1 | // $Id: latex.lib,v 1.1 1998-05-17 17:39:51 obachman Exp $ |
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2 | // 1998/04/17 |
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3 | // author : Christian Gorzel email: gorzelc@math.uni-muenster.de |
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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 | LIBRARY: latex.lib PROCEDURES FOR TYPESET OF SINGULAROBJECTS IN LATEX2E |
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9 | by Christian Gorzel, send bugs and |
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10 | comments to gorzelc@math.uni-muenster.de |
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11 | |
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12 | closetex(fnm); writes closing line for TeX-document |
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13 | opentex(fnm); writes header for TeX-file fnm |
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14 | tex(fnm); calls LaTeX2e for TeX-file fnm |
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15 | texdemo([n]); produces a file explaining the features of this lib |
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16 | texfactorize(fnm,f); creates string in TeX-Symbolformat for factors of poly f |
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17 | texmap(fnm,m,r1,r2); creates string in TeX-Symbolformat for map m:r1->r2 |
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18 | texname(fnm,s); creates string in TeX-Symbolformat for identifier |
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19 | texobj(l); creates string in TeX-Symbolformat for any (basic) type |
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20 | texpoly(f,n[,l]); creates string in TeX-Symbolformat for poly |
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21 | texproc(fnm,p); creates string in TeX-Symbolformat of text from proc p |
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22 | texring(fnm,r[,l]); creates string in TeX-Symbolformat for ring/qring |
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23 | rmx(s); removes .aux and .log files of TeXfile s |
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24 | xdvi(s); calls xdvi for dvi-file s |
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25 | (parameters in square brackets [] are optional) |
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26 | |
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27 | Global Variables: |
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28 | TeXwidth, TeXnofrac, TeXbrack, TeXproj, TeXaligned, TeXreplace, NoDollars |
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29 | are used to control the typesetting |
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30 | Call example texdemo; to become familiar with the features of latex.lib |
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31 | |
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32 | |
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33 | TeXwidth : int: -1,0,1..9, >9 controls the breaking of long polynomials |
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34 | TeXnofrac : (int) flag, write 1/2 instead of \\frac{1}{2} |
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35 | TeXbrack : string: possible values {,(,<,|, \"\" |
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36 | controls brackets around ideals and matrices |
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37 | TeXproj : (int) flag, write : instead of , in intvecs and vectors |
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38 | TeXaligned : (int) flag, write maps (and ideals) aligned |
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39 | TeXreplace : list, entries twoelemented list for replacing symbols |
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40 | NoDollars : (int) flag, suppresses surrounding "$" signs |
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41 | |
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42 | |
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43 | /////////////////////////////////////////////////////////////////////////////// |
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44 | |
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45 | proc closetex(string fname, list #) |
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46 | USAGE: closetex(fname[,style]); fname,style = string |
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47 | RETURN: nothing; writes a LaTeX2e closing line into file fname |
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48 | NOTE: style overwrites the default setting latex2e; maybe latex,amstex,tex |
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49 | preceeding ">>" end ending ".tex" may miss in fname; |
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50 | overwriting an existing file is not possible |
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51 | EXAMPLE: example closetex; shows an example |
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52 | { |
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53 | string default = "latex2e"; |
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54 | string s; |
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55 | int i = 1; |
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56 | int flag; |
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57 | |
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58 | if (size(#)) { default = #[1];} |
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59 | |
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60 | if (default=="latex2e" or default == "latex") |
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61 | { s = "\\end{document}"; flag = 1;} |
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62 | if (default=="amstex") {s = "\\enddocument"; flag = 1;} |
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63 | if (default=="tex") {s = "\\bye"; flag = 1;} |
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64 | if (not(flag)) { s = "";} |
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65 | |
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66 | if (size(fname)) |
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67 | { |
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68 | while (fname[i]==">"){i++;} |
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69 | fname = fname[i,size(fname)-i+1]; |
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70 | |
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71 | if (size(fname)>=4) // check if filename is ending with ".tex" |
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72 | { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; } |
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73 | } |
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74 | else {fname = fname + ".tex";} |
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75 | write(fname, s); |
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76 | write(fname," - Thanks latex.lib and Singular - "); |
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77 | } |
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78 | else {return(s);} |
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79 | } |
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80 | example |
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81 | { "EXAMPLE:"; echo=2; |
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82 | opentex("exmpl"); |
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83 | texobj("exmpl","{\\large \\bf hello}"); |
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84 | closetex("exmpl"); |
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85 | } |
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86 | /////////////////////////////////////////////////////////////////////////////// |
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87 | |
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88 | proc tex(string fname, list #) |
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89 | USAGE: tex(fname[,style]); fname,style = string |
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90 | RETURN: nothing; calls latex2e for compiling the file fname |
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91 | NOTE: style overwrites the default setting latex2e; maybe latex,amstex,tex |
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92 | ending ".tex" may miss in fname |
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93 | EXAMPLE: example tex; shows an example |
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94 | { |
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95 | string default = "latex2e"; |
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96 | int retval; |
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97 | int i=1; |
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98 | |
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99 | if (size(#)) {default = string(#[1]);} |
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100 | |
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101 | if (size(fname)) |
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102 | { |
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103 | while (fname[i]==">"){i++;} |
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104 | fname = fname[i,size(fname)-i+1]; |
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105 | |
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106 | if (size(fname)>=4) // check if filename is ending with ".tex" |
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107 | { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; } |
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108 | } |
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109 | else {fname = fname + ".tex";} |
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110 | "calling ",default, " for :",fname,newline; |
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111 | |
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112 | retval = system("sh",default + " " + fname); |
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113 | } |
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114 | else |
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115 | { " -- Need a filename "; |
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116 | return(); |
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117 | } |
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118 | } |
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119 | example |
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120 | { "EXAMPLE:"; echo =2; |
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121 | ring r; |
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122 | ideal I = maxideal(7); |
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123 | opentex("exp001"); // defaulted latex2e document |
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124 | texobj("exp001","An ideal ",I); |
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125 | closetex("exp001"); |
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126 | tex("exp001"); |
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127 | |
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128 | opentex("exp002","tex"); // create a texdocument |
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129 | texobj("exp002","An ideal",I); |
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130 | closetex("exp002"); |
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131 | tex("exp002","tex"); |
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132 | echo = 0; |
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133 | print("the created files will be deleted after pressing <RETURN> "); |
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134 | pause; |
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135 | echo = 2; |
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136 | system("sh","rm -i exp00?.*"); |
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137 | } |
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138 | /////////////////////////////////////////////////////////////////////////////// |
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139 | |
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140 | proc opentex(string fname, list #) |
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141 | USAGE: opentex(fname[,style]); fname,style = string |
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142 | RETURN: nothing; writes as LaTeX2e header into a new file fname |
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143 | NOTE: suffix .tex may miss in fname |
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144 | style overwrites the default setting latex2e; may be latex,amstex,tex |
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145 | EXAMPLE: example opentex; shows an example |
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146 | { |
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147 | string default = "latex2e"; |
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148 | string s; |
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149 | int i =1; |
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150 | int flag; |
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151 | |
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152 | if (size(#)) { default = #[1];} |
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153 | |
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154 | if (default == "latex2e") // the default latex2e header |
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155 | { s = |
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156 | "\\documentclass[12pt]{article}" + newline + |
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157 | // "\\usepackage{fullpage,amsmath,amscd,amsthm,amssymb,amsxtra,latexsym,epsfig}" + newline + |
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158 | "\\usepackage{amsmath,amssymb}" + newline + |
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159 | "\\parindent=0pt" + newline + |
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160 | "\\newcommand{\\C}{{\\Bbb C}}" + newline + |
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161 | "\\newcommand{\\F}{{\\Bbb F}}" + newline + |
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162 | "\\newcommand{\\N}{{\\Bbb N}}" + newline + |
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163 | // "\\newcommand{\\P}{{\\Bbb P}}" + newline + |
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164 | "\\newcommand{\\Q}{{\\Bbb Q}}" + newline + |
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165 | "\\newcommand{\\R}{{\\Bbb R}}" + newline + |
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166 | "\\newcommand{\\T}{{\\Bbb T}}" + newline + |
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167 | "\\newcommand{\\Z}{{\\Bbb Z}}" + newline + newline + |
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168 | "\\begin{document}"; |
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169 | flag = 1; |
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170 | } |
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171 | if (default == "latex") |
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172 | { s = |
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173 | "\\documentstyle[12pt,amstex]{article}" + newline + |
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174 | "\\parindent=0pt" + newline + |
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175 | "\\newcommand{\\C}{{\\Bbb C}}" + newline + |
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176 | "\\newcommand{\\F}{{\\Bbb F}}" + newline + |
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177 | "\\newcommand{\\N}{{\\Bbb N}}" + newline + |
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178 | // "\\newcommand{\\P}{{\\Bbb P}}" + newline + |
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179 | "\\newcommand{\\Q}{{\\Bbb Q}}" + newline + |
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180 | "\\newcommand{\\R}{{\\Bbb R}}" + newline + |
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181 | "\\newcommand{\\T}{{\\Bbb T}}" + newline + |
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182 | "\\newcommand{\\Z}{{\\Bbb Z}}" + newline + newline + |
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183 | "\\begin{document}"; |
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184 | flag = 1; |
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185 | } |
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186 | if (default == "amstex") |
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187 | { s = |
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188 | "\\documentstyle{amsppt} " + newline + newline + |
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189 | "\\document"; |
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190 | flag = 1; |
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191 | } |
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192 | |
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193 | if (default == "tex") |
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194 | { s = |
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195 | ""; |
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196 | flag = 1; |
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197 | } |
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198 | if (default == "own") // the proper own header |
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199 | { s = ""; |
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200 | flag = 1; |
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201 | } |
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202 | if (not(flag)) { s = "";} |
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203 | |
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204 | if (size(fname)) |
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205 | { |
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206 | while (fname[i]==">"){i++;} |
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207 | fname = fname[i,size(fname)-i+1]; |
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208 | |
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209 | if (size(fname)>=4) // check if filename is ending with ".tex" |
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210 | { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; } |
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211 | } |
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212 | else {fname = fname + ".tex";} |
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213 | fname = ">" + fname; |
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214 | write(fname,s); |
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215 | } |
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216 | else {return(s);} |
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217 | } |
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218 | example |
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219 | { "EXAMPLE:"; echo=2; |
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220 | opentex("exmpl"); |
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221 | texobj("exmpl","hello"); |
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222 | closetex("exmpl"); |
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223 | } |
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224 | /////////////////////////////////////////////////////////////////////////////// |
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225 | |
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226 | proc texdemo(list #) |
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227 | USAGE: texdemo(); |
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228 | RETURN: nothing; generates automatically a LaTeX2e file called: texlibdemo.tex |
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229 | explaining the features of tex.lib and its gloabl variables |
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230 | NOTE: this proc takes some minutes |
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231 | EXAMPLE: example texdemo; executes the generation |
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232 | { int TeXdemostart = system("pid"); |
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233 | string fname = "texlibdemo"; |
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234 | string fnamet = fname+ ".tex"; |
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235 | |
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236 | if (size(#)) |
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237 | { if (typeof(#[1])=="int") {TeXdemostart = #[1];} |
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238 | } |
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239 | system("random",TeXdemostart); |
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240 | |
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241 | if (size(#) ==2) |
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242 | { if (typeof(#[2]) == "string") { fname = #[2];} |
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243 | } |
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244 | |
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245 | if (size(fname)) |
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246 | { |
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247 | if (size(fname)>=4) // check if filename is ending with ".tex" |
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248 | { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; } |
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249 | } else {fname = fname + ".tex";} |
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250 | } |
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251 | |
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252 | |
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253 | part0(fname); |
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254 | part1(fname); |
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255 | part2(fname); |
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256 | part3(fname); |
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257 | print(" Demofile generated ..."); |
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258 | if (size(fname)) |
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259 | { |
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260 | print(" call latex now by tex(\"" + fname + "\");" ); |
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261 | print(" .log and .aux files may be deleted with rmx(\"texlibdemo\");"); |
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262 | } |
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263 | return(); |
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264 | } |
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265 | example |
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266 | { "EXAMPLE:"; |
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267 | texdemo(); |
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268 | } |
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269 | /////////////////////////////////////////////////////////////////////////////// |
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270 | |
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271 | proc texfactorize(string fname, poly f, list #) |
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272 | USAGE: opentex(fname,f); fname = string; f = poly |
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273 | RETURN: string, the poly as as product of its irreducible factors |
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274 | in TeX-typesetting if fname == empty string; |
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275 | otherwise append this to file fname.tex; return nothing |
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276 | NOTE: preceeding ">>" end ending ".tex" may miss in fname |
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277 | EXAMPLE: example texfactorize; shows an example |
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278 | { |
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279 | def @r = basering; |
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280 | list l; |
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281 | int i,j,k,Tw,TW,ND;; |
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282 | intvec v; |
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283 | string s,t; |
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284 | string D = "$"; |
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285 | poly g; |
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286 | |
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287 | ND = defined(NoDollars); |
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288 | if (!(ND)) {int NoDollars; export NoDollars;} |
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289 | else { D = ""; } |
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290 | TW = defined(TeXwidth); |
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291 | if (TW) {Tw = TeXwidth; TeXwidth = -1;} |
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292 | else {int TeXwidth = -1; export TeXwidth;} |
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293 | |
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294 | if (f==0) {s= D + "0" + D;} |
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295 | else |
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296 | { |
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297 | l = factorize(f); // sollte auch fuer f== 0 direkt funktionieren |
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298 | if (l[1][1]<>1){s = texpoly("",l[1][1]);} |
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299 | for(i=2;i<=size(l[1]);i++) |
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300 | { |
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301 | if(size(s)){s = s+"\\cdot ";} |
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302 | g = l[1][i]; |
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303 | v = leadexp(g); |
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304 | k=0; |
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305 | for(j=1;j<=size(v);j++){k = k + v[j];} |
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306 | if(size(g)>1 or (size(g)==1 and k>1)) |
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307 | { t = "(" + texpoly("",l[1][i]) + ")";} |
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308 | else { t = texpoly("",l[1][i]);} |
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309 | if (l[2][i]>1) |
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310 | { t = t+"^{" +string(l[2][i]) + "}";} |
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311 | s = s + t; |
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312 | } |
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313 | if (!(ND)) { kill NoDollars;} |
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314 | s = D + s + D; |
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315 | if (TW) {TeXwidth = Tw;} |
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316 | } |
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317 | if(size(fname)) |
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318 | { i=1; |
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319 | while (fname[i]==">"){i++;} |
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320 | fname = fname[i,size(fname)-i+1]; |
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321 | |
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322 | if (size(fname)>=4) // check if filename is ending with ".tex" |
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323 | { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; } |
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324 | } |
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325 | else {fname = fname + ".tex";} |
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326 | write(fname,s); |
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327 | } |
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328 | else{return(s);} |
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329 | } |
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330 | example |
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331 | { "EXAMPLE:"; echo=2; |
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332 | ring r2=13,(x,y),dp; |
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333 | poly f = (x+1+y)^2*x3y*(2x -2y)*y12; |
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334 | texfactorize("",f); |
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335 | ring R49 = (7,a),x,dp; |
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336 | minpoly = a2 +a +3; |
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337 | poly f = (a24x5 + x3)*a2x6*(x+1)^2; |
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338 | f; |
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339 | texfactorize("",f); |
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340 | } |
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341 | /////////////////////////////////////////////////////////////////////////////// |
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342 | |
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343 | proc texmap(string fname, def m, def @r1, def @r2, list #) |
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344 | USAGE: texmap(fname,f); fname = string; m = string/map, @r1,@r2 = ring |
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345 | RETURN: string, the map m from @r1 to @r2 preeceded by its name if m = string |
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346 | in TeX-typesetting if fname == empty string; |
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347 | otherwise append this to file fname.tex; return nothing |
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348 | NOTE: preceeding ">>" end ending ".tex" may miss in fname |
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349 | EXAMPLE: example texmap; shows an example |
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350 | { |
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351 | int saveDollars= defined(NoDollars); |
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352 | int TX = defined(TeXwidth); |
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353 | int Tw; |
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354 | int i,n; |
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355 | string r1str,r2str, varr1str, varr2str; |
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356 | string mapname,t,s; |
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357 | string D,DD,vrg = "$","$$",","; |
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358 | def @r = basering; |
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359 | def themap; |
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360 | list l1,l2; |
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361 | string rr1,rr2 = "@r1","@r2"; |
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362 | |
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363 | proc rp(string s) |
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364 | { int i; |
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365 | |
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366 | for(i=1;i<=size(TeXreplace);i++) |
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367 | { if (TeXreplace[i][1]==s) {s= TeXreplace[i][2]; break;}} |
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368 | return(s); |
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369 | } |
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370 | |
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371 | // --- store all actual informations |
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372 | if(TX) { Tw = TeXwidth; TeXwidth = -1;} |
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373 | else { int TeXwidth = -1; export TeXwidth;} |
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374 | if (!(saveDollars)) { int NoDollars; export NoDollars;} |
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375 | if (defined(TeXproj)) {vrg = ":";} |
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376 | |
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377 | if (size(#)) |
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378 | { if (typeof(#[1])=="list") |
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379 | { l1 = #[1]; |
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380 | if(size(#)==2) { l2 = #[2];} |
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381 | } |
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382 | else {l1=#; l2 =#;} |
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383 | } |
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384 | // --- tex the information in preimring r1 |
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385 | |
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386 | setring(@r1); |
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387 | r1str = texring("",@r1,l1); |
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388 | // --- avoid an execute; hence construct an ideal |
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389 | |
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390 | n = nvars(@r1); |
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391 | if (n>1) { t = "\\left(";} |
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392 | ideal @I = var(1); |
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393 | t = t + texpoly("",var(1)); |
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394 | for(i=2;i<=n;i++) |
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395 | { @I = @I + var(i); |
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396 | t = t + vrg + texpoly("",var(i)); |
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397 | } |
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398 | if (n>1) { t = t + "\\right)";} |
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399 | varr1str = t; |
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400 | |
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401 | // --- now the things in ring ring r2 |
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402 | |
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403 | setring(@r2); |
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404 | // listvar(); |
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405 | |
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406 | if (typeof(m)=="string") |
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407 | { themap = `m`; |
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408 | mapname = m; |
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409 | if (defined(TeXreplace)) |
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410 | { mapname = rp(mapname); // rp ausschreiben ! |
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411 | } |
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412 | mapname = mapname + ":"; |
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413 | } |
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414 | if (typeof(m)=="map") { themap = m;} |
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415 | |
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416 | r2str = texring("",@r2,l2); |
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417 | ideal @J = themap(@I); |
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418 | n = size(matrix(@J)); |
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419 | if (n>1) { t = " \\left(";} |
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420 | if (!(defined(TeXaligned)) and (n>1)) |
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421 | { t = t + newline + "\\begin{array}{c}" + newline;} |
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422 | t = t + texpoly("",@J[1]); |
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423 | for (i=2;i<=n; i++) |
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424 | {if(defined(TeXaligned)) |
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425 | { t = t + vrg + texpoly("",@J[i]); } |
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426 | else { t = t + "\\\\" + newline + texpoly("",@J[i]);} |
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427 | } |
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428 | if (!(defined(TeXaligned)) and (n>1)) |
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429 | { t = t + newline + "\\end{array}" + newline;} |
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430 | if (n>1) {t = t + "\\right)";} |
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431 | varr2str = t; |
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432 | |
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433 | // --- go back to ring r1 to kill @I |
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434 | |
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435 | setring(@r1); |
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436 | kill @I; |
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437 | |
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438 | // --- now reset the old settings and stick all the information together |
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439 | |
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440 | setring(@r); |
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441 | if (!(saveDollars)) { kill NoDollars;} |
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442 | if (TX) {TeXwidth = Tw;} |
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443 | else { kill TeXwidth;} |
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444 | if (defined(NoDollars)) |
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445 | { D,DD = "",""; } |
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446 | |
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447 | if (defined(TeXaligned)) |
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448 | { s = D + mapname; |
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449 | s = s + r1str + "\\longrightarrow" + r2str + ", \\ " + |
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450 | varr1str + "\\longmapsto" + varr2str + D; } |
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451 | else |
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452 | { s = DD; |
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453 | s = s + newline + "\\begin{array}{rcc}" + newline; |
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454 | s = s + mapname + r1str + " & \\longrightarrow & " + r2str + "\\\\[2mm]" |
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455 | + newline; |
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456 | s = s + varr1str + " & \\longmapsto & " + newline + varr2str + newline; |
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457 | s = s + "\\end{array}" + newline; |
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458 | s = s + DD; |
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459 | } |
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460 | |
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461 | if (size(fname)) |
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462 | { i=1; |
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463 | while (fname[i]==">"){i++;} |
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464 | fname = fname[i,size(fname)-i+1]; |
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465 | |
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466 | if (size(fname)>=4) // check if filename is ending with ".tex" |
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467 | { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; } |
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468 | } |
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469 | else {fname = fname + ".tex";} |
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470 | write(fname,s); |
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471 | } |
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472 | else {return(s);} |
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473 | } |
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474 | example |
---|
475 | { "EXAMPLE:"; echo = 2; |
---|
476 | string fname = "tldemo"; |
---|
477 | ring r1=0,(x,y,z),dp; export r1; |
---|
478 | ring r2=0,(u,v),dp; |
---|
479 | map phi =(r1,u2,uv -v,v2); export phi; |
---|
480 | list TeXreplace; |
---|
481 | TeXreplace[1] = list("phi","\\phi"); |
---|
482 | export TeXreplace; |
---|
483 | texmap("","phi",r1,r2); |
---|
484 | int TeXaligned; export TeXaligned; |
---|
485 | texmap("",phi,r1,r2,"\\C"); |
---|
486 | kill r1,r2,TeXreplace,TeXaligned; |
---|
487 | } |
---|
488 | /////////////////////////////////////////////////////////////////////////////// |
---|
489 | |
---|
490 | proc texname(string fname, string s) |
---|
491 | USAGE: texname(fname,s); fname,s = string |
---|
492 | RETURN: the string s if fname == the empty string "" ; |
---|
493 | otherwise append s to file fname.tex; return nothing |
---|
494 | NOTE: preceeding ">>" end ending ".tex" may miss in fname; |
---|
495 | EXAMPLE: example texname; shows an example |
---|
496 | { |
---|
497 | string st, extr; |
---|
498 | int i,anf,end,op,bigch; |
---|
499 | int n; |
---|
500 | |
---|
501 | if (s[1]=="{") { return(s[2,size(s)-2]);} |
---|
502 | if (s=="") { return(s);} |
---|
503 | s = s + newline; // add a terminating sign |
---|
504 | anf=1; |
---|
505 | while(s[i]!=newline) |
---|
506 | { |
---|
507 | i =anf; |
---|
508 | |
---|
509 | while(s[i]<"0" or s[i]>"9" and s[i]!="'" and s[i]!= "_" and s[i]!="~" and |
---|
510 | s[i]!="(" and s[i]!=")" and s[i]!= "[" and s[i]!=newline) {i++;} |
---|
511 | if (s[i]==newline){st = st + s[anf,i-anf]; n = n +10*(i-anf); return(st);} |
---|
512 | st = st + s[anf,i-anf]; // the starting letters |
---|
513 | if (s[anf]>="A" and s[anf]<="Z") {bigch=1;} |
---|
514 | if (s[i]=="'") { st = st + "'";i++;} |
---|
515 | if (s[i]=="~") { st = "\\tilde{" + st + "}"; i++;} |
---|
516 | if (s[i]=="_") { i++;} |
---|
517 | if (s[i]=="(") { op =1;i++;} |
---|
518 | if (s[i]=="[") { anf = i+1; |
---|
519 | while(s[i]!="]"){i++;} // matrices and vectors |
---|
520 | st = st + "_{" + s[anf,i-anf] + "}"; n = n+ 5*(i-anf); i++; |
---|
521 | // besser: while s[i]<> nwline : scan forward: end, return |
---|
522 | } |
---|
523 | if (s[i]==newline) {return(st);} |
---|
524 | anf =i; |
---|
525 | while (s[i]>="0" and s[i]<="9") {i++;} // parse the number after the letters |
---|
526 | if (bigch and not(op)) { st = st + "^{" + s[anf,i-anf] + "}"; bigch =0;} |
---|
527 | else { st = st + "_{" + s[anf,i-anf] + "}";} |
---|
528 | n = n+5*(i-anf); |
---|
529 | anf =i; // the next text in ( , ) as exponent |
---|
530 | if (op) { if (s[i]== ","){anf = anf+1;} |
---|
531 | while(s[i] !=")"){ i++;} |
---|
532 | if (i<>anf){st = st + "^{" + s[anf,i-anf] + "}"; n = n +5*(i-anf);} |
---|
533 | i++; |
---|
534 | } |
---|
535 | anf =i; |
---|
536 | } |
---|
537 | if (size(fname)) |
---|
538 | { i=1; |
---|
539 | while (fname[i]==">"){i++;} |
---|
540 | fname = fname[i,size(fname)-i+1]; |
---|
541 | |
---|
542 | if (size(fname)>=4) // check if filename is ending with ".tex" |
---|
543 | { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; } |
---|
544 | } |
---|
545 | else {fname = fname + ".tex";} |
---|
546 | write(fname,st); |
---|
547 | } |
---|
548 | else {return(st);} |
---|
549 | } |
---|
550 | example |
---|
551 | { "EXAMPLE:"; echo =2; |
---|
552 | ring r = 0,(x,y),lp; |
---|
553 | poly f = 3xy4 + 2xy2 + x5y3 + x + y6; |
---|
554 | texname("","{f(10)}"); |
---|
555 | texname("","f(10) ="); |
---|
556 | texname("","n1"); |
---|
557 | texname("","T1_12"); |
---|
558 | texname("","g'_11"); |
---|
559 | texname("","f23"); |
---|
560 | texname("","M[2,3]"); |
---|
561 | texname("","A(0,3);"); |
---|
562 | texname("","E~(3)"); |
---|
563 | } |
---|
564 | /////////////////////////////////////////////////////////////////////////////// |
---|
565 | |
---|
566 | proc texobj(string fname, list #) |
---|
567 | USAGE: texobj(fname,l); fname = string,l = list of Singular dataypes |
---|
568 | RETURN: string, the objects in TeX-typesetting if fname == empty string; |
---|
569 | otherwise append this to file fname.tex; return nothing |
---|
570 | NOTE: preceeding ">>" end ending ".tex" may miss in fname; |
---|
571 | EXAMPLE: example texobj; shows an example |
---|
572 | { |
---|
573 | int i,j,k,nr,nc,linear,Tw,Dollars; |
---|
574 | int ND = defined(NoDollars); |
---|
575 | int TW = defined(TeXwidth); |
---|
576 | |
---|
577 | if(defined(basering)){ poly g,h; matrix M;} |
---|
578 | string s,t,l,ineq,sg,Iname; |
---|
579 | string sep= ","; |
---|
580 | string D,DA,DE = "$","\\begin{equation*}" + newline, |
---|
581 | "\\end{equation*}"+ newline; |
---|
582 | string OB,CB = "(",")"; |
---|
583 | if (defined(TeXbrack)) |
---|
584 | {// if (TeXbrack=="(") {OB = "("; CB = ")";} |
---|
585 | if (TeXbrack=="<") {OB = "<"; CB = ">";} |
---|
586 | if (TeXbrack=="{") {OB = "{"; CB = "}";} |
---|
587 | if (TeXbrack=="|") {OB = "|"; CB = "|";} |
---|
588 | if (TeXbrack=="" ) {OB = "."; CB = ".";} |
---|
589 | } |
---|
590 | |
---|
591 | |
---|
592 | if (!(TW)) { int TeXwidth = -1; export TeXwidth; } |
---|
593 | Tw = TeXwidth; |
---|
594 | |
---|
595 | if (defined(TeXproj)){ sep = ":";} |
---|
596 | if(ND) { D,DA,DE="","","";} |
---|
597 | else {int NoDollars; export NoDollars;} |
---|
598 | |
---|
599 | proc absterm(poly f) |
---|
600 | { int k; |
---|
601 | |
---|
602 | for (k=1; k<=nvars(basering); k++) |
---|
603 | { f = subst(f,var(k),0); } |
---|
604 | return(f); |
---|
605 | } |
---|
606 | |
---|
607 | |
---|
608 | if (size(#)==1) |
---|
609 | { if (typeof(#[1])=="int" or typeof(#[1])=="intvec" or typeof(#[1])=="vector" |
---|
610 | or typeof(#[1])=="number" or defined(TeXaligned)) { DA = D; DE = D; } } |
---|
611 | |
---|
612 | s = DA; |
---|
613 | |
---|
614 | for (k=1; k<=size(#); k++) |
---|
615 | { def obj = #[k]; |
---|
616 | if (typeof(obj) == "string") |
---|
617 | { if (defined(`obj`)) |
---|
618 | { if (typeof(`obj`)=="ideal") |
---|
619 | { Iname = obj; def e = `obj`; |
---|
620 | kill obj; def obj = e; kill e;} |
---|
621 | else {s = s + obj + newline;} |
---|
622 | } |
---|
623 | else { s = s + obj + newline;} |
---|
624 | } |
---|
625 | if (typeof(obj) == "int") { s = s + " " + string(obj) + " ";} |
---|
626 | |
---|
627 | if (typeof(obj) == "intvec") |
---|
628 | { s = s + " ("; |
---|
629 | for(j=1; j<size(obj);j++) { s = s + string(obj[j]) + sep;} |
---|
630 | s = s + string(obj[j]) + ") "; |
---|
631 | } |
---|
632 | |
---|
633 | if (typeof(obj) == "number" ) |
---|
634 | { s = s + texpoly("",obj) + newline; |
---|
635 | } |
---|
636 | |
---|
637 | if (typeof(obj) == "poly") |
---|
638 | { int TeXdisplay; export TeXdisplay; |
---|
639 | s = s + "\\begin{split}" + newline; |
---|
640 | s = s + texpoly("",obj) + "\\\\" + newline; |
---|
641 | s = s + "\\end{split}" + newline; |
---|
642 | kill TeXdisplay; |
---|
643 | } |
---|
644 | |
---|
645 | if (typeof(obj) == "vector") |
---|
646 | { if (obj==0) { s = s + "0" ;} |
---|
647 | else |
---|
648 | { if (Tw==0) { TeXwidth = -1;} |
---|
649 | s = s + "\\left" + OB; |
---|
650 | for(j=1; j<nrows(obj); j++) {s = s + texpoly("",obj[j]) + sep;} |
---|
651 | s = s + texpoly("",obj[j]) + "\\right" + CB + newline; |
---|
652 | TeXwidth = Tw; |
---|
653 | } |
---|
654 | } |
---|
655 | |
---|
656 | if (typeof(obj) == "ideal") |
---|
657 | { if (size(Iname)) // verwende hier align |
---|
658 | { if (Tw==0) {TeXwidth = -1;} |
---|
659 | |
---|
660 | // Lasse hier TeXwidth == 0 zu ! |
---|
661 | // if (!(defined(TeXaligned))) |
---|
662 | // { untereinander } |
---|
663 | // else { hintereinander } |
---|
664 | // |
---|
665 | // |
---|
666 | // s = s + Iname + "=" + texpoly("",obj,","); |
---|
667 | // siehe ebenso noch einmal am Ende : ! (TeXwidth <> 0 !? ) |
---|
668 | |
---|
669 | s = s + "\\begin{array}{rcl}" + newline; |
---|
670 | for (i=1;i<=size(matrix(obj));i++) |
---|
671 | { s = s + Iname+ "_{" + string(i) + "} & = & " |
---|
672 | + texpoly("",obj[i]); |
---|
673 | if (i<size(matrix(obj))){ s = s + "\\\\" + newline;} |
---|
674 | } |
---|
675 | s = s + newline; |
---|
676 | s = s + "\\end{array}" + newline; |
---|
677 | TeXwidth = Tw; |
---|
678 | Iname =""; |
---|
679 | } |
---|
680 | else |
---|
681 | { |
---|
682 | if (TeXwidth==0) |
---|
683 | { TeXwidth = -1; |
---|
684 | obj= simplify(obj,2); |
---|
685 | linear = 1; |
---|
686 | for (j=1;j<=size(obj);j++) |
---|
687 | { if (deg(obj[j])>1){linear =0; break;} |
---|
688 | } |
---|
689 | if (!(linear)) |
---|
690 | { s = s + "\\begin{array}{rcl}" + newline; |
---|
691 | for(j=1;j<=size(obj);j++) |
---|
692 | { h = absterm(obj[j]); |
---|
693 | ineq = attrib(obj[j],"ineq"); |
---|
694 | if(!(size(ineq))) { ineq = "=" ; } |
---|
695 | l = texpoly("",obj[j]-h) + " & " + ineq + " & " + texpoly("",-h); |
---|
696 | if(j<size(obj)) { l = l + " \\\\";} |
---|
697 | s =s+ l + newline; |
---|
698 | } |
---|
699 | s = s + "\\end{array}" + newline; |
---|
700 | } |
---|
701 | else // linear |
---|
702 | { s = s + |
---|
703 | "\\begin{array}{*{" + string(2*nvars(basering)-1) + "}{c}cr}" + newline; |
---|
704 | for(j=1; j<=size(obj);j++) |
---|
705 | { h = absterm(obj[j]); |
---|
706 | ineq = attrib(obj[j],"ineq"); |
---|
707 | if(!(size(ineq))) { ineq = "=" ; } |
---|
708 | l = ""; nc = 0; |
---|
709 | for (i=1; i<=nvars(basering);i++) |
---|
710 | { t = " "; sg =""; |
---|
711 | g = obj[j]-subst(obj[j],var(i),0); |
---|
712 | if (g!=0) { t = texpoly("",g);} |
---|
713 | if (i>1) |
---|
714 | { if (t[1]!="-" and t[1]!= " " and nc ){sg = "+";} |
---|
715 | if (t[1]=="-") { sg = "-"; nc =1; t=t[2,size(t)-1];} |
---|
716 | if (t==" ") {sg ="";} |
---|
717 | l = l + " & " + sg + " & " + t; |
---|
718 | } |
---|
719 | else { l = t;} |
---|
720 | if (g!=0) {nc = 1;} |
---|
721 | } |
---|
722 | |
---|
723 | l = l + " & " + ineq + " & " + texpoly("",-h); |
---|
724 | if (j < size(obj)) { l = l + " \\\\";} |
---|
725 | s = s + l + newline; |
---|
726 | } // end for (j) |
---|
727 | s = s + "\\end{array}"; |
---|
728 | } // end else linear |
---|
729 | TeXwidth = 0; |
---|
730 | } // end TeXwidth == 0 |
---|
731 | else // TeXwidth <> 0 |
---|
732 | { s = s + "\\left"+ OB; |
---|
733 | if (defined(TeXaligned)) |
---|
734 | { s = s + texpoly("",obj,","); |
---|
735 | } |
---|
736 | else |
---|
737 | { s = s + newline + "\\begin{array}{c}" + newline + |
---|
738 | texpoly("",obj,", \\\\" + newline) + |
---|
739 | newline + "\\end{array}" + newline; |
---|
740 | } |
---|
741 | s = s + "\\right" + CB; |
---|
742 | } // end TeXwidth <> 0 |
---|
743 | } // not Iname |
---|
744 | // s; |
---|
745 | } |
---|
746 | |
---|
747 | if (typeof(obj) == "module") |
---|
748 | { M = matrix(obj); |
---|
749 | if (Tw ==0 or Tw > 9) { TeXwidth = -1;} |
---|
750 | s = s + "\\left" + OB + newline; |
---|
751 | if (!(defined(TeXaligned))) |
---|
752 | { // Naechste Zeile nicht notwendig ! |
---|
753 | // s = s + "\\begin{array}{*{"+ string(ncols(M)) + "}{c}}" + newline; |
---|
754 | for(j=1;j<=ncols(M);j++) |
---|
755 | { l = "\\left" + OB + newline + "\\begin{array}{c}" + newline; |
---|
756 | l = l + texpoly("",ideal(M[1..nrows(M),j]), " \\\\" + newline) |
---|
757 | + newline + "\\end{array}" +newline + "\\right" + CB + newline; |
---|
758 | if (j< ncols(M)) { l = l + " , " + newline;} |
---|
759 | s = s + l ; |
---|
760 | } |
---|
761 | } |
---|
762 | else // TeXaligned |
---|
763 | { |
---|
764 | for(j=1;j<=ncols(M);j++) |
---|
765 | { s = s + "\\left" + OB + newline + |
---|
766 | texpoly("",ideal(M[1..nrows(M),j]),",") + newline + "\\right" + CB; |
---|
767 | if (j<ncols(M)) { s = s + "," + newline; } |
---|
768 | } |
---|
769 | } |
---|
770 | s = s + "\\right" + CB + newline; |
---|
771 | } // module part |
---|
772 | |
---|
773 | |
---|
774 | if (typeof(obj) == "matrix") |
---|
775 | { if (Tw==0 or Tw > 9) {TeXwidth = -1;} |
---|
776 | l = ""; |
---|
777 | // M = transpose(obj); |
---|
778 | s = s + "\\left" + OB + newline + |
---|
779 | "\\begin{array}{*{"+ string(ncols(obj)) + "}{c}" + "}"+ newline; |
---|
780 | for(i=1;i<=nrows(obj);i++) |
---|
781 | { l = l + texpoly("",ideal(obj[i,1..ncols(obj)])," & "); |
---|
782 | if (i<nrows(obj)) { l = l + " \\\\" + newline;} |
---|
783 | } |
---|
784 | l = l + newline; |
---|
785 | s = s + l + "\\end{array}" + newline + |
---|
786 | "\\right" + CB + newline; |
---|
787 | TeXwidth = Tw; |
---|
788 | } |
---|
789 | |
---|
790 | if (typeof(obj) == "intmat") |
---|
791 | { nr,nc = nrows(obj),ncols(obj); |
---|
792 | l = ""; |
---|
793 | l = "\\left" + OB + newline + |
---|
794 | "\\begin{array}{*{"+ string(nc) + "}{r}}"+ newline; |
---|
795 | for(i=1;i<=nr;i++) |
---|
796 | { for(j=1;j<=nc;j++) |
---|
797 | { l = l + string(obj[i,j]); |
---|
798 | if (j <nc ) { l = l + " & ";} |
---|
799 | else {if( i < nr) { l = l + "\\\\" + newline;}} |
---|
800 | } |
---|
801 | } |
---|
802 | l = l + newline + "\\end{array}" + newline + |
---|
803 | "\\right" + CB + newline; |
---|
804 | s = s + l; |
---|
805 | } |
---|
806 | |
---|
807 | if (typeof(obj) == "ring" or |
---|
808 | typeof(obj) == "qring") { s = s + D + texring("",obj) + D + newline;} |
---|
809 | |
---|
810 | kill obj; |
---|
811 | } |
---|
812 | |
---|
813 | s = s + DE + newline; |
---|
814 | |
---|
815 | if(!(ND)) { kill NoDollars;} |
---|
816 | |
---|
817 | // s; |
---|
818 | if(size(fname)) |
---|
819 | { i=1; |
---|
820 | while (fname[i]==">"){i++;} |
---|
821 | fname = fname[i,size(fname)-i+1]; |
---|
822 | if (size(fname)>=4) // check if filename is ending with ".tex" |
---|
823 | { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; } |
---|
824 | } |
---|
825 | else {fname = fname + ".tex";} |
---|
826 | write(fname,s); |
---|
827 | } |
---|
828 | else {return(s);} |
---|
829 | } |
---|
830 | example |
---|
831 | { "EXAMPLE:"; echo =2; |
---|
832 | ring r = 0,(x,y),lp; |
---|
833 | poly f = 3xy4 + 2xy2 + x5y3 + x + y6; |
---|
834 | ideal G = jacob(f); |
---|
835 | texobj("",G); |
---|
836 | matrix J = jacob(G); |
---|
837 | texobj("",J); |
---|
838 | intmat m[3,4] = 9,2,4,5,2,5,-2,4,-6,10,-1,2,7; |
---|
839 | texobj("",m); |
---|
840 | ring r0 = 0,(x,y,z),dp; |
---|
841 | ideal I = 2x2-4yz3+2-4,zy2+2x,y5z-6x2+7y4z2 +5; |
---|
842 | } |
---|
843 | /////////////////////////////////////////////////////////////////////////////// |
---|
844 | |
---|
845 | proc texproc(string fname,string pname) |
---|
846 | USAGE: opentex(fname,pname); fname,pname = string |
---|
847 | RETURN: string, the proc in a verbatim environment in TeX-typesetting |
---|
848 | if fname == empty string; |
---|
849 | otherwise append this to file fname.tex; return nothing |
---|
850 | NOTE: preceeding ">>" end ending ".tex" may miss in fname; |
---|
851 | CAUTION: texproc cannot applied on itself correctly |
---|
852 | EXAMPLE: example texproc; shows an example |
---|
853 | { |
---|
854 | int i,j=1,1; |
---|
855 | string p,s,t; |
---|
856 | |
---|
857 | if (defined(pname)) |
---|
858 | { if (typeof(`pname`)=="proc") |
---|
859 | { p = string(`pname`); |
---|
860 | s = "\\begin{verbatim}" + newline; |
---|
861 | s = s + "proc " + pname + "("; |
---|
862 | i = find(p,"parameter"); // collecting the parameters |
---|
863 | while(i) |
---|
864 | { j=find(p,";",i); |
---|
865 | t = p[i+10,j-i-10]; |
---|
866 | if(i>1){s = s + ",";}; |
---|
867 | s = s + t; |
---|
868 | i = find(p,"parameter",j); |
---|
869 | } |
---|
870 | s = s + ")" + newline; |
---|
871 | j++; // skip one for the newline |
---|
872 | i = find(p,"return();",j); |
---|
873 | if (!(i)) |
---|
874 | { i = find(p,";RETURN();",j); } // j kann hier weg |
---|
875 | s = s + "{" + p[j,i-j-1] + "}" + newline; |
---|
876 | s = s + "\\end{verbatim}" + newline; |
---|
877 | } |
---|
878 | } |
---|
879 | else |
---|
880 | { print(" --Error: No such proc defined"); |
---|
881 | return(); |
---|
882 | } |
---|
883 | if(size(fname)) |
---|
884 | { i=1; |
---|
885 | while (fname[i]==">"){i++;} |
---|
886 | fname = fname[i,size(fname)-i+1]; |
---|
887 | if (size(fname)>=4) // check if filename is ending with ".tex" |
---|
888 | { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; } |
---|
889 | } |
---|
890 | else {fname = fname + ".tex";} |
---|
891 | write(fname,s); |
---|
892 | } |
---|
893 | else{return(s);} |
---|
894 | } |
---|
895 | example |
---|
896 | { "EXAMPLE:"; echo=2; |
---|
897 | proc exp(int i,int j,list #) |
---|
898 | { string s; |
---|
899 | |
---|
900 | if (size(#)) |
---|
901 | { |
---|
902 | for(i;i<=j;i++) |
---|
903 | { s = s + string(j) + string(#); } |
---|
904 | } |
---|
905 | return(s); |
---|
906 | } |
---|
907 | export exp; |
---|
908 | texproc("","exp"); |
---|
909 | } |
---|
910 | |
---|
911 | /////////////////////////////////////////////////////////////////////////////// |
---|
912 | |
---|
913 | proc texring(string fname, def r, list #) |
---|
914 | USAGE: texring(fname, r[,l]); fname = string; r = ring; |
---|
915 | l=list of strings : controls the symbol for |
---|
916 | coefficint field etc. see example texdemo(); |
---|
917 | RETURN: string, the ring in TeX-typesetting if fname == empty string; |
---|
918 | otherwise append this to file fname.tex; return nothing |
---|
919 | NOTE: preceeding ">>" end ending ".tex" may miss in fname; |
---|
920 | EXAMPLE: example texring; shows an example |
---|
921 | { |
---|
922 | int i,galT,flag,mipo,nopar,Dollars,TB,TA; |
---|
923 | string ob,cb,cf,en,s,t,savebrack; //opening bracket, closing br, coef.field |
---|
924 | intvec v; |
---|
925 | |
---|
926 | |
---|
927 | proc tvar(intvec v) |
---|
928 | { |
---|
929 | int i,j,ldots; |
---|
930 | string s; |
---|
931 | |
---|
932 | j = 1; |
---|
933 | s = texpoly("",var(1)); |
---|
934 | |
---|
935 | if (nvars(basering)==1) { return(s);} |
---|
936 | if (nvars(basering)==2) { return(s + "," + texpoly("",var(2)));} |
---|
937 | if (size(v)==1 and v[1] == 1) |
---|
938 | {return(s + ",\\ldots,"+ texpoly("",var(nvars(basering))));} |
---|
939 | if (v[1]==1 and size(v) >1) {j++;} |
---|
940 | |
---|
941 | for(i=2;i<nvars(basering);i++) |
---|
942 | { if (i<v[j] and !(ldots)) |
---|
943 | { s = s + ",\\ldots"; |
---|
944 | ldots =1; |
---|
945 | } |
---|
946 | if (i== v[j]) |
---|
947 | { s = s + "," + texpoly("",var(i)); |
---|
948 | ldots =0; |
---|
949 | if (j< size(v)) {j++;} |
---|
950 | } |
---|
951 | } |
---|
952 | if (v[j]<nvars(basering)-1) { s = s + ",\\dotsc";} |
---|
953 | return(s + "," + texpoly("",var(nvars(basering)))); |
---|
954 | } |
---|
955 | |
---|
956 | |
---|
957 | setring r; |
---|
958 | if (!(defined(NoDollars))){ Dollars = 1; int NoDollars; export NoDollars;} |
---|
959 | ob,cb = "[","]"; |
---|
960 | if (find(ordstr(r),"s")) { ob,cb="\\{","\\}";} |
---|
961 | if(char(r)==0){cf="\\Q";} |
---|
962 | if(charstr(r)=="real"){cf="\\R";} |
---|
963 | if(char(r)==prime(char(r))){cf="\\Z_{"+string(char(r))+"}";} |
---|
964 | if(char(r)>0) |
---|
965 | { i = find(charstr(r),","); |
---|
966 | if(i) |
---|
967 | { t= charstr(r)[1,i-1]; |
---|
968 | galT = (t <> string(char(r))); |
---|
969 | if (galT) { cf = "\\F_{"+ t + "}";} |
---|
970 | } |
---|
971 | } // all other cases are cover already by char(r)=? prime(char) |
---|
972 | |
---|
973 | if (size(#)) |
---|
974 | { if (typeof(#[1])=="list") { # = #[1];} |
---|
975 | } |
---|
976 | for (i=1;i<=size(#);i++) |
---|
977 | { flag =0; |
---|
978 | if(typeof(#[i])=="string") |
---|
979 | { |
---|
980 | if(#[i][1]=="^" or #[i][1]=="_"){en=en+#[i];flag = 1;} |
---|
981 | if(#[i]=="mipo"){mipo=1; flag = 1;} |
---|
982 | if(#[i]=="{"){ob,cb="\\{","\\}";flag=1;} |
---|
983 | if(#[i]=="{{"){ob,cb="\\{\\{","\\}\\}";flag=1;} |
---|
984 | if(#[i]=="["){ob,cb="[","]";flag=1;} |
---|
985 | if(#[i]=="[["){ob,cb="[[","]]";flag=1;} |
---|
986 | if(#[i]=="<"){ob,cb="<",">";flag=1;} |
---|
987 | if(#[i]=="<<"){ob,cb="{\\ll}","{\\gg}";flag=1;} |
---|
988 | if(#[i]=="C"){cf="\\C";flag=1;} |
---|
989 | if(#[i]=="Q"){cf="\\Q";flag=1;} |
---|
990 | if((#[i]=="k" or #[i]=="K" or #[i]=="R") and !(galT)) |
---|
991 | {cf=#[i]; flag=1; nopar=1;} |
---|
992 | if (flag!=1) {cf = #[i];} // for all the cases not covered here e.g Z_(p) |
---|
993 | } // or Q[i] |
---|
994 | |
---|
995 | if ((typeof(#[i])=="intvec") or |
---|
996 | (typeof(#[i])=="int")){v=#[i];} |
---|
997 | } |
---|
998 | s = cf; |
---|
999 | // now the parameters |
---|
1000 | // t; |
---|
1001 | if(npars(r) and ((t==string(char(r))) or char(r)==0) and !(nopar)) |
---|
1002 | { |
---|
1003 | s = s + "("; // !! mit ideal !! |
---|
1004 | for(i=1;i<npars(r);i++) {s = s + texpoly("",par(i)) + ",";} |
---|
1005 | s = s + texpoly("",par(npars(r))) + ")"; |
---|
1006 | } // parameters done |
---|
1007 | if (!(galT) and mipo and minpoly!=0) |
---|
1008 | { s = s + "/" + list(parsp(string(minpoly),0))[1];} |
---|
1009 | s = s + ob; |
---|
1010 | if (v!=0 and nvars(r)>3) |
---|
1011 | { s = s + tvar(v);} |
---|
1012 | else |
---|
1013 | { s = s + texpoly("",maxideal(1),","); } |
---|
1014 | s = s + cb + en; |
---|
1015 | |
---|
1016 | if (typeof(r)=="qring") |
---|
1017 | { ideal @I = ideal(r); |
---|
1018 | if (defined(TeXbrack)) |
---|
1019 | { |
---|
1020 | TB =1; savebrack = TeXbrack; |
---|
1021 | if (TeXbrack!= "<" and TeXbrack!="(") { TeXbrack = "<";} |
---|
1022 | } |
---|
1023 | TA = defined(TeXaligned); |
---|
1024 | if (!(TA)) { int TeXaligned; export TeXaligned; } |
---|
1025 | t = texobj("",@I); |
---|
1026 | // @I; |
---|
1027 | // t; |
---|
1028 | if (TB) { TeXbrack = savebrack;} |
---|
1029 | if (!(TA)) { kill TeXaligned;} |
---|
1030 | s = s + "/" + t; |
---|
1031 | } |
---|
1032 | |
---|
1033 | if (Dollars) |
---|
1034 | { kill NoDollars; |
---|
1035 | s = "$" + s + "$"; |
---|
1036 | } |
---|
1037 | if (size(fname)) |
---|
1038 | { i=1; |
---|
1039 | while (fname[i]==">"){i++;} |
---|
1040 | fname = fname[i,size(fname)-i+1]; |
---|
1041 | |
---|
1042 | if (size(fname)>=4) // check if filename is ending with ".tex" |
---|
1043 | { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; } |
---|
1044 | } |
---|
1045 | else {fname = fname + ".tex";} |
---|
1046 | write(fname,s); |
---|
1047 | } |
---|
1048 | else{return(s);} |
---|
1049 | } |
---|
1050 | example |
---|
1051 | { "EXAMPLE:"; echo=2; |
---|
1052 | ring r0 = 0,(x,y,z),dp; // short varnames polynomial ordering |
---|
1053 | texring("",r0); |
---|
1054 | ring r7 =0,(x(0..2)),ds; // char =7, long varnames |
---|
1055 | texring("",r7); |
---|
1056 | ring r1 = 0,(x1,x2,y1,y2),wp(1,2,3,4); |
---|
1057 | texring("",r1); |
---|
1058 | ring r2= 0,(x_10,x_11),M(1,2,3,4); |
---|
1059 | texring("",r2); |
---|
1060 | ring rr = real,(x),dp; // real numbers |
---|
1061 | texring("",rr); |
---|
1062 | ring r; |
---|
1063 | texring("",r); |
---|
1064 | ring rabc =(0,t1,t2,t3),(x,y),dp; // parameters |
---|
1065 | texring("",rabc); |
---|
1066 | ring ralg = (7,a),(x1,x2),(ds,dp); // algebraic extension |
---|
1067 | minpoly = a2-a+3; |
---|
1068 | texring("",ralg); |
---|
1069 | texring("",ralg,"mipo"); |
---|
1070 | ring r49=(49,a),x,dp; // Galoisfield |
---|
1071 | texring("",r49); |
---|
1072 | setring r0; |
---|
1073 | ideal i = x2-z,xy2+1; |
---|
1074 | qring q = std(i); |
---|
1075 | q; |
---|
1076 | texring("",q); |
---|
1077 | // -------- additional features ------------- |
---|
1078 | ring r10 =0,(x(0..10)),dp; |
---|
1079 | texring("",r10,1); |
---|
1080 | ring rxy = 0,(x(1..5),y(1..6)),ds; |
---|
1081 | intvec v = 5,6; |
---|
1082 | texring("",rxy,v); |
---|
1083 | texring("",r0,"C","{"); |
---|
1084 | texring("",ralg,"k"); |
---|
1085 | texring("",r7,"^G"); |
---|
1086 | list TeXreplace; |
---|
1087 | TeXreplace[1] = list("x","\\xi"); |
---|
1088 | TeXreplace[2] = list ("t","\\lambda"); |
---|
1089 | export TeXreplace; |
---|
1090 | texring("",rabc); |
---|
1091 | texring("",r7); |
---|
1092 | kill TeXreplace; |
---|
1093 | } |
---|
1094 | |
---|
1095 | /////////////////////////////////////////////////////////////////////////////// |
---|
1096 | |
---|
1097 | proc rmx(string fname) |
---|
1098 | USAGE: rmx(fname); fname = string |
---|
1099 | RETURN: nothing; removes .log and .aux files associated to file <fname> |
---|
1100 | removes tex and xdvi file too, if suffix ".tex" or ".dvi" is given |
---|
1101 | NOTE: if fname ends by .dvi or .tex |
---|
1102 | fname.dvi or fname.dvi and fname.tex will be deleted, too |
---|
1103 | EXAMPLE: example rmx; shows an example |
---|
1104 | { |
---|
1105 | int i,suffix= 1,0; |
---|
1106 | int retval; |
---|
1107 | |
---|
1108 | if (size(fname)) |
---|
1109 | { |
---|
1110 | while (fname[i]==">"){i++;} |
---|
1111 | fname = fname[i,size(fname)-i+1]; |
---|
1112 | if (size(fname)>4) |
---|
1113 | { if (fname[size(fname)-3,4]==".tex") { suffix = 2;} |
---|
1114 | if (fname[size(fname)-3,4]==".dvi") { suffix = 1; } |
---|
1115 | if (suffix) { fname = fname[1,size(fname)-4]; } |
---|
1116 | } |
---|
1117 | retval = system("sh","rm " + fname + ".aux"); |
---|
1118 | retval = system("sh","rm " + fname + ".log"); |
---|
1119 | if (suffix==2) {retval = system("sh","/bin/rm -i " + fname +".tex");} |
---|
1120 | if (suffix>=1) {retval = system("sh","/bin/rm -i " + fname +".dvi");} |
---|
1121 | } |
---|
1122 | else |
---|
1123 | {" -- Need a filename "; |
---|
1124 | return(); |
---|
1125 | } |
---|
1126 | } |
---|
1127 | example |
---|
1128 | { "EXAMPLE:"; echo =2; |
---|
1129 | ring r; |
---|
1130 | poly f = x+y+z; |
---|
1131 | opentex("exp001"); // defaulted latex2e document |
---|
1132 | texobj("exp001","A polynom",f); |
---|
1133 | closetex("exp001"); |
---|
1134 | tex("exp001"); |
---|
1135 | rmx("exp001"); // removes aux and log file of exp001 |
---|
1136 | |
---|
1137 | opentex("exp002","tex"); // create a texdocument |
---|
1138 | texpoly("exp002",f); |
---|
1139 | closetex("exp002"); |
---|
1140 | tex("exp002","tex"); |
---|
1141 | rmx("exp002.tex"); // removes aux, log, dvi and tex file of exp002 |
---|
1142 | echo = 0; |
---|
1143 | print("remaining files will be deleted after pressing <RETURN> "); |
---|
1144 | pause; |
---|
1145 | echo = 2; |
---|
1146 | system("sh","rm -i exp00?.*"); |
---|
1147 | } |
---|
1148 | /////////////////////////////////////////////////////////////////////////////// |
---|
1149 | |
---|
1150 | proc xdvi(string fname, list #) |
---|
1151 | USAGE: xdvi(fname[,style]); fname,style = string |
---|
1152 | RETURN: nothing; displays dvi-file fname.dvi with previewer xdvi |
---|
1153 | NOTE: ending .dvi may miss in fname |
---|
1154 | style overwrites the default setting xdvi |
---|
1155 | EXAMPLE: example xdvi ; shows an example |
---|
1156 | { |
---|
1157 | int i=1; |
---|
1158 | int retval; |
---|
1159 | string default = "xdvi"; |
---|
1160 | |
---|
1161 | if (size(#)) {default = string(#[1]);} |
---|
1162 | |
---|
1163 | if (size(fname)) |
---|
1164 | { |
---|
1165 | while (fname[i]==">") {i++;} |
---|
1166 | fname = fname[i,size(fname)-i+1]; |
---|
1167 | |
---|
1168 | if (size(fname)>=4) |
---|
1169 | { if(fname[size(fname)-3,4]==".tex") {fname = fname[1,size(fname)-4];}} |
---|
1170 | |
---|
1171 | "calling ",default, " for :",fname,newline; |
---|
1172 | |
---|
1173 | retval = system("sh",default + " " + fname + " &"); |
---|
1174 | } |
---|
1175 | else |
---|
1176 | { " -- Need a filename "; |
---|
1177 | return(); |
---|
1178 | } |
---|
1179 | } |
---|
1180 | example |
---|
1181 | { "EXAMPLE:"; echo = 2; |
---|
1182 | ring r; |
---|
1183 | ideal i = maxideal(7); |
---|
1184 | opentex("exp001"); // defaulted latex2e document |
---|
1185 | texobj("exp001","An ideal",i); |
---|
1186 | closetex("exp001"); |
---|
1187 | tex("exp001"); |
---|
1188 | xdvi("exp001"); |
---|
1189 | echo = 0; |
---|
1190 | print("the created files will be deleted after pressing <RETURN> "); |
---|
1191 | pause; |
---|
1192 | echo = 2; |
---|
1193 | system("sh","rm -i exp00?.*"); |
---|
1194 | } |
---|
1195 | /////////////////////////////////////////////////////////////////////////////// |
---|
1196 | |
---|
1197 | proc texpoly(string fname,def p,list #) |
---|
1198 | { |
---|
1199 | def @r = basering; |
---|
1200 | |
---|
1201 | poly f,monom; |
---|
1202 | ideal I; |
---|
1203 | number cfm; |
---|
1204 | string sign,cfmt,pt,s,bg,t,monomt, lnbreak; |
---|
1205 | string sep = newline; |
---|
1206 | int i,b,b2,n, msz,linesz, count,k; |
---|
1207 | int realT, parT, galT; |
---|
1208 | int C = 2 + defined(TeXdisplay); |
---|
1209 | |
---|
1210 | string notvalid = "intvec intmat vector matrix module map "; |
---|
1211 | |
---|
1212 | if (typeof(p) == "int") { return(p);} |
---|
1213 | if (typeof(p) == "ring" or typeof(p) == "qring") |
---|
1214 | { " -- Call texring instead "; return();} |
---|
1215 | if (find(notvalid,typeof(p))) |
---|
1216 | { " -- Call texobj instead "; return();} |
---|
1217 | if (typeof(p) == "map") |
---|
1218 | { " -- Call texmap instead "; return();} |
---|
1219 | if (typeof(p) == "proc") |
---|
1220 | { " -- Call texmap instead "; return();} |
---|
1221 | if (typeof(p) == "link" or typeof(p) == "list" or typeof(p) == "resolution") |
---|
1222 | { " -- Object can not translated into tex "; return();} |
---|
1223 | |
---|
1224 | if (!(defined(TeXdisplay))){ lnbreak = "\\\\[2mm]" + newline;} |
---|
1225 | else { lnbreak = "\\\\" + newline;} |
---|
1226 | |
---|
1227 | proc parsr(string s) // parse real |
---|
1228 | { string t; |
---|
1229 | |
---|
1230 | if (s==" Inf") { return("\\infty",3);} |
---|
1231 | if (s==" -Inf") { return("\\-infty",6);} |
---|
1232 | if (s[7]=="-"){t ="-";} |
---|
1233 | if (s[8]<>"0"){t = t + s[8];} |
---|
1234 | if (s[9]<>"0" or s[8]<>"0"){t = t + s[9];} |
---|
1235 | if (size(t)) |
---|
1236 | { if (t=="1") {return(s[1,5]+"*10",21);} |
---|
1237 | if (size(t)>1) {return(s[1,5]+"*10^{"+t+"}",21+2*size(t));} |
---|
1238 | else {return(s[1,5]+"*10^"+t,23);} |
---|
1239 | } |
---|
1240 | else {return(s[1,5],12);} |
---|
1241 | } |
---|
1242 | |
---|
1243 | proc parsg(string s) // parse Galoisfield |
---|
1244 | { int i,j = 1,1; |
---|
1245 | string t; |
---|
1246 | |
---|
1247 | if (short) |
---|
1248 | { t =s[1]; |
---|
1249 | if(size(s)>1) {return(t+"^{" + s[2,size(s)-1] + "}",3+2*(size(s)-1));} |
---|
1250 | else{return(t,5);} |
---|
1251 | } |
---|
1252 | else |
---|
1253 | { return(parselong(s+"!"));} |
---|
1254 | } |
---|
1255 | |
---|
1256 | if (defined(TeXdisplay)) { bg = "& ";} |
---|
1257 | if (!(defined(TeXwidth))) { int TeXwidth = -1; export TeXwidth;} |
---|
1258 | |
---|
1259 | |
---|
1260 | // -- Type check |
---|
1261 | |
---|
1262 | if (typeof(p)=="string") |
---|
1263 | { if(defined(`p`)) |
---|
1264 | { pt = p + " = "; |
---|
1265 | p = `p`; |
---|
1266 | } |
---|
1267 | } |
---|
1268 | if (typeof(p)=="poly" or typeof(p)=="number") {I = p;} |
---|
1269 | |
---|
1270 | if (typeof(p)=="ideal") |
---|
1271 | { I = p; |
---|
1272 | if(size(#)){ sep = #[1];} |
---|
1273 | } |
---|
1274 | |
---|
1275 | if (I==0) |
---|
1276 | { if (!(defined(NoDollars))){return("$0$");} |
---|
1277 | else {return("0");} |
---|
1278 | } |
---|
1279 | |
---|
1280 | // -- Type check ende |
---|
1281 | |
---|
1282 | //--------------------- |
---|
1283 | |
---|
1284 | |
---|
1285 | //------- set flags: -------------------------------------------------------- |
---|
1286 | |
---|
1287 | if (size(#)) |
---|
1288 | { if (typeof(#[1])=="int") { linesz = #[1];} |
---|
1289 | // if (typeof(#[1])=="string") { linesz = #[1];} |
---|
1290 | } |
---|
1291 | |
---|
1292 | parT = npars(@r); |
---|
1293 | realT = (charstr(@r)=="real"); |
---|
1294 | i = find(charstr(@r),","); |
---|
1295 | if (i) |
---|
1296 | { t = charstr(@r)[1,i-1]; |
---|
1297 | galT = (t <> string(char(@r))); // the char is not the same as the ... |
---|
1298 | } |
---|
1299 | i = 0; |
---|
1300 | |
---|
1301 | //------- parse the polynom |
---|
1302 | pt = bg; |
---|
1303 | |
---|
1304 | for(k=1;k<=size(matrix(I));k++) |
---|
1305 | { i = 0; linesz = 0; count =0; |
---|
1306 | sign =""; |
---|
1307 | f = I[k]; |
---|
1308 | if (f==0) { pt = pt + "0";} |
---|
1309 | while(f<>0) |
---|
1310 | { count++; msz = 0; |
---|
1311 | |
---|
1312 | // ------ tex the coefficient |
---|
1313 | monom = lead(f); |
---|
1314 | f = f - monom; |
---|
1315 | cfm = leadcoef(monom); |
---|
1316 | if (cfm*1 != 0) { monom = monom/cfm;} // the normalized monom |
---|
1317 | s = string(monom) + "!"; // add a terminating sign |
---|
1318 | cfmt = ""; |
---|
1319 | |
---|
1320 | if (defined(TeXreplace)) { short =0;} // this is essential |
---|
1321 | cfmt = string(cfm); |
---|
1322 | if (size(cfmt)>1) // check if sign is < 0 |
---|
1323 | { if (cfmt[2]=="-") { cfm = (-1) *cfm; sign = "-";}} |
---|
1324 | if (cfmt[1] == "-") { cfm = (-1) * cfm; sign = "-";} |
---|
1325 | if (cfm!=1 or monom==1) {cfmt = string(cfm);} |
---|
1326 | else {cfmt="";} |
---|
1327 | |
---|
1328 | if (defined(TeXwidth) and TeXwidth > 0 and TeXwidth <9 and count> TeXwidth) |
---|
1329 | { pt = pt + sign + "\\dotsb"; break;} |
---|
1330 | // ---------------------------------------- linesz ?? |
---|
1331 | |
---|
1332 | if (size(cfmt)) // parse the coefficient |
---|
1333 | { |
---|
1334 | monomt = cfmt; // (already a good choice for integers) |
---|
1335 | msz = 3*size(cfmt); |
---|
1336 | |
---|
1337 | if(realT) { monomt,msz = parsr(cfmt);} |
---|
1338 | if (galT) { monomt,msz = parsg(cfmt);} |
---|
1339 | b = find(cfmt,")/("); // look if fraction |
---|
1340 | b2 = find(cfmt,"/"); |
---|
1341 | if (b) {b++;} |
---|
1342 | n = size(cfmt); |
---|
1343 | if (!(parT) and !(realT) and !(galT)) |
---|
1344 | { if( !(b2) or defined(TeXnofrac)) |
---|
1345 | { monomt = cfmt; msz = 3*size(monomt);} |
---|
1346 | else |
---|
1347 | { monomt = "\\frac{" + cfmt[1,b2-1] + "}{" + cfmt[b2+1,n-b2] + "}"; |
---|
1348 | if (n-2*b2>0) {msz = C*(n-b2);} |
---|
1349 | else {msz = C*b2;} |
---|
1350 | } |
---|
1351 | } |
---|
1352 | if (parT and !(galT)) |
---|
1353 | { monomt,msz = parsp(cfmt,b);} |
---|
1354 | } |
---|
1355 | |
---|
1356 | // -- now parse the monom |
---|
1357 | if (monom <> 1) |
---|
1358 | { i = 1; |
---|
1359 | if(short) |
---|
1360 | { while(s[i]<>"!") |
---|
1361 | { monomt = monomt + s[i]; i++; |
---|
1362 | b = i; |
---|
1363 | msz = msz + 3; // it was a single lettered var |
---|
1364 | while(s[i]!="!" and s[i]>="0" and s[i]<="9"){i++;} |
---|
1365 | if (i-b) |
---|
1366 | { monomt = monomt + "^{" + s[b,i-b] + "}"; |
---|
1367 | msz = msz + 2*(i-b); |
---|
1368 | } |
---|
1369 | } |
---|
1370 | } |
---|
1371 | else // not short |
---|
1372 | { t,i = parselong(s); |
---|
1373 | monomt = monomt + t; |
---|
1374 | msz = msz + i; |
---|
1375 | } |
---|
1376 | } |
---|
1377 | |
---|
1378 | |
---|
1379 | |
---|
1380 | msz = msz + 6*size(sign); // Wieso mal 6 ?? |
---|
1381 | // string(msz) + " ," + string(linesz) + " " + string(cfm*monom); |
---|
1382 | |
---|
1383 | if (TeXwidth > 10 and (linesz + msz > 3*TeXwidth) and linesz) |
---|
1384 | { pt = pt + lnbreak + bg; |
---|
1385 | linesz = msz; |
---|
1386 | } |
---|
1387 | else { linesz = linesz + msz; } // 3 for sign |
---|
1388 | pt = pt + sign + monomt; |
---|
1389 | sign = "+"; |
---|
1390 | monomt = ""; |
---|
1391 | } |
---|
1392 | |
---|
1393 | if (k<size(matrix(I))){ pt = pt + sep;} |
---|
1394 | } |
---|
1395 | |
---|
1396 | if (TeXwidth==0 and typeof(p)=="poly"){ pt = pt + "= 0";} |
---|
1397 | if (not(defined(NoDollars))) { pt = "$"+pt+"$";} |
---|
1398 | |
---|
1399 | if (size(fname)) |
---|
1400 | { i=1; |
---|
1401 | while (fname[i]==">"){i++;} |
---|
1402 | fname = fname[i,size(fname)-i+1]; |
---|
1403 | |
---|
1404 | if (size(fname)>=4) // check if filename is ending with ".tex" |
---|
1405 | { if(fname[size(fname)-3,4]!=".tex") {fname = fname +".tex"; } |
---|
1406 | } |
---|
1407 | else {fname = fname + ".tex";} |
---|
1408 | write(fname,pt); |
---|
1409 | } |
---|
1410 | else {return(pt);} |
---|
1411 | } |
---|
1412 | example |
---|
1413 | { "EXAMPLE:"; echo =2; |
---|
1414 | ring r0=0,(x,y,z),dp; |
---|
1415 | poly f = -1x^2 + 2; |
---|
1416 | texpoly("",f); |
---|
1417 | texpoly("",2x2y23z); |
---|
1418 | |
---|
1419 | |
---|
1420 | ring rr= real,(x,y),dp; |
---|
1421 | |
---|
1422 | ring r7= 7,(x,y,z),dp; |
---|
1423 | poly f = 2x2y23z; |
---|
1424 | texpoly("",f); |
---|
1425 | ring rab =(0,a,b),(x,y,z),dp; |
---|
1426 | poly f = (-2a2 +b3 -2)/a * x2y4z5 + (a2+1)*x + a+1; |
---|
1427 | f; |
---|
1428 | texpoly("",f); |
---|
1429 | } |
---|
1430 | |
---|
1431 | proc parsp(string cfmt, int b) |
---|
1432 | { string mt, nom,denom; |
---|
1433 | int fl1,fl2,sz1,sz2,msz; |
---|
1434 | |
---|
1435 | if (!(b)) |
---|
1436 | { mt,fl1 = parst(cfmt,0); msz = size(cfmt)-2; |
---|
1437 | if (fl1) { mt = "(" + mt + ")"; msz = msz +1; } |
---|
1438 | } |
---|
1439 | else |
---|
1440 | { nom,fl1 = parst(cfmt[1,b-1],1); |
---|
1441 | denom,fl2 = parst(cfmt[b+1,size(cfmt)-b],1); |
---|
1442 | if (defined(TeXnofrac)) |
---|
1443 | { if(fl1) { nom = "(" + nom + ")"; sz1++;} |
---|
1444 | if(fl2) {denom = "(" + denom + ")"; sz2++;} |
---|
1445 | mt = nom+ "/"+ denom; msz = sz1+sz2 +1; |
---|
1446 | } |
---|
1447 | else |
---|
1448 | { mt = "\\frac{" + nom + "}{" + denom + "}"; |
---|
1449 | if (sz1-sz2) { msz = 5*sz1;} |
---|
1450 | else {msz = 5*sz2;} |
---|
1451 | } |
---|
1452 | } |
---|
1453 | return(mt,msz); |
---|
1454 | } |
---|
1455 | example |
---|
1456 | {"EXAMPLE:"; echo =2; |
---|
1457 | ring r=(0,a,b),x,dp; |
---|
1458 | int i; |
---|
1459 | poly f = (a2b12 + 23a2 -b13-1)/(a2+2b -1); |
---|
1460 | f; |
---|
1461 | string s; |
---|
1462 | s= string(f); |
---|
1463 | i = find(s,")/("); |
---|
1464 | parsp(s,i); |
---|
1465 | } |
---|
1466 | |
---|
1467 | proc parst(string s,int sec) // parse parameter |
---|
1468 | // sec parameter to see if in parsp a fraction follows |
---|
1469 | { int i,j =1,-1; |
---|
1470 | int b,k,jj,mz; // begin and end |
---|
1471 | int saveshort=short; |
---|
1472 | string t,c,vn,nom,denom,sg; |
---|
1473 | |
---|
1474 | s = s[2,size(s)-2]; s = s + "!"; |
---|
1475 | |
---|
1476 | if(defined(TeXreplace)){ short =0;} // only then replacing works correctly |
---|
1477 | if (short) |
---|
1478 | { while(s[i]<>"!") |
---|
1479 | { b=i; j++; |
---|
1480 | while(s[i]>="0" and s[i]<="9" or (s[i]=="+" or s[i]=="-") and s[i]!="!") |
---|
1481 | {i++;} // scan the number |
---|
1482 | t =s[b,i-b]; |
---|
1483 | // if (t=="-1" and s[i]!="!" and s[i]!="-" and s[i]!="+"){t = "-";} |
---|
1484 | if (t=="-1" and (s[i]<="0" or s[i]>="9") and s[i]!= "/" and s[i]!="!") |
---|
1485 | { |
---|
1486 | t = "-";} |
---|
1487 | if (s[i]=="/") |
---|
1488 | { i++; |
---|
1489 | sg = ""; |
---|
1490 | if (t[1]=="+" or t[1]=="-") |
---|
1491 | { nom = t[2,size(t)-1]; |
---|
1492 | sg = t[1]; |
---|
1493 | } |
---|
1494 | else { nom = t;} |
---|
1495 | b =i; |
---|
1496 | while(s[i]>="0" and s[i]<="9") {i++;} |
---|
1497 | denom = s[b,i-b]; |
---|
1498 | if (!(sec) and (!(defined(TeXaligned)))) |
---|
1499 | { t = sg + "\\frac{" + nom + "}{" + denom + "}";} |
---|
1500 | else |
---|
1501 | { t = sg + "(" + nom + "/" + denom + ")"; |
---|
1502 | } |
---|
1503 | } |
---|
1504 | c = c + t; |
---|
1505 | if(s[i]!="!"){c = c + s[i]; i++;} // the parameter |
---|
1506 | b=i; |
---|
1507 | while(s[i]>="0" and s[i]<="9") |
---|
1508 | {i++;} //the exponent |
---|
1509 | if(i-b){ c = c + "^{" + s[b,i-b]+"}";} |
---|
1510 | } |
---|
1511 | } |
---|
1512 | else // if not short .... |
---|
1513 | { while (s[i] <> "!") |
---|
1514 | { b=i; j++; |
---|
1515 | while(s[i]=="-" or s[i]=="+" or (s[i]>="0" and s[i]<="9")){i++;} |
---|
1516 | t = s[b,i-b]; |
---|
1517 | if (t=="-1" and s[i]=="*" ) {t="-";} |
---|
1518 | if (s[i]=="/") |
---|
1519 | { i++; |
---|
1520 | sg = ""; |
---|
1521 | if (t[1]=="+" or t[1]=="-") |
---|
1522 | { nom = t[2,size(t)-1]; |
---|
1523 | sg = t[1]; |
---|
1524 | } |
---|
1525 | else { nom = t;} |
---|
1526 | b =i; |
---|
1527 | while(s[i]>="0" and s[i]<="9") {i++;} |
---|
1528 | denom = s[b,i-b]; |
---|
1529 | if (!(sec) and (!(defined(TeXaligned)))) |
---|
1530 | { t = sg + "\\frac{" + nom + "}{" + denom + "}";} |
---|
1531 | else |
---|
1532 | { t = sg + "(" + nom + "/" + denom + ")"; |
---|
1533 | } |
---|
1534 | } |
---|
1535 | c = c+t; t=""; |
---|
1536 | if (s[i]=="*"){i++;} |
---|
1537 | b=i; |
---|
1538 | while(s[i]!="+" and s[i]!="-" and s[i]!="!") //pass a monom |
---|
1539 | { // start with letters |
---|
1540 | // alternativ: |
---|
1541 | while((s[i]>="a" and s[i]<="z") or (s[i]>="A" and s[i]<="Z")){i++;} |
---|
1542 | k = i-b; |
---|
1543 | vn = s[b,k]; |
---|
1544 | if (defined(TeXreplace)) |
---|
1545 | { for (jj=1; jj<= size(TeXreplace);jj++) |
---|
1546 | { if (vn == TeXreplace[jj][1]) |
---|
1547 | {vn = TeXreplace[jj][2]; k=1; |
---|
1548 | if (s[i]=="*") {vn = vn + " ";} |
---|
1549 | break;} //suppose replacing by a single sign |
---|
1550 | } |
---|
1551 | } |
---|
1552 | t = t + vn; |
---|
1553 | mz = mz + 10*k; |
---|
1554 | if (s[i]=="_" or s[i]=="(") { i++;} // the index is coming |
---|
1555 | b = i; |
---|
1556 | while(s[i]>="0" and s[i]<="9"){ i++;} |
---|
1557 | k = i-b; |
---|
1558 | if (k){ t = t + "_{" +s[b,k] + "}";} |
---|
1559 | if(s[i]==")") {i++;} |
---|
1560 | if (s[i]=="^") |
---|
1561 | { i++; b = i; |
---|
1562 | while(s[i]>="0" and s[i]<="9"){ i++;} // for neg. expon. |
---|
1563 | if (b-i) { t = t + "^{" + s[b,i-b] + "}";} |
---|
1564 | } |
---|
1565 | if (i-b > k) { mz = mz + 5*(i-b);} |
---|
1566 | else {mz = mz + 5*k;} |
---|
1567 | if (s[i]=="*"){i++;} |
---|
1568 | b=i; |
---|
1569 | } |
---|
1570 | c =c+t; |
---|
1571 | } |
---|
1572 | } |
---|
1573 | short = saveshort; |
---|
1574 | return(c,j); |
---|
1575 | } |
---|
1576 | example |
---|
1577 | { "EXAMPLE:"; echo =2; |
---|
1578 | ring r=(0,a,b),x,dp; |
---|
1579 | poly f = (a2b12 + 23a2 -b13-1); |
---|
1580 | f; |
---|
1581 | parst(string(f)); |
---|
1582 | |
---|
1583 | f =(-a +4b2 -2); |
---|
1584 | f; |
---|
1585 | parst(string(f)); |
---|
1586 | |
---|
1587 | f = a23; |
---|
1588 | f; |
---|
1589 | parst(string(f)); |
---|
1590 | f = 2a12b3 -4ab15 +2a4b12 -2; |
---|
1591 | short =0; |
---|
1592 | f; |
---|
1593 | parst(string(f)); |
---|
1594 | ring r2=(0,a1,b1),x,dp; |
---|
1595 | poly f = 2*a1^12*b1^3 -4*a1*b1^15 +2*a1^4*b1^12 -2; |
---|
1596 | f; |
---|
1597 | parst(string(f)); |
---|
1598 | } |
---|
1599 | |
---|
1600 | |
---|
1601 | proc parselong(string s) |
---|
1602 | { |
---|
1603 | int i,j,k,b,mz; |
---|
1604 | string t,vn; // varname |
---|
1605 | |
---|
1606 | // "s=" + s; |
---|
1607 | i = 1; |
---|
1608 | while (s[i] <> "!") |
---|
1609 | { b=i; |
---|
1610 | |
---|
1611 | // -- scan now the letter ... |
---|
1612 | |
---|
1613 | // while(s[i]!="!" and ) |
---|
1614 | |
---|
1615 | // alternativ: |
---|
1616 | while((s[i]>="a" and s[i]<="z") or (s[i]>="A" and s[i]<="Z")) |
---|
1617 | { i++;} |
---|
1618 | // s[i]; i; |
---|
1619 | k = i-b; |
---|
1620 | vn = s[b,k]; |
---|
1621 | |
---|
1622 | if (defined(TeXreplace)) |
---|
1623 | { for (j=1; j<= size(TeXreplace);j++) |
---|
1624 | { if (vn == TeXreplace[j][1]) |
---|
1625 | {vn = TeXreplace[j][2]; k=1; |
---|
1626 | if (s[i]=="*") {vn = vn + " ";} |
---|
1627 | break;} //suppose replacing by a single sign |
---|
1628 | } |
---|
1629 | } |
---|
1630 | t = t + vn; |
---|
1631 | mz = mz + 10*k; |
---|
1632 | if (s[i]=="_" or s[i]=="(") { i++;} // the index is coming |
---|
1633 | b = i; |
---|
1634 | while(s[i]>="0" and s[i]<="9"){ i++;} |
---|
1635 | j = i-b; |
---|
1636 | if (j){ t = t + "_{" +s[b,j] + "}";} |
---|
1637 | if(s[i]==")") {i++;} |
---|
1638 | if (s[i]=="^") |
---|
1639 | { i++; b = i; |
---|
1640 | while(s[i]>="0" and s[i]<="9" or s[i]=="-") |
---|
1641 | { i++;} // for neg. expon. |
---|
1642 | if (b-i) { t = t + "^{" + s[b,i-b] + "}";} |
---|
1643 | } |
---|
1644 | if (i-b > j) { mz = mz + 5*(i-b);} |
---|
1645 | else {mz = mz + 5*j;} |
---|
1646 | if (s[i]=="*"){i++;} |
---|
1647 | } |
---|
1648 | return(t,mz); |
---|
1649 | } |
---|
1650 | example |
---|
1651 | { "EXAMPLE:"; echo =2; |
---|
1652 | ring r =(49,a),x,dp; |
---|
1653 | number f = a13; |
---|
1654 | parsg(string(f)); |
---|
1655 | list TeXreplace; export TeXreplace; |
---|
1656 | TeXreplace[1] = list("b","\\beta"); |
---|
1657 | TeXreplace[2] = list("a","\\alpha"); |
---|
1658 | TeXreplace[3] = list("c","\\gamma"); |
---|
1659 | parselong(string(f)+"!"); |
---|
1660 | } |
---|
1661 | /////////////////////////////////////////////////////////////////////////////// |
---|
1662 | |
---|
1663 | ///////////////////////////// PART0 ////////////////////////////////////////// |
---|
1664 | |
---|
1665 | proc part0(string fname) |
---|
1666 | { |
---|
1667 | int texdemopart =0; |
---|
1668 | export texdemopart; |
---|
1669 | |
---|
1670 | |
---|
1671 | // Singular script for generating tldemo.tex |
---|
1672 | |
---|
1673 | // int TeXwidth =-1; |
---|
1674 | // export TeXwidth; |
---|
1675 | // if(defined(NoDollars)) {kill NoDollars;} |
---|
1676 | //echo =2; |
---|
1677 | |
---|
1678 | proc randompoly(int n,int cm,int em) |
---|
1679 | { |
---|
1680 | int i,j,k; |
---|
1681 | number nm,nom,denom; |
---|
1682 | poly f,g; |
---|
1683 | int nv,np=nvars(basering),npars(basering); |
---|
1684 | |
---|
1685 | for (i=1; i<=n; i++) |
---|
1686 | { |
---|
1687 | if (np) |
---|
1688 | { |
---|
1689 | // for(k=1; k<=2;k++) // zwei Terme |
---|
1690 | // { |
---|
1691 | nm=random(-cm,cm); |
---|
1692 | for (j=1;j<=np;j++) |
---|
1693 | { nm=nm*par(j)^random(-em/ 2,em/ 2);} |
---|
1694 | nom = nom + nm; |
---|
1695 | // } |
---|
1696 | // for(k=1; k<=2;k++) // zwei Terme |
---|
1697 | // { |
---|
1698 | nm=random(-cm,cm); |
---|
1699 | for (j=1;j<=np;j++) |
---|
1700 | { nm=nm*par(j)^random(-em/ 2,em/ 2);} |
---|
1701 | denom = denom + nm; |
---|
1702 | // } |
---|
1703 | if (denom!=0) {g = nom*denom^-1;} |
---|
1704 | else {g = 0;} |
---|
1705 | } |
---|
1706 | else |
---|
1707 | { g = random(-cm,cm); |
---|
1708 | } |
---|
1709 | for (j=1; j<=nv; j++) |
---|
1710 | { g=g*var(j)^random(0,em);} |
---|
1711 | f = f + g; |
---|
1712 | } |
---|
1713 | return(f); |
---|
1714 | } |
---|
1715 | |
---|
1716 | |
---|
1717 | |
---|
1718 | export randompoly; |
---|
1719 | |
---|
1720 | proc randomintv(int n, int m) |
---|
1721 | { |
---|
1722 | int i; |
---|
1723 | |
---|
1724 | for(i=1; i<=n; i++) |
---|
1725 | { |
---|
1726 | v[i]; |
---|
1727 | } |
---|
1728 | } |
---|
1729 | |
---|
1730 | |
---|
1731 | proc splt(string s) |
---|
1732 | { int n,i= size(s),1; |
---|
1733 | int p; |
---|
1734 | string t; |
---|
1735 | |
---|
1736 | while(n-i+1 >pagewidth) |
---|
1737 | { p = find(s,newline,i); |
---|
1738 | if (p and (p-i)<pagewidth) |
---|
1739 | { t = t + s[i,p]; |
---|
1740 | i = i + p; |
---|
1741 | } |
---|
1742 | else |
---|
1743 | { |
---|
1744 | t = t+ s[i,pagewidth] + newline; |
---|
1745 | i = i + pagewidth; |
---|
1746 | } |
---|
1747 | } |
---|
1748 | if (n) { t= t + s[i,n-i+1];} |
---|
1749 | return(t); |
---|
1750 | } |
---|
1751 | |
---|
1752 | export splt; |
---|
1753 | |
---|
1754 | // string fname = "texlibdemo.tex"; |
---|
1755 | string nl = newline; |
---|
1756 | string nl2 = newline + newline; |
---|
1757 | string lb = "\\\\"; |
---|
1758 | string bv = "\\begin{verbatim}" + newline ; |
---|
1759 | string ev = "\\end{verbatim}" ; |
---|
1760 | export nl,nl2,lb,bv,ev; //fname |
---|
1761 | |
---|
1762 | "generating part0 of " + fname + nl; |
---|
1763 | |
---|
1764 | opentex(fname); |
---|
1765 | |
---|
1766 | |
---|
1767 | write(fname,"\\newcommand{\\Line}{\\rule{\\textwidth}{0.25mm}\\\\[5mm]}"); |
---|
1768 | |
---|
1769 | write(fname,"\\centerline{\\large \\bf Demo file for latex.lib 1.0.0}"); |
---|
1770 | write(fname,"\\centerline{\\bf Christian Gorzel}"); |
---|
1771 | write(fname,"\\vspace{1cm}"); |
---|
1772 | |
---|
1773 | |
---|
1774 | //-- |
---|
1775 | |
---|
1776 | write(fname,"\\section{Introduction}"); |
---|
1777 | write(fname,"The procedures in \\verb|tex.lib| translate the output of |
---|
1778 | Singular in \\LaTeX text. Most of the examples in this document are generated |
---|
1779 | randomly by Singular itself and passed through the procs from \\verb|tex.lib|. |
---|
1780 | Consequently, every document doesnot show merely how the \\verb|tex.lib| works |
---|
1781 | but looks differently in large parts."); |
---|
1782 | write(fname,bv + |
---|
1783 | " |
---|
1784 | |
---|
1785 | LIBRARY: tex.lib PROCEDURES FOR TYPESET OF SINGULAROBJECTS IN TEX |
---|
1786 | |
---|
1787 | closetex(s); writes closing line for TeX-document |
---|
1788 | opentex(s); writes header for TeX-file s |
---|
1789 | tex(s); call latex for TeX-file s |
---|
1790 | texdemo(); produces a latex file explaining the features of this lib |
---|
1791 | texfactorize(fname,f); create string in TeX-Symbolformat for factors of poly f |
---|
1792 | texmap(fname,m,r1,r2); create string in TeX-Symbolformat for map m:r1->r2 |
---|
1793 | texname(fname,s); create string in TeX-Symbolformat for identifier |
---|
1794 | texobj(l); creates string in TeX-Symbolformat for any (basic) type |
---|
1795 | texpoly(f,n[,l]); creates string in TeX-Symbolformat for poly |
---|
1796 | texproc(fname,p); create string in TeX-Symbolformat of text from proc p |
---|
1797 | texring(fname,r[,l]); create string in TeX-Symbolformat for ring/qring |
---|
1798 | rmx(s); remove .aux and .log files of TeXfile s |
---|
1799 | xdvi(s); call xdvi for dvi-file s |
---|
1800 | (parameters in square brackets [] are optional) |
---|
1801 | |
---|
1802 | Global Variables: |
---|
1803 | TeXwidth, TeXnofrac, TeXbrack, TeXproj, TeXaligned, TeXreplace, NoDollars |
---|
1804 | are used to control the typesetting |
---|
1805 | Call example texdemo; to become familiar with the features of tex.lib |
---|
1806 | |
---|
1807 | " + |
---|
1808 | ev); |
---|
1809 | |
---|
1810 | write(fname,"A flag means in the following that a variable with the indicated |
---|
1811 | name has to be defined. Usually it is from type \\verb|int|."); |
---|
1812 | |
---|
1813 | |
---|
1814 | write(fname, |
---|
1815 | bv + |
---|
1816 | " |
---|
1817 | TeXwidth : int: -1,0,1..9, >9 controls the breaking of long polynomials |
---|
1818 | TeXnofrac : (int) flag, write 1/2 instead of \\frac{1}{2} |
---|
1819 | TeXbrack : string: possible values {,(,<,|, \"\" |
---|
1820 | controls brackets around ideals |
---|
1821 | TeXproj : (int) flag, write : instead of , in intvecs |
---|
1822 | TeXaligned : (int) flag, write mappings (and ideals) aligned |
---|
1823 | TeXreplace : list, entries twoelemented list for replacing symbols |
---|
1824 | NoDollars : (int) flag, suppresses surrounding \\$ signs |
---|
1825 | |
---|
1826 | " + |
---|
1827 | ev); |
---|
1828 | |
---|
1829 | //% The procs and |
---|
1830 | //% the global variables |
---|
1831 | |
---|
1832 | //----------------------- opentex ----------------------------- |
---|
1833 | write(fname,"\\section{Opening a \\LaTeX\\ file}"); |
---|
1834 | write(fname,"All starts by defining a variable " + nl |
---|
1835 | + bv + "> string fname = \"tldemo.tex\";" + nl + |
---|
1836 | "> texopen(fname);" + ev + nl); |
---|
1837 | write(fname,"This variable \\verb|fname| has to given as first argument to |
---|
1838 | all procedures in \\verb|tex.lib|"); |
---|
1839 | |
---|
1840 | //% opentex, defaulted to latex, possibly extension are ... and |
---|
1841 | //% ``own'' |
---|
1842 | |
---|
1843 | |
---|
1844 | pagewidth = 65; |
---|
1845 | int TeXwidth = 80; export TeXwidth; |
---|
1846 | "part 0 generated " + nl; |
---|
1847 | } //part0 |
---|
1848 | |
---|
1849 | |
---|
1850 | ///////////////////////////// PART1 ////////////////////////////////////////// |
---|
1851 | |
---|
1852 | |
---|
1853 | proc part1(string fname) |
---|
1854 | { int st = defined(texdemopart); |
---|
1855 | |
---|
1856 | if (not(st) or texdemopart>=1) |
---|
1857 | { print(" Call part0 first"); |
---|
1858 | return(); |
---|
1859 | } |
---|
1860 | else { texdemopart=1; } |
---|
1861 | |
---|
1862 | "Continuing part1 of " + fname + nl; |
---|
1863 | |
---|
1864 | write(fname, |
---|
1865 | "\\section{Rings and polynomials}"+nl2); |
---|
1866 | |
---|
1867 | // -1a------ a ring in char 0, short varnames and poly. ordering ---------- |
---|
1868 | write(fname, |
---|
1869 | " A ring in characteristic 0 with short variablenames and polynomial ordering. |
---|
1870 | " +nl); |
---|
1871 | ring r0=0,(x,y,z),dp; export r0; |
---|
1872 | poly g = -x2y +2y13z +1; export g; |
---|
1873 | poly f = randompoly(5,25,25); f; export f; |
---|
1874 | write(fname, |
---|
1875 | bv + |
---|
1876 | "> ring r0=0,(x,y,z),dp; texring(fname,r0); |
---|
1877 | > poly g = -x2y +2y13z +1; g; texpoly(fname,g);" +nl + |
---|
1878 | string(g) + nl + |
---|
1879 | "> poly f = randompoly(5,25,25); f; texpoly(fname,f);" +nl + |
---|
1880 | splt(string(f)) + nl2 + |
---|
1881 | ev |
---|
1882 | ); |
---|
1883 | texring(fname,r0); write(fname,nl2); |
---|
1884 | texpoly(fname,g); write(fname,nl2); |
---|
1885 | texpoly(fname,f); write(fname,nl2); |
---|
1886 | // write(fname,"\\Line"); |
---|
1887 | |
---|
1888 | // -1b------ stil in the same ring, the poly with rational coefs -------- |
---|
1889 | write(fname, |
---|
1890 | " The polynomial with rational coefficients. |
---|
1891 | " +nl); |
---|
1892 | f = f/280; |
---|
1893 | write(fname, |
---|
1894 | bv + |
---|
1895 | "> f = f/280; |
---|
1896 | > texpoly(fname,f);" +nl + |
---|
1897 | splt(string(f)) + nl2 + |
---|
1898 | ev |
---|
1899 | ); |
---|
1900 | texpoly(fname,f); write(fname,nl2); |
---|
1901 | write(fname,"\\Line"); |
---|
1902 | // -2-------- a ring in char 7, indexed varnames and series ordering ---------- |
---|
1903 | write(fname, |
---|
1904 | " A ring in characteristic 7 with indexed variablenames and local ordering. |
---|
1905 | " +nl); |
---|
1906 | ring r1=7,(x1,x2,x3,x4),Ds; export r1; |
---|
1907 | poly g = -2*x1 +x4 -1; |
---|
1908 | poly f = randompoly(5,25,25); f; export f; |
---|
1909 | write(fname, |
---|
1910 | bv + |
---|
1911 | "> ring r1=7,(x1,x2,x3,x4),Ds; texring(fname,r1); |
---|
1912 | > poly g = -2*x1 +x4 -1; g; texpoly(fname,g);" +nl + |
---|
1913 | string(g) + nl + |
---|
1914 | "> poly f = randompoly(5,25,25); f; texpoly(fname,f);" +nl + |
---|
1915 | splt(string(f)) + nl2 + |
---|
1916 | ev |
---|
1917 | ); |
---|
1918 | texring(fname,r1); write(fname,lb); |
---|
1919 | texpoly(fname,g); write(fname,lb); |
---|
1920 | texpoly(fname,f); write(fname,lb); |
---|
1921 | write(fname,"\\Line"); |
---|
1922 | |
---|
1923 | // -3-------- a ring in char 0, indexed varnames and mixed ordering ---------- |
---|
1924 | write(fname, |
---|
1925 | " A ring in characteristic 0 with indexed variablenames and mixed ordering. |
---|
1926 | " +nl); |
---|
1927 | ring r2=0,(x(1..5),y(1..2)),(ds(5),dp(2)); |
---|
1928 | poly g = -y(1)*x(5) +y(1)*x(2); g; |
---|
1929 | poly f = randompoly(5,25,25); f; |
---|
1930 | write(fname, |
---|
1931 | bv + |
---|
1932 | "> ring r2=0,(x(1..5),y(1..2)),(ds(5),dp(2)); texring(fname,r2); |
---|
1933 | > poly g = -y(1)*x(5) +y(1)*x(2); g; texpoly(fname,g);" +nl + |
---|
1934 | string(g) + nl + |
---|
1935 | "> poly f = randompoly(5,25,25); f; texpoly(fname,f);" +nl + |
---|
1936 | splt(string(f)) + nl2 + |
---|
1937 | ev |
---|
1938 | ); |
---|
1939 | texring(fname,r2); write(fname,lb); |
---|
1940 | texpoly(fname,g); write(fname,lb); |
---|
1941 | texpoly(fname,f); write(fname,lb); |
---|
1942 | write(fname,"\\Line"); |
---|
1943 | |
---|
1944 | // -4-------- a ring in char 0, indexed varnames and weighted ordering ------ |
---|
1945 | write(fname, |
---|
1946 | " A ring in characteristic 0 with indexed variablenames and weighted ordering. |
---|
1947 | " +nl); |
---|
1948 | ring r3=0,(x_1,x_2,x_3),wp(3,2,1); export r3; |
---|
1949 | poly g = -x_1*x_2 + 2*x_2*x_3 + x_1*x_3; g; |
---|
1950 | poly f = randompoly(5,25,25); f; export f; |
---|
1951 | write(fname, |
---|
1952 | bv + |
---|
1953 | "> ring r3=0,(x_1,x_2,x_3),wp(3,2,1); texring(fname,r3); |
---|
1954 | > poly g = -x_1*x_2 + 2*x_2*x_3 + x_1*x_3; g; texpoly(fname,g);" +nl + |
---|
1955 | string(g) + nl + |
---|
1956 | "> poly f = randompoly(5,25,25); f; texpoly(fname,f);" +nl + |
---|
1957 | splt(string(f)) + nl2 + |
---|
1958 | ev |
---|
1959 | ); |
---|
1960 | texring(fname,r3); write(fname,lb); |
---|
1961 | texpoly(fname,g); write(fname,lb); |
---|
1962 | texpoly(fname,f); write(fname,lb); |
---|
1963 | write(fname,"\\Line"); |
---|
1964 | |
---|
1965 | // -5-------- a ring with real coeff and matrix ordering ------------------- |
---|
1966 | write(fname, |
---|
1967 | " A ring with real coefficients and matrix ordering. |
---|
1968 | " +nl); |
---|
1969 | ring rr =real,(x,y),M(1,2,3,4); |
---|
1970 | poly g = -1.2e-10*x + y +1; |
---|
1971 | poly f = randompoly(5,25,25); f; |
---|
1972 | write(fname, |
---|
1973 | bv + |
---|
1974 | "> ring rr =real,(x,y),M(1,2,3,4); texring(fname,rr); |
---|
1975 | > poly g = -1.2e-10*x + y +1; g; texpoly(fname,g);" +nl + |
---|
1976 | string(g) + nl + |
---|
1977 | "> poly f = randompoly(5,25,25); f; texpoly(fname,f);" +nl + |
---|
1978 | splt(string(f)) + nl2 + |
---|
1979 | ev |
---|
1980 | ); |
---|
1981 | texring(fname,rr); write(fname,lb); |
---|
1982 | texpoly(fname,g); write(fname,lb); |
---|
1983 | texpoly(fname,f); write(fname,lb); |
---|
1984 | write(fname,"\\Line"); |
---|
1985 | |
---|
1986 | // -6a-------- a ring in char 0, and indexed parameters --------- ---------- |
---|
1987 | write(fname, |
---|
1988 | " A ring in characteristic 0 and indexed parameters. |
---|
1989 | " +nl); |
---|
1990 | ring r0t=(0,s,t),(x,y),dp; export r0t; |
---|
1991 | poly g = 8*(-s+2t)/(st+t3)*x + t2*x -1; g; |
---|
1992 | poly f = randompoly(5,25,25); f; export f; |
---|
1993 | write(fname, |
---|
1994 | bv + |
---|
1995 | "> ring r0t=(0,s,t),(x,y),dp; texring(fname,r0t); |
---|
1996 | > poly g = 8*(-s+2t)/(st+t3)*x + t2*x -1; g; texpoly(fname,g);" +nl + |
---|
1997 | string(g) + nl + |
---|
1998 | "> poly f = randompoly(5,25,25); f; texpoly(fname,f);" +nl + |
---|
1999 | splt(string(f)) + nl2 + |
---|
2000 | ev |
---|
2001 | ); |
---|
2002 | texring(fname,r0t); write(fname,lb); |
---|
2003 | texpoly(fname,g); write(fname,lb); |
---|
2004 | texpoly(fname,f); write(fname,lb); |
---|
2005 | write(fname,"\\Line"); |
---|
2006 | |
---|
2007 | |
---|
2008 | // -6b------- a ring in char 11, and indexed parameters --------- ---------- |
---|
2009 | write(fname, |
---|
2010 | " A ring in characteristic 11 and indexed parameters. |
---|
2011 | " +nl); |
---|
2012 | ring rt=(11111,t1,t2,t3),(X,Y),dp; |
---|
2013 | poly g = 8*(-t1+t2)/(t1+t3)*X + t2*Y -1; g; |
---|
2014 | poly f = randompoly(5,25,25); f; |
---|
2015 | write(fname, |
---|
2016 | bv + |
---|
2017 | "> ring rt=(11111,t1,t2,t3),(X,Y),dp; texring(fname,rt); |
---|
2018 | > poly g = 8*(-t1+t2)/(t1+t3)*X + t2*Y -1; g; texpoly(fname,g);" +nl + |
---|
2019 | string(g) + nl + |
---|
2020 | "> poly f = randompoly(5,25,25); f; texpoly(fname,f);" +nl + |
---|
2021 | splt(string(f)) + nl2 + |
---|
2022 | ev |
---|
2023 | ); |
---|
2024 | texring(fname,rt); write(fname,lb); |
---|
2025 | texpoly(fname,g); write(fname,lb); |
---|
2026 | texpoly(fname,f); write(fname,lb); |
---|
2027 | write(fname,"\\Line"); |
---|
2028 | |
---|
2029 | // -7-------- a ring over an algebraic extension in char 7 --------------- |
---|
2030 | write(fname, |
---|
2031 | " A ring over an algebraic extension in char 7. |
---|
2032 | " +nl); |
---|
2033 | ring ralg = (7,a),x,dp; |
---|
2034 | minpoly = a2-a+3; |
---|
2035 | poly g = -(2a13 +a)*x2 + a2*x -a +1; g; |
---|
2036 | poly f = randompoly(5,25,25); f; |
---|
2037 | write(fname, |
---|
2038 | bv + |
---|
2039 | "> ring ralg = (7,a),x,dp; |
---|
2040 | > minpoly = a2-a+3; texring(fname,ralg); |
---|
2041 | > poly g = -(2a13 +a)*x2 + a2*x -a +1; g; texpoly(fname,g);" +nl + |
---|
2042 | string(g) + nl + |
---|
2043 | "> poly f = randompoly(5,25,25); f; texpoly(fname,f);" +nl + |
---|
2044 | splt(string(f)) + nl2 + |
---|
2045 | ev |
---|
2046 | ); |
---|
2047 | texring(fname,ralg); write(fname,lb); |
---|
2048 | texpoly(fname,g); write(fname,lb); |
---|
2049 | texpoly(fname,f); write(fname,lb); |
---|
2050 | write(fname,"\\Line"); |
---|
2051 | |
---|
2052 | // -8-------- the same ring a in 7 ralg, defined with gftables -- F_49 ------- |
---|
2053 | write(fname, |
---|
2054 | " A ring defined with \\verb|gftables|, the same as \\verb|ralg| before, but |
---|
2055 | with primitive element in the Galoisfield $\\F_{49}$." +nl); |
---|
2056 | ring r49 =(49,a),x,dp; export r49; |
---|
2057 | poly g = -(2a13 +a)*x2 + a2*x -a +1; g; export g; |
---|
2058 | poly f = randompoly(5,25,25); f; |
---|
2059 | write(fname, |
---|
2060 | bv + |
---|
2061 | "> ring r49 =(49,a),x,dp; texring(fname,r49); |
---|
2062 | > poly g = -(2a13 +a)*x2 + a2*x -a +1; g; texpoly(fname,g);" +nl + |
---|
2063 | string(g) + nl + |
---|
2064 | "> poly f = randompoly(5,25,25); f; texpoly(fname,f);" +nl + |
---|
2065 | splt(string(f)) + nl2 + |
---|
2066 | ev |
---|
2067 | ); |
---|
2068 | texring(fname,r49); write(fname,lb); |
---|
2069 | texpoly(fname,g); write(fname,lb); |
---|
2070 | texpoly(fname,f); write(fname,lb); |
---|
2071 | write(fname,"\\Line"); |
---|
2072 | |
---|
2073 | // -9-------- a ring over the Gaussian numbers ---------- |
---|
2074 | write(fname, |
---|
2075 | " A ring over the Gaussian numbers. |
---|
2076 | " +nl); |
---|
2077 | ring ri=(0,i),(x,y,z),ls; |
---|
2078 | minpoly = i2 +1; |
---|
2079 | poly g = -(i+1)*x +2i2y2 +i +x; g; |
---|
2080 | poly f = randompoly(5,25,25); f; |
---|
2081 | write(fname, |
---|
2082 | bv + |
---|
2083 | "> ring ri=(0,i),(x,y,z),ls; |
---|
2084 | > minpoly = i2 +1; texring(fname,ri); |
---|
2085 | > poly g = -(i+1)*x +2i2y2 +i +x; g; texpoly(fname,g);" +nl + |
---|
2086 | string(g) + nl + |
---|
2087 | "> poly f = randompoly(5,25,25); f; texpoly(fname,f);" +nl + |
---|
2088 | splt(string(f)) + nl2 + |
---|
2089 | ev |
---|
2090 | ); |
---|
2091 | texring(fname,ri); write(fname,lb); |
---|
2092 | texpoly(fname,g); write(fname,lb); |
---|
2093 | texpoly(fname,f); write(fname,lb); |
---|
2094 | write(fname,"\\Line"); |
---|
2095 | |
---|
2096 | // -10--------- a quotient ring performed from ---------- |
---|
2097 | write(fname, |
---|
2098 | " A quotient ring . |
---|
2099 | " +nl); |
---|
2100 | setring r0; |
---|
2101 | ideal I = x2-y,y+z2, xy; |
---|
2102 | I = std(I); |
---|
2103 | string sI = string(I); |
---|
2104 | qring qr = I; |
---|
2105 | write(fname, |
---|
2106 | bv + |
---|
2107 | "> setring r0; |
---|
2108 | > ideal I = x2-y,y+z2, xy; |
---|
2109 | > I = std(I); |
---|
2110 | > string(I);" + nl + |
---|
2111 | splt(sI) + nl + |
---|
2112 | "> qring qr = I; texring(fname,qr);" + |
---|
2113 | ev |
---|
2114 | ); |
---|
2115 | texring(fname,qr); write(fname,lb); |
---|
2116 | |
---|
2117 | write(fname,"\\Line"); |
---|
2118 | |
---|
2119 | // ------------------------- Features for rings |
---|
2120 | |
---|
2121 | write(fname,"\\subsection{Features for rings}"); |
---|
2122 | |
---|
2123 | write(fname,"The printed form of the ring may be modified in a great variety"); |
---|
2124 | |
---|
2125 | // changing the brackets |
---|
2126 | |
---|
2127 | write(fname,"If the displayed and defaulted brackets for the ring are not |
---|
2128 | the rigth one, |
---|
2129 | correct brackets my be passed over to \\verb|texring|",nl, |
---|
2130 | "Predefined and accepted brackets are \\verb|\"\\{\"|,\\verb|\"\\{\"|, |
---|
2131 | \\verb|\"\\{\\{\"|,\\verb|\"[\"|,\\verb|\"[[\"|,\\verb|\"<\"|, |
---|
2132 | \\verb|\"<<\"|."); |
---|
2133 | |
---|
2134 | |
---|
2135 | write(fname, |
---|
2136 | bv + |
---|
2137 | "> texring(fname,rr,\"{{\");" + nl + |
---|
2138 | ev |
---|
2139 | ); |
---|
2140 | |
---|
2141 | texring(fname,rr,"{{"); |
---|
2142 | |
---|
2143 | write(fname, |
---|
2144 | bv + |
---|
2145 | "> texring(fname,r2,\"[\");" + nl + |
---|
2146 | ev |
---|
2147 | ); |
---|
2148 | |
---|
2149 | texring(fname,r2,"["); |
---|
2150 | |
---|
2151 | write(fname,nl2); |
---|
2152 | |
---|
2153 | write(fname,nl2,"The brackets around the ideal in a quotientring can be |
---|
2154 | changed with the global variable \\verb|TeXbrack| (see the section |
---|
2155 | {\\tt ideal}).",nl); |
---|
2156 | |
---|
2157 | |
---|
2158 | write(fname, |
---|
2159 | bv + |
---|
2160 | "> string TeXbrack = \"<\"; |
---|
2161 | > texring(fname,qr); |
---|
2162 | > kill TeXbrack;" + nl + |
---|
2163 | ev |
---|
2164 | ); |
---|
2165 | |
---|
2166 | string TeXbrack = "<"; export TeXbrack; |
---|
2167 | texring(fname,qr); |
---|
2168 | kill TeXbrack; |
---|
2169 | |
---|
2170 | write(fname,nl2,"\\Line"); |
---|
2171 | |
---|
2172 | // changing the coeffield |
---|
2173 | // ------------------------------------------------- |
---|
2174 | write(fname,"If the coefficientfield in charcteristic 0 should be written as |
---|
2175 | $\\C$ instead of $\\Q$ use this as additonal argument.",nl); |
---|
2176 | |
---|
2177 | |
---|
2178 | write(fname, |
---|
2179 | bv + |
---|
2180 | "> texring(fname,r3,\"\\\\C\");" + nl + |
---|
2181 | ev |
---|
2182 | ); |
---|
2183 | |
---|
2184 | texring(fname,r3,"\\C"); |
---|
2185 | write(fname,nl2); |
---|
2186 | |
---|
2187 | write(fname,nl2, "naechster abschnitt stimmt nicht"+lb,nl2); |
---|
2188 | |
---|
2189 | write(fname,"Predefined and accepted values here are |
---|
2190 | \\verb|\"\\\\C\"|, \\verb|\"\\\\R\"|, |
---|
2191 | \\verb|\"\\\\C\"|, \\verb|\"k\"|, \\verb|\"K\"|, \\verb|\"R\"|."); |
---|
2192 | write(fname,"The latter are useful to print a ring whose coefficientfield is |
---|
2193 | defined by an algebraic extension. Now the parameters will omitted completely. |
---|
2194 | "); |
---|
2195 | write(fname,"The user may specify then the field in more detail."+lb,nl2); |
---|
2196 | |
---|
2197 | write(fname,"Any correct letter in \\LaTeX \\ notation may be used to describe |
---|
2198 | the coefficientfield. If the letter is k, K or R it should ! forcew texring |
---|
2199 | not to print the parameters. This will be useful for a ring described by an |
---|
2200 | algebraic extension",nl2); |
---|
2201 | |
---|
2202 | write(fname, |
---|
2203 | bv + |
---|
2204 | "> texring(fname,ralg,\"k\");" + nl + |
---|
2205 | ev |
---|
2206 | ); |
---|
2207 | |
---|
2208 | texring(fname, ralg,"k"); |
---|
2209 | |
---|
2210 | // texobj(fname,"with k = "); |
---|
2211 | |
---|
2212 | write(fname,nl,"\\Line"); |
---|
2213 | // displaying only certain vars |
---|
2214 | |
---|
2215 | write(fname,"By default all variables of a ring will be typed. It is possible |
---|
2216 | to print only certain variables filled up with $\\ldots$ between them. Define |
---|
2217 | therefore an \\verb|intvec| with the marked places."); |
---|
2218 | |
---|
2219 | write(fname, |
---|
2220 | bv + |
---|
2221 | "> intvec v = 5,6; |
---|
2222 | > texring(fname,r2,v); |
---|
2223 | > kill v;" + nl + |
---|
2224 | ev |
---|
2225 | ); |
---|
2226 | |
---|
2227 | intvec v = 5,6; |
---|
2228 | texring(fname,r2,v); |
---|
2229 | kill v; |
---|
2230 | |
---|
2231 | write(fname,nl2,"The first and last variable |
---|
2232 | will be printed always, to print only these it is sufficient to give a 1 as |
---|
2233 | third argument."); |
---|
2234 | |
---|
2235 | write(fname, |
---|
2236 | bv + |
---|
2237 | "> texring(fname,r1,1);" + nl + |
---|
2238 | ev |
---|
2239 | ); |
---|
2240 | texring(fname,r1,1); |
---|
2241 | |
---|
2242 | |
---|
2243 | write(fname,nl2,"\\Line",nl); |
---|
2244 | |
---|
2245 | // passing over additional information |
---|
2246 | |
---|
2247 | write(fname,"If you want to mark a ring as the Invariantring under a group, |
---|
2248 | additional informations starting with \\verb|^| will be added.",nl2); |
---|
2249 | |
---|
2250 | write(fname, |
---|
2251 | bv + |
---|
2252 | "> texring(fname,r0,\"^G\");" + nl + |
---|
2253 | ev |
---|
2254 | ); |
---|
2255 | |
---|
2256 | texring(fname, r0,"^G"); |
---|
2257 | |
---|
2258 | write(fname,nl2,"All these arguments may be passed over in any order as |
---|
2259 | optional arguments, but it may completely --- result if too much of them |
---|
2260 | are used at the same time",nl); |
---|
2261 | |
---|
2262 | write(fname, |
---|
2263 | bv + |
---|
2264 | "> texring(fname,r3,\"\\\\R\",1,\"{{\",\"^G\");" + nl + |
---|
2265 | ev |
---|
2266 | ); |
---|
2267 | |
---|
2268 | texring(fname, r3,"\\R",1,"<<","^G"); |
---|
2269 | |
---|
2270 | write(fname,nl2); |
---|
2271 | |
---|
2272 | export r0,ralg; |
---|
2273 | "end part 1" + nl; |
---|
2274 | } |
---|
2275 | |
---|
2276 | |
---|
2277 | ///////////////////////////// PART2 ////////////////////////////////////////// |
---|
2278 | |
---|
2279 | |
---|
2280 | proc part2(string fname) |
---|
2281 | { int st = defined(texdemopart); |
---|
2282 | |
---|
2283 | if (not(st) or texdemopart>=2) |
---|
2284 | { print(" Call part1 first"); |
---|
2285 | return(); |
---|
2286 | } |
---|
2287 | else { texdemopart=2; } |
---|
2288 | |
---|
2289 | "Continuing Part2 of " + fname + nl; |
---|
2290 | |
---|
2291 | //-------------------- texfactorize ------------------------------ |
---|
2292 | write(fname,"\\subsection{Factorized polynomials}"); |
---|
2293 | |
---|
2294 | write(fname,"The command \\verb|texfactorize| calls internally the Singular |
---|
2295 | command \\verb|factorize| and returns the product of the irreducible factors. |
---|
2296 | at the present it is not possible to pass the optional arguments of |
---|
2297 | \\verb|factorize| through \\verb|texfactorize|."+lb); |
---|
2298 | |
---|
2299 | setring r0; |
---|
2300 | poly h = (x+1+y)^2*x3y*(2x -2y)*y12*x2*z2; |
---|
2301 | //h; |
---|
2302 | write(fname, |
---|
2303 | bv + |
---|
2304 | "> setring r0; |
---|
2305 | > poly h = (x+1+y)^2*x3y*(2x -2y)*y12*z2; |
---|
2306 | > h; |
---|
2307 | > " + splt(string(h)) + nl + |
---|
2308 | "> texfactorize(fname,h); |
---|
2309 | " + nl + |
---|
2310 | ev); |
---|
2311 | |
---|
2312 | texfactorize(fname,h); |
---|
2313 | |
---|
2314 | setring ralg; |
---|
2315 | poly h = (a24x5 + x3)*a2x6*(x+1)^2; |
---|
2316 | //h; |
---|
2317 | write(fname, |
---|
2318 | bv + |
---|
2319 | "> setring ralg; |
---|
2320 | > poly h = (a24x5 + x3)*a2x6*(x+1)^2; |
---|
2321 | > h; |
---|
2322 | > " + splt(string(h)) + nl + |
---|
2323 | "> texfactorize(fname,h); |
---|
2324 | " + nl + |
---|
2325 | ev); |
---|
2326 | |
---|
2327 | texfactorize(fname,h); |
---|
2328 | |
---|
2329 | |
---|
2330 | write(fname,nl2,"If \\verb|texfactorize| is called by the name of the polynom, |
---|
2331 | the result is the following" + lb,nl); |
---|
2332 | |
---|
2333 | |
---|
2334 | write(fname,nl2, "Noch nicht implemtiert" + lb,nl2); |
---|
2335 | |
---|
2336 | |
---|
2337 | //write(fname,"\\subsection{Hilbertpolynomials}"); |
---|
2338 | |
---|
2339 | //--------------------- features for polynomials ----------------- |
---|
2340 | write(fname,"\\subsection{Features for polynomials}"); |
---|
2341 | |
---|
2342 | |
---|
2343 | write(fname,"very long variables will be set correctly too. Furthermore, |
---|
2344 | but we cannot demonstrate it here, |
---|
2345 | the Laurentpolynomials with negative exponents will be translated."+ lb); |
---|
2346 | |
---|
2347 | |
---|
2348 | |
---|
2349 | // TeXreplace |
---|
2350 | // --------------------------------------------- |
---|
2351 | write(fname,"The global variable \\verb|TeXreplace| must be a list |
---|
2352 | whose entries are twoelemented lists again; wherby the first entry is the |
---|
2353 | word which should be replaced and second is the replacing word." + lb + |
---|
2354 | "---- ---- this holds for texname anmd texmap too ---- ---- " + lb + |
---|
2355 | "It is most usefule to write the greec letters correctly. Notice to write |
---|
2356 | a \\verb|\\\\\ | at the beginning of a \\TeX \\ symbol." + lb); |
---|
2357 | |
---|
2358 | |
---|
2359 | // Example |
---|
2360 | |
---|
2361 | write(fname,"Usually we write $\\xi$ for the primitive element:"+ lb); |
---|
2362 | list TeXreplace; export TeXreplace; |
---|
2363 | TeXreplace[1] = list("a","\\xi"); |
---|
2364 | setring r49; |
---|
2365 | |
---|
2366 | write(fname, |
---|
2367 | bv + |
---|
2368 | "> list TeXreplace; |
---|
2369 | > TeXreplace[1] = list(\"a\",\"\\\\xi\"); |
---|
2370 | > setring r49; |
---|
2371 | > texpoly(fname,g); |
---|
2372 | " + nl + |
---|
2373 | ev); |
---|
2374 | |
---|
2375 | texpoly(fname,g); |
---|
2376 | |
---|
2377 | write(fname,nl2,"Let us write $\\lambda$ and $\\mu$ for deforming parameters" |
---|
2378 | +lb); |
---|
2379 | TeXreplace[2]= list("s","\\lambda"); |
---|
2380 | TeXreplace[3]= list("t","\\mu"); |
---|
2381 | setring(r0t); |
---|
2382 | |
---|
2383 | write(fname, |
---|
2384 | bv + |
---|
2385 | "> TeXreplace[2]= list(\"s\",\"\\\\lambda\"); |
---|
2386 | > TeXreplace[3]= list(\"t\",\"\\\\mu\"); |
---|
2387 | > setring(r0t); |
---|
2388 | > texpoly(fname,f); |
---|
2389 | " + nl + |
---|
2390 | ev); |
---|
2391 | |
---|
2392 | texpoly(fname,f); |
---|
2393 | |
---|
2394 | |
---|
2395 | write(fname,nl2,"let us write $\\tilde{y}$ for $x$" + lb); |
---|
2396 | |
---|
2397 | TeXreplace[4] = list("x","\\tilde{y}"); |
---|
2398 | setring r1; |
---|
2399 | |
---|
2400 | |
---|
2401 | write(fname, |
---|
2402 | bv + |
---|
2403 | "> TeXreplace[4] = list(\"x\",\"\\\\tilde{y}\"); |
---|
2404 | > setring r1; |
---|
2405 | > texpoly(fname,f); |
---|
2406 | > kill TeXreplace; |
---|
2407 | " + nl + |
---|
2408 | ev); |
---|
2409 | |
---|
2410 | texobj(fname,f); |
---|
2411 | kill TeXreplace; |
---|
2412 | |
---|
2413 | write(fname,"If \\verb|TeXreplace| is defined, the translation into \\TeX--code |
---|
2414 | runs significantly slower, because every polynom will be compiled in the |
---|
2415 | \\verb|non short| mode."+ lb ); |
---|
2416 | |
---|
2417 | |
---|
2418 | write(fname,nl,"\\Line"); |
---|
2419 | //linebreaking TeXwdith |
---|
2420 | //----------------------------------------------------------------------- |
---|
2421 | write(fname,"The global variable \\verb|TeXwidth| controls the wrapping of |
---|
2422 | polynomials; possible values are:" + lb); |
---|
2423 | |
---|
2424 | write(fname, |
---|
2425 | "\\[ " + nl + |
---|
2426 | "TeXwidth = ", |
---|
2427 | "\\begin{cases} ", |
---|
2428 | " -1 & \\text{no linebreaking} \\\\ ", |
---|
2429 | " 0 & \\text{print the polynom as equation} f=0 \\\\ ", |
---|
2430 | " 1,\\ldots,5 & \\text{ the first n termes followed by the sign of the next |
---|
2431 | term} \\\\ ", |
---|
2432 | " > 5 & \\text{wrapping after n letters corresponding x} ", |
---|
2433 | "\\end{cases}", |
---|
2434 | "\\]",nl); |
---|
2435 | |
---|
2436 | write(fname,"Notice that two letters as x counts as three subscripts or |
---|
2437 | exponents",nl); |
---|
2438 | |
---|
2439 | |
---|
2440 | write(fname,nl,"\\Line",nl); |
---|
2441 | //---------------------------------------------------------- |
---|
2442 | |
---|
2443 | write(fname,"\\verb|TeXwidth| is the only global variable which will be |
---|
2444 | from Singular automatically. Its default value is -1 |
---|
2445 | i.e. wrapping is set off"+ lb); |
---|
2446 | |
---|
2447 | // Examples: |
---|
2448 | |
---|
2449 | write(fname,"\\begin{itemize}",nl); |
---|
2450 | write(fname,"\\item",nl); |
---|
2451 | |
---|
2452 | write(fname,"Up to now the value is -1"); |
---|
2453 | |
---|
2454 | write(fname, |
---|
2455 | bv + |
---|
2456 | "> TeXwidth; |
---|
2457 | " + nl + |
---|
2458 | string(TeXwidth) + |
---|
2459 | ev); |
---|
2460 | |
---|
2461 | |
---|
2462 | write(fname, |
---|
2463 | bv + |
---|
2464 | "> setring r0; |
---|
2465 | > poly h = f^2; |
---|
2466 | > texpoly(fname,h); |
---|
2467 | " + nl + |
---|
2468 | ev); |
---|
2469 | |
---|
2470 | setring r0; |
---|
2471 | poly h = f^2; |
---|
2472 | texpoly(fname,h); |
---|
2473 | |
---|
2474 | write(fname,"\\item",nl); |
---|
2475 | |
---|
2476 | write(fname, |
---|
2477 | bv + |
---|
2478 | "> TeXwidth =0; |
---|
2479 | > texpoly(fname,g); |
---|
2480 | " + nl + |
---|
2481 | ev); |
---|
2482 | TeXwidth = 0; |
---|
2483 | texpoly(fname,g); |
---|
2484 | |
---|
2485 | write(fname,"\\item",nl); |
---|
2486 | |
---|
2487 | write(fname, |
---|
2488 | bv + |
---|
2489 | "> TeXwidth = 2; |
---|
2490 | > texpoly(fname,f); |
---|
2491 | " + nl + |
---|
2492 | ev); |
---|
2493 | TeXwidth = 2; |
---|
2494 | texpoly(fname,h); |
---|
2495 | write(fname,"\\item",nl); |
---|
2496 | |
---|
2497 | write(fname, |
---|
2498 | bv + |
---|
2499 | "> TeXwidth = 60; |
---|
2500 | > texobj(fname,h); |
---|
2501 | " + nl + |
---|
2502 | ev); |
---|
2503 | TeXwidth = 60; |
---|
2504 | texobj(fname,h); |
---|
2505 | |
---|
2506 | write(fname,"\\end{itemize}",nl); |
---|
2507 | |
---|
2508 | // overread for \[ and \] ??? |
---|
2509 | |
---|
2510 | // offset for texpoly |
---|
2511 | |
---|
2512 | write(fname,nl2,"\\Line",nl); |
---|
2513 | |
---|
2514 | write(fname,nl2, " offset for poly " + lb, nl); |
---|
2515 | |
---|
2516 | write(fname,nl2,"\\Line",nl); |
---|
2517 | |
---|
2518 | write(fname,"As seen there are two possibilities to tex a polynomial. The |
---|
2519 | command \\verb|texpoly| is the most basic one and sets the polynomials in |
---|
2520 | textmode. Notice that it counts the length of the terms convenientely." + lb + |
---|
2521 | " The command \\verb|texobj| is the most general one, if a polynomial |
---|
2522 | will be texed with this command, it will be written in display mode and |
---|
2523 | the length of the terms will be counted .... ." + lb,nl2, |
---|
2524 | "Let us compare the output for \\verb|texpoly| and \\verb|texobj|."+lb); |
---|
2525 | |
---|
2526 | |
---|
2527 | write(fname, |
---|
2528 | bv + |
---|
2529 | "> setring r3; |
---|
2530 | > texpoly(fname,f);" + nl + |
---|
2531 | ev); |
---|
2532 | |
---|
2533 | |
---|
2534 | setring r3; |
---|
2535 | texpoly(fname,f); |
---|
2536 | |
---|
2537 | write(fname,nl2, "Now the same again with \\verb|texobj| "+ lb,nl); |
---|
2538 | |
---|
2539 | write(fname, |
---|
2540 | bv + |
---|
2541 | "> texobj(fname,f); |
---|
2542 | " + nl + |
---|
2543 | ev); |
---|
2544 | |
---|
2545 | texobj(fname,f); |
---|
2546 | |
---|
2547 | |
---|
2548 | write(fname,"Some explaination how it works: if \\verb|texobj| is called for |
---|
2549 | a polynomial, then it defines a global variable \\verb|TeXdisp| which forces |
---|
2550 | \\verb|texpoly| to count fraction with space corresponding |
---|
2551 | the displaymode."+lb,nl2); |
---|
2552 | |
---|
2553 | |
---|
2554 | |
---|
2555 | //---------------------texobj for ideal --------------- |
---|
2556 | write(fname,"\\section{ideal}"); |
---|
2557 | write(fname,"Ideal will just be printed as they are"); |
---|
2558 | |
---|
2559 | |
---|
2560 | ring r; |
---|
2561 | ideal I = 3xz5+x2y3-3z,7xz5+y3z+x-z,-xyz2+4yz+2x; |
---|
2562 | |
---|
2563 | |
---|
2564 | write(fname, |
---|
2565 | bv + |
---|
2566 | "> ring r; // the default one |
---|
2567 | > ideal I = 3xz5+x2y3-3z,7xz5+y3z+x-z,-xyz2+4yz+2x; |
---|
2568 | > texobj(fname,I);" + nl + |
---|
2569 | ev + nl); |
---|
2570 | |
---|
2571 | texobj(fname,I); |
---|
2572 | |
---|
2573 | write(fname,"\\subsection{Features for ideals}"); |
---|
2574 | //---------------------------------------------------------------------- |
---|
2575 | write(fname," With setting of \\verb|TeXaligned| the ideal will be set in |
---|
2576 | line "); |
---|
2577 | |
---|
2578 | write(fname, |
---|
2579 | bv + |
---|
2580 | "> int TeXaligned; |
---|
2581 | > texobj(fname,I);" + nl + |
---|
2582 | ev); |
---|
2583 | |
---|
2584 | int TeXaligned; export TeXaligned; |
---|
2585 | texobj(fname,I); |
---|
2586 | |
---|
2587 | write(fname,"\\Line"); |
---|
2588 | //---------------------------------------------------------------------- |
---|
2589 | write(fname,"If you prefer other brackets just set them"); |
---|
2590 | |
---|
2591 | write(fname, |
---|
2592 | bv + |
---|
2593 | "> string TeXbrack = \"<\"; |
---|
2594 | > texobj(fname,I); |
---|
2595 | > kill TeXbrack, TeXaligned;" + nl + |
---|
2596 | ev); |
---|
2597 | |
---|
2598 | |
---|
2599 | string TeXbrack = "<"; export TeXbrack; |
---|
2600 | texobj(fname,I); |
---|
2601 | kill TeXbrack,TeXaligned; |
---|
2602 | write(fname,"\\Line"); |
---|
2603 | //---------------------------------------------------------------------- |
---|
2604 | write(fname, |
---|
2605 | " If \\verb|TeXwidth| is set 0, an ideal will be set as an equation system |
---|
2606 | " +nl); |
---|
2607 | |
---|
2608 | |
---|
2609 | // ------------- a linear equation system |
---|
2610 | |
---|
2611 | ring r5 = 0,x(1..5),dp; |
---|
2612 | ideal I = -x(1) + 2*x(3) + x(5),x(2) -x(4) +2*x(5) -1,8*x(1) +x(4) +2; |
---|
2613 | |
---|
2614 | TeXwidth = 0; |
---|
2615 | write(fname, |
---|
2616 | bv + |
---|
2617 | "> ring r5 = 0,x(1..5),dp ; |
---|
2618 | > ideal I = -x(1) + 2*x(3) + x(5),x(2) -x(4) +2*x(5) -1,8*x(1) +x(4) +2; |
---|
2619 | > string(I);" + nl + |
---|
2620 | splt(string(I)) + nl2 + |
---|
2621 | "> TeXwidth = 0; |
---|
2622 | > texobj(fname,I);" + |
---|
2623 | //> TeXwidth = 0;" + |
---|
2624 | ev |
---|
2625 | ); |
---|
2626 | |
---|
2627 | texobj(fname,I); |
---|
2628 | // TeXwidth = -1; |
---|
2629 | |
---|
2630 | setring r; |
---|
2631 | ideal J; |
---|
2632 | J[1] = randompoly(2,5,25); |
---|
2633 | J[2] = randompoly(4,15,25); |
---|
2634 | J[3] = randompoly(2,5,25); |
---|
2635 | J[4] = randompoly(3,10,25); |
---|
2636 | J[5] = randompoly(2,20,25); |
---|
2637 | |
---|
2638 | string(J); |
---|
2639 | |
---|
2640 | write(fname, |
---|
2641 | bv + |
---|
2642 | "> setring r; |
---|
2643 | > J[1] = randompoly(2,5,25); |
---|
2644 | > J[2] = randompoly(4,15,25); |
---|
2645 | > J[3] = randompoly(2,5,25); |
---|
2646 | > J[4] = randompoly(3,10,25); |
---|
2647 | > J[5] = randompoly(2,20,25); |
---|
2648 | > string(J); |
---|
2649 | " + nl + string(J) + |
---|
2650 | ev |
---|
2651 | ); |
---|
2652 | |
---|
2653 | |
---|
2654 | write(fname, |
---|
2655 | bv + |
---|
2656 | "> texobj(fname,J);" + |
---|
2657 | ev |
---|
2658 | ); |
---|
2659 | |
---|
2660 | texobj(fname,J); |
---|
2661 | //% TeXwidth = 0; TeXbrackets |
---|
2662 | |
---|
2663 | write(fname,"\\Line"); |
---|
2664 | //----------------------------------------------------------------------- |
---|
2665 | write(fname,"Call the ideal by its name and it will be printed as follows"); |
---|
2666 | write(fname, |
---|
2667 | bv + |
---|
2668 | "> setring r; |
---|
2669 | > ideal I = 3xz5+x2y3-3z,7xz5+y3z+x-z,-xyz2+4yz+2x; |
---|
2670 | > texobj(fname,\"I\");" + nl + |
---|
2671 | ev); |
---|
2672 | |
---|
2673 | setring r; |
---|
2674 | ideal I = 3xz5+x2y3-3z,7xz5+y3z+x-z,-xyz2+4yz+2x; |
---|
2675 | export r; |
---|
2676 | export I; |
---|
2677 | listvar(r); |
---|
2678 | texobj(fname,"I"); |
---|
2679 | |
---|
2680 | // kill r; |
---|
2681 | " end part 2 " + nl; |
---|
2682 | } |
---|
2683 | |
---|
2684 | ///////////////////////////// PART3 ////////////////////////////////////////// |
---|
2685 | |
---|
2686 | |
---|
2687 | proc part3(string fname) |
---|
2688 | { int st = defined(texdemopart); |
---|
2689 | |
---|
2690 | if (not(st) or st>=3) |
---|
2691 | { print(" Call part2 first"); |
---|
2692 | return(); |
---|
2693 | } |
---|
2694 | else { texdemopart=3; } |
---|
2695 | |
---|
2696 | " Continuing part 3 of " + fname + |
---|
2697 | " : map,matrices,vectors,intvec,intmats,proc"; |
---|
2698 | |
---|
2699 | //---------------------- texmap ------------------------------ |
---|
2700 | write(fname,"\\section{maps}"); |
---|
2701 | // TeXwidth; |
---|
2702 | // int TeXwidth =-1; |
---|
2703 | write(fname,bv + |
---|
2704 | "> ring r1=0,(x,y,z),dp; |
---|
2705 | > ring r2=0,(u,v),dp; |
---|
2706 | > map phi = r1,u2,uv -v,v2; |
---|
2707 | > texmap(fname,phi,r1,r2,\"\\\\C\");" + nl + |
---|
2708 | ev ); |
---|
2709 | ring r1=0,(x,y,z),dp; export r1; |
---|
2710 | ring r2=0,(u,v),dp; |
---|
2711 | map phi =r1,u2,uv -v,v2; export phi; |
---|
2712 | texmap(fname,phi,r1,r2,"\\C"); |
---|
2713 | |
---|
2714 | |
---|
2715 | write(fname,"\\subsection{Features for maps}"); |
---|
2716 | //-------------------------------------------------------------------- |
---|
2717 | |
---|
2718 | |
---|
2719 | write(fname,"\\begin{itemize}",nl); |
---|
2720 | |
---|
2721 | write(fname,"\\item",nl); |
---|
2722 | |
---|
2723 | write(fname,"If the map will be called by its name \\verb|texmap| can in |
---|
2724 | combination with \\verb|TeXreplace| print the name of the map." + lb ,nl); |
---|
2725 | |
---|
2726 | write(fname,bv + |
---|
2727 | "> list TeXreplace; |
---|
2728 | > TeXreplace[1] = list(\"phi\",\"\\\\phi\"); |
---|
2729 | > texmap(fname,\"phi\",r1,r2);" + nl + |
---|
2730 | ev); |
---|
2731 | |
---|
2732 | list TeXreplace; |
---|
2733 | TeXreplace[1] = list("phi","\\phi"); |
---|
2734 | export TeXreplace; |
---|
2735 | texmap(fname,"phi",r1,r2); |
---|
2736 | |
---|
2737 | write(fname,"\\item",nl); |
---|
2738 | |
---|
2739 | write(fname,"With \\verb|TeXaligned| the map will be printed in a line"+lb,nl); |
---|
2740 | |
---|
2741 | write(fname,bv + |
---|
2742 | "> int TeXaligned; |
---|
2743 | > texmap(fname,phi,r1,r2,\"\\\\C\");" + nl + |
---|
2744 | ev ); |
---|
2745 | |
---|
2746 | int TeXaligned; export TeXaligned; |
---|
2747 | texmap(fname,phi,r1,r2,"\\C"); |
---|
2748 | |
---|
2749 | write(fname,"\\item",nl); |
---|
2750 | |
---|
2751 | write(fname,nl2,"The addtional arguments for \\verb|rings| may be passed over |
---|
2752 | in \\verb|texmap|.",nl); |
---|
2753 | |
---|
2754 | write(fname,"In the following form the arguments are valid for both |
---|
2755 | \\verb|rings|.",nl); |
---|
2756 | |
---|
2757 | write(fname,bv + |
---|
2758 | "> texmap(fname,\"phi\",r1,r2,\"\\\\C\",\"{\",1); " + nl + |
---|
2759 | ev ); |
---|
2760 | |
---|
2761 | texmap(fname,"phi",r1,r2,"\\C","{",1); |
---|
2762 | |
---|
2763 | write(fname,"\\\\",nl2,"If they are enclosed in \\verb|list( )| the arguments |
---|
2764 | may specialized in ",nl); |
---|
2765 | |
---|
2766 | |
---|
2767 | write(fname,bv + |
---|
2768 | "> intvec v = 2;", |
---|
2769 | "> texmap(fname,\"phi\",r1,r2,list(),list(v,\"{\"));", |
---|
2770 | "> kill r1,r2,TeXreplace,TeXaligned;" + nl + |
---|
2771 | ev ); |
---|
2772 | |
---|
2773 | intvec v = 2; |
---|
2774 | texmap(fname,"phi",r1,r2,list(),list(v,"{")); |
---|
2775 | |
---|
2776 | "map _Ende"; |
---|
2777 | kill r1,r2,TeXreplace,TeXaligned; |
---|
2778 | |
---|
2779 | write(fname,"\\end{itemize}",nl); |
---|
2780 | |
---|
2781 | //% the texobj part |
---|
2782 | write(fname,"\\section{basic, composed data}"); |
---|
2783 | //======================================================================= |
---|
2784 | |
---|
2785 | write(fname, "Now we present the most general procedure \\verb|texobj| to |
---|
2786 | translate composed Singularobjects into \\LaTeX \\ code"+lb,nl); |
---|
2787 | |
---|
2788 | write(fname,"\\section{matrices and vectors}"); |
---|
2789 | //======================================================================= |
---|
2790 | |
---|
2791 | write(fname,bv + |
---|
2792 | "> ring r;", |
---|
2793 | "> poly h = 2xy3-x2z+x4z7 + y4z2;", |
---|
2794 | "> matrix H = jacob(jacob(h));", |
---|
2795 | "> texobj(fname,H);", |
---|
2796 | ev ); |
---|
2797 | |
---|
2798 | ring r; |
---|
2799 | poly h = 2xy3-x2z+x4z7 + y4z2; |
---|
2800 | matrix H = jacob(jacob(h)); |
---|
2801 | |
---|
2802 | texobj(fname,H); |
---|
2803 | |
---|
2804 | // probiere auch V = 0 bei texobj aus |
---|
2805 | matrix M = H; |
---|
2806 | |
---|
2807 | write(fname,"A \\verb|vector| will be set as one column:"+lb ,nl); |
---|
2808 | |
---|
2809 | // Das geht nicht ? |
---|
2810 | vector V = M[2]; |
---|
2811 | |
---|
2812 | vector W= [x,y,0,z]; |
---|
2813 | |
---|
2814 | write(fname,bv + |
---|
2815 | "> matrix M = H;", |
---|
2816 | "> vector V = M[2];", |
---|
2817 | "> vector W= [x,y,0,z];", |
---|
2818 | "> texobj(fname,V);", |
---|
2819 | ev ); |
---|
2820 | |
---|
2821 | texobj(fname,V); |
---|
2822 | |
---|
2823 | write(fname,bv + |
---|
2824 | "> texobj(fname,W);", |
---|
2825 | ev ); |
---|
2826 | |
---|
2827 | |
---|
2828 | texobj(fname,W); |
---|
2829 | |
---|
2830 | |
---|
2831 | write(fname,"To turn it just the cast \\verb|matrix| here"+ lb,nl); |
---|
2832 | write(fname,bv + |
---|
2833 | "> texobj(fname,matrix(V));", |
---|
2834 | ev ); |
---|
2835 | |
---|
2836 | |
---|
2837 | texobj(fname,matrix(V)); |
---|
2838 | |
---|
2839 | write(fname,"\\subsection{Features for matrices and vectors}"); |
---|
2840 | //------------------------------------------------------------------------ |
---|
2841 | |
---|
2842 | write(fname,"All the features for \\verb|poly| and the features for |
---|
2843 | \\verb|intmat| or \\verb|intvec| hold here, too."); |
---|
2844 | |
---|
2845 | write(fname,"Display only the jet of the Hessian"); |
---|
2846 | |
---|
2847 | write(fname,bv + |
---|
2848 | "> TeXwidth = 1;", |
---|
2849 | "> texobj(fname,H);", |
---|
2850 | "> TeXwidth = -1;", |
---|
2851 | ev ); |
---|
2852 | |
---|
2853 | TeXwidth = 1; |
---|
2854 | texobj(fname,H); |
---|
2855 | TeXwidth = -1; |
---|
2856 | |
---|
2857 | write(fname,nl,"\\Line"); |
---|
2858 | //------------------------------------------------------------------------ |
---|
2859 | write(fname,"Set rational numbers as you like"+lb,nl); |
---|
2860 | |
---|
2861 | write(fname,bv + |
---|
2862 | "> ring r0 = 0,x,dp;", |
---|
2863 | "> matrix M[2][3] = 1/2, 0, 1/2, 0, 1/3, 2/3;", |
---|
2864 | "> texobj(fname,M);", |
---|
2865 | ev); |
---|
2866 | |
---|
2867 | |
---|
2868 | ring r0 = 0,x,dp; |
---|
2869 | matrix M[2][3] = 1/2, 0, 1/2, 0, 1/3, 2/3; |
---|
2870 | texobj(fname,M); |
---|
2871 | |
---|
2872 | write(fname,bv + |
---|
2873 | "> int TeXnofrac;", |
---|
2874 | "> texobj(fname,M);", |
---|
2875 | "> kill TeXnofrac;", |
---|
2876 | ev ); |
---|
2877 | |
---|
2878 | int TeXnofrac; export TeXnofrac; |
---|
2879 | texobj(fname,M); |
---|
2880 | kill TeXnofrac; |
---|
2881 | |
---|
2882 | write(fname,nl,"\\Line"); |
---|
2883 | //------------------------------------------------------------------------ |
---|
2884 | |
---|
2885 | write(fname,nl,"Print a vector with homogenous coordinates "); |
---|
2886 | write(fname,bv + |
---|
2887 | "> setring r;", |
---|
2888 | "> int TeXproj;", |
---|
2889 | "> texobj(fname,V);", |
---|
2890 | "> kill TeXproj;", |
---|
2891 | ev ); |
---|
2892 | |
---|
2893 | setring r; |
---|
2894 | int TeXproj; export TeXproj; |
---|
2895 | texobj(fname,V); |
---|
2896 | kill TeXproj; |
---|
2897 | |
---|
2898 | write(fname,"\\section{modules}",nl2); |
---|
2899 | |
---|
2900 | write(fname,bv + |
---|
2901 | "> setring r;", |
---|
2902 | "> module md = module(H);", |
---|
2903 | "> texobj(fname,md);", |
---|
2904 | ev ); |
---|
2905 | |
---|
2906 | setring r; |
---|
2907 | module md = module(H); |
---|
2908 | texobj(fname,md); |
---|
2909 | |
---|
2910 | write(fname,"\\subsection{Features for modules}"); |
---|
2911 | |
---|
2912 | write(fname,"Set a module aligned",nl2); |
---|
2913 | |
---|
2914 | write(fname,bv + |
---|
2915 | "> int TeXaligned;", |
---|
2916 | "> texobj(fname,md);", |
---|
2917 | "> kill TeXaligned;", |
---|
2918 | ev ); |
---|
2919 | |
---|
2920 | int TeXaligned; export TeXaligned; |
---|
2921 | texobj(fname,md); |
---|
2922 | kill TeXaligned; |
---|
2923 | |
---|
2924 | // write(fname,"\\section{Bettinumbers}"); |
---|
2925 | |
---|
2926 | |
---|
2927 | //---------------------------------------------------------------- |
---|
2928 | write(fname,"\\section{intvec and intmat}"); |
---|
2929 | |
---|
2930 | write(fname,"Despite of the fact that a \\verb|intvec| is in Singular a column |
---|
2931 | vector, the \\verb|tex.lib| sets it as a row vector ust as Singular displays it |
---|
2932 | "); |
---|
2933 | intvec v = 1..4; |
---|
2934 | write(fname, |
---|
2935 | bv + |
---|
2936 | "> intvec v = 1..4; |
---|
2937 | > v;" + nl + |
---|
2938 | string(v) + nl + |
---|
2939 | "> nrows(v);" + nl + |
---|
2940 | string(nrows(v)) + nl + |
---|
2941 | "texobj(fname,v);" + nl2 + |
---|
2942 | ev ); |
---|
2943 | |
---|
2944 | texobj(fname,v); |
---|
2945 | |
---|
2946 | |
---|
2947 | intmat m[3][4] = -1,3,5,2,-2,8,6,0,2,5,8,7; |
---|
2948 | m; |
---|
2949 | |
---|
2950 | write(fname, |
---|
2951 | bv + |
---|
2952 | "> intmat m[3][4] = -1,3,5,2,-2,8,6,0,2,5,8,7;" + nl + |
---|
2953 | "> m;" + nl + |
---|
2954 | string(m) + nl + |
---|
2955 | "> texobj(fname,m);" + nl2 + |
---|
2956 | ev ); |
---|
2957 | |
---|
2958 | texobj(fname,m); |
---|
2959 | |
---|
2960 | //----------------------------------------------------------------- |
---|
2961 | write(fname,"\\subsection{Features for intvec and intmat}"); |
---|
2962 | |
---|
2963 | write(fname,"If the \\verb|intvec| should represent homogemous coordinates |
---|
2964 | set \\verb|TeXproc|."); |
---|
2965 | write(fname, |
---|
2966 | bv + |
---|
2967 | "> int TeXproj;" + nl + |
---|
2968 | "> texobj(fname,v);" + nl + |
---|
2969 | "> kill TeXproj;" + nl2 + |
---|
2970 | ev ); |
---|
2971 | |
---|
2972 | int TeXproj; export TeXproj; |
---|
2973 | texobj(fname,v); |
---|
2974 | kill TeXproj; |
---|
2975 | |
---|
2976 | write(fname,nl2); |
---|
2977 | |
---|
2978 | //----------------------------------------------- |
---|
2979 | write(fname,"\\Line"); |
---|
2980 | write(fname,"For writing an \\verb|intvec| as row vector as it is use the |
---|
2981 | cast \\verb|intmat|"); |
---|
2982 | |
---|
2983 | write(fname, |
---|
2984 | bv + |
---|
2985 | "> texobj(fname,intmat(v));" + nl2 + |
---|
2986 | ev ); |
---|
2987 | |
---|
2988 | texobj(fname,intmat(v)); |
---|
2989 | |
---|
2990 | write(fname, |
---|
2991 | bv + |
---|
2992 | "> texobj(fname,intmat(m*v),\"=\",m,\"*\",intmat(v));" + nl2 + |
---|
2993 | ev ); |
---|
2994 | |
---|
2995 | texobj(fname,intmat(m*v),"=",m,"*",intmat(v)); |
---|
2996 | |
---|
2997 | //----------------------------------------------------------------- |
---|
2998 | write(fname,"\\Line"); |
---|
2999 | |
---|
3000 | write(fname,"The brackets of a \\verb|intmat| can be set with \\verb|TeXproj| |
---|
3001 | as usual"); |
---|
3002 | |
---|
3003 | write(fname, |
---|
3004 | bv + |
---|
3005 | "> intmat mat[3][3] = 1,2,3,4,5,6,7,8,9;" + nl + |
---|
3006 | "> string TeXbrack = \"|\";" + nl + |
---|
3007 | "> texobj(fname,mat,\"=\",det(mat)); " + nl2 + |
---|
3008 | ev ); |
---|
3009 | |
---|
3010 | intmat mat[3][3] = 1,2,3,4,5,6,7,8,9; |
---|
3011 | string TeXbrack = "|"; export TeXbrack; |
---|
3012 | texobj(fname,mat,"=",det(mat)); |
---|
3013 | kill TeXbrack; |
---|
3014 | |
---|
3015 | //----------------------------------texname------------------- |
---|
3016 | |
---|
3017 | write(fname,"\\section{Names of identifiers}"); |
---|
3018 | |
---|
3019 | |
---|
3020 | write(fname,"The proc \\verb|texname| is used to write indexed names in a |
---|
3021 | correct way"+lb,nl); |
---|
3022 | |
---|
3023 | |
---|
3024 | |
---|
3025 | // ------------------------------- texproc ------------------------------- |
---|
3026 | write(fname,"\\section{procs}"); |
---|
3027 | write(fname,"Finally, here is the procedure we used to generate the random |
---|
3028 | polynomials."); |
---|
3029 | write(fname,"\\newpage"); |
---|
3030 | texproc(fname,"randompoly"); |
---|
3031 | |
---|
3032 | |
---|
3033 | // ------------------------------ closing the tex file ------------------- |
---|
3034 | write(fname,"\\section{Closing the \\LaTeX\\ file}"); |
---|
3035 | write(fname,"The file will be closed by \\verb|closetex(fname);|. It should |
---|
3036 | contain now purely correct \\LaTeX code and may be compiled with " + |
---|
3037 | "\\verb|tex(fname)| and displayed with \\verb|xdvi(fname)|"); |
---|
3038 | |
---|
3039 | write(fname,"\\section{Remarks}"); |
---|
3040 | closetex(fname); |
---|
3041 | |
---|
3042 | "end of part3" + nl; |
---|
3043 | } |
---|
3044 | |
---|
3045 | |
---|
3046 | proc cleantexdemo() |
---|
3047 | { |
---|
3048 | kill fname,nl,nl2,lb,bv,ev; |
---|
3049 | return(); |
---|
3050 | } |
---|