1 |
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2 |
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3 |
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4 |
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5 |
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6 |
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7 |
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8 |
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9 | Eval_derivative = ->
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10 |
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11 |
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12 |
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13 | i = 0
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14 | p1 = cdr(p1)
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15 | push(car(p1))
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16 | Eval()
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17 |
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18 |
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19 |
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20 |
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21 |
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22 |
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23 |
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24 |
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25 |
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26 |
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27 |
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28 | p1 = cdr(p1)
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29 | push(car(p1))
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30 | Eval()
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31 |
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32 | p2 = pop()
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33 | if (p2 == symbol(NIL))
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34 | guess()
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35 | push(symbol(NIL))
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36 | else if (isnum(p2))
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37 | guess()
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38 | push(p2)
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39 | else
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40 | push(p2)
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41 | p1 = cdr(p1)
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42 | push(car(p1))
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43 | Eval()
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44 |
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45 | p5 = pop();
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46 | p4 = pop();
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47 | p3 = pop();
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48 |
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49 | while (1)
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50 |
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51 |
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52 |
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53 | if (isnum(p5))
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54 | push(p5);
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55 | n = pop_integer()
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56 | if (isNaN(n))
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57 | stop("nth derivative: check n")
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58 | else
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59 | n = 1
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60 |
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61 | push(p3);
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62 |
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63 | if (n >= 0)
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64 | for i in [0...n]
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65 | push(p4);
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66 | derivative()
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67 | else
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68 | n = -n
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69 | for i in [0...n]
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70 | push(p4);
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71 | integral()
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72 |
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73 | p3 = pop();
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74 |
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75 |
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76 |
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77 | if (p5 == symbol(NIL))
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78 | break
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79 |
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80 |
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81 |
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82 |
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83 |
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84 |
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85 |
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86 |
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87 |
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88 |
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89 |
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90 |
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91 |
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92 | if (isnum(p5))
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93 | p1 = cdr(p1)
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94 | push(car(p1))
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95 | Eval()
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96 | p5 = pop();
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97 | if (p5 == symbol(NIL))
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98 | break;
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99 | if (isnum(p5))
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100 | doNothing = 1
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101 | else
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102 | p4 = p5;
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103 | p1 = cdr(p1)
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104 | push(car(p1))
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105 | Eval()
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106 | p5 = pop();
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107 | else
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108 | p4 = p5;
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109 | p1 = cdr(p1)
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110 | push(car(p1))
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111 | Eval()
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112 | p5 = pop();
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113 |
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114 | push(p3);
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115 |
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116 | derivative = ->
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117 | save()
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118 | p2 = pop()
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119 | p1 = pop()
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120 | if (isnum(p2))
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121 | stop("undefined function")
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122 | if (istensor(p1))
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123 | if (istensor(p2))
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124 | d_tensor_tensor()
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125 | else
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126 | d_tensor_scalar()
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127 | else
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128 | if (istensor(p2))
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129 | d_scalar_tensor()
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130 | else
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131 | d_scalar_scalar()
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132 | restore()
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133 |
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134 | d_scalar_scalar = ->
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135 | if (issymbol(p2))
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136 | d_scalar_scalar_1()
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137 | else
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138 |
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139 |
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140 | push(p1);
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141 | push(p2);
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142 | push(symbol(SECRETX));
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143 | subst();
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144 | push(symbol(SECRETX));
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145 | derivative()
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146 | push(symbol(SECRETX));
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147 | push(p2);
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148 | subst();
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149 |
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150 | d_scalar_scalar_1 = ->
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151 |
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152 |
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153 | if (equal(p1, p2))
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154 | push(one)
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155 | return
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156 |
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157 |
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158 |
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159 | if (!iscons(p1))
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160 | push(zero)
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161 | return
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162 |
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163 | if (isadd(p1))
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164 | dsum()
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165 | return
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166 |
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167 | if (car(p1) == symbol(MULTIPLY))
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168 | dproduct()
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169 | return
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170 |
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171 | if (car(p1) == symbol(POWER))
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172 | dpower()
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173 | return
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174 |
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175 | if (car(p1) == symbol(DERIVATIVE))
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176 | dd()
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177 | return
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178 |
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179 | if (car(p1) == symbol(LOG))
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180 | dlog()
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181 | return
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182 |
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183 | if (car(p1) == symbol(SIN))
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184 | dsin()
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185 | return
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186 |
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187 | if (car(p1) == symbol(COS))
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188 | dcos()
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189 | return
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190 |
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191 | if (car(p1) == symbol(TAN))
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192 | dtan()
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193 | return
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194 |
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195 | if (car(p1) == symbol(ARCSIN))
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196 | darcsin()
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197 | return
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198 |
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199 | if (car(p1) == symbol(ARCCOS))
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200 | darccos()
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201 | return
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202 |
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203 | if (car(p1) == symbol(ARCTAN))
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204 | darctan()
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205 | return
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206 |
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207 | if (car(p1) == symbol(SINH))
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208 | dsinh()
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209 | return
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210 |
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211 | if (car(p1) == symbol(COSH))
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212 | dcosh()
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213 | return
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214 |
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215 | if (car(p1) == symbol(TANH))
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216 | dtanh()
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217 | return
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218 |
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219 | if (car(p1) == symbol(ARCSINH))
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220 | darcsinh()
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221 | return
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222 |
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223 | if (car(p1) == symbol(ARCCOSH))
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224 | darccosh()
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225 | return
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226 |
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227 | if (car(p1) == symbol(ARCTANH))
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228 | darctanh()
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229 | return
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230 |
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231 | if (car(p1) == symbol(ABS))
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232 | dabs()
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233 | return
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234 |
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235 | if (car(p1) == symbol(SGN))
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236 | dsgn()
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237 | return
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238 |
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239 | if (car(p1) == symbol(HERMITE))
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240 | dhermite()
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241 | return
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242 |
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243 | if (car(p1) == symbol(ERF))
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244 | derf()
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245 | return
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246 |
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247 | if (car(p1) == symbol(ERFC))
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248 | derfc()
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249 | return
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250 |
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251 | if (car(p1) == symbol(BESSELJ))
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252 | if (iszero(caddr(p1)))
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253 | dbesselj0()
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254 | else
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255 | dbesseljn()
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256 | return
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257 |
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258 | if (car(p1) == symbol(BESSELY))
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259 | if (iszero(caddr(p1)))
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260 | dbessely0()
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261 | else
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262 | dbesselyn()
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263 | return
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264 |
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265 | if (car(p1) == symbol(INTEGRAL) && caddr(p1) == p2)
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266 | derivative_of_integral()
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267 | return
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268 |
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269 | dfunction()
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270 |
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271 | dsum = ->
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272 | h = tos
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273 | p1 = cdr(p1)
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274 | while (iscons(p1))
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275 | push(car(p1))
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276 | push(p2)
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277 | derivative()
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278 | p1 = cdr(p1)
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279 | add_all(tos - h)
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280 |
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281 | dproduct = ->
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282 | i = 0
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283 | j = 0
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284 | n = 0
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285 | n = length(p1) - 1
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286 | for i in [0...n]
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287 | p3 = cdr(p1)
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288 | for j in [0...n]
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289 | push(car(p3))
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290 | if (i == j)
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291 | push(p2)
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292 | derivative()
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293 | p3 = cdr(p3)
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294 | multiply_all(n)
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295 | add_all(n)
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296 |
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297 |
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298 |
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299 |
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300 |
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301 |
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302 |
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303 |
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304 |
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305 |
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306 |
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307 |
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308 |
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309 |
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310 |
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311 |
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312 |
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313 |
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314 | dpower = ->
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315 | push(caddr(p1));
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316 | push(cadr(p1))
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317 | divide()
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318 |
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319 | push(cadr(p1));
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320 | push(p2)
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321 | derivative()
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322 |
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323 | multiply()
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324 |
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325 | push(cadr(p1));
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326 | logarithm()
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327 |
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328 | push(caddr(p1));
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329 | push(p2)
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330 | derivative()
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331 |
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332 | multiply()
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333 |
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334 | add()
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335 |
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336 | push(p1);
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337 |
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338 | multiply()
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339 |
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340 | dlog = ->
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341 | push(cadr(p1))
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342 | push(p2)
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343 | derivative()
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344 | push(cadr(p1))
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345 | divide()
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346 |
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347 |
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348 |
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349 |
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350 |
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351 |
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352 |
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353 |
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354 |
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355 |
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356 |
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357 |
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358 |
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359 | dd = ->
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360 |
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361 |
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362 | push(cadr(p1))
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363 | push(p2)
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364 | derivative()
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365 |
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366 | p3 = pop()
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367 |
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368 | if (car(p3) == symbol(DERIVATIVE))
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369 |
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370 |
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371 |
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372 | push_symbol(DERIVATIVE)
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373 | push_symbol(DERIVATIVE)
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374 | push(cadr(p3))
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375 |
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376 | if (lessp(caddr(p3), caddr(p1)))
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377 | push(caddr(p3))
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378 | list(3)
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379 | push(caddr(p1))
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380 | else
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381 | push(caddr(p1))
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382 | list(3)
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383 | push(caddr(p3))
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384 |
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385 | list(3)
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386 |
|
387 | else
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388 | push(p3)
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389 | push(caddr(p1))
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390 | derivative()
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391 |
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392 |
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393 |
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394 | dfunction = ->
|
395 | p3 = cdr(p1);
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396 |
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397 | if (p3 == symbol(NIL) || Find(p3, p2))
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398 | push_symbol(DERIVATIVE)
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399 | push(p1)
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400 | push(p2)
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401 | list(3)
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402 | else
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403 | push(zero)
|
404 |
|
405 | dsin = ->
|
406 | push(cadr(p1))
|
407 | push(p2)
|
408 | derivative()
|
409 | push(cadr(p1))
|
410 | cosine()
|
411 | multiply()
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412 |
|
413 | dcos = ->
|
414 | push(cadr(p1))
|
415 | push(p2)
|
416 | derivative()
|
417 | push(cadr(p1))
|
418 | sine()
|
419 | multiply()
|
420 | negate()
|
421 |
|
422 | dtan = ->
|
423 | push(cadr(p1))
|
424 | push(p2)
|
425 | derivative()
|
426 | push(cadr(p1))
|
427 | cosine()
|
428 | push_integer(-2)
|
429 | power()
|
430 | multiply()
|
431 |
|
432 | darcsin = ->
|
433 | push(cadr(p1))
|
434 | push(p2)
|
435 | derivative()
|
436 | push_integer(1)
|
437 | push(cadr(p1))
|
438 | push_integer(2)
|
439 | power()
|
440 | subtract()
|
441 | push_rational(-1, 2)
|
442 | power()
|
443 | multiply()
|
444 |
|
445 | darccos = ->
|
446 | push(cadr(p1))
|
447 | push(p2)
|
448 | derivative()
|
449 | push_integer(1)
|
450 | push(cadr(p1))
|
451 | push_integer(2)
|
452 | power()
|
453 | subtract()
|
454 | push_rational(-1, 2)
|
455 | power()
|
456 | multiply()
|
457 | negate()
|
458 |
|
459 |
|
460 |
|
461 |
|
462 |
|
463 |
|
464 |
|
465 | darctan = ->
|
466 | push(cadr(p1))
|
467 | push(p2)
|
468 | derivative()
|
469 | push_integer(1)
|
470 | push(cadr(p1))
|
471 | push_integer(2)
|
472 | power()
|
473 | add()
|
474 | inverse()
|
475 | multiply()
|
476 | simplify()
|
477 |
|
478 | dsinh = ->
|
479 | push(cadr(p1))
|
480 | push(p2)
|
481 | derivative()
|
482 | push(cadr(p1))
|
483 | ycosh()
|
484 | multiply()
|
485 |
|
486 | dcosh = ->
|
487 | push(cadr(p1))
|
488 | push(p2)
|
489 | derivative()
|
490 | push(cadr(p1))
|
491 | ysinh()
|
492 | multiply()
|
493 |
|
494 | dtanh = ->
|
495 | push(cadr(p1))
|
496 | push(p2)
|
497 | derivative()
|
498 | push(cadr(p1))
|
499 | ycosh()
|
500 | push_integer(-2)
|
501 | power()
|
502 | multiply()
|
503 |
|
504 | darcsinh = ->
|
505 | push(cadr(p1))
|
506 | push(p2)
|
507 | derivative()
|
508 | push(cadr(p1))
|
509 | push_integer(2)
|
510 | power()
|
511 | push_integer(1)
|
512 | add()
|
513 | push_rational(-1, 2)
|
514 | power()
|
515 | multiply()
|
516 |
|
517 | darccosh = ->
|
518 | push(cadr(p1))
|
519 | push(p2)
|
520 | derivative()
|
521 | push(cadr(p1))
|
522 | push_integer(2)
|
523 | power()
|
524 | push_integer(-1)
|
525 | add()
|
526 | push_rational(-1, 2)
|
527 | power()
|
528 | multiply()
|
529 |
|
530 | darctanh = ->
|
531 | push(cadr(p1))
|
532 | push(p2)
|
533 | derivative()
|
534 | push_integer(1)
|
535 | push(cadr(p1))
|
536 | push_integer(2)
|
537 | power()
|
538 | subtract()
|
539 | inverse()
|
540 | multiply()
|
541 |
|
542 | dabs = ->
|
543 | push(cadr(p1))
|
544 | push(p2)
|
545 | derivative()
|
546 | push(cadr(p1))
|
547 | sgn()
|
548 | multiply()
|
549 |
|
550 | dsgn = ->
|
551 | push(cadr(p1))
|
552 | push(p2)
|
553 | derivative()
|
554 | push(cadr(p1))
|
555 | dirac()
|
556 | multiply()
|
557 | push_integer(2)
|
558 | multiply()
|
559 |
|
560 | dhermite = ->
|
561 | push(cadr(p1))
|
562 | push(p2)
|
563 | derivative()
|
564 | push_integer(2)
|
565 | push(caddr(p1))
|
566 | multiply()
|
567 | multiply()
|
568 | push(cadr(p1))
|
569 | push(caddr(p1))
|
570 | push_integer(-1)
|
571 | add()
|
572 | hermite()
|
573 | multiply()
|
574 |
|
575 | derf = ->
|
576 | push(cadr(p1))
|
577 | push_integer(2)
|
578 | power()
|
579 | push_integer(-1)
|
580 | multiply()
|
581 | exponential()
|
582 | if evaluatingAsFloats
|
583 | push_double(Math.PI)
|
584 | else
|
585 | push_symbol(PI)
|
586 | push_rational(-1,2)
|
587 | power()
|
588 | multiply()
|
589 | push_integer(2)
|
590 | multiply()
|
591 | push(cadr(p1))
|
592 | push(p2)
|
593 | derivative()
|
594 | multiply()
|
595 |
|
596 | derfc = ->
|
597 | push(cadr(p1))
|
598 | push_integer(2)
|
599 | power()
|
600 | push_integer(-1)
|
601 | multiply()
|
602 | exponential()
|
603 | if evaluatingAsFloats
|
604 | push_double(Math.PI)
|
605 | else
|
606 | push_symbol(PI)
|
607 | push_rational(-1,2)
|
608 | power()
|
609 | multiply()
|
610 | push_integer(-2)
|
611 | multiply()
|
612 | push(cadr(p1))
|
613 | push(p2)
|
614 | derivative()
|
615 | multiply()
|
616 |
|
617 | dbesselj0 = ->
|
618 | push(cadr(p1))
|
619 | push(p2)
|
620 | derivative()
|
621 | push(cadr(p1))
|
622 | push_integer(1)
|
623 | besselj()
|
624 | multiply()
|
625 | push_integer(-1)
|
626 | multiply()
|
627 |
|
628 | dbesseljn = ->
|
629 | push(cadr(p1))
|
630 | push(p2)
|
631 | derivative()
|
632 | push(cadr(p1))
|
633 | push(caddr(p1))
|
634 | push_integer(-1)
|
635 | add()
|
636 | besselj()
|
637 | push(caddr(p1))
|
638 | push_integer(-1)
|
639 | multiply()
|
640 | push(cadr(p1))
|
641 | divide()
|
642 | push(cadr(p1))
|
643 | push(caddr(p1))
|
644 | besselj()
|
645 | multiply()
|
646 | add()
|
647 | multiply()
|
648 |
|
649 | dbessely0 = ->
|
650 | push(cadr(p1))
|
651 | push(p2)
|
652 | derivative()
|
653 | push(cadr(p1))
|
654 | push_integer(1)
|
655 | besselj()
|
656 | multiply()
|
657 | push_integer(-1)
|
658 | multiply()
|
659 |
|
660 | dbesselyn = ->
|
661 | push(cadr(p1))
|
662 | push(p2)
|
663 | derivative()
|
664 | push(cadr(p1))
|
665 | push(caddr(p1))
|
666 | push_integer(-1)
|
667 | add()
|
668 | bessely()
|
669 | push(caddr(p1))
|
670 | push_integer(-1)
|
671 | multiply()
|
672 | push(cadr(p1))
|
673 | divide()
|
674 | push(cadr(p1))
|
675 | push(caddr(p1))
|
676 | bessely()
|
677 | multiply()
|
678 | add()
|
679 | multiply()
|
680 |
|
681 | derivative_of_integral = ->
|
682 | push(cadr(p1))
|
683 |
|
684 |
|