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Adding Ben Sapp's symbolic toolbox (but not GinaC, cln, or gmp on which it depends)
author pkienzle
date Wed, 14 Nov 2001 15:09:50 +0000
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children 9585f93393ab
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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&nbsp; <a href="http://www.ginac.de">GiNaC</a>
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10 .&nbsp;&nbsp; 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:&nbsp;
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15 sym_matrix = [x+1, x+5; x^2+4,x^2+2*x+1];&nbsp; I could make a function
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16 like sym_matrix(the_rows,the_columns,x+1, ... )&nbsp; 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.&nbsp; For example:&nbsp; vpa("1")/vpa("7") is represented
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20 internally as exactly 1/7.&nbsp;&nbsp; However,&nbsp; vpa("1")/7 or 1/vpa("7")&nbsp;
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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.&nbsp;&nbsp;
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24 I handle some of them at this time, but I do not handle all of them.&nbsp;&nbsp;
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25 This can cause octave to terminate prematurely.&nbsp;&nbsp; For example,
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26 try vpa("1")/vpa("0").&nbsp;&nbsp; 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.&nbsp; 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.&nbsp;&nbsp; This package uses both exceptions and run-time type
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32 identification.&nbsp;&nbsp;&nbsp; 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 .&nbsp; 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.&nbsp; 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.&nbsp;
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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.&nbsp;
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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>&nbsp; - 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>&nbsp; - 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>&nbsp; - 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>&nbsp; - 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>&nbsp; - returns true if an object a
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62 symbolic expression (i.e.&nbsp; 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>&nbsp; - 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>
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69 <font color="#009900">digits</font>&nbsp; - set or view the number of digits
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70 that newly created vpa object should have</li>
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71
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72 <li>
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73 <font color="#CC0000">Abs</font>&nbsp; - Absolute value</li>
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74
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75 <li>
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76 <font color="#CC0000">csgn</font>&nbsp; -</li>
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77
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78 <li>
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79 <font color="#CC0000">Sqrt</font>&nbsp; - Sqrt(x)&nbsp; => x^(vpa(1)/2)
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80 or x^(1/vpa(2))</li>
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81
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82 <li>
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83 <font color="#009900">Cos</font>&nbsp; - the cosine of a sym, vpa , or
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84 ex variable</li>
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85
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86 <li>
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87 <font color="#009900">Sin</font> - the sine of a sym, vpa , or ex variable</li>
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88
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89 <li>
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90 <font color="#009900">Tan</font> - the tangent 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">aCos</font>&nbsp; - the inverse cosine of a sym,
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94 vpa , or ex variable</li>
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95
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96 <li>
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97 <font color="#009900">aSin</font>&nbsp; - the inverse sin of a sym, vpa
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98 , or ex variable</li>
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99
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100 <li>
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101 <font color="#009900">aTan</font>&nbsp; - the inverse tangent of a sym,
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102 vpa , or ex variable</li>
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103
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104 <li>
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105 <font color="#CC0000">aTan2</font>&nbsp; -</li>
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106
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107 <li>
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108 <font color="#009900">Cosh</font>&nbsp; - the hyperbolic cosine of a sym,
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109 vpa , or ex variable</li>
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110
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111 <li>
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112 <font color="#009900">Sinh</font>&nbsp; - the hyperbolic sine of a sym,
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113 vpa , or ex variable</li>
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114
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115 <li>
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116 <font color="#009900">Tanh</font>&nbsp; - the hyperbolic tangent of a sym,
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117 vpa , or ex variable</li>
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118
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119 <li>
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120 <font color="#009900">aCosh</font> - the inverse hyperbolic cosine of a
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121 sym, vpa , or ex variable</li>
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122
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123 <li>
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124 <font color="#009900">aSinh</font> - the inverse hyperbolic sine of a sym,
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125 vpa , or ex variable</li>
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126
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127 <li>
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128 <font color="#009900">aTanh</font>&nbsp; - the inverse hyperbolic tangent
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129 of a sym, vpa , or ex variable</li>
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130
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131 <li>
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132 <font color="#009900">Exp</font>&nbsp; - the cosine of a sym, vpa , or
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133 ex variable</li>
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134
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135 <li>
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136 <font color="#009900">Log</font>&nbsp; - the cosine of a sym, vpa , or
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137 ex variable</li>
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138
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139 <li>
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140 <font color="#CC0000">Zeta</font>&nbsp; -</li>
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141
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142 <li>
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143 <font color="#CC0000">Tgamma</font>&nbsp; -</li>
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144
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145 <li>
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146 <font color="#CC0000">Lgamma</font>&nbsp; -</li>
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147
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148 <li>
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149 <font color="#CC0000">Beta</font>&nbsp; -</li>
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150
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151 <li>
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152 <font color="#CC0000">Factorial</font>&nbsp; -</li>
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153
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154 <li>
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155 <font color="#CC0000">Binomial</font>&nbsp; -</li>
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156
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157 <li>
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158 <font color="#CC0000">Order</font> -</li>
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159
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160 <li>
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161 <font color="#009900">subs</font> - perform a substitution in an expression</li>
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162
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163 <li>
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164 <font color="#009900">differentiate</font>&nbsp; - differentiate an expression</li>
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165
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166 <li>
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167 <font color="#009900">expand</font>&nbsp; -&nbsp; multiply all of the terms
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168 in an expression out:&nbsp; (x+y)*(x+z) => x^2+x*y+x*z+y*z</li>
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169
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170 <li>
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171 <font color="#009900">collect</font>&nbsp; - collect similar terms in an
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172 already expanded expression</li>
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173
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174 <li>
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175 <font color="#009900">coeff</font>&nbsp; - return the nth coefficient in
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176 a polynomial</li>
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177
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178 <li>
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179 <font color="#009900">lcoeff</font>&nbsp; - leading coefficient of a polynomial
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180 (4x^2+2x+5 => 4)</li>
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181
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182 <li>
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183 <font color="#009900">tcoeff</font>&nbsp; - trailing coefficient of a polynomial
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184 (4x^2+2x+5 => 5)</li>
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185
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186 <li>
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187 <font color="#009900">degree</font>&nbsp; - The degree of a polynomial
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188 (i.e. x^2+2x+1 => 2)</li>
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189
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190 <li>
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191 <font color="#009900">ldegree</font>&nbsp; - The low degree of a polynomial
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192 (i.e. x^2+2x+1&nbsp; => 0)</li>
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193
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194 <li>
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195 <font color="#009900">quotient</font>&nbsp; -</li>
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196
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197 <li>
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198 <font color="#009900">remainder</font>&nbsp; -</li>
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199
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200 <li>
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201 <font color="#009900">premainder</font>&nbsp; -</li>
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202
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203 <li>
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204 <font color="#CC0000">unit</font>&nbsp; -</li>
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205
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206 <li>
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207 <font color="#CC0000">content</font>&nbsp; -</li>
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208
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209 <li>
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210 <font color="#CC0000">primpart</font>&nbsp; -</li>
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211
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212 <li>
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213 <font color="#CC0000">Gcd</font>&nbsp; - greatest common denominator of
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214 a polynomial expression</li>
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215
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216 <li>
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217 <font color="#CC0000">Lcm</font>&nbsp; - least common multiple of a polynomial
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218 expression</li>
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219
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220 <li>
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221 <font color="#CC0000">numer</font>&nbsp; -</li>
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222
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223 <li>
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224 <font color="#CC0000">denom</font>&nbsp; -</li>
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225
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226 <li>
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227 normal&nbsp; - ?</li>
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228
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229 <li>
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230 <font color="#CC0000">to_rational</font>&nbsp; -</li>
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231
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232 <li>
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233 <font color="#CC0000">Series</font>&nbsp; -</li>
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234
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235 <li>
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236 <font color="#009900">Pi</font>&nbsp; - pi evaluated to the current value
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237 of digits accuracy.</li>
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238
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239 <li>
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240 <font color="#009900">splot</font>&nbsp; -plot a symbolic functin over
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241 a range of values</li>
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242
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243 <li>
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244 <font color="#CC0000">Saving of expressions, Retrieving of expressions</font></li>
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245 </ul>
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246
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247 </body>
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248 </html>