1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: syz0.cc,v 1.9 1997-04-17 17:52:22 Singular Exp $ */ |
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5 | /* |
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6 | * ABSTRACT: resolutions |
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7 | */ |
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8 | |
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9 | |
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10 | #include "mod2.h" |
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11 | #include "mmemory.h" |
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12 | #include "polys.h" |
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13 | #include "febase.h" |
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14 | #include "kstd1.h" |
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15 | #include "kutil.h" |
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16 | #include "spolys.h" |
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17 | #include "stairc.h" |
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18 | #include "ipid.h" |
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19 | #include "cntrlc.h" |
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20 | #include "ipid.h" |
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21 | #include "intvec.h" |
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22 | #include "ipshell.h" |
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23 | #include "tok.h" |
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24 | #include "numbers.h" |
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25 | #include "ideals.h" |
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26 | #include "intvec.h" |
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27 | #include "ring.h" |
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28 | #include "syz.h" |
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29 | |
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30 | static polyset syInitSort(polyset oldF,int rkF,int Fmax, |
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31 | int syComponentOrder,intvec **modcomp) |
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32 | { |
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33 | int i,j,k,kk,kkk,jj; |
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34 | polyset F; |
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35 | int Fl=Fmax; |
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36 | |
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37 | while ((Fl!=0) && (oldF[Fl-1]==NULL)) Fl--; |
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38 | if (*modcomp!=NULL) delete modcomp; |
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39 | *modcomp = new intvec(rkF+2); |
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40 | F=(polyset)Alloc0(Fmax*sizeof(poly)); |
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41 | j=0; |
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42 | for(i=0;i<=rkF;i++) |
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43 | { |
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44 | k=0; |
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45 | jj = j; |
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46 | (**modcomp)[i] = j; |
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47 | while (k<Fl) |
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48 | { |
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49 | while ((k<Fl) && (pGetComp(oldF[k]) != i)) k++; |
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50 | if (k<Fl) |
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51 | { |
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52 | kk=jj; |
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53 | while ((kk<Fl) && (F[kk]) && (pComp0(oldF[k],F[kk])!=syComponentOrder)) |
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54 | { |
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55 | kk++; |
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56 | } |
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57 | for (kkk=j;kkk>kk;kkk--) |
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58 | { |
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59 | F[kkk] = F[kkk-1]; |
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60 | } |
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61 | F[kk] = oldF[k]; |
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62 | //Print("Element %d: ",kk);pWrite(F[kk]); |
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63 | j++; |
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64 | k++; |
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65 | } |
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66 | } |
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67 | } |
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68 | (**modcomp)[rkF+1] = Fl; |
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69 | return F; |
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70 | } |
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71 | |
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72 | static void syCreatePairs(polyset F,int lini,int wend,int k,int j,int i, |
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73 | polyset pairs,int regularPairs=0,ideal mW=NULL) |
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74 | { |
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75 | int l,ii=0,jj; |
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76 | poly p,q; |
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77 | |
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78 | while (((k<wend) && (pGetComp(F[k]) == i)) || |
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79 | ((currQuotient!=NULL) && (k<regularPairs+IDELEMS(currQuotient)))) |
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80 | { |
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81 | p = pOne(); |
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82 | if ((k<wend) && (pGetComp(F[k]) == i) && (k!=j)) |
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83 | pLcm(F[j],F[k],p); |
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84 | else if (ii<IDELEMS(currQuotient)) |
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85 | { |
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86 | q = pHead(F[j]); |
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87 | if (mW!=NULL) |
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88 | { |
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89 | for(jj=1;jj<=pVariables;jj++) |
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90 | pSetExp(q,jj,pGetExp(q,jj) -pGetExp(mW->m[pGetComp(q)-1],jj)); |
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91 | pSetm(q); |
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92 | } |
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93 | pLcm(q,currQuotient->m[ii],p); |
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94 | if (mW!=NULL) |
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95 | { |
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96 | for(jj=1;jj<=pVariables;jj++) |
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97 | pSetExp(p,jj,pGetExp(p,jj) +pGetExp(mW->m[pGetComp(p)-1],jj)); |
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98 | pSetm(p); |
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99 | } |
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100 | pDelete(&q); |
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101 | k = regularPairs+ii; |
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102 | ii++; |
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103 | } |
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104 | l=lini; |
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105 | while ((l<k) && ((pairs[l]==NULL) || (!pDivisibleBy(pairs[l],p)))) |
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106 | { |
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107 | if ((pairs[l]!=NULL) && (pDivisibleBy(p,pairs[l]))) |
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108 | pDelete(&(pairs[l])); |
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109 | l++; |
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110 | } |
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111 | if (l==k) |
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112 | { |
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113 | pSetm(p); |
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114 | pairs[l] = p; |
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115 | } |
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116 | else |
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117 | pDelete(&p); |
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118 | k++; |
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119 | } |
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120 | } |
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121 | |
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122 | inline BOOLEAN syDivisibleBy2(poly a, poly b) |
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123 | { |
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124 | //if (a->exp[0]==b->exp[0]) |
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125 | { |
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126 | int i=pVariables-1; |
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127 | short *e1=&(a->exp[1]); |
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128 | short *e2=&(b->exp[1]); |
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129 | if ((*e1) > (*e2)) return FALSE; |
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130 | do |
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131 | { |
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132 | i--; |
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133 | e1++; |
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134 | e2++; |
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135 | if ((*e1) > (*e2)) return FALSE; |
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136 | } while (i>0); |
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137 | return TRUE; |
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138 | } |
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139 | //else |
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140 | //{ |
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141 | //Print("Fehler"); |
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142 | //return FALSE; |
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143 | //} |
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144 | } |
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145 | |
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146 | static poly syRedtail2(poly p, polyset redWith, intvec *modcomp) |
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147 | { |
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148 | poly h, hn; |
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149 | int hncomp,nxt; |
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150 | int j; |
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151 | |
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152 | h = p; |
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153 | hn = pNext(h); |
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154 | while(hn != NULL) |
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155 | { |
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156 | hncomp = pGetComp(hn); |
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157 | j = (*modcomp)[hncomp]; |
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158 | nxt = (*modcomp)[hncomp+1]; |
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159 | while (j < nxt) |
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160 | { |
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161 | if (syDivisibleBy2(redWith[j], hn)) |
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162 | { |
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163 | //if (TEST_OPT_PROT) Print("r"); |
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164 | hn = spSpolyRed(redWith[j],hn,NULL); |
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165 | if (hn == NULL) |
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166 | { |
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167 | pNext(h) = NULL; |
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168 | return p; |
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169 | } |
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170 | hncomp = pGetComp(hn); |
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171 | j = (*modcomp)[hncomp]; |
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172 | nxt = (*modcomp)[hncomp+1]; |
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173 | } |
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174 | else |
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175 | { |
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176 | j++; |
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177 | } |
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178 | } |
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179 | h = pNext(h) = hn; |
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180 | hn = pNext(h); |
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181 | } |
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182 | return p; |
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183 | } |
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184 | |
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185 | /*2 |
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186 | * computes the Schreyer syzygies in the local case |
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187 | * input: F, Fmax, noSort: F is already ordered by: Schreyer-order |
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188 | * (only allocated: Shdl, Smax) |
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189 | * output: Shdl, Smax |
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190 | */ |
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191 | void sySchreyersSyzygiesFM(polyset F,int Fmax,polyset* Shdl,int* Smax, |
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192 | BOOLEAN noSort) |
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193 | { |
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194 | int Fl=Fmax; |
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195 | while ((Fl!=0) && (F[Fl-1]==NULL)) Fl--; |
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196 | if (Fl==0) return; |
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197 | |
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198 | int i,j,l,k,totalToRed,ecartToRed,kk,bestEcart,totalmax,rkF, |
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199 | Sl=0,smax,tmax,tl; |
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200 | int *ecartS, *ecartT, *totalS, |
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201 | *totalT=NULL, *temp=NULL; |
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202 | intvec * modcomp=NULL; |
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203 | polyset pairs,S,T,ST,oldF; |
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204 | poly p,q,toRed; |
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205 | BOOLEAN notFound = FALSE; |
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206 | |
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207 | /*-------------initializing the sets--------------------*/ |
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208 | ideal idF=(ideal)Alloc(sizeof(ip_sideal)); |
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209 | ST=(polyset)Alloc0(Fl*sizeof(poly)); |
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210 | S=(polyset)Alloc0(Fl*sizeof(poly)); |
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211 | ecartS=(int*)Alloc(Fl*sizeof(int)); |
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212 | totalS=(int*)Alloc(Fl*sizeof(int)); |
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213 | T=(polyset)Alloc0(2*Fl*sizeof(poly)); |
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214 | ecartT=(int*)Alloc(2*Fl*sizeof(int)); |
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215 | totalT=(int*)Alloc(2*Fl*sizeof(int)); |
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216 | pairs=(polyset)Alloc0(Fl*sizeof(poly)); |
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217 | |
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218 | smax = Fl; |
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219 | tmax = 2*Fl; |
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220 | idF->m=F;IDELEMS(idF)=Fmax; |
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221 | rkF=idRankFreeModule(idF); |
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222 | Free((ADDRESS)idF,sizeof(ip_sideal)); |
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223 | spSet(currRing); |
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224 | /*-------------sorting of F for index handling------------*/ |
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225 | if (noSort) |
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226 | { |
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227 | oldF = F; |
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228 | F=syInitSort(F,rkF,Fmax,1,&modcomp); |
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229 | } |
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230 | /*----------------construction of the new ordering----------*/ |
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231 | pSetSchreyerOrdM(F,Fl,rkF); |
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232 | /*----------------creating S--------------------------------*/ |
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233 | for(j=0;j<Fl;j++) |
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234 | { |
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235 | S[j] = pCopy(F[j]); |
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236 | totalS[j] = pLDeg(S[j],&k); |
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237 | ecartS[j] = totalS[j]-pFDeg(S[j]); |
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238 | //Print("%d", pGetComp(S[j]));PrintS(" "); |
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239 | p = S[j]; |
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240 | if (rkF==0) pSetCompP(p,1); |
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241 | while (pNext(p)!=NULL) pIter(p); |
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242 | pNext(p) = pHead(F[j]); |
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243 | pIter(p); |
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244 | if (rkF==0) |
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245 | pSetComp(p,j+2); |
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246 | else |
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247 | pSetComp(p,rkF+j+1); |
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248 | } |
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249 | //PrintLn(); |
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250 | if (rkF==0) rkF = 1; |
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251 | /*---------------creating the initial for T----------------*/ |
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252 | j=0; |
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253 | l=-1; |
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254 | totalmax=-1; |
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255 | for (k=0;k<smax;k++) |
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256 | if (totalS[k]>totalmax) totalmax=totalS[k]; |
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257 | for (kk=1;kk<=rkF;kk++) |
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258 | { |
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259 | for (k=0;k<=totalmax;k++) |
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260 | { |
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261 | for (l=0;l<smax;l++) |
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262 | { |
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263 | if ((pGetComp(S[l])==kk) && (totalS[l]==k)) |
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264 | { |
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265 | ST[j] = S[l]; |
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266 | totalT[j] = totalS[l]; |
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267 | ecartT[j] = ecartS[l]; |
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268 | //Print("%d", totalS[l]);PrintS(" "); |
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269 | j++; |
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270 | } |
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271 | } |
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272 | } |
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273 | } |
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274 | //PrintLn(); |
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275 | for (j=0;j<smax;j++) |
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276 | { |
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277 | totalS[j] = totalT[j]; |
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278 | ecartS[j] = ecartT[j]; |
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279 | } |
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280 | |
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281 | /*---------------computing---------------------------------*/ |
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282 | for(j=0;j<smax;j++) |
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283 | { |
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284 | i = pGetComp(S[j]); |
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285 | k=j+1; |
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286 | /*----------------constructing all pairs with S[j]---------*/ |
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287 | if (TEST_OPT_PROT) |
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288 | { |
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289 | Print("(%d)",Fl-j); |
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290 | mflush(); |
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291 | } |
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292 | syCreatePairs(S,j+1,Fl,k,j,i,pairs); |
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293 | /*--------------computing the syzygies----------------------*/ |
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294 | for (k=j+1;k<Fl;k++) |
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295 | { |
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296 | if (pairs[k]!=NULL) |
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297 | { |
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298 | /*--------------creating T----------------------------------*/ |
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299 | for (l=0;l<smax;l++) |
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300 | { |
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301 | ecartT[l] = ecartS[l]; |
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302 | totalT[l] = totalS[l]; |
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303 | T[l] = ST[l]; |
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304 | } |
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305 | tl = smax; |
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306 | /*--------------begin to reduce-----------------------------*/ |
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307 | toRed = spSpolyCreate(S[j],S[k],NULL); |
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308 | ecartToRed = 1; |
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309 | bestEcart = 1; |
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310 | if (BTEST1(6)) |
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311 | { |
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312 | PrintS("pair: ");pWrite0(S[j]);PrintS(" ");pWrite(S[k]); |
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313 | } |
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314 | if (TEST_OPT_PROT) |
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315 | { |
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316 | PrintS("."); |
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317 | mflush(); |
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318 | } |
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319 | while (pGetComp(toRed)<=rkF) |
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320 | { |
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321 | if (BTEST1(6)) |
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322 | { |
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323 | PrintS("toRed: ");pWrite(toRed); |
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324 | } |
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325 | /* |
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326 | * if ((bestEcart) || (ecartToRed!=0)) |
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327 | * { |
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328 | */ |
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329 | totalToRed = pLDeg(toRed,&kk); |
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330 | ecartToRed = totalToRed-pFDeg(toRed); |
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331 | /* |
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332 | * } |
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333 | */ |
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334 | notFound = TRUE; |
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335 | l=0; |
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336 | bestEcart = 32000; //a very large integer |
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337 | p = NULL; |
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338 | while ((l<tl) && (pGetComp(T[l])<pGetComp(toRed))) l++; |
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339 | while ((l<tl) && (notFound)) |
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340 | { |
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341 | if ((ecartT[l]<bestEcart) && (pDivisibleBy(T[l],toRed))) |
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342 | { |
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343 | if (ecartT[l]<=ecartToRed) notFound = FALSE; |
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344 | p = T[l]; |
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345 | bestEcart = ecartT[l]; |
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346 | } |
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347 | l++; |
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348 | } |
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349 | if (p==NULL) |
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350 | { |
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351 | WerrorS("ideal not a standardbasis");//no polynom for reduction |
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352 | pDelete(&toRed); |
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353 | for(k=j;k<Fl;k++) pDelete(&(pairs[k])); |
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354 | Free((ADDRESS)pairs,Fl*sizeof(poly)); |
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355 | Free((ADDRESS)ST,Fl*sizeof(poly)); |
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356 | Free((ADDRESS)S,Fl*sizeof(poly)); |
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357 | Free((ADDRESS)T,tmax*sizeof(poly)); |
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358 | Free((ADDRESS)ecartT,tmax*sizeof(int)); |
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359 | Free((ADDRESS)totalT,tmax*sizeof(int)); |
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360 | Free((ADDRESS)ecartS,Fl*sizeof(int)); |
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361 | Free((ADDRESS)totalS,Fl*sizeof(int)); |
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362 | if (noSort) |
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363 | { |
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364 | Free((ADDRESS)F,Fl*sizeof(poly)); |
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365 | F = oldF; |
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366 | } |
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367 | for(k=0;k<*Smax;k++) pDelete(&((*Shdl)[k])); |
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368 | return; |
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369 | } |
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370 | else |
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371 | { |
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372 | //PrintS("reduced with: ");pWrite(p);PrintLn(); |
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373 | if (notFound) |
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374 | { |
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375 | if (tl>=tmax) |
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376 | { |
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377 | pEnlargeSet(&T,tmax,16); |
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378 | tmax += 16; |
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379 | temp = (int*)Alloc((tmax+16)*sizeof(int)); |
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380 | for(l=0;l<tmax;l++) temp[l]=totalT[l]; |
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381 | totalT = temp; |
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382 | temp = (int*)Alloc((tmax+16)*sizeof(int)); |
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383 | for(l=0;l<tmax;l++) temp[l]=ecartT[l]; |
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384 | ecartT = temp; |
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385 | } |
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386 | //PrintS("t"); |
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387 | l=0; |
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388 | while ((l<tl) && (pGetComp(toRed)>pGetComp(T[l]))) l++; |
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389 | while ((l<tl) && (totalT[l]<=totalToRed)) l++; |
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390 | for (kk=tl;kk>l;kk--) |
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391 | { |
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392 | T[kk]=T[kk-1]; |
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393 | totalT[kk]=totalT[kk-1]; |
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394 | ecartT[kk]=ecartT[kk-1]; |
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395 | } |
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396 | q = pCopy(toRed); |
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397 | pNorm(q); |
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398 | T[l] = q; |
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399 | totalT[l] = totalToRed; |
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400 | ecartT[l] = ecartToRed; |
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401 | tl++; |
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402 | } |
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403 | |
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404 | toRed = spSpolyRed(p,toRed,NULL); |
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405 | } |
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406 | } |
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407 | //PrintS("s"); |
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408 | if (pGetComp(toRed)>rkF) |
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409 | { |
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410 | if (Sl>=*Smax) |
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411 | { |
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412 | pEnlargeSet(Shdl,*Smax,16); |
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413 | *Smax += 16; |
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414 | } |
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415 | pShift(&toRed,-rkF); |
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416 | pNorm(toRed); |
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417 | (*Shdl)[Sl] = toRed; |
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418 | Sl++; |
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419 | } |
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420 | /*----------------deleting all polys not from ST--------------*/ |
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421 | for(l=0;l<tl;l++) |
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422 | { |
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423 | kk=0; |
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424 | while ((kk<smax) && (T[l] != S[kk])) kk++; |
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425 | if (kk>=smax) |
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426 | { |
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427 | pDelete(&T[l]); |
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428 | //Print ("#"); |
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429 | } |
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430 | } |
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431 | } |
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432 | } |
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433 | for(k=j;k<Fl;k++) pDelete(&(pairs[k])); |
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434 | } |
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435 | Free((ADDRESS)pairs,Fl*sizeof(poly)); |
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436 | Free((ADDRESS)ST,Fl*sizeof(poly)); |
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437 | Free((ADDRESS)S,Fl*sizeof(poly)); |
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438 | Free((ADDRESS)T,tmax*sizeof(poly)); |
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439 | Free((ADDRESS)ecartT,tmax*sizeof(int)); |
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440 | Free((ADDRESS)totalT,tmax*sizeof(int)); |
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441 | Free((ADDRESS)ecartS,Fl*sizeof(int)); |
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442 | Free((ADDRESS)totalS,Fl*sizeof(int)); |
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443 | if (noSort) |
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444 | { |
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445 | if (modcomp!=NULL) delete modcomp; |
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446 | Free((ADDRESS)F,Fl*sizeof(poly)); |
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447 | F = oldF; |
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448 | } |
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449 | } |
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450 | |
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451 | /*3 |
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452 | *special Normalform for Schreyer in factor rings |
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453 | */ |
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454 | poly sySpecNormalize(poly toNorm,ideal mW=NULL) |
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455 | { |
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456 | int j,i=0; |
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457 | poly p; |
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458 | |
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459 | if (toNorm==NULL) return NULL; |
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460 | p = pHead(toNorm); |
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461 | if (mW!=NULL) |
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462 | { |
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463 | for(j=1;j<=pVariables;j++) |
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464 | pSetExp(p,j,pGetExp(p,j) -pGetExp(mW->m[pGetComp(p)-1],j)); |
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465 | } |
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466 | while ((p!=NULL) && (i<IDELEMS(currQuotient))) |
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467 | { |
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468 | if (pDivisibleBy(currQuotient->m[i],p)) |
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469 | { |
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470 | //pNorm(toNorm); |
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471 | toNorm = spSpolyRed(currQuotient->m[i],toNorm,NULL); |
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472 | pDelete(&p); |
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473 | if (toNorm==NULL) return NULL; |
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474 | p = pHead(toNorm); |
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475 | if (mW!=NULL) |
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476 | { |
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477 | for(j=1;j<=pVariables;j++) |
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478 | pSetExp(p,j,pGetExp(p,j) -pGetExp(mW->m[pGetComp(p)-1],j)); |
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479 | } |
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480 | i = 0; |
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481 | } |
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482 | else |
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483 | { |
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484 | i++; |
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485 | } |
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486 | } |
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487 | pDelete(&p); |
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488 | return toNorm; |
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489 | } |
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490 | |
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491 | /*2 |
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492 | * computes the Schreyer syzygies in the global case |
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493 | * input: F, Fmax, noSort: F is already ordered by: Schreyer-order |
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494 | * (only allocated: Shdl, Smax) |
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495 | * output: Shdl, Smax |
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496 | * modcomp, length stores the start position of the module comp. in FF |
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497 | */ |
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498 | void sySchreyersSyzygiesFB(polyset *FF,int Fmax,polyset* Shdl,int* Smax, |
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499 | BOOLEAN noSort,intvec ** modcomp, int * length,ideal mW) |
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500 | { |
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501 | int i,j,l,k,kkk,rkF,Sl=0,Fl=Fmax,syComponentOrder=pModuleOrder(); |
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502 | int fstart,wend,lini; |
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503 | intvec *newmodcomp; |
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504 | polyset pairs,oldF,F=*FF; |
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505 | poly p,q,toRed,syz,lastmonom,multWith; |
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506 | ideal idF=(ideal)Alloc(sizeof(*idF)),null; |
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507 | BOOLEAN isNotReduced=TRUE; |
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508 | |
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509 | while ((Fl!=0) && (F[Fl-1]==NULL)) Fl--; |
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510 | newmodcomp = new intvec(Fl+2); |
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511 | //for (j=0;j<Fl;j++) pWrite(F[j]); |
---|
512 | //PrintLn(); |
---|
513 | if (currQuotient==NULL) |
---|
514 | pairs=(polyset)Alloc0(Fl*sizeof(poly)); |
---|
515 | else |
---|
516 | pairs=(polyset)Alloc0((Fl+IDELEMS(currQuotient))*sizeof(poly)); |
---|
517 | idF->m=F;IDELEMS(idF)=Fmax; |
---|
518 | rkF=idRankFreeModule(idF); |
---|
519 | null = idInit(1,rkF); |
---|
520 | Free((ADDRESS)idF,sizeof(*idF)); |
---|
521 | if (noSort) |
---|
522 | { |
---|
523 | oldF = *FF; |
---|
524 | F=syInitSort(*FF,rkF,Fmax,syComponentOrder,modcomp); |
---|
525 | } |
---|
526 | else |
---|
527 | { |
---|
528 | F = *FF; |
---|
529 | } |
---|
530 | for(j=0;j<Fl;j++) |
---|
531 | { |
---|
532 | (*newmodcomp)[j+1] = Sl; |
---|
533 | if (TEST_OPT_PROT) |
---|
534 | { |
---|
535 | Print("(%d)",Fl-j); |
---|
536 | mflush(); |
---|
537 | } |
---|
538 | i = pGetComp(F[j]); |
---|
539 | if (syComponentOrder==1) |
---|
540 | { |
---|
541 | lini=k=j+1; |
---|
542 | wend=Fl; |
---|
543 | } |
---|
544 | else |
---|
545 | { |
---|
546 | lini=k=0; |
---|
547 | while ((k<j) && (pGetComp(F[k]) != i)) k++; |
---|
548 | wend=j; |
---|
549 | } |
---|
550 | syCreatePairs(F,lini,wend,k,j,i,pairs,Fl,mW); |
---|
551 | if (currQuotient!=NULL) wend = Fl+IDELEMS(currQuotient); |
---|
552 | for (k=lini;k<wend;k++) |
---|
553 | { |
---|
554 | if (pairs[k]!=NULL) |
---|
555 | { |
---|
556 | if (TEST_OPT_PROT) |
---|
557 | { |
---|
558 | PrintS("."); |
---|
559 | mflush(); |
---|
560 | } |
---|
561 | //begins to construct the syzygy |
---|
562 | if (k<Fl) |
---|
563 | { |
---|
564 | syz = pCopy(pairs[k]); |
---|
565 | syz->coef = nCopy(F[k]->coef); |
---|
566 | syz->coef = nNeg(syz->coef); |
---|
567 | pNext(syz) = pairs[k]; |
---|
568 | lastmonom = pNext(syz); |
---|
569 | lastmonom->coef = nCopy(F[j]->coef); |
---|
570 | pSetComp(lastmonom,k+1); |
---|
571 | } |
---|
572 | else |
---|
573 | { |
---|
574 | syz = pairs[k]; |
---|
575 | syz->coef = nCopy(currQuotient->m[k-Fl]->coef); |
---|
576 | lastmonom = syz; |
---|
577 | multWith = pDivide(syz,F[j]); |
---|
578 | multWith->coef = nCopy(currQuotient->m[k-Fl]->coef); |
---|
579 | } |
---|
580 | pSetComp(syz,j+1); |
---|
581 | pairs[k] = NULL; |
---|
582 | //the next term of the syzygy |
---|
583 | //constructs the spoly |
---|
584 | if (BTEST1(6)) |
---|
585 | { |
---|
586 | if (k<Fl) |
---|
587 | { |
---|
588 | PrintS("pair: ");pWrite0(F[j]);PrintS(" ");pWrite(F[k]); |
---|
589 | } |
---|
590 | else |
---|
591 | { |
---|
592 | PrintS("pair: ");pWrite0(F[j]);PrintS(" ");pWrite(currQuotient->m[k-Fl]); |
---|
593 | } |
---|
594 | } |
---|
595 | if (k<Fl) |
---|
596 | toRed = spSpolyCreate(F[j],F[k],NULL); |
---|
597 | else |
---|
598 | { |
---|
599 | q = pMultT(pCopy(F[j]),multWith); |
---|
600 | toRed = sySpecNormalize(q,mW); |
---|
601 | pDelete(&multWith); |
---|
602 | } |
---|
603 | isNotReduced = TRUE; |
---|
604 | while (toRed!=NULL) |
---|
605 | { |
---|
606 | if (BTEST1(6)) |
---|
607 | { |
---|
608 | PrintS("toRed: ");pWrite(toRed); |
---|
609 | } |
---|
610 | // l=0; |
---|
611 | // while ((l<Fl) && (!pDivisibleBy(F[l],toRed))) l++; |
---|
612 | // if (l>=Fl) |
---|
613 | l = (**modcomp)[pGetComp(toRed)+1]-1; |
---|
614 | kkk = (**modcomp)[pGetComp(toRed)]; |
---|
615 | while ((l>=kkk) && (!pDivisibleBy(F[l],toRed))) l--; |
---|
616 | if (l<kkk) |
---|
617 | { |
---|
618 | if ((currQuotient!=NULL) && (isNotReduced)) |
---|
619 | { |
---|
620 | toRed = sySpecNormalize(toRed,mW); |
---|
621 | isNotReduced = FALSE; |
---|
622 | } |
---|
623 | else |
---|
624 | { |
---|
625 | //no polynom for reduction |
---|
626 | WerrorS("ideal not a standardbasis"); |
---|
627 | pDelete(&toRed); |
---|
628 | pDelete(&syz); |
---|
629 | for(k=j;k<Fl;k++) pDelete(&(pairs[k])); |
---|
630 | Free((ADDRESS)pairs,Fl*sizeof(poly)); |
---|
631 | if (noSort) |
---|
632 | { |
---|
633 | Free((ADDRESS)F,Fl*sizeof(poly)); |
---|
634 | F = oldF; |
---|
635 | } |
---|
636 | for(k=0;k<*Smax;k++) pDelete(&((*Shdl)[k])); |
---|
637 | return; |
---|
638 | } |
---|
639 | } |
---|
640 | else |
---|
641 | { |
---|
642 | //the next monom of the syzygy |
---|
643 | isNotReduced = TRUE; |
---|
644 | if (BTEST1(6)) |
---|
645 | { |
---|
646 | PrintS("reduced with: ");pWrite(F[l]); |
---|
647 | } |
---|
648 | multWith = pDivide(toRed,F[l]); |
---|
649 | multWith->coef = nDiv(toRed->coef,F[l]->coef); |
---|
650 | multWith->coef = nNeg(multWith->coef); |
---|
651 | pNext(lastmonom) = toRed; |
---|
652 | pIter(lastmonom); |
---|
653 | pIter(toRed); |
---|
654 | pNext(lastmonom) = NULL; |
---|
655 | lastmonom->coef = nDiv(lastmonom->coef,F[l]->coef); |
---|
656 | lastmonom->coef = nNeg(lastmonom->coef); |
---|
657 | pSetComp(lastmonom,l+1); |
---|
658 | //computes the new toRed |
---|
659 | p = pCopy(pNext(F[l])); |
---|
660 | p = pMultT(p,multWith); |
---|
661 | pDelete(&multWith); |
---|
662 | toRed = pAdd(toRed,p); |
---|
663 | //the module component of the new monom |
---|
664 | //pWrite(toRed); |
---|
665 | } |
---|
666 | } |
---|
667 | //PrintLn(); |
---|
668 | if (syz!=NULL) |
---|
669 | { |
---|
670 | if (Sl>=*Smax) |
---|
671 | { |
---|
672 | pEnlargeSet(Shdl,*Smax,16); |
---|
673 | *Smax += 16; |
---|
674 | } |
---|
675 | pNorm(syz); |
---|
676 | if (BTEST1(OPT_REDTAIL)) |
---|
677 | { |
---|
678 | (*newmodcomp)[j+2] = Sl; |
---|
679 | (*Shdl)[Sl] = syRedtail2(syz,*Shdl,newmodcomp); |
---|
680 | (*newmodcomp)[j+2] = 0; |
---|
681 | } |
---|
682 | else |
---|
683 | (*Shdl)[Sl] = syz; |
---|
684 | Sl++; |
---|
685 | } |
---|
686 | } |
---|
687 | } |
---|
688 | // for(k=j;k<Fl;k++) pDelete(&(pairs[k])); |
---|
689 | } |
---|
690 | (*newmodcomp)[Fl+1] = Sl; |
---|
691 | if (currQuotient==NULL) |
---|
692 | Free((ADDRESS)pairs,Fl*sizeof(poly)); |
---|
693 | else |
---|
694 | Free((ADDRESS)pairs,(Fl+IDELEMS(currQuotient))*sizeof(poly)); |
---|
695 | if (noSort) |
---|
696 | { |
---|
697 | Free((ADDRESS)oldF,Fmax*sizeof(poly)); |
---|
698 | *FF = F; |
---|
699 | } |
---|
700 | delete *modcomp; |
---|
701 | *length = Fl+2; |
---|
702 | *modcomp = newmodcomp; |
---|
703 | } |
---|
704 | |
---|
705 | void syReOrderResolventFB(resolvente res,int length, int initial) |
---|
706 | { |
---|
707 | int syzIndex=length-1,i,j; |
---|
708 | poly p; |
---|
709 | |
---|
710 | while ((syzIndex!=0) && (res[syzIndex]==NULL)) syzIndex--; |
---|
711 | while (syzIndex>=initial) |
---|
712 | { |
---|
713 | for(i=0;i<IDELEMS(res[syzIndex]);i++) |
---|
714 | { |
---|
715 | p = res[syzIndex]->m[i]; |
---|
716 | while (p!=NULL) |
---|
717 | { |
---|
718 | if (res[syzIndex-1]->m[pGetComp(p)-1]!=NULL) |
---|
719 | { |
---|
720 | for(j=1;j<=pVariables;j++) |
---|
721 | { |
---|
722 | pSetExp(p,j,pGetExp(p,j) |
---|
723 | -pGetExp(res[syzIndex-1]->m[pGetComp(p)-1],j)); |
---|
724 | } |
---|
725 | } |
---|
726 | else |
---|
727 | PrintS("error in the resolvent\n"); |
---|
728 | pSetm(p); |
---|
729 | pIter(p); |
---|
730 | } |
---|
731 | } |
---|
732 | syzIndex--; |
---|
733 | } |
---|
734 | } |
---|
735 | |
---|
736 | BOOLEAN syTestOrder(ideal M) |
---|
737 | { |
---|
738 | int i=idRankFreeModule(M); |
---|
739 | int j=0; |
---|
740 | |
---|
741 | while ((currRing->order[j]!=ringorder_c) && (currRing->order[j]!=ringorder_C)) |
---|
742 | j++; |
---|
743 | if ((i>0) && (currRing->order[j+1]!=0)) |
---|
744 | { |
---|
745 | return TRUE; |
---|
746 | } |
---|
747 | return FALSE; |
---|
748 | } |
---|
749 | |
---|
750 | resolvente sySchreyerResolvente(ideal arg, int maxlength, int * length, |
---|
751 | BOOLEAN isMonomial,BOOLEAN notReplace) |
---|
752 | { |
---|
753 | ideal mW=NULL; |
---|
754 | int i,syzIndex = 0,j=0,lgth,*ord=NULL,*bl0=NULL,*bl1=NULL; |
---|
755 | intvec * modcomp=NULL,*w=NULL; |
---|
756 | short ** wv=NULL; |
---|
757 | BOOLEAN sort = TRUE; |
---|
758 | tHomog hom=(tHomog)idHomModule(arg,NULL,&w); |
---|
759 | |
---|
760 | if((hom==isHomog) |
---|
761 | &&(maxlength==pVariables-1) |
---|
762 | &&(currQuotient==NULL) |
---|
763 | &&(idRankFreeModule(arg)==0) |
---|
764 | &&(!idIs0(arg))) |
---|
765 | { |
---|
766 | return syLaScala1(arg,length); |
---|
767 | } |
---|
768 | |
---|
769 | if ((!isMonomial) && syTestOrder(arg)) |
---|
770 | { |
---|
771 | WerrorS("sres only implemented for modules with ordering ..,c or ..,C"); |
---|
772 | return NULL; |
---|
773 | } |
---|
774 | *length = 4; |
---|
775 | resolvente res = (resolvente)Alloc0(4*sizeof(ideal)),newres; |
---|
776 | res[0] = idCopy(arg); |
---|
777 | while ((!idIs0(res[syzIndex])) && ((maxlength==-1) || (syzIndex<maxlength))) |
---|
778 | { |
---|
779 | i = IDELEMS(res[syzIndex]); |
---|
780 | //while ((i!=0) && (!res[syzIndex]->m[i-1])) i--; |
---|
781 | if (syzIndex+1==*length) |
---|
782 | { |
---|
783 | newres = (resolvente)Alloc((*length+4)*sizeof(ideal)); |
---|
784 | for (j=0;j<*length+4;j++) newres[j] = NULL; |
---|
785 | for (j=0;j<*length;j++) newres[j] = res[j]; |
---|
786 | Free((ADDRESS)res,*length*sizeof(ideal)); |
---|
787 | *length += 4; |
---|
788 | res=newres; |
---|
789 | } |
---|
790 | res[syzIndex+1] = idInit(16,1); |
---|
791 | if ((currRing->OrdSgn == 1) || (hom==isHomog)) |
---|
792 | { |
---|
793 | sySchreyersSyzygiesFB(&(res[syzIndex]->m),i,&(res[syzIndex+1]->m), |
---|
794 | &(IDELEMS(res[syzIndex+1])),sort,&modcomp,&lgth,mW); |
---|
795 | mW = res[syzIndex]; |
---|
796 | } |
---|
797 | else |
---|
798 | sySchreyersSyzygiesFM(res[syzIndex]->m,i,&(res[syzIndex+1]->m), |
---|
799 | &(IDELEMS(res[syzIndex+1])),sort); |
---|
800 | //idPrint(res[syzIndex+1]); |
---|
801 | if ((syzIndex==0) && (currRing->OrdSgn==1)) |
---|
802 | { |
---|
803 | j = 0; |
---|
804 | while ((currRing->order[j]!=ringorder_c) |
---|
805 | && (currRing->order[j]!=ringorder_C)) |
---|
806 | j++; |
---|
807 | if ((!notReplace) && (currRing->order[j]!=0)) |
---|
808 | { |
---|
809 | while (currRing->order[j]!=0) j++; |
---|
810 | ord = (int*)Alloc0((j+2)*sizeof(int)); |
---|
811 | wv = (short**)Alloc0((j+2)*sizeof(short*)); |
---|
812 | bl0 = (int*)Alloc0((j+2)*sizeof(int)); |
---|
813 | bl1 = (int*)Alloc0((j+2)*sizeof(int)); |
---|
814 | j = 0; |
---|
815 | while ((currRing->order[j]!=ringorder_c) |
---|
816 | && (currRing->order[j]!=ringorder_C)) |
---|
817 | { |
---|
818 | ord[j] = currRing->order[j]; |
---|
819 | bl0[j] = currRing->block0[j]; |
---|
820 | bl1[j] = currRing->block1[j]; |
---|
821 | wv[j] = currRing->wvhdl[j]; |
---|
822 | j++; |
---|
823 | } |
---|
824 | int m_order=j; |
---|
825 | while (currRing->order[j+1]!=0) |
---|
826 | { |
---|
827 | ord[j] = currRing->order[j+1]; |
---|
828 | bl0[j] = currRing->block0[j+1]; |
---|
829 | bl1[j] = currRing->block1[j+1]; |
---|
830 | wv[j] = currRing->wvhdl[j+1]; |
---|
831 | j++; |
---|
832 | } |
---|
833 | ord[j] = currRing->order[m_order]; |
---|
834 | bl0[j] = currRing->block0[m_order]; |
---|
835 | bl1[j] = currRing->block1[m_order]; |
---|
836 | wv[j] = currRing->wvhdl[m_order]; |
---|
837 | pChangeRing(pVariables,currRing->OrdSgn,ord,bl0,bl1,wv); |
---|
838 | } |
---|
839 | } |
---|
840 | if (sort) sort=FALSE; |
---|
841 | syzIndex++; |
---|
842 | if (TEST_OPT_PROT) Print("[%d]\n",syzIndex); |
---|
843 | } |
---|
844 | if (currRing->OrdSgn == -1) |
---|
845 | pSetSchreyerOrdM(NULL,0,0); |
---|
846 | syReOrderResolventFB(res,*length); |
---|
847 | syzIndex = 1; |
---|
848 | if (/*ringOrderChanged:*/ ord!=NULL) |
---|
849 | { |
---|
850 | j = 0; |
---|
851 | while (currRing->order[j]!=0) j++; |
---|
852 | Free((ADDRESS)ord,(j+2)*sizeof(int)); |
---|
853 | Free((ADDRESS)bl0,(j+2)*sizeof(int)); |
---|
854 | Free((ADDRESS)bl1,(j+2)*sizeof(int)); |
---|
855 | Free((ADDRESS)wv,(j+2)*sizeof(short*)); |
---|
856 | pChangeRing(pVariables,currRing->OrdSgn,currRing->order,currRing->block0, |
---|
857 | currRing->block1,currRing->wvhdl); |
---|
858 | } |
---|
859 | while ((syzIndex < *length) && (res[syzIndex])) |
---|
860 | { |
---|
861 | for (i=0;i<IDELEMS(res[syzIndex]);i++) |
---|
862 | { |
---|
863 | if (res[syzIndex]->m[i]) |
---|
864 | res[syzIndex]->m[i] = pOrdPolySchreyer(res[syzIndex]->m[i]); |
---|
865 | } |
---|
866 | syzIndex++; |
---|
867 | } |
---|
868 | if (modcomp!=NULL) delete modcomp; |
---|
869 | if (w!=NULL) delete w; |
---|
870 | return res; |
---|
871 | } |
---|