1 | // $Id: standard.lib,v 1.15 1998-05-25 08:44:14 obachman Exp $ |
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2 | ////////////////////////////////////////////////////////////////////////////// |
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3 | |
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4 | version="$Id: standard.lib,v 1.15 1998-05-25 08:44:14 obachman Exp $"; |
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5 | info=" |
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6 | LIBRARY: standard.lib PROCEDURES WHICH ARE ALWAYS LOADED AT START-UP |
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7 | |
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8 | stdfglm(ideal[,ord]) standard basis of the ideal via fglm [and ordering ord] |
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9 | stdhilb(ideal) standard basis of the ideal using the Hilbert function |
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10 | groebner(ideal/module) standard basis of ideal or module using a |
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11 | heuristically choosen method |
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12 | "; |
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13 | |
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14 | ////////////////////////////////////////////////////////////////////////////// |
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15 | |
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16 | proc stdfglm (ideal i, list #) |
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17 | "USAGE: stdfglm(i[,s]); i ideal, s string (any allowed ordstr of a ring) |
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18 | RETURN: stdfglm(i): standard basis of i in the basering, calculated via fglm |
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19 | from ordering \"dp\" to the ordering of the basering. |
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20 | stdfglm(i,s): standard basis of i in the basering, calculated via |
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21 | fglm from ordering s to the ordering of the basering. |
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22 | EXAMPLE: example stdfglm; shows an example" |
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23 | { |
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24 | string os; |
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25 | def dr= basering; |
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26 | if( (size(#)==0) or (typeof(#[1]) != "string") ) |
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27 | { |
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28 | os = "dp(" + string( nvars(dr) ) + ")"; |
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29 | if ( (find( ordstr(dr), os ) != 0) and (find( ordstr(dr), "a") == 0) ) |
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30 | { |
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31 | os= "Dp"; |
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32 | } |
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33 | else |
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34 | { |
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35 | os= "dp"; |
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36 | } |
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37 | } |
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38 | else { os = #[1]; } |
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39 | execute "ring sr=("+charstr(dr)+"),("+varstr(dr)+"),"+os+";"; |
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40 | ideal i= fetch(dr,i); |
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41 | intvec opt= option(get); |
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42 | option(redSB); |
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43 | i=std(i); |
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44 | option(set,opt); |
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45 | setring dr; |
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46 | return (fglm(sr,i)); |
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47 | } |
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48 | example |
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49 | { "EXAMPLE:"; echo = 2; |
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50 | ring r = 0,(x,y,z),lp; |
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51 | ideal i = y3+x2, x2y+x2, x3-x2, z4-x2-y; |
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52 | ideal i1= stdfglm(i); //uses fglm from "dp" to "lp" |
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53 | i1; |
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54 | ideal i2= stdfglm(i,"Dp"); //uses fglm from "Dp" to "lp" |
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55 | i2; |
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56 | } |
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57 | ///////////////////////////////////////////////////////////////////////////// |
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58 | |
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59 | proc stdhilb(ideal i,list #) |
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60 | "USAGE: stdhilb(i); i ideal |
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61 | stdhilb(i,v); i homogeneous ideal, v intvec (the Hilbert function) |
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62 | RETURN: stdhilb(i): a standard basis of i (computing v internally) |
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63 | stdhilb(i,v): standard basis of i, using the given Hilbert function |
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64 | EXAMPLE: example stdhilb; shows an example" |
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65 | { |
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66 | def R=basering; |
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67 | |
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68 | if((homog(i)==1)||(ordstr(basering)[1]=="d")) |
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69 | { |
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70 | if ((size(#)!=0)&&(homog(i)==1)) |
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71 | { |
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72 | return(std(i,#[1])); |
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73 | } |
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74 | return(std(i)); |
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75 | } |
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76 | |
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77 | execute "ring S = ("+charstr(R)+"),("+varstr(R)+",@t),dp;"; |
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78 | ideal i=homog(imap(R,i),@t); |
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79 | intvec v=hilb(std(i),1); |
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80 | execute "ring T = ("+charstr(R)+"),("+varstr(R)+",@t),("+ordstr(R)+");"; |
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81 | ideal i=fetch(S,i); |
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82 | ideal a=std(i,v); |
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83 | setring R; |
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84 | map phi=T,maxideal(1),1; |
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85 | ideal a=phi(a); |
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86 | |
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87 | int k,j; |
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88 | poly m; |
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89 | int c=size(i); |
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90 | |
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91 | for(j=1;j<c;j++) |
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92 | { |
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93 | if(deg(a[j])==0) |
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94 | { |
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95 | a=ideal(1); |
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96 | attrib(a,"isSB",1); |
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97 | return(a); |
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98 | } |
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99 | if(deg(a[j])>0) |
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100 | { |
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101 | m=lead(a[j]); |
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102 | for(k=j+1;k<=c;k++) |
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103 | { |
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104 | if(size(lead(a[k])/m)>0) |
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105 | { |
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106 | a[k]=0; |
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107 | } |
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108 | } |
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109 | } |
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110 | } |
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111 | a=simplify(a,2); |
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112 | attrib(a,"isSB",1); |
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113 | return(a); |
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114 | } |
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115 | example |
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116 | { "EXAMPLE:"; echo = 2; |
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117 | ring r = 0,(x,y,z),lp; |
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118 | ideal i = y3+x2, x2y+x2, x3-x2, z4-x2-y; |
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119 | ideal i1= stdhilb(i); i1; |
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120 | // is in this case equivalent to: |
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121 | intvec v=1,0,0,-3,0,1,0,3,-1,-1; |
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122 | ideal i2=stdhilb(i,v); |
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123 | } |
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124 | ////////////////////////////////////////////////////////////////////////// |
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125 | |
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126 | proc groebner(def i, list #) |
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127 | "USAGE: groebner(i[, wait]) i -- ideal/module; wait -- int |
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128 | RETURNS: Standard basis of ideal or module which is computed using a |
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129 | heuristically choosen method: |
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130 | If the ordering of the current ring is a local ordering, or |
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131 | if it is a non-block ordering and the current ring has no |
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132 | parameters, then std(i) is returned. |
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133 | Otherwise, i is mapped into a ring with no parameters and |
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134 | ordering dp, where its Hilbert series is computed. This is |
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135 | followed by a Hilbert-series based std computation in the |
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136 | original ring. |
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137 | NOTE: If a 2nd argument 'wait' is given, then the computation proceeds |
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138 | at most 'wait' seconds. That is, if no result could be computed in |
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139 | 'wait' seconds, then the computation is interrupted, 0 is returned, |
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140 | a warning message is displayed, and the global variable |
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141 | 'groebner_error' is defined. |
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142 | EXAMPLE: example groebner; shows an example" |
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143 | { |
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144 | def P=basering; |
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145 | |
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146 | // we have two arguments -- try to use MPfork links |
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147 | if (size(#) > 0) |
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148 | { |
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149 | if (system("with", "MP")) |
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150 | { |
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151 | if (typeof(#[1]) == "int") |
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152 | { |
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153 | int wait = #[1] * 1000000; |
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154 | int j,k = 10, 0; |
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155 | string bs = nameof(basering); |
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156 | link l_fork = "MPtcp:fork"; |
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157 | open(l_fork); |
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158 | write(l_fork, quote(system("pid"))); |
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159 | int pid = read(l_fork); |
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160 | write(l_fork, quote(groebner(eval(i)))); |
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161 | |
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162 | while(k < wait) |
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163 | { |
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164 | if (status(l_fork, "read", "ready", j)) {break;} |
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165 | k = k + j; |
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166 | j = j + j; |
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167 | } |
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168 | |
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169 | if (status(l_fork, "read", "ready")) |
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170 | { |
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171 | def result = read(l_fork); |
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172 | if (bs != nameof(basering)) |
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173 | { |
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174 | def PP = basering; |
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175 | setring P; |
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176 | def result = imap(PP, result); |
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177 | kill PP; |
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178 | } |
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179 | if (defined(groebner_error)) |
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180 | { |
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181 | kill(groebner_error); |
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182 | } |
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183 | kill (l_fork); |
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184 | } |
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185 | else |
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186 | { |
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187 | ideal result; |
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188 | if (! defined(groebner_error)) |
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189 | { |
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190 | int groebner_error = 1; |
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191 | export groebner_error; |
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192 | } |
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193 | "// ** groebner did not finish"; |
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194 | j = system("sh", "kill " + string(pid)); |
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195 | } |
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196 | return (result); |
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197 | } |
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198 | else |
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199 | { |
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200 | "// ** groebner needs int as 2nd arg"; |
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201 | } |
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202 | } |
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203 | else |
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204 | { |
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205 | "// ** groebner with two args not supported in this configuration"; |
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206 | } |
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207 | } |
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208 | |
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209 | // we are still here -- do the actual computation |
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210 | string ordstr_P = ordstr(P); |
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211 | if (find(ordstr_P,"s") > 0) |
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212 | { |
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213 | //spaeter den lokalen fall ueber lp oder aehnlich behandeln |
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214 | return(std(i)); |
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215 | } |
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216 | |
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217 | int IsSimple_P; |
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218 | if (system("nblocks") <= 2) |
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219 | { |
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220 | if (find(ordstr_P, "M") <= 0) |
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221 | { |
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222 | IsSimple_P = 1; |
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223 | } |
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224 | } |
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225 | int npars_P = npars(P); |
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226 | |
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227 | // return std if no parameters and (dp or wp) |
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228 | if ((npars_P == 0) && IsSimple_P) |
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229 | { |
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230 | if (find(ordstr_P, "d") > 0) |
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231 | { |
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232 | return (std(i)); |
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233 | } |
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234 | if (find(ordstr_P,"w") > 0) |
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235 | { |
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236 | return (std(i)); |
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237 | } |
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238 | } |
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239 | |
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240 | // reset options |
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241 | intvec opt=option(get); |
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242 | int p_opt; |
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243 | string s_opt = option(); |
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244 | option(none); |
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245 | // turn on option(prot) and/or option(mem), if previously set |
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246 | if (find(s_opt, "prot")) |
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247 | { |
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248 | option(prot); |
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249 | p_opt = 1; |
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250 | } |
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251 | if (find(s_opt, "mem")) |
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252 | { |
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253 | option(mem); |
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254 | } |
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255 | |
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256 | // construct ring in which first std computation is done |
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257 | string varstr_P = varstr(P); |
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258 | string parstr_P = parstr(P); |
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259 | int is_homog = (homog(i) && (npars_P == 0)); |
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260 | |
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261 | string ri = "ring Phelp =" + string(char(P)) + ",(" + varstr_P; |
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262 | // parameters are converted to ring variables |
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263 | if (npars_P > 0) |
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264 | { |
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265 | ri = ri + "," + parstr_P; |
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266 | } |
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267 | // a homogenizing variable is added, if necessary |
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268 | if (! is_homog) |
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269 | { |
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270 | ri = ri + ",@t"; |
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271 | } |
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272 | // ordering is set to (dp, C) |
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273 | ri = ri + "),(dp,C);"; |
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274 | |
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275 | // change the ring |
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276 | execute(ri); |
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277 | |
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278 | // get ideal from previous ring |
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279 | if (is_homog) |
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280 | { |
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281 | ideal qh = imap(P, i); |
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282 | } |
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283 | else |
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284 | { |
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285 | // and homogenize |
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286 | ideal qh=homog(imap(P,i),@t); |
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287 | } |
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288 | |
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289 | // compute std and hilbert series |
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290 | if (p_opt) |
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291 | { |
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292 | "std in " + ri[13, size(ri) - 13]; |
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293 | } |
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294 | ideal qh1=std(qh); |
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295 | intvec hi=hilb(qh1,1); |
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296 | |
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297 | if (is_homog && (npars_P == 0)) |
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298 | { |
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299 | // no additional variables were introduced |
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300 | setring P; // can immediately change to original ring |
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301 | // simply compute std with hilbert series in original ring |
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302 | if (p_opt) |
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303 | { |
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304 | "std with hilb in basering"; |
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305 | i = std(i, hi); |
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306 | } |
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307 | } |
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308 | else |
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309 | { |
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310 | // additional variables were introduced |
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311 | // need another intermediate ring |
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312 | ri = "ring Phelp1 =" + string(char(P)) |
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313 | + ",(" + varstr(Phelp) + "),(" + ordstr_P; |
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314 | |
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315 | // for lp without parameters, we do not need a block ordering |
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316 | if ( ! (IsSimple_P && (npars_P + is_homog < 2) && find(ordstr_P, "l"))) |
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317 | { |
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318 | // need block ordering |
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319 | ri = ri + ", dp(" + string(npars_P + is_homog) + ")"; |
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320 | } |
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321 | ri = ri + ");"; |
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322 | |
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323 | // change to intermediate ring |
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324 | execute(ri); |
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325 | ideal qh = imap(Phelp, qh); |
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326 | kill Phelp; |
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327 | if (p_opt) |
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328 | { |
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329 | "std with hilb in " + ri[14,size(ri)-14]; |
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330 | } |
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331 | // compute std with Hilbert series |
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332 | qh = std(qh, hi); |
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333 | // subst 1 for homogenizing var |
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334 | if (!is_homog) |
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335 | { |
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336 | qh = subst(qh, @t, 1); |
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337 | } |
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338 | |
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339 | // go back to original ring |
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340 | setring P; |
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341 | // get ideal, delete zeros and clean SB |
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342 | i = imap(Phelp1,qh); |
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343 | i = simplify(i, 34); |
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344 | kill Phelp1; |
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345 | } |
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346 | |
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347 | // clean-up time |
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348 | option(set, opt); |
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349 | if (find(s_opt, "redSB") > 0) |
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350 | { |
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351 | i=interred(i); |
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352 | } |
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353 | attrib(i, "isSB", 1); |
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354 | return (i); |
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355 | } |
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356 | example |
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357 | { |
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358 | "EXAMPLE: "; echo = 2; |
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359 | ring r = 0, (a,b,c,d), lp; |
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360 | option(prot); |
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361 | ideal i = a+b+c+d, ab+ad+bc+cd, abc+abd+acd+bcd, abcd-1; // cyclic 4 |
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362 | groebner(i); |
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363 | ring rp = (0, a, b), (c,d), lp; |
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364 | ideal i = imap(r, i); |
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365 | ideal j = groebner(i); |
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366 | option(noprot); |
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367 | j; simplify(j, 1); std(i); |
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368 | if (system("with", "MP")) {groebner(i, 0);} |
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369 | defined(groebner_error); |
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370 | } |
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371 | |
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372 | |
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373 | ////////////////////////////////////////////////////////////////////////// |
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374 | proc resu(list #) |
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375 | { |
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376 | def P=basering; |
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377 | list result; |
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378 | def m=#[1]; //the ideal or module |
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379 | |
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380 | int i=#[2]; //the length of the resolution |
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381 | //if size(#)>2 a minimal resolution is computed |
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382 | |
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383 | //LaScala for the homogeneous case |
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384 | if(homog(m)==1) |
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385 | { |
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386 | resolution re=lres(m,i); |
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387 | if(size(#)>2) |
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388 | { |
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389 | re=minres(re); |
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390 | } |
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391 | return(re); |
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392 | } |
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393 | |
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394 | //mres for the global non homogeneous case |
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395 | if(find(ordstr(P),"s")==0) |
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396 | { |
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397 | string ri= "ring Phelp =" |
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398 | +string(char(P))+",("+varstr_P+"),(dp,C);"; |
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399 | execute(ri); |
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400 | def m=imap(P,m); |
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401 | list re=mres(m,i); |
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402 | setring P; |
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403 | result=imap(Phelp,re); |
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404 | return(result); |
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405 | } |
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406 | |
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407 | //sres for the local case and not minimal resolution |
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408 | if(size(#)<=2) |
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409 | { |
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410 | string ri= "ring Phelp =" |
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411 | +string(char(P))+",("+varstr_P+"),(ls,c);"; |
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412 | execute(ri); |
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413 | def m=imap(P,m); |
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414 | m=std(m); |
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415 | list re=sres(m,i); |
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416 | setring P; |
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417 | result=imap(Phelp,re); |
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418 | return(result); |
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419 | } |
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420 | |
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421 | //mres for the local case and minimal resolution |
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422 | string ri= "ring Phelp =" |
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423 | +string(char(P))+",("+varstr_P+"),(ls,C);"; |
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424 | execute(ri); |
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425 | def m=imap(P,m); |
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426 | list re=mres(m,i); |
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427 | setring P; |
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428 | result=imap(Phelp,re); |
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429 | return(result); |
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430 | } |
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431 | |
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432 | proc minresu(list #) |
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433 | { |
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434 | return(resu(#[1],#[2],1)); |
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435 | } |
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