1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: maps.cc,v 1.4 2004-05-25 12:01:50 levandov Exp $ */ |
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5 | /* |
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6 | * ABSTRACT - the mapping of polynomials to other rings |
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7 | */ |
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8 | |
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9 | #include "mod2.h" |
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10 | #include "structs.h" |
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11 | #include "febase.h" |
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12 | #include "polys.h" |
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13 | #include "numbers.h" |
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14 | #include "ring.h" |
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15 | #include "ideals.h" |
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16 | #include "matpol.h" |
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17 | #include "omalloc.h" |
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18 | #include "kstd1.h" |
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19 | #include "longalg.h" |
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20 | #include "maps.h" |
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21 | #include "prCopy.h" |
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22 | |
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23 | // This is a very dirty way to "normalize" numbers w.r.t. a |
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24 | // MinPoly |
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25 | |
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26 | /* debug output: Tok2Cmdname in maApplyFetch*/ |
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27 | //#include "ipshell.h" |
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28 | |
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29 | #define MAX_MAP_DEG 128 |
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30 | |
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31 | /*2 |
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32 | * copy a map |
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33 | */ |
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34 | map maCopy(map theMap) |
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35 | { |
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36 | int i; |
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37 | map m=(map)idInit(IDELEMS(theMap),0); |
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38 | for (i=IDELEMS(theMap)-1; i>=0; i--) |
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39 | m->m[i] = pCopy(theMap->m[i]); |
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40 | m->preimage=omStrDup(theMap->preimage); |
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41 | return m; |
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42 | } |
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43 | |
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44 | |
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45 | /*2 |
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46 | * return the image of var(v)^pExp, where var(v) maps to p |
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47 | */ |
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48 | poly maEvalVariable(poly p, int v,int pExp,matrix s) |
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49 | { |
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50 | if (pExp==1) |
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51 | return pCopy(p); |
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52 | |
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53 | poly res; |
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54 | |
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55 | if((s!=NULL)&&(pExp<MAX_MAP_DEG)) |
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56 | { |
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57 | int j=2; |
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58 | poly p0=p; |
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59 | // find starting point |
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60 | if(MATELEM(s,v,1)==NULL) |
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61 | { |
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62 | MATELEM(s,v,1)=pCopy(p/*theMap->m[v-1]*/); |
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63 | } |
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64 | else |
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65 | { |
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66 | while((j<=pExp)&&(MATELEM(s,v,j)!=NULL)) |
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67 | { |
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68 | j++; |
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69 | } |
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70 | p0=MATELEM(s,v,j-1); |
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71 | } |
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72 | // multiply |
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73 | for(;j<=pExp;j++) |
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74 | { |
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75 | p0=MATELEM(s,v,j)=ppMult_qq(p0, p); |
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76 | pNormalize(p0); |
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77 | } |
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78 | res=pCopy(p0/*MATELEM(s,v,pExp)*/); |
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79 | } |
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80 | else //if ((p->next!=NULL)&&(p->next->next==NULL)) |
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81 | { |
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82 | res=pPower(pCopy(p),pExp); |
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83 | } |
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84 | return res; |
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85 | } |
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86 | |
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87 | static poly maEvalMonom(map theMap, poly p,ring preimage_r,matrix s, nMapFunc nMap) |
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88 | { |
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89 | poly q=pNSet(nMap(pGetCoeff(p))); |
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90 | |
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91 | int i; |
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92 | for(i=1;i<=preimage_r->N; i++) |
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93 | { |
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94 | int pExp=p_GetExp( p,i,preimage_r); |
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95 | if (pExp != 0) |
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96 | { |
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97 | if (theMap->m[i-1]!=NULL) |
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98 | { |
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99 | poly p1=theMap->m[i-1]; |
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100 | poly pp=maEvalVariable(p1,i,pExp,s); |
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101 | q = pMult(q,pp); |
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102 | } |
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103 | else |
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104 | { |
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105 | pDelete(&q); |
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106 | break; |
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107 | } |
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108 | } |
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109 | } |
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110 | int modulComp = p_GetComp( p,preimage_r); |
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111 | if (q!=NULL) pSetCompP(q,modulComp); |
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112 | return q; |
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113 | } |
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114 | |
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115 | poly maEval(map theMap, poly p,ring preimage_r,nMapFunc nMap,matrix s) |
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116 | { |
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117 | poly result = NULL; |
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118 | int i; |
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119 | |
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120 | // for(i=1; i<=preimage_r->N; i++) |
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121 | // { |
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122 | // pTest(theMap->m[i-1]); |
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123 | // } |
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124 | // while (p!=NULL) |
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125 | // { |
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126 | // poly q=maEvalMonom(theMap,p,preimage_r,s); |
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127 | // result = pAdd(result,q); |
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128 | // pIter(p); |
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129 | // } |
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130 | if (p!=NULL) |
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131 | { |
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132 | int l = pLength(p)-1; |
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133 | poly* monoms; |
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134 | if (l>0) |
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135 | { |
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136 | monoms = (poly*) omAlloc(l*sizeof(poly)); |
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137 | |
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138 | for (i=0; i<l; i++) |
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139 | { |
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140 | monoms[i]=maEvalMonom(theMap,p,preimage_r,s, nMap); |
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141 | pIter(p); |
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142 | } |
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143 | } |
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144 | result=maEvalMonom(theMap,p,preimage_r,s, nMap); |
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145 | if (l>0) |
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146 | { |
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147 | for(i = l-1; i>=0; i--) |
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148 | { |
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149 | result=pAdd(result, monoms[i]); |
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150 | } |
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151 | omFreeSize((ADDRESS)monoms,l*sizeof(poly)); |
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152 | } |
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153 | if (currRing->minpoly!=NULL) result=pMinPolyNormalize(result); |
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154 | } |
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155 | pTest(result); |
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156 | return result; |
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157 | } |
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158 | |
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159 | /*2 |
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160 | *shifts the variables between minvar and maxvar of p \in p_ring to the |
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161 | *first maxvar-minvar+1 variables in the actual ring |
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162 | *be carefull: there is no range check for the variables of p |
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163 | */ |
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164 | static poly pChangeSizeOfPoly(ring p_ring, poly p,int minvar,int maxvar) |
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165 | { |
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166 | int i; |
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167 | poly result = NULL,resultWorkP; |
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168 | number n; |
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169 | |
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170 | if (p==NULL) return result; |
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171 | else result = pInit(); |
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172 | resultWorkP = result; |
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173 | while (p!=NULL) |
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174 | { |
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175 | for (i=minvar;i<=maxvar;i++) |
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176 | pSetExp(resultWorkP,i-minvar+1,p_GetExp(p,i,p_ring)); |
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177 | pSetComp(resultWorkP,p_GetComp(p,p_ring)); |
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178 | n=nCopy(pGetCoeff(p)); |
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179 | pSetCoeff(resultWorkP,n); |
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180 | pSetm(resultWorkP); |
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181 | pIter(p); |
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182 | if (p!=NULL) |
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183 | { |
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184 | pNext(resultWorkP) = pInit(); |
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185 | pIter(resultWorkP); |
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186 | } |
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187 | } |
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188 | return result; |
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189 | } |
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190 | |
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191 | |
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192 | /*2 |
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193 | *returns the preimage of id under theMap, |
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194 | *if id is empty or zero the kernel is computed |
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195 | * (assumes) that both ring have the same coeff.field |
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196 | */ |
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197 | ideal maGetPreimage(ring theImageRing, map theMap, ideal id) |
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198 | { |
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199 | int i,j; |
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200 | int ordersize = rBlocks(currRing) + 1; |
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201 | poly p,pp,q; |
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202 | ideal temp1; |
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203 | ideal temp2; |
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204 | int *orders = (int*) omAlloc0(sizeof(int)*(ordersize)); |
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205 | int *block0 = (int*) omAlloc0(sizeof(int)*(ordersize)); |
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206 | int *block1 = (int*) omAlloc0(sizeof(int)*(ordersize)); |
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207 | int **wv = (int **) omAlloc0(ordersize * sizeof(int *)); |
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208 | |
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209 | int imagepvariables = theImageRing->N; |
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210 | ring sourcering = currRing; |
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211 | int N = pVariables+imagepvariables; |
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212 | char** names = (char**) omAlloc0(N*sizeof(char*)); |
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213 | |
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214 | memcpy(names, currRing->names, currRing->N*sizeof(char*)); |
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215 | memcpy(&(names[currRing->N]), theImageRing->names, |
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216 | (theImageRing->N*sizeof(char*))); |
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217 | sip_sring tmpR; |
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218 | |
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219 | //if (theImageRing->OrdSgn == 1)s |
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220 | orders[0] = ringorder_dp; |
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221 | //else orders[0] = ringorder_ls; |
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222 | block1[0] = imagepvariables; |
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223 | block0[0] = 1; |
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224 | /* |
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225 | *if (sourcering->order[blockmax]) |
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226 | *{ |
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227 | * if (sourcering->OrdSgn == 1) orders[1] = ringorder_dp; |
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228 | * else orders[1] = ringorder_ls; |
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229 | * block1[1] = N; |
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230 | *} |
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231 | *else |
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232 | */ |
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233 | for (i=0; i<ordersize - 1; i++) |
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234 | { |
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235 | orders[i+1] = sourcering->order[i]; |
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236 | block0[i+1] = sourcering->block0[i]+imagepvariables; |
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237 | block1[i+1] = sourcering->block1[i]+imagepvariables; |
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238 | wv[i+1] = sourcering->wvhdl[i]; |
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239 | } |
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240 | tmpR = *currRing; |
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241 | tmpR.N = N; |
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242 | tmpR.order = orders; |
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243 | tmpR.block0 = block0; |
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244 | tmpR.block1 = block1; |
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245 | tmpR.wvhdl = wv; |
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246 | tmpR.names = names; |
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247 | rComplete(&tmpR, 1); |
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248 | rTest(&tmpR); |
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249 | |
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250 | #ifdef HAVE_PLURAL |
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251 | if (rIsPluralRing(theImageRing)) |
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252 | { |
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253 | rUnComplete(&tmpR); |
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254 | omFreeSize(orders, sizeof(int)*(ordersize));orders=NULL; |
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255 | omFreeSize(block0, sizeof(int)*(ordersize));block0=NULL; |
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256 | omFreeSize(block1, sizeof(int)*(ordersize));block1=NULL; |
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257 | omFreeSize(wv, sizeof(int*)*(ordersize)); wv=NULL; |
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258 | omFreeSize(names, (currRing->N)*sizeof(char*)); names=NULL; |
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259 | memset(&tmpR,0,sizeof(tmpR)); |
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260 | if ((rIsPluralRing(sourcering)) && (sourcering->nc->type!=nc_comm)) |
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261 | { |
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262 | Werror("Sorry, not yet implemented for noncomm. rings"); |
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263 | return NULL; |
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264 | } |
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265 | ring tmpR_ptr; |
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266 | if ( rSum(theImageRing, sourcering, tmpR_ptr ) !=1 ) |
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267 | { |
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268 | /* something is wrong with the rings... */ |
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269 | Werror("Error in rSum"); |
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270 | return NULL; |
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271 | } |
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272 | memcpy(&tmpR,tmpR_ptr,sizeof(tmpR)); |
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273 | // Action! |
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274 | } |
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275 | if (nSetMap(theImageRing) != nCopy) |
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276 | { |
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277 | Werror("Coefficient fields must be equal"); |
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278 | } |
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279 | #endif |
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280 | |
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281 | // change to new ring |
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282 | rChangeCurrRing(&tmpR); |
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283 | if (id==NULL) |
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284 | j = 0; |
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285 | else |
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286 | j = IDELEMS(id); |
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287 | int j0=j; |
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288 | if (theImageRing->qideal!=NULL) j+=IDELEMS(theImageRing->qideal); |
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289 | temp1 = idInit(sourcering->N+j,1); |
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290 | for (i=0;i<sourcering->N;i++) |
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291 | { |
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292 | q = pISet(-1); |
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293 | pSetExp(q,i+1+imagepvariables,1); |
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294 | pSetm(q); |
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295 | if ((i<IDELEMS(theMap)) && (theMap->m[i]!=NULL)) |
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296 | { |
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297 | p = pSort(pChangeSizeOfPoly(theImageRing,theMap->m[i],1,imagepvariables)); |
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298 | p=pAdd(p,q); |
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299 | } |
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300 | else |
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301 | { |
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302 | p = q; |
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303 | } |
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304 | temp1->m[i] = p; |
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305 | } |
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306 | idTest(temp1); |
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307 | for (i=sourcering->N;i<sourcering->N+j0;i++) |
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308 | { |
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309 | temp1->m[i] = pSort(pChangeSizeOfPoly(theImageRing, |
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310 | id->m[i-sourcering->N],1,imagepvariables)); |
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311 | } |
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312 | for (i=sourcering->N+j0;i<sourcering->N+j;i++) |
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313 | { |
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314 | temp1->m[i] = pSort(pChangeSizeOfPoly(theImageRing, |
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315 | theImageRing->qideal->m[i-sourcering->N-j0], |
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316 | 1,imagepvariables)); |
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317 | } |
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318 | // we ignore here homogenity - may be changed later: |
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319 | temp2 = kStd(temp1,NULL,isNotHomog,NULL); |
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320 | idDelete(&temp1); |
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321 | for (i=0;i<IDELEMS(temp2);i++) |
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322 | { |
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323 | if (pLowVar(temp2->m[i])<imagepvariables) pDelete(&(temp2->m[i])); |
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324 | } |
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325 | |
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326 | // let's get back to the original ring |
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327 | rChangeCurrRing(sourcering); |
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328 | temp1 = idInit(5,1); |
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329 | j = 0; |
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330 | for (i=0;i<IDELEMS(temp2);i++) |
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331 | { |
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332 | p = temp2->m[i]; |
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333 | if (p!=NULL) |
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334 | { |
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335 | q = pChangeSizeOfPoly(&tmpR, p,imagepvariables+1,N); |
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336 | if (j>=IDELEMS(temp1)) |
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337 | { |
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338 | pEnlargeSet(&(temp1->m),IDELEMS(temp1),5); |
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339 | IDELEMS(temp1)+=5; |
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340 | } |
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341 | temp1->m[j] = q; |
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342 | j++; |
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343 | } |
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344 | } |
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345 | id_Delete(&temp2, &tmpR); |
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346 | idSkipZeroes(temp1); |
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347 | rUnComplete(&tmpR); |
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348 | if (orders!=NULL) |
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349 | { |
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350 | omFreeSize(orders, sizeof(int)*(ordersize)); |
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351 | omFreeSize(block0, sizeof(int)*(ordersize)); |
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352 | omFreeSize(block1, sizeof(int)*(ordersize)); |
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353 | omFreeSize(wv, sizeof(int*)*(ordersize)); |
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354 | omFreeSize(names, (currRing->N)*sizeof(char*)); |
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355 | } |
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356 | return temp1; |
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357 | } |
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358 | |
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359 | void maFindPerm(char **preim_names, int preim_n, char **preim_par, int preim_p, |
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360 | char **names, int n, char **par, int nop, |
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361 | int * perm, int *par_perm, int ch) |
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362 | { |
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363 | int i,j; |
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364 | /* find correspondig vars */ |
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365 | for (i=0; i<preim_n; i++) |
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366 | { |
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367 | for(j=0; j<n; j++) |
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368 | { |
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369 | if (strcmp(preim_names[i],names[j])==0) |
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370 | { |
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371 | if (BVERBOSE(V_IMAP)) |
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372 | Print("// var %s: nr %d -> nr %d\n",preim_names[i],i+1,j+1); |
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373 | /* var i+1 from preimage ring is var j+1 (index j+1) from image ring */ |
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374 | perm[i+1]=j+1; |
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375 | break; |
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376 | } |
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377 | } |
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378 | if ((perm[i+1]==0)&&(par!=NULL) |
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379 | // do not consider par of Fq |
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380 | && (ch < 2)) |
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381 | { |
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382 | for(j=0; j<nop; j++) |
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383 | { |
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384 | if (strcmp(preim_names[i],par[j])==0) |
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385 | { |
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386 | if (BVERBOSE(V_IMAP)) |
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387 | Print("// var %s: nr %d -> par %d\n",preim_names[i],i+1,j+1); |
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388 | /* var i+1 from preimage ring is par j+1 (index j) from image ring */ |
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389 | perm[i+1]=-(j+1); |
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390 | } |
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391 | } |
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392 | } |
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393 | } |
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394 | if (par_perm!=NULL) |
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395 | { |
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396 | for (i=0; i<preim_p; i++) |
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397 | { |
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398 | for(j=0; j<n; j++) |
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399 | { |
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400 | if (strcmp(preim_par[i],names[j])==0) |
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401 | { |
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402 | if (BVERBOSE(V_IMAP)) |
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403 | Print("// par %s: par %d -> nr %d\n",preim_par[i],i+1,j+1); |
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404 | /*par i+1 from preimage ring is var j+1 (index j+1) from image ring*/ |
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405 | par_perm[i]=j+1; |
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406 | break; |
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407 | } |
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408 | } |
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409 | if ((par!=NULL) && (par_perm[i]==0)) |
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410 | { |
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411 | for(j=0; j<nop; j++) |
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412 | { |
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413 | if (strcmp(preim_par[i],par[j])==0) |
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414 | { |
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415 | if (BVERBOSE(V_IMAP)) |
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416 | Print("// par %s: nr %d -> par %d\n",preim_par[i],i+1,j+1); |
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417 | /*par i+1 from preimage ring is par j+1 (index j) from image ring */ |
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418 | par_perm[i]=-(j+1); |
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419 | } |
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420 | } |
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421 | } |
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422 | } |
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423 | } |
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424 | } |
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425 | |
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426 | /*2 |
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427 | * embeds poly p from the subring r into the current ring |
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428 | */ |
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429 | poly maIMap(ring r, poly p) |
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430 | { |
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431 | /* the simplest case:*/ |
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432 | if(r==currRing) return pCopy(p); |
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433 | nMapFunc nMap=nSetMap(r); |
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434 | int *perm=(int *)omAlloc0((r->N+1)*sizeof(int)); |
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435 | //int *par_perm=(int *)omAlloc0(rPar(r)*sizeof(int)); |
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436 | maFindPerm(r->names,r->N, r->parameter, r->P, |
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437 | currRing->names,currRing->N,currRing->parameter, currRing->P, |
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438 | perm,NULL, currRing->ch); |
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439 | poly res=pPermPoly(p,perm,r, nMap /*,par_perm,rPar(r)*/); |
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440 | omFreeSize((ADDRESS)perm,(r->N+1)*sizeof(int)); |
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441 | //omFreeSize((ADDRESS)par_perm,rPar(r)*sizeof(int)); |
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442 | return res; |
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443 | } |
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444 | |
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445 | /*3 |
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446 | * find the max. degree in one variable, but not larger than MAX_MAP_DEG |
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447 | */ |
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448 | int maMaxDeg_Ma(ideal a,ring preimage_r) |
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449 | { |
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450 | int i,j; |
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451 | int N = preimage_r->N; |
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452 | poly p; |
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453 | int *m=(int *)omAlloc0(N*sizeof(int)); |
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454 | |
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455 | for (i=MATROWS(a)*MATCOLS(a)-1;i>=0;i--) |
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456 | { |
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457 | p=a->m[i]; |
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458 | //pTest(p); // cannot test p because it is from another ring |
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459 | while(p!=NULL) |
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460 | { |
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461 | for(j=N-1;j>=0;j--) |
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462 | { |
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463 | m[j]=si_max(m[j],p_GetExp( p,j+1,preimage_r)); |
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464 | if (m[j]>=MAX_MAP_DEG) |
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465 | { |
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466 | i=MAX_MAP_DEG; |
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467 | goto max_deg_fertig_id; |
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468 | } |
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469 | } |
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470 | pIter(p); |
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471 | } |
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472 | } |
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473 | i=m[0]; |
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474 | for(j=N-1;j>0;j--) |
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475 | { |
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476 | i=si_max(i,m[j]); |
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477 | } |
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478 | max_deg_fertig_id: |
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479 | omFreeSize((ADDRESS)m,N*sizeof(int)); |
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480 | return i; |
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481 | } |
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482 | |
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483 | /*3 |
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484 | * find the max. degree in one variable, but not larger than MAX_MAP_DEG |
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485 | */ |
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486 | int maMaxDeg_P(poly p,ring preimage_r) |
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487 | { |
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488 | int i,j; |
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489 | int N = preimage_r->N; |
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490 | int *m=(int *)omAlloc0(N*sizeof(int)); |
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491 | |
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492 | // pTest(p); |
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493 | while(p!=NULL) |
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494 | { |
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495 | for(j=N-1;j>=0;j--) |
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496 | { |
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497 | m[j]=si_max(m[j],p_GetExp(p,j+1,preimage_r)); |
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498 | if (m[j]>=MAX_MAP_DEG) |
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499 | { |
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500 | i=MAX_MAP_DEG; |
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501 | goto max_deg_fertig_p; |
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502 | } |
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503 | } |
---|
504 | pIter(p); |
---|
505 | } |
---|
506 | i=m[0]; |
---|
507 | for(j=N-1;j>0;j--) |
---|
508 | { |
---|
509 | i=si_max(i,m[j]); |
---|
510 | } |
---|
511 | max_deg_fertig_p: |
---|
512 | omFreeSize((ADDRESS)m,N*sizeof(int)); |
---|
513 | return i; |
---|
514 | } |
---|
515 | |
---|
516 | // This is a very dirty way to cancel monoms whose number equals the |
---|
517 | // MinPoly |
---|
518 | poly pMinPolyNormalize(poly p) |
---|
519 | { |
---|
520 | number one = nInit(1); |
---|
521 | spolyrec rp; |
---|
522 | |
---|
523 | poly q = &rp; |
---|
524 | |
---|
525 | while (p != NULL) |
---|
526 | { |
---|
527 | // this returns 0, if p == MinPoly |
---|
528 | number product = nMult(pGetCoeff(p), one); |
---|
529 | if (product == NULL) |
---|
530 | { |
---|
531 | pDeleteLm(&p); |
---|
532 | } |
---|
533 | else |
---|
534 | { |
---|
535 | pSetCoeff(p, product); |
---|
536 | pNext(q) = p; |
---|
537 | q = p; |
---|
538 | p = pNext(p); |
---|
539 | } |
---|
540 | } |
---|
541 | pNext(q) = NULL; |
---|
542 | return rp.next; |
---|
543 | } |
---|