1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* |
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5 | * ABSTRACT: resolutions |
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6 | */ |
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7 | |
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8 | #include "kernel/mod2.h" |
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9 | #include "misc/options.h" |
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10 | #include "kernel/polys.h" |
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11 | #include "kernel/GBEngine/kstd1.h" |
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12 | #include "kernel/GBEngine/kutil.h" |
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13 | #include "kernel/combinatorics/stairc.h" |
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14 | #include "misc/intvec.h" |
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15 | #include "coeffs/numbers.h" |
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16 | #include "kernel/ideals.h" |
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17 | #include "misc/intvec.h" |
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18 | #include "polys/monomials/ring.h" |
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19 | #include "kernel/GBEngine/syz.h" |
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20 | #include "polys/kbuckets.h" |
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21 | #include "polys/prCopy.h" |
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22 | |
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23 | static void syInitSort(ideal arg,intvec **modcomp) |
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24 | { |
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25 | int i,j,k,kk,kkk,jj; |
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26 | idSkipZeroes(arg); |
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27 | polyset F,oldF=arg->m; |
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28 | int Fl=IDELEMS(arg); |
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29 | int rkF=id_RankFreeModule(arg,currRing); |
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30 | int syComponentOrder=currRing->ComponentOrder; |
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31 | |
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32 | while ((Fl!=0) && (oldF[Fl-1]==NULL)) Fl--; |
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33 | if (*modcomp!=NULL) delete modcomp; |
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34 | *modcomp = new intvec(rkF+2); |
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35 | F=(polyset)omAlloc0(IDELEMS(arg)*sizeof(poly)); |
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36 | j=0; |
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37 | for(i=0;i<=rkF;i++) |
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38 | { |
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39 | k=0; |
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40 | jj = j; |
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41 | (**modcomp)[i] = j; |
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42 | while (k<Fl) |
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43 | { |
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44 | while ((k<Fl) && (pGetComp(oldF[k]) != i)) k++; |
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45 | if (k<Fl) |
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46 | { |
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47 | kk=jj; |
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48 | while ((kk<Fl) && (F[kk]) && (pLmCmp(oldF[k],F[kk])!=syComponentOrder)) |
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49 | { |
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50 | kk++; |
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51 | } |
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52 | for (kkk=j;kkk>kk;kkk--) |
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53 | { |
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54 | F[kkk] = F[kkk-1]; |
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55 | } |
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56 | F[kk] = oldF[k]; |
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57 | //Print("Element %d: ",kk);pWrite(F[kk]); |
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58 | j++; |
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59 | k++; |
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60 | } |
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61 | } |
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62 | } |
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63 | (**modcomp)[rkF+1] = Fl; |
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64 | arg->m = F; |
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65 | omFreeSize((ADDRESS)oldF,IDELEMS(arg)*sizeof(poly)); |
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66 | } |
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67 | |
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68 | static void syCreatePairs(polyset F,int lini,int wend,int k,int j,int i, |
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69 | polyset pairs,int regularPairs=0,ideal mW=NULL) |
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70 | { |
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71 | int l,ii=0,jj; |
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72 | poly p,q; |
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73 | |
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74 | while (((k<wend) && (pGetComp(F[k]) == i)) || |
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75 | ((currRing->qideal!=NULL) && (k<regularPairs+IDELEMS(currRing->qideal)))) |
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76 | { |
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77 | p = pOne(); |
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78 | if ((k<wend) && (pGetComp(F[k]) == i) && (k!=j)) |
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79 | pLcm(F[j],F[k],p); |
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80 | else if (ii<IDELEMS(currRing->qideal)) |
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81 | { |
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82 | q = pHead(F[j]); |
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83 | if (mW!=NULL) |
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84 | { |
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85 | for(jj=1;jj<=(currRing->N);jj++) |
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86 | pSetExp(q,jj,pGetExp(q,jj) -pGetExp(mW->m[pGetComp(q)-1],jj)); |
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87 | pSetm(q); |
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88 | } |
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89 | pLcm(q,currRing->qideal->m[ii],p); |
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90 | if (mW!=NULL) |
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91 | { |
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92 | for(jj=1;jj<=(currRing->N);jj++) |
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93 | pSetExp(p,jj,pGetExp(p,jj) +pGetExp(mW->m[pGetComp(p)-1],jj)); |
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94 | pSetm(p); |
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95 | } |
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96 | pDelete(&q); |
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97 | k = regularPairs+ii; |
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98 | ii++; |
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99 | } |
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100 | l=lini; |
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101 | while ((l<k) && ((pairs[l]==NULL) || (!pDivisibleBy(pairs[l],p)))) |
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102 | { |
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103 | if ((pairs[l]!=NULL) && (pDivisibleBy(p,pairs[l]))) |
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104 | pDelete(&(pairs[l])); |
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105 | l++; |
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106 | } |
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107 | if (l==k) |
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108 | { |
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109 | pSetm(p); |
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110 | pairs[l] = p; |
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111 | } |
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112 | else |
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113 | pDelete(&p); |
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114 | k++; |
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115 | } |
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116 | } |
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117 | |
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118 | static poly syRedtail2(poly p, polyset redWith, intvec *modcomp) |
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119 | { |
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120 | poly h, hn; |
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121 | int hncomp,nxt; |
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122 | int j; |
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123 | |
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124 | h = p; |
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125 | hn = pNext(h); |
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126 | while(hn != NULL) |
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127 | { |
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128 | hncomp = pGetComp(hn); |
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129 | j = (*modcomp)[hncomp]; |
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130 | nxt = (*modcomp)[hncomp+1]; |
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131 | while (j < nxt) |
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132 | { |
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133 | if (pLmDivisibleByNoComp(redWith[j], hn)) |
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134 | { |
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135 | //if (TEST_OPT_PROT) PrintS("r"); |
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136 | hn = ksOldSpolyRed(redWith[j],hn); |
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137 | if (hn == NULL) |
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138 | { |
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139 | pNext(h) = NULL; |
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140 | return p; |
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141 | } |
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142 | hncomp = pGetComp(hn); |
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143 | j = (*modcomp)[hncomp]; |
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144 | nxt = (*modcomp)[hncomp+1]; |
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145 | } |
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146 | else |
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147 | { |
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148 | j++; |
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149 | } |
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150 | } |
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151 | h = pNext(h) = hn; |
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152 | hn = pNext(h); |
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153 | } |
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154 | return p; |
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155 | } |
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156 | |
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157 | /*2 |
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158 | * computes the Schreyer syzygies in the local case |
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159 | * input: arg (only allocated: Shdl, Smax) |
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160 | * output: Shdl, Smax |
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161 | */ |
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162 | static ideal sySchreyersSyzygiesFM(ideal arg,intvec ** modcomp) |
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163 | { |
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164 | int Fl=IDELEMS(arg); |
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165 | while ((Fl!=0) && (arg->m[Fl-1]==NULL)) Fl--; |
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166 | ideal result=idInit(16,arg->rank+Fl); |
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167 | polyset F=arg->m,*Shdl=&(result->m); |
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168 | if (Fl==0) return result; |
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169 | |
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170 | int i,j,l,k,totalToRed,ecartToRed,kk; |
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171 | int bestEcart,totalmax,rkF,Sl=0,smax,tmax,tl; |
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172 | int *ecartS, *ecartT, *totalS, |
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173 | *totalT=NULL, *temp=NULL; |
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174 | polyset pairs,S,T,ST/*,oldF*/; |
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175 | poly p,q,toRed; |
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176 | BOOLEAN notFound = FALSE; |
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177 | intvec * newmodcomp = new intvec(Fl+2); |
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178 | intvec * tempcomp; |
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179 | |
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180 | //Print("Naechster Modul\n"); |
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181 | //idPrint(arg); |
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182 | /*-------------initializing the sets--------------------*/ |
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183 | ST=(polyset)omAlloc0(Fl*sizeof(poly)); |
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184 | S=(polyset)omAlloc0(Fl*sizeof(poly)); |
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185 | ecartS=(int*)omAlloc(Fl*sizeof(int)); |
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186 | totalS=(int*)omAlloc(Fl*sizeof(int)); |
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187 | T=(polyset)omAlloc0(2*Fl*sizeof(poly)); |
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188 | ecartT=(int*)omAlloc(2*Fl*sizeof(int)); |
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189 | totalT=(int*)omAlloc(2*Fl*sizeof(int)); |
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190 | pairs=(polyset)omAlloc0(Fl*sizeof(poly)); |
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191 | |
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192 | smax = Fl; |
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193 | tmax = 2*Fl; |
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194 | for (j=1;j<IDELEMS(arg);j++) |
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195 | { |
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196 | if (arg->m[j] != NULL) |
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197 | { |
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198 | assume (arg->m[j-1] != NULL); |
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199 | assume (pGetComp(arg->m[j-1])-pGetComp(arg->m[j])<=0); |
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200 | } |
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201 | } |
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202 | rkF=id_RankFreeModule(arg,currRing); |
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203 | /*----------------construction of the new ordering----------*/ |
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204 | if (rkF>0) |
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205 | rSetSyzComp(rkF, currRing); |
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206 | else |
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207 | rSetSyzComp(1, currRing); |
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208 | /*----------------creating S--------------------------------*/ |
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209 | for(j=0;j<Fl;j++) |
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210 | { |
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211 | S[j] = pCopy(F[j]); |
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212 | totalS[j] = p_LDeg(S[j],&k,currRing); |
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213 | ecartS[j] = totalS[j]-p_FDeg(S[j],currRing); |
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214 | //Print("%d", pGetComp(S[j]));PrintS(" "); |
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215 | p = S[j]; |
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216 | if (rkF==0) pSetCompP(p,1); |
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217 | while (pNext(p)!=NULL) pIter(p); |
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218 | pNext(p) = pHead(F[j]); |
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219 | pIter(p); |
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220 | if (rkF==0) |
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221 | pSetComp(p,j+2); |
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222 | else |
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223 | pSetComp(p,rkF+j+1); |
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224 | pSetmComp(p); |
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225 | } |
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226 | //PrintLn(); |
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227 | if (rkF==0) rkF = 1; |
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228 | /*---------------creating the initial for T----------------*/ |
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229 | j=0; |
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230 | l=-1; |
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231 | totalmax=-1; |
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232 | for (k=0;k<smax;k++) |
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233 | if (totalS[k]>totalmax) totalmax=totalS[k]; |
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234 | for (kk=1;kk<=rkF;kk++) |
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235 | { |
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236 | for (k=0;k<=totalmax;k++) |
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237 | { |
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238 | for (l=0;l<smax;l++) |
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239 | { |
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240 | if ((pGetComp(S[l])==kk) && (totalS[l]==k)) |
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241 | { |
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242 | ST[j] = S[l]; |
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243 | totalT[j] = totalS[l]; |
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244 | ecartT[j] = ecartS[l]; |
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245 | //Print("%d", totalS[l]);PrintS(" "); |
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246 | j++; |
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247 | } |
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248 | } |
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249 | } |
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250 | } |
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251 | //PrintLn(); |
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252 | for (j=0;j<smax;j++) |
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253 | { |
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254 | totalS[j] = totalT[j]; |
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255 | ecartS[j] = ecartT[j]; |
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256 | } |
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257 | |
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258 | /*---------------computing---------------------------------*/ |
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259 | for(j=0;j<smax;j++) |
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260 | { |
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261 | (*newmodcomp)[j+1] = Sl; |
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262 | i = pGetComp(S[j]); |
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263 | int syComponentOrder= currRing->ComponentOrder; |
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264 | int lini,wend; |
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265 | if (syComponentOrder==1) |
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266 | { |
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267 | lini=k=j+1; |
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268 | wend=Fl; |
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269 | } |
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270 | else |
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271 | { |
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272 | lini=k=0; |
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273 | while ((k<j) && (pGetComp(S[k]) != i)) k++; |
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274 | wend=j; |
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275 | } |
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276 | if (TEST_OPT_PROT) |
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277 | { |
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278 | Print("(%d)",Fl-j); |
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279 | mflush(); |
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280 | } |
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281 | syCreatePairs(S,lini,wend,k,j,i,pairs); |
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282 | for (k=lini;k<wend;k++) |
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283 | { |
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284 | if (pairs[k]!=NULL) |
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285 | { |
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286 | /*--------------creating T----------------------------------*/ |
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287 | for (l=0;l<smax;l++) |
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288 | { |
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289 | ecartT[l] = ecartS[l]; |
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290 | totalT[l] = totalS[l]; |
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291 | T[l] = ST[l]; |
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292 | } |
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293 | tl = smax; |
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294 | tempcomp = ivCopy(*modcomp); |
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295 | /*--------------begin to reduce-----------------------------*/ |
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296 | toRed = ksOldCreateSpoly(S[j],S[k]); |
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297 | ecartToRed = 1; |
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298 | bestEcart = 1; |
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299 | if (TEST_OPT_DEBUG) |
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300 | { |
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301 | PrintS("pair: ");pWrite0(S[j]);PrintS(" ");pWrite(S[k]); |
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302 | } |
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303 | if (TEST_OPT_PROT) |
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304 | { |
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305 | PrintS("."); |
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306 | mflush(); |
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307 | } |
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308 | //Print("Reduziere Paar %d,%d (ecart %d): \n",j,k,ecartToRed); |
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309 | //Print("Poly %d: ",j);pWrite(S[j]); |
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310 | //Print("Poly %d: ",k);pWrite(S[k]); |
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311 | //Print("Spoly: ");pWrite(toRed); |
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312 | while (pGetComp(toRed)<=rkF) |
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313 | { |
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314 | if (TEST_OPT_DEBUG) |
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315 | { |
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316 | PrintS("toRed: ");pWrite(toRed); |
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317 | } |
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318 | /* |
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319 | * if ((bestEcart) || (ecartToRed!=0)) |
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320 | * { |
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321 | */ |
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322 | totalToRed = p_LDeg(toRed,&kk,currRing); |
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323 | ecartToRed = totalToRed-p_FDeg(toRed,currRing); |
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324 | /* |
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325 | * } |
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326 | */ |
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327 | //Print("toRed now (neuer ecart %d): ",ecartToRed);pWrite(toRed); |
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328 | notFound = TRUE; |
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329 | bestEcart = 32000; //a very large integer |
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330 | p = NULL; |
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331 | int l=0; |
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332 | #define OLD_SEARCH |
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333 | #ifdef OLD_SEARCH |
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334 | while ((l<tl) && (pGetComp(T[l])<pGetComp(toRed))) l++; |
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335 | //assume (l==(**modcomp)[pGetComp(toRed)]); |
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336 | while ((l<tl) && (notFound)) |
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337 | #else |
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338 | l = (**modcomp)[pGetComp(toRed)]; |
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339 | int kkk = (**modcomp)[pGetComp(toRed)+1]; |
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340 | while ((l<kkk) && (notFound)) |
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341 | #endif |
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342 | { |
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343 | if ((ecartT[l]<bestEcart) && (pDivisibleBy(T[l],toRed))) |
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344 | { |
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345 | if (ecartT[l]<=ecartToRed) notFound = FALSE; |
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346 | p = T[l]; |
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347 | bestEcart = ecartT[l]; |
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348 | } |
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349 | l++; |
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350 | } |
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351 | if (p==NULL) |
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352 | { |
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353 | pDelete(&toRed); |
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354 | for(k=j;k<Fl;k++) pDelete(&(pairs[k])); |
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355 | omFreeSize((ADDRESS)pairs,Fl*sizeof(poly)); |
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356 | omFreeSize((ADDRESS)ST,Fl*sizeof(poly)); |
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357 | omFreeSize((ADDRESS)S,Fl*sizeof(poly)); |
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358 | omFreeSize((ADDRESS)T,tmax*sizeof(poly)); |
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359 | omFreeSize((ADDRESS)ecartT,tmax*sizeof(int)); |
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360 | omFreeSize((ADDRESS)totalT,tmax*sizeof(int)); |
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361 | omFreeSize((ADDRESS)ecartS,Fl*sizeof(int)); |
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362 | omFreeSize((ADDRESS)totalS,Fl*sizeof(int)); |
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363 | for(k=0;k<IDELEMS(result);k++) pDelete(&((*Shdl)[k])); |
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364 | WerrorS("ideal not a standard basis");//no polynom for reduction |
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365 | return result; |
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366 | } |
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367 | else |
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368 | { |
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369 | //Print("reduced with (ecart %d): ",bestEcart);wrp(p);PrintLn(); |
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370 | if (notFound) |
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371 | { |
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372 | if (tl>=tmax) |
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373 | { |
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374 | pEnlargeSet(&T,tmax,16); |
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375 | tmax += 16; |
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376 | temp = (int*)omAlloc((tmax+16)*sizeof(int)); |
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377 | for(l=0;l<tmax;l++) temp[l]=totalT[l]; |
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378 | totalT = temp; |
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379 | temp = (int*)omAlloc((tmax+16)*sizeof(int)); |
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380 | for(l=0;l<tmax;l++) temp[l]=ecartT[l]; |
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381 | ecartT = temp; |
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382 | } |
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383 | //PrintS("t"); |
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384 | int comptR=pGetComp(toRed); |
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385 | for (l=tempcomp->length()-1;l>comptR;l--) |
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386 | { |
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387 | if ((*tempcomp)[l]>0) |
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388 | (*tempcomp)[l]++; |
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389 | } |
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390 | l=0; |
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391 | while ((l<tl) && (comptR>pGetComp(T[l]))) l++; |
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392 | while ((l<tl) && (totalT[l]<=totalToRed)) l++; |
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393 | for (kk=tl;kk>l;kk--) |
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394 | { |
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395 | T[kk]=T[kk-1]; |
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396 | totalT[kk]=totalT[kk-1]; |
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397 | ecartT[kk]=ecartT[kk-1]; |
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398 | } |
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399 | q = pCopy(toRed); |
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400 | pNorm(q); |
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401 | T[l] = q; |
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402 | totalT[l] = totalToRed; |
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403 | ecartT[l] = ecartToRed; |
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404 | tl++; |
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405 | } |
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406 | toRed = ksOldSpolyRed(p,toRed); |
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407 | } |
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408 | } |
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409 | //Print("toRed finally (neuer ecart %d): ",ecartToRed);pWrite(toRed); |
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410 | //PrintS("s"); |
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411 | if (pGetComp(toRed)>rkF) |
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412 | { |
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413 | if (Sl>=IDELEMS(result)) |
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414 | { |
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415 | pEnlargeSet(Shdl,IDELEMS(result),16); |
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416 | IDELEMS(result) += 16; |
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417 | } |
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418 | //p_Shift(&toRed,-rkF,currRing); |
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419 | pNorm(toRed); |
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420 | (*Shdl)[Sl] = toRed; |
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421 | Sl++; |
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422 | } |
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423 | /*----------------deleting all polys not from ST--------------*/ |
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424 | for(l=0;l<tl;l++) |
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425 | { |
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426 | kk=0; |
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427 | while ((kk<smax) && (T[l] != S[kk])) kk++; |
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428 | if (kk>=smax) |
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429 | { |
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430 | pDelete(&T[l]); |
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431 | //Print ("#"); |
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432 | } |
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433 | } |
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434 | delete tempcomp; |
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435 | } |
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436 | } |
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437 | for(k=lini;k<wend;k++) pDelete(&(pairs[k])); |
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438 | } |
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439 | (*newmodcomp)[Fl+1] = Sl; |
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440 | omFreeSize((ADDRESS)pairs,Fl*sizeof(poly)); |
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441 | omFreeSize((ADDRESS)ST,Fl*sizeof(poly)); |
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442 | omFreeSize((ADDRESS)S,Fl*sizeof(poly)); |
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443 | omFreeSize((ADDRESS)T,tmax*sizeof(poly)); |
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444 | omFreeSize((ADDRESS)ecartT,tmax*sizeof(int)); |
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445 | omFreeSize((ADDRESS)totalT,tmax*sizeof(int)); |
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446 | omFreeSize((ADDRESS)ecartS,Fl*sizeof(int)); |
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447 | omFreeSize((ADDRESS)totalS,Fl*sizeof(int)); |
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448 | delete *modcomp; |
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449 | *modcomp = newmodcomp; |
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450 | return result; |
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451 | } |
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452 | |
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453 | /*3 |
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454 | *special Normalform for Schreyer in factor rings |
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455 | */ |
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456 | poly sySpecNormalize(poly toNorm,ideal mW=NULL) |
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457 | { |
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458 | int j,i=0; |
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459 | poly p; |
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460 | |
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461 | if (toNorm==NULL) return NULL; |
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462 | p = pHead(toNorm); |
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463 | if (mW!=NULL) |
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464 | { |
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465 | for(j=1;j<=(currRing->N);j++) |
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466 | pSetExp(p,j,pGetExp(p,j) -pGetExp(mW->m[pGetComp(p)-1],j)); |
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467 | } |
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468 | while ((p!=NULL) && (i<IDELEMS(currRing->qideal))) |
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469 | { |
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470 | if (pDivisibleBy(currRing->qideal->m[i],p)) |
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471 | { |
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472 | //pNorm(toNorm); |
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473 | toNorm = ksOldSpolyRed(currRing->qideal->m[i],toNorm); |
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474 | pDelete(&p); |
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475 | if (toNorm==NULL) return NULL; |
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476 | p = pHead(toNorm); |
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477 | if (mW!=NULL) |
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478 | { |
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479 | for(j=1;j<=(currRing->N);j++) |
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480 | pSetExp(p,j,pGetExp(p,j) -pGetExp(mW->m[pGetComp(p)-1],j)); |
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481 | } |
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482 | i = 0; |
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483 | } |
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484 | else |
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485 | { |
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486 | i++; |
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487 | } |
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488 | } |
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489 | pDelete(&p); |
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490 | return toNorm; |
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491 | } |
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492 | |
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493 | /*2 |
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494 | * computes the Schreyer syzygies in the global case |
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495 | * input: F |
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496 | * output: Shdl, Smax |
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497 | * modcomp, length stores the start position of the module comp. in arg |
---|
498 | */ |
---|
499 | static ideal sySchreyersSyzygiesFB(ideal arg,intvec ** modcomp,ideal mW,BOOLEAN redTail=TRUE) |
---|
500 | { |
---|
501 | kBucket_pt sy0buck = kBucketCreate(currRing); |
---|
502 | |
---|
503 | int Fl=IDELEMS(arg); |
---|
504 | while ((Fl!=0) && (arg->m[Fl-1]==NULL)) Fl--; |
---|
505 | ideal result=idInit(16,Fl); |
---|
506 | int i,j,l,k,kkk,/*rkF,*/Sl=0,syComponentOrder=currRing->ComponentOrder; |
---|
507 | int /*fstart,*/wend,lini,ltR,gencQ=0; |
---|
508 | intvec *newmodcomp; |
---|
509 | int *Flength; |
---|
510 | polyset pairs,F=arg->m,*Shdl=&(result->m); |
---|
511 | poly /*p,*/q,toRed,syz,lastmonom,multWith; |
---|
512 | BOOLEAN isNotReduced=TRUE; |
---|
513 | |
---|
514 | //#define WRITE_BUCKETS |
---|
515 | #ifdef WRITE_BUCKETS |
---|
516 | PrintS("Input: \n"); |
---|
517 | ideal twr=idHead(arg); |
---|
518 | idPrint(arg); |
---|
519 | idDelete(&twr); |
---|
520 | if (modcomp!=NULL) (*modcomp)->show(0,0); |
---|
521 | #endif |
---|
522 | |
---|
523 | newmodcomp = new intvec(Fl+2); |
---|
524 | //for (j=0;j<Fl;j++) pWrite(F[j]); |
---|
525 | //PrintLn(); |
---|
526 | if (currRing->qideal==NULL) |
---|
527 | pairs=(polyset)omAlloc0(Fl*sizeof(poly)); |
---|
528 | else |
---|
529 | { |
---|
530 | gencQ = IDELEMS(currRing->qideal); |
---|
531 | pairs=(polyset)omAlloc0((Fl+gencQ)*sizeof(poly)); |
---|
532 | } |
---|
533 | // rkF=id_RankFreeModule(arg,currRing); |
---|
534 | Flength = (int*)omAlloc0(Fl*sizeof(int)); |
---|
535 | for(j=0;j<Fl;j++) |
---|
536 | { |
---|
537 | Flength[j] = pLength(F[j]); |
---|
538 | } |
---|
539 | for(j=0;j<Fl;j++) |
---|
540 | { |
---|
541 | (*newmodcomp)[j+1] = Sl; |
---|
542 | if (TEST_OPT_PROT) |
---|
543 | { |
---|
544 | Print("(%d)",Fl-j); |
---|
545 | mflush(); |
---|
546 | } |
---|
547 | i = pGetComp(F[j]); |
---|
548 | if (syComponentOrder==1) |
---|
549 | { |
---|
550 | lini=k=j+1; |
---|
551 | wend=Fl; |
---|
552 | } |
---|
553 | else |
---|
554 | { |
---|
555 | lini=k=0; |
---|
556 | while ((k<j) && (pGetComp(F[k]) != i)) k++; |
---|
557 | wend=j; |
---|
558 | } |
---|
559 | syCreatePairs(F,lini,wend,k,j,i,pairs,Fl,mW); |
---|
560 | if (currRing->qideal!=NULL) wend = Fl+gencQ; |
---|
561 | for (k=lini;k<wend;k++) |
---|
562 | { |
---|
563 | if (pairs[k]!=NULL) |
---|
564 | { |
---|
565 | if (TEST_OPT_PROT) |
---|
566 | { |
---|
567 | PrintS("."); |
---|
568 | mflush(); |
---|
569 | } |
---|
570 | //begins to construct the syzygy |
---|
571 | if (k<Fl) |
---|
572 | { |
---|
573 | number an=nCopy(pGetCoeff(F[k])),bn=nCopy(pGetCoeff(F[j])); |
---|
574 | /*int ct =*/ (void) ksCheckCoeff(&an, &bn, currRing->cf); |
---|
575 | syz = pCopy(pairs[k]); |
---|
576 | //syz->coef = nCopy(F[k]->coef); |
---|
577 | syz->coef = an; |
---|
578 | //syz->coef = nInpNeg(syz->coef); |
---|
579 | pNext(syz) = pairs[k]; |
---|
580 | lastmonom = pNext(syz); |
---|
581 | //lastmonom->coef = nCopy(F[j]->coef); |
---|
582 | lastmonom->coef = bn; |
---|
583 | lastmonom->coef = nInpNeg(lastmonom->coef); |
---|
584 | pSetComp(lastmonom,k+1); |
---|
585 | } |
---|
586 | else |
---|
587 | { |
---|
588 | syz = pairs[k]; |
---|
589 | syz->coef = nCopy(currRing->qideal->m[k-Fl]->coef); |
---|
590 | syz->coef = nInpNeg(syz->coef); |
---|
591 | lastmonom = syz; |
---|
592 | multWith = pMDivide(syz,F[j]); |
---|
593 | multWith->coef = nCopy(currRing->qideal->m[k-Fl]->coef); |
---|
594 | } |
---|
595 | pSetComp(syz,j+1); |
---|
596 | pairs[k] = NULL; |
---|
597 | //the next term of the syzygy |
---|
598 | //constructs the spoly |
---|
599 | if (TEST_OPT_DEBUG) |
---|
600 | { |
---|
601 | if (k<Fl) |
---|
602 | { |
---|
603 | PrintS("pair: ");pWrite0(F[j]);PrintS(" ");pWrite(F[k]); |
---|
604 | } |
---|
605 | else |
---|
606 | { |
---|
607 | PrintS("pair: ");pWrite0(F[j]);PrintS(" ");pWrite(currRing->qideal->m[k-Fl]); |
---|
608 | } |
---|
609 | } |
---|
610 | if (k<Fl) |
---|
611 | toRed = ksOldCreateSpoly(F[j],F[k]); |
---|
612 | else |
---|
613 | { |
---|
614 | q = pMult_mm(pCopy(F[j]),multWith); |
---|
615 | toRed = sySpecNormalize(q,mW); |
---|
616 | pDelete(&multWith); |
---|
617 | } |
---|
618 | kBucketInit(sy0buck,toRed,-1); |
---|
619 | toRed = kBucketGetLm(sy0buck); |
---|
620 | isNotReduced = TRUE; |
---|
621 | while (toRed!=NULL) |
---|
622 | { |
---|
623 | if (TEST_OPT_DEBUG) |
---|
624 | { |
---|
625 | PrintS("toRed: ");pWrite(toRed); |
---|
626 | } |
---|
627 | // l=0; |
---|
628 | // while ((l<Fl) && (!pDivisibleBy(F[l],toRed))) l++; |
---|
629 | // if (l>=Fl) |
---|
630 | l = (**modcomp)[pGetComp(toRed)+1]-1; |
---|
631 | kkk = (**modcomp)[pGetComp(toRed)]; |
---|
632 | while ((l>=kkk) && (!pDivisibleBy(F[l],toRed))) l--; |
---|
633 | #ifdef WRITE_BUCKETS |
---|
634 | kBucketClear(sy0buck,&toRed,<R); |
---|
635 | printf("toRed in Pair[%d, %d]:", j, k); |
---|
636 | pWrite(toRed); |
---|
637 | kBucketInit(sy0buck,toRed,-1); |
---|
638 | #endif |
---|
639 | |
---|
640 | if (l<kkk) |
---|
641 | { |
---|
642 | if ((currRing->qideal!=NULL) && (isNotReduced)) |
---|
643 | { |
---|
644 | kBucketClear(sy0buck,&toRed,<R); |
---|
645 | toRed = sySpecNormalize(toRed,mW); |
---|
646 | #ifdef WRITE_BUCKETS |
---|
647 | printf("toRed in Pair[%d, %d]:", j, k); |
---|
648 | pWrite(toRed); |
---|
649 | #endif |
---|
650 | kBucketInit(sy0buck,toRed,-1); |
---|
651 | toRed = kBucketGetLm(sy0buck); |
---|
652 | isNotReduced = FALSE; |
---|
653 | } |
---|
654 | else |
---|
655 | { |
---|
656 | pDelete(&toRed); |
---|
657 | |
---|
658 | pDelete(&syz); |
---|
659 | for(k=j;k<Fl;k++) pDelete(&(pairs[k])); |
---|
660 | omFreeSize((ADDRESS)pairs,(Fl + gencQ)*sizeof(poly)); |
---|
661 | |
---|
662 | |
---|
663 | for(k=0;k<IDELEMS(result);k++) pDelete(&((*Shdl)[k])); |
---|
664 | |
---|
665 | kBucketDestroy(&(sy0buck)); |
---|
666 | |
---|
667 | //no polynom for reduction |
---|
668 | WerrorS("ideal not a standard basis"); |
---|
669 | |
---|
670 | return result; |
---|
671 | } |
---|
672 | } |
---|
673 | else |
---|
674 | { |
---|
675 | //the next monom of the syzygy |
---|
676 | isNotReduced = TRUE; |
---|
677 | if (TEST_OPT_DEBUG) |
---|
678 | { |
---|
679 | PrintS("reduced with: ");pWrite(F[l]); |
---|
680 | } |
---|
681 | pNext(lastmonom) = pHead(toRed); |
---|
682 | pIter(lastmonom); |
---|
683 | lastmonom->coef = nDiv(lastmonom->coef,F[l]->coef); |
---|
684 | //lastmonom->coef = nInpNeg(lastmonom->coef); |
---|
685 | pSetComp(lastmonom,l+1); |
---|
686 | //computes the new toRed |
---|
687 | number up = kBucketPolyRed(sy0buck,F[l],Flength[l],NULL); |
---|
688 | if (! nIsOne(up)) |
---|
689 | { |
---|
690 | // Thomas: Now do whatever you need to do |
---|
691 | #ifdef WRITE_BUCKETS |
---|
692 | PrintS("multiplied with: ");nWrite(up);PrintLn(); |
---|
693 | #endif |
---|
694 | syz=__p_Mult_nn(syz,up,currRing); |
---|
695 | } |
---|
696 | nDelete(&up); |
---|
697 | |
---|
698 | toRed = kBucketGetLm(sy0buck); |
---|
699 | //the module component of the new monom |
---|
700 | //pWrite(toRed); |
---|
701 | } |
---|
702 | } |
---|
703 | kBucketClear(sy0buck,&toRed,<R); //Zur Sichereheit |
---|
704 | //PrintLn(); |
---|
705 | if (syz!=NULL) |
---|
706 | { |
---|
707 | if (Sl>=IDELEMS(result)) |
---|
708 | { |
---|
709 | pEnlargeSet(Shdl,IDELEMS(result),16); |
---|
710 | IDELEMS(result) += 16; |
---|
711 | } |
---|
712 | pNorm(syz); |
---|
713 | if (BTEST1(OPT_REDTAIL) && redTail) |
---|
714 | { |
---|
715 | (*newmodcomp)[j+2] = Sl; |
---|
716 | (*Shdl)[Sl] = syRedtail2(syz,*Shdl,newmodcomp); |
---|
717 | (*newmodcomp)[j+2] = 0; |
---|
718 | } |
---|
719 | else |
---|
720 | (*Shdl)[Sl] = syz; |
---|
721 | Sl++; |
---|
722 | } |
---|
723 | } |
---|
724 | } |
---|
725 | // for(k=j;k<Fl;k++) pDelete(&(pairs[k])); |
---|
726 | } |
---|
727 | (*newmodcomp)[Fl+1] = Sl; |
---|
728 | if (currRing->qideal==NULL) |
---|
729 | omFreeSize((ADDRESS)pairs,Fl*sizeof(poly)); |
---|
730 | else |
---|
731 | omFreeSize((ADDRESS)pairs,(Fl+IDELEMS(currRing->qideal))*sizeof(poly)); |
---|
732 | omFreeSize((ADDRESS)Flength,Fl*sizeof(int)); |
---|
733 | delete *modcomp; |
---|
734 | *modcomp = newmodcomp; |
---|
735 | |
---|
736 | kBucketDestroy(&(sy0buck)); |
---|
737 | return result; |
---|
738 | } |
---|
739 | |
---|
740 | void syReOrderResolventFB(resolvente res,int length, int initial) |
---|
741 | { |
---|
742 | int syzIndex=length-1,i,j; |
---|
743 | poly p; |
---|
744 | |
---|
745 | while ((syzIndex!=0) && (res[syzIndex]==NULL)) syzIndex--; |
---|
746 | while (syzIndex>=initial) |
---|
747 | { |
---|
748 | for(i=0;i<IDELEMS(res[syzIndex]);i++) |
---|
749 | { |
---|
750 | p = res[syzIndex]->m[i]; |
---|
751 | |
---|
752 | while (p!=NULL) |
---|
753 | { |
---|
754 | if (res[syzIndex-1]->m[pGetComp(p)-1]!=NULL) |
---|
755 | { |
---|
756 | for(j=1;j<=(currRing->N);j++) |
---|
757 | { |
---|
758 | pSetExp(p,j,pGetExp(p,j) |
---|
759 | -pGetExp(res[syzIndex-1]->m[pGetComp(p)-1],j)); |
---|
760 | } |
---|
761 | } |
---|
762 | else |
---|
763 | PrintS("error in the resolvent\n"); |
---|
764 | pSetm(p); |
---|
765 | pIter(p); |
---|
766 | } |
---|
767 | } |
---|
768 | syzIndex--; |
---|
769 | } |
---|
770 | } |
---|
771 | |
---|
772 | #if 0 |
---|
773 | static void syMergeSortResolventFB(resolvente res,int length, int initial=1) |
---|
774 | { |
---|
775 | int syzIndex=length-1,i,j; |
---|
776 | poly qq,pp,result=NULL; |
---|
777 | poly p; |
---|
778 | |
---|
779 | while ((syzIndex!=0) && (res[syzIndex]==NULL)) syzIndex--; |
---|
780 | while (syzIndex>=initial) |
---|
781 | { |
---|
782 | for(i=0;i<IDELEMS(res[syzIndex]);i++) |
---|
783 | { |
---|
784 | p = res[syzIndex]->m[i]; |
---|
785 | if (p != NULL) |
---|
786 | { |
---|
787 | for (;;) |
---|
788 | { |
---|
789 | qq = p; |
---|
790 | for(j=1;j<=(currRing->N);j++) |
---|
791 | { |
---|
792 | pSetExp(p,j,pGetExp(p,j) |
---|
793 | -pGetExp(res[syzIndex-1]->m[pGetComp(p)-1],j)); |
---|
794 | } |
---|
795 | pSetm(p); |
---|
796 | for (;;) |
---|
797 | { |
---|
798 | if (pNext(p) == NULL) |
---|
799 | { |
---|
800 | pAdd(result, qq); |
---|
801 | break; |
---|
802 | } |
---|
803 | pp = pNext(p); |
---|
804 | for(j=1;j<=(currRing->N);j++) |
---|
805 | { |
---|
806 | pSetExp(pp,j,pGetExp(pp,j) |
---|
807 | -pGetExp(res[syzIndex-1]->m[pGetComp(pp)-1],j)); |
---|
808 | } |
---|
809 | pSetm(pp); |
---|
810 | if (pCmp(p,pNext(p)) != 1) |
---|
811 | { |
---|
812 | pp = p; |
---|
813 | pIter(p); |
---|
814 | pNext(pp) = NULL; |
---|
815 | result = pAdd(result, qq); |
---|
816 | break; |
---|
817 | } |
---|
818 | pIter(p); |
---|
819 | } |
---|
820 | } |
---|
821 | } |
---|
822 | res[syzIndex]->m[i] = p; |
---|
823 | } |
---|
824 | syzIndex--; |
---|
825 | } |
---|
826 | } |
---|
827 | #endif |
---|
828 | |
---|
829 | BOOLEAN syTestOrder(ideal M) |
---|
830 | { |
---|
831 | int i=id_RankFreeModule(M,currRing); |
---|
832 | if (i == 0) return FALSE; |
---|
833 | int j=0; |
---|
834 | |
---|
835 | while ((currRing->order[j]!=ringorder_c) && (currRing->order[j]!=ringorder_C)) |
---|
836 | j++; |
---|
837 | if (currRing->order[j+1]!=0) |
---|
838 | return TRUE; |
---|
839 | return FALSE; |
---|
840 | } |
---|
841 | |
---|
842 | #if 0 /*debug only */ |
---|
843 | static void syPrintResolution(resolvente res,int start,int length) |
---|
844 | { |
---|
845 | while ((start < length) && (res[start])) |
---|
846 | { |
---|
847 | Print("Syz(%d): \n",start); |
---|
848 | idTest(res[start]); |
---|
849 | //idPrint(res[start]); |
---|
850 | start++; |
---|
851 | } |
---|
852 | } |
---|
853 | #endif |
---|
854 | |
---|
855 | resolvente sySchreyerResolvente(ideal arg, int maxlength, int * length, |
---|
856 | BOOLEAN isMonomial, BOOLEAN /*notReplace*/) |
---|
857 | { |
---|
858 | ideal mW=NULL; |
---|
859 | int i,syzIndex = 0,j=0; |
---|
860 | intvec * modcomp=NULL,*w=NULL; |
---|
861 | // int ** wv=NULL; |
---|
862 | tHomog hom=(tHomog)idHomModule(arg,NULL,&w); |
---|
863 | ring origR = currRing; |
---|
864 | ring syRing = NULL; |
---|
865 | |
---|
866 | if ((!isMonomial) && syTestOrder(arg)) |
---|
867 | { |
---|
868 | WerrorS("sres only implemented for modules with ordering ..,c or ..,C"); |
---|
869 | return NULL; |
---|
870 | } |
---|
871 | *length = 4; |
---|
872 | resolvente res = (resolvente)omAlloc0(4*sizeof(ideal)),newres; |
---|
873 | res[0] = idCopy(arg); |
---|
874 | |
---|
875 | while ((!idIs0(res[syzIndex])) && ((maxlength==-1) || (syzIndex<maxlength))) |
---|
876 | { |
---|
877 | i = IDELEMS(res[syzIndex]); |
---|
878 | //while ((i!=0) && (!res[syzIndex]->m[i-1])) i--; |
---|
879 | if (syzIndex+1==*length) |
---|
880 | { |
---|
881 | newres = (resolvente)omAlloc0((*length+4)*sizeof(ideal)); |
---|
882 | // for (j=0;j<*length+4;j++) newres[j] = NULL; |
---|
883 | for (j=0;j<*length;j++) newres[j] = res[j]; |
---|
884 | omFreeSize((ADDRESS)res,*length*sizeof(ideal)); |
---|
885 | *length += 4; |
---|
886 | res=newres; |
---|
887 | } |
---|
888 | |
---|
889 | if ((hom==isHomog)|| (rHasGlobalOrdering(origR))) |
---|
890 | { |
---|
891 | if (syzIndex==0) syInitSort(res[0],&modcomp); |
---|
892 | |
---|
893 | if ((syzIndex==0) && !rRing_has_CompLastBlock(currRing)) |
---|
894 | res[syzIndex+1] = sySchreyersSyzygiesFB(res[syzIndex],&modcomp,mW,FALSE); |
---|
895 | else |
---|
896 | res[syzIndex+1] = sySchreyersSyzygiesFB(res[syzIndex],&modcomp,mW); |
---|
897 | |
---|
898 | if (errorreported) |
---|
899 | { |
---|
900 | for (j=0;j<*length;j++) idDelete( &res[j] ); |
---|
901 | omFreeSize((ADDRESS)res,*length*sizeof(ideal)); |
---|
902 | return NULL; |
---|
903 | } |
---|
904 | |
---|
905 | mW = res[syzIndex]; |
---|
906 | } |
---|
907 | //idPrint(res[syzIndex+1]); |
---|
908 | |
---|
909 | if ( /*(*/ syzIndex==0 /*)*/ ) |
---|
910 | { |
---|
911 | if ((hom==isHomog)|| (rHasGlobalOrdering(origR))) |
---|
912 | { |
---|
913 | syRing = rAssure_CompLastBlock(origR, TRUE); |
---|
914 | if (syRing != origR) |
---|
915 | { |
---|
916 | rChangeCurrRing(syRing); |
---|
917 | for (i=0; i<IDELEMS(res[1]); i++) |
---|
918 | { |
---|
919 | res[1]->m[i] = prMoveR( res[1]->m[i], origR, syRing); |
---|
920 | } |
---|
921 | } |
---|
922 | idTest(res[1]); |
---|
923 | } |
---|
924 | else |
---|
925 | { |
---|
926 | syRing = rAssure_SyzComp_CompLastBlock(origR); |
---|
927 | if (syRing != origR) |
---|
928 | { |
---|
929 | rChangeCurrRing(syRing); |
---|
930 | for (i=0; i<IDELEMS(res[0]); i++) |
---|
931 | { |
---|
932 | res[0]->m[i] = prMoveR( res[0]->m[i], origR, syRing); |
---|
933 | } |
---|
934 | } |
---|
935 | idTest(res[0]); |
---|
936 | } |
---|
937 | } |
---|
938 | if ((hom!=isHomog) && (rHasLocalOrMixedOrdering(origR))) |
---|
939 | { |
---|
940 | if (syzIndex==0) syInitSort(res[0],&modcomp); |
---|
941 | res[syzIndex+1] = sySchreyersSyzygiesFM(res[syzIndex],&modcomp); |
---|
942 | if (errorreported) |
---|
943 | { |
---|
944 | for (j=0;j<*length;j++) idDelete( &res[j] ); |
---|
945 | omFreeSize((ADDRESS)res,*length*sizeof(ideal)); |
---|
946 | return NULL; |
---|
947 | } |
---|
948 | } |
---|
949 | syzIndex++; |
---|
950 | if (TEST_OPT_PROT) Print("[%d]\n",syzIndex); |
---|
951 | } |
---|
952 | //syPrintResolution(res,1,*length); |
---|
953 | if ((hom!=isHomog) && (rHasLocalOrMixedOrdering(origR))) |
---|
954 | { |
---|
955 | syzIndex = 1; |
---|
956 | while ((syzIndex < *length) && (!idIs0(res[syzIndex]))) |
---|
957 | { |
---|
958 | id_Shift(res[syzIndex],-rGetMaxSyzComp(syzIndex, currRing),currRing); |
---|
959 | syzIndex++; |
---|
960 | } |
---|
961 | } |
---|
962 | if ((hom==isHomog) || (rHasGlobalOrdering(origR))) |
---|
963 | syzIndex = 1; |
---|
964 | else |
---|
965 | syzIndex = 0; |
---|
966 | syReOrderResolventFB(res,*length,syzIndex+1); |
---|
967 | if (/*ringOrderChanged:*/ origR!=syRing && syRing != NULL) |
---|
968 | { |
---|
969 | rChangeCurrRing(origR); |
---|
970 | // Thomas: Here I assume that all (!) polys of res live in tmpR |
---|
971 | while ((syzIndex < *length) && (res[syzIndex])) |
---|
972 | { |
---|
973 | for (i=0;i<IDELEMS(res[syzIndex]);i++) |
---|
974 | { |
---|
975 | if (res[syzIndex]->m[i]) |
---|
976 | { |
---|
977 | res[syzIndex]->m[i] = prMoveR( res[syzIndex]->m[i], syRing, origR); |
---|
978 | } |
---|
979 | } |
---|
980 | syzIndex++; |
---|
981 | } |
---|
982 | // j = 0; while (currRing->order[j]!=0) j++; // What was this for???! |
---|
983 | rDelete(syRing); |
---|
984 | } |
---|
985 | else |
---|
986 | { |
---|
987 | // Thomas -- are you sure that you have to "reorder" here? |
---|
988 | while ((syzIndex < *length) && (res[syzIndex])) |
---|
989 | { |
---|
990 | for (i=0;i<IDELEMS(res[syzIndex]);i++) |
---|
991 | { |
---|
992 | if (res[syzIndex]->m[i]) |
---|
993 | res[syzIndex]->m[i] = pSortCompCorrect(res[syzIndex]->m[i]); |
---|
994 | } |
---|
995 | syzIndex++; |
---|
996 | } |
---|
997 | } |
---|
998 | if ((hom==isHomog) || (rHasGlobalOrdering(origR))) |
---|
999 | { |
---|
1000 | if (res[1]!=NULL) |
---|
1001 | { |
---|
1002 | syReOrderResolventFB(res,2,1); |
---|
1003 | for (i=0;i<IDELEMS(res[1]);i++) |
---|
1004 | { |
---|
1005 | if (res[1]->m[i]) |
---|
1006 | res[1]->m[i] = pSort(res[1]->m[i]); |
---|
1007 | } |
---|
1008 | } |
---|
1009 | } |
---|
1010 | //syPrintResolution(res,0,*length); |
---|
1011 | |
---|
1012 | //syMergeSortResolventFB(res,*length); |
---|
1013 | if (modcomp!=NULL) delete modcomp; |
---|
1014 | if (w!=NULL) delete w; |
---|
1015 | return res; |
---|
1016 | } |
---|
1017 | |
---|
1018 | syStrategy sySchreyer(ideal arg, int maxlength) |
---|
1019 | { |
---|
1020 | int rl; |
---|
1021 | resolvente fr = sySchreyerResolvente(arg,maxlength,&(rl)); |
---|
1022 | if (fr==NULL) return NULL; |
---|
1023 | |
---|
1024 | // int typ0; |
---|
1025 | syStrategy result=(syStrategy)omAlloc0(sizeof(ssyStrategy)); |
---|
1026 | result->length=rl; |
---|
1027 | result->fullres = (resolvente)omAlloc0((rl /*result->length*/+1)*sizeof(ideal)); |
---|
1028 | for (int i=rl /*result->length*/-1;i>=0;i--) |
---|
1029 | { |
---|
1030 | if (fr[i]!=NULL) |
---|
1031 | { |
---|
1032 | idSkipZeroes(fr[i]); |
---|
1033 | result->fullres[i] = fr[i]; |
---|
1034 | fr[i] = NULL; |
---|
1035 | } |
---|
1036 | } |
---|
1037 | if (currRing->qideal!=NULL) |
---|
1038 | { |
---|
1039 | for (int i=0; i<rl; i++) |
---|
1040 | { |
---|
1041 | if (result->fullres[i]!=NULL) |
---|
1042 | { |
---|
1043 | ideal t=kNF(currRing->qideal,NULL,result->fullres[i]); |
---|
1044 | idDelete(&result->fullres[i]); |
---|
1045 | result->fullres[i]=t; |
---|
1046 | if (i<rl-1) |
---|
1047 | { |
---|
1048 | for(int j=IDELEMS(t)-1;j>=0; j--) |
---|
1049 | { |
---|
1050 | if ((t->m[j]==NULL) && (result->fullres[i+1]!=NULL)) |
---|
1051 | { |
---|
1052 | for(int k=IDELEMS(result->fullres[i+1])-1;k>=0; k--) |
---|
1053 | { |
---|
1054 | if (result->fullres[i+1]->m[k]!=NULL) |
---|
1055 | { |
---|
1056 | pDeleteComp(&(result->fullres[i+1]->m[k]),j+1); |
---|
1057 | } |
---|
1058 | } |
---|
1059 | } |
---|
1060 | } |
---|
1061 | } |
---|
1062 | idSkipZeroes(result->fullres[i]); |
---|
1063 | } |
---|
1064 | } |
---|
1065 | if ((rl>maxlength) && (result->fullres[rl-1]!=NULL)) |
---|
1066 | { |
---|
1067 | idDelete(&result->fullres[rl-1]); |
---|
1068 | } |
---|
1069 | } |
---|
1070 | omFreeSize((ADDRESS)fr,(rl /*result->length*/)*sizeof(ideal)); |
---|
1071 | return result; |
---|
1072 | } |
---|
1073 | |
---|