3189 | push_rational(1, 6);
|
| 3190 | if (evaluatingAsFloats) {
|
| 3191 | push_double(Math.PI);
|
| 3192 | } else {
|
| 3193 | push(symbol(PI));
|
| 3194 | }
|
| 3195 | multiply();
|
| 3196 | restore();
|
| 3197 | return;
|
| 3198 | }
|
| 3199 | if (equaln(p1, 1)) {
|
| 3200 | push_rational(1, 4);
|
| 3201 | if (evaluatingAsFloats) {
|
| 3202 | push_double(Math.PI);
|
| 3203 | } else {
|
| 3204 | push(symbol(PI));
|
| 3205 | }
|
| 3206 | multiply();
|
| 3207 | restore();
|
| 3208 | return;
|
| 3209 | }
|
| 3210 | if (car(p1) === symbol(POWER) && equaln(cadr(p1), 3) && equalq(caddr(p1), 1, 2)) {
|
| 3211 | push_rational(1, 3);
|
| 3212 | if (evaluatingAsFloats) {
|
| 3213 | push_double(Math.PI);
|
| 3214 | } else {
|
| 3215 | push(symbol(PI));
|
| 3216 | }
|
| 3217 | multiply();
|
| 3218 | restore();
|
| 3219 | return;
|
| 3220 | }
|
| 3221 | push_symbol(ARCTAN);
|
| 3222 | push(p1);
|
| 3223 | list(2);
|
| 3224 | return restore();
|
| 3225 | };
|
| 3226 |
|
| 3227 |
|
| 3228 | |
| 3229 | |
| 3230 | |
| 3231 | |
| 3232 | |
| 3233 | |
| 3234 | |
| 3235 | |
| 3236 | |
| 3237 | |
| 3238 | |
| 3239 | |
| 3240 | |
| 3241 |
|
| 3242 |
|
| 3243 | Eval_arctanh = function() {
|
| 3244 | push(cadr(p1));
|
| 3245 | Eval();
|
| 3246 | return arctanh();
|
| 3247 | };
|
| 3248 |
|
| 3249 | arctanh = function() {
|
| 3250 | var d;
|
| 3251 | d = 0.0;
|
| 3252 | save();
|
| 3253 | p1 = pop();
|
| 3254 | if (car(p1) === symbol(TANH)) {
|
| 3255 | push(cadr(p1));
|
| 3256 | restore();
|
| 3257 | return;
|
| 3258 | }
|
| 3259 | if (isdouble(p1)) {
|
| 3260 | d = p1.d;
|
| 3261 | if (d < -1.0 || d > 1.0) {
|
| 3262 | stop("arctanh function argument is not in the interval [-1,1]");
|
| 3263 | }
|
| 3264 | d = Math.log((1.0 + d) / (1.0 - d)) / 2.0;
|
| 3265 | push_double(d);
|
| 3266 | restore();
|
| 3267 | return;
|
| 3268 | }
|
| 3269 | if (iszero(p1)) {
|
| 3270 | push(zero);
|
| 3271 | restore();
|
| 3272 | return;
|
| 3273 | }
|
| 3274 | push_symbol(ARCTANH);
|
| 3275 | push(p1);
|
| 3276 | list(2);
|
| 3277 | return restore();
|
| 3278 | };
|
| 3279 |
|
| 3280 |
|
| 3281 | |
| 3282 | |
| 3283 | |
| 3284 | |
| 3285 | |
| 3286 | |
| 3287 | |
| 3288 | |
| 3289 | |
| 3290 | |
| 3291 | |
| 3292 | |
| 3293 | |
| 3294 |
|
| 3295 |
|
| 3296 |
|
| 3297 | |
| 3298 | |
| 3299 | |
| 3300 | |
| 3301 | |
| 3302 | |
| 3303 | |
| 3304 | |
| 3305 | |
| 3306 | |
| 3307 | |
| 3308 | |
| 3309 | |
| 3310 | |
| 3311 | |
| 3312 | |
| 3313 | |
| 3314 | |
| 3315 | |
| 3316 | |
| 3317 | |
| 3318 | |
| 3319 | |
| 3320 | |
| 3321 | |
| 3322 | |
| 3323 | |
| 3324 | |
| 3325 | |
| 3326 | |
| 3327 | |
| 3328 | |
| 3329 | |
| 3330 | |
| 3331 | |
| 3332 | |
| 3333 | |
| 3334 | |
| 3335 | |
| 3336 | |
| 3337 | |
| 3338 | |
| 3339 | |
| 3340 | |
| 3341 | |
| 3342 | |
| 3343 | |
| 3344 |
|
| 3345 |
|
| 3346 | DEBUG_ARG = false;
|
| 3347 |
|
| 3348 | Eval_arg = function() {
|
| 3349 | push(cadr(p1));
|
| 3350 | Eval();
|
| 3351 | return arg();
|
| 3352 | };
|
| 3353 |
|
| 3354 | arg = function() {
|
| 3355 | save();
|
| 3356 | p1 = pop();
|
| 3357 | push(p1);
|
| 3358 | numerator();
|
| 3359 | yyarg();
|
| 3360 | push(p1);
|
| 3361 | denominator();
|
| 3362 | yyarg();
|
| 3363 | subtract();
|
| 3364 | return restore();
|
| 3365 | };
|
| 3366 |
|
| 3367 | yyarg = function() {
|
| 3368 | save();
|
| 3369 | p1 = pop();
|
| 3370 | if (ispositivenumber(p1) || p1 === symbol(PI)) {
|
| 3371 | if (isdouble(p1) || evaluatingAsFloats) {
|
| 3372 | push_double(0);
|
| 3373 | } else {
|
| 3374 | push_integer(0);
|
| 3375 | }
|
| 3376 | } else if (isnegativenumber(p1)) {
|
| 3377 | if (isdouble(p1) || evaluatingAsFloats) {
|
| 3378 | push_double(Math.PI);
|
| 3379 | } else {
|
| 3380 | push(symbol(PI));
|
| 3381 | }
|
| 3382 | negate();
|
| 3383 | } else if (issymbol(p1)) {
|
| 3384 | push_symbol(ARG);
|
| 3385 | push(p1);
|
| 3386 | list(2);
|
| 3387 | } else if (car(p1) === symbol(POWER) && equaln(cadr(p1), -1)) {
|
| 3388 | if (evaluatingAsFloats) {
|
| 3389 | push_double(Math.PI);
|
| 3390 | } else {
|
| 3391 | push(symbol(PI));
|
| 3392 | }
|
| 3393 | push(caddr(p1));
|
| 3394 | multiply();
|
| 3395 | } else if (car(p1) === symbol(POWER) && cadr(p1) === symbol(E)) {
|
| 3396 | push(caddr(p1));
|
| 3397 | imag();
|
| 3398 | } else if (car(p1) === symbol(POWER) && isoneovertwo(caddr(p1))) {
|
| 3399 | if (DEBUG_ARG) {
|
| 3400 | console.log("arg of a sqrt: " + p1);
|
| 3401 | }
|
| 3402 | if (DEBUG_ARG) {
|
| 3403 | debugger;
|
| 3404 | }
|
| 3405 | push(cadr(p1));
|
| 3406 | arg();
|
| 3407 | if (DEBUG_ARG) {
|
| 3408 | console.log(" = 1/2 * " + stack[tos - 1]);
|
| 3409 | }
|
| 3410 | push(caddr(p1));
|
| 3411 | multiply();
|
| 3412 | } else if (car(p1) === symbol(MULTIPLY)) {
|
| 3413 | push_integer(0);
|
| 3414 | p1 = cdr(p1);
|
| 3415 | while (iscons(p1)) {
|
| 3416 | push(car(p1));
|
| 3417 | arg();
|
| 3418 | add();
|
| 3419 | p1 = cdr(p1);
|
| 3420 | }
|
| 3421 | } else if (car(p1) === symbol(ADD)) {
|
| 3422 | push(p1);
|
| 3423 | rect();
|
| 3424 | p1 = pop();
|
| 3425 | push(p1);
|
| 3426 | real();
|
| 3427 | p2 = pop();
|
| 3428 | push(p1);
|
| 3429 | imag();
|
| 3430 | p3 = pop();
|
| 3431 | if (iszero(p2)) {
|
| 3432 | if (evaluatingAsFloats) {
|
| 3433 | push_double(Math.PI);
|
| 3434 | } else {
|
| 3435 | push(symbol(PI));
|
| 3436 | }
|
| 3437 | if (isnegative(p3)) {
|
| 3438 | negate();
|
| 3439 | }
|
| 3440 | } else {
|
| 3441 | push(p3);
|
| 3442 | push(p2);
|
| 3443 | divide();
|
| 3444 | arctan();
|
| 3445 | if (isnegative(p2)) {
|
| 3446 | if (evaluatingAsFloats) {
|
| 3447 | push_double(Math.PI);
|
| 3448 | } else {
|
| 3449 | push_symbol(PI);
|
| 3450 | }
|
| 3451 | if (isnegative(p3)) {
|
| 3452 | subtract();
|
| 3453 | } else {
|
| 3454 | add();
|
| 3455 | }
|
| 3456 | }
|
| 3457 | }
|
| 3458 | } else {
|
| 3459 | if (!iszero(get_binding(symbol(ASSUME_REAL_VARIABLES)))) {
|
| 3460 | push_integer(0);
|
| 3461 | } else {
|
| 3462 | push_symbol(ARG);
|
| 3463 | push(p1);
|
| 3464 | list(2);
|
| 3465 | }
|
| 3466 | }
|
| 3467 | return restore();
|
| 3468 | };
|
| 3469 |
|
| 3470 | bake = function() {
|
| 3471 | var h, s, t, x, y, z;
|
| 3472 | h = 0;
|
| 3473 | s = 0;
|
| 3474 | t = 0;
|
| 3475 | x = 0;
|
| 3476 | y = 0;
|
| 3477 | z = 0;
|
| 3478 | expanding++;
|
| 3479 | save();
|
| 3480 | p1 = pop();
|
| 3481 | s = ispoly(p1, symbol(SYMBOL_S));
|
| 3482 | t = ispoly(p1, symbol(SYMBOL_T));
|
| 3483 | x = ispoly(p1, symbol(SYMBOL_X));
|
| 3484 | y = ispoly(p1, symbol(SYMBOL_Y));
|
| 3485 | z = ispoly(p1, symbol(SYMBOL_Z));
|
| 3486 | if (s === 1 && t === 0 && x === 0 && y === 0 && z === 0) {
|
| 3487 | p2 = symbol(SYMBOL_S);
|
| 3488 | bake_poly();
|
| 3489 | } else if (s === 0 && t === 1 && x === 0 && y === 0 && z === 0) {
|
| 3490 | p2 = symbol(SYMBOL_T);
|
| 3491 | bake_poly();
|
| 3492 | } else if (s === 0 && t === 0 && x === 1 && y === 0 && z === 0) {
|
| 3493 | p2 = symbol(SYMBOL_X);
|
| 3494 | bake_poly();
|
| 3495 | } else if (s === 0 && t === 0 && x === 0 && y === 1 && z === 0) {
|
| 3496 | p2 = symbol(SYMBOL_Y);
|
| 3497 | bake_poly();
|
| 3498 | } else if (s === 0 && t === 0 && x === 0 && y === 0 && z === 1) {
|
| 3499 | p2 = symbol(SYMBOL_Z);
|
| 3500 | bake_poly();
|
| 3501 | } else if ((iscons(p1)) && car(p1) !== symbol(FOR)) {
|
| 3502 | h = tos;
|
| 3503 | push(car(p1));
|
| 3504 | p1 = cdr(p1);
|
| 3505 | while (iscons(p1)) {
|
| 3506 | push(car(p1));
|
| 3507 | bake();
|
| 3508 | p1 = cdr(p1);
|
| 3509 | }
|
| 3510 | list(tos - h);
|
| 3511 | } else {
|
| 3512 | push(p1);
|
| 3513 | }
|
| 3514 | restore();
|
| 3515 | return expanding--;
|
| 3516 | };
|
| 3517 |
|
| 3518 | polyform = function() {
|
| 3519 | var h;
|
| 3520 | h = 0;
|
| 3521 | save();
|
| 3522 | p2 = pop();
|
| 3523 | p1 = pop();
|
| 3524 | if (ispoly(p1, p2)) {
|
| 3525 | bake_poly();
|
| 3526 | } else if (iscons(p1)) {
|
| 3527 | h = tos;
|
| 3528 | push(car(p1));
|
| 3529 | p1 = cdr(p1);
|
| 3530 | while (iscons(p1)) {
|
| 3531 | push(car(p1));
|
| 3532 | push(p2);
|
| 3533 | polyform();
|
| 3534 | p1 = cdr(p1);
|
| 3535 | }
|
| 3536 | list(tos - h);
|
| 3537 | } else {
|
| 3538 | push(p1);
|
| 3539 | }
|
| 3540 | return restore();
|
| 3541 | };
|
| 3542 |
|
| 3543 | bake_poly = function() {
|
| 3544 | var a, h, i, k, n, o, ref;
|
| 3545 | h = 0;
|
| 3546 | i = 0;
|
| 3547 | k = 0;
|
| 3548 | n = 0;
|
| 3549 | a = tos;
|
| 3550 | push(p1);
|
| 3551 | push(p2);
|
| 3552 | k = coeff();
|
| 3553 | h = tos;
|
| 3554 | for (i = o = ref = k - 1; o >= 0; i = o += -1) {
|
| 3555 | p1 = stack[a + i];
|
| 3556 | bake_poly_term(i);
|
| 3557 | }
|
| 3558 | n = tos - h;
|
| 3559 | if (n > 1) {
|
| 3560 | list(n);
|
| 3561 | push(symbol(ADD));
|
| 3562 | swap();
|
| 3563 | cons();
|
| 3564 | }
|
| 3565 | p1 = pop();
|
| 3566 | moveTos(tos - k);
|
| 3567 | return push(p1);
|
| 3568 | };
|
| 3569 |
|
| 3570 | bake_poly_term = function(k) {
|
| 3571 | var h, n;
|
| 3572 | h = 0;
|
| 3573 | n = 0;
|
| 3574 | if (iszero(p1)) {
|
| 3575 | return;
|
| 3576 | }
|
| 3577 | if (k === 0) {
|
| 3578 | if (car(p1) === symbol(ADD)) {
|
| 3579 | p1 = cdr(p1);
|
| 3580 | while (iscons(p1)) {
|
| 3581 | push(car(p1));
|
| 3582 | p1 = cdr(p1);
|
| 3583 | }
|
| 3584 | } else {
|
| 3585 | push(p1);
|
| 3586 | }
|
| 3587 | return;
|
| 3588 | }
|
| 3589 | h = tos;
|
| 3590 | if (car(p1) === symbol(MULTIPLY)) {
|
| 3591 | p1 = cdr(p1);
|
| 3592 | while (iscons(p1)) {
|
| 3593 | push(car(p1));
|
| 3594 | p1 = cdr(p1);
|
| 3595 | }
|
| 3596 | } else if (!equaln(p1, 1)) {
|
| 3597 | push(p1);
|
| 3598 | }
|
| 3599 | if (k === 1) {
|
| 3600 | push(p2);
|
| 3601 | } else {
|
| 3602 | push(symbol(POWER));
|
| 3603 | push(p2);
|
| 3604 | push_integer(k);
|
| 3605 | list(3);
|
| 3606 | }
|
| 3607 | n = tos - h;
|
| 3608 | if (n > 1) {
|
| 3609 | list(n);
|
| 3610 | push(symbol(MULTIPLY));
|
| 3611 | swap();
|
| 3612 | return cons();
|
| 3613 | }
|
| 3614 | };
|
| 3615 |
|
| 3616 |
|
| 3617 | |
| 3618 | |
| 3619 | |
| 3620 | |
| 3621 | |
| 3622 | |
| 3623 | |
| 3624 | |
| 3625 | |
| 3626 | |
| 3627 | |
| 3628 | |
| 3629 | |
| 3630 | |
| 3631 | |
| 3632 | |
| 3633 | |
| 3634 | |
| 3635 | |
| 3636 | |
| 3637 | |
| 3638 | |
| 3639 | |
| 3640 | |
| 3641 | |
| 3642 | |
| 3643 | |
| 3644 | |
| 3645 | |
| 3646 | |
| 3647 | |
| 3648 | |
| 3649 | |
| 3650 | |
| 3651 | |
| 3652 | |
| 3653 |
|
| 3654 |
|
| 3655 | Eval_besselj = function() {
|
| 3656 | push(cadr(p1));
|
| 3657 | Eval();
|
| 3658 | push(caddr(p1));
|
| 3659 | Eval();
|
| 3660 | return besselj();
|
| 3661 | };
|
| 3662 |
|
| 3663 | besselj = function() {
|
| 3664 | save();
|
| 3665 | yybesselj();
|
| 3666 | return restore();
|
| 3667 | };
|
| 3668 |
|
| 3669 | yybesselj = function() {
|
| 3670 | var d, n;
|
| 3671 | d = 0.0;
|
| 3672 | n = 0;
|
| 3673 | p2 = pop();
|
| 3674 | p1 = pop();
|
| 3675 | push(p2);
|
| 3676 | n = pop_integer();
|
| 3677 | if (isdouble(p1) && !isNaN(n)) {
|
| 3678 | d = jn(n, p1.d);
|
| 3679 | push_double(d);
|
| 3680 | return;
|
| 3681 | }
|
| 3682 | if (iszero(p1) && iszero(p2)) {
|
| 3683 | push_integer(1);
|
| 3684 | return;
|
| 3685 | }
|
| 3686 | if (iszero(p1) && !isNaN(n)) {
|
| 3687 | push_integer(0);
|
| 3688 | return;
|
| 3689 | }
|
| 3690 | if (p2.k === NUM && MEQUAL(p2.q.b, 2)) {
|
| 3691 | if (MEQUAL(p2.q.a, 1)) {
|
| 3692 | if (evaluatingAsFloats) {
|
| 3693 | push_double(2.0 / Math.PI);
|
| 3694 | } else {
|
| 3695 | push_integer(2);
|
| 3696 | push_symbol(PI);
|
| 3697 | divide();
|
| 3698 | }
|
| 3699 | push(p1);
|
| 3700 | divide();
|
| 3701 | push_rational(1, 2);
|
| 3702 | power();
|
| 3703 | push(p1);
|
| 3704 | sine();
|
| 3705 | multiply();
|
| 3706 | return;
|
| 3707 | }
|
| 3708 | if (MEQUAL(p2.q.a, -1)) {
|
| 3709 | if (evaluatingAsFloats) {
|
| 3710 | push_double(2.0 / Math.PI);
|
| 3711 | } else {
|
| 3712 | push_integer(2);
|
| 3713 | push_symbol(PI);
|
| 3714 | divide();
|
| 3715 | }
|
| 3716 | push(p1);
|
| 3717 | divide();
|
| 3718 | push_rational(1, 2);
|
| 3719 | power();
|
| 3720 | push(p1);
|
| 3721 | cosine();
|
| 3722 | multiply();
|
| 3723 | return;
|
| 3724 | }
|
| 3725 | push_integer(MSIGN(p2.q.a));
|
| 3726 | p3 = pop();
|
| 3727 | push_integer(2);
|
| 3728 | push(p1);
|
| 3729 | divide();
|
| 3730 | push(p2);
|
| 3731 | push(p3);
|
| 3732 | subtract();
|
| 3733 | multiply();
|
| 3734 | push(p1);
|
| 3735 | push(p2);
|
| 3736 | push(p3);
|
| 3737 | subtract();
|
| 3738 | besselj();
|
| 3739 | multiply();
|
| 3740 | push(p1);
|
| 3741 | push(p2);
|
| 3742 | push_integer(2);
|
| 3743 | push(p3);
|
| 3744 | multiply();
|
| 3745 | subtract();
|
| 3746 | besselj();
|
| 3747 | subtract();
|
| 3748 | return;
|
| 3749 | }
|
| 3750 | if (isnegativeterm(p1)) {
|
| 3751 | push(p1);
|
| 3752 | negate();
|
| 3753 | push(p2);
|
| 3754 | power();
|
| 3755 | push(p1);
|
| 3756 | push(p2);
|
| 3757 | negate();
|
| 3758 | power();
|
| 3759 | multiply();
|
| 3760 | push_symbol(BESSELJ);
|
| 3761 | push(p1);
|
| 3762 | negate();
|
| 3763 | push(p2);
|
| 3764 | list(3);
|
| 3765 | multiply();
|
| 3766 | return;
|
| 3767 | }
|
| 3768 | if (isnegativeterm(p2)) {
|
| 3769 | push_integer(-1);
|
| 3770 | push(p2);
|
| 3771 | power();
|
| 3772 | push_symbol(BESSELJ);
|
| 3773 | push(p1);
|
| 3774 | push(p2);
|
| 3775 | negate();
|
| 3776 | list(3);
|
| 3777 | multiply();
|
| 3778 | return;
|
| 3779 | }
|
| 3780 | push(symbol(BESSELJ));
|
| 3781 | push(p1);
|
| 3782 | push(p2);
|
| 3783 | return list(3);
|
| 3784 | };
|
| 3785 |
|
| 3786 |
|
| 3787 | |
| 3788 | |
| 3789 | |
| 3790 | |
| 3791 | |
| 3792 | |
| 3793 | |
| 3794 | |
| 3795 | |
| 3796 | |
| 3797 | |
| 3798 | |
| 3799 | |
| 3800 | |
| 3801 |
|
| 3802 |
|
| 3803 | Eval_bessely = function() {
|
| 3804 | push(cadr(p1));
|
| 3805 | Eval();
|
| 3806 | push(caddr(p1));
|
| 3807 | Eval();
|
| 3808 | return bessely();
|
| 3809 | };
|
| 3810 |
|
| 3811 | bessely = function() {
|
| 3812 | save();
|
| 3813 | yybessely();
|
| 3814 | return restore();
|
| 3815 | };
|
| 3816 |
|
| 3817 | yybessely = function() {
|
| 3818 | var d, n;
|
| 3819 | d = 0.0;
|
| 3820 | n = 0;
|
| 3821 | p2 = pop();
|
| 3822 | p1 = pop();
|
| 3823 | push(p2);
|
| 3824 | n = pop_integer();
|
| 3825 | if (isdouble(p1) && !isNaN(n)) {
|
| 3826 | d = yn(n, p1.d);
|
| 3827 | push_double(d);
|
| 3828 | return;
|
| 3829 | }
|
| 3830 | if (isnegativeterm(p2)) {
|
| 3831 | push_integer(-1);
|
| 3832 | push(p2);
|
| 3833 | power();
|
| 3834 | push_symbol(BESSELY);
|
| 3835 | push(p1);
|
| 3836 | push(p2);
|
| 3837 | negate();
|
| 3838 | list(3);
|
| 3839 | multiply();
|
| 3840 | return;
|
| 3841 | }
|
| 3842 | push_symbol(BESSELY);
|
| 3843 | push(p1);
|
| 3844 | push(p2);
|
| 3845 | list(3);
|
| 3846 | };
|
| 3847 |
|
| 3848 | mint = function(a) {
|
| 3849 | return bigInt(a);
|
| 3850 | };
|
| 3851 |
|
| 3852 | setSignTo = function(a, b) {
|
| 3853 | if (a.isPositive()) {
|
| 3854 | if (b < 0) {
|
| 3855 | return a.multiply(bigInt(-1));
|
| 3856 | }
|
| 3857 | } else {
|
| 3858 | if (b > 0) {
|
| 3859 | return a.multiply(bigInt(-1));
|
| 3860 | }
|
| 3861 | }
|
| 3862 | return a;
|
| 3863 | };
|
| 3864 |
|
| 3865 | makeSignSameAs = function(a, b) {
|
| 3866 | if (a.isPositive()) {
|
| 3867 | if (b.isNegative()) {
|
| 3868 | return a.multiply(bigInt(-1));
|
| 3869 | }
|
| 3870 | } else {
|
| 3871 | if (b.isPositive()) {
|
| 3872 | return a.multiply(bigInt(-1));
|
| 3873 | }
|
| 3874 | }
|
| 3875 | return a;
|
| 3876 | };
|
| 3877 |
|
| 3878 | makePositive = function(a) {
|
| 3879 | if (a.isNegative()) {
|
| 3880 | return a.multiply(bigInt(-1));
|
| 3881 | }
|
| 3882 | return a;
|
| 3883 | };
|
| 3884 |
|
| 3885 |
|
| 3886 | |
| 3887 | |
| 3888 | |
| 3889 | |
| 3890 | |
| 3891 | |
| 3892 | |
| 3893 | |
| 3894 | |
| 3895 | |
| 3896 | |
| 3897 | |
| 3898 | |
| 3899 | |
| 3900 | |
| 3901 | |
| 3902 | |
| 3903 |
|
| 3904 |
|
| 3905 |
|
| 3906 | |
| 3907 | |
| 3908 | |
| 3909 | |
| 3910 | |
| 3911 | |
| 3912 | |
| 3913 | |
| 3914 | |
| 3915 | |
| 3916 |
|
| 3917 |
|
| 3918 |
|
| 3919 | |
| 3920 | |
| 3921 | |
| 3922 | |
| 3923 | |
| 3924 | |
| 3925 | |
| 3926 | |
| 3927 | |
| 3928 | |
| 3929 | |
| 3930 | |
| 3931 | |
| 3932 | |
| 3933 | |
| 3934 |
|
| 3935 |
|
| 3936 |
|
| 3937 | |
| 3938 | |
| 3939 | |
| 3940 | |
| 3941 | |
| 3942 | |
| 3943 | |
| 3944 | |
| 3945 | |
| 3946 | |
| 3947 | |
| 3948 | |
| 3949 | |
| 3950 | |
| 3951 |
|
| 3952 |
|
| 3953 |
|
| 3954 | |
| 3955 | |
| 3956 | |
| 3957 | |
| 3958 | |
| 3959 | |
| 3960 | |
| 3961 | |
| 3962 | |
| 3963 | |
| 3964 | |
| 3965 | |
| 3966 | |
| 3967 | |
| 3968 | |
| 3969 | |
| 3970 | |
| 3971 | |
| 3972 | |
| 3973 |
|
| 3974 |
|
| 3975 | add_numbers = function() {
|
| 3976 | var a, b, theResult;
|
| 3977 | a = 1.0;
|
| 3978 | b = 1.0;
|
| 3979 | if (isrational(stack[tos - 1]) && isrational(stack[tos - 2])) {
|
| 3980 | qadd();
|
| 3981 | return;
|
| 3982 | }
|
| 3983 | save();
|
| 3984 | p2 = pop();
|
| 3985 | p1 = pop();
|
| 3986 | if (isdouble(p1)) {
|
| 3987 | a = p1.d;
|
| 3988 | } else {
|
| 3989 | a = convert_rational_to_double(p1);
|
| 3990 | }
|
| 3991 | if (isdouble(p2)) {
|
| 3992 | b = p2.d;
|
| 3993 | } else {
|
| 3994 | b = convert_rational_to_double(p2);
|
| 3995 | }
|
| 3996 | theResult = a + b;
|
| 3997 | push_double(theResult);
|
| 3998 | return restore();
|
| 3999 | };
|
| 4000 |
|
| 4001 | subtract_numbers = function() {
|
| 4002 | var a, b;
|
| 4003 | a = 0.0;
|
| 4004 | b = 0.0;
|
| 4005 | if (isrational(stack[tos - 1]) && isrational(stack[tos - 2])) {
|
| 4006 | qsub();
|
| 4007 | return;
|
| 4008 | }
|
| 4009 | save();
|
| 4010 | p2 = pop();
|
| 4011 | p1 = pop();
|
| 4012 | if (isdouble(p1)) {
|
| 4013 | a = p1.d;
|
| 4014 | } else {
|
| 4015 | a = convert_rational_to_double(p1);
|
| 4016 | }
|
| 4017 | if (isdouble(p2)) {
|
| 4018 | b = p2.d;
|
| 4019 | } else {
|
| 4020 | b = convert_rational_to_double(p2);
|
| 4021 | }
|
| 4022 | push_double(a - b);
|
| 4023 | return restore();
|
| 4024 | };
|
| 4025 |
|
| 4026 | multiply_numbers = function() {
|
| 4027 | var a, b;
|
| 4028 | a = 0.0;
|
| 4029 | b = 0.0;
|
| 4030 | if (isrational(stack[tos - 1]) && isrational(stack[tos - 2])) {
|
| 4031 | qmul();
|
| 4032 | return;
|
| 4033 | }
|
| 4034 | save();
|
| 4035 | p2 = pop();
|
| 4036 | p1 = pop();
|
| 4037 | if (isdouble(p1)) {
|
| 4038 | a = p1.d;
|
| 4039 | } else {
|
| 4040 | a = convert_rational_to_double(p1);
|
| 4041 | }
|
| 4042 | if (isdouble(p2)) {
|
| 4043 | b = p2.d;
|
| 4044 | } else {
|
| 4045 | b = convert_rational_to_double(p2);
|
| 4046 | }
|
| 4047 | push_double(a * b);
|
| 4048 | return restore();
|
| 4049 | };
|
| 4050 |
|
| 4051 | divide_numbers = function() {
|
| 4052 | var a, b;
|
| 4053 | a = 0.0;
|
| 4054 | b = 0.0;
|
| 4055 | if (isrational(stack[tos - 1]) && isrational(stack[tos - 2])) {
|
| 4056 | qdiv();
|
| 4057 | return;
|
| 4058 | }
|
| 4059 | save();
|
| 4060 | p2 = pop();
|
| 4061 | p1 = pop();
|
| 4062 | if (iszero(p2)) {
|
| 4063 | stop("divide by zero");
|
| 4064 | }
|
| 4065 | if (isdouble(p1)) {
|
| 4066 | a = p1.d;
|
| 4067 | } else {
|
| 4068 | a = convert_rational_to_double(p1);
|
| 4069 | }
|
| 4070 | if (isdouble(p2)) {
|
| 4071 | b = p2.d;
|
| 4072 | } else {
|
| 4073 | b = convert_rational_to_double(p2);
|
| 4074 | }
|
| 4075 | push_double(a / b);
|
| 4076 | return restore();
|
| 4077 | };
|
| 4078 |
|
| 4079 | invert_number = function() {
|
| 4080 | var a, b;
|
| 4081 | save();
|
| 4082 | p1 = pop();
|
| 4083 | if (iszero(p1)) {
|
| 4084 | stop("divide by zero");
|
| 4085 | }
|
| 4086 | if (isdouble(p1)) {
|
| 4087 | push_double(1 / p1.d);
|
| 4088 | restore();
|
| 4089 | return;
|
| 4090 | }
|
| 4091 | a = bigInt(p1.q.a);
|
| 4092 | b = bigInt(p1.q.b);
|
| 4093 | b = makeSignSameAs(b, a);
|
| 4094 | a = setSignTo(a, 1);
|
| 4095 | p1 = new U();
|
| 4096 | p1.k = NUM;
|
| 4097 | p1.q.a = b;
|
| 4098 | p1.q.b = a;
|
| 4099 | push(p1);
|
| 4100 | return restore();
|
| 4101 | };
|
| 4102 |
|
| 4103 | compare_rationals = function(a, b) {
|
| 4104 | var ab, ba, t;
|
| 4105 | t = 0;
|
| 4106 | ab = mmul(a.q.a, b.q.b);
|
| 4107 | ba = mmul(a.q.b, b.q.a);
|
| 4108 | t = mcmp(ab, ba);
|
| 4109 | return t;
|
| 4110 | };
|
| 4111 |
|
| 4112 | compare_numbers = function(a, b) {
|
| 4113 | var x, y;
|
| 4114 | x = 0.0;
|
| 4115 | y = 0.0;
|
| 4116 | if (isrational(a) && isrational(b)) {
|
| 4117 | return compare_rationals(a, b);
|
| 4118 | }
|
| 4119 | if (isdouble(a)) {
|
| 4120 | x = a.d;
|
| 4121 | } else {
|
| 4122 | x = convert_rational_to_double(a);
|
| 4123 | }
|
| 4124 | if (isdouble(b)) {
|
| 4125 | y = b.d;
|
| 4126 | } else {
|
| 4127 | y = convert_rational_to_double(b);
|
| 4128 | }
|
| 4129 | if (x < y) {
|
| 4130 | return -1;
|
| 4131 | }
|
| 4132 | if (x > y) {
|
| 4133 | return 1;
|
| 4134 | }
|
| 4135 | return 0;
|
| 4136 | };
|
| 4137 |
|
| 4138 | negate_number = function() {
|
| 4139 | save();
|
| 4140 | p1 = pop();
|
| 4141 | if (iszero(p1)) {
|
| 4142 | push(p1);
|
| 4143 | restore();
|
| 4144 | return;
|
| 4145 | }
|
| 4146 | switch (p1.k) {
|
| 4147 | case NUM:
|
| 4148 | p2 = new U();
|
| 4149 | p2.k = NUM;
|
| 4150 | p2.q.a = bigInt(p1.q.a.multiply(bigInt.minusOne));
|
| 4151 | p2.q.b = bigInt(p1.q.b);
|
| 4152 | push(p2);
|
| 4153 | break;
|
| 4154 | case DOUBLE:
|
| 4155 | push_double(-p1.d);
|
| 4156 | break;
|
| 4157 | default:
|
| 4158 | stop("bug caught in mp_negate_number");
|
| 4159 | }
|
| 4160 | return restore();
|
| 4161 | };
|
| 4162 |
|
| 4163 | bignum_truncate = function() {
|
| 4164 | var a;
|
| 4165 | save();
|
| 4166 | p1 = pop();
|
| 4167 | a = mdiv(p1.q.a, p1.q.b);
|
| 4168 | p1 = new U();
|
| 4169 | p1.k = NUM;
|
| 4170 | p1.q.a = a;
|
| 4171 | p1.q.b = bigInt(1);
|
| 4172 | push(p1);
|
| 4173 | return restore();
|
| 4174 | };
|
| 4175 |
|
| 4176 | mp_numerator = function() {
|
| 4177 | save();
|
| 4178 | p1 = pop();
|
| 4179 | if (p1.k !== NUM) {
|
| 4180 | push(one);
|
| 4181 | restore();
|
| 4182 | return;
|
| 4183 | }
|
| 4184 | p2 = new U();
|
| 4185 | p2.k = NUM;
|
| 4186 | p2.q.a = bigInt(p1.q.a);
|
| 4187 | p2.q.b = bigInt(1);
|
| 4188 | push(p2);
|
| 4189 | return restore();
|
| 4190 | };
|
| 4191 |
|
| 4192 | mp_denominator = function() {
|
| 4193 | save();
|
| 4194 | p1 = pop();
|
| 4195 | if (p1.k !== NUM) {
|
| 4196 | push(one);
|
| 4197 | restore();
|
| 4198 | return;
|
| 4199 | }
|
| 4200 | p2 = new U();
|
| 4201 | p2.k = NUM;
|
| 4202 | p2.q.a = bigInt(p1.q.b);
|
| 4203 | p2.q.b = bigInt(1);
|
| 4204 | push(p2);
|
| 4205 | return restore();
|
| 4206 | };
|
| 4207 |
|
| 4208 | bignum_power_number = function(expo) {
|
| 4209 | var a, b, t;
|
| 4210 | save();
|
| 4211 | p1 = pop();
|
| 4212 | a = mpow(p1.q.a, Math.abs(expo));
|
| 4213 | b = mpow(p1.q.b, Math.abs(expo));
|
| 4214 | if (expo < 0) {
|
| 4215 | t = a;
|
| 4216 | a = b;
|
| 4217 | b = t;
|
| 4218 | a = makeSignSameAs(a, b);
|
| 4219 | b = setSignTo(b, 1);
|
| 4220 | }
|
| 4221 | p1 = new U();
|
| 4222 | p1.k = NUM;
|
| 4223 | p1.q.a = a;
|
| 4224 | p1.q.b = b;
|
| 4225 | push(p1);
|
| 4226 | return restore();
|
| 4227 | };
|
| 4228 |
|
| 4229 | convert_bignum_to_double = function(p) {
|
| 4230 | return p.toJSNumber();
|
| 4231 | };
|
| 4232 |
|
| 4233 | convert_rational_to_double = function(p) {
|
| 4234 | var quotientAndRemainder, result;
|
| 4235 | if (p.q == null) {
|
| 4236 | debugger;
|
| 4237 | }
|
| 4238 | quotientAndRemainder = p.q.a.divmod(p.q.b);
|
| 4239 | result = quotientAndRemainder.quotient + quotientAndRemainder.remainder / p.q.b.toJSNumber();
|
| 4240 | return result;
|
| 4241 | };
|
| 4242 |
|
| 4243 | push_integer = function(n) {
|
| 4244 | if (DEBUG) {
|
| 4245 | console.log("pushing integer " + n);
|
| 4246 | }
|
| 4247 | save();
|
| 4248 | p1 = new U();
|
| 4249 | p1.k = NUM;
|
| 4250 | p1.q.a = bigInt(n);
|
| 4251 | p1.q.b = bigInt(1);
|
| 4252 | push(p1);
|
| 4253 | return restore();
|
| 4254 | };
|
| 4255 |
|
| 4256 | push_double = function(d) {
|
| 4257 | save();
|
| 4258 | p1 = new U();
|
| 4259 | p1.k = DOUBLE;
|
| 4260 | p1.d = d;
|
| 4261 | push(p1);
|
| 4262 | return restore();
|
| 4263 | };
|
| 4264 |
|
| 4265 | push_rational = function(a, b) {
|
| 4266 |
|
| 4267 | |
| 4268 | |
| 4269 | |
| 4270 | |
| 4271 | |
| 4272 | |
| 4273 | |
| 4274 | |
| 4275 | |
| 4276 |
|
| 4277 | var p;
|
| 4278 | p = new U();
|
| 4279 | p.k = NUM;
|
| 4280 | p.q.a = bigInt(a);
|
| 4281 | p.q.b = bigInt(b);
|
| 4282 | return push(p);
|
| 4283 | };
|
| 4284 |
|
| 4285 | pop_integer = function() {
|
| 4286 | var n;
|
| 4287 | n = 0/0;
|
| 4288 | save();
|
| 4289 | p1 = pop();
|
| 4290 | switch (p1.k) {
|
| 4291 | case NUM:
|
| 4292 | if (isinteger(p1) && p1.q.a.isSmall) {
|
| 4293 | n = p1.q.a.toJSNumber();
|
| 4294 | }
|
| 4295 | break;
|
| 4296 | case DOUBLE:
|
| 4297 | if (DEBUG) {
|
| 4298 | console.log("popping integer but double is found");
|
| 4299 | }
|
| 4300 | if (Math.floor(p1.d) === p1.d) {
|
| 4301 | if (DEBUG) {
|
| 4302 | console.log("...altough it's an integer");
|
| 4303 | }
|
| 4304 | n = p1.d;
|
| 4305 | }
|
| 4306 | }
|
| 4307 | restore();
|
| 4308 | return n;
|
| 4309 | };
|
| 4310 |
|
| 4311 | print_double = function(p, flag) {
|
| 4312 | var accumulator, buf;
|
| 4313 | accumulator = "";
|
| 4314 | buf = doubleToReasonableString(p.d);
|
| 4315 | if (flag === 1 && buf === '-') {
|
| 4316 | accumulator += print_str(buf + 1);
|
| 4317 | } else {
|
| 4318 | accumulator += print_str(buf);
|
| 4319 | }
|
| 4320 | return accumulator;
|
| 4321 | };
|
| 4322 |
|
| 4323 | bignum_scan_integer = function(s) {
|
| 4324 | var a, scounter, sign_;
|
| 4325 | save();
|
| 4326 | scounter = 0;
|
| 4327 | sign_ = s[scounter];
|
| 4328 | if (sign_ === '+' || sign_ === '-') {
|
| 4329 | scounter++;
|
| 4330 | }
|
| 4331 | a = bigInt(s.substring(scounter));
|
| 4332 | p1 = new U();
|
| 4333 | p1.k = NUM;
|
| 4334 | p1.q.a = a;
|
| 4335 | p1.q.b = bigInt(1);
|
| 4336 | push(p1);
|
| 4337 | if (sign_ === '-') {
|
| 4338 | negate();
|
| 4339 | }
|
| 4340 | return restore();
|
| 4341 | };
|
| 4342 |
|
| 4343 | bignum_scan_float = function(s) {
|
| 4344 | return push_double(parseFloat(s));
|
| 4345 | };
|
| 4346 |
|
| 4347 | print_number = function(p, signed) {
|
| 4348 | var aAsString, accumulator, buf, denominatorString;
|
| 4349 | accumulator = "";
|
| 4350 | denominatorString = "";
|
| 4351 | buf = "";
|
| 4352 | switch (p.k) {
|
| 4353 | case NUM:
|
| 4354 | aAsString = p.q.a.toString();
|
| 4355 | if (!signed) {
|
| 4356 | if (aAsString[0] === "-") {
|
| 4357 | aAsString = aAsString.substring(1);
|
| 4358 | }
|
| 4359 | }
|
| 4360 | if (printMode === PRINTMODE_LATEX && isfraction(p)) {
|
| 4361 | aAsString = "\\frac{" + aAsString + "}{";
|
| 4362 | }
|
| 4363 | accumulator += aAsString;
|
| 4364 | if (isfraction(p)) {
|
| 4365 | if (printMode !== PRINTMODE_LATEX) {
|
| 4366 | accumulator += "/";
|
| 4367 | }
|
| 4368 | denominatorString = p.q.b.toString();
|
| 4369 | if (printMode === PRINTMODE_LATEX) {
|
| 4370 | denominatorString += "}";
|
| 4371 | }
|
| 4372 | accumulator += denominatorString;
|
| 4373 | }
|
| 4374 | break;
|
| 4375 | case DOUBLE:
|
| 4376 | aAsString = doubleToReasonableString(p.d);
|
| 4377 | if (!signed) {
|
| 4378 | if (aAsString[0] === "-") {
|
| 4379 | aAsString = aAsString.substring(1);
|
| 4380 | }
|
| 4381 | }
|
| 4382 | accumulator += aAsString;
|
| 4383 | }
|
| 4384 | return accumulator;
|
| 4385 | };
|
| 4386 |
|
| 4387 | gcd_numbers = function() {
|
| 4388 | save();
|
| 4389 | p2 = pop();
|
| 4390 | p1 = pop();
|
| 4391 | p3 = new U();
|
| 4392 | p3.k = NUM;
|
| 4393 | p3.q.a = mgcd(p1.q.a, p2.q.a);
|
| 4394 | p3.q.b = mgcd(p1.q.b, p2.q.b);
|
| 4395 | p3.q.a = setSignTo(p3.q.a, 1);
|
| 4396 | push(p3);
|
| 4397 | return restore();
|
| 4398 | };
|
| 4399 |
|
| 4400 | pop_double = function() {
|
| 4401 | var d;
|
| 4402 | d = 0.0;
|
| 4403 | save();
|
| 4404 | p1 = pop();
|
| 4405 | switch (p1.k) {
|
| 4406 | case NUM:
|
| 4407 | d = convert_rational_to_double(p1);
|
| 4408 | break;
|
| 4409 | case DOUBLE:
|
| 4410 | d = p1.d;
|
| 4411 | break;
|
| 4412 | default:
|
| 4413 | d = 0.0;
|
| 4414 | }
|
| 4415 | restore();
|
| 4416 | return d;
|
| 4417 | };
|
| 4418 |
|
| 4419 | bignum_float = function() {
|
| 4420 | var d;
|
| 4421 | d = 0.0;
|
| 4422 | d = convert_rational_to_double(pop());
|
| 4423 | return push_double(d);
|
| 4424 | };
|
| 4425 |
|
| 4426 | bignum_factorial = function(n) {
|
| 4427 | save();
|
| 4428 | p1 = new U();
|
| 4429 | p1.k = NUM;
|
| 4430 | p1.q.a = __factorial(n);
|
| 4431 | p1.q.b = bigInt(1);
|
| 4432 | push(p1);
|
| 4433 | return restore();
|
| 4434 | };
|
| 4435 |
|
| 4436 | __factorial = function(n) {
|
| 4437 | var a, b, i, o, ref, t;
|
| 4438 | i = 0;
|
| 4439 | if (n === 0 || n === 1) {
|
| 4440 | a = bigInt(1);
|
| 4441 | return a;
|
| 4442 | }
|
| 4443 | a = bigInt(2);
|
| 4444 | b = bigInt(0);
|
| 4445 | if (3 <= n) {
|
| 4446 | for (i = o = 3, ref = n; 3 <= ref ? o <= ref : o >= ref; i = 3 <= ref ? ++o : --o) {
|
| 4447 | b = bigInt(i);
|
| 4448 | t = mmul(a, b);
|
| 4449 | a = t;
|
| 4450 | }
|
| 4451 | }
|
| 4452 | return a;
|
| 4453 | };
|
| 4454 |
|
| 4455 | mask = [0x00000001, 0x00000002, 0x00000004, 0x00000008, 0x00000010, 0x00000020, 0x00000040, 0x00000080, 0x00000100, 0x00000200, 0x00000400, 0x00000800, 0x00001000, 0x00002000, 0x00004000, 0x00008000, 0x00010000, 0x00020000, 0x00040000, 0x00080000, 0x00100000, 0x00200000, 0x00400000, 0x00800000, 0x01000000, 0x02000000, 0x04000000, 0x08000000, 0x10000000, 0x20000000, 0x40000000, 0x80000000];
|
| 4456 |
|
| 4457 | mp_set_bit = function(x, k) {
|
| 4458 | console.log("not implemented yet");
|
| 4459 | debugger;
|
| 4460 | return x[k / 32] |= mask[k % 32];
|
| 4461 | };
|
| 4462 |
|
| 4463 | mp_clr_bit = function(x, k) {
|
| 4464 | console.log("not implemented yet");
|
| 4465 | debugger;
|
| 4466 | return x[k / 32] &= ~mask[k % 32];
|
| 4467 | };
|
| 4468 |
|
| 4469 | mshiftright = function(a) {
|
| 4470 | return a = a.shiftRight();
|
| 4471 | };
|
| 4472 |
|
| 4473 | Eval_binomial = function() {
|
| 4474 | push(cadr(p1));
|
| 4475 | Eval();
|
| 4476 | push(caddr(p1));
|
| 4477 | Eval();
|
| 4478 | return binomial();
|
| 4479 | };
|
| 4480 |
|
| 4481 | binomial = function() {
|
| 4482 | save();
|
| 4483 | ybinomial();
|
| 4484 | return restore();
|
| 4485 | };
|
| 4486 |
|
| 4487 | ybinomial = function() {
|
| 4488 | p2 = pop();
|
| 4489 | p1 = pop();
|
| 4490 | if (BINOM_check_args() === 0) {
|
| 4491 | push(zero);
|
| 4492 | return;
|
| 4493 | }
|
| 4494 | push(p1);
|
| 4495 | factorial();
|
| 4496 | push(p2);
|
| 4497 | factorial();
|
| 4498 | divide();
|
| 4499 | push(p1);
|
| 4500 | push(p2);
|
| 4501 | subtract();
|
| 4502 | factorial();
|
| 4503 | return divide();
|
| 4504 | };
|
| 4505 |
|
| 4506 | BINOM_check_args = function() {
|
| 4507 | if (isnum(p1) && lessp(p1, zero)) {
|
| 4508 | return 0;
|
| 4509 | } else if (isnum(p2) && lessp(p2, zero)) {
|
| 4510 | return 0;
|
| 4511 | } else if (isnum(p1) && isnum(p2) && lessp(p1, p2)) {
|
| 4512 | return 0;
|
| 4513 | } else {
|
| 4514 | return 1;
|
| 4515 | }
|
| 4516 | };
|
| 4517 |
|
| 4518 |
|
| 4519 | |
| 4520 | |
| 4521 | |
| 4522 | |
| 4523 | |
| 4524 | |
| 4525 | |
| 4526 | |
| 4527 | |
| 4528 | |
| 4529 | |
| 4530 | |
| 4531 | |
| 4532 | |
| 4533 |
|
| 4534 |
|
| 4535 | Eval_ceiling = function() {
|
| 4536 | push(cadr(p1));
|
| 4537 | Eval();
|
| 4538 | return ceiling();
|
| 4539 | };
|
| 4540 |
|
| 4541 | ceiling = function() {
|
| 4542 | save();
|
| 4543 | yyceiling();
|
| 4544 | return restore();
|
| 4545 | };
|
| 4546 |
|
| 4547 | yyceiling = function() {
|
| 4548 | var d, doNothing;
|
| 4549 | d = 0.0;
|
| 4550 | p1 = pop();
|
| 4551 | if (!isnum(p1)) {
|
| 4552 | push_symbol(CEILING);
|
| 4553 | push(p1);
|
| 4554 | list(2);
|
| 4555 | return;
|
| 4556 | }
|
| 4557 | if (isdouble(p1)) {
|
| 4558 | d = Math.ceil(p1.d);
|
| 4559 | push_double(d);
|
| 4560 | return;
|
| 4561 | }
|
| 4562 | if (isinteger(p1)) {
|
| 4563 | push(p1);
|
| 4564 | return;
|
| 4565 | }
|
| 4566 | p3 = new U();
|
| 4567 | p3.k = NUM;
|
| 4568 | p3.q.a = mdiv(p1.q.a, p1.q.b);
|
| 4569 | p3.q.b = mint(1);
|
| 4570 | push(p3);
|
| 4571 | if (isnegativenumber(p1)) {
|
| 4572 | return doNothing = 1;
|
| 4573 | } else {
|
| 4574 | push_integer(1);
|
| 4575 | return add();
|
| 4576 | }
|
| 4577 | };
|
| 4578 |
|
| 4579 |
|
| 4580 | |
| 4581 | |
| 4582 | |
| 4583 | |
| 4584 | |
| 4585 | |
| 4586 | |
| 4587 | |
| 4588 | |
| 4589 | |
| 4590 | |
| 4591 | |
| 4592 | |
| 4593 | |
| 4594 | |
| 4595 | |
| 4596 | |
| 4597 | |
| 4598 | |
| 4599 | |
| 4600 | |
| 4601 | |
| 4602 |
|
| 4603 |
|
| 4604 | Eval_choose = function() {
|
| 4605 | push(cadr(p1));
|
| 4606 | Eval();
|
| 4607 | push(caddr(p1));
|
| 4608 | Eval();
|
| 4609 | return choose();
|
| 4610 | };
|
| 4611 |
|
| 4612 | choose = function() {
|
| 4613 | save();
|
| 4614 | p2 = pop();
|
| 4615 | p1 = pop();
|
| 4616 | if (choose_check_args() === 0) {
|
| 4617 | push_integer(0);
|
| 4618 | restore();
|
| 4619 | return;
|
| 4620 | }
|
| 4621 | push(p1);
|
| 4622 | factorial();
|
| 4623 | push(p2);
|
| 4624 | factorial();
|
| 4625 | divide();
|
| 4626 | push(p1);
|
| 4627 | push(p2);
|
| 4628 | subtract();
|
| 4629 | factorial();
|
| 4630 | divide();
|
| 4631 | return restore();
|
| 4632 | };
|
| 4633 |
|
| 4634 | choose_check_args = function() {
|
| 4635 | if (isnum(p1) && lessp(p1, zero)) {
|
| 4636 | return 0;
|
| 4637 | } else if (isnum(p2) && lessp(p2, zero)) {
|
| 4638 | return 0;
|
| 4639 | } else if (isnum(p1) && isnum(p2) && lessp(p1, p2)) {
|
| 4640 | return 0;
|
| 4641 | } else {
|
| 4642 | return 1;
|
| 4643 | }
|
| 4644 | };
|
| 4645 |
|
| 4646 |
|
| 4647 | |
| 4648 | |
| 4649 | |
| 4650 | |
| 4651 | |
| 4652 | |
| 4653 | |
| 4654 | |
| 4655 | |
| 4656 | |
| 4657 | |
| 4658 | |
| 4659 | |
| 4660 | |
| 4661 |
|
| 4662 |
|
| 4663 | Eval_circexp = function() {
|
| 4664 | push(cadr(p1));
|
| 4665 | Eval();
|
| 4666 | circexp();
|
| 4667 | return Eval();
|
| 4668 | };
|
| 4669 |
|
| 4670 | circexp = function() {
|
| 4671 | var h, i, o, ref;
|
| 4672 | i = 0;
|
| 4673 | h = 0;
|
| 4674 | save();
|
| 4675 | p1 = pop();
|
| 4676 | if (car(p1) === symbol(COS)) {
|
| 4677 | push(cadr(p1));
|
| 4678 | expcos();
|
| 4679 | restore();
|
| 4680 | return;
|
| 4681 | }
|
| 4682 | if (car(p1) === symbol(SIN)) {
|
| 4683 | push(cadr(p1));
|
| 4684 | expsin();
|
| 4685 | restore();
|
| 4686 | return;
|
| 4687 | }
|
| 4688 | if (car(p1) === symbol(TAN)) {
|
| 4689 | p1 = cadr(p1);
|
| 4690 | push(imaginaryunit);
|
| 4691 | push(p1);
|
| 4692 | multiply();
|
| 4693 | exponential();
|
| 4694 | p2 = pop();
|
| 4695 | push(imaginaryunit);
|
| 4696 | push(p1);
|
| 4697 | multiply();
|
| 4698 | negate();
|
| 4699 | exponential();
|
| 4700 | p3 = pop();
|
| 4701 | push(p3);
|
| 4702 | push(p2);
|
| 4703 | subtract();
|
| 4704 | push(imaginaryunit);
|
| 4705 | multiply();
|
| 4706 | push(p2);
|
| 4707 | push(p3);
|
| 4708 | add();
|
| 4709 | divide();
|
| 4710 | restore();
|
| 4711 | return;
|
| 4712 | }
|
| 4713 | if (car(p1) === symbol(COSH)) {
|
| 4714 | p1 = cadr(p1);
|
| 4715 | push(p1);
|
| 4716 | exponential();
|
| 4717 | push(p1);
|
| 4718 | negate();
|
| 4719 | exponential();
|
| 4720 | add();
|
| 4721 | push_rational(1, 2);
|
| 4722 | multiply();
|
| 4723 | restore();
|
| 4724 | return;
|
| 4725 | }
|
| 4726 | if (car(p1) === symbol(SINH)) {
|
| 4727 | p1 = cadr(p1);
|
| 4728 | push(p1);
|
| 4729 | exponential();
|
| 4730 | push(p1);
|
| 4731 | negate();
|
| 4732 | exponential();
|
| 4733 | subtract();
|
| 4734 | push_rational(1, 2);
|
| 4735 | multiply();
|
| 4736 | restore();
|
| 4737 | return;
|
| 4738 | }
|
| 4739 | if (car(p1) === symbol(TANH)) {
|
| 4740 | p1 = cadr(p1);
|
| 4741 | push(p1);
|
| 4742 | push_integer(2);
|
| 4743 | multiply();
|
| 4744 | exponential();
|
| 4745 | p1 = pop();
|
| 4746 | push(p1);
|
| 4747 | push_integer(1);
|
| 4748 | subtract();
|
| 4749 | push(p1);
|
| 4750 | push_integer(1);
|
| 4751 | add();
|
| 4752 | divide();
|
| 4753 | restore();
|
| 4754 | return;
|
| 4755 | }
|
| 4756 | if (iscons(p1)) {
|
| 4757 | h = tos;
|
| 4758 | while (iscons(p1)) {
|
| 4759 | push(car(p1));
|
| 4760 | circexp();
|
| 4761 | p1 = cdr(p1);
|
| 4762 | }
|
| 4763 | list(tos - h);
|
| 4764 | restore();
|
| 4765 | return;
|
| 4766 | }
|
| 4767 | if (p1.k === TENSOR) {
|
| 4768 | push(p1);
|
| 4769 | copy_tensor();
|
| 4770 | p1 = pop();
|
| 4771 | for (i = o = 0, ref = p1.tensor.nelem; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 4772 | push(p1.tensor.elem[i]);
|
| 4773 | circexp();
|
| 4774 | p1.tensor.elem[i] = pop();
|
| 4775 | }
|
| 4776 | push(p1);
|
| 4777 | restore();
|
| 4778 | return;
|
| 4779 | }
|
| 4780 | push(p1);
|
| 4781 | return restore();
|
| 4782 | };
|
| 4783 |
|
| 4784 |
|
| 4785 | |
| 4786 | |
| 4787 | |
| 4788 | |
| 4789 | |
| 4790 | |
| 4791 | |
| 4792 | |
| 4793 | |
| 4794 | |
| 4795 | |
| 4796 |
|
| 4797 |
|
| 4798 | Eval_clearall = function() {
|
| 4799 | do_clearall();
|
| 4800 | return push(symbol(NIL));
|
| 4801 | };
|
| 4802 |
|
| 4803 | do_clearall = function() {
|
| 4804 | if (test_flag === 0) {
|
| 4805 | clear_term();
|
| 4806 | }
|
| 4807 | do_clearPatterns();
|
| 4808 | clear_symbols();
|
| 4809 | defn();
|
| 4810 | return codeGen = false;
|
| 4811 | };
|
| 4812 |
|
| 4813 | clearall = function() {
|
| 4814 | return run("clearall");
|
| 4815 | };
|
| 4816 |
|
| 4817 | clearRenamedVariablesToAvoidBindingToExternalScope = function() {
|
| 4818 | var i, o, ref, results;
|
| 4819 | results = [];
|
| 4820 | for (i = o = 0, ref = symtab.length; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 4821 | if (symtab[i].printname.indexOf("AVOID_BINDING_TO_EXTERNAL_SCOPE_VALUE") !== -1) {
|
| 4822 | symtab[i].k = SYM;
|
| 4823 | symtab[i].printname = "";
|
| 4824 | binding[i] = symtab[i];
|
| 4825 | results.push(isSymbolReclaimable[i] = true);
|
| 4826 | } else {
|
| 4827 | results.push(void 0);
|
| 4828 | }
|
| 4829 | }
|
| 4830 | return results;
|
| 4831 | };
|
| 4832 |
|
| 4833 |
|
| 4834 | |
| 4835 | |
| 4836 | |
| 4837 | |
| 4838 | |
| 4839 | |
| 4840 | |
| 4841 | |
| 4842 | |
| 4843 | |
| 4844 | |
| 4845 | |
| 4846 | |
| 4847 | |
| 4848 |
|
| 4849 |
|
| 4850 | Eval_clear = function() {
|
| 4851 | var indexFound, variableToBeCleared;
|
| 4852 | p2 = cdr(p1);
|
| 4853 | while (iscons(p2)) {
|
| 4854 | variableToBeCleared = car(p2);
|
| 4855 | if (variableToBeCleared.k !== SYM) {
|
| 4856 | stop("symbol error");
|
| 4857 | }
|
| 4858 | indexFound = symtab.indexOf(variableToBeCleared);
|
| 4859 | symtab[indexFound].k = SYM;
|
| 4860 | symtab[indexFound].printname = "";
|
| 4861 | binding[indexFound] = symtab[indexFound];
|
| 4862 | isSymbolReclaimable[indexFound] = true;
|
| 4863 | p2 = cdr(p2);
|
| 4864 | }
|
| 4865 | return push(symbol(NIL));
|
| 4866 | };
|
| 4867 |
|
| 4868 |
|
| 4869 | |
| 4870 | |
| 4871 | |
| 4872 | |
| 4873 | |
| 4874 | |
| 4875 | |
| 4876 | |
| 4877 | |
| 4878 | |
| 4879 |
|
| 4880 |
|
| 4881 | DEBUG_CLOCKFORM = false;
|
| 4882 |
|
| 4883 | Eval_clock = function() {
|
| 4884 | push(cadr(p1));
|
| 4885 | Eval();
|
| 4886 | return clockform();
|
| 4887 | };
|
| 4888 |
|
| 4889 | clockform = function() {
|
| 4890 | save();
|
| 4891 | p1 = pop();
|
| 4892 | push(p1);
|
| 4893 | abs();
|
| 4894 | if (DEBUG_CLOCKFORM) {
|
| 4895 | console.log("clockform: abs of " + p1 + " : " + stack[tos - 1]);
|
| 4896 | }
|
| 4897 | push_symbol(POWER);
|
| 4898 | push_integer(-1);
|
| 4899 | push(p1);
|
| 4900 | arg();
|
| 4901 | if (DEBUG_CLOCKFORM) {
|
| 4902 | console.log("clockform: arg of " + p1 + " : " + stack[tos - 1]);
|
| 4903 | }
|
| 4904 | if (evaluatingAsFloats) {
|
| 4905 | push_double(Math.PI);
|
| 4906 | } else {
|
| 4907 | push(symbol(PI));
|
| 4908 | }
|
| 4909 | divide();
|
| 4910 | if (DEBUG_CLOCKFORM) {
|
| 4911 | console.log("clockform: divide : " + stack[tos - 1]);
|
| 4912 | }
|
| 4913 | list(3);
|
| 4914 | if (DEBUG_CLOCKFORM) {
|
| 4915 | console.log("clockform: power : " + stack[tos - 1]);
|
| 4916 | }
|
| 4917 | multiply();
|
| 4918 | if (DEBUG_CLOCKFORM) {
|
| 4919 | console.log("clockform: multiply : " + stack[tos - 1]);
|
| 4920 | }
|
| 4921 |
|
| 4922 | |
| 4923 | |
| 4924 | |
| 4925 | |
| 4926 | |
| 4927 | |
| 4928 | |
| 4929 | |
| 4930 | |
| 4931 | |
| 4932 | |
| 4933 |
|
| 4934 | return restore();
|
| 4935 | };
|
| 4936 |
|
| 4937 |
|
| 4938 | |
| 4939 | |
| 4940 | |
| 4941 | |
| 4942 | |
| 4943 | |
| 4944 | |
| 4945 | |
| 4946 | |
| 4947 | |
| 4948 | |
| 4949 | |
| 4950 | |
| 4951 |
|
| 4952 |
|
| 4953 | Eval_coeff = function() {
|
| 4954 | push(cadr(p1));
|
| 4955 | Eval();
|
| 4956 | push(caddr(p1));
|
| 4957 | Eval();
|
| 4958 | push(cadddr(p1));
|
| 4959 | Eval();
|
| 4960 | p3 = pop();
|
| 4961 | p2 = pop();
|
| 4962 | p1 = pop();
|
| 4963 | if (p3 === symbol(NIL)) {
|
| 4964 | p3 = p2;
|
| 4965 | p2 = symbol(SYMBOL_X);
|
| 4966 | }
|
| 4967 | push(p1);
|
| 4968 | push(p2);
|
| 4969 | push(p3);
|
| 4970 | power();
|
| 4971 | divide();
|
| 4972 | push(p2);
|
| 4973 | return filter();
|
| 4974 | };
|
| 4975 |
|
| 4976 | coeff = function() {
|
| 4977 | var h, n, prev_expanding;
|
| 4978 | save();
|
| 4979 | p2 = pop();
|
| 4980 | p1 = pop();
|
| 4981 | h = tos;
|
| 4982 | while (1) {
|
| 4983 | push(p1);
|
| 4984 | push(p2);
|
| 4985 | push(zero);
|
| 4986 | subst();
|
| 4987 | Eval();
|
| 4988 | p3 = pop();
|
| 4989 | push(p3);
|
| 4990 | push(p1);
|
| 4991 | push(p3);
|
| 4992 | subtract();
|
| 4993 | p1 = pop();
|
| 4994 | if (equal(p1, zero)) {
|
| 4995 | n = tos - h;
|
| 4996 | restore();
|
| 4997 | return n;
|
| 4998 | }
|
| 4999 | push(p1);
|
| 5000 | push(p2);
|
| 5001 | prev_expanding = expanding;
|
| 5002 | expanding = 1;
|
| 5003 | divide();
|
| 5004 | expanding = prev_expanding;
|
| 5005 | p1 = pop();
|
| 5006 | }
|
| 5007 | };
|
| 5008 |
|
| 5009 |
|
| 5010 | |
| 5011 | |
| 5012 | |
| 5013 | |
| 5014 | |
| 5015 | |
| 5016 | |
| 5017 | |
| 5018 | |
| 5019 | |
| 5020 | |
| 5021 | |
| 5022 | |
| 5023 | |
| 5024 | |
| 5025 |
|
| 5026 |
|
| 5027 | Eval_cofactor = function() {
|
| 5028 | var doNothing, i, j, n;
|
| 5029 | i = 0;
|
| 5030 | j = 0;
|
| 5031 | n = 0;
|
| 5032 | push(cadr(p1));
|
| 5033 | Eval();
|
| 5034 | p2 = pop();
|
| 5035 | if (istensor(p2) && p2.tensor.ndim === 2 && p2.tensor.dim[0] === p2.tensor.dim[1]) {
|
| 5036 | doNothing = 1;
|
| 5037 | } else {
|
| 5038 | stop("cofactor: 1st arg: square matrix expected");
|
| 5039 | }
|
| 5040 | n = p2.tensor.dim[0];
|
| 5041 | push(caddr(p1));
|
| 5042 | Eval();
|
| 5043 | i = pop_integer();
|
| 5044 | if (i < 1 || i > n) {
|
| 5045 | stop("cofactor: 2nd arg: row index expected");
|
| 5046 | }
|
| 5047 | push(cadddr(p1));
|
| 5048 | Eval();
|
| 5049 | j = pop_integer();
|
| 5050 | if (j < 1 || j > n) {
|
| 5051 | stop("cofactor: 3rd arg: column index expected");
|
| 5052 | }
|
| 5053 | return cofactor(p2, n, i - 1, j - 1);
|
| 5054 | };
|
| 5055 |
|
| 5056 | cofactor = function(p, n, row, col) {
|
| 5057 | var i, i1, j, o, ref, ref1;
|
| 5058 | i = 0;
|
| 5059 | j = 0;
|
| 5060 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 5061 | for (j = i1 = 0, ref1 = n; 0 <= ref1 ? i1 < ref1 : i1 > ref1; j = 0 <= ref1 ? ++i1 : --i1) {
|
| 5062 | if (i !== row && j !== col) {
|
| 5063 | push(p.tensor.elem[n * i + j]);
|
| 5064 | }
|
| 5065 | }
|
| 5066 | }
|
| 5067 | determinant(n - 1);
|
| 5068 | if ((row + col) % 2) {
|
| 5069 | return negate();
|
| 5070 | }
|
| 5071 | };
|
| 5072 |
|
| 5073 | Eval_condense = function() {
|
| 5074 | push(cadr(p1));
|
| 5075 | Eval();
|
| 5076 | return Condense();
|
| 5077 | };
|
| 5078 |
|
| 5079 | Condense = function() {
|
| 5080 | var prev_expanding;
|
| 5081 | prev_expanding = expanding;
|
| 5082 | expanding = 0;
|
| 5083 | save();
|
| 5084 | yycondense();
|
| 5085 | restore();
|
| 5086 | return expanding = prev_expanding;
|
| 5087 | };
|
| 5088 |
|
| 5089 | yycondense = function() {
|
| 5090 | p1 = pop();
|
| 5091 | if (car(p1) !== symbol(ADD)) {
|
| 5092 | push(p1);
|
| 5093 | return;
|
| 5094 | }
|
| 5095 | p3 = cdr(p1);
|
| 5096 | push(car(p3));
|
| 5097 | p3 = cdr(p3);
|
| 5098 | while (iscons(p3)) {
|
| 5099 | push(car(p3));
|
| 5100 | gcd();
|
| 5101 | p3 = cdr(p3);
|
| 5102 | }
|
| 5103 | inverse();
|
| 5104 | p2 = pop();
|
| 5105 | push(zero);
|
| 5106 | p3 = cdr(p1);
|
| 5107 | while (iscons(p3)) {
|
| 5108 | push(p2);
|
| 5109 | push(car(p3));
|
| 5110 | multiply();
|
| 5111 | add();
|
| 5112 | p3 = cdr(p3);
|
| 5113 | }
|
| 5114 | yyexpand();
|
| 5115 | push(p2);
|
| 5116 | return divide();
|
| 5117 | };
|
| 5118 |
|
| 5119 |
|
| 5120 | |
| 5121 | |
| 5122 | |
| 5123 | |
| 5124 | |
| 5125 | |
| 5126 | |
| 5127 | |
| 5128 | |
| 5129 | |
| 5130 | |
| 5131 | |
| 5132 | |
| 5133 |
|
| 5134 |
|
| 5135 | Eval_conj = function() {
|
| 5136 | push(cadr(p1));
|
| 5137 | Eval();
|
| 5138 | p1 = pop();
|
| 5139 | push(p1);
|
| 5140 | if (!Find(p1, imaginaryunit)) {
|
| 5141 | polar();
|
| 5142 | conjugate();
|
| 5143 | return clockform();
|
| 5144 | } else {
|
| 5145 | return conjugate();
|
| 5146 | }
|
| 5147 | };
|
| 5148 |
|
| 5149 | conjugate = function() {
|
| 5150 | push(imaginaryunit);
|
| 5151 | push(imaginaryunit);
|
| 5152 | negate();
|
| 5153 | subst();
|
| 5154 | return Eval();
|
| 5155 | };
|
| 5156 |
|
| 5157 | consCount = 0;
|
| 5158 |
|
| 5159 | cons = function() {
|
| 5160 | var p;
|
| 5161 | consCount++;
|
| 5162 | if (DEBUG) {
|
| 5163 | console.log("cons tos: " + tos + " # " + consCount);
|
| 5164 | }
|
| 5165 | p = new U();
|
| 5166 | p.k = CONS;
|
| 5167 | p.cons.cdr = pop();
|
| 5168 | if (p === p.cons.cdr) {
|
| 5169 | debugger;
|
| 5170 | console.log("something wrong p == its cdr");
|
| 5171 | }
|
| 5172 | p.cons.car = pop();
|
| 5173 |
|
| 5174 | |
| 5175 | |
| 5176 | |
| 5177 | |
| 5178 | |
| 5179 |
|
| 5180 | return push(p);
|
| 5181 | };
|
| 5182 |
|
| 5183 |
|
| 5184 | |
| 5185 | |
| 5186 | |
| 5187 | |
| 5188 | |
| 5189 | |
| 5190 | |
| 5191 | |
| 5192 | |
| 5193 | |
| 5194 | |
| 5195 | |
| 5196 | |
| 5197 | |
| 5198 | |
| 5199 |
|
| 5200 |
|
| 5201 | Eval_contract = function() {
|
| 5202 | push(cadr(p1));
|
| 5203 | Eval();
|
| 5204 | if (cddr(p1) === symbol(NIL)) {
|
| 5205 | push_integer(1);
|
| 5206 | push_integer(2);
|
| 5207 | } else {
|
| 5208 | push(caddr(p1));
|
| 5209 | Eval();
|
| 5210 | push(cadddr(p1));
|
| 5211 | Eval();
|
| 5212 | }
|
| 5213 | return contract();
|
| 5214 | };
|
| 5215 |
|
| 5216 | contract = function() {
|
| 5217 | save();
|
| 5218 | yycontract();
|
| 5219 | return restore();
|
| 5220 | };
|
| 5221 |
|
| 5222 | yycontract = function() {
|
| 5223 | var a, ai, an, b, h, i, i1, j, j1, k, l, l1, m, m1, n, n1, ndim, nelem, o, o1, ref, ref1, ref2, ref3, ref4, ref5, ref6;
|
| 5224 | h = 0;
|
| 5225 | i = 0;
|
| 5226 | j = 0;
|
| 5227 | k = 0;
|
| 5228 | l = 0;
|
| 5229 | m = 0;
|
| 5230 | n = 0;
|
| 5231 | ndim = 0;
|
| 5232 | nelem = 0;
|
| 5233 | ai = [];
|
| 5234 | an = [];
|
| 5235 | p3 = pop();
|
| 5236 | p2 = pop();
|
| 5237 | p1 = pop();
|
| 5238 | if (!istensor(p1)) {
|
| 5239 | if (!iszero(p1)) {
|
| 5240 | stop("contract: tensor expected, 1st arg is not a tensor");
|
| 5241 | }
|
| 5242 | push(zero);
|
| 5243 | return;
|
| 5244 | }
|
| 5245 | push(p2);
|
| 5246 | l = pop_integer();
|
| 5247 | push(p3);
|
| 5248 | m = pop_integer();
|
| 5249 | ndim = p1.tensor.ndim;
|
| 5250 | if (l < 1 || l > ndim || m < 1 || m > ndim || l === m || p1.tensor.dim[l - 1] !== p1.tensor.dim[m - 1]) {
|
| 5251 | stop("contract: index out of range");
|
| 5252 | }
|
| 5253 | l--;
|
| 5254 | m--;
|
| 5255 | n = p1.tensor.dim[l];
|
| 5256 | nelem = 1;
|
| 5257 | for (i = o = 0, ref = ndim; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 5258 | if (i !== l && i !== m) {
|
| 5259 | nelem *= p1.tensor.dim[i];
|
| 5260 | }
|
| 5261 | }
|
| 5262 | p2 = alloc_tensor(nelem);
|
| 5263 | p2.tensor.ndim = ndim - 2;
|
| 5264 | j = 0;
|
| 5265 | for (i = i1 = 0, ref1 = ndim; 0 <= ref1 ? i1 < ref1 : i1 > ref1; i = 0 <= ref1 ? ++i1 : --i1) {
|
| 5266 | if (i !== l && i !== m) {
|
| 5267 | p2.tensor.dim[j++] = p1.tensor.dim[i];
|
| 5268 | }
|
| 5269 | }
|
| 5270 | a = p1.tensor.elem;
|
| 5271 | b = p2.tensor.elem;
|
| 5272 | for (i = j1 = 0, ref2 = ndim; 0 <= ref2 ? j1 < ref2 : j1 > ref2; i = 0 <= ref2 ? ++j1 : --j1) {
|
| 5273 | ai[i] = 0;
|
| 5274 | an[i] = p1.tensor.dim[i];
|
| 5275 | }
|
| 5276 | for (i = l1 = 0, ref3 = nelem; 0 <= ref3 ? l1 < ref3 : l1 > ref3; i = 0 <= ref3 ? ++l1 : --l1) {
|
| 5277 | push(zero);
|
| 5278 | for (j = m1 = 0, ref4 = n; 0 <= ref4 ? m1 < ref4 : m1 > ref4; j = 0 <= ref4 ? ++m1 : --m1) {
|
| 5279 | ai[l] = j;
|
| 5280 | ai[m] = j;
|
| 5281 | h = 0;
|
| 5282 | for (k = n1 = 0, ref5 = ndim; 0 <= ref5 ? n1 < ref5 : n1 > ref5; k = 0 <= ref5 ? ++n1 : --n1) {
|
| 5283 | h = (h * an[k]) + ai[k];
|
| 5284 | }
|
| 5285 | push(a[h]);
|
| 5286 | add();
|
| 5287 | }
|
| 5288 | b[i] = pop();
|
| 5289 | for (j = o1 = ref6 = ndim - 1; ref6 <= 0 ? o1 <= 0 : o1 >= 0; j = ref6 <= 0 ? ++o1 : --o1) {
|
| 5290 | if (j === l || j === m) {
|
| 5291 | continue;
|
| 5292 | }
|
| 5293 | if (++ai[j] < an[j]) {
|
| 5294 | break;
|
| 5295 | }
|
| 5296 | ai[j] = 0;
|
| 5297 | }
|
| 5298 | }
|
| 5299 | if (nelem === 1) {
|
| 5300 | return push(b[0]);
|
| 5301 | } else {
|
| 5302 | return push(p2);
|
| 5303 | }
|
| 5304 | };
|
| 5305 |
|
| 5306 |
|
| 5307 | |
| 5308 | |
| 5309 | |
| 5310 | |
| 5311 | |
| 5312 | |
| 5313 | |
| 5314 | |
| 5315 | |
| 5316 | |
| 5317 | |
| 5318 | |
| 5319 | |
| 5320 |
|
| 5321 |
|
| 5322 | Eval_cos = function() {
|
| 5323 | push(cadr(p1));
|
| 5324 | Eval();
|
| 5325 | return cosine();
|
| 5326 | };
|
| 5327 |
|
| 5328 | cosine = function() {
|
| 5329 | save();
|
| 5330 | p1 = pop();
|
| 5331 | if (car(p1) === symbol(ADD)) {
|
| 5332 | cosine_of_angle_sum();
|
| 5333 | } else {
|
| 5334 | cosine_of_angle();
|
| 5335 | }
|
| 5336 | return restore();
|
| 5337 | };
|
| 5338 |
|
| 5339 | cosine_of_angle_sum = function() {
|
| 5340 | p2 = cdr(p1);
|
| 5341 | while (iscons(p2)) {
|
| 5342 | p4 = car(p2);
|
| 5343 | if (isnpi(p4)) {
|
| 5344 | push(p1);
|
| 5345 | push(p4);
|
| 5346 | subtract();
|
| 5347 | p3 = pop();
|
| 5348 | push(p3);
|
| 5349 | cosine();
|
| 5350 | push(p4);
|
| 5351 | cosine();
|
| 5352 | multiply();
|
| 5353 | push(p3);
|
| 5354 | sine();
|
| 5355 | push(p4);
|
| 5356 | sine();
|
| 5357 | multiply();
|
| 5358 | subtract();
|
| 5359 | return;
|
| 5360 | }
|
| 5361 | p2 = cdr(p2);
|
| 5362 | }
|
| 5363 | return cosine_of_angle();
|
| 5364 | };
|
| 5365 |
|
| 5366 | cosine_of_angle = function() {
|
| 5367 | var d, n;
|
| 5368 | if (car(p1) === symbol(ARCCOS)) {
|
| 5369 | push(cadr(p1));
|
| 5370 | return;
|
| 5371 | }
|
| 5372 | if (isdouble(p1)) {
|
| 5373 | d = Math.cos(p1.d);
|
| 5374 | if (Math.abs(d) < 1e-10) {
|
| 5375 | d = 0.0;
|
| 5376 | }
|
| 5377 | push_double(d);
|
| 5378 | return;
|
| 5379 | }
|
| 5380 | if (isnegative(p1)) {
|
| 5381 | push(p1);
|
| 5382 | negate();
|
| 5383 | p1 = pop();
|
| 5384 | }
|
| 5385 | if (car(p1) === symbol(ARCTAN)) {
|
| 5386 | push_integer(1);
|
| 5387 | push(cadr(p1));
|
| 5388 | push_integer(2);
|
| 5389 | power();
|
| 5390 | add();
|
| 5391 | push_rational(-1, 2);
|
| 5392 | power();
|
| 5393 | return;
|
| 5394 | }
|
| 5395 | push(p1);
|
| 5396 | push_integer(180);
|
| 5397 | multiply();
|
| 5398 | if (evaluatingAsFloats) {
|
| 5399 | push_double(Math.PI);
|
| 5400 | } else {
|
| 5401 | push_symbol(PI);
|
| 5402 | }
|
| 5403 | divide();
|
| 5404 | n = pop_integer();
|
| 5405 | if (n < 0 || isNaN(n)) {
|
| 5406 | push(symbol(COS));
|
| 5407 | push(p1);
|
| 5408 | list(2);
|
| 5409 | return;
|
| 5410 | }
|
| 5411 | switch (n % 360) {
|
| 5412 | case 90:
|
| 5413 | case 270:
|
| 5414 | return push_integer(0);
|
| 5415 | case 60:
|
| 5416 | case 300:
|
| 5417 | return push_rational(1, 2);
|
| 5418 | case 120:
|
| 5419 | case 240:
|
| 5420 | return push_rational(-1, 2);
|
| 5421 | case 45:
|
| 5422 | case 315:
|
| 5423 | push_rational(1, 2);
|
| 5424 | push_integer(2);
|
| 5425 | push_rational(1, 2);
|
| 5426 | power();
|
| 5427 | return multiply();
|
| 5428 | case 135:
|
| 5429 | case 225:
|
| 5430 | push_rational(-1, 2);
|
| 5431 | push_integer(2);
|
| 5432 | push_rational(1, 2);
|
| 5433 | power();
|
| 5434 | return multiply();
|
| 5435 | case 30:
|
| 5436 | case 330:
|
| 5437 | push_rational(1, 2);
|
| 5438 | push_integer(3);
|
| 5439 | push_rational(1, 2);
|
| 5440 | power();
|
| 5441 | return multiply();
|
| 5442 | case 150:
|
| 5443 | case 210:
|
| 5444 | push_rational(-1, 2);
|
| 5445 | push_integer(3);
|
| 5446 | push_rational(1, 2);
|
| 5447 | power();
|
| 5448 | return multiply();
|
| 5449 | case 0:
|
| 5450 | return push_integer(1);
|
| 5451 | case 180:
|
| 5452 | return push_integer(-1);
|
| 5453 | default:
|
| 5454 | push(symbol(COS));
|
| 5455 | push(p1);
|
| 5456 | return list(2);
|
| 5457 | }
|
| 5458 | };
|
| 5459 |
|
| 5460 |
|
| 5461 | |
| 5462 | |
| 5463 | |
| 5464 | |
| 5465 | |
| 5466 | |
| 5467 | |
| 5468 | |
| 5469 | |
| 5470 | |
| 5471 | |
| 5472 | |
| 5473 | |
| 5474 | |
| 5475 | |
| 5476 | |
| 5477 | |
| 5478 | |
| 5479 | |
| 5480 |
|
| 5481 |
|
| 5482 | Eval_cosh = function() {
|
| 5483 | push(cadr(p1));
|
| 5484 | Eval();
|
| 5485 | return ycosh();
|
| 5486 | };
|
| 5487 |
|
| 5488 | ycosh = function() {
|
| 5489 | save();
|
| 5490 | yycosh();
|
| 5491 | return restore();
|
| 5492 | };
|
| 5493 |
|
| 5494 | yycosh = function() {
|
| 5495 | var d;
|
| 5496 | d = 0.0;
|
| 5497 | p1 = pop();
|
| 5498 | if (car(p1) === symbol(ARCCOSH)) {
|
| 5499 | push(cadr(p1));
|
| 5500 | return;
|
| 5501 | }
|
| 5502 | if (isdouble(p1)) {
|
| 5503 | d = Math.cosh(p1.d);
|
| 5504 | if (Math.abs(d) < 1e-10) {
|
| 5505 | d = 0.0;
|
| 5506 | }
|
| 5507 | push_double(d);
|
| 5508 | return;
|
| 5509 | }
|
| 5510 | if (iszero(p1)) {
|
| 5511 | push(one);
|
| 5512 | return;
|
| 5513 | }
|
| 5514 | push_symbol(COSH);
|
| 5515 | push(p1);
|
| 5516 | return list(2);
|
| 5517 | };
|
| 5518 |
|
| 5519 | Eval_decomp = function() {
|
| 5520 | var h;
|
| 5521 | save();
|
| 5522 | console.log("Eval_decomp is being called!!!!!!!!!!!!!!!!!!!!");
|
| 5523 | h = tos;
|
| 5524 | push(symbol(NIL));
|
| 5525 | push(cadr(p1));
|
| 5526 | Eval();
|
| 5527 | push(caddr(p1));
|
| 5528 | Eval();
|
| 5529 | p1 = pop();
|
| 5530 | if (p1 === symbol(NIL)) {
|
| 5531 | guess();
|
| 5532 | } else {
|
| 5533 | push(p1);
|
| 5534 | }
|
| 5535 | decomp(false);
|
| 5536 | list(tos - h);
|
| 5537 | return restore();
|
| 5538 | };
|
| 5539 |
|
| 5540 | pushTryNotToDuplicate = function(toBePushed) {
|
| 5541 | if (tos > 0) {
|
| 5542 | if (DEBUG) {
|
| 5543 | console.log("comparing " + toBePushed + " to: " + stack[tos - 1]);
|
| 5544 | }
|
| 5545 | if (equal(toBePushed, stack[tos - 1])) {
|
| 5546 | if (DEBUG) {
|
| 5547 | console.log("skipping " + toBePushed + " because it's already on stack ");
|
| 5548 | }
|
| 5549 | return;
|
| 5550 | }
|
| 5551 | }
|
| 5552 | return push(toBePushed);
|
| 5553 | };
|
| 5554 |
|
| 5555 | decomp = function(generalTransform) {
|
| 5556 | save();
|
| 5557 | p2 = pop();
|
| 5558 | p1 = pop();
|
| 5559 | if (DEBUG) {
|
| 5560 | console.log("DECOMPOSING " + p1);
|
| 5561 | }
|
| 5562 | if (generalTransform) {
|
| 5563 | if (!iscons(p1)) {
|
| 5564 | if (DEBUG) {
|
| 5565 | console.log(" ground thing: " + p1);
|
| 5566 | }
|
| 5567 | pushTryNotToDuplicate(p1);
|
| 5568 | restore();
|
| 5569 | return;
|
| 5570 | }
|
| 5571 | } else {
|
| 5572 | if (Find(p1, p2) === 0) {
|
| 5573 | if (DEBUG) {
|
| 5574 | console.log(" entire expression is constant");
|
| 5575 | }
|
| 5576 | pushTryNotToDuplicate(p1);
|
| 5577 | restore();
|
| 5578 | return;
|
| 5579 | }
|
| 5580 | }
|
| 5581 | if (isadd(p1)) {
|
| 5582 | decomp_sum(generalTransform);
|
| 5583 | restore();
|
| 5584 | return;
|
| 5585 | }
|
| 5586 | if (ismultiply(p1)) {
|
| 5587 | decomp_product(generalTransform);
|
| 5588 | restore();
|
| 5589 | return;
|
| 5590 | }
|
| 5591 | if (DEBUG) {
|
| 5592 | console.log(" naive decomp");
|
| 5593 | }
|
| 5594 | p3 = cdr(p1);
|
| 5595 | if (DEBUG) {
|
| 5596 | console.log("startig p3: " + p3);
|
| 5597 | }
|
| 5598 | while (iscons(p3)) {
|
| 5599 | if (generalTransform) {
|
| 5600 | push(car(p3));
|
| 5601 | }
|
| 5602 | if (DEBUG) {
|
| 5603 | console.log("recursive decomposition");
|
| 5604 | }
|
| 5605 | push(car(p3));
|
| 5606 | if (DEBUG) {
|
| 5607 | console.log("car(p3): " + car(p3));
|
| 5608 | }
|
| 5609 | push(p2);
|
| 5610 | if (DEBUG) {
|
| 5611 | console.log("p2: " + p2);
|
| 5612 | }
|
| 5613 | decomp(generalTransform);
|
| 5614 | p3 = cdr(p3);
|
| 5615 | }
|
| 5616 | return restore();
|
| 5617 | };
|
| 5618 |
|
| 5619 | decomp_sum = function(generalTransform) {
|
| 5620 | var h;
|
| 5621 | if (DEBUG) {
|
| 5622 | console.log(" decomposing the sum ");
|
| 5623 | }
|
| 5624 | h = 0;
|
| 5625 | p3 = cdr(p1);
|
| 5626 | while (iscons(p3)) {
|
| 5627 | if (Find(car(p3), p2) || generalTransform) {
|
| 5628 | push(car(p3));
|
| 5629 | push(p2);
|
| 5630 | decomp(generalTransform);
|
| 5631 | }
|
| 5632 | p3 = cdr(p3);
|
| 5633 | }
|
| 5634 | h = tos;
|
| 5635 | p3 = cdr(p1);
|
| 5636 | while (iscons(p3)) {
|
| 5637 | if (Find(car(p3), p2) === 0) {
|
| 5638 | pushTryNotToDuplicate(car(p3));
|
| 5639 | }
|
| 5640 | p3 = cdr(p3);
|
| 5641 | }
|
| 5642 | if (tos - h) {
|
| 5643 | add_all(tos - h);
|
| 5644 | p3 = pop();
|
| 5645 | pushTryNotToDuplicate(p3);
|
| 5646 | push(p3);
|
| 5647 | return negate();
|
| 5648 | }
|
| 5649 | };
|
| 5650 |
|
| 5651 | decomp_product = function(generalTransform) {
|
| 5652 | var h;
|
| 5653 | if (DEBUG) {
|
| 5654 | console.log(" decomposing the product ");
|
| 5655 | }
|
| 5656 | h = 0;
|
| 5657 | p3 = cdr(p1);
|
| 5658 | while (iscons(p3)) {
|
| 5659 | if (Find(car(p3), p2) || generalTransform) {
|
| 5660 | push(car(p3));
|
| 5661 | push(p2);
|
| 5662 | decomp(generalTransform);
|
| 5663 | }
|
| 5664 | p3 = cdr(p3);
|
| 5665 | }
|
| 5666 | h = tos;
|
| 5667 | p3 = cdr(p1);
|
| 5668 | while (iscons(p3)) {
|
| 5669 | if (Find(car(p3), p2) === 0) {
|
| 5670 | pushTryNotToDuplicate(car(p3));
|
| 5671 | }
|
| 5672 | p3 = cdr(p3);
|
| 5673 | }
|
| 5674 | if (tos - h) {
|
| 5675 | return multiply_all(tos - h);
|
| 5676 | }
|
| 5677 | };
|
| 5678 |
|
| 5679 | define_user_function = function() {
|
| 5680 | p3 = caadr(p1);
|
| 5681 | p4 = cdadr(p1);
|
| 5682 | p5 = caddr(p1);
|
| 5683 | if (!issymbol(p3)) {
|
| 5684 | stop("function name?");
|
| 5685 | }
|
| 5686 | if (car(p5) === symbol(EVAL)) {
|
| 5687 | push(cadr(p5));
|
| 5688 | Eval();
|
| 5689 | p5 = pop();
|
| 5690 | }
|
| 5691 | push_symbol(FUNCTION);
|
| 5692 | push(p5);
|
| 5693 | push(p4);
|
| 5694 | list(3);
|
| 5695 | p5 = pop();
|
| 5696 | set_binding(p3, p5);
|
| 5697 | return push_symbol(NIL);
|
| 5698 | };
|
| 5699 |
|
| 5700 | Eval_function_reference = function() {
|
| 5701 | return push(p1);
|
| 5702 | };
|
| 5703 |
|
| 5704 |
|
| 5705 | |
| 5706 | |
| 5707 | |
| 5708 | |
| 5709 | |
| 5710 | |
| 5711 | |
| 5712 | |
| 5713 | |
| 5714 | |
| 5715 | |
| 5716 | |
| 5717 | |
| 5718 | |
| 5719 | |
| 5720 | |
| 5721 | |
| 5722 |
|
| 5723 |
|
| 5724 | Eval_defint = function() {
|
| 5725 | push(cadr(p1));
|
| 5726 | Eval();
|
| 5727 | p2 = pop();
|
| 5728 | p1 = cddr(p1);
|
| 5729 | while (iscons(p1)) {
|
| 5730 | push(car(p1));
|
| 5731 | p1 = cdr(p1);
|
| 5732 | Eval();
|
| 5733 | p3 = pop();
|
| 5734 | push(car(p1));
|
| 5735 | p1 = cdr(p1);
|
| 5736 | Eval();
|
| 5737 | p4 = pop();
|
| 5738 | push(car(p1));
|
| 5739 | p1 = cdr(p1);
|
| 5740 | Eval();
|
| 5741 | p5 = pop();
|
| 5742 | push(p2);
|
| 5743 | push(p3);
|
| 5744 | integral();
|
| 5745 | p2 = pop();
|
| 5746 | push(p2);
|
| 5747 | push(p3);
|
| 5748 | push(p5);
|
| 5749 | subst();
|
| 5750 | Eval();
|
| 5751 | push(p2);
|
| 5752 | push(p3);
|
| 5753 | push(p4);
|
| 5754 | subst();
|
| 5755 | Eval();
|
| 5756 | subtract();
|
| 5757 | p2 = pop();
|
| 5758 | }
|
| 5759 | return push(p2);
|
| 5760 | };
|
| 5761 |
|
| 5762 |
|
| 5763 | |
| 5764 | |
| 5765 | |
| 5766 | |
| 5767 | |
| 5768 | |
| 5769 | |
| 5770 | |
| 5771 | |
| 5772 | |
| 5773 | |
| 5774 | |
| 5775 | |
| 5776 |
|
| 5777 |
|
| 5778 | Eval_degree = function() {
|
| 5779 | push(cadr(p1));
|
| 5780 | Eval();
|
| 5781 | push(caddr(p1));
|
| 5782 | Eval();
|
| 5783 | p1 = pop();
|
| 5784 | if (p1 === symbol(NIL)) {
|
| 5785 | guess();
|
| 5786 | } else {
|
| 5787 | push(p1);
|
| 5788 | }
|
| 5789 | return degree();
|
| 5790 | };
|
| 5791 |
|
| 5792 | degree = function() {
|
| 5793 | save();
|
| 5794 | p2 = pop();
|
| 5795 | p1 = pop();
|
| 5796 | p3 = zero;
|
| 5797 | yydegree(p1);
|
| 5798 | push(p3);
|
| 5799 | return restore();
|
| 5800 | };
|
| 5801 |
|
| 5802 | yydegree = function(p) {
|
| 5803 | var results;
|
| 5804 | if (equal(p, p2)) {
|
| 5805 | if (iszero(p3)) {
|
| 5806 | return p3 = one;
|
| 5807 | }
|
| 5808 | } else if (car(p) === symbol(POWER)) {
|
| 5809 | if (equal(cadr(p), p2) && isnum(caddr(p)) && lessp(p3, caddr(p))) {
|
| 5810 | return p3 = caddr(p);
|
| 5811 | }
|
| 5812 | } else if (iscons(p)) {
|
| 5813 | p = cdr(p);
|
| 5814 | results = [];
|
| 5815 | while (iscons(p)) {
|
| 5816 | yydegree(car(p));
|
| 5817 | results.push(p = cdr(p));
|
| 5818 | }
|
| 5819 | return results;
|
| 5820 | }
|
| 5821 | };
|
| 5822 |
|
| 5823 |
|
| 5824 | |
| 5825 | |
| 5826 | |
| 5827 | |
| 5828 | |
| 5829 | |
| 5830 | |
| 5831 | |
| 5832 | |
| 5833 | |
| 5834 | |
| 5835 | |
| 5836 | |
| 5837 |
|
| 5838 |
|
| 5839 | Eval_denominator = function() {
|
| 5840 | push(cadr(p1));
|
| 5841 | Eval();
|
| 5842 | return denominator();
|
| 5843 | };
|
| 5844 |
|
| 5845 | denominator = function() {
|
| 5846 | var h;
|
| 5847 | h = 0;
|
| 5848 | save();
|
| 5849 | p1 = pop();
|
| 5850 | if (car(p1) === symbol(ADD)) {
|
| 5851 | push(p1);
|
| 5852 | rationalize();
|
| 5853 | p1 = pop();
|
| 5854 | }
|
| 5855 | if (car(p1) === symbol(MULTIPLY)) {
|
| 5856 | h = tos;
|
| 5857 | p1 = cdr(p1);
|
| 5858 | while (iscons(p1)) {
|
| 5859 | push(car(p1));
|
| 5860 | denominator();
|
| 5861 | p1 = cdr(p1);
|
| 5862 | }
|
| 5863 | multiply_all(tos - h);
|
| 5864 | } else if (isrational(p1)) {
|
| 5865 | push(p1);
|
| 5866 | mp_denominator();
|
| 5867 | } else if (car(p1) === symbol(POWER) && isnegativeterm(caddr(p1))) {
|
| 5868 | push(p1);
|
| 5869 | reciprocate();
|
| 5870 | } else {
|
| 5871 | push(one);
|
| 5872 | }
|
| 5873 | return restore();
|
| 5874 | };
|
| 5875 |
|
| 5876 | Eval_derivative = function() {
|
| 5877 | var doNothing, i, i1, n, o, ref, ref1;
|
| 5878 | i = 0;
|
| 5879 | p1 = cdr(p1);
|
| 5880 | push(car(p1));
|
| 5881 | Eval();
|
| 5882 | p1 = cdr(p1);
|
| 5883 | push(car(p1));
|
| 5884 | Eval();
|
| 5885 | p2 = pop();
|
| 5886 | if (p2 === symbol(NIL)) {
|
| 5887 | guess();
|
| 5888 | push(symbol(NIL));
|
| 5889 | } else if (isnum(p2)) {
|
| 5890 | guess();
|
| 5891 | push(p2);
|
| 5892 | } else {
|
| 5893 | push(p2);
|
| 5894 | p1 = cdr(p1);
|
| 5895 | push(car(p1));
|
| 5896 | Eval();
|
| 5897 | }
|
| 5898 | p5 = pop();
|
| 5899 | p4 = pop();
|
| 5900 | p3 = pop();
|
| 5901 | while (1) {
|
| 5902 | if (isnum(p5)) {
|
| 5903 | push(p5);
|
| 5904 | n = pop_integer();
|
| 5905 | if (isNaN(n)) {
|
| 5906 | stop("nth derivative: check n");
|
| 5907 | }
|
| 5908 | } else {
|
| 5909 | n = 1;
|
| 5910 | }
|
| 5911 | push(p3);
|
| 5912 | if (n >= 0) {
|
| 5913 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 5914 | push(p4);
|
| 5915 | derivative();
|
| 5916 | }
|
| 5917 | } else {
|
| 5918 | n = -n;
|
| 5919 | for (i = i1 = 0, ref1 = n; 0 <= ref1 ? i1 < ref1 : i1 > ref1; i = 0 <= ref1 ? ++i1 : --i1) {
|
| 5920 | push(p4);
|
| 5921 | integral();
|
| 5922 | }
|
| 5923 | }
|
| 5924 | p3 = pop();
|
| 5925 | if (p5 === symbol(NIL)) {
|
| 5926 | break;
|
| 5927 | }
|
| 5928 | if (isnum(p5)) {
|
| 5929 | p1 = cdr(p1);
|
| 5930 | push(car(p1));
|
| 5931 | Eval();
|
| 5932 | p5 = pop();
|
| 5933 | if (p5 === symbol(NIL)) {
|
| 5934 | break;
|
| 5935 | }
|
| 5936 | if (isnum(p5)) {
|
| 5937 | doNothing = 1;
|
| 5938 | } else {
|
| 5939 | p4 = p5;
|
| 5940 | p1 = cdr(p1);
|
| 5941 | push(car(p1));
|
| 5942 | Eval();
|
| 5943 | p5 = pop();
|
| 5944 | }
|
| 5945 | } else {
|
| 5946 | p4 = p5;
|
| 5947 | p1 = cdr(p1);
|
| 5948 | push(car(p1));
|
| 5949 | Eval();
|
| 5950 | p5 = pop();
|
| 5951 | }
|
| 5952 | }
|
| 5953 | return push(p3);
|
| 5954 | };
|
| 5955 |
|
| 5956 | derivative = function() {
|
| 5957 | save();
|
| 5958 | p2 = pop();
|
| 5959 | p1 = pop();
|
| 5960 | if (isnum(p2)) {
|
| 5961 | stop("undefined function");
|
| 5962 | }
|
| 5963 | if (istensor(p1)) {
|
| 5964 | if (istensor(p2)) {
|
| 5965 | d_tensor_tensor();
|
| 5966 | } else {
|
| 5967 | d_tensor_scalar();
|
| 5968 | }
|
| 5969 | } else {
|
| 5970 | if (istensor(p2)) {
|
| 5971 | d_scalar_tensor();
|
| 5972 | } else {
|
| 5973 | d_scalar_scalar();
|
| 5974 | }
|
| 5975 | }
|
| 5976 | return restore();
|
| 5977 | };
|
| 5978 |
|
| 5979 | d_scalar_scalar = function() {
|
| 5980 | if (issymbol(p2)) {
|
| 5981 | return d_scalar_scalar_1();
|
| 5982 | } else {
|
| 5983 | push(p1);
|
| 5984 | push(p2);
|
| 5985 | push(symbol(SECRETX));
|
| 5986 | subst();
|
| 5987 | push(symbol(SECRETX));
|
| 5988 | derivative();
|
| 5989 | push(symbol(SECRETX));
|
| 5990 | push(p2);
|
| 5991 | return subst();
|
| 5992 | }
|
| 5993 | };
|
| 5994 |
|
| 5995 | d_scalar_scalar_1 = function() {
|
| 5996 | if (equal(p1, p2)) {
|
| 5997 | push(one);
|
| 5998 | return;
|
| 5999 | }
|
| 6000 | if (!iscons(p1)) {
|
| 6001 | push(zero);
|
| 6002 | return;
|
| 6003 | }
|
| 6004 | if (isadd(p1)) {
|
| 6005 | dsum();
|
| 6006 | return;
|
| 6007 | }
|
| 6008 | if (car(p1) === symbol(MULTIPLY)) {
|
| 6009 | dproduct();
|
| 6010 | return;
|
| 6011 | }
|
| 6012 | if (car(p1) === symbol(POWER)) {
|
| 6013 | dpower();
|
| 6014 | return;
|
| 6015 | }
|
| 6016 | if (car(p1) === symbol(DERIVATIVE)) {
|
| 6017 | dd();
|
| 6018 | return;
|
| 6019 | }
|
| 6020 | if (car(p1) === symbol(LOG)) {
|
| 6021 | dlog();
|
| 6022 | return;
|
| 6023 | }
|
| 6024 | if (car(p1) === symbol(SIN)) {
|
| 6025 | dsin();
|
| 6026 | return;
|
| 6027 | }
|
| 6028 | if (car(p1) === symbol(COS)) {
|
| 6029 | dcos();
|
| 6030 | return;
|
| 6031 | }
|
| 6032 | if (car(p1) === symbol(TAN)) {
|
| 6033 | dtan();
|
| 6034 | return;
|
| 6035 | }
|
| 6036 | if (car(p1) === symbol(ARCSIN)) {
|
| 6037 | darcsin();
|
| 6038 | return;
|
| 6039 | }
|
| 6040 | if (car(p1) === symbol(ARCCOS)) {
|
| 6041 | darccos();
|
| 6042 | return;
|
| 6043 | }
|
| 6044 | if (car(p1) === symbol(ARCTAN)) {
|
| 6045 | darctan();
|
| 6046 | return;
|
| 6047 | }
|
| 6048 | if (car(p1) === symbol(SINH)) {
|
| 6049 | dsinh();
|
| 6050 | return;
|
| 6051 | }
|
| 6052 | if (car(p1) === symbol(COSH)) {
|
| 6053 | dcosh();
|
| 6054 | return;
|
| 6055 | }
|
| 6056 | if (car(p1) === symbol(TANH)) {
|
| 6057 | dtanh();
|
| 6058 | return;
|
| 6059 | }
|
| 6060 | if (car(p1) === symbol(ARCSINH)) {
|
| 6061 | darcsinh();
|
| 6062 | return;
|
| 6063 | }
|
| 6064 | if (car(p1) === symbol(ARCCOSH)) {
|
| 6065 | darccosh();
|
| 6066 | return;
|
| 6067 | }
|
| 6068 | if (car(p1) === symbol(ARCTANH)) {
|
| 6069 | darctanh();
|
| 6070 | return;
|
| 6071 | }
|
| 6072 | if (car(p1) === symbol(ABS)) {
|
| 6073 | dabs();
|
| 6074 | return;
|
| 6075 | }
|
| 6076 | if (car(p1) === symbol(SGN)) {
|
| 6077 | dsgn();
|
| 6078 | return;
|
| 6079 | }
|
| 6080 | if (car(p1) === symbol(HERMITE)) {
|
| 6081 | dhermite();
|
| 6082 | return;
|
| 6083 | }
|
| 6084 | if (car(p1) === symbol(ERF)) {
|
| 6085 | derf();
|
| 6086 | return;
|
| 6087 | }
|
| 6088 | if (car(p1) === symbol(ERFC)) {
|
| 6089 | derfc();
|
| 6090 | return;
|
| 6091 | }
|
| 6092 | if (car(p1) === symbol(BESSELJ)) {
|
| 6093 | if (iszero(caddr(p1))) {
|
| 6094 | dbesselj0();
|
| 6095 | } else {
|
| 6096 | dbesseljn();
|
| 6097 | }
|
| 6098 | return;
|
| 6099 | }
|
| 6100 | if (car(p1) === symbol(BESSELY)) {
|
| 6101 | if (iszero(caddr(p1))) {
|
| 6102 | dbessely0();
|
| 6103 | } else {
|
| 6104 | dbesselyn();
|
| 6105 | }
|
| 6106 | return;
|
| 6107 | }
|
| 6108 | if (car(p1) === symbol(INTEGRAL) && caddr(p1) === p2) {
|
| 6109 | derivative_of_integral();
|
| 6110 | return;
|
| 6111 | }
|
| 6112 | return dfunction();
|
| 6113 | };
|
| 6114 |
|
| 6115 | dsum = function() {
|
| 6116 | var h;
|
| 6117 | h = tos;
|
| 6118 | p1 = cdr(p1);
|
| 6119 | while (iscons(p1)) {
|
| 6120 | push(car(p1));
|
| 6121 | push(p2);
|
| 6122 | derivative();
|
| 6123 | p1 = cdr(p1);
|
| 6124 | }
|
| 6125 | return add_all(tos - h);
|
| 6126 | };
|
| 6127 |
|
| 6128 | dproduct = function() {
|
| 6129 | var i, i1, j, n, o, ref, ref1;
|
| 6130 | i = 0;
|
| 6131 | j = 0;
|
| 6132 | n = 0;
|
| 6133 | n = length(p1) - 1;
|
| 6134 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 6135 | p3 = cdr(p1);
|
| 6136 | for (j = i1 = 0, ref1 = n; 0 <= ref1 ? i1 < ref1 : i1 > ref1; j = 0 <= ref1 ? ++i1 : --i1) {
|
| 6137 | push(car(p3));
|
| 6138 | if (i === j) {
|
| 6139 | push(p2);
|
| 6140 | derivative();
|
| 6141 | }
|
| 6142 | p3 = cdr(p3);
|
| 6143 | }
|
| 6144 | multiply_all(n);
|
| 6145 | }
|
| 6146 | return add_all(n);
|
| 6147 | };
|
| 6148 |
|
| 6149 | dpower = function() {
|
| 6150 | push(caddr(p1));
|
| 6151 | push(cadr(p1));
|
| 6152 | divide();
|
| 6153 | push(cadr(p1));
|
| 6154 | push(p2);
|
| 6155 | derivative();
|
| 6156 | multiply();
|
| 6157 | push(cadr(p1));
|
| 6158 | logarithm();
|
| 6159 | push(caddr(p1));
|
| 6160 | push(p2);
|
| 6161 | derivative();
|
| 6162 | multiply();
|
| 6163 | add();
|
| 6164 | push(p1);
|
| 6165 | return multiply();
|
| 6166 | };
|
| 6167 |
|
| 6168 | dlog = function() {
|
| 6169 | push(cadr(p1));
|
| 6170 | push(p2);
|
| 6171 | derivative();
|
| 6172 | push(cadr(p1));
|
| 6173 | return divide();
|
| 6174 | };
|
| 6175 |
|
| 6176 | dd = function() {
|
| 6177 | push(cadr(p1));
|
| 6178 | push(p2);
|
| 6179 | derivative();
|
| 6180 | p3 = pop();
|
| 6181 | if (car(p3) === symbol(DERIVATIVE)) {
|
| 6182 | push_symbol(DERIVATIVE);
|
| 6183 | push_symbol(DERIVATIVE);
|
| 6184 | push(cadr(p3));
|
| 6185 | if (lessp(caddr(p3), caddr(p1))) {
|
| 6186 | push(caddr(p3));
|
| 6187 | list(3);
|
| 6188 | push(caddr(p1));
|
| 6189 | } else {
|
| 6190 | push(caddr(p1));
|
| 6191 | list(3);
|
| 6192 | push(caddr(p3));
|
| 6193 | }
|
| 6194 | return list(3);
|
| 6195 | } else {
|
| 6196 | push(p3);
|
| 6197 | push(caddr(p1));
|
| 6198 | return derivative();
|
| 6199 | }
|
| 6200 | };
|
| 6201 |
|
| 6202 | dfunction = function() {
|
| 6203 | p3 = cdr(p1);
|
| 6204 | if (p3 === symbol(NIL) || Find(p3, p2)) {
|
| 6205 | push_symbol(DERIVATIVE);
|
| 6206 | push(p1);
|
| 6207 | push(p2);
|
| 6208 | return list(3);
|
| 6209 | } else {
|
| 6210 | return push(zero);
|
| 6211 | }
|
| 6212 | };
|
| 6213 |
|
| 6214 | dsin = function() {
|
| 6215 | push(cadr(p1));
|
| 6216 | push(p2);
|
| 6217 | derivative();
|
| 6218 | push(cadr(p1));
|
| 6219 | cosine();
|
| 6220 | return multiply();
|
| 6221 | };
|
| 6222 |
|
| 6223 | dcos = function() {
|
| 6224 | push(cadr(p1));
|
| 6225 | push(p2);
|
| 6226 | derivative();
|
| 6227 | push(cadr(p1));
|
| 6228 | sine();
|
| 6229 | multiply();
|
| 6230 | return negate();
|
| 6231 | };
|
| 6232 |
|
| 6233 | dtan = function() {
|
| 6234 | push(cadr(p1));
|
| 6235 | push(p2);
|
| 6236 | derivative();
|
| 6237 | push(cadr(p1));
|
| 6238 | cosine();
|
| 6239 | push_integer(-2);
|
| 6240 | power();
|
| 6241 | return multiply();
|
| 6242 | };
|
| 6243 |
|
| 6244 | darcsin = function() {
|
| 6245 | push(cadr(p1));
|
| 6246 | push(p2);
|
| 6247 | derivative();
|
| 6248 | push_integer(1);
|
| 6249 | push(cadr(p1));
|
| 6250 | push_integer(2);
|
| 6251 | power();
|
| 6252 | subtract();
|
| 6253 | push_rational(-1, 2);
|
| 6254 | power();
|
| 6255 | return multiply();
|
| 6256 | };
|
| 6257 |
|
| 6258 | darccos = function() {
|
| 6259 | push(cadr(p1));
|
| 6260 | push(p2);
|
| 6261 | derivative();
|
| 6262 | push_integer(1);
|
| 6263 | push(cadr(p1));
|
| 6264 | push_integer(2);
|
| 6265 | power();
|
| 6266 | subtract();
|
| 6267 | push_rational(-1, 2);
|
| 6268 | power();
|
| 6269 | multiply();
|
| 6270 | return negate();
|
| 6271 | };
|
| 6272 |
|
| 6273 | darctan = function() {
|
| 6274 | push(cadr(p1));
|
| 6275 | push(p2);
|
| 6276 | derivative();
|
| 6277 | push_integer(1);
|
| 6278 | push(cadr(p1));
|
| 6279 | push_integer(2);
|
| 6280 | power();
|
| 6281 | add();
|
| 6282 | inverse();
|
| 6283 | multiply();
|
| 6284 | return simplify();
|
| 6285 | };
|
| 6286 |
|
| 6287 | dsinh = function() {
|
| 6288 | push(cadr(p1));
|
| 6289 | push(p2);
|
| 6290 | derivative();
|
| 6291 | push(cadr(p1));
|
| 6292 | ycosh();
|
| 6293 | return multiply();
|
| 6294 | };
|
| 6295 |
|
| 6296 | dcosh = function() {
|
| 6297 | push(cadr(p1));
|
| 6298 | push(p2);
|
| 6299 | derivative();
|
| 6300 | push(cadr(p1));
|
| 6301 | ysinh();
|
| 6302 | return multiply();
|
| 6303 | };
|
| 6304 |
|
| 6305 | dtanh = function() {
|
| 6306 | push(cadr(p1));
|
| 6307 | push(p2);
|
| 6308 | derivative();
|
| 6309 | push(cadr(p1));
|
| 6310 | ycosh();
|
| 6311 | push_integer(-2);
|
| 6312 | power();
|
| 6313 | return multiply();
|
| 6314 | };
|
| 6315 |
|
| 6316 | darcsinh = function() {
|
| 6317 | push(cadr(p1));
|
| 6318 | push(p2);
|
| 6319 | derivative();
|
| 6320 | push(cadr(p1));
|
| 6321 | push_integer(2);
|
| 6322 | power();
|
| 6323 | push_integer(1);
|
| 6324 | add();
|
| 6325 | push_rational(-1, 2);
|
| 6326 | power();
|
| 6327 | return multiply();
|
| 6328 | };
|
| 6329 |
|
| 6330 | darccosh = function() {
|
| 6331 | push(cadr(p1));
|
| 6332 | push(p2);
|
| 6333 | derivative();
|
| 6334 | push(cadr(p1));
|
| 6335 | push_integer(2);
|
| 6336 | power();
|
| 6337 | push_integer(-1);
|
| 6338 | add();
|
| 6339 | push_rational(-1, 2);
|
| 6340 | power();
|
| 6341 | return multiply();
|
| 6342 | };
|
| 6343 |
|
| 6344 | darctanh = function() {
|
| 6345 | push(cadr(p1));
|
| 6346 | push(p2);
|
| 6347 | derivative();
|
| 6348 | push_integer(1);
|
| 6349 | push(cadr(p1));
|
| 6350 | push_integer(2);
|
| 6351 | power();
|
| 6352 | subtract();
|
| 6353 | inverse();
|
| 6354 | return multiply();
|
| 6355 | };
|
| 6356 |
|
| 6357 | dabs = function() {
|
| 6358 | push(cadr(p1));
|
| 6359 | push(p2);
|
| 6360 | derivative();
|
| 6361 | push(cadr(p1));
|
| 6362 | sgn();
|
| 6363 | return multiply();
|
| 6364 | };
|
| 6365 |
|
| 6366 | dsgn = function() {
|
| 6367 | push(cadr(p1));
|
| 6368 | push(p2);
|
| 6369 | derivative();
|
| 6370 | push(cadr(p1));
|
| 6371 | dirac();
|
| 6372 | multiply();
|
| 6373 | push_integer(2);
|
| 6374 | return multiply();
|
| 6375 | };
|
| 6376 |
|
| 6377 | dhermite = function() {
|
| 6378 | push(cadr(p1));
|
| 6379 | push(p2);
|
| 6380 | derivative();
|
| 6381 | push_integer(2);
|
| 6382 | push(caddr(p1));
|
| 6383 | multiply();
|
| 6384 | multiply();
|
| 6385 | push(cadr(p1));
|
| 6386 | push(caddr(p1));
|
| 6387 | push_integer(-1);
|
| 6388 | add();
|
| 6389 | hermite();
|
| 6390 | return multiply();
|
| 6391 | };
|
| 6392 |
|
| 6393 | derf = function() {
|
| 6394 | push(cadr(p1));
|
| 6395 | push_integer(2);
|
| 6396 | power();
|
| 6397 | push_integer(-1);
|
| 6398 | multiply();
|
| 6399 | exponential();
|
| 6400 | if (evaluatingAsFloats) {
|
| 6401 | push_double(Math.PI);
|
| 6402 | } else {
|
| 6403 | push_symbol(PI);
|
| 6404 | }
|
| 6405 | push_rational(-1, 2);
|
| 6406 | power();
|
| 6407 | multiply();
|
| 6408 | push_integer(2);
|
| 6409 | multiply();
|
| 6410 | push(cadr(p1));
|
| 6411 | push(p2);
|
| 6412 | derivative();
|
| 6413 | return multiply();
|
| 6414 | };
|
| 6415 |
|
| 6416 | derfc = function() {
|
| 6417 | push(cadr(p1));
|
| 6418 | push_integer(2);
|
| 6419 | power();
|
| 6420 | push_integer(-1);
|
| 6421 | multiply();
|
| 6422 | exponential();
|
| 6423 | if (evaluatingAsFloats) {
|
| 6424 | push_double(Math.PI);
|
| 6425 | } else {
|
| 6426 | push_symbol(PI);
|
| 6427 | }
|
| 6428 | push_rational(-1, 2);
|
| 6429 | power();
|
| 6430 | multiply();
|
| 6431 | push_integer(-2);
|
| 6432 | multiply();
|
| 6433 | push(cadr(p1));
|
| 6434 | push(p2);
|
| 6435 | derivative();
|
| 6436 | return multiply();
|
| 6437 | };
|
| 6438 |
|
| 6439 | dbesselj0 = function() {
|
| 6440 | push(cadr(p1));
|
| 6441 | push(p2);
|
| 6442 | derivative();
|
| 6443 | push(cadr(p1));
|
| 6444 | push_integer(1);
|
| 6445 | besselj();
|
| 6446 | multiply();
|
| 6447 | push_integer(-1);
|
| 6448 | return multiply();
|
| 6449 | };
|
| 6450 |
|
| 6451 | dbesseljn = function() {
|
| 6452 | push(cadr(p1));
|
| 6453 | push(p2);
|
| 6454 | derivative();
|
| 6455 | push(cadr(p1));
|
| 6456 | push(caddr(p1));
|
| 6457 | push_integer(-1);
|
| 6458 | add();
|
| 6459 | besselj();
|
| 6460 | push(caddr(p1));
|
| 6461 | push_integer(-1);
|
| 6462 | multiply();
|
| 6463 | push(cadr(p1));
|
| 6464 | divide();
|
| 6465 | push(cadr(p1));
|
| 6466 | push(caddr(p1));
|
| 6467 | besselj();
|
| 6468 | multiply();
|
| 6469 | add();
|
| 6470 | return multiply();
|
| 6471 | };
|
| 6472 |
|
| 6473 | dbessely0 = function() {
|
| 6474 | push(cadr(p1));
|
| 6475 | push(p2);
|
| 6476 | derivative();
|
| 6477 | push(cadr(p1));
|
| 6478 | push_integer(1);
|
| 6479 | besselj();
|
| 6480 | multiply();
|
| 6481 | push_integer(-1);
|
| 6482 | return multiply();
|
| 6483 | };
|
| 6484 |
|
| 6485 | dbesselyn = function() {
|
| 6486 | push(cadr(p1));
|
| 6487 | push(p2);
|
| 6488 | derivative();
|
| 6489 | push(cadr(p1));
|
| 6490 | push(caddr(p1));
|
| 6491 | push_integer(-1);
|
| 6492 | add();
|
| 6493 | bessely();
|
| 6494 | push(caddr(p1));
|
| 6495 | push_integer(-1);
|
| 6496 | multiply();
|
| 6497 | push(cadr(p1));
|
| 6498 | divide();
|
| 6499 | push(cadr(p1));
|
| 6500 | push(caddr(p1));
|
| 6501 | bessely();
|
| 6502 | multiply();
|
| 6503 | add();
|
| 6504 | return multiply();
|
| 6505 | };
|
| 6506 |
|
| 6507 | derivative_of_integral = function() {
|
| 6508 | return push(cadr(p1));
|
| 6509 | };
|
| 6510 |
|
| 6511 |
|
| 6512 | |
| 6513 | |
| 6514 | |
| 6515 | |
| 6516 | |
| 6517 | |
| 6518 | |
| 6519 | |
| 6520 | |
| 6521 | |
| 6522 | |
| 6523 | |
| 6524 | |
| 6525 | |
| 6526 | |
| 6527 | |
| 6528 | |
| 6529 | |
| 6530 | |
| 6531 |
|
| 6532 |
|
| 6533 | DET_check_arg = function() {
|
| 6534 | if (!istensor(p1)) {
|
| 6535 | return 0;
|
| 6536 | } else if (p1.tensor.ndim !== 2) {
|
| 6537 | return 0;
|
| 6538 | } else if (p1.tensor.dim[0] !== p1.tensor.dim[1]) {
|
| 6539 | return 0;
|
| 6540 | } else {
|
| 6541 | return 1;
|
| 6542 | }
|
| 6543 | };
|
| 6544 |
|
| 6545 | det = function() {
|
| 6546 | var a, i, i1, n, o, ref, ref1;
|
| 6547 | i = 0;
|
| 6548 | n = 0;
|
| 6549 | save();
|
| 6550 | p1 = pop();
|
| 6551 | if (DET_check_arg() === 0) {
|
| 6552 | push_symbol(DET);
|
| 6553 | push(p1);
|
| 6554 | list(2);
|
| 6555 | restore();
|
| 6556 | return;
|
| 6557 | }
|
| 6558 | n = p1.tensor.nelem;
|
| 6559 | a = p1.tensor.elem;
|
| 6560 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 6561 | if (!isnum(a[i])) {
|
| 6562 | break;
|
| 6563 | }
|
| 6564 | }
|
| 6565 | if (i === n) {
|
| 6566 | yydetg();
|
| 6567 | } else {
|
| 6568 | for (i = i1 = 0, ref1 = p1.tensor.nelem; 0 <= ref1 ? i1 < ref1 : i1 > ref1; i = 0 <= ref1 ? ++i1 : --i1) {
|
| 6569 | push(p1.tensor.elem[i]);
|
| 6570 | }
|
| 6571 | determinant(p1.tensor.dim[0]);
|
| 6572 | }
|
| 6573 | return restore();
|
| 6574 | };
|
| 6575 |
|
| 6576 | determinant = function(n) {
|
| 6577 | var a, breakFromOutherWhile, h, i, i1, j, k, o, q, ref, ref1, s, sign_, t;
|
| 6578 | h = 0;
|
| 6579 | i = 0;
|
| 6580 | j = 0;
|
| 6581 | k = 0;
|
| 6582 | q = 0;
|
| 6583 | s = 0;
|
| 6584 | sign_ = 0;
|
| 6585 | t = 0;
|
| 6586 | a = [];
|
| 6587 | h = tos - n * n;
|
| 6588 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 6589 | a[i] = i;
|
| 6590 | a[i + n] = 0;
|
| 6591 | a[i + n + n] = 1;
|
| 6592 | }
|
| 6593 | sign_ = 1;
|
| 6594 | push(zero);
|
| 6595 | while (1) {
|
| 6596 | if (sign_ === 1) {
|
| 6597 | push_integer(1);
|
| 6598 | } else {
|
| 6599 | push_integer(-1);
|
| 6600 | }
|
| 6601 | for (i = i1 = 0, ref1 = n; 0 <= ref1 ? i1 < ref1 : i1 > ref1; i = 0 <= ref1 ? ++i1 : --i1) {
|
| 6602 | k = n * a[i] + i;
|
| 6603 | push(stack[h + k]);
|
| 6604 | multiply();
|
| 6605 | }
|
| 6606 | add();
|
| 6607 | j = n - 1;
|
| 6608 | s = 0;
|
| 6609 | breakFromOutherWhile = false;
|
| 6610 | while (1) {
|
| 6611 | q = a[n + j] + a[n + n + j];
|
| 6612 | if (q < 0) {
|
| 6613 | a[n + n + j] = -a[n + n + j];
|
| 6614 | j--;
|
| 6615 | continue;
|
| 6616 | }
|
| 6617 | if (q === j + 1) {
|
| 6618 | if (j === 0) {
|
| 6619 | breakFromOutherWhile = true;
|
| 6620 | break;
|
| 6621 | }
|
| 6622 | s++;
|
| 6623 | a[n + n + j] = -a[n + n + j];
|
| 6624 | j--;
|
| 6625 | continue;
|
| 6626 | }
|
| 6627 | break;
|
| 6628 | }
|
| 6629 | if (breakFromOutherWhile) {
|
| 6630 | break;
|
| 6631 | }
|
| 6632 | t = a[j - a[n + j] + s];
|
| 6633 | a[j - a[n + j] + s] = a[j - q + s];
|
| 6634 | a[j - q + s] = t;
|
| 6635 | a[n + j] = q;
|
| 6636 | sign_ = -sign_;
|
| 6637 | }
|
| 6638 | stack[h] = stack[tos - 1];
|
| 6639 | return moveTos(h + 1);
|
| 6640 | };
|
| 6641 |
|
| 6642 | detg = function() {
|
| 6643 | save();
|
| 6644 | p1 = pop();
|
| 6645 | if (DET_check_arg() === 0) {
|
| 6646 | push_symbol(DET);
|
| 6647 | push(p1);
|
| 6648 | list(2);
|
| 6649 | restore();
|
| 6650 | return;
|
| 6651 | }
|
| 6652 | yydetg();
|
| 6653 | return restore();
|
| 6654 | };
|
| 6655 |
|
| 6656 | yydetg = function() {
|
| 6657 | var i, n, o, ref;
|
| 6658 | i = 0;
|
| 6659 | n = 0;
|
| 6660 | n = p1.tensor.dim[0];
|
| 6661 | for (i = o = 0, ref = n * n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 6662 | push(p1.tensor.elem[i]);
|
| 6663 | }
|
| 6664 | lu_decomp(n);
|
| 6665 | moveTos(tos - n * n);
|
| 6666 | return push(p1);
|
| 6667 | };
|
| 6668 |
|
| 6669 | M = function(h, n, i, j) {
|
| 6670 | return stack[h + n * i + j];
|
| 6671 | };
|
| 6672 |
|
| 6673 | setM = function(h, n, i, j, value) {
|
| 6674 | return stack[h + n * i + j] = value;
|
| 6675 | };
|
| 6676 |
|
| 6677 | lu_decomp = function(n) {
|
| 6678 | var d, h, i, i1, j, j1, l1, m1, o, ref, ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8;
|
| 6679 | d = 0;
|
| 6680 | h = 0;
|
| 6681 | i = 0;
|
| 6682 | j = 0;
|
| 6683 | h = tos - n * n;
|
| 6684 | p1 = one;
|
| 6685 | for (d = o = 0, ref = n - 1; 0 <= ref ? o < ref : o > ref; d = 0 <= ref ? ++o : --o) {
|
| 6686 | if (equal(M(h, n, d, d), zero)) {
|
| 6687 | for (i = i1 = ref1 = d + 1, ref2 = n; ref1 <= ref2 ? i1 < ref2 : i1 > ref2; i = ref1 <= ref2 ? ++i1 : --i1) {
|
| 6688 | if (!equal(M(h, n, i, d), zero)) {
|
| 6689 | break;
|
| 6690 | }
|
| 6691 | }
|
| 6692 | if (i === n) {
|
| 6693 | p1 = zero;
|
| 6694 | break;
|
| 6695 | }
|
| 6696 | for (j = j1 = ref3 = d, ref4 = n; ref3 <= ref4 ? j1 < ref4 : j1 > ref4; j = ref3 <= ref4 ? ++j1 : --j1) {
|
| 6697 | p2 = M(h, n, d, j);
|
| 6698 | setM(h, n, d, j, M(h, n, i, j));
|
| 6699 | setM(h, n, i, j, p2);
|
| 6700 | }
|
| 6701 | push(p1);
|
| 6702 | negate();
|
| 6703 | p1 = pop();
|
| 6704 | }
|
| 6705 | push(p1);
|
| 6706 | push(M(h, n, d, d));
|
| 6707 | multiply();
|
| 6708 | p1 = pop();
|
| 6709 | for (i = l1 = ref5 = d + 1, ref6 = n; ref5 <= ref6 ? l1 < ref6 : l1 > ref6; i = ref5 <= ref6 ? ++l1 : --l1) {
|
| 6710 | push(M(h, n, i, d));
|
| 6711 | push(M(h, n, d, d));
|
| 6712 | divide();
|
| 6713 | negate();
|
| 6714 | p2 = pop();
|
| 6715 | setM(h, n, i, d, zero);
|
| 6716 | for (j = m1 = ref7 = d + 1, ref8 = n; ref7 <= ref8 ? m1 < ref8 : m1 > ref8; j = ref7 <= ref8 ? ++m1 : --m1) {
|
| 6717 | push(M(h, n, d, j));
|
| 6718 | push(p2);
|
| 6719 | multiply();
|
| 6720 | push(M(h, n, i, j));
|
| 6721 | add();
|
| 6722 | setM(h, n, i, j, pop());
|
| 6723 | }
|
| 6724 | }
|
| 6725 | }
|
| 6726 | push(p1);
|
| 6727 | push(M(h, n, n - 1, n - 1));
|
| 6728 | multiply();
|
| 6729 | return p1 = pop();
|
| 6730 | };
|
| 6731 |
|
| 6732 | Eval_dirac = function() {
|
| 6733 | push(cadr(p1));
|
| 6734 | Eval();
|
| 6735 | return dirac();
|
| 6736 | };
|
| 6737 |
|
| 6738 | dirac = function() {
|
| 6739 | save();
|
| 6740 | ydirac();
|
| 6741 | return restore();
|
| 6742 | };
|
| 6743 |
|
| 6744 | ydirac = function() {
|
| 6745 | p1 = pop();
|
| 6746 | if (isdouble(p1)) {
|
| 6747 | if (p1.d === 0) {
|
| 6748 | push_integer(1);
|
| 6749 | return;
|
| 6750 | } else {
|
| 6751 | push_integer(0);
|
| 6752 | return;
|
| 6753 | }
|
| 6754 | }
|
| 6755 | if (isrational(p1)) {
|
| 6756 | if (MZERO(mmul(p1.q.a, p1.q.b))) {
|
| 6757 | push_integer(1);
|
| 6758 | return;
|
| 6759 | } else {
|
| 6760 | push_integer(0);
|
| 6761 | return;
|
| 6762 | }
|
| 6763 | }
|
| 6764 | if (car(p1) === symbol(POWER)) {
|
| 6765 | push_symbol(DIRAC);
|
| 6766 | push(cadr(p1));
|
| 6767 | list(2);
|
| 6768 | return;
|
| 6769 | }
|
| 6770 | if (isnegativeterm(p1)) {
|
| 6771 | push_symbol(DIRAC);
|
| 6772 | push(p1);
|
| 6773 | negate();
|
| 6774 | list(2);
|
| 6775 | return;
|
| 6776 | }
|
| 6777 | if (isnegativeterm(p1) || (car(p1) === symbol(ADD) && isnegativeterm(cadr(p1)))) {
|
| 6778 | push(p1);
|
| 6779 | negate();
|
| 6780 | p1 = pop();
|
| 6781 | }
|
| 6782 | push_symbol(DIRAC);
|
| 6783 | push(p1);
|
| 6784 | return list(2);
|
| 6785 | };
|
| 6786 |
|
| 6787 | divisors = function() {
|
| 6788 | var h, i, n, o, ref, subsetOfStack;
|
| 6789 | i = 0;
|
| 6790 | h = 0;
|
| 6791 | n = 0;
|
| 6792 | save();
|
| 6793 | h = tos - 1;
|
| 6794 | divisors_onstack();
|
| 6795 | n = tos - h;
|
| 6796 | subsetOfStack = stack.slice(h, h + n);
|
| 6797 | subsetOfStack.sort(cmp_expr);
|
| 6798 | stack = stack.slice(0, h).concat(subsetOfStack).concat(stack.slice(h + n));
|
| 6799 | p1 = alloc_tensor(n);
|
| 6800 | p1.tensor.ndim = 1;
|
| 6801 | p1.tensor.dim[0] = n;
|
| 6802 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 6803 | p1.tensor.elem[i] = stack[h + i];
|
| 6804 | }
|
| 6805 | moveTos(h);
|
| 6806 | push(p1);
|
| 6807 | return restore();
|
| 6808 | };
|
| 6809 |
|
| 6810 | divisors_onstack = function() {
|
| 6811 | var h, i, k, n, o, ref;
|
| 6812 | h = 0;
|
| 6813 | i = 0;
|
| 6814 | k = 0;
|
| 6815 | n = 0;
|
| 6816 | save();
|
| 6817 | p1 = pop();
|
| 6818 | h = tos;
|
| 6819 | if (isnum(p1)) {
|
| 6820 | push(p1);
|
| 6821 | factor_small_number();
|
| 6822 | } else if (car(p1) === symbol(ADD)) {
|
| 6823 | push(p1);
|
| 6824 | __factor_add();
|
| 6825 | } else if (car(p1) === symbol(MULTIPLY)) {
|
| 6826 | p1 = cdr(p1);
|
| 6827 | if (isnum(car(p1))) {
|
| 6828 | push(car(p1));
|
| 6829 | factor_small_number();
|
| 6830 | p1 = cdr(p1);
|
| 6831 | }
|
| 6832 | while (iscons(p1)) {
|
| 6833 | p2 = car(p1);
|
| 6834 | if (car(p2) === symbol(POWER)) {
|
| 6835 | push(cadr(p2));
|
| 6836 | push(caddr(p2));
|
| 6837 | } else {
|
| 6838 | push(p2);
|
| 6839 | push(one);
|
| 6840 | }
|
| 6841 | p1 = cdr(p1);
|
| 6842 | }
|
| 6843 | } else if (car(p1) === symbol(POWER)) {
|
| 6844 | push(cadr(p1));
|
| 6845 | push(caddr(p1));
|
| 6846 | } else {
|
| 6847 | push(p1);
|
| 6848 | push(one);
|
| 6849 | }
|
| 6850 | k = tos;
|
| 6851 | push(one);
|
| 6852 | gen(h, k);
|
| 6853 | n = tos - k;
|
| 6854 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 6855 | stack[h + i] = stack[k + i];
|
| 6856 | }
|
| 6857 | moveTos(h + n);
|
| 6858 | return restore();
|
| 6859 | };
|
| 6860 |
|
| 6861 | gen = function(h, k) {
|
| 6862 | var expo, i, o, ref;
|
| 6863 | expo = 0;
|
| 6864 | i = 0;
|
| 6865 | save();
|
| 6866 | p1 = pop();
|
| 6867 | if (h === k) {
|
| 6868 | push(p1);
|
| 6869 | restore();
|
| 6870 | return;
|
| 6871 | }
|
| 6872 | p2 = stack[h + 0];
|
| 6873 | p3 = stack[h + 1];
|
| 6874 | push(p3);
|
| 6875 | expo = pop_integer();
|
| 6876 | if (!isNaN(expo)) {
|
| 6877 | for (i = o = 0, ref = Math.abs(expo); 0 <= ref ? o <= ref : o >= ref; i = 0 <= ref ? ++o : --o) {
|
| 6878 | push(p1);
|
| 6879 | push(p2);
|
| 6880 | push_integer(sign(expo) * i);
|
| 6881 | power();
|
| 6882 | multiply();
|
| 6883 | gen(h + 2, k);
|
| 6884 | }
|
| 6885 | }
|
| 6886 | return restore();
|
| 6887 | };
|
| 6888 |
|
| 6889 | __factor_add = function() {
|
| 6890 | save();
|
| 6891 | p1 = pop();
|
| 6892 | p3 = cdr(p1);
|
| 6893 | push(car(p3));
|
| 6894 | p3 = cdr(p3);
|
| 6895 | while (iscons(p3)) {
|
| 6896 | push(car(p3));
|
| 6897 | gcd();
|
| 6898 | p3 = cdr(p3);
|
| 6899 | }
|
| 6900 | p2 = pop();
|
| 6901 | if (isplusone(p2)) {
|
| 6902 | push(p1);
|
| 6903 | push(one);
|
| 6904 | restore();
|
| 6905 | return;
|
| 6906 | }
|
| 6907 | if (isnum(p2)) {
|
| 6908 | push(p2);
|
| 6909 | factor_small_number();
|
| 6910 | } else if (car(p2) === symbol(MULTIPLY)) {
|
| 6911 | p3 = cdr(p2);
|
| 6912 | if (isnum(car(p3))) {
|
| 6913 | push(car(p3));
|
| 6914 | factor_small_number();
|
| 6915 | } else {
|
| 6916 | push(car(p3));
|
| 6917 | push(one);
|
| 6918 | }
|
| 6919 | p3 = cdr(p3);
|
| 6920 | while (iscons(p3)) {
|
| 6921 | push(car(p3));
|
| 6922 | push(one);
|
| 6923 | p3 = cdr(p3);
|
| 6924 | }
|
| 6925 | } else {
|
| 6926 | push(p2);
|
| 6927 | push(one);
|
| 6928 | }
|
| 6929 | push(p2);
|
| 6930 | inverse();
|
| 6931 | p2 = pop();
|
| 6932 | push(zero);
|
| 6933 | p3 = cdr(p1);
|
| 6934 | while (iscons(p3)) {
|
| 6935 | push(p2);
|
| 6936 | push(car(p3));
|
| 6937 | multiply();
|
| 6938 | add();
|
| 6939 | p3 = cdr(p3);
|
| 6940 | }
|
| 6941 | push(one);
|
| 6942 | return restore();
|
| 6943 | };
|
| 6944 |
|
| 6945 | dpow = function() {
|
| 6946 | var a, b, base, expo, result, theta;
|
| 6947 | a = 0.0;
|
| 6948 | b = 0.0;
|
| 6949 | base = 0.0;
|
| 6950 | expo = 0.0;
|
| 6951 | result = 0.0;
|
| 6952 | theta = 0.0;
|
| 6953 | expo = pop_double();
|
| 6954 | base = pop_double();
|
| 6955 | if (base === 0.0 && expo < 0.0) {
|
| 6956 | stop("divide by zero");
|
| 6957 | }
|
| 6958 | if (base >= 0.0 || (expo % 1.0) === 0.0) {
|
| 6959 | result = Math.pow(base, expo);
|
| 6960 | push_double(result);
|
| 6961 | return;
|
| 6962 | }
|
| 6963 | result = Math.pow(Math.abs(base), expo);
|
| 6964 | theta = Math.PI * expo;
|
| 6965 | if ((expo % 0.5) === 0.0) {
|
| 6966 | a = 0.0;
|
| 6967 | b = Math.sin(theta);
|
| 6968 | } else {
|
| 6969 | a = Math.cos(theta);
|
| 6970 | b = Math.sin(theta);
|
| 6971 | }
|
| 6972 | push_double(a * result);
|
| 6973 | push_double(b * result);
|
| 6974 | push(imaginaryunit);
|
| 6975 | multiply();
|
| 6976 | return add();
|
| 6977 | };
|
| 6978 |
|
| 6979 |
|
| 6980 | |
| 6981 | |
| 6982 | |
| 6983 | |
| 6984 | |
| 6985 | |
| 6986 | |
| 6987 | |
| 6988 | |
| 6989 | |
| 6990 | |
| 6991 | |
| 6992 | |
| 6993 | |
| 6994 | |
| 6995 | |
| 6996 | |
| 6997 | |
| 6998 | |
| 6999 | |
| 7000 | |
| 7001 | |
| 7002 | |
| 7003 | |
| 7004 | |
| 7005 | |
| 7006 | |
| 7007 | |
| 7008 | |
| 7009 | |
| 7010 | |
| 7011 | |
| 7012 | |
| 7013 | |
| 7014 | |
| 7015 | |
| 7016 | |
| 7017 | |
| 7018 | |
| 7019 | |
| 7020 | |
| 7021 | |
| 7022 | |
| 7023 | |
| 7024 | |
| 7025 | |
| 7026 | |
| 7027 | |
| 7028 | |
| 7029 | |
| 7030 | |
| 7031 | |
| 7032 | |
| 7033 | |
| 7034 | |
| 7035 | |
| 7036 | |
| 7037 | |
| 7038 | |
| 7039 | |
| 7040 | |
| 7041 | |
| 7042 | |
| 7043 | |
| 7044 | |
| 7045 | |
| 7046 | |
| 7047 | |
| 7048 | |
| 7049 | |
| 7050 | |
| 7051 | |
| 7052 | |
| 7053 | |
| 7054 | |
| 7055 | |
| 7056 | |
| 7057 |
|
| 7058 |
|
| 7059 | EIG_N = 0;
|
| 7060 |
|
| 7061 | EIG_yydd = [];
|
| 7062 |
|
| 7063 | EIG_yyqq = [];
|
| 7064 |
|
| 7065 | Eval_eigen = function() {
|
| 7066 | if (EIG_check_arg() === 0) {
|
| 7067 | stop("eigen: argument is not a square matrix");
|
| 7068 | }
|
| 7069 | eigen(EIGEN);
|
| 7070 | p1 = usr_symbol("D");
|
| 7071 | set_binding(p1, p2);
|
| 7072 | p1 = usr_symbol("Q");
|
| 7073 | set_binding(p1, p3);
|
| 7074 | return push(symbol(NIL));
|
| 7075 | };
|
| 7076 |
|
| 7077 |
|
| 7078 | |
| 7079 | |
| 7080 | |
| 7081 | |
| 7082 | |
| 7083 | |
| 7084 | |
| 7085 | |
| 7086 | |
| 7087 | |
| 7088 | |
| 7089 | |
| 7090 | |
| 7091 |
|
| 7092 |
|
| 7093 | Eval_eigenval = function() {
|
| 7094 | if (EIG_check_arg() === 0) {
|
| 7095 | push_symbol(EIGENVAL);
|
| 7096 | push(p1);
|
| 7097 | list(2);
|
| 7098 | return;
|
| 7099 | }
|
| 7100 | eigen(EIGENVAL);
|
| 7101 | return push(p2);
|
| 7102 | };
|
| 7103 |
|
| 7104 |
|
| 7105 | |
| 7106 | |
| 7107 | |
| 7108 | |
| 7109 | |
| 7110 | |
| 7111 | |
| 7112 | |
| 7113 | |
| 7114 | |
| 7115 | |
| 7116 | |
| 7117 | |
| 7118 |
|
| 7119 |
|
| 7120 | Eval_eigenvec = function() {
|
| 7121 | if (EIG_check_arg() === 0) {
|
| 7122 | push_symbol(EIGENVEC);
|
| 7123 | push(p1);
|
| 7124 | list(2);
|
| 7125 | return;
|
| 7126 | }
|
| 7127 | eigen(EIGENVEC);
|
| 7128 | return push(p3);
|
| 7129 | };
|
| 7130 |
|
| 7131 | EIG_check_arg = function() {
|
| 7132 | var i, i1, j, j1, l1, o, ref, ref1, ref2, ref3, ref4;
|
| 7133 | i = 0;
|
| 7134 | j = 0;
|
| 7135 | push(cadr(p1));
|
| 7136 | Eval();
|
| 7137 | yyfloat();
|
| 7138 | Eval();
|
| 7139 | p1 = pop();
|
| 7140 | if (!istensor(p1)) {
|
| 7141 | return 0;
|
| 7142 | }
|
| 7143 | if (p1.tensor.ndim !== 2 || p1.tensor.dim[0] !== p1.tensor.dim[1]) {
|
| 7144 | stop("eigen: argument is not a square matrix");
|
| 7145 | }
|
| 7146 | EIG_N = p1.tensor.dim[0];
|
| 7147 | for (i = o = 0, ref = EIG_N; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 7148 | for (j = i1 = 0, ref1 = EIG_N; 0 <= ref1 ? i1 < ref1 : i1 > ref1; j = 0 <= ref1 ? ++i1 : --i1) {
|
| 7149 | if (!isdouble(p1.tensor.elem[EIG_N * i + j])) {
|
| 7150 | stop("eigen: matrix is not numerical");
|
| 7151 | }
|
| 7152 | }
|
| 7153 | }
|
| 7154 | for (i = j1 = 0, ref2 = EIG_N - 1; 0 <= ref2 ? j1 < ref2 : j1 > ref2; i = 0 <= ref2 ? ++j1 : --j1) {
|
| 7155 | for (j = l1 = ref3 = i + 1, ref4 = EIG_N; ref3 <= ref4 ? l1 < ref4 : l1 > ref4; j = ref3 <= ref4 ? ++l1 : --l1) {
|
| 7156 | if (Math.abs(p1.tensor.elem[EIG_N * i + j].d - p1.tensor.elem[EIG_N * j + i].d) > 1e-10) {
|
| 7157 | stop("eigen: matrix is not symmetrical");
|
| 7158 | }
|
| 7159 | }
|
| 7160 | }
|
| 7161 | return 1;
|
| 7162 | };
|
| 7163 |
|
| 7164 | eigen = function(op) {
|
| 7165 | var i, i1, j, j1, l1, m1, n1, o, o1, q1, r1, ref, ref1, ref10, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, results, s1;
|
| 7166 | i = 0;
|
| 7167 | j = 0;
|
| 7168 | for (i = o = 0, ref = EIG_N * EIG_N; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 7169 | EIG_yydd[i] = 0.0;
|
| 7170 | }
|
| 7171 | for (i = i1 = 0, ref1 = EIG_N * EIG_N; 0 <= ref1 ? i1 < ref1 : i1 > ref1; i = 0 <= ref1 ? ++i1 : --i1) {
|
| 7172 | EIG_yyqq[i] = 0.0;
|
| 7173 | }
|
| 7174 | for (i = j1 = 0, ref2 = EIG_N; 0 <= ref2 ? j1 < ref2 : j1 > ref2; i = 0 <= ref2 ? ++j1 : --j1) {
|
| 7175 | EIG_yydd[EIG_N * i + i] = p1.tensor.elem[EIG_N * i + i].d;
|
| 7176 | for (j = l1 = ref3 = i + 1, ref4 = EIG_N; ref3 <= ref4 ? l1 < ref4 : l1 > ref4; j = ref3 <= ref4 ? ++l1 : --l1) {
|
| 7177 | EIG_yydd[EIG_N * i + j] = p1.tensor.elem[EIG_N * i + j].d;
|
| 7178 | EIG_yydd[EIG_N * j + i] = p1.tensor.elem[EIG_N * i + j].d;
|
| 7179 | }
|
| 7180 | }
|
| 7181 | for (i = m1 = 0, ref5 = EIG_N; 0 <= ref5 ? m1 < ref5 : m1 > ref5; i = 0 <= ref5 ? ++m1 : --m1) {
|
| 7182 | EIG_yyqq[EIG_N * i + i] = 1.0;
|
| 7183 | for (j = n1 = ref6 = i + 1, ref7 = EIG_N; ref6 <= ref7 ? n1 < ref7 : n1 > ref7; j = ref6 <= ref7 ? ++n1 : --n1) {
|
| 7184 | EIG_yyqq[EIG_N * i + j] = 0.0;
|
| 7185 | EIG_yyqq[EIG_N * j + i] = 0.0;
|
| 7186 | }
|
| 7187 | }
|
| 7188 | for (i = o1 = 0; o1 < 100; i = ++o1) {
|
| 7189 | if (step() === 0) {
|
| 7190 | break;
|
| 7191 | }
|
| 7192 | }
|
| 7193 | if (i === 100) {
|
| 7194 | printstr("\nnote: eigen did not converge\n");
|
| 7195 | }
|
| 7196 | if (op === EIGEN || op === EIGENVAL) {
|
| 7197 | push(p1);
|
| 7198 | copy_tensor();
|
| 7199 | p2 = pop();
|
| 7200 | for (i = q1 = 0, ref8 = EIG_N; 0 <= ref8 ? q1 < ref8 : q1 > ref8; i = 0 <= ref8 ? ++q1 : --q1) {
|
| 7201 | for (j = r1 = 0, ref9 = EIG_N; 0 <= ref9 ? r1 < ref9 : r1 > ref9; j = 0 <= ref9 ? ++r1 : --r1) {
|
| 7202 | push_double(EIG_yydd[EIG_N * i + j]);
|
| 7203 | p2.tensor.elem[EIG_N * i + j] = pop();
|
| 7204 | }
|
| 7205 | }
|
| 7206 | }
|
| 7207 | if (op === EIGEN || op === EIGENVEC) {
|
| 7208 | push(p1);
|
| 7209 | copy_tensor();
|
| 7210 | p3 = pop();
|
| 7211 | results = [];
|
| 7212 | for (i = s1 = 0, ref10 = EIG_N; 0 <= ref10 ? s1 < ref10 : s1 > ref10; i = 0 <= ref10 ? ++s1 : --s1) {
|
| 7213 | results.push((function() {
|
| 7214 | var ref11, results1, t1;
|
| 7215 | results1 = [];
|
| 7216 | for (j = t1 = 0, ref11 = EIG_N; 0 <= ref11 ? t1 < ref11 : t1 > ref11; j = 0 <= ref11 ? ++t1 : --t1) {
|
| 7217 | push_double(EIG_yyqq[EIG_N * i + j]);
|
| 7218 | results1.push(p3.tensor.elem[EIG_N * i + j] = pop());
|
| 7219 | }
|
| 7220 | return results1;
|
| 7221 | })());
|
| 7222 | }
|
| 7223 | return results;
|
| 7224 | }
|
| 7225 | };
|
| 7226 |
|
| 7227 | step = function() {
|
| 7228 | var count, i, i1, j, o, ref, ref1, ref2;
|
| 7229 | i = 0;
|
| 7230 | j = 0;
|
| 7231 | count = 0;
|
| 7232 | for (i = o = 0, ref = EIG_N - 1; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 7233 | for (j = i1 = ref1 = i + 1, ref2 = EIG_N; ref1 <= ref2 ? i1 < ref2 : i1 > ref2; j = ref1 <= ref2 ? ++i1 : --i1) {
|
| 7234 | if (EIG_yydd[EIG_N * i + j] !== 0.0) {
|
| 7235 | step2(i, j);
|
| 7236 | count++;
|
| 7237 | }
|
| 7238 | }
|
| 7239 | }
|
| 7240 | return count;
|
| 7241 | };
|
| 7242 |
|
| 7243 | step2 = function(p, q) {
|
| 7244 | var c, cc, i1, j1, k, o, ref, ref1, ref2, s, ss, t, theta;
|
| 7245 | k = 0;
|
| 7246 | t = 0.0;
|
| 7247 | theta = 0.0;
|
| 7248 | c = 0.0;
|
| 7249 | cc = 0.0;
|
| 7250 | s = 0.0;
|
| 7251 | ss = 0.0;
|
| 7252 | theta = 0.5 * (EIG_yydd[EIG_N * p + p] - EIG_yydd[EIG_N * q + q]) / EIG_yydd[EIG_N * p + q];
|
| 7253 | t = 1.0 / (Math.abs(theta) + Math.sqrt(theta * theta + 1.0));
|
| 7254 | if (theta < 0.0) {
|
| 7255 | t = -t;
|
| 7256 | }
|
| 7257 | c = 1.0 / Math.sqrt(t * t + 1.0);
|
| 7258 | s = t * c;
|
| 7259 | for (k = o = 0, ref = EIG_N; 0 <= ref ? o < ref : o > ref; k = 0 <= ref ? ++o : --o) {
|
| 7260 | cc = EIG_yydd[EIG_N * p + k];
|
| 7261 | ss = EIG_yydd[EIG_N * q + k];
|
| 7262 | EIG_yydd[EIG_N * p + k] = c * cc + s * ss;
|
| 7263 | EIG_yydd[EIG_N * q + k] = c * ss - s * cc;
|
| 7264 | }
|
| 7265 | for (k = i1 = 0, ref1 = EIG_N; 0 <= ref1 ? i1 < ref1 : i1 > ref1; k = 0 <= ref1 ? ++i1 : --i1) {
|
| 7266 | cc = EIG_yydd[EIG_N * k + p];
|
| 7267 | ss = EIG_yydd[EIG_N * k + q];
|
| 7268 | EIG_yydd[EIG_N * k + p] = c * cc + s * ss;
|
| 7269 | EIG_yydd[EIG_N * k + q] = c * ss - s * cc;
|
| 7270 | }
|
| 7271 | for (k = j1 = 0, ref2 = EIG_N; 0 <= ref2 ? j1 < ref2 : j1 > ref2; k = 0 <= ref2 ? ++j1 : --j1) {
|
| 7272 | cc = EIG_yyqq[EIG_N * p + k];
|
| 7273 | ss = EIG_yyqq[EIG_N * q + k];
|
| 7274 | EIG_yyqq[EIG_N * p + k] = c * cc + s * ss;
|
| 7275 | EIG_yyqq[EIG_N * q + k] = c * ss - s * cc;
|
| 7276 | }
|
| 7277 | EIG_yydd[EIG_N * p + q] = 0.0;
|
| 7278 | return EIG_yydd[EIG_N * q + p] = 0.0;
|
| 7279 | };
|
| 7280 |
|
| 7281 |
|
| 7282 | |
| 7283 | |
| 7284 | |
| 7285 | |
| 7286 | |
| 7287 | |
| 7288 | |
| 7289 | |
| 7290 | |
| 7291 | |
| 7292 | |
| 7293 | |
| 7294 | |
| 7295 | |
| 7296 | |
| 7297 | |
| 7298 | |
| 7299 | |
| 7300 |
|
| 7301 |
|
| 7302 | Eval_erf = function() {
|
| 7303 | push(cadr(p1));
|
| 7304 | Eval();
|
| 7305 | return yerf();
|
| 7306 | };
|
| 7307 |
|
| 7308 | yerf = function() {
|
| 7309 | save();
|
| 7310 | yyerf();
|
| 7311 | return restore();
|
| 7312 | };
|
| 7313 |
|
| 7314 | yyerf = function() {
|
| 7315 | var d;
|
| 7316 | d = 0.0;
|
| 7317 | p1 = pop();
|
| 7318 | if (isdouble(p1)) {
|
| 7319 | d = 1.0 - erfc(p1.d);
|
| 7320 | push_double(d);
|
| 7321 | return;
|
| 7322 | }
|
| 7323 | if (isnegativeterm(p1)) {
|
| 7324 | push_symbol(ERF);
|
| 7325 | push(p1);
|
| 7326 | negate();
|
| 7327 | list(2);
|
| 7328 | negate();
|
| 7329 | return;
|
| 7330 | }
|
| 7331 | push_symbol(ERF);
|
| 7332 | push(p1);
|
| 7333 | list(2);
|
| 7334 | };
|
| 7335 |
|
| 7336 | Eval_erfc = function() {
|
| 7337 | push(cadr(p1));
|
| 7338 | Eval();
|
| 7339 | return yerfc();
|
| 7340 | };
|
| 7341 |
|
| 7342 | yerfc = function() {
|
| 7343 | save();
|
| 7344 | yyerfc();
|
| 7345 | return restore();
|
| 7346 | };
|
| 7347 |
|
| 7348 | yyerfc = function() {
|
| 7349 | var d;
|
| 7350 | d = 0.0;
|
| 7351 | p1 = pop();
|
| 7352 | if (isdouble(p1)) {
|
| 7353 | d = erfc(p1.d);
|
| 7354 | push_double(d);
|
| 7355 | return;
|
| 7356 | }
|
| 7357 | push_symbol(ERFC);
|
| 7358 | push(p1);
|
| 7359 | list(2);
|
| 7360 | };
|
| 7361 |
|
| 7362 | erfc = function(x) {
|
| 7363 | var ans, t, z;
|
| 7364 | t = 0.0;
|
| 7365 | z = 0.0;
|
| 7366 | ans = 0.0;
|
| 7367 | z = Math.abs(x);
|
| 7368 | t = 1.0 / (1.0 + 0.5 * z);
|
| 7369 | ans = t * Math.exp(-z * z - 1.26551223 + t * (1.00002368 + t * (0.37409196 + t * (0.09678418 + t * (-0.18628806 + t * (0.27886807 + t * (-1.13520398 + t * (1.48851587 + t * (-0.82215223 + t * 0.17087277)))))))));
|
| 7370 | if (x >= 0.0) {
|
| 7371 | return ans;
|
| 7372 | } else {
|
| 7373 | return 2.0 - ans;
|
| 7374 | }
|
| 7375 | };
|
| 7376 |
|
| 7377 |
|
| 7378 | |
| 7379 | |
| 7380 | |
| 7381 | |
| 7382 |
|
| 7383 |
|
| 7384 | Eval = function() {
|
| 7385 | var willEvaluateAsFloats;
|
| 7386 | check_esc_flag();
|
| 7387 | save();
|
| 7388 | p1 = pop();
|
| 7389 | if (p1 == null) {
|
| 7390 | debugger;
|
| 7391 | }
|
| 7392 | if (!evaluatingAsFloats && isfloating(p1)) {
|
| 7393 | willEvaluateAsFloats = true;
|
| 7394 | evaluatingAsFloats++;
|
| 7395 | }
|
| 7396 | switch (p1.k) {
|
| 7397 | case CONS:
|
| 7398 | Eval_cons();
|
| 7399 | break;
|
| 7400 | case NUM:
|
| 7401 | if (evaluatingAsFloats) {
|
| 7402 | push_double(convert_rational_to_double(p1));
|
| 7403 | } else {
|
| 7404 | push(p1);
|
| 7405 | }
|
| 7406 | break;
|
| 7407 | case DOUBLE:
|
| 7408 | case STR:
|
| 7409 | push(p1);
|
| 7410 | break;
|
| 7411 | case TENSOR:
|
| 7412 | Eval_tensor();
|
| 7413 | break;
|
| 7414 | case SYM:
|
| 7415 | Eval_sym();
|
| 7416 | break;
|
| 7417 | default:
|
| 7418 | stop("atom?");
|
| 7419 | }
|
| 7420 | if (willEvaluateAsFloats) {
|
| 7421 | evaluatingAsFloats--;
|
| 7422 | }
|
| 7423 | return restore();
|
| 7424 | };
|
| 7425 |
|
| 7426 | Eval_sym = function() {
|
| 7427 | var cycleString, i, o, positionIfSymbolAlreadyBeingEvaluated, ref, ref1;
|
| 7428 | if (iskeyword(p1)) {
|
| 7429 | push(p1);
|
| 7430 | push(symbol(LAST));
|
| 7431 | list(2);
|
| 7432 | Eval();
|
| 7433 | return;
|
| 7434 | } else if (p1 === symbol(PI) && evaluatingAsFloats) {
|
| 7435 | push_double(Math.PI);
|
| 7436 | return;
|
| 7437 | }
|
| 7438 | p2 = get_binding(p1);
|
| 7439 | if (DEBUG) {
|
| 7440 | console.log("looked up: " + p1 + " which contains: " + p2);
|
| 7441 | }
|
| 7442 | push(p2);
|
| 7443 | if (p1 !== p2) {
|
| 7444 | positionIfSymbolAlreadyBeingEvaluated = chainOfUserSymbolsNotFunctionsBeingEvaluated.indexOf(p1);
|
| 7445 | if (positionIfSymbolAlreadyBeingEvaluated !== -1) {
|
| 7446 | cycleString = "";
|
| 7447 | for (i = o = ref = positionIfSymbolAlreadyBeingEvaluated, ref1 = chainOfUserSymbolsNotFunctionsBeingEvaluated.length; ref <= ref1 ? o < ref1 : o > ref1; i = ref <= ref1 ? ++o : --o) {
|
| 7448 | cycleString += chainOfUserSymbolsNotFunctionsBeingEvaluated[i].printname + " -> ";
|
| 7449 | }
|
| 7450 | cycleString += p1.printname;
|
| 7451 | stop("recursive evaluation of symbols: " + cycleString);
|
| 7452 | return;
|
| 7453 | }
|
| 7454 | chainOfUserSymbolsNotFunctionsBeingEvaluated.push(p1);
|
| 7455 | Eval();
|
| 7456 | return chainOfUserSymbolsNotFunctionsBeingEvaluated.pop();
|
| 7457 | }
|
| 7458 | };
|
| 7459 |
|
| 7460 | Eval_cons = function() {
|
| 7461 | var cons_head;
|
| 7462 | cons_head = car(p1);
|
| 7463 | if (car(cons_head) === symbol(EVAL)) {
|
| 7464 | Eval_user_function();
|
| 7465 | return;
|
| 7466 | }
|
| 7467 | if (!issymbol(cons_head)) {
|
| 7468 | stop("cons?");
|
| 7469 | }
|
| 7470 | switch (symnum(cons_head)) {
|
| 7471 | case ABS:
|
| 7472 | return Eval_abs();
|
| 7473 | case ADD:
|
| 7474 | return Eval_add();
|
| 7475 | case ADJ:
|
| 7476 | return Eval_adj();
|
| 7477 | case AND:
|
| 7478 | return Eval_and();
|
| 7479 | case ARCCOS:
|
| 7480 | return Eval_arccos();
|
| 7481 | case ARCCOSH:
|
| 7482 | return Eval_arccosh();
|
| 7483 | case ARCSIN:
|
| 7484 | return Eval_arcsin();
|
| 7485 | case ARCSINH:
|
| 7486 | return Eval_arcsinh();
|
| 7487 | case ARCTAN:
|
| 7488 | return Eval_arctan();
|
| 7489 | case ARCTANH:
|
| 7490 | return Eval_arctanh();
|
| 7491 | case ARG:
|
| 7492 | return Eval_arg();
|
| 7493 | case ATOMIZE:
|
| 7494 | return Eval_atomize();
|
| 7495 | case BESSELJ:
|
| 7496 | return Eval_besselj();
|
| 7497 | case BESSELY:
|
| 7498 | return Eval_bessely();
|
| 7499 | case BINDING:
|
| 7500 | return Eval_binding();
|
| 7501 | case BINOMIAL:
|
| 7502 | return Eval_binomial();
|
| 7503 | case CEILING:
|
| 7504 | return Eval_ceiling();
|
| 7505 | case CHECK:
|
| 7506 | return Eval_check();
|
| 7507 | case CHOOSE:
|
| 7508 | return Eval_choose();
|
| 7509 | case CIRCEXP:
|
| 7510 | return Eval_circexp();
|
| 7511 | case CLEAR:
|
| 7512 | return Eval_clear();
|
| 7513 | case CLEARALL:
|
| 7514 | return Eval_clearall();
|
| 7515 | case CLEARPATTERNS:
|
| 7516 | return Eval_clearpatterns();
|
| 7517 | case CLOCK:
|
| 7518 | return Eval_clock();
|
| 7519 | case COEFF:
|
| 7520 | return Eval_coeff();
|
| 7521 | case COFACTOR:
|
| 7522 | return Eval_cofactor();
|
| 7523 | case CONDENSE:
|
| 7524 | return Eval_condense();
|
| 7525 | case CONJ:
|
| 7526 | return Eval_conj();
|
| 7527 | case CONTRACT:
|
| 7528 | return Eval_contract();
|
| 7529 | case COS:
|
| 7530 | return Eval_cos();
|
| 7531 | case COSH:
|
| 7532 | return Eval_cosh();
|
| 7533 | case DECOMP:
|
| 7534 | return Eval_decomp();
|
| 7535 | case DEGREE:
|
| 7536 | return Eval_degree();
|
| 7537 | case DEFINT:
|
| 7538 | return Eval_defint();
|
| 7539 | case DENOMINATOR:
|
| 7540 | return Eval_denominator();
|
| 7541 | case DERIVATIVE:
|
| 7542 | return Eval_derivative();
|
| 7543 | case DET:
|
| 7544 | return Eval_det();
|
| 7545 | case DIM:
|
| 7546 | return Eval_dim();
|
| 7547 | case DIRAC:
|
| 7548 | return Eval_dirac();
|
| 7549 | case DIVISORS:
|
| 7550 | return Eval_divisors();
|
| 7551 | case DO:
|
| 7552 | return Eval_do();
|
| 7553 | case DOT:
|
| 7554 | return Eval_inner();
|
| 7555 | case DRAW:
|
| 7556 | return Eval_draw();
|
| 7557 | case DSOLVE:
|
| 7558 | return Eval_dsolve();
|
| 7559 | case EIGEN:
|
| 7560 | return Eval_eigen();
|
| 7561 | case EIGENVAL:
|
| 7562 | return Eval_eigenval();
|
| 7563 | case EIGENVEC:
|
| 7564 | return Eval_eigenvec();
|
| 7565 | case ERF:
|
| 7566 | return Eval_erf();
|
| 7567 | case ERFC:
|
| 7568 | return Eval_erfc();
|
| 7569 | case EVAL:
|
| 7570 | return Eval_Eval();
|
| 7571 | case EXP:
|
| 7572 | return Eval_exp();
|
| 7573 | case EXPAND:
|
| 7574 | return Eval_expand();
|
| 7575 | case EXPCOS:
|
| 7576 | return Eval_expcos();
|
| 7577 | case EXPSIN:
|
| 7578 | return Eval_expsin();
|
| 7579 | case FACTOR:
|
| 7580 | return Eval_factor();
|
| 7581 | case FACTORIAL:
|
| 7582 | return Eval_factorial();
|
| 7583 | case FACTORPOLY:
|
| 7584 | return Eval_factorpoly();
|
| 7585 | case FILTER:
|
| 7586 | return Eval_filter();
|
| 7587 | case FLOATF:
|
| 7588 | return Eval_float();
|
| 7589 | case APPROXRATIO:
|
| 7590 | return Eval_approxratio();
|
| 7591 | case FLOOR:
|
| 7592 | return Eval_floor();
|
| 7593 | case FOR:
|
| 7594 | return Eval_for();
|
| 7595 | case FUNCTION:
|
| 7596 | return Eval_function_reference();
|
| 7597 | case GAMMA:
|
| 7598 | return Eval_gamma();
|
| 7599 | case GCD:
|
| 7600 | return Eval_gcd();
|
| 7601 | case HERMITE:
|
| 7602 | return Eval_hermite();
|
| 7603 | case HILBERT:
|
| 7604 | return Eval_hilbert();
|
| 7605 | case IMAG:
|
| 7606 | return Eval_imag();
|
| 7607 | case INDEX:
|
| 7608 | return Eval_index();
|
| 7609 | case INNER:
|
| 7610 | return Eval_inner();
|
| 7611 | case INTEGRAL:
|
| 7612 | return Eval_integral();
|
| 7613 | case INV:
|
| 7614 | return Eval_inv();
|
| 7615 | case INVG:
|
| 7616 | return Eval_invg();
|
| 7617 | case ISINTEGER:
|
| 7618 | return Eval_isinteger();
|
| 7619 | case ISPRIME:
|
| 7620 | return Eval_isprime();
|
| 7621 | case LAGUERRE:
|
| 7622 | return Eval_laguerre();
|
| 7623 | case LCM:
|
| 7624 | return Eval_lcm();
|
| 7625 | case LEADING:
|
| 7626 | return Eval_leading();
|
| 7627 | case LEGENDRE:
|
| 7628 | return Eval_legendre();
|
| 7629 | case LOG:
|
| 7630 | return Eval_log();
|
| 7631 | case LOOKUP:
|
| 7632 | return Eval_lookup();
|
| 7633 | case MOD:
|
| 7634 | return Eval_mod();
|
| 7635 | case MULTIPLY:
|
| 7636 | return Eval_multiply();
|
| 7637 | case NOT:
|
| 7638 | return Eval_not();
|
| 7639 | case NROOTS:
|
| 7640 | return Eval_nroots();
|
| 7641 | case NUMBER:
|
| 7642 | return Eval_number();
|
| 7643 | case NUMERATOR:
|
| 7644 | return Eval_numerator();
|
| 7645 | case OPERATOR:
|
| 7646 | return Eval_operator();
|
| 7647 | case OR:
|
| 7648 | return Eval_or();
|
| 7649 | case OUTER:
|
| 7650 | return Eval_outer();
|
| 7651 | case PATTERN:
|
| 7652 | return Eval_pattern();
|
| 7653 | case PATTERNSINFO:
|
| 7654 | return Eval_patternsinfo();
|
| 7655 | case POLAR:
|
| 7656 | return Eval_polar();
|
| 7657 | case POWER:
|
| 7658 | return Eval_power();
|
| 7659 | case PRIME:
|
| 7660 | return Eval_prime();
|
| 7661 | case PRINT:
|
| 7662 | return Eval_print();
|
| 7663 | case PRINT2DASCII:
|
| 7664 | return Eval_print2dascii();
|
| 7665 | case PRINTFULL:
|
| 7666 | return Eval_printfull();
|
| 7667 | case PRINTLATEX:
|
| 7668 | return Eval_printlatex();
|
| 7669 | case PRINTLIST:
|
| 7670 | return Eval_printlist();
|
| 7671 | case PRINTPLAIN:
|
| 7672 | return Eval_printplain();
|
| 7673 | case PRODUCT:
|
| 7674 | return Eval_product();
|
| 7675 | case QUOTE:
|
| 7676 | return Eval_quote();
|
| 7677 | case QUOTIENT:
|
| 7678 | return Eval_quotient();
|
| 7679 | case RANK:
|
| 7680 | return Eval_rank();
|
| 7681 | case RATIONALIZE:
|
| 7682 | return Eval_rationalize();
|
| 7683 | case REAL:
|
| 7684 | return Eval_real();
|
| 7685 | case ROUND:
|
| 7686 | return Eval_round();
|
| 7687 | case YYRECT:
|
| 7688 | return Eval_rect();
|
| 7689 | case ROOTS:
|
| 7690 | return Eval_roots();
|
| 7691 | case SETQ:
|
| 7692 | return Eval_setq();
|
| 7693 | case SGN:
|
| 7694 | return Eval_sgn();
|
| 7695 | case SILENTPATTERN:
|
| 7696 | return Eval_silentpattern();
|
| 7697 | case SIMPLIFY:
|
| 7698 | return Eval_simplify();
|
| 7699 | case SIN:
|
| 7700 | return Eval_sin();
|
| 7701 | case SINH:
|
| 7702 | return Eval_sinh();
|
| 7703 | case SHAPE:
|
| 7704 | return Eval_shape();
|
| 7705 | case SQRT:
|
| 7706 | return Eval_sqrt();
|
| 7707 | case STOP:
|
| 7708 | return Eval_stop();
|
| 7709 | case SUBST:
|
| 7710 | return Eval_subst();
|
| 7711 | case SUM:
|
| 7712 | return Eval_sum();
|
| 7713 | case SYMBOLSINFO:
|
| 7714 | return Eval_symbolsinfo();
|
| 7715 | case TAN:
|
| 7716 | return Eval_tan();
|
| 7717 | case TANH:
|
| 7718 | return Eval_tanh();
|
| 7719 | case TAYLOR:
|
| 7720 | return Eval_taylor();
|
| 7721 | case TEST:
|
| 7722 | return Eval_test();
|
| 7723 | case TESTEQ:
|
| 7724 | return Eval_testeq();
|
| 7725 | case TESTGE:
|
| 7726 | return Eval_testge();
|
| 7727 | case TESTGT:
|
| 7728 | return Eval_testgt();
|
| 7729 | case TESTLE:
|
| 7730 | return Eval_testle();
|
| 7731 | case TESTLT:
|
| 7732 | return Eval_testlt();
|
| 7733 | case TRANSPOSE:
|
| 7734 | return Eval_transpose();
|
| 7735 | case UNIT:
|
| 7736 | return Eval_unit();
|
| 7737 | case ZERO:
|
| 7738 | return Eval_zero();
|
| 7739 | default:
|
| 7740 | return Eval_user_function();
|
| 7741 | }
|
| 7742 | };
|
| 7743 |
|
| 7744 | Eval_binding = function() {
|
| 7745 | return push(get_binding(cadr(p1)));
|
| 7746 | };
|
| 7747 |
|
| 7748 |
|
| 7749 | |
| 7750 | |
| 7751 | |
| 7752 | |
| 7753 | |
| 7754 | |
| 7755 | |
| 7756 | |
| 7757 | |
| 7758 | |
| 7759 | |
| 7760 | |
| 7761 | |
| 7762 | |
| 7763 | |
| 7764 |
|
| 7765 |
|
| 7766 | Eval_check = function() {
|
| 7767 | push(cadr(p1));
|
| 7768 | Eval_predicate();
|
| 7769 | p1 = pop();
|
| 7770 | return push(p1);
|
| 7771 | };
|
| 7772 |
|
| 7773 | Eval_det = function() {
|
| 7774 | push(cadr(p1));
|
| 7775 | Eval();
|
| 7776 | return det();
|
| 7777 | };
|
| 7778 |
|
| 7779 |
|
| 7780 | |
| 7781 | |
| 7782 | |
| 7783 | |
| 7784 | |
| 7785 | |
| 7786 | |
| 7787 | |
| 7788 | |
| 7789 | |
| 7790 | |
| 7791 | |
| 7792 | |
| 7793 |
|
| 7794 |
|
| 7795 | Eval_dim = function() {
|
| 7796 | var n;
|
| 7797 | push(cadr(p1));
|
| 7798 | Eval();
|
| 7799 | p2 = pop();
|
| 7800 | if (iscons(cddr(p1))) {
|
| 7801 | push(caddr(p1));
|
| 7802 | Eval();
|
| 7803 | n = pop_integer();
|
| 7804 | } else {
|
| 7805 | n = 1;
|
| 7806 | }
|
| 7807 | if (!istensor(p2)) {
|
| 7808 | return push_integer(1);
|
| 7809 | } else if (n < 1 || n > p2.tensor.ndim) {
|
| 7810 | return push(p1);
|
| 7811 | } else {
|
| 7812 | return push_integer(p2.tensor.dim[n - 1]);
|
| 7813 | }
|
| 7814 | };
|
| 7815 |
|
| 7816 | Eval_divisors = function() {
|
| 7817 | push(cadr(p1));
|
| 7818 | Eval();
|
| 7819 | return divisors();
|
| 7820 | };
|
| 7821 |
|
| 7822 |
|
| 7823 | |
| 7824 | |
| 7825 | |
| 7826 | |
| 7827 | |
| 7828 | |
| 7829 | |
| 7830 | |
| 7831 | |
| 7832 | |
| 7833 | |
| 7834 | |
| 7835 | |
| 7836 |
|
| 7837 |
|
| 7838 | Eval_do = function() {
|
| 7839 | var results;
|
| 7840 | push(car(p1));
|
| 7841 | p1 = cdr(p1);
|
| 7842 | results = [];
|
| 7843 | while (iscons(p1)) {
|
| 7844 | pop();
|
| 7845 | push(car(p1));
|
| 7846 | Eval();
|
| 7847 | results.push(p1 = cdr(p1));
|
| 7848 | }
|
| 7849 | return results;
|
| 7850 | };
|
| 7851 |
|
| 7852 | Eval_dsolve = function() {
|
| 7853 | push(cadr(p1));
|
| 7854 | Eval();
|
| 7855 | push(caddr(p1));
|
| 7856 | Eval();
|
| 7857 | push(cadddr(p1));
|
| 7858 | Eval();
|
| 7859 | return dsolve();
|
| 7860 | };
|
| 7861 |
|
| 7862 | Eval_Eval = function() {
|
| 7863 | push(cadr(p1));
|
| 7864 | Eval();
|
| 7865 | p1 = cddr(p1);
|
| 7866 | while (iscons(p1)) {
|
| 7867 | push(car(p1));
|
| 7868 | Eval();
|
| 7869 | push(cadr(p1));
|
| 7870 | Eval();
|
| 7871 | subst();
|
| 7872 | p1 = cddr(p1);
|
| 7873 | }
|
| 7874 | return Eval();
|
| 7875 | };
|
| 7876 |
|
| 7877 | Eval_exp = function() {
|
| 7878 | push(cadr(p1));
|
| 7879 | Eval();
|
| 7880 | return exponential();
|
| 7881 | };
|
| 7882 |
|
| 7883 | Eval_factorial = function() {
|
| 7884 | push(cadr(p1));
|
| 7885 | Eval();
|
| 7886 | return factorial();
|
| 7887 | };
|
| 7888 |
|
| 7889 | Eval_factorpoly = function() {
|
| 7890 | var results;
|
| 7891 | p1 = cdr(p1);
|
| 7892 | push(car(p1));
|
| 7893 | Eval();
|
| 7894 | p1 = cdr(p1);
|
| 7895 | push(car(p1));
|
| 7896 | Eval();
|
| 7897 | factorpoly();
|
| 7898 | p1 = cdr(p1);
|
| 7899 | results = [];
|
| 7900 | while (iscons(p1)) {
|
| 7901 | push(car(p1));
|
| 7902 | Eval();
|
| 7903 | factorpoly();
|
| 7904 | results.push(p1 = cdr(p1));
|
| 7905 | }
|
| 7906 | return results;
|
| 7907 | };
|
| 7908 |
|
| 7909 | Eval_hermite = function() {
|
| 7910 | push(cadr(p1));
|
| 7911 | Eval();
|
| 7912 | push(caddr(p1));
|
| 7913 | Eval();
|
| 7914 | return hermite();
|
| 7915 | };
|
| 7916 |
|
| 7917 | Eval_hilbert = function() {
|
| 7918 | push(cadr(p1));
|
| 7919 | Eval();
|
| 7920 | return hilbert();
|
| 7921 | };
|
| 7922 |
|
| 7923 | Eval_index = function() {
|
| 7924 | var h, orig, theTensor;
|
| 7925 | h = tos;
|
| 7926 | orig = p1;
|
| 7927 | p1 = cdr(p1);
|
| 7928 | push(car(p1));
|
| 7929 | Eval();
|
| 7930 | theTensor = stack[tos - 1];
|
| 7931 | if (isnum(theTensor)) {
|
| 7932 | stop("trying to access a scalar as a tensor");
|
| 7933 | }
|
| 7934 | if (!istensor(theTensor)) {
|
| 7935 | moveTos(h);
|
| 7936 | push(orig);
|
| 7937 | return;
|
| 7938 | }
|
| 7939 | p1 = cdr(p1);
|
| 7940 | while (iscons(p1)) {
|
| 7941 | push(car(p1));
|
| 7942 | Eval();
|
| 7943 | if (!isintegerorintegerfloat(stack[tos - 1])) {
|
| 7944 | moveTos(h);
|
| 7945 | push(orig);
|
| 7946 | return;
|
| 7947 | }
|
| 7948 | p1 = cdr(p1);
|
| 7949 | }
|
| 7950 | return index_function(tos - h);
|
| 7951 | };
|
| 7952 |
|
| 7953 | Eval_inv = function() {
|
| 7954 | push(cadr(p1));
|
| 7955 | Eval();
|
| 7956 | return inv();
|
| 7957 | };
|
| 7958 |
|
| 7959 | Eval_invg = function() {
|
| 7960 | push(cadr(p1));
|
| 7961 | Eval();
|
| 7962 | return invg();
|
| 7963 | };
|
| 7964 |
|
| 7965 | Eval_isinteger = function() {
|
| 7966 | var n;
|
| 7967 | push(cadr(p1));
|
| 7968 | Eval();
|
| 7969 | p1 = pop();
|
| 7970 | if (isrational(p1)) {
|
| 7971 | if (isinteger(p1)) {
|
| 7972 | push(one);
|
| 7973 | } else {
|
| 7974 | push(zero);
|
| 7975 | }
|
| 7976 | return;
|
| 7977 | }
|
| 7978 | if (isdouble(p1)) {
|
| 7979 | n = Math.floor(p1.d);
|
| 7980 | if (n === p1.d) {
|
| 7981 | push(one);
|
| 7982 | } else {
|
| 7983 | push(zero);
|
| 7984 | }
|
| 7985 | return;
|
| 7986 | }
|
| 7987 | push_symbol(ISINTEGER);
|
| 7988 | push(p1);
|
| 7989 | return list(2);
|
| 7990 | };
|
| 7991 |
|
| 7992 | Eval_number = function() {
|
| 7993 | push(cadr(p1));
|
| 7994 | Eval();
|
| 7995 | p1 = pop();
|
| 7996 | if (p1.k === NUM || p1.k === DOUBLE) {
|
| 7997 | return push_integer(1);
|
| 7998 | } else {
|
| 7999 | return push_integer(0);
|
| 8000 | }
|
| 8001 | };
|
| 8002 |
|
| 8003 | Eval_operator = function() {
|
| 8004 | var h;
|
| 8005 | h = tos;
|
| 8006 | push_symbol(OPERATOR);
|
| 8007 | p1 = cdr(p1);
|
| 8008 | while (iscons(p1)) {
|
| 8009 | push(car(p1));
|
| 8010 | Eval();
|
| 8011 | p1 = cdr(p1);
|
| 8012 | }
|
| 8013 | return list(tos - h);
|
| 8014 | };
|
| 8015 |
|
| 8016 | Eval_quote = function() {
|
| 8017 | return push(cadr(p1));
|
| 8018 | };
|
| 8019 |
|
| 8020 | Eval_rank = function() {
|
| 8021 | push(cadr(p1));
|
| 8022 | Eval();
|
| 8023 | p1 = pop();
|
| 8024 | if (istensor(p1)) {
|
| 8025 | return push_integer(p1.tensor.ndim);
|
| 8026 | } else {
|
| 8027 | return push(zero);
|
| 8028 | }
|
| 8029 | };
|
| 8030 |
|
| 8031 | Eval_setq = function() {
|
| 8032 | if (caadr(p1) === symbol(INDEX)) {
|
| 8033 | setq_indexed();
|
| 8034 | return;
|
| 8035 | }
|
| 8036 | if (iscons(cadr(p1))) {
|
| 8037 | define_user_function();
|
| 8038 | return;
|
| 8039 | }
|
| 8040 | if (!issymbol(cadr(p1))) {
|
| 8041 | stop("symbol assignment: error in symbol");
|
| 8042 | }
|
| 8043 | push(caddr(p1));
|
| 8044 | Eval();
|
| 8045 | p2 = pop();
|
| 8046 | set_binding(cadr(p1), p2);
|
| 8047 | return push(symbol(NIL));
|
| 8048 | };
|
| 8049 |
|
| 8050 | setq_indexed = function() {
|
| 8051 | var h;
|
| 8052 | p4 = cadadr(p1);
|
| 8053 | if (!issymbol(p4)) {
|
| 8054 | stop("indexed assignment: error in symbol");
|
| 8055 | }
|
| 8056 | h = tos;
|
| 8057 | push(caddr(p1));
|
| 8058 | Eval();
|
| 8059 | p2 = cdadr(p1);
|
| 8060 | while (iscons(p2)) {
|
| 8061 | push(car(p2));
|
| 8062 | Eval();
|
| 8063 | p2 = cdr(p2);
|
| 8064 | }
|
| 8065 | set_component(tos - h);
|
| 8066 | p3 = pop();
|
| 8067 | set_binding(p4, p3);
|
| 8068 | return push(symbol(NIL));
|
| 8069 | };
|
| 8070 |
|
| 8071 | Eval_sqrt = function() {
|
| 8072 | push(cadr(p1));
|
| 8073 | Eval();
|
| 8074 | push_rational(1, 2);
|
| 8075 | return power();
|
| 8076 | };
|
| 8077 |
|
| 8078 | Eval_stop = function() {
|
| 8079 | return stop("user stop");
|
| 8080 | };
|
| 8081 |
|
| 8082 | Eval_subst = function() {
|
| 8083 | push(cadddr(p1));
|
| 8084 | Eval();
|
| 8085 | push(caddr(p1));
|
| 8086 | Eval();
|
| 8087 | push(cadr(p1));
|
| 8088 | Eval();
|
| 8089 | subst();
|
| 8090 | return Eval();
|
| 8091 | };
|
| 8092 |
|
| 8093 | Eval_unit = function() {
|
| 8094 | var i, n, o, ref;
|
| 8095 | i = 0;
|
| 8096 | n = 0;
|
| 8097 | push(cadr(p1));
|
| 8098 | Eval();
|
| 8099 | n = pop_integer();
|
| 8100 | if (isNaN(n)) {
|
| 8101 | push(p1);
|
| 8102 | return;
|
| 8103 | }
|
| 8104 | if (n < 1) {
|
| 8105 | push(p1);
|
| 8106 | return;
|
| 8107 | }
|
| 8108 | p1 = alloc_tensor(n * n);
|
| 8109 | p1.tensor.ndim = 2;
|
| 8110 | p1.tensor.dim[0] = n;
|
| 8111 | p1.tensor.dim[1] = n;
|
| 8112 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 8113 | p1.tensor.elem[n * i + i] = one;
|
| 8114 | }
|
| 8115 | check_tensor_dimensions(p1);
|
| 8116 | return push(p1);
|
| 8117 | };
|
| 8118 |
|
| 8119 | Eval_noexpand = function() {
|
| 8120 | var prev_expanding;
|
| 8121 | prev_expanding = expanding;
|
| 8122 | expanding = 0;
|
| 8123 | Eval();
|
| 8124 | return expanding = prev_expanding;
|
| 8125 | };
|
| 8126 |
|
| 8127 | Eval_predicate = function() {
|
| 8128 | save();
|
| 8129 | p1 = top();
|
| 8130 | if (car(p1) === symbol(SETQ)) {
|
| 8131 | pop();
|
| 8132 | push_symbol(TESTEQ);
|
| 8133 | push(cadr(p1));
|
| 8134 | push(caddr(p1));
|
| 8135 | list(3);
|
| 8136 | }
|
| 8137 | Eval();
|
| 8138 | return restore();
|
| 8139 | };
|
| 8140 |
|
| 8141 | Eval_expand = function() {
|
| 8142 | push(cadr(p1));
|
| 8143 | Eval();
|
| 8144 | push(caddr(p1));
|
| 8145 | Eval();
|
| 8146 | p2 = pop();
|
| 8147 | if (p2 === symbol(NIL)) {
|
| 8148 | guess();
|
| 8149 | } else {
|
| 8150 | push(p2);
|
| 8151 | }
|
| 8152 | return expand();
|
| 8153 | };
|
| 8154 |
|
| 8155 | expand = function() {
|
| 8156 | var prev_expanding;
|
| 8157 | save();
|
| 8158 | p9 = pop();
|
| 8159 | p5 = pop();
|
| 8160 | if (istensor(p5)) {
|
| 8161 | expand_tensor();
|
| 8162 | restore();
|
| 8163 | return;
|
| 8164 | }
|
| 8165 | if (car(p5) === symbol(ADD)) {
|
| 8166 | push_integer(0);
|
| 8167 | p1 = cdr(p5);
|
| 8168 | while (iscons(p1)) {
|
| 8169 | push(car(p1));
|
| 8170 | push(p9);
|
| 8171 | expand();
|
| 8172 | add();
|
| 8173 | p1 = cdr(p1);
|
| 8174 | }
|
| 8175 | restore();
|
| 8176 | return;
|
| 8177 | }
|
| 8178 | push(p5);
|
| 8179 | numerator();
|
| 8180 | p3 = pop();
|
| 8181 | push(p5);
|
| 8182 | denominator();
|
| 8183 | p2 = pop();
|
| 8184 | remove_negative_exponents();
|
| 8185 | push(p3);
|
| 8186 | push(p2);
|
| 8187 | push(p9);
|
| 8188 | if (isone(p3) || isone(p2)) {
|
| 8189 | if (!ispoly(p2, p9) || isone(p2)) {
|
| 8190 | pop();
|
| 8191 | pop();
|
| 8192 | pop();
|
| 8193 | push(p5);
|
| 8194 | restore();
|
| 8195 | return;
|
| 8196 | }
|
| 8197 | }
|
| 8198 | divpoly();
|
| 8199 | p7 = pop();
|
| 8200 | push(p3);
|
| 8201 | push(p2);
|
| 8202 | push(p7);
|
| 8203 | multiply();
|
| 8204 | subtract();
|
| 8205 | p3 = pop();
|
| 8206 | if (iszero(p3)) {
|
| 8207 | push(p7);
|
| 8208 | restore();
|
| 8209 | return;
|
| 8210 | }
|
| 8211 | push(p2);
|
| 8212 | push(p9);
|
| 8213 | factorpoly();
|
| 8214 | p2 = pop();
|
| 8215 | expand_get_C();
|
| 8216 | expand_get_B();
|
| 8217 | expand_get_A();
|
| 8218 | if (istensor(p4)) {
|
| 8219 | push(p4);
|
| 8220 | prev_expanding = expanding;
|
| 8221 | expanding = 1;
|
| 8222 | inv();
|
| 8223 | expanding = prev_expanding;
|
| 8224 | push(p3);
|
| 8225 | inner();
|
| 8226 | push(p2);
|
| 8227 | inner();
|
| 8228 | } else {
|
| 8229 | push(p3);
|
| 8230 | push(p4);
|
| 8231 | prev_expanding = expanding;
|
| 8232 | expanding = 1;
|
| 8233 | divide();
|
| 8234 | expanding = prev_expanding;
|
| 8235 | push(p2);
|
| 8236 | multiply();
|
| 8237 | }
|
| 8238 | push(p7);
|
| 8239 | add();
|
| 8240 | return restore();
|
| 8241 | };
|
| 8242 |
|
| 8243 | expand_tensor = function() {
|
| 8244 | var i, o, ref;
|
| 8245 | i = 0;
|
| 8246 | push(p5);
|
| 8247 | copy_tensor();
|
| 8248 | p5 = pop();
|
| 8249 | for (i = o = 0, ref = p5.tensor.nelem; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 8250 | push(p5.tensor.elem[i]);
|
| 8251 | push(p9);
|
| 8252 | expand();
|
| 8253 | p5.tensor.elem[i] = pop();
|
| 8254 | }
|
| 8255 | return push(p5);
|
| 8256 | };
|
| 8257 |
|
| 8258 | remove_negative_exponents = function() {
|
| 8259 | var h, i, j, k, n, o, ref;
|
| 8260 | h = 0;
|
| 8261 | i = 0;
|
| 8262 | j = 0;
|
| 8263 | k = 0;
|
| 8264 | n = 0;
|
| 8265 | h = tos;
|
| 8266 | factors(p2);
|
| 8267 | factors(p3);
|
| 8268 | n = tos - h;
|
| 8269 | j = 0;
|
| 8270 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 8271 | p1 = stack[h + i];
|
| 8272 | if (car(p1) !== symbol(POWER)) {
|
| 8273 | continue;
|
| 8274 | }
|
| 8275 | if (cadr(p1) !== p9) {
|
| 8276 | continue;
|
| 8277 | }
|
| 8278 | push(caddr(p1));
|
| 8279 | k = pop_integer();
|
| 8280 | if (isNaN(k)) {
|
| 8281 | continue;
|
| 8282 | }
|
| 8283 | if (k < j) {
|
| 8284 | j = k;
|
| 8285 | }
|
| 8286 | }
|
| 8287 | moveTos(h);
|
| 8288 | if (j === 0) {
|
| 8289 | return;
|
| 8290 | }
|
| 8291 | push(p2);
|
| 8292 | push(p9);
|
| 8293 | push_integer(-j);
|
| 8294 | power();
|
| 8295 | multiply();
|
| 8296 | p2 = pop();
|
| 8297 | push(p3);
|
| 8298 | push(p9);
|
| 8299 | push_integer(-j);
|
| 8300 | power();
|
| 8301 | multiply();
|
| 8302 | return p3 = pop();
|
| 8303 | };
|
| 8304 |
|
| 8305 | expand_get_C = function() {
|
| 8306 | var a, h, i, i1, j, n, o, prev_expanding, ref, ref1;
|
| 8307 | h = 0;
|
| 8308 | i = 0;
|
| 8309 | j = 0;
|
| 8310 | n = 0;
|
| 8311 | h = tos;
|
| 8312 | if (car(p2) === symbol(MULTIPLY)) {
|
| 8313 | p1 = cdr(p2);
|
| 8314 | while (iscons(p1)) {
|
| 8315 | p5 = car(p1);
|
| 8316 | expand_get_CF();
|
| 8317 | p1 = cdr(p1);
|
| 8318 | }
|
| 8319 | } else {
|
| 8320 | p5 = p2;
|
| 8321 | expand_get_CF();
|
| 8322 | }
|
| 8323 | n = tos - h;
|
| 8324 | if (n === 1) {
|
| 8325 | p4 = pop();
|
| 8326 | return;
|
| 8327 | }
|
| 8328 | p4 = alloc_tensor(n * n);
|
| 8329 | p4.tensor.ndim = 2;
|
| 8330 | p4.tensor.dim[0] = n;
|
| 8331 | p4.tensor.dim[1] = n;
|
| 8332 | a = h;
|
| 8333 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 8334 | for (j = i1 = 0, ref1 = n; 0 <= ref1 ? i1 < ref1 : i1 > ref1; j = 0 <= ref1 ? ++i1 : --i1) {
|
| 8335 | push(stack[a + j]);
|
| 8336 | push(p9);
|
| 8337 | push_integer(i);
|
| 8338 | power();
|
| 8339 | prev_expanding = expanding;
|
| 8340 | expanding = 1;
|
| 8341 | divide();
|
| 8342 | expanding = prev_expanding;
|
| 8343 | push(p9);
|
| 8344 | filter();
|
| 8345 | p4.tensor.elem[n * i + j] = pop();
|
| 8346 | }
|
| 8347 | }
|
| 8348 | return moveTos(tos - n);
|
| 8349 | };
|
| 8350 |
|
| 8351 | expand_get_CF = function() {
|
| 8352 | var d, i, j, n, o, prev_expanding, ref, results;
|
| 8353 | d = 0;
|
| 8354 | i = 0;
|
| 8355 | j = 0;
|
| 8356 | n = 0;
|
| 8357 | if (!Find(p5, p9)) {
|
| 8358 | return;
|
| 8359 | }
|
| 8360 | prev_expanding = expanding;
|
| 8361 | expanding = 1;
|
| 8362 | trivial_divide();
|
| 8363 | expanding = prev_expanding;
|
| 8364 | if (car(p5) === symbol(POWER)) {
|
| 8365 | push(caddr(p5));
|
| 8366 | n = pop_integer();
|
| 8367 | p6 = cadr(p5);
|
| 8368 | } else {
|
| 8369 | n = 1;
|
| 8370 | p6 = p5;
|
| 8371 | }
|
| 8372 | push(p6);
|
| 8373 | push(p9);
|
| 8374 | degree();
|
| 8375 | d = pop_integer();
|
| 8376 | results = [];
|
| 8377 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 8378 | results.push((function() {
|
| 8379 | var i1, ref1, results1;
|
| 8380 | results1 = [];
|
| 8381 | for (j = i1 = 0, ref1 = d; 0 <= ref1 ? i1 < ref1 : i1 > ref1; j = 0 <= ref1 ? ++i1 : --i1) {
|
| 8382 | push(p8);
|
| 8383 | push(p6);
|
| 8384 | push_integer(i);
|
| 8385 | power();
|
| 8386 | prev_expanding = expanding;
|
| 8387 | expanding = 1;
|
| 8388 | multiply();
|
| 8389 | expanding = prev_expanding;
|
| 8390 | push(p9);
|
| 8391 | push_integer(j);
|
| 8392 | power();
|
| 8393 | prev_expanding = expanding;
|
| 8394 | expanding = 1;
|
| 8395 | multiply();
|
| 8396 | results1.push(expanding = prev_expanding);
|
| 8397 | }
|
| 8398 | return results1;
|
| 8399 | })());
|
| 8400 | }
|
| 8401 | return results;
|
| 8402 | };
|
| 8403 |
|
| 8404 | trivial_divide = function() {
|
| 8405 | var h;
|
| 8406 | h = 0;
|
| 8407 | if (car(p2) === symbol(MULTIPLY)) {
|
| 8408 | h = tos;
|
| 8409 | p0 = cdr(p2);
|
| 8410 | while (iscons(p0)) {
|
| 8411 | if (!equal(car(p0), p5)) {
|
| 8412 | push(car(p0));
|
| 8413 | Eval();
|
| 8414 | }
|
| 8415 | p0 = cdr(p0);
|
| 8416 | }
|
| 8417 | multiply_all(tos - h);
|
| 8418 | } else {
|
| 8419 | push_integer(1);
|
| 8420 | }
|
| 8421 | return p8 = pop();
|
| 8422 | };
|
| 8423 |
|
| 8424 | expand_get_B = function() {
|
| 8425 | var i, n, o, prev_expanding, ref;
|
| 8426 | i = 0;
|
| 8427 | n = 0;
|
| 8428 | if (!istensor(p4)) {
|
| 8429 | return;
|
| 8430 | }
|
| 8431 | n = p4.tensor.dim[0];
|
| 8432 | p8 = alloc_tensor(n);
|
| 8433 | p8.tensor.ndim = 1;
|
| 8434 | p8.tensor.dim[0] = n;
|
| 8435 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 8436 | push(p3);
|
| 8437 | push(p9);
|
| 8438 | push_integer(i);
|
| 8439 | power();
|
| 8440 | prev_expanding = expanding;
|
| 8441 | expanding = 1;
|
| 8442 | divide();
|
| 8443 | expanding = prev_expanding;
|
| 8444 | push(p9);
|
| 8445 | filter();
|
| 8446 | p8.tensor.elem[i] = pop();
|
| 8447 | }
|
| 8448 | return p3 = p8;
|
| 8449 | };
|
| 8450 |
|
| 8451 | expand_get_A = function() {
|
| 8452 | var h, i, n, o, ref;
|
| 8453 | h = 0;
|
| 8454 | i = 0;
|
| 8455 | n = 0;
|
| 8456 | if (!istensor(p4)) {
|
| 8457 | push(p2);
|
| 8458 | reciprocate();
|
| 8459 | p2 = pop();
|
| 8460 | return;
|
| 8461 | }
|
| 8462 | h = tos;
|
| 8463 | if (car(p2) === symbol(MULTIPLY)) {
|
| 8464 | p8 = cdr(p2);
|
| 8465 | while (iscons(p8)) {
|
| 8466 | p5 = car(p8);
|
| 8467 | expand_get_AF();
|
| 8468 | p8 = cdr(p8);
|
| 8469 | }
|
| 8470 | } else {
|
| 8471 | p5 = p2;
|
| 8472 | expand_get_AF();
|
| 8473 | }
|
| 8474 | n = tos - h;
|
| 8475 | p8 = alloc_tensor(n);
|
| 8476 | p8.tensor.ndim = 1;
|
| 8477 | p8.tensor.dim[0] = n;
|
| 8478 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 8479 | p8.tensor.elem[i] = stack[h + i];
|
| 8480 | }
|
| 8481 | moveTos(h);
|
| 8482 | return p2 = p8;
|
| 8483 | };
|
| 8484 |
|
| 8485 | expand_get_AF = function() {
|
| 8486 | var d, i, j, n, o, ref, results;
|
| 8487 | d = 0;
|
| 8488 | i = 0;
|
| 8489 | j = 0;
|
| 8490 | n = 1;
|
| 8491 | if (!Find(p5, p9)) {
|
| 8492 | return;
|
| 8493 | }
|
| 8494 | if (car(p5) === symbol(POWER)) {
|
| 8495 | push(caddr(p5));
|
| 8496 | n = pop_integer();
|
| 8497 | p5 = cadr(p5);
|
| 8498 | }
|
| 8499 | push(p5);
|
| 8500 | push(p9);
|
| 8501 | degree();
|
| 8502 | d = pop_integer();
|
| 8503 | results = [];
|
| 8504 | for (i = o = ref = n; ref <= 0 ? o < 0 : o > 0; i = ref <= 0 ? ++o : --o) {
|
| 8505 | results.push((function() {
|
| 8506 | var i1, ref1, results1;
|
| 8507 | results1 = [];
|
| 8508 | for (j = i1 = 0, ref1 = d; 0 <= ref1 ? i1 < ref1 : i1 > ref1; j = 0 <= ref1 ? ++i1 : --i1) {
|
| 8509 | push(p5);
|
| 8510 | push_integer(i);
|
| 8511 | power();
|
| 8512 | reciprocate();
|
| 8513 | push(p9);
|
| 8514 | push_integer(j);
|
| 8515 | power();
|
| 8516 | results1.push(multiply());
|
| 8517 | }
|
| 8518 | return results1;
|
| 8519 | })());
|
| 8520 | }
|
| 8521 | return results;
|
| 8522 | };
|
| 8523 |
|
| 8524 | Eval_expcos = function() {
|
| 8525 | push(cadr(p1));
|
| 8526 | Eval();
|
| 8527 | return expcos();
|
| 8528 | };
|
| 8529 |
|
| 8530 | expcos = function() {
|
| 8531 | save();
|
| 8532 | p1 = pop();
|
| 8533 | push(imaginaryunit);
|
| 8534 | push(p1);
|
| 8535 | multiply();
|
| 8536 | exponential();
|
| 8537 | push_rational(1, 2);
|
| 8538 | multiply();
|
| 8539 | push(imaginaryunit);
|
| 8540 | negate();
|
| 8541 | push(p1);
|
| 8542 | multiply();
|
| 8543 | exponential();
|
| 8544 | push_rational(1, 2);
|
| 8545 | multiply();
|
| 8546 | add();
|
| 8547 | return restore();
|
| 8548 | };
|
| 8549 |
|
| 8550 | Eval_expsin = function() {
|
| 8551 | push(cadr(p1));
|
| 8552 | Eval();
|
| 8553 | return expsin();
|
| 8554 | };
|
| 8555 |
|
| 8556 | expsin = function() {
|
| 8557 | save();
|
| 8558 | p1 = pop();
|
| 8559 | push(imaginaryunit);
|
| 8560 | push(p1);
|
| 8561 | multiply();
|
| 8562 | exponential();
|
| 8563 | push(imaginaryunit);
|
| 8564 | divide();
|
| 8565 | push_rational(1, 2);
|
| 8566 | multiply();
|
| 8567 | push(imaginaryunit);
|
| 8568 | negate();
|
| 8569 | push(p1);
|
| 8570 | multiply();
|
| 8571 | exponential();
|
| 8572 | push(imaginaryunit);
|
| 8573 | divide();
|
| 8574 | push_rational(1, 2);
|
| 8575 | multiply();
|
| 8576 | subtract();
|
| 8577 | return restore();
|
| 8578 | };
|
| 8579 |
|
| 8580 | Eval_factor = function() {
|
| 8581 | var results;
|
| 8582 | push(cadr(p1));
|
| 8583 | Eval();
|
| 8584 | push(caddr(p1));
|
| 8585 | Eval();
|
| 8586 | p2 = pop();
|
| 8587 | if (p2 === symbol(NIL)) {
|
| 8588 | guess();
|
| 8589 | } else {
|
| 8590 | push(p2);
|
| 8591 | }
|
| 8592 | factor();
|
| 8593 | p1 = cdddr(p1);
|
| 8594 | results = [];
|
| 8595 | while (iscons(p1)) {
|
| 8596 | push(car(p1));
|
| 8597 | Eval();
|
| 8598 | factor_again();
|
| 8599 | results.push(p1 = cdr(p1));
|
| 8600 | }
|
| 8601 | return results;
|
| 8602 | };
|
| 8603 |
|
| 8604 | factor_again = function() {
|
| 8605 | var h, n;
|
| 8606 | save();
|
| 8607 | p2 = pop();
|
| 8608 | p1 = pop();
|
| 8609 | h = tos;
|
| 8610 | if (car(p1) === symbol(MULTIPLY)) {
|
| 8611 | p1 = cdr(p1);
|
| 8612 | while (iscons(p1)) {
|
| 8613 | push(car(p1));
|
| 8614 | push(p2);
|
| 8615 | factor_term();
|
| 8616 | p1 = cdr(p1);
|
| 8617 | }
|
| 8618 | } else {
|
| 8619 | push(p1);
|
| 8620 | push(p2);
|
| 8621 | factor_term();
|
| 8622 | }
|
| 8623 | n = tos - h;
|
| 8624 | if (n > 1) {
|
| 8625 | multiply_all_noexpand(n);
|
| 8626 | }
|
| 8627 | return restore();
|
| 8628 | };
|
| 8629 |
|
| 8630 | factor_term = function() {
|
| 8631 | save();
|
| 8632 | factorpoly();
|
| 8633 | p1 = pop();
|
| 8634 | if (car(p1) === symbol(MULTIPLY)) {
|
| 8635 | p1 = cdr(p1);
|
| 8636 | while (iscons(p1)) {
|
| 8637 | push(car(p1));
|
| 8638 | p1 = cdr(p1);
|
| 8639 | }
|
| 8640 | } else {
|
| 8641 | push(p1);
|
| 8642 | }
|
| 8643 | return restore();
|
| 8644 | };
|
| 8645 |
|
| 8646 | factor = function() {
|
| 8647 | save();
|
| 8648 | p2 = pop();
|
| 8649 | p1 = pop();
|
| 8650 | if (isinteger(p1)) {
|
| 8651 | push(p1);
|
| 8652 | factor_number();
|
| 8653 | } else {
|
| 8654 | push(p1);
|
| 8655 | push(p2);
|
| 8656 | factorpoly();
|
| 8657 | }
|
| 8658 | return restore();
|
| 8659 | };
|
| 8660 |
|
| 8661 | factor_small_number = function() {
|
| 8662 | var d, expo, i, n, o, ref;
|
| 8663 | i = 0;
|
| 8664 | save();
|
| 8665 | n = pop_integer();
|
| 8666 | if (isNaN(n)) {
|
| 8667 | stop("number too big to factor");
|
| 8668 | }
|
| 8669 | if (n < 0) {
|
| 8670 | n = -n;
|
| 8671 | }
|
| 8672 | for (i = o = 0, ref = MAXPRIMETAB; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 8673 | d = primetab[i];
|
| 8674 | if (d > n / d) {
|
| 8675 | break;
|
| 8676 | }
|
| 8677 | expo = 0;
|
| 8678 | while (n % d === 0) {
|
| 8679 | n /= d;
|
| 8680 | expo++;
|
| 8681 | }
|
| 8682 | if (expo) {
|
| 8683 | push_integer(d);
|
| 8684 | push_integer(expo);
|
| 8685 | }
|
| 8686 | }
|
| 8687 | if (n > 1) {
|
| 8688 | push_integer(n);
|
| 8689 | push_integer(1);
|
| 8690 | }
|
| 8691 | return restore();
|
| 8692 | };
|
| 8693 |
|
| 8694 | factorial = function() {
|
| 8695 | var n;
|
| 8696 | n = 0;
|
| 8697 | save();
|
| 8698 | p1 = pop();
|
| 8699 | push(p1);
|
| 8700 | n = pop_integer();
|
| 8701 | if (n < 0 || isNaN(n)) {
|
| 8702 | push_symbol(FACTORIAL);
|
| 8703 | push(p1);
|
| 8704 | list(2);
|
| 8705 | restore();
|
| 8706 | return;
|
| 8707 | }
|
| 8708 | bignum_factorial(n);
|
| 8709 | return restore();
|
| 8710 | };
|
| 8711 |
|
| 8712 | simplifyfactorials = function() {
|
| 8713 | var x;
|
| 8714 | x = 0;
|
| 8715 | save();
|
| 8716 | x = expanding;
|
| 8717 | expanding = 0;
|
| 8718 | p1 = pop();
|
| 8719 | if (car(p1) === symbol(ADD)) {
|
| 8720 | push(zero);
|
| 8721 | p1 = cdr(p1);
|
| 8722 | while (iscons(p1)) {
|
| 8723 | push(car(p1));
|
| 8724 | simplifyfactorials();
|
| 8725 | add();
|
| 8726 | p1 = cdr(p1);
|
| 8727 | }
|
| 8728 | expanding = x;
|
| 8729 | restore();
|
| 8730 | return;
|
| 8731 | }
|
| 8732 | if (car(p1) === symbol(MULTIPLY)) {
|
| 8733 | sfac_product();
|
| 8734 | expanding = x;
|
| 8735 | restore();
|
| 8736 | return;
|
| 8737 | }
|
| 8738 | push(p1);
|
| 8739 | expanding = x;
|
| 8740 | return restore();
|
| 8741 | };
|
| 8742 |
|
| 8743 | sfac_product = function() {
|
| 8744 | var i, i1, j, j1, n, o, ref, ref1, ref2, ref3, s;
|
| 8745 | i = 0;
|
| 8746 | j = 0;
|
| 8747 | n = 0;
|
| 8748 | s = tos;
|
| 8749 | p1 = cdr(p1);
|
| 8750 | n = 0;
|
| 8751 | while (iscons(p1)) {
|
| 8752 | push(car(p1));
|
| 8753 | p1 = cdr(p1);
|
| 8754 | n++;
|
| 8755 | }
|
| 8756 | for (i = o = 0, ref = n - 1; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 8757 | if (stack[s + i] === symbol(NIL)) {
|
| 8758 | continue;
|
| 8759 | }
|
| 8760 | for (j = i1 = ref1 = i + 1, ref2 = n; ref1 <= ref2 ? i1 < ref2 : i1 > ref2; j = ref1 <= ref2 ? ++i1 : --i1) {
|
| 8761 | if (stack[s + j] === symbol(NIL)) {
|
| 8762 | continue;
|
| 8763 | }
|
| 8764 | sfac_product_f(s, i, j);
|
| 8765 | }
|
| 8766 | }
|
| 8767 | push(one);
|
| 8768 | for (i = j1 = 0, ref3 = n; 0 <= ref3 ? j1 < ref3 : j1 > ref3; i = 0 <= ref3 ? ++j1 : --j1) {
|
| 8769 | if (stack[s + i] === symbol(NIL)) {
|
| 8770 | continue;
|
| 8771 | }
|
| 8772 | push(stack[s + i]);
|
| 8773 | multiply();
|
| 8774 | }
|
| 8775 | p1 = pop();
|
| 8776 | moveTos(tos - n);
|
| 8777 | return push(p1);
|
| 8778 | };
|
| 8779 |
|
| 8780 | sfac_product_f = function(s, a, b) {
|
| 8781 | var i, n, o, ref;
|
| 8782 | i = 0;
|
| 8783 | n = 0;
|
| 8784 | p1 = stack[s + a];
|
| 8785 | p2 = stack[s + b];
|
| 8786 | if (ispower(p1)) {
|
| 8787 | p3 = caddr(p1);
|
| 8788 | p1 = cadr(p1);
|
| 8789 | } else {
|
| 8790 | p3 = one;
|
| 8791 | }
|
| 8792 | if (ispower(p2)) {
|
| 8793 | p4 = caddr(p2);
|
| 8794 | p2 = cadr(p2);
|
| 8795 | } else {
|
| 8796 | p4 = one;
|
| 8797 | }
|
| 8798 | if (isfactorial(p1) && isfactorial(p2)) {
|
| 8799 | push(p3);
|
| 8800 | push(p4);
|
| 8801 | add();
|
| 8802 | yyexpand();
|
| 8803 | n = pop_integer();
|
| 8804 | if (n !== 0) {
|
| 8805 | return;
|
| 8806 | }
|
| 8807 | push(cadr(p1));
|
| 8808 | push(cadr(p2));
|
| 8809 | subtract();
|
| 8810 | yyexpand();
|
| 8811 | n = pop_integer();
|
| 8812 | if (n === 0 || isNaN(n)) {
|
| 8813 | return;
|
| 8814 | }
|
| 8815 | if (n < 0) {
|
| 8816 | n = -n;
|
| 8817 | p5 = p1;
|
| 8818 | p1 = p2;
|
| 8819 | p2 = p5;
|
| 8820 | p5 = p3;
|
| 8821 | p3 = p4;
|
| 8822 | p4 = p5;
|
| 8823 | }
|
| 8824 | push(one);
|
| 8825 | for (i = o = 1, ref = n; 1 <= ref ? o <= ref : o >= ref; i = 1 <= ref ? ++o : --o) {
|
| 8826 | push(cadr(p2));
|
| 8827 | push_integer(i);
|
| 8828 | add();
|
| 8829 | push(p3);
|
| 8830 | power();
|
| 8831 | multiply();
|
| 8832 | }
|
| 8833 | stack[s + a] = pop();
|
| 8834 | return stack[s + b] = symbol(NIL);
|
| 8835 | }
|
| 8836 | };
|
| 8837 |
|
| 8838 | polycoeff = 0;
|
| 8839 |
|
| 8840 | factpoly_expo = 0;
|
| 8841 |
|
| 8842 | factorpoly = function() {
|
| 8843 | save();
|
| 8844 | p2 = pop();
|
| 8845 | p1 = pop();
|
| 8846 | if (!Find(p1, p2)) {
|
| 8847 | push(p1);
|
| 8848 | restore();
|
| 8849 | return;
|
| 8850 | }
|
| 8851 | if (!ispoly(p1, p2)) {
|
| 8852 | push(p1);
|
| 8853 | restore();
|
| 8854 | return;
|
| 8855 | }
|
| 8856 | if (!issymbol(p2)) {
|
| 8857 | push(p1);
|
| 8858 | restore();
|
| 8859 | return;
|
| 8860 | }
|
| 8861 | push(p1);
|
| 8862 | push(p2);
|
| 8863 | yyfactorpoly();
|
| 8864 | return restore();
|
| 8865 | };
|
| 8866 |
|
| 8867 | yyfactorpoly = function() {
|
| 8868 | var checkingTheDivision, dividend, foundComplexRoot, foundRealRoot, h, i, i1, j1, l1, o, prev_expanding, previousFactorisation, ref, ref1, ref2, ref3, remainingPoly, whichRootsAreWeFinding;
|
| 8869 | h = 0;
|
| 8870 | i = 0;
|
| 8871 | save();
|
| 8872 | p2 = pop();
|
| 8873 | p1 = pop();
|
| 8874 | h = tos;
|
| 8875 | if (isfloating(p1)) {
|
| 8876 | stop("floating point numbers in polynomial");
|
| 8877 | }
|
| 8878 | polycoeff = tos;
|
| 8879 | push(p1);
|
| 8880 | push(p2);
|
| 8881 | factpoly_expo = coeff() - 1;
|
| 8882 | rationalize_coefficients(h);
|
| 8883 | whichRootsAreWeFinding = "real";
|
| 8884 | remainingPoly = null;
|
| 8885 | while (factpoly_expo > 0) {
|
| 8886 | if (iszero(stack[polycoeff + 0])) {
|
| 8887 | push_integer(1);
|
| 8888 | p4 = pop();
|
| 8889 | push_integer(0);
|
| 8890 | p5 = pop();
|
| 8891 | } else {
|
| 8892 | if (whichRootsAreWeFinding === "real") {
|
| 8893 | foundRealRoot = get_factor_from_real_root();
|
| 8894 | } else if (whichRootsAreWeFinding === "complex") {
|
| 8895 | foundComplexRoot = get_factor_from_complex_root(remainingPoly);
|
| 8896 | }
|
| 8897 | }
|
| 8898 | if (whichRootsAreWeFinding === "real") {
|
| 8899 | if (foundRealRoot === 0) {
|
| 8900 | whichRootsAreWeFinding = "complex";
|
| 8901 | continue;
|
| 8902 | } else {
|
| 8903 | push(p4);
|
| 8904 | push(p2);
|
| 8905 | multiply();
|
| 8906 | push(p5);
|
| 8907 | add();
|
| 8908 | p8 = pop();
|
| 8909 | if (DEBUG) {
|
| 8910 | console.log("success\nFACTOR=" + p8);
|
| 8911 | }
|
| 8912 |
|
| 8913 | |
| 8914 | |
| 8915 | |
| 8916 | |
| 8917 | |
| 8918 | |
| 8919 | |
| 8920 | |
| 8921 |
|
| 8922 | push(p7);
|
| 8923 | push(p8);
|
| 8924 | multiply_noexpand();
|
| 8925 | p7 = pop();
|
| 8926 | yydivpoly();
|
| 8927 | while (factpoly_expo && iszero(stack[polycoeff + factpoly_expo])) {
|
| 8928 | factpoly_expo--;
|
| 8929 | }
|
| 8930 | push(zero);
|
| 8931 | for (i = o = 0, ref = factpoly_expo; 0 <= ref ? o <= ref : o >= ref; i = 0 <= ref ? ++o : --o) {
|
| 8932 | push(stack[polycoeff + i]);
|
| 8933 | push(p2);
|
| 8934 | push_integer(i);
|
| 8935 | power();
|
| 8936 | multiply();
|
| 8937 | add();
|
| 8938 | }
|
| 8939 | remainingPoly = pop();
|
| 8940 | }
|
| 8941 | } else if (whichRootsAreWeFinding === "complex") {
|
| 8942 | if (foundComplexRoot === 0) {
|
| 8943 | break;
|
| 8944 | } else {
|
| 8945 | push(p4);
|
| 8946 | push(p2);
|
| 8947 | subtract();
|
| 8948 | push(p4);
|
| 8949 | conjugate();
|
| 8950 | push(p2);
|
| 8951 | subtract();
|
| 8952 | multiply();
|
| 8953 | p8 = pop();
|
| 8954 | if (DEBUG) {
|
| 8955 | console.log("success\nFACTOR=" + p8);
|
| 8956 | }
|
| 8957 |
|
| 8958 | |
| 8959 | |
| 8960 | |
| 8961 | |
| 8962 | |
| 8963 | |
| 8964 | |
| 8965 | |
| 8966 |
|
| 8967 | push(p7);
|
| 8968 | previousFactorisation = pop();
|
| 8969 | push(p7);
|
| 8970 | push(p8);
|
| 8971 | multiply_noexpand();
|
| 8972 | p7 = pop();
|
| 8973 | if (remainingPoly == null) {
|
| 8974 | push(zero);
|
| 8975 | for (i = i1 = 0, ref1 = factpoly_expo; 0 <= ref1 ? i1 <= ref1 : i1 >= ref1; i = 0 <= ref1 ? ++i1 : --i1) {
|
| 8976 | push(stack[polycoeff + i]);
|
| 8977 | push(p2);
|
| 8978 | push_integer(i);
|
| 8979 | power();
|
| 8980 | multiply();
|
| 8981 | add();
|
| 8982 | }
|
| 8983 | remainingPoly = pop();
|
| 8984 | }
|
| 8985 | dividend = remainingPoly;
|
| 8986 | push(dividend);
|
| 8987 | push(p8);
|
| 8988 | push(p2);
|
| 8989 | divpoly();
|
| 8990 | remainingPoly = pop();
|
| 8991 | push(remainingPoly);
|
| 8992 | push(p8);
|
| 8993 | multiply();
|
| 8994 | checkingTheDivision = pop();
|
| 8995 | if (!equal(checkingTheDivision, dividend)) {
|
| 8996 | if (DEBUG) {
|
| 8997 | console.log("we found a polynomial based on complex root and its conj but it doesn't divide the poly, quitting");
|
| 8998 | }
|
| 8999 | if (DEBUG) {
|
| 9000 | console.log("so just returning previousFactorisation times dividend: " + previousFactorisation + " * " + dividend);
|
| 9001 | }
|
| 9002 | push(previousFactorisation);
|
| 9003 | push(dividend);
|
| 9004 | prev_expanding = expanding;
|
| 9005 | expanding = 0;
|
| 9006 | yycondense();
|
| 9007 | expanding = prev_expanding;
|
| 9008 | multiply_noexpand();
|
| 9009 | p7 = pop();
|
| 9010 | stack[h] = p7;
|
| 9011 | moveTos(h + 1);
|
| 9012 | restore();
|
| 9013 | return;
|
| 9014 | }
|
| 9015 |
|
| 9016 | |
| 9017 | |
| 9018 | |
| 9019 | |
| 9020 | |
| 9021 | |
| 9022 | |
| 9023 | |
| 9024 |
|
| 9025 | for (i = j1 = 0, ref2 = factpoly_expo; 0 <= ref2 ? j1 <= ref2 : j1 >= ref2; i = 0 <= ref2 ? ++j1 : --j1) {
|
| 9026 | pop();
|
| 9027 | }
|
| 9028 | push(remainingPoly);
|
| 9029 | push(p2);
|
| 9030 | coeff();
|
| 9031 | factpoly_expo -= 2;
|
| 9032 | }
|
| 9033 | }
|
| 9034 | }
|
| 9035 | push(zero);
|
| 9036 | for (i = l1 = 0, ref3 = factpoly_expo; 0 <= ref3 ? l1 <= ref3 : l1 >= ref3; i = 0 <= ref3 ? ++l1 : --l1) {
|
| 9037 | push(stack[polycoeff + i]);
|
| 9038 | push(p2);
|
| 9039 | push_integer(i);
|
| 9040 | power();
|
| 9041 | multiply();
|
| 9042 | add();
|
| 9043 | }
|
| 9044 | p1 = pop();
|
| 9045 | if (DEBUG) {
|
| 9046 | console.log("POLY=" + p1);
|
| 9047 | }
|
| 9048 | push(p1);
|
| 9049 | prev_expanding = expanding;
|
| 9050 | expanding = 0;
|
| 9051 | yycondense();
|
| 9052 | expanding = prev_expanding;
|
| 9053 | p1 = pop();
|
| 9054 | if (factpoly_expo > 0 && isnegativeterm(stack[polycoeff + factpoly_expo])) {
|
| 9055 | push(p1);
|
| 9056 | negate();
|
| 9057 | p1 = pop();
|
| 9058 | push(p7);
|
| 9059 | negate_noexpand();
|
| 9060 | p7 = pop();
|
| 9061 | }
|
| 9062 | push(p7);
|
| 9063 | push(p1);
|
| 9064 | multiply_noexpand();
|
| 9065 | p7 = pop();
|
| 9066 | if (DEBUG) {
|
| 9067 | console.log("RESULT=" + p7);
|
| 9068 | }
|
| 9069 | stack[h] = p7;
|
| 9070 | moveTos(h + 1);
|
| 9071 | return restore();
|
| 9072 | };
|
| 9073 |
|
| 9074 | rationalize_coefficients = function(h) {
|
| 9075 | var i, i1, o, ref, ref1, ref2, ref3;
|
| 9076 | i = 0;
|
| 9077 | p7 = one;
|
| 9078 | for (i = o = ref = h, ref1 = tos; ref <= ref1 ? o < ref1 : o > ref1; i = ref <= ref1 ? ++o : --o) {
|
| 9079 | push(stack[i]);
|
| 9080 | denominator();
|
| 9081 | push(p7);
|
| 9082 | lcm();
|
| 9083 | p7 = pop();
|
| 9084 | }
|
| 9085 | for (i = i1 = ref2 = h, ref3 = tos; ref2 <= ref3 ? i1 < ref3 : i1 > ref3; i = ref2 <= ref3 ? ++i1 : --i1) {
|
| 9086 | push(p7);
|
| 9087 | push(stack[i]);
|
| 9088 | multiply();
|
| 9089 | stack[i] = pop();
|
| 9090 | }
|
| 9091 | push(p7);
|
| 9092 | reciprocate();
|
| 9093 | p7 = pop();
|
| 9094 | if (DEBUG) {
|
| 9095 | return console.log("rationalize_coefficients result");
|
| 9096 | }
|
| 9097 | };
|
| 9098 |
|
| 9099 | get_factor_from_real_root = function() {
|
| 9100 | var a0, an, h, i, i1, j, j1, l1, m1, na0, nan, o, ref, ref1, ref2, ref3, ref4, rootsTries_i, rootsTries_j;
|
| 9101 | i = 0;
|
| 9102 | j = 0;
|
| 9103 | h = 0;
|
| 9104 | a0 = 0;
|
| 9105 | an = 0;
|
| 9106 | na0 = 0;
|
| 9107 | nan = 0;
|
| 9108 | if (DEBUG) {
|
| 9109 | push(zero);
|
| 9110 | for (i = o = 0, ref = factpoly_expo; 0 <= ref ? o <= ref : o >= ref; i = 0 <= ref ? ++o : --o) {
|
| 9111 | push(stack[polycoeff + i]);
|
| 9112 | push(p2);
|
| 9113 | push_integer(i);
|
| 9114 | power();
|
| 9115 | multiply();
|
| 9116 | add();
|
| 9117 | }
|
| 9118 | p1 = pop();
|
| 9119 | console.log("POLY=" + p1);
|
| 9120 | }
|
| 9121 | h = tos;
|
| 9122 | an = tos;
|
| 9123 | push(stack[polycoeff + factpoly_expo]);
|
| 9124 | divisors_onstack();
|
| 9125 | nan = tos - an;
|
| 9126 | a0 = tos;
|
| 9127 | push(stack[polycoeff + 0]);
|
| 9128 | divisors_onstack();
|
| 9129 | na0 = tos - a0;
|
| 9130 | if (DEBUG) {
|
| 9131 | console.log("divisors of base term");
|
| 9132 | for (i = i1 = 0, ref1 = na0; 0 <= ref1 ? i1 < ref1 : i1 > ref1; i = 0 <= ref1 ? ++i1 : --i1) {
|
| 9133 | console.log(", " + stack[a0 + i]);
|
| 9134 | }
|
| 9135 | console.log("divisors of leading term");
|
| 9136 | for (i = j1 = 0, ref2 = nan; 0 <= ref2 ? j1 < ref2 : j1 > ref2; i = 0 <= ref2 ? ++j1 : --j1) {
|
| 9137 | console.log(", " + stack[an + i]);
|
| 9138 | }
|
| 9139 | }
|
| 9140 | for (rootsTries_i = l1 = 0, ref3 = nan; 0 <= ref3 ? l1 < ref3 : l1 > ref3; rootsTries_i = 0 <= ref3 ? ++l1 : --l1) {
|
| 9141 | for (rootsTries_j = m1 = 0, ref4 = na0; 0 <= ref4 ? m1 < ref4 : m1 > ref4; rootsTries_j = 0 <= ref4 ? ++m1 : --m1) {
|
| 9142 | p4 = stack[an + rootsTries_i];
|
| 9143 | p5 = stack[a0 + rootsTries_j];
|
| 9144 | push(p5);
|
| 9145 | push(p4);
|
| 9146 | divide();
|
| 9147 | negate();
|
| 9148 | p3 = pop();
|
| 9149 | Evalpoly();
|
| 9150 | if (DEBUG) {
|
| 9151 | console.log("try A=" + p4);
|
| 9152 | console.log(", B=" + p5);
|
| 9153 | console.log(", root " + p2);
|
| 9154 | console.log("=-B/A=" + p3);
|
| 9155 | console.log(", POLY(" + p3);
|
| 9156 | console.log(")=" + p6);
|
| 9157 | }
|
| 9158 | if (iszero(p6)) {
|
| 9159 | moveTos(h);
|
| 9160 | if (DEBUG) {
|
| 9161 | console.log("get_factor_from_real_root returning 1");
|
| 9162 | }
|
| 9163 | return 1;
|
| 9164 | }
|
| 9165 | push(p5);
|
| 9166 | negate();
|
| 9167 | p5 = pop();
|
| 9168 | push(p3);
|
| 9169 | negate();
|
| 9170 | p3 = pop();
|
| 9171 | Evalpoly();
|
| 9172 | if (DEBUG) {
|
| 9173 | console.log("try A=" + p4);
|
| 9174 | console.log(", B=" + p5);
|
| 9175 | console.log(", root " + p2);
|
| 9176 | console.log("=-B/A=" + p3);
|
| 9177 | console.log(", POLY(" + p3);
|
| 9178 | console.log(")=" + p6);
|
| 9179 | }
|
| 9180 | if (iszero(p6)) {
|
| 9181 | moveTos(h);
|
| 9182 | if (DEBUG) {
|
| 9183 | console.log("get_factor_from_real_root returning 1");
|
| 9184 | }
|
| 9185 | return 1;
|
| 9186 | }
|
| 9187 | }
|
| 9188 | }
|
| 9189 | moveTos(h);
|
| 9190 | if (DEBUG) {
|
| 9191 | console.log("get_factor_from_real_root returning 0");
|
| 9192 | }
|
| 9193 | return 0;
|
| 9194 | };
|
| 9195 |
|
| 9196 | get_factor_from_complex_root = function(remainingPoly) {
|
| 9197 | var a0, an, h, i, i1, j, na0, nan, o, rootsTries_i, rootsTries_j;
|
| 9198 | i = 0;
|
| 9199 | j = 0;
|
| 9200 | h = 0;
|
| 9201 | a0 = 0;
|
| 9202 | an = 0;
|
| 9203 | na0 = 0;
|
| 9204 | nan = 0;
|
| 9205 | if (factpoly_expo <= 2) {
|
| 9206 | if (DEBUG) {
|
| 9207 | console.log("no more factoring via complex roots to be found in polynomial of degree <= 2");
|
| 9208 | }
|
| 9209 | return 0;
|
| 9210 | }
|
| 9211 | p1 = remainingPoly;
|
| 9212 | if (DEBUG) {
|
| 9213 | console.log("complex root finding for POLY=" + p1);
|
| 9214 | }
|
| 9215 | h = tos;
|
| 9216 | an = tos;
|
| 9217 | push_integer(-1);
|
| 9218 | push_rational(2, 3);
|
| 9219 | power();
|
| 9220 | rect();
|
| 9221 | p4 = pop();
|
| 9222 | if (DEBUG) {
|
| 9223 | console.log("complex root finding: trying with " + p4);
|
| 9224 | }
|
| 9225 | push(p4);
|
| 9226 | p3 = pop();
|
| 9227 | push(p3);
|
| 9228 | Evalpoly();
|
| 9229 | if (DEBUG) {
|
| 9230 | console.log("complex root finding result: " + p6);
|
| 9231 | }
|
| 9232 | if (iszero(p6)) {
|
| 9233 | moveTos(h);
|
| 9234 | if (DEBUG) {
|
| 9235 | console.log("get_factor_from_complex_root returning 1");
|
| 9236 | }
|
| 9237 | return 1;
|
| 9238 | }
|
| 9239 | push_integer(1);
|
| 9240 | push_rational(2, 3);
|
| 9241 | power();
|
| 9242 | rect();
|
| 9243 | p4 = pop();
|
| 9244 | if (DEBUG) {
|
| 9245 | console.log("complex root finding: trying with " + p4);
|
| 9246 | }
|
| 9247 | push(p4);
|
| 9248 | p3 = pop();
|
| 9249 | push(p3);
|
| 9250 | Evalpoly();
|
| 9251 | if (DEBUG) {
|
| 9252 | console.log("complex root finding result: " + p6);
|
| 9253 | }
|
| 9254 | if (iszero(p6)) {
|
| 9255 | moveTos(h);
|
| 9256 | if (DEBUG) {
|
| 9257 | console.log("get_factor_from_complex_root returning 1");
|
| 9258 | }
|
| 9259 | return 1;
|
| 9260 | }
|
| 9261 | for (rootsTries_i = o = -10; o <= 10; rootsTries_i = ++o) {
|
| 9262 | for (rootsTries_j = i1 = 1; i1 <= 5; rootsTries_j = ++i1) {
|
| 9263 | push_integer(rootsTries_i);
|
| 9264 | push_integer(rootsTries_j);
|
| 9265 | push(imaginaryunit);
|
| 9266 | multiply();
|
| 9267 | add();
|
| 9268 | rect();
|
| 9269 | p4 = pop();
|
| 9270 | push(p4);
|
| 9271 | p3 = pop();
|
| 9272 | push(p3);
|
| 9273 | Evalpoly();
|
| 9274 | if (iszero(p6)) {
|
| 9275 | moveTos(h);
|
| 9276 | if (DEBUG) {
|
| 9277 | console.log("found complex root: " + p6);
|
| 9278 | }
|
| 9279 | return 1;
|
| 9280 | }
|
| 9281 | }
|
| 9282 | }
|
| 9283 | moveTos(h);
|
| 9284 | if (DEBUG) {
|
| 9285 | console.log("get_factor_from_complex_root returning 0");
|
| 9286 | }
|
| 9287 | return 0;
|
| 9288 | };
|
| 9289 |
|
| 9290 | yydivpoly = function() {
|
| 9291 | var i, o, ref;
|
| 9292 | i = 0;
|
| 9293 | p6 = zero;
|
| 9294 | for (i = o = ref = factpoly_expo; ref <= 0 ? o < 0 : o > 0; i = ref <= 0 ? ++o : --o) {
|
| 9295 | push(stack[polycoeff + i]);
|
| 9296 | stack[polycoeff + i] = p6;
|
| 9297 | push(p4);
|
| 9298 | divide();
|
| 9299 | p6 = pop();
|
| 9300 | push(stack[polycoeff + i - 1]);
|
| 9301 | push(p6);
|
| 9302 | push(p5);
|
| 9303 | multiply();
|
| 9304 | subtract();
|
| 9305 | stack[polycoeff + i - 1] = pop();
|
| 9306 | }
|
| 9307 | stack[polycoeff + 0] = p6;
|
| 9308 | if (DEBUG) {
|
| 9309 | return console.log("yydivpoly Q:");
|
| 9310 | }
|
| 9311 | };
|
| 9312 |
|
| 9313 | Evalpoly = function() {
|
| 9314 | var i, o, ref;
|
| 9315 | i = 0;
|
| 9316 | push(zero);
|
| 9317 | for (i = o = ref = factpoly_expo; ref <= 0 ? o <= 0 : o >= 0; i = ref <= 0 ? ++o : --o) {
|
| 9318 | push(p3);
|
| 9319 | multiply();
|
| 9320 | push(stack[polycoeff + i]);
|
| 9321 | if (DEBUG) {
|
| 9322 | console.log("Evalpoly top of stack:");
|
| 9323 | console.log(print_list(stack[tos - i]));
|
| 9324 | }
|
| 9325 | add();
|
| 9326 | }
|
| 9327 | return p6 = pop();
|
| 9328 | };
|
| 9329 |
|
| 9330 | factors = function(p) {
|
| 9331 | var h;
|
| 9332 | h = tos;
|
| 9333 | if (car(p) === symbol(ADD)) {
|
| 9334 | p = cdr(p);
|
| 9335 | while (iscons(p)) {
|
| 9336 | push_term_factors(car(p));
|
| 9337 | p = cdr(p);
|
| 9338 | }
|
| 9339 | } else {
|
| 9340 | push_term_factors(p);
|
| 9341 | }
|
| 9342 | return tos - h;
|
| 9343 | };
|
| 9344 |
|
| 9345 | push_term_factors = function(p) {
|
| 9346 | var results;
|
| 9347 | if (car(p) === symbol(MULTIPLY)) {
|
| 9348 | p = cdr(p);
|
| 9349 | results = [];
|
| 9350 | while (iscons(p)) {
|
| 9351 | push(car(p));
|
| 9352 | results.push(p = cdr(p));
|
| 9353 | }
|
| 9354 | return results;
|
| 9355 | } else {
|
| 9356 | return push(p);
|
| 9357 | }
|
| 9358 | };
|
| 9359 |
|
| 9360 |
|
| 9361 | |
| 9362 | |
| 9363 | |
| 9364 | |
| 9365 | |
| 9366 | |
| 9367 |
|
| 9368 |
|
| 9369 | Eval_filter = function() {
|
| 9370 | var results;
|
| 9371 | p1 = cdr(p1);
|
| 9372 | push(car(p1));
|
| 9373 | Eval();
|
| 9374 | p1 = cdr(p1);
|
| 9375 | results = [];
|
| 9376 | while (iscons(p1)) {
|
| 9377 | push(car(p1));
|
| 9378 | Eval();
|
| 9379 | filter();
|
| 9380 | results.push(p1 = cdr(p1));
|
| 9381 | }
|
| 9382 | return results;
|
| 9383 | };
|
| 9384 |
|
| 9385 |
|
| 9386 | |
| 9387 | |
| 9388 | |
| 9389 | |
| 9390 | |
| 9391 | |
| 9392 | |
| 9393 |
|
| 9394 |
|
| 9395 | filter = function() {
|
| 9396 | save();
|
| 9397 | p2 = pop();
|
| 9398 | p1 = pop();
|
| 9399 | filter_main();
|
| 9400 | return restore();
|
| 9401 | };
|
| 9402 |
|
| 9403 | filter_main = function() {
|
| 9404 | if (car(p1) === symbol(ADD)) {
|
| 9405 | return filter_sum();
|
| 9406 | } else if (istensor(p1)) {
|
| 9407 | return filter_tensor();
|
| 9408 | } else if (Find(p1, p2)) {
|
| 9409 | return push_integer(0);
|
| 9410 | } else {
|
| 9411 | return push(p1);
|
| 9412 | }
|
| 9413 | };
|
| 9414 |
|
| 9415 | filter_sum = function() {
|
| 9416 | var results;
|
| 9417 | push_integer(0);
|
| 9418 | p1 = cdr(p1);
|
| 9419 | results = [];
|
| 9420 | while (iscons(p1)) {
|
| 9421 | push(car(p1));
|
| 9422 | push(p2);
|
| 9423 | filter();
|
| 9424 | add();
|
| 9425 | results.push(p1 = cdr(p1));
|
| 9426 | }
|
| 9427 | return results;
|
| 9428 | };
|
| 9429 |
|
| 9430 | filter_tensor = function() {
|
| 9431 | var i, i1, n, o, ref, ref1;
|
| 9432 | i = 0;
|
| 9433 | n = 0;
|
| 9434 | n = p1.tensor.nelem;
|
| 9435 | p3 = alloc_tensor(n);
|
| 9436 | p3.tensor.ndim = p1.tensor.ndim;
|
| 9437 | for (i = o = 0, ref = p1.tensor.ndim; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 9438 | p3.tensor.dim[i] = p1.tensor.dim[i];
|
| 9439 | }
|
| 9440 | for (i = i1 = 0, ref1 = n; 0 <= ref1 ? i1 < ref1 : i1 > ref1; i = 0 <= ref1 ? ++i1 : --i1) {
|
| 9441 | push(p1.tensor.elem[i]);
|
| 9442 | push(p2);
|
| 9443 | filter();
|
| 9444 | p3.tensor.elem[i] = pop();
|
| 9445 | }
|
| 9446 | return push(p3);
|
| 9447 | };
|
| 9448 |
|
| 9449 | Eval_float = function() {
|
| 9450 | evaluatingAsFloats++;
|
| 9451 | push(cadr(p1));
|
| 9452 | Eval();
|
| 9453 | yyfloat();
|
| 9454 | Eval();
|
| 9455 | return evaluatingAsFloats--;
|
| 9456 | };
|
| 9457 |
|
| 9458 | checkFloatHasWorkedOutCompletely = function(nodeToCheck) {
|
| 9459 | var numberOfEs, numberOfMults, numberOfPIs, numberOfPowers, numberOfSums;
|
| 9460 | numberOfPowers = countOccurrencesOfSymbol(symbol(POWER), nodeToCheck);
|
| 9461 | numberOfPIs = countOccurrencesOfSymbol(symbol(PI), nodeToCheck);
|
| 9462 | numberOfEs = countOccurrencesOfSymbol(symbol(E), nodeToCheck);
|
| 9463 | numberOfMults = countOccurrencesOfSymbol(symbol(MULTIPLY), nodeToCheck);
|
| 9464 | numberOfSums = countOccurrencesOfSymbol(symbol(ADD), nodeToCheck);
|
| 9465 | if (DEBUG) {
|
| 9466 | console.log(" ... numberOfPowers: " + numberOfPowers);
|
| 9467 | console.log(" ... numberOfPIs: " + numberOfPIs);
|
| 9468 | console.log(" ... numberOfEs: " + numberOfEs);
|
| 9469 | console.log(" ... numberOfMults: " + numberOfMults);
|
| 9470 | console.log(" ... numberOfSums: " + numberOfSums);
|
| 9471 | }
|
| 9472 | if (numberOfPowers > 1 || numberOfPIs > 0 || numberOfEs > 0 || numberOfMults > 1 || numberOfSums > 1) {
|
| 9473 | return stop("float: some unevalued parts in " + nodeToCheck);
|
| 9474 | }
|
| 9475 | };
|
| 9476 |
|
| 9477 | zzfloat = function() {
|
| 9478 | save();
|
| 9479 | evaluatingAsFloats++;
|
| 9480 | Eval();
|
| 9481 | yyfloat();
|
| 9482 | Eval();
|
| 9483 | evaluatingAsFloats--;
|
| 9484 | return restore();
|
| 9485 | };
|
| 9486 |
|
| 9487 | yyfloat = function() {
|
| 9488 | var h, i, o, ref;
|
| 9489 | i = 0;
|
| 9490 | h = 0;
|
| 9491 | evaluatingAsFloats++;
|
| 9492 | save();
|
| 9493 | p1 = pop();
|
| 9494 | if (iscons(p1)) {
|
| 9495 | h = tos;
|
| 9496 | while (iscons(p1)) {
|
| 9497 | push(car(p1));
|
| 9498 | yyfloat();
|
| 9499 | p1 = cdr(p1);
|
| 9500 | }
|
| 9501 | list(tos - h);
|
| 9502 | } else if (p1.k === TENSOR) {
|
| 9503 | push(p1);
|
| 9504 | copy_tensor();
|
| 9505 | p1 = pop();
|
| 9506 | for (i = o = 0, ref = p1.tensor.nelem; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 9507 | push(p1.tensor.elem[i]);
|
| 9508 | yyfloat();
|
| 9509 | p1.tensor.elem[i] = pop();
|
| 9510 | }
|
| 9511 | push(p1);
|
| 9512 | } else if (p1.k === NUM) {
|
| 9513 | push(p1);
|
| 9514 | bignum_float();
|
| 9515 | } else if (p1 === symbol(PI)) {
|
| 9516 | push_double(Math.PI);
|
| 9517 | } else if (p1 === symbol(E)) {
|
| 9518 | push_double(Math.E);
|
| 9519 | } else {
|
| 9520 | push(p1);
|
| 9521 | }
|
| 9522 | restore();
|
| 9523 | return evaluatingAsFloats--;
|
| 9524 | };
|
| 9525 |
|
| 9526 | Eval_floor = function() {
|
| 9527 | push(cadr(p1));
|
| 9528 | Eval();
|
| 9529 | return yfloor();
|
| 9530 | };
|
| 9531 |
|
| 9532 | yfloor = function() {
|
| 9533 | save();
|
| 9534 | yyfloor();
|
| 9535 | return restore();
|
| 9536 | };
|
| 9537 |
|
| 9538 | yyfloor = function() {
|
| 9539 | var d;
|
| 9540 | d = 0.0;
|
| 9541 | p1 = pop();
|
| 9542 | if (!isnum(p1)) {
|
| 9543 | push_symbol(FLOOR);
|
| 9544 | push(p1);
|
| 9545 | list(2);
|
| 9546 | return;
|
| 9547 | }
|
| 9548 | if (isdouble(p1)) {
|
| 9549 | d = Math.floor(p1.d);
|
| 9550 | push_double(d);
|
| 9551 | return;
|
| 9552 | }
|
| 9553 | if (isinteger(p1)) {
|
| 9554 | push(p1);
|
| 9555 | return;
|
| 9556 | }
|
| 9557 | p3 = new U();
|
| 9558 | p3.k = NUM;
|
| 9559 | p3.q.a = mdiv(p1.q.a, p1.q.b);
|
| 9560 | p3.q.b = mint(1);
|
| 9561 | push(p3);
|
| 9562 | if (isnegativenumber(p1)) {
|
| 9563 | push_integer(-1);
|
| 9564 | return add();
|
| 9565 | }
|
| 9566 | };
|
| 9567 |
|
| 9568 |
|
| 9569 | |
| 9570 | |
| 9571 | |
| 9572 | |
| 9573 | |
| 9574 | |
| 9575 | |
| 9576 | |
| 9577 | |
| 9578 | |
| 9579 | |
| 9580 | |
| 9581 |
|
| 9582 |
|
| 9583 | Eval_for = function() {
|
| 9584 | var i, j, k, loopingVariable, o, ref, ref1;
|
| 9585 | i = 0;
|
| 9586 | j = 0;
|
| 9587 | k = 0;
|
| 9588 | loopingVariable = caddr(p1);
|
| 9589 | if (!issymbol(loopingVariable)) {
|
| 9590 | stop("for: 2nd arg should be the variable to loop over");
|
| 9591 | }
|
| 9592 | push(cadddr(p1));
|
| 9593 | Eval();
|
| 9594 | j = pop_integer();
|
| 9595 | if (isNaN(j)) {
|
| 9596 | push(p1);
|
| 9597 | return;
|
| 9598 | }
|
| 9599 | push(caddddr(p1));
|
| 9600 | Eval();
|
| 9601 | k = pop_integer();
|
| 9602 | if (isNaN(k)) {
|
| 9603 | push(p1);
|
| 9604 | return;
|
| 9605 | }
|
| 9606 | p4 = get_binding(loopingVariable);
|
| 9607 | for (i = o = ref = j, ref1 = k; ref <= ref1 ? o <= ref1 : o >= ref1; i = ref <= ref1 ? ++o : --o) {
|
| 9608 | push_integer(i);
|
| 9609 | p5 = pop();
|
| 9610 | set_binding(loopingVariable, p5);
|
| 9611 | push(cadr(p1));
|
| 9612 | Eval();
|
| 9613 | pop();
|
| 9614 | }
|
| 9615 | set_binding(loopingVariable, p4);
|
| 9616 | return push_symbol(NIL);
|
| 9617 | };
|
| 9618 |
|
| 9619 | Eval_gamma = function() {
|
| 9620 | push(cadr(p1));
|
| 9621 | Eval();
|
| 9622 | return gamma();
|
| 9623 | };
|
| 9624 |
|
| 9625 | gamma = function() {
|
| 9626 | save();
|
| 9627 | gammaf();
|
| 9628 | return restore();
|
| 9629 | };
|
| 9630 |
|
| 9631 | gammaf = function() {
|
| 9632 | p1 = pop();
|
| 9633 | if (isrational(p1) && MEQUAL(p1.q.a, 1) && MEQUAL(p1.q.b, 2)) {
|
| 9634 | if (evaluatingAsFloats) {
|
| 9635 | push_double(Math.PI);
|
| 9636 | } else {
|
| 9637 | push_symbol(PI);
|
| 9638 | }
|
| 9639 | push_rational(1, 2);
|
| 9640 | power();
|
| 9641 | return;
|
| 9642 | }
|
| 9643 | if (isrational(p1) && MEQUAL(p1.q.a, 3) && MEQUAL(p1.q.b, 2)) {
|
| 9644 | if (evaluatingAsFloats) {
|
| 9645 | push_double(Math.PI);
|
| 9646 | } else {
|
| 9647 | push_symbol(PI);
|
| 9648 | }
|
| 9649 | push_rational(1, 2);
|
| 9650 | power();
|
| 9651 | push_rational(1, 2);
|
| 9652 | multiply();
|
| 9653 | return;
|
| 9654 | }
|
| 9655 | if (isnegativeterm(p1)) {
|
| 9656 | if (evaluatingAsFloats) {
|
| 9657 | push_double(Math.PI);
|
| 9658 | } else {
|
| 9659 | push_symbol(PI);
|
| 9660 | }
|
| 9661 | push_integer(-1);
|
| 9662 | multiply();
|
| 9663 | if (evaluatingAsFloats) {
|
| 9664 | push_double(Math.PI);
|
| 9665 | } else {
|
| 9666 | push_symbol(PI);
|
| 9667 | }
|
| 9668 | push(p1);
|
| 9669 | multiply();
|
| 9670 | sine();
|
| 9671 | push(p1);
|
| 9672 | multiply();
|
| 9673 | push(p1);
|
| 9674 | negate();
|
| 9675 | gamma();
|
| 9676 | multiply();
|
| 9677 | divide();
|
| 9678 | return;
|
| 9679 | }
|
| 9680 | if (car(p1) === symbol(ADD)) {
|
| 9681 | gamma_of_sum();
|
| 9682 | return;
|
| 9683 | }
|
| 9684 | push_symbol(GAMMA);
|
| 9685 | push(p1);
|
| 9686 | list(2);
|
| 9687 | };
|
| 9688 |
|
| 9689 | gamma_of_sum = function() {
|
| 9690 | p3 = cdr(p1);
|
| 9691 | if (isrational(car(p3)) && MEQUAL(car(p3).q.a, 1) && MEQUAL(car(p3).q.b, 1)) {
|
| 9692 | push(cadr(p3));
|
| 9693 | push(cadr(p3));
|
| 9694 | gamma();
|
| 9695 | return multiply();
|
| 9696 | } else {
|
| 9697 | if (isrational(car(p3)) && MEQUAL(car(p3).q.a, -1) && MEQUAL(car(p3).q.b, 1)) {
|
| 9698 | push(cadr(p3));
|
| 9699 | gamma();
|
| 9700 | push(cadr(p3));
|
| 9701 | push_integer(-1);
|
| 9702 | add();
|
| 9703 | return divide();
|
| 9704 | } else {
|
| 9705 | push_symbol(GAMMA);
|
| 9706 | push(p1);
|
| 9707 | list(2);
|
| 9708 | }
|
| 9709 | }
|
| 9710 | };
|
| 9711 |
|
| 9712 | Eval_gcd = function() {
|
| 9713 | var results;
|
| 9714 | p1 = cdr(p1);
|
| 9715 | push(car(p1));
|
| 9716 | Eval();
|
| 9717 | p1 = cdr(p1);
|
| 9718 | results = [];
|
| 9719 | while (iscons(p1)) {
|
| 9720 | push(car(p1));
|
| 9721 | Eval();
|
| 9722 | gcd();
|
| 9723 | results.push(p1 = cdr(p1));
|
| 9724 | }
|
| 9725 | return results;
|
| 9726 | };
|
| 9727 |
|
| 9728 | gcd = function() {
|
| 9729 | var prev_expanding;
|
| 9730 | prev_expanding = expanding;
|
| 9731 | save();
|
| 9732 | gcd_main();
|
| 9733 | restore();
|
| 9734 | return expanding = prev_expanding;
|
| 9735 | };
|
| 9736 |
|
| 9737 | gcd_main = function() {
|
| 9738 | expanding = 1;
|
| 9739 | p2 = pop();
|
| 9740 | p1 = pop();
|
| 9741 | if (equal(p1, p2)) {
|
| 9742 | push(p1);
|
| 9743 | return;
|
| 9744 | }
|
| 9745 | if (isrational(p1) && isrational(p2)) {
|
| 9746 | push(p1);
|
| 9747 | push(p2);
|
| 9748 | gcd_numbers();
|
| 9749 | return;
|
| 9750 | }
|
| 9751 | if (car(p1) === symbol(ADD) && car(p2) === symbol(ADD)) {
|
| 9752 | gcd_expr_expr();
|
| 9753 | return;
|
| 9754 | }
|
| 9755 | if (car(p1) === symbol(ADD)) {
|
| 9756 | gcd_expr(p1);
|
| 9757 | p1 = pop();
|
| 9758 | }
|
| 9759 | if (car(p2) === symbol(ADD)) {
|
| 9760 | gcd_expr(p2);
|
| 9761 | p2 = pop();
|
| 9762 | }
|
| 9763 | if (car(p1) === symbol(MULTIPLY) && car(p2) === symbol(MULTIPLY)) {
|
| 9764 | gcd_term_term();
|
| 9765 | return;
|
| 9766 | }
|
| 9767 | if (car(p1) === symbol(MULTIPLY)) {
|
| 9768 | gcd_term_factor();
|
| 9769 | return;
|
| 9770 | }
|
| 9771 | if (car(p2) === symbol(MULTIPLY)) {
|
| 9772 | gcd_factor_term();
|
| 9773 | return;
|
| 9774 | }
|
| 9775 | if (car(p1) === symbol(POWER)) {
|
| 9776 | p3 = caddr(p1);
|
| 9777 | p1 = cadr(p1);
|
| 9778 | } else {
|
| 9779 | p3 = one;
|
| 9780 | }
|
| 9781 | if (car(p2) === symbol(POWER)) {
|
| 9782 | p4 = caddr(p2);
|
| 9783 | p2 = cadr(p2);
|
| 9784 | } else {
|
| 9785 | p4 = one;
|
| 9786 | }
|
| 9787 | if (!equal(p1, p2)) {
|
| 9788 | push(one);
|
| 9789 | return;
|
| 9790 | }
|
| 9791 | if (isnum(p3) && isnum(p4)) {
|
| 9792 | push(p1);
|
| 9793 | if (lessp(p3, p4)) {
|
| 9794 | push(p3);
|
| 9795 | } else {
|
| 9796 | push(p4);
|
| 9797 | }
|
| 9798 | power();
|
| 9799 | return;
|
| 9800 | }
|
| 9801 | push(p3);
|
| 9802 | push(p4);
|
| 9803 | divide();
|
| 9804 | p5 = pop();
|
| 9805 | if (isnum(p5)) {
|
| 9806 | push(p1);
|
| 9807 | if (car(p3) === symbol(MULTIPLY) && isnum(cadr(p3))) {
|
| 9808 | p5 = cadr(p3);
|
| 9809 | } else {
|
| 9810 | p5 = one;
|
| 9811 | }
|
| 9812 | if (car(p4) === symbol(MULTIPLY) && isnum(cadr(p4))) {
|
| 9813 | p6 = cadr(p4);
|
| 9814 | } else {
|
| 9815 | p6 = one;
|
| 9816 | }
|
| 9817 | if (lessp(p5, p6)) {
|
| 9818 | push(p3);
|
| 9819 | } else {
|
| 9820 | push(p4);
|
| 9821 | }
|
| 9822 | power();
|
| 9823 | return;
|
| 9824 | }
|
| 9825 | push(p3);
|
| 9826 | push(p4);
|
| 9827 | subtract();
|
| 9828 | p5 = pop();
|
| 9829 | if (!isnum(p5)) {
|
| 9830 | push(one);
|
| 9831 | return;
|
| 9832 | }
|
| 9833 | push(p1);
|
| 9834 | if (isnegativenumber(p5)) {
|
| 9835 | push(p3);
|
| 9836 | } else {
|
| 9837 | push(p4);
|
| 9838 | }
|
| 9839 | return power();
|
| 9840 | };
|
| 9841 |
|
| 9842 | gcd_expr_expr = function() {
|
| 9843 | if (length(p1) !== length(p2)) {
|
| 9844 | push(one);
|
| 9845 | return;
|
| 9846 | }
|
| 9847 | p3 = cdr(p1);
|
| 9848 | push(car(p3));
|
| 9849 | p3 = cdr(p3);
|
| 9850 | while (iscons(p3)) {
|
| 9851 | push(car(p3));
|
| 9852 | gcd();
|
| 9853 | p3 = cdr(p3);
|
| 9854 | }
|
| 9855 | p3 = pop();
|
| 9856 | p4 = cdr(p2);
|
| 9857 | push(car(p4));
|
| 9858 | p4 = cdr(p4);
|
| 9859 | while (iscons(p4)) {
|
| 9860 | push(car(p4));
|
| 9861 | gcd();
|
| 9862 | p4 = cdr(p4);
|
| 9863 | }
|
| 9864 | p4 = pop();
|
| 9865 | push(p1);
|
| 9866 | push(p3);
|
| 9867 | divide();
|
| 9868 | p5 = pop();
|
| 9869 | push(p2);
|
| 9870 | push(p4);
|
| 9871 | divide();
|
| 9872 | p6 = pop();
|
| 9873 | if (equal(p5, p6)) {
|
| 9874 | push(p5);
|
| 9875 | push(p3);
|
| 9876 | push(p4);
|
| 9877 | gcd();
|
| 9878 | return multiply();
|
| 9879 | } else {
|
| 9880 | return push(one);
|
| 9881 | }
|
| 9882 | };
|
| 9883 |
|
| 9884 | gcd_expr = function(p) {
|
| 9885 | var results;
|
| 9886 | p = cdr(p);
|
| 9887 | push(car(p));
|
| 9888 | p = cdr(p);
|
| 9889 | results = [];
|
| 9890 | while (iscons(p)) {
|
| 9891 | push(car(p));
|
| 9892 | gcd();
|
| 9893 | results.push(p = cdr(p));
|
| 9894 | }
|
| 9895 | return results;
|
| 9896 | };
|
| 9897 |
|
| 9898 | gcd_term_term = function() {
|
| 9899 | var results;
|
| 9900 | push(one);
|
| 9901 | p3 = cdr(p1);
|
| 9902 | results = [];
|
| 9903 | while (iscons(p3)) {
|
| 9904 | p4 = cdr(p2);
|
| 9905 | while (iscons(p4)) {
|
| 9906 | push(car(p3));
|
| 9907 | push(car(p4));
|
| 9908 | gcd();
|
| 9909 | multiply();
|
| 9910 | p4 = cdr(p4);
|
| 9911 | }
|
| 9912 | results.push(p3 = cdr(p3));
|
| 9913 | }
|
| 9914 | return results;
|
| 9915 | };
|
| 9916 |
|
| 9917 | gcd_term_factor = function() {
|
| 9918 | var results;
|
| 9919 | push(one);
|
| 9920 | p3 = cdr(p1);
|
| 9921 | results = [];
|
| 9922 | while (iscons(p3)) {
|
| 9923 | push(car(p3));
|
| 9924 | push(p2);
|
| 9925 | gcd();
|
| 9926 | multiply();
|
| 9927 | results.push(p3 = cdr(p3));
|
| 9928 | }
|
| 9929 | return results;
|
| 9930 | };
|
| 9931 |
|
| 9932 | gcd_factor_term = function() {
|
| 9933 | var results;
|
| 9934 | push(one);
|
| 9935 | p4 = cdr(p2);
|
| 9936 | results = [];
|
| 9937 | while (iscons(p4)) {
|
| 9938 | push(p1);
|
| 9939 | push(car(p4));
|
| 9940 | gcd();
|
| 9941 | multiply();
|
| 9942 | results.push(p4 = cdr(p4));
|
| 9943 | }
|
| 9944 | return results;
|
| 9945 | };
|
| 9946 |
|
| 9947 | guess = function() {
|
| 9948 | var p;
|
| 9949 | p = pop();
|
| 9950 | push(p);
|
| 9951 | if (Find(p, symbol(SYMBOL_X))) {
|
| 9952 | return push_symbol(SYMBOL_X);
|
| 9953 | } else if (Find(p, symbol(SYMBOL_Y))) {
|
| 9954 | return push_symbol(SYMBOL_Y);
|
| 9955 | } else if (Find(p, symbol(SYMBOL_Z))) {
|
| 9956 | return push_symbol(SYMBOL_Z);
|
| 9957 | } else if (Find(p, symbol(SYMBOL_T))) {
|
| 9958 | return push_symbol(SYMBOL_T);
|
| 9959 | } else if (Find(p, symbol(SYMBOL_S))) {
|
| 9960 | return push_symbol(SYMBOL_S);
|
| 9961 | } else {
|
| 9962 | return push_symbol(SYMBOL_X);
|
| 9963 | }
|
| 9964 | };
|
| 9965 |
|
| 9966 | hermite = function() {
|
| 9967 | save();
|
| 9968 | yyhermite();
|
| 9969 | return restore();
|
| 9970 | };
|
| 9971 |
|
| 9972 | yyhermite = function() {
|
| 9973 | var n;
|
| 9974 | n = 0;
|
| 9975 | p2 = pop();
|
| 9976 | p1 = pop();
|
| 9977 | push(p2);
|
| 9978 | n = pop_integer();
|
| 9979 | if (n < 0 || isNaN(n)) {
|
| 9980 | push_symbol(HERMITE);
|
| 9981 | push(p1);
|
| 9982 | push(p2);
|
| 9983 | list(3);
|
| 9984 | return;
|
| 9985 | }
|
| 9986 | if (issymbol(p1)) {
|
| 9987 | return yyhermite2(n);
|
| 9988 | } else {
|
| 9989 | p3 = p1;
|
| 9990 | p1 = symbol(SECRETX);
|
| 9991 | yyhermite2(n);
|
| 9992 | p1 = p3;
|
| 9993 | push(symbol(SECRETX));
|
| 9994 | push(p1);
|
| 9995 | subst();
|
| 9996 | return Eval();
|
| 9997 | }
|
| 9998 | };
|
| 9999 |
|
| 10000 | yyhermite2 = function(n) {
|
| 10001 | var i, o, ref, results;
|
| 10002 | i = 0;
|
| 10003 | push_integer(1);
|
| 10004 | push_integer(0);
|
| 10005 | p4 = pop();
|
| 10006 | results = [];
|
| 10007 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 10008 | p5 = p4;
|
| 10009 | p4 = pop();
|
| 10010 | push(p1);
|
| 10011 | push(p4);
|
| 10012 | multiply();
|
| 10013 | push_integer(i);
|
| 10014 | push(p5);
|
| 10015 | multiply();
|
| 10016 | subtract();
|
| 10017 | push_integer(2);
|
| 10018 | results.push(multiply());
|
| 10019 | }
|
| 10020 | return results;
|
| 10021 | };
|
| 10022 |
|
| 10023 | hilbert = function() {
|
| 10024 | var i, i1, j, n, o, ref, ref1;
|
| 10025 | i = 0;
|
| 10026 | j = 0;
|
| 10027 | n = 0;
|
| 10028 | save();
|
| 10029 | p2 = pop();
|
| 10030 | push(p2);
|
| 10031 | n = pop_integer();
|
| 10032 | if (n < 2) {
|
| 10033 | push_symbol(HILBERT);
|
| 10034 | push(p2);
|
| 10035 | list(2);
|
| 10036 | restore();
|
| 10037 | return;
|
| 10038 | }
|
| 10039 | push_zero_matrix(n, n);
|
| 10040 | p1 = pop();
|
| 10041 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 10042 | for (j = i1 = 0, ref1 = n; 0 <= ref1 ? i1 < ref1 : i1 > ref1; j = 0 <= ref1 ? ++i1 : --i1) {
|
| 10043 | push_integer(i + j + 1);
|
| 10044 | inverse();
|
| 10045 | p1.tensor.elem[i * n + j] = pop();
|
| 10046 | }
|
| 10047 | }
|
| 10048 | push(p1);
|
| 10049 | return restore();
|
| 10050 | };
|
| 10051 |
|
| 10052 |
|
| 10053 | |
| 10054 | |
| 10055 | |
| 10056 | |
| 10057 | |
| 10058 | |
| 10059 | |
| 10060 | |
| 10061 | |
| 10062 |
|
| 10063 |
|
| 10064 | DEBUG_IMAG = false;
|
| 10065 |
|
| 10066 | Eval_imag = function() {
|
| 10067 | push(cadr(p1));
|
| 10068 | Eval();
|
| 10069 | return imag();
|
| 10070 | };
|
| 10071 |
|
| 10072 | imag = function() {
|
| 10073 | save();
|
| 10074 | rect();
|
| 10075 | p1 = pop();
|
| 10076 | if (DEBUG_IMAG) {
|
| 10077 | console.log("IMAGE of " + p1);
|
| 10078 | }
|
| 10079 | push(p1);
|
| 10080 | push(p1);
|
| 10081 | conjugate();
|
| 10082 | if (DEBUG_IMAG) {
|
| 10083 | console.log(" image: conjugate result: " + stack[tos - 1]);
|
| 10084 | }
|
| 10085 | subtract();
|
| 10086 | push_integer(2);
|
| 10087 | divide();
|
| 10088 | if (DEBUG_IMAG) {
|
| 10089 | console.log(" image: 1st divide result: " + stack[tos - 1]);
|
| 10090 | }
|
| 10091 | push(imaginaryunit);
|
| 10092 | divide();
|
| 10093 | if (DEBUG_IMAG) {
|
| 10094 | console.log(" image: 2nd divide result: " + stack[tos - 1]);
|
| 10095 | }
|
| 10096 | return restore();
|
| 10097 | };
|
| 10098 |
|
| 10099 | index_function = function(n) {
|
| 10100 | var i, i1, j1, k, l1, m, m1, ndim, nelem, o, ref, ref1, ref2, ref3, ref4, ref5, ref6, ref7, s, t;
|
| 10101 | i = 0;
|
| 10102 | k = 0;
|
| 10103 | m = 0;
|
| 10104 | ndim = 0;
|
| 10105 | nelem = 0;
|
| 10106 | t = 0;
|
| 10107 | save();
|
| 10108 | s = tos - n;
|
| 10109 | p1 = stack[s];
|
| 10110 | ndim = p1.tensor.ndim;
|
| 10111 | m = n - 1;
|
| 10112 | if (m > ndim) {
|
| 10113 | stop("too many indices for tensor");
|
| 10114 | }
|
| 10115 | k = 0;
|
| 10116 | for (i = o = 0, ref = m; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 10117 | push(stack[s + i + 1]);
|
| 10118 | t = pop_integer();
|
| 10119 | if (t < 1 || t > p1.tensor.dim[i]) {
|
| 10120 | stop("index out of range");
|
| 10121 | }
|
| 10122 | k = k * p1.tensor.dim[i] + t - 1;
|
| 10123 | }
|
| 10124 | if (ndim === m) {
|
| 10125 | moveTos(tos - n);
|
| 10126 | push(p1.tensor.elem[k]);
|
| 10127 | restore();
|
| 10128 | return;
|
| 10129 | }
|
| 10130 | for (i = i1 = ref1 = m, ref2 = ndim; ref1 <= ref2 ? i1 < ref2 : i1 > ref2; i = ref1 <= ref2 ? ++i1 : --i1) {
|
| 10131 | k = k * p1.tensor.dim[i] + 0;
|
| 10132 | }
|
| 10133 | nelem = 1;
|
| 10134 | for (i = j1 = ref3 = m, ref4 = ndim; ref3 <= ref4 ? j1 < ref4 : j1 > ref4; i = ref3 <= ref4 ? ++j1 : --j1) {
|
| 10135 | nelem *= p1.tensor.dim[i];
|
| 10136 | }
|
| 10137 | p2 = alloc_tensor(nelem);
|
| 10138 | p2.tensor.ndim = ndim - m;
|
| 10139 | for (i = l1 = ref5 = m, ref6 = ndim; ref5 <= ref6 ? l1 < ref6 : l1 > ref6; i = ref5 <= ref6 ? ++l1 : --l1) {
|
| 10140 | p2.tensor.dim[i - m] = p1.tensor.dim[i];
|
| 10141 | }
|
| 10142 | for (i = m1 = 0, ref7 = nelem; 0 <= ref7 ? m1 < ref7 : m1 > ref7; i = 0 <= ref7 ? ++m1 : --m1) {
|
| 10143 | p2.tensor.elem[i] = p1.tensor.elem[k + i];
|
| 10144 | }
|
| 10145 | check_tensor_dimensions(p1);
|
| 10146 | check_tensor_dimensions(p2);
|
| 10147 | moveTos(tos - n);
|
| 10148 | push(p2);
|
| 10149 | return restore();
|
| 10150 | };
|
| 10151 |
|
| 10152 | set_component = function(n) {
|
| 10153 | var i, i1, j1, k, l1, m, m1, n1, ndim, o, ref, ref1, ref2, ref3, ref4, ref5, ref6, s, t;
|
| 10154 | i = 0;
|
| 10155 | k = 0;
|
| 10156 | m = 0;
|
| 10157 | ndim = 0;
|
| 10158 | t = 0;
|
| 10159 | save();
|
| 10160 | if (n < 3) {
|
| 10161 | stop("error in indexed assign");
|
| 10162 | }
|
| 10163 | s = tos - n;
|
| 10164 | p2 = stack[s];
|
| 10165 | p1 = stack[s + 1];
|
| 10166 | if (!istensor(p1)) {
|
| 10167 | stop("error in indexed assign");
|
| 10168 | }
|
| 10169 | ndim = p1.tensor.ndim;
|
| 10170 | m = n - 2;
|
| 10171 | if (m > ndim) {
|
| 10172 | stop("error in indexed assign");
|
| 10173 | }
|
| 10174 | k = 0;
|
| 10175 | for (i = o = 0, ref = m; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 10176 | push(stack[s + i + 2]);
|
| 10177 | t = pop_integer();
|
| 10178 | if (t < 1 || t > p1.tensor.dim[i]) {
|
| 10179 | stop("error in indexed assign\n");
|
| 10180 | }
|
| 10181 | k = k * p1.tensor.dim[i] + t - 1;
|
| 10182 | }
|
| 10183 | for (i = i1 = ref1 = m, ref2 = ndim; ref1 <= ref2 ? i1 < ref2 : i1 > ref2; i = ref1 <= ref2 ? ++i1 : --i1) {
|
| 10184 | k = k * p1.tensor.dim[i] + 0;
|
| 10185 | }
|
| 10186 | p3 = alloc_tensor(p1.tensor.nelem);
|
| 10187 | p3.tensor.ndim = p1.tensor.ndim;
|
| 10188 | for (i = j1 = 0, ref3 = p1.tensor.ndim; 0 <= ref3 ? j1 < ref3 : j1 > ref3; i = 0 <= ref3 ? ++j1 : --j1) {
|
| 10189 | p3.tensor.dim[i] = p1.tensor.dim[i];
|
| 10190 | }
|
| 10191 | for (i = l1 = 0, ref4 = p1.tensor.nelem; 0 <= ref4 ? l1 < ref4 : l1 > ref4; i = 0 <= ref4 ? ++l1 : --l1) {
|
| 10192 | p3.tensor.elem[i] = p1.tensor.elem[i];
|
| 10193 | }
|
| 10194 | check_tensor_dimensions(p1);
|
| 10195 | check_tensor_dimensions(p3);
|
| 10196 | p1 = p3;
|
| 10197 | if (ndim === m) {
|
| 10198 | if (istensor(p2)) {
|
| 10199 | stop("error in indexed assign");
|
| 10200 | }
|
| 10201 | p1.tensor.elem[k] = p2;
|
| 10202 | check_tensor_dimensions(p1);
|
| 10203 | moveTos(tos - n);
|
| 10204 | push(p1);
|
| 10205 | restore();
|
| 10206 | return;
|
| 10207 | }
|
| 10208 | if (!istensor(p2)) {
|
| 10209 | stop("error in indexed assign");
|
| 10210 | }
|
| 10211 | if (ndim - m !== p2.tensor.ndim) {
|
| 10212 | stop("error in indexed assign");
|
| 10213 | }
|
| 10214 | for (i = m1 = 0, ref5 = p2.tensor.ndim; 0 <= ref5 ? m1 < ref5 : m1 > ref5; i = 0 <= ref5 ? ++m1 : --m1) {
|
| 10215 | if (p1.tensor.dim[m + i] !== p2.tensor.dim[i]) {
|
| 10216 | stop("error in indexed assign");
|
| 10217 | }
|
| 10218 | }
|
| 10219 | for (i = n1 = 0, ref6 = p2.tensor.nelem; 0 <= ref6 ? n1 < ref6 : n1 > ref6; i = 0 <= ref6 ? ++n1 : --n1) {
|
| 10220 | p1.tensor.elem[k + i] = p2.tensor.elem[i];
|
| 10221 | }
|
| 10222 | check_tensor_dimensions(p1);
|
| 10223 | check_tensor_dimensions(p2);
|
| 10224 | moveTos(tos - n);
|
| 10225 | push(p1);
|
| 10226 | return restore();
|
| 10227 | };
|
| 10228 |
|
| 10229 |
|
| 10230 | |
| 10231 | |
| 10232 | |
| 10233 | |
| 10234 | |
| 10235 | |
| 10236 | |
| 10237 | |
| 10238 | |
| 10239 | |
| 10240 | |
| 10241 | |
| 10242 | |
| 10243 | |
| 10244 | |
| 10245 | |
| 10246 | |
| 10247 | |
| 10248 | |
| 10249 | |
| 10250 | |
| 10251 | |
| 10252 | |
| 10253 | |
| 10254 | |
| 10255 | |
| 10256 | |
| 10257 | |
| 10258 | |
| 10259 | |
| 10260 | |
| 10261 | |
| 10262 | |
| 10263 | |
| 10264 | |
| 10265 | |
| 10266 | |
| 10267 | |
| 10268 | |
| 10269 | |
| 10270 | |
| 10271 | |
| 10272 | |
| 10273 | |
| 10274 | |
| 10275 | |
| 10276 | |
| 10277 | |
| 10278 | |
| 10279 | |
| 10280 | |
| 10281 | |
| 10282 | |
| 10283 | |
| 10284 | |
| 10285 | |
| 10286 | |
| 10287 | |
| 10288 | |
| 10289 | |
| 10290 | |
| 10291 | |
| 10292 | |
| 10293 | |
| 10294 | |
| 10295 | |
| 10296 | |
| 10297 | |
| 10298 | |
| 10299 |
|
| 10300 |
|
| 10301 | Eval_inner = function() {
|
| 10302 | var difference, i, i1, j1, l1, moretheArguments, o, operands, ref, ref1, ref2, ref3, refinedOperands, results, secondArgument, shift, theArguments;
|
| 10303 | theArguments = [];
|
| 10304 | theArguments.push(car(cdr(p1)));
|
| 10305 | secondArgument = car(cdr(cdr(p1)));
|
| 10306 | if (secondArgument === symbol(NIL)) {
|
| 10307 | stop("pattern needs at least a template and a transformed version");
|
| 10308 | }
|
| 10309 | moretheArguments = cdr(cdr(p1));
|
| 10310 | while (moretheArguments !== symbol(NIL)) {
|
| 10311 | theArguments.push(car(moretheArguments));
|
| 10312 | moretheArguments = cdr(moretheArguments);
|
| 10313 | }
|
| 10314 | if (theArguments.length > 2) {
|
| 10315 | push_symbol(INNER);
|
| 10316 | push(theArguments[theArguments.length - 2]);
|
| 10317 | push(theArguments[theArguments.length - 1]);
|
| 10318 | list(3);
|
| 10319 | for (i = o = 2, ref = theArguments.length; 2 <= ref ? o < ref : o > ref; i = 2 <= ref ? ++o : --o) {
|
| 10320 | push_symbol(INNER);
|
| 10321 | swap();
|
| 10322 | push(theArguments[theArguments.length - i - 1]);
|
| 10323 | swap();
|
| 10324 | list(3);
|
| 10325 | }
|
| 10326 | p1 = pop();
|
| 10327 | Eval_inner();
|
| 10328 | return;
|
| 10329 | }
|
| 10330 | operands = [];
|
| 10331 | get_innerprod_factors(p1, operands);
|
| 10332 | refinedOperands = [];
|
| 10333 | for (i = i1 = 0, ref1 = operands.length; 0 <= ref1 ? i1 < ref1 : i1 > ref1; i = 0 <= ref1 ? ++i1 : --i1) {
|
| 10334 | if (operands[i] === symbol(SYMBOL_IDENTITY_MATRIX)) {
|
| 10335 | continue;
|
| 10336 | } else {
|
| 10337 | refinedOperands.push(operands[i]);
|
| 10338 | }
|
| 10339 | }
|
| 10340 | operands = refinedOperands;
|
| 10341 | refinedOperands = [];
|
| 10342 | if (operands.length > 1) {
|
| 10343 | shift = 0;
|
| 10344 | for (i = j1 = 0, ref2 = operands.length; 0 <= ref2 ? j1 < ref2 : j1 > ref2; i = 0 <= ref2 ? ++j1 : --j1) {
|
| 10345 | if ((i + shift + 1) <= (operands.length - 1)) {
|
| 10346 | if (!(isnumerictensor(operands[i + shift]) || isnumerictensor(operands[i + shift + 1]))) {
|
| 10347 | push(operands[i + shift]);
|
| 10348 | Eval();
|
| 10349 | inv();
|
| 10350 | push(operands[i + shift + 1]);
|
| 10351 | Eval();
|
| 10352 | subtract();
|
| 10353 | difference = pop();
|
| 10354 | if (iszero(difference)) {
|
| 10355 | shift += 1;
|
| 10356 | } else {
|
| 10357 | refinedOperands.push(operands[i + shift]);
|
| 10358 | }
|
| 10359 | } else {
|
| 10360 | refinedOperands.push(operands[i + shift]);
|
| 10361 | }
|
| 10362 | } else {
|
| 10363 | break;
|
| 10364 | }
|
| 10365 | if (i + shift === operands.length - 2) {
|
| 10366 | refinedOperands.push(operands[operands.length - 1]);
|
| 10367 | }
|
| 10368 | if (i + shift >= operands.length - 1) {
|
| 10369 | break;
|
| 10370 | }
|
| 10371 | }
|
| 10372 | operands = refinedOperands;
|
| 10373 | }
|
| 10374 | push(symbol(INNER));
|
| 10375 | if (operands.length > 0) {
|
| 10376 | for (i = l1 = 0, ref3 = operands.length; 0 <= ref3 ? l1 < ref3 : l1 > ref3; i = 0 <= ref3 ? ++l1 : --l1) {
|
| 10377 | push(operands[i]);
|
| 10378 | }
|
| 10379 | } else {
|
| 10380 | pop();
|
| 10381 | push(symbol(SYMBOL_IDENTITY_MATRIX));
|
| 10382 | return;
|
| 10383 | }
|
| 10384 | list(operands.length + 1);
|
| 10385 | p1 = pop();
|
| 10386 | p1 = cdr(p1);
|
| 10387 | push(car(p1));
|
| 10388 | Eval();
|
| 10389 | p1 = cdr(p1);
|
| 10390 | results = [];
|
| 10391 | while (iscons(p1)) {
|
| 10392 | push(car(p1));
|
| 10393 | Eval();
|
| 10394 | inner();
|
| 10395 | results.push(p1 = cdr(p1));
|
| 10396 | }
|
| 10397 | return results;
|
| 10398 | };
|
| 10399 |
|
| 10400 | inner = function() {
|
| 10401 | var arg1, arg2, arg3, subtractionResult;
|
| 10402 | save();
|
| 10403 | p2 = pop();
|
| 10404 | p1 = pop();
|
| 10405 | if (isnegativeterm(p2) && isnegativeterm(p1)) {
|
| 10406 | push(p2);
|
| 10407 | negate();
|
| 10408 | p2 = pop();
|
| 10409 | push(p1);
|
| 10410 | negate();
|
| 10411 | p1 = pop();
|
| 10412 | }
|
| 10413 | if (isinnerordot(p1)) {
|
| 10414 | arg1 = car(cdr(p1));
|
| 10415 | arg2 = car(cdr(cdr(p1)));
|
| 10416 | arg3 = p2;
|
| 10417 | p1 = arg1;
|
| 10418 | push(arg2);
|
| 10419 | push(arg3);
|
| 10420 | inner();
|
| 10421 | p2 = pop();
|
| 10422 | }
|
| 10423 | if (p1 === symbol(SYMBOL_IDENTITY_MATRIX)) {
|
| 10424 | push(p2);
|
| 10425 | restore();
|
| 10426 | return;
|
| 10427 | } else if (p2 === symbol(SYMBOL_IDENTITY_MATRIX)) {
|
| 10428 | push(p1);
|
| 10429 | restore();
|
| 10430 | return;
|
| 10431 | }
|
| 10432 | if (istensor(p1) && istensor(p2)) {
|
| 10433 | inner_f();
|
| 10434 | } else {
|
| 10435 | if (!(isnumerictensor(p1) || isnumerictensor(p2))) {
|
| 10436 | push(p1);
|
| 10437 | push(p2);
|
| 10438 | inv();
|
| 10439 | subtract();
|
| 10440 | subtractionResult = pop();
|
| 10441 | if (iszero(subtractionResult)) {
|
| 10442 | push_symbol(SYMBOL_IDENTITY_MATRIX);
|
| 10443 | restore();
|
| 10444 | return;
|
| 10445 | }
|
| 10446 | }
|
| 10447 | if (expanding && isadd(p1)) {
|
| 10448 | p1 = cdr(p1);
|
| 10449 | push(zero);
|
| 10450 | while (iscons(p1)) {
|
| 10451 | push(car(p1));
|
| 10452 | push(p2);
|
| 10453 | inner();
|
| 10454 | add();
|
| 10455 | p1 = cdr(p1);
|
| 10456 | }
|
| 10457 | restore();
|
| 10458 | return;
|
| 10459 | }
|
| 10460 | if (expanding && isadd(p2)) {
|
| 10461 | p2 = cdr(p2);
|
| 10462 | push(zero);
|
| 10463 | while (iscons(p2)) {
|
| 10464 | push(p1);
|
| 10465 | push(car(p2));
|
| 10466 | inner();
|
| 10467 | add();
|
| 10468 | p2 = cdr(p2);
|
| 10469 | }
|
| 10470 | restore();
|
| 10471 | return;
|
| 10472 | }
|
| 10473 | push(p1);
|
| 10474 | push(p2);
|
| 10475 | if (istensor(p1) && isnum(p2)) {
|
| 10476 | tensor_times_scalar();
|
| 10477 | } else if (isnum(p1) && istensor(p2)) {
|
| 10478 | scalar_times_tensor();
|
| 10479 | } else {
|
| 10480 | if (isnum(p1) || isnum(p2)) {
|
| 10481 | multiply();
|
| 10482 | } else {
|
| 10483 | pop();
|
| 10484 | pop();
|
| 10485 | push_symbol(INNER);
|
| 10486 | push(p1);
|
| 10487 | push(p2);
|
| 10488 | list(3);
|
| 10489 | restore();
|
| 10490 | return;
|
| 10491 | }
|
| 10492 | }
|
| 10493 | }
|
| 10494 | return restore();
|
| 10495 | };
|
| 10496 |
|
| 10497 | inner_f = function() {
|
| 10498 | var a, ak, b, bk, c, i, i1, j, j1, k, l1, m1, n, n1, ndim, o, o1, ref, ref1, ref2, ref3, ref4, ref5, ref6;
|
| 10499 | i = 0;
|
| 10500 | n = p1.tensor.dim[p1.tensor.ndim - 1];
|
| 10501 | if (n !== p2.tensor.dim[0]) {
|
| 10502 | debugger;
|
| 10503 | stop("inner: tensor dimension check");
|
| 10504 | }
|
| 10505 | ndim = p1.tensor.ndim + p2.tensor.ndim - 2;
|
| 10506 | if (ndim > MAXDIM) {
|
| 10507 | stop("inner: rank of result exceeds maximum");
|
| 10508 | }
|
| 10509 | a = p1.tensor.elem;
|
| 10510 | b = p2.tensor.elem;
|
| 10511 | ak = 1;
|
| 10512 | for (i = o = 0, ref = p1.tensor.ndim - 1; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 10513 | ak *= p1.tensor.dim[i];
|
| 10514 | }
|
| 10515 | bk = 1;
|
| 10516 | for (i = i1 = 1, ref1 = p2.tensor.ndim; 1 <= ref1 ? i1 < ref1 : i1 > ref1; i = 1 <= ref1 ? ++i1 : --i1) {
|
| 10517 | bk *= p2.tensor.dim[i];
|
| 10518 | }
|
| 10519 | p3 = alloc_tensor(ak * bk);
|
| 10520 | c = p3.tensor.elem;
|
| 10521 | for (i = j1 = 0, ref2 = ak; 0 <= ref2 ? j1 < ref2 : j1 > ref2; i = 0 <= ref2 ? ++j1 : --j1) {
|
| 10522 | for (j = l1 = 0, ref3 = n; 0 <= ref3 ? l1 < ref3 : l1 > ref3; j = 0 <= ref3 ? ++l1 : --l1) {
|
| 10523 | if (iszero(a[i * n + j])) {
|
| 10524 | continue;
|
| 10525 | }
|
| 10526 | for (k = m1 = 0, ref4 = bk; 0 <= ref4 ? m1 < ref4 : m1 > ref4; k = 0 <= ref4 ? ++m1 : --m1) {
|
| 10527 | push(a[i * n + j]);
|
| 10528 | push(b[j * bk + k]);
|
| 10529 | multiply();
|
| 10530 | push(c[i * bk + k]);
|
| 10531 | add();
|
| 10532 | c[i * bk + k] = pop();
|
| 10533 | }
|
| 10534 | }
|
| 10535 | }
|
| 10536 | if (ndim === 0) {
|
| 10537 | return push(p3.tensor.elem[0]);
|
| 10538 | } else {
|
| 10539 | p3.tensor.ndim = ndim;
|
| 10540 | j = 0;
|
| 10541 | for (i = n1 = 0, ref5 = p1.tensor.ndim - 1; 0 <= ref5 ? n1 < ref5 : n1 > ref5; i = 0 <= ref5 ? ++n1 : --n1) {
|
| 10542 | p3.tensor.dim[i] = p1.tensor.dim[i];
|
| 10543 | }
|
| 10544 | j = p1.tensor.ndim - 1;
|
| 10545 | for (i = o1 = 0, ref6 = p2.tensor.ndim - 1; 0 <= ref6 ? o1 < ref6 : o1 > ref6; i = 0 <= ref6 ? ++o1 : --o1) {
|
| 10546 | p3.tensor.dim[j + i] = p2.tensor.dim[i + 1];
|
| 10547 | }
|
| 10548 | return push(p3);
|
| 10549 | }
|
| 10550 | };
|
| 10551 |
|
| 10552 | get_innerprod_factors = function(tree, factors_accumulator) {
|
| 10553 | if (!iscons(tree)) {
|
| 10554 | add_factor_to_accumulator(tree, factors_accumulator);
|
| 10555 | return;
|
| 10556 | }
|
| 10557 | if (cdr(tree) === symbol(NIL)) {
|
| 10558 | tree = get_innerprod_factors(car(tree), factors_accumulator);
|
| 10559 | return;
|
| 10560 | }
|
| 10561 | if (isinnerordot(tree)) {
|
| 10562 | get_innerprod_factors(car(cdr(tree)), factors_accumulator);
|
| 10563 | get_innerprod_factors(cdr(cdr(tree)), factors_accumulator);
|
| 10564 | return;
|
| 10565 | }
|
| 10566 | return add_factor_to_accumulator(tree, factors_accumulator);
|
| 10567 | };
|
| 10568 |
|
| 10569 | add_factor_to_accumulator = function(tree, factors_accumulator) {
|
| 10570 | if (tree !== symbol(NIL)) {
|
| 10571 | return factors_accumulator.push(tree);
|
| 10572 | }
|
| 10573 | };
|
| 10574 |
|
| 10575 |
|
| 10576 | |
| 10577 | |
| 10578 | |
| 10579 | |
| 10580 | |
| 10581 | |
| 10582 | |
| 10583 | |
| 10584 | |
| 10585 | |
| 10586 |
|
| 10587 |
|
| 10588 | itab = ["f(a,a*x)", "f(1/x,log(x))", "f(x^a,x^(a+1)/(a+1))", "f(exp(a*x),1/a*exp(a*x))", "f(exp(a*x+b),1/a*exp(a*x+b))", "f(x*exp(a*x^2),exp(a*x^2)/(2*a))", "f(x*exp(a*x^2+b),exp(a*x^2+b)/(2*a))", "f(log(a*x),x*log(a*x)-x)", "f(a^x,a^x/log(a),or(not(number(a)),a>0))", "f(1/(a+x^2),1/sqrt(a)*arctan(x/sqrt(a)),or(not(number(a)),a>0))", "f(1/(a-x^2),1/sqrt(a)*arctanh(x/sqrt(a)))", "f(1/sqrt(a-x^2),arcsin(x/(sqrt(a))))", "f(1/sqrt(a+x^2),log(x+sqrt(a+x^2)))", "f(1/(a+b*x),1/b*log(a+b*x))", "f(1/(a+b*x)^2,-1/(b*(a+b*x)))", "f(1/(a+b*x)^3,-1/(2*b)*1/(a+b*x)^2)", "f(x/(a+b*x),x/b-a*log(a+b*x)/b/b)", "f(x/(a+b*x)^2,1/b^2*(log(a+b*x)+a/(a+b*x)))", "f(x^2/(a+b*x),1/b^2*(1/2*(a+b*x)^2-2*a*(a+b*x)+a^2*log(a+b*x)))", "f(x^2/(a+b*x)^2,1/b^3*(a+b*x-2*a*log(a+b*x)-a^2/(a+b*x)))", "f(x^2/(a+b*x)^3,1/b^3*(log(a+b*x)+2*a/(a+b*x)-1/2*a^2/(a+b*x)^2))", "f(1/x*1/(a+b*x),-1/a*log((a+b*x)/x))", "f(1/x*1/(a+b*x)^2,1/a*1/(a+b*x)-1/a^2*log((a+b*x)/x))", "f(1/x*1/(a+b*x)^3,1/a^3*(1/2*((2*a+b*x)/(a+b*x))^2+log(x/(a+b*x))))", "f(1/x^2*1/(a+b*x),-1/(a*x)+b/a^2*log((a+b*x)/x))", "f(1/x^3*1/(a+b*x),(2*b*x-a)/(2*a^2*x^2)+b^2/a^3*log(x/(a+b*x)))", "f(1/x^2*1/(a+b*x)^2,-(a+2*b*x)/(a^2*x*(a+b*x))+2*b/a^3*log((a+b*x)/x))", "f(1/(a+b*x^2),1/sqrt(a*b)*arctan(x*sqrt(a*b)/a),or(not(number(a*b)),a*b>0))", "f(1/(a+b*x^2),1/(2*sqrt(-a*b))*log((a+x*sqrt(-a*b))/(a-x*sqrt(-a*b))),or(not(number(a*b)),a*b<0))", "f(x/(a+b*x^2),1/2*1/b*log(a+b*x^2))", "f(x^2/(a+b*x^2),x/b-a/b*integral(1/(a+b*x^2),x))", "f(1/(a+b*x^2)^2,x/(2*a*(a+b*x^2))+1/2*1/a*integral(1/(a+b*x^2),x))", "f(1/x*1/(a+b*x^2),1/2*1/a*log(x^2/(a+b*x^2)))", "f(1/x^2*1/(a+b*x^2),-1/(a*x)-b/a*integral(1/(a+b*x^2),x))", "f(1/(a+b*x^3),1/3*1/a*(a/b)^(1/3)*(1/2*log(((a/b)^(1/3)+x)^3/(a+b*x^3))+sqrt(3)*arctan((2*x-(a/b)^(1/3))*(a/b)^(-1/3)/sqrt(3))))", "f(x^2/(a+b*x^3),1/3*1/b*log(a+b*x^3))", "f(x/(a+b*x^4),1/2*sqrt(b/a)/b*arctan(x^2*sqrt(b/a)),or(not(number(a*b)),a*b>0))", "f(x/(a+b*x^4),1/4*sqrt(-b/a)/b*log((x^2-sqrt(-a/b))/(x^2+sqrt(-a/b))),or(not(number(a*b)),a*b<0))", "f(x^3/(a+b*x^4),1/4*1/b*log(a+b*x^4))", "f(sqrt(a+b*x),2/3*1/b*sqrt((a+b*x)^3))", "f(x*sqrt(a+b*x),-2*(2*a-3*b*x)*sqrt((a+b*x)^3)/15/b^2)", "f(x^2*sqrt(a+b*x),2*(8*a^2-12*a*b*x+15*b^2*x^2)*sqrt((a+b*x)^3)/105/b^3)", "f(sqrt(a+b*x)/x,2*sqrt(a+b*x)+a*integral(1/x*1/sqrt(a+b*x),x))", "f(sqrt(a+b*x)/x^2,-sqrt(a+b*x)/x+b/2*integral(1/x*1/sqrt(a+b*x),x))", "f(1/sqrt(a+b*x),2*sqrt(a+b*x)/b)", "f(x/sqrt(a+b*x),-2/3*(2*a-b*x)*sqrt(a+b*x)/b^2)", "f(x^2/sqrt(a+b*x),2/15*(8*a^2-4*a*b*x+3*b^2*x^2)*sqrt(a+b*x)/b^3)", "f(1/x*1/sqrt(a+b*x),1/sqrt(a)*log((sqrt(a+b*x)-sqrt(a))/(sqrt(a+b*x)+sqrt(a))),or(not(number(a)),a>0))", "f(1/x*1/sqrt(a+b*x),2/sqrt(-a)*arctan(sqrt(-(a+b*x)/a)),or(not(number(a)),a<0))", "f(1/x^2*1/sqrt(a+b*x),-sqrt(a+b*x)/a/x-1/2*b/a*integral(1/x*1/sqrt(a+b*x),x))", "f(sqrt(x^2+a),1/2*(x*sqrt(x^2+a)+a*log(x+sqrt(x^2+a))))", "f(1/sqrt(x^2+a),log(x+sqrt(x^2+a)))", "f(1/x*1/sqrt(x^2+a),arcsec(x/sqrt(-a))/sqrt(-a),or(not(number(a)),a<0))", "f(1/x*1/sqrt(x^2+a),-1/sqrt(a)*log((sqrt(a)+sqrt(x^2+a))/x),or(not(number(a)),a>0))", "f(sqrt(x^2+a)/x,sqrt(x^2+a)-sqrt(a)*log((sqrt(a)+sqrt(x^2+a))/x),or(not(number(a)),a>0))", "f(sqrt(x^2+a)/x,sqrt(x^2+a)-sqrt(-a)*arcsec(x/sqrt(-a)),or(not(number(a)),a<0))", "f(x/sqrt(x^2+a),sqrt(x^2+a))", "f(x*sqrt(x^2+a),1/3*sqrt((x^2+a)^3))", "f(sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),1/4*(x*sqrt((x^2+a^(1/3))^3)+3/2*a^(1/3)*x*sqrt(x^2+a^(1/3))+3/2*a^(2/3)*log(x+sqrt(x^2+a^(1/3)))))", "f(sqrt(-a+x^6-3*a^(1/3)*x^4+3*a^(2/3)*x^2),1/4*(x*sqrt((x^2-a^(1/3))^3)-3/2*a^(1/3)*x*sqrt(x^2-a^(1/3))+3/2*a^(2/3)*log(x+sqrt(x^2-a^(1/3)))))", "f(1/sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),x/a^(1/3)/sqrt(x^2+a^(1/3)))", "f(x/sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),-1/sqrt(x^2+a^(1/3)))", "f(x*sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),1/5*sqrt((x^2+a^(1/3))^5))", "f(x^2*sqrt(x^2+a),1/4*x*sqrt((x^2+a)^3)-1/8*a*x*sqrt(x^2+a)-1/8*a^2*log(x+sqrt(x^2+a)))", "f(x^3*sqrt(x^2+a),(1/5*x^2-2/15*a)*sqrt((x^2+a)^3),and(number(a),a>0))", "f(x^3*sqrt(x^2+a),sqrt((x^2+a)^5)/5-a*sqrt((x^2+a)^3)/3,and(number(a),a<0))", "f(x^2/sqrt(x^2+a),1/2*x*sqrt(x^2+a)-1/2*a*log(x+sqrt(x^2+a)))", "f(x^3/sqrt(x^2+a),1/3*sqrt((x^2+a)^3)-a*sqrt(x^2+a))", "f(1/x^2*1/sqrt(x^2+a),-sqrt(x^2+a)/a/x)", "f(1/x^3*1/sqrt(x^2+a),-1/2*sqrt(x^2+a)/a/x^2+1/2*log((sqrt(a)+sqrt(x^2+a))/x)/a^(3/2),or(not(number(a)),a>0))", "f(1/x^3*1/sqrt(x^2-a),1/2*sqrt(x^2-a)/a/x^2+1/2*1/(a^(3/2))*arcsec(x/(a^(1/2))),or(not(number(a)),a>0))", "f(x^2*sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),1/6*x*sqrt((x^2+a^(1/3))^5)-1/24*a^(1/3)*x*sqrt((x^2+a^(1/3))^3)-1/16*a^(2/3)*x*sqrt(x^2+a^(1/3))-1/16*a*log(x+sqrt(x^2+a^(1/3))),or(not(number(a)),a>0))", "f(x^2*sqrt(-a-3*a^(1/3)*x^4+3*a^(2/3)*x^2+x^6),1/6*x*sqrt((x^2-a^(1/3))^5)+1/24*a^(1/3)*x*sqrt((x^2-a^(1/3))^3)-1/16*a^(2/3)*x*sqrt(x^2-a^(1/3))+1/16*a*log(x+sqrt(x^2-a^(1/3))),or(not(number(a)),a>0))", "f(x^3*sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),1/7*sqrt((x^2+a^(1/3))^7)-1/5*a^(1/3)*sqrt((x^2+a^(1/3))^5),or(not(number(a)),a>0))", "f(x^3*sqrt(-a-3*a^(1/3)*x^4+3*a^(2/3)*x^2+x^6),1/7*sqrt((x^2-a^(1/3))^7)+1/5*a^(1/3)*sqrt((x^2-a^(1/3))^5),or(not(number(a)),a>0))", "f(1/(x-a)/sqrt(x^2-a^2),-sqrt(x^2-a^2)/a/(x-a))", "f(1/(x+a)/sqrt(x^2-a^2),sqrt(x^2-a^2)/a/(x+a))", "f(sqrt(a-x^2),1/2*(x*sqrt(a-x^2)+a*arcsin(x/sqrt(abs(a)))))", "f(1/x*1/sqrt(a-x^2),-1/sqrt(a)*log((sqrt(a)+sqrt(a-x^2))/x),or(not(number(a)),a>0))", "f(sqrt(a-x^2)/x,sqrt(a-x^2)-sqrt(a)*log((sqrt(a)+sqrt(a-x^2))/x),or(not(number(a)),a>0))", "f(x/sqrt(a-x^2),-sqrt(a-x^2))", "f(x*sqrt(a-x^2),-1/3*sqrt((a-x^2)^3))", "f(x^2*sqrt(a-x^2),-x/4*sqrt((a-x^2)^3)+1/8*a*(x*sqrt(a-x^2)+a*arcsin(x/sqrt(a))),or(not(number(a)),a>0))", "f(x^3*sqrt(a-x^2),(-1/5*x^2-2/15*a)*sqrt((a-x^2)^3),or(not(number(a)),a>0))", "f(x^2/sqrt(a-x^2),-x/2*sqrt(a-x^2)+a/2*arcsin(x/sqrt(a)),or(not(number(a)),a>0))", "f(1/x^2*1/sqrt(a-x^2),-sqrt(a-x^2)/a/x,or(not(number(a)),a>0))", "f(sqrt(a-x^2)/x^2,-sqrt(a-x^2)/x-arcsin(x/sqrt(a)),or(not(number(a)),a>0))", "f(sqrt(a-x^2)/x^3,-1/2*sqrt(a-x^2)/x^2+1/2*log((sqrt(a)+sqrt(a-x^2))/x)/sqrt(a),or(not(number(a)),a>0))", "f(sqrt(a-x^2)/x^4,-1/3*sqrt((a-x^2)^3)/a/x^3,or(not(number(a)),a>0))", "f(sqrt(a*x^2+b),x*sqrt(a*x^2+b)/2+b*log(x*sqrt(a)+sqrt(a*x^2+b))/2/sqrt(a),and(number(a),a>0))", "f(sqrt(a*x^2+b),x*sqrt(a*x^2+b)/2+b*arcsin(x*sqrt(-a/b))/2/sqrt(-a),and(number(a),a<0))", "f(sin(a*x),-cos(a*x)/a)", "f(cos(a*x),sin(a*x)/a)", "f(tan(a*x),-log(cos(a*x))/a)", "f(1/tan(a*x),log(sin(a*x))/a)", "f(1/cos(a*x),log(tan(pi/4+a*x/2))/a)", "f(1/sin(a*x),log(tan(a*x/2))/a)", "f(sin(a*x)^2,x/2-sin(2*a*x)/(4*a))", "f(sin(a*x)^3,-cos(a*x)*(sin(a*x)^2+2)/(3*a))", "f(sin(a*x)^4,3/8*x-sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a))", "f(cos(a*x)^2,x/2+sin(2*a*x)/(4*a))", "f(cos(a*x)^3,sin(a*x)*(cos(a*x)^2+2)/(3*a))", "f(cos(a*x)^4,3/8*x+sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a))", "f(1/sin(a*x)^2,-1/(a*tan(a*x)))", "f(1/cos(a*x)^2,tan(a*x)/a)", "f(sin(a*x)*cos(a*x),sin(a*x)^2/(2*a))", "f(sin(a*x)^2*cos(a*x)^2,-sin(4*a*x)/(32*a)+x/8)", "f(sin(a*x)/cos(a*x)^2,1/(a*cos(a*x)))", "f(sin(a*x)^2/cos(a*x),(log(tan(pi/4+a*x/2))-sin(a*x))/a)", "f(cos(a*x)/sin(a*x)^2,-1/(a*sin(a*x)))", "f(1/(sin(a*x)*cos(a*x)),log(tan(a*x))/a)", "f(1/(sin(a*x)*cos(a*x)^2),(1/cos(a*x)+log(tan(a*x/2)))/a)", "f(1/(sin(a*x)^2*cos(a*x)),(log(tan(pi/4+a*x/2))-1/sin(a*x))/a)", "f(1/(sin(a*x)^2*cos(a*x)^2),-2/(a*tan(2*a*x)))", "f(sin(a+b*x),-cos(a+b*x)/b)", "f(cos(a+b*x),sin(a+b*x)/b)", "f(1/(b+b*sin(a*x)),-tan(pi/4-a*x/2)/a/b)", "f(1/(b-b*sin(a*x)),tan(pi/4+a*x/2)/a/b)", "f(1/(b+b*cos(a*x)),tan(a*x/2)/a/b)", "f(1/(b-b*cos(a*x)),-1/tan(a*x/2)/a/b)", "f(1/(a+b*sin(x)),1/sqrt(b^2-a^2)*log((a*tan(x/2)+b-sqrt(b^2-a^2))/(a*tan(x/2)+b+sqrt(b^2-a^2))),b^2-a^2)", "f(1/(a+b*cos(x)),1/sqrt(b^2-a^2)*log((sqrt(b^2-a^2)*tan(x/2)+a+b)/(sqrt(b^2-a^2)*tan(x/2)-a-b)),b^2-a^2)", "f(x*sin(a*x),sin(a*x)/a^2-x*cos(a*x)/a)", "f(x^2*sin(a*x),2*x*sin(a*x)/a^2-(a^2*x^2-2)*cos(a*x)/a^3)", "f(x*cos(a*x),cos(a*x)/a^2+x*sin(a*x)/a)", "f(x^2*cos(a*x),2*x*cos(a*x)/a^2+(a^2*x^2-2)*sin(a*x)/a^3)", "f(arcsin(a*x),x*arcsin(a*x)+sqrt(1-a^2*x^2)/a)", "f(arccos(a*x),x*arccos(a*x)-sqrt(1-a^2*x^2)/a)", "f(arctan(a*x),x*arctan(a*x)-1/2*log(1+a^2*x^2)/a)", "f(log(a*x),x*log(a*x)-x)", "f(x*log(a*x),x^2*log(a*x)/2-x^2/4)", "f(x^2*log(a*x),x^3*log(a*x)/3-1/9*x^3)", "f(log(x)^2,x*log(x)^2-2*x*log(x)+2*x)", "f(1/x*1/(a+log(x)),log(a+log(x)))", "f(log(a*x+b),(a*x+b)*log(a*x+b)/a-x)", "f(log(a*x+b)/x^2,a/b*log(x)-(a*x+b)*log(a*x+b)/b/x)", "f(sinh(x),cosh(x))", "f(cosh(x),sinh(x))", "f(tanh(x),log(cosh(x)))", "f(x*sinh(x),x*cosh(x)-sinh(x))", "f(x*cosh(x),x*sinh(x)-cosh(x))", "f(sinh(x)^2,sinh(2*x)/4-x/2)", "f(tanh(x)^2,x-tanh(x))", "f(cosh(x)^2,sinh(2*x)/4+x/2)", "f(x^3*exp(a*x^2),exp(a*x^2)*(x^2/a-1/(a^2))/2)", "f(x^3*exp(a*x^2+b),exp(a*x^2)*exp(b)*(x^2/a-1/(a^2))/2)", "f(exp(a*x^2),-i*sqrt(pi)*erf(i*sqrt(a)*x)/sqrt(a)/2)", "f(erf(a*x),x*erf(a*x)+exp(-a^2*x^2)/a/sqrt(pi))", "f(x^2*(1-x^2)^(3/2),(x*sqrt(1-x^2)*(-8*x^4+14*x^2-3)+3*arcsin(x))/48)", "f(x^2*(1-x^2)^(5/2),(x*sqrt(1-x^2)*(48*x^6-136*x^4+118*x^2-15)+15*arcsin(x))/384)", "f(x^4*(1-x^2)^(3/2),(-x*sqrt(1-x^2)*(16*x^6-24*x^4+2*x^2+3)+3*arcsin(x))/128)", "f(x*exp(a*x),exp(a*x)*(a*x-1)/(a^2))", "f(x*exp(a*x+b),exp(a*x+b)*(a*x-1)/(a^2))", "f(x^2*exp(a*x),exp(a*x)*(a^2*x^2-2*a*x+2)/(a^3))", "f(x^2*exp(a*x+b),exp(a*x+b)*(a^2*x^2-2*a*x+2)/(a^3))", "f(x^3*exp(a*x),exp(a*x)*x^3/a-3/a*integral(x^2*exp(a*x),x))", "f(x^3*exp(a*x+b),exp(a*x+b)*x^3/a-3/a*integral(x^2*exp(a*x+b),x))", 0];
|
| 10589 |
|
| 10590 | Eval_integral = function() {
|
| 10591 | var doNothing, i, i1, n, o, ref, ref1;
|
| 10592 | i = 0;
|
| 10593 | n = 0;
|
| 10594 | p1 = cdr(p1);
|
| 10595 | push(car(p1));
|
| 10596 | Eval();
|
| 10597 | p1 = cdr(p1);
|
| 10598 | push(car(p1));
|
| 10599 | Eval();
|
| 10600 | p2 = pop();
|
| 10601 | if (p2 === symbol(NIL)) {
|
| 10602 | guess();
|
| 10603 | push(symbol(NIL));
|
| 10604 | } else if (isnum(p2)) {
|
| 10605 | guess();
|
| 10606 | push(p2);
|
| 10607 | } else {
|
| 10608 | push(p2);
|
| 10609 | p1 = cdr(p1);
|
| 10610 | push(car(p1));
|
| 10611 | Eval();
|
| 10612 | }
|
| 10613 | p5 = pop();
|
| 10614 | p4 = pop();
|
| 10615 | p3 = pop();
|
| 10616 | while (1) {
|
| 10617 | if (isnum(p5)) {
|
| 10618 | push(p5);
|
| 10619 | n = pop_integer();
|
| 10620 | if (isNaN(n)) {
|
| 10621 | stop("nth integral: check n");
|
| 10622 | }
|
| 10623 | } else {
|
| 10624 | n = 1;
|
| 10625 | }
|
| 10626 | push(p3);
|
| 10627 | if (n >= 0) {
|
| 10628 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 10629 | push(p4);
|
| 10630 | integral();
|
| 10631 | }
|
| 10632 | } else {
|
| 10633 | n = -n;
|
| 10634 | for (i = i1 = 0, ref1 = n; 0 <= ref1 ? i1 < ref1 : i1 > ref1; i = 0 <= ref1 ? ++i1 : --i1) {
|
| 10635 | push(p4);
|
| 10636 | derivative();
|
| 10637 | }
|
| 10638 | }
|
| 10639 | p3 = pop();
|
| 10640 | if (p5 === symbol(NIL)) {
|
| 10641 | break;
|
| 10642 | }
|
| 10643 | if (isnum(p5)) {
|
| 10644 | p1 = cdr(p1);
|
| 10645 | push(car(p1));
|
| 10646 | Eval();
|
| 10647 | p5 = pop();
|
| 10648 | if (p5 === symbol(NIL)) {
|
| 10649 | break;
|
| 10650 | }
|
| 10651 | if (isnum(p5)) {
|
| 10652 | doNothing = 1;
|
| 10653 | } else {
|
| 10654 | p4 = p5;
|
| 10655 | p1 = cdr(p1);
|
| 10656 | push(car(p1));
|
| 10657 | Eval();
|
| 10658 | p5 = pop();
|
| 10659 | }
|
| 10660 | } else {
|
| 10661 | p4 = p5;
|
| 10662 | p1 = cdr(p1);
|
| 10663 | push(car(p1));
|
| 10664 | Eval();
|
| 10665 | p5 = pop();
|
| 10666 | }
|
| 10667 | }
|
| 10668 | return push(p3);
|
| 10669 | };
|
| 10670 |
|
| 10671 | integral = function() {
|
| 10672 | save();
|
| 10673 | p2 = pop();
|
| 10674 | p1 = pop();
|
| 10675 | if (car(p1) === symbol(ADD)) {
|
| 10676 | integral_of_sum();
|
| 10677 | } else if (car(p1) === symbol(MULTIPLY)) {
|
| 10678 | integral_of_product();
|
| 10679 | } else {
|
| 10680 | integral_of_form();
|
| 10681 | }
|
| 10682 | p1 = pop();
|
| 10683 | if (Find(p1, symbol(INTEGRAL))) {
|
| 10684 | stop("integral: sorry, could not find a solution");
|
| 10685 | }
|
| 10686 | push(p1);
|
| 10687 | simplify();
|
| 10688 | Eval();
|
| 10689 | return restore();
|
| 10690 | };
|
| 10691 |
|
| 10692 | integral_of_sum = function() {
|
| 10693 | var results;
|
| 10694 | p1 = cdr(p1);
|
| 10695 | push(car(p1));
|
| 10696 | push(p2);
|
| 10697 | integral();
|
| 10698 | p1 = cdr(p1);
|
| 10699 | results = [];
|
| 10700 | while (iscons(p1)) {
|
| 10701 | push(car(p1));
|
| 10702 | push(p2);
|
| 10703 | integral();
|
| 10704 | add();
|
| 10705 | results.push(p1 = cdr(p1));
|
| 10706 | }
|
| 10707 | return results;
|
| 10708 | };
|
| 10709 |
|
| 10710 | integral_of_product = function() {
|
| 10711 | push(p1);
|
| 10712 | push(p2);
|
| 10713 | partition();
|
| 10714 | p1 = pop();
|
| 10715 | integral_of_form();
|
| 10716 | return multiply();
|
| 10717 | };
|
| 10718 |
|
| 10719 | integral_of_form = function() {
|
| 10720 | push(p1);
|
| 10721 | push(p2);
|
| 10722 | transform(itab, false);
|
| 10723 | p3 = pop();
|
| 10724 | if (p3 === symbol(NIL)) {
|
| 10725 | push_symbol(INTEGRAL);
|
| 10726 | push(p1);
|
| 10727 | push(p2);
|
| 10728 | return list(3);
|
| 10729 | } else {
|
| 10730 | return push(p3);
|
| 10731 | }
|
| 10732 | };
|
| 10733 |
|
| 10734 | INV_check_arg = function() {
|
| 10735 | if (!istensor(p1)) {
|
| 10736 | return 0;
|
| 10737 | } else if (p1.tensor.ndim !== 2) {
|
| 10738 | return 0;
|
| 10739 | } else if (p1.tensor.dim[0] !== p1.tensor.dim[1]) {
|
| 10740 | return 0;
|
| 10741 | } else {
|
| 10742 | return 1;
|
| 10743 | }
|
| 10744 | };
|
| 10745 |
|
| 10746 | inv = function() {
|
| 10747 | var accumulator, eachEntry, i, n, o, ref;
|
| 10748 | i = 0;
|
| 10749 | n = 0;
|
| 10750 | save();
|
| 10751 | p1 = pop();
|
| 10752 | if (isinv(p1)) {
|
| 10753 | push(car(cdr(p1)));
|
| 10754 | restore();
|
| 10755 | return;
|
| 10756 | }
|
| 10757 | if (isidentitymatrix(p1)) {
|
| 10758 | push(p1);
|
| 10759 | restore();
|
| 10760 | return;
|
| 10761 | }
|
| 10762 | if (expanding && isinnerordot(p1)) {
|
| 10763 | p1 = cdr(p1);
|
| 10764 | accumulator = [];
|
| 10765 | while (iscons(p1)) {
|
| 10766 | accumulator.push(car(p1));
|
| 10767 | p1 = cdr(p1);
|
| 10768 | }
|
| 10769 | for (eachEntry = o = ref = accumulator.length - 1; ref <= 0 ? o <= 0 : o >= 0; eachEntry = ref <= 0 ? ++o : --o) {
|
| 10770 | push(accumulator[eachEntry]);
|
| 10771 | inv();
|
| 10772 | if (eachEntry !== accumulator.length - 1) {
|
| 10773 | inner();
|
| 10774 | }
|
| 10775 | }
|
| 10776 | restore();
|
| 10777 | return;
|
| 10778 | }
|
| 10779 | if (INV_check_arg() === 0) {
|
| 10780 | push_symbol(INV);
|
| 10781 | push(p1);
|
| 10782 | list(2);
|
| 10783 | restore();
|
| 10784 | return;
|
| 10785 | }
|
| 10786 | if (isnumerictensor(p1)) {
|
| 10787 | yyinvg();
|
| 10788 | } else {
|
| 10789 | push(p1);
|
| 10790 | adj();
|
| 10791 | push(p1);
|
| 10792 | det();
|
| 10793 | p2 = pop();
|
| 10794 | if (iszero(p2)) {
|
| 10795 | stop("inverse of singular matrix");
|
| 10796 | }
|
| 10797 | push(p2);
|
| 10798 | divide();
|
| 10799 | }
|
| 10800 | return restore();
|
| 10801 | };
|
| 10802 |
|
| 10803 | invg = function() {
|
| 10804 | save();
|
| 10805 | p1 = pop();
|
| 10806 | if (INV_check_arg() === 0) {
|
| 10807 | push_symbol(INVG);
|
| 10808 | push(p1);
|
| 10809 | list(2);
|
| 10810 | restore();
|
| 10811 | return;
|
| 10812 | }
|
| 10813 | yyinvg();
|
| 10814 | return restore();
|
| 10815 | };
|
| 10816 |
|
| 10817 | yyinvg = function() {
|
| 10818 | var h, i, i1, j, j1, l1, n, o, ref, ref1, ref2, ref3;
|
| 10819 | h = 0;
|
| 10820 | i = 0;
|
| 10821 | j = 0;
|
| 10822 | n = 0;
|
| 10823 | n = p1.tensor.dim[0];
|
| 10824 | h = tos;
|
| 10825 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 10826 | for (j = i1 = 0, ref1 = n; 0 <= ref1 ? i1 < ref1 : i1 > ref1; j = 0 <= ref1 ? ++i1 : --i1) {
|
| 10827 | if (i === j) {
|
| 10828 | push(one);
|
| 10829 | } else {
|
| 10830 | push(zero);
|
| 10831 | }
|
| 10832 | }
|
| 10833 | }
|
| 10834 | for (i = j1 = 0, ref2 = n * n; 0 <= ref2 ? j1 < ref2 : j1 > ref2; i = 0 <= ref2 ? ++j1 : --j1) {
|
| 10835 | push(p1.tensor.elem[i]);
|
| 10836 | }
|
| 10837 | INV_decomp(n);
|
| 10838 | p1 = alloc_tensor(n * n);
|
| 10839 | p1.tensor.ndim = 2;
|
| 10840 | p1.tensor.dim[0] = n;
|
| 10841 | p1.tensor.dim[1] = n;
|
| 10842 | for (i = l1 = 0, ref3 = n * n; 0 <= ref3 ? l1 < ref3 : l1 > ref3; i = 0 <= ref3 ? ++l1 : --l1) {
|
| 10843 | p1.tensor.elem[i] = stack[h + i];
|
| 10844 | }
|
| 10845 | moveTos(tos - 2 * n * n);
|
| 10846 | return push(p1);
|
| 10847 | };
|
| 10848 |
|
| 10849 | INV_decomp = function(n) {
|
| 10850 | var a, d, i, i1, j, j1, l1, o, ref, ref1, ref2, ref3, ref4, results, u;
|
| 10851 | a = 0;
|
| 10852 | d = 0;
|
| 10853 | i = 0;
|
| 10854 | j = 0;
|
| 10855 | u = 0;
|
| 10856 | a = tos - n * n;
|
| 10857 | u = a - n * n;
|
| 10858 | results = [];
|
| 10859 | for (d = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; d = 0 <= ref ? ++o : --o) {
|
| 10860 | if (equal(stack[a + n * d + d], zero)) {
|
| 10861 | for (i = i1 = ref1 = d + 1, ref2 = n; ref1 <= ref2 ? i1 < ref2 : i1 > ref2; i = ref1 <= ref2 ? ++i1 : --i1) {
|
| 10862 | if (!equal(stack[a + n * i + d], zero)) {
|
| 10863 | break;
|
| 10864 | }
|
| 10865 | }
|
| 10866 | if (i === n) {
|
| 10867 | stop("inverse of singular matrix");
|
| 10868 | }
|
| 10869 | for (j = j1 = 0, ref3 = n; 0 <= ref3 ? j1 < ref3 : j1 > ref3; j = 0 <= ref3 ? ++j1 : --j1) {
|
| 10870 | p2 = stack[a + n * d + j];
|
| 10871 | stack[a + n * d + j] = stack[a + n * i + j];
|
| 10872 | stack[a + n * i + j] = p2;
|
| 10873 | p2 = stack[u + n * d + j];
|
| 10874 | stack[u + n * d + j] = stack[u + n * i + j];
|
| 10875 | stack[u + n * i + j] = p2;
|
| 10876 | }
|
| 10877 | }
|
| 10878 | p2 = stack[a + n * d + d];
|
| 10879 | for (j = l1 = 0, ref4 = n; 0 <= ref4 ? l1 < ref4 : l1 > ref4; j = 0 <= ref4 ? ++l1 : --l1) {
|
| 10880 | if (j > d) {
|
| 10881 | push(stack[a + n * d + j]);
|
| 10882 | push(p2);
|
| 10883 | divide();
|
| 10884 | stack[a + n * d + j] = pop();
|
| 10885 | }
|
| 10886 | push(stack[u + n * d + j]);
|
| 10887 | push(p2);
|
| 10888 | divide();
|
| 10889 | stack[u + n * d + j] = pop();
|
| 10890 | }
|
| 10891 | results.push((function() {
|
| 10892 | var m1, ref5, results1;
|
| 10893 | results1 = [];
|
| 10894 | for (i = m1 = 0, ref5 = n; 0 <= ref5 ? m1 < ref5 : m1 > ref5; i = 0 <= ref5 ? ++m1 : --m1) {
|
| 10895 | if (i === d) {
|
| 10896 | continue;
|
| 10897 | }
|
| 10898 | p2 = stack[a + n * i + d];
|
| 10899 | results1.push((function() {
|
| 10900 | var n1, ref6, results2;
|
| 10901 | results2 = [];
|
| 10902 | for (j = n1 = 0, ref6 = n; 0 <= ref6 ? n1 < ref6 : n1 > ref6; j = 0 <= ref6 ? ++n1 : --n1) {
|
| 10903 | if (j > d) {
|
| 10904 | push(stack[a + n * i + j]);
|
| 10905 | push(stack[a + n * d + j]);
|
| 10906 | push(p2);
|
| 10907 | multiply();
|
| 10908 | subtract();
|
| 10909 | stack[a + n * i + j] = pop();
|
| 10910 | }
|
| 10911 | push(stack[u + n * i + j]);
|
| 10912 | push(stack[u + n * d + j]);
|
| 10913 | push(p2);
|
| 10914 | multiply();
|
| 10915 | subtract();
|
| 10916 | results2.push(stack[u + n * i + j] = pop());
|
| 10917 | }
|
| 10918 | return results2;
|
| 10919 | })());
|
| 10920 | }
|
| 10921 | return results1;
|
| 10922 | })());
|
| 10923 | }
|
| 10924 | return results;
|
| 10925 | };
|
| 10926 |
|
| 10927 | DEBUG_IS = false;
|
| 10928 |
|
| 10929 | iszero = function(p) {
|
| 10930 | var i, o, ref;
|
| 10931 | i = 0;
|
| 10932 | switch (p.k) {
|
| 10933 | case NUM:
|
| 10934 | if (MZERO(p.q.a)) {
|
| 10935 | return 1;
|
| 10936 | }
|
| 10937 | break;
|
| 10938 | case DOUBLE:
|
| 10939 | if (p.d === 0.0) {
|
| 10940 | return 1;
|
| 10941 | }
|
| 10942 | break;
|
| 10943 | case TENSOR:
|
| 10944 | for (i = o = 0, ref = p.tensor.nelem; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 10945 | if (!iszero(p.tensor.elem[i])) {
|
| 10946 | return 0;
|
| 10947 | }
|
| 10948 | }
|
| 10949 | return 1;
|
| 10950 | }
|
| 10951 | return 0;
|
| 10952 | };
|
| 10953 |
|
| 10954 | isnegativenumber = function(p) {
|
| 10955 | switch (p.k) {
|
| 10956 | case NUM:
|
| 10957 | if (MSIGN(p.q.a) === -1) {
|
| 10958 | return 1;
|
| 10959 | }
|
| 10960 | break;
|
| 10961 | case DOUBLE:
|
| 10962 | if (p.d < 0.0) {
|
| 10963 | return 1;
|
| 10964 | }
|
| 10965 | }
|
| 10966 | return 0;
|
| 10967 | };
|
| 10968 |
|
| 10969 | ispositivenumber = function(p) {
|
| 10970 | switch (p.k) {
|
| 10971 | case NUM:
|
| 10972 | if (MSIGN(p.q.a) === 1) {
|
| 10973 | return 1;
|
| 10974 | }
|
| 10975 | break;
|
| 10976 | case DOUBLE:
|
| 10977 | if (p.d > 0.0) {
|
| 10978 | return 1;
|
| 10979 | }
|
| 10980 | }
|
| 10981 | return 0;
|
| 10982 | };
|
| 10983 |
|
| 10984 | isplustwo = function(p) {
|
| 10985 | switch (p.k) {
|
| 10986 | case NUM:
|
| 10987 | if (MEQUAL(p.q.a, 2) && MEQUAL(p.q.b, 1)) {
|
| 10988 | return 1;
|
| 10989 | }
|
| 10990 | break;
|
| 10991 | case DOUBLE:
|
| 10992 | if (p.d === 2.0) {
|
| 10993 | return 1;
|
| 10994 | }
|
| 10995 | }
|
| 10996 | return 0;
|
| 10997 | };
|
| 10998 |
|
| 10999 | isplusone = function(p) {
|
| 11000 | switch (p.k) {
|
| 11001 | case NUM:
|
| 11002 | if (MEQUAL(p.q.a, 1) && MEQUAL(p.q.b, 1)) {
|
| 11003 | return 1;
|
| 11004 | }
|
| 11005 | break;
|
| 11006 | case DOUBLE:
|
| 11007 | if (p.d === 1.0) {
|
| 11008 | return 1;
|
| 11009 | }
|
| 11010 | }
|
| 11011 | return 0;
|
| 11012 | };
|
| 11013 |
|
| 11014 | isminusone = function(p) {
|
| 11015 | switch (p.k) {
|
| 11016 | case NUM:
|
| 11017 | if (MEQUAL(p.q.a, -1) && MEQUAL(p.q.b, 1)) {
|
| 11018 | return 1;
|
| 11019 | }
|
| 11020 | break;
|
| 11021 | case DOUBLE:
|
| 11022 | if (p.d === -1.0) {
|
| 11023 | return 1;
|
| 11024 | }
|
| 11025 | }
|
| 11026 | return 0;
|
| 11027 | };
|
| 11028 |
|
| 11029 | isone = function(p) {
|
| 11030 | return isplusone(p) || isminusone(p);
|
| 11031 | };
|
| 11032 |
|
| 11033 | isinteger = function(p) {
|
| 11034 | if (p.k === NUM && MEQUAL(p.q.b, 1)) {
|
| 11035 | return 1;
|
| 11036 | } else {
|
| 11037 | return 0;
|
| 11038 | }
|
| 11039 | };
|
| 11040 |
|
| 11041 | isintegerorintegerfloat = function(p) {
|
| 11042 | if (p.k === DOUBLE) {
|
| 11043 | if (p.d === Math.round(p.d)) {
|
| 11044 | return 1;
|
| 11045 | }
|
| 11046 | return 0;
|
| 11047 | }
|
| 11048 | return isinteger(p);
|
| 11049 | };
|
| 11050 |
|
| 11051 | isnonnegativeinteger = function(p) {
|
| 11052 | if (isrational(p) && MEQUAL(p.q.b, 1) && MSIGN(p.q.a) === 1) {
|
| 11053 | return 1;
|
| 11054 | } else {
|
| 11055 | return 0;
|
| 11056 | }
|
| 11057 | };
|
| 11058 |
|
| 11059 | isposint = function(p) {
|
| 11060 | if (isinteger(p) && MSIGN(p.q.a) === 1) {
|
| 11061 | return 1;
|
| 11062 | } else {
|
| 11063 | return 0;
|
| 11064 | }
|
| 11065 | };
|
| 11066 |
|
| 11067 | ispoly = function(p, x) {
|
| 11068 | if (Find(p, x)) {
|
| 11069 | return ispoly_expr(p, x);
|
| 11070 | } else {
|
| 11071 | return 0;
|
| 11072 | }
|
| 11073 | };
|
| 11074 |
|
| 11075 | ispoly_expr = function(p, x) {
|
| 11076 | if (car(p) === symbol(ADD)) {
|
| 11077 | p = cdr(p);
|
| 11078 | while (iscons(p)) {
|
| 11079 | if (!ispoly_term(car(p), x)) {
|
| 11080 | return 0;
|
| 11081 | }
|
| 11082 | p = cdr(p);
|
| 11083 | }
|
| 11084 | return 1;
|
| 11085 | } else {
|
| 11086 | return ispoly_term(p, x);
|
| 11087 | }
|
| 11088 | };
|
| 11089 |
|
| 11090 | ispoly_term = function(p, x) {
|
| 11091 | if (car(p) === symbol(MULTIPLY)) {
|
| 11092 | p = cdr(p);
|
| 11093 | while (iscons(p)) {
|
| 11094 | if (!ispoly_factor(car(p), x)) {
|
| 11095 | return 0;
|
| 11096 | }
|
| 11097 | p = cdr(p);
|
| 11098 | }
|
| 11099 | return 1;
|
| 11100 | } else {
|
| 11101 | return ispoly_factor(p, x);
|
| 11102 | }
|
| 11103 | };
|
| 11104 |
|
| 11105 | ispoly_factor = function(p, x) {
|
| 11106 | if (equal(p, x)) {
|
| 11107 | return 1;
|
| 11108 | }
|
| 11109 | if (car(p) === symbol(POWER) && equal(cadr(p), x)) {
|
| 11110 | if (isposint(caddr(p))) {
|
| 11111 | return 1;
|
| 11112 | } else {
|
| 11113 | return 0;
|
| 11114 | }
|
| 11115 | }
|
| 11116 | if (Find(p, x)) {
|
| 11117 | return 0;
|
| 11118 | } else {
|
| 11119 | return 1;
|
| 11120 | }
|
| 11121 | };
|
| 11122 |
|
| 11123 | isnegativeterm = function(p) {
|
| 11124 | if (isnegativenumber(p)) {
|
| 11125 | return 1;
|
| 11126 | } else if (car(p) === symbol(MULTIPLY) && isnegativenumber(cadr(p))) {
|
| 11127 | return 1;
|
| 11128 | } else {
|
| 11129 | return 0;
|
| 11130 | }
|
| 11131 | };
|
| 11132 |
|
| 11133 | hasNegativeRationalExponent = function(p) {
|
| 11134 | if (car(p) === symbol(POWER) && isrational(car(cdr(cdr(p)))) && isnegativenumber(car(cdr(p)))) {
|
| 11135 | if (DEBUG_IS) {
|
| 11136 | console.log("hasNegativeRationalExponent: " + p.toString() + " has imaginary component");
|
| 11137 | }
|
| 11138 | return 1;
|
| 11139 | } else {
|
| 11140 | if (DEBUG_IS) {
|
| 11141 | console.log("hasNegativeRationalExponent: " + p.toString() + " has NO imaginary component");
|
| 11142 | }
|
| 11143 | return 0;
|
| 11144 | }
|
| 11145 | };
|
| 11146 |
|
| 11147 | isimaginarynumberdouble = function(p) {
|
| 11148 | if ((car(p) === symbol(MULTIPLY) && length(p) === 3 && isdouble(cadr(p)) && hasNegativeRationalExponent(caddr(p))) || equal(p, imaginaryunit)) {
|
| 11149 | return 1;
|
| 11150 | } else {
|
| 11151 | return 0;
|
| 11152 | }
|
| 11153 | };
|
| 11154 |
|
| 11155 | isimaginarynumber = function(p) {
|
| 11156 | if ((car(p) === symbol(MULTIPLY) && length(p) === 3 && isnum(cadr(p)) && equal(caddr(p), imaginaryunit)) || equal(p, imaginaryunit) || hasNegativeRationalExponent(caddr(p))) {
|
| 11157 | if (DEBUG_IS) {
|
| 11158 | console.log("isimaginarynumber: " + p.toString() + " is imaginary number");
|
| 11159 | }
|
| 11160 | return 1;
|
| 11161 | } else {
|
| 11162 | if (DEBUG_IS) {
|
| 11163 | console.log("isimaginarynumber: " + p.toString() + " isn't an imaginary number");
|
| 11164 | }
|
| 11165 | return 0;
|
| 11166 | }
|
| 11167 | };
|
| 11168 |
|
| 11169 | iscomplexnumberdouble = function(p) {
|
| 11170 | if ((car(p) === symbol(ADD) && length(p) === 3 && isdouble(cadr(p)) && isimaginarynumberdouble(caddr(p))) || isimaginarynumberdouble(p)) {
|
| 11171 | return 1;
|
| 11172 | } else {
|
| 11173 | return 0;
|
| 11174 | }
|
| 11175 | };
|
| 11176 |
|
| 11177 | iscomplexnumber = function(p) {
|
| 11178 | if (DEBUG_IS) {
|
| 11179 | debugger;
|
| 11180 | }
|
| 11181 | if ((car(p) === symbol(ADD) && length(p) === 3 && isnum(cadr(p)) && isimaginarynumber(caddr(p))) || isimaginarynumber(p)) {
|
| 11182 | if (DEBUG) {
|
| 11183 | console.log("iscomplexnumber: " + p.toString() + " is imaginary number");
|
| 11184 | }
|
| 11185 | return 1;
|
| 11186 | } else {
|
| 11187 | if (DEBUG) {
|
| 11188 | console.log("iscomplexnumber: " + p.toString() + " is imaginary number");
|
| 11189 | }
|
| 11190 | return 0;
|
| 11191 | }
|
| 11192 | };
|
| 11193 |
|
| 11194 | iseveninteger = function(p) {
|
| 11195 | if (isinteger(p) && p.q.a.isEven()) {
|
| 11196 | return 1;
|
| 11197 | } else {
|
| 11198 | return 0;
|
| 11199 | }
|
| 11200 | };
|
| 11201 |
|
| 11202 | isnegative = function(p) {
|
| 11203 | if (car(p) === symbol(ADD) && isnegativeterm(cadr(p))) {
|
| 11204 | return 1;
|
| 11205 | } else if (isnegativeterm(p)) {
|
| 11206 | return 1;
|
| 11207 | } else {
|
| 11208 | return 0;
|
| 11209 | }
|
| 11210 | };
|
| 11211 |
|
| 11212 | issymbolic = function(p) {
|
| 11213 | if (issymbol(p)) {
|
| 11214 | return 1;
|
| 11215 | } else {
|
| 11216 | while (iscons(p)) {
|
| 11217 | if (issymbolic(car(p))) {
|
| 11218 | return 1;
|
| 11219 | }
|
| 11220 | p = cdr(p);
|
| 11221 | }
|
| 11222 | return 0;
|
| 11223 | }
|
| 11224 | };
|
| 11225 |
|
| 11226 | isintegerfactor = function(p) {
|
| 11227 | if (isinteger(p) || car(p) === symbol(POWER) && isinteger(cadr(p)) && isinteger(caddr(p))) {
|
| 11228 | return 1;
|
| 11229 | } else {
|
| 11230 | return 0;
|
| 11231 | }
|
| 11232 | };
|
| 11233 |
|
| 11234 | isnumberoneoversomething = function(p) {
|
| 11235 | if (isfraction(p) && Math.abs(p.q.a.value) === 1) {
|
| 11236 | return 1;
|
| 11237 | } else {
|
| 11238 | return 0;
|
| 11239 | }
|
| 11240 | };
|
| 11241 |
|
| 11242 | isoneover = function(p) {
|
| 11243 | if (car(p) === symbol(POWER) && isminusone(caddr(p))) {
|
| 11244 | return 1;
|
| 11245 | } else {
|
| 11246 | return 0;
|
| 11247 | }
|
| 11248 | };
|
| 11249 |
|
| 11250 | isfraction = function(p) {
|
| 11251 | if (p.k === NUM && !MEQUAL(p.q.b, 1)) {
|
| 11252 | return 1;
|
| 11253 | } else {
|
| 11254 | return 0;
|
| 11255 | }
|
| 11256 | };
|
| 11257 |
|
| 11258 | equaln = function(p, n) {
|
| 11259 | switch (p.k) {
|
| 11260 | case NUM:
|
| 11261 | if (MEQUAL(p.q.a, n) && MEQUAL(p.q.b, 1)) {
|
| 11262 | return 1;
|
| 11263 | }
|
| 11264 | break;
|
| 11265 | case DOUBLE:
|
| 11266 | if (p.d === n) {
|
| 11267 | return 1;
|
| 11268 | }
|
| 11269 | }
|
| 11270 | return 0;
|
| 11271 | };
|
| 11272 |
|
| 11273 | equalq = function(p, a, b) {
|
| 11274 | switch (p.k) {
|
| 11275 | case NUM:
|
| 11276 | if (MEQUAL(p.q.a, a) && MEQUAL(p.q.b, b)) {
|
| 11277 | return 1;
|
| 11278 | }
|
| 11279 | break;
|
| 11280 | case DOUBLE:
|
| 11281 | if (p.d === a / b) {
|
| 11282 | return 1;
|
| 11283 | }
|
| 11284 | }
|
| 11285 | return 0;
|
| 11286 | };
|
| 11287 |
|
| 11288 | isoneovertwo = function(p) {
|
| 11289 | if (equalq(p, 1, 2)) {
|
| 11290 | return 1;
|
| 11291 | } else {
|
| 11292 | return 0;
|
| 11293 | }
|
| 11294 | };
|
| 11295 |
|
| 11296 | isminusoneovertwo = function(p) {
|
| 11297 | if (equalq(p, -1, 2)) {
|
| 11298 | return 1;
|
| 11299 | } else {
|
| 11300 | return 0;
|
| 11301 | }
|
| 11302 | };
|
| 11303 |
|
| 11304 | isoneoversqrttwo = function(p) {
|
| 11305 | if (car(p) === symbol(POWER) && equaln(cadr(p), 2) && equalq(caddr(p), -1, 2)) {
|
| 11306 | return 1;
|
| 11307 | } else {
|
| 11308 | return 0;
|
| 11309 | }
|
| 11310 | };
|
| 11311 |
|
| 11312 | isminusoneoversqrttwo = function(p) {
|
| 11313 | if (car(p) === symbol(MULTIPLY) && equaln(cadr(p), -1) && isoneoversqrttwo(caddr(p)) && length(p) === 3) {
|
| 11314 | return 1;
|
| 11315 | } else {
|
| 11316 | return 0;
|
| 11317 | }
|
| 11318 | };
|
| 11319 |
|
| 11320 | isfloating = function(p) {
|
| 11321 | if (p.k === DOUBLE || p === symbol(FLOATF)) {
|
| 11322 | return 1;
|
| 11323 | }
|
| 11324 | while (iscons(p)) {
|
| 11325 | if (isfloating(car(p))) {
|
| 11326 | return 1;
|
| 11327 | }
|
| 11328 | p = cdr(p);
|
| 11329 | }
|
| 11330 | return 0;
|
| 11331 | };
|
| 11332 |
|
| 11333 | isimaginaryunit = function(p) {
|
| 11334 | if (equal(p, imaginaryunit)) {
|
| 11335 | return 1;
|
| 11336 | } else {
|
| 11337 | return 0;
|
| 11338 | }
|
| 11339 | };
|
| 11340 |
|
| 11341 | isquarterturn = function(p) {
|
| 11342 | var minussign, n;
|
| 11343 | n = 0;
|
| 11344 | minussign = 0;
|
| 11345 | if (car(p) !== symbol(MULTIPLY)) {
|
| 11346 | return 0;
|
| 11347 | }
|
| 11348 | if (equal(cadr(p), imaginaryunit)) {
|
| 11349 | if (caddr(p) !== symbol(PI)) {
|
| 11350 | return 0;
|
| 11351 | }
|
| 11352 | if (length(p) !== 3) {
|
| 11353 | return 0;
|
| 11354 | }
|
| 11355 | return 2;
|
| 11356 | }
|
| 11357 | if (!isnum(cadr(p))) {
|
| 11358 | return 0;
|
| 11359 | }
|
| 11360 | if (!equal(caddr(p), imaginaryunit)) {
|
| 11361 | return 0;
|
| 11362 | }
|
| 11363 | if (cadddr(p) !== symbol(PI)) {
|
| 11364 | return 0;
|
| 11365 | }
|
| 11366 | if (length(p) !== 4) {
|
| 11367 | return 0;
|
| 11368 | }
|
| 11369 | push(cadr(p));
|
| 11370 | push_integer(2);
|
| 11371 | multiply();
|
| 11372 | n = pop_integer();
|
| 11373 | if (isNaN(n)) {
|
| 11374 | return 0;
|
| 11375 | }
|
| 11376 | if (n < 1) {
|
| 11377 | minussign = 1;
|
| 11378 | n = -n;
|
| 11379 | }
|
| 11380 | switch (n % 4) {
|
| 11381 | case 0:
|
| 11382 | n = 1;
|
| 11383 | break;
|
| 11384 | case 1:
|
| 11385 | if (minussign) {
|
| 11386 | n = 4;
|
| 11387 | } else {
|
| 11388 | n = 3;
|
| 11389 | }
|
| 11390 | break;
|
| 11391 | case 2:
|
| 11392 | n = 2;
|
| 11393 | break;
|
| 11394 | case 3:
|
| 11395 | if (minussign) {
|
| 11396 | n = 3;
|
| 11397 | } else {
|
| 11398 | n = 4;
|
| 11399 | }
|
| 11400 | }
|
| 11401 | return n;
|
| 11402 | };
|
| 11403 |
|
| 11404 | isnpi = function(p) {
|
| 11405 | var doNothing, n;
|
| 11406 | n = 0;
|
| 11407 | if (p === symbol(PI)) {
|
| 11408 | return 2;
|
| 11409 | }
|
| 11410 | if (car(p) === symbol(MULTIPLY) && isnum(cadr(p)) && caddr(p) === symbol(PI) && length(p) === 3) {
|
| 11411 | doNothing = 0;
|
| 11412 | } else {
|
| 11413 | return 0;
|
| 11414 | }
|
| 11415 | push(cadr(p));
|
| 11416 | push_integer(2);
|
| 11417 | multiply();
|
| 11418 | n = pop_integer();
|
| 11419 | if (isNaN(n)) {
|
| 11420 | return 0;
|
| 11421 | }
|
| 11422 | if (n < 0) {
|
| 11423 | n = 4 - (-n) % 4;
|
| 11424 | } else {
|
| 11425 | n = 1 + (n - 1) % 4;
|
| 11426 | }
|
| 11427 | return n;
|
| 11428 | };
|
| 11429 |
|
| 11430 | $.iszero = iszero;
|
| 11431 |
|
| 11432 | $.isnegativenumber = isnegativenumber;
|
| 11433 |
|
| 11434 | $.isplusone = isplusone;
|
| 11435 |
|
| 11436 | $.isminusone = isminusone;
|
| 11437 |
|
| 11438 | $.isinteger = isinteger;
|
| 11439 |
|
| 11440 | $.isnonnegativeinteger = isnonnegativeinteger;
|
| 11441 |
|
| 11442 | $.isposint = isposint;
|
| 11443 |
|
| 11444 | $.isnegativeterm = isnegativeterm;
|
| 11445 |
|
| 11446 | $.isimaginarynumber = isimaginarynumber;
|
| 11447 |
|
| 11448 | $.iscomplexnumber = iscomplexnumber;
|
| 11449 |
|
| 11450 | $.iseveninteger = iseveninteger;
|
| 11451 |
|
| 11452 | $.isnegative = isnegative;
|
| 11453 |
|
| 11454 | $.issymbolic = issymbolic;
|
| 11455 |
|
| 11456 | $.isintegerfactor = isintegerfactor;
|
| 11457 |
|
| 11458 | $.isoneover = isoneover;
|
| 11459 |
|
| 11460 | $.isfraction = isfraction;
|
| 11461 |
|
| 11462 | $.isoneoversqrttwo = isoneoversqrttwo;
|
| 11463 |
|
| 11464 | $.isminusoneoversqrttwo = isminusoneoversqrttwo;
|
| 11465 |
|
| 11466 | $.isfloating = isfloating;
|
| 11467 |
|
| 11468 | $.isimaginaryunit = isimaginaryunit;
|
| 11469 |
|
| 11470 | $.isquarterturn = isquarterturn;
|
| 11471 |
|
| 11472 | $.isnpi = isnpi;
|
| 11473 |
|
| 11474 | Eval_isprime = function() {
|
| 11475 | push(cadr(p1));
|
| 11476 | Eval();
|
| 11477 | p1 = pop();
|
| 11478 | if (isnonnegativeinteger(p1) && mprime(p1.q.a)) {
|
| 11479 | return push_integer(1);
|
| 11480 | } else {
|
| 11481 | return push_integer(0);
|
| 11482 | }
|
| 11483 | };
|
| 11484 |
|
| 11485 |
|
| 11486 | |
| 11487 | |
| 11488 | |
| 11489 | |
| 11490 | |
| 11491 | |
| 11492 | |
| 11493 | |
| 11494 | |
| 11495 | |
| 11496 | |
| 11497 | |
| 11498 | |
| 11499 | |
| 11500 | |
| 11501 | |
| 11502 | |
| 11503 | |
| 11504 | |
| 11505 | |
| 11506 | |
| 11507 | |
| 11508 | |
| 11509 | |
| 11510 |
|
| 11511 |
|
| 11512 | Eval_laguerre = function() {
|
| 11513 | push(cadr(p1));
|
| 11514 | Eval();
|
| 11515 | push(caddr(p1));
|
| 11516 | Eval();
|
| 11517 | push(cadddr(p1));
|
| 11518 | Eval();
|
| 11519 | p2 = pop();
|
| 11520 | if (p2 === symbol(NIL)) {
|
| 11521 | push_integer(0);
|
| 11522 | } else {
|
| 11523 | push(p2);
|
| 11524 | }
|
| 11525 | return laguerre();
|
| 11526 | };
|
| 11527 |
|
| 11528 | laguerre = function() {
|
| 11529 | var n;
|
| 11530 | n = 0;
|
| 11531 | save();
|
| 11532 | p3 = pop();
|
| 11533 | p2 = pop();
|
| 11534 | p1 = pop();
|
| 11535 | push(p2);
|
| 11536 | n = pop_integer();
|
| 11537 | if (n < 0 || isNaN(n)) {
|
| 11538 | push_symbol(LAGUERRE);
|
| 11539 | push(p1);
|
| 11540 | push(p2);
|
| 11541 | push(p3);
|
| 11542 | list(4);
|
| 11543 | restore();
|
| 11544 | return;
|
| 11545 | }
|
| 11546 | if (issymbol(p1)) {
|
| 11547 | laguerre2(n);
|
| 11548 | } else {
|
| 11549 | p4 = p1;
|
| 11550 | p1 = symbol(SECRETX);
|
| 11551 | laguerre2(n);
|
| 11552 | p1 = p4;
|
| 11553 | push(symbol(SECRETX));
|
| 11554 | push(p1);
|
| 11555 | subst();
|
| 11556 | Eval();
|
| 11557 | }
|
| 11558 | return restore();
|
| 11559 | };
|
| 11560 |
|
| 11561 | laguerre2 = function(n) {
|
| 11562 | var i, o, ref, results;
|
| 11563 | i = 0;
|
| 11564 | push_integer(1);
|
| 11565 | push_integer(0);
|
| 11566 | p6 = pop();
|
| 11567 | results = [];
|
| 11568 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 11569 | p5 = p6;
|
| 11570 | p6 = pop();
|
| 11571 | push_integer(2 * i + 1);
|
| 11572 | push(p1);
|
| 11573 | subtract();
|
| 11574 | push(p3);
|
| 11575 | add();
|
| 11576 | push(p6);
|
| 11577 | multiply();
|
| 11578 | push_integer(i);
|
| 11579 | push(p3);
|
| 11580 | add();
|
| 11581 | push(p5);
|
| 11582 | multiply();
|
| 11583 | subtract();
|
| 11584 | push_integer(i + 1);
|
| 11585 | results.push(divide());
|
| 11586 | }
|
| 11587 | return results;
|
| 11588 | };
|
| 11589 |
|
| 11590 | Eval_lcm = function() {
|
| 11591 | var results;
|
| 11592 | p1 = cdr(p1);
|
| 11593 | push(car(p1));
|
| 11594 | Eval();
|
| 11595 | p1 = cdr(p1);
|
| 11596 | results = [];
|
| 11597 | while (iscons(p1)) {
|
| 11598 | push(car(p1));
|
| 11599 | Eval();
|
| 11600 | lcm();
|
| 11601 | results.push(p1 = cdr(p1));
|
| 11602 | }
|
| 11603 | return results;
|
| 11604 | };
|
| 11605 |
|
| 11606 | lcm = function() {
|
| 11607 | var prev_expanding;
|
| 11608 | prev_expanding = expanding;
|
| 11609 | save();
|
| 11610 | yylcm();
|
| 11611 | restore();
|
| 11612 | return expanding = prev_expanding;
|
| 11613 | };
|
| 11614 |
|
| 11615 | yylcm = function() {
|
| 11616 | expanding = 1;
|
| 11617 | p2 = pop();
|
| 11618 | p1 = pop();
|
| 11619 | push(p1);
|
| 11620 | push(p2);
|
| 11621 | gcd();
|
| 11622 | push(p1);
|
| 11623 | divide();
|
| 11624 | push(p2);
|
| 11625 | divide();
|
| 11626 | return inverse();
|
| 11627 | };
|
| 11628 |
|
| 11629 |
|
| 11630 | |
| 11631 | |
| 11632 | |
| 11633 | |
| 11634 | |
| 11635 | |
| 11636 | |
| 11637 | |
| 11638 | |
| 11639 | |
| 11640 | |
| 11641 | |
| 11642 |
|
| 11643 |
|
| 11644 | Eval_leading = function() {
|
| 11645 | push(cadr(p1));
|
| 11646 | Eval();
|
| 11647 | push(caddr(p1));
|
| 11648 | Eval();
|
| 11649 | p1 = pop();
|
| 11650 | if (p1 === symbol(NIL)) {
|
| 11651 | guess();
|
| 11652 | } else {
|
| 11653 | push(p1);
|
| 11654 | }
|
| 11655 | return leading();
|
| 11656 | };
|
| 11657 |
|
| 11658 | leading = function() {
|
| 11659 | save();
|
| 11660 | p2 = pop();
|
| 11661 | p1 = pop();
|
| 11662 | push(p1);
|
| 11663 | push(p2);
|
| 11664 | degree();
|
| 11665 | p3 = pop();
|
| 11666 | push(p1);
|
| 11667 | push(p2);
|
| 11668 | push(p3);
|
| 11669 | power();
|
| 11670 | divide();
|
| 11671 | push(p2);
|
| 11672 | filter();
|
| 11673 | return restore();
|
| 11674 | };
|
| 11675 |
|
| 11676 |
|
| 11677 | |
| 11678 | |
| 11679 | |
| 11680 | |
| 11681 | |
| 11682 | |
| 11683 | |
| 11684 | |
| 11685 | |
| 11686 | |
| 11687 | |
| 11688 | |
| 11689 | |
| 11690 | |
| 11691 | |
| 11692 | |
| 11693 | |
| 11694 | |
| 11695 | |
| 11696 | |
| 11697 | |
| 11698 | |
| 11699 | |
| 11700 | |
| 11701 | |
| 11702 | |
| 11703 | |
| 11704 | |
| 11705 |
|
| 11706 |
|
| 11707 | Eval_legendre = function() {
|
| 11708 | push(cadr(p1));
|
| 11709 | Eval();
|
| 11710 | push(caddr(p1));
|
| 11711 | Eval();
|
| 11712 | push(cadddr(p1));
|
| 11713 | Eval();
|
| 11714 | p2 = pop();
|
| 11715 | if (p2 === symbol(NIL)) {
|
| 11716 | push_integer(0);
|
| 11717 | } else {
|
| 11718 | push(p2);
|
| 11719 | }
|
| 11720 | return legendre();
|
| 11721 | };
|
| 11722 |
|
| 11723 | legendre = function() {
|
| 11724 | save();
|
| 11725 | __legendre();
|
| 11726 | return restore();
|
| 11727 | };
|
| 11728 |
|
| 11729 | __legendre = function() {
|
| 11730 | var m, n;
|
| 11731 | m = 0;
|
| 11732 | n = 0;
|
| 11733 | p3 = pop();
|
| 11734 | p2 = pop();
|
| 11735 | p1 = pop();
|
| 11736 | push(p2);
|
| 11737 | n = pop_integer();
|
| 11738 | push(p3);
|
| 11739 | m = pop_integer();
|
| 11740 | if (n < 0 || isNaN(n) || m < 0 || isNaN(m)) {
|
| 11741 | push_symbol(LEGENDRE);
|
| 11742 | push(p1);
|
| 11743 | push(p2);
|
| 11744 | push(p3);
|
| 11745 | list(4);
|
| 11746 | return;
|
| 11747 | }
|
| 11748 | if (issymbol(p1)) {
|
| 11749 | __legendre2(n, m);
|
| 11750 | } else {
|
| 11751 | p4 = p1;
|
| 11752 | p1 = symbol(SECRETX);
|
| 11753 | __legendre2(n, m);
|
| 11754 | p1 = p4;
|
| 11755 | push(symbol(SECRETX));
|
| 11756 | push(p1);
|
| 11757 | subst();
|
| 11758 | Eval();
|
| 11759 | }
|
| 11760 | return __legendre3(m);
|
| 11761 | };
|
| 11762 |
|
| 11763 | __legendre2 = function(n, m) {
|
| 11764 | var i, i1, o, ref, ref1, results;
|
| 11765 | i = 0;
|
| 11766 | push_integer(1);
|
| 11767 | push_integer(0);
|
| 11768 | p6 = pop();
|
| 11769 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 11770 | p5 = p6;
|
| 11771 | p6 = pop();
|
| 11772 | push_integer(2 * i + 1);
|
| 11773 | push(p1);
|
| 11774 | multiply();
|
| 11775 | push(p6);
|
| 11776 | multiply();
|
| 11777 | push_integer(i);
|
| 11778 | push(p5);
|
| 11779 | multiply();
|
| 11780 | subtract();
|
| 11781 | push_integer(i + 1);
|
| 11782 | divide();
|
| 11783 | }
|
| 11784 | results = [];
|
| 11785 | for (i = i1 = 0, ref1 = m; 0 <= ref1 ? i1 < ref1 : i1 > ref1; i = 0 <= ref1 ? ++i1 : --i1) {
|
| 11786 | push(p1);
|
| 11787 | results.push(derivative());
|
| 11788 | }
|
| 11789 | return results;
|
| 11790 | };
|
| 11791 |
|
| 11792 | __legendre3 = function(m) {
|
| 11793 | if (m === 0) {
|
| 11794 | return;
|
| 11795 | }
|
| 11796 | if (car(p1) === symbol(COS)) {
|
| 11797 | push(cadr(p1));
|
| 11798 | sine();
|
| 11799 | square();
|
| 11800 | } else if (car(p1) === symbol(SIN)) {
|
| 11801 | push(cadr(p1));
|
| 11802 | cosine();
|
| 11803 | square();
|
| 11804 | } else {
|
| 11805 | push_integer(1);
|
| 11806 | push(p1);
|
| 11807 | square();
|
| 11808 | subtract();
|
| 11809 | }
|
| 11810 | push_integer(m);
|
| 11811 | push_rational(1, 2);
|
| 11812 | multiply();
|
| 11813 | power();
|
| 11814 | multiply();
|
| 11815 | if (m % 2) {
|
| 11816 | return negate();
|
| 11817 | }
|
| 11818 | };
|
| 11819 |
|
| 11820 | list = function(n) {
|
| 11821 | var listIterator, o, ref, results;
|
| 11822 | listIterator = 0;
|
| 11823 | push(symbol(NIL));
|
| 11824 | results = [];
|
| 11825 | for (listIterator = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; listIterator = 0 <= ref ? ++o : --o) {
|
| 11826 | results.push(cons());
|
| 11827 | }
|
| 11828 | return results;
|
| 11829 | };
|
| 11830 |
|
| 11831 | Eval_log = function() {
|
| 11832 | push(cadr(p1));
|
| 11833 | Eval();
|
| 11834 | return logarithm();
|
| 11835 | };
|
| 11836 |
|
| 11837 | logarithm = function() {
|
| 11838 | save();
|
| 11839 | yylog();
|
| 11840 | return restore();
|
| 11841 | };
|
| 11842 |
|
| 11843 | yylog = function() {
|
| 11844 | var d;
|
| 11845 | d = 0.0;
|
| 11846 | p1 = pop();
|
| 11847 | if (p1 === symbol(E)) {
|
| 11848 | push_integer(1);
|
| 11849 | return;
|
| 11850 | }
|
| 11851 | if (equaln(p1, 1)) {
|
| 11852 | push_integer(0);
|
| 11853 | return;
|
| 11854 | }
|
| 11855 | if (isnegativenumber(p1)) {
|
| 11856 | push(p1);
|
| 11857 | negate();
|
| 11858 | logarithm();
|
| 11859 | push(imaginaryunit);
|
| 11860 | if (evaluatingAsFloats) {
|
| 11861 | push_double(Math.PI);
|
| 11862 | } else {
|
| 11863 | push_symbol(PI);
|
| 11864 | }
|
| 11865 | multiply();
|
| 11866 | add();
|
| 11867 | return;
|
| 11868 | }
|
| 11869 | if (isdouble(p1)) {
|
| 11870 | d = Math.log(p1.d);
|
| 11871 | push_double(d);
|
| 11872 | return;
|
| 11873 | }
|
| 11874 | if (isfraction(p1)) {
|
| 11875 | push(p1);
|
| 11876 | numerator();
|
| 11877 | logarithm();
|
| 11878 | push(p1);
|
| 11879 | denominator();
|
| 11880 | logarithm();
|
| 11881 | subtract();
|
| 11882 | return;
|
| 11883 | }
|
| 11884 | if (car(p1) === symbol(POWER)) {
|
| 11885 | push(caddr(p1));
|
| 11886 | push(cadr(p1));
|
| 11887 | logarithm();
|
| 11888 | multiply();
|
| 11889 | return;
|
| 11890 | }
|
| 11891 | if (car(p1) === symbol(MULTIPLY)) {
|
| 11892 | push_integer(0);
|
| 11893 | p1 = cdr(p1);
|
| 11894 | while (iscons(p1)) {
|
| 11895 | push(car(p1));
|
| 11896 | logarithm();
|
| 11897 | add();
|
| 11898 | p1 = cdr(p1);
|
| 11899 | }
|
| 11900 | return;
|
| 11901 | }
|
| 11902 | push_symbol(LOG);
|
| 11903 | push(p1);
|
| 11904 | return list(2);
|
| 11905 | };
|
| 11906 |
|
| 11907 | Eval_lookup = function() {
|
| 11908 | p1 = cadr(p1);
|
| 11909 | if (!iscons(p1) && cadr(p1).k === SYM) {
|
| 11910 | p1 = get_binding(p1);
|
| 11911 | }
|
| 11912 | return push(p1);
|
| 11913 | };
|
| 11914 |
|
| 11915 | madd = function(a, b) {
|
| 11916 | return a.add(b);
|
| 11917 | };
|
| 11918 |
|
| 11919 | msub = function(a, b) {
|
| 11920 | return a.subtract(b);
|
| 11921 | };
|
| 11922 |
|
| 11923 | addf = function(a, b) {
|
| 11924 | return a.add(b);
|
| 11925 | };
|
| 11926 |
|
| 11927 | subf = function(a, b) {
|
| 11928 | return a.subtract(b);
|
| 11929 | };
|
| 11930 |
|
| 11931 | ucmp = function(a, b) {
|
| 11932 | return a.compareAbs(b);
|
| 11933 | };
|
| 11934 |
|
| 11935 | mgcd = function(u, v) {
|
| 11936 | return bigInt.gcd(u, v);
|
| 11937 | };
|
| 11938 |
|
| 11939 | new_string = function(s) {
|
| 11940 | save();
|
| 11941 | p1 = new U();
|
| 11942 | p1.k = STR;
|
| 11943 | p1.str = s;
|
| 11944 | push(p1);
|
| 11945 | return restore();
|
| 11946 | };
|
| 11947 |
|
| 11948 | out_of_memory = function() {
|
| 11949 | return stop("out of memory");
|
| 11950 | };
|
| 11951 |
|
| 11952 | push_zero_matrix = function(i, j) {
|
| 11953 | push(alloc_tensor(i * j));
|
| 11954 | stack[tos - 1].tensor.ndim = 2;
|
| 11955 | stack[tos - 1].tensor.dim[0] = i;
|
| 11956 | return stack[tos - 1].tensor.dim[1] = j;
|
| 11957 | };
|
| 11958 |
|
| 11959 | push_identity_matrix = function(n) {
|
| 11960 | var i, o, ref;
|
| 11961 | push_zero_matrix(n, n);
|
| 11962 | i = 0;
|
| 11963 | for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 11964 | stack[tos - 1].tensor.elem[i * n + i] = one;
|
| 11965 | }
|
| 11966 | return check_tensor_dimensions(stack[tos - 1]);
|
| 11967 | };
|
| 11968 |
|
| 11969 | push_cars = function(p) {
|
| 11970 | var results;
|
| 11971 | results = [];
|
| 11972 | while (iscons(p)) {
|
| 11973 | push(car(p));
|
| 11974 | results.push(p = cdr(p));
|
| 11975 | }
|
| 11976 | return results;
|
| 11977 | };
|
| 11978 |
|
| 11979 | peek = function() {
|
| 11980 | save();
|
| 11981 | p1 = pop();
|
| 11982 | push(p1);
|
| 11983 | return restore();
|
| 11984 | };
|
| 11985 |
|
| 11986 | equal = function(p1, p2) {
|
| 11987 | if (cmp_expr(p1, p2) === 0) {
|
| 11988 | return 1;
|
| 11989 | } else {
|
| 11990 | return 0;
|
| 11991 | }
|
| 11992 | };
|
| 11993 |
|
| 11994 | lessp = function(p1, p2) {
|
| 11995 | if (cmp_expr(p1, p2) < 0) {
|
| 11996 | return 1;
|
| 11997 | } else {
|
| 11998 | return 0;
|
| 11999 | }
|
| 12000 | };
|
| 12001 |
|
| 12002 | sign = function(n) {
|
| 12003 | if (n < 0) {
|
| 12004 | return -1;
|
| 12005 | } else if (n > 0) {
|
| 12006 | return 1;
|
| 12007 | } else {
|
| 12008 | return 0;
|
| 12009 | }
|
| 12010 | };
|
| 12011 |
|
| 12012 | cmp_expr = function(p1, p2) {
|
| 12013 | var n;
|
| 12014 | n = 0;
|
| 12015 | if (p1 === p2) {
|
| 12016 | return 0;
|
| 12017 | }
|
| 12018 | if (p1 === symbol(NIL)) {
|
| 12019 | return -1;
|
| 12020 | }
|
| 12021 | if (p2 === symbol(NIL)) {
|
| 12022 | return 1;
|
| 12023 | }
|
| 12024 | if (isnum(p1) && isnum(p2)) {
|
| 12025 | return sign(compare_numbers(p1, p2));
|
| 12026 | }
|
| 12027 | if (isnum(p1)) {
|
| 12028 | return -1;
|
| 12029 | }
|
| 12030 | if (isnum(p2)) {
|
| 12031 | return 1;
|
| 12032 | }
|
| 12033 | if (isstr(p1) && isstr(p2)) {
|
| 12034 | return sign(strcmp(p1.str, p2.str));
|
| 12035 | }
|
| 12036 | if (isstr(p1)) {
|
| 12037 | return -1;
|
| 12038 | }
|
| 12039 | if (isstr(p2)) {
|
| 12040 | return 1;
|
| 12041 | }
|
| 12042 | if (issymbol(p1) && issymbol(p2)) {
|
| 12043 | return sign(strcmp(get_printname(p1), get_printname(p2)));
|
| 12044 | }
|
| 12045 | if (issymbol(p1)) {
|
| 12046 | return -1;
|
| 12047 | }
|
| 12048 | if (issymbol(p2)) {
|
| 12049 | return 1;
|
| 12050 | }
|
| 12051 | if (istensor(p1) && istensor(p2)) {
|
| 12052 | return compare_tensors(p1, p2);
|
| 12053 | }
|
| 12054 | if (istensor(p1)) {
|
| 12055 | return -1;
|
| 12056 | }
|
| 12057 | if (istensor(p2)) {
|
| 12058 | return 1;
|
| 12059 | }
|
| 12060 | while (iscons(p1) && iscons(p2)) {
|
| 12061 | n = cmp_expr(car(p1), car(p2));
|
| 12062 | if (n !== 0) {
|
| 12063 | return n;
|
| 12064 | }
|
| 12065 | p1 = cdr(p1);
|
| 12066 | p2 = cdr(p2);
|
| 12067 | }
|
| 12068 | if (iscons(p2)) {
|
| 12069 | return -1;
|
| 12070 | }
|
| 12071 | if (iscons(p1)) {
|
| 12072 | return 1;
|
| 12073 | }
|
| 12074 | return 0;
|
| 12075 | };
|
| 12076 |
|
| 12077 | length = function(p) {
|
| 12078 | var n;
|
| 12079 | n = 0;
|
| 12080 | while (iscons(p)) {
|
| 12081 | p = cdr(p);
|
| 12082 | n++;
|
| 12083 | }
|
| 12084 | return n;
|
| 12085 | };
|
| 12086 |
|
| 12087 | unique = function(p) {
|
| 12088 | save();
|
| 12089 | p1 = symbol(NIL);
|
| 12090 | p2 = symbol(NIL);
|
| 12091 | unique_f(p);
|
| 12092 | if (p2 !== symbol(NIL)) {
|
| 12093 | p1 = symbol(NIL);
|
| 12094 | }
|
| 12095 | p = p1;
|
| 12096 | restore();
|
| 12097 | return p;
|
| 12098 | };
|
| 12099 |
|
| 12100 | unique_f = function(p) {
|
| 12101 | if (isstr(p)) {
|
| 12102 | if (p1 === symbol(NIL)) {
|
| 12103 | p1 = p;
|
| 12104 | } else if (p !== p1) {
|
| 12105 | p2 = p;
|
| 12106 | }
|
| 12107 | return;
|
| 12108 | }
|
| 12109 | while (iscons(p)) {
|
| 12110 | unique_f(car(p));
|
| 12111 | if (p2 !== symbol(NIL)) {
|
| 12112 | return;
|
| 12113 | }
|
| 12114 | p = cdr(p);
|
| 12115 | }
|
| 12116 | };
|
| 12117 |
|
| 12118 | ssqrt = function() {
|
| 12119 | push_rational(1, 2);
|
| 12120 | return power();
|
| 12121 | };
|
| 12122 |
|
| 12123 | yyexpand = function() {
|
| 12124 | var prev_expanding;
|
| 12125 | prev_expanding = expanding;
|
| 12126 | expanding = 1;
|
| 12127 | Eval();
|
| 12128 | return expanding = prev_expanding;
|
| 12129 | };
|
| 12130 |
|
| 12131 | exponential = function() {
|
| 12132 | push_symbol(E);
|
| 12133 | swap();
|
| 12134 | return power();
|
| 12135 | };
|
| 12136 |
|
| 12137 | square = function() {
|
| 12138 | push_integer(2);
|
| 12139 | return power();
|
| 12140 | };
|
| 12141 |
|
| 12142 | sort_stack = function(n) {
|
| 12143 | var h, subsetOfStack;
|
| 12144 | h = tos - n;
|
| 12145 | subsetOfStack = stack.slice(h, h + n);
|
| 12146 | subsetOfStack.sort(cmp_expr);
|
| 12147 | return stack = stack.slice(0, h).concat(subsetOfStack).concat(stack.slice(h + n));
|
| 12148 | };
|
| 12149 |
|
| 12150 | $.equal = equal;
|
| 12151 |
|
| 12152 | $.length = length;
|
| 12153 |
|
| 12154 | mmul = function(a, b) {
|
| 12155 | return a.multiply(b);
|
| 12156 | };
|
| 12157 |
|
| 12158 | mdiv = function(a, b) {
|
| 12159 | return a.divide(b);
|
| 12160 | };
|
| 12161 |
|
| 12162 |
|
| 12163 | |
| 12164 | |
| 12165 | |
| 12166 | |
| 12167 | |
| 12168 | |
| 12169 | |
| 12170 | |
| 12171 | |
| 12172 | |
| 12173 | |
| 12174 | |
| 12175 | |
| 12176 | |
| 12177 | |
| 12178 | |
| 12179 | |
| 12180 | |
| 12181 | |
| 12182 | |
| 12183 | |
| 12184 | |
| 12185 | |
| 12186 | |
| 12187 | |
| 12188 | |
| 12189 | |
| 12190 | |
| 12191 | |
| 12192 | |
| 12193 | |
| 12194 | |
| 12195 | |
| 12196 | |
| 12197 | |
| 12198 | |
| 12199 | |
| 12200 | |
| 12201 | |
| 12202 | |
| 12203 | |
| 12204 | |
| 12205 | |
| 12206 |
|
| 12207 |
|
| 12208 | mmod = function(a, b) {
|
| 12209 | return a.mod(b);
|
| 12210 | };
|
| 12211 |
|
| 12212 | mdivrem = function(a, b) {
|
| 12213 | var toReturn;
|
| 12214 | toReturn = a.divmod(b);
|
| 12215 | return [toReturn.quotient, toReturn.remainder];
|
| 12216 | };
|
| 12217 |
|
| 12218 | Eval_mod = function() {
|
| 12219 | push(cadr(p1));
|
| 12220 | Eval();
|
| 12221 | push(caddr(p1));
|
| 12222 | Eval();
|
| 12223 | return mod();
|
| 12224 | };
|
| 12225 |
|
| 12226 | mod = function() {
|
| 12227 | var n;
|
| 12228 | n = 0;
|
| 12229 | save();
|
| 12230 | p2 = pop();
|
| 12231 | p1 = pop();
|
| 12232 | if (iszero(p2)) {
|
| 12233 | stop("mod function: divide by zero");
|
| 12234 | }
|
| 12235 | if (!isnum(p1) || !isnum(p2)) {
|
| 12236 | push_symbol(MOD);
|
| 12237 | push(p1);
|
| 12238 | push(p2);
|
| 12239 | list(3);
|
| 12240 | restore();
|
| 12241 | return;
|
| 12242 | }
|
| 12243 | if (isdouble(p1)) {
|
| 12244 | push(p1);
|
| 12245 | n = pop_integer();
|
| 12246 | if (isNaN(n)) {
|
| 12247 | stop("mod function: cannot convert float value to integer");
|
| 12248 | }
|
| 12249 | push_integer(n);
|
| 12250 | p1 = pop();
|
| 12251 | }
|
| 12252 | if (isdouble(p2)) {
|
| 12253 | push(p2);
|
| 12254 | n = pop_integer();
|
| 12255 | if (isNaN(n)) {
|
| 12256 | stop("mod function: cannot convert float value to integer");
|
| 12257 | }
|
| 12258 | push_integer(n);
|
| 12259 | p2 = pop();
|
| 12260 | }
|
| 12261 | if (!isinteger(p1) || !isinteger(p2)) {
|
| 12262 | stop("mod function: integer arguments expected");
|
| 12263 | }
|
| 12264 | p3 = new U();
|
| 12265 | p3.k = NUM;
|
| 12266 | p3.q.a = mmod(p1.q.a, p2.q.a);
|
| 12267 | p3.q.b = mint(1);
|
| 12268 | push(p3);
|
| 12269 | return restore();
|
| 12270 | };
|
| 12271 |
|
| 12272 | mpow = function(a, n) {
|
| 12273 | return a.pow(n);
|
| 12274 | };
|
| 12275 |
|
| 12276 | mprime = function(n) {
|
| 12277 | return n.isProbablePrime();
|
| 12278 | };
|
| 12279 |
|
| 12280 | mroot = function(n, index) {
|
| 12281 | var i, j, k, o, ref, x, y;
|
| 12282 | n = n.abs();
|
| 12283 | i = 0;
|
| 12284 | j = 0;
|
| 12285 | k = 0;
|
| 12286 | if (index === 0) {
|
| 12287 | stop("root index is zero");
|
| 12288 | }
|
| 12289 | k = 0;
|
| 12290 | while (n.shiftRight(k) > 0) {
|
| 12291 | k++;
|
| 12292 | }
|
| 12293 | if (k === 0) {
|
| 12294 | return mint(0);
|
| 12295 | }
|
| 12296 | k = Math.floor((k - 1) / index);
|
| 12297 | j = Math.floor(k / 32 + 1);
|
| 12298 | x = bigInt(j);
|
| 12299 | for (i = o = 0, ref = j; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
|
| 12300 | x = x.and(bigInt(1).shiftLeft(i).not());
|
| 12301 | }
|
| 12302 | while (k >= 0) {
|
| 12303 | x = x.or(bigInt(1).shiftLeft(k));
|
| 12304 | y = mpow(x, index);
|
| 12305 | switch (mcmp(y, n)) {
|
| 12306 | case 0:
|
| 12307 | return x;
|
| 12308 | case 1:
|
| 12309 | x = x.and(bigInt(1).shiftLeft(k).not());
|
| 12310 | }
|
| 12311 | k--;
|
| 12312 | }
|
| 12313 | return 0;
|
| 12314 | };
|
| 12315 |
|
| 12316 | Eval_multiply = function() {
|
| 12317 | var results;
|
| 12318 | push(cadr(p1));
|
| 12319 | Eval();
|
| 12320 | p1 = cddr(p1);
|
| 12321 | results = [];
|
| 12322 | while (iscons(p1)) {
|
| 12323 | push(car(p1));
|
| 12324 | Eval();
|
| 12325 | multiply();
|
| 12326 | results.push(p1 = cdr(p1));
|
| 12327 | }
|
| 12328 | return results;
|
| 12329 | };
|
| 12330 |
|
| 12331 | multiply = function() {
|
| 12332 | if (esc_flag) {
|
| 12333 | stop("escape key stop");
|
| 12334 | }
|
| 12335 | if (isnum(stack[tos - 2]) && isnum(stack[tos - 1])) {
|
| 12336 | return multiply_numbers();
|
| 12337 | } else {
|
| 12338 | save();
|
| 12339 | yymultiply();
|
| 12340 | return restore();
|
| 12341 | }
|
| 12342 | };
|
| 12343 |
|
| 12344 | yymultiply = function() {
|
| 12345 | var h, i, n, o, ref, ref1;
|
| 12346 | h = 0;
|
| 12347 | i = 0;
|
| 12348 | n = 0;
|
| 12349 | p2 = pop();
|
| 12350 | p1 = pop();
|
| 12351 | h = tos;
|
| 12352 | if (iszero(p1) || iszero(p2)) {
|
| 12353 | if (evaluatingAsFloats) {
|
| 12354 | push_double(0.0);
|
| 12355 | } else {
|
| 12356 | push(zero);
|
| 12357 | }
|
| 12358 | return;
|
| 12359 | }
|
| 12360 | if (expanding && isadd(p1)) {
|
| 12361 | p1 = cdr(p1);
|
| 12362 | if (evaluatingAsFloats) {
|
| 12363 | push_double(0.0);
|
| 12364 | } else {
|
| 12365 | push(zero);
|
| 12366 | }
|
| 12367 | while (iscons(p1)) {
|
| 12368 | push(car(p1));
|
| 12369 | push(p2);
|
| 12370 | multiply();
|
| 12371 | add();
|
| 12372 | p1 = cdr(p1);
|
| 12373 | }
|
| 12374 | return;
|
| 12375 | }
|
| 12376 | if (expanding && isadd(p2)) {
|
| 12377 | p2 = cdr(p2);
|
| 12378 | if (evaluatingAsFloats) {
|
| 12379 | push_double(0.0);
|
| 12380 | } else {
|
| 12381 | push(zero);
|
| 12382 | }
|
| 12383 | while (iscons(p2)) {
|
| 12384 | push(p1);
|
| 12385 | push(car(p2));
|
| 12386 | multiply();
|
| 12387 | add();
|
| 12388 | p2 = cdr(p2);
|
| 12389 | }
|
| 12390 | return;
|
| 12391 | }
|
| 12392 | if (!istensor(p1) && istensor(p2)) {
|
| 12393 | push(p1);
|
| 12394 | push(p2);
|
| 12395 | scalar_times_tensor();
|
| 12396 | return;
|
| 12397 | }
|
| 12398 | if (istensor(p1) && !istensor(p2)) {
|
| 12399 | push(p1);
|
| 12400 | push(p2);
|
| 12401 | tensor_times_scalar();
|
| 12402 | return;
|
| 12403 | }
|
| 12404 | if (car(p1) === symbol(MULTIPLY)) {
|
| 12405 | p1 = cdr(p1);
|
| 12406 | } else {
|
| 12407 | push(p1);
|
| 12408 | list(1);
|
| 12409 | p1 = pop();
|
| 12410 | }
|
| 12411 | if (car(p2) === symbol(MULTIPLY)) {
|
| 12412 | p2 = cdr(p2);
|
| 12413 | } else {
|
| 12414 | push(p2);
|
| 12415 | list(1);
|
| 12416 | p2 = pop();
|
| 12417 | }
|
| 12418 | if (isnum(car(p1)) && isnum(car(p2))) {
|
| 12419 | push(car(p1));
|
| 12420 | push(car(p2));
|
| 12421 | multiply_numbers();
|
| 12422 | p1 = cdr(p1);
|
| 12423 | p2 = cdr(p2);
|
| 12424 | } else if (isnum(car(p1))) {
|
| 12425 | push(car(p1));
|
| 12426 | p1 = cdr(p1);
|
| 12427 | } else if (isnum(car(p2))) {
|
| 12428 | push(car(p2));
|
| 12429 | p2 = cdr(p2);
|
| 12430 | } else {
|
| 12431 | if (evaluatingAsFloats) {
|
| 12432 | push_double(1.0);
|
| 12433 | } else {
|
| 12434 | push(one);
|
| 12435 | }
|
| 12436 | }
|
| 12437 | parse_p1();
|
| 12438 | parse_p2();
|
| 12439 | while (iscons(p1) && iscons(p2)) {
|
| 12440 | if (caar(p1) === symbol(OPERATOR) && caar(p2) === symbol(OPERATOR)) {
|
| 12441 | push_symbol(OPERATOR);
|
| 12442 | push(cdar(p1));
|
| 12443 | push(cdar(p2));
|
| 12444 | append();
|
| 12445 | cons();
|
| 12446 | p1 = cdr(p1);
|
| 12447 | p2 = cdr(p2);
|
| 12448 | parse_p1();
|
| 12449 | parse_p2();
|
| 12450 | continue;
|
| 12451 | }
|
| 12452 | switch (cmp_expr(p3, p4)) {
|
| 12453 | case -1:
|
| 12454 | push(car(p1));
|
| 12455 | p1 = cdr(p1);
|
| 12456 | parse_p1();
|
| 12457 | break;
|
| 12458 | case 1:
|
| 12459 | push(car(p2));
|
| 12460 | p2 = cdr(p2);
|
| 12461 | parse_p2();
|
| 12462 | break;
|
| 12463 | case 0:
|
| 12464 | combine_factors(h);
|
| 12465 | p1 = cdr(p1);
|
| 12466 | p2 = cdr(p2);
|
| 12467 | parse_p1();
|
| 12468 | parse_p2();
|
| 12469 | break;
|
| 12470 | default:
|
| 12471 | stop("internal error 2");
|
| 12472 | }
|
| 12473 | }
|
| 12474 | while (iscons(p1)) {
|
| 12475 | push(car(p1));
|
| 12476 | p1 = cdr(p1);
|
| 12477 | }
|
| 12478 | while (iscons(p2)) {
|
| 12479 | push(car(p2));
|
| 12480 | p2 = cdr(p2);
|
| 12481 | }
|
| 12482 | __normalize_radical_factors(h);
|
| 12483 | if (expanding) {
|
| 12484 | for (i = o = ref = h, ref1 = tos; ref <= ref1 ? o < ref1 : o > ref1; i = ref <= ref1 ? ++o : --o) {
|
| 12485 | if (isadd(stack[i])) {
|
| 12486 | multiply_all(tos - h);
|
| 12487 | return;
|
| 12488 | }
|
| 12489 | }
|
| 12490 | }
|
| 12491 | n = tos - h;
|
| 12492 | if (n === 1) {
|
| 12493 | return;
|
| 12494 | }
|
| 12495 | if (isrational(stack[h]) && equaln(stack[h], 1)) {
|
| 12496 | if (n === 2) {
|
| 12497 | p7 = pop();
|
| 12498 | pop();
|
| 12499 | push(p7);
|
| 12500 | } else {
|
| 12501 | stack[h] = symbol(MULTIPLY);
|
| 12502 | list(n);
|
| 12503 | }
|
| 12504 | return;
|
| 12505 | }
|
| 12506 | list(n);
|
| 12507 | p7 = pop();
|
| 12508 | push_symbol(MULTIPLY);
|
| 12509 | push(p7);
|
| 12510 | return cons();
|
| 12511 | };
|
| 12512 |
|
| 12513 | parse_p1 = function() {
|
| 12514 | p3 = car(p1);
|
| 12515 | p5 = evaluatingAsFloats ? one_as_double : one;
|
| 12516 | if (car(p3) === symbol(POWER)) {
|
| 12517 | p5 = caddr(p3);
|
| 12518 | return p3 = cadr(p3);
|
| 12519 | }
|
| 12520 | };
|
| 12521 |
|
| 12522 | parse_p2 = function() {
|
| 12523 | p4 = car(p2);
|
| 12524 | p6 = evaluatingAsFloats ? one_as_double : one;
|
| 12525 | if (car(p4) === symbol(POWER)) {
|
| 12526 | p6 = caddr(p4);
|
| 12527 | return p4 = cadr(p4);
|
| 12528 | }
|
| 12529 | };
|
| 12530 |
|
| 12531 | combine_factors = function(h) {
|
| 12532 | push(p4);
|
| 12533 | push(p5);
|
| 12534 | push(p6);
|
| 12535 | add();
|
| 12536 | power();
|
| 12537 | p7 = pop();
|
| 12538 | if (isnum(p7)) {
|
| 12539 | push(stack[h]);
|
| 12540 | push(p7);
|
| 12541 | multiply_numbers();
|
| 12542 | return stack[h] = pop();
|
| 12543 | } else if (car(p7) === symbol(MULTIPLY)) {
|
| 12544 | if (isnum(cadr(p7)) && cdddr(p7) === symbol(NIL)) {
|
| 12545 | push(stack[h]);
|
| 12546 | push(cadr(p7));
|
| 12547 | multiply_numbers();
|
| 12548 | stack[h] = pop();
|
| 12549 | return push(caddr(p7));
|
| 12550 | } else {
|
| 12551 | return push(p7);
|
| 12552 | }
|
| 12553 | } else {
|
| 12554 | return push(p7);
|
| 12555 | }
|
| 12556 | };
|
| 12557 |
|
| 12558 | gp = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, -6, -7, -8, -3, -4, -5, 13, 14, 15, -16, 9, 10, 11, -12], [0, 0, 6, -1, -11, 10, -2, -15, 14, 12, -5, 4, -9, 16, -8, 7, -13], [0, 0, 7, 11, -1, -9, 15, -2, -13, 5, 12, -3, -10, 8, 16, -6, -14], [0, 0, 8, -10, 9, -1, -14, 13, -2, -4, 3, 12, -11, -7, 6, 16, -15], [0, 0, 3, 2, 15, -14, 1, 11, -10, 16, -8, 7, 13, 12, -5, 4, 9], [0, 0, 4, -15, 2, 13, -11, 1, 9, 8, 16, -6, 14, 5, 12, -3, 10], [0, 0, 5, 14, -13, 2, 10, -9, 1, -7, 6, 16, 15, -4, 3, 12, 11], [0, 0, 13, 12, -5, 4, 16, -8, 7, -1, -11, 10, -3, -2, -15, 14, -6], [0, 0, 14, 5, 12, -3, 8, 16, -6, 11, -1, -9, -4, 15, -2, -13, -7], [0, 0, 15, -4, 3, 12, -7, 6, 16, -10, 9, -1, -5, -14, 13, -2, -8], [0, 0, 16, -9, -10, -11, -13, -14, -15, -3, -4, -5, 1, -6, -7, -8, 2], [0, 0, 9, -16, 8, -7, -12, 5, -4, -2, -15, 14, 6, -1, -11, 10, 3], [0, 0, 10, -8, -16, 6, -5, -12, 3, 15, -2, -13, 7, 11, -1, -9, 4], [0, 0, 11, 7, -6, -16, 4, -3, -12, -14, 13, -2, 8, -10, 9, -1, 5], [0, 0, 12, 13, 14, 15, 9, 10, 11, -6, -7, -8, -2, -3, -4, -5, -1]];
|
| 12559 |
|
| 12560 | combine_gammas = function(h) {
|
| 12561 | var n;
|
| 12562 | n = gp[Math.floor(p1.gamma)][Math.floor(p2.gamma)];
|
| 12563 | if (n < 0) {
|
| 12564 | n = -n;
|
| 12565 | push(stack[h]);
|
| 12566 | negate();
|
| 12567 | stack[h] = pop();
|
| 12568 | }
|
| 12569 | if (n > 1) {
|
| 12570 | return push(_gamma[n]);
|
| 12571 | }
|
| 12572 | };
|
| 12573 |
|
| 12574 | multiply_noexpand = function() {
|
| 12575 | var prev_expanding;
|
| 12576 | prev_expanding = expanding;
|
| 12577 | expanding = 0;
|
| 12578 | multiply();
|
| 12579 | return expanding = prev_expanding;
|
| 12580 | };
|
| 12581 |
|
| 12582 | multiply_all = function(n) {
|
| 12583 | var h, i, o, ref;
|
| 12584 | i = 0;
|
| 12585 | if (n === 1) {
|
| 12586 | return;
|
| 12587 | }
|
| 12588 | if (n === 0) {
|
| 12589 | push(evaluatingAsFloats ? one_as_double : one);
|
| 12590 | return;
|
| 12591 | }
|
| 12592 | h = tos - n;
|
| 12593 | push(stack[h]);
|
| 12594 | for (i = o = 1, ref = n; 1 <= ref ? o < ref : o > ref; i = 1 <= ref ? ++o : --o) {
|
| 12595 | push(stack[h + i]);
|
| 12596 | multiply();
|
| 12597 | }
|
| 12598 | stack[h] = pop();
|
| 12599 | return moveTos(h + 1);
|
| 12600 | };
|
| 12601 |
|
| 12602 | multiply_all_noexpand = function(n) {
|
| 12603 | var prev_expanding;
|
| 12604 | prev_expanding = expanding;
|
| 12605 | expanding = 0;
|
| 12606 | multiply_all(n);
|
| 12607 | return expanding = prev_expanding;
|
| 12608 | };
|
| 12609 |
|
| 12610 | divide = function() {
|
| 12611 | if (isnum(stack[tos - 2]) && isnum(stack[tos - 1])) {
|
| 12612 | return divide_numbers();
|
| 12613 | } else {
|
| 12614 | inverse();
|
| 12615 | return multiply();
|
| 12616 | }
|
| 12617 | };
|
| 12618 |
|
| 12619 | inverse = function() {
|
| 12620 | if (isnum(stack[tos - 1])) {
|
| 12621 | return invert_number();
|
| 12622 | } else {
|
| 12623 | push_integer(-1);
|
| 12624 | return power();
|
| 12625 | }
|
| 12626 | };
|
| 12627 |
|
| 12628 | reciprocate = function() {
|
| 12629 | return inverse();
|
| 12630 | };
|
| 12631 |
|
| 12632 | negate = function() {
|
| 12633 | if (isnum(stack[tos - 1])) {
|
| 12634 | return negate_number();
|
| 12635 | } else {
|
| 12636 | if (evaluatingAsFloats) {
|
| 12637 | push_double(-1.0);
|
| 12638 | } else {
|
| 12639 | push_integer(-1);
|
| 12640 | }
|
| 12641 | return multiply();
|
| 12642 | }
|
| 12643 | };
|
| 12644 |
|
| 12645 | negate_expand = function() {
|
| 12646 | var prev_expanding;
|
| 12647 | prev_expanding = expanding;
|
| 12648 | expanding = 1;
|
| 12649 | negate();
|
| 12650 | return expanding = prev_expanding;
|
| 12651 | };
|
| 12652 |
|
| 12653 | negate_noexpand = function() {
|
| 12654 | var prev_expanding;
|
| 12655 | prev_expanding = expanding;
|
| 12656 | expanding = 0;
|
| 12657 | negate();
|
| 12658 | return expanding = prev_expanding;
|
| 12659 | };
|
| 12660 |
|
| 12661 | __normalize_radical_factors = function(h) {
|
| 12662 | var i, i1, j1, o, ref, ref1, ref2, ref3, ref4, ref5;
|
| 12663 | i = 0;
|
| 12664 | if (isplusone(stack[h]) || isminusone(stack[h]) || isdouble(stack[h])) {
|
| 12665 | return;
|
| 12666 | }
|
| 12667 | for (i = o = ref = h + 1, ref1 = tos; ref <= ref1 ? o < ref1 : o > ref1; i = ref <= ref1 ? ++o : --o) {
|
| 12668 | if (__is_radical_number(stack[i])) {
|
| 12669 | break;
|
| 12670 | }
|
| 12671 | }
|
| 12672 | if (i === tos) {
|
| 12673 | return;
|
| 12674 | }
|
| 12675 | save();
|
| 12676 | push(stack[h]);
|
| 12677 | mp_numerator();
|
| 12678 | p1 = pop();
|
| 12679 | for (i = i1 = ref2 = h + 1, ref3 = tos; ref2 <= ref3 ? i1 < ref3 : i1 > ref3; i = ref2 <= ref3 ? ++i1 : --i1) {
|
| 12680 | if (isplusone(p1) || isminusone(p1)) {
|
| 12681 | break;
|
| 12682 | }
|
| 12683 | if (!__is_radical_number(stack[i])) {
|
| 12684 | continue;
|
| 12685 | }
|
| 12686 | p3 = cadr(stack[i]);
|
| 12687 | p4 = caddr(stack[i]);
|
| 12688 | if (!isnegativenumber(p4)) {
|
| 12689 | continue;
|
| 12690 | }
|
| 12691 | push(p1);
|
| 12692 | push(p3);
|
| 12693 | divide();
|
| 12694 | p5 = pop();
|
| 12695 | if (!isinteger(p5)) {
|
| 12696 | continue;
|
| 12697 | }
|
| 12698 | p1 = p5;
|
| 12699 | push_symbol(POWER);
|
| 12700 | push(p3);
|
| 12701 | push(evaluatingAsFloats ? one_as_double : one);
|
| 12702 | push(p4);
|
| 12703 | add();
|
| 12704 | list(3);
|
| 12705 | stack[i] = pop();
|
| 12706 | }
|
| 12707 | push(stack[h]);
|
| 12708 | mp_denominator();
|
| 12709 | p2 = pop();
|
| 12710 | for (i = j1 = ref4 = h + 1, ref5 = tos; ref4 <= ref5 ? j1 < ref5 : j1 > ref5; i = ref4 <= ref5 ? ++j1 : --j1) {
|
| 12711 | if (isplusone(p2)) {
|
| 12712 | break;
|
| 12713 | }
|
| 12714 | if (!__is_radical_number(stack[i])) {
|
| 12715 | continue;
|
| 12716 | }
|
| 12717 | p3 = cadr(stack[i]);
|
| 12718 | p4 = caddr(stack[i]);
|
| 12719 | if (isnegativenumber(p4)) {
|
| 12720 | continue;
|
| 12721 | }
|
| 12722 | push(p2);
|
| 12723 | push(p3);
|
| 12724 | divide();
|
| 12725 | p5 = pop();
|
| 12726 | if (!isinteger(p5)) {
|
| 12727 | continue;
|
| 12728 | }
|
| 12729 | p2 = p5;
|
| 12730 | push_symbol(POWER);
|
| 12731 | push(p3);
|
| 12732 | push(p4);
|
| 12733 | push(one);
|
| 12734 | subtract();
|
| 12735 | if (dontCreateNewRadicalsInDenominatorWhenEvalingMultiplication) {
|
| 12736 | if (isinteger(p3) && !isinteger(stack[tos - 1]) && isnegativenumber(stack[tos - 1])) {
|
| 12737 | pop();
|
| 12738 | pop();
|
| 12739 | pop();
|
| 12740 | push(p1);
|
| 12741 | push(p3);
|
| 12742 | divide();
|
| 12743 | p1 = pop();
|
| 12744 | break;
|
| 12745 | }
|
| 12746 | }
|
| 12747 | list(3);
|
| 12748 | stack[i] = pop();
|
| 12749 | }
|
| 12750 | push(p1);
|
| 12751 | push(p2);
|
| 12752 | divide();
|
| 12753 | stack[h] = pop();
|
| 12754 | return restore();
|
| 12755 | };
|
| 12756 |
|
| 12757 | __is_radical_number = function(p) {
|
| 12758 | if (car(p) === symbol(POWER) && isnum(cadr(p)) && isnum(caddr(p)) && !isminusone(cadr(p))) {
|
| 12759 | return 1;
|
| 12760 | } else {
|
| 12761 | return 0;
|
| 12762 | }
|
| 12763 | };
|
| 12764 |
|
| 12765 | NROOTS_YMAX = 101;
|
| 12766 |
|
| 12767 | NROOTS_DELTA = 1.0e-6;
|
| 12768 |
|
| 12769 | NROOTS_EPSILON = 1.0e-9;
|
| 12770 |
|
| 12771 | NROOTS_ABS = function(z) {
|
| 12772 | return Math.sqrt(z.r * z.r + z.i * z.i);
|
| 12773 | };
|
| 12774 |
|
| 12775 | theRandom = 0.0;
|
| 12776 |
|
| 12777 | NROOTS_RANDOM = function() {
|
| 12778 | return 4.0 * Math.random() - 2.0;
|
| 12779 | };
|
| 12780 |
|
| 12781 | numericRootOfPolynomial = (function() {
|
| 12782 | function numericRootOfPolynomial() {}
|
| 12783 |
|
| 12784 | numericRootOfPolynomial.prototype.r = 0.0;
|
| 12785 |
|
| 12786 | numericRootOfPolynomial.prototype.i = 0.0;
|
| 12787 |
|
| 12788 | return numericRootOfPolynomial;
|
| 12789 |
|
| 12790 | })();
|
| 12791 |
|
| 12792 | nroots_a = new numericRootOfPolynomial();
|
| 12793 |
|
| 12794 | nroots_b = new numericRootOfPolynomial();
|
| 12795 |
|
| 12796 | nroots_x = new numericRootOfPolynomial();
|
| 12797 |
|
| 12798 | nroots_y = new numericRootOfPolynomial();
|
| 12799 |
|
| 12800 | nroots_fa = new numericRootOfPolynomial();
|
| 12801 |
|
| 12802 | nroots_fb = new numericRootOfPolynomial();
|
| 12803 |
|
| 12804 | nroots_dx = new numericRootOfPolynomial();
|
| 12805 |
|
| 12806 | nroots_df = new numericRootOfPolynomial();
|
| 12807 |
|
| 12808 | nroots_c = [];
|
| 12809 |
|
| 12810 | for (initNRoots = o = 0, ref = NROOTS_YMAX; 0 <= ref ? o < ref : o > ref; initNRoots = 0 <= ref ? ++o : --o) {
|
| 12811 | nroots_c[initNRoots] = new numericRootOfPolynomial();
|
| 12812 | }
|
| 12813 |
|
| 12814 | Eval_nroots = function() {
|
| 12815 | var h, i, i1, j1, k, l1, n, ref1, ref2, ref3;
|
| 12816 | h = 0;
|
| 12817 | i = 0;
|
| 12818 | k = 0;
|
| 12819 | n = 0;
|
| 12820 | push(cadr(p1));
|
| 12821 | Eval();
|
| 12822 | push(caddr(p1));
|
| 12823 | Eval();
|
| 12824 | p2 = pop();
|
| 12825 | if (p2 === symbol(NIL)) {
|
| 12826 | guess();
|
| 12827 | } else {
|
| 12828 | push(p2);
|
| 12829 | }
|
| 12830 | p2 = pop();
|
| 12831 | p1 = pop();
|
| 12832 | if (!ispoly(p1, p2)) {
|
| 12833 | stop("nroots: polynomial?");
|
| 12834 | }
|
| 12835 | h = tos;
|
| 12836 | push(p1);
|
| 12837 | push(p2);
|
| 12838 | n = coeff();
|
| 12839 | if (n > NROOTS_YMAX) {
|
| 12840 | stop("nroots: degree?");
|
| 12841 | }
|
| 12842 | for (i = i1 = 0, ref1 = n; 0 <= ref1 ? i1 < ref1 : i1 > ref1; i = 0 <= ref1 ? ++i1 : --i1) {
|
| 12843 | push(stack[h + i]);
|
| 12844 | real();
|
| 12845 | yyfloat();
|
| 12846 | Eval();
|
| 12847 | p1 = pop();
|
| 12848 | push(stack[h + i]);
|
| 12849 | imag();
|
| 12850 | yyfloat();
|
| 12851 | Eval();
|
| 12852 | p2 = pop();
|
| 12853 | if (!isdouble(p1) || !isdouble(p2)) {
|
| 12854 | stop("nroots: coefficients?");
|
| 12855 | }
|
| 12856 | nroots_c[i].r = p1.d;
|
| 12857 | nroots_c[i].i = p2.d;
|
| 12858 | }
|
| 12859 | moveTos(h);
|
| 12860 | monic(n);
|
| 12861 | for (k = j1 = ref2 = n; j1 > 1; k = j1 += -1) {
|
| 12862 | findroot(k);
|
| 12863 | if (Math.abs(nroots_a.r) < NROOTS_DELTA) {
|
| 12864 | nroots_a.r = 0.0;
|
| 12865 | }
|
| 12866 | if (Math.abs(nroots_a.i) < NROOTS_DELTA) {
|
| 12867 | nroots_a.i = 0.0;
|
| 12868 | }
|
| 12869 | push_double(nroots_a.r);
|
| 12870 | push_double(nroots_a.i);
|
| 12871 | push(imaginaryunit);
|
| 12872 | multiply();
|
| 12873 | add();
|
| 12874 | NROOTS_divpoly(k);
|
| 12875 | }
|
| 12876 | n = tos - h;
|
| 12877 | if (n > 1) {
|
| 12878 | sort_stack(n);
|
| 12879 | p1 = alloc_tensor(n);
|
| 12880 | p1.tensor.ndim = 1;
|
| 12881 | p1.tensor.dim[0] = n;
|
| 12882 | for (i = l1 = 0, ref3 = n; 0 <= ref3 ? l1 < ref3 : l1 > ref3; i = 0 <= ref3 ? ++l1 : --l1) {
|
| 12883 | p1.tensor.elem[i] = stack[h + i];
|
| 12884 | }
|
| 12885 | moveTos(h);
|
| 12886 | return push(p1);
|
| 12887 | }
|
| 12888 | };
|
| 12889 |
|
| 12890 | monic = function(n) {
|
| 12891 | var i1, k, ref1, t;
|
| 12892 | k = 0;
|
| 12893 | t = 0.0;
|
| 12894 | nroots_y.r = nroots_c[n - 1].r;
|
| 12895 | nroots_y.i = nroots_c[n - 1].i;
|
| 12896 | t = nroots_y.r * nroots_y.r + nroots_y.i * nroots_y.i;
|
| 12897 | for (k = i1 = 0, ref1 = n - 1; 0 <= ref1 ? i1 < ref1 : i1 > ref1; k = 0 <= ref1 ? ++i1 : --i1) {
|
| 12898 | nroots_c[k].r = (nroots_c[k].r * nroots_y.r + nroots_c[k].i * nroots_y.i) / t;
|
| 12899 | nroots_c[k].i = (nroots_c[k].i * nroots_y.r - nroots_c[k].r * nroots_y.i) / t;
|
| 12900 | }
|
| 12901 | nroots_c[n - 1].r = 1.0;
|
| 12902 | return nroots_c[n - 1].i = 0.0;
|
| 12903 | };
|
| 12904 |
|
| 12905 | findroot = function(n) {
|
| 12906 | var i1, j, j1, k, nrabs, t;
|
| 12907 | j = 0;
|
| 12908 | k = 0;
|
| 12909 | t = 0.0;
|
| 12910 | if (NROOTS_ABS(nroots_c[0]) < NROOTS_DELTA) {
|
| 12911 | nroots_a.r = 0.0;
|
| 12912 | nroots_a.i = 0.0;
|
| 12913 | return;
|
| 12914 | }
|
| 12915 | for (j = i1 = 0; i1 < 100; j = ++i1) {
|
| 12916 | nroots_a.r = NROOTS_RANDOM();
|
| 12917 | nroots_a.i = NROOTS_RANDOM();
|
| 12918 | compute_fa(n);
|
| 12919 | nroots_b.r = nroots_a.r;
|
| 12920 | nroots_b.i = nroots_a.i;
|
| 12921 | nroots_fb.r = nroots_fa.r;
|
| 12922 | nroots_fb.i = nroots_fa.i;
|
| 12923 | nroots_a.r = NROOTS_RANDOM();
|
| 12924 | nroots_a.i = NROOTS_RANDOM();
|
| 12925 | for (k = j1 = 0; j1 < 1000; k = ++j1) {
|
| 12926 | compute_fa(n);
|
| 12927 | nrabs = NROOTS_ABS(nroots_fa);
|
| 12928 | if (DEBUG) {
|
| 12929 | console.log("nrabs: " + nrabs);
|
| 12930 | }
|
| 12931 | if (nrabs < NROOTS_EPSILON) {
|
| 12932 | return;
|
| 12933 | }
|
| 12934 | if (NROOTS_ABS(nroots_fa) < NROOTS_ABS(nroots_fb)) {
|
| 12935 | nroots_x.r = nroots_a.r;
|
| 12936 | nroots_x.i = nroots_a.i;
|
| 12937 | nroots_a.r = nroots_b.r;
|
| 12938 | nroots_a.i = nroots_b.i;
|
| 12939 | nroots_b.r = nroots_x.r;
|
| 12940 | nroots_b.i = nroots_x.i;
|
| 12941 | nroots_x.r = nroots_fa.r;
|
| 12942 | nroots_x.i = nroots_fa.i;
|
| 12943 | nroots_fa.r = nroots_fb.r;
|
| 12944 | nroots_fa.i = nroots_fb.i;
|
| 12945 | nroots_fb.r = nroots_x.r;
|
| 12946 | nroots_fb.i = nroots_x.i;
|
| 12947 | }
|
| 12948 | nroots_dx.r = nroots_b.r - nroots_a.r;
|
| 12949 | nroots_dx.i = nroots_b.i - nroots_a.i;
|
| 12950 | nroots_df.r = nroots_fb.r - nroots_fa.r;
|
| 12951 | nroots_df.i = nroots_fb.i - nroots_fa.i;
|
| 12952 | t = nroots_df.r * nroots_df.r + nroots_df.i * nroots_df.i;
|
| 12953 | if (t === 0.0) {
|
| 12954 | break;
|
| 12955 | }
|
| 12956 | nroots_y.r = (nroots_dx.r * nroots_df.r + nroots_dx.i * nroots_df.i) / t;
|
| 12957 | nroots_y.i = (nroots_dx.i * nroots_df.r - nroots_dx.r * nroots_df.i) / t;
|
| 12958 | nroots_a.r = nroots_b.r - (nroots_y.r * nroots_fb.r - nroots_y.i * nroots_fb.i);
|
| 12959 | nroots_a.i = nroots_b.i - (nroots_y.r * nroots_fb.i + nroots_y.i * nroots_fb.r);
|
| 12960 | }
|
| 12961 | }
|
| 12962 | return stop("nroots: convergence error");
|
| 12963 | };
|
| 12964 |
|
| 12965 | compute_fa = function(n) {
|
| 12966 | var i1, k, ref1, results, t;
|
| 12967 | k = 0;
|
| 12968 | t = 0.0;
|
| 12969 | nroots_x.r = nroots_a.r;
|
| 12970 | nroots_x.i = nroots_a.i;
|
| 12971 | nroots_fa.r = nroots_c[0].r + nroots_c[1].r * nroots_x.r - nroots_c[1].i * nroots_x.i;
|
| 12972 | nroots_fa.i = nroots_c[0].i + nroots_c[1].r * nroots_x.i + nroots_c[1].i * nroots_x.r;
|
| 12973 | results = [];
|
| 12974 | for (k = i1 = 2, ref1 = n; 2 <= ref1 ? i1 < ref1 : i1 > ref1; k = 2 <= ref1 ? ++i1 : --i1) {
|
| 12975 | t = nroots_a.r * nroots_x.r - nroots_a.i * nroots_x.i;
|
| 12976 | nroots_x.i = nroots_a.r * nroots_x.i + nroots_a.i * nroots_x.r;
|
| 12977 | nroots_x.r = t;
|
| 12978 | nroots_fa.r += nroots_c[k].r * nroots_x.r - nroots_c[k].i * nroots_x.i;
|
| 12979 | results.push(nroots_fa.i += nroots_c[k].r * nroots_x.i + nroots_c[k].i * nroots_x.r);
|
| 12980 | }
|
| 12981 | return results;
|
| 12982 | };
|
| 12983 |
|
| 12984 | NROOTS_divpoly = function(n) {
|
| 12985 | var i1, j1, k, ref1, ref2, results;
|
| 12986 | k = 0;
|
| 12987 | for (k = i1 = ref1 = n - 1; ref1 <= 0 ? i1 < 0 : i1 > 0; k = ref1 <= 0 ? ++i1 : --i1) {
|
| 12988 | nroots_c[k - 1].r += nroots_c[k].r * nroots_a.r - nroots_c[k].i * nroots_a.i;
|
| 12989 | nroots_c[k - 1].i += nroots_c[k].i * nroots_a.r + nroots_c[k].r * nroots_a.i;
|
| 12990 | }
|
| 12991 | if (NROOTS_ABS(nroots_c[0]) > NROOTS_DELTA) {
|
| 12992 | stop("nroots: residual error");
|
| 12993 | }
|
| 12994 | results = [];
|
| 12995 | for (k = j1 = 0, ref2 = n - 1; 0 <= ref2 ? j1 < ref2 : j1 > ref2; k = 0 <= ref2 ? ++j1 : --j1) {
|
| 12996 | nroots_c[k].r = nroots_c[k + 1].r;
|
| 12997 | results.push(nroots_c[k].i = nroots_c[k + 1].i);
|
| 12998 | }
|
| 12999 | return results;
|
| 13000 | };
|
| 13001 |
|
| 13002 | Eval_numerator = function() {
|
| 13003 | push(cadr(p1));
|
| 13004 | Eval();
|
| 13005 | return numerator();
|
| 13006 | };
|
| 13007 |
|
| 13008 | numerator = function() {
|
| 13009 | var h;
|
| 13010 | h = 0;
|
| 13011 | save();
|
| 13012 | p1 = pop();
|
| 13013 | if (car(p1) === symbol(ADD)) {
|
| 13014 | push(p1);
|
| 13015 | rationalize();
|
| 13016 | p1 = pop();
|
| 13017 | }
|
| 13018 | if (car(p1) === symbol(MULTIPLY)) {
|
| 13019 | h = tos;
|
| 13020 | p1 = cdr(p1);
|
| 13021 | while (iscons(p1)) {
|
| 13022 | push(car(p1));
|
| 13023 | numerator();
|
| 13024 | p1 = cdr(p1);
|
| 13025 | }
|
| 13026 | multiply_all(tos - h);
|
| 13027 | } else if (isrational(p1)) {
|
| 13028 | push(p1);
|
| 13029 | mp_numerator();
|
| 13030 | } else if (car(p1) === symbol(POWER) && isnegativeterm(caddr(p1))) {
|
| 13031 | push(one);
|
| 13032 | } else {
|
| 13033 | push(p1);
|
| 13034 | }
|
| 13035 | return restore();
|
| 13036 | };
|
| 13037 |
|
| 13038 | Eval_outer = function() {
|
| 13039 | var results;
|
| 13040 | p1 = cdr(p1);
|
| 13041 | push(car(p1));
|
| 13042 | Eval();
|
| 13043 | p1 = cdr(p1);
|
| 13044 | results = [];
|
| 13045 | while (iscons(p1)) {
|
| 13046 | push(car(p1));
|
| 13047 | Eval();
|
| 13048 | outer();
|
| 13049 | results.push(p1 = cdr(p1));
|
| 13050 | }
|
| 13051 | return results;
|
| 13052 | };
|
| 13053 |
|
| 13054 | outer = function() {
|
| 13055 | save();
|
| 13056 | p2 = pop();
|
| 13057 | p1 = pop();
|
| 13058 | if (istensor(p1) && istensor(p2)) {
|
| 13059 | yyouter();
|
| 13060 | } else {
|
| 13061 | push(p1);
|
| 13062 | push(p2);
|
| 13063 | if (istensor(p1)) {
|
| 13064 | tensor_times_scalar();
|
| 13065 | } else if (istensor(p2)) {
|
| 13066 | scalar_times_tensor();
|
| 13067 | } else {
|
| 13068 | multiply();
|
| 13069 | }
|
| 13070 | }
|
| 13071 | return restore();
|
| 13072 | };
|
| 13073 |
|
| 13074 | yyouter = function() {
|
| 13075 | var i, i1, j, j1, k, l1, m1, ndim, nelem, ref1, ref2, ref3, ref4;
|
| 13076 | i = 0;
|
| 13077 | j = 0;
|
| 13078 | k = 0;
|
| 13079 | ndim = 0;
|
| 13080 | nelem = 0;
|
| 13081 | ndim = p1.tensor.ndim + p2.tensor.ndim;
|
| 13082 | if (ndim > MAXDIM) {
|
| 13083 | stop("outer: rank of result exceeds maximum");
|
| 13084 | }
|
| 13085 | nelem = p1.tensor.nelem * p2.tensor.nelem;
|
| 13086 | p3 = alloc_tensor(nelem);
|
| 13087 | p3.tensor.ndim = ndim;
|
| 13088 | for (i = i1 = 0, ref1 = p1.tensor.ndim; 0 <= ref1 ? i1 < ref1 : i1 > ref1; i = 0 <= ref1 ? ++i1 : --i1) {
|
| 13089 | p3.tensor.dim[i] = p1.tensor.dim[i];
|
| 13090 | }
|
| 13091 | j = i;
|
| 13092 | for (i = j1 = 0, ref2 = p2.tensor.ndim; 0 <= ref2 ? j1 < ref2 : j1 > ref2; i = 0 <= ref2 ? ++j1 : --j1) {
|
| 13093 | p3.tensor.dim[j + i] = p2.tensor.dim[i];
|
| 13094 | }
|
| 13095 | k = 0;
|
| 13096 | for (i = l1 = 0, ref3 = p1.tensor.nelem; 0 <= ref3 ? l1 < ref3 : l1 > ref3; i = 0 <= ref3 ? ++l1 : --l1) {
|
| 13097 | for (j = m1 = 0, ref4 = p2.tensor.nelem; 0 <= ref4 ? m1 < ref4 : m1 > ref4; j = 0 <= ref4 ? ++m1 : --m1) {
|
| 13098 | push(p1.tensor.elem[i]);
|
| 13099 | push(p2.tensor.elem[j]);
|
| 13100 | multiply();
|
| 13101 | p3.tensor.elem[k++] = pop();
|
| 13102 | }
|
| 13103 | }
|
| 13104 | return push(p3);
|
| 13105 | };
|
| 13106 |
|
| 13107 |
|
| 13108 | |
| 13109 | |
| 13110 | |
| 13111 | |
| 13112 | |
| 13113 | |
| 13114 | |
| 13115 | |
| 13116 | |
| 13117 | |
| 13118 | |
| 13119 | |
| 13120 | |
| 13121 | |
| 13122 |
|
| 13123 |
|
| 13124 | partition = function() {
|
| 13125 | save();
|
| 13126 | p2 = pop();
|
| 13127 | p1 = pop();
|
| 13128 | push_integer(1);
|
| 13129 | p3 = pop();
|
| 13130 | p4 = p3;
|
| 13131 | p1 = cdr(p1);
|
| 13132 | while (iscons(p1)) {
|
| 13133 | if (Find(car(p1), p2)) {
|
| 13134 | push(p4);
|
| 13135 | push(car(p1));
|
| 13136 | multiply();
|
| 13137 | p4 = pop();
|
| 13138 | } else {
|
| 13139 | push(p3);
|
| 13140 | push(car(p1));
|
| 13141 | multiply();
|
| 13142 | p3 = pop();
|
| 13143 | }
|
| 13144 | p1 = cdr(p1);
|
| 13145 | }
|
| 13146 | push(p3);
|
| 13147 | push(p4);
|
| 13148 | return restore();
|
| 13149 | };
|
| 13150 |
|
| 13151 |
|
| 13152 | |
| 13153 | |
| 13154 | |
| 13155 | |
| 13156 | |
| 13157 | |
| 13158 |
|
| 13159 |
|
| 13160 | Eval_silentpattern = function() {
|
| 13161 | Eval_pattern();
|
| 13162 | pop();
|
| 13163 | return push_symbol(NIL);
|
| 13164 | };
|
| 13165 |
|
| 13166 | Eval_pattern = function() {
|
| 13167 | var firstArgument, patternPosition, secondArgument, stringKey, thirdArgument;
|
| 13168 | if (!iscons(cdr(p1))) {
|
| 13169 | stop("pattern needs at least a template and a transformed version");
|
| 13170 | }
|
| 13171 | firstArgument = car(cdr(p1));
|
| 13172 | secondArgument = car(cdr(cdr(p1)));
|
| 13173 | if (secondArgument === symbol(NIL)) {
|
| 13174 | stop("pattern needs at least a template and a transformed version");
|
| 13175 | }
|
| 13176 | if (!iscons(cdr(cdr(p1)))) {
|
| 13177 | thirdArgument = symbol(NIL);
|
| 13178 | } else {
|
| 13179 | thirdArgument = car(cdr(cdr(cdr(p1))));
|
| 13180 | }
|
| 13181 | if (equal(firstArgument, secondArgument)) {
|
| 13182 | stop("recursive pattern");
|
| 13183 | }
|
| 13184 | stringKey = "template: " + print_list(firstArgument);
|
| 13185 | stringKey += " tests: " + print_list(thirdArgument);
|
| 13186 | if (DEBUG) {
|
| 13187 | console.log("pattern stringkey: " + stringKey);
|
| 13188 | }
|
| 13189 | patternPosition = userSimplificationsInStringForm.indexOf(stringKey);
|
| 13190 | if (patternPosition === -1) {
|
| 13191 | userSimplificationsInStringForm.push(stringKey);
|
| 13192 | userSimplificationsInListForm.push(cdr(p1));
|
| 13193 | } else {
|
| 13194 | if (DEBUG) {
|
| 13195 | console.log("pattern already exists, replacing. " + cdr(p1));
|
| 13196 | }
|
| 13197 | userSimplificationsInStringForm[patternPosition] = stringKey;
|
| 13198 | userSimplificationsInListForm[patternPosition] = cdr(p1);
|
| 13199 | }
|
| 13200 | push_symbol(PATTERN);
|
| 13201 | push(cdr(p1));
|
| 13202 | return list(2);
|
| 13203 | };
|
| 13204 |
|
| 13205 |
|
| 13206 | |
| 13207 | |
| 13208 |
|
| 13209 |
|
| 13210 | do_clearPatterns = function() {
|
| 13211 | userSimplificationsInListForm = [];
|
| 13212 | return userSimplificationsInStringForm = [];
|
| 13213 | };
|
| 13214 |
|
| 13215 | Eval_clearpatterns = function() {
|
| 13216 | do_clearPatterns();
|
| 13217 | return push_symbol(NIL);
|
| 13218 | };
|
| 13219 |
|
| 13220 | Eval_patternsinfo = function() {
|
| 13221 | var patternsinfoToBePrinted;
|
| 13222 | patternsinfoToBePrinted = patternsinfo();
|
| 13223 | if (patternsinfoToBePrinted !== "") {
|
| 13224 | return new_string(patternsinfoToBePrinted);
|
| 13225 | } else {
|
| 13226 | return push_symbol(NIL);
|
| 13227 | }
|
| 13228 | };
|
| 13229 |
|
| 13230 | patternsinfo = function() {
|
| 13231 | var i, i1, len, patternsinfoToBePrinted;
|
| 13232 | patternsinfoToBePrinted = "";
|
| 13233 | for (i1 = 0, len = userSimplificationsInListForm.length; i1 < len; i1++) {
|
| 13234 | i = userSimplificationsInListForm[i1];
|
| 13235 | patternsinfoToBePrinted += userSimplificationsInListForm + "\n";
|
| 13236 | }
|
| 13237 | return patternsinfoToBePrinted;
|
| 13238 | };
|
| 13239 |
|
| 13240 |
|
| 13241 | |
| 13242 | |
| 13243 | |
| 13244 | |
| 13245 | |
| 13246 | |
| 13247 | |
| 13248 | |
| 13249 |
|
| 13250 |
|
| 13251 | Eval_polar = function() {
|
| 13252 | push(cadr(p1));
|
| 13253 | Eval();
|
| 13254 | return polar();
|
| 13255 | };
|
| 13256 |
|
| 13257 | polar = function() {
|
| 13258 | evaluatingPolar++;
|
| 13259 | save();
|
| 13260 | p1 = pop();
|
| 13261 | push(p1);
|
| 13262 | abs();
|
| 13263 | push(imaginaryunit);
|
| 13264 | push(p1);
|
| 13265 | arg();
|
| 13266 | multiply();
|
| 13267 | exponential();
|
| 13268 | multiply();
|
| 13269 | evaluatingPolar--;
|
| 13270 | return restore();
|
| 13271 | };
|
| 13272 |
|
| 13273 | n_factor_number = 0;
|
| 13274 |
|
| 13275 | factor_number = function() {
|
| 13276 | var h;
|
| 13277 | h = 0;
|
| 13278 | save();
|
| 13279 | p1 = pop();
|
| 13280 | if (equaln(p1, 0) || equaln(p1, 1) || equaln(p1, -1)) {
|
| 13281 | push(p1);
|
| 13282 | restore();
|
| 13283 | return;
|
| 13284 | }
|
| 13285 | n_factor_number = p1.q.a;
|
| 13286 | h = tos;
|
| 13287 | factor_a();
|
| 13288 | if (tos - h > 1) {
|
| 13289 | list(tos - h);
|
| 13290 | push_symbol(MULTIPLY);
|
| 13291 | swap();
|
| 13292 | cons();
|
| 13293 | }
|
| 13294 | return restore();
|
| 13295 | };
|
| 13296 |
|
| 13297 | factor_a = function() {
|
| 13298 | var i1, k;
|
| 13299 | k = 0;
|
| 13300 | if (n_factor_number.isNegative()) {
|
| 13301 | n_factor_number = setSignTo(n_factor_number, 1);
|
| 13302 | push_integer(-1);
|
| 13303 | }
|
| 13304 | for (k = i1 = 0; i1 < 10000; k = ++i1) {
|
| 13305 | try_kth_prime(k);
|
| 13306 | if (n_factor_number.compare(1) === 0) {
|
| 13307 | return;
|
| 13308 | }
|
| 13309 | }
|
| 13310 | return factor_b();
|
| 13311 | };
|
| 13312 |
|
| 13313 | try_kth_prime = function(k) {
|
| 13314 | var count, d, q, r, ref1;
|
| 13315 | count = 0;
|
| 13316 | d = mint(primetab[k]);
|
| 13317 | count = 0;
|
| 13318 | while (1) {
|
| 13319 | if (n_factor_number.compare(1) === 0) {
|
| 13320 | if (count) {
|
| 13321 | push_factor(d, count);
|
| 13322 | }
|
| 13323 | return;
|
| 13324 | }
|
| 13325 | ref1 = mdivrem(n_factor_number, d), q = ref1[0], r = ref1[1];
|
| 13326 | if (r.isZero()) {
|
| 13327 | count++;
|
| 13328 | n_factor_number = q;
|
| 13329 | } else {
|
| 13330 | break;
|
| 13331 | }
|
| 13332 | }
|
| 13333 | if (count) {
|
| 13334 | push_factor(d, count);
|
| 13335 | }
|
| 13336 | if (mcmp(q, d) === -1) {
|
| 13337 | push_factor(n_factor_number, 1);
|
| 13338 | return n_factor_number = mint(1);
|
| 13339 | }
|
| 13340 | };
|
| 13341 |
|
| 13342 | factor_b = function() {
|
| 13343 | var bigint_one, g, k, l, t, x, xprime;
|
| 13344 | k = 0;
|
| 13345 | l = 0;
|
| 13346 | bigint_one = mint(1);
|
| 13347 | x = mint(5);
|
| 13348 | xprime = mint(2);
|
| 13349 | k = 1;
|
| 13350 | l = 1;
|
| 13351 | while (1) {
|
| 13352 | if (mprime(n_factor_number)) {
|
| 13353 | push_factor(n_factor_number, 1);
|
| 13354 | return 0;
|
| 13355 | }
|
| 13356 | while (1) {
|
| 13357 | if (esc_flag) {
|
| 13358 | stop("esc");
|
| 13359 | }
|
| 13360 | t = msub(xprime, x);
|
| 13361 | t = setSignTo(t, 1);
|
| 13362 | g = mgcd(t, n_factor_number);
|
| 13363 | if (MEQUAL(g, 1)) {
|
| 13364 | if (--k === 0) {
|
| 13365 | xprime = x;
|
| 13366 | l *= 2;
|
| 13367 | k = l;
|
| 13368 | }
|
| 13369 | t = mmul(x, x);
|
| 13370 | x = madd(t, bigint_one);
|
| 13371 | t = mmod(x, n_factor_number);
|
| 13372 | x = t;
|
| 13373 | continue;
|
| 13374 | }
|
| 13375 | push_factor(g, 1);
|
| 13376 | if (mcmp(g, n_factor_number) === 0) {
|
| 13377 | return -1;
|
| 13378 | }
|
| 13379 | t = mdiv(n_factor_number, g);
|
| 13380 | n_factor_number = t;
|
| 13381 | t = mmod(x, n_factor_number);
|
| 13382 | x = t;
|
| 13383 | t = mmod(xprime, n_factor_number);
|
| 13384 | xprime = t;
|
| 13385 | break;
|
| 13386 | }
|
| 13387 | }
|
| 13388 | };
|
| 13389 |
|
| 13390 | push_factor = function(d, count) {
|
| 13391 | p1 = new U();
|
| 13392 | p1.k = NUM;
|
| 13393 | p1.q.a = d;
|
| 13394 | p1.q.b = mint(1);
|
| 13395 | push(p1);
|
| 13396 | if (count > 1) {
|
| 13397 | push_symbol(POWER);
|
| 13398 | swap();
|
| 13399 | p1 = new U();
|
| 13400 | p1.k = NUM;
|
| 13401 | p1.q.a = mint(count);
|
| 13402 | p1.q.b = mint(1);
|
| 13403 | push(p1);
|
| 13404 | return list(3);
|
| 13405 | }
|
| 13406 | };
|
| 13407 |
|
| 13408 |
|
| 13409 | |
| 13410 | |
| 13411 | |
| 13412 | |
| 13413 | |
| 13414 | |
| 13415 | |
| 13416 |
|
| 13417 |
|
| 13418 | DEBUG_POWER = false;
|
| 13419 |
|
| 13420 | Eval_power = function() {
|
| 13421 | if (DEBUG_POWER) {
|
| 13422 | debugger;
|
| 13423 | }
|
| 13424 | push(cadr(p1));
|
| 13425 | Eval();
|
| 13426 | push(caddr(p1));
|
| 13427 | Eval();
|
| 13428 | return power();
|
| 13429 | };
|
| 13430 |
|
| 13431 | power = function() {
|
| 13432 | save();
|
| 13433 | yypower();
|
| 13434 | return restore();
|
| 13435 | };
|
| 13436 |
|
| 13437 | yypower = function() {
|
| 13438 | var b_isEven_and_c_isItsInverse, hopefullySimplified, inputBase, inputExp, isThisOne, is_a_moreThanZero, n;
|
| 13439 | if (DEBUG_POWER) {
|
| 13440 | debugger;
|
| 13441 | }
|
| 13442 | n = 0;
|
| 13443 | p2 = pop();
|
| 13444 | p1 = pop();
|
| 13445 | inputExp = p2;
|
| 13446 | inputBase = p1;
|
| 13447 | if (DEBUG_POWER) {
|
| 13448 | console.log("POWER: " + p1 + " ^ " + p2);
|
| 13449 | }
|
| 13450 | if (equal(p1, one) || iszero(p2)) {
|
| 13451 | if (evaluatingAsFloats) {
|
| 13452 | push_double(1.0);
|
| 13453 | } else {
|
| 13454 | push(one);
|
| 13455 | }
|
| 13456 | if (DEBUG_POWER) {
|
| 13457 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13458 | }
|
| 13459 | return;
|
| 13460 | }
|
| 13461 | if (equal(p2, one)) {
|
| 13462 | push(p1);
|
| 13463 | if (DEBUG_POWER) {
|
| 13464 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13465 | }
|
| 13466 | return;
|
| 13467 | }
|
| 13468 | if (isminusone(p1) && isminusone(p2)) {
|
| 13469 | if (evaluatingAsFloats) {
|
| 13470 | push_double(1.0);
|
| 13471 | } else {
|
| 13472 | push(one);
|
| 13473 | }
|
| 13474 | negate();
|
| 13475 | if (DEBUG_POWER) {
|
| 13476 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13477 | }
|
| 13478 | return;
|
| 13479 | }
|
| 13480 | if (isminusone(p1) && (isoneovertwo(p2))) {
|
| 13481 | push(imaginaryunit);
|
| 13482 | if (DEBUG_POWER) {
|
| 13483 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13484 | }
|
| 13485 | return;
|
| 13486 | }
|
| 13487 | if (isminusone(p1) && isminusoneovertwo(p2)) {
|
| 13488 | push(imaginaryunit);
|
| 13489 | negate();
|
| 13490 | if (DEBUG_POWER) {
|
| 13491 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13492 | }
|
| 13493 | return;
|
| 13494 | }
|
| 13495 | if (isminusone(p1) && !isdouble(p1) && isrational(p2) && !isinteger(p2) && ispositivenumber(p2) && !evaluatingAsFloats) {
|
| 13496 | if (DEBUG_POWER) {
|
| 13497 | console.log(" power: -1 ^ rational");
|
| 13498 | }
|
| 13499 | if (DEBUG_POWER) {
|
| 13500 | console.log(" trick: p2.q.a , p2.q.b " + p2.q.a + " , " + p2.q.b);
|
| 13501 | }
|
| 13502 | if (p2.q.a < p2.q.b) {
|
| 13503 | push_symbol(POWER);
|
| 13504 | push(p1);
|
| 13505 | push(p2);
|
| 13506 | list(3);
|
| 13507 | } else {
|
| 13508 | push_symbol(MULTIPLY);
|
| 13509 | push(p1);
|
| 13510 | push_symbol(POWER);
|
| 13511 | push(p1);
|
| 13512 | push_rational(p2.q.a.mod(p2.q.b), p2.q.b);
|
| 13513 | list(3);
|
| 13514 | list(3);
|
| 13515 | if (DEBUG_POWER) {
|
| 13516 | console.log(" trick applied : " + stack[tos - 1]);
|
| 13517 | }
|
| 13518 | }
|
| 13519 | rect();
|
| 13520 | if (DEBUG_POWER) {
|
| 13521 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13522 | }
|
| 13523 | return;
|
| 13524 | }
|
| 13525 | if (isrational(p1) && isrational(p2)) {
|
| 13526 | if (DEBUG_POWER) {
|
| 13527 | console.log(" power: isrational(p1) && isrational(p2)");
|
| 13528 | }
|
| 13529 | push(p1);
|
| 13530 | push(p2);
|
| 13531 | qpow();
|
| 13532 | if (DEBUG_POWER) {
|
| 13533 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13534 | }
|
| 13535 | return;
|
| 13536 | }
|
| 13537 | if (isnum(p1) && isnum(p2)) {
|
| 13538 | if (DEBUG_POWER) {
|
| 13539 | console.log(" power: both base and exponent are either rational or double ");
|
| 13540 | }
|
| 13541 | if (DEBUG_POWER) {
|
| 13542 | console.log("POWER - isnum(p1) && isnum(p2)");
|
| 13543 | }
|
| 13544 | push(p1);
|
| 13545 | push(p2);
|
| 13546 | dpow();
|
| 13547 | if (DEBUG_POWER) {
|
| 13548 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13549 | }
|
| 13550 | return;
|
| 13551 | }
|
| 13552 | if (istensor(p1)) {
|
| 13553 | if (DEBUG_POWER) {
|
| 13554 | console.log(" power: istensor(p1) ");
|
| 13555 | }
|
| 13556 | power_tensor();
|
| 13557 | if (DEBUG_POWER) {
|
| 13558 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13559 | }
|
| 13560 | return;
|
| 13561 | }
|
| 13562 | if (car(p1) === symbol(ABS) && iseveninteger(p2) && !iszero(get_binding(symbol(ASSUME_REAL_VARIABLES)))) {
|
| 13563 | if (DEBUG_POWER) {
|
| 13564 | console.log(" power: even power of absolute of real value ");
|
| 13565 | }
|
| 13566 | push(cadr(p1));
|
| 13567 | push(p2);
|
| 13568 | power();
|
| 13569 | if (DEBUG_POWER) {
|
| 13570 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13571 | }
|
| 13572 | return;
|
| 13573 | }
|
| 13574 | if (p1 === symbol(E) && car(p2) === symbol(LOG)) {
|
| 13575 | push(cadr(p2));
|
| 13576 | if (DEBUG_POWER) {
|
| 13577 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13578 | }
|
| 13579 | return;
|
| 13580 | }
|
| 13581 | if (p1 === symbol(E) && isdouble(p2)) {
|
| 13582 | if (DEBUG_POWER) {
|
| 13583 | console.log(" power: p1 == symbol(E) && isdouble(p2) ");
|
| 13584 | }
|
| 13585 | push_double(Math.exp(p2.d));
|
| 13586 | if (DEBUG_POWER) {
|
| 13587 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13588 | }
|
| 13589 | return;
|
| 13590 | }
|
| 13591 | if (p1 === symbol(E) && Find(p2, imaginaryunit) !== 0 && Find(p2, symbol(PI)) !== 0 && !evaluatingPolar) {
|
| 13592 | push_symbol(POWER);
|
| 13593 | push(p1);
|
| 13594 | push(p2);
|
| 13595 | list(3);
|
| 13596 | if (DEBUG_POWER) {
|
| 13597 | console.log(" power: turning complex exponential to rect: " + stack[tos - 1]);
|
| 13598 | }
|
| 13599 | rect();
|
| 13600 | hopefullySimplified = pop();
|
| 13601 | if (Find(hopefullySimplified, symbol(PI)) === 0) {
|
| 13602 | if (DEBUG_POWER) {
|
| 13603 | console.log(" power: turned complex exponential to rect: " + hopefullySimplified);
|
| 13604 | }
|
| 13605 | push(hopefullySimplified);
|
| 13606 | return;
|
| 13607 | }
|
| 13608 | }
|
| 13609 | if (car(p1) === symbol(MULTIPLY) && isinteger(p2)) {
|
| 13610 | if (DEBUG_POWER) {
|
| 13611 | console.log(" power: (a * b) ^ c -> (a ^ c) * (b ^ c) ");
|
| 13612 | }
|
| 13613 | p1 = cdr(p1);
|
| 13614 | push(car(p1));
|
| 13615 | push(p2);
|
| 13616 | power();
|
| 13617 | p1 = cdr(p1);
|
| 13618 | while (iscons(p1)) {
|
| 13619 | push(car(p1));
|
| 13620 | push(p2);
|
| 13621 | power();
|
| 13622 | multiply();
|
| 13623 | p1 = cdr(p1);
|
| 13624 | }
|
| 13625 | if (DEBUG_POWER) {
|
| 13626 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13627 | }
|
| 13628 | return;
|
| 13629 | }
|
| 13630 | is_a_moreThanZero = false;
|
| 13631 | if (isnum(cadr(p1))) {
|
| 13632 | is_a_moreThanZero = sign(compare_numbers(cadr(p1), zero));
|
| 13633 | }
|
| 13634 | if (car(p1) === symbol(POWER) && (isinteger(p2) || is_a_moreThanZero)) {
|
| 13635 | push(cadr(p1));
|
| 13636 | push(caddr(p1));
|
| 13637 | push(p2);
|
| 13638 | multiply();
|
| 13639 | power();
|
| 13640 | if (DEBUG_POWER) {
|
| 13641 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13642 | }
|
| 13643 | return;
|
| 13644 | }
|
| 13645 | b_isEven_and_c_isItsInverse = false;
|
| 13646 | if (iseveninteger(caddr(p1))) {
|
| 13647 | push(caddr(p1));
|
| 13648 | push(p2);
|
| 13649 | multiply();
|
| 13650 | isThisOne = pop();
|
| 13651 | if (isone(isThisOne)) {
|
| 13652 | b_isEven_and_c_isItsInverse = true;
|
| 13653 | }
|
| 13654 | }
|
| 13655 | if (car(p1) === symbol(POWER) && b_isEven_and_c_isItsInverse) {
|
| 13656 | if (DEBUG_POWER) {
|
| 13657 | console.log(" power: car(p1) == symbol(POWER) && b_isEven_and_c_isItsInverse ");
|
| 13658 | }
|
| 13659 | push(cadr(p1));
|
| 13660 | abs();
|
| 13661 | if (DEBUG_POWER) {
|
| 13662 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13663 | }
|
| 13664 | return;
|
| 13665 | }
|
| 13666 | if (expanding && isadd(p1) && isnum(p2)) {
|
| 13667 | push(p2);
|
| 13668 | n = pop_integer();
|
| 13669 | if (n > 1 && !isNaN(n)) {
|
| 13670 | if (DEBUG_POWER) {
|
| 13671 | console.log(" power: expanding && isadd(p1) && isnum(p2) ");
|
| 13672 | }
|
| 13673 | power_sum(n);
|
| 13674 | if (DEBUG_POWER) {
|
| 13675 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13676 | }
|
| 13677 | return;
|
| 13678 | }
|
| 13679 | }
|
| 13680 | if (trigmode === 1 && car(p1) === symbol(SIN) && iseveninteger(p2)) {
|
| 13681 | if (DEBUG_POWER) {
|
| 13682 | console.log(" power: trigmode == 1 && car(p1) == symbol(SIN) && iseveninteger(p2) ");
|
| 13683 | }
|
| 13684 | push_integer(1);
|
| 13685 | push(cadr(p1));
|
| 13686 | cosine();
|
| 13687 | push_integer(2);
|
| 13688 | power();
|
| 13689 | subtract();
|
| 13690 | push(p2);
|
| 13691 | push_rational(1, 2);
|
| 13692 | multiply();
|
| 13693 | power();
|
| 13694 | if (DEBUG_POWER) {
|
| 13695 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13696 | }
|
| 13697 | return;
|
| 13698 | }
|
| 13699 | if (trigmode === 2 && car(p1) === symbol(COS) && iseveninteger(p2)) {
|
| 13700 | if (DEBUG_POWER) {
|
| 13701 | console.log(" power: trigmode == 2 && car(p1) == symbol(COS) && iseveninteger(p2) ");
|
| 13702 | }
|
| 13703 | push_integer(1);
|
| 13704 | push(cadr(p1));
|
| 13705 | sine();
|
| 13706 | push_integer(2);
|
| 13707 | power();
|
| 13708 | subtract();
|
| 13709 | push(p2);
|
| 13710 | push_rational(1, 2);
|
| 13711 | multiply();
|
| 13712 | power();
|
| 13713 | if (DEBUG_POWER) {
|
| 13714 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13715 | }
|
| 13716 | return;
|
| 13717 | }
|
| 13718 | if (iscomplexnumber(p1)) {
|
| 13719 | if (DEBUG_POWER) {
|
| 13720 | console.log(" power - handling the case (a + ib) ^ n");
|
| 13721 | }
|
| 13722 | if (isinteger(p2)) {
|
| 13723 | push(p1);
|
| 13724 | conjugate();
|
| 13725 | p3 = pop();
|
| 13726 | push(p3);
|
| 13727 | push(p3);
|
| 13728 | push(p1);
|
| 13729 | multiply();
|
| 13730 | divide();
|
| 13731 | if (!isone(p2)) {
|
| 13732 | push(p2);
|
| 13733 | negate();
|
| 13734 | power();
|
| 13735 | }
|
| 13736 | if (DEBUG_POWER) {
|
| 13737 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13738 | }
|
| 13739 | return;
|
| 13740 | }
|
| 13741 | if (isnum(p2)) {
|
| 13742 | push(p1);
|
| 13743 | abs();
|
| 13744 | push(p2);
|
| 13745 | power();
|
| 13746 | push_integer(-1);
|
| 13747 | push(p1);
|
| 13748 | arg();
|
| 13749 | push(p2);
|
| 13750 | multiply();
|
| 13751 | if (evaluatingAsFloats || (iscomplexnumberdouble(p1) && isdouble(p2))) {
|
| 13752 | push_double(Math.PI);
|
| 13753 | } else {
|
| 13754 | push(symbol(PI));
|
| 13755 | }
|
| 13756 | divide();
|
| 13757 | power();
|
| 13758 | multiply();
|
| 13759 | if (avoidCalculatingPowersIntoArctans) {
|
| 13760 | if (Find(stack[tos - 1], symbol(ARCTAN))) {
|
| 13761 | pop();
|
| 13762 | push_symbol(POWER);
|
| 13763 | push(p1);
|
| 13764 | push(p2);
|
| 13765 | list(3);
|
| 13766 | }
|
| 13767 | }
|
| 13768 | if (DEBUG_POWER) {
|
| 13769 | console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13770 | }
|
| 13771 | return;
|
| 13772 | }
|
| 13773 | }
|
| 13774 | if (simplify_polar()) {
|
| 13775 | if (DEBUG_POWER) {
|
| 13776 | console.log(" power: using simplify_polar");
|
| 13777 | }
|
| 13778 | return;
|
| 13779 | }
|
| 13780 | if (DEBUG_POWER) {
|
| 13781 | console.log(" power: nothing can be done ");
|
| 13782 | }
|
| 13783 | push_symbol(POWER);
|
| 13784 | push(p1);
|
| 13785 | push(p2);
|
| 13786 | list(3);
|
| 13787 | if (DEBUG_POWER) {
|
| 13788 | return console.log(" power of " + inputBase + " ^ " + inputExp + ": " + stack[tos - 1]);
|
| 13789 | }
|
| 13790 | };
|
| 13791 |
|
| 13792 | power_sum = function(n) {
|
| 13793 | var a, i, i1, j, j1, k, l1, ref1, ref2, ref3;
|
| 13794 | a = [];
|
| 13795 | i = 0;
|
| 13796 | j = 0;
|
| 13797 | k = 0;
|
| 13798 | k = length(p1) - 1;
|
| 13799 | push_frame(k * (n + 1));
|
| 13800 | p1 = cdr(p1);
|
| 13801 | for (i = i1 = 0, ref1 = k; 0 <= ref1 ? i1 < ref1 : i1 > ref1; i = 0 <= ref1 ? ++i1 : --i1) {
|
| 13802 | for (j = j1 = 0, ref2 = n; 0 <= ref2 ? j1 <= ref2 : j1 >= ref2; j = 0 <= ref2 ? ++j1 : --j1) {
|
| 13803 | push(car(p1));
|
| 13804 | push_integer(j);
|
| 13805 | power();
|
| 13806 | stack[frame + i * (n + 1) + j] = pop();
|
| 13807 | }
|
| 13808 | p1 = cdr(p1);
|
| 13809 | }
|
| 13810 | push_integer(n);
|
| 13811 | factorial();
|
| 13812 | p1 = pop();
|
| 13813 | for (i = l1 = 0, ref3 = k; 0 <= ref3 ? l1 < ref3 : l1 > ref3; i = 0 <= ref3 ? ++l1 : --l1) {
|
| 13814 | a[i] = 0;
|
| 13815 | }
|
| 13816 | push(zero);
|
| 13817 | multinomial_sum(k, n, a, 0, n);
|
| 13818 | return pop_frame(k * (n + 1));
|
| 13819 | };
|
| 13820 |
|
| 13821 | multinomial_sum = function(k, n, a, i, m) {
|
| 13822 | var i1, j, j1, l1, ref1, ref2, ref3;
|
| 13823 | j = 0;
|
| 13824 | if (i < k - 1) {
|
| 13825 | for (j = i1 = 0, ref1 = m; 0 <= ref1 ? i1 <= ref1 : i1 >= ref1; j = 0 <= ref1 ? ++i1 : --i1) {
|
| 13826 | a[i] = j;
|
| 13827 | multinomial_sum(k, n, a, i + 1, m - j);
|
| 13828 | }
|
| 13829 | return;
|
| 13830 | }
|
| 13831 | a[i] = m;
|
| 13832 | push(p1);
|
| 13833 | for (j = j1 = 0, ref2 = k; 0 <= ref2 ? j1 < ref2 : j1 > ref2; j = 0 <= ref2 ? ++j1 : --j1) {
|
| 13834 | push_integer(a[j]);
|
| 13835 | factorial();
|
| 13836 | divide();
|
| 13837 | }
|
| 13838 | for (j = l1 = 0, ref3 = k; 0 <= ref3 ? l1 < ref3 : l1 > ref3; j = 0 <= ref3 ? ++l1 : --l1) {
|
| 13839 | push(stack[frame + j * (n + 1) + a[j]]);
|
| 13840 | multiply();
|
| 13841 | }
|
| 13842 | return add();
|
| 13843 | };
|
| 13844 |
|
| 13845 | simplify_polar = function() {
|
| 13846 | var doNothing, n;
|
| 13847 | n = 0;
|
| 13848 | n = isquarterturn(p2);
|
| 13849 | switch (n) {
|
| 13850 | case 0:
|
| 13851 | doNothing = 1;
|
| 13852 | break;
|
| 13853 | case 1:
|
| 13854 | push_integer(1);
|
| 13855 | return 1;
|
| 13856 | case 2:
|
| 13857 | push_integer(-1);
|
| 13858 | return 1;
|
| 13859 | case 3:
|
| 13860 | push(imaginaryunit);
|
| 13861 | return 1;
|
| 13862 | case 4:
|
| 13863 | push(imaginaryunit);
|
| 13864 | negate();
|
| 13865 | return 1;
|
| 13866 | }
|
| 13867 | if (car(p2) === symbol(ADD)) {
|
| 13868 | p3 = cdr(p2);
|
| 13869 | while (iscons(p3)) {
|
| 13870 | n = isquarterturn(car(p3));
|
| 13871 | if (n) {
|
| 13872 | break;
|
| 13873 | }
|
| 13874 | p3 = cdr(p3);
|
| 13875 | }
|
| 13876 | switch (n) {
|
| 13877 | case 0:
|
| 13878 | return 0;
|
| 13879 | case 1:
|
| 13880 | push_integer(1);
|
| 13881 | break;
|
| 13882 | case 2:
|
| 13883 | push_integer(-1);
|
| 13884 | break;
|
| 13885 | case 3:
|
| 13886 | push(imaginaryunit);
|
| 13887 | break;
|
| 13888 | case 4:
|
| 13889 | push(imaginaryunit);
|
| 13890 | negate();
|
| 13891 | }
|
| 13892 | push(p2);
|
| 13893 | push(car(p3));
|
| 13894 | subtract();
|
| 13895 | exponential();
|
| 13896 | multiply();
|
| 13897 | return 1;
|
| 13898 | }
|
| 13899 | return 0;
|
| 13900 | };
|
| 13901 |
|
| 13902 | Eval_prime = function() {
|
| 13903 | push(cadr(p1));
|
| 13904 | Eval();
|
| 13905 | return prime();
|
| 13906 | };
|
| 13907 |
|
| 13908 | prime = function() {
|
| 13909 | var n;
|
| 13910 | n = 0;
|
| 13911 | n = pop_integer();
|
| 13912 | if (n < 1 || n > MAXPRIMETAB) {
|
| 13913 | stop("prime: Argument out of range.");
|
| 13914 | }
|
| 13915 | n = primetab[n - 1];
|
| 13916 | return push_integer(n);
|
| 13917 | };
|
| 13918 |
|
| 13919 | power_str = "^";
|
| 13920 |
|
| 13921 | codeGen = false;
|
| 13922 |
|
| 13923 | Eval_print = function() {
|
| 13924 | stringsEmittedByUserPrintouts += _print(cdr(p1), environment_printmode);
|
| 13925 | return push(symbol(NIL));
|
| 13926 | };
|
| 13927 |
|
| 13928 | Eval_print2dascii = function() {
|
| 13929 | stringsEmittedByUserPrintouts += _print(cdr(p1), PRINTMODE_2DASCII);
|
| 13930 | return push(symbol(NIL));
|
| 13931 | };
|
| 13932 |
|
| 13933 | Eval_printfull = function() {
|
| 13934 | stringsEmittedByUserPrintouts += _print(cdr(p1), PRINTMODE_FULL);
|
| 13935 | return push(symbol(NIL));
|
| 13936 | };
|
| 13937 |
|
| 13938 | Eval_printlatex = function() {
|
| 13939 | stringsEmittedByUserPrintouts += _print(cdr(p1), PRINTMODE_LATEX);
|
| 13940 | return push(symbol(NIL));
|
| 13941 | };
|
| 13942 |
|
| 13943 | Eval_printplain = function() {
|
| 13944 | var original_test_flag;
|
| 13945 | original_test_flag = test_flag;
|
| 13946 | test_flag = 0;
|
| 13947 | stringsEmittedByUserPrintouts += _print(cdr(p1), PRINTMODE_PLAIN);
|
| 13948 | test_flag = original_test_flag;
|
| 13949 | return push(symbol(NIL));
|
| 13950 | };
|
| 13951 |
|
| 13952 | Eval_printlist = function() {
|
| 13953 | var beenPrinted;
|
| 13954 | beenPrinted = _print(cdr(p1), PRINTMODE_LIST);
|
| 13955 | stringsEmittedByUserPrintouts += beenPrinted;
|
| 13956 | return push(symbol(NIL));
|
| 13957 | };
|
| 13958 |
|
| 13959 | _print = function(p, passedPrintMode) {
|
| 13960 | var accumulator, origPrintMode;
|
| 13961 | accumulator = "";
|
| 13962 | while (iscons(p)) {
|
| 13963 | push(car(p));
|
| 13964 | Eval();
|
| 13965 | p2 = pop();
|
| 13966 |
|
| 13967 | |
| 13968 | |
| 13969 | |
| 13970 | |
| 13971 | |
| 13972 | |
| 13973 | |
| 13974 |
|
| 13975 | origPrintMode = printMode;
|
| 13976 | if (passedPrintMode === PRINTMODE_FULL) {
|
| 13977 | printMode = PRINTMODE_FULL;
|
| 13978 | accumulator = printline(p2);
|
| 13979 | rememberPrint(accumulator, LAST_FULL_PRINT);
|
| 13980 | } else if (passedPrintMode === PRINTMODE_PLAIN) {
|
| 13981 | printMode = PRINTMODE_PLAIN;
|
| 13982 | accumulator = printline(p2);
|
| 13983 | rememberPrint(accumulator, LAST_PLAIN_PRINT);
|
| 13984 | } else if (passedPrintMode === PRINTMODE_2DASCII) {
|
| 13985 | printMode = PRINTMODE_2DASCII;
|
| 13986 | accumulator = print2dascii(p2);
|
| 13987 | rememberPrint(accumulator, LAST_2DASCII_PRINT);
|
| 13988 | } else if (passedPrintMode === PRINTMODE_LATEX) {
|
| 13989 | printMode = PRINTMODE_LATEX;
|
| 13990 | accumulator = printline(p2);
|
| 13991 | rememberPrint(accumulator, LAST_LATEX_PRINT);
|
| 13992 | } else if (passedPrintMode === PRINTMODE_LIST) {
|
| 13993 | printMode = PRINTMODE_LIST;
|
| 13994 | accumulator = print_list(p2);
|
| 13995 | rememberPrint(accumulator, LAST_LIST_PRINT);
|
| 13996 | }
|
| 13997 | printMode = origPrintMode;
|
| 13998 | p = cdr(p);
|
| 13999 | }
|
| 14000 | if (DEBUG) {
|
| 14001 | console.log("emttedString from display: " + stringsEmittedByUserPrintouts);
|
| 14002 | }
|
| 14003 | return accumulator;
|
| 14004 | };
|
| 14005 |
|
| 14006 | rememberPrint = function(theString, theTypeOfPrint) {
|
| 14007 | var parsedString;
|
| 14008 | scan('"' + theString + '"');
|
| 14009 | parsedString = pop();
|
| 14010 | return set_binding(symbol(theTypeOfPrint), parsedString);
|
| 14011 | };
|
| 14012 |
|
| 14013 | print_str = function(s) {
|
| 14014 | if (DEBUG) {
|
| 14015 | console.log("emttedString from print_str: " + stringsEmittedByUserPrintouts);
|
| 14016 | }
|
| 14017 | return s;
|
| 14018 | };
|
| 14019 |
|
| 14020 | print_char = function(c) {
|
| 14021 | return c;
|
| 14022 | };
|
| 14023 |
|
| 14024 | collectLatexStringFromReturnValue = function(p) {
|
| 14025 | var origPrintMode, originalCodeGen, returnedString;
|
| 14026 | origPrintMode = printMode;
|
| 14027 | printMode = PRINTMODE_LATEX;
|
| 14028 | originalCodeGen = codeGen;
|
| 14029 | codeGen = false;
|
| 14030 | returnedString = print_expr(p);
|
| 14031 | returnedString = returnedString.replace(/_/g, "\\_");
|
| 14032 | printMode = origPrintMode;
|
| 14033 | codeGen = originalCodeGen;
|
| 14034 | if (DEBUG) {
|
| 14035 | console.log("emttedString from collectLatexStringFromReturnValue: " + stringsEmittedByUserPrintouts);
|
| 14036 | }
|
| 14037 | return returnedString;
|
| 14038 | };
|
| 14039 |
|
| 14040 | printline = function(p) {
|
| 14041 | var accumulator;
|
| 14042 | accumulator = "";
|
| 14043 | accumulator += print_expr(p);
|
| 14044 | return accumulator;
|
| 14045 | };
|
| 14046 |
|
| 14047 | print_base_of_denom = function(p1) {
|
| 14048 | var accumulator;
|
| 14049 | accumulator = "";
|
| 14050 | if (isfraction(p1) || car(p1) === symbol(ADD) || car(p1) === symbol(MULTIPLY) || car(p1) === symbol(POWER) || lessp(p1, zero)) {
|
| 14051 | accumulator += print_char('(');
|
| 14052 | accumulator += print_expr(p1);
|
| 14053 | accumulator += print_char(')');
|
| 14054 | } else {
|
| 14055 | accumulator += print_expr(p1);
|
| 14056 | }
|
| 14057 | return accumulator;
|
| 14058 | };
|
| 14059 |
|
| 14060 | print_expo_of_denom = function(p2) {
|
| 14061 | var accumulator;
|
| 14062 | accumulator = "";
|
| 14063 | if (isfraction(p2) || car(p2) === symbol(ADD) || car(p2) === symbol(MULTIPLY) || car(p2) === symbol(POWER)) {
|
| 14064 | accumulator += print_char('(');
|
| 14065 | accumulator += print_expr(p2);
|
| 14066 | accumulator += print_char(')');
|
| 14067 | } else {
|
| 14068 | accumulator += print_expr(p2);
|
| 14069 | }
|
| 14070 | return accumulator;
|
| 14071 | };
|
| 14072 |
|
| 14073 | print_denom = function(p, d) {
|
| 14074 | var accumulator;
|
| 14075 | accumulator = "";
|
| 14076 | save();
|
| 14077 | p1 = cadr(p);
|
| 14078 | p2 = caddr(p);
|
| 14079 | if (isminusone(p2)) {
|
| 14080 | accumulator += print_base_of_denom(p1);
|
| 14081 | restore();
|
| 14082 | return accumulator;
|
| 14083 | }
|
| 14084 | if (d === 1) {
|
| 14085 | accumulator += print_char('(');
|
| 14086 | }
|
| 14087 | push(p2);
|
| 14088 | negate();
|
| 14089 | p2 = pop();
|
| 14090 | accumulator += print_power(p1, p2);
|
| 14091 | if (d === 1) {
|
| 14092 | accumulator += print_char(')');
|
| 14093 | }
|
| 14094 | restore();
|
| 14095 | return accumulator;
|
| 14096 | };
|
| 14097 |
|
| 14098 | print_a_over_b = function(p) {
|
| 14099 | var accumulator, d, doNothing, n;
|
| 14100 | accumulator = "";
|
| 14101 | flag = 0;
|
| 14102 | n = 0;
|
| 14103 | d = 0;
|
| 14104 | save();
|
| 14105 | n = 0;
|
| 14106 | d = 0;
|
| 14107 | p1 = cdr(p);
|
| 14108 | p2 = car(p1);
|
| 14109 | if (isrational(p2)) {
|
| 14110 | push(p2);
|
| 14111 | mp_numerator();
|
| 14112 | absval();
|
| 14113 | p3 = pop();
|
| 14114 | push(p2);
|
| 14115 | mp_denominator();
|
| 14116 | p4 = pop();
|
| 14117 | if (!isplusone(p3)) {
|
| 14118 | n++;
|
| 14119 | }
|
| 14120 | if (!isplusone(p4)) {
|
| 14121 | d++;
|
| 14122 | }
|
| 14123 | p1 = cdr(p1);
|
| 14124 | } else {
|
| 14125 | p3 = one;
|
| 14126 | p4 = one;
|
| 14127 | }
|
| 14128 | while (iscons(p1)) {
|
| 14129 | p2 = car(p1);
|
| 14130 | if (is_denominator(p2)) {
|
| 14131 | d++;
|
| 14132 | } else {
|
| 14133 | n++;
|
| 14134 | }
|
| 14135 | p1 = cdr(p1);
|
| 14136 | }
|
| 14137 | if (printMode === PRINTMODE_LATEX) {
|
| 14138 | accumulator += print_str('\\frac{');
|
| 14139 | }
|
| 14140 | if (n === 0) {
|
| 14141 | accumulator += print_char('1');
|
| 14142 | } else {
|
| 14143 | flag = 0;
|
| 14144 | p1 = cdr(p);
|
| 14145 | if (isrational(car(p1))) {
|
| 14146 | p1 = cdr(p1);
|
| 14147 | }
|
| 14148 | if (!isplusone(p3)) {
|
| 14149 | accumulator += print_factor(p3);
|
| 14150 | flag = 1;
|
| 14151 | }
|
| 14152 | while (iscons(p1)) {
|
| 14153 | p2 = car(p1);
|
| 14154 | if (is_denominator(p2)) {
|
| 14155 | doNothing = 1;
|
| 14156 | } else {
|
| 14157 | if (flag) {
|
| 14158 | accumulator += print_multiply_sign();
|
| 14159 | }
|
| 14160 | accumulator += print_factor(p2);
|
| 14161 | flag = 1;
|
| 14162 | }
|
| 14163 | p1 = cdr(p1);
|
| 14164 | }
|
| 14165 | }
|
| 14166 | if (printMode === PRINTMODE_LATEX) {
|
| 14167 | accumulator += print_str('}{');
|
| 14168 | } else if (printMode === PRINTMODE_PLAIN && !test_flag) {
|
| 14169 | accumulator += print_str(" / ");
|
| 14170 | } else {
|
| 14171 | accumulator += print_str("/");
|
| 14172 | }
|
| 14173 | if (d > 1 && printMode !== PRINTMODE_LATEX) {
|
| 14174 | accumulator += print_char('(');
|
| 14175 | }
|
| 14176 | flag = 0;
|
| 14177 | p1 = cdr(p);
|
| 14178 | if (isrational(car(p1))) {
|
| 14179 | p1 = cdr(p1);
|
| 14180 | }
|
| 14181 | if (!isplusone(p4)) {
|
| 14182 | accumulator += print_factor(p4);
|
| 14183 | flag = 1;
|
| 14184 | }
|
| 14185 | while (iscons(p1)) {
|
| 14186 | p2 = car(p1);
|
| 14187 | if (is_denominator(p2)) {
|
| 14188 | if (flag) {
|
| 14189 | accumulator += print_multiply_sign();
|
| 14190 | }
|
| 14191 | accumulator += print_denom(p2, d);
|
| 14192 | flag = 1;
|
| 14193 | }
|
| 14194 | p1 = cdr(p1);
|
| 14195 | }
|
| 14196 | if (d > 1 && printMode !== PRINTMODE_LATEX) {
|
| 14197 | accumulator += print_char(')');
|
| 14198 | }
|
| 14199 | if (printMode === PRINTMODE_LATEX) {
|
| 14200 | accumulator += print_str('}');
|
| 14201 | }
|
| 14202 | restore();
|
| 14203 | return accumulator;
|
| 14204 | };
|
| 14205 |
|
| 14206 | print_expr = function(p) {
|
| 14207 | var accumulator;
|
| 14208 | accumulator = "";
|
| 14209 | if (isadd(p)) {
|
| 14210 | p = cdr(p);
|
| 14211 | if (sign_of_term(car(p)) === '-') {
|
| 14212 | accumulator += print_str("-");
|
| 14213 | }
|
| 14214 | accumulator += print_term(car(p));
|
| 14215 | p = cdr(p);
|
| 14216 | while (iscons(p)) {
|
| 14217 | if (sign_of_term(car(p)) === '+') {
|
| 14218 | if (printMode === PRINTMODE_PLAIN && !test_flag) {
|
| 14219 | accumulator += print_str(" + ");
|
| 14220 | } else {
|
| 14221 | accumulator += print_str("+");
|
| 14222 | }
|
| 14223 | } else {
|
| 14224 | if (printMode === PRINTMODE_PLAIN && !test_flag) {
|
| 14225 | accumulator += print_str(" - ");
|
| 14226 | } else {
|
| 14227 | accumulator += print_str("-");
|
| 14228 | }
|
| 14229 | }
|
| 14230 | accumulator += print_term(car(p));
|
| 14231 | p = cdr(p);
|
| 14232 | }
|
| 14233 | } else {
|
| 14234 | if (sign_of_term(p) === '-') {
|
| 14235 | accumulator += print_str("-");
|
| 14236 | }
|
| 14237 | accumulator += print_term(p);
|
| 14238 | }
|
| 14239 | return accumulator;
|
| 14240 | };
|
| 14241 |
|
| 14242 | sign_of_term = function(p) {
|
| 14243 | var accumulator;
|
| 14244 | accumulator = "";
|
| 14245 | if (car(p) === symbol(MULTIPLY) && isnum(cadr(p)) && lessp(cadr(p), zero)) {
|
| 14246 | accumulator += '-';
|
| 14247 | } else if (isnum(p) && lessp(p, zero)) {
|
| 14248 | accumulator += '-';
|
| 14249 | } else {
|
| 14250 | accumulator += '+';
|
| 14251 | }
|
| 14252 | return accumulator;
|
| 14253 | };
|
| 14254 |
|
| 14255 | print_term = function(p) {
|
| 14256 | var accumulator, denom, numberOneOverSomething, origAccumulator, previousFactorWasANumber;
|
| 14257 | accumulator = "";
|
| 14258 | if (car(p) === symbol(MULTIPLY) && any_denominators(p)) {
|
| 14259 | accumulator += print_a_over_b(p);
|
| 14260 | return accumulator;
|
| 14261 | }
|
| 14262 | if (car(p) === symbol(MULTIPLY)) {
|
| 14263 | p = cdr(p);
|
| 14264 | if (isminusone(car(p))) {
|
| 14265 | p = cdr(p);
|
| 14266 | }
|
| 14267 | previousFactorWasANumber = false;
|
| 14268 | if (isnum(car(p))) {
|
| 14269 | previousFactorWasANumber = true;
|
| 14270 | }
|
| 14271 | numberOneOverSomething = false;
|
| 14272 | if (printMode === PRINTMODE_LATEX && iscons(cdr(p)) && isnumberoneoversomething(car(p))) {
|
| 14273 | numberOneOverSomething = true;
|
| 14274 | denom = car(p).q.b.toString();
|
| 14275 | }
|
| 14276 | if (numberOneOverSomething) {
|
| 14277 | origAccumulator = accumulator;
|
| 14278 | accumulator = "";
|
| 14279 | } else {
|
| 14280 | accumulator += print_factor(car(p));
|
| 14281 | }
|
| 14282 | p = cdr(p);
|
| 14283 | while (iscons(p)) {
|
| 14284 | if (printMode === PRINTMODE_LATEX) {
|
| 14285 | if (previousFactorWasANumber) {
|
| 14286 | if (caar(p) === symbol(POWER)) {
|
| 14287 | if (isnum(car(cdr(car(p))))) {
|
| 14288 | if (!isfraction(car(cdr(cdr(car(p)))))) {
|
| 14289 | accumulator += " \\cdot ";
|
| 14290 | }
|
| 14291 | }
|
| 14292 | }
|
| 14293 | }
|
| 14294 | }
|
| 14295 | accumulator += print_multiply_sign();
|
| 14296 | accumulator += print_factor(car(p));
|
| 14297 | previousFactorWasANumber = false;
|
| 14298 | if (isnum(car(p))) {
|
| 14299 | previousFactorWasANumber = true;
|
| 14300 | }
|
| 14301 | p = cdr(p);
|
| 14302 | }
|
| 14303 | if (numberOneOverSomething) {
|
| 14304 | accumulator = origAccumulator + "\\frac{" + accumulator + "}{" + denom + "}";
|
| 14305 | }
|
| 14306 | } else {
|
| 14307 | accumulator += print_factor(p);
|
| 14308 | }
|
| 14309 | return accumulator;
|
| 14310 | };
|
| 14311 |
|
| 14312 | print_subexpr = function(p) {
|
| 14313 | var accumulator;
|
| 14314 | accumulator = "";
|
| 14315 | accumulator += print_char('(');
|
| 14316 | accumulator += print_expr(p);
|
| 14317 | accumulator += print_char(')');
|
| 14318 | return accumulator;
|
| 14319 | };
|
| 14320 |
|
| 14321 | print_factorial_function = function(p) {
|
| 14322 | var accumulator;
|
| 14323 | accumulator = "";
|
| 14324 | p = cadr(p);
|
| 14325 | if (car(p) === symbol(ADD) || car(p) === symbol(MULTIPLY) || car(p) === symbol(POWER) || car(p) === symbol(FACTORIAL)) {
|
| 14326 | accumulator += print_subexpr(p);
|
| 14327 | } else {
|
| 14328 | accumulator += print_expr(p);
|
| 14329 | }
|
| 14330 | accumulator += print_char('!');
|
| 14331 | return accumulator;
|
| 14332 | };
|
| 14333 |
|
| 14334 | print_ABS_latex = function(p) {
|
| 14335 | var accumulator;
|
| 14336 | accumulator = "";
|
| 14337 | accumulator += print_str("\\left |");
|
| 14338 | accumulator += print_expr(cadr(p));
|
| 14339 | accumulator += print_str(" \\right |");
|
| 14340 | return accumulator;
|
| 14341 | };
|
| 14342 |
|
| 14343 | print_BINOMIAL_latex = function(p) {
|
| 14344 | var accumulator;
|
| 14345 | accumulator = "";
|
| 14346 | accumulator += print_str("\\binom{");
|
| 14347 | accumulator += print_expr(cadr(p));
|
| 14348 | accumulator += print_str("}{");
|
| 14349 | accumulator += print_expr(caddr(p));
|
| 14350 | accumulator += print_str("} ");
|
| 14351 | return accumulator;
|
| 14352 | };
|
| 14353 |
|
| 14354 | print_DOT_latex = function(p) {
|
| 14355 | var accumulator;
|
| 14356 | accumulator = "";
|
| 14357 | accumulator += print_expr(cadr(p));
|
| 14358 | accumulator += print_str(" \\cdot ");
|
| 14359 | accumulator += print_expr(caddr(p));
|
| 14360 | return accumulator;
|
| 14361 | };
|
| 14362 |
|
| 14363 | print_DOT_codegen = function(p) {
|
| 14364 | var accumulator;
|
| 14365 | accumulator = "dot(";
|
| 14366 | accumulator += print_expr(cadr(p));
|
| 14367 | accumulator += ", ";
|
| 14368 | accumulator += print_expr(caddr(p));
|
| 14369 | accumulator += ")";
|
| 14370 | return accumulator;
|
| 14371 | };
|
| 14372 |
|
| 14373 | print_SIN_codegen = function(p) {
|
| 14374 | var accumulator;
|
| 14375 | accumulator = "Math.sin(";
|
| 14376 | accumulator += print_expr(cadr(p));
|
| 14377 | accumulator += ")";
|
| 14378 | return accumulator;
|
| 14379 | };
|
| 14380 |
|
| 14381 | print_COS_codegen = function(p) {
|
| 14382 | var accumulator;
|
| 14383 | accumulator = "Math.cos(";
|
| 14384 | accumulator += print_expr(cadr(p));
|
| 14385 | accumulator += ")";
|
| 14386 | return accumulator;
|
| 14387 | };
|
| 14388 |
|
| 14389 | print_TAN_codegen = function(p) {
|
| 14390 | var accumulator;
|
| 14391 | accumulator = "Math.tan(";
|
| 14392 | accumulator += print_expr(cadr(p));
|
| 14393 | accumulator += ")";
|
| 14394 | return accumulator;
|
| 14395 | };
|
| 14396 |
|
| 14397 | print_ARCSIN_codegen = function(p) {
|
| 14398 | var accumulator;
|
| 14399 | accumulator = "Math.asin(";
|
| 14400 | accumulator += print_expr(cadr(p));
|
| 14401 | accumulator += ")";
|
| 14402 | return accumulator;
|
| 14403 | };
|
| 14404 |
|
| 14405 | print_ARCCOS_codegen = function(p) {
|
| 14406 | var accumulator;
|
| 14407 | accumulator = "Math.acos(";
|
| 14408 | accumulator += print_expr(cadr(p));
|
| 14409 | accumulator += ")";
|
| 14410 | return accumulator;
|
| 14411 | };
|
| 14412 |
|
| 14413 | print_ARCTAN_codegen = function(p) {
|
| 14414 | var accumulator;
|
| 14415 | accumulator = "Math.atan(";
|
| 14416 | accumulator += print_expr(cadr(p));
|
| 14417 | accumulator += ")";
|
| 14418 | return accumulator;
|
| 14419 | };
|
| 14420 |
|
| 14421 | print_SQRT_latex = function(p) {
|
| 14422 | var accumulator;
|
| 14423 | accumulator = "";
|
| 14424 | accumulator += print_str("\\sqrt{");
|
| 14425 | accumulator += print_expr(cadr(p));
|
| 14426 | accumulator += print_str("} ");
|
| 14427 | return accumulator;
|
| 14428 | };
|
| 14429 |
|
| 14430 | print_TRANSPOSE_latex = function(p) {
|
| 14431 | var accumulator;
|
| 14432 | accumulator = "";
|
| 14433 | accumulator += print_str("{");
|
| 14434 | if (iscons(cadr(p))) {
|
| 14435 | accumulator += print_str('(');
|
| 14436 | }
|
| 14437 | accumulator += print_expr(cadr(p));
|
| 14438 | if (iscons(cadr(p))) {
|
| 14439 | accumulator += print_str(')');
|
| 14440 | }
|
| 14441 | accumulator += print_str("}");
|
| 14442 | accumulator += print_str("^T");
|
| 14443 | return accumulator;
|
| 14444 | };
|
| 14445 |
|
| 14446 | print_TRANSPOSE_codegen = function(p) {
|
| 14447 | var accumulator;
|
| 14448 | accumulator = "";
|
| 14449 | accumulator += print_str("transpose(");
|
| 14450 | accumulator += print_expr(cadr(p));
|
| 14451 | accumulator += print_str(')');
|
| 14452 | return accumulator;
|
| 14453 | };
|
| 14454 |
|
| 14455 | print_UNIT_codegen = function(p) {
|
| 14456 | var accumulator;
|
| 14457 | accumulator = "";
|
| 14458 | accumulator += print_str("identity(");
|
| 14459 | accumulator += print_expr(cadr(p));
|
| 14460 | accumulator += print_str(')');
|
| 14461 | return accumulator;
|
| 14462 | };
|
| 14463 |
|
| 14464 | print_INV_latex = function(p) {
|
| 14465 | var accumulator;
|
| 14466 | accumulator = "";
|
| 14467 | accumulator += print_str("{");
|
| 14468 | if (iscons(cadr(p))) {
|
| 14469 | accumulator += print_str('(');
|
| 14470 | }
|
| 14471 | accumulator += print_expr(cadr(p));
|
| 14472 | if (iscons(cadr(p))) {
|
| 14473 | accumulator += print_str(')');
|
| 14474 | }
|
| 14475 | accumulator += print_str("}");
|
| 14476 | accumulator += print_str("^{-1}");
|
| 14477 | return accumulator;
|
| 14478 | };
|
| 14479 |
|
| 14480 | print_INV_codegen = function(p) {
|
| 14481 | var accumulator;
|
| 14482 | accumulator = "";
|
| 14483 | accumulator += print_str("inv(");
|
| 14484 | accumulator += print_expr(cadr(p));
|
| 14485 | accumulator += print_str(')');
|
| 14486 | return accumulator;
|
| 14487 | };
|
| 14488 |
|
| 14489 | print_DEFINT_latex = function(p) {
|
| 14490 | var accumulator, functionBody, i, i1, numberOfIntegrals, originalIntegral, ref1, theIntegral, theVariable;
|
| 14491 | accumulator = "";
|
| 14492 | functionBody = car(cdr(p));
|
| 14493 | p = cdr(p);
|
| 14494 | originalIntegral = p;
|
| 14495 | numberOfIntegrals = 0;
|
| 14496 | while (iscons(cdr(cdr(p)))) {
|
| 14497 | numberOfIntegrals++;
|
| 14498 | theIntegral = cdr(cdr(p));
|
| 14499 | accumulator += print_str("\\int^{");
|
| 14500 | accumulator += print_expr(car(cdr(theIntegral)));
|
| 14501 | accumulator += print_str("}_{");
|
| 14502 | accumulator += print_expr(car(theIntegral));
|
| 14503 | accumulator += print_str("} \\! ");
|
| 14504 | p = cdr(theIntegral);
|
| 14505 | }
|
| 14506 | accumulator += print_expr(functionBody);
|
| 14507 | accumulator += print_str(" \\,");
|
| 14508 | p = originalIntegral;
|
| 14509 | for (i = i1 = 1, ref1 = numberOfIntegrals; 1 <= ref1 ? i1 <= ref1 : i1 >= ref1; i = 1 <= ref1 ? ++i1 : --i1) {
|
| 14510 | theVariable = cdr(p);
|
| 14511 | accumulator += print_str(" \\mathrm{d} ");
|
| 14512 | accumulator += print_expr(car(theVariable));
|
| 14513 | if (i < numberOfIntegrals) {
|
| 14514 | accumulator += print_str(" \\, ");
|
| 14515 | }
|
| 14516 | p = cdr(cdr(theVariable));
|
| 14517 | }
|
| 14518 | return accumulator;
|
| 14519 | };
|
| 14520 |
|
| 14521 | print_tensor = function(p) {
|
| 14522 | var accumulator;
|
| 14523 | accumulator = "";
|
| 14524 | accumulator += print_tensor_inner(p, 0, 0)[1];
|
| 14525 | return accumulator;
|
| 14526 | };
|
| 14527 |
|
| 14528 | print_tensor_inner = function(p, j, k) {
|
| 14529 | var accumulator, i, i1, j1, ref1, ref2, ref3, retString;
|
| 14530 | accumulator = "";
|
| 14531 | accumulator += print_str("[");
|
| 14532 | if (j < p.tensor.ndim - 1) {
|
| 14533 | for (i = i1 = 0, ref1 = p.tensor.dim[j]; 0 <= ref1 ? i1 < ref1 : i1 > ref1; i = 0 <= ref1 ? ++i1 : --i1) {
|
| 14534 | ref2 = print_tensor_inner(p, j + 1, k), k = ref2[0], retString = ref2[1];
|
| 14535 | accumulator += retString;
|
| 14536 | if (i !== p.tensor.dim[j] - 1) {
|
| 14537 | accumulator += print_str(",");
|
| 14538 | }
|
| 14539 | }
|
| 14540 | } else {
|
| 14541 | for (i = j1 = 0, ref3 = p.tensor.dim[j]; 0 <= ref3 ? j1 < ref3 : j1 > ref3; i = 0 <= ref3 ? ++j1 : --j1) {
|
| 14542 | accumulator += print_expr(p.tensor.elem[k]);
|
| 14543 | if (i !== p.tensor.dim[j] - 1) {
|
| 14544 | accumulator += print_str(",");
|
| 14545 | }
|
| 14546 | k++;
|
| 14547 | }
|
| 14548 | }
|
| 14549 | accumulator += print_str("]");
|
| 14550 | return [k, accumulator];
|
| 14551 | };
|
| 14552 |
|
| 14553 | print_tensor_latex = function(p) {
|
| 14554 | var accumulator;
|
| 14555 | accumulator = "";
|
| 14556 | if (p.tensor.ndim <= 2) {
|
| 14557 | accumulator += print_tensor_inner_latex(true, p, 0, 0)[1];
|
| 14558 | }
|
| 14559 | return accumulator;
|
| 14560 | };
|
| 14561 |
|
| 14562 | print_tensor_inner_latex = function(firstLevel, p, j, k) {
|
| 14563 | var accumulator, i, i1, j1, ref1, ref2, ref3, retString;
|
| 14564 | accumulator = "";
|
| 14565 | if (firstLevel) {
|
| 14566 | accumulator += "\\begin{bmatrix} ";
|
| 14567 | }
|
| 14568 | if (j < p.tensor.ndim - 1) {
|
| 14569 | for (i = i1 = 0, ref1 = p.tensor.dim[j]; 0 <= ref1 ? i1 < ref1 : i1 > ref1; i = 0 <= ref1 ? ++i1 : --i1) {
|
| 14570 | ref2 = print_tensor_inner_latex(0, p, j + 1, k), k = ref2[0], retString = ref2[1];
|
| 14571 | accumulator += retString;
|
| 14572 | if (i !== p.tensor.dim[j] - 1) {
|
| 14573 | accumulator += print_str(" \\\\ ");
|
| 14574 | }
|
| 14575 | }
|
| 14576 | } else {
|
| 14577 | for (i = j1 = 0, ref3 = p.tensor.dim[j]; 0 <= ref3 ? j1 < ref3 : j1 > ref3; i = 0 <= ref3 ? ++j1 : --j1) {
|
| 14578 | accumulator += print_expr(p.tensor.elem[k]);
|
| 14579 | if (i !== p.tensor.dim[j] - 1) {
|
| 14580 | accumulator += print_str(" & ");
|
| 14581 | }
|
| 14582 | k++;
|
| 14583 | }
|
| 14584 | }
|
| 14585 | if (firstLevel) {
|
| 14586 | accumulator += " \\end{bmatrix}";
|
| 14587 | }
|
| 14588 | return [k, accumulator];
|
| 14589 | };
|
| 14590 |
|
| 14591 | print_SUM_latex = function(p) {
|
| 14592 | var accumulator;
|
| 14593 | accumulator = "\\sum_{";
|
| 14594 | accumulator += print_expr(caddr(p));
|
| 14595 | accumulator += "=";
|
| 14596 | accumulator += print_expr(cadddr(p));
|
| 14597 | accumulator += "}^{";
|
| 14598 | accumulator += print_expr(caddddr(p));
|
| 14599 | accumulator += "}{";
|
| 14600 | accumulator += print_expr(cadr(p));
|
| 14601 | accumulator += "}";
|
| 14602 | return accumulator;
|
| 14603 | };
|
| 14604 |
|
| 14605 | print_SUM_codegen = function(p) {
|
| 14606 | var accumulator, body, lowerlimit, upperlimit, variable;
|
| 14607 | body = cadr(p);
|
| 14608 | variable = caddr(p);
|
| 14609 | lowerlimit = cadddr(p);
|
| 14610 | upperlimit = caddddr(p);
|
| 14611 | accumulator = "(function(){" + " var " + variable + "; " + " var holderSum = 0; " + " var lowerlimit = " + print_expr(lowerlimit) + "; " + " var upperlimit = " + print_expr(upperlimit) + "; " + " for (" + variable + " = lowerlimit; " + variable + " < upperlimit; " + variable + "++) { " + " holderSum += " + print_expr(body) + ";" + " } " + " return holderSum;" + "})()";
|
| 14612 | return accumulator;
|
| 14613 | };
|
| 14614 |
|
| 14615 | print_TEST_latex = function(p) {
|
| 14616 | var accumulator;
|
| 14617 | accumulator = "\\left\\{ \\begin{array}{ll}";
|
| 14618 | p = cdr(p);
|
| 14619 | while (iscons(p)) {
|
| 14620 | if (cdr(p) === symbol(NIL)) {
|
| 14621 | accumulator += "{";
|
| 14622 | accumulator += print_expr(car(p));
|
| 14623 | accumulator += "} & otherwise ";
|
| 14624 | accumulator += " \\\\\\\\";
|
| 14625 | break;
|
| 14626 | }
|
| 14627 | accumulator += "{";
|
| 14628 | accumulator += print_expr(cadr(p));
|
| 14629 | accumulator += "} & if & ";
|
| 14630 | accumulator += print_expr(car(p));
|
| 14631 | accumulator += " \\\\\\\\";
|
| 14632 | p = cddr(p);
|
| 14633 | }
|
| 14634 | accumulator = accumulator.substring(0, accumulator.length - 4);
|
| 14635 | return accumulator += "\\end{array} \\right.";
|
| 14636 | };
|
| 14637 |
|
| 14638 | print_TEST_codegen = function(p) {
|
| 14639 | var accumulator, howManyIfs;
|
| 14640 | accumulator = "(function(){";
|
| 14641 | p = cdr(p);
|
| 14642 | howManyIfs = 0;
|
| 14643 | while (iscons(p)) {
|
| 14644 | if (cdr(p) === symbol(NIL)) {
|
| 14645 | accumulator += "else {";
|
| 14646 | accumulator += "return (" + print_expr(car(p)) + ");";
|
| 14647 | accumulator += "}";
|
| 14648 | break;
|
| 14649 | }
|
| 14650 | if (howManyIfs) {
|
| 14651 | accumulator += " else ";
|
| 14652 | }
|
| 14653 | accumulator += "if (" + print_expr(car(p)) + "){";
|
| 14654 | accumulator += "return (" + print_expr(cadr(p)) + ");";
|
| 14655 | accumulator += "}";
|
| 14656 | howManyIfs++;
|
| 14657 | p = cddr(p);
|
| 14658 | }
|
| 14659 | accumulator += "})()";
|
| 14660 | return accumulator;
|
| 14661 | };
|
| 14662 |
|
| 14663 | print_TESTLT_latex = function(p) {
|
| 14664 | var accumulator;
|
| 14665 | accumulator = "{";
|
| 14666 | accumulator += print_expr(cadr(p));
|
| 14667 | accumulator += "}";
|
| 14668 | accumulator += " < ";
|
| 14669 | accumulator += "{";
|
| 14670 | accumulator += print_expr(caddr(p));
|
| 14671 | return accumulator += "}";
|
| 14672 | };
|
| 14673 |
|
| 14674 | print_TESTLE_latex = function(p) {
|
| 14675 | var accumulator;
|
| 14676 | accumulator = "{";
|
| 14677 | accumulator += print_expr(cadr(p));
|
| 14678 | accumulator += "}";
|
| 14679 | accumulator += " \\leq ";
|
| 14680 | accumulator += "{";
|
| 14681 | accumulator += print_expr(caddr(p));
|
| 14682 | return accumulator += "}";
|
| 14683 | };
|
| 14684 |
|
| 14685 | print_TESTGT_latex = function(p) {
|
| 14686 | var accumulator;
|
| 14687 | accumulator = "{";
|
| 14688 | accumulator += print_expr(cadr(p));
|
| 14689 | accumulator += "}";
|
| 14690 | accumulator += " > ";
|
| 14691 | accumulator += "{";
|
| 14692 | accumulator += print_expr(caddr(p));
|
| 14693 | return accumulator += "}";
|
| 14694 | };
|
| 14695 |
|
| 14696 | print_TESTGE_latex = function(p) {
|
| 14697 | var accumulator;
|
| 14698 | accumulator = "{";
|
| 14699 | accumulator += print_expr(cadr(p));
|
| 14700 | accumulator += "}";
|
| 14701 | accumulator += " \\geq ";
|
| 14702 | accumulator += "{";
|
| 14703 | accumulator += print_expr(caddr(p));
|
| 14704 | return accumulator += "}";
|
| 14705 | };
|
| 14706 |
|
| 14707 | print_TESTEQ_latex = function(p) {
|
| 14708 | var accumulator;
|
| 14709 | accumulator = "{";
|
| 14710 | accumulator += print_expr(cadr(p));
|
| 14711 | accumulator += "}";
|
| 14712 | accumulator += " = ";
|
| 14713 | accumulator += "{";
|
| 14714 | accumulator += print_expr(caddr(p));
|
| 14715 | return accumulator += "}";
|
| 14716 | };
|
| 14717 |
|
| 14718 | print_FOR_codegen = function(p) {
|
| 14719 | var accumulator, body, lowerlimit, upperlimit, variable;
|
| 14720 | body = cadr(p);
|
| 14721 | variable = caddr(p);
|
| 14722 | lowerlimit = cadddr(p);
|
| 14723 | upperlimit = caddddr(p);
|
| 14724 | accumulator = "(function(){" + " var " + variable + "; " + " var lowerlimit = " + print_expr(lowerlimit) + "; " + " var upperlimit = " + print_expr(upperlimit) + "; " + " for (" + variable + " = lowerlimit; " + variable + " < upperlimit; " + variable + "++) { " + " " + print_expr(body) + " } " + "})()";
|
| 14725 | return accumulator;
|
| 14726 | };
|
| 14727 |
|
| 14728 | print_DO_codegen = function(p) {
|
| 14729 | var accumulator;
|
| 14730 | accumulator = "";
|
| 14731 | p = cdr(p);
|
| 14732 | while (iscons(p)) {
|
| 14733 | accumulator += print_expr(car(p));
|
| 14734 | p = cdr(p);
|
| 14735 | }
|
| 14736 | return accumulator;
|
| 14737 | };
|
| 14738 |
|
| 14739 | print_SETQ_codegen = function(p) {
|
| 14740 | var accumulator;
|
| 14741 | accumulator = "";
|
| 14742 | accumulator += print_expr(cadr(p));
|
| 14743 | accumulator += " = ";
|
| 14744 | accumulator += print_expr(caddr(p));
|
| 14745 | accumulator += "; ";
|
| 14746 | return accumulator;
|
| 14747 | };
|
| 14748 |
|
| 14749 | print_PRODUCT_latex = function(p) {
|
| 14750 | var accumulator;
|
| 14751 | accumulator = "\\prod_{";
|
| 14752 | accumulator += print_expr(caddr(p));
|
| 14753 | accumulator += "=";
|
| 14754 | accumulator += print_expr(cadddr(p));
|
| 14755 | accumulator += "}^{";
|
| 14756 | accumulator += print_expr(caddddr(p));
|
| 14757 | accumulator += "}{";
|
| 14758 | accumulator += print_expr(cadr(p));
|
| 14759 | accumulator += "}";
|
| 14760 | return accumulator;
|
| 14761 | };
|
| 14762 |
|
| 14763 | print_PRODUCT_codegen = function(p) {
|
| 14764 | var accumulator, body, lowerlimit, upperlimit, variable;
|
| 14765 | body = cadr(p);
|
| 14766 | variable = caddr(p);
|
| 14767 | lowerlimit = cadddr(p);
|
| 14768 | upperlimit = caddddr(p);
|
| 14769 | accumulator = "(function(){" + " var " + variable + "; " + " var holderProduct = 1; " + " var lowerlimit = " + print_expr(lowerlimit) + "; " + " var upperlimit = " + print_expr(upperlimit) + "; " + " for (" + variable + " = lowerlimit; " + variable + " < upperlimit; " + variable + "++) { " + " holderProduct *= " + print_expr(body) + ";" + " } " + " return holderProduct;" + "})()";
|
| 14770 | return accumulator;
|
| 14771 | };
|
| 14772 |
|
| 14773 | print_base = function(p) {
|
| 14774 | var accumulator;
|
| 14775 | accumulator = "";
|
| 14776 | if (isadd(cadr(p)) || caadr(p) === symbol(MULTIPLY) || caadr(p) === symbol(POWER) || isnegativenumber(cadr(p))) {
|
| 14777 | accumulator += print_str('(');
|
| 14778 | accumulator += print_expr(cadr(p));
|
| 14779 | accumulator += print_str(')');
|
| 14780 | } else if (isnum(cadr(p)) && (lessp(cadr(p), zero) || isfraction(cadr(p)))) {
|
| 14781 | accumulator += print_str('(');
|
| 14782 | accumulator += print_factor(cadr(p));
|
| 14783 | accumulator += print_str(')');
|
| 14784 | } else {
|
| 14785 | accumulator += print_factor(cadr(p));
|
| 14786 | }
|
| 14787 | return accumulator;
|
| 14788 | };
|
| 14789 |
|
| 14790 | print_exponent = function(p) {
|
| 14791 | var accumulator;
|
| 14792 | accumulator = "";
|
| 14793 | if (iscons(caddr(p)) || isfraction(caddr(p)) || (isnum(caddr(p)) && lessp(caddr(p), zero))) {
|
| 14794 | accumulator += print_str('(');
|
| 14795 | accumulator += print_expr(caddr(p));
|
| 14796 | accumulator += print_str(')');
|
| 14797 | } else {
|
| 14798 | accumulator += print_factor(caddr(p));
|
| 14799 | }
|
| 14800 | return accumulator;
|
| 14801 | };
|
| 14802 |
|
| 14803 | print_power = function(base, exponent) {
|
| 14804 | var accumulator, denomExponent, newExponent, numExponent;
|
| 14805 | accumulator = "";
|
| 14806 | if (DEBUG) {
|
| 14807 | console.log("power base: " + base + " " + " exponent: " + exponent);
|
| 14808 | }
|
| 14809 | if (isoneovertwo(exponent)) {
|
| 14810 | if (equaln(base, 2)) {
|
| 14811 | if (codeGen) {
|
| 14812 | accumulator += print_str("Math.SQRT2");
|
| 14813 | return accumulator;
|
| 14814 | }
|
| 14815 | } else {
|
| 14816 | if (printMode === PRINTMODE_LATEX) {
|
| 14817 | accumulator += print_str("\\sqrt{");
|
| 14818 | accumulator += print_expr(base);
|
| 14819 | accumulator += print_str("}");
|
| 14820 | return accumulator;
|
| 14821 | } else if (codeGen) {
|
| 14822 | accumulator += print_str("Math.sqrt(");
|
| 14823 | accumulator += print_expr(base);
|
| 14824 | accumulator += print_str(')');
|
| 14825 | return accumulator;
|
| 14826 | }
|
| 14827 | }
|
| 14828 | }
|
| 14829 | if ((equaln(get_binding(symbol(PRINT_LEAVE_E_ALONE)), 1)) && base === symbol(E)) {
|
| 14830 | if (codeGen) {
|
| 14831 | accumulator += print_str("Math.exp(");
|
| 14832 | accumulator += print_expo_of_denom(exponent);
|
| 14833 | accumulator += print_str(')');
|
| 14834 | return accumulator;
|
| 14835 | }
|
| 14836 | if (printMode === PRINTMODE_LATEX) {
|
| 14837 | accumulator += print_str("e^{");
|
| 14838 | accumulator += print_expr(exponent);
|
| 14839 | accumulator += print_str("}");
|
| 14840 | } else {
|
| 14841 | accumulator += print_str("exp(");
|
| 14842 | accumulator += print_expr(exponent);
|
| 14843 | accumulator += print_str(')');
|
| 14844 | }
|
| 14845 | return accumulator;
|
| 14846 | }
|
| 14847 | if (codeGen) {
|
| 14848 | accumulator += print_str("Math.pow(");
|
| 14849 | accumulator += print_base_of_denom(base);
|
| 14850 | accumulator += print_str(", ");
|
| 14851 | accumulator += print_expo_of_denom(exponent);
|
| 14852 | accumulator += print_str(')');
|
| 14853 | return accumulator;
|
| 14854 | }
|
| 14855 | if ((equaln(get_binding(symbol(PRINT_LEAVE_X_ALONE)), 0)) || base.printname !== "x") {
|
| 14856 | if (base !== symbol(E)) {
|
| 14857 | if (isminusone(exponent)) {
|
| 14858 | if (printMode === PRINTMODE_LATEX) {
|
| 14859 | accumulator += print_str("\\frac{1}{");
|
| 14860 | } else if (printMode === PRINTMODE_PLAIN && !test_flag) {
|
| 14861 | accumulator += print_str("1 / ");
|
| 14862 | } else {
|
| 14863 | accumulator += print_str("1/");
|
| 14864 | }
|
| 14865 | if (iscons(base) && printMode !== PRINTMODE_LATEX) {
|
| 14866 | accumulator += print_str('(');
|
| 14867 | accumulator += print_expr(base);
|
| 14868 | accumulator += print_str(')');
|
| 14869 | } else {
|
| 14870 | accumulator += print_expr(base);
|
| 14871 | }
|
| 14872 | if (printMode === PRINTMODE_LATEX) {
|
| 14873 | accumulator += print_str("}");
|
| 14874 | }
|
| 14875 | return accumulator;
|
| 14876 | }
|
| 14877 | if (isnegativeterm(exponent)) {
|
| 14878 | if (printMode === PRINTMODE_LATEX) {
|
| 14879 | accumulator += print_str("\\frac{1}{");
|
| 14880 | } else if (printMode === PRINTMODE_PLAIN && !test_flag) {
|
| 14881 | accumulator += print_str("1 / ");
|
| 14882 | } else {
|
| 14883 | accumulator += print_str("1/");
|
| 14884 | }
|
| 14885 | push(exponent);
|
| 14886 | push_integer(-1);
|
| 14887 | multiply();
|
| 14888 | newExponent = pop();
|
| 14889 | if (iscons(base) && printMode !== PRINTMODE_LATEX) {
|
| 14890 | accumulator += print_str('(');
|
| 14891 | accumulator += print_power(base, newExponent);
|
| 14892 | accumulator += print_str(')');
|
| 14893 | } else {
|
| 14894 | accumulator += print_power(base, newExponent);
|
| 14895 | }
|
| 14896 | if (printMode === PRINTMODE_LATEX) {
|
| 14897 | accumulator += print_str("}");
|
| 14898 | }
|
| 14899 | return accumulator;
|
| 14900 | }
|
| 14901 | }
|
| 14902 | if (isfraction(exponent) && printMode === PRINTMODE_LATEX) {
|
| 14903 | accumulator += print_str("\\sqrt");
|
| 14904 | push(exponent);
|
| 14905 | denominator();
|
| 14906 | denomExponent = pop();
|
| 14907 | if (!isplustwo(denomExponent)) {
|
| 14908 | accumulator += print_str("[");
|
| 14909 | accumulator += print_expr(denomExponent);
|
| 14910 | accumulator += print_str("]");
|
| 14911 | }
|
| 14912 | accumulator += print_str("{");
|
| 14913 | push(exponent);
|
| 14914 | numerator();
|
| 14915 | numExponent = pop();
|
| 14916 | exponent = numExponent;
|
| 14917 | accumulator += print_power(base, exponent);
|
| 14918 | accumulator += print_str("}");
|
| 14919 | return accumulator;
|
| 14920 | }
|
| 14921 | }
|
| 14922 | if (printMode === PRINTMODE_LATEX && isplusone(exponent)) {
|
| 14923 | accumulator += print_expr(base);
|
| 14924 | } else {
|
| 14925 | if (isadd(base) || isnegativenumber(base)) {
|
| 14926 | accumulator += print_str('(');
|
| 14927 | accumulator += print_expr(base);
|
| 14928 | accumulator += print_str(')');
|
| 14929 | } else if (car(base) === symbol(MULTIPLY) || car(base) === symbol(POWER)) {
|
| 14930 | if (printMode !== PRINTMODE_LATEX) {
|
| 14931 | accumulator += print_str('(');
|
| 14932 | }
|
| 14933 | accumulator += print_factor(base, true);
|
| 14934 | if (printMode !== PRINTMODE_LATEX) {
|
| 14935 | accumulator += print_str(')');
|
| 14936 | }
|
| 14937 | } else if (isnum(base) && (lessp(base, zero) || isfraction(base))) {
|
| 14938 | accumulator += print_str('(');
|
| 14939 | accumulator += print_factor(base);
|
| 14940 | accumulator += print_str(')');
|
| 14941 | } else {
|
| 14942 | accumulator += print_factor(base);
|
| 14943 | }
|
| 14944 | if (printMode === PRINTMODE_PLAIN && !test_flag) {
|
| 14945 | accumulator += print_str(power_str);
|
| 14946 | } else {
|
| 14947 | accumulator += print_str("^");
|
| 14948 | }
|
| 14949 | if (printMode === PRINTMODE_LATEX) {
|
| 14950 | if (print_expr(exponent).length > 1) {
|
| 14951 | accumulator += print_str("{");
|
| 14952 | accumulator += print_expr(exponent);
|
| 14953 | accumulator += print_str("}");
|
| 14954 | } else {
|
| 14955 | accumulator += print_expr(exponent);
|
| 14956 | }
|
| 14957 | } else if (iscons(exponent) || isfraction(exponent) || (isnum(exponent) && lessp(exponent, zero))) {
|
| 14958 | accumulator += print_str('(');
|
| 14959 | accumulator += print_expr(exponent);
|
| 14960 | accumulator += print_str(')');
|
| 14961 | } else {
|
| 14962 | accumulator += print_factor(exponent);
|
| 14963 | }
|
| 14964 | }
|
| 14965 | return accumulator;
|
| 14966 | };
|
| 14967 |
|
| 14968 | print_index_function = function(p) {
|
| 14969 | var accumulator;
|
| 14970 | accumulator = "";
|
| 14971 | p = cdr(p);
|
| 14972 | if (caar(p) === symbol(ADD) || caar(p) === symbol(MULTIPLY) || caar(p) === symbol(POWER) || caar(p) === symbol(FACTORIAL)) {
|
| 14973 | accumulator += print_subexpr(car(p));
|
| 14974 | } else {
|
| 14975 | accumulator += print_expr(car(p));
|
| 14976 | }
|
| 14977 | accumulator += print_str('[');
|
| 14978 | p = cdr(p);
|
| 14979 | if (iscons(p)) {
|
| 14980 | accumulator += print_expr(car(p));
|
| 14981 | p = cdr(p);
|
| 14982 | while (iscons(p)) {
|
| 14983 | accumulator += print_str(',');
|
| 14984 | accumulator += print_expr(car(p));
|
| 14985 | p = cdr(p);
|
| 14986 | }
|
| 14987 | }
|
| 14988 | accumulator += print_str(']');
|
| 14989 | return accumulator;
|
| 14990 | };
|
| 14991 |
|
| 14992 | print_factor = function(p, omitParens) {
|
| 14993 | var accumulator, base, exponent, fbody, parameters, returned;
|
| 14994 | accumulator = "";
|
| 14995 | if (isnum(p)) {
|
| 14996 | accumulator += print_number(p, false);
|
| 14997 | return accumulator;
|
| 14998 | }
|
| 14999 | if (isstr(p)) {
|
| 15000 | accumulator += print_str("\"");
|
| 15001 | accumulator += print_str(p.str);
|
| 15002 | accumulator += print_str("\"");
|
| 15003 | return accumulator;
|
| 15004 | }
|
| 15005 | if (istensor(p)) {
|
| 15006 | if (printMode === PRINTMODE_LATEX) {
|
| 15007 | accumulator += print_tensor_latex(p);
|
| 15008 | } else {
|
| 15009 | accumulator += print_tensor(p);
|
| 15010 | }
|
| 15011 | return accumulator;
|
| 15012 | }
|
| 15013 | if (car(p) === symbol(MULTIPLY)) {
|
| 15014 | if (!omitParens) {
|
| 15015 | if (sign_of_term(p) === '-' || printMode !== PRINTMODE_LATEX) {
|
| 15016 | if (printMode === PRINTMODE_LATEX) {
|
| 15017 | accumulator += print_str(" \\left (");
|
| 15018 | } else {
|
| 15019 | accumulator += print_str('(');
|
| 15020 | }
|
| 15021 | }
|
| 15022 | }
|
| 15023 | accumulator += print_expr(p);
|
| 15024 | if (!omitParens) {
|
| 15025 | if (sign_of_term(p) === '-' || printMode !== PRINTMODE_LATEX) {
|
| 15026 | if (printMode === PRINTMODE_LATEX) {
|
| 15027 | accumulator += print_str(" \\right ) ");
|
| 15028 | } else {
|
| 15029 | accumulator += print_str(')');
|
| 15030 | }
|
| 15031 | }
|
| 15032 | }
|
| 15033 | return accumulator;
|
| 15034 | } else if (isadd(p)) {
|
| 15035 | if (!omitParens) {
|
| 15036 | accumulator += print_str('(');
|
| 15037 | }
|
| 15038 | accumulator += print_expr(p);
|
| 15039 | if (!omitParens) {
|
| 15040 | accumulator += print_str(')');
|
| 15041 | }
|
| 15042 | return accumulator;
|
| 15043 | }
|
| 15044 | if (car(p) === symbol(POWER)) {
|
| 15045 | base = cadr(p);
|
| 15046 | exponent = caddr(p);
|
| 15047 | accumulator += print_power(base, exponent);
|
| 15048 | return accumulator;
|
| 15049 | }
|
| 15050 | if (car(p) === symbol(FUNCTION)) {
|
| 15051 | fbody = cadr(p);
|
| 15052 | if (!codeGen) {
|
| 15053 | parameters = caddr(p);
|
| 15054 | accumulator += print_str("function ");
|
| 15055 | if (DEBUG) {
|
| 15056 | console.log("emittedString from print_factor " + stringsEmittedByUserPrintouts);
|
| 15057 | }
|
| 15058 | returned = print_list(parameters);
|
| 15059 | accumulator += returned;
|
| 15060 | accumulator += print_str(" -> ");
|
| 15061 | }
|
| 15062 | accumulator += print_expr(fbody);
|
| 15063 | return accumulator;
|
| 15064 | }
|
| 15065 | if (car(p) === symbol(PATTERN)) {
|
| 15066 | accumulator += print_expr(caadr(p));
|
| 15067 | if (printMode === PRINTMODE_LATEX) {
|
| 15068 | accumulator += print_str(" \\rightarrow ");
|
| 15069 | } else {
|
| 15070 | if (printMode === PRINTMODE_PLAIN && !test_flag) {
|
| 15071 | accumulator += print_str(" -> ");
|
| 15072 | } else {
|
| 15073 | accumulator += print_str("->");
|
| 15074 | }
|
| 15075 | }
|
| 15076 | accumulator += print_expr(car(cdr(cadr(p))));
|
| 15077 | return accumulator;
|
| 15078 | }
|
| 15079 | if (car(p) === symbol(INDEX) && issymbol(cadr(p))) {
|
| 15080 | accumulator += print_index_function(p);
|
| 15081 | return accumulator;
|
| 15082 | }
|
| 15083 | if (car(p) === symbol(FACTORIAL)) {
|
| 15084 | accumulator += print_factorial_function(p);
|
| 15085 | return accumulator;
|
| 15086 | } else if (car(p) === symbol(ABS) && printMode === PRINTMODE_LATEX) {
|
| 15087 | accumulator += print_ABS_latex(p);
|
| 15088 | return accumulator;
|
| 15089 | } else if (car(p) === symbol(SQRT) && printMode === PRINTMODE_LATEX) {
|
| 15090 | accumulator += print_SQRT_latex(p);
|
| 15091 | return accumulator;
|
| 15092 | } else if (car(p) === symbol(TRANSPOSE)) {
|
| 15093 | if (printMode === PRINTMODE_LATEX) {
|
| 15094 | accumulator += print_TRANSPOSE_latex(p);
|
| 15095 | return accumulator;
|
| 15096 | } else if (codeGen) {
|
| 15097 | accumulator += print_TRANSPOSE_codegen(p);
|
| 15098 | return accumulator;
|
| 15099 | }
|
| 15100 | } else if (car(p) === symbol(UNIT)) {
|
| 15101 | if (codeGen) {
|
| 15102 | accumulator += print_UNIT_codegen(p);
|
| 15103 | return accumulator;
|
| 15104 | }
|
| 15105 | } else if (car(p) === symbol(INV)) {
|
| 15106 | if (printMode === PRINTMODE_LATEX) {
|
| 15107 | accumulator += print_INV_latex(p);
|
| 15108 | return accumulator;
|
| 15109 | } else if (codeGen) {
|
| 15110 | accumulator += print_INV_codegen(p);
|
| 15111 | return accumulator;
|
| 15112 | }
|
| 15113 | } else if (car(p) === symbol(BINOMIAL) && printMode === PRINTMODE_LATEX) {
|
| 15114 | accumulator += print_BINOMIAL_latex(p);
|
| 15115 | return accumulator;
|
| 15116 | } else if (car(p) === symbol(DEFINT) && printMode === PRINTMODE_LATEX) {
|
| 15117 | accumulator += print_DEFINT_latex(p);
|
| 15118 | return accumulator;
|
| 15119 | } else if (isinnerordot(p)) {
|
| 15120 | if (printMode === PRINTMODE_LATEX) {
|
| 15121 | accumulator += print_DOT_latex(p);
|
| 15122 | return accumulator;
|
| 15123 | } else if (codeGen) {
|
| 15124 | accumulator += print_DOT_codegen(p);
|
| 15125 | return accumulator;
|
| 15126 | }
|
| 15127 | } else if (car(p) === symbol(SIN)) {
|
| 15128 | if (codeGen) {
|
| 15129 | accumulator += print_SIN_codegen(p);
|
| 15130 | return accumulator;
|
| 15131 | }
|
| 15132 | } else if (car(p) === symbol(COS)) {
|
| 15133 | if (codeGen) {
|
| 15134 | accumulator += print_COS_codegen(p);
|
| 15135 | return accumulator;
|
| 15136 | }
|
| 15137 | } else if (car(p) === symbol(TAN)) {
|
| 15138 | if (codeGen) {
|
| 15139 | accumulator += print_TAN_codegen(p);
|
| 15140 | return accumulator;
|
| 15141 | }
|
| 15142 | } else if (car(p) === symbol(ARCSIN)) {
|
| 15143 | if (codeGen) {
|
| 15144 | accumulator += print_ARCSIN_codegen(p);
|
| 15145 | return accumulator;
|
| 15146 | }
|
| 15147 | } else if (car(p) === symbol(ARCCOS)) {
|
| 15148 | if (codeGen) {
|
| 15149 | accumulator += print_ARCCOS_codegen(p);
|
| 15150 | return accumulator;
|
| 15151 | }
|
| 15152 | } else if (car(p) === symbol(ARCTAN)) {
|
| 15153 | if (codeGen) {
|
| 15154 | accumulator += print_ARCTAN_codegen(p);
|
| 15155 | return accumulator;
|
| 15156 | }
|
| 15157 | } else if (car(p) === symbol(SUM)) {
|
| 15158 | if (printMode === PRINTMODE_LATEX) {
|
| 15159 | accumulator += print_SUM_latex(p);
|
| 15160 | return accumulator;
|
| 15161 | } else if (codeGen) {
|
| 15162 | accumulator += print_SUM_codegen(p);
|
| 15163 | return accumulator;
|
| 15164 | }
|
| 15165 | } else if (car(p) === symbol(PRODUCT)) {
|
| 15166 | if (printMode === PRINTMODE_LATEX) {
|
| 15167 | accumulator += print_PRODUCT_latex(p);
|
| 15168 | return accumulator;
|
| 15169 | } else if (codeGen) {
|
| 15170 | accumulator += print_PRODUCT_codegen(p);
|
| 15171 | return accumulator;
|
| 15172 | }
|
| 15173 | } else if (car(p) === symbol(FOR)) {
|
| 15174 | if (codeGen) {
|
| 15175 | accumulator += print_FOR_codegen(p);
|
| 15176 | return accumulator;
|
| 15177 | }
|
| 15178 | } else if (car(p) === symbol(DO)) {
|
| 15179 | if (codeGen) {
|
| 15180 | accumulator += print_DO_codegen(p);
|
| 15181 | return accumulator;
|
| 15182 | }
|
| 15183 | } else if (car(p) === symbol(TEST)) {
|
| 15184 | if (codeGen) {
|
| 15185 | accumulator += print_TEST_codegen(p);
|
| 15186 | return accumulator;
|
| 15187 | }
|
| 15188 | if (printMode === PRINTMODE_LATEX) {
|
| 15189 | accumulator += print_TEST_latex(p);
|
| 15190 | return accumulator;
|
| 15191 | }
|
| 15192 | } else if (car(p) === symbol(TESTLT)) {
|
| 15193 | if (codeGen) {
|
| 15194 | accumulator += "((" + print_expr(cadr(p)) + ") < (" + print_expr(caddr(p)) + "))";
|
| 15195 | return accumulator;
|
| 15196 | }
|
| 15197 | if (printMode === PRINTMODE_LATEX) {
|
| 15198 | accumulator += print_TESTLT_latex(p);
|
| 15199 | return accumulator;
|
| 15200 | }
|
| 15201 | } else if (car(p) === symbol(TESTLE)) {
|
| 15202 | if (codeGen) {
|
| 15203 | accumulator += "((" + print_expr(cadr(p)) + ") <= (" + print_expr(caddr(p)) + "))";
|
| 15204 | return accumulator;
|
| 15205 | }
|
| 15206 | if (printMode === PRINTMODE_LATEX) {
|
| 15207 | accumulator += print_TESTLE_latex(p);
|
| 15208 | return accumulator;
|
| 15209 | }
|
| 15210 | } else if (car(p) === symbol(TESTGT)) {
|
| 15211 | if (codeGen) {
|
| 15212 | accumulator += "((" + print_expr(cadr(p)) + ") > (" + print_expr(caddr(p)) + "))";
|
| 15213 | return accumulator;
|
| 15214 | }
|
| 15215 | if (printMode === PRINTMODE_LATEX) {
|
| 15216 | accumulator += print_TESTGT_latex(p);
|
| 15217 | return accumulator;
|
| 15218 | }
|
| 15219 | } else if (car(p) === symbol(TESTGE)) {
|
| 15220 | if (codeGen) {
|
| 15221 | accumulator += "((" + print_expr(cadr(p)) + ") >= (" + print_expr(caddr(p)) + "))";
|
| 15222 | return accumulator;
|
| 15223 | }
|
| 15224 | if (printMode === PRINTMODE_LATEX) {
|
| 15225 | accumulator += print_TESTGE_latex(p);
|
| 15226 | return accumulator;
|
| 15227 | }
|
| 15228 | } else if (car(p) === symbol(TESTEQ)) {
|
| 15229 | if (codeGen) {
|
| 15230 | accumulator += "((" + print_expr(cadr(p)) + ") === (" + print_expr(caddr(p)) + "))";
|
| 15231 | return accumulator;
|
| 15232 | }
|
| 15233 | if (printMode === PRINTMODE_LATEX) {
|
| 15234 | accumulator += print_TESTEQ_latex(p);
|
| 15235 | return accumulator;
|
| 15236 | }
|
| 15237 | } else if (car(p) === symbol(FLOOR)) {
|
| 15238 | if (codeGen) {
|
| 15239 | accumulator += "Math.floor(" + print_expr(cadr(p)) + ")";
|
| 15240 | return accumulator;
|
| 15241 | }
|
| 15242 | if (printMode === PRINTMODE_LATEX) {
|
| 15243 | accumulator += " \\lfloor {" + print_expr(cadr(p)) + "} \\rfloor ";
|
| 15244 | return accumulator;
|
| 15245 | }
|
| 15246 | } else if (car(p) === symbol(CEILING)) {
|
| 15247 | debugger;
|
| 15248 | if (codeGen) {
|
| 15249 | accumulator += "Math.ceiling(" + print_expr(cadr(p)) + ")";
|
| 15250 | return accumulator;
|
| 15251 | }
|
| 15252 | if (printMode === PRINTMODE_LATEX) {
|
| 15253 | accumulator += " \\lceil {" + print_expr(cadr(p)) + "} \\rceil ";
|
| 15254 | return accumulator;
|
| 15255 | }
|
| 15256 | } else if (car(p) === symbol(ROUND)) {
|
| 15257 | if (codeGen) {
|
| 15258 | accumulator += "Math.round(" + print_expr(cadr(p)) + ")";
|
| 15259 | return accumulator;
|
| 15260 | }
|
| 15261 | } else if (car(p) === symbol(SETQ)) {
|
| 15262 | if (codeGen) {
|
| 15263 | accumulator += print_SETQ_codegen(p);
|
| 15264 | return accumulator;
|
| 15265 | } else {
|
| 15266 | accumulator += print_expr(cadr(p));
|
| 15267 | accumulator += print_str("=");
|
| 15268 | accumulator += print_expr(caddr(p));
|
| 15269 | return accumulator;
|
| 15270 | }
|
| 15271 | }
|
| 15272 | if (iscons(p)) {
|
| 15273 | accumulator += print_factor(car(p));
|
| 15274 | p = cdr(p);
|
| 15275 | if (!omitParens) {
|
| 15276 | accumulator += print_str('(');
|
| 15277 | }
|
| 15278 | if (iscons(p)) {
|
| 15279 | accumulator += print_expr(car(p));
|
| 15280 | p = cdr(p);
|
| 15281 | while (iscons(p)) {
|
| 15282 | accumulator += print_str(",");
|
| 15283 | accumulator += print_expr(car(p));
|
| 15284 | p = cdr(p);
|
| 15285 | }
|
| 15286 | }
|
| 15287 | if (!omitParens) {
|
| 15288 | accumulator += print_str(')');
|
| 15289 | }
|
| 15290 | return accumulator;
|
| 15291 | }
|
| 15292 | if (p === symbol(DERIVATIVE)) {
|
| 15293 | accumulator += print_char('d');
|
| 15294 | } else if (p === symbol(E)) {
|
| 15295 | if (codeGen) {
|
| 15296 | accumulator += print_str("Math.E");
|
| 15297 | } else {
|
| 15298 | accumulator += print_str("e");
|
| 15299 | }
|
| 15300 | } else if (p === symbol(PI)) {
|
| 15301 | if (printMode === PRINTMODE_LATEX) {
|
| 15302 | accumulator += print_str("\\pi");
|
| 15303 | } else {
|
| 15304 | accumulator += print_str("pi");
|
| 15305 | }
|
| 15306 | } else {
|
| 15307 | accumulator += print_str(get_printname(p));
|
| 15308 | }
|
| 15309 | return accumulator;
|
| 15310 | };
|
| 15311 |
|
| 15312 | print_list = function(p) {
|
| 15313 | var accumulator;
|
| 15314 | accumulator = "";
|
| 15315 | switch (p.k) {
|
| 15316 | case CONS:
|
| 15317 | accumulator += '(';
|
| 15318 | accumulator += print_list(car(p));
|
| 15319 | if (p === cdr(p) && p !== symbol(NIL)) {
|
| 15320 | console.log("oh no recursive!");
|
| 15321 | debugger;
|
| 15322 | }
|
| 15323 | p = cdr(p);
|
| 15324 | while (iscons(p)) {
|
| 15325 | accumulator += " ";
|
| 15326 | accumulator += print_list(car(p));
|
| 15327 | p = cdr(p);
|
| 15328 | if (p === cdr(p) && p !== symbol(NIL)) {
|
| 15329 | console.log("oh no recursive!");
|
| 15330 | debugger;
|
| 15331 | }
|
| 15332 | }
|
| 15333 | if (p !== symbol(NIL)) {
|
| 15334 | accumulator += " . ";
|
| 15335 | accumulator += print_list(p);
|
| 15336 | }
|
| 15337 | accumulator += ')';
|
| 15338 | break;
|
| 15339 | case STR:
|
| 15340 | accumulator += p.str;
|
| 15341 | break;
|
| 15342 | case NUM:
|
| 15343 | case DOUBLE:
|
| 15344 | accumulator += print_number(p, true);
|
| 15345 | break;
|
| 15346 | case SYM:
|
| 15347 | accumulator += get_printname(p);
|
| 15348 | break;
|
| 15349 | default:
|
| 15350 | accumulator += "<tensor>";
|
| 15351 | }
|
| 15352 | return accumulator;
|
| 15353 | };
|
| 15354 |
|
| 15355 | print_multiply_sign = function() {
|
| 15356 | var accumulator;
|
| 15357 | accumulator = "";
|
| 15358 | if (printMode === PRINTMODE_LATEX) {
|
| 15359 | if (printMode === PRINTMODE_PLAIN && !test_flag) {
|
| 15360 | accumulator += print_str(" ");
|
| 15361 | } else {
|
| 15362 | return accumulator;
|
| 15363 | }
|
| 15364 | }
|
| 15365 | if (printMode === PRINTMODE_PLAIN && !test_flag && !codeGen) {
|
| 15366 | accumulator += print_str(" ");
|
| 15367 | } else {
|
| 15368 | accumulator += print_str("*");
|
| 15369 | }
|
| 15370 | return accumulator;
|
| 15371 | };
|
| 15372 |
|
| 15373 | is_denominator = function(p) {
|
| 15374 | if (car(p) === symbol(POWER) && cadr(p) !== symbol(E) && isnegativeterm(caddr(p))) {
|
| 15375 | return 1;
|
| 15376 | } else {
|
| 15377 | return 0;
|
| 15378 | }
|
| 15379 | };
|
| 15380 |
|
| 15381 | any_denominators = function(p) {
|
| 15382 | var q;
|
| 15383 | p = cdr(p);
|
| 15384 | while (iscons(p)) {
|
| 15385 | q = car(p);
|
| 15386 | if (is_denominator(q)) {
|
| 15387 | return 1;
|
| 15388 | }
|
| 15389 | p = cdr(p);
|
| 15390 | }
|
| 15391 | return 0;
|
| 15392 | };
|
| 15393 |
|
| 15394 |
|
| 15395 | |
| 15396 | |
| 15397 | |
| 15398 | |
| 15399 | |
| 15400 | |
| 15401 | |
| 15402 | |
| 15403 | |
| 15404 | |
| 15405 | |
| 15406 | |
| 15407 | |
| 15408 | |
| 15409 | |
| 15410 | |
| 15411 | |
| 15412 | |
| 15413 |
|
| 15414 |
|
| 15415 | YMAX = 10000;
|
| 15416 |
|
| 15417 | glyph = (function() {
|
| 15418 | function glyph() {}
|
| 15419 |
|
| 15420 | glyph.prototype.c = 0;
|
| 15421 |
|
| 15422 | glyph.prototype.x = 0;
|
| 15423 |
|
| 15424 | glyph.prototype.y = 0;
|
| 15425 |
|
| 15426 | return glyph;
|
| 15427 |
|
| 15428 | })();
|
| 15429 |
|
| 15430 | chartab = [];
|
| 15431 |
|
| 15432 | for (charTabIndex = i1 = 0, ref1 = YMAX; 0 <= ref1 ? i1 < ref1 : i1 > ref1; charTabIndex = 0 <= ref1 ? ++i1 : --i1) {
|
| 15433 | chartab[charTabIndex] = new glyph();
|
| 15434 | }
|
| 15435 |
|
| 15436 | yindex = 0;
|
| 15437 |
|
| 15438 | level = 0;
|
| 15439 |
|
| 15440 | emit_x = 0;
|
| 15441 |
|
| 15442 | expr_level = 0;
|
| 15443 |
|
| 15444 | display_flag = 0;
|
| 15445 |
|
| 15446 | printchar_nowrap = function(character) {
|
| 15447 | var accumulator;
|
| 15448 | accumulator = "";
|
| 15449 | accumulator += character;
|
| 15450 | return accumulator;
|
| 15451 | };
|
| 15452 |
|
| 15453 | printchar = function(character) {
|
| 15454 | return printchar_nowrap(character);
|
| 15455 | };
|
| 15456 |
|
| 15457 | print2dascii = function(p) {
|
| 15458 | var beenPrinted, h, ref2, w, y;
|
| 15459 | h = 0;
|
| 15460 | w = 0;
|
| 15461 | y = 0;
|
| 15462 | save();
|
| 15463 | yindex = 0;
|
| 15464 | level = 0;
|
| 15465 | emit_x = 0;
|
| 15466 | emit_top_expr(p);
|
| 15467 | ref2 = get_size(0, yindex), h = ref2[0], w = ref2[1], y = ref2[2];
|
| 15468 | if (w > 100) {
|
| 15469 | printline(p);
|
| 15470 | restore();
|
| 15471 | return;
|
| 15472 | }
|
| 15473 | beenPrinted = print_glyphs();
|
| 15474 | restore();
|
| 15475 | return beenPrinted;
|
| 15476 | };
|
| 15477 |
|
| 15478 | emit_top_expr = function(p) {
|
| 15479 | if (car(p) === symbol(SETQ)) {
|
| 15480 | emit_expr(cadr(p));
|
| 15481 | __emit_str(" = ");
|
| 15482 | emit_expr(caddr(p));
|
| 15483 | return;
|
| 15484 | }
|
| 15485 | if (istensor(p)) {
|
| 15486 | return emit_tensor(p);
|
| 15487 | } else {
|
| 15488 | return emit_expr(p);
|
| 15489 | }
|
| 15490 | };
|
| 15491 |
|
| 15492 | will_be_displayed_as_fraction = function(p) {
|
| 15493 | if (level > 0) {
|
| 15494 | return 0;
|
| 15495 | }
|
| 15496 | if (isfraction(p)) {
|
| 15497 | return 1;
|
| 15498 | }
|
| 15499 | if (car(p) !== symbol(MULTIPLY)) {
|
| 15500 | return 0;
|
| 15501 | }
|
| 15502 | if (isfraction(cadr(p))) {
|
| 15503 | return 1;
|
| 15504 | }
|
| 15505 | while (iscons(p)) {
|
| 15506 | if (isdenominator(car(p))) {
|
| 15507 | return 1;
|
| 15508 | }
|
| 15509 | p = cdr(p);
|
| 15510 | }
|
| 15511 | return 0;
|
| 15512 | };
|
| 15513 |
|
| 15514 | emit_expr = function(p) {
|
| 15515 | expr_level++;
|
| 15516 | if (car(p) === symbol(ADD)) {
|
| 15517 | p = cdr(p);
|
| 15518 | if (__is_negative(car(p))) {
|
| 15519 | __emit_char('-');
|
| 15520 | if (will_be_displayed_as_fraction(car(p))) {
|
| 15521 | __emit_char(' ');
|
| 15522 | }
|
| 15523 | }
|
| 15524 | emit_term(car(p));
|
| 15525 | p = cdr(p);
|
| 15526 | while (iscons(p)) {
|
| 15527 | if (__is_negative(car(p))) {
|
| 15528 | __emit_char(' ');
|
| 15529 | __emit_char('-');
|
| 15530 | __emit_char(' ');
|
| 15531 | } else {
|
| 15532 | __emit_char(' ');
|
| 15533 | __emit_char('+');
|
| 15534 | __emit_char(' ');
|
| 15535 | }
|
| 15536 | emit_term(car(p));
|
| 15537 | p = cdr(p);
|
| 15538 | }
|
| 15539 | } else {
|
| 15540 | if (__is_negative(p)) {
|
| 15541 | __emit_char('-');
|
| 15542 | if (will_be_displayed_as_fraction(p)) {
|
| 15543 | __emit_char(' ');
|
| 15544 | }
|
| 15545 | }
|
| 15546 | emit_term(p);
|
| 15547 | }
|
| 15548 | return expr_level--;
|
| 15549 | };
|
| 15550 |
|
| 15551 | emit_unsigned_expr = function(p) {
|
| 15552 | var results;
|
| 15553 | if (car(p) === symbol(ADD)) {
|
| 15554 | p = cdr(p);
|
| 15555 | emit_term(car(p));
|
| 15556 | p = cdr(p);
|
| 15557 | results = [];
|
| 15558 | while (iscons(p)) {
|
| 15559 | if (__is_negative(car(p))) {
|
| 15560 | __emit_char(' ');
|
| 15561 | __emit_char('-');
|
| 15562 | __emit_char(' ');
|
| 15563 | } else {
|
| 15564 | __emit_char(' ');
|
| 15565 | __emit_char('+');
|
| 15566 | __emit_char(' ');
|
| 15567 | }
|
| 15568 | emit_term(car(p));
|
| 15569 | results.push(p = cdr(p));
|
| 15570 | }
|
| 15571 | return results;
|
| 15572 | } else {
|
| 15573 | return emit_term(p);
|
| 15574 | }
|
| 15575 | };
|
| 15576 |
|
| 15577 | __is_negative = function(p) {
|
| 15578 | if (isnegativenumber(p)) {
|
| 15579 | return 1;
|
| 15580 | }
|
| 15581 | if (car(p) === symbol(MULTIPLY) && isnegativenumber(cadr(p))) {
|
| 15582 | return 1;
|
| 15583 | }
|
| 15584 | return 0;
|
| 15585 | };
|
| 15586 |
|
| 15587 | emit_term = function(p) {
|
| 15588 | var n;
|
| 15589 | if (car(p) === symbol(MULTIPLY)) {
|
| 15590 | n = count_denominators(p);
|
| 15591 | if (n && level === 0) {
|
| 15592 | return emit_fraction(p, n);
|
| 15593 | } else {
|
| 15594 | return emit_multiply(p, n);
|
| 15595 | }
|
| 15596 | } else {
|
| 15597 | return emit_factor(p);
|
| 15598 | }
|
| 15599 | };
|
| 15600 |
|
| 15601 | isdenominator = function(p) {
|
| 15602 | if (car(p) === symbol(POWER) && cadr(p) !== symbol(E) && __is_negative(caddr(p))) {
|
| 15603 | return 1;
|
| 15604 | } else {
|
| 15605 | return 0;
|
| 15606 | }
|
| 15607 | };
|
| 15608 |
|
| 15609 | count_denominators = function(p) {
|
| 15610 | var count, q;
|
| 15611 | count = 0;
|
| 15612 | p = cdr(p);
|
| 15613 | while (iscons(p)) {
|
| 15614 | q = car(p);
|
| 15615 | if (isdenominator(q)) {
|
| 15616 | count++;
|
| 15617 | }
|
| 15618 | p = cdr(p);
|
| 15619 | }
|
| 15620 | return count;
|
| 15621 | };
|
| 15622 |
|
| 15623 | emit_multiply = function(p, n) {
|
| 15624 | var results;
|
| 15625 | if (n === 0) {
|
| 15626 | p = cdr(p);
|
| 15627 | if (isplusone(car(p)) || isminusone(car(p))) {
|
| 15628 | p = cdr(p);
|
| 15629 | }
|
| 15630 | emit_factor(car(p));
|
| 15631 | p = cdr(p);
|
| 15632 | results = [];
|
| 15633 | while (iscons(p)) {
|
| 15634 | __emit_char(' ');
|
| 15635 | emit_factor(car(p));
|
| 15636 | results.push(p = cdr(p));
|
| 15637 | }
|
| 15638 | return results;
|
| 15639 | } else {
|
| 15640 | emit_numerators(p);
|
| 15641 | __emit_char('/');
|
| 15642 | if (n > 1 || isfraction(cadr(p))) {
|
| 15643 | __emit_char('(');
|
| 15644 | emit_denominators(p);
|
| 15645 | return __emit_char(')');
|
| 15646 | } else {
|
| 15647 | return emit_denominators(p);
|
| 15648 | }
|
| 15649 | }
|
| 15650 | };
|
| 15651 |
|
| 15652 | emit_fraction = function(p, d) {
|
| 15653 | var count, doNothing, k1, k2, n, x;
|
| 15654 | count = 0;
|
| 15655 | k1 = 0;
|
| 15656 | k2 = 0;
|
| 15657 | n = 0;
|
| 15658 | x = 0;
|
| 15659 | save();
|
| 15660 | p3 = one;
|
| 15661 | p4 = one;
|
| 15662 | if (isrational(cadr(p))) {
|
| 15663 | push(cadr(p));
|
| 15664 | mp_numerator();
|
| 15665 | absval();
|
| 15666 | p3 = pop();
|
| 15667 | push(cadr(p));
|
| 15668 | mp_denominator();
|
| 15669 | p4 = pop();
|
| 15670 | }
|
| 15671 | if (isdouble(cadr(p))) {
|
| 15672 | push(cadr(p));
|
| 15673 | absval();
|
| 15674 | p3 = pop();
|
| 15675 | }
|
| 15676 | if (isplusone(p3)) {
|
| 15677 | n = 0;
|
| 15678 | } else {
|
| 15679 | n = 1;
|
| 15680 | }
|
| 15681 | p1 = cdr(p);
|
| 15682 | if (isnum(car(p1))) {
|
| 15683 | p1 = cdr(p1);
|
| 15684 | }
|
| 15685 | while (iscons(p1)) {
|
| 15686 | p2 = car(p1);
|
| 15687 | if (isdenominator(p2)) {
|
| 15688 | doNothing = 1;
|
| 15689 | } else {
|
| 15690 | n++;
|
| 15691 | }
|
| 15692 | p1 = cdr(p1);
|
| 15693 | }
|
| 15694 | x = emit_x;
|
| 15695 | k1 = yindex;
|
| 15696 | count = 0;
|
| 15697 | if (!isplusone(p3)) {
|
| 15698 | emit_number(p3, 0);
|
| 15699 | count++;
|
| 15700 | }
|
| 15701 | p1 = cdr(p);
|
| 15702 | if (isnum(car(p1))) {
|
| 15703 | p1 = cdr(p1);
|
| 15704 | }
|
| 15705 | while (iscons(p1)) {
|
| 15706 | p2 = car(p1);
|
| 15707 | if (isdenominator(p2)) {
|
| 15708 | doNothing = 1;
|
| 15709 | } else {
|
| 15710 | if (count > 0) {
|
| 15711 | __emit_char(' ');
|
| 15712 | }
|
| 15713 | if (n === 1) {
|
| 15714 | emit_expr(p2);
|
| 15715 | } else {
|
| 15716 | emit_factor(p2);
|
| 15717 | }
|
| 15718 | count++;
|
| 15719 | }
|
| 15720 | p1 = cdr(p1);
|
| 15721 | }
|
| 15722 | if (count === 0) {
|
| 15723 | __emit_char('1');
|
| 15724 | }
|
| 15725 | k2 = yindex;
|
| 15726 | count = 0;
|
| 15727 | if (!isplusone(p4)) {
|
| 15728 | emit_number(p4, 0);
|
| 15729 | count++;
|
| 15730 | d++;
|
| 15731 | }
|
| 15732 | p1 = cdr(p);
|
| 15733 | if (isrational(car(p1))) {
|
| 15734 | p1 = cdr(p1);
|
| 15735 | }
|
| 15736 | while (iscons(p1)) {
|
| 15737 | p2 = car(p1);
|
| 15738 | if (isdenominator(p2)) {
|
| 15739 | if (count > 0) {
|
| 15740 | __emit_char(' ');
|
| 15741 | }
|
| 15742 | emit_denominator(p2, d);
|
| 15743 | count++;
|
| 15744 | }
|
| 15745 | p1 = cdr(p1);
|
| 15746 | }
|
| 15747 | fixup_fraction(x, k1, k2);
|
| 15748 | return restore();
|
| 15749 | };
|
| 15750 |
|
| 15751 | emit_numerators = function(p) {
|
| 15752 | var doNothing, n;
|
| 15753 | save();
|
| 15754 | n = 0;
|
| 15755 | p1 = one;
|
| 15756 | p = cdr(p);
|
| 15757 | if (isrational(car(p))) {
|
| 15758 | push(car(p));
|
| 15759 | mp_numerator();
|
| 15760 | absval();
|
| 15761 | p1 = pop();
|
| 15762 | p = cdr(p);
|
| 15763 | } else if (isdouble(car(p))) {
|
| 15764 | push(car(p));
|
| 15765 | absval();
|
| 15766 | p1 = pop();
|
| 15767 | p = cdr(p);
|
| 15768 | }
|
| 15769 | n = 0;
|
| 15770 | if (!isplusone(p1)) {
|
| 15771 | emit_number(p1, 0);
|
| 15772 | n++;
|
| 15773 | }
|
| 15774 | while (iscons(p)) {
|
| 15775 | if (isdenominator(car(p))) {
|
| 15776 | doNothing = 1;
|
| 15777 | } else {
|
| 15778 | if (n > 0) {
|
| 15779 | __emit_char(' ');
|
| 15780 | }
|
| 15781 | emit_factor(car(p));
|
| 15782 | n++;
|
| 15783 | }
|
| 15784 | p = cdr(p);
|
| 15785 | }
|
| 15786 | if (n === 0) {
|
| 15787 | __emit_char('1');
|
| 15788 | }
|
| 15789 | return restore();
|
| 15790 | };
|
| 15791 |
|
| 15792 | emit_denominators = function(p) {
|
| 15793 | var n;
|
| 15794 | save();
|
| 15795 | n = 0;
|
| 15796 | p = cdr(p);
|
| 15797 | if (isfraction(car(p))) {
|
| 15798 | push(car(p));
|
| 15799 | mp_denominator();
|
| 15800 | p1 = pop();
|
| 15801 | emit_number(p1, 0);
|
| 15802 | n++;
|
| 15803 | p = cdr(p);
|
| 15804 | }
|
| 15805 | while (iscons(p)) {
|
| 15806 | if (isdenominator(car(p))) {
|
| 15807 | if (n > 0) {
|
| 15808 | __emit_char(' ');
|
| 15809 | }
|
| 15810 | emit_denominator(car(p), 0);
|
| 15811 | n++;
|
| 15812 | }
|
| 15813 | p = cdr(p);
|
| 15814 | }
|
| 15815 | return restore();
|
| 15816 | };
|
| 15817 |
|
| 15818 | emit_factor = function(p) {
|
| 15819 | if (istensor(p)) {
|
| 15820 | if (level === 0) {
|
| 15821 | emit_flat_tensor(p);
|
| 15822 | } else {
|
| 15823 | emit_flat_tensor(p);
|
| 15824 | }
|
| 15825 | return;
|
| 15826 | }
|
| 15827 | if (isdouble(p)) {
|
| 15828 | emit_number(p, 0);
|
| 15829 | return;
|
| 15830 | }
|
| 15831 | if (car(p) === symbol(ADD) || car(p) === symbol(MULTIPLY)) {
|
| 15832 | emit_subexpr(p);
|
| 15833 | return;
|
| 15834 | }
|
| 15835 | if (car(p) === symbol(POWER)) {
|
| 15836 | emit_power(p);
|
| 15837 | return;
|
| 15838 | }
|
| 15839 | if (iscons(p)) {
|
| 15840 | emit_function(p);
|
| 15841 | return;
|
| 15842 | }
|
| 15843 | if (isnum(p)) {
|
| 15844 | if (level === 0) {
|
| 15845 | emit_numerical_fraction(p);
|
| 15846 | } else {
|
| 15847 | emit_number(p, 0);
|
| 15848 | }
|
| 15849 | return;
|
| 15850 | }
|
| 15851 | if (issymbol(p)) {
|
| 15852 | emit_symbol(p);
|
| 15853 | return;
|
| 15854 | }
|
| 15855 | if (isstr(p)) {
|
| 15856 | emit_string(p);
|
| 15857 | }
|
| 15858 | };
|
| 15859 |
|
| 15860 | emit_numerical_fraction = function(p) {
|
| 15861 | var k1, k2, x;
|
| 15862 | k1 = 0;
|
| 15863 | k2 = 0;
|
| 15864 | x = 0;
|
| 15865 | save();
|
| 15866 | push(p);
|
| 15867 | mp_numerator();
|
| 15868 | absval();
|
| 15869 | p3 = pop();
|
| 15870 | push(p);
|
| 15871 | mp_denominator();
|
| 15872 | p4 = pop();
|
| 15873 | if (isplusone(p4)) {
|
| 15874 | emit_number(p3, 0);
|
| 15875 | restore();
|
| 15876 | return;
|
| 15877 | }
|
| 15878 | x = emit_x;
|
| 15879 | k1 = yindex;
|
| 15880 | emit_number(p3, 0);
|
| 15881 | k2 = yindex;
|
| 15882 | emit_number(p4, 0);
|
| 15883 | fixup_fraction(x, k1, k2);
|
| 15884 | return restore();
|
| 15885 | };
|
| 15886 |
|
| 15887 | isfactor = function(p) {
|
| 15888 | if (iscons(p) && car(p) !== symbol(ADD) && car(p) !== symbol(MULTIPLY) && car(p) !== symbol(POWER)) {
|
| 15889 | return 1;
|
| 15890 | }
|
| 15891 | if (issymbol(p)) {
|
| 15892 | return 1;
|
| 15893 | }
|
| 15894 | if (isfraction(p)) {
|
| 15895 | return 0;
|
| 15896 | }
|
| 15897 | if (isnegativenumber(p)) {
|
| 15898 | return 0;
|
| 15899 | }
|
| 15900 | if (isnum(p)) {
|
| 15901 | return 1;
|
| 15902 | }
|
| 15903 | return 0;
|
| 15904 | };
|
| 15905 |
|
| 15906 | emit_power = function(p) {
|
| 15907 | var k1, k2, x;
|
| 15908 | k1 = 0;
|
| 15909 | k2 = 0;
|
| 15910 | x = 0;
|
| 15911 | if (cadr(p) === symbol(E)) {
|
| 15912 | __emit_str("exp(");
|
| 15913 | emit_expr(caddr(p));
|
| 15914 | __emit_char(')');
|
| 15915 | return;
|
| 15916 | }
|
| 15917 | if (level > 0) {
|
| 15918 | if (isminusone(caddr(p))) {
|
| 15919 | __emit_char('1');
|
| 15920 | __emit_char('/');
|
| 15921 | if (isfactor(cadr(p))) {
|
| 15922 | emit_factor(cadr(p));
|
| 15923 | } else {
|
| 15924 | emit_subexpr(cadr(p));
|
| 15925 | }
|
| 15926 | } else {
|
| 15927 | if (isfactor(cadr(p))) {
|
| 15928 | emit_factor(cadr(p));
|
| 15929 | } else {
|
| 15930 | emit_subexpr(cadr(p));
|
| 15931 | }
|
| 15932 | __emit_char('^');
|
| 15933 | if (isfactor(caddr(p))) {
|
| 15934 | emit_factor(caddr(p));
|
| 15935 | } else {
|
| 15936 | emit_subexpr(caddr(p));
|
| 15937 | }
|
| 15938 | }
|
| 15939 | return;
|
| 15940 | }
|
| 15941 | if (__is_negative(caddr(p))) {
|
| 15942 | x = emit_x;
|
| 15943 | k1 = yindex;
|
| 15944 | __emit_char('1');
|
| 15945 | k2 = yindex;
|
| 15946 | emit_denominator(p, 1);
|
| 15947 | fixup_fraction(x, k1, k2);
|
| 15948 | return;
|
| 15949 | }
|
| 15950 | k1 = yindex;
|
| 15951 | if (isfactor(cadr(p))) {
|
| 15952 | emit_factor(cadr(p));
|
| 15953 | } else {
|
| 15954 | emit_subexpr(cadr(p));
|
| 15955 | }
|
| 15956 | k2 = yindex;
|
| 15957 | level++;
|
| 15958 | emit_expr(caddr(p));
|
| 15959 | level--;
|
| 15960 | return fixup_power(k1, k2);
|
| 15961 | };
|
| 15962 |
|
| 15963 | emit_denominator = function(p, n) {
|
| 15964 | var k1, k2;
|
| 15965 | k1 = 0;
|
| 15966 | k2 = 0;
|
| 15967 | if (isminusone(caddr(p))) {
|
| 15968 | if (n === 1) {
|
| 15969 | emit_expr(cadr(p));
|
| 15970 | } else {
|
| 15971 | emit_factor(cadr(p));
|
| 15972 | }
|
| 15973 | return;
|
| 15974 | }
|
| 15975 | k1 = yindex;
|
| 15976 | if (isfactor(cadr(p))) {
|
| 15977 | emit_factor(cadr(p));
|
| 15978 | } else {
|
| 15979 | emit_subexpr(cadr(p));
|
| 15980 | }
|
| 15981 | k2 = yindex;
|
| 15982 | level++;
|
| 15983 | emit_unsigned_expr(caddr(p));
|
| 15984 | level--;
|
| 15985 | return fixup_power(k1, k2);
|
| 15986 | };
|
| 15987 |
|
| 15988 | emit_function = function(p) {
|
| 15989 | if (car(p) === symbol(INDEX) && issymbol(cadr(p))) {
|
| 15990 | emit_index_function(p);
|
| 15991 | return;
|
| 15992 | }
|
| 15993 | if (car(p) === symbol(FACTORIAL)) {
|
| 15994 | emit_factorial_function(p);
|
| 15995 | return;
|
| 15996 | }
|
| 15997 | if (car(p) === symbol(DERIVATIVE)) {
|
| 15998 | __emit_char('d');
|
| 15999 | } else {
|
| 16000 | emit_symbol(car(p));
|
| 16001 | }
|
| 16002 | __emit_char('(');
|
| 16003 | p = cdr(p);
|
| 16004 | if (iscons(p)) {
|
| 16005 | emit_expr(car(p));
|
| 16006 | p = cdr(p);
|
| 16007 | while (iscons(p)) {
|
| 16008 | __emit_char(',');
|
| 16009 | emit_expr(car(p));
|
| 16010 | p = cdr(p);
|
| 16011 | }
|
| 16012 | }
|
| 16013 | return __emit_char(')');
|
| 16014 | };
|
| 16015 |
|
| 16016 | emit_index_function = function(p) {
|
| 16017 | p = cdr(p);
|
| 16018 | if (caar(p) === symbol(ADD) || caar(p) === symbol(MULTIPLY) || caar(p) === symbol(POWER) || caar(p) === symbol(FACTORIAL)) {
|
| 16019 | emit_subexpr(car(p));
|
| 16020 | } else {
|
| 16021 | emit_expr(car(p));
|
| 16022 | }
|
| 16023 | __emit_char('[');
|
| 16024 | p = cdr(p);
|
| 16025 | if (iscons(p)) {
|
| 16026 | emit_expr(car(p));
|
| 16027 | p = cdr(p);
|
| 16028 | while (iscons(p)) {
|
| 16029 | __emit_char(',');
|
| 16030 | emit_expr(car(p));
|
| 16031 | p = cdr(p);
|
| 16032 | }
|
| 16033 | }
|
| 16034 | return __emit_char(']');
|
| 16035 | };
|
| 16036 |
|
| 16037 | emit_factorial_function = function(p) {
|
| 16038 | p = cadr(p);
|
| 16039 | if (car(p) === symbol(ADD) || car(p) === symbol(MULTIPLY) || car(p) === symbol(POWER) || car(p) === symbol(FACTORIAL)) {
|
| 16040 | emit_subexpr(p);
|
| 16041 | } else {
|
| 16042 | emit_expr(p);
|
| 16043 | }
|
| 16044 | return __emit_char('!');
|
| 16045 | };
|
| 16046 |
|
| 16047 | emit_subexpr = function(p) {
|
| 16048 | __emit_char('(');
|
| 16049 | emit_expr(p);
|
| 16050 | return __emit_char(')');
|
| 16051 | };
|
| 16052 |
|
| 16053 | emit_symbol = function(p) {
|
| 16054 | var i, j1, pPrintName, ref2, results;
|
| 16055 | i = 0;
|
| 16056 | if (p === symbol(E)) {
|
| 16057 | __emit_str("exp(1)");
|
| 16058 | return;
|
| 16059 | }
|
| 16060 | pPrintName = get_printname(p);
|
| 16061 | results = [];
|
| 16062 | for (i = j1 = 0, ref2 = pPrintName.length; 0 <= ref2 ? j1 < ref2 : j1 > ref2; i = 0 <= ref2 ? ++j1 : --j1) {
|
| 16063 | results.push(__emit_char(pPrintName[i]));
|
| 16064 | }
|
| 16065 | return results;
|
| 16066 | };
|
| 16067 |
|
| 16068 | emit_string = function(p) {
|
| 16069 | var i, j1, pString, ref2;
|
| 16070 | i = 0;
|
| 16071 | pString = p.str;
|
| 16072 | __emit_char('"');
|
| 16073 | for (i = j1 = 0, ref2 = pString.length; 0 <= ref2 ? j1 < ref2 : j1 > ref2; i = 0 <= ref2 ? ++j1 : --j1) {
|
| 16074 | __emit_char(pString[i]);
|
| 16075 | }
|
| 16076 | return __emit_char('"');
|
| 16077 | };
|
| 16078 |
|
| 16079 | fixup_fraction = function(x, k1, k2) {
|
| 16080 | var dx, dy, h1, h2, i, j1, ref2, ref3, ref4, results, w, w1, w2, y, y1, y2;
|
| 16081 | dx = 0;
|
| 16082 | dy = 0;
|
| 16083 | i = 0;
|
| 16084 | w = 0;
|
| 16085 | y = 0;
|
| 16086 | h1 = 0;
|
| 16087 | w1 = 0;
|
| 16088 | y1 = 0;
|
| 16089 | h2 = 0;
|
| 16090 | w2 = 0;
|
| 16091 | y2 = 0;
|
| 16092 | ref2 = get_size(k1, k2), h1 = ref2[0], w1 = ref2[1], y1 = ref2[2];
|
| 16093 | ref3 = get_size(k2, yindex), h2 = ref3[0], w2 = ref3[1], y2 = ref3[2];
|
| 16094 | if (w2 > w1) {
|
| 16095 | dx = (w2 - w1) / 2;
|
| 16096 | } else {
|
| 16097 | dx = 0;
|
| 16098 | }
|
| 16099 | dx++;
|
| 16100 | y = y1 + h1 - 1;
|
| 16101 | dy = -y - 1;
|
| 16102 | move(k1, k2, dx, dy);
|
| 16103 | if (w2 > w1) {
|
| 16104 | dx = -w1;
|
| 16105 | } else {
|
| 16106 | dx = -w1 + (w1 - w2) / 2;
|
| 16107 | }
|
| 16108 | dx++;
|
| 16109 | dy = -y2 + 1;
|
| 16110 | move(k2, yindex, dx, dy);
|
| 16111 | if (w2 > w1) {
|
| 16112 | w = w2;
|
| 16113 | } else {
|
| 16114 | w = w1;
|
| 16115 | }
|
| 16116 | w += 2;
|
| 16117 | emit_x = x;
|
| 16118 | results = [];
|
| 16119 | for (i = j1 = 0, ref4 = w; 0 <= ref4 ? j1 < ref4 : j1 > ref4; i = 0 <= ref4 ? ++j1 : --j1) {
|
| 16120 | results.push(__emit_char('-'));
|
| 16121 | }
|
| 16122 | return results;
|
| 16123 | };
|
| 16124 |
|
| 16125 | fixup_power = function(k1, k2) {
|
| 16126 | var dy, h1, h2, ref2, ref3, w1, w2, y1, y2;
|
| 16127 | dy = 0;
|
| 16128 | h1 = 0;
|
| 16129 | w1 = 0;
|
| 16130 | y1 = 0;
|
| 16131 | h2 = 0;
|
| 16132 | w2 = 0;
|
| 16133 | y2 = 0;
|
| 16134 | ref2 = get_size(k1, k2), h1 = ref2[0], w1 = ref2[1], y1 = ref2[2];
|
| 16135 | ref3 = get_size(k2, yindex), h2 = ref3[0], w2 = ref3[1], y2 = ref3[2];
|
| 16136 | dy = -y2 - h2 + 1;
|
| 16137 | dy += y1 - 1;
|
| 16138 | return move(k2, yindex, 0, dy);
|
| 16139 | };
|
| 16140 |
|
| 16141 | move = function(j, k, dx, dy) {
|
| 16142 | var i, j1, ref2, ref3, results;
|
| 16143 | i = 0;
|
| 16144 | results = [];
|
| 16145 | for (i = j1 = ref2 = j, ref3 = k; ref2 <= ref3 ? j1 < ref3 : j1 > ref3; i = ref2 <= ref3 ? ++j1 : --j1) {
|
| 16146 | chartab[i].x += dx;
|
| 16147 | results.push(chartab[i].y += dy);
|
| 16148 | }
|
| 16149 | return results;
|
| 16150 | };
|
| 16151 |
|
| 16152 | get_size = function(j, k) {
|
| 16153 | var h, i, j1, max_x, max_y, min_x, min_y, ref2, ref3, w, y;
|
| 16154 | i = 0;
|
| 16155 | min_x = chartab[j].x;
|
| 16156 | max_x = chartab[j].x;
|
| 16157 | min_y = chartab[j].y;
|
| 16158 | max_y = chartab[j].y;
|
| 16159 | for (i = j1 = ref2 = j + 1, ref3 = k; ref2 <= ref3 ? j1 < ref3 : j1 > ref3; i = ref2 <= ref3 ? ++j1 : --j1) {
|
| 16160 | if (chartab[i].x < min_x) {
|
| 16161 | min_x = chartab[i].x;
|
| 16162 | }
|
| 16163 | if (chartab[i].x > max_x) {
|
| 16164 | max_x = chartab[i].x;
|
| 16165 | }
|
| 16166 | if (chartab[i].y < min_y) {
|
| 16167 | min_y = chartab[i].y;
|
| 16168 | }
|
| 16169 | if (chartab[i].y > max_y) {
|
| 16170 | max_y = chartab[i].y;
|
| 16171 | }
|
| 16172 | }
|
| 16173 | h = max_y - min_y + 1;
|
| 16174 | w = max_x - min_x + 1;
|
| 16175 | y = min_y;
|
| 16176 | return [h, w, y];
|
| 16177 | };
|
| 16178 |
|
| 16179 | displaychar = function(c) {
|
| 16180 | return __emit_char(c);
|
| 16181 | };
|
| 16182 |
|
| 16183 | __emit_char = function(c) {
|
| 16184 | if (yindex === YMAX) {
|
| 16185 | return;
|
| 16186 | }
|
| 16187 | if (chartab[yindex] == null) {
|
| 16188 | debugger;
|
| 16189 | }
|
| 16190 | chartab[yindex].c = c;
|
| 16191 | chartab[yindex].x = emit_x;
|
| 16192 | chartab[yindex].y = 0;
|
| 16193 | yindex++;
|
| 16194 | return emit_x++;
|
| 16195 | };
|
| 16196 |
|
| 16197 | __emit_str = function(s) {
|
| 16198 | var i, j1, ref2, results;
|
| 16199 | i = 0;
|
| 16200 | results = [];
|
| 16201 | for (i = j1 = 0, ref2 = s.length; 0 <= ref2 ? j1 < ref2 : j1 > ref2; i = 0 <= ref2 ? ++j1 : --j1) {
|
| 16202 | results.push(__emit_char(s[i]));
|
| 16203 | }
|
| 16204 | return results;
|
| 16205 | };
|
| 16206 |
|
| 16207 | emit_number = function(p, emit_sign) {
|
| 16208 | var i, j1, l1, m1, ref2, ref3, ref4, results, results1, tmpString;
|
| 16209 | tmpString = "";
|
| 16210 | i = 0;
|
| 16211 | switch (p.k) {
|
| 16212 | case NUM:
|
| 16213 | tmpString = p.q.a.toString();
|
| 16214 | if (tmpString[0] === '-' && emit_sign === 0) {
|
| 16215 | tmpString = tmpString.substring(1);
|
| 16216 | }
|
| 16217 | for (i = j1 = 0, ref2 = tmpString.length; 0 <= ref2 ? j1 < ref2 : j1 > ref2; i = 0 <= ref2 ? ++j1 : --j1) {
|
| 16218 | __emit_char(tmpString[i]);
|
| 16219 | }
|
| 16220 | tmpString = p.q.b.toString();
|
| 16221 | if (tmpString === "1") {
|
| 16222 | break;
|
| 16223 | }
|
| 16224 | __emit_char('/');
|
| 16225 | results = [];
|
| 16226 | for (i = l1 = 0, ref3 = tmpString.length; 0 <= ref3 ? l1 < ref3 : l1 > ref3; i = 0 <= ref3 ? ++l1 : --l1) {
|
| 16227 | results.push(__emit_char(tmpString[i]));
|
| 16228 | }
|
| 16229 | return results;
|
| 16230 | break;
|
| 16231 | case DOUBLE:
|
| 16232 | tmpString = doubleToReasonableString(p.d);
|
| 16233 | if (tmpString[0] === '-' && emit_sign === 0) {
|
| 16234 | tmpString = tmpString.substring(1);
|
| 16235 | }
|
| 16236 | results1 = [];
|
| 16237 | for (i = m1 = 0, ref4 = tmpString.length; 0 <= ref4 ? m1 < ref4 : m1 > ref4; i = 0 <= ref4 ? ++m1 : --m1) {
|
| 16238 | results1.push(__emit_char(tmpString[i]));
|
| 16239 | }
|
| 16240 | return results1;
|
| 16241 | }
|
| 16242 | };
|
| 16243 |
|
| 16244 | cmpGlyphs = function(a, b) {
|
| 16245 | if (a.y < b.y) {
|
| 16246 | return -1;
|
| 16247 | }
|
| 16248 | if (a.y > b.y) {
|
| 16249 | return 1;
|
| 16250 | }
|
| 16251 | if (a.x < b.x) {
|
| 16252 | return -1;
|
| 16253 | }
|
| 16254 | if (a.x > b.x) {
|
| 16255 | return 1;
|
| 16256 | }
|
| 16257 | return 0;
|
| 16258 | };
|
| 16259 |
|
| 16260 | print_glyphs = function() {
|
| 16261 | var accumulator, i, j1, ref2, subsetOfStack, x, y;
|
| 16262 | i = 0;
|
| 16263 | accumulator = "";
|
| 16264 | subsetOfStack = chartab.slice(0, yindex);
|
| 16265 | subsetOfStack.sort(cmpGlyphs);
|
| 16266 | chartab = [].concat(subsetOfStack).concat(chartab.slice(yindex));
|
| 16267 | x = 0;
|
| 16268 | y = chartab[0].y;
|
| 16269 | for (i = j1 = 0, ref2 = yindex; 0 <= ref2 ? j1 < ref2 : j1 > ref2; i = 0 <= ref2 ? ++j1 : --j1) {
|
| 16270 | while (chartab[i].y > y) {
|
| 16271 | accumulator += printchar('\n');
|
| 16272 | x = 0;
|
| 16273 | y++;
|
| 16274 | }
|
| 16275 | while (chartab[i].x > x) {
|
| 16276 | accumulator += printchar_nowrap(' ');
|
| 16277 | x++;
|
| 16278 | }
|
| 16279 | accumulator += printchar_nowrap(chartab[i].c);
|
| 16280 | x++;
|
| 16281 | }
|
| 16282 | return accumulator;
|
| 16283 | };
|
| 16284 |
|
| 16285 | buffer = "";
|
| 16286 |
|
| 16287 | getdisplaystr = function() {
|
| 16288 | yindex = 0;
|
| 16289 | level = 0;
|
| 16290 | emit_x = 0;
|
| 16291 | emit_expr(pop());
|
| 16292 | fill_buf();
|
| 16293 | return buffer;
|
| 16294 | };
|
| 16295 |
|
| 16296 | fill_buf = function() {
|
| 16297 | var i, j1, ref2, sIndex, subsetOfStack, tmpBuffer, x, y;
|
| 16298 | tmpBuffer = buffer;
|
| 16299 | sIndex = 0;
|
| 16300 | i = 0;
|
| 16301 | subsetOfStack = chartab.slice(0, yindex);
|
| 16302 | subsetOfStack.sort(cmpGlyphs);
|
| 16303 | chartab = [].concat(subsetOfStack).concat(chartab.slice(yindex));
|
| 16304 | x = 0;
|
| 16305 | y = chartab[0].y;
|
| 16306 | for (i = j1 = 0, ref2 = yindex; 0 <= ref2 ? j1 < ref2 : j1 > ref2; i = 0 <= ref2 ? ++j1 : --j1) {
|
| 16307 | while (chartab[i].y > y) {
|
| 16308 | tmpBuffer[sIndex++] = '\n';
|
| 16309 | x = 0;
|
| 16310 | y++;
|
| 16311 | }
|
| 16312 | while (chartab[i].x > x) {
|
| 16313 | tmpBuffer[sIndex++] = ' ';
|
| 16314 | x++;
|
| 16315 | }
|
| 16316 | tmpBuffer[sIndex++] = chartab[i].c;
|
| 16317 | x++;
|
| 16318 | }
|
| 16319 | return tmpBuffer[sIndex++] = '\n';
|
| 16320 | };
|
| 16321 |
|
| 16322 | N = 100;
|
| 16323 |
|
| 16324 | oneElement = (function() {
|
| 16325 | function oneElement() {}
|
| 16326 |
|
| 16327 | oneElement.prototype.x = 0;
|
| 16328 |
|
| 16329 | oneElement.prototype.y = 0;
|
| 16330 |
|
| 16331 | oneElement.prototype.h = 0;
|
| 16332 |
|
| 16333 | oneElement.prototype.w = 0;
|
| 16334 |
|
| 16335 | oneElement.prototype.index = 0;
|
| 16336 |
|
| 16337 | oneElement.prototype.count = 0;
|
| 16338 |
|
| 16339 | return oneElement;
|
| 16340 |
|
| 16341 | })();
|
| 16342 |
|
| 16343 | elem = [];
|
| 16344 |
|
| 16345 | for (elelmIndex = j1 = 0; j1 < 10000; elelmIndex = ++j1) {
|
| 16346 | elem[elelmIndex] = new oneElement;
|
| 16347 | }
|
| 16348 |
|
| 16349 | SPACE_BETWEEN_COLUMNS = 3;
|
| 16350 |
|
| 16351 | SPACE_BETWEEN_ROWS = 1;
|
| 16352 |
|
| 16353 | emit_tensor = function(p) {
|
| 16354 | var col, dx, dy, eh, ew, h, i, l1, m1, n, n1, ncol, nrow, o1, ref2, ref3, ref4, ref5, ref6, row, w, x, y;
|
| 16355 | i = 0;
|
| 16356 | n = 0;
|
| 16357 | nrow = 0;
|
| 16358 | ncol = 0;
|
| 16359 | x = 0;
|
| 16360 | y = 0;
|
| 16361 | h = 0;
|
| 16362 | w = 0;
|
| 16363 | dx = 0;
|
| 16364 | dy = 0;
|
| 16365 | eh = 0;
|
| 16366 | ew = 0;
|
| 16367 | row = 0;
|
| 16368 | col = 0;
|
| 16369 | if (p.tensor.ndim > 2) {
|
| 16370 | emit_flat_tensor(p);
|
| 16371 | return;
|
| 16372 | }
|
| 16373 | nrow = p.tensor.dim[0];
|
| 16374 | if (p.tensor.ndim === 2) {
|
| 16375 | ncol = p.tensor.dim[1];
|
| 16376 | } else {
|
| 16377 | ncol = 1;
|
| 16378 | }
|
| 16379 | n = nrow * ncol;
|
| 16380 | if (n > N) {
|
| 16381 | emit_flat_tensor(p);
|
| 16382 | return;
|
| 16383 | }
|
| 16384 | x = emit_x;
|
| 16385 | for (i = l1 = 0, ref2 = n; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 16386 | elem[i].index = yindex;
|
| 16387 | elem[i].x = emit_x;
|
| 16388 | emit_expr(p.tensor.elem[i]);
|
| 16389 | elem[i].count = yindex - elem[i].index;
|
| 16390 | ref3 = get_size(elem[i].index, yindex), elem[i].h = ref3[0], elem[i].w = ref3[1], elem[i].y = ref3[2];
|
| 16391 | }
|
| 16392 | eh = 0;
|
| 16393 | ew = 0;
|
| 16394 | for (i = m1 = 0, ref4 = n; 0 <= ref4 ? m1 < ref4 : m1 > ref4; i = 0 <= ref4 ? ++m1 : --m1) {
|
| 16395 | if (elem[i].h > eh) {
|
| 16396 | eh = elem[i].h;
|
| 16397 | }
|
| 16398 | if (elem[i].w > ew) {
|
| 16399 | ew = elem[i].w;
|
| 16400 | }
|
| 16401 | }
|
| 16402 | h = nrow * eh + (nrow - 1) * SPACE_BETWEEN_ROWS;
|
| 16403 | w = ncol * ew + (ncol - 1) * SPACE_BETWEEN_COLUMNS;
|
| 16404 | y = -(h / 2);
|
| 16405 | for (row = n1 = 0, ref5 = nrow; 0 <= ref5 ? n1 < ref5 : n1 > ref5; row = 0 <= ref5 ? ++n1 : --n1) {
|
| 16406 | for (col = o1 = 0, ref6 = ncol; 0 <= ref6 ? o1 < ref6 : o1 > ref6; col = 0 <= ref6 ? ++o1 : --o1) {
|
| 16407 | i = row * ncol + col;
|
| 16408 | dx = x - elem[i].x;
|
| 16409 | dy = y - elem[i].y;
|
| 16410 | move(elem[i].index, elem[i].index + elem[i].count, dx, dy);
|
| 16411 | dx = 0;
|
| 16412 | if (col > 0) {
|
| 16413 | dx = col * (ew + SPACE_BETWEEN_COLUMNS);
|
| 16414 | }
|
| 16415 | dy = 0;
|
| 16416 | if (row > 0) {
|
| 16417 | dy = row * (eh + SPACE_BETWEEN_ROWS);
|
| 16418 | }
|
| 16419 | dx += (ew - elem[i].w) / 2;
|
| 16420 | dy += (eh - elem[i].h) / 2;
|
| 16421 | move(elem[i].index, elem[i].index + elem[i].count, dx, dy);
|
| 16422 | }
|
| 16423 | }
|
| 16424 | return emit_x = x + w;
|
| 16425 |
|
| 16426 | |
| 16427 | |
| 16428 | |
| 16429 | |
| 16430 | |
| 16431 | |
| 16432 | |
| 16433 | |
| 16434 | |
| 16435 | |
| 16436 | |
| 16437 | |
| 16438 | |
| 16439 | |
| 16440 | |
| 16441 | |
| 16442 | |
| 16443 | |
| 16444 | |
| 16445 | |
| 16446 | |
| 16447 | |
| 16448 | |
| 16449 | |
| 16450 | |
| 16451 | |
| 16452 | |
| 16453 | |
| 16454 | |
| 16455 | |
| 16456 |
|
| 16457 | };
|
| 16458 |
|
| 16459 | emit_flat_tensor = function(p) {
|
| 16460 | return emit_tensor_inner(p, 0, 0);
|
| 16461 | };
|
| 16462 |
|
| 16463 | emit_tensor_inner = function(p, j, k) {
|
| 16464 | var i, l1, ref2;
|
| 16465 | i = 0;
|
| 16466 | __emit_char('(');
|
| 16467 | for (i = l1 = 0, ref2 = p.tensor.dim[j]; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 16468 | if (j + 1 === p.tensor.ndim) {
|
| 16469 | emit_expr(p.tensor.elem[k]);
|
| 16470 | k = k + 1;
|
| 16471 | } else {
|
| 16472 | k = emit_tensor_inner(p, j + 1, k);
|
| 16473 | }
|
| 16474 | if (i + 1 < p.tensor.dim[j]) {
|
| 16475 | __emit_char(',');
|
| 16476 | }
|
| 16477 | }
|
| 16478 | __emit_char(')');
|
| 16479 | return k;
|
| 16480 | };
|
| 16481 |
|
| 16482 | Eval_product = function() {
|
| 16483 | var body, i, indexVariable, j, k, l1, oldIndexVariableValue, ref2, ref3;
|
| 16484 | i = 0;
|
| 16485 | j = 0;
|
| 16486 | k = 0;
|
| 16487 | body = cadr(p1);
|
| 16488 | indexVariable = caddr(p1);
|
| 16489 | if (!issymbol(p6)) {
|
| 16490 | stop("sum: 1st arg?");
|
| 16491 | }
|
| 16492 | push(cadddr(p1));
|
| 16493 | Eval();
|
| 16494 | j = pop_integer();
|
| 16495 | if (isNaN(j)) {
|
| 16496 | push(p1);
|
| 16497 | return;
|
| 16498 | }
|
| 16499 | push(caddddr(p1));
|
| 16500 | Eval();
|
| 16501 | k = pop_integer();
|
| 16502 | if (isNaN(k)) {
|
| 16503 | push(p1);
|
| 16504 | return;
|
| 16505 | }
|
| 16506 | oldIndexVariableValue = get_binding(indexVariable);
|
| 16507 | push_integer(1);
|
| 16508 | for (i = l1 = ref2 = j, ref3 = k; ref2 <= ref3 ? l1 <= ref3 : l1 >= ref3; i = ref2 <= ref3 ? ++l1 : --l1) {
|
| 16509 | push_integer(i);
|
| 16510 | p5 = pop();
|
| 16511 | set_binding(indexVariable, p5);
|
| 16512 | push(body);
|
| 16513 | Eval();
|
| 16514 | if (DEBUG) {
|
| 16515 | console.log("product - factor 1: " + stack[tos - 1].toString());
|
| 16516 | console.log("product - factor 2: " + stack[tos - 2].toString());
|
| 16517 | }
|
| 16518 | multiply();
|
| 16519 | if (DEBUG) {
|
| 16520 | console.log("product - result: " + stack[tos - 1].toString());
|
| 16521 | }
|
| 16522 | }
|
| 16523 | return set_binding(indexVariable, oldIndexVariableValue);
|
| 16524 | };
|
| 16525 |
|
| 16526 | qadd = function() {
|
| 16527 | var a, ab, b, ba, c;
|
| 16528 | save();
|
| 16529 | p2 = pop();
|
| 16530 | p1 = pop();
|
| 16531 | ab = mmul(p1.q.a, p2.q.b);
|
| 16532 | ba = mmul(p1.q.b, p2.q.a);
|
| 16533 | a = madd(ab, ba);
|
| 16534 | if (MZERO(a)) {
|
| 16535 | push(zero);
|
| 16536 | restore();
|
| 16537 | return;
|
| 16538 | }
|
| 16539 | b = mmul(p1.q.b, p2.q.b);
|
| 16540 | c = mgcd(a, b);
|
| 16541 | c = makeSignSameAs(c, b);
|
| 16542 | p1 = new U();
|
| 16543 | p1.k = NUM;
|
| 16544 | p1.q.a = mdiv(a, c);
|
| 16545 | p1.q.b = mdiv(b, c);
|
| 16546 | push(p1);
|
| 16547 | return restore();
|
| 16548 | };
|
| 16549 |
|
| 16550 | qdiv = function() {
|
| 16551 | var aa, bb, c;
|
| 16552 | save();
|
| 16553 | p2 = pop();
|
| 16554 | p1 = pop();
|
| 16555 | if (MZERO(p2.q.a)) {
|
| 16556 | stop("divide by zero");
|
| 16557 | }
|
| 16558 | if (MZERO(p1.q.a)) {
|
| 16559 | push(zero);
|
| 16560 | restore();
|
| 16561 | return;
|
| 16562 | }
|
| 16563 | aa = mmul(p1.q.a, p2.q.b);
|
| 16564 | bb = mmul(p1.q.b, p2.q.a);
|
| 16565 | c = mgcd(aa, bb);
|
| 16566 | c = makeSignSameAs(c, bb);
|
| 16567 | p1 = new U();
|
| 16568 | p1.k = NUM;
|
| 16569 | p1.q.a = mdiv(aa, c);
|
| 16570 | p1.q.b = mdiv(bb, c);
|
| 16571 | push(p1);
|
| 16572 | return restore();
|
| 16573 | };
|
| 16574 |
|
| 16575 | qmul = function() {
|
| 16576 | var aa, bb, c;
|
| 16577 | save();
|
| 16578 | p2 = pop();
|
| 16579 | p1 = pop();
|
| 16580 | if (MZERO(p1.q.a) || MZERO(p2.q.a)) {
|
| 16581 | push(zero);
|
| 16582 | restore();
|
| 16583 | return;
|
| 16584 | }
|
| 16585 | aa = mmul(p1.q.a, p2.q.a);
|
| 16586 | bb = mmul(p1.q.b, p2.q.b);
|
| 16587 | c = mgcd(aa, bb);
|
| 16588 | c = makeSignSameAs(c, bb);
|
| 16589 | p1 = new U();
|
| 16590 | p1.k = NUM;
|
| 16591 | p1.q.a = mdiv(aa, c);
|
| 16592 | p1.q.b = mdiv(bb, c);
|
| 16593 | push(p1);
|
| 16594 | return restore();
|
| 16595 | };
|
| 16596 |
|
| 16597 | qpow = function() {
|
| 16598 | save();
|
| 16599 | qpowf();
|
| 16600 | return restore();
|
| 16601 | };
|
| 16602 |
|
| 16603 | qpowf = function() {
|
| 16604 | var a, b, expo, t, x, y;
|
| 16605 | expo = 0;
|
| 16606 | p2 = pop();
|
| 16607 | p1 = pop();
|
| 16608 | if (isplusone(p1) || iszero(p2)) {
|
| 16609 | push_integer(1);
|
| 16610 | return;
|
| 16611 | }
|
| 16612 | if (isminusone(p1) && isoneovertwo(p2)) {
|
| 16613 | push(imaginaryunit);
|
| 16614 | return;
|
| 16615 | }
|
| 16616 | if (iszero(p1)) {
|
| 16617 | if (isnegativenumber(p2)) {
|
| 16618 | stop("divide by zero");
|
| 16619 | }
|
| 16620 | push(zero);
|
| 16621 | return;
|
| 16622 | }
|
| 16623 | if (isplusone(p2)) {
|
| 16624 | push(p1);
|
| 16625 | return;
|
| 16626 | }
|
| 16627 | if (isinteger(p2)) {
|
| 16628 | push(p2);
|
| 16629 | expo = pop_integer();
|
| 16630 | if (isNaN(expo)) {
|
| 16631 | push_symbol(POWER);
|
| 16632 | push(p1);
|
| 16633 | push(p2);
|
| 16634 | list(3);
|
| 16635 | return;
|
| 16636 | }
|
| 16637 | x = mpow(p1.q.a, Math.abs(expo));
|
| 16638 | y = mpow(p1.q.b, Math.abs(expo));
|
| 16639 | if (expo < 0) {
|
| 16640 | t = x;
|
| 16641 | x = y;
|
| 16642 | y = t;
|
| 16643 | x = makeSignSameAs(x, y);
|
| 16644 | y = makePositive(y);
|
| 16645 | }
|
| 16646 | p3 = new U();
|
| 16647 | p3.k = NUM;
|
| 16648 | p3.q.a = x;
|
| 16649 | p3.q.b = y;
|
| 16650 | push(p3);
|
| 16651 | return;
|
| 16652 | }
|
| 16653 | if (isminusone(p1)) {
|
| 16654 | push(p2);
|
| 16655 | normalize_angle();
|
| 16656 | return;
|
| 16657 | }
|
| 16658 | if (isnegativenumber(p1)) {
|
| 16659 | push(p1);
|
| 16660 | negate();
|
| 16661 | push(p2);
|
| 16662 | qpow();
|
| 16663 | push_integer(-1);
|
| 16664 | push(p2);
|
| 16665 | qpow();
|
| 16666 | multiply();
|
| 16667 | return;
|
| 16668 | }
|
| 16669 | if (!isinteger(p1)) {
|
| 16670 | push(p1);
|
| 16671 | mp_numerator();
|
| 16672 | push(p2);
|
| 16673 | qpow();
|
| 16674 | push(p1);
|
| 16675 | mp_denominator();
|
| 16676 | push(p2);
|
| 16677 | negate();
|
| 16678 | qpow();
|
| 16679 | multiply();
|
| 16680 | return;
|
| 16681 | }
|
| 16682 | if (is_small_integer(p1)) {
|
| 16683 | push(p1);
|
| 16684 | push(p2);
|
| 16685 | quickfactor();
|
| 16686 | return;
|
| 16687 | }
|
| 16688 | if (!p2.q.a.isSmall || !p2.q.b.isSmall) {
|
| 16689 | push_symbol(POWER);
|
| 16690 | push(p1);
|
| 16691 | push(p2);
|
| 16692 | list(3);
|
| 16693 | return;
|
| 16694 | }
|
| 16695 | a = p2.q.a;
|
| 16696 | b = p2.q.b;
|
| 16697 | x = mroot(p1.q.a, b);
|
| 16698 | if (x === 0) {
|
| 16699 | push_symbol(POWER);
|
| 16700 | push(p1);
|
| 16701 | push(p2);
|
| 16702 | list(3);
|
| 16703 | return;
|
| 16704 | }
|
| 16705 | y = mpow(x, a);
|
| 16706 | p3 = new U();
|
| 16707 | p3.k = NUM;
|
| 16708 | if (p2.q.a.isNegative()) {
|
| 16709 | p3.q.a = bigInt(1);
|
| 16710 | p3.q.b = y;
|
| 16711 | } else {
|
| 16712 | p3.q.a = y;
|
| 16713 | p3.q.b = bigInt(1);
|
| 16714 | }
|
| 16715 | return push(p3);
|
| 16716 | };
|
| 16717 |
|
| 16718 | normalize_angle = function() {
|
| 16719 | save();
|
| 16720 | p1 = pop();
|
| 16721 | if (isinteger(p1)) {
|
| 16722 | if (p1.q.a.isOdd()) {
|
| 16723 | push_integer(-1);
|
| 16724 | } else {
|
| 16725 | push_integer(1);
|
| 16726 | }
|
| 16727 | restore();
|
| 16728 | return;
|
| 16729 | }
|
| 16730 | push(p1);
|
| 16731 | bignum_truncate();
|
| 16732 | p2 = pop();
|
| 16733 | if (isnegativenumber(p1)) {
|
| 16734 | push(p2);
|
| 16735 | push_integer(-1);
|
| 16736 | add();
|
| 16737 | p2 = pop();
|
| 16738 | }
|
| 16739 | push(p1);
|
| 16740 | push(p2);
|
| 16741 | subtract();
|
| 16742 | p3 = pop();
|
| 16743 | push_symbol(POWER);
|
| 16744 | push_integer(-1);
|
| 16745 | push(p3);
|
| 16746 | list(3);
|
| 16747 | if (p2.q.a.isOdd()) {
|
| 16748 | negate();
|
| 16749 | }
|
| 16750 | return restore();
|
| 16751 | };
|
| 16752 |
|
| 16753 | is_small_integer = function(p) {
|
| 16754 | return p.q.a.isSmall;
|
| 16755 | };
|
| 16756 |
|
| 16757 | quickfactor = function() {
|
| 16758 | var h, i, l1, n, ref2, stackIndex;
|
| 16759 | i = 0;
|
| 16760 | save();
|
| 16761 | p2 = pop();
|
| 16762 | p1 = pop();
|
| 16763 | h = tos;
|
| 16764 | push(p1);
|
| 16765 | factor_small_number();
|
| 16766 | n = tos - h;
|
| 16767 | stackIndex = h;
|
| 16768 | for (i = l1 = 0, ref2 = n; l1 < ref2; i = l1 += 2) {
|
| 16769 | push(stack[stackIndex + i]);
|
| 16770 | push(stack[stackIndex + i + 1]);
|
| 16771 | push(p2);
|
| 16772 | multiply();
|
| 16773 | quickpower();
|
| 16774 | }
|
| 16775 | multiply_all(tos - h - n);
|
| 16776 | p1 = pop();
|
| 16777 | moveTos(h);
|
| 16778 | push(p1);
|
| 16779 | return restore();
|
| 16780 | };
|
| 16781 |
|
| 16782 | quickpower = function() {
|
| 16783 | var expo;
|
| 16784 | expo = 0;
|
| 16785 | save();
|
| 16786 | p2 = pop();
|
| 16787 | p1 = pop();
|
| 16788 | push(p2);
|
| 16789 | bignum_truncate();
|
| 16790 | p3 = pop();
|
| 16791 | push(p2);
|
| 16792 | push(p3);
|
| 16793 | subtract();
|
| 16794 | p4 = pop();
|
| 16795 | if (!iszero(p4)) {
|
| 16796 | push_symbol(POWER);
|
| 16797 | push(p1);
|
| 16798 | push(p4);
|
| 16799 | list(3);
|
| 16800 | }
|
| 16801 | push(p3);
|
| 16802 | expo = pop_integer();
|
| 16803 | if (isNaN(expo)) {
|
| 16804 | push_symbol(POWER);
|
| 16805 | push(p1);
|
| 16806 | push(p3);
|
| 16807 | list(3);
|
| 16808 | restore();
|
| 16809 | return;
|
| 16810 | }
|
| 16811 | if (expo === 0) {
|
| 16812 | restore();
|
| 16813 | return;
|
| 16814 | }
|
| 16815 | push(p1);
|
| 16816 | bignum_power_number(expo);
|
| 16817 | return restore();
|
| 16818 | };
|
| 16819 |
|
| 16820 | Eval_quotient = function() {
|
| 16821 | push(cadr(p1));
|
| 16822 | Eval();
|
| 16823 | push(caddr(p1));
|
| 16824 | Eval();
|
| 16825 | push(cadddr(p1));
|
| 16826 | Eval();
|
| 16827 | p1 = pop();
|
| 16828 | if (p1 === symbol(NIL)) {
|
| 16829 | p1 = symbol(SYMBOL_X);
|
| 16830 | }
|
| 16831 | push(p1);
|
| 16832 | return divpoly();
|
| 16833 | };
|
| 16834 |
|
| 16835 | divpoly = function() {
|
| 16836 | var dividend, divisor, h, i, l1, m, n, ref2, x;
|
| 16837 | h = 0;
|
| 16838 | i = 0;
|
| 16839 | m = 0;
|
| 16840 | n = 0;
|
| 16841 | x = 0;
|
| 16842 | save();
|
| 16843 | p3 = pop();
|
| 16844 | p2 = pop();
|
| 16845 | p1 = pop();
|
| 16846 | h = tos;
|
| 16847 | dividend = tos;
|
| 16848 | push(p1);
|
| 16849 | push(p3);
|
| 16850 | m = coeff() - 1;
|
| 16851 | divisor = tos;
|
| 16852 | push(p2);
|
| 16853 | push(p3);
|
| 16854 | n = coeff() - 1;
|
| 16855 | x = m - n;
|
| 16856 | push_integer(0);
|
| 16857 | p5 = pop();
|
| 16858 | while (x >= 0) {
|
| 16859 | push(stack[dividend + m]);
|
| 16860 | push(stack[divisor + n]);
|
| 16861 | divide();
|
| 16862 | p4 = pop();
|
| 16863 | for (i = l1 = 0, ref2 = n; 0 <= ref2 ? l1 <= ref2 : l1 >= ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 16864 | push(stack[dividend + x + i]);
|
| 16865 | push(stack[divisor + i]);
|
| 16866 | push(p4);
|
| 16867 | multiply();
|
| 16868 | subtract();
|
| 16869 | stack[dividend + x + i] = pop();
|
| 16870 | }
|
| 16871 | push(p5);
|
| 16872 | push(p4);
|
| 16873 | push(p3);
|
| 16874 | push_integer(x);
|
| 16875 | power();
|
| 16876 | multiply();
|
| 16877 | add();
|
| 16878 | p5 = pop();
|
| 16879 | m--;
|
| 16880 | x--;
|
| 16881 | }
|
| 16882 | moveTos(h);
|
| 16883 | push(p5);
|
| 16884 | return restore();
|
| 16885 | };
|
| 16886 |
|
| 16887 | Eval_rationalize = function() {
|
| 16888 | push(cadr(p1));
|
| 16889 | Eval();
|
| 16890 | return rationalize();
|
| 16891 | };
|
| 16892 |
|
| 16893 | rationalize = function() {
|
| 16894 | var x;
|
| 16895 | x = expanding;
|
| 16896 | save();
|
| 16897 | yyrationalize();
|
| 16898 | restore();
|
| 16899 | return expanding = x;
|
| 16900 | };
|
| 16901 |
|
| 16902 | yyrationalize = function() {
|
| 16903 | p1 = pop();
|
| 16904 | if (istensor(p1)) {
|
| 16905 | __rationalize_tensor();
|
| 16906 | return;
|
| 16907 | }
|
| 16908 | expanding = 0;
|
| 16909 | if (car(p1) !== symbol(ADD)) {
|
| 16910 | push(p1);
|
| 16911 | return;
|
| 16912 | }
|
| 16913 | if (DEBUG) {
|
| 16914 | printf("rationalize: this is the input expr:\n");
|
| 16915 | printline(p1);
|
| 16916 | }
|
| 16917 | push(one);
|
| 16918 | multiply_denominators(p1);
|
| 16919 | p2 = pop();
|
| 16920 | if (DEBUG) {
|
| 16921 | printf("rationalize: this is the common denominator:\n");
|
| 16922 | printline(p2);
|
| 16923 | }
|
| 16924 | push(zero);
|
| 16925 | p3 = cdr(p1);
|
| 16926 | while (iscons(p3)) {
|
| 16927 | push(p2);
|
| 16928 | push(car(p3));
|
| 16929 | multiply();
|
| 16930 | add();
|
| 16931 | p3 = cdr(p3);
|
| 16932 | }
|
| 16933 | if (DEBUG) {
|
| 16934 | printf("rationalize: original expr times common denominator:\n");
|
| 16935 | printline(stack[tos - 1]);
|
| 16936 | }
|
| 16937 | Condense();
|
| 16938 | if (DEBUG) {
|
| 16939 | printf("rationalize: after factoring:\n");
|
| 16940 | printline(stack[tos - 1]);
|
| 16941 | }
|
| 16942 | push(p2);
|
| 16943 | divide();
|
| 16944 | if (DEBUG) {
|
| 16945 | printf("rationalize: after dividing by common denom. (and we're done):\n");
|
| 16946 | return printline(stack[tos - 1]);
|
| 16947 | }
|
| 16948 | };
|
| 16949 |
|
| 16950 | multiply_denominators = function(p) {
|
| 16951 | var results;
|
| 16952 | if (car(p) === symbol(ADD)) {
|
| 16953 | p = cdr(p);
|
| 16954 | results = [];
|
| 16955 | while (iscons(p)) {
|
| 16956 | multiply_denominators_term(car(p));
|
| 16957 | results.push(p = cdr(p));
|
| 16958 | }
|
| 16959 | return results;
|
| 16960 | } else {
|
| 16961 | return multiply_denominators_term(p);
|
| 16962 | }
|
| 16963 | };
|
| 16964 |
|
| 16965 | multiply_denominators_term = function(p) {
|
| 16966 | var results;
|
| 16967 | if (car(p) === symbol(MULTIPLY)) {
|
| 16968 | p = cdr(p);
|
| 16969 | results = [];
|
| 16970 | while (iscons(p)) {
|
| 16971 | multiply_denominators_factor(car(p));
|
| 16972 | results.push(p = cdr(p));
|
| 16973 | }
|
| 16974 | return results;
|
| 16975 | } else {
|
| 16976 | return multiply_denominators_factor(p);
|
| 16977 | }
|
| 16978 | };
|
| 16979 |
|
| 16980 | multiply_denominators_factor = function(p) {
|
| 16981 | if (car(p) !== symbol(POWER)) {
|
| 16982 | return;
|
| 16983 | }
|
| 16984 | push(p);
|
| 16985 | p = caddr(p);
|
| 16986 | if (isnegativenumber(p)) {
|
| 16987 | inverse();
|
| 16988 | __lcm();
|
| 16989 | return;
|
| 16990 | }
|
| 16991 | if (car(p) === symbol(MULTIPLY) && isnegativenumber(cadr(p))) {
|
| 16992 | inverse();
|
| 16993 | __lcm();
|
| 16994 | return;
|
| 16995 | }
|
| 16996 | return pop();
|
| 16997 | };
|
| 16998 |
|
| 16999 | __rationalize_tensor = function() {
|
| 17000 | var i, l1, n, ref2;
|
| 17001 | i = 0;
|
| 17002 | push(p1);
|
| 17003 | Eval();
|
| 17004 | p1 = pop();
|
| 17005 | if (!istensor(p1)) {
|
| 17006 | push(p1);
|
| 17007 | return;
|
| 17008 | }
|
| 17009 | n = p1.tensor.nelem;
|
| 17010 | for (i = l1 = 0, ref2 = n; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 17011 | push(p1.tensor.elem[i]);
|
| 17012 | rationalize();
|
| 17013 | p1.tensor.elem[i] = pop();
|
| 17014 | }
|
| 17015 | check_tensor_dimensions(p1);
|
| 17016 | return push(p1);
|
| 17017 | };
|
| 17018 |
|
| 17019 | __lcm = function() {
|
| 17020 | save();
|
| 17021 | p1 = pop();
|
| 17022 | p2 = pop();
|
| 17023 | push(p1);
|
| 17024 | push(p2);
|
| 17025 | multiply();
|
| 17026 | push(p1);
|
| 17027 | push(p2);
|
| 17028 | gcd();
|
| 17029 | divide();
|
| 17030 | return restore();
|
| 17031 | };
|
| 17032 |
|
| 17033 |
|
| 17034 | |
| 17035 | |
| 17036 | |
| 17037 | |
| 17038 | |
| 17039 | |
| 17040 | |
| 17041 | |
| 17042 | |
| 17043 |
|
| 17044 |
|
| 17045 | Eval_real = function() {
|
| 17046 | push(cadr(p1));
|
| 17047 | Eval();
|
| 17048 | return real();
|
| 17049 | };
|
| 17050 |
|
| 17051 | real = function() {
|
| 17052 | save();
|
| 17053 | rect();
|
| 17054 | p1 = pop();
|
| 17055 | push(p1);
|
| 17056 | push(p1);
|
| 17057 | conjugate();
|
| 17058 | add();
|
| 17059 | push_integer(2);
|
| 17060 | divide();
|
| 17061 | return restore();
|
| 17062 | };
|
| 17063 |
|
| 17064 |
|
| 17065 | |
| 17066 | |
| 17067 | |
| 17068 | |
| 17069 | |
| 17070 | |
| 17071 |
|
| 17072 |
|
| 17073 | DEBUG_RECT = false;
|
| 17074 |
|
| 17075 | Eval_rect = function() {
|
| 17076 | push(cadr(p1));
|
| 17077 | Eval();
|
| 17078 | return rect();
|
| 17079 | };
|
| 17080 |
|
| 17081 | rect = function() {
|
| 17082 | var input;
|
| 17083 | save();
|
| 17084 | p1 = pop();
|
| 17085 | input = p1;
|
| 17086 | if (DEBUG_RECT) {
|
| 17087 | console.log("RECT of " + input);
|
| 17088 | }
|
| 17089 | if (DEBUG_RECT) {
|
| 17090 | console.log("any clock forms in : " + input + " ? " + findPossibleClockForm(input));
|
| 17091 | }
|
| 17092 | if (issymbol(p1)) {
|
| 17093 | if (DEBUG_RECT) {
|
| 17094 | console.log(" rect: simple symbol: " + input);
|
| 17095 | }
|
| 17096 | if (!iszero(get_binding(symbol(ASSUME_REAL_VARIABLES)))) {
|
| 17097 | push(p1);
|
| 17098 | } else {
|
| 17099 | push_symbol(YYRECT);
|
| 17100 | push(p1);
|
| 17101 | list(2);
|
| 17102 | }
|
| 17103 | } else if (!iszero(get_binding(symbol(ASSUME_REAL_VARIABLES))) && !findPossibleExponentialForm(p1) && !findPossibleClockForm(p1) && !(Find(p1, symbol(SIN)) && Find(p1, symbol(COS)) && Find(p1, imaginaryunit))) {
|
| 17104 | if (DEBUG_RECT) {
|
| 17105 | console.log(" rect: simple symbol: " + input);
|
| 17106 | }
|
| 17107 | push(p1);
|
| 17108 | } else if (car(p1) === symbol(MULTIPLY) && isimaginaryunit(cadr(p1)) && !iszero(get_binding(symbol(ASSUME_REAL_VARIABLES)))) {
|
| 17109 | push(p1);
|
| 17110 | } else if (car(p1) === symbol(ADD)) {
|
| 17111 | if (DEBUG_RECT) {
|
| 17112 | console.log(" rect - " + input + " is a sum ");
|
| 17113 | }
|
| 17114 | push_integer(0);
|
| 17115 | p1 = cdr(p1);
|
| 17116 | while (iscons(p1)) {
|
| 17117 | push(car(p1));
|
| 17118 | rect();
|
| 17119 | add();
|
| 17120 | p1 = cdr(p1);
|
| 17121 | }
|
| 17122 | } else {
|
| 17123 | if (DEBUG_RECT) {
|
| 17124 | console.log(" rect - " + input + " is NOT a sum ");
|
| 17125 | }
|
| 17126 | push(p1);
|
| 17127 | abs();
|
| 17128 | if (DEBUG_RECT) {
|
| 17129 | console.log(" rect - " + input + " abs: " + stack[tos - 1].toString());
|
| 17130 | }
|
| 17131 | push(p1);
|
| 17132 | arg();
|
| 17133 | if (DEBUG_RECT) {
|
| 17134 | console.log(" rect - " + input + " arg of " + p1 + " : " + stack[tos - 1].toString());
|
| 17135 | }
|
| 17136 | p1 = pop();
|
| 17137 | push(p1);
|
| 17138 | cosine();
|
| 17139 | if (DEBUG_RECT) {
|
| 17140 | console.log(" rect - " + input + " cosine: " + stack[tos - 1].toString());
|
| 17141 | }
|
| 17142 | push(imaginaryunit);
|
| 17143 | push(p1);
|
| 17144 | sine();
|
| 17145 | if (DEBUG_RECT) {
|
| 17146 | console.log(" rect - " + input + " sine: " + stack[tos - 1].toString());
|
| 17147 | }
|
| 17148 | multiply();
|
| 17149 | if (DEBUG_RECT) {
|
| 17150 | console.log(" rect - " + input + " i * sine: " + stack[tos - 1].toString());
|
| 17151 | }
|
| 17152 | add();
|
| 17153 | if (DEBUG_RECT) {
|
| 17154 | console.log(" rect - " + input + " cos + i * sine: " + stack[tos - 1].toString());
|
| 17155 | }
|
| 17156 | multiply();
|
| 17157 | }
|
| 17158 | restore();
|
| 17159 | if (DEBUG_RECT) {
|
| 17160 | return console.log("rect of " + input + " : " + stack[tos - 1]);
|
| 17161 | }
|
| 17162 | };
|
| 17163 |
|
| 17164 | show_power_debug = false;
|
| 17165 |
|
| 17166 | performing_roots = false;
|
| 17167 |
|
| 17168 | Eval_roots = function() {
|
| 17169 | p2 = cadr(p1);
|
| 17170 | if (car(p2) === symbol(SETQ) || car(p2) === symbol(TESTEQ)) {
|
| 17171 | push(cadr(p2));
|
| 17172 | Eval();
|
| 17173 | push(caddr(p2));
|
| 17174 | Eval();
|
| 17175 | subtract();
|
| 17176 | } else {
|
| 17177 | push(p2);
|
| 17178 | Eval();
|
| 17179 | p2 = pop();
|
| 17180 | if (car(p2) === symbol(SETQ) || car(p2) === symbol(TESTEQ)) {
|
| 17181 | push(cadr(p2));
|
| 17182 | Eval();
|
| 17183 | push(caddr(p2));
|
| 17184 | Eval();
|
| 17185 | subtract();
|
| 17186 | } else {
|
| 17187 | push(p2);
|
| 17188 | }
|
| 17189 | }
|
| 17190 | push(caddr(p1));
|
| 17191 | Eval();
|
| 17192 | p2 = pop();
|
| 17193 | if (p2 === symbol(NIL)) {
|
| 17194 | guess();
|
| 17195 | } else {
|
| 17196 | push(p2);
|
| 17197 | }
|
| 17198 | p2 = pop();
|
| 17199 | p1 = pop();
|
| 17200 | if (!ispoly(p1, p2)) {
|
| 17201 | stop("roots: 1st argument is not a polynomial");
|
| 17202 | }
|
| 17203 | push(p1);
|
| 17204 | push(p2);
|
| 17205 | return roots();
|
| 17206 | };
|
| 17207 |
|
| 17208 | hasImaginaryCoeff = function(k) {
|
| 17209 | var h, i, imaginaryCoefficients, l1, ref2;
|
| 17210 | imaginaryCoefficients = false;
|
| 17211 | h = tos;
|
| 17212 | for (i = l1 = ref2 = k; l1 > 0; i = l1 += -1) {
|
| 17213 | if (iscomplexnumber(stack[tos - i])) {
|
| 17214 | imaginaryCoefficients = true;
|
| 17215 | break;
|
| 17216 | }
|
| 17217 | }
|
| 17218 | return imaginaryCoefficients;
|
| 17219 | };
|
| 17220 |
|
| 17221 | isSimpleRoot = function(k) {
|
| 17222 | var h, i, isSimpleRootPolynomial, l1, ref2;
|
| 17223 | if (k > 2) {
|
| 17224 | isSimpleRootPolynomial = true;
|
| 17225 | h = tos;
|
| 17226 | if (iszero(stack[tos - k])) {
|
| 17227 | isSimpleRootPolynomial = false;
|
| 17228 | }
|
| 17229 | for (i = l1 = ref2 = k - 1; l1 > 1; i = l1 += -1) {
|
| 17230 | if (!iszero(stack[tos - i])) {
|
| 17231 | isSimpleRootPolynomial = false;
|
| 17232 | break;
|
| 17233 | }
|
| 17234 | }
|
| 17235 | } else {
|
| 17236 | isSimpleRootPolynomial = false;
|
| 17237 | }
|
| 17238 | return isSimpleRootPolynomial;
|
| 17239 | };
|
| 17240 |
|
| 17241 | normalisedCoeff = function() {
|
| 17242 | var divideBy, i, k, l1, m1, miniStack, ref2, ref3;
|
| 17243 | k = coeff();
|
| 17244 | divideBy = stack[tos - 1];
|
| 17245 | miniStack = [];
|
| 17246 | for (i = l1 = 1, ref2 = k; 1 <= ref2 ? l1 <= ref2 : l1 >= ref2; i = 1 <= ref2 ? ++l1 : --l1) {
|
| 17247 | miniStack.push(pop());
|
| 17248 | }
|
| 17249 | for (i = m1 = ref3 = k - 1; ref3 <= 0 ? m1 <= 0 : m1 >= 0; i = ref3 <= 0 ? ++m1 : --m1) {
|
| 17250 | push(miniStack[i]);
|
| 17251 | push(divideBy);
|
| 17252 | divide();
|
| 17253 | }
|
| 17254 | return k;
|
| 17255 | };
|
| 17256 |
|
| 17257 | roots = function() {
|
| 17258 | var h, i, k, l1, lastCoeff, leadingCoeff, n, ref2;
|
| 17259 | h = 0;
|
| 17260 | i = 0;
|
| 17261 | n = 0;
|
| 17262 | save();
|
| 17263 | if (recursionLevelNestedRadicalsRemoval > 1) {
|
| 17264 | pop();
|
| 17265 | pop();
|
| 17266 | push(symbol(NIL));
|
| 17267 | restore();
|
| 17268 | return;
|
| 17269 | }
|
| 17270 | performing_roots = true;
|
| 17271 | h = tos - 2;
|
| 17272 | if (DEBUG) {
|
| 17273 | console.log("checking if " + stack[tos - 1].toString() + " is a case of simple roots");
|
| 17274 | }
|
| 17275 | p2 = pop();
|
| 17276 | p1 = pop();
|
| 17277 | push(p1);
|
| 17278 | push(p2);
|
| 17279 | push(p1);
|
| 17280 | push(p2);
|
| 17281 | k = normalisedCoeff();
|
| 17282 | if (isSimpleRoot(k)) {
|
| 17283 | if (DEBUG) {
|
| 17284 | console.log("yes, " + stack[tos - 1].toString() + " is a case of simple roots");
|
| 17285 | }
|
| 17286 | lastCoeff = stack[tos - k];
|
| 17287 | leadingCoeff = stack[tos - 1];
|
| 17288 | moveTos(tos - k);
|
| 17289 | pop();
|
| 17290 | pop();
|
| 17291 | getSimpleRoots(k, leadingCoeff, lastCoeff);
|
| 17292 | } else {
|
| 17293 | moveTos(tos - k);
|
| 17294 | roots2();
|
| 17295 | }
|
| 17296 | n = tos - h;
|
| 17297 | if (n === 0) {
|
| 17298 | stop("roots: the polynomial is not factorable, try nroots");
|
| 17299 | }
|
| 17300 | if (n === 1) {
|
| 17301 | performing_roots = false;
|
| 17302 | restore();
|
| 17303 | return;
|
| 17304 | }
|
| 17305 | sort_stack(n);
|
| 17306 | p1 = alloc_tensor(n);
|
| 17307 | p1.tensor.ndim = 1;
|
| 17308 | p1.tensor.dim[0] = n;
|
| 17309 | for (i = l1 = 0, ref2 = n; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 17310 | p1.tensor.elem[i] = stack[h + i];
|
| 17311 | }
|
| 17312 | moveTos(h);
|
| 17313 | push(p1);
|
| 17314 | restore();
|
| 17315 | return performing_roots = false;
|
| 17316 | };
|
| 17317 |
|
| 17318 | getSimpleRoots = function(n, leadingCoeff, lastCoeff) {
|
| 17319 | var aSol, commonPart, l1, m1, ref2, ref3, rootsOfOne;
|
| 17320 | if (DEBUG) {
|
| 17321 | console.log("getSimpleRoots");
|
| 17322 | }
|
| 17323 | save();
|
| 17324 | n = n - 1;
|
| 17325 | push(lastCoeff);
|
| 17326 | push_rational(1, n);
|
| 17327 | power();
|
| 17328 | push(leadingCoeff);
|
| 17329 | push_rational(1, n);
|
| 17330 | power();
|
| 17331 | divide();
|
| 17332 | commonPart = pop();
|
| 17333 | if (n % 2 === 0) {
|
| 17334 | for (rootsOfOne = l1 = 1, ref2 = n; l1 <= ref2; rootsOfOne = l1 += 2) {
|
| 17335 | push(commonPart);
|
| 17336 | push_integer(-1);
|
| 17337 | push_rational(rootsOfOne, n);
|
| 17338 | power();
|
| 17339 | multiply();
|
| 17340 | aSol = pop();
|
| 17341 | push(aSol);
|
| 17342 | push(aSol);
|
| 17343 | negate();
|
| 17344 | }
|
| 17345 | } else {
|
| 17346 | for (rootsOfOne = m1 = 1, ref3 = n; 1 <= ref3 ? m1 <= ref3 : m1 >= ref3; rootsOfOne = 1 <= ref3 ? ++m1 : --m1) {
|
| 17347 | push(commonPart);
|
| 17348 | push_integer(-1);
|
| 17349 | push_rational(rootsOfOne, n);
|
| 17350 | power();
|
| 17351 | multiply();
|
| 17352 | if (rootsOfOne % 2 === 0) {
|
| 17353 | negate();
|
| 17354 | }
|
| 17355 | }
|
| 17356 | }
|
| 17357 | return restore();
|
| 17358 | };
|
| 17359 |
|
| 17360 | roots2 = function() {
|
| 17361 | var k;
|
| 17362 | save();
|
| 17363 | p2 = pop();
|
| 17364 | p1 = pop();
|
| 17365 | push(p1);
|
| 17366 | push(p2);
|
| 17367 | push(p1);
|
| 17368 | push(p2);
|
| 17369 | k = normalisedCoeff();
|
| 17370 | if (!hasImaginaryCoeff(k)) {
|
| 17371 | moveTos(tos - k);
|
| 17372 | factorpoly();
|
| 17373 | p1 = pop();
|
| 17374 | } else {
|
| 17375 | moveTos(tos - k);
|
| 17376 | pop();
|
| 17377 | pop();
|
| 17378 | }
|
| 17379 | if (car(p1) === symbol(MULTIPLY)) {
|
| 17380 | p1 = cdr(p1);
|
| 17381 | while (iscons(p1)) {
|
| 17382 | push(car(p1));
|
| 17383 | push(p2);
|
| 17384 | roots3();
|
| 17385 | p1 = cdr(p1);
|
| 17386 | }
|
| 17387 | } else {
|
| 17388 | push(p1);
|
| 17389 | push(p2);
|
| 17390 | roots3();
|
| 17391 | }
|
| 17392 | return restore();
|
| 17393 | };
|
| 17394 |
|
| 17395 | roots3 = function() {
|
| 17396 | var n;
|
| 17397 | save();
|
| 17398 | p2 = pop();
|
| 17399 | p1 = pop();
|
| 17400 | if (car(p1) === symbol(POWER) && ispoly(cadr(p1), p2) && isposint(caddr(p1))) {
|
| 17401 | push(cadr(p1));
|
| 17402 | push(p2);
|
| 17403 | n = normalisedCoeff();
|
| 17404 | mini_solve(n);
|
| 17405 | } else if (ispoly(p1, p2)) {
|
| 17406 | push(p1);
|
| 17407 | push(p2);
|
| 17408 | n = normalisedCoeff();
|
| 17409 | mini_solve(n);
|
| 17410 | }
|
| 17411 | return restore();
|
| 17412 | };
|
| 17413 |
|
| 17414 | mini_solve = function(n) {
|
| 17415 | var C_CHECKED_AS_NOT_ZERO, Q_CHECKED_AS_NOT_ZERO, R_18_a_b_c_d, R_27_a2_d, R_2_b3, R_3_a, R_3_a_C, R_3_a_c, R_4_DELTA03, R_6_a, R_6_a_C, R_C, R_C_over_3a, R_C_simplified_toCheckIfZero, R_DELTA0, R_DELTA0_simplified_toCheckIfZero, R_DELTA0_toBeCheckedIfZero, R_DELTA1, R_Q, R_Q_simplified_toCheckIfZero, R_S, R_S_simplified_toCheckIfZero, R_a2, R_a2_d, R_a2_d2, R_a3, R_a_b_c, R_a_b_c_d, R_a_c, R_b2, R_b2_c2, R_b3, R_b3_d, R_c2, R_c3, R_d2, R_determinant, R_determinant_simplified_toCheckIfZero, R_e2, R_e3, R_m, R_m27_a2_d2, R_m4_a_c3, R_m4_b3_d, R_m9_a_b_c, R_m_b_over_3a, R_minus_4S2_minus_2p, R_minus_b_over_4a, R_p, R_principalCubicRoot, R_q, R_q_over_S, R_r, S_CHECKED_AS_NOT_ZERO, ThreePPlus2M, TwoQOversqrtPPlus2M, biquadraticSolutions, choiceOfRadicalInQSoSIsNotZero, coeff2, coeff3, coeff4, depressedSolutions, eachSolution, flipSignOFQSoCIsNotZero, flipSignOFRadicalSoQIsNotZero, i_sqrt3, l1, len, len1, len2, m1, n1, one_minus_i_sqrt3, one_plus_i_sqrt3, ref2, ref3, ref4, resolventCubicSolutions, root_solution, sqrtPPlus2M, toBeCheckedIFZero;
|
| 17416 | save();
|
| 17417 | if (n === 2) {
|
| 17418 | p3 = pop();
|
| 17419 | p4 = pop();
|
| 17420 | push(p4);
|
| 17421 | push(p3);
|
| 17422 | divide();
|
| 17423 | negate();
|
| 17424 | restore();
|
| 17425 | return;
|
| 17426 | }
|
| 17427 | if (n === 3) {
|
| 17428 | p3 = pop();
|
| 17429 | p4 = pop();
|
| 17430 | p5 = pop();
|
| 17431 | push(p4);
|
| 17432 | push_integer(2);
|
| 17433 | power();
|
| 17434 | push_integer(4);
|
| 17435 | push(p3);
|
| 17436 | multiply();
|
| 17437 | push(p5);
|
| 17438 | multiply();
|
| 17439 | subtract();
|
| 17440 | push_rational(1, 2);
|
| 17441 | power();
|
| 17442 | p6 = pop();
|
| 17443 | push(p6);
|
| 17444 | push(p4);
|
| 17445 | subtract();
|
| 17446 | push(p3);
|
| 17447 | push_integer(2);
|
| 17448 | multiply();
|
| 17449 | divide();
|
| 17450 | push(p6);
|
| 17451 | push(p4);
|
| 17452 | add();
|
| 17453 | negate();
|
| 17454 | push(p3);
|
| 17455 | divide();
|
| 17456 | push_rational(1, 2);
|
| 17457 | multiply();
|
| 17458 | restore();
|
| 17459 | return;
|
| 17460 | }
|
| 17461 | if (n === 4 || n === 5) {
|
| 17462 | p3 = pop();
|
| 17463 | p4 = pop();
|
| 17464 | p5 = pop();
|
| 17465 | p6 = pop();
|
| 17466 | push(p5);
|
| 17467 | push(p5);
|
| 17468 | multiply();
|
| 17469 | R_c2 = pop();
|
| 17470 | push(R_c2);
|
| 17471 | push(p5);
|
| 17472 | multiply();
|
| 17473 | R_c3 = pop();
|
| 17474 | push(p4);
|
| 17475 | push(p4);
|
| 17476 | multiply();
|
| 17477 | R_b2 = pop();
|
| 17478 | push(R_b2);
|
| 17479 | push(p4);
|
| 17480 | multiply();
|
| 17481 | R_b3 = pop();
|
| 17482 | push(R_b3);
|
| 17483 | push(p6);
|
| 17484 | multiply();
|
| 17485 | R_b3_d = pop();
|
| 17486 | push(R_b3_d);
|
| 17487 | push_integer(-4);
|
| 17488 | multiply();
|
| 17489 | R_m4_b3_d = pop();
|
| 17490 | push(R_b3);
|
| 17491 | push_integer(2);
|
| 17492 | multiply();
|
| 17493 | R_2_b3 = pop();
|
| 17494 | push(p3);
|
| 17495 | push(p3);
|
| 17496 | multiply();
|
| 17497 | R_a2 = pop();
|
| 17498 | push(R_a2);
|
| 17499 | push(p3);
|
| 17500 | multiply();
|
| 17501 | R_a3 = pop();
|
| 17502 | push_integer(3);
|
| 17503 | push(p3);
|
| 17504 | multiply();
|
| 17505 | R_3_a = pop();
|
| 17506 | push(R_a2);
|
| 17507 | push(p6);
|
| 17508 | multiply();
|
| 17509 | R_a2_d = pop();
|
| 17510 | push(R_a2_d);
|
| 17511 | push(p6);
|
| 17512 | multiply();
|
| 17513 | R_a2_d2 = pop();
|
| 17514 | push(R_a2_d);
|
| 17515 | push_integer(27);
|
| 17516 | multiply();
|
| 17517 | R_27_a2_d = pop();
|
| 17518 | push(R_a2_d2);
|
| 17519 | push_integer(-27);
|
| 17520 | multiply();
|
| 17521 | R_m27_a2_d2 = pop();
|
| 17522 | push(R_3_a);
|
| 17523 | push_integer(2);
|
| 17524 | multiply();
|
| 17525 | R_6_a = pop();
|
| 17526 | push(p3);
|
| 17527 | push(p5);
|
| 17528 | multiply();
|
| 17529 | R_a_c = pop();
|
| 17530 | push(R_a_c);
|
| 17531 | push(p4);
|
| 17532 | multiply();
|
| 17533 | R_a_b_c = pop();
|
| 17534 | push(R_a_b_c);
|
| 17535 | push(p6);
|
| 17536 | multiply();
|
| 17537 | R_a_b_c_d = pop();
|
| 17538 | push(R_a_c);
|
| 17539 | push_integer(3);
|
| 17540 | multiply();
|
| 17541 | R_3_a_c = pop();
|
| 17542 | push_integer(-4);
|
| 17543 | push(p3);
|
| 17544 | push(R_c3);
|
| 17545 | multiply();
|
| 17546 | multiply();
|
| 17547 | R_m4_a_c3 = pop();
|
| 17548 | push(R_a_b_c);
|
| 17549 | push_integer(9);
|
| 17550 | multiply();
|
| 17551 | negate();
|
| 17552 | R_m9_a_b_c = pop();
|
| 17553 | push(R_a_b_c_d);
|
| 17554 | push_integer(18);
|
| 17555 | multiply();
|
| 17556 | R_18_a_b_c_d = pop();
|
| 17557 | push(R_b2);
|
| 17558 | push(R_3_a_c);
|
| 17559 | subtract();
|
| 17560 | R_DELTA0 = pop();
|
| 17561 | push(R_b2);
|
| 17562 | push(R_c2);
|
| 17563 | multiply();
|
| 17564 | R_b2_c2 = pop();
|
| 17565 | push(p4);
|
| 17566 | negate();
|
| 17567 | push(R_3_a);
|
| 17568 | divide();
|
| 17569 | R_m_b_over_3a = pop();
|
| 17570 | if (n === 4) {
|
| 17571 | if (DEBUG) {
|
| 17572 | console.log(">>>>>>>>>>>>>>>> actually using cubic formula <<<<<<<<<<<<<<< ");
|
| 17573 | }
|
| 17574 | if (DEBUG) {
|
| 17575 | console.log("cubic: D0: " + R_DELTA0.toString());
|
| 17576 | }
|
| 17577 | push(R_DELTA0);
|
| 17578 | push_integer(3);
|
| 17579 | power();
|
| 17580 | push_integer(4);
|
| 17581 | multiply();
|
| 17582 | R_4_DELTA03 = pop();
|
| 17583 | push(R_DELTA0);
|
| 17584 | simplify();
|
| 17585 | absValFloat();
|
| 17586 | R_DELTA0_toBeCheckedIfZero = pop();
|
| 17587 | if (DEBUG) {
|
| 17588 | console.log("cubic: D0 as float: " + R_DELTA0_toBeCheckedIfZero.toString());
|
| 17589 | }
|
| 17590 | push(R_18_a_b_c_d);
|
| 17591 | push(R_m4_b3_d);
|
| 17592 | push(R_b2_c2);
|
| 17593 | push(R_m4_a_c3);
|
| 17594 | push(R_m27_a2_d2);
|
| 17595 | add();
|
| 17596 | add();
|
| 17597 | add();
|
| 17598 | add();
|
| 17599 | simplify();
|
| 17600 | absValFloat();
|
| 17601 | R_determinant = pop();
|
| 17602 | if (DEBUG) {
|
| 17603 | console.log("cubic: DETERMINANT: " + R_determinant.toString());
|
| 17604 | }
|
| 17605 | push(R_2_b3);
|
| 17606 | push(R_m9_a_b_c);
|
| 17607 | push(R_27_a2_d);
|
| 17608 | add();
|
| 17609 | add();
|
| 17610 | R_DELTA1 = pop();
|
| 17611 | if (DEBUG) {
|
| 17612 | console.log("cubic: D1: " + R_DELTA1.toString());
|
| 17613 | }
|
| 17614 | push(R_DELTA1);
|
| 17615 | push_integer(2);
|
| 17616 | power();
|
| 17617 | push(R_4_DELTA03);
|
| 17618 | subtract();
|
| 17619 | push_rational(1, 2);
|
| 17620 | power();
|
| 17621 | simplify();
|
| 17622 | R_Q = pop();
|
| 17623 | if (iszero(R_determinant)) {
|
| 17624 | if (iszero(R_DELTA0_toBeCheckedIfZero)) {
|
| 17625 | if (DEBUG) {
|
| 17626 | console.log(" cubic: DETERMINANT IS ZERO and delta0 is zero");
|
| 17627 | }
|
| 17628 | push(R_m_b_over_3a);
|
| 17629 | restore();
|
| 17630 | return;
|
| 17631 | } else {
|
| 17632 | if (DEBUG) {
|
| 17633 | console.log(" cubic: DETERMINANT IS ZERO and delta0 is not zero");
|
| 17634 | }
|
| 17635 | push(p3);
|
| 17636 | push(p6);
|
| 17637 | push_integer(9);
|
| 17638 | multiply();
|
| 17639 | multiply();
|
| 17640 | push(p4);
|
| 17641 | push(p5);
|
| 17642 | multiply();
|
| 17643 | subtract();
|
| 17644 | push(R_DELTA0);
|
| 17645 | push_integer(2);
|
| 17646 | multiply();
|
| 17647 | divide();
|
| 17648 | root_solution = pop();
|
| 17649 | push(root_solution);
|
| 17650 | push(root_solution);
|
| 17651 | push(R_a_b_c);
|
| 17652 | push_integer(4);
|
| 17653 | multiply();
|
| 17654 | push(p3);
|
| 17655 | push(p3);
|
| 17656 | push(p6);
|
| 17657 | push_integer(9);
|
| 17658 | multiply();
|
| 17659 | multiply();
|
| 17660 | multiply();
|
| 17661 | negate();
|
| 17662 | push(R_b3);
|
| 17663 | negate();
|
| 17664 | add();
|
| 17665 | add();
|
| 17666 | push(p3);
|
| 17667 | push(R_DELTA0);
|
| 17668 | multiply();
|
| 17669 | divide();
|
| 17670 | restore();
|
| 17671 | return;
|
| 17672 | }
|
| 17673 | }
|
| 17674 | C_CHECKED_AS_NOT_ZERO = false;
|
| 17675 | flipSignOFQSoCIsNotZero = false;
|
| 17676 | while (!C_CHECKED_AS_NOT_ZERO) {
|
| 17677 | push(R_Q);
|
| 17678 | if (flipSignOFQSoCIsNotZero) {
|
| 17679 | negate();
|
| 17680 | }
|
| 17681 | push(R_DELTA1);
|
| 17682 | add();
|
| 17683 | push_rational(1, 2);
|
| 17684 | multiply();
|
| 17685 | push_rational(1, 3);
|
| 17686 | power();
|
| 17687 | simplify();
|
| 17688 | R_C = pop();
|
| 17689 | if (DEBUG) {
|
| 17690 | console.log("cubic: C: " + R_C.toString());
|
| 17691 | }
|
| 17692 | push(R_C);
|
| 17693 | simplify();
|
| 17694 | absValFloat();
|
| 17695 | R_C_simplified_toCheckIfZero = pop();
|
| 17696 | if (DEBUG) {
|
| 17697 | console.log("cubic: C as absval and float: " + R_C_simplified_toCheckIfZero.toString());
|
| 17698 | }
|
| 17699 | if (iszero(R_C_simplified_toCheckIfZero)) {
|
| 17700 | if (DEBUG) {
|
| 17701 | console.log(" cubic: C IS ZERO flipping the sign");
|
| 17702 | }
|
| 17703 | flipSignOFQSoCIsNotZero = true;
|
| 17704 | } else {
|
| 17705 | C_CHECKED_AS_NOT_ZERO = true;
|
| 17706 | }
|
| 17707 | }
|
| 17708 | push(R_C);
|
| 17709 | push(R_3_a);
|
| 17710 | multiply();
|
| 17711 | R_3_a_C = pop();
|
| 17712 | push(R_3_a_C);
|
| 17713 | push_integer(2);
|
| 17714 | multiply();
|
| 17715 | R_6_a_C = pop();
|
| 17716 | push(imaginaryunit);
|
| 17717 | push_integer(3);
|
| 17718 | push_rational(1, 2);
|
| 17719 | power();
|
| 17720 | multiply();
|
| 17721 | i_sqrt3 = pop();
|
| 17722 | push_integer(1);
|
| 17723 | push(i_sqrt3);
|
| 17724 | add();
|
| 17725 | one_plus_i_sqrt3 = pop();
|
| 17726 | push_integer(1);
|
| 17727 | push(i_sqrt3);
|
| 17728 | subtract();
|
| 17729 | one_minus_i_sqrt3 = pop();
|
| 17730 | push(R_C);
|
| 17731 | push(R_3_a);
|
| 17732 | divide();
|
| 17733 | R_C_over_3a = pop();
|
| 17734 | push(R_m_b_over_3a);
|
| 17735 | push(R_C_over_3a);
|
| 17736 | negate();
|
| 17737 | push(R_DELTA0);
|
| 17738 | push(R_3_a_C);
|
| 17739 | divide();
|
| 17740 | negate();
|
| 17741 | add();
|
| 17742 | add();
|
| 17743 | simplify();
|
| 17744 | push(R_m_b_over_3a);
|
| 17745 | push(R_C_over_3a);
|
| 17746 | push(one_plus_i_sqrt3);
|
| 17747 | multiply();
|
| 17748 | push_integer(2);
|
| 17749 | divide();
|
| 17750 | push(one_minus_i_sqrt3);
|
| 17751 | push(R_DELTA0);
|
| 17752 | multiply();
|
| 17753 | push(R_6_a_C);
|
| 17754 | divide();
|
| 17755 | add();
|
| 17756 | add();
|
| 17757 | simplify();
|
| 17758 | push(R_m_b_over_3a);
|
| 17759 | push(R_C_over_3a);
|
| 17760 | push(one_minus_i_sqrt3);
|
| 17761 | multiply();
|
| 17762 | push_integer(2);
|
| 17763 | divide();
|
| 17764 | push(one_plus_i_sqrt3);
|
| 17765 | push(R_DELTA0);
|
| 17766 | multiply();
|
| 17767 | push(R_6_a_C);
|
| 17768 | divide();
|
| 17769 | add();
|
| 17770 | add();
|
| 17771 | simplify();
|
| 17772 | restore();
|
| 17773 | return;
|
| 17774 | }
|
| 17775 | if (n === 5) {
|
| 17776 | if (DEBUG) {
|
| 17777 | console.log(">>>>>>>>>>>>>>>> actually using quartic formula <<<<<<<<<<<<<<< ");
|
| 17778 | }
|
| 17779 | p7 = pop();
|
| 17780 | if (iszero(p4) && iszero(p6) && !iszero(p5) && !iszero(p7)) {
|
| 17781 | if (DEBUG) {
|
| 17782 | console.log("biquadratic case");
|
| 17783 | }
|
| 17784 | push(p3);
|
| 17785 | push(symbol(SECRETX));
|
| 17786 | push_integer(2);
|
| 17787 | power();
|
| 17788 | multiply();
|
| 17789 | push(p5);
|
| 17790 | push(symbol(SECRETX));
|
| 17791 | multiply();
|
| 17792 | push(p7);
|
| 17793 | add();
|
| 17794 | add();
|
| 17795 | push(symbol(SECRETX));
|
| 17796 | roots();
|
| 17797 | biquadraticSolutions = pop();
|
| 17798 | ref2 = biquadraticSolutions.tensor.elem;
|
| 17799 | for (l1 = 0, len = ref2.length; l1 < len; l1++) {
|
| 17800 | eachSolution = ref2[l1];
|
| 17801 | push(eachSolution);
|
| 17802 | push_rational(1, 2);
|
| 17803 | power();
|
| 17804 | simplify();
|
| 17805 | push(eachSolution);
|
| 17806 | push_rational(1, 2);
|
| 17807 | power();
|
| 17808 | negate();
|
| 17809 | simplify();
|
| 17810 | }
|
| 17811 | restore();
|
| 17812 | return;
|
| 17813 | }
|
| 17814 | push(p6);
|
| 17815 | push(p6);
|
| 17816 | multiply();
|
| 17817 | R_d2 = pop();
|
| 17818 | push(p7);
|
| 17819 | push(p7);
|
| 17820 | multiply();
|
| 17821 | R_e2 = pop();
|
| 17822 | push(R_e2);
|
| 17823 | push(p7);
|
| 17824 | multiply();
|
| 17825 | R_e3 = pop();
|
| 17826 | push_integer(256);
|
| 17827 | push(R_a3);
|
| 17828 | push(R_e3);
|
| 17829 | multiply();
|
| 17830 | multiply();
|
| 17831 | push_integer(-192);
|
| 17832 | push(R_a2_d);
|
| 17833 | push(R_e2);
|
| 17834 | push(p4);
|
| 17835 | multiply();
|
| 17836 | multiply();
|
| 17837 | multiply();
|
| 17838 | push_integer(-128);
|
| 17839 | push(R_a2);
|
| 17840 | push(R_c2);
|
| 17841 | push(R_e2);
|
| 17842 | multiply();
|
| 17843 | multiply();
|
| 17844 | multiply();
|
| 17845 | push_integer(144);
|
| 17846 | push(R_a2_d2);
|
| 17847 | push(p5);
|
| 17848 | push(p7);
|
| 17849 | multiply();
|
| 17850 | multiply();
|
| 17851 | multiply();
|
| 17852 | push(R_m27_a2_d2);
|
| 17853 | push(R_d2);
|
| 17854 | multiply();
|
| 17855 | push_integer(144);
|
| 17856 | push(R_a_b_c);
|
| 17857 | push(p4);
|
| 17858 | push(R_e2);
|
| 17859 | multiply();
|
| 17860 | multiply();
|
| 17861 | multiply();
|
| 17862 | push_integer(-6);
|
| 17863 | push(p3);
|
| 17864 | push(R_b2);
|
| 17865 | push(R_d2);
|
| 17866 | push(p7);
|
| 17867 | multiply();
|
| 17868 | multiply();
|
| 17869 | multiply();
|
| 17870 | multiply();
|
| 17871 | push_integer(-80);
|
| 17872 | push(R_a_b_c_d);
|
| 17873 | push(p5);
|
| 17874 | push(p7);
|
| 17875 | multiply();
|
| 17876 | multiply();
|
| 17877 | multiply();
|
| 17878 | push_integer(18);
|
| 17879 | push(R_a_b_c_d);
|
| 17880 | push(R_d2);
|
| 17881 | multiply();
|
| 17882 | multiply();
|
| 17883 | push_integer(16);
|
| 17884 | push(R_a_c);
|
| 17885 | push(R_c3);
|
| 17886 | push(p7);
|
| 17887 | multiply();
|
| 17888 | multiply();
|
| 17889 | multiply();
|
| 17890 | push_integer(-4);
|
| 17891 | push(R_a_c);
|
| 17892 | push(R_c2);
|
| 17893 | push(R_d2);
|
| 17894 | multiply();
|
| 17895 | multiply();
|
| 17896 | multiply();
|
| 17897 | push_integer(-27);
|
| 17898 | push(R_b3);
|
| 17899 | push(p4);
|
| 17900 | push(R_e2);
|
| 17901 | multiply();
|
| 17902 | multiply();
|
| 17903 | multiply();
|
| 17904 | push_integer(18);
|
| 17905 | push(R_b3_d);
|
| 17906 | push(p5);
|
| 17907 | push(p7);
|
| 17908 | multiply();
|
| 17909 | multiply();
|
| 17910 | multiply();
|
| 17911 | push(R_m4_b3_d);
|
| 17912 | push(R_d2);
|
| 17913 | multiply();
|
| 17914 | push_integer(-4);
|
| 17915 | push(R_b2_c2);
|
| 17916 | push(p5);
|
| 17917 | push(p7);
|
| 17918 | multiply();
|
| 17919 | multiply();
|
| 17920 | multiply();
|
| 17921 | push(R_b2_c2);
|
| 17922 | push(R_d2);
|
| 17923 | multiply();
|
| 17924 | add();
|
| 17925 | add();
|
| 17926 | add();
|
| 17927 | add();
|
| 17928 | add();
|
| 17929 | add();
|
| 17930 | add();
|
| 17931 | add();
|
| 17932 | add();
|
| 17933 | add();
|
| 17934 | add();
|
| 17935 | add();
|
| 17936 | add();
|
| 17937 | add();
|
| 17938 | add();
|
| 17939 | R_determinant = pop();
|
| 17940 | if (DEBUG) {
|
| 17941 | console.log("R_determinant: " + R_determinant.toString());
|
| 17942 | }
|
| 17943 | push(R_c2);
|
| 17944 | push_integer(-3);
|
| 17945 | push(p4);
|
| 17946 | push(p6);
|
| 17947 | multiply();
|
| 17948 | multiply();
|
| 17949 | push_integer(12);
|
| 17950 | push(p3);
|
| 17951 | push(p7);
|
| 17952 | multiply();
|
| 17953 | multiply();
|
| 17954 | add();
|
| 17955 | add();
|
| 17956 | R_DELTA0 = pop();
|
| 17957 | if (DEBUG) {
|
| 17958 | console.log("R_DELTA0: " + R_DELTA0.toString());
|
| 17959 | }
|
| 17960 | push_integer(2);
|
| 17961 | push(R_c3);
|
| 17962 | multiply();
|
| 17963 | push_integer(-9);
|
| 17964 | push(p4);
|
| 17965 | push(p5);
|
| 17966 | push(p6);
|
| 17967 | multiply();
|
| 17968 | multiply();
|
| 17969 | multiply();
|
| 17970 | push_integer(27);
|
| 17971 | push(R_b2);
|
| 17972 | push(p7);
|
| 17973 | multiply();
|
| 17974 | multiply();
|
| 17975 | push_integer(27);
|
| 17976 | push(p3);
|
| 17977 | push(R_d2);
|
| 17978 | multiply();
|
| 17979 | multiply();
|
| 17980 | push_integer(-72);
|
| 17981 | push(R_a_c);
|
| 17982 | push(p7);
|
| 17983 | multiply();
|
| 17984 | multiply();
|
| 17985 | add();
|
| 17986 | add();
|
| 17987 | add();
|
| 17988 | add();
|
| 17989 | R_DELTA1 = pop();
|
| 17990 | if (DEBUG) {
|
| 17991 | console.log("R_DELTA1: " + R_DELTA1.toString());
|
| 17992 | }
|
| 17993 | push_integer(8);
|
| 17994 | push(R_a_c);
|
| 17995 | multiply();
|
| 17996 | push_integer(-3);
|
| 17997 | push(R_b2);
|
| 17998 | multiply();
|
| 17999 | add();
|
| 18000 | push_integer(8);
|
| 18001 | push(R_a2);
|
| 18002 | multiply();
|
| 18003 | divide();
|
| 18004 | R_p = pop();
|
| 18005 | if (DEBUG) {
|
| 18006 | console.log("p: " + R_p.toString());
|
| 18007 | }
|
| 18008 | push(R_b3);
|
| 18009 | push_integer(-4);
|
| 18010 | push(R_a_b_c);
|
| 18011 | multiply();
|
| 18012 | push_integer(8);
|
| 18013 | push(R_a2_d);
|
| 18014 | multiply();
|
| 18015 | add();
|
| 18016 | add();
|
| 18017 | push_integer(8);
|
| 18018 | push(R_a3);
|
| 18019 | multiply();
|
| 18020 | divide();
|
| 18021 | R_q = pop();
|
| 18022 | if (DEBUG) {
|
| 18023 | console.log("q: " + R_q.toString());
|
| 18024 | }
|
| 18025 | if (DEBUG) {
|
| 18026 | console.log("tos 1 " + tos);
|
| 18027 | }
|
| 18028 | if (!iszero(p4)) {
|
| 18029 | if (DEBUG) {
|
| 18030 | console.log("tos 2 " + tos);
|
| 18031 | }
|
| 18032 | push_integer(8);
|
| 18033 | push(p5);
|
| 18034 | push(p3);
|
| 18035 | multiply();
|
| 18036 | multiply();
|
| 18037 | push_integer(-3);
|
| 18038 | push(p4);
|
| 18039 | push_integer(2);
|
| 18040 | power();
|
| 18041 | multiply();
|
| 18042 | add();
|
| 18043 | push_integer(8);
|
| 18044 | push(p3);
|
| 18045 | push_integer(2);
|
| 18046 | power();
|
| 18047 | multiply();
|
| 18048 | divide();
|
| 18049 | R_p = pop();
|
| 18050 | if (DEBUG) {
|
| 18051 | console.log("p for depressed quartic: " + R_p.toString());
|
| 18052 | }
|
| 18053 | push(p4);
|
| 18054 | push_integer(3);
|
| 18055 | power();
|
| 18056 | push_integer(-4);
|
| 18057 | push(p3);
|
| 18058 | push(p4);
|
| 18059 | push(p5);
|
| 18060 | multiply();
|
| 18061 | multiply();
|
| 18062 | multiply();
|
| 18063 | push_integer(8);
|
| 18064 | push(p6);
|
| 18065 | push(p3);
|
| 18066 | push_integer(2);
|
| 18067 | power();
|
| 18068 | multiply();
|
| 18069 | multiply();
|
| 18070 | add();
|
| 18071 | add();
|
| 18072 | push_integer(8);
|
| 18073 | push(p3);
|
| 18074 | push_integer(3);
|
| 18075 | power();
|
| 18076 | multiply();
|
| 18077 | divide();
|
| 18078 | R_q = pop();
|
| 18079 | if (DEBUG) {
|
| 18080 | console.log("q for depressed quartic: " + R_q.toString());
|
| 18081 | }
|
| 18082 | push(p4);
|
| 18083 | push_integer(4);
|
| 18084 | power();
|
| 18085 | push_integer(-3);
|
| 18086 | multiply();
|
| 18087 | push_integer(256);
|
| 18088 | push(R_a3);
|
| 18089 | push(p7);
|
| 18090 | multiply();
|
| 18091 | multiply();
|
| 18092 | push_integer(-64);
|
| 18093 | push(R_a2_d);
|
| 18094 | push(p4);
|
| 18095 | multiply();
|
| 18096 | multiply();
|
| 18097 | push_integer(16);
|
| 18098 | push(R_b2);
|
| 18099 | push(p3);
|
| 18100 | push(p5);
|
| 18101 | multiply();
|
| 18102 | multiply();
|
| 18103 | multiply();
|
| 18104 | add();
|
| 18105 | add();
|
| 18106 | add();
|
| 18107 | push_integer(256);
|
| 18108 | push(p3);
|
| 18109 | push_integer(4);
|
| 18110 | power();
|
| 18111 | multiply();
|
| 18112 | divide();
|
| 18113 | R_r = pop();
|
| 18114 | if (DEBUG) {
|
| 18115 | console.log("r for depressed quartic: " + R_r.toString());
|
| 18116 | }
|
| 18117 | if (DEBUG) {
|
| 18118 | console.log("tos 4 " + tos);
|
| 18119 | }
|
| 18120 | push(symbol(SECRETX));
|
| 18121 | push_integer(4);
|
| 18122 | power();
|
| 18123 | if (DEBUG) {
|
| 18124 | console.log("4 * x^4: " + stack[tos - 1].toString());
|
| 18125 | }
|
| 18126 | push(R_p);
|
| 18127 | push(symbol(SECRETX));
|
| 18128 | push_integer(2);
|
| 18129 | power();
|
| 18130 | multiply();
|
| 18131 | if (DEBUG) {
|
| 18132 | console.log("R_p * x^2: " + stack[tos - 1].toString());
|
| 18133 | }
|
| 18134 | push(R_q);
|
| 18135 | push(symbol(SECRETX));
|
| 18136 | multiply();
|
| 18137 | if (DEBUG) {
|
| 18138 | console.log("R_q * x: " + stack[tos - 1].toString());
|
| 18139 | }
|
| 18140 | push(R_r);
|
| 18141 | if (DEBUG) {
|
| 18142 | console.log("R_r: " + stack[tos - 1].toString());
|
| 18143 | }
|
| 18144 | add();
|
| 18145 | add();
|
| 18146 | add();
|
| 18147 | simplify();
|
| 18148 | if (DEBUG) {
|
| 18149 | console.log("solving depressed quartic: " + stack[tos - 1].toString());
|
| 18150 | }
|
| 18151 | push(symbol(SECRETX));
|
| 18152 | roots();
|
| 18153 | depressedSolutions = pop();
|
| 18154 | if (DEBUG) {
|
| 18155 | console.log("depressedSolutions: " + depressedSolutions);
|
| 18156 | }
|
| 18157 | ref3 = depressedSolutions.tensor.elem;
|
| 18158 | for (m1 = 0, len1 = ref3.length; m1 < len1; m1++) {
|
| 18159 | eachSolution = ref3[m1];
|
| 18160 | push(eachSolution);
|
| 18161 | push(p4);
|
| 18162 | push_integer(4);
|
| 18163 | push(p3);
|
| 18164 | multiply();
|
| 18165 | divide();
|
| 18166 | subtract();
|
| 18167 | simplify();
|
| 18168 | if (DEBUG) {
|
| 18169 | console.log("solution from depressed: " + stack[tos - 1].toString());
|
| 18170 | }
|
| 18171 | }
|
| 18172 | restore();
|
| 18173 | return;
|
| 18174 | } else {
|
| 18175 | R_p = p5;
|
| 18176 | R_q = p6;
|
| 18177 | R_r = p7;
|
| 18178 |
|
| 18179 | |
| 18180 | |
| 18181 | |
| 18182 | |
| 18183 | |
| 18184 | |
| 18185 | |
| 18186 | |
| 18187 | |
| 18188 | |
| 18189 | |
| 18190 | |
| 18191 | |
| 18192 | |
| 18193 | |
| 18194 | |
| 18195 | |
| 18196 | |
| 18197 | |
| 18198 | |
| 18199 | |
| 18200 | |
| 18201 | |
| 18202 | |
| 18203 | |
| 18204 | |
| 18205 | |
| 18206 | |
| 18207 | |
| 18208 | |
| 18209 | |
| 18210 | |
| 18211 | |
| 18212 | |
| 18213 | |
| 18214 | |
| 18215 | |
| 18216 | |
| 18217 | |
| 18218 | |
| 18219 | |
| 18220 | |
| 18221 | |
| 18222 | |
| 18223 | |
| 18224 | |
| 18225 | |
| 18226 | |
| 18227 | |
| 18228 | |
| 18229 | |
| 18230 | |
| 18231 | |
| 18232 | |
| 18233 | |
| 18234 | |
| 18235 | |
| 18236 | |
| 18237 | |
| 18238 | |
| 18239 | |
| 18240 | |
| 18241 | |
| 18242 | |
| 18243 | |
| 18244 | |
| 18245 | |
| 18246 | |
| 18247 | |
| 18248 | |
| 18249 | |
| 18250 | |
| 18251 | |
| 18252 | |
| 18253 | |
| 18254 | |
| 18255 | |
| 18256 | |
| 18257 | |
| 18258 | |
| 18259 | |
| 18260 | |
| 18261 | |
| 18262 | |
| 18263 | |
| 18264 | |
| 18265 | |
| 18266 | |
| 18267 | |
| 18268 | |
| 18269 | |
| 18270 | |
| 18271 | |
| 18272 | |
| 18273 | |
| 18274 | |
| 18275 | |
| 18276 | |
| 18277 | |
| 18278 | |
| 18279 | |
| 18280 | |
| 18281 | |
| 18282 | |
| 18283 | |
| 18284 | |
| 18285 | |
| 18286 | |
| 18287 | |
| 18288 | |
| 18289 | |
| 18290 | |
| 18291 | |
| 18292 | |
| 18293 | |
| 18294 | |
| 18295 | |
| 18296 | |
| 18297 | |
| 18298 | |
| 18299 | |
| 18300 | |
| 18301 | |
| 18302 | |
| 18303 | |
| 18304 | |
| 18305 | |
| 18306 | |
| 18307 | |
| 18308 | |
| 18309 | |
| 18310 | |
| 18311 | |
| 18312 | |
| 18313 | |
| 18314 | |
| 18315 | |
| 18316 | |
| 18317 | |
| 18318 | |
| 18319 |
|
| 18320 | push_rational(5, 2);
|
| 18321 | push(R_p);
|
| 18322 | multiply();
|
| 18323 | coeff2 = pop();
|
| 18324 | push_integer(2);
|
| 18325 | push(R_p);
|
| 18326 | push_integer(2);
|
| 18327 | power();
|
| 18328 | multiply();
|
| 18329 | push(R_r);
|
| 18330 | subtract();
|
| 18331 | coeff3 = pop();
|
| 18332 | push(R_p);
|
| 18333 | push_integer(3);
|
| 18334 | power();
|
| 18335 | push_integer(2);
|
| 18336 | divide();
|
| 18337 | push_rational(-1, 2);
|
| 18338 | push(R_p);
|
| 18339 | push(R_r);
|
| 18340 | multiply();
|
| 18341 | multiply();
|
| 18342 | push_rational(-1, 8);
|
| 18343 | push(R_q);
|
| 18344 | push_integer(2);
|
| 18345 | power();
|
| 18346 | multiply();
|
| 18347 | add();
|
| 18348 | add();
|
| 18349 | coeff4 = pop();
|
| 18350 | push(symbol(SECRETX));
|
| 18351 | push_integer(3);
|
| 18352 | power();
|
| 18353 | push(coeff2);
|
| 18354 | push(symbol(SECRETX));
|
| 18355 | push_integer(2);
|
| 18356 | power();
|
| 18357 | multiply();
|
| 18358 | push(coeff3);
|
| 18359 | push(symbol(SECRETX));
|
| 18360 | multiply();
|
| 18361 | push(coeff4);
|
| 18362 | add();
|
| 18363 | add();
|
| 18364 | add();
|
| 18365 | if (DEBUG) {
|
| 18366 | console.log("resolventCubic: " + stack[tos - 1].toString());
|
| 18367 | }
|
| 18368 | push(symbol(SECRETX));
|
| 18369 | roots();
|
| 18370 | resolventCubicSolutions = pop();
|
| 18371 | if (DEBUG) {
|
| 18372 | console.log("resolventCubicSolutions: " + resolventCubicSolutions);
|
| 18373 | }
|
| 18374 | R_m = null;
|
| 18375 | ref4 = resolventCubicSolutions.tensor.elem;
|
| 18376 | for (n1 = 0, len2 = ref4.length; n1 < len2; n1++) {
|
| 18377 | eachSolution = ref4[n1];
|
| 18378 | if (DEBUG) {
|
| 18379 | console.log("examining solution: " + eachSolution);
|
| 18380 | }
|
| 18381 | push(eachSolution);
|
| 18382 | push_integer(2);
|
| 18383 | multiply();
|
| 18384 | push(R_p);
|
| 18385 | add();
|
| 18386 | absValFloat();
|
| 18387 | toBeCheckedIFZero = pop();
|
| 18388 | if (DEBUG) {
|
| 18389 | console.log("abs value is: " + eachSolution);
|
| 18390 | }
|
| 18391 | if (!iszero(toBeCheckedIFZero)) {
|
| 18392 | R_m = eachSolution;
|
| 18393 | break;
|
| 18394 | }
|
| 18395 | }
|
| 18396 | if (DEBUG) {
|
| 18397 | console.log("chosen solution: " + R_m);
|
| 18398 | }
|
| 18399 | push(R_m);
|
| 18400 | push_integer(2);
|
| 18401 | multiply();
|
| 18402 | push(R_p);
|
| 18403 | add();
|
| 18404 | push_rational(1, 2);
|
| 18405 | power();
|
| 18406 | simplify();
|
| 18407 | sqrtPPlus2M = pop();
|
| 18408 | push(R_q);
|
| 18409 | push_integer(2);
|
| 18410 | multiply();
|
| 18411 | push(sqrtPPlus2M);
|
| 18412 | divide();
|
| 18413 | simplify();
|
| 18414 | TwoQOversqrtPPlus2M = pop();
|
| 18415 | push(R_p);
|
| 18416 | push_integer(3);
|
| 18417 | multiply();
|
| 18418 | push(R_m);
|
| 18419 | push_integer(2);
|
| 18420 | multiply();
|
| 18421 | add();
|
| 18422 | ThreePPlus2M = pop();
|
| 18423 | push(sqrtPPlus2M);
|
| 18424 | push(ThreePPlus2M);
|
| 18425 | push(TwoQOversqrtPPlus2M);
|
| 18426 | add();
|
| 18427 | negate();
|
| 18428 | push_rational(1, 2);
|
| 18429 | power();
|
| 18430 | simplify();
|
| 18431 | add();
|
| 18432 | push_integer(2);
|
| 18433 | divide();
|
| 18434 | push(sqrtPPlus2M);
|
| 18435 | push(ThreePPlus2M);
|
| 18436 | push(TwoQOversqrtPPlus2M);
|
| 18437 | add();
|
| 18438 | negate();
|
| 18439 | push_rational(1, 2);
|
| 18440 | power();
|
| 18441 | simplify();
|
| 18442 | subtract();
|
| 18443 | push_integer(2);
|
| 18444 | divide();
|
| 18445 | push(sqrtPPlus2M);
|
| 18446 | negate();
|
| 18447 | push(ThreePPlus2M);
|
| 18448 | push(TwoQOversqrtPPlus2M);
|
| 18449 | subtract();
|
| 18450 | negate();
|
| 18451 | push_rational(1, 2);
|
| 18452 | power();
|
| 18453 | simplify();
|
| 18454 | add();
|
| 18455 | push_integer(2);
|
| 18456 | divide();
|
| 18457 | push(sqrtPPlus2M);
|
| 18458 | negate();
|
| 18459 | push(ThreePPlus2M);
|
| 18460 | push(TwoQOversqrtPPlus2M);
|
| 18461 | subtract();
|
| 18462 | negate();
|
| 18463 | push_rational(1, 2);
|
| 18464 | power();
|
| 18465 | simplify();
|
| 18466 | subtract();
|
| 18467 | push_integer(2);
|
| 18468 | divide();
|
| 18469 | restore();
|
| 18470 | return;
|
| 18471 | }
|
| 18472 | push(R_determinant);
|
| 18473 | simplify();
|
| 18474 | absValFloat();
|
| 18475 | R_determinant_simplified_toCheckIfZero = pop();
|
| 18476 | push(R_DELTA0);
|
| 18477 | simplify();
|
| 18478 | absValFloat();
|
| 18479 | R_DELTA0_simplified_toCheckIfZero = pop();
|
| 18480 | S_CHECKED_AS_NOT_ZERO = false;
|
| 18481 | choiceOfRadicalInQSoSIsNotZero = 0;
|
| 18482 | while (!S_CHECKED_AS_NOT_ZERO) {
|
| 18483 | Q_CHECKED_AS_NOT_ZERO = false;
|
| 18484 | flipSignOFRadicalSoQIsNotZero = false;
|
| 18485 | while (!Q_CHECKED_AS_NOT_ZERO) {
|
| 18486 | push(R_DELTA1);
|
| 18487 | push(R_DELTA1);
|
| 18488 | push_integer(2);
|
| 18489 | power();
|
| 18490 | push_integer(-4);
|
| 18491 | push(R_DELTA0);
|
| 18492 | push_integer(3);
|
| 18493 | power();
|
| 18494 | multiply();
|
| 18495 | add();
|
| 18496 | push_rational(1, 2);
|
| 18497 | power();
|
| 18498 | if (flipSignOFRadicalSoQIsNotZero) {
|
| 18499 | negate();
|
| 18500 | }
|
| 18501 | add();
|
| 18502 | push_integer(2);
|
| 18503 | divide();
|
| 18504 | if (DEBUG) {
|
| 18505 | console.log("content of cubic root: " + stack[tos - 1].toString());
|
| 18506 | }
|
| 18507 | push_rational(1, 3);
|
| 18508 | power();
|
| 18509 | simplify();
|
| 18510 | R_principalCubicRoot = pop();
|
| 18511 | if (DEBUG) {
|
| 18512 | console.log("principal cubic root: " + R_principalCubicRoot.toString());
|
| 18513 | }
|
| 18514 | if (DEBUG) {
|
| 18515 | console.log("tos : " + tos);
|
| 18516 | }
|
| 18517 | if (choiceOfRadicalInQSoSIsNotZero === 0) {
|
| 18518 | if (DEBUG) {
|
| 18519 | console.log("chosing principal cubic root");
|
| 18520 | }
|
| 18521 | push(R_principalCubicRoot);
|
| 18522 | } else if (choiceOfRadicalInQSoSIsNotZero === 1) {
|
| 18523 | if (DEBUG) {
|
| 18524 | console.log("chosing cubic root beyond principal");
|
| 18525 | }
|
| 18526 | push(R_principalCubicRoot);
|
| 18527 | push_rational(-1, 2);
|
| 18528 | multiply();
|
| 18529 | push_integer(3);
|
| 18530 | push_rational(1, 2);
|
| 18531 | power();
|
| 18532 | push(imaginaryunit);
|
| 18533 | multiply();
|
| 18534 | push_rational(-1, 2);
|
| 18535 | multiply();
|
| 18536 | push(R_principalCubicRoot);
|
| 18537 | multiply();
|
| 18538 | add();
|
| 18539 | } else if (choiceOfRadicalInQSoSIsNotZero === 1) {
|
| 18540 | if (DEBUG) {
|
| 18541 | console.log("chosing cubic root beyond beyond principal");
|
| 18542 | }
|
| 18543 | push(R_principalCubicRoot);
|
| 18544 | push_rational(-1, 2);
|
| 18545 | multiply();
|
| 18546 | push_integer(3);
|
| 18547 | push_rational(1, 2);
|
| 18548 | power();
|
| 18549 | push(imaginaryunit);
|
| 18550 | multiply();
|
| 18551 | push_rational(1, 2);
|
| 18552 | multiply();
|
| 18553 | push(R_principalCubicRoot);
|
| 18554 | multiply();
|
| 18555 | add();
|
| 18556 | }
|
| 18557 | simplify();
|
| 18558 | R_Q = pop();
|
| 18559 | if (DEBUG) {
|
| 18560 | console.log("Q " + R_Q.toString());
|
| 18561 | }
|
| 18562 | if (DEBUG) {
|
| 18563 | console.log("tos: " + tos);
|
| 18564 | }
|
| 18565 | push(R_Q);
|
| 18566 | simplify();
|
| 18567 | absValFloat();
|
| 18568 | R_Q_simplified_toCheckIfZero = pop();
|
| 18569 | if (DEBUG) {
|
| 18570 | console.log("Q simplified and abs" + R_Q_simplified_toCheckIfZero.toString());
|
| 18571 | }
|
| 18572 | if (iszero(R_Q_simplified_toCheckIfZero) && (!iszero(R_determinant_simplified_toCheckIfZero) && iszero(R_DELTA0_simplified_toCheckIfZero))) {
|
| 18573 | if (DEBUG) {
|
| 18574 | console.log(" *********************************** Q IS ZERO and it matters, flipping the sign");
|
| 18575 | }
|
| 18576 | flipSignOFRadicalSoQIsNotZero = true;
|
| 18577 | } else {
|
| 18578 | Q_CHECKED_AS_NOT_ZERO = true;
|
| 18579 | }
|
| 18580 | if (DEBUG) {
|
| 18581 | console.log("tos: " + tos);
|
| 18582 | }
|
| 18583 | }
|
| 18584 | push_rational(-2, 3);
|
| 18585 | push(R_p);
|
| 18586 | multiply();
|
| 18587 | push(R_Q);
|
| 18588 | push(R_DELTA0);
|
| 18589 | push(R_Q);
|
| 18590 | divide();
|
| 18591 | add();
|
| 18592 | push(R_3_a);
|
| 18593 | divide();
|
| 18594 | add();
|
| 18595 | push_rational(1, 2);
|
| 18596 | power();
|
| 18597 | push_integer(2);
|
| 18598 | divide();
|
| 18599 | show_power_debug = true;
|
| 18600 | simplify();
|
| 18601 | R_S = pop();
|
| 18602 | if (DEBUG) {
|
| 18603 | console.log("S " + R_S.toString());
|
| 18604 | }
|
| 18605 | push(R_S);
|
| 18606 | simplify();
|
| 18607 | absValFloat();
|
| 18608 | R_S_simplified_toCheckIfZero = pop();
|
| 18609 | if (DEBUG) {
|
| 18610 | console.log("S " + R_S_simplified_toCheckIfZero.toString());
|
| 18611 | }
|
| 18612 | if (iszero(R_S_simplified_toCheckIfZero)) {
|
| 18613 | if (DEBUG) {
|
| 18614 | console.log(" *********************************** S IS ZERO chosing another cubic root");
|
| 18615 | }
|
| 18616 | choiceOfRadicalInQSoSIsNotZero++;
|
| 18617 | } else {
|
| 18618 | S_CHECKED_AS_NOT_ZERO = true;
|
| 18619 | }
|
| 18620 | if (DEBUG) {
|
| 18621 | console.log("tos: " + tos);
|
| 18622 | }
|
| 18623 | }
|
| 18624 | if (DEBUG) {
|
| 18625 | console.log("tos: " + tos);
|
| 18626 | }
|
| 18627 | push(p4);
|
| 18628 | negate();
|
| 18629 | push(p3);
|
| 18630 | push_integer(4);
|
| 18631 | multiply();
|
| 18632 | divide();
|
| 18633 | R_minus_b_over_4a = pop();
|
| 18634 | push_integer(-4);
|
| 18635 | push(R_S);
|
| 18636 | push_integer(2);
|
| 18637 | power();
|
| 18638 | multiply();
|
| 18639 | push_integer(2);
|
| 18640 | push(R_p);
|
| 18641 | multiply();
|
| 18642 | subtract();
|
| 18643 | R_minus_4S2_minus_2p = pop();
|
| 18644 | push(R_q);
|
| 18645 | push(R_S);
|
| 18646 | divide();
|
| 18647 | R_q_over_S = pop();
|
| 18648 | if (DEBUG) {
|
| 18649 | console.log("tos before putting together the 4 solutions: " + tos);
|
| 18650 | }
|
| 18651 | push(R_minus_b_over_4a);
|
| 18652 | push(R_S);
|
| 18653 | subtract();
|
| 18654 | push(R_minus_4S2_minus_2p);
|
| 18655 | push(R_q_over_S);
|
| 18656 | add();
|
| 18657 | push_rational(1, 2);
|
| 18658 | power();
|
| 18659 | push_integer(2);
|
| 18660 | divide();
|
| 18661 | add();
|
| 18662 | simplify();
|
| 18663 | push(R_minus_b_over_4a);
|
| 18664 | push(R_S);
|
| 18665 | subtract();
|
| 18666 | push(R_minus_4S2_minus_2p);
|
| 18667 | push(R_q_over_S);
|
| 18668 | add();
|
| 18669 | push_rational(1, 2);
|
| 18670 | power();
|
| 18671 | push_integer(2);
|
| 18672 | divide();
|
| 18673 | subtract();
|
| 18674 | simplify();
|
| 18675 | push(R_minus_b_over_4a);
|
| 18676 | push(R_S);
|
| 18677 | add();
|
| 18678 | push(R_minus_4S2_minus_2p);
|
| 18679 | push(R_q_over_S);
|
| 18680 | subtract();
|
| 18681 | push_rational(1, 2);
|
| 18682 | power();
|
| 18683 | push_integer(2);
|
| 18684 | divide();
|
| 18685 | add();
|
| 18686 | simplify();
|
| 18687 | push(R_minus_b_over_4a);
|
| 18688 | push(R_S);
|
| 18689 | add();
|
| 18690 | push(R_minus_4S2_minus_2p);
|
| 18691 | push(R_q_over_S);
|
| 18692 | subtract();
|
| 18693 | push_rational(1, 2);
|
| 18694 | power();
|
| 18695 | push_integer(2);
|
| 18696 | divide();
|
| 18697 | subtract();
|
| 18698 | simplify();
|
| 18699 | restore();
|
| 18700 | return;
|
| 18701 | }
|
| 18702 | }
|
| 18703 | moveTos(tos - n);
|
| 18704 | return restore();
|
| 18705 | };
|
| 18706 |
|
| 18707 | Eval_round = function() {
|
| 18708 | push(cadr(p1));
|
| 18709 | Eval();
|
| 18710 | return yround();
|
| 18711 | };
|
| 18712 |
|
| 18713 | yround = function() {
|
| 18714 | save();
|
| 18715 | yyround();
|
| 18716 | return restore();
|
| 18717 | };
|
| 18718 |
|
| 18719 | yyround = function() {
|
| 18720 | var d;
|
| 18721 | d = 0.0;
|
| 18722 | p1 = pop();
|
| 18723 | if (!isnum(p1)) {
|
| 18724 | push_symbol(ROUND);
|
| 18725 | push(p1);
|
| 18726 | list(2);
|
| 18727 | return;
|
| 18728 | }
|
| 18729 | if (isdouble(p1)) {
|
| 18730 | d = Math.round(p1.d);
|
| 18731 | push_double(d);
|
| 18732 | return;
|
| 18733 | }
|
| 18734 | if (isinteger(p1)) {
|
| 18735 | push(p1);
|
| 18736 | return;
|
| 18737 | }
|
| 18738 | push(p1);
|
| 18739 | yyfloat();
|
| 18740 | p1 = pop();
|
| 18741 | return push_integer(Math.round(p1.d));
|
| 18742 | };
|
| 18743 |
|
| 18744 | T_INTEGER = 1001;
|
| 18745 |
|
| 18746 | T_DOUBLE = 1002;
|
| 18747 |
|
| 18748 | T_SYMBOL = 1003;
|
| 18749 |
|
| 18750 | T_FUNCTION = 1004;
|
| 18751 |
|
| 18752 | T_NEWLINE = 1006;
|
| 18753 |
|
| 18754 | T_STRING = 1007;
|
| 18755 |
|
| 18756 | T_GTEQ = 1008;
|
| 18757 |
|
| 18758 | T_LTEQ = 1009;
|
| 18759 |
|
| 18760 | T_EQ = 1010;
|
| 18761 |
|
| 18762 | T_NEQ = 1011;
|
| 18763 |
|
| 18764 | T_QUOTASSIGN = 1012;
|
| 18765 |
|
| 18766 | token = "";
|
| 18767 |
|
| 18768 | newline_flag = 0;
|
| 18769 |
|
| 18770 | meta_mode = 0;
|
| 18771 |
|
| 18772 | input_str = 0;
|
| 18773 |
|
| 18774 | scan_str = 0;
|
| 18775 |
|
| 18776 | token_str = 0;
|
| 18777 |
|
| 18778 | token_buf = 0;
|
| 18779 |
|
| 18780 | lastFoundSymbol = null;
|
| 18781 |
|
| 18782 | symbolsRightOfAssignment = null;
|
| 18783 |
|
| 18784 | symbolsLeftOfAssignment = null;
|
| 18785 |
|
| 18786 | isSymbolLeftOfAssignment = null;
|
| 18787 |
|
| 18788 | scanningParameters = null;
|
| 18789 |
|
| 18790 | functionInvokationsScanningStack = null;
|
| 18791 |
|
| 18792 | skipRootVariableToBeSolved = false;
|
| 18793 |
|
| 18794 | assignmentFound = null;
|
| 18795 |
|
| 18796 | scanned = "";
|
| 18797 |
|
| 18798 | scan = function(s) {
|
| 18799 | if (DEBUG) {
|
| 18800 | console.log("#### scanning " + s);
|
| 18801 | }
|
| 18802 | lastFoundSymbol = null;
|
| 18803 | symbolsRightOfAssignment = [];
|
| 18804 | symbolsLeftOfAssignment = [];
|
| 18805 | isSymbolLeftOfAssignment = true;
|
| 18806 | scanningParameters = [];
|
| 18807 | functionInvokationsScanningStack = [""];
|
| 18808 | assignmentFound = false;
|
| 18809 | scanned = s;
|
| 18810 | meta_mode = 0;
|
| 18811 | expanding++;
|
| 18812 | input_str = 0;
|
| 18813 | scan_str = 0;
|
| 18814 | get_next_token();
|
| 18815 | if (token === "") {
|
| 18816 | push(symbol(NIL));
|
| 18817 | expanding--;
|
| 18818 | return 0;
|
| 18819 | }
|
| 18820 | scan_stmt();
|
| 18821 | expanding--;
|
| 18822 | if (!assignmentFound) {
|
| 18823 | symbolsInExpressionsWithoutAssignments = symbolsInExpressionsWithoutAssignments.concat(symbolsLeftOfAssignment);
|
| 18824 | }
|
| 18825 | return token_str - input_str;
|
| 18826 | };
|
| 18827 |
|
| 18828 | scan_meta = function(s) {
|
| 18829 | scanned = s;
|
| 18830 | meta_mode = 1;
|
| 18831 | expanding++;
|
| 18832 | input_str = 0;
|
| 18833 | scan_str = 0;
|
| 18834 | get_next_token();
|
| 18835 | if (token === "") {
|
| 18836 | push(symbol(NIL));
|
| 18837 | expanding--;
|
| 18838 | return 0;
|
| 18839 | }
|
| 18840 | scan_stmt();
|
| 18841 | expanding--;
|
| 18842 | return token_str - input_str;
|
| 18843 | };
|
| 18844 |
|
| 18845 | scan_stmt = function() {
|
| 18846 | var assignmentIsOfQuotedType, existingDependencies, i, indexOfSymbolLeftOfAssignment, l1, len, len1, m1, symbolLeftOfAssignment;
|
| 18847 | scan_relation();
|
| 18848 | assignmentIsOfQuotedType = false;
|
| 18849 | if (token === T_QUOTASSIGN) {
|
| 18850 | assignmentIsOfQuotedType = true;
|
| 18851 | }
|
| 18852 | if (token === T_QUOTASSIGN || token === '=') {
|
| 18853 | symbolLeftOfAssignment = lastFoundSymbol;
|
| 18854 | if (DEBUG) {
|
| 18855 | console.log("assignment!");
|
| 18856 | }
|
| 18857 | assignmentFound = true;
|
| 18858 | isSymbolLeftOfAssignment = false;
|
| 18859 | get_next_token();
|
| 18860 | push_symbol(SETQ);
|
| 18861 | swap();
|
| 18862 | if (assignmentIsOfQuotedType) {
|
| 18863 | push_symbol(QUOTE);
|
| 18864 | }
|
| 18865 | scan_relation();
|
| 18866 | if (assignmentIsOfQuotedType) {
|
| 18867 | list(2);
|
| 18868 | }
|
| 18869 | list(3);
|
| 18870 | isSymbolLeftOfAssignment = true;
|
| 18871 | if (codeGen) {
|
| 18872 | indexOfSymbolLeftOfAssignment = symbolsRightOfAssignment.indexOf(symbolLeftOfAssignment);
|
| 18873 | if (indexOfSymbolLeftOfAssignment !== -1) {
|
| 18874 | symbolsRightOfAssignment.splice(indexOfSymbolLeftOfAssignment, 1);
|
| 18875 | symbolsHavingReassignments.push(symbolLeftOfAssignment);
|
| 18876 | }
|
| 18877 | if (DEBUG) {
|
| 18878 | console.log("locally, " + symbolLeftOfAssignment + " depends on: ");
|
| 18879 | for (l1 = 0, len = symbolsRightOfAssignment.length; l1 < len; l1++) {
|
| 18880 | i = symbolsRightOfAssignment[l1];
|
| 18881 | console.log(" " + i);
|
| 18882 | }
|
| 18883 | }
|
| 18884 | if (symbolsDependencies[symbolLeftOfAssignment] == null) {
|
| 18885 | symbolsDependencies[symbolLeftOfAssignment] = [];
|
| 18886 | }
|
| 18887 | existingDependencies = symbolsDependencies[symbolLeftOfAssignment];
|
| 18888 | for (m1 = 0, len1 = symbolsRightOfAssignment.length; m1 < len1; m1++) {
|
| 18889 | i = symbolsRightOfAssignment[m1];
|
| 18890 | if (existingDependencies.indexOf(i) === -1) {
|
| 18891 | existingDependencies.push(i);
|
| 18892 | }
|
| 18893 | }
|
| 18894 | return symbolsRightOfAssignment = [];
|
| 18895 | }
|
| 18896 | }
|
| 18897 | };
|
| 18898 |
|
| 18899 | scan_relation = function() {
|
| 18900 | scan_expression();
|
| 18901 | switch (token) {
|
| 18902 | case T_EQ:
|
| 18903 | push_symbol(TESTEQ);
|
| 18904 | swap();
|
| 18905 | get_next_token();
|
| 18906 | scan_expression();
|
| 18907 | return list(3);
|
| 18908 | case T_NEQ:
|
| 18909 | push_symbol(NOT);
|
| 18910 | swap();
|
| 18911 | push_symbol(TESTEQ);
|
| 18912 | swap();
|
| 18913 | get_next_token();
|
| 18914 | scan_expression();
|
| 18915 | list(3);
|
| 18916 | return list(2);
|
| 18917 | case T_LTEQ:
|
| 18918 | push_symbol(TESTLE);
|
| 18919 | swap();
|
| 18920 | get_next_token();
|
| 18921 | scan_expression();
|
| 18922 | return list(3);
|
| 18923 | case T_GTEQ:
|
| 18924 | push_symbol(TESTGE);
|
| 18925 | swap();
|
| 18926 | get_next_token();
|
| 18927 | scan_expression();
|
| 18928 | return list(3);
|
| 18929 | case '<':
|
| 18930 | push_symbol(TESTLT);
|
| 18931 | swap();
|
| 18932 | get_next_token();
|
| 18933 | scan_expression();
|
| 18934 | return list(3);
|
| 18935 | case '>':
|
| 18936 | push_symbol(TESTGT);
|
| 18937 | swap();
|
| 18938 | get_next_token();
|
| 18939 | scan_expression();
|
| 18940 | return list(3);
|
| 18941 | }
|
| 18942 | };
|
| 18943 |
|
| 18944 | scan_expression = function() {
|
| 18945 | var h;
|
| 18946 | h = tos;
|
| 18947 | switch (token) {
|
| 18948 | case '+':
|
| 18949 | get_next_token();
|
| 18950 | scan_term();
|
| 18951 | break;
|
| 18952 | case '-':
|
| 18953 | get_next_token();
|
| 18954 | scan_term();
|
| 18955 | negate();
|
| 18956 | break;
|
| 18957 | default:
|
| 18958 | scan_term();
|
| 18959 | }
|
| 18960 | while (newline_flag === 0 && (token === '+' || token === '-')) {
|
| 18961 | if (token === '+') {
|
| 18962 | get_next_token();
|
| 18963 | scan_term();
|
| 18964 | } else {
|
| 18965 | get_next_token();
|
| 18966 | scan_term();
|
| 18967 | negate();
|
| 18968 | }
|
| 18969 | }
|
| 18970 | if (tos - h > 1) {
|
| 18971 | list(tos - h);
|
| 18972 | push_symbol(ADD);
|
| 18973 | swap();
|
| 18974 | return cons();
|
| 18975 | }
|
| 18976 | };
|
| 18977 |
|
| 18978 | is_factor = function() {
|
| 18979 | if ((typeof token.charCodeAt === "function" ? token.charCodeAt(0) : void 0) === dotprod_unicode) {
|
| 18980 | return 1;
|
| 18981 | }
|
| 18982 | switch (token) {
|
| 18983 | case '*':
|
| 18984 | case '/':
|
| 18985 | return 1;
|
| 18986 | case '(':
|
| 18987 | case T_SYMBOL:
|
| 18988 | case T_FUNCTION:
|
| 18989 | case T_INTEGER:
|
| 18990 | case T_DOUBLE:
|
| 18991 | case T_STRING:
|
| 18992 | if (newline_flag) {
|
| 18993 | scan_str = token_str;
|
| 18994 | return 0;
|
| 18995 | } else {
|
| 18996 | return 1;
|
| 18997 | }
|
| 18998 | }
|
| 18999 | return 0;
|
| 19000 | };
|
| 19001 |
|
| 19002 | simplify_1_in_products = function(tos, h) {
|
| 19003 | if (tos > h && isrational(stack[tos - 1]) && equaln(stack[tos - 1], 1)) {
|
| 19004 | return pop();
|
| 19005 | }
|
| 19006 | };
|
| 19007 |
|
| 19008 | multiply_consecutive_constants = function(tos, h) {
|
| 19009 | if (tos > h + 1 && isnum(stack[tos - 2]) && isnum(stack[tos - 1])) {
|
| 19010 | return multiply();
|
| 19011 | }
|
| 19012 | };
|
| 19013 |
|
| 19014 | scan_term = function() {
|
| 19015 | var h;
|
| 19016 | h = tos;
|
| 19017 | scan_factor();
|
| 19018 | if (parse_time_simplifications) {
|
| 19019 | simplify_1_in_products(tos, h);
|
| 19020 | }
|
| 19021 | while (is_factor()) {
|
| 19022 | if (token === '*') {
|
| 19023 | get_next_token();
|
| 19024 | scan_factor();
|
| 19025 | } else if (token === '/') {
|
| 19026 | simplify_1_in_products(tos, h);
|
| 19027 | get_next_token();
|
| 19028 | scan_factor();
|
| 19029 | inverse();
|
| 19030 | } else if ((typeof token.charCodeAt === "function" ? token.charCodeAt(0) : void 0) === dotprod_unicode) {
|
| 19031 | get_next_token();
|
| 19032 | push_symbol(INNER);
|
| 19033 | swap();
|
| 19034 | scan_factor();
|
| 19035 | list(3);
|
| 19036 | } else {
|
| 19037 | scan_factor();
|
| 19038 | }
|
| 19039 | if (parse_time_simplifications) {
|
| 19040 | multiply_consecutive_constants(tos, h);
|
| 19041 | simplify_1_in_products(tos, h);
|
| 19042 | }
|
| 19043 | }
|
| 19044 | if (h === tos) {
|
| 19045 | return push_integer(1);
|
| 19046 | } else if (tos - h > 1) {
|
| 19047 | list(tos - h);
|
| 19048 | push_symbol(MULTIPLY);
|
| 19049 | swap();
|
| 19050 | return cons();
|
| 19051 | }
|
| 19052 | };
|
| 19053 |
|
| 19054 | scan_power = function() {
|
| 19055 | if (token === '^') {
|
| 19056 | get_next_token();
|
| 19057 | push_symbol(POWER);
|
| 19058 | swap();
|
| 19059 | scan_factor();
|
| 19060 | return list(3);
|
| 19061 | }
|
| 19062 | };
|
| 19063 |
|
| 19064 | scan_index = function(h) {
|
| 19065 | get_next_token();
|
| 19066 | push_symbol(INDEX);
|
| 19067 | swap();
|
| 19068 | scan_expression();
|
| 19069 | while (token === ',') {
|
| 19070 | get_next_token();
|
| 19071 | scan_expression();
|
| 19072 | }
|
| 19073 | if (token !== ']') {
|
| 19074 | scan_error("] expected");
|
| 19075 | }
|
| 19076 | get_next_token();
|
| 19077 | return list(tos - h);
|
| 19078 | };
|
| 19079 |
|
| 19080 | scan_factor = function() {
|
| 19081 | var h;
|
| 19082 | h = tos;
|
| 19083 | if (token === '(') {
|
| 19084 | scan_subexpr();
|
| 19085 | } else if (token === T_SYMBOL) {
|
| 19086 | scan_symbol();
|
| 19087 | } else if (token === T_FUNCTION) {
|
| 19088 | scan_function_call_with_function_name();
|
| 19089 | } else if (token === '[') {
|
| 19090 | scan_tensor();
|
| 19091 | } else if (token === T_INTEGER) {
|
| 19092 | bignum_scan_integer(token_buf);
|
| 19093 | get_next_token();
|
| 19094 | } else if (token === T_DOUBLE) {
|
| 19095 | bignum_scan_float(token_buf);
|
| 19096 | get_next_token();
|
| 19097 | } else if (token === T_STRING) {
|
| 19098 | scan_string();
|
| 19099 | } else {
|
| 19100 | scan_error("syntax error");
|
| 19101 | }
|
| 19102 | while (token === '[' || token === '(' && newline_flag === 0) {
|
| 19103 | if (token === '[') {
|
| 19104 | scan_index(h);
|
| 19105 | } else if (token === '(') {
|
| 19106 | scan_function_call_without_function_name();
|
| 19107 | }
|
| 19108 | }
|
| 19109 | while (token === '!') {
|
| 19110 | get_next_token();
|
| 19111 | push_symbol(FACTORIAL);
|
| 19112 | swap();
|
| 19113 | list(2);
|
| 19114 | }
|
| 19115 | while ((typeof token.charCodeAt === "function" ? token.charCodeAt(0) : void 0) === transpose_unicode) {
|
| 19116 | get_next_token();
|
| 19117 | push_symbol(TRANSPOSE);
|
| 19118 | swap();
|
| 19119 | list(2);
|
| 19120 | }
|
| 19121 | return scan_power();
|
| 19122 | };
|
| 19123 |
|
| 19124 | addSymbolRightOfAssignment = function(theSymbol) {
|
| 19125 | var i, l1, prefixVar, ref2;
|
| 19126 | if (predefinedSymbolsInGlobalScope_doNotTrackInDependencies.indexOf(theSymbol) === -1 && symbolsRightOfAssignment.indexOf(theSymbol) === -1 && symbolsRightOfAssignment.indexOf("'" + theSymbol) === -1 && !skipRootVariableToBeSolved) {
|
| 19127 | if (DEBUG) {
|
| 19128 | console.log("... adding symbol: " + theSymbol + " to the set of the symbols right of assignment");
|
| 19129 | }
|
| 19130 | prefixVar = "";
|
| 19131 | for (i = l1 = 1, ref2 = functionInvokationsScanningStack.length; 1 <= ref2 ? l1 < ref2 : l1 > ref2; i = 1 <= ref2 ? ++l1 : --l1) {
|
| 19132 | if (functionInvokationsScanningStack[i] !== "") {
|
| 19133 | prefixVar += functionInvokationsScanningStack[i] + "_" + i + "_";
|
| 19134 | }
|
| 19135 | }
|
| 19136 | theSymbol = prefixVar + theSymbol;
|
| 19137 | return symbolsRightOfAssignment.push(theSymbol);
|
| 19138 | }
|
| 19139 | };
|
| 19140 |
|
| 19141 | addSymbolLeftOfAssignment = function(theSymbol) {
|
| 19142 | var i, l1, prefixVar, ref2;
|
| 19143 | if (predefinedSymbolsInGlobalScope_doNotTrackInDependencies.indexOf(theSymbol) === -1 && symbolsLeftOfAssignment.indexOf(theSymbol) === -1 && symbolsLeftOfAssignment.indexOf("'" + theSymbol) === -1 && !skipRootVariableToBeSolved) {
|
| 19144 | if (DEBUG) {
|
| 19145 | console.log("... adding symbol: " + theSymbol + " to the set of the symbols left of assignment");
|
| 19146 | }
|
| 19147 | prefixVar = "";
|
| 19148 | for (i = l1 = 1, ref2 = functionInvokationsScanningStack.length; 1 <= ref2 ? l1 < ref2 : l1 > ref2; i = 1 <= ref2 ? ++l1 : --l1) {
|
| 19149 | if (functionInvokationsScanningStack[i] !== "") {
|
| 19150 | prefixVar += functionInvokationsScanningStack[i] + "_" + i + "_";
|
| 19151 | }
|
| 19152 | }
|
| 19153 | theSymbol = prefixVar + theSymbol;
|
| 19154 | return symbolsLeftOfAssignment.push(theSymbol);
|
| 19155 | }
|
| 19156 | };
|
| 19157 |
|
| 19158 | scan_symbol = function() {
|
| 19159 | if (token !== T_SYMBOL) {
|
| 19160 | scan_error("symbol expected");
|
| 19161 | }
|
| 19162 | if (meta_mode && token_buf.length === 1) {
|
| 19163 | switch (token_buf[0]) {
|
| 19164 | case 'a':
|
| 19165 | push(symbol(METAA));
|
| 19166 | break;
|
| 19167 | case 'b':
|
| 19168 | push(symbol(METAB));
|
| 19169 | break;
|
| 19170 | case 'x':
|
| 19171 | push(symbol(METAX));
|
| 19172 | break;
|
| 19173 | default:
|
| 19174 | push(usr_symbol(token_buf));
|
| 19175 | }
|
| 19176 | } else {
|
| 19177 | push(usr_symbol(token_buf));
|
| 19178 | }
|
| 19179 | if (scanningParameters.length === 0) {
|
| 19180 | if (DEBUG) {
|
| 19181 | console.log("out of scanning parameters, processing " + token_buf);
|
| 19182 | }
|
| 19183 | lastFoundSymbol = token_buf;
|
| 19184 | if (isSymbolLeftOfAssignment) {
|
| 19185 | addSymbolLeftOfAssignment(token_buf);
|
| 19186 | }
|
| 19187 | } else {
|
| 19188 | if (DEBUG) {
|
| 19189 | console.log("still scanning parameters, skipping " + token_buf);
|
| 19190 | }
|
| 19191 | if (isSymbolLeftOfAssignment) {
|
| 19192 | addSymbolRightOfAssignment("'" + token_buf);
|
| 19193 | }
|
| 19194 | }
|
| 19195 | if (DEBUG) {
|
| 19196 | console.log("found symbol: " + token_buf + " left of assignment: " + isSymbolLeftOfAssignment);
|
| 19197 | }
|
| 19198 | if (!isSymbolLeftOfAssignment) {
|
| 19199 | addSymbolRightOfAssignment(token_buf);
|
| 19200 | }
|
| 19201 | return get_next_token();
|
| 19202 | };
|
| 19203 |
|
| 19204 | scan_string = function() {
|
| 19205 | new_string(token_buf);
|
| 19206 | return get_next_token();
|
| 19207 | };
|
| 19208 |
|
| 19209 | scan_function_call_with_function_name = function() {
|
| 19210 | var functionName, i, l1, n, p, ref2;
|
| 19211 | if (DEBUG) {
|
| 19212 | console.log("-- scan_function_call_with_function_name start");
|
| 19213 | }
|
| 19214 | n = 1;
|
| 19215 | p = new U();
|
| 19216 | p = usr_symbol(token_buf);
|
| 19217 | push(p);
|
| 19218 | get_next_token();
|
| 19219 | functionName = token_buf;
|
| 19220 | if (functionName === "roots" || functionName === "defint" || functionName === "sum" || functionName === "product" || functionName === "for") {
|
| 19221 | functionInvokationsScanningStack.push(token_buf);
|
| 19222 | }
|
| 19223 | lastFoundSymbol = token_buf;
|
| 19224 | if (!isSymbolLeftOfAssignment) {
|
| 19225 | addSymbolRightOfAssignment(token_buf);
|
| 19226 | }
|
| 19227 | get_next_token();
|
| 19228 | scanningParameters.push(true);
|
| 19229 | if (token !== ')') {
|
| 19230 | scan_stmt();
|
| 19231 | n++;
|
| 19232 | while (token === ',') {
|
| 19233 | get_next_token();
|
| 19234 | if (n === 2 && functionInvokationsScanningStack[functionInvokationsScanningStack.length - 1].indexOf("roots") !== -1) {
|
| 19235 | symbolsRightOfAssignment = symbolsRightOfAssignment.filter(function(x) {
|
| 19236 | return !(new RegExp("roots_" + (functionInvokationsScanningStack.length - 1) + "_" + token_buf)).test(x);
|
| 19237 | });
|
| 19238 | skipRootVariableToBeSolved = true;
|
| 19239 | }
|
| 19240 | if (n === 2 && functionInvokationsScanningStack[functionInvokationsScanningStack.length - 1].indexOf("sum") !== -1) {
|
| 19241 | symbolsRightOfAssignment = symbolsRightOfAssignment.filter(function(x) {
|
| 19242 | return !(new RegExp("sum_" + (functionInvokationsScanningStack.length - 1) + "_" + token_buf)).test(x);
|
| 19243 | });
|
| 19244 | skipRootVariableToBeSolved = true;
|
| 19245 | }
|
| 19246 | if (n === 2 && functionInvokationsScanningStack[functionInvokationsScanningStack.length - 1].indexOf("product") !== -1) {
|
| 19247 | symbolsRightOfAssignment = symbolsRightOfAssignment.filter(function(x) {
|
| 19248 | return !(new RegExp("product_" + (functionInvokationsScanningStack.length - 1) + "_" + token_buf)).test(x);
|
| 19249 | });
|
| 19250 | skipRootVariableToBeSolved = true;
|
| 19251 | }
|
| 19252 | if (n === 2 && functionInvokationsScanningStack[functionInvokationsScanningStack.length - 1].indexOf("for") !== -1) {
|
| 19253 | symbolsRightOfAssignment = symbolsRightOfAssignment.filter(function(x) {
|
| 19254 | return !(new RegExp("for_" + (functionInvokationsScanningStack.length - 1) + "_" + token_buf)).test(x);
|
| 19255 | });
|
| 19256 | skipRootVariableToBeSolved = true;
|
| 19257 | }
|
| 19258 | if (functionInvokationsScanningStack[functionInvokationsScanningStack.length - 1].indexOf("defint") !== -1 && (n === 2 || (n > 2 && ((n - 2) % 3 === 0)))) {
|
| 19259 | symbolsRightOfAssignment = symbolsRightOfAssignment.filter(function(x) {
|
| 19260 | return !(new RegExp("defint_" + (functionInvokationsScanningStack.length - 1) + "_" + token_buf)).test(x);
|
| 19261 | });
|
| 19262 | skipRootVariableToBeSolved = true;
|
| 19263 | }
|
| 19264 | scan_stmt();
|
| 19265 | skipRootVariableToBeSolved = false;
|
| 19266 | n++;
|
| 19267 | }
|
| 19268 | if (n === 2 && functionInvokationsScanningStack[functionInvokationsScanningStack.length - 1].indexOf("roots") !== -1) {
|
| 19269 | symbolsRightOfAssignment = symbolsRightOfAssignment.filter(function(x) {
|
| 19270 | return !(new RegExp("roots_" + (functionInvokationsScanningStack.length - 1) + "_" + "x")).test(x);
|
| 19271 | });
|
| 19272 | }
|
| 19273 | }
|
| 19274 | scanningParameters.pop();
|
| 19275 | for (i = l1 = 0, ref2 = symbolsRightOfAssignment.length; 0 <= ref2 ? l1 <= ref2 : l1 >= ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 19276 | if (symbolsRightOfAssignment[i] != null) {
|
| 19277 | if (functionName === "roots") {
|
| 19278 | symbolsRightOfAssignment[i] = symbolsRightOfAssignment[i].replace(new RegExp("roots_" + (functionInvokationsScanningStack.length - 1) + "_"), "");
|
| 19279 | }
|
| 19280 | if (functionName === "defint") {
|
| 19281 | symbolsRightOfAssignment[i] = symbolsRightOfAssignment[i].replace(new RegExp("defint_" + (functionInvokationsScanningStack.length - 1) + "_"), "");
|
| 19282 | }
|
| 19283 | if (functionName === "sum") {
|
| 19284 | symbolsRightOfAssignment[i] = symbolsRightOfAssignment[i].replace(new RegExp("sum_" + (functionInvokationsScanningStack.length - 1) + "_"), "");
|
| 19285 | }
|
| 19286 | if (functionName === "product") {
|
| 19287 | symbolsRightOfAssignment[i] = symbolsRightOfAssignment[i].replace(new RegExp("product_" + (functionInvokationsScanningStack.length - 1) + "_"), "");
|
| 19288 | }
|
| 19289 | if (functionName === "for") {
|
| 19290 | symbolsRightOfAssignment[i] = symbolsRightOfAssignment[i].replace(new RegExp("for_" + (functionInvokationsScanningStack.length - 1) + "_"), "");
|
| 19291 | }
|
| 19292 | }
|
| 19293 | }
|
| 19294 | if (token !== ')') {
|
| 19295 | scan_error(") expected");
|
| 19296 | }
|
| 19297 | get_next_token();
|
| 19298 | list(n);
|
| 19299 | if (functionName === "roots" || functionName === "defint" || functionName === "sum" || functionName === "product" || functionName === "for") {
|
| 19300 | functionInvokationsScanningStack.pop();
|
| 19301 | }
|
| 19302 | if (functionName === symbol(PATTERN).printname) {
|
| 19303 | patternHasBeenFound = true;
|
| 19304 | }
|
| 19305 | if (DEBUG) {
|
| 19306 | return console.log("-- scan_function_call_with_function_name end");
|
| 19307 | }
|
| 19308 | };
|
| 19309 |
|
| 19310 | scan_function_call_without_function_name = function() {
|
| 19311 | var n;
|
| 19312 | if (DEBUG) {
|
| 19313 | console.log("-- scan_function_call_without_function_name start");
|
| 19314 | }
|
| 19315 | push_symbol(EVAL);
|
| 19316 | swap();
|
| 19317 | list(2);
|
| 19318 | n = 1;
|
| 19319 | get_next_token();
|
| 19320 | scanningParameters.push(true);
|
| 19321 | if (token !== ')') {
|
| 19322 | scan_stmt();
|
| 19323 | n++;
|
| 19324 | while (token === ',') {
|
| 19325 | get_next_token();
|
| 19326 | scan_stmt();
|
| 19327 | n++;
|
| 19328 | }
|
| 19329 | }
|
| 19330 | scanningParameters.pop();
|
| 19331 | if (token !== ')') {
|
| 19332 | scan_error(") expected");
|
| 19333 | }
|
| 19334 | get_next_token();
|
| 19335 | list(n);
|
| 19336 | if (DEBUG) {
|
| 19337 | return console.log("-- scan_function_call_without_function_name end: " + stack[tos - 1]);
|
| 19338 | }
|
| 19339 | };
|
| 19340 |
|
| 19341 | scan_subexpr = function() {
|
| 19342 | var n;
|
| 19343 | n = 0;
|
| 19344 | if (token !== '(') {
|
| 19345 | scan_error("( expected");
|
| 19346 | }
|
| 19347 | get_next_token();
|
| 19348 | scan_stmt();
|
| 19349 | if (token !== ')') {
|
| 19350 | scan_error(") expected");
|
| 19351 | }
|
| 19352 | return get_next_token();
|
| 19353 | };
|
| 19354 |
|
| 19355 | scan_tensor = function() {
|
| 19356 | var n;
|
| 19357 | n = 0;
|
| 19358 | if (token !== '[') {
|
| 19359 | scan_error("[ expected");
|
| 19360 | }
|
| 19361 | get_next_token();
|
| 19362 | scan_stmt();
|
| 19363 | n = 1;
|
| 19364 | while (token === ',') {
|
| 19365 | get_next_token();
|
| 19366 | scan_stmt();
|
| 19367 | n++;
|
| 19368 | }
|
| 19369 | build_tensor(n);
|
| 19370 | if (token !== ']') {
|
| 19371 | scan_error("] expected");
|
| 19372 | }
|
| 19373 | return get_next_token();
|
| 19374 | };
|
| 19375 |
|
| 19376 | scan_error = function(errmsg) {
|
| 19377 | errorMessage = "";
|
| 19378 | while (input_str !== scan_str) {
|
| 19379 | if ((scanned[input_str] === '\n' || scanned[input_str] === '\r') && input_str + 1 === scan_str) {
|
| 19380 | break;
|
| 19381 | }
|
| 19382 | errorMessage += scanned[input_str++];
|
| 19383 | }
|
| 19384 | errorMessage += " ? ";
|
| 19385 | while (scanned[input_str] && (scanned[input_str] !== '\n' && scanned[input_str] !== '\r')) {
|
| 19386 | errorMessage += scanned[input_str++];
|
| 19387 | }
|
| 19388 | errorMessage += '\n';
|
| 19389 | return stop(errmsg);
|
| 19390 | };
|
| 19391 |
|
| 19392 | build_tensor = function(n) {
|
| 19393 | var i, l1, ref2;
|
| 19394 | i = 0;
|
| 19395 | save();
|
| 19396 | p2 = alloc_tensor(n);
|
| 19397 | p2.tensor.ndim = 1;
|
| 19398 | p2.tensor.dim[0] = n;
|
| 19399 | for (i = l1 = 0, ref2 = n; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 19400 | p2.tensor.elem[i] = stack[tos - n + i];
|
| 19401 | }
|
| 19402 | check_tensor_dimensions(p2);
|
| 19403 | moveTos(tos - n);
|
| 19404 | push(p2);
|
| 19405 | return restore();
|
| 19406 | };
|
| 19407 |
|
| 19408 | get_next_token = function() {
|
| 19409 | newline_flag = 0;
|
| 19410 | while (1) {
|
| 19411 | get_token();
|
| 19412 | if (token !== T_NEWLINE) {
|
| 19413 | break;
|
| 19414 | }
|
| 19415 | newline_flag = 1;
|
| 19416 | }
|
| 19417 | if (DEBUG) {
|
| 19418 | return console.log("get_next_token token: " + token);
|
| 19419 | }
|
| 19420 | };
|
| 19421 |
|
| 19422 | get_token = function() {
|
| 19423 | while (isspace(scanned[scan_str])) {
|
| 19424 | if (scanned[scan_str] === '\n' || scanned[scan_str] === '\r') {
|
| 19425 | token = T_NEWLINE;
|
| 19426 | scan_str++;
|
| 19427 | return;
|
| 19428 | }
|
| 19429 | scan_str++;
|
| 19430 | }
|
| 19431 | token_str = scan_str;
|
| 19432 | if (scan_str === scanned.length) {
|
| 19433 | token = "";
|
| 19434 | return;
|
| 19435 | }
|
| 19436 | if (isdigit(scanned[scan_str]) || scanned[scan_str] === '.') {
|
| 19437 | while (isdigit(scanned[scan_str])) {
|
| 19438 | scan_str++;
|
| 19439 | }
|
| 19440 | if (scanned[scan_str] === '.') {
|
| 19441 | scan_str++;
|
| 19442 | while (isdigit(scanned[scan_str])) {
|
| 19443 | scan_str++;
|
| 19444 | }
|
| 19445 | if (scanned[scan_str] === 'e' && (scanned[scan_str + 1] === '+' || scanned[scan_str + 1] === '-' || isdigit(scanned[scan_str + 1]))) {
|
| 19446 | scan_str += 2;
|
| 19447 | while (isdigit(scanned[scan_str])) {
|
| 19448 | scan_str++;
|
| 19449 | }
|
| 19450 | }
|
| 19451 | token = T_DOUBLE;
|
| 19452 | } else {
|
| 19453 | token = T_INTEGER;
|
| 19454 | }
|
| 19455 | update_token_buf(token_str, scan_str);
|
| 19456 | return;
|
| 19457 | }
|
| 19458 | if (isalpha(scanned[scan_str])) {
|
| 19459 | while (isalnumorunderscore(scanned[scan_str])) {
|
| 19460 | scan_str++;
|
| 19461 | }
|
| 19462 | if (scanned[scan_str] === '(') {
|
| 19463 | token = T_FUNCTION;
|
| 19464 | } else {
|
| 19465 | token = T_SYMBOL;
|
| 19466 | }
|
| 19467 | update_token_buf(token_str, scan_str);
|
| 19468 | return;
|
| 19469 | }
|
| 19470 | if (scanned[scan_str] === '"') {
|
| 19471 | scan_str++;
|
| 19472 | while (scanned[scan_str] !== '"') {
|
| 19473 | if (scan_str === scanned.length - 1) {
|
| 19474 | scan_str++;
|
| 19475 | scan_error("runaway string");
|
| 19476 | scan_str--;
|
| 19477 | }
|
| 19478 | scan_str++;
|
| 19479 | }
|
| 19480 | scan_str++;
|
| 19481 | token = T_STRING;
|
| 19482 | update_token_buf(token_str + 1, scan_str - 1);
|
| 19483 | return;
|
| 19484 | }
|
| 19485 | if (scanned[scan_str] === '#' || scanned[scan_str] === '-' && scanned[scan_str + 1] === '-') {
|
| 19486 | while (scanned[scan_str] && scanned[scan_str] !== '\n' && scanned[scan_str] !== '\r') {
|
| 19487 | scan_str++;
|
| 19488 | }
|
| 19489 | if (scanned[scan_str]) {
|
| 19490 | scan_str++;
|
| 19491 | }
|
| 19492 | token = T_NEWLINE;
|
| 19493 | return;
|
| 19494 | }
|
| 19495 | if (scanned[scan_str] === ':' && scanned[scan_str + 1] === '=') {
|
| 19496 | scan_str += 2;
|
| 19497 | token = T_QUOTASSIGN;
|
| 19498 | return;
|
| 19499 | }
|
| 19500 | if (scanned[scan_str] === '=' && scanned[scan_str + 1] === '=') {
|
| 19501 | scan_str += 2;
|
| 19502 | token = T_EQ;
|
| 19503 | return;
|
| 19504 | }
|
| 19505 | if (scanned[scan_str] === '!' && scanned[scan_str + 1] === '=') {
|
| 19506 | scan_str += 2;
|
| 19507 | token = T_NEQ;
|
| 19508 | return;
|
| 19509 | }
|
| 19510 | if (scanned[scan_str] === '<' && scanned[scan_str + 1] === '=') {
|
| 19511 | scan_str += 2;
|
| 19512 | token = T_LTEQ;
|
| 19513 | return;
|
| 19514 | }
|
| 19515 | if (scanned[scan_str] === '>' && scanned[scan_str + 1] === '=') {
|
| 19516 | scan_str += 2;
|
| 19517 | token = T_GTEQ;
|
| 19518 | return;
|
| 19519 | }
|
| 19520 | return token = scanned[scan_str++];
|
| 19521 | };
|
| 19522 |
|
| 19523 | update_token_buf = function(a, b) {
|
| 19524 | return token_buf = scanned.substring(a, b);
|
| 19525 | };
|
| 19526 |
|
| 19527 | $.scan = scan;
|
| 19528 |
|
| 19529 | Eval_sgn = function() {
|
| 19530 | push(cadr(p1));
|
| 19531 | Eval();
|
| 19532 | return sgn();
|
| 19533 | };
|
| 19534 |
|
| 19535 | sgn = function() {
|
| 19536 | save();
|
| 19537 | yysgn();
|
| 19538 | return restore();
|
| 19539 | };
|
| 19540 |
|
| 19541 | yysgn = function() {
|
| 19542 | p1 = pop();
|
| 19543 | if (isdouble(p1)) {
|
| 19544 | if (p1.d > 0) {
|
| 19545 | push_integer(1);
|
| 19546 | return;
|
| 19547 | } else {
|
| 19548 | if (p1.d === 0) {
|
| 19549 | push_integer(1);
|
| 19550 | return;
|
| 19551 | } else {
|
| 19552 | push_integer(-1);
|
| 19553 | return;
|
| 19554 | }
|
| 19555 | }
|
| 19556 | }
|
| 19557 | if (isrational(p1)) {
|
| 19558 | if (MSIGN(mmul(p1.q.a, p1.q.b)) === -1) {
|
| 19559 | push_integer(-1);
|
| 19560 | return;
|
| 19561 | } else {
|
| 19562 | if (MZERO(mmul(p1.q.a, p1.q.b))) {
|
| 19563 | push_integer(0);
|
| 19564 | return;
|
| 19565 | } else {
|
| 19566 | push_integer(1);
|
| 19567 | return;
|
| 19568 | }
|
| 19569 | }
|
| 19570 | }
|
| 19571 | if (iscomplexnumber(p1)) {
|
| 19572 | push_integer(-1);
|
| 19573 | push(p1);
|
| 19574 | absval();
|
| 19575 | power();
|
| 19576 | push(p1);
|
| 19577 | multiply();
|
| 19578 | return;
|
| 19579 | }
|
| 19580 | if (isnegativeterm(p1)) {
|
| 19581 | push_symbol(SGN);
|
| 19582 | push(p1);
|
| 19583 | negate();
|
| 19584 | list(2);
|
| 19585 | push_integer(-1);
|
| 19586 | multiply();
|
| 19587 | return;
|
| 19588 | }
|
| 19589 |
|
| 19590 | |
| 19591 | |
| 19592 | |
| 19593 | |
| 19594 | |
| 19595 | |
| 19596 | |
| 19597 |
|
| 19598 | push_symbol(SGN);
|
| 19599 | push(p1);
|
| 19600 | return list(2);
|
| 19601 | };
|
| 19602 |
|
| 19603 | Eval_shape = function() {
|
| 19604 | push(cadr(p1));
|
| 19605 | Eval();
|
| 19606 | return shape();
|
| 19607 | };
|
| 19608 |
|
| 19609 | shape = function() {
|
| 19610 | var ai, an, i, l1, m1, ndim, ref2, ref3, t;
|
| 19611 | i = 0;
|
| 19612 | ndim = 0;
|
| 19613 | t = 0;
|
| 19614 | ai = [];
|
| 19615 | an = [];
|
| 19616 | for (i = l1 = 0, ref2 = MAXDIM; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 19617 | ai[i] = 0;
|
| 19618 | an[i] = 0;
|
| 19619 | }
|
| 19620 | save();
|
| 19621 | p1 = pop();
|
| 19622 | if (!istensor(p1)) {
|
| 19623 | if (!iszero(p1)) {
|
| 19624 | stop("transpose: tensor expected, 1st arg is not a tensor");
|
| 19625 | }
|
| 19626 | push(zero);
|
| 19627 | restore();
|
| 19628 | return;
|
| 19629 | }
|
| 19630 | ndim = p1.tensor.ndim;
|
| 19631 | p2 = alloc_tensor(ndim);
|
| 19632 | p2.tensor.ndim = 1;
|
| 19633 | p2.tensor.dim[0] = ndim;
|
| 19634 | for (i = m1 = 0, ref3 = ndim; 0 <= ref3 ? m1 < ref3 : m1 > ref3; i = 0 <= ref3 ? ++m1 : --m1) {
|
| 19635 | push_integer(p1.tensor.dim[i]);
|
| 19636 | p2.tensor.elem[i] = pop();
|
| 19637 | }
|
| 19638 | push(p2);
|
| 19639 | return restore();
|
| 19640 | };
|
| 19641 |
|
| 19642 |
|
| 19643 | |
| 19644 | |
| 19645 | |
| 19646 | |
| 19647 | |
| 19648 | |
| 19649 | |
| 19650 | |
| 19651 | |
| 19652 | |
| 19653 | |
| 19654 | |
| 19655 | |
| 19656 | |
| 19657 | |
| 19658 | |
| 19659 | |
| 19660 | |
| 19661 | |
| 19662 | |
| 19663 | |
| 19664 | |
| 19665 | |
| 19666 | |
| 19667 | |
| 19668 |
|
| 19669 |
|
| 19670 | Eval_simfac = function() {
|
| 19671 | push(cadr(p1));
|
| 19672 | Eval();
|
| 19673 | return simfac();
|
| 19674 | };
|
| 19675 |
|
| 19676 | simfac = function() {
|
| 19677 | var h;
|
| 19678 | h = 0;
|
| 19679 | save();
|
| 19680 | p1 = pop();
|
| 19681 | if (car(p1) === symbol(ADD)) {
|
| 19682 | h = tos;
|
| 19683 | p1 = cdr(p1);
|
| 19684 | while (p1 !== symbol(NIL)) {
|
| 19685 | push(car(p1));
|
| 19686 | simfac_term();
|
| 19687 | p1 = cdr(p1);
|
| 19688 | }
|
| 19689 | add_all(tos - h);
|
| 19690 | } else {
|
| 19691 | push(p1);
|
| 19692 | simfac_term();
|
| 19693 | }
|
| 19694 | return restore();
|
| 19695 | };
|
| 19696 |
|
| 19697 |
|
| 19698 | |
| 19699 | |
| 19700 | |
| 19701 | |
| 19702 | |
| 19703 | |
| 19704 | |
| 19705 | |
| 19706 | |
| 19707 | |
| 19708 | |
| 19709 | |
| 19710 | |
| 19711 | |
| 19712 | |
| 19713 | |
| 19714 | |
| 19715 | |
| 19716 | |
| 19717 | |
| 19718 | |
| 19719 | |
| 19720 | |
| 19721 | |
| 19722 | |
| 19723 | |
| 19724 | |
| 19725 | |
| 19726 | |
| 19727 | |
| 19728 | |
| 19729 | |
| 19730 |
|
| 19731 |
|
| 19732 | simfac_term = function() {
|
| 19733 | var doNothing, h;
|
| 19734 | h = 0;
|
| 19735 | save();
|
| 19736 | p1 = pop();
|
| 19737 | if (car(p1) !== symbol(MULTIPLY)) {
|
| 19738 | push(p1);
|
| 19739 | restore();
|
| 19740 | return;
|
| 19741 | }
|
| 19742 | h = tos;
|
| 19743 | p1 = cdr(p1);
|
| 19744 | while (p1 !== symbol(NIL)) {
|
| 19745 | push(car(p1));
|
| 19746 | p1 = cdr(p1);
|
| 19747 | }
|
| 19748 | while (yysimfac(h)) {
|
| 19749 | doNothing = 1;
|
| 19750 | }
|
| 19751 | multiply_all_noexpand(tos - h);
|
| 19752 | return restore();
|
| 19753 | };
|
| 19754 |
|
| 19755 | yysimfac = function(h) {
|
| 19756 | var i, j, l1, m1, ref2, ref3, ref4, ref5;
|
| 19757 | i = 0;
|
| 19758 | j = 0;
|
| 19759 | for (i = l1 = ref2 = h, ref3 = tos; ref2 <= ref3 ? l1 < ref3 : l1 > ref3; i = ref2 <= ref3 ? ++l1 : --l1) {
|
| 19760 | p1 = stack[i];
|
| 19761 | for (j = m1 = ref4 = h, ref5 = tos; ref4 <= ref5 ? m1 < ref5 : m1 > ref5; j = ref4 <= ref5 ? ++m1 : --m1) {
|
| 19762 | if (i === j) {
|
| 19763 | continue;
|
| 19764 | }
|
| 19765 | p2 = stack[j];
|
| 19766 | if (car(p1) === symbol(FACTORIAL) && car(p2) === symbol(POWER) && isminusone(caddr(p2)) && equal(cadr(p1), cadr(p2))) {
|
| 19767 | push(cadr(p1));
|
| 19768 | push(one);
|
| 19769 | subtract();
|
| 19770 | factorial();
|
| 19771 | stack[i] = pop();
|
| 19772 | stack[j] = one;
|
| 19773 | return 1;
|
| 19774 | }
|
| 19775 | if (car(p2) === symbol(POWER) && isminusone(caddr(p2)) && caadr(p2) === symbol(FACTORIAL) && equal(p1, cadadr(p2))) {
|
| 19776 | push(p1);
|
| 19777 | push_integer(-1);
|
| 19778 | add();
|
| 19779 | factorial();
|
| 19780 | reciprocate();
|
| 19781 | stack[i] = pop();
|
| 19782 | stack[j] = one;
|
| 19783 | return 1;
|
| 19784 | }
|
| 19785 | if (car(p2) === symbol(FACTORIAL)) {
|
| 19786 | push(p1);
|
| 19787 | push(cadr(p2));
|
| 19788 | subtract();
|
| 19789 | p3 = pop();
|
| 19790 | if (isplusone(p3)) {
|
| 19791 | push(p1);
|
| 19792 | factorial();
|
| 19793 | stack[i] = pop();
|
| 19794 | stack[j] = one;
|
| 19795 | return 1;
|
| 19796 | }
|
| 19797 | }
|
| 19798 | if (car(p1) === symbol(POWER) && isminusone(caddr(p1)) && car(p2) === symbol(POWER) && isminusone(caddr(p2)) && caadr(p2) === symbol(FACTORIAL)) {
|
| 19799 | push(cadr(p1));
|
| 19800 | push(cadr(cadr(p2)));
|
| 19801 | subtract();
|
| 19802 | p3 = pop();
|
| 19803 | if (isplusone(p3)) {
|
| 19804 | push(cadr(p1));
|
| 19805 | factorial();
|
| 19806 | reciprocate();
|
| 19807 | stack[i] = pop();
|
| 19808 | stack[j] = one;
|
| 19809 | return 1;
|
| 19810 | }
|
| 19811 | }
|
| 19812 | if (car(p1) === symbol(FACTORIAL) && car(p2) === symbol(POWER) && isminusone(caddr(p2)) && caadr(p2) === symbol(FACTORIAL)) {
|
| 19813 | push(cadr(p1));
|
| 19814 | push(cadr(cadr(p2)));
|
| 19815 | subtract();
|
| 19816 | p3 = pop();
|
| 19817 | if (isplusone(p3)) {
|
| 19818 | stack[i] = cadr(p1);
|
| 19819 | stack[j] = one;
|
| 19820 | return 1;
|
| 19821 | }
|
| 19822 | if (isminusone(p3)) {
|
| 19823 | push(cadr(cadr(p2)));
|
| 19824 | reciprocate();
|
| 19825 | stack[i] = pop();
|
| 19826 | stack[j] = one;
|
| 19827 | return 1;
|
| 19828 | }
|
| 19829 | if (equaln(p3, 2)) {
|
| 19830 | stack[i] = cadr(p1);
|
| 19831 | push(cadr(p1));
|
| 19832 | push_integer(-1);
|
| 19833 | add();
|
| 19834 | stack[j] = pop();
|
| 19835 | return 1;
|
| 19836 | }
|
| 19837 | if (equaln(p3, -2)) {
|
| 19838 | push(cadr(cadr(p2)));
|
| 19839 | reciprocate();
|
| 19840 | stack[i] = pop();
|
| 19841 | push(cadr(cadr(p2)));
|
| 19842 | push_integer(-1);
|
| 19843 | add();
|
| 19844 | reciprocate();
|
| 19845 | stack[j] = pop();
|
| 19846 | return 1;
|
| 19847 | }
|
| 19848 | }
|
| 19849 | }
|
| 19850 | }
|
| 19851 | return 0;
|
| 19852 | };
|
| 19853 |
|
| 19854 | Eval_simplify = function() {
|
| 19855 | push(cadr(p1));
|
| 19856 | runUserDefinedSimplifications();
|
| 19857 | Eval();
|
| 19858 | return simplify();
|
| 19859 | };
|
| 19860 |
|
| 19861 | runUserDefinedSimplifications = function() {
|
| 19862 | var atLeastOneSuccessInRouldOfRulesApplications, eachConsecutiveRuleApplication, eachSimplification, l1, len, len1, m1, numberOfRulesApplications, originalexpanding, success;
|
| 19863 | if (userSimplificationsInListForm.length !== 0 && !Find(cadr(p1), symbol(INTEGRAL))) {
|
| 19864 | originalexpanding = expanding;
|
| 19865 | expanding = false;
|
| 19866 | if (DEBUG) {
|
| 19867 | console.log("runUserDefinedSimplifications passed: " + stack[tos - 1].toString());
|
| 19868 | }
|
| 19869 | Eval();
|
| 19870 | if (DEBUG) {
|
| 19871 | console.log("runUserDefinedSimplifications after eval no expanding: " + stack[tos - 1].toString());
|
| 19872 | }
|
| 19873 | expanding = originalexpanding;
|
| 19874 | p1 = stack[tos - 1];
|
| 19875 | if (DEBUG) {
|
| 19876 | console.log("patterns to be checked: ");
|
| 19877 | }
|
| 19878 | for (l1 = 0, len = userSimplificationsInListForm.length; l1 < len; l1++) {
|
| 19879 | eachSimplification = userSimplificationsInListForm[l1];
|
| 19880 | if (DEBUG) {
|
| 19881 | console.log("..." + eachSimplification);
|
| 19882 | }
|
| 19883 | }
|
| 19884 | atLeastOneSuccessInRouldOfRulesApplications = true;
|
| 19885 | numberOfRulesApplications = 0;
|
| 19886 | while (atLeastOneSuccessInRouldOfRulesApplications && numberOfRulesApplications < MAX_CONSECUTIVE_APPLICATIONS_OF_ALL_RULES) {
|
| 19887 | atLeastOneSuccessInRouldOfRulesApplications = false;
|
| 19888 | numberOfRulesApplications++;
|
| 19889 | for (m1 = 0, len1 = userSimplificationsInListForm.length; m1 < len1; m1++) {
|
| 19890 | eachSimplification = userSimplificationsInListForm[m1];
|
| 19891 | success = true;
|
| 19892 | eachConsecutiveRuleApplication = 0;
|
| 19893 | while (success && eachConsecutiveRuleApplication < MAX_CONSECUTIVE_APPLICATIONS_OF_SINGLE_RULE) {
|
| 19894 | eachConsecutiveRuleApplication++;
|
| 19895 | if (DEBUG) {
|
| 19896 | console.log("simplify - tos: " + tos + " checking pattern: " + eachSimplification + " on: " + p1);
|
| 19897 | }
|
| 19898 | push_symbol(NIL);
|
| 19899 | success = transform(eachSimplification, true);
|
| 19900 | if (success) {
|
| 19901 | atLeastOneSuccessInRouldOfRulesApplications = true;
|
| 19902 | }
|
| 19903 | p1 = stack[tos - 1];
|
| 19904 | if (DEBUG) {
|
| 19905 | console.log("p1 at this stage of simplification: " + p1);
|
| 19906 | }
|
| 19907 | }
|
| 19908 | if (eachConsecutiveRuleApplication === MAX_CONSECUTIVE_APPLICATIONS_OF_SINGLE_RULE) {
|
| 19909 | stop("maximum application of single transformation rule exceeded: " + eachSimplification);
|
| 19910 | }
|
| 19911 | }
|
| 19912 | }
|
| 19913 | if (numberOfRulesApplications === MAX_CONSECUTIVE_APPLICATIONS_OF_ALL_RULES) {
|
| 19914 | stop("maximum application of all transformation rules exceeded ");
|
| 19915 | }
|
| 19916 | if (DEBUG) {
|
| 19917 | console.log("METAX = " + get_binding(symbol(METAX)));
|
| 19918 | console.log("METAA = " + get_binding(symbol(METAA)));
|
| 19919 | return console.log("METAB = " + get_binding(symbol(METAB)));
|
| 19920 | }
|
| 19921 | }
|
| 19922 | };
|
| 19923 |
|
| 19924 | simplifyForCodeGeneration = function() {
|
| 19925 | save();
|
| 19926 | runUserDefinedSimplifications();
|
| 19927 | codeGen = true;
|
| 19928 | simplify_main();
|
| 19929 | codeGen = false;
|
| 19930 | return restore();
|
| 19931 | };
|
| 19932 |
|
| 19933 | simplify = function() {
|
| 19934 | save();
|
| 19935 | simplify_main();
|
| 19936 | return restore();
|
| 19937 | };
|
| 19938 |
|
| 19939 | simplify_main = function() {
|
| 19940 | var args, fbody;
|
| 19941 | p1 = pop();
|
| 19942 | if (codeGen && car(p1) === symbol(FUNCTION)) {
|
| 19943 | fbody = cadr(p1);
|
| 19944 | push(fbody);
|
| 19945 | eval();
|
| 19946 | simplify();
|
| 19947 | p3 = pop();
|
| 19948 | args = caddr(p1);
|
| 19949 | push_symbol(FUNCTION);
|
| 19950 | push(p3);
|
| 19951 | push(args);
|
| 19952 | list(3);
|
| 19953 | p1 = pop();
|
| 19954 | }
|
| 19955 | if (istensor(p1)) {
|
| 19956 | simplify_tensor();
|
| 19957 | return;
|
| 19958 | }
|
| 19959 | if (Find(p1, symbol(FACTORIAL))) {
|
| 19960 | push(p1);
|
| 19961 | simfac();
|
| 19962 | p2 = pop();
|
| 19963 | push(p1);
|
| 19964 | rationalize();
|
| 19965 | simfac();
|
| 19966 | p3 = pop();
|
| 19967 | if (count(p2) < count(p3)) {
|
| 19968 | p1 = p2;
|
| 19969 | } else {
|
| 19970 | p1 = p3;
|
| 19971 | }
|
| 19972 | }
|
| 19973 | f10();
|
| 19974 | f1();
|
| 19975 | f2();
|
| 19976 | f3();
|
| 19977 | f4();
|
| 19978 | f5();
|
| 19979 | f9();
|
| 19980 | simplify_polarRect();
|
| 19981 | if (do_simplify_nested_radicals) {
|
| 19982 | if (simplify_nested_radicals()) {
|
| 19983 | if (DEBUG) {
|
| 19984 | console.log("de-nesting successful into: " + p1.toString());
|
| 19985 | }
|
| 19986 | push(p1);
|
| 19987 | simplify();
|
| 19988 | return;
|
| 19989 | }
|
| 19990 | }
|
| 19991 | simplify_rectToClock();
|
| 19992 | return push(p1);
|
| 19993 | };
|
| 19994 |
|
| 19995 | simplify_tensor = function() {
|
| 19996 | var i, l1, m1, ref2, ref3;
|
| 19997 | i = 0;
|
| 19998 | p2 = alloc_tensor(p1.tensor.nelem);
|
| 19999 | p2.tensor.ndim = p1.tensor.ndim;
|
| 20000 | for (i = l1 = 0, ref2 = p1.tensor.ndim; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 20001 | p2.tensor.dim[i] = p1.tensor.dim[i];
|
| 20002 | }
|
| 20003 | for (i = m1 = 0, ref3 = p1.tensor.nelem; 0 <= ref3 ? m1 < ref3 : m1 > ref3; i = 0 <= ref3 ? ++m1 : --m1) {
|
| 20004 | push(p1.tensor.elem[i]);
|
| 20005 | simplify();
|
| 20006 | p2.tensor.elem[i] = pop();
|
| 20007 | }
|
| 20008 | check_tensor_dimensions(p2);
|
| 20009 | if (iszero(p2)) {
|
| 20010 | p2 = zero;
|
| 20011 | }
|
| 20012 | return push(p2);
|
| 20013 | };
|
| 20014 |
|
| 20015 | f1 = function() {
|
| 20016 | if (car(p1) !== symbol(ADD)) {
|
| 20017 | return;
|
| 20018 | }
|
| 20019 | push(p1);
|
| 20020 | rationalize();
|
| 20021 | p2 = pop();
|
| 20022 | if (count(p2) < count(p1)) {
|
| 20023 | return p1 = p2;
|
| 20024 | }
|
| 20025 | };
|
| 20026 |
|
| 20027 | f2 = function() {
|
| 20028 | if (car(p1) !== symbol(ADD)) {
|
| 20029 | return;
|
| 20030 | }
|
| 20031 | push(p1);
|
| 20032 | Condense();
|
| 20033 | p2 = pop();
|
| 20034 | if (count(p2) <= count(p1)) {
|
| 20035 | return p1 = p2;
|
| 20036 | }
|
| 20037 | };
|
| 20038 |
|
| 20039 | f3 = function() {
|
| 20040 | push(p1);
|
| 20041 | rationalize();
|
| 20042 | negate();
|
| 20043 | rationalize();
|
| 20044 | negate();
|
| 20045 | rationalize();
|
| 20046 | p2 = pop();
|
| 20047 | if (count(p2) < count(p1)) {
|
| 20048 | return p1 = p2;
|
| 20049 | }
|
| 20050 | };
|
| 20051 |
|
| 20052 | f10 = function() {
|
| 20053 | var a, b, carp1, miao, originalexpanding;
|
| 20054 | carp1 = car(p1);
|
| 20055 | miao = cdr(p1);
|
| 20056 | if (carp1 === symbol(MULTIPLY) || isinnerordot(p1)) {
|
| 20057 | if ((car(car(cdr(p1))) === symbol(TRANSPOSE)) && (car(car(cdr(cdr(p1)))) === symbol(TRANSPOSE))) {
|
| 20058 | if (DEBUG) {
|
| 20059 | console.log("maybe collecting a transpose " + p1);
|
| 20060 | }
|
| 20061 | a = cadr(car(cdr(p1)));
|
| 20062 | b = cadr(car(cdr(cdr(p1))));
|
| 20063 | if (carp1 === symbol(MULTIPLY)) {
|
| 20064 | push(a);
|
| 20065 | push(b);
|
| 20066 | multiply();
|
| 20067 | } else if (isinnerordot(p1)) {
|
| 20068 | push(b);
|
| 20069 | push(a);
|
| 20070 | inner();
|
| 20071 | }
|
| 20072 | push_integer(1);
|
| 20073 | push_integer(2);
|
| 20074 | originalexpanding = expanding;
|
| 20075 | expanding = false;
|
| 20076 | transpose();
|
| 20077 | expanding = originalexpanding;
|
| 20078 | p2 = pop();
|
| 20079 | if (count(p2) < count(p1)) {
|
| 20080 | p1 = p2;
|
| 20081 | }
|
| 20082 | if (DEBUG) {
|
| 20083 | return console.log("collecting a transpose " + p2);
|
| 20084 | }
|
| 20085 | }
|
| 20086 | }
|
| 20087 | };
|
| 20088 |
|
| 20089 | f4 = function() {
|
| 20090 | if (iszero(p1)) {
|
| 20091 | return;
|
| 20092 | }
|
| 20093 | push(p1);
|
| 20094 | rationalize();
|
| 20095 | inverse();
|
| 20096 | rationalize();
|
| 20097 | inverse();
|
| 20098 | rationalize();
|
| 20099 | p2 = pop();
|
| 20100 | if (count(p2) < count(p1)) {
|
| 20101 | return p1 = p2;
|
| 20102 | }
|
| 20103 | };
|
| 20104 |
|
| 20105 | simplify_trig = function() {
|
| 20106 | save();
|
| 20107 | p1 = pop();
|
| 20108 | f5();
|
| 20109 | push(p1);
|
| 20110 | return restore();
|
| 20111 | };
|
| 20112 |
|
| 20113 | f5 = function() {
|
| 20114 | if (Find(p1, symbol(SIN)) === 0 && Find(p1, symbol(COS)) === 0) {
|
| 20115 | return;
|
| 20116 | }
|
| 20117 | p2 = p1;
|
| 20118 | trigmode = 1;
|
| 20119 | push(p2);
|
| 20120 | Eval();
|
| 20121 | p3 = pop();
|
| 20122 | trigmode = 2;
|
| 20123 | push(p2);
|
| 20124 | Eval();
|
| 20125 | p4 = pop();
|
| 20126 | trigmode = 0;
|
| 20127 | if (count(p4) < count(p3) || nterms(p4) < nterms(p3)) {
|
| 20128 | p3 = p4;
|
| 20129 | }
|
| 20130 | if (count(p3) < count(p1) || nterms(p3) < nterms(p1)) {
|
| 20131 | return p1 = p3;
|
| 20132 | }
|
| 20133 | };
|
| 20134 |
|
| 20135 | f9 = function() {
|
| 20136 | if (car(p1) !== symbol(ADD)) {
|
| 20137 | return;
|
| 20138 | }
|
| 20139 | push_integer(0);
|
| 20140 | p2 = cdr(p1);
|
| 20141 | while (iscons(p2)) {
|
| 20142 | push(car(p2));
|
| 20143 | simplify();
|
| 20144 | add();
|
| 20145 | p2 = cdr(p2);
|
| 20146 | }
|
| 20147 | p2 = pop();
|
| 20148 | if (count(p2) < count(p1)) {
|
| 20149 | return p1 = p2;
|
| 20150 | }
|
| 20151 | };
|
| 20152 |
|
| 20153 | simplify_rectToClock = function() {
|
| 20154 | if (Find(p1, symbol(SIN)) === 0 && Find(p1, symbol(COS)) === 0) {
|
| 20155 | return;
|
| 20156 | }
|
| 20157 | push(p1);
|
| 20158 | Eval();
|
| 20159 | clockform();
|
| 20160 | p2 = pop();
|
| 20161 | if (DEBUG) {
|
| 20162 | console.log("before simplification clockform: " + p1 + " after: " + p2);
|
| 20163 | }
|
| 20164 | if (count(p2) < count(p1)) {
|
| 20165 | return p1 = p2;
|
| 20166 | }
|
| 20167 | };
|
| 20168 |
|
| 20169 | simplify_polarRect = function() {
|
| 20170 | push(p1);
|
| 20171 | polarRectAMinusOneBase();
|
| 20172 | Eval();
|
| 20173 | p2 = pop();
|
| 20174 | if (count(p2) < count(p1)) {
|
| 20175 | return p1 = p2;
|
| 20176 | }
|
| 20177 | };
|
| 20178 |
|
| 20179 | polarRectAMinusOneBase = function() {
|
| 20180 | var h;
|
| 20181 | save();
|
| 20182 | p1 = pop();
|
| 20183 | if (isimaginaryunit(p1)) {
|
| 20184 | push(p1);
|
| 20185 | restore();
|
| 20186 | return;
|
| 20187 | }
|
| 20188 | if (equal(car(p1), symbol(POWER)) && isminusone(cadr(p1))) {
|
| 20189 | push(one);
|
| 20190 | negate();
|
| 20191 | push(caddr(p1));
|
| 20192 | polarRectAMinusOneBase();
|
| 20193 | power();
|
| 20194 | polar();
|
| 20195 | rect();
|
| 20196 | } else if (iscons(p1)) {
|
| 20197 | h = tos;
|
| 20198 | while (iscons(p1)) {
|
| 20199 | push(car(p1));
|
| 20200 | polarRectAMinusOneBase();
|
| 20201 | p1 = cdr(p1);
|
| 20202 | }
|
| 20203 | list(tos - h);
|
| 20204 | } else {
|
| 20205 | push(p1);
|
| 20206 | }
|
| 20207 | restore();
|
| 20208 | };
|
| 20209 |
|
| 20210 | nterms = function(p) {
|
| 20211 | if (car(p) !== symbol(ADD)) {
|
| 20212 | return 1;
|
| 20213 | } else {
|
| 20214 | return length(p) - 1;
|
| 20215 | }
|
| 20216 | };
|
| 20217 |
|
| 20218 | simplify_nested_radicals = function() {
|
| 20219 | var prev_expanding, simplificationWithCondense, simplificationWithoutCondense, somethingSimplified;
|
| 20220 | if (recursionLevelNestedRadicalsRemoval > 0) {
|
| 20221 | if (DEBUG) {
|
| 20222 | console.log("denesting bailing out because of too much recursion");
|
| 20223 | }
|
| 20224 | return false;
|
| 20225 | }
|
| 20226 | push(p1);
|
| 20227 | somethingSimplified = take_care_of_nested_radicals();
|
| 20228 | simplificationWithoutCondense = stack[tos - 1];
|
| 20229 | prev_expanding = expanding;
|
| 20230 | expanding = 0;
|
| 20231 | yycondense();
|
| 20232 | expanding = prev_expanding;
|
| 20233 | simplificationWithCondense = pop();
|
| 20234 | if (countOccurrencesOfSymbol(symbol(POWER), simplificationWithoutCondense) < countOccurrencesOfSymbol(symbol(POWER), simplificationWithCondense)) {
|
| 20235 | push(simplificationWithoutCondense);
|
| 20236 | } else {
|
| 20237 | push(simplificationWithCondense);
|
| 20238 | }
|
| 20239 | p1 = pop();
|
| 20240 | return somethingSimplified;
|
| 20241 | };
|
| 20242 |
|
| 20243 | take_care_of_nested_radicals = function() {
|
| 20244 | var A, B, C, SOLUTION, anyRadicalSimplificationWorked, base, checkSize, commonBases, commonInnerExponent, countingTerms, eachSolution, exponent, firstTerm, h, i, innerbase, innerexponent, l1, len, len1, len2, len3, lowercase_a, lowercase_b, m1, n1, numberOfTerms, o1, possibleNewExpression, possibleNewExpressionValue, possibleRationalSolutions, possibleSolutions, potentialPower, realOfpossibleRationalSolutions, ref2, secondTerm, secondTermFactor, termsThatAreNotPowers, whichRationalSolution;
|
| 20245 | if (recursionLevelNestedRadicalsRemoval > 0) {
|
| 20246 | if (DEBUG) {
|
| 20247 | console.log("denesting bailing out because of too much recursion");
|
| 20248 | }
|
| 20249 | return false;
|
| 20250 | }
|
| 20251 | save();
|
| 20252 | p1 = pop();
|
| 20253 | if (equal(car(p1), symbol(POWER))) {
|
| 20254 | base = cadr(p1);
|
| 20255 | exponent = caddr(p1);
|
| 20256 | if (!isminusone(exponent) && equal(car(base), symbol(ADD)) && isfraction(exponent) && (equalq(exponent, 1, 3) || equalq(exponent, 1, 2))) {
|
| 20257 | firstTerm = cadr(base);
|
| 20258 | push(firstTerm);
|
| 20259 | take_care_of_nested_radicals();
|
| 20260 | pop();
|
| 20261 | secondTerm = caddr(base);
|
| 20262 | push(secondTerm);
|
| 20263 | take_care_of_nested_radicals();
|
| 20264 | pop();
|
| 20265 | numberOfTerms = 0;
|
| 20266 | countingTerms = base;
|
| 20267 | while (cdr(countingTerms) !== symbol(NIL)) {
|
| 20268 | numberOfTerms++;
|
| 20269 | countingTerms = cdr(countingTerms);
|
| 20270 | }
|
| 20271 | if (numberOfTerms > 2) {
|
| 20272 | push(p1);
|
| 20273 | restore();
|
| 20274 | return false;
|
| 20275 | }
|
| 20276 | commonInnerExponent = null;
|
| 20277 | commonBases = [];
|
| 20278 | termsThatAreNotPowers = [];
|
| 20279 | if (car(secondTerm) === symbol(MULTIPLY)) {
|
| 20280 | secondTermFactor = cdr(secondTerm);
|
| 20281 | if (iscons(secondTermFactor)) {
|
| 20282 | while (iscons(secondTermFactor)) {
|
| 20283 | potentialPower = car(secondTermFactor);
|
| 20284 | if (car(potentialPower) === symbol(POWER)) {
|
| 20285 | innerbase = cadr(potentialPower);
|
| 20286 | innerexponent = caddr(potentialPower);
|
| 20287 | if (equalq(innerexponent, 1, 2)) {
|
| 20288 | if (commonInnerExponent == null) {
|
| 20289 | commonInnerExponent = innerexponent;
|
| 20290 | commonBases.push(innerbase);
|
| 20291 | } else {
|
| 20292 | if (equal(innerexponent, commonInnerExponent)) {
|
| 20293 | commonBases.push(innerbase);
|
| 20294 | } else {
|
| 20295 |
|
| 20296 | }
|
| 20297 | }
|
| 20298 | }
|
| 20299 | } else {
|
| 20300 | termsThatAreNotPowers.push(potentialPower);
|
| 20301 | }
|
| 20302 | secondTermFactor = cdr(secondTermFactor);
|
| 20303 | }
|
| 20304 | }
|
| 20305 | } else if (car(secondTerm) === symbol(POWER)) {
|
| 20306 | innerbase = cadr(secondTerm);
|
| 20307 | innerexponent = caddr(secondTerm);
|
| 20308 | if ((commonInnerExponent == null) && equalq(innerexponent, 1, 2)) {
|
| 20309 | commonInnerExponent = innerexponent;
|
| 20310 | commonBases.push(innerbase);
|
| 20311 | }
|
| 20312 | }
|
| 20313 | if (commonBases.length === 0) {
|
| 20314 | push(p1);
|
| 20315 | restore();
|
| 20316 | return false;
|
| 20317 | }
|
| 20318 | A = firstTerm;
|
| 20319 | push_integer(1);
|
| 20320 | for (l1 = 0, len = commonBases.length; l1 < len; l1++) {
|
| 20321 | i = commonBases[l1];
|
| 20322 | push(i);
|
| 20323 | multiply();
|
| 20324 | }
|
| 20325 | C = pop();
|
| 20326 | push_integer(1);
|
| 20327 | for (m1 = 0, len1 = termsThatAreNotPowers.length; m1 < len1; m1++) {
|
| 20328 | i = termsThatAreNotPowers[m1];
|
| 20329 | push(i);
|
| 20330 | multiply();
|
| 20331 | }
|
| 20332 | B = pop();
|
| 20333 | if (equalq(exponent, 1, 3)) {
|
| 20334 | push(A);
|
| 20335 | negate();
|
| 20336 | push(C);
|
| 20337 | multiply();
|
| 20338 | push(B);
|
| 20339 | divide();
|
| 20340 | checkSize = pop();
|
| 20341 | push(checkSize);
|
| 20342 | real();
|
| 20343 | yyfloat();
|
| 20344 | if (Math.abs(pop().d) > Math.pow(2, 32)) {
|
| 20345 | push(p1);
|
| 20346 | restore();
|
| 20347 | return false;
|
| 20348 | }
|
| 20349 | push(checkSize);
|
| 20350 | push_integer(3);
|
| 20351 | push(C);
|
| 20352 | multiply();
|
| 20353 | checkSize = pop();
|
| 20354 | push(checkSize);
|
| 20355 | real();
|
| 20356 | yyfloat();
|
| 20357 | if (Math.abs(pop().d) > Math.pow(2, 32)) {
|
| 20358 | pop();
|
| 20359 | push(p1);
|
| 20360 | restore();
|
| 20361 | return false;
|
| 20362 | }
|
| 20363 | push(checkSize);
|
| 20364 | push(symbol(SECRETX));
|
| 20365 | multiply();
|
| 20366 | push_integer(-3);
|
| 20367 | push(A);
|
| 20368 | multiply();
|
| 20369 | push(B);
|
| 20370 | divide();
|
| 20371 | checkSize = pop();
|
| 20372 | push(checkSize);
|
| 20373 | real();
|
| 20374 | yyfloat();
|
| 20375 | if (Math.abs(pop().d) > Math.pow(2, 32)) {
|
| 20376 | pop();
|
| 20377 | pop();
|
| 20378 | push(p1);
|
| 20379 | restore();
|
| 20380 | return false;
|
| 20381 | }
|
| 20382 | push(checkSize);
|
| 20383 | push(symbol(SECRETX));
|
| 20384 | push_integer(2);
|
| 20385 | power();
|
| 20386 | multiply();
|
| 20387 | push_integer(1);
|
| 20388 | push(symbol(SECRETX));
|
| 20389 | push_integer(3);
|
| 20390 | power();
|
| 20391 | multiply();
|
| 20392 | add();
|
| 20393 | add();
|
| 20394 | add();
|
| 20395 | } else if (equalq(exponent, 1, 2)) {
|
| 20396 | push(C);
|
| 20397 | checkSize = pop();
|
| 20398 | push(checkSize);
|
| 20399 | real();
|
| 20400 | yyfloat();
|
| 20401 | if (Math.abs(pop().d) > Math.pow(2, 32)) {
|
| 20402 | push(p1);
|
| 20403 | restore();
|
| 20404 | return false;
|
| 20405 | }
|
| 20406 | push(checkSize);
|
| 20407 | push_integer(-2);
|
| 20408 | push(A);
|
| 20409 | multiply();
|
| 20410 | push(B);
|
| 20411 | divide();
|
| 20412 | checkSize = pop();
|
| 20413 | push(checkSize);
|
| 20414 | real();
|
| 20415 | yyfloat();
|
| 20416 | if (Math.abs(pop().d) > Math.pow(2, 32)) {
|
| 20417 | pop();
|
| 20418 | push(p1);
|
| 20419 | restore();
|
| 20420 | return false;
|
| 20421 | }
|
| 20422 | push(checkSize);
|
| 20423 | push(symbol(SECRETX));
|
| 20424 | multiply();
|
| 20425 | push_integer(1);
|
| 20426 | push(symbol(SECRETX));
|
| 20427 | push_integer(2);
|
| 20428 | power();
|
| 20429 | multiply();
|
| 20430 | add();
|
| 20431 | add();
|
| 20432 | }
|
| 20433 | push(symbol(SECRETX));
|
| 20434 | recursionLevelNestedRadicalsRemoval++;
|
| 20435 | roots();
|
| 20436 | recursionLevelNestedRadicalsRemoval--;
|
| 20437 | if (equal(stack[tos - 1], symbol(NIL))) {
|
| 20438 | if (DEBUG) {
|
| 20439 | console.log("roots bailed out because of too much recursion");
|
| 20440 | }
|
| 20441 | pop();
|
| 20442 | push(p1);
|
| 20443 | restore();
|
| 20444 | return false;
|
| 20445 | }
|
| 20446 | possibleSolutions = [];
|
| 20447 | ref2 = stack[tos - 1].tensor.elem;
|
| 20448 | for (n1 = 0, len2 = ref2.length; n1 < len2; n1++) {
|
| 20449 | eachSolution = ref2[n1];
|
| 20450 | if (!Find(eachSolution, symbol(POWER))) {
|
| 20451 | possibleSolutions.push(eachSolution);
|
| 20452 | }
|
| 20453 | }
|
| 20454 | pop();
|
| 20455 | if (possibleSolutions.length === 0) {
|
| 20456 | push(p1);
|
| 20457 | restore();
|
| 20458 | return false;
|
| 20459 | }
|
| 20460 | possibleRationalSolutions = [];
|
| 20461 | realOfpossibleRationalSolutions = [];
|
| 20462 | for (o1 = 0, len3 = possibleSolutions.length; o1 < len3; o1++) {
|
| 20463 | i = possibleSolutions[o1];
|
| 20464 | push(i);
|
| 20465 | real();
|
| 20466 | yyfloat();
|
| 20467 | possibleRationalSolutions.push(i);
|
| 20468 | realOfpossibleRationalSolutions.push(pop().d);
|
| 20469 | }
|
| 20470 | whichRationalSolution = realOfpossibleRationalSolutions.indexOf(Math.max.apply(Math, realOfpossibleRationalSolutions));
|
| 20471 | SOLUTION = possibleRationalSolutions[whichRationalSolution];
|
| 20472 |
|
| 20473 | |
| 20474 | |
| 20475 | |
| 20476 | |
| 20477 | |
| 20478 | |
| 20479 | |
| 20480 | |
| 20481 | |
| 20482 | |
| 20483 | |
| 20484 | |
| 20485 | |
| 20486 | |
| 20487 | |
| 20488 | |
| 20489 | |
| 20490 | |
| 20491 | |
| 20492 | |
| 20493 | |
| 20494 | |
| 20495 | |
| 20496 | |
| 20497 | |
| 20498 | |
| 20499 | |
| 20500 | |
| 20501 | |
| 20502 | |
| 20503 | |
| 20504 | |
| 20505 | |
| 20506 | |
| 20507 | |
| 20508 | |
| 20509 | |
| 20510 | |
| 20511 | |
| 20512 | |
| 20513 | |
| 20514 |
|
| 20515 | if (equalq(exponent, 1, 3)) {
|
| 20516 | push(A);
|
| 20517 | push(SOLUTION);
|
| 20518 | push_integer(3);
|
| 20519 | power();
|
| 20520 | push_integer(3);
|
| 20521 | push(C);
|
| 20522 | multiply();
|
| 20523 | push(SOLUTION);
|
| 20524 | multiply();
|
| 20525 | add();
|
| 20526 | divide();
|
| 20527 | push_rational(1, 3);
|
| 20528 | power();
|
| 20529 | } else if (equalq(exponent, 1, 2)) {
|
| 20530 | push(A);
|
| 20531 | push(SOLUTION);
|
| 20532 | push_integer(2);
|
| 20533 | power();
|
| 20534 | push(C);
|
| 20535 | add();
|
| 20536 | divide();
|
| 20537 | push_rational(1, 2);
|
| 20538 | power();
|
| 20539 | }
|
| 20540 | lowercase_b = pop();
|
| 20541 | if (lowercase_b == null) {
|
| 20542 | push(p1);
|
| 20543 | restore();
|
| 20544 | return false;
|
| 20545 | }
|
| 20546 | push(lowercase_b);
|
| 20547 | push(SOLUTION);
|
| 20548 | multiply();
|
| 20549 | if (equalq(exponent, 1, 3)) {
|
| 20550 | lowercase_a = pop();
|
| 20551 | push(lowercase_b);
|
| 20552 | push(C);
|
| 20553 | push_rational(1, 2);
|
| 20554 | power();
|
| 20555 | multiply();
|
| 20556 | push(lowercase_a);
|
| 20557 | add();
|
| 20558 | simplify();
|
| 20559 | } else if (equalq(exponent, 1, 2)) {
|
| 20560 | lowercase_a = pop();
|
| 20561 | push(lowercase_b);
|
| 20562 | push(C);
|
| 20563 | push_rational(1, 2);
|
| 20564 | power();
|
| 20565 | multiply();
|
| 20566 | push(lowercase_a);
|
| 20567 | add();
|
| 20568 | simplify();
|
| 20569 | possibleNewExpression = pop();
|
| 20570 | push(possibleNewExpression);
|
| 20571 | real();
|
| 20572 | yyfloat();
|
| 20573 | possibleNewExpressionValue = pop();
|
| 20574 | if (!isnegativenumber(possibleNewExpressionValue)) {
|
| 20575 | push(possibleNewExpression);
|
| 20576 | } else {
|
| 20577 | push(lowercase_b);
|
| 20578 | negate();
|
| 20579 | lowercase_b = pop();
|
| 20580 | push(lowercase_a);
|
| 20581 | negate();
|
| 20582 | lowercase_a = pop();
|
| 20583 | push(lowercase_b);
|
| 20584 | push(C);
|
| 20585 | push_rational(1, 2);
|
| 20586 | power();
|
| 20587 | multiply();
|
| 20588 | push(lowercase_a);
|
| 20589 | add();
|
| 20590 | simplify();
|
| 20591 | }
|
| 20592 | }
|
| 20593 | p1 = pop();
|
| 20594 | push(p1);
|
| 20595 | restore();
|
| 20596 | return true;
|
| 20597 | } else {
|
| 20598 | push(p1);
|
| 20599 | restore();
|
| 20600 | return false;
|
| 20601 | }
|
| 20602 | } else if (iscons(p1)) {
|
| 20603 | h = tos;
|
| 20604 | anyRadicalSimplificationWorked = false;
|
| 20605 | while (iscons(p1)) {
|
| 20606 | push(car(p1));
|
| 20607 | anyRadicalSimplificationWorked = anyRadicalSimplificationWorked || take_care_of_nested_radicals();
|
| 20608 | p1 = cdr(p1);
|
| 20609 | }
|
| 20610 | list(tos - h);
|
| 20611 | restore();
|
| 20612 | return anyRadicalSimplificationWorked;
|
| 20613 | } else {
|
| 20614 | push(p1);
|
| 20615 | restore();
|
| 20616 | return false;
|
| 20617 | }
|
| 20618 | throw new Error("control flow should never reach here");
|
| 20619 | };
|
| 20620 |
|
| 20621 | Eval_sin = function() {
|
| 20622 | push(cadr(p1));
|
| 20623 | Eval();
|
| 20624 | return sine();
|
| 20625 | };
|
| 20626 |
|
| 20627 | sine = function() {
|
| 20628 | save();
|
| 20629 | p1 = pop();
|
| 20630 | if (car(p1) === symbol(ADD)) {
|
| 20631 | sine_of_angle_sum();
|
| 20632 | } else {
|
| 20633 | sine_of_angle();
|
| 20634 | }
|
| 20635 | return restore();
|
| 20636 | };
|
| 20637 |
|
| 20638 | sine_of_angle_sum = function() {
|
| 20639 | p2 = cdr(p1);
|
| 20640 | while (iscons(p2)) {
|
| 20641 | p4 = car(p2);
|
| 20642 | if (isnpi(p4)) {
|
| 20643 | push(p1);
|
| 20644 | push(p4);
|
| 20645 | subtract();
|
| 20646 | p3 = pop();
|
| 20647 | push(p3);
|
| 20648 | sine();
|
| 20649 | push(p4);
|
| 20650 | cosine();
|
| 20651 | multiply();
|
| 20652 | push(p3);
|
| 20653 | cosine();
|
| 20654 | push(p4);
|
| 20655 | sine();
|
| 20656 | multiply();
|
| 20657 | add();
|
| 20658 | return;
|
| 20659 | }
|
| 20660 | p2 = cdr(p2);
|
| 20661 | }
|
| 20662 | return sine_of_angle();
|
| 20663 | };
|
| 20664 |
|
| 20665 | sine_of_angle = function() {
|
| 20666 | var d, n;
|
| 20667 | if (car(p1) === symbol(ARCSIN)) {
|
| 20668 | push(cadr(p1));
|
| 20669 | return;
|
| 20670 | }
|
| 20671 | if (isdouble(p1)) {
|
| 20672 | d = Math.sin(p1.d);
|
| 20673 | if (Math.abs(d) < 1e-10) {
|
| 20674 | d = 0.0;
|
| 20675 | }
|
| 20676 | push_double(d);
|
| 20677 | return;
|
| 20678 | }
|
| 20679 | if (isnegative(p1)) {
|
| 20680 | push(p1);
|
| 20681 | negate();
|
| 20682 | sine();
|
| 20683 | negate();
|
| 20684 | return;
|
| 20685 | }
|
| 20686 | if (car(p1) === symbol(ARCTAN)) {
|
| 20687 | push(cadr(p1));
|
| 20688 | push_integer(1);
|
| 20689 | push(cadr(p1));
|
| 20690 | push_integer(2);
|
| 20691 | power();
|
| 20692 | add();
|
| 20693 | push_rational(-1, 2);
|
| 20694 | power();
|
| 20695 | multiply();
|
| 20696 | return;
|
| 20697 | }
|
| 20698 | push(p1);
|
| 20699 | push_integer(180);
|
| 20700 | multiply();
|
| 20701 | if (evaluatingAsFloats) {
|
| 20702 | push_double(Math.PI);
|
| 20703 | } else {
|
| 20704 | push_symbol(PI);
|
| 20705 | }
|
| 20706 | divide();
|
| 20707 | n = pop_integer();
|
| 20708 | if (n < 0 || isNaN(n)) {
|
| 20709 | push(symbol(SIN));
|
| 20710 | push(p1);
|
| 20711 | list(2);
|
| 20712 | return;
|
| 20713 | }
|
| 20714 | switch (n % 360) {
|
| 20715 | case 0:
|
| 20716 | case 180:
|
| 20717 | return push_integer(0);
|
| 20718 | case 30:
|
| 20719 | case 150:
|
| 20720 | return push_rational(1, 2);
|
| 20721 | case 210:
|
| 20722 | case 330:
|
| 20723 | return push_rational(-1, 2);
|
| 20724 | case 45:
|
| 20725 | case 135:
|
| 20726 | push_rational(1, 2);
|
| 20727 | push_integer(2);
|
| 20728 | push_rational(1, 2);
|
| 20729 | power();
|
| 20730 | return multiply();
|
| 20731 | case 225:
|
| 20732 | case 315:
|
| 20733 | push_rational(-1, 2);
|
| 20734 | push_integer(2);
|
| 20735 | push_rational(1, 2);
|
| 20736 | power();
|
| 20737 | return multiply();
|
| 20738 | case 60:
|
| 20739 | case 120:
|
| 20740 | push_rational(1, 2);
|
| 20741 | push_integer(3);
|
| 20742 | push_rational(1, 2);
|
| 20743 | power();
|
| 20744 | return multiply();
|
| 20745 | case 240:
|
| 20746 | case 300:
|
| 20747 | push_rational(-1, 2);
|
| 20748 | push_integer(3);
|
| 20749 | push_rational(1, 2);
|
| 20750 | power();
|
| 20751 | return multiply();
|
| 20752 | case 90:
|
| 20753 | return push_integer(1);
|
| 20754 | case 270:
|
| 20755 | return push_integer(-1);
|
| 20756 | default:
|
| 20757 | push(symbol(SIN));
|
| 20758 | push(p1);
|
| 20759 | return list(2);
|
| 20760 | }
|
| 20761 | };
|
| 20762 |
|
| 20763 | Eval_sinh = function() {
|
| 20764 | push(cadr(p1));
|
| 20765 | Eval();
|
| 20766 | return ysinh();
|
| 20767 | };
|
| 20768 |
|
| 20769 | ysinh = function() {
|
| 20770 | save();
|
| 20771 | yysinh();
|
| 20772 | return restore();
|
| 20773 | };
|
| 20774 |
|
| 20775 | yysinh = function() {
|
| 20776 | var d;
|
| 20777 | d = 0.0;
|
| 20778 | p1 = pop();
|
| 20779 | if (car(p1) === symbol(ARCSINH)) {
|
| 20780 | push(cadr(p1));
|
| 20781 | return;
|
| 20782 | }
|
| 20783 | if (isdouble(p1)) {
|
| 20784 | d = Math.sinh(p1.d);
|
| 20785 | if (Math.abs(d) < 1e-10) {
|
| 20786 | d = 0.0;
|
| 20787 | }
|
| 20788 | push_double(d);
|
| 20789 | return;
|
| 20790 | }
|
| 20791 | if (iszero(p1)) {
|
| 20792 | push(zero);
|
| 20793 | return;
|
| 20794 | }
|
| 20795 | push_symbol(SINH);
|
| 20796 | push(p1);
|
| 20797 | return list(2);
|
| 20798 | };
|
| 20799 |
|
| 20800 |
|
| 20801 | |
| 20802 | |
| 20803 | |
| 20804 | |
| 20805 | |
| 20806 | |
| 20807 | |
| 20808 | |
| 20809 | |
| 20810 | |
| 20811 |
|
| 20812 |
|
| 20813 | subst = function() {
|
| 20814 | var i, l1, m1, ref2, ref3;
|
| 20815 | i = 0;
|
| 20816 | save();
|
| 20817 | p3 = pop();
|
| 20818 | p2 = pop();
|
| 20819 | if (p2 === symbol(NIL) || p3 === symbol(NIL)) {
|
| 20820 | restore();
|
| 20821 | return;
|
| 20822 | }
|
| 20823 | p1 = pop();
|
| 20824 | if (istensor(p1)) {
|
| 20825 | p4 = alloc_tensor(p1.tensor.nelem);
|
| 20826 | p4.tensor.ndim = p1.tensor.ndim;
|
| 20827 | for (i = l1 = 0, ref2 = p1.tensor.ndim; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 20828 | p4.tensor.dim[i] = p1.tensor.dim[i];
|
| 20829 | }
|
| 20830 | for (i = m1 = 0, ref3 = p1.tensor.nelem; 0 <= ref3 ? m1 < ref3 : m1 > ref3; i = 0 <= ref3 ? ++m1 : --m1) {
|
| 20831 | push(p1.tensor.elem[i]);
|
| 20832 | push(p2);
|
| 20833 | push(p3);
|
| 20834 | subst();
|
| 20835 | p4.tensor.elem[i] = pop();
|
| 20836 | check_tensor_dimensions(p4);
|
| 20837 | }
|
| 20838 | push(p4);
|
| 20839 | } else if (equal(p1, p2)) {
|
| 20840 | push(p3);
|
| 20841 | } else if (iscons(p1)) {
|
| 20842 | push(car(p1));
|
| 20843 | push(p2);
|
| 20844 | push(p3);
|
| 20845 | subst();
|
| 20846 | push(cdr(p1));
|
| 20847 | push(p2);
|
| 20848 | push(p3);
|
| 20849 | subst();
|
| 20850 | cons();
|
| 20851 | } else {
|
| 20852 | push(p1);
|
| 20853 | }
|
| 20854 | return restore();
|
| 20855 | };
|
| 20856 |
|
| 20857 | Eval_sum = function() {
|
| 20858 | var body, i, indexVariable, j, k, l1, ref2, ref3;
|
| 20859 | i = 0;
|
| 20860 | j = 0;
|
| 20861 | k = 0;
|
| 20862 | body = cadr(p1);
|
| 20863 | indexVariable = caddr(p1);
|
| 20864 | if (!issymbol(p6)) {
|
| 20865 | stop("sum: 1st arg?");
|
| 20866 | }
|
| 20867 | push(cadddr(p1));
|
| 20868 | Eval();
|
| 20869 | j = pop_integer();
|
| 20870 | if (isNaN(j)) {
|
| 20871 | push(p1);
|
| 20872 | return;
|
| 20873 | }
|
| 20874 | push(caddddr(p1));
|
| 20875 | Eval();
|
| 20876 | k = pop_integer();
|
| 20877 | if (isNaN(k)) {
|
| 20878 | push(p1);
|
| 20879 | return;
|
| 20880 | }
|
| 20881 | p4 = get_binding(indexVariable);
|
| 20882 | push_integer(0);
|
| 20883 | for (i = l1 = ref2 = j, ref3 = k; ref2 <= ref3 ? l1 <= ref3 : l1 >= ref3; i = ref2 <= ref3 ? ++l1 : --l1) {
|
| 20884 | push_integer(i);
|
| 20885 | p5 = pop();
|
| 20886 | set_binding(indexVariable, p5);
|
| 20887 | push(body);
|
| 20888 | Eval();
|
| 20889 | add();
|
| 20890 | }
|
| 20891 | return set_binding(indexVariable, p4);
|
| 20892 | };
|
| 20893 |
|
| 20894 | Eval_tan = function() {
|
| 20895 | push(cadr(p1));
|
| 20896 | Eval();
|
| 20897 | return tangent();
|
| 20898 | };
|
| 20899 |
|
| 20900 | tangent = function() {
|
| 20901 | save();
|
| 20902 | yytangent();
|
| 20903 | return restore();
|
| 20904 | };
|
| 20905 |
|
| 20906 | yytangent = function() {
|
| 20907 | var d, n;
|
| 20908 | n = 0;
|
| 20909 | d = 0.0;
|
| 20910 | p1 = pop();
|
| 20911 | if (car(p1) === symbol(ARCTAN)) {
|
| 20912 | push(cadr(p1));
|
| 20913 | return;
|
| 20914 | }
|
| 20915 | if (isdouble(p1)) {
|
| 20916 | d = Math.tan(p1.d);
|
| 20917 | if (Math.abs(d) < 1e-10) {
|
| 20918 | d = 0.0;
|
| 20919 | }
|
| 20920 | push_double(d);
|
| 20921 | return;
|
| 20922 | }
|
| 20923 | if (isnegative(p1)) {
|
| 20924 | push(p1);
|
| 20925 | negate();
|
| 20926 | tangent();
|
| 20927 | negate();
|
| 20928 | return;
|
| 20929 | }
|
| 20930 | push(p1);
|
| 20931 | push_integer(180);
|
| 20932 | multiply();
|
| 20933 | if (evaluatingAsFloats) {
|
| 20934 | push_double(Math.PI);
|
| 20935 | } else {
|
| 20936 | push_symbol(PI);
|
| 20937 | }
|
| 20938 | divide();
|
| 20939 | n = pop_integer();
|
| 20940 | if (n < 0 || isNaN(n)) {
|
| 20941 | push(symbol(TAN));
|
| 20942 | push(p1);
|
| 20943 | list(2);
|
| 20944 | return;
|
| 20945 | }
|
| 20946 | switch (n % 360) {
|
| 20947 | case 0:
|
| 20948 | case 180:
|
| 20949 | return push_integer(0);
|
| 20950 | case 30:
|
| 20951 | case 210:
|
| 20952 | push_rational(1, 3);
|
| 20953 | push_integer(3);
|
| 20954 | push_rational(1, 2);
|
| 20955 | power();
|
| 20956 | return multiply();
|
| 20957 | case 150:
|
| 20958 | case 330:
|
| 20959 | push_rational(-1, 3);
|
| 20960 | push_integer(3);
|
| 20961 | push_rational(1, 2);
|
| 20962 | power();
|
| 20963 | return multiply();
|
| 20964 | case 45:
|
| 20965 | case 225:
|
| 20966 | return push_integer(1);
|
| 20967 | case 135:
|
| 20968 | case 315:
|
| 20969 | return push_integer(-1);
|
| 20970 | case 60:
|
| 20971 | case 240:
|
| 20972 | push_integer(3);
|
| 20973 | push_rational(1, 2);
|
| 20974 | return power();
|
| 20975 | case 120:
|
| 20976 | case 300:
|
| 20977 | push_integer(3);
|
| 20978 | push_rational(1, 2);
|
| 20979 | power();
|
| 20980 | return negate();
|
| 20981 | default:
|
| 20982 | push(symbol(TAN));
|
| 20983 | push(p1);
|
| 20984 | return list(2);
|
| 20985 | }
|
| 20986 | };
|
| 20987 |
|
| 20988 | Eval_tanh = function() {
|
| 20989 | var d;
|
| 20990 | d = 0.0;
|
| 20991 | push(cadr(p1));
|
| 20992 | Eval();
|
| 20993 | p1 = pop();
|
| 20994 | if (car(p1) === symbol(ARCTANH)) {
|
| 20995 | push(cadr(p1));
|
| 20996 | return;
|
| 20997 | }
|
| 20998 | if (isdouble(p1)) {
|
| 20999 | d = Math.tanh(p1.d);
|
| 21000 | if (Math.abs(d) < 1e-10) {
|
| 21001 | d = 0.0;
|
| 21002 | }
|
| 21003 | push_double(d);
|
| 21004 | return;
|
| 21005 | }
|
| 21006 | if (iszero(p1)) {
|
| 21007 | push(zero);
|
| 21008 | return;
|
| 21009 | }
|
| 21010 | push_symbol(TANH);
|
| 21011 | push(p1);
|
| 21012 | return list(2);
|
| 21013 | };
|
| 21014 |
|
| 21015 |
|
| 21016 | |
| 21017 | |
| 21018 | |
| 21019 | |
| 21020 | |
| 21021 | |
| 21022 | |
| 21023 | |
| 21024 |
|
| 21025 |
|
| 21026 | Eval_taylor = function() {
|
| 21027 | p1 = cdr(p1);
|
| 21028 | push(car(p1));
|
| 21029 | Eval();
|
| 21030 | p1 = cdr(p1);
|
| 21031 | push(car(p1));
|
| 21032 | Eval();
|
| 21033 | p2 = pop();
|
| 21034 | if (p2 === symbol(NIL)) {
|
| 21035 | guess();
|
| 21036 | } else {
|
| 21037 | push(p2);
|
| 21038 | }
|
| 21039 | p1 = cdr(p1);
|
| 21040 | push(car(p1));
|
| 21041 | Eval();
|
| 21042 | p2 = pop();
|
| 21043 | if (p2 === symbol(NIL)) {
|
| 21044 | push_integer(24);
|
| 21045 | } else {
|
| 21046 | push(p2);
|
| 21047 | }
|
| 21048 | p1 = cdr(p1);
|
| 21049 | push(car(p1));
|
| 21050 | Eval();
|
| 21051 | p2 = pop();
|
| 21052 | if (p2 === symbol(NIL)) {
|
| 21053 | push_integer(0);
|
| 21054 | } else {
|
| 21055 | push(p2);
|
| 21056 | }
|
| 21057 | return taylor();
|
| 21058 | };
|
| 21059 |
|
| 21060 | taylor = function() {
|
| 21061 | var i, k, l1, ref2;
|
| 21062 | i = 0;
|
| 21063 | k = 0;
|
| 21064 | save();
|
| 21065 | p4 = pop();
|
| 21066 | p3 = pop();
|
| 21067 | p2 = pop();
|
| 21068 | p1 = pop();
|
| 21069 | push(p3);
|
| 21070 | k = pop_integer();
|
| 21071 | if (isNaN(k)) {
|
| 21072 | push_symbol(TAYLOR);
|
| 21073 | push(p1);
|
| 21074 | push(p2);
|
| 21075 | push(p3);
|
| 21076 | push(p4);
|
| 21077 | list(5);
|
| 21078 | restore();
|
| 21079 | return;
|
| 21080 | }
|
| 21081 | push(p1);
|
| 21082 | push(p2);
|
| 21083 | push(p4);
|
| 21084 | subst();
|
| 21085 | Eval();
|
| 21086 | push_integer(1);
|
| 21087 | p5 = pop();
|
| 21088 | for (i = l1 = 1, ref2 = k; 1 <= ref2 ? l1 <= ref2 : l1 >= ref2; i = 1 <= ref2 ? ++l1 : --l1) {
|
| 21089 | push(p1);
|
| 21090 | push(p2);
|
| 21091 | derivative();
|
| 21092 | p1 = pop();
|
| 21093 | if (iszero(p1)) {
|
| 21094 | break;
|
| 21095 | }
|
| 21096 | push(p5);
|
| 21097 | push(p2);
|
| 21098 | push(p4);
|
| 21099 | subtract();
|
| 21100 | multiply();
|
| 21101 | p5 = pop();
|
| 21102 | push(p1);
|
| 21103 | push(p2);
|
| 21104 | push(p4);
|
| 21105 | subst();
|
| 21106 | Eval();
|
| 21107 | push(p5);
|
| 21108 | multiply();
|
| 21109 | push_integer(i);
|
| 21110 | factorial();
|
| 21111 | divide();
|
| 21112 | add();
|
| 21113 | }
|
| 21114 | return restore();
|
| 21115 | };
|
| 21116 |
|
| 21117 |
|
| 21118 | |
| 21119 | |
| 21120 | |
| 21121 | |
| 21122 | |
| 21123 | |
| 21124 | |
| 21125 | |
| 21126 | |
| 21127 | |
| 21128 | |
| 21129 | |
| 21130 | |
| 21131 | |
| 21132 | |
| 21133 | |
| 21134 | |
| 21135 | |
| 21136 | |
| 21137 | |
| 21138 | |
| 21139 | |
| 21140 | |
| 21141 | |
| 21142 | |
| 21143 | |
| 21144 | |
| 21145 | |
| 21146 | |
| 21147 | |
| 21148 | |
| 21149 | |
| 21150 | |
| 21151 | |
| 21152 | |
| 21153 | |
| 21154 | |
| 21155 | |
| 21156 | |
| 21157 | |
| 21158 | |
| 21159 | |
| 21160 | |
| 21161 | |
| 21162 | |
| 21163 | |
| 21164 |
|
| 21165 |
|
| 21166 | Eval_tensor = function() {
|
| 21167 | var a, b, i, l1, m1, ndim, nelem, ref2, ref3;
|
| 21168 | i = 0;
|
| 21169 | ndim = 0;
|
| 21170 | nelem = 0;
|
| 21171 | check_tensor_dimensions(p1);
|
| 21172 | nelem = p1.tensor.nelem;
|
| 21173 | ndim = p1.tensor.ndim;
|
| 21174 | p2 = alloc_tensor(nelem);
|
| 21175 | p2.tensor.ndim = ndim;
|
| 21176 | for (i = l1 = 0, ref2 = ndim; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 21177 | p2.tensor.dim[i] = p1.tensor.dim[i];
|
| 21178 | }
|
| 21179 | a = p1.tensor.elem;
|
| 21180 | b = p2.tensor.elem;
|
| 21181 | check_tensor_dimensions(p2);
|
| 21182 | for (i = m1 = 0, ref3 = nelem; 0 <= ref3 ? m1 < ref3 : m1 > ref3; i = 0 <= ref3 ? ++m1 : --m1) {
|
| 21183 | push(a[i]);
|
| 21184 | Eval();
|
| 21185 | b[i] = pop();
|
| 21186 | }
|
| 21187 | check_tensor_dimensions(p1);
|
| 21188 | check_tensor_dimensions(p2);
|
| 21189 | push(p2);
|
| 21190 | return promote_tensor();
|
| 21191 | };
|
| 21192 |
|
| 21193 | tensor_plus_tensor = function() {
|
| 21194 | var a, b, c, i, l1, m1, n1, ndim, nelem, ref2, ref3, ref4;
|
| 21195 | i = 0;
|
| 21196 | ndim = 0;
|
| 21197 | nelem = 0;
|
| 21198 | save();
|
| 21199 | p2 = pop();
|
| 21200 | p1 = pop();
|
| 21201 | ndim = p1.tensor.ndim;
|
| 21202 | if (ndim !== p2.tensor.ndim) {
|
| 21203 | push(symbol(NIL));
|
| 21204 | restore();
|
| 21205 | return;
|
| 21206 | }
|
| 21207 | for (i = l1 = 0, ref2 = ndim; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 21208 | if (p1.tensor.dim[i] !== p2.tensor.dim[i]) {
|
| 21209 | push(symbol(NIL));
|
| 21210 | restore();
|
| 21211 | return;
|
| 21212 | }
|
| 21213 | }
|
| 21214 | nelem = p1.tensor.nelem;
|
| 21215 | p3 = alloc_tensor(nelem);
|
| 21216 | p3.tensor.ndim = ndim;
|
| 21217 | for (i = m1 = 0, ref3 = ndim; 0 <= ref3 ? m1 < ref3 : m1 > ref3; i = 0 <= ref3 ? ++m1 : --m1) {
|
| 21218 | p3.tensor.dim[i] = p1.tensor.dim[i];
|
| 21219 | }
|
| 21220 | a = p1.tensor.elem;
|
| 21221 | b = p2.tensor.elem;
|
| 21222 | c = p3.tensor.elem;
|
| 21223 | for (i = n1 = 0, ref4 = nelem; 0 <= ref4 ? n1 < ref4 : n1 > ref4; i = 0 <= ref4 ? ++n1 : --n1) {
|
| 21224 | push(a[i]);
|
| 21225 | push(b[i]);
|
| 21226 | add();
|
| 21227 | c[i] = pop();
|
| 21228 | }
|
| 21229 | push(p3);
|
| 21230 | return restore();
|
| 21231 | };
|
| 21232 |
|
| 21233 | tensor_times_scalar = function() {
|
| 21234 | var a, b, i, l1, m1, ndim, nelem, ref2, ref3;
|
| 21235 | i = 0;
|
| 21236 | ndim = 0;
|
| 21237 | nelem = 0;
|
| 21238 | save();
|
| 21239 | p2 = pop();
|
| 21240 | p1 = pop();
|
| 21241 | ndim = p1.tensor.ndim;
|
| 21242 | nelem = p1.tensor.nelem;
|
| 21243 | p3 = alloc_tensor(nelem);
|
| 21244 | p3.tensor.ndim = ndim;
|
| 21245 | for (i = l1 = 0, ref2 = ndim; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 21246 | p3.tensor.dim[i] = p1.tensor.dim[i];
|
| 21247 | }
|
| 21248 | a = p1.tensor.elem;
|
| 21249 | b = p3.tensor.elem;
|
| 21250 | for (i = m1 = 0, ref3 = nelem; 0 <= ref3 ? m1 < ref3 : m1 > ref3; i = 0 <= ref3 ? ++m1 : --m1) {
|
| 21251 | push(a[i]);
|
| 21252 | push(p2);
|
| 21253 | multiply();
|
| 21254 | b[i] = pop();
|
| 21255 | }
|
| 21256 | push(p3);
|
| 21257 | return restore();
|
| 21258 | };
|
| 21259 |
|
| 21260 | scalar_times_tensor = function() {
|
| 21261 | var a, b, i, l1, m1, ndim, nelem, ref2, ref3;
|
| 21262 | i = 0;
|
| 21263 | ndim = 0;
|
| 21264 | nelem = 0;
|
| 21265 | save();
|
| 21266 | p2 = pop();
|
| 21267 | p1 = pop();
|
| 21268 | ndim = p2.tensor.ndim;
|
| 21269 | nelem = p2.tensor.nelem;
|
| 21270 | p3 = alloc_tensor(nelem);
|
| 21271 | p3.tensor.ndim = ndim;
|
| 21272 | for (i = l1 = 0, ref2 = ndim; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 21273 | p3.tensor.dim[i] = p2.tensor.dim[i];
|
| 21274 | }
|
| 21275 | a = p2.tensor.elem;
|
| 21276 | b = p3.tensor.elem;
|
| 21277 | for (i = m1 = 0, ref3 = nelem; 0 <= ref3 ? m1 < ref3 : m1 > ref3; i = 0 <= ref3 ? ++m1 : --m1) {
|
| 21278 | push(p1);
|
| 21279 | push(a[i]);
|
| 21280 | multiply();
|
| 21281 | b[i] = pop();
|
| 21282 | }
|
| 21283 | push(p3);
|
| 21284 | return restore();
|
| 21285 | };
|
| 21286 |
|
| 21287 | check_tensor_dimensions = function(p) {
|
| 21288 | if (p.tensor.nelem !== p.tensor.elem.length) {
|
| 21289 | console.log("something wrong in tensor dimensions");
|
| 21290 | debugger;
|
| 21291 | }
|
| 21292 | };
|
| 21293 |
|
| 21294 | is_square_matrix = function(p) {
|
| 21295 | if (istensor(p) && p.tensor.ndim === 2 && p.tensor.dim[0] === p.tensor.dim[1]) {
|
| 21296 | return 1;
|
| 21297 | } else {
|
| 21298 | return 0;
|
| 21299 | }
|
| 21300 | };
|
| 21301 |
|
| 21302 | d_tensor_tensor = function() {
|
| 21303 | var a, b, c, i, j, l1, m1, n1, ndim, nelem, ref2, ref3, ref4;
|
| 21304 | i = 0;
|
| 21305 | j = 0;
|
| 21306 | ndim = 0;
|
| 21307 | nelem = 0;
|
| 21308 | ndim = p1.tensor.ndim;
|
| 21309 | nelem = p1.tensor.nelem;
|
| 21310 | if (ndim + 1 >= MAXDIM) {
|
| 21311 | push_symbol(DERIVATIVE);
|
| 21312 | push(p1);
|
| 21313 | push(p2);
|
| 21314 | list(3);
|
| 21315 | return;
|
| 21316 | }
|
| 21317 | p3 = alloc_tensor(nelem * p2.tensor.nelem);
|
| 21318 | p3.tensor.ndim = ndim + 1;
|
| 21319 | for (i = l1 = 0, ref2 = ndim; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 21320 | p3.tensor.dim[i] = p1.tensor.dim[i];
|
| 21321 | }
|
| 21322 | p3.tensor.dim[ndim] = p2.tensor.dim[0];
|
| 21323 | a = p1.tensor.elem;
|
| 21324 | b = p2.tensor.elem;
|
| 21325 | c = p3.tensor.elem;
|
| 21326 | for (i = m1 = 0, ref3 = nelem; 0 <= ref3 ? m1 < ref3 : m1 > ref3; i = 0 <= ref3 ? ++m1 : --m1) {
|
| 21327 | for (j = n1 = 0, ref4 = p2.tensor.nelem; 0 <= ref4 ? n1 < ref4 : n1 > ref4; j = 0 <= ref4 ? ++n1 : --n1) {
|
| 21328 | push(a[i]);
|
| 21329 | push(b[j]);
|
| 21330 | derivative();
|
| 21331 | c[i * p2.tensor.nelem + j] = pop();
|
| 21332 | }
|
| 21333 | }
|
| 21334 | return push(p3);
|
| 21335 | };
|
| 21336 |
|
| 21337 | d_scalar_tensor = function() {
|
| 21338 | var a, b, i, l1, ref2;
|
| 21339 | p3 = alloc_tensor(p2.tensor.nelem);
|
| 21340 | p3.tensor.ndim = 1;
|
| 21341 | p3.tensor.dim[0] = p2.tensor.dim[0];
|
| 21342 | a = p2.tensor.elem;
|
| 21343 | b = p3.tensor.elem;
|
| 21344 | for (i = l1 = 0, ref2 = p2.tensor.nelem; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 21345 | push(p1);
|
| 21346 | push(a[i]);
|
| 21347 | derivative();
|
| 21348 | b[i] = pop();
|
| 21349 | }
|
| 21350 | return push(p3);
|
| 21351 | };
|
| 21352 |
|
| 21353 | d_tensor_scalar = function() {
|
| 21354 | var a, b, i, l1, m1, ref2, ref3;
|
| 21355 | i = 0;
|
| 21356 | p3 = alloc_tensor(p1.tensor.nelem);
|
| 21357 | p3.tensor.ndim = p1.tensor.ndim;
|
| 21358 | for (i = l1 = 0, ref2 = p1.tensor.ndim; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 21359 | p3.tensor.dim[i] = p1.tensor.dim[i];
|
| 21360 | }
|
| 21361 | a = p1.tensor.elem;
|
| 21362 | b = p3.tensor.elem;
|
| 21363 | for (i = m1 = 0, ref3 = p1.tensor.nelem; 0 <= ref3 ? m1 < ref3 : m1 > ref3; i = 0 <= ref3 ? ++m1 : --m1) {
|
| 21364 | push(a[i]);
|
| 21365 | push(p2);
|
| 21366 | derivative();
|
| 21367 | b[i] = pop();
|
| 21368 | }
|
| 21369 | return push(p3);
|
| 21370 | };
|
| 21371 |
|
| 21372 | compare_tensors = function(p1, p2) {
|
| 21373 | var i, l1, m1, ref2, ref3;
|
| 21374 | i = 0;
|
| 21375 | if (p1.tensor.ndim < p2.tensor.ndim) {
|
| 21376 | return -1;
|
| 21377 | }
|
| 21378 | if (p1.tensor.ndim > p2.tensor.ndim) {
|
| 21379 | return 1;
|
| 21380 | }
|
| 21381 | for (i = l1 = 0, ref2 = p1.tensor.ndim; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 21382 | if (p1.tensor.dim[i] < p2.tensor.dim[i]) {
|
| 21383 | return -1;
|
| 21384 | }
|
| 21385 | if (p1.tensor.dim[i] > p2.tensor.dim[i]) {
|
| 21386 | return 1;
|
| 21387 | }
|
| 21388 | }
|
| 21389 | for (i = m1 = 0, ref3 = p1.tensor.nelem; 0 <= ref3 ? m1 < ref3 : m1 > ref3; i = 0 <= ref3 ? ++m1 : --m1) {
|
| 21390 | if (equal(p1.tensor.elem[i], p2.tensor.elem[i])) {
|
| 21391 | continue;
|
| 21392 | }
|
| 21393 | if (lessp(p1.tensor.elem[i], p2.tensor.elem[i])) {
|
| 21394 | return -1;
|
| 21395 | } else {
|
| 21396 | return 1;
|
| 21397 | }
|
| 21398 | }
|
| 21399 | return 0;
|
| 21400 | };
|
| 21401 |
|
| 21402 | power_tensor = function() {
|
| 21403 | var i, k, l1, m1, n, ref2, ref3, results;
|
| 21404 | i = 0;
|
| 21405 | k = 0;
|
| 21406 | n = 0;
|
| 21407 | k = p1.tensor.ndim - 1;
|
| 21408 | if (p1.tensor.dim[0] !== p1.tensor.dim[k]) {
|
| 21409 | push_symbol(POWER);
|
| 21410 | push(p1);
|
| 21411 | push(p2);
|
| 21412 | list(3);
|
| 21413 | return;
|
| 21414 | }
|
| 21415 | push(p2);
|
| 21416 | n = pop_integer();
|
| 21417 | if (isNaN(n)) {
|
| 21418 | push_symbol(POWER);
|
| 21419 | push(p1);
|
| 21420 | push(p2);
|
| 21421 | list(3);
|
| 21422 | return;
|
| 21423 | }
|
| 21424 | if (n === 0) {
|
| 21425 | if (p1.tensor.ndim !== 2) {
|
| 21426 | stop("power(tensor,0) with tensor rank not equal to 2");
|
| 21427 | }
|
| 21428 | n = p1.tensor.dim[0];
|
| 21429 | p1 = alloc_tensor(n * n);
|
| 21430 | p1.tensor.ndim = 2;
|
| 21431 | p1.tensor.dim[0] = n;
|
| 21432 | p1.tensor.dim[1] = n;
|
| 21433 | for (i = l1 = 0, ref2 = n; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 21434 | p1.tensor.elem[n * i + i] = one;
|
| 21435 | }
|
| 21436 | check_tensor_dimensions(p1);
|
| 21437 | push(p1);
|
| 21438 | return;
|
| 21439 | }
|
| 21440 | if (n < 0) {
|
| 21441 | n = -n;
|
| 21442 | push(p1);
|
| 21443 | inv();
|
| 21444 | p1 = pop();
|
| 21445 | }
|
| 21446 | push(p1);
|
| 21447 | results = [];
|
| 21448 | for (i = m1 = 1, ref3 = n; 1 <= ref3 ? m1 < ref3 : m1 > ref3; i = 1 <= ref3 ? ++m1 : --m1) {
|
| 21449 | push(p1);
|
| 21450 | inner();
|
| 21451 | if (iszero(stack[tos - 1])) {
|
| 21452 | break;
|
| 21453 | } else {
|
| 21454 | results.push(void 0);
|
| 21455 | }
|
| 21456 | }
|
| 21457 | return results;
|
| 21458 | };
|
| 21459 |
|
| 21460 | copy_tensor = function() {
|
| 21461 | var i, l1, m1, ref2, ref3;
|
| 21462 | i = 0;
|
| 21463 | save();
|
| 21464 | p1 = pop();
|
| 21465 | p2 = alloc_tensor(p1.tensor.nelem);
|
| 21466 | p2.tensor.ndim = p1.tensor.ndim;
|
| 21467 | for (i = l1 = 0, ref2 = p1.tensor.ndim; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 21468 | p2.tensor.dim[i] = p1.tensor.dim[i];
|
| 21469 | }
|
| 21470 | for (i = m1 = 0, ref3 = p1.tensor.nelem; 0 <= ref3 ? m1 < ref3 : m1 > ref3; i = 0 <= ref3 ? ++m1 : --m1) {
|
| 21471 | p2.tensor.elem[i] = p1.tensor.elem[i];
|
| 21472 | }
|
| 21473 | check_tensor_dimensions(p1);
|
| 21474 | check_tensor_dimensions(p2);
|
| 21475 | push(p2);
|
| 21476 | return restore();
|
| 21477 | };
|
| 21478 |
|
| 21479 | promote_tensor = function() {
|
| 21480 | var i, j, k, l1, m1, n1, ndim, nelem, o1, q1, ref2, ref3, ref4, ref5, ref6;
|
| 21481 | i = 0;
|
| 21482 | j = 0;
|
| 21483 | k = 0;
|
| 21484 | nelem = 0;
|
| 21485 | ndim = 0;
|
| 21486 | save();
|
| 21487 | p1 = pop();
|
| 21488 | if (!istensor(p1)) {
|
| 21489 | push(p1);
|
| 21490 | restore();
|
| 21491 | return;
|
| 21492 | }
|
| 21493 | p2 = p1.tensor.elem[0];
|
| 21494 | for (i = l1 = 1, ref2 = p1.tensor.nelem; 1 <= ref2 ? l1 < ref2 : l1 > ref2; i = 1 <= ref2 ? ++l1 : --l1) {
|
| 21495 | if (!compatible(p2, p1.tensor.elem[i])) {
|
| 21496 | stop("Cannot promote tensor due to inconsistent tensor components.");
|
| 21497 | }
|
| 21498 | }
|
| 21499 | if (!istensor(p2)) {
|
| 21500 | push(p1);
|
| 21501 | restore();
|
| 21502 | return;
|
| 21503 | }
|
| 21504 | ndim = p1.tensor.ndim + p2.tensor.ndim;
|
| 21505 | if (ndim > MAXDIM) {
|
| 21506 | stop("tensor rank > " + MAXDIM);
|
| 21507 | }
|
| 21508 | nelem = p1.tensor.nelem * p2.tensor.nelem;
|
| 21509 | p3 = alloc_tensor(nelem);
|
| 21510 | p3.tensor.ndim = ndim;
|
| 21511 | for (i = m1 = 0, ref3 = p1.tensor.ndim; 0 <= ref3 ? m1 < ref3 : m1 > ref3; i = 0 <= ref3 ? ++m1 : --m1) {
|
| 21512 | p3.tensor.dim[i] = p1.tensor.dim[i];
|
| 21513 | }
|
| 21514 | for (j = n1 = 0, ref4 = p2.tensor.ndim; 0 <= ref4 ? n1 < ref4 : n1 > ref4; j = 0 <= ref4 ? ++n1 : --n1) {
|
| 21515 | p3.tensor.dim[i + j] = p2.tensor.dim[j];
|
| 21516 | }
|
| 21517 | k = 0;
|
| 21518 | for (i = o1 = 0, ref5 = p1.tensor.nelem; 0 <= ref5 ? o1 < ref5 : o1 > ref5; i = 0 <= ref5 ? ++o1 : --o1) {
|
| 21519 | p2 = p1.tensor.elem[i];
|
| 21520 | for (j = q1 = 0, ref6 = p2.tensor.nelem; 0 <= ref6 ? q1 < ref6 : q1 > ref6; j = 0 <= ref6 ? ++q1 : --q1) {
|
| 21521 | p3.tensor.elem[k++] = p2.tensor.elem[j];
|
| 21522 | }
|
| 21523 | }
|
| 21524 | check_tensor_dimensions(p2);
|
| 21525 | check_tensor_dimensions(p3);
|
| 21526 | push(p3);
|
| 21527 | return restore();
|
| 21528 | };
|
| 21529 |
|
| 21530 | compatible = function(p, q) {
|
| 21531 | var i, l1, ref2;
|
| 21532 | if (!istensor(p) && !istensor(q)) {
|
| 21533 | return 1;
|
| 21534 | }
|
| 21535 | if (!istensor(p) || !istensor(q)) {
|
| 21536 | return 0;
|
| 21537 | }
|
| 21538 | if (p.tensor.ndim !== q.tensor.ndim) {
|
| 21539 | return 0;
|
| 21540 | }
|
| 21541 | for (i = l1 = 0, ref2 = p.tensor.ndim; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 21542 | if (p.tensor.dim[i] !== q.tensor.dim[i]) {
|
| 21543 | return 0;
|
| 21544 | }
|
| 21545 | }
|
| 21546 | return 1;
|
| 21547 | };
|
| 21548 |
|
| 21549 | Eval_test = function() {
|
| 21550 | var orig;
|
| 21551 | orig = p1;
|
| 21552 | p1 = cdr(p1);
|
| 21553 | while (iscons(p1)) {
|
| 21554 | if (cdr(p1) === symbol(NIL)) {
|
| 21555 | push(car(p1));
|
| 21556 | Eval();
|
| 21557 | return;
|
| 21558 | }
|
| 21559 | push(car(p1));
|
| 21560 | Eval_predicate();
|
| 21561 | p2 = pop();
|
| 21562 | if (isone(p2)) {
|
| 21563 | push(cadr(p1));
|
| 21564 | Eval();
|
| 21565 | return;
|
| 21566 | } else if (!iszero(p2)) {
|
| 21567 | push(orig);
|
| 21568 | return;
|
| 21569 | }
|
| 21570 | p1 = cddr(p1);
|
| 21571 | }
|
| 21572 | return push_integer(0);
|
| 21573 | };
|
| 21574 |
|
| 21575 | Eval_testeq = function() {
|
| 21576 | var orig, subtractionResult;
|
| 21577 | orig = p1;
|
| 21578 | push(cadr(p1));
|
| 21579 | Eval();
|
| 21580 | push(caddr(p1));
|
| 21581 | Eval();
|
| 21582 | subtract();
|
| 21583 | subtractionResult = pop();
|
| 21584 | if (iszero(subtractionResult)) {
|
| 21585 | p1 = subtractionResult;
|
| 21586 | return push_integer(1);
|
| 21587 | } else {
|
| 21588 | push(cadr(p1));
|
| 21589 | Eval();
|
| 21590 | simplify();
|
| 21591 | push(caddr(p1));
|
| 21592 | Eval();
|
| 21593 | simplify();
|
| 21594 | subtract();
|
| 21595 | p1 = pop();
|
| 21596 | if (iszero(p1)) {
|
| 21597 | return push_integer(1);
|
| 21598 | } else {
|
| 21599 | push(p1);
|
| 21600 | yyfloat();
|
| 21601 | p1 = pop();
|
| 21602 | if (iszero(p1)) {
|
| 21603 | return push_integer(1);
|
| 21604 | } else if (isnum(p1)) {
|
| 21605 | return push_integer(0);
|
| 21606 | } else {
|
| 21607 | return push(orig);
|
| 21608 | }
|
| 21609 | }
|
| 21610 | }
|
| 21611 | };
|
| 21612 |
|
| 21613 | Eval_testge = function() {
|
| 21614 | var comparison, orig;
|
| 21615 | orig = p1;
|
| 21616 | comparison = cmp_args();
|
| 21617 | if (comparison == null) {
|
| 21618 | push(orig);
|
| 21619 | return;
|
| 21620 | }
|
| 21621 | if (comparison >= 0) {
|
| 21622 | return push_integer(1);
|
| 21623 | } else {
|
| 21624 | return push_integer(0);
|
| 21625 | }
|
| 21626 | };
|
| 21627 |
|
| 21628 | Eval_testgt = function() {
|
| 21629 | var comparison, orig;
|
| 21630 | orig = p1;
|
| 21631 | comparison = cmp_args();
|
| 21632 | if (comparison == null) {
|
| 21633 | push(orig);
|
| 21634 | return;
|
| 21635 | }
|
| 21636 | if (comparison > 0) {
|
| 21637 | return push_integer(1);
|
| 21638 | } else {
|
| 21639 | return push_integer(0);
|
| 21640 | }
|
| 21641 | };
|
| 21642 |
|
| 21643 | Eval_testle = function() {
|
| 21644 | var comparison, orig;
|
| 21645 | orig = p1;
|
| 21646 | comparison = cmp_args();
|
| 21647 | if (comparison == null) {
|
| 21648 | push(orig);
|
| 21649 | return;
|
| 21650 | }
|
| 21651 | if (comparison <= 0) {
|
| 21652 | return push_integer(1);
|
| 21653 | } else {
|
| 21654 | return push_integer(0);
|
| 21655 | }
|
| 21656 | };
|
| 21657 |
|
| 21658 | Eval_testlt = function() {
|
| 21659 | var comparison, orig;
|
| 21660 | orig = p1;
|
| 21661 | comparison = cmp_args();
|
| 21662 | if (comparison == null) {
|
| 21663 | push(orig);
|
| 21664 | return;
|
| 21665 | }
|
| 21666 | if (comparison < 0) {
|
| 21667 | return push_integer(1);
|
| 21668 | } else {
|
| 21669 | return push_integer(0);
|
| 21670 | }
|
| 21671 | };
|
| 21672 |
|
| 21673 | Eval_not = function() {
|
| 21674 | push(cadr(p1));
|
| 21675 | Eval_predicate();
|
| 21676 | p1 = pop();
|
| 21677 | if (iszero(p1)) {
|
| 21678 | return push_integer(1);
|
| 21679 | } else {
|
| 21680 | return push_integer(0);
|
| 21681 | }
|
| 21682 | };
|
| 21683 |
|
| 21684 |
|
| 21685 | |
| 21686 | |
| 21687 | |
| 21688 | |
| 21689 | |
| 21690 | |
| 21691 | |
| 21692 | |
| 21693 | |
| 21694 | |
| 21695 | |
| 21696 | |
| 21697 | |
| 21698 |
|
| 21699 |
|
| 21700 | Eval_and = function() {
|
| 21701 | p1 = cdr(p1);
|
| 21702 | while (iscons(p1)) {
|
| 21703 | push(car(p1));
|
| 21704 | Eval_predicate();
|
| 21705 | p2 = pop();
|
| 21706 | if (iszero(p2)) {
|
| 21707 | push_integer(0);
|
| 21708 | return;
|
| 21709 | }
|
| 21710 | p1 = cdr(p1);
|
| 21711 | }
|
| 21712 | return push_integer(1);
|
| 21713 | };
|
| 21714 |
|
| 21715 | Eval_or = function() {
|
| 21716 | p1 = cdr(p1);
|
| 21717 | while (iscons(p1)) {
|
| 21718 | push(car(p1));
|
| 21719 | Eval_predicate();
|
| 21720 | p2 = pop();
|
| 21721 | if (!iszero(p2)) {
|
| 21722 | push_integer(1);
|
| 21723 | return;
|
| 21724 | }
|
| 21725 | p1 = cdr(p1);
|
| 21726 | }
|
| 21727 | return push_integer(0);
|
| 21728 | };
|
| 21729 |
|
| 21730 | cmp_args = function() {
|
| 21731 | var t;
|
| 21732 | t = 0;
|
| 21733 | push(cadr(p1));
|
| 21734 | Eval();
|
| 21735 | simplify();
|
| 21736 | push(caddr(p1));
|
| 21737 | Eval();
|
| 21738 | simplify();
|
| 21739 | subtract();
|
| 21740 | p1 = pop();
|
| 21741 | if (p1.k !== NUM && p1.k !== DOUBLE) {
|
| 21742 | push(p1);
|
| 21743 | yyfloat();
|
| 21744 | Eval();
|
| 21745 | p1 = pop();
|
| 21746 | }
|
| 21747 | if (iszero(p1)) {
|
| 21748 | return 0;
|
| 21749 | }
|
| 21750 | switch (p1.k) {
|
| 21751 | case NUM:
|
| 21752 | if (MSIGN(p1.q.a) === -1) {
|
| 21753 | t = -1;
|
| 21754 | } else {
|
| 21755 | t = 1;
|
| 21756 | }
|
| 21757 | break;
|
| 21758 | case DOUBLE:
|
| 21759 | if (p1.d < 0.0) {
|
| 21760 | t = -1;
|
| 21761 | } else {
|
| 21762 | t = 1;
|
| 21763 | }
|
| 21764 | break;
|
| 21765 | default:
|
| 21766 | t = null;
|
| 21767 | }
|
| 21768 | return t;
|
| 21769 | };
|
| 21770 |
|
| 21771 |
|
| 21772 | |
| 21773 | |
| 21774 | |
| 21775 | |
| 21776 | |
| 21777 | |
| 21778 | |
| 21779 | |
| 21780 | |
| 21781 | |
| 21782 | |
| 21783 | |
| 21784 | |
| 21785 | |
| 21786 | |
| 21787 | |
| 21788 | |
| 21789 | |
| 21790 | |
| 21791 | |
| 21792 | |
| 21793 | |
| 21794 | |
| 21795 | |
| 21796 | |
| 21797 | |
| 21798 |
|
| 21799 |
|
| 21800 | transform = function(s, generalTransform) {
|
| 21801 | var bookmarkTosToPrintDecomps, eachTransformEntry, i, l1, len, len1, m1, n1, numberOfDecomps, ref2, restTerm, secondTerm, success, theTransform, transform_h, transformationSuccessful, transformedTerms;
|
| 21802 | transform_h = 0;
|
| 21803 | save();
|
| 21804 | p1 = null;
|
| 21805 | p4 = pop();
|
| 21806 | p3 = pop();
|
| 21807 | if (DEBUG) {
|
| 21808 | console.log(" !!!!!!!!! transform on: " + p3);
|
| 21809 | }
|
| 21810 | saveMetaBindings();
|
| 21811 | set_binding(symbol(METAX), p4);
|
| 21812 | transform_h = tos;
|
| 21813 | push_integer(1);
|
| 21814 | push(p3);
|
| 21815 | push(p4);
|
| 21816 | polyform();
|
| 21817 | push(p4);
|
| 21818 | bookmarkTosToPrintDecomps = tos - 2;
|
| 21819 | decomp(generalTransform);
|
| 21820 | numberOfDecomps = tos - bookmarkTosToPrintDecomps;
|
| 21821 | if (DEBUG) {
|
| 21822 | console.log(" " + numberOfDecomps + " decomposed elements ====== ");
|
| 21823 | for (i = l1 = 0, ref2 = numberOfDecomps; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 21824 | console.log(" decomposition element " + i + ": " + stack[tos - 1 - i]);
|
| 21825 | }
|
| 21826 | }
|
| 21827 | transformationSuccessful = false;
|
| 21828 | if (generalTransform) {
|
| 21829 | if (!isnum(p3)) {
|
| 21830 | theTransform = s;
|
| 21831 | if (DEBUG) {
|
| 21832 | console.log("applying transform: " + theTransform);
|
| 21833 | }
|
| 21834 | if (DEBUG) {
|
| 21835 | console.log("scanning table entry " + theTransform);
|
| 21836 | }
|
| 21837 | push(theTransform);
|
| 21838 | push(symbol(SYMBOL_A_UNDERSCORE));
|
| 21839 | push(symbol(METAA));
|
| 21840 | subst();
|
| 21841 | push(symbol(SYMBOL_B_UNDERSCORE));
|
| 21842 | push(symbol(METAB));
|
| 21843 | subst();
|
| 21844 | push(symbol(SYMBOL_X_UNDERSCORE));
|
| 21845 | push(symbol(METAX));
|
| 21846 | subst();
|
| 21847 | p1 = pop();
|
| 21848 | p5 = car(p1);
|
| 21849 | if (DEBUG) {
|
| 21850 | console.log("template expression: " + p5);
|
| 21851 | }
|
| 21852 | p6 = cadr(p1);
|
| 21853 | p7 = cddr(p1);
|
| 21854 |
|
| 21855 | |
| 21856 | |
| 21857 | |
| 21858 | |
| 21859 | |
| 21860 | |
| 21861 | |
| 21862 |
|
| 21863 | if (f_equals_a(transform_h, generalTransform)) {
|
| 21864 | transformationSuccessful = true;
|
| 21865 | } else {
|
| 21866 | if (DEBUG) {
|
| 21867 | console.log("p3 at this point: " + p3);
|
| 21868 | }
|
| 21869 | transformedTerms = [];
|
| 21870 | if (DEBUG) {
|
| 21871 | console.log("car(p3): " + car(p3));
|
| 21872 | }
|
| 21873 | restTerm = p3;
|
| 21874 | if (iscons(restTerm)) {
|
| 21875 | transformedTerms.push(car(p3));
|
| 21876 | restTerm = cdr(p3);
|
| 21877 | }
|
| 21878 | while (iscons(restTerm)) {
|
| 21879 | secondTerm = car(restTerm);
|
| 21880 | restTerm = cdr(restTerm);
|
| 21881 | if (DEBUG) {
|
| 21882 | console.log("tos before recursive transform: " + tos);
|
| 21883 | }
|
| 21884 | push(secondTerm);
|
| 21885 | push_symbol(NIL);
|
| 21886 | if (DEBUG) {
|
| 21887 | console.log("testing: " + secondTerm);
|
| 21888 | }
|
| 21889 | if (DEBUG) {
|
| 21890 | console.log("about to try to simplify other term: " + secondTerm);
|
| 21891 | }
|
| 21892 | success = transform(s, generalTransform);
|
| 21893 | transformationSuccessful = transformationSuccessful || success;
|
| 21894 | transformedTerms.push(pop());
|
| 21895 | if (DEBUG) {
|
| 21896 | console.log("tried to simplify other term: " + secondTerm + " ...successful?: " + success + " ...transformed: " + transformedTerms[transformedTerms.length - 1]);
|
| 21897 | }
|
| 21898 | }
|
| 21899 | if (transformedTerms.length !== 0) {
|
| 21900 | for (m1 = 0, len = transformedTerms.length; m1 < len; m1++) {
|
| 21901 | i = transformedTerms[m1];
|
| 21902 | push(i);
|
| 21903 | }
|
| 21904 | list(transformedTerms.length);
|
| 21905 | p6 = pop();
|
| 21906 | }
|
| 21907 | }
|
| 21908 | }
|
| 21909 | } else {
|
| 21910 | for (n1 = 0, len1 = s.length; n1 < len1; n1++) {
|
| 21911 | eachTransformEntry = s[n1];
|
| 21912 | if (DEBUG) {
|
| 21913 | console.log("scanning table entry " + eachTransformEntry);
|
| 21914 | if ((eachTransformEntry + "").indexOf("f(sqrt(a+b*x),2/3*1/b*sqrt((a+b*x)^3))") !== -1) {
|
| 21915 | debugger;
|
| 21916 | }
|
| 21917 | }
|
| 21918 | if (eachTransformEntry) {
|
| 21919 | scan_meta(eachTransformEntry);
|
| 21920 | p1 = pop();
|
| 21921 | p5 = cadr(p1);
|
| 21922 | p6 = caddr(p1);
|
| 21923 | p7 = cdddr(p1);
|
| 21924 |
|
| 21925 | |
| 21926 | |
| 21927 | |
| 21928 | |
| 21929 | |
| 21930 | |
| 21931 | |
| 21932 |
|
| 21933 | if (f_equals_a(transform_h, generalTransform)) {
|
| 21934 | transformationSuccessful = true;
|
| 21935 | break;
|
| 21936 | }
|
| 21937 | }
|
| 21938 | }
|
| 21939 | }
|
| 21940 | moveTos(transform_h);
|
| 21941 | if (transformationSuccessful) {
|
| 21942 | push(p6);
|
| 21943 | Eval();
|
| 21944 | p1 = pop();
|
| 21945 | transformationSuccessful = true;
|
| 21946 | } else {
|
| 21947 | if (generalTransform) {
|
| 21948 | p1 = p3;
|
| 21949 | } else {
|
| 21950 | p1 = symbol(NIL);
|
| 21951 | }
|
| 21952 | }
|
| 21953 | restoreMetaBindings();
|
| 21954 | push(p1);
|
| 21955 | restore();
|
| 21956 | return transformationSuccessful;
|
| 21957 | };
|
| 21958 |
|
| 21959 | saveMetaBindings = function() {
|
| 21960 | push(get_binding(symbol(METAA)));
|
| 21961 | push(get_binding(symbol(METAB)));
|
| 21962 | return push(get_binding(symbol(METAX)));
|
| 21963 | };
|
| 21964 |
|
| 21965 | restoreMetaBindings = function() {
|
| 21966 | set_binding(symbol(METAX), pop());
|
| 21967 | set_binding(symbol(METAB), pop());
|
| 21968 | return set_binding(symbol(METAA), pop());
|
| 21969 | };
|
| 21970 |
|
| 21971 | f_equals_a = function(h, generalTransform) {
|
| 21972 | var fea_i, fea_j, l1, m1, originalexpanding, ref2, ref3, ref4, ref5;
|
| 21973 | fea_i = 0;
|
| 21974 | fea_j = 0;
|
| 21975 | for (fea_i = l1 = ref2 = h, ref3 = tos; ref2 <= ref3 ? l1 < ref3 : l1 > ref3; fea_i = ref2 <= ref3 ? ++l1 : --l1) {
|
| 21976 | set_binding(symbol(METAA), stack[fea_i]);
|
| 21977 | if (DEBUG) {
|
| 21978 | console.log(" binding METAA to " + get_binding(symbol(METAA)));
|
| 21979 | }
|
| 21980 | for (fea_j = m1 = ref4 = h, ref5 = tos; ref4 <= ref5 ? m1 < ref5 : m1 > ref5; fea_j = ref4 <= ref5 ? ++m1 : --m1) {
|
| 21981 | set_binding(symbol(METAB), stack[fea_j]);
|
| 21982 | if (DEBUG) {
|
| 21983 | console.log(" binding METAB to " + get_binding(symbol(METAB)));
|
| 21984 | }
|
| 21985 | p1 = p7;
|
| 21986 | while (iscons(p1)) {
|
| 21987 | push(car(p1));
|
| 21988 | Eval();
|
| 21989 | p2 = pop();
|
| 21990 | if (iszero(p2)) {
|
| 21991 | break;
|
| 21992 | }
|
| 21993 | p1 = cdr(p1);
|
| 21994 | }
|
| 21995 | if (iscons(p1)) {
|
| 21996 | continue;
|
| 21997 | }
|
| 21998 | push(p3);
|
| 21999 | if (DEBUG) {
|
| 22000 | console.log("about to evaluate template expression: " + p5 + " binding METAA to " + get_binding(symbol(METAA)) + " and binding METAB to " + get_binding(symbol(METAB)) + " and binding METAX to " + get_binding(symbol(METAX)));
|
| 22001 | }
|
| 22002 | push(p5);
|
| 22003 | if (generalTransform) {
|
| 22004 | originalexpanding = expanding;
|
| 22005 | expanding = false;
|
| 22006 | }
|
| 22007 | Eval();
|
| 22008 | if (generalTransform) {
|
| 22009 | expanding = originalexpanding;
|
| 22010 | }
|
| 22011 | if (DEBUG) {
|
| 22012 | console.log(" comparing " + stack[tos - 1] + " to: " + stack[tos - 2]);
|
| 22013 | }
|
| 22014 | subtract();
|
| 22015 | p1 = pop();
|
| 22016 | if (iszero(p1)) {
|
| 22017 | if (DEBUG) {
|
| 22018 | console.log("binding METAA to " + get_binding(symbol(METAA)));
|
| 22019 | console.log("binding METAB to " + get_binding(symbol(METAB)));
|
| 22020 | console.log("binding METAX to " + get_binding(symbol(METAX)));
|
| 22021 | console.log("comparing " + p3 + " to: " + p5);
|
| 22022 | }
|
| 22023 | return 1;
|
| 22024 | }
|
| 22025 | }
|
| 22026 | }
|
| 22027 | return 0;
|
| 22028 | };
|
| 22029 |
|
| 22030 | Eval_transpose = function() {
|
| 22031 | push(cadr(p1));
|
| 22032 | Eval();
|
| 22033 | if (cddr(p1) === symbol(NIL)) {
|
| 22034 | push_integer(1);
|
| 22035 | push_integer(2);
|
| 22036 | } else {
|
| 22037 | push(caddr(p1));
|
| 22038 | Eval();
|
| 22039 | push(cadddr(p1));
|
| 22040 | Eval();
|
| 22041 | }
|
| 22042 | return transpose();
|
| 22043 | };
|
| 22044 |
|
| 22045 | transpose = function() {
|
| 22046 | var a, accumulator, ai, an, b, eachEntry, i, innerTranspSwitch1, innerTranspSwitch2, j, k, l, l1, m, m1, n1, ndim, nelem, o1, q1, r1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, s1, t;
|
| 22047 | i = 0;
|
| 22048 | j = 0;
|
| 22049 | k = 0;
|
| 22050 | l = 0;
|
| 22051 | m = 0;
|
| 22052 | ndim = 0;
|
| 22053 | nelem = 0;
|
| 22054 | t = 0;
|
| 22055 | ai = [];
|
| 22056 | an = [];
|
| 22057 | for (i = l1 = 0, ref2 = MAXDIM; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 22058 | ai[i] = 0;
|
| 22059 | an[i] = 0;
|
| 22060 | }
|
| 22061 | save();
|
| 22062 | p3 = pop();
|
| 22063 | p2 = pop();
|
| 22064 | p1 = pop();
|
| 22065 | if (isnum(p1)) {
|
| 22066 | push(p1);
|
| 22067 | restore();
|
| 22068 | return;
|
| 22069 | }
|
| 22070 | if ((isplusone(p2) && isplustwo(p3)) || (isplusone(p3) && isplustwo(p2))) {
|
| 22071 | if (isidentitymatrix(p1)) {
|
| 22072 | push(p1);
|
| 22073 | restore();
|
| 22074 | return;
|
| 22075 | }
|
| 22076 | }
|
| 22077 | if (istranspose(p1)) {
|
| 22078 | innerTranspSwitch1 = car(cdr(cdr(p1)));
|
| 22079 | innerTranspSwitch2 = car(cdr(cdr(cdr(p1))));
|
| 22080 | if ((equal(innerTranspSwitch1, p3) && equal(innerTranspSwitch2, p2)) || (equal(innerTranspSwitch2, p3) && equal(innerTranspSwitch1, p2)) || ((equal(innerTranspSwitch1, symbol(NIL)) && equal(innerTranspSwitch2, symbol(NIL))) && ((isplusone(p3) && isplustwo(p2)) || (isplusone(p2) && isplustwo(p3))))) {
|
| 22081 | push(car(cdr(p1)));
|
| 22082 | restore();
|
| 22083 | return;
|
| 22084 | }
|
| 22085 | }
|
| 22086 | if (expanding && isadd(p1)) {
|
| 22087 | p1 = cdr(p1);
|
| 22088 | push(zero);
|
| 22089 | while (iscons(p1)) {
|
| 22090 | push(car(p1));
|
| 22091 | push(p2);
|
| 22092 | push(p3);
|
| 22093 | transpose();
|
| 22094 | add();
|
| 22095 | p1 = cdr(p1);
|
| 22096 | }
|
| 22097 | restore();
|
| 22098 | return;
|
| 22099 | }
|
| 22100 | if (expanding && ismultiply(p1)) {
|
| 22101 | p1 = cdr(p1);
|
| 22102 | push(one);
|
| 22103 | while (iscons(p1)) {
|
| 22104 | push(car(p1));
|
| 22105 | push(p2);
|
| 22106 | push(p3);
|
| 22107 | transpose();
|
| 22108 | multiply();
|
| 22109 | p1 = cdr(p1);
|
| 22110 | }
|
| 22111 | restore();
|
| 22112 | return;
|
| 22113 | }
|
| 22114 | if (expanding && isinnerordot(p1)) {
|
| 22115 | p1 = cdr(p1);
|
| 22116 | accumulator = [];
|
| 22117 | while (iscons(p1)) {
|
| 22118 | accumulator.push([car(p1), p2, p3]);
|
| 22119 | p1 = cdr(p1);
|
| 22120 | }
|
| 22121 | for (eachEntry = m1 = ref3 = accumulator.length - 1; ref3 <= 0 ? m1 <= 0 : m1 >= 0; eachEntry = ref3 <= 0 ? ++m1 : --m1) {
|
| 22122 | push(accumulator[eachEntry][0]);
|
| 22123 | push(accumulator[eachEntry][1]);
|
| 22124 | push(accumulator[eachEntry][2]);
|
| 22125 | transpose();
|
| 22126 | if (eachEntry !== accumulator.length - 1) {
|
| 22127 | inner();
|
| 22128 | }
|
| 22129 | }
|
| 22130 | restore();
|
| 22131 | return;
|
| 22132 | }
|
| 22133 | if (!istensor(p1)) {
|
| 22134 | if (!iszero(p1)) {
|
| 22135 | push_symbol(TRANSPOSE);
|
| 22136 | push(p1);
|
| 22137 | if ((!isplusone(p2) || !isplustwo(p3)) && (!isplusone(p3) || !isplustwo(p2))) {
|
| 22138 | push(p2);
|
| 22139 | push(p3);
|
| 22140 | list(4);
|
| 22141 | } else {
|
| 22142 | list(2);
|
| 22143 | }
|
| 22144 | restore();
|
| 22145 | return;
|
| 22146 | }
|
| 22147 | push(zero);
|
| 22148 | restore();
|
| 22149 | return;
|
| 22150 | }
|
| 22151 | ndim = p1.tensor.ndim;
|
| 22152 | nelem = p1.tensor.nelem;
|
| 22153 | if (ndim === 1) {
|
| 22154 | push(p1);
|
| 22155 | restore();
|
| 22156 | return;
|
| 22157 | }
|
| 22158 | push(p2);
|
| 22159 | l = pop_integer();
|
| 22160 | push(p3);
|
| 22161 | m = pop_integer();
|
| 22162 | if (l < 1 || l > ndim || m < 1 || m > ndim) {
|
| 22163 | stop("transpose: index out of range");
|
| 22164 | }
|
| 22165 | l--;
|
| 22166 | m--;
|
| 22167 | p2 = alloc_tensor(nelem);
|
| 22168 | p2.tensor.ndim = ndim;
|
| 22169 | for (i = n1 = 0, ref4 = ndim; 0 <= ref4 ? n1 < ref4 : n1 > ref4; i = 0 <= ref4 ? ++n1 : --n1) {
|
| 22170 | p2.tensor.dim[i] = p1.tensor.dim[i];
|
| 22171 | }
|
| 22172 | p2.tensor.dim[l] = p1.tensor.dim[m];
|
| 22173 | p2.tensor.dim[m] = p1.tensor.dim[l];
|
| 22174 | a = p1.tensor.elem;
|
| 22175 | b = p2.tensor.elem;
|
| 22176 | for (i = o1 = 0, ref5 = ndim; 0 <= ref5 ? o1 < ref5 : o1 > ref5; i = 0 <= ref5 ? ++o1 : --o1) {
|
| 22177 | ai[i] = 0;
|
| 22178 | an[i] = p1.tensor.dim[i];
|
| 22179 | }
|
| 22180 | for (i = q1 = 0, ref6 = nelem; 0 <= ref6 ? q1 < ref6 : q1 > ref6; i = 0 <= ref6 ? ++q1 : --q1) {
|
| 22181 | t = ai[l];
|
| 22182 | ai[l] = ai[m];
|
| 22183 | ai[m] = t;
|
| 22184 | t = an[l];
|
| 22185 | an[l] = an[m];
|
| 22186 | an[m] = t;
|
| 22187 | k = 0;
|
| 22188 | for (j = r1 = 0, ref7 = ndim; 0 <= ref7 ? r1 < ref7 : r1 > ref7; j = 0 <= ref7 ? ++r1 : --r1) {
|
| 22189 | k = (k * an[j]) + ai[j];
|
| 22190 | }
|
| 22191 | t = ai[l];
|
| 22192 | ai[l] = ai[m];
|
| 22193 | ai[m] = t;
|
| 22194 | t = an[l];
|
| 22195 | an[l] = an[m];
|
| 22196 | an[m] = t;
|
| 22197 | b[k] = a[i];
|
| 22198 | for (j = s1 = ref8 = ndim - 1; ref8 <= 0 ? s1 <= 0 : s1 >= 0; j = ref8 <= 0 ? ++s1 : --s1) {
|
| 22199 | if (++ai[j] < an[j]) {
|
| 22200 | break;
|
| 22201 | }
|
| 22202 | ai[j] = 0;
|
| 22203 | }
|
| 22204 | }
|
| 22205 | push(p2);
|
| 22206 | return restore();
|
| 22207 | };
|
| 22208 |
|
| 22209 |
|
| 22210 | |
| 22211 | |
| 22212 | |
| 22213 | |
| 22214 | |
| 22215 | |
| 22216 | |
| 22217 | |
| 22218 | |
| 22219 | |
| 22220 | |
| 22221 | |
| 22222 | |
| 22223 |
|
| 22224 |
|
| 22225 | Eval_user_function = function() {
|
| 22226 | var bodyAndFormalArguments, h;
|
| 22227 | if (DEBUG) {
|
| 22228 | console.log("Eval_user_function evaluating: " + car(p1));
|
| 22229 | }
|
| 22230 | if (car(p1) === symbol(SYMBOL_D) && get_binding(symbol(SYMBOL_D)) === symbol(SYMBOL_D)) {
|
| 22231 | Eval_derivative();
|
| 22232 | return;
|
| 22233 | }
|
| 22234 | push(car(p1));
|
| 22235 | Eval();
|
| 22236 | bodyAndFormalArguments = pop();
|
| 22237 | p3 = car(cdr(bodyAndFormalArguments));
|
| 22238 | p4 = car(cdr(cdr(bodyAndFormalArguments)));
|
| 22239 | p5 = cdr(p1);
|
| 22240 | if (bodyAndFormalArguments === car(p1)) {
|
| 22241 | h = tos;
|
| 22242 | push(bodyAndFormalArguments);
|
| 22243 | p1 = p5;
|
| 22244 | while (iscons(p1)) {
|
| 22245 | push(car(p1));
|
| 22246 | Eval();
|
| 22247 | p1 = cdr(p1);
|
| 22248 | }
|
| 22249 | list(tos - h);
|
| 22250 | return;
|
| 22251 | }
|
| 22252 | p1 = p4;
|
| 22253 | p2 = p5;
|
| 22254 | h = tos;
|
| 22255 | while (iscons(p1) && iscons(p2)) {
|
| 22256 | push(car(p1));
|
| 22257 | push(car(p2));
|
| 22258 | p1 = cdr(p1);
|
| 22259 | p2 = cdr(p2);
|
| 22260 | }
|
| 22261 | list(tos - h);
|
| 22262 | p6 = pop();
|
| 22263 | push(p3);
|
| 22264 | if (iscons(p6)) {
|
| 22265 | push(p6);
|
| 22266 | rewrite_args();
|
| 22267 | }
|
| 22268 | return Eval();
|
| 22269 | };
|
| 22270 |
|
| 22271 | rewrite_args = function() {
|
| 22272 | var h, n;
|
| 22273 | n = 0;
|
| 22274 | save();
|
| 22275 | p2 = pop();
|
| 22276 | p1 = pop();
|
| 22277 | if (istensor(p1)) {
|
| 22278 | n = rewrite_args_tensor();
|
| 22279 | restore();
|
| 22280 | return n;
|
| 22281 | }
|
| 22282 | if (iscons(p1)) {
|
| 22283 | h = tos;
|
| 22284 | if (car(p1) === car(p2)) {
|
| 22285 | push_symbol(EVAL);
|
| 22286 | push(car(cdr(p2)));
|
| 22287 | list(2);
|
| 22288 | } else {
|
| 22289 | push(car(p1));
|
| 22290 | }
|
| 22291 | p1 = cdr(p1);
|
| 22292 | while (iscons(p1)) {
|
| 22293 | push(car(p1));
|
| 22294 | push(p2);
|
| 22295 | n += rewrite_args();
|
| 22296 | p1 = cdr(p1);
|
| 22297 | }
|
| 22298 | list(tos - h);
|
| 22299 | restore();
|
| 22300 | return n;
|
| 22301 | }
|
| 22302 | if (!issymbol(p1)) {
|
| 22303 | push(p1);
|
| 22304 | restore();
|
| 22305 | return 0;
|
| 22306 | }
|
| 22307 | p3 = p2;
|
| 22308 | while (iscons(p3)) {
|
| 22309 | if (p1 === car(p3)) {
|
| 22310 | push(cadr(p3));
|
| 22311 | restore();
|
| 22312 | return 1;
|
| 22313 | }
|
| 22314 | p3 = cddr(p3);
|
| 22315 | }
|
| 22316 | p3 = get_binding(p1);
|
| 22317 | push(p3);
|
| 22318 | if (p1 !== p3) {
|
| 22319 | push(p2);
|
| 22320 | n = rewrite_args();
|
| 22321 | if (n === 0) {
|
| 22322 | pop();
|
| 22323 | push(p1);
|
| 22324 | }
|
| 22325 | }
|
| 22326 | restore();
|
| 22327 | return n;
|
| 22328 | };
|
| 22329 |
|
| 22330 | rewrite_args_tensor = function() {
|
| 22331 | var i, l1, n, ref2;
|
| 22332 | n = 0;
|
| 22333 | i = 0;
|
| 22334 | push(p1);
|
| 22335 | copy_tensor();
|
| 22336 | p1 = pop();
|
| 22337 | for (i = l1 = 0, ref2 = p1.tensor.nelem; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 22338 | push(p1.tensor.elem[i]);
|
| 22339 | push(p2);
|
| 22340 | n += rewrite_args();
|
| 22341 | p1.tensor.elem[i] = pop();
|
| 22342 | }
|
| 22343 | check_tensor_dimensions(p1);
|
| 22344 | push(p1);
|
| 22345 | return n;
|
| 22346 | };
|
| 22347 |
|
| 22348 | Eval_zero = function() {
|
| 22349 | var i, k, l1, m, m1, n, ref2, ref3;
|
| 22350 | i = 0;
|
| 22351 | k = [];
|
| 22352 | m = 0;
|
| 22353 | n = 0;
|
| 22354 | for (i = l1 = 0, ref2 = MAXDIM; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 22355 | k[i] = 0;
|
| 22356 | }
|
| 22357 | m = 1;
|
| 22358 | n = 0;
|
| 22359 | p2 = cdr(p1);
|
| 22360 | while (iscons(p2)) {
|
| 22361 | push(car(p2));
|
| 22362 | Eval();
|
| 22363 | i = pop_integer();
|
| 22364 | if (i < 1 || isNaN(i)) {
|
| 22365 | push(zero);
|
| 22366 | return;
|
| 22367 | }
|
| 22368 | m *= i;
|
| 22369 | k[n++] = i;
|
| 22370 | p2 = cdr(p2);
|
| 22371 | }
|
| 22372 | if (n === 0) {
|
| 22373 | push(zero);
|
| 22374 | return;
|
| 22375 | }
|
| 22376 | p1 = alloc_tensor(m);
|
| 22377 | p1.tensor.ndim = n;
|
| 22378 | for (i = m1 = 0, ref3 = n; 0 <= ref3 ? m1 < ref3 : m1 > ref3; i = 0 <= ref3 ? ++m1 : --m1) {
|
| 22379 | p1.tensor.dim[i] = k[i];
|
| 22380 | }
|
| 22381 | return push(p1);
|
| 22382 | };
|
| 22383 |
|
| 22384 |
|
| 22385 | |
| 22386 | |
| 22387 | |
| 22388 | |
| 22389 | |
| 22390 | |
| 22391 | |
| 22392 | |
| 22393 | |
| 22394 | |
| 22395 | |
| 22396 | |
| 22397 | |
| 22398 | |
| 22399 | |
| 22400 | |
| 22401 | |
| 22402 | |
| 22403 | |
| 22404 | |
| 22405 | |
| 22406 | |
| 22407 | |
| 22408 | |
| 22409 | |
| 22410 | |
| 22411 | |
| 22412 | |
| 22413 | |
| 22414 | |
| 22415 | |
| 22416 | |
| 22417 |
|
| 22418 |
|
| 22419 | allocatedId = 0;
|
| 22420 |
|
| 22421 | alloc_tensor = function(nelem) {
|
| 22422 | var i, l1, p, ref2;
|
| 22423 | i = 0;
|
| 22424 | p = new U();
|
| 22425 | p.k = TENSOR;
|
| 22426 | p.tensor = new tensor();
|
| 22427 | p.tensor.nelem = nelem;
|
| 22428 | for (i = l1 = 0, ref2 = nelem; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 22429 | p.tensor.elem[i] = zero;
|
| 22430 | }
|
| 22431 | p.tensor.allocatedId = allocatedId;
|
| 22432 | allocatedId++;
|
| 22433 | check_tensor_dimensions(p);
|
| 22434 | return p;
|
| 22435 | };
|
| 22436 |
|
| 22437 |
|
| 22438 | |
| 22439 | |
| 22440 | |
| 22441 | |
| 22442 | |
| 22443 | |
| 22444 | |
| 22445 | |
| 22446 | |
| 22447 | |
| 22448 | |
| 22449 | |
| 22450 | |
| 22451 | |
| 22452 | |
| 22453 | |
| 22454 | |
| 22455 | |
| 22456 | |
| 22457 | |
| 22458 | |
| 22459 | |
| 22460 | |
| 22461 | |
| 22462 | |
| 22463 | |
| 22464 | |
| 22465 | |
| 22466 | |
| 22467 | |
| 22468 | |
| 22469 | |
| 22470 | |
| 22471 | |
| 22472 | |
| 22473 | |
| 22474 | |
| 22475 | |
| 22476 | |
| 22477 | |
| 22478 | |
| 22479 | |
| 22480 | |
| 22481 | |
| 22482 | |
| 22483 | |
| 22484 | |
| 22485 | |
| 22486 | |
| 22487 | |
| 22488 | |
| 22489 | |
| 22490 | |
| 22491 | |
| 22492 | |
| 22493 | |
| 22494 | |
| 22495 | |
| 22496 | |
| 22497 | |
| 22498 | |
| 22499 | |
| 22500 | |
| 22501 | |
| 22502 | |
| 22503 | |
| 22504 | |
| 22505 | |
| 22506 | |
| 22507 | |
| 22508 | |
| 22509 | |
| 22510 | |
| 22511 | |
| 22512 | |
| 22513 | |
| 22514 | |
| 22515 | |
| 22516 | |
| 22517 | |
| 22518 | |
| 22519 | |
| 22520 | |
| 22521 | |
| 22522 | |
| 22523 | |
| 22524 | |
| 22525 | |
| 22526 | |
| 22527 | |
| 22528 | |
| 22529 | |
| 22530 | |
| 22531 | |
| 22532 | |
| 22533 | |
| 22534 | |
| 22535 | |
| 22536 | |
| 22537 | |
| 22538 | |
| 22539 | |
| 22540 | |
| 22541 | |
| 22542 | |
| 22543 | |
| 22544 | |
| 22545 | |
| 22546 | |
| 22547 | |
| 22548 | |
| 22549 | |
| 22550 | |
| 22551 | |
| 22552 | |
| 22553 | |
| 22554 | |
| 22555 | |
| 22556 | |
| 22557 | |
| 22558 | |
| 22559 | |
| 22560 | |
| 22561 | |
| 22562 | |
| 22563 | |
| 22564 | |
| 22565 | |
| 22566 | |
| 22567 | |
| 22568 | |
| 22569 | |
| 22570 | |
| 22571 | |
| 22572 | |
| 22573 | |
| 22574 | |
| 22575 |
|
| 22576 |
|
| 22577 | Find = function(p, q) {
|
| 22578 | var i, l1, ref2;
|
| 22579 | i = 0;
|
| 22580 | if (equal(p, q)) {
|
| 22581 | return 1;
|
| 22582 | }
|
| 22583 | if (istensor(p)) {
|
| 22584 | for (i = l1 = 0, ref2 = p.tensor.nelem; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 22585 | if (Find(p.tensor.elem[i], q)) {
|
| 22586 | return 1;
|
| 22587 | }
|
| 22588 | }
|
| 22589 | return 0;
|
| 22590 | }
|
| 22591 | while (iscons(p)) {
|
| 22592 | if (Find(car(p), q)) {
|
| 22593 | return 1;
|
| 22594 | }
|
| 22595 | p = cdr(p);
|
| 22596 | }
|
| 22597 | return 0;
|
| 22598 | };
|
| 22599 |
|
| 22600 | findPossibleClockForm = function(p) {
|
| 22601 | var i, l1, ref2;
|
| 22602 | i = 0;
|
| 22603 | if (isimaginaryunit(p)) {
|
| 22604 | return 0;
|
| 22605 | }
|
| 22606 | if (car(p) === symbol(POWER) && !isinteger(caddr(p1))) {
|
| 22607 | if (Find(cadr(p), imaginaryunit)) {
|
| 22608 | return 1;
|
| 22609 | }
|
| 22610 | }
|
| 22611 | if (car(p) === symbol(POWER) && equaln(cadr(p), -1) && !isinteger(caddr(p1))) {
|
| 22612 | return 1;
|
| 22613 | }
|
| 22614 | if (istensor(p)) {
|
| 22615 | for (i = l1 = 0, ref2 = p.tensor.nelem; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 22616 | if (findPossibleClockForm(p.tensor.elem[i])) {
|
| 22617 | return 1;
|
| 22618 | }
|
| 22619 | }
|
| 22620 | return 0;
|
| 22621 | }
|
| 22622 | while (iscons(p)) {
|
| 22623 | if (findPossibleClockForm(car(p))) {
|
| 22624 | return 1;
|
| 22625 | }
|
| 22626 | p = cdr(p);
|
| 22627 | }
|
| 22628 | return 0;
|
| 22629 | };
|
| 22630 |
|
| 22631 | findPossibleExponentialForm = function(p) {
|
| 22632 | var i, l1, ref2;
|
| 22633 | i = 0;
|
| 22634 | if (car(p) === symbol(POWER) && cadr(p) === symbol(E)) {
|
| 22635 | return Find(caddr(p), imaginaryunit);
|
| 22636 | }
|
| 22637 | if (istensor(p)) {
|
| 22638 | for (i = l1 = 0, ref2 = p.tensor.nelem; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 22639 | if (findPossibleExponentialForm(p.tensor.elem[i])) {
|
| 22640 | return 1;
|
| 22641 | }
|
| 22642 | }
|
| 22643 | return 0;
|
| 22644 | }
|
| 22645 | while (iscons(p)) {
|
| 22646 | if (findPossibleExponentialForm(car(p))) {
|
| 22647 | return 1;
|
| 22648 | }
|
| 22649 | p = cdr(p);
|
| 22650 | }
|
| 22651 | return 0;
|
| 22652 | };
|
| 22653 |
|
| 22654 | $.Find = Find;
|
| 22655 |
|
| 22656 | init = function() {
|
| 22657 | var i, l1, ref2;
|
| 22658 | i = 0;
|
| 22659 | flag = 0;
|
| 22660 | reset_after_error();
|
| 22661 | chainOfUserSymbolsNotFunctionsBeingEvaluated = [];
|
| 22662 | if (flag) {
|
| 22663 | return;
|
| 22664 | }
|
| 22665 | flag = 1;
|
| 22666 | for (i = l1 = 0, ref2 = NSYM; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 22667 | symtab[i] = new U();
|
| 22668 | symtab[i].k = SYM;
|
| 22669 | binding[i] = symtab[i];
|
| 22670 | isSymbolReclaimable[i] = false;
|
| 22671 | }
|
| 22672 | return defn();
|
| 22673 | };
|
| 22674 |
|
| 22675 |
|
| 22676 | |
| 22677 | |
| 22678 | |
| 22679 | |
| 22680 | |
| 22681 | |
| 22682 | |
| 22683 | |
| 22684 | |
| 22685 | |
| 22686 | |
| 22687 | |
| 22688 | |
| 22689 |
|
| 22690 |
|
| 22691 |
|
| 22692 | |
| 22693 | |
| 22694 | |
| 22695 | |
| 22696 | |
| 22697 | |
| 22698 | |
| 22699 | |
| 22700 | |
| 22701 | |
| 22702 | |
| 22703 | |
| 22704 | |
| 22705 |
|
| 22706 |
|
| 22707 | defn_str = ["version=\"" + version + "\"", "e=exp(1)", "i=sqrt(-1)", "autoexpand=1", "assumeRealVariables=1", "trange=[-pi,pi]", "xrange=[-10,10]", "yrange=[-10,10]", "last=0", "trace=0", "printLeaveEAlone=1", "printLeaveXAlone=0", "cross(u,v)=[u[2]*v[3]-u[3]*v[2],u[3]*v[1]-u[1]*v[3],u[1]*v[2]-u[2]*v[1]]", "curl(v)=[d(v[3],y)-d(v[2],z),d(v[1],z)-d(v[3],x),d(v[2],x)-d(v[1],y)]", "div(v)=d(v[1],x)+d(v[2],y)+d(v[3],z)", "ln(x)=log(x)"];
|
| 22708 |
|
| 22709 | defn = function() {
|
| 22710 | var definitionOfInterest, defn_i, l1, originalCodeGen, ref2;
|
| 22711 | p0 = symbol(NIL);
|
| 22712 | p1 = symbol(NIL);
|
| 22713 | p2 = symbol(NIL);
|
| 22714 | p3 = symbol(NIL);
|
| 22715 | p4 = symbol(NIL);
|
| 22716 | p5 = symbol(NIL);
|
| 22717 | p6 = symbol(NIL);
|
| 22718 | p7 = symbol(NIL);
|
| 22719 | p8 = symbol(NIL);
|
| 22720 | p9 = symbol(NIL);
|
| 22721 | std_symbol("abs", ABS);
|
| 22722 | std_symbol("add", ADD);
|
| 22723 | std_symbol("adj", ADJ);
|
| 22724 | std_symbol("and", AND);
|
| 22725 | std_symbol("approxratio", APPROXRATIO);
|
| 22726 | std_symbol("arccos", ARCCOS);
|
| 22727 | std_symbol("arccosh", ARCCOSH);
|
| 22728 | std_symbol("arcsin", ARCSIN);
|
| 22729 | std_symbol("arcsinh", ARCSINH);
|
| 22730 | std_symbol("arctan", ARCTAN);
|
| 22731 | std_symbol("arctanh", ARCTANH);
|
| 22732 | std_symbol("arg", ARG);
|
| 22733 | std_symbol("atomize", ATOMIZE);
|
| 22734 | std_symbol("besselj", BESSELJ);
|
| 22735 | std_symbol("bessely", BESSELY);
|
| 22736 | std_symbol("binding", BINDING);
|
| 22737 | std_symbol("binomial", BINOMIAL);
|
| 22738 | std_symbol("ceiling", CEILING);
|
| 22739 | std_symbol("check", CHECK);
|
| 22740 | std_symbol("choose", CHOOSE);
|
| 22741 | std_symbol("circexp", CIRCEXP);
|
| 22742 | std_symbol("clear", CLEAR);
|
| 22743 | std_symbol("clearall", CLEARALL);
|
| 22744 | std_symbol("clearpatterns", CLEARPATTERNS);
|
| 22745 | std_symbol("clock", CLOCK);
|
| 22746 | std_symbol("coeff", COEFF);
|
| 22747 | std_symbol("cofactor", COFACTOR);
|
| 22748 | std_symbol("condense", CONDENSE);
|
| 22749 | std_symbol("conj", CONJ);
|
| 22750 | std_symbol("contract", CONTRACT);
|
| 22751 | std_symbol("cos", COS);
|
| 22752 | std_symbol("cosh", COSH);
|
| 22753 | std_symbol("decomp", DECOMP);
|
| 22754 | std_symbol("defint", DEFINT);
|
| 22755 | std_symbol("deg", DEGREE);
|
| 22756 | std_symbol("denominator", DENOMINATOR);
|
| 22757 | std_symbol("det", DET);
|
| 22758 | std_symbol("derivative", DERIVATIVE);
|
| 22759 | std_symbol("dim", DIM);
|
| 22760 | std_symbol("dirac", DIRAC);
|
| 22761 | std_symbol("divisors", DIVISORS);
|
| 22762 | std_symbol("do", DO);
|
| 22763 | std_symbol("dot", DOT);
|
| 22764 | std_symbol("draw", DRAW);
|
| 22765 | std_symbol("dsolve", DSOLVE);
|
| 22766 | std_symbol("erf", ERF);
|
| 22767 | std_symbol("erfc", ERFC);
|
| 22768 | std_symbol("eigen", EIGEN);
|
| 22769 | std_symbol("eigenval", EIGENVAL);
|
| 22770 | std_symbol("eigenvec", EIGENVEC);
|
| 22771 | std_symbol("eval", EVAL);
|
| 22772 | std_symbol("exp", EXP);
|
| 22773 | std_symbol("expand", EXPAND);
|
| 22774 | std_symbol("expcos", EXPCOS);
|
| 22775 | std_symbol("expsin", EXPSIN);
|
| 22776 | std_symbol("factor", FACTOR);
|
| 22777 | std_symbol("factorial", FACTORIAL);
|
| 22778 | std_symbol("factorpoly", FACTORPOLY);
|
| 22779 | std_symbol("filter", FILTER);
|
| 22780 | std_symbol("float", FLOATF);
|
| 22781 | std_symbol("floor", FLOOR);
|
| 22782 | std_symbol("for", FOR);
|
| 22783 | std_symbol("function", FUNCTION);
|
| 22784 | std_symbol("Gamma", GAMMA);
|
| 22785 | std_symbol("gcd", GCD);
|
| 22786 | std_symbol("hermite", HERMITE);
|
| 22787 | std_symbol("hilbert", HILBERT);
|
| 22788 | std_symbol("imag", IMAG);
|
| 22789 | std_symbol("component", INDEX);
|
| 22790 | std_symbol("inner", INNER);
|
| 22791 | std_symbol("integral", INTEGRAL);
|
| 22792 | std_symbol("inv", INV);
|
| 22793 | std_symbol("invg", INVG);
|
| 22794 | std_symbol("isinteger", ISINTEGER);
|
| 22795 | std_symbol("isprime", ISPRIME);
|
| 22796 | std_symbol("laguerre", LAGUERRE);
|
| 22797 | std_symbol("lcm", LCM);
|
| 22798 | std_symbol("leading", LEADING);
|
| 22799 | std_symbol("legendre", LEGENDRE);
|
| 22800 | std_symbol("log", LOG);
|
| 22801 | std_symbol("lookup", LOOKUP);
|
| 22802 | std_symbol("mod", MOD);
|
| 22803 | std_symbol("multiply", MULTIPLY);
|
| 22804 | std_symbol("not", NOT);
|
| 22805 | std_symbol("nroots", NROOTS);
|
| 22806 | std_symbol("number", NUMBER);
|
| 22807 | std_symbol("numerator", NUMERATOR);
|
| 22808 | std_symbol("operator", OPERATOR);
|
| 22809 | std_symbol("or", OR);
|
| 22810 | std_symbol("outer", OUTER);
|
| 22811 | std_symbol("pattern", PATTERN);
|
| 22812 | std_symbol("patternsinfo", PATTERNSINFO);
|
| 22813 | std_symbol("polar", POLAR);
|
| 22814 | std_symbol("power", POWER);
|
| 22815 | std_symbol("prime", PRIME);
|
| 22816 | std_symbol("print", PRINT);
|
| 22817 | std_symbol("print2dascii", PRINT2DASCII);
|
| 22818 | std_symbol("printfull", PRINTFULL);
|
| 22819 | std_symbol("printlatex", PRINTLATEX);
|
| 22820 | std_symbol("printlist", PRINTLIST);
|
| 22821 | std_symbol("printplain", PRINTPLAIN);
|
| 22822 | std_symbol("printLeaveEAlone", PRINT_LEAVE_E_ALONE);
|
| 22823 | std_symbol("printLeaveXAlone", PRINT_LEAVE_X_ALONE);
|
| 22824 | std_symbol("product", PRODUCT);
|
| 22825 | std_symbol("quote", QUOTE);
|
| 22826 | std_symbol("quotient", QUOTIENT);
|
| 22827 | std_symbol("rank", RANK);
|
| 22828 | std_symbol("rationalize", RATIONALIZE);
|
| 22829 | std_symbol("real", REAL);
|
| 22830 | std_symbol("rect", YYRECT);
|
| 22831 | std_symbol("roots", ROOTS);
|
| 22832 | std_symbol("round", ROUND);
|
| 22833 | std_symbol("equals", SETQ);
|
| 22834 | std_symbol("sgn", SGN);
|
| 22835 | std_symbol("silentpattern", SILENTPATTERN);
|
| 22836 | std_symbol("simplify", SIMPLIFY);
|
| 22837 | std_symbol("sin", SIN);
|
| 22838 | std_symbol("sinh", SINH);
|
| 22839 | std_symbol("shape", SHAPE);
|
| 22840 | std_symbol("sqrt", SQRT);
|
| 22841 | std_symbol("stop", STOP);
|
| 22842 | std_symbol("subst", SUBST);
|
| 22843 | std_symbol("sum", SUM);
|
| 22844 | std_symbol("symbolsinfo", SYMBOLSINFO);
|
| 22845 | std_symbol("tan", TAN);
|
| 22846 | std_symbol("tanh", TANH);
|
| 22847 | std_symbol("taylor", TAYLOR);
|
| 22848 | std_symbol("test", TEST);
|
| 22849 | std_symbol("testeq", TESTEQ);
|
| 22850 | std_symbol("testge", TESTGE);
|
| 22851 | std_symbol("testgt", TESTGT);
|
| 22852 | std_symbol("testle", TESTLE);
|
| 22853 | std_symbol("testlt", TESTLT);
|
| 22854 | std_symbol("transpose", TRANSPOSE);
|
| 22855 | std_symbol("unit", UNIT);
|
| 22856 | std_symbol("zero", ZERO);
|
| 22857 | std_symbol("nil", NIL);
|
| 22858 | std_symbol("autoexpand", AUTOEXPAND);
|
| 22859 | std_symbol("bake", BAKE);
|
| 22860 | std_symbol("assumeRealVariables", ASSUME_REAL_VARIABLES);
|
| 22861 | std_symbol("last", LAST);
|
| 22862 | std_symbol("lastprint", LAST_PRINT);
|
| 22863 | std_symbol("last2dasciiprint", LAST_2DASCII_PRINT);
|
| 22864 | std_symbol("lastfullprint", LAST_FULL_PRINT);
|
| 22865 | std_symbol("lastlatexprint", LAST_LATEX_PRINT);
|
| 22866 | std_symbol("lastlistprint", LAST_LIST_PRINT);
|
| 22867 | std_symbol("lastplainprint", LAST_PLAIN_PRINT);
|
| 22868 | std_symbol("trace", TRACE);
|
| 22869 | std_symbol("~", YYE);
|
| 22870 | std_symbol("$DRAWX", DRAWX);
|
| 22871 | std_symbol("$METAA", METAA);
|
| 22872 | std_symbol("$METAB", METAB);
|
| 22873 | std_symbol("$METAX", METAX);
|
| 22874 | std_symbol("$SECRETX", SECRETX);
|
| 22875 | std_symbol("version", VERSION);
|
| 22876 | std_symbol("pi", PI);
|
| 22877 | std_symbol("a", SYMBOL_A);
|
| 22878 | std_symbol("b", SYMBOL_B);
|
| 22879 | std_symbol("c", SYMBOL_C);
|
| 22880 | std_symbol("d", SYMBOL_D);
|
| 22881 | std_symbol("i", SYMBOL_I);
|
| 22882 | std_symbol("j", SYMBOL_J);
|
| 22883 | std_symbol("n", SYMBOL_N);
|
| 22884 | std_symbol("r", SYMBOL_R);
|
| 22885 | std_symbol("s", SYMBOL_S);
|
| 22886 | std_symbol("t", SYMBOL_T);
|
| 22887 | std_symbol("x", SYMBOL_X);
|
| 22888 | std_symbol("y", SYMBOL_Y);
|
| 22889 | std_symbol("z", SYMBOL_Z);
|
| 22890 | std_symbol("I", SYMBOL_IDENTITY_MATRIX);
|
| 22891 | std_symbol("a_", SYMBOL_A_UNDERSCORE);
|
| 22892 | std_symbol("b_", SYMBOL_B_UNDERSCORE);
|
| 22893 | std_symbol("x_", SYMBOL_X_UNDERSCORE);
|
| 22894 | std_symbol("$C1", C1);
|
| 22895 | std_symbol("$C2", C2);
|
| 22896 | std_symbol("$C3", C3);
|
| 22897 | std_symbol("$C4", C4);
|
| 22898 | std_symbol("$C5", C5);
|
| 22899 | std_symbol("$C6", C6);
|
| 22900 | defineSomeHandyConstants();
|
| 22901 | originalCodeGen = codeGen;
|
| 22902 | codeGen = false;
|
| 22903 | for (defn_i = l1 = 0, ref2 = defn_str.length; 0 <= ref2 ? l1 < ref2 : l1 > ref2; defn_i = 0 <= ref2 ? ++l1 : --l1) {
|
| 22904 | definitionOfInterest = defn_str[defn_i];
|
| 22905 | scan(definitionOfInterest);
|
| 22906 | if (DEBUG) {
|
| 22907 | console.log("... evaling " + definitionOfInterest);
|
| 22908 | console.log("top of stack:");
|
| 22909 | console.log(print_list(stack[tos - 1]));
|
| 22910 | }
|
| 22911 | Eval();
|
| 22912 | pop();
|
| 22913 | }
|
| 22914 | return codeGen = originalCodeGen;
|
| 22915 | };
|
| 22916 |
|
| 22917 | defineSomeHandyConstants = function() {
|
| 22918 | push_integer(0);
|
| 22919 | zero = pop();
|
| 22920 | push_integer(1);
|
| 22921 | one = pop();
|
| 22922 | push_double(1.0);
|
| 22923 | one_as_double = pop();
|
| 22924 | push_symbol(POWER);
|
| 22925 | if (DEBUG) {
|
| 22926 | console.log(print_list(stack[tos - 1]));
|
| 22927 | }
|
| 22928 | push_integer(-1);
|
| 22929 | if (DEBUG) {
|
| 22930 | console.log(print_list(stack[tos - 1]));
|
| 22931 | }
|
| 22932 | push_rational(1, 2);
|
| 22933 | if (DEBUG) {
|
| 22934 | console.log(print_list(stack[tos - 1]));
|
| 22935 | }
|
| 22936 | list(3);
|
| 22937 | if (DEBUG) {
|
| 22938 | console.log(print_list(stack[tos - 1]));
|
| 22939 | }
|
| 22940 | return imaginaryunit = pop();
|
| 22941 | };
|
| 22942 |
|
| 22943 | mcmp = function(a, b) {
|
| 22944 | return a.compare(b);
|
| 22945 | };
|
| 22946 |
|
| 22947 | mcmpint = function(a, n) {
|
| 22948 | var b, t;
|
| 22949 | b = bigInt(n);
|
| 22950 | t = mcmp(a, b);
|
| 22951 | return t;
|
| 22952 | };
|
| 22953 |
|
| 22954 |
|
| 22955 | |
| 22956 | |
| 22957 | |
| 22958 | |
| 22959 | |
| 22960 | |
| 22961 | |
| 22962 | |
| 22963 | |
| 22964 | |
| 22965 | |
| 22966 | |
| 22967 | |
| 22968 | |
| 22969 | |
| 22970 | |
| 22971 | |
| 22972 | |
| 22973 | |
| 22974 | |
| 22975 | |
| 22976 | |
| 22977 | |
| 22978 | |
| 22979 | |
| 22980 | |
| 22981 | |
| 22982 | |
| 22983 | |
| 22984 | |
| 22985 | |
| 22986 | |
| 22987 | |
| 22988 | |
| 22989 |
|
| 22990 |
|
| 22991 | strcmp = function(str1, str2) {
|
| 22992 | if (str1 === str2) {
|
| 22993 | return 0;
|
| 22994 | } else if (str1 > str2) {
|
| 22995 | return 1;
|
| 22996 | } else {
|
| 22997 | return -1;
|
| 22998 | }
|
| 22999 | };
|
| 23000 |
|
| 23001 | doubleToReasonableString = function(d) {
|
| 23002 | var stringRepresentation;
|
| 23003 | if (codeGen) {
|
| 23004 | return d + "";
|
| 23005 | }
|
| 23006 | stringRepresentation = "" + parseFloat(d.toPrecision(6));
|
| 23007 | if (stringRepresentation.indexOf(".") === -1) {
|
| 23008 | stringRepresentation += ".0";
|
| 23009 | }
|
| 23010 | return stringRepresentation;
|
| 23011 | };
|
| 23012 |
|
| 23013 | clear_term = function() {};
|
| 23014 |
|
| 23015 | isspace = function(s) {
|
| 23016 | if (s == null) {
|
| 23017 | return false;
|
| 23018 | }
|
| 23019 | return s === ' ' || s === '\t' || s === '\n' || s === '\v' || s === '\f' || s === '\r';
|
| 23020 | };
|
| 23021 |
|
| 23022 | isdigit = function(str) {
|
| 23023 | if (str == null) {
|
| 23024 | return false;
|
| 23025 | }
|
| 23026 | return /^\d+$/.test(str);
|
| 23027 | };
|
| 23028 |
|
| 23029 | isalpha = function(str) {
|
| 23030 | if (str == null) {
|
| 23031 | return false;
|
| 23032 | }
|
| 23033 | return str.search(/[^A-Za-z]/) === -1;
|
| 23034 | };
|
| 23035 |
|
| 23036 | isalphaOrUnderscore = function(str) {
|
| 23037 | if (str == null) {
|
| 23038 | return false;
|
| 23039 | }
|
| 23040 | return str.search(/[^A-Za-z_]/) === -1;
|
| 23041 | };
|
| 23042 |
|
| 23043 | isunderscore = function(str) {
|
| 23044 | if (str == null) {
|
| 23045 | return false;
|
| 23046 | }
|
| 23047 | return str.search(/_/) === -1;
|
| 23048 | };
|
| 23049 |
|
| 23050 | isalnumorunderscore = function(str) {
|
| 23051 | if (str == null) {
|
| 23052 | return false;
|
| 23053 | }
|
| 23054 | return isalphaOrUnderscore(str) || isdigit(str);
|
| 23055 | };
|
| 23056 |
|
| 23057 | count = function(p) {
|
| 23058 | var n;
|
| 23059 | if (iscons(p)) {
|
| 23060 | n = 0;
|
| 23061 | while (iscons(p)) {
|
| 23062 | n += count(car(p)) + 1;
|
| 23063 | p = cdr(p);
|
| 23064 | }
|
| 23065 | } else {
|
| 23066 | n = 1;
|
| 23067 | }
|
| 23068 | return n;
|
| 23069 | };
|
| 23070 |
|
| 23071 | countOccurrencesOfSymbol = function(needle, p) {
|
| 23072 | var n;
|
| 23073 | n = 0;
|
| 23074 | if (iscons(p)) {
|
| 23075 | while (iscons(p)) {
|
| 23076 | n += countOccurrencesOfSymbol(needle, car(p));
|
| 23077 | p = cdr(p);
|
| 23078 | }
|
| 23079 | } else {
|
| 23080 | if (equal(needle, p)) {
|
| 23081 | n = 1;
|
| 23082 | }
|
| 23083 | }
|
| 23084 | return n;
|
| 23085 | };
|
| 23086 |
|
| 23087 | countsize = function(p) {
|
| 23088 | var i, l1, n, ref2;
|
| 23089 | n = 0;
|
| 23090 | if (istensor(p)) {
|
| 23091 | for (i = l1 = 0, ref2 = p.tensor.nelem; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 23092 | n += p.tensor.elem[i];
|
| 23093 | }
|
| 23094 | } else if (iscons(p)) {
|
| 23095 | while (iscons(p)) {
|
| 23096 | n += count(car(p)) + 1;
|
| 23097 | p = cdr(p);
|
| 23098 | }
|
| 23099 | } else {
|
| 23100 | n = 1;
|
| 23101 | }
|
| 23102 | return n;
|
| 23103 | };
|
| 23104 |
|
| 23105 | stop = function(s) {
|
| 23106 | var message;
|
| 23107 | errorMessage += "Stop: ";
|
| 23108 | errorMessage += s;
|
| 23109 | message = errorMessage;
|
| 23110 | errorMessage = '';
|
| 23111 | moveTos(0);
|
| 23112 | throw new Error(message);
|
| 23113 | };
|
| 23114 |
|
| 23115 | findDependenciesInScript = function(stringToBeParsed, dontGenerateCode) {
|
| 23116 | var allReturnedLatexStrings, allReturnedPlainStrings, bodyForReadableSummaryOfGeneratedCode, cacheKey, cacheMissPenalty, currentStateHash, cyclesDescriptions, deQuotedDep, dependencyInfo, eachDependency, error, frozen, generatedBody, generatedCode, i, indexOfEachReplacement, indexOfPartRemainingToBeParsed, inited, key, l1, len, len1, len2, len3, len4, len5, len6, len7, m1, n, n1, newUserSymbol, o1, origPrintMode, originalUserSymbol, parameters, possiblyCached, q1, r1, readableSummaryOfGeneratedCode, recursedDependencies, ref2, replacementsFrom, replacementsTo, s1, scriptEvaluation, stringToBeRun, t1, testableString, timeStartFromAlgebra, toBeFrozen, toBePrinted, totalTime, u1, userVariablesMentioned, value, variablesWithCycles;
|
| 23117 | if (DEBUG) {
|
| 23118 | console.log("stringToBeParsed: " + stringToBeParsed);
|
| 23119 | }
|
| 23120 | timeStartFromAlgebra = new Date().getTime();
|
| 23121 | if (CACHE_DEBUGS || CACHE_HITSMISS_DEBUGS || TIMING_DEBUGS) {
|
| 23122 | console.log(" --------- findDependenciesInScript input: " + stringToBeParsed + " at: " + (new Date()));
|
| 23123 | currentStateHash = getStateHash();
|
| 23124 | console.log("state hash: " + currentStateHash);
|
| 23125 | }
|
| 23126 | inited = true;
|
| 23127 | codeGen = true;
|
| 23128 | symbolsDependencies = {};
|
| 23129 | symbolsHavingReassignments = [];
|
| 23130 | symbolsInExpressionsWithoutAssignments = [];
|
| 23131 | patternHasBeenFound = false;
|
| 23132 | indexOfPartRemainingToBeParsed = 0;
|
| 23133 | allReturnedPlainStrings = "";
|
| 23134 | allReturnedLatexStrings = "";
|
| 23135 | n = 0;
|
| 23136 | dependencyInfo = {
|
| 23137 | affectsVariables: [],
|
| 23138 | affectedBy: []
|
| 23139 | };
|
| 23140 | stringToBeRun = stringToBeParsed;
|
| 23141 | if (ENABLE_CACHING && stringToBeRun !== "clearall") {
|
| 23142 | currentStateHash = getStateHash();
|
| 23143 | cacheKey = currentStateHash + " stringToBeRun: " + stringToBeRun + " - " + dontGenerateCode;
|
| 23144 | if (CACHE_DEBUGS) {
|
| 23145 | console.log("cached_findDependenciesInScript key: " + cacheKey);
|
| 23146 | }
|
| 23147 | possiblyCached = cached_findDependenciesInScript.get(cacheKey);
|
| 23148 | if (possiblyCached != null) {
|
| 23149 | if (CACHE_HITSMISS_DEBUGS) {
|
| 23150 | console.log("cached_findDependenciesInScript hit on " + stringToBeRun);
|
| 23151 | }
|
| 23152 | unfreeze(possiblyCached);
|
| 23153 | if (TIMING_DEBUGS) {
|
| 23154 | totalTime = new Date().getTime() - timeStartFromAlgebra;
|
| 23155 | console.log("findDependenciesInScript input: " + stringToBeRun + " time: " + totalTime + "ms, saved " + (possiblyCached[possiblyCached.length - 5] - totalTime) + "ms due to cache hit");
|
| 23156 | }
|
| 23157 | return [possiblyCached[possiblyCached.length - 7], possiblyCached[possiblyCached.length - 6], possiblyCached[possiblyCached.length - 5], possiblyCached[possiblyCached.length - 4], possiblyCached[possiblyCached.length - 3], possiblyCached[possiblyCached.length - 2], possiblyCached[possiblyCached.length - 1]];
|
| 23158 | } else {
|
| 23159 | if (CACHE_HITSMISS_DEBUGS) {
|
| 23160 | console.log("cached_findDependenciesInScript miss on: " + stringToBeRun);
|
| 23161 | }
|
| 23162 | if (TIMING_DEBUGS) {
|
| 23163 | cacheMissPenalty = new Date().getTime() - timeStartFromAlgebra;
|
| 23164 | }
|
| 23165 | }
|
| 23166 | }
|
| 23167 | while (1) {
|
| 23168 | try {
|
| 23169 | errorMessage = "";
|
| 23170 | check_stack();
|
| 23171 | if (DEBUG) {
|
| 23172 | console.log("findDependenciesInScript: scanning");
|
| 23173 | }
|
| 23174 | n = scan(stringToBeParsed.substring(indexOfPartRemainingToBeParsed));
|
| 23175 | if (DEBUG) {
|
| 23176 | console.log("scanned");
|
| 23177 | }
|
| 23178 | pop();
|
| 23179 | check_stack();
|
| 23180 | } catch (error1) {
|
| 23181 | error = error1;
|
| 23182 | if (PRINTOUTRESULT) {
|
| 23183 | console.log(error);
|
| 23184 | }
|
| 23185 | errorMessage = error + "";
|
| 23186 | reset_after_error();
|
| 23187 | break;
|
| 23188 | }
|
| 23189 | if (n === 0) {
|
| 23190 | break;
|
| 23191 | }
|
| 23192 | indexOfPartRemainingToBeParsed += n;
|
| 23193 | }
|
| 23194 | testableString = "";
|
| 23195 | if (DEBUG) {
|
| 23196 | console.log("all local dependencies ----------------");
|
| 23197 | }
|
| 23198 | testableString += "All local dependencies: ";
|
| 23199 | for (key in symbolsDependencies) {
|
| 23200 | value = symbolsDependencies[key];
|
| 23201 | if (DEBUG) {
|
| 23202 | console.log("variable " + key + " depends on: ");
|
| 23203 | }
|
| 23204 | dependencyInfo.affectsVariables.push(key);
|
| 23205 | testableString += " variable " + key + " depends on: ";
|
| 23206 | for (l1 = 0, len = value.length; l1 < len; l1++) {
|
| 23207 | i = value[l1];
|
| 23208 | if (DEBUG) {
|
| 23209 | console.log(" " + i);
|
| 23210 | }
|
| 23211 | if (i[0] !== "'") {
|
| 23212 | dependencyInfo.affectedBy.push(i);
|
| 23213 | }
|
| 23214 | testableString += i + ", ";
|
| 23215 | }
|
| 23216 | testableString += "; ";
|
| 23217 | }
|
| 23218 | testableString += ". ";
|
| 23219 | if (DEBUG) {
|
| 23220 | console.log("Symbols with reassignments ----------------");
|
| 23221 | }
|
| 23222 | testableString += "Symbols with reassignments: ";
|
| 23223 | for (m1 = 0, len1 = symbolsHavingReassignments.length; m1 < len1; m1++) {
|
| 23224 | key = symbolsHavingReassignments[m1];
|
| 23225 | if (dependencyInfo.affectedBy.indexOf(key) === -1) {
|
| 23226 | dependencyInfo.affectedBy.push(key);
|
| 23227 | testableString += key + ", ";
|
| 23228 | }
|
| 23229 | }
|
| 23230 | testableString += ". ";
|
| 23231 | if (DEBUG) {
|
| 23232 | console.log("Symbols in expressions without assignments ----------------");
|
| 23233 | }
|
| 23234 | testableString += "Symbols in expressions without assignments: ";
|
| 23235 | for (n1 = 0, len2 = symbolsInExpressionsWithoutAssignments.length; n1 < len2; n1++) {
|
| 23236 | key = symbolsInExpressionsWithoutAssignments[n1];
|
| 23237 | if (dependencyInfo.affectedBy.indexOf(key) === -1) {
|
| 23238 | dependencyInfo.affectedBy.push(key);
|
| 23239 | testableString += key + ", ";
|
| 23240 | }
|
| 23241 | }
|
| 23242 | testableString += ". ";
|
| 23243 | dependencyInfo.affectedBy.push("PATTERN_DEPENDENCY");
|
| 23244 | if (patternHasBeenFound) {
|
| 23245 | dependencyInfo.affectsVariables.push("PATTERN_DEPENDENCY");
|
| 23246 | testableString += " - PATTERN_DEPENDENCY inserted - ";
|
| 23247 | }
|
| 23248 | if (DEBUG) {
|
| 23249 | console.log("All dependencies recursively ----------------");
|
| 23250 | }
|
| 23251 | testableString += "All dependencies recursively: ";
|
| 23252 | scriptEvaluation = ["", ""];
|
| 23253 | generatedCode = "";
|
| 23254 | readableSummaryOfGeneratedCode = "";
|
| 23255 | if (errorMessage === "" && !dontGenerateCode) {
|
| 23256 | try {
|
| 23257 | allReturnedPlainStrings = "";
|
| 23258 | allReturnedLatexStrings = "";
|
| 23259 | scriptEvaluation = run(stringToBeParsed, true);
|
| 23260 | allReturnedPlainStrings = "";
|
| 23261 | allReturnedLatexStrings = "";
|
| 23262 | } catch (error1) {
|
| 23263 | error = error1;
|
| 23264 | if (PRINTOUTRESULT) {
|
| 23265 | console.log(error);
|
| 23266 | }
|
| 23267 | errorMessage = error + "";
|
| 23268 | init();
|
| 23269 | }
|
| 23270 | if (errorMessage === "") {
|
| 23271 | for (key in symbolsDependencies) {
|
| 23272 | codeGen = true;
|
| 23273 | if (DEBUG) {
|
| 23274 | console.log(" variable " + key + " is: " + get_binding(usr_symbol(key)).toString());
|
| 23275 | }
|
| 23276 | codeGen = false;
|
| 23277 | if (DEBUG) {
|
| 23278 | console.log(" variable " + key + " depends on: ");
|
| 23279 | }
|
| 23280 | testableString += " variable " + key + " depends on: ";
|
| 23281 | recursedDependencies = [];
|
| 23282 | variablesWithCycles = [];
|
| 23283 | cyclesDescriptions = [];
|
| 23284 | recursiveDependencies(key, recursedDependencies, [], variablesWithCycles, [], cyclesDescriptions);
|
| 23285 | for (o1 = 0, len3 = variablesWithCycles.length; o1 < len3; o1++) {
|
| 23286 | i = variablesWithCycles[o1];
|
| 23287 | if (DEBUG) {
|
| 23288 | console.log(" --> cycle through " + i);
|
| 23289 | }
|
| 23290 | }
|
| 23291 | for (q1 = 0, len4 = recursedDependencies.length; q1 < len4; q1++) {
|
| 23292 | i = recursedDependencies[q1];
|
| 23293 | if (DEBUG) {
|
| 23294 | console.log(" " + i);
|
| 23295 | }
|
| 23296 | testableString += i + ", ";
|
| 23297 | }
|
| 23298 | testableString += "; ";
|
| 23299 | for (r1 = 0, len5 = cyclesDescriptions.length; r1 < len5; r1++) {
|
| 23300 | i = cyclesDescriptions[r1];
|
| 23301 | testableString += " " + i + ", ";
|
| 23302 | }
|
| 23303 | if (DEBUG) {
|
| 23304 | console.log(" code generation:" + key + " is: " + get_binding(usr_symbol(key)).toString());
|
| 23305 | }
|
| 23306 | push(get_binding(usr_symbol(key)));
|
| 23307 | replacementsFrom = [];
|
| 23308 | replacementsTo = [];
|
| 23309 | for (s1 = 0, len6 = recursedDependencies.length; s1 < len6; s1++) {
|
| 23310 | eachDependency = recursedDependencies[s1];
|
| 23311 | if (eachDependency[0] === "'") {
|
| 23312 | deQuotedDep = eachDependency.substring(1);
|
| 23313 | originalUserSymbol = usr_symbol(deQuotedDep);
|
| 23314 | newUserSymbol = usr_symbol("AVOID_BINDING_TO_EXTERNAL_SCOPE_VALUE" + deQuotedDep);
|
| 23315 | replacementsFrom.push(originalUserSymbol);
|
| 23316 | replacementsTo.push(newUserSymbol);
|
| 23317 | push(originalUserSymbol);
|
| 23318 | push(newUserSymbol);
|
| 23319 | subst();
|
| 23320 | if (DEBUG) {
|
| 23321 | console.log("after substitution: " + stack[tos - 1]);
|
| 23322 | }
|
| 23323 | }
|
| 23324 | }
|
| 23325 | try {
|
| 23326 | simplifyForCodeGeneration();
|
| 23327 | } catch (error1) {
|
| 23328 | error = error1;
|
| 23329 | if (PRINTOUTRESULT) {
|
| 23330 | console.log(error);
|
| 23331 | }
|
| 23332 | errorMessage = error + "";
|
| 23333 | init();
|
| 23334 | }
|
| 23335 | for (indexOfEachReplacement = t1 = 0, ref2 = replacementsFrom.length; 0 <= ref2 ? t1 < ref2 : t1 > ref2; indexOfEachReplacement = 0 <= ref2 ? ++t1 : --t1) {
|
| 23336 | push(replacementsTo[indexOfEachReplacement]);
|
| 23337 | push(replacementsFrom[indexOfEachReplacement]);
|
| 23338 | subst();
|
| 23339 | }
|
| 23340 | clearRenamedVariablesToAvoidBindingToExternalScope();
|
| 23341 | if (errorMessage === "") {
|
| 23342 | toBePrinted = pop();
|
| 23343 | userVariablesMentioned = [];
|
| 23344 | collectUserSymbols(toBePrinted, userVariablesMentioned);
|
| 23345 | allReturnedPlainStrings = "";
|
| 23346 | allReturnedLatexStrings = "";
|
| 23347 | codeGen = true;
|
| 23348 | generatedBody = toBePrinted.toString();
|
| 23349 | codeGen = false;
|
| 23350 | origPrintMode = printMode;
|
| 23351 | printMode = PRINTMODE_LATEX;
|
| 23352 | bodyForReadableSummaryOfGeneratedCode = toBePrinted.toString();
|
| 23353 | printMode = origPrintMode;
|
| 23354 | if (variablesWithCycles.indexOf(key) !== -1) {
|
| 23355 | generatedCode += "// " + key + " is part of a cyclic dependency, no code generated.";
|
| 23356 | readableSummaryOfGeneratedCode += "#" + key + " is part of a cyclic dependency, no code generated.";
|
| 23357 | } else {
|
| 23358 |
|
| 23359 | |
| 23360 | |
| 23361 | |
| 23362 | |
| 23363 | |
| 23364 | |
| 23365 | |
| 23366 | |
| 23367 | |
| 23368 | |
| 23369 | |
| 23370 | |
| 23371 | |
| 23372 | |
| 23373 | |
| 23374 | |
| 23375 | |
| 23376 | |
| 23377 | |
| 23378 |
|
| 23379 | userVariablesMentioned = userVariablesMentioned.filter(function(x) {
|
| 23380 | return predefinedSymbolsInGlobalScope_doNotTrackInDependencies.indexOf(x + "") === -1;
|
| 23381 | });
|
| 23382 | userVariablesMentioned = userVariablesMentioned.filter(function(x) {
|
| 23383 | return recursedDependencies.indexOf(x + "") !== -1 || recursedDependencies.indexOf("\'" + x + "") !== -1;
|
| 23384 | });
|
| 23385 | if (userVariablesMentioned.length !== 0) {
|
| 23386 | parameters = "(";
|
| 23387 | for (u1 = 0, len7 = userVariablesMentioned.length; u1 < len7; u1++) {
|
| 23388 | i = userVariablesMentioned[u1];
|
| 23389 | if (i.printname !== key) {
|
| 23390 | parameters += i.printname + ", ";
|
| 23391 | }
|
| 23392 | }
|
| 23393 | parameters = parameters.replace(/, $/gm, "");
|
| 23394 | parameters += ")";
|
| 23395 | generatedCode += key + " = function " + parameters + " { return ( " + generatedBody + " ); }";
|
| 23396 | readableSummaryOfGeneratedCode += key + parameters + " = " + bodyForReadableSummaryOfGeneratedCode;
|
| 23397 | } else {
|
| 23398 | generatedCode += key + " = " + generatedBody + ";";
|
| 23399 | readableSummaryOfGeneratedCode += key + " = " + bodyForReadableSummaryOfGeneratedCode;
|
| 23400 | }
|
| 23401 | }
|
| 23402 | generatedCode += "\n";
|
| 23403 | readableSummaryOfGeneratedCode += "\n";
|
| 23404 | if (DEBUG) {
|
| 23405 | console.log(" " + generatedCode);
|
| 23406 | }
|
| 23407 | }
|
| 23408 | }
|
| 23409 | }
|
| 23410 | }
|
| 23411 | generatedCode = generatedCode.replace(/\n$/gm, "");
|
| 23412 | readableSummaryOfGeneratedCode = readableSummaryOfGeneratedCode.replace(/\n$/gm, "");
|
| 23413 | symbolsDependencies = {};
|
| 23414 | symbolsHavingReassignments = [];
|
| 23415 | patternHasBeenFound = false;
|
| 23416 | symbolsInExpressionsWithoutAssignments = [];
|
| 23417 | if (DEBUG) {
|
| 23418 | console.log("testable string: " + testableString);
|
| 23419 | }
|
| 23420 | if (TIMING_DEBUGS) {
|
| 23421 | console.log("findDependenciesInScript time for: " + stringToBeRun + " : " + ((new Date().getTime()) - timeStartFromAlgebra) + "ms");
|
| 23422 | }
|
| 23423 | if (ENABLE_CACHING && stringToBeRun !== "clearall" && errorMessage === "") {
|
| 23424 | frozen = freeze();
|
| 23425 | toBeFrozen = [frozen[0], frozen[1], frozen[2], frozen[3], frozen[4], frozen[5], new Date().getTime() - timeStartFromAlgebra, testableString, scriptEvaluation[0], generatedCode, readableSummaryOfGeneratedCode, scriptEvaluation[1], errorMessage, dependencyInfo];
|
| 23426 | if (CACHE_DEBUGS) {
|
| 23427 | console.log("setting cached_findDependenciesInScript on key: " + cacheKey);
|
| 23428 | }
|
| 23429 | cached_findDependenciesInScript.set(cacheKey, toBeFrozen);
|
| 23430 | }
|
| 23431 | return [testableString, scriptEvaluation[0], generatedCode, readableSummaryOfGeneratedCode, scriptEvaluation[1], errorMessage, dependencyInfo];
|
| 23432 | };
|
| 23433 |
|
| 23434 | recursiveDependencies = function(variableToBeChecked, arrayWhereDependenciesWillBeAdded, variablesAlreadyFleshedOut, variablesWithCycles, chainBeingChecked, cyclesDescriptions) {
|
| 23435 | var cyclesDescription, i, k, l1, len, len1, m1, ref2;
|
| 23436 | variablesAlreadyFleshedOut.push(variableToBeChecked);
|
| 23437 | if (symbolsDependencies[chainBeingChecked[chainBeingChecked.length - 1]] != null) {
|
| 23438 | if (symbolsDependencies[chainBeingChecked[chainBeingChecked.length - 1]].indexOf("'" + variableToBeChecked) !== -1) {
|
| 23439 | if (DEBUG) {
|
| 23440 | console.log("can't keep following the chain of " + variableToBeChecked + " because it's actually a variable bound to a parameter");
|
| 23441 | }
|
| 23442 | if (arrayWhereDependenciesWillBeAdded.indexOf("'" + variableToBeChecked) === -1 && arrayWhereDependenciesWillBeAdded.indexOf(variableToBeChecked) === -1) {
|
| 23443 | arrayWhereDependenciesWillBeAdded.push(variableToBeChecked);
|
| 23444 | }
|
| 23445 | return arrayWhereDependenciesWillBeAdded;
|
| 23446 | }
|
| 23447 | }
|
| 23448 | chainBeingChecked.push(variableToBeChecked);
|
| 23449 | if (symbolsDependencies[variableToBeChecked] == null) {
|
| 23450 | if (arrayWhereDependenciesWillBeAdded.indexOf(variableToBeChecked) === -1) {
|
| 23451 | arrayWhereDependenciesWillBeAdded.push(variableToBeChecked);
|
| 23452 | }
|
| 23453 | return arrayWhereDependenciesWillBeAdded;
|
| 23454 | } else {
|
| 23455 | ref2 = symbolsDependencies[variableToBeChecked];
|
| 23456 | for (l1 = 0, len = ref2.length; l1 < len; l1++) {
|
| 23457 | i = ref2[l1];
|
| 23458 | if (chainBeingChecked.indexOf(i) !== -1) {
|
| 23459 | if (DEBUG) {
|
| 23460 | console.log(" found cycle:");
|
| 23461 | }
|
| 23462 | cyclesDescription = "";
|
| 23463 | for (m1 = 0, len1 = chainBeingChecked.length; m1 < len1; m1++) {
|
| 23464 | k = chainBeingChecked[m1];
|
| 23465 | if (variablesWithCycles.indexOf(k) === -1) {
|
| 23466 | variablesWithCycles.push(k);
|
| 23467 | }
|
| 23468 | if (DEBUG) {
|
| 23469 | console.log(k + " --> ");
|
| 23470 | }
|
| 23471 | cyclesDescription += k + " --> ";
|
| 23472 | }
|
| 23473 | if (DEBUG) {
|
| 23474 | console.log(" ... then " + i + " again");
|
| 23475 | }
|
| 23476 | cyclesDescription += " ... then " + i + " again";
|
| 23477 | cyclesDescriptions.push(cyclesDescription);
|
| 23478 | if (variablesWithCycles.indexOf(i) === -1) {
|
| 23479 | variablesWithCycles.push(i);
|
| 23480 | }
|
| 23481 | } else {
|
| 23482 | recursiveDependencies(i, arrayWhereDependenciesWillBeAdded, variablesAlreadyFleshedOut, variablesWithCycles, chainBeingChecked, cyclesDescriptions);
|
| 23483 | chainBeingChecked.pop();
|
| 23484 | }
|
| 23485 | }
|
| 23486 | return arrayWhereDependenciesWillBeAdded;
|
| 23487 | }
|
| 23488 | };
|
| 23489 |
|
| 23490 | inited = false;
|
| 23491 |
|
| 23492 | latexErrorSign = "\\rlap{\\large\\color{red}\\bigtriangleup}{\\ \\ \\tiny\\color{red}!}";
|
| 23493 |
|
| 23494 | turnErrorMessageToLatex = function(theErrorMessage) {
|
| 23495 | theErrorMessage = theErrorMessage.replace(/\n/g, "");
|
| 23496 | theErrorMessage = theErrorMessage.replace(/_/g, "} \\_ \\text{");
|
| 23497 | theErrorMessage = theErrorMessage.replace(new RegExp(String.fromCharCode(transpose_unicode), 'g'), "}{}^{T}\\text{");
|
| 23498 | theErrorMessage = theErrorMessage.replace(new RegExp(String.fromCharCode(dotprod_unicode), 'g'), "}\\cdot \\text{");
|
| 23499 | theErrorMessage = theErrorMessage.replace("Stop:", "} \\quad \\text{Stop:");
|
| 23500 | theErrorMessage = theErrorMessage.replace("->", "} \\rightarrow \\text{");
|
| 23501 | theErrorMessage = theErrorMessage.replace("?", "}\\enspace " + latexErrorSign + " \\enspace \\text{");
|
| 23502 | theErrorMessage = "$$\\text{" + theErrorMessage.replace(/\n/g, "") + "}$$";
|
| 23503 | return theErrorMessage;
|
| 23504 | };
|
| 23505 |
|
| 23506 | normaliseDots = function(stringToNormalise) {
|
| 23507 | stringToNormalise = stringToNormalise.replace(new RegExp(String.fromCharCode(8901), 'g'), String.fromCharCode(dotprod_unicode));
|
| 23508 | stringToNormalise = stringToNormalise.replace(new RegExp(String.fromCharCode(8226), 'g'), String.fromCharCode(dotprod_unicode));
|
| 23509 | stringToNormalise = stringToNormalise.replace(new RegExp(String.fromCharCode(12539), 'g'), String.fromCharCode(dotprod_unicode));
|
| 23510 | stringToNormalise = stringToNormalise.replace(new RegExp(String.fromCharCode(55296), 'g'), String.fromCharCode(dotprod_unicode));
|
| 23511 | stringToNormalise = stringToNormalise.replace(new RegExp(String.fromCharCode(65381), 'g'), String.fromCharCode(dotprod_unicode));
|
| 23512 | return stringToNormalise;
|
| 23513 | };
|
| 23514 |
|
| 23515 | CACHE_DEBUGS = false;
|
| 23516 |
|
| 23517 | CACHE_HITSMISS_DEBUGS = false;
|
| 23518 |
|
| 23519 | TIMING_DEBUGS = false;
|
| 23520 |
|
| 23521 | cacheMissPenalty = 0;
|
| 23522 |
|
| 23523 | run = function(stringToBeRun, generateLatex) {
|
| 23524 | var allReturnedLatexStrings, allReturnedPlainStrings, cacheKey, collectedLatexResult, collectedPlainResult, currentStateHash, error, errorWhileExecution, frozen, i, indexOfPartRemainingToBeParsed, n, possiblyCached, stringToBeReturned, theErrorMessage, timeStart, timingDebugWrite, toBeFrozen, totalTime;
|
| 23525 | if (generateLatex == null) {
|
| 23526 | generateLatex = false;
|
| 23527 | }
|
| 23528 | timeStart = new Date().getTime();
|
| 23529 | stringToBeRun = normaliseDots(stringToBeRun);
|
| 23530 | if (ENABLE_CACHING && stringToBeRun !== "clearall") {
|
| 23531 | currentStateHash = getStateHash();
|
| 23532 | cacheKey = currentStateHash + " stringToBeRun: " + stringToBeRun;
|
| 23533 | if (CACHE_DEBUGS) {
|
| 23534 | console.log("cached_runs key: " + cacheKey);
|
| 23535 | }
|
| 23536 | possiblyCached = cached_runs.get(cacheKey);
|
| 23537 | if (possiblyCached != null) {
|
| 23538 | if (CACHE_HITSMISS_DEBUGS) {
|
| 23539 | console.log("cached_runs hit on: " + stringToBeRun);
|
| 23540 | }
|
| 23541 | unfreeze(possiblyCached);
|
| 23542 | if (TIMING_DEBUGS) {
|
| 23543 | totalTime = new Date().getTime() - timeStart;
|
| 23544 | console.log("run time: " + totalTime + "ms, saved " + (possiblyCached[possiblyCached.length - 2] - totalTime) + "ms due to cache hit");
|
| 23545 | }
|
| 23546 | return possiblyCached[possiblyCached.length - 1];
|
| 23547 | } else {
|
| 23548 | if (CACHE_HITSMISS_DEBUGS) {
|
| 23549 | console.log("cached_runs miss on: " + stringToBeRun);
|
| 23550 | }
|
| 23551 | if (TIMING_DEBUGS) {
|
| 23552 | cacheMissPenalty = new Date().getTime() - timeStart;
|
| 23553 | }
|
| 23554 | }
|
| 23555 | }
|
| 23556 | if (stringToBeRun === "selftest") {
|
| 23557 | selftest();
|
| 23558 | return;
|
| 23559 | }
|
| 23560 | if (!inited) {
|
| 23561 | inited = true;
|
| 23562 | init();
|
| 23563 | }
|
| 23564 | i = 0;
|
| 23565 | n = 0;
|
| 23566 | indexOfPartRemainingToBeParsed = 0;
|
| 23567 | allReturnedPlainStrings = "";
|
| 23568 | allReturnedLatexStrings = "";
|
| 23569 | while (1) {
|
| 23570 | try {
|
| 23571 | errorMessage = "";
|
| 23572 | check_stack();
|
| 23573 | n = scan(stringToBeRun.substring(indexOfPartRemainingToBeParsed));
|
| 23574 | p1 = pop();
|
| 23575 | check_stack();
|
| 23576 | } catch (error1) {
|
| 23577 | error = error1;
|
| 23578 | if (PRINTOUTRESULT) {
|
| 23579 | console.log(error);
|
| 23580 | }
|
| 23581 | allReturnedPlainStrings += error.message;
|
| 23582 | if (generateLatex) {
|
| 23583 | theErrorMessage = turnErrorMessageToLatex(error.message);
|
| 23584 | allReturnedLatexStrings += theErrorMessage;
|
| 23585 | }
|
| 23586 | reset_after_error();
|
| 23587 | break;
|
| 23588 | }
|
| 23589 | if (n === 0) {
|
| 23590 | break;
|
| 23591 | }
|
| 23592 | indexOfPartRemainingToBeParsed += n;
|
| 23593 | push(p1);
|
| 23594 | errorWhileExecution = false;
|
| 23595 | try {
|
| 23596 | stringsEmittedByUserPrintouts = "";
|
| 23597 | top_level_eval();
|
| 23598 | p2 = pop();
|
| 23599 | check_stack();
|
| 23600 | if (isstr(p2)) {
|
| 23601 | if (DEBUG) {
|
| 23602 | console.log(p2.str);
|
| 23603 | }
|
| 23604 | if (DEBUG) {
|
| 23605 | console.log("\n");
|
| 23606 | }
|
| 23607 | }
|
| 23608 | if (p2 === symbol(NIL)) {
|
| 23609 | collectedPlainResult = stringsEmittedByUserPrintouts;
|
| 23610 | if (generateLatex) {
|
| 23611 | collectedLatexResult = "$$" + stringsEmittedByUserPrintouts + "$$";
|
| 23612 | }
|
| 23613 | } else {
|
| 23614 | collectedPlainResult = print_expr(p2);
|
| 23615 | collectedPlainResult += "\n";
|
| 23616 | if (generateLatex) {
|
| 23617 | collectedLatexResult = "$$" + collectLatexStringFromReturnValue(p2) + "$$";
|
| 23618 | if (DEBUG) {
|
| 23619 | console.log("collectedLatexResult: " + collectedLatexResult);
|
| 23620 | }
|
| 23621 | }
|
| 23622 | }
|
| 23623 | allReturnedPlainStrings += collectedPlainResult;
|
| 23624 | if (generateLatex) {
|
| 23625 | allReturnedLatexStrings += collectedLatexResult;
|
| 23626 | }
|
| 23627 | if (PRINTOUTRESULT) {
|
| 23628 | if (DEBUG) {
|
| 23629 | console.log("printline");
|
| 23630 | }
|
| 23631 | if (DEBUG) {
|
| 23632 | console.log(collectedPlainResult);
|
| 23633 | }
|
| 23634 | }
|
| 23635 | if (PRINTOUTRESULT) {
|
| 23636 | if (DEBUG) {
|
| 23637 | console.log("display:");
|
| 23638 | }
|
| 23639 | print2dascii(p2);
|
| 23640 | }
|
| 23641 | if (generateLatex) {
|
| 23642 | allReturnedLatexStrings += "\n";
|
| 23643 | }
|
| 23644 | } catch (error1) {
|
| 23645 | error = error1;
|
| 23646 | errorWhileExecution = true;
|
| 23647 | collectedPlainResult = error.message;
|
| 23648 | if (generateLatex) {
|
| 23649 | collectedLatexResult = turnErrorMessageToLatex(error.message);
|
| 23650 | }
|
| 23651 | if (PRINTOUTRESULT) {
|
| 23652 | console.log(collectedPlainResult);
|
| 23653 | }
|
| 23654 | allReturnedPlainStrings += collectedPlainResult;
|
| 23655 | if (collectedPlainResult !== "") {
|
| 23656 | allReturnedPlainStrings += "\n";
|
| 23657 | }
|
| 23658 | if (generateLatex) {
|
| 23659 | allReturnedLatexStrings += collectedLatexResult;
|
| 23660 | allReturnedLatexStrings += "\n";
|
| 23661 | }
|
| 23662 | resetCache();
|
| 23663 | init();
|
| 23664 | }
|
| 23665 | }
|
| 23666 | if (allReturnedPlainStrings[allReturnedPlainStrings.length - 1] === "\n") {
|
| 23667 | allReturnedPlainStrings = allReturnedPlainStrings.substring(0, allReturnedPlainStrings.length - 1);
|
| 23668 | }
|
| 23669 | if (generateLatex) {
|
| 23670 | if (allReturnedLatexStrings[allReturnedLatexStrings.length - 1] === "\n") {
|
| 23671 | allReturnedLatexStrings = allReturnedLatexStrings.substring(0, allReturnedLatexStrings.length - 1);
|
| 23672 | }
|
| 23673 | }
|
| 23674 | if (generateLatex) {
|
| 23675 | if (DEBUG) {
|
| 23676 | console.log("allReturnedLatexStrings: " + allReturnedLatexStrings);
|
| 23677 | }
|
| 23678 | stringToBeReturned = [allReturnedPlainStrings, allReturnedLatexStrings];
|
| 23679 | } else {
|
| 23680 | stringToBeReturned = allReturnedPlainStrings;
|
| 23681 | }
|
| 23682 | if (ENABLE_CACHING && stringToBeRun !== "clearall" && !errorWhileExecution) {
|
| 23683 | frozen = freeze();
|
| 23684 | toBeFrozen = [frozen[0], frozen[1], frozen[2], frozen[3], frozen[4], frozen[5], new Date().getTime() - timeStart, stringToBeReturned];
|
| 23685 | if (CACHE_DEBUGS) {
|
| 23686 | console.log("setting cached_runs on key: " + cacheKey);
|
| 23687 | }
|
| 23688 | cached_runs.set(cacheKey, toBeFrozen);
|
| 23689 | }
|
| 23690 | if (TIMING_DEBUGS) {
|
| 23691 | timingDebugWrite = "run time on: " + stringToBeRun + " : " + (new Date().getTime() - timeStart) + "ms";
|
| 23692 | if (ENABLE_CACHING && stringToBeRun !== "clearall") {
|
| 23693 | timingDebugWrite += ", of which cache miss penalty: " + cacheMissPenalty + "ms";
|
| 23694 | }
|
| 23695 | console.log(timingDebugWrite);
|
| 23696 | }
|
| 23697 | allReturnedPlainStrings = "";
|
| 23698 | allReturnedLatexStrings = "";
|
| 23699 | return stringToBeReturned;
|
| 23700 | };
|
| 23701 |
|
| 23702 | check_stack = function() {
|
| 23703 | if (tos !== 0) {
|
| 23704 | debugger;
|
| 23705 | stop("stack error");
|
| 23706 | }
|
| 23707 | if (frame !== TOS) {
|
| 23708 | debugger;
|
| 23709 | stop("frame error");
|
| 23710 | }
|
| 23711 | if (chainOfUserSymbolsNotFunctionsBeingEvaluated.length !== 0) {
|
| 23712 | debugger;
|
| 23713 | stop("symbols evaluation still ongoing?");
|
| 23714 | }
|
| 23715 | if (evaluatingAsFloats !== 0) {
|
| 23716 | debugger;
|
| 23717 | stop("numeric evaluation still ongoing?");
|
| 23718 | }
|
| 23719 | if (evaluatingPolar !== 0) {
|
| 23720 | debugger;
|
| 23721 | return stop("evaluation of polar still ongoing?");
|
| 23722 | }
|
| 23723 | };
|
| 23724 |
|
| 23725 | top_level_eval = function() {
|
| 23726 | var doNothing;
|
| 23727 | if (DEBUG) {
|
| 23728 | console.log("#### top level eval");
|
| 23729 | }
|
| 23730 | save();
|
| 23731 | trigmode = 0;
|
| 23732 | p1 = symbol(AUTOEXPAND);
|
| 23733 | if (iszero(get_binding(p1))) {
|
| 23734 | expanding = 0;
|
| 23735 | } else {
|
| 23736 | expanding = 1;
|
| 23737 | }
|
| 23738 | p1 = pop();
|
| 23739 | push(p1);
|
| 23740 | Eval();
|
| 23741 | p2 = pop();
|
| 23742 | if (p2 === symbol(NIL)) {
|
| 23743 | push(p2);
|
| 23744 | restore();
|
| 23745 | return;
|
| 23746 | }
|
| 23747 | set_binding(symbol(LAST), p2);
|
| 23748 | if (!iszero(get_binding(symbol(BAKE)))) {
|
| 23749 | push(p2);
|
| 23750 | bake();
|
| 23751 | p2 = pop();
|
| 23752 | }
|
| 23753 | if ((p1 === symbol(SYMBOL_I) || p1 === symbol(SYMBOL_J)) && isimaginaryunit(p2)) {
|
| 23754 | doNothing = 0;
|
| 23755 | } else if (isimaginaryunit(get_binding(symbol(SYMBOL_J)))) {
|
| 23756 | push(p2);
|
| 23757 | push(imaginaryunit);
|
| 23758 | push_symbol(SYMBOL_J);
|
| 23759 | subst();
|
| 23760 | p2 = pop();
|
| 23761 | } else if (isimaginaryunit(get_binding(symbol(SYMBOL_I)))) {
|
| 23762 | push(p2);
|
| 23763 | push(imaginaryunit);
|
| 23764 | push_symbol(SYMBOL_I);
|
| 23765 | subst();
|
| 23766 | p2 = pop();
|
| 23767 | }
|
| 23768 | push(p2);
|
| 23769 | return restore();
|
| 23770 | };
|
| 23771 |
|
| 23772 | check_esc_flag = function() {
|
| 23773 | if (esc_flag) {
|
| 23774 | return stop("esc key");
|
| 23775 | }
|
| 23776 | };
|
| 23777 |
|
| 23778 | clearAlgebraEnvironment = function() {
|
| 23779 | return do_clearall();
|
| 23780 | };
|
| 23781 |
|
| 23782 | computeDependenciesFromAlgebra = function(codeFromAlgebraBlock) {
|
| 23783 | var i, keepState, l1, len, len1, m1, originalcodeFromAlgebraBlock, userSimplificationsInProgramForm;
|
| 23784 | if (DEBUG) {
|
| 23785 | console.log("computeDependenciesFromAlgebra!!!");
|
| 23786 | }
|
| 23787 | originalcodeFromAlgebraBlock = codeFromAlgebraBlock;
|
| 23788 | keepState = true;
|
| 23789 | called_from_Algebra_block = true;
|
| 23790 | codeFromAlgebraBlock = normaliseDots(codeFromAlgebraBlock);
|
| 23791 | if (!keepState) {
|
| 23792 | userSimplificationsInListForm = [];
|
| 23793 | userSimplificationsInProgramForm = "";
|
| 23794 | for (l1 = 0, len = userSimplificationsInListForm.length; l1 < len; l1++) {
|
| 23795 | i = userSimplificationsInListForm[l1];
|
| 23796 | userSimplificationsInProgramForm += "silentpattern(" + car(i) + "," + car(cdr(i)) + "," + car(cdr(cdr(i))) + ")\n";
|
| 23797 | }
|
| 23798 | do_clearall();
|
| 23799 | codeFromAlgebraBlock = userSimplificationsInProgramForm + codeFromAlgebraBlock;
|
| 23800 | if (DEBUG) {
|
| 23801 | console.log("codeFromAlgebraBlock including patterns: " + codeFromAlgebraBlock);
|
| 23802 | }
|
| 23803 | }
|
| 23804 | if (DEBUG) {
|
| 23805 | console.log("computeDependenciesFromAlgebra: patterns in the list --------------- ");
|
| 23806 | for (m1 = 0, len1 = userSimplificationsInListForm.length; m1 < len1; m1++) {
|
| 23807 | i = userSimplificationsInListForm[m1];
|
| 23808 | console.log(car(i) + "," + cdr(i) + ")");
|
| 23809 | }
|
| 23810 | console.log("...end of list --------------- ");
|
| 23811 | }
|
| 23812 | called_from_Algebra_block = false;
|
| 23813 | return findDependenciesInScript(codeFromAlgebraBlock, true)[6];
|
| 23814 | };
|
| 23815 |
|
| 23816 | computeResultsAndJavaScriptFromAlgebra = function(codeFromAlgebraBlock) {
|
| 23817 | var code, dependencyInfo, i, keepState, l1, latexResult, len, len1, m1, originalcodeFromAlgebraBlock, readableSummaryOfCode, ref2, result, stringToBeRun, testableStringIsIgnoredHere, timeStartFromAlgebra, userSimplificationsInProgramForm;
|
| 23818 | originalcodeFromAlgebraBlock = codeFromAlgebraBlock;
|
| 23819 | keepState = true;
|
| 23820 | called_from_Algebra_block = true;
|
| 23821 | timeStartFromAlgebra = new Date().getTime();
|
| 23822 | if (TIMING_DEBUGS) {
|
| 23823 | console.log(" --------- computeResultsAndJavaScriptFromAlgebra input: " + codeFromAlgebraBlock + " at: " + (new Date()));
|
| 23824 | }
|
| 23825 | codeFromAlgebraBlock = normaliseDots(codeFromAlgebraBlock);
|
| 23826 | stringToBeRun = codeFromAlgebraBlock;
|
| 23827 | if (DEBUG) {
|
| 23828 | console.log("computeResultsAndJavaScriptFromAlgebra: patterns in the list --------------- ");
|
| 23829 | for (l1 = 0, len = userSimplificationsInListForm.length; l1 < len; l1++) {
|
| 23830 | i = userSimplificationsInListForm[l1];
|
| 23831 | console.log(car(i) + "," + cdr(i) + ")");
|
| 23832 | }
|
| 23833 | console.log("...end of list --------------- ");
|
| 23834 | }
|
| 23835 | if (!keepState) {
|
| 23836 | userSimplificationsInListForm = [];
|
| 23837 | userSimplificationsInProgramForm = "";
|
| 23838 | for (m1 = 0, len1 = userSimplificationsInListForm.length; m1 < len1; m1++) {
|
| 23839 | i = userSimplificationsInListForm[m1];
|
| 23840 | userSimplificationsInProgramForm += "silentpattern(" + car(i) + "," + car(cdr(i)) + "," + car(cdr(cdr(i))) + ")\n";
|
| 23841 | }
|
| 23842 | do_clearall();
|
| 23843 | codeFromAlgebraBlock = userSimplificationsInProgramForm + codeFromAlgebraBlock;
|
| 23844 | if (DEBUG) {
|
| 23845 | console.log("codeFromAlgebraBlock including patterns: " + codeFromAlgebraBlock);
|
| 23846 | }
|
| 23847 | }
|
| 23848 | ref2 = findDependenciesInScript(codeFromAlgebraBlock), testableStringIsIgnoredHere = ref2[0], result = ref2[1], code = ref2[2], readableSummaryOfCode = ref2[3], latexResult = ref2[4], errorMessage = ref2[5], dependencyInfo = ref2[6];
|
| 23849 | called_from_Algebra_block = false;
|
| 23850 | if (readableSummaryOfCode !== "" || errorMessage !== "") {
|
| 23851 | result += "\n" + readableSummaryOfCode;
|
| 23852 | if (errorMessage !== "") {
|
| 23853 | result += "\n" + errorMessage;
|
| 23854 | }
|
| 23855 | result = result.replace(/\n/g, "\n\n");
|
| 23856 | latexResult += "\n" + "$$" + readableSummaryOfCode + "$$";
|
| 23857 | if (errorMessage !== "") {
|
| 23858 | latexResult += turnErrorMessageToLatex(errorMessage);
|
| 23859 | }
|
| 23860 | latexResult = latexResult.replace(/\n/g, "\n\n");
|
| 23861 | }
|
| 23862 | latexResult = latexResult.replace(/\n*/, "");
|
| 23863 | latexResult = latexResult.replace(/\$\$\$\$\n*/g, "");
|
| 23864 | code = code.replace(/Math\./g, "");
|
| 23865 | code = code.replace(/\n/g, "\n\n");
|
| 23866 | if (TIMING_DEBUGS) {
|
| 23867 | console.log("computeResultsAndJavaScriptFromAlgebra time (total time from notebook and back) for: " + stringToBeRun + " : " + ((new Date().getTime()) - timeStartFromAlgebra) + "ms");
|
| 23868 | }
|
| 23869 | return {
|
| 23870 | code: code,
|
| 23871 | result: latexResult,
|
| 23872 | latexResult: latexResult,
|
| 23873 | dependencyInfo: dependencyInfo
|
| 23874 | };
|
| 23875 | };
|
| 23876 |
|
| 23877 | enableCaching = function() {
|
| 23878 | return ENABLE_CACHING = true;
|
| 23879 | };
|
| 23880 |
|
| 23881 | disableCaching = function() {
|
| 23882 | return ENABLE_CACHING = false;
|
| 23883 | };
|
| 23884 |
|
| 23885 | (typeof exports !== "undefined" && exports !== null ? exports : this).run = run;
|
| 23886 |
|
| 23887 | (typeof exports !== "undefined" && exports !== null ? exports : this).findDependenciesInScript = findDependenciesInScript;
|
| 23888 |
|
| 23889 | (typeof exports !== "undefined" && exports !== null ? exports : this).computeDependenciesFromAlgebra = computeDependenciesFromAlgebra;
|
| 23890 |
|
| 23891 | (typeof exports !== "undefined" && exports !== null ? exports : this).computeResultsAndJavaScriptFromAlgebra = computeResultsAndJavaScriptFromAlgebra;
|
| 23892 |
|
| 23893 | (typeof exports !== "undefined" && exports !== null ? exports : this).clearAlgebraEnvironment = clearAlgebraEnvironment;
|
| 23894 |
|
| 23895 | (typeof exports !== "undefined" && exports !== null ? exports : this).enableCaching = enableCaching;
|
| 23896 |
|
| 23897 | (typeof exports !== "undefined" && exports !== null ? exports : this).disableCaching = disableCaching;
|
| 23898 |
|
| 23899 | tos = 0;
|
| 23900 |
|
| 23901 | nil_symbols = 0;
|
| 23902 |
|
| 23903 | push = function(p) {
|
| 23904 | if (p == null) {
|
| 23905 | debugger;
|
| 23906 | }
|
| 23907 | if (p.isZero != null) {
|
| 23908 | debugger;
|
| 23909 | }
|
| 23910 | if (p === symbol(NIL)) {
|
| 23911 | nil_symbols++;
|
| 23912 | if (DEBUG) {
|
| 23913 | console.log("pushing symbol(NIL) #" + nil_symbols);
|
| 23914 | }
|
| 23915 | }
|
| 23916 | if (tos >= frame) {
|
| 23917 | stop("stack overflow");
|
| 23918 | }
|
| 23919 | return stack[tos++] = p;
|
| 23920 | };
|
| 23921 |
|
| 23922 | moveTos = function(stackPos) {
|
| 23923 | if (tos <= stackPos) {
|
| 23924 | tos = stackPos;
|
| 23925 | return;
|
| 23926 | }
|
| 23927 | while (tos > stackPos) {
|
| 23928 | stack[tos] = null;
|
| 23929 | tos--;
|
| 23930 | }
|
| 23931 | };
|
| 23932 |
|
| 23933 | top = function() {
|
| 23934 | return stack[tos - 1];
|
| 23935 | };
|
| 23936 |
|
| 23937 | pop = function() {
|
| 23938 | var elementToBeReturned;
|
| 23939 | if (tos === 0) {
|
| 23940 | debugger;
|
| 23941 | stop("stack underflow");
|
| 23942 | }
|
| 23943 | if (stack[tos - 1] == null) {
|
| 23944 | debugger;
|
| 23945 | }
|
| 23946 | elementToBeReturned = stack[--tos];
|
| 23947 | stack[tos] = null;
|
| 23948 | return elementToBeReturned;
|
| 23949 | };
|
| 23950 |
|
| 23951 | push_frame = function(n) {
|
| 23952 | var i, l1, ref2, results;
|
| 23953 | i = 0;
|
| 23954 | frame -= n;
|
| 23955 | if (frame < tos) {
|
| 23956 | debugger;
|
| 23957 | stop("frame overflow, circular reference?");
|
| 23958 | }
|
| 23959 | results = [];
|
| 23960 | for (i = l1 = 0, ref2 = n; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 23961 | results.push(stack[frame + i] = symbol(NIL));
|
| 23962 | }
|
| 23963 | return results;
|
| 23964 | };
|
| 23965 |
|
| 23966 | pop_frame = function(n) {
|
| 23967 | frame += n;
|
| 23968 | if (frame > TOS) {
|
| 23969 | return stop("frame underflow");
|
| 23970 | }
|
| 23971 | };
|
| 23972 |
|
| 23973 | save = function() {
|
| 23974 | frame -= 10;
|
| 23975 | if (frame < tos) {
|
| 23976 | debugger;
|
| 23977 | stop("frame overflow, circular reference?");
|
| 23978 | }
|
| 23979 | stack[frame + 0] = p0;
|
| 23980 | stack[frame + 1] = p1;
|
| 23981 | stack[frame + 2] = p2;
|
| 23982 | stack[frame + 3] = p3;
|
| 23983 | stack[frame + 4] = p4;
|
| 23984 | stack[frame + 5] = p5;
|
| 23985 | stack[frame + 6] = p6;
|
| 23986 | stack[frame + 7] = p7;
|
| 23987 | stack[frame + 8] = p8;
|
| 23988 | return stack[frame + 9] = p9;
|
| 23989 | };
|
| 23990 |
|
| 23991 | restore = function() {
|
| 23992 | if (frame > TOS - 10) {
|
| 23993 | stop("frame underflow");
|
| 23994 | }
|
| 23995 | p0 = stack[frame + 0];
|
| 23996 | p1 = stack[frame + 1];
|
| 23997 | p2 = stack[frame + 2];
|
| 23998 | p3 = stack[frame + 3];
|
| 23999 | p4 = stack[frame + 4];
|
| 24000 | p5 = stack[frame + 5];
|
| 24001 | p6 = stack[frame + 6];
|
| 24002 | p7 = stack[frame + 7];
|
| 24003 | p8 = stack[frame + 8];
|
| 24004 | p9 = stack[frame + 9];
|
| 24005 | return frame += 10;
|
| 24006 | };
|
| 24007 |
|
| 24008 | swap = function() {
|
| 24009 | var p, q;
|
| 24010 | p = pop();
|
| 24011 | q = pop();
|
| 24012 | push(p);
|
| 24013 | return push(q);
|
| 24014 | };
|
| 24015 |
|
| 24016 | dupl = function() {
|
| 24017 | var p;
|
| 24018 | p = pop();
|
| 24019 | push(p);
|
| 24020 | return push(p);
|
| 24021 | };
|
| 24022 |
|
| 24023 | $.dupl = dupl;
|
| 24024 |
|
| 24025 | $.swap = swap;
|
| 24026 |
|
| 24027 | $.restore = restore;
|
| 24028 |
|
| 24029 | $.save = save;
|
| 24030 |
|
| 24031 | $.push = push;
|
| 24032 |
|
| 24033 | $.pop = pop;
|
| 24034 |
|
| 24035 | Eval_symbolsinfo = function() {
|
| 24036 | var symbolsinfoToBePrinted;
|
| 24037 | symbolsinfoToBePrinted = symbolsinfo();
|
| 24038 | if (symbolsinfoToBePrinted !== "") {
|
| 24039 | return new_string(symbolsinfoToBePrinted);
|
| 24040 | } else {
|
| 24041 | return push_symbol(NIL);
|
| 24042 | }
|
| 24043 | };
|
| 24044 |
|
| 24045 | symbolsinfo = function() {
|
| 24046 | var bindingi, i, l1, ref2, ref3, symbolsinfoToBePrinted, symtabi;
|
| 24047 | symbolsinfoToBePrinted = "";
|
| 24048 | for (i = l1 = ref2 = NIL + 1, ref3 = symtab.length; ref2 <= ref3 ? l1 < ref3 : l1 > ref3; i = ref2 <= ref3 ? ++l1 : --l1) {
|
| 24049 | if (symtab[i].printname === "") {
|
| 24050 | if (isSymbolReclaimable[i] === false) {
|
| 24051 | break;
|
| 24052 | } else {
|
| 24053 | continue;
|
| 24054 | }
|
| 24055 | }
|
| 24056 | symtabi = symtab[i] + "";
|
| 24057 | bindingi = (binding[i] + "").substring(0, 4);
|
| 24058 | symbolsinfoToBePrinted += "symbol: " + symtabi + " size: " + countsize(binding[i]) + " value: " + bindingi + "...\n";
|
| 24059 | }
|
| 24060 | return symbolsinfoToBePrinted;
|
| 24061 | };
|
| 24062 |
|
| 24063 | std_symbol = function(s, n, latexPrint) {
|
| 24064 | var p;
|
| 24065 | p = symtab[n];
|
| 24066 | if (p == null) {
|
| 24067 | debugger;
|
| 24068 | }
|
| 24069 | p.printname = s;
|
| 24070 | if (latexPrint != null) {
|
| 24071 | return p.latexPrint = latexPrint;
|
| 24072 | } else {
|
| 24073 | return p.latexPrint = s;
|
| 24074 | }
|
| 24075 | };
|
| 24076 |
|
| 24077 | usr_symbol = function(s) {
|
| 24078 | var i, l1, ref2;
|
| 24079 | i = 0;
|
| 24080 | for (i = l1 = 0, ref2 = NSYM; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 24081 | if (symtab[i].printname === "") {
|
| 24082 | break;
|
| 24083 | }
|
| 24084 | if (s === symtab[i].printname) {
|
| 24085 | return symtab[i];
|
| 24086 | }
|
| 24087 | }
|
| 24088 | if (i === NSYM) {
|
| 24089 | stop("symbol table overflow");
|
| 24090 | }
|
| 24091 | symtab[i] = new U();
|
| 24092 | symtab[i].k = SYM;
|
| 24093 | symtab[i].printname = s;
|
| 24094 | binding[i] = symtab[i];
|
| 24095 | isSymbolReclaimable[i] = false;
|
| 24096 | return symtab[i];
|
| 24097 | };
|
| 24098 |
|
| 24099 | get_printname = function(p) {
|
| 24100 | if (p.k !== SYM) {
|
| 24101 | stop("symbol error");
|
| 24102 | }
|
| 24103 | return p.printname;
|
| 24104 | };
|
| 24105 |
|
| 24106 | set_binding = function(p, q) {
|
| 24107 | var indexFound;
|
| 24108 | if (p.k !== SYM) {
|
| 24109 | stop("symbol error");
|
| 24110 | }
|
| 24111 | indexFound = symtab.indexOf(p);
|
| 24112 |
|
| 24113 | |
| 24114 | |
| 24115 | |
| 24116 | |
| 24117 | |
| 24118 | |
| 24119 | |
| 24120 | |
| 24121 |
|
| 24122 | if (symtab.indexOf(p, indexFound + 1) !== -1) {
|
| 24123 | console.log("ops, more than one element!");
|
| 24124 | debugger;
|
| 24125 | }
|
| 24126 | if (DEBUG) {
|
| 24127 | console.log("lookup >> set_binding lookup " + indexFound);
|
| 24128 | }
|
| 24129 | isSymbolReclaimable[indexFound] = false;
|
| 24130 | return binding[indexFound] = q;
|
| 24131 | };
|
| 24132 |
|
| 24133 | get_binding = function(p) {
|
| 24134 | var indexFound;
|
| 24135 | if (p.k !== SYM) {
|
| 24136 | stop("symbol error");
|
| 24137 | }
|
| 24138 | indexFound = symtab.indexOf(p);
|
| 24139 |
|
| 24140 | |
| 24141 | |
| 24142 | |
| 24143 | |
| 24144 | |
| 24145 | |
| 24146 | |
| 24147 | |
| 24148 |
|
| 24149 | if (symtab.indexOf(p, indexFound + 1) !== -1) {
|
| 24150 | console.log("ops, more than one element!");
|
| 24151 | debugger;
|
| 24152 | }
|
| 24153 | if (DEBUG) {
|
| 24154 | console.log("lookup >> get_binding lookup " + indexFound);
|
| 24155 | }
|
| 24156 | return binding[indexFound];
|
| 24157 | };
|
| 24158 |
|
| 24159 | is_usr_symbol = function(p) {
|
| 24160 | var theSymnum;
|
| 24161 | if (p.k !== SYM) {
|
| 24162 | return false;
|
| 24163 | }
|
| 24164 | theSymnum = symnum(p);
|
| 24165 | if (theSymnum > PI && theSymnum !== SYMBOL_I && theSymnum !== SYMBOL_IDENTITY_MATRIX) {
|
| 24166 | return true;
|
| 24167 | }
|
| 24168 | return false;
|
| 24169 | };
|
| 24170 |
|
| 24171 | lookupsTotal = 0;
|
| 24172 |
|
| 24173 | symnum = function(p) {
|
| 24174 | var indexFound;
|
| 24175 | lookupsTotal++;
|
| 24176 | if (p.k !== SYM) {
|
| 24177 | stop("symbol error");
|
| 24178 | }
|
| 24179 | indexFound = symtab.indexOf(p);
|
| 24180 | if (symtab.indexOf(p, indexFound + 1) !== -1) {
|
| 24181 | console.log("ops, more than one element!");
|
| 24182 | debugger;
|
| 24183 | }
|
| 24184 | if (DEBUG) {
|
| 24185 | console.log("lookup >> symnum lookup " + indexFound + " lookup # " + lookupsTotal);
|
| 24186 | }
|
| 24187 | return indexFound;
|
| 24188 | };
|
| 24189 |
|
| 24190 | push_symbol = function(k) {
|
| 24191 | return push(symtab[k]);
|
| 24192 | };
|
| 24193 |
|
| 24194 | clear_symbols = function() {
|
| 24195 | var i, l1, ref2, ref3, results;
|
| 24196 | results = [];
|
| 24197 | for (i = l1 = ref2 = NIL + 1, ref3 = NSYM; ref2 <= ref3 ? l1 < ref3 : l1 > ref3; i = ref2 <= ref3 ? ++l1 : --l1) {
|
| 24198 | if (symtab[i].printname === "") {
|
| 24199 | if (isSymbolReclaimable[i] === false) {
|
| 24200 | break;
|
| 24201 | } else {
|
| 24202 | continue;
|
| 24203 | }
|
| 24204 | }
|
| 24205 | symtab[i] = new U();
|
| 24206 | symtab[i].k = SYM;
|
| 24207 | binding[i] = symtab[i];
|
| 24208 | results.push(isSymbolReclaimable[i] = false);
|
| 24209 | }
|
| 24210 | return results;
|
| 24211 | };
|
| 24212 |
|
| 24213 | collectUserSymbols = function(p, accumulator) {
|
| 24214 | var i, l1, ref2;
|
| 24215 | if (accumulator == null) {
|
| 24216 | accumulator = [];
|
| 24217 | }
|
| 24218 | if (is_usr_symbol(p)) {
|
| 24219 | if (accumulator.indexOf(p) === -1) {
|
| 24220 | accumulator.push(p);
|
| 24221 | return;
|
| 24222 | }
|
| 24223 | }
|
| 24224 | if (istensor(p)) {
|
| 24225 | for (i = l1 = 0, ref2 = p.tensor.nelem; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 24226 | collectUserSymbols(p.tensor.elem[i], accumulator);
|
| 24227 | }
|
| 24228 | return;
|
| 24229 | }
|
| 24230 | while (iscons(p)) {
|
| 24231 | collectUserSymbols(car(p), accumulator);
|
| 24232 | p = cdr(p);
|
| 24233 | }
|
| 24234 | };
|
| 24235 |
|
| 24236 | $.get_binding = get_binding;
|
| 24237 |
|
| 24238 | $.set_binding = set_binding;
|
| 24239 |
|
| 24240 | $.usr_symbol = usr_symbol;
|
| 24241 |
|
| 24242 | $.symbolsinfo = symbolsinfo;
|
| 24243 |
|
| 24244 | $.collectUserSymbols = collectUserSymbols;
|
| 24245 |
|
| 24246 | if (!inited) {
|
| 24247 | inited = true;
|
| 24248 | init();
|
| 24249 | }
|
| 24250 |
|
| 24251 | $.init = init;
|
| 24252 |
|
| 24253 | parse_internal = function(argu) {
|
| 24254 | if (typeof argu === 'string') {
|
| 24255 | return scan(argu);
|
| 24256 | } else if (typeof argu === 'number') {
|
| 24257 | if (argu % 1 === 0) {
|
| 24258 | return push_integer(argu);
|
| 24259 | } else {
|
| 24260 | return push_double(argu);
|
| 24261 | }
|
| 24262 | } else if (argu instanceof U) {
|
| 24263 | return push(argu);
|
| 24264 | } else {
|
| 24265 | console.warn('unknown argument type', argu);
|
| 24266 | return push(symbol(NIL));
|
| 24267 | }
|
| 24268 | };
|
| 24269 |
|
| 24270 | parse = function(argu) {
|
| 24271 | var data, error;
|
| 24272 | try {
|
| 24273 | parse_internal(argu);
|
| 24274 | data = pop();
|
| 24275 | check_stack();
|
| 24276 | } catch (error1) {
|
| 24277 | error = error1;
|
| 24278 | reset_after_error();
|
| 24279 | throw error;
|
| 24280 | }
|
| 24281 | return data;
|
| 24282 | };
|
| 24283 |
|
| 24284 | exec = function() {
|
| 24285 | var argu, argus, error, fn, l1, len, name, result;
|
| 24286 | name = arguments[0], argus = 2 <= arguments.length ? slice.call(arguments, 1) : [];
|
| 24287 | fn = get_binding(usr_symbol(name));
|
| 24288 | check_stack();
|
| 24289 | push(fn);
|
| 24290 | for (l1 = 0, len = argus.length; l1 < len; l1++) {
|
| 24291 | argu = argus[l1];
|
| 24292 | parse_internal(argu);
|
| 24293 | }
|
| 24294 | list(1 + argus.length);
|
| 24295 | p1 = pop();
|
| 24296 | push(p1);
|
| 24297 | try {
|
| 24298 | fixed_top_level_eval();
|
| 24299 | result = pop();
|
| 24300 | check_stack();
|
| 24301 | } catch (error1) {
|
| 24302 | error = error1;
|
| 24303 | reset_after_error();
|
| 24304 | throw error;
|
| 24305 | }
|
| 24306 | return result;
|
| 24307 | };
|
| 24308 |
|
| 24309 | fixed_top_level_eval = function() {
|
| 24310 | save();
|
| 24311 | trigmode = 0;
|
| 24312 | p1 = symbol(AUTOEXPAND);
|
| 24313 | if (iszero(get_binding(p1))) {
|
| 24314 | expanding = 0;
|
| 24315 | } else {
|
| 24316 | expanding = 1;
|
| 24317 | }
|
| 24318 | p1 = pop();
|
| 24319 | push(p1);
|
| 24320 | Eval();
|
| 24321 | p2 = pop();
|
| 24322 | if (p2 === symbol(NIL)) {
|
| 24323 | push(p2);
|
| 24324 | restore();
|
| 24325 | return;
|
| 24326 | }
|
| 24327 | if (!iszero(get_binding(symbol(BAKE)))) {
|
| 24328 | push(p2);
|
| 24329 | bake();
|
| 24330 | p2 = pop();
|
| 24331 | }
|
| 24332 | push(p2);
|
| 24333 | return restore();
|
| 24334 | };
|
| 24335 |
|
| 24336 | $.exec = exec;
|
| 24337 |
|
| 24338 | $.parse = parse;
|
| 24339 |
|
| 24340 | (function() {
|
| 24341 | var builtin_fns, fn, l1, len, results;
|
| 24342 | builtin_fns = ["abs", "add", "adj", "and", "approxratio", "arccos", "arccosh", "arcsin", "arcsinh", "arctan", "arctanh", "arg", "atomize", "besselj", "bessely", "binding", "binomial", "ceiling", "check", "choose", "circexp", "clear", "clearall", "clearpatterns", "clock", "coeff", "cofactor", "condense", "conj", "contract", "cos", "cosh", "decomp", "defint", "deg", "denominator", "det", "derivative", "dim", "dirac", "divisors", "do", "dot", "draw", "dsolve", "eigen", "eigenval", "eigenvec", "erf", "erfc", "eval", "exp", "expand", "expcos", "expsin", "factor", "factorial", "factorpoly", "filter", "float", "floor", "for", "Gamma", "gcd", "hermite", "hilbert", "imag", "component", "inner", "integral", "inv", "invg", "isinteger", "isprime", "laguerre", "lcm", "leading", "legendre", "log", "mod", "multiply", "not", "nroots", "number", "numerator", "operator", "or", "outer", "pattern", "patternsinfo", "polar", "power", "prime", "print", "print2dascii", "printfull", "printlatex", "printlist", "printplain", "product", "quote", "quotient", "rank", "rationalize", "real", "rect", "roots", "round", "equals", "shape", "sgn", "silentpattern", "simplify", "sin", "sinh", "sqrt", "stop", "subst", "sum", "symbolsinfo", "tan", "tanh", "taylor", "test", "testeq", "testge", "testgt", "testle", "testlt", "transpose", "unit", "zero"];
|
| 24343 | results = [];
|
| 24344 | for (l1 = 0, len = builtin_fns.length; l1 < len; l1++) {
|
| 24345 | fn = builtin_fns[l1];
|
| 24346 | results.push($[fn] = exec.bind(this, fn));
|
| 24347 | }
|
| 24348 | return results;
|
| 24349 | })();
|
| 24350 |
|
| 24351 | DoubleLinkedList = (function() {
|
| 24352 | function DoubleLinkedList() {
|
| 24353 | this.headNode = this.tailNode = null;
|
| 24354 | }
|
| 24355 |
|
| 24356 | DoubleLinkedList.prototype.remove = function(node) {
|
| 24357 | if (node.pre) {
|
| 24358 | node.pre.next = node.next;
|
| 24359 | } else {
|
| 24360 | this.headNode = node.next;
|
| 24361 | }
|
| 24362 | if (node.next) {
|
| 24363 | return node.next.pre = node.pre;
|
| 24364 | } else {
|
| 24365 | return this.tailNode = node.pre;
|
| 24366 | }
|
| 24367 | };
|
| 24368 |
|
| 24369 | DoubleLinkedList.prototype.insertBeginning = function(node) {
|
| 24370 | if (this.headNode) {
|
| 24371 | node.next = this.headNode;
|
| 24372 | this.headNode.pre = node;
|
| 24373 | return this.headNode = node;
|
| 24374 | } else {
|
| 24375 | return this.headNode = this.tailNode = node;
|
| 24376 | }
|
| 24377 | };
|
| 24378 |
|
| 24379 | DoubleLinkedList.prototype.moveToHead = function(node) {
|
| 24380 | this.remove(node);
|
| 24381 | return this.insertBeginning(node);
|
| 24382 | };
|
| 24383 |
|
| 24384 | DoubleLinkedList.prototype.clear = function() {
|
| 24385 | return this.headNode = this.tailNode = null;
|
| 24386 | };
|
| 24387 |
|
| 24388 | return DoubleLinkedList;
|
| 24389 |
|
| 24390 | })();
|
| 24391 |
|
| 24392 | LRUCache = (function() {
|
| 24393 | function LRUCache(capacity, maxAge) {
|
| 24394 | this.capacity = capacity != null ? capacity : 10;
|
| 24395 | this.maxAge = maxAge != null ? maxAge : 60000;
|
| 24396 | this._linkList = new DoubleLinkedList();
|
| 24397 | this.reset();
|
| 24398 | this.hitCount = this.missCount = 0;
|
| 24399 | }
|
| 24400 |
|
| 24401 | LRUCache.prototype.resetHitMissCount = function() {
|
| 24402 | return this.hitCount = this.missCount = 0;
|
| 24403 | };
|
| 24404 |
|
| 24405 | LRUCache.prototype.keys = function() {
|
| 24406 | return Object.keys(this._hash);
|
| 24407 | };
|
| 24408 |
|
| 24409 | LRUCache.prototype.values = function() {
|
| 24410 | var values;
|
| 24411 | values = this.keys().map((function(_this) {
|
| 24412 | return function(key) {
|
| 24413 | return _this.get(key);
|
| 24414 | };
|
| 24415 | })(this));
|
| 24416 | return values.filter(function(v) {
|
| 24417 | return v !== void 0;
|
| 24418 | });
|
| 24419 | };
|
| 24420 |
|
| 24421 | LRUCache.prototype.remove = function(key) {
|
| 24422 | var node;
|
| 24423 | if (this._hash[key] != null) {
|
| 24424 | node = this._hash[key];
|
| 24425 | this._linkList.remove(node);
|
| 24426 | delete this._hash[key];
|
| 24427 | if (node.data.onDispose) {
|
| 24428 | node.data.onDispose.call(this, node.data.key, node.data.value);
|
| 24429 | }
|
| 24430 | return this.size--;
|
| 24431 | }
|
| 24432 | };
|
| 24433 |
|
| 24434 | LRUCache.prototype.reset = function() {
|
| 24435 | this._hash = {};
|
| 24436 | this.size = 0;
|
| 24437 | this.resetHitMissCount();
|
| 24438 | return this._linkList.clear();
|
| 24439 | };
|
| 24440 |
|
| 24441 | LRUCache.prototype.set = function(key, value, onDispose) {
|
| 24442 | var createNode, node;
|
| 24443 | node = this._hash[key];
|
| 24444 | if (node) {
|
| 24445 | node.data.value = value;
|
| 24446 | node.data.onDispose = onDispose;
|
| 24447 | return this._refreshNode(node);
|
| 24448 | } else {
|
| 24449 | if (this.size === this.capacity) {
|
| 24450 | this.remove(this._linkList.tailNode.data.key);
|
| 24451 | }
|
| 24452 | createNode = function(data, pre, next) {
|
| 24453 | return {
|
| 24454 | data: data,
|
| 24455 | pre: pre,
|
| 24456 | next: next
|
| 24457 | };
|
| 24458 | };
|
| 24459 | node = createNode({
|
| 24460 | key: key,
|
| 24461 | value: value,
|
| 24462 | onDispose: onDispose
|
| 24463 | });
|
| 24464 | node.data.lastVisitTime = Date.now();
|
| 24465 | this._linkList.insertBeginning(node);
|
| 24466 | this._hash[key] = node;
|
| 24467 | this.size++;
|
| 24468 | }
|
| 24469 | };
|
| 24470 |
|
| 24471 | LRUCache.prototype.get = function(key) {
|
| 24472 | var node;
|
| 24473 | node = this._hash[key];
|
| 24474 | if (!node) {
|
| 24475 | this.missCount++;
|
| 24476 | return void 0;
|
| 24477 | }
|
| 24478 | if (this._isExpiredNode(node)) {
|
| 24479 | this.remove(key);
|
| 24480 | this.missCount++;
|
| 24481 | return void 0;
|
| 24482 | }
|
| 24483 | this._refreshNode(node);
|
| 24484 | this.hitCount++;
|
| 24485 | return node.data.value;
|
| 24486 | };
|
| 24487 |
|
| 24488 | LRUCache.prototype._refreshNode = function(node) {
|
| 24489 | node.data.lastVisitTime = Date.now();
|
| 24490 | return this._linkList.moveToHead(node);
|
| 24491 | };
|
| 24492 |
|
| 24493 | LRUCache.prototype._isExpiredNode = function(node) {
|
| 24494 | return Date.now() - node.data.lastVisitTime > this.maxAge;
|
| 24495 | };
|
| 24496 |
|
| 24497 | LRUCache.prototype.has = function(key) {
|
| 24498 | return this._hash[key] != null;
|
| 24499 | };
|
| 24500 |
|
| 24501 | return LRUCache;
|
| 24502 |
|
| 24503 | })();
|
| 24504 |
|
| 24505 | cached_runs = new LRUCache(100, 60000 * 60 * 24 * 265);
|
| 24506 |
|
| 24507 | cached_findDependenciesInScript = new LRUCache(100, 60000 * 60 * 24 * 265);
|
| 24508 |
|
| 24509 | freeze = function() {
|
| 24510 | var frozenContents, frozenHash, frozenPatterns, frozenSymbols, i, l1, ref2;
|
| 24511 | frozenSymbols = [];
|
| 24512 | frozenContents = [];
|
| 24513 | frozenPatterns = [];
|
| 24514 | frozenHash = "";
|
| 24515 | for (i = l1 = 0, ref2 = symtab.length; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 24516 | if (isSymbolReclaimable[i] === false) {
|
| 24517 | frozenSymbols.push(symtab[i]);
|
| 24518 | frozenContents.push(binding[i]);
|
| 24519 | }
|
| 24520 | }
|
| 24521 | frozenPatterns = userSimplificationsInListForm.slice(0);
|
| 24522 | return [frozenSymbols, frozenContents, frozenPatterns, zero, one, imaginaryunit, getStateHash()];
|
| 24523 | };
|
| 24524 |
|
| 24525 | unfreeze = function(frozen) {
|
| 24526 | var frozenContents, frozenPatterns, frozenSymbols, i, l1, ref2;
|
| 24527 | frozenSymbols = frozen[0], frozenContents = frozen[1], frozenPatterns = frozen[2], zero = frozen[3], one = frozen[4], imaginaryunit = frozen[5];
|
| 24528 | for (i = l1 = 0, ref2 = frozenSymbols.length; 0 <= ref2 ? l1 < ref2 : l1 > ref2; i = 0 <= ref2 ? ++l1 : --l1) {
|
| 24529 | symtab[i] = frozenSymbols[i];
|
| 24530 | binding[i] = frozenContents[i];
|
| 24531 | }
|
| 24532 | return userSimplificationsInListForm = frozenPatterns.slice(0);
|
| 24533 | };
|
| 24534 |
|
| 24535 | compareState = function(previousHash) {
|
| 24536 | var frozenHash;
|
| 24537 | frozenHash = getStateHash();
|
| 24538 | if (frozenHash === previousHash) {
|
| 24539 | return true;
|
| 24540 | } else {
|
| 24541 | return false;
|
| 24542 | }
|
| 24543 | };
|
| 24544 |
|
| 24545 | resetCache = function() {
|
| 24546 | if (cached_runs != null) {
|
| 24547 | cached_runs.reset();
|
| 24548 | if (DEBUG) {
|
| 24549 | console.log("resetting cached_runs");
|
| 24550 | }
|
| 24551 | }
|
| 24552 | if (cached_findDependenciesInScript != null) {
|
| 24553 | cached_findDependenciesInScript.reset();
|
| 24554 | if (DEBUG) {
|
| 24555 | return console.log("resetting cached_findDependenciesInScript");
|
| 24556 | }
|
| 24557 | }
|
| 24558 | };
|
| 24559 |
|
| 24560 | resetCacheHitMissCounts = function() {
|
| 24561 | if (cached_runs != null) {
|
| 24562 | cached_runs.resetHitMissCount();
|
| 24563 | }
|
| 24564 | if (cached_findDependenciesInScript != null) {
|
| 24565 | return cached_findDependenciesInScript.resetHitMissCount();
|
| 24566 | }
|
| 24567 | };
|
| 24568 |
|
| 24569 | totalAllCachesHits = function() {
|
| 24570 | return cached_runs.hitCount + cached_findDependenciesInScript.hitCount;
|
| 24571 | };
|
| 24572 |
|
| 24573 | totalAllCachesMisses = function() {
|
| 24574 | return cached_runs.missCount + cached_findDependenciesInScript.missCount;
|
| 24575 | };
|
| 24576 |
|
| 24577 | getStateHash = function() {
|
| 24578 | var bindingi, frozenHash, i, l1, len, m1, ref2, ref3, symtabi;
|
| 24579 | frozenHash = "";
|
| 24580 | for (i = l1 = ref2 = NIL + 1, ref3 = symtab.length; ref2 <= ref3 ? l1 < ref3 : l1 > ref3; i = ref2 <= ref3 ? ++l1 : --l1) {
|
| 24581 | if (symtab[i].printname === "") {
|
| 24582 | if (isSymbolReclaimable[i] === false) {
|
| 24583 | break;
|
| 24584 | } else {
|
| 24585 | continue;
|
| 24586 | }
|
| 24587 | }
|
| 24588 | symtabi = print_list(symtab[i]);
|
| 24589 | bindingi = print_list(binding[i]);
|
| 24590 | frozenHash += " //" + symtabi + " : " + bindingi;
|
| 24591 | }
|
| 24592 | for (m1 = 0, len = userSimplificationsInListForm.length; m1 < len; m1++) {
|
| 24593 | i = userSimplificationsInListForm[m1];
|
| 24594 | frozenHash += " pattern: " + i;
|
| 24595 | }
|
| 24596 | if (DEBUG) {
|
| 24597 | console.log("frozenHash: " + frozenHash);
|
| 24598 | }
|
| 24599 | return frozenHash;
|
| 24600 | };
|
| 24601 |
|
| 24602 | }).call(this);
|