1 | # Function reference
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2 |
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3 | ## Core functions
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4 |
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5 | Function | Description
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6 | ---- | -----------
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7 | [math.config(config: Object): Object](functions/config.md) | Set configuration options for math.
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8 | [math.import(object, override)](functions/import.md) | Import functions from an object or a module.
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9 | [math.typed(name, signatures) : function](functions/typed.md) | Create a typed-function which checks the types of the arguments and can match them against multiple provided signatures.
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10 |
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11 | ## Construction functions
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12 |
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13 | Function | Description
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14 | ---- | -----------
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15 | [math.bignumber(x)](functions/bignumber.md) | Create a BigNumber, which can store numbers with arbitrary precision.
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16 | [math.boolean(x)](functions/boolean.md) | Create a boolean or convert a string or number to a boolean.
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17 | [math.chain(value)](functions/chain.md) | Wrap any value in a chain, allowing to perform chained operations on the value.
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18 | [math.complex(re, im)](functions/complex.md) | Create a complex value or convert a value to a complex value.
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19 | [math.createUnit(units)](functions/createUnit.md) | Create a user-defined unit and register it with the Unit type.
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20 | [math.fraction(numerator, denominator)](functions/fraction.md) | Create a fraction convert a value to a fraction.
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21 | [math.index(range1, range2, ...)](functions/index.md) | Create an index.
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22 | [math.matrix(x)](functions/matrix.md) | Create a Matrix.
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23 | [math.number(value)](functions/number.md) | Create a number or convert a string, boolean, or unit to a number.
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24 | [math.sparse(x)](functions/sparse.md) | Create a Sparse Matrix.
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25 | [math.splitUnit(unit, parts)](functions/splitUnit.md) | Split a unit in an array of units whose sum is equal to the original unit.
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26 | [math.string(value)](functions/string.md) | Create a string or convert any object into a string.
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27 | [math.unit(x)](functions/unit.md) | Create a unit.
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28 |
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29 | ## Expression functions
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30 |
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31 | Function | Description
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32 | ---- | -----------
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33 | [math.compile(expr)](functions/compile.md) | Parse and compile an expression.
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34 | [math.eval(expr [, scope])](functions/eval.md) | Evaluate an expression.
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35 | [math.help(search)](functions/help.md) | Retrieve help on a function or data type.
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36 | [math.parse(expr [, scope])](functions/parse.md) | Parse an expression.
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37 | [math.parser()](functions/parser.md) | Create a parser.
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38 |
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39 | ## Algebra functions
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40 |
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41 | Function | Description
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42 | ---- | -----------
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43 | [derivative(expr, variable)](functions/derivative.md) | Takes the derivative of an expression expressed in parser Nodes.
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44 | [math.lsolve(L, b)](functions/lsolve.md) | Solves the linear equation system by forwards substitution.
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45 | [math.lup(A)](functions/lup.md) | Calculate the Matrix LU decomposition with partial pivoting.
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46 | [math.lusolve(A, b)](functions/lusolve.md) | Solves the linear system `A * x = b` where `A` is an [n x n] matrix and `b` is a [n] column vector.
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47 | [math.qr(A)](functions/qr.md) | Calculate the Matrix QR decomposition.
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48 | [rationalize(expr)](functions/rationalize.md) | Transform a rationalizable expression in a rational fraction.
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49 | [simplify(expr)](functions/simplify.md) | Simplify an expression tree.
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50 | [math.slu(A, order, threshold)](functions/slu.md) | Calculate the Sparse Matrix LU decomposition with full pivoting.
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51 | [math.usolve(U, b)](functions/usolve.md) | Solves the linear equation system by backward substitution.
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52 |
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53 | ## Arithmetic functions
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54 |
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55 | Function | Description
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56 | ---- | -----------
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57 | [math.abs(x)](functions/abs.md) | Calculate the absolute value of a number.
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58 | [math.add(x, y)](functions/add.md) | Add two or more values, `x + y`.
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59 | [math.cbrt(x [, allRoots])](functions/cbrt.md) | Calculate the cubic root of a value.
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60 | [math.ceil(x)](functions/ceil.md) | Round a value towards plus infinity If `x` is complex, both real and imaginary part are rounded towards plus infinity.
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61 | [math.cube(x)](functions/cube.md) | Compute the cube of a value, `x * x * x`.
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62 | [math.divide(x, y)](functions/divide.md) | Divide two values, `x / y`.
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63 | [math.dotDivide(x, y)](functions/dotDivide.md) | Divide two matrices element wise.
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64 | [math.dotMultiply(x, y)](functions/dotMultiply.md) | Multiply two matrices element wise.
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65 | [math.dotPow(x, y)](functions/dotPow.md) | Calculates the power of x to y element wise.
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66 | [math.exp(x)](functions/exp.md) | Calculate the exponent of a value.
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67 | [math.expm1(x)](functions/expm1.md) | Calculate the value of subtracting 1 from the exponential value.
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68 | [math.fix(x)](functions/fix.md) | Round a value towards zero.
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69 | [math.floor(x)](functions/floor.md) | Round a value towards minus infinity.
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70 | [math.gcd(a, b)](functions/gcd.md) | Calculate the greatest common divisor for two or more values or arrays.
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71 | [math.hypot(a, b, ...)](functions/hypot.md) | Calculate the hypotenusa of a list with values.
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72 | [math.lcm(a, b)](functions/lcm.md) | Calculate the least common multiple for two or more values or arrays.
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73 | [math.log(x [, base])](functions/log.md) | Calculate the logarithm of a value.
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74 | [math.log10(x)](functions/log10.md) | Calculate the 10-base logarithm of a value.
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75 | [math.log1p(x)](functions/log1p.md) | Calculate the logarithm of a `value+1`.
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76 | [math.log2(x)](functions/log2.md) | Calculate the 2-base of a value.
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77 | [math.mod(x, y)](functions/mod.md) | Calculates the modulus, the remainder of an integer division.
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78 | [math.multiply(x, y)](functions/multiply.md) | Multiply two or more values, `x * y`.
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79 | [math.norm(x [, p])](functions/norm.md) | Calculate the norm of a number, vector or matrix.
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80 | [math.nthRoot(a)](functions/nthRoot.md) | Calculate the nth root of a value.
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81 | [math.nthRoots(x)](functions/nthRoots.md) | Calculate the nth roots of a value.
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82 | [math.pow(x, y)](functions/pow.md) | Calculates the power of x to y, `x ^ y`.
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83 | [math.round(x [, n])](functions/round.md) | Round a value towards the nearest integer.
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84 | [math.sign(x)](functions/sign.md) | Compute the sign of a value.
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85 | [math.sqrt(x)](functions/sqrt.md) | Calculate the square root of a value.
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86 | [math.square(x)](functions/square.md) | Compute the square of a value, `x * x`.
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87 | [math.subtract(x, y)](functions/subtract.md) | Subtract two values, `x - y`.
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88 | [math.unaryMinus(x)](functions/unaryMinus.md) | Inverse the sign of a value, apply a unary minus operation.
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89 | [math.unaryPlus(x)](functions/unaryPlus.md) | Unary plus operation.
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90 | [math.xgcd(a, b)](functions/xgcd.md) | Calculate the extended greatest common divisor for two values.
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91 |
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92 | ## Bitwise functions
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93 |
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94 | Function | Description
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95 | ---- | -----------
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96 | [math.bitAnd(x, y)](functions/bitAnd.md) | Bitwise AND two values, `x & y`.
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97 | [math.bitNot(x)](functions/bitNot.md) | Bitwise NOT value, `~x`.
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98 | [math.bitOr(x, y)](functions/bitOr.md) | Bitwise OR two values, `x | y`.
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99 | [math.bitXor(x, y)](functions/bitXor.md) | Bitwise XOR two values, `x ^ y`.
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100 | [math.leftShift(x, y)](functions/leftShift.md) | Bitwise left logical shift of a value x by y number of bits, `x << y`.
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101 | [math.rightArithShift(x, y)](functions/rightArithShift.md) | Bitwise right arithmetic shift of a value x by y number of bits, `x >> y`.
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102 | [math.rightLogShift(x, y)](functions/rightLogShift.md) | Bitwise right logical shift of value x by y number of bits, `x >>> y`.
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103 |
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104 | ## Combinatorics functions
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105 |
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106 | Function | Description
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107 | ---- | -----------
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108 | [math.bellNumbers(n)](functions/bellNumbers.md) | The Bell Numbers count the number of partitions of a set.
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109 | [math.catalan(n)](functions/catalan.md) | The Catalan Numbers enumerate combinatorial structures of many different types.
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110 | [math.composition(n, k)](functions/composition.md) | The composition counts of n into k parts.
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111 | [math.stirlingS2(n, k)](functions/stirlingS2.md) | The Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets.
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112 |
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113 | ## Complex functions
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114 |
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115 | Function | Description
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116 | ---- | -----------
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117 | [math.arg(x)](functions/arg.md) | Compute the argument of a complex value.
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118 | [math.conj(x)](functions/conj.md) | Compute the complex conjugate of a complex value.
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119 | [math.im(x)](functions/im.md) | Get the imaginary part of a complex number.
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120 | [math.re(x)](functions/re.md) | Get the real part of a complex number.
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121 |
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122 | ## Geometry functions
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123 |
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124 | Function | Description
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125 | ---- | -----------
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126 | [math.distance([x1, y1], [x2, y2])](functions/distance.md) | Calculates: The eucledian distance between two points in 2 and 3 dimensional spaces.
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127 | [math.intersect(endPoint1Line1, endPoint2Line1, endPoint1Line2, endPoint2Line2)](functions/intersect.md) | Calculates the point of intersection of two lines in two or three dimensions and of a line and a plane in three dimensions.
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128 |
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129 | ## Logical functions
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130 |
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131 | Function | Description
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132 | ---- | -----------
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133 | [math.and(x, y)](functions/and.md) | Logical `and`.
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134 | [math.not(x)](functions/not.md) | Logical `not`.
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135 | [math.or(x, y)](functions/or.md) | Logical `or`.
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136 | [math.xor(x, y)](functions/xor.md) | Logical `xor`.
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137 |
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138 | ## Matrix functions
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139 |
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140 | Function | Description
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141 | ---- | -----------
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142 | [math.apply(A, dim, callback)](functions/apply.md) | Apply a function that maps an array to a scalar along a given axis of a matrix or array.
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143 | [math.column(value, index)](functions/column.md) | Return column in Matrix.
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144 | [math.concat(a, b, c, ... [, dim])](functions/concat.md) | Concatenate two or more matrices.
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145 | [math.cross(x, y)](functions/cross.md) | Calculate the cross product for two vectors in three dimensional space.
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146 | [math.ctranspose(x)](functions/ctranspose.md) | Transpose and complex conjugate a matrix.
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147 | [math.det(x)](functions/det.md) | Calculate the determinant of a matrix.
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148 | [math.diag(X)](functions/diag.md) | Create a diagonal matrix or retrieve the diagonal of a matrix When `x` is a vector, a matrix with vector `x` on the diagonal will be returned.
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149 | [math.dot(x, y)](functions/dot.md) | Calculate the dot product of two vectors.
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150 | [math.expm(x)](functions/expm.md) | Compute the matrix exponential, expm(A) = e^A.
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151 | [math.filter(x, test)](functions/filter.md) | Filter the items in an array or one dimensional matrix.
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152 | [math.flatten(x)](functions/flatten.md) | Flatten a multi dimensional matrix into a single dimensional matrix.
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153 | [math.forEach(x, callback)](functions/forEach.md) | Iterate over all elements of a matrix/array, and executes the given callback function.
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154 | [math.getMatrixDataType(x)](functions/getMatrixDataType.md) | Find the data type of all elements in a matrix or array, for example 'number' if all items are a number and 'Complex' if all values are complex numbers.
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155 | [math.identity(n)](functions/identity.md) | Create a 2-dimensional identity matrix with size m x n or n x n.
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156 | [math.inv(x)](functions/inv.md) | Calculate the inverse of a square matrix.
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157 | [math.kron(x, y)](functions/kron.md) | Calculates the kronecker product of 2 matrices or vectors.
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158 | [math.map(x, callback)](functions/map.md) | Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array.
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159 | [math.ones(m, n, p, ...)](functions/ones.md) | Create a matrix filled with ones.
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160 | [math.partitionSelect(x, k)](functions/partitionSelect.md) | Partition-based selection of an array or 1D matrix.
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161 | [math.range(start, end [, step])](functions/range.md) | Create an array from a range.
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162 | [math.reshape(x, sizes)](functions/reshape.md) | Reshape a multi dimensional array to fit the specified dimensions.
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163 | [math.resize(x, size [, defaultValue])](functions/resize.md) | Resize a matrix.
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164 | [math.row(value, index)](functions/row.md) | Return row in Matrix.
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165 | [math.size(x)](functions/size.md) | Calculate the size of a matrix or scalar.
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166 | [math.sort(x)](functions/sort.md) | Sort the items in a matrix.
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167 | [X = math.sqrtm(A)](functions/sqrtm.md) | Calculate the principal square root of a square matrix.
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168 | [math.squeeze(x)](functions/squeeze.md) | Squeeze a matrix, remove inner and outer singleton dimensions from a matrix.
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169 | [math.subset(x, index [, replacement])](functions/subset.md) | Get or set a subset of a matrix or string.
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170 | [math.trace(x)](functions/trace.md) | Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.
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171 | [math.transpose(x)](functions/transpose.md) | Transpose a matrix.
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172 | [math.zeros(m, n, p, ...)](functions/zeros.md) | Create a matrix filled with zeros.
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173 |
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174 | ## Probability functions
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175 |
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176 | Function | Description
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177 | ---- | -----------
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178 | [math.combinations(n, k)](functions/combinations.md) | Compute the number of ways of picking `k` unordered outcomes from `n` possibilities.
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179 | [math.factorial(n)](functions/factorial.md) | Compute the factorial of a value Factorial only supports an integer value as argument.
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180 | [math.gamma(n)](functions/gamma.md) | Compute the gamma function of a value using Lanczos approximation for small values, and an extended Stirling approximation for large values.
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181 | [math.kldivergence(x, y)](functions/kldivergence.md) | Calculate the Kullback-Leibler (KL) divergence between two distributions.
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182 | [math.multinomial(a)](functions/multinomial.md) | Multinomial Coefficients compute the number of ways of picking a1, a2, .
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183 | [math.permutations(n [, k])](functions/permutations.md) | Compute the number of ways of obtaining an ordered subset of `k` elements from a set of `n` elements.
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184 | [math.pickRandom(array)](functions/pickRandom.md) | Random pick one or more values from a one dimensional array.
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185 | [math.random([min, max])](functions/random.md) | Return a random number larger or equal to `min` and smaller than `max` using a uniform distribution.
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186 | [math.randomInt([min, max])](functions/randomInt.md) | Return a random integer number larger or equal to `min` and smaller than `max` using a uniform distribution.
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187 |
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188 | ## Relational functions
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189 |
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190 | Function | Description
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191 | ---- | -----------
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192 | [math.compare(x, y)](functions/compare.md) | Compare two values.
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193 | [math.compareNatural(x, y)](functions/compareNatural.md) | Compare two values of any type in a deterministic, natural way.
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194 | [math.compareText(x, y)](functions/compareText.md) | Compare two strings lexically.
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195 | [math.deepEqual(x, y)](functions/deepEqual.md) | Test element wise whether two matrices are equal.
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196 | [math.equal(x, y)](functions/equal.md) | Test whether two values are equal.
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197 | [math.equalText(x, y)](functions/equalText.md) | Check equality of two strings.
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198 | [math.larger(x, y)](functions/larger.md) | Test whether value x is larger than y.
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199 | [math.largerEq(x, y)](functions/largerEq.md) | Test whether value x is larger or equal to y.
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200 | [math.smaller(x, y)](functions/smaller.md) | Test whether value x is smaller than y.
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201 | [math.smallerEq(x, y)](functions/smallerEq.md) | Test whether value x is smaller or equal to y.
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202 | [math.unequal(x, y)](functions/unequal.md) | Test whether two values are unequal.
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203 |
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204 | ## Set functions
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205 |
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206 | Function | Description
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207 | ---- | -----------
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208 | [math.setCartesian(set1, set2)](functions/setCartesian.md) | Create the cartesian product of two (multi)sets.
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209 | [math.setDifference(set1, set2)](functions/setDifference.md) | Create the difference of two (multi)sets: every element of set1, that is not the element of set2.
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210 | [math.setDistinct(set)](functions/setDistinct.md) | Collect the distinct elements of a multiset.
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211 | [math.setIntersect(set1, set2)](functions/setIntersect.md) | Create the intersection of two (multi)sets.
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212 | [math.setIsSubset(set1, set2)](functions/setIsSubset.md) | Check whether a (multi)set is a subset of another (multi)set.
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213 | [math.setMultiplicity(element, set)](functions/setMultiplicity.md) | Count the multiplicity of an element in a multiset.
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214 | [math.setPowerset(set)](functions/setPowerset.md) | Create the powerset of a (multi)set.
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215 | [math.setSize(set)](functions/setSize.md) | Count the number of elements of a (multi)set.
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216 | [math.setSymDifference(set1, set2)](functions/setSymDifference.md) | Create the symmetric difference of two (multi)sets.
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217 | [math.setUnion(set1, set2)](functions/setUnion.md) | Create the union of two (multi)sets.
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218 |
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219 | ## Special functions
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220 |
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221 | Function | Description
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222 | ---- | -----------
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223 | [math.erf(x)](functions/erf.md) | Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x.
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224 |
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225 | ## Statistics functions
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226 |
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227 | Function | Description
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228 | ---- | -----------
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229 | [math.mad(a, b, c, ...)](functions/mad.md) | Compute the median absolute deviation of a matrix or a list with values.
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230 | [math.max(a, b, c, ...)](functions/max.md) | Compute the maximum value of a matrix or a list with values.
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231 | [math.mean(a, b, c, ...)](functions/mean.md) | Compute the mean value of matrix or a list with values.
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232 | [math.median(a, b, c, ...)](functions/median.md) | Compute the median of a matrix or a list with values.
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233 | [math.min(a, b, c, ...)](functions/min.md) | Compute the minimum value of a matrix or a list of values.
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234 | [math.mode(a, b, c, ...)](functions/mode.md) | Computes the mode of a set of numbers or a list with values(numbers or characters).
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235 | [math.prod(a, b, c, ...)](functions/prod.md) | Compute the product of a matrix or a list with values.
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236 | [math.quantileSeq(A, prob[, sorted])](functions/quantileSeq.md) | Compute the prob order quantile of a matrix or a list with values.
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237 | [math.std(a, b, c, ...)](functions/std.md) | Compute the standard deviation of a matrix or a list with values.
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238 | [math.sum(a, b, c, ...)](functions/sum.md) | Compute the sum of a matrix or a list with values.
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239 | [math.var(a, b, c, ...)](functions/var.md) | Compute the variance of a matrix or a list with values.
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240 |
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241 | ## String functions
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242 |
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243 | Function | Description
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244 | ---- | -----------
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245 | [math.format(value [, precision])](functions/format.md) | Format a value of any type into a string.
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246 | [math.print(template, values [, precision])](functions/print.md) | Interpolate values into a string template.
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247 |
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248 | ## Trigonometry functions
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249 |
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250 | Function | Description
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251 | ---- | -----------
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252 | [math.acos(x)](functions/acos.md) | Calculate the inverse cosine of a value.
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253 | [math.acosh(x)](functions/acosh.md) | Calculate the hyperbolic arccos of a value, defined as `acosh(x) = ln(sqrt(x^2 - 1) + x)`.
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254 | [math.acot(x)](functions/acot.md) | Calculate the inverse cotangent of a value, defined as `acot(x) = atan(1/x)`.
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255 | [math.acoth(x)](functions/acoth.md) | Calculate the hyperbolic arccotangent of a value, defined as `acoth(x) = atanh(1/x) = (ln((x+1)/x) + ln(x/(x-1))) / 2`.
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256 | [math.acsc(x)](functions/acsc.md) | Calculate the inverse cosecant of a value, defined as `acsc(x) = asin(1/x)`.
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257 | [math.acsch(x)](functions/acsch.md) | Calculate the hyperbolic arccosecant of a value, defined as `acsch(x) = asinh(1/x) = ln(1/x + sqrt(1/x^2 + 1))`.
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258 | [math.asec(x)](functions/asec.md) | Calculate the inverse secant of a value.
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259 | [math.asech(x)](functions/asech.md) | Calculate the hyperbolic arcsecant of a value, defined as `asech(x) = acosh(1/x) = ln(sqrt(1/x^2 - 1) + 1/x)`.
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260 | [math.asin(x)](functions/asin.md) | Calculate the inverse sine of a value.
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261 | [math.asinh(x)](functions/asinh.md) | Calculate the hyperbolic arcsine of a value, defined as `asinh(x) = ln(x + sqrt(x^2 + 1))`.
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262 | [math.atan(x)](functions/atan.md) | Calculate the inverse tangent of a value.
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263 | [math.atan2(y, x)](functions/atan2.md) | Calculate the inverse tangent function with two arguments, y/x.
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264 | [math.atanh(x)](functions/atanh.md) | Calculate the hyperbolic arctangent of a value, defined as `atanh(x) = ln((1 + x)/(1 - x)) / 2`.
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265 | [math.cos(x)](functions/cos.md) | Calculate the cosine of a value.
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266 | [math.cosh(x)](functions/cosh.md) | Calculate the hyperbolic cosine of a value, defined as `cosh(x) = 1/2 * (exp(x) + exp(-x))`.
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267 | [math.cot(x)](functions/cot.md) | Calculate the cotangent of a value.
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268 | [math.coth(x)](functions/coth.md) | Calculate the hyperbolic cotangent of a value, defined as `coth(x) = 1 / tanh(x)`.
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269 | [math.csc(x)](functions/csc.md) | Calculate the cosecant of a value, defined as `csc(x) = 1/sin(x)`.
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270 | [math.csch(x)](functions/csch.md) | Calculate the hyperbolic cosecant of a value, defined as `csch(x) = 1 / sinh(x)`.
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271 | [math.sec(x)](functions/sec.md) | Calculate the secant of a value, defined as `sec(x) = 1/cos(x)`.
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272 | [math.sech(x)](functions/sech.md) | Calculate the hyperbolic secant of a value, defined as `sech(x) = 1 / cosh(x)`.
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273 | [math.sin(x)](functions/sin.md) | Calculate the sine of a value.
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274 | [math.sinh(x)](functions/sinh.md) | Calculate the hyperbolic sine of a value, defined as `sinh(x) = 1/2 * (exp(x) - exp(-x))`.
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275 | [math.tan(x)](functions/tan.md) | Calculate the tangent of a value.
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276 | [math.tanh(x)](functions/tanh.md) | Calculate the hyperbolic tangent of a value, defined as `tanh(x) = (exp(2 * x) - 1) / (exp(2 * x) + 1)`.
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277 |
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278 | ## Unit functions
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279 |
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280 | Function | Description
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281 | ---- | -----------
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282 | [math.to(x, unit)](functions/to.md) | Change the unit of a value.
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283 |
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284 | ## Utils functions
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285 |
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286 | Function | Description
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287 | ---- | -----------
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288 | [math.clone(x)](functions/clone.md) | Clone an object.
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289 | [math.hasNumericValue(x)](functions/hasNumericValue.md) | Test whether a value is an numeric value.
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290 | [math.isInteger(x)](functions/isInteger.md) | Test whether a value is an integer number.
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291 | [math.isNaN(x)](functions/isNaN.md) | Test whether a value is NaN (not a number).
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292 | [math.isNegative(x)](functions/isNegative.md) | Test whether a value is negative: smaller than zero.
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293 | [math.isNumeric(x)](functions/isNumeric.md) | Test whether a value is an numeric value.
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294 | [math.isPositive(x)](functions/isPositive.md) | Test whether a value is positive: larger than zero.
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295 | [math.isPrime(x)](functions/isPrime.md) | Test whether a value is prime: has no divisors other than itself and one.
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296 | [math.isZero(x)](functions/isZero.md) | Test whether a value is zero.
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297 | [math.typeof(x)](functions/typeof.md) | Determine the type of a variable.
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298 |
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299 |
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300 |
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301 |
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