Mercurial > forge
annotate main/symbolic/doc/symbolic.html @ 11613:e4cb1c2c39c4 octave-forge
Fix for functions of >2 variables, reported by Hershal.
author | i7tiol |
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date | Mon, 08 Apr 2013 11:52:52 +0000 |
parents | 9585f93393ab |
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rev | line source |
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1 <!doctype html public "-//w3c//dtd html 4.0 transitional//en"> |
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2 <html> |
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3 <head> |
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4 <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> |
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5 <meta name="GENERATOR" content="Mozilla/4.75C-SGI [en] (X11; U; IRIX 6.5 IP22) [Netscape]"> |
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6 </head> |
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7 <body text="#000000" bgcolor="#FFFFFF" link="#0000FF" vlink="#FF0000" alink="#000088"> |
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8 <font size=+2>Octave Symbolic Manipulation Toolbox</font> |
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9 <p>The Octave Symbolic Manipulation Toolbox is based upon <a href="http://www.ginac.de">GiNaC</a> |
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10 . The goal is to simply provide the capabilities of GiNaC in |
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11 the easy to use environment provided by Octave. |
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12 <p><font size=+1>Limitations/Features</font> |
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13 <br>Currently there is no support for symbolic matrices. I think it would |
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14 require a few changes to the parser to do it nicely: for example: |
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15 sym_matrix = [x+1, x+5; x^2+4,x^2+2*x+1]; I could make a function |
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16 like sym_matrix(the_rows,the_columns,x+1, ... ) that returned a symbolic |
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17 matrix but this would be a bit of a kludge. |
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18 <p>In order to do exact arithmetic you need to deal with strings and the |
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19 vpa command. For example: vpa("1")/vpa("7") is represented |
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20 internally as exactly 1/7. However, vpa("1")/7 or 1/vpa("7") |
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21 is an approximation to 1/7 that is accurate to roughly the accuracy of |
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22 the current value of digits. |
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23 <p>GiNaC throws exceptions when there are problems with computations. |
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24 I handle some of them at this time, but I do not handle all of them. |
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25 This can cause octave to terminate prematurely. For example, |
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26 try vpa("1")/vpa("0"). This will eventually be fixed. |
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27 <p><font size=+1>Download and install</font> |
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28 <p>You will need to install cln-1.0.1, GiNaC-0.8.0 and octave-2.1.33 or |
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29 later to use this package. You may be able to get by with an earlier |
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30 version of octave if you compiled without the "-fno-rtti -fno-exceptions" |
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31 options. This package uses both exceptions and run-time type |
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32 identification. There is an INSTALL file in the package |
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33 which will tell you how to install the package. |
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34 <p><font size=+1>Functions</font> |
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35 <br>Below I provide a list of function that I have implemented or have |
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36 plans to implement as of the latest release . If the function name |
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37 is <font color="#009900">green</font><font color="#330000"> </font><font color="#000000">then |
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38 the function is implemented and to the best of my knowledge there are no |
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39 problems with it. If the function is </font><font color="#CC0000">red |
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40 </font><font color="#000000">then it has not been implemented yet. |
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41 If the function is </font><font color="#000099">blue</font><font color="#000000"> |
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42 then it has been implemented but is known not to work correctly. |
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43 Blues will appear only very rarely.</font> |
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44 <ul> |
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45 <li> |
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46 <font color="#009900">vpa</font> - create a variable precision arithmetic |
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47 variable from a string, double, or an appropriate expression.</li> |
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48 |
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49 <li> |
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50 <font color="#009900">sym</font> - create a symbolic variable</li> |
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51 |
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52 <li> |
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53 <font color="#009900">is_vpa</font> - returns true if an object is |
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54 a vpa object</li> |
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55 |
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56 <li> |
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57 <font color="#009900">is_sym</font> - return true if the argument |
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58 is a symbolic variable</li> |
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59 |
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60 <li> |
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61 <font color="#009900">is_ex</font> - returns true if an object a |
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62 symbolic expression (i.e. x+y)</li> |
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63 |
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64 <li> |
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65 <font color="#009900">to_double</font> - convert a vpa, ex or string |
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66 to a double value.</li> |
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67 |
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68 <li> |
4522 | 69 <font color="#009900">to_char</font> - convert a vpa, ex to a string.</li> |
70 | |
71 <li> | |
49
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72 <font color="#009900">digits</font> - set or view the number of digits |
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73 that newly created vpa object should have</li> |
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74 |
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75 <li> |
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76 <font color="#CC0000">Abs</font> - Absolute value</li> |
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77 |
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78 <li> |
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79 <font color="#CC0000">csgn</font> -</li> |
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80 |
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81 <li> |
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82 <font color="#CC0000">Sqrt</font> - Sqrt(x) => x^(vpa(1)/2) |
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83 or x^(1/vpa(2))</li> |
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84 |
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85 <li> |
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86 <font color="#009900">Cos</font> - the cosine of a sym, vpa , or |
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87 ex variable</li> |
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88 |
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89 <li> |
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90 <font color="#009900">Sin</font> - the sine of a sym, vpa , or ex variable</li> |
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91 |
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92 <li> |
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93 <font color="#009900">Tan</font> - the tangent of a sym, vpa , or ex variable</li> |
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94 |
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95 <li> |
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96 <font color="#009900">aCos</font> - the inverse cosine of a sym, |
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97 vpa , or ex variable</li> |
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98 |
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99 <li> |
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100 <font color="#009900">aSin</font> - the inverse sin of a sym, vpa |
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101 , or ex variable</li> |
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102 |
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103 <li> |
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104 <font color="#009900">aTan</font> - the inverse tangent of a sym, |
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105 vpa , or ex variable</li> |
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106 |
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107 <li> |
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108 <font color="#CC0000">aTan2</font> -</li> |
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109 |
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110 <li> |
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111 <font color="#009900">Cosh</font> - the hyperbolic cosine of a sym, |
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112 vpa , or ex variable</li> |
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113 |
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114 <li> |
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115 <font color="#009900">Sinh</font> - the hyperbolic sine of a sym, |
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116 vpa , or ex variable</li> |
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117 |
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118 <li> |
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119 <font color="#009900">Tanh</font> - the hyperbolic tangent of a sym, |
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120 vpa , or ex variable</li> |
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121 |
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122 <li> |
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123 <font color="#009900">aCosh</font> - the inverse hyperbolic cosine of a |
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124 sym, vpa , or ex variable</li> |
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125 |
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126 <li> |
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127 <font color="#009900">aSinh</font> - the inverse hyperbolic sine of a sym, |
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128 vpa , or ex variable</li> |
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129 |
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130 <li> |
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131 <font color="#009900">aTanh</font> - the inverse hyperbolic tangent |
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132 of a sym, vpa , or ex variable</li> |
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133 |
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134 <li> |
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135 <font color="#009900">Exp</font> - the cosine of a sym, vpa , or |
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136 ex variable</li> |
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137 |
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138 <li> |
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139 <font color="#009900">Log</font> - the cosine of a sym, vpa , or |
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140 ex variable</li> |
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141 |
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142 <li> |
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143 <font color="#CC0000">Zeta</font> -</li> |
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144 |
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145 <li> |
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146 <font color="#CC0000">Tgamma</font> -</li> |
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147 |
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148 <li> |
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149 <font color="#CC0000">Lgamma</font> -</li> |
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150 |
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151 <li> |
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152 <font color="#CC0000">Beta</font> -</li> |
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153 |
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154 <li> |
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155 <font color="#CC0000">Factorial</font> -</li> |
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156 |
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157 <li> |
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158 <font color="#CC0000">Binomial</font> -</li> |
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159 |
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160 <li> |
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161 <font color="#CC0000">Order</font> -</li> |
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162 |
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163 <li> |
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164 <font color="#009900">subs</font> - perform a substitution in an expression</li> |
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165 |
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166 <li> |
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167 <font color="#009900">differentiate</font> - differentiate an expression</li> |
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168 |
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169 <li> |
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170 <font color="#009900">expand</font> - multiply all of the terms |
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171 in an expression out: (x+y)*(x+z) => x^2+x*y+x*z+y*z</li> |
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172 |
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173 <li> |
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174 <font color="#009900">collect</font> - collect similar terms in an |
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175 already expanded expression</li> |
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176 |
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177 <li> |
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178 <font color="#009900">coeff</font> - return the nth coefficient in |
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179 a polynomial</li> |
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180 |
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181 <li> |
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182 <font color="#009900">lcoeff</font> - leading coefficient of a polynomial |
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183 (4x^2+2x+5 => 4)</li> |
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184 |
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185 <li> |
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186 <font color="#009900">tcoeff</font> - trailing coefficient of a polynomial |
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187 (4x^2+2x+5 => 5)</li> |
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188 |
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189 <li> |
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190 <font color="#009900">degree</font> - The degree of a polynomial |
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191 (i.e. x^2+2x+1 => 2)</li> |
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192 |
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193 <li> |
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194 <font color="#009900">ldegree</font> - The low degree of a polynomial |
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195 (i.e. x^2+2x+1 => 0)</li> |
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196 |
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197 <li> |
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198 <font color="#009900">quotient</font> -</li> |
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199 |
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200 <li> |
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201 <font color="#009900">remainder</font> -</li> |
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202 |
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203 <li> |
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204 <font color="#009900">premainder</font> -</li> |
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205 |
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206 <li> |
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207 <font color="#CC0000">unit</font> -</li> |
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208 |
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209 <li> |
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210 <font color="#CC0000">content</font> -</li> |
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211 |
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212 <li> |
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213 <font color="#CC0000">primpart</font> -</li> |
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214 |
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215 <li> |
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216 <font color="#CC0000">Gcd</font> - greatest common denominator of |
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217 a polynomial expression</li> |
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218 |
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219 <li> |
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220 <font color="#CC0000">Lcm</font> - least common multiple of a polynomial |
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221 expression</li> |
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222 |
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223 <li> |
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224 <font color="#CC0000">numer</font> -</li> |
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225 |
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226 <li> |
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227 <font color="#CC0000">denom</font> -</li> |
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228 |
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229 <li> |
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230 normal - ?</li> |
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231 |
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232 <li> |
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233 <font color="#CC0000">to_rational</font> -</li> |
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234 |
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235 <li> |
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236 <font color="#CC0000">Series</font> -</li> |
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237 |
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238 <li> |
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239 <font color="#009900">Pi</font> - pi evaluated to the current value |
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240 of digits accuracy.</li> |
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241 |
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242 <li> |
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243 <font color="#009900">splot</font> -plot a symbolic functin over |
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244 a range of values</li> |
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245 |
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246 <li> |
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247 <font color="#CC0000">Saving of expressions, Retrieving of expressions</font></li> |
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248 </ul> |
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249 |
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250 </body> |
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251 </html> |