1 | // $Id: surf.lib,v 1.12 2000-12-04 13:05:57 Singular Exp $ |
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2 | // |
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3 | // author : Hans Schoenemann |
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4 | // |
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5 | /////////////////////////////////////////////////////////////////////////////// |
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6 | version="$Id: surf.lib,v 1.12 2000-12-04 13:05:57 Singular Exp $"; |
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7 | info=" |
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8 | LIBRARY: surf.lib PROCEDURES FOR GRAPHICS WITH SURF |
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9 | |
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10 | AUTHOR: surf is written by Stefan Endrass |
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11 | |
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12 | NOTE: |
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13 | @texinfo |
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14 | To use this library requires the program @code{surf} to be installed. |
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15 | @code{surf} is only available for Linux PCs and Sun workstations. |
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16 | You can download @code{surf} either from |
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17 | @uref{http://sourceforge.net/projects/surf} |
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18 | or from @uref{ftp://www.mathematik.uni-kl.de/pub/Math/Singular/utils/}. |
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19 | @end texinfo |
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20 | |
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21 | PROCEDURES: |
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22 | plot(I); plots curves and surfaces |
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23 | "; |
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24 | |
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25 | /////////////////////////////////////////////////////////////////////////////// |
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26 | static proc num_of_vars(ideal I) |
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27 | { |
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28 | intvec v; |
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29 | int i; |
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30 | poly p; |
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31 | for(i=size(I);i>0;i--) |
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32 | { |
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33 | p=I[i]; |
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34 | while(p!=0) |
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35 | { |
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36 | v=v+leadexp(p); |
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37 | p=p-lead(p); |
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38 | } |
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39 | } |
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40 | return(v); |
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41 | } |
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42 | |
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43 | proc plot(ideal I) |
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44 | "USAGE: plot(I); I ideal |
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45 | RETURN: nothing |
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46 | NOTE: requires the external program 'surf' to be installed |
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47 | EXAMPLE: example plot; shows an example |
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48 | " |
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49 | { |
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50 | string l="/tmp/surf"+string(system("pid")); |
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51 | def base=basering; |
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52 | intvec v=num_of_vars(I); |
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53 | int i,j,n; |
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54 | for(i=size(v);i>0;i--) |
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55 | { |
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56 | if (v[i]!=0) { n++; } |
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57 | } |
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58 | if (n==0 or n>3) |
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59 | { |
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60 | ERROR("Cannot plot equations with", n, "variables"); |
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61 | } |
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62 | ring r=0,(x,y,z),dp; |
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63 | short=0; |
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64 | map phi=base,0; |
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65 | j=1; |
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66 | for(i=1;i<=size(v);i++) |
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67 | { |
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68 | if (v[i]!=0) |
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69 | { |
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70 | phi[i]=var(j); |
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71 | j++; |
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72 | if(j==4) break; |
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73 | } |
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74 | } |
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75 | ideal I=simplify(phi(I),2); |
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76 | if (ncols(I)==1 and n<=2) // curve |
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77 | { |
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78 | write(":w "+l,"clip=none;"); |
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79 | write(l, "width=500; height=500; set_size; do_background=yes; background_red=255; background_green=255; background_blue=255;"); |
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80 | write(l, |
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81 | "root_finder=d_chain_bisection;epsilon=0.0000000001;iterations=20000;"); |
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82 | write(l, "curve_green=0; curve_blue=0; curve_width=1.5;"); |
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83 | write(l,"curve=",I[1],";"); |
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84 | write(l,"draw_curve;"); |
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85 | } |
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86 | else |
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87 | { |
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88 | if (ncols(I)==1 and n==3) // surface |
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89 | { |
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90 | write(":w "+l, |
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91 | "root_finder=d_chain_bisection;epsilon=0.0000000001;iterations=20000;"); |
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92 | write(l, "width=500; height=500; set_size; do_background=yes; background_red=255; background_green=255; background_blue=255;"); |
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93 | write(l,"rot_x=0.14; rot_y=-0.3;"); |
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94 | write(l,"surface=",I[1],";"); |
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95 | write(l,"draw_surface;"); |
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96 | } |
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97 | else |
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98 | { |
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99 | ERROR("cannot plot"+string(ncols(I))+"equations in" |
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100 | +string(n)+"variables"); |
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101 | } |
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102 | } |
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103 | string surf_call = "surf "; |
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104 | if (defined(extra_surf_opts)) |
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105 | { |
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106 | surf_call = surf_call + extra_surf_opts + " "; |
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107 | } |
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108 | // "calling surf (by Stephan Endrass) for drawing"; |
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109 | i=system("sh",surf_call + l +" >/dev/null 2>&1"); |
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110 | if (i!=0) |
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111 | { |
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112 | ERROR("calling `surf` failed. (the shell return the error code" |
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113 | +string(i)+")."+newline+ |
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114 | "probably the executable `surf` is not found."); |
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115 | } |
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116 | i=system("sh","/bin/rm "+l); |
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117 | } |
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118 | example |
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119 | { "EXAMPLE:"; echo =2; |
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120 | // --------- plane curves ------------ |
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121 | ring rr0 = 0,(x1,x2),dp; |
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122 | |
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123 | ideal I = x1^3 - x2^2; |
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124 | plot(I); |
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125 | ideal J = x1^2-x1-x2^3; |
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126 | plot(J); |
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127 | |
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128 | ring rr1 = 0,(x,y,z),dp; |
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129 | ideal I(1) = 2x2-1/2x3 +1-y+1; |
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130 | plot(I(1)); |
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131 | ideal I(2) = x3-x-y; |
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132 | plot(I(2)); |
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133 | |
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134 | // ---- Singular Logo -------------- |
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135 | poly logo = ((x+3)^3 + 2*(x+3)^2 - y^2)*(x^3 - y^2)*((x-3)^3-2*(x-3)^2-y^2); |
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136 | plot(logo); |
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137 | |
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138 | |
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139 | // --------- implicit curves ------------ |
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140 | // implicit curves |
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141 | ideal I(1) = y,-x2; |
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142 | plot(I(1)); |
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143 | ideal I(2) = x2,-y2 +4; |
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144 | plot(I(2)); |
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145 | |
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146 | //the lemniscate |
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147 | |
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148 | ideal I(3) = x4+2x2y2 + y4, x2-y2; |
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149 | plot(I(3)); |
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150 | |
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151 | // a critical part |
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152 | // adjust the plotregion properly to get a good picture |
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153 | |
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154 | poly f = (x-y)*(x2+y); |
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155 | plot(f,1); |
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156 | ideal J = jacob(f); |
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157 | J; |
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158 | plot(J); // bad resolution |
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159 | |
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160 | // ----------- surfaces ------------------- |
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161 | ideal J(1) = 3xy4 + 2xy2, x5y3 + x + y6,10x2; |
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162 | plot(J(1)); |
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163 | |
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164 | // Steiner surface |
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165 | |
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166 | ideal J(2) = x^2*y^2+x^2*z^2+y^2*z^2-17*x*y*z; |
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167 | plot(J(2)); |
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168 | |
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169 | plot(x*(x2-y2)+z2); |
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170 | |
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171 | // E7 |
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172 | plot(x^3-x*y^3+z^2); |
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173 | |
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174 | // Whitney umbrella |
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175 | plot(z^2-x^2*y); |
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176 | |
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177 | // A1 |
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178 | plot(y2-xz); |
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179 | |
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180 | |
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181 | } |
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182 | /////////////////////////////////////////////////////////////////////////////// |
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