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 - all basic methods to manipulate ideals |
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6 | */ |
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7 | |
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8 | /* includes */ |
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9 | |
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10 | #include "kernel/mod2.h" |
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11 | |
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12 | #include "omalloc/omalloc.h" |
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13 | |
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14 | #include "misc/options.h" |
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15 | #include "misc/intvec.h" |
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16 | |
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17 | #include "coeffs/coeffs.h" |
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18 | #include "coeffs/numbers.h" |
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19 | // #include "coeffs/longrat.h" |
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20 | |
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21 | |
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22 | #include "polys/monomials/ring.h" |
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23 | #include "polys/matpol.h" |
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24 | #include "polys/weight.h" |
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25 | #include "polys/sparsmat.h" |
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26 | #include "polys/prCopy.h" |
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27 | #include "polys/nc/nc.h" |
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28 | |
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29 | |
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30 | #include "kernel/ideals.h" |
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31 | |
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32 | #include "kernel/polys.h" |
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33 | |
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34 | #include "kernel/GBEngine/kstd1.h" |
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35 | #include "kernel/GBEngine/kutil.h" |
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36 | #include "kernel/GBEngine/tgb.h" |
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37 | #include "kernel/GBEngine/syz.h" |
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38 | #include "Singular/ipshell.h" // iiCallLibProc1 |
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39 | #include "Singular/ipid.h" // ggetid |
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40 | |
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41 | |
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42 | /* #define WITH_OLD_MINOR */ |
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43 | |
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44 | /*0 implementation*/ |
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45 | |
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46 | /*2 |
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47 | *returns a minimized set of generators of h1 |
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48 | */ |
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49 | ideal idMinBase (ideal h1) |
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50 | { |
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51 | ideal h2, h3,h4,e; |
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52 | int j,k; |
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53 | int i,l,ll; |
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54 | intvec * wth; |
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55 | BOOLEAN homog; |
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56 | if(rField_is_Ring(currRing)) |
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57 | { |
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58 | WarnS("minbase applies only to the local or homogeneous case over coefficient fields"); |
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59 | e=idCopy(h1); |
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60 | return e; |
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61 | } |
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62 | homog = idHomModule(h1,currRing->qideal,&wth); |
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63 | if (rHasGlobalOrdering(currRing)) |
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64 | { |
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65 | if(!homog) |
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66 | { |
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67 | WarnS("minbase applies only to the local or homogeneous case over coefficient fields"); |
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68 | e=idCopy(h1); |
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69 | return e; |
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70 | } |
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71 | else |
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72 | { |
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73 | ideal re=kMin_std(h1,currRing->qideal,(tHomog)homog,&wth,h2,NULL,0,3); |
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74 | idDelete(&re); |
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75 | return h2; |
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76 | } |
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77 | } |
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78 | e=idInit(1,h1->rank); |
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79 | if (idIs0(h1)) |
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80 | { |
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81 | return e; |
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82 | } |
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83 | pEnlargeSet(&(e->m),IDELEMS(e),15); |
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84 | IDELEMS(e) = 16; |
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85 | h2 = kStd(h1,currRing->qideal,isNotHomog,NULL); |
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86 | h3 = idMaxIdeal(1); |
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87 | h4=idMult(h2,h3); |
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88 | idDelete(&h3); |
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89 | h3=kStd(h4,currRing->qideal,isNotHomog,NULL); |
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90 | k = IDELEMS(h3); |
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91 | while ((k > 0) && (h3->m[k-1] == NULL)) k--; |
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92 | j = -1; |
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93 | l = IDELEMS(h2); |
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94 | while ((l > 0) && (h2->m[l-1] == NULL)) l--; |
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95 | for (i=l-1; i>=0; i--) |
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96 | { |
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97 | if (h2->m[i] != NULL) |
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98 | { |
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99 | ll = 0; |
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100 | while ((ll < k) && ((h3->m[ll] == NULL) |
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101 | || !pDivisibleBy(h3->m[ll],h2->m[i]))) |
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102 | ll++; |
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103 | if (ll >= k) |
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104 | { |
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105 | j++; |
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106 | if (j > IDELEMS(e)-1) |
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107 | { |
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108 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
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109 | IDELEMS(e) += 16; |
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110 | } |
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111 | e->m[j] = pCopy(h2->m[i]); |
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112 | } |
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113 | } |
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114 | } |
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115 | idDelete(&h2); |
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116 | idDelete(&h3); |
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117 | idDelete(&h4); |
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118 | if (currRing->qideal!=NULL) |
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119 | { |
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120 | h3=idInit(1,e->rank); |
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121 | h2=kNF(h3,currRing->qideal,e); |
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122 | idDelete(&h3); |
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123 | idDelete(&e); |
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124 | e=h2; |
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125 | } |
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126 | idSkipZeroes(e); |
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127 | return e; |
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128 | } |
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129 | |
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130 | |
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131 | /*2 |
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132 | *initialized a field with r numbers between beg and end for the |
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133 | *procedure idNextChoise |
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134 | */ |
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135 | ideal idSectWithElim (ideal h1,ideal h2) |
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136 | // does not destroy h1,h2 |
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137 | { |
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138 | if (TEST_OPT_PROT) PrintS("intersect by elimination method\n"); |
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139 | assume(!idIs0(h1)); |
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140 | assume(!idIs0(h2)); |
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141 | assume(IDELEMS(h1)<=IDELEMS(h2)); |
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142 | assume(id_RankFreeModule(h1,currRing)==0); |
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143 | assume(id_RankFreeModule(h2,currRing)==0); |
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144 | // add a new variable: |
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145 | int j; |
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146 | ring origRing=currRing; |
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147 | ring r=rCopy0(origRing); |
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148 | r->N++; |
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149 | r->block0[0]=1; |
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150 | r->block1[0]= r->N; |
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151 | omFree(r->order); |
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152 | r->order=(rRingOrder_t*)omAlloc0(3*sizeof(rRingOrder_t)); |
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153 | r->order[0]=ringorder_dp; |
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154 | r->order[1]=ringorder_C; |
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155 | char **names=(char**)omAlloc0(rVar(r) * sizeof(char_ptr)); |
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156 | for (j=0;j<r->N-1;j++) names[j]=r->names[j]; |
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157 | names[r->N-1]=omStrDup("@"); |
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158 | omFree(r->names); |
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159 | r->names=names; |
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160 | rComplete(r,TRUE); |
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161 | // fetch h1, h2 |
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162 | ideal h; |
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163 | h1=idrCopyR(h1,origRing,r); |
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164 | h2=idrCopyR(h2,origRing,r); |
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165 | // switch to temp. ring r |
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166 | rChangeCurrRing(r); |
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167 | // create 1-t, t |
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168 | poly omt=p_One(currRing); |
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169 | p_SetExp(omt,r->N,1,currRing); |
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170 | poly t=p_Copy(omt,currRing); |
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171 | p_Setm(omt,currRing); |
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172 | omt=p_Neg(omt,currRing); |
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173 | omt=p_Add_q(omt,pOne(),currRing); |
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174 | // compute (1-t)*h1 |
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175 | h1=(ideal)mp_MultP((matrix)h1,omt,currRing); |
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176 | // compute t*h2 |
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177 | h2=(ideal)mp_MultP((matrix)h2,pCopy(t),currRing); |
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178 | // (1-t)h1 + t*h2 |
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179 | h=idInit(IDELEMS(h1)+IDELEMS(h2),1); |
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180 | int l; |
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181 | for (l=IDELEMS(h1)-1; l>=0; l--) |
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182 | { |
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183 | h->m[l] = h1->m[l]; h1->m[l]=NULL; |
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184 | } |
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185 | j=IDELEMS(h1); |
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186 | for (l=IDELEMS(h2)-1; l>=0; l--) |
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187 | { |
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188 | h->m[l+j] = h2->m[l]; h2->m[l]=NULL; |
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189 | } |
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190 | idDelete(&h1); |
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191 | idDelete(&h2); |
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192 | // eliminate t: |
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193 | |
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194 | ideal res=idElimination(h,t); |
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195 | // cleanup |
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196 | idDelete(&h); |
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197 | if (res!=NULL) res=idrMoveR(res,r,origRing); |
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198 | rChangeCurrRing(origRing); |
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199 | rDelete(r); |
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200 | return res; |
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201 | } |
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202 | /*2 |
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203 | * h3 := h1 intersect h2 |
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204 | */ |
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205 | ideal idSect (ideal h1,ideal h2, GbVariant alg) |
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206 | { |
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207 | int i,j,k; |
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208 | unsigned length; |
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209 | int flength = id_RankFreeModule(h1,currRing); |
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210 | int slength = id_RankFreeModule(h2,currRing); |
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211 | int rank=si_max(h1->rank,h2->rank); |
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212 | if ((idIs0(h1)) || (idIs0(h2))) return idInit(1,rank); |
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213 | |
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214 | ideal first,second,temp,temp1,result; |
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215 | poly p,q; |
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216 | |
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217 | if (IDELEMS(h1)<IDELEMS(h2)) |
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218 | { |
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219 | first = h1; |
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220 | second = h2; |
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221 | } |
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222 | else |
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223 | { |
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224 | first = h2; |
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225 | second = h1; |
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226 | int t=flength; flength=slength; slength=t; |
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227 | } |
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228 | length = si_max(flength,slength); |
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229 | if (length==0) |
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230 | { |
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231 | if ((currRing->qideal==NULL) |
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232 | && (currRing->OrdSgn==1) |
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233 | && (!rIsPluralRing(currRing)) |
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234 | && ((TEST_V_INTERSECT_ELIM) || (!TEST_V_INTERSECT_SYZ))) |
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235 | return idSectWithElim(first,second); |
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236 | else length = 1; |
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237 | } |
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238 | if (TEST_OPT_PROT) PrintS("intersect by syzygy methods\n"); |
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239 | j = IDELEMS(first); |
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240 | |
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241 | ring orig_ring=currRing; |
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242 | ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE); |
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243 | rSetSyzComp(length,syz_ring); |
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244 | rChangeCurrRing(syz_ring); |
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245 | |
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246 | while ((j>0) && (first->m[j-1]==NULL)) j--; |
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247 | temp = idInit(j /*IDELEMS(first)*/+IDELEMS(second),length+j); |
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248 | k = 0; |
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249 | for (i=0;i<j;i++) |
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250 | { |
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251 | if (first->m[i]!=NULL) |
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252 | { |
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253 | if (syz_ring==orig_ring) |
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254 | temp->m[k] = pCopy(first->m[i]); |
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255 | else |
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256 | temp->m[k] = prCopyR(first->m[i], orig_ring, syz_ring); |
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257 | q = pOne(); |
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258 | pSetComp(q,i+1+length); |
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259 | pSetmComp(q); |
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260 | if (flength==0) p_Shift(&(temp->m[k]),1,currRing); |
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261 | p = temp->m[k]; |
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262 | while (pNext(p)!=NULL) pIter(p); |
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263 | pNext(p) = q; |
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264 | k++; |
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265 | } |
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266 | } |
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267 | for (i=0;i<IDELEMS(second);i++) |
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268 | { |
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269 | if (second->m[i]!=NULL) |
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270 | { |
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271 | if (syz_ring==orig_ring) |
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272 | temp->m[k] = pCopy(second->m[i]); |
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273 | else |
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274 | temp->m[k] = prCopyR(second->m[i], orig_ring,currRing); |
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275 | if (slength==0) p_Shift(&(temp->m[k]),1,currRing); |
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276 | k++; |
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277 | } |
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278 | } |
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279 | intvec *w=NULL; |
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280 | if (alg==GbDefault) alg=GbStd; |
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281 | if (alg==GbStd) |
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282 | { |
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283 | if (TEST_OPT_PROT) { PrintS("std:"); mflush(); } |
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284 | temp1 = kStd(temp,currRing->qideal,testHomog,&w,NULL,length); |
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285 | if (w!=NULL) delete w; |
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286 | idDelete(&temp); |
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287 | } |
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288 | else if (alg==GbSlimgb) |
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289 | { |
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290 | if (TEST_OPT_PROT) { PrintS("slimgb:"); mflush(); } |
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291 | temp1 = t_rep_gb(currRing, temp, temp->rank); |
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292 | idDelete(&temp); |
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293 | } |
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294 | else if (alg==GbGroebner) |
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295 | { |
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296 | if (TEST_OPT_PROT) { PrintS("groebner:"); mflush(); } |
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297 | BOOLEAN err; |
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298 | temp1=(ideal)iiCallLibProc1("groebner",temp,MODUL_CMD,err); |
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299 | if (err) |
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300 | { |
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301 | Werror("error %d in >>groebner<<",err); |
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302 | temp1=idInit(1,1); |
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303 | } |
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304 | } |
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305 | else if (alg==GbModstd) |
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306 | { |
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307 | if (TEST_OPT_PROT) { PrintS("modStd:"); mflush(); } |
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308 | BOOLEAN err; |
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309 | void *args[]={temp,(void*)1,NULL}; |
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310 | int arg_t[]={MODUL_CMD,INT_CMD,0}; |
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311 | temp1=(ideal)iiCallLibProcM("modStd",args,arg_t,err); |
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312 | if (err) |
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313 | { |
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314 | Werror("error %d in >>modStd<<",err); |
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315 | temp1=idInit(1,1); |
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316 | } |
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317 | } |
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318 | else if (alg==GbStdSat) |
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319 | { |
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320 | if (TEST_OPT_PROT) { PrintS("std:sat:"); mflush(); } |
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321 | BOOLEAN err; |
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322 | // search for 2nd block of vars |
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323 | int i=0; |
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324 | int block=-1; |
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325 | loop |
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326 | { |
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327 | if ((currRing->order[i]!=ringorder_c) |
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328 | && (currRing->order[i]!=ringorder_C) |
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329 | && (currRing->order[i]!=ringorder_s)) |
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330 | { |
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331 | if (currRing->order[i]==0) { err=TRUE;break;} |
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332 | block++; |
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333 | if (block==1) { block=i; break;} |
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334 | } |
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335 | i++; |
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336 | } |
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337 | if (block>0) |
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338 | { |
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339 | if (TEST_OPT_PROT) |
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340 | { |
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341 | Print("sat(%d..%d)\n",currRing->block0[block],currRing->block1[block]); |
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342 | mflush(); |
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343 | } |
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344 | ideal v=idInit(currRing->block1[block]-currRing->block0[block]+1,1); |
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345 | for(i=currRing->block0[block];i<=currRing->block1[block];i++) |
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346 | { |
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347 | v->m[i-currRing->block0[block]]=pOne(); |
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348 | pSetExp(v->m[i-currRing->block0[block]],i,1); |
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349 | pSetm(v->m[i-currRing->block0[block]]); |
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350 | } |
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351 | void *args[]={temp,v,NULL}; |
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352 | int arg_t[]={MODUL_CMD,IDEAL_CMD,0}; |
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353 | temp1=(ideal)iiCallLibProcM("satstd",args,arg_t,err); |
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354 | } |
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355 | if (err) |
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356 | { |
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357 | Werror("error %d in >>satstd<<",err); |
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358 | temp1=idInit(1,1); |
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359 | } |
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360 | } |
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361 | |
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362 | if(syz_ring!=orig_ring) |
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363 | rChangeCurrRing(orig_ring); |
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364 | |
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365 | result = idInit(IDELEMS(temp1),rank); |
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366 | j = 0; |
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367 | for (i=0;i<IDELEMS(temp1);i++) |
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368 | { |
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369 | if ((temp1->m[i]!=NULL) |
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370 | && (__p_GetComp(temp1->m[i],syz_ring)>length)) |
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371 | { |
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372 | if(syz_ring==orig_ring) |
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373 | { |
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374 | p = temp1->m[i]; |
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375 | } |
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376 | else |
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377 | { |
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378 | p = prMoveR(temp1->m[i], syz_ring,orig_ring); |
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379 | } |
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380 | temp1->m[i]=NULL; |
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381 | while (p!=NULL) |
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382 | { |
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383 | q = pNext(p); |
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384 | pNext(p) = NULL; |
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385 | k = pGetComp(p)-1-length; |
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386 | pSetComp(p,0); |
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387 | pSetmComp(p); |
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388 | /* Warning! multiply only from the left! it's very important for Plural */ |
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389 | result->m[j] = pAdd(result->m[j],pMult(p,pCopy(first->m[k]))); |
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390 | p = q; |
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391 | } |
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392 | j++; |
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393 | } |
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394 | } |
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395 | if(syz_ring!=orig_ring) |
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396 | { |
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397 | rChangeCurrRing(syz_ring); |
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398 | idDelete(&temp1); |
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399 | rChangeCurrRing(orig_ring); |
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400 | rDelete(syz_ring); |
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401 | } |
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402 | else |
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403 | { |
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404 | idDelete(&temp1); |
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405 | } |
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406 | |
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407 | idSkipZeroes(result); |
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408 | if (TEST_OPT_RETURN_SB) |
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409 | { |
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410 | w=NULL; |
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411 | temp1=kStd(result,currRing->qideal,testHomog,&w); |
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412 | if (w!=NULL) delete w; |
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413 | idDelete(&result); |
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414 | idSkipZeroes(temp1); |
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415 | return temp1; |
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416 | } |
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417 | else //temp1=kInterRed(result,currRing->qideal); |
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418 | return result; |
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419 | } |
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420 | |
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421 | /*2 |
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422 | * ideal/module intersection for a list of objects |
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423 | * given as 'resolvente' |
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424 | */ |
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425 | ideal idMultSect(resolvente arg, int length, GbVariant alg) |
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426 | { |
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427 | int i,j=0,k=0,l,maxrk=-1,realrki; |
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428 | unsigned syzComp; |
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429 | ideal bigmat,tempstd,result; |
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430 | poly p; |
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431 | int isIdeal=0; |
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432 | intvec * w=NULL; |
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433 | |
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434 | /* find 0-ideals and max rank -----------------------------------*/ |
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435 | for (i=0;i<length;i++) |
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436 | { |
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437 | if (!idIs0(arg[i])) |
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438 | { |
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439 | realrki=id_RankFreeModule(arg[i],currRing); |
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440 | k++; |
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441 | j += IDELEMS(arg[i]); |
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442 | if (realrki>maxrk) maxrk = realrki; |
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443 | } |
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444 | else |
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445 | { |
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446 | if (arg[i]!=NULL) |
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447 | { |
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448 | return idInit(1,arg[i]->rank); |
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449 | } |
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450 | } |
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451 | } |
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452 | if (maxrk == 0) |
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453 | { |
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454 | isIdeal = 1; |
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455 | maxrk = 1; |
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456 | } |
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457 | /* init -----------------------------------------------------------*/ |
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458 | j += maxrk; |
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459 | syzComp = k*maxrk; |
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460 | |
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461 | ring orig_ring=currRing; |
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462 | ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE); |
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463 | rSetSyzComp(syzComp,syz_ring); |
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464 | rChangeCurrRing(syz_ring); |
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465 | |
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466 | bigmat = idInit(j,(k+1)*maxrk); |
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467 | /* create unit matrices ------------------------------------------*/ |
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468 | for (i=0;i<maxrk;i++) |
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469 | { |
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470 | for (j=0;j<=k;j++) |
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471 | { |
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472 | p = pOne(); |
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473 | pSetComp(p,i+1+j*maxrk); |
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474 | pSetmComp(p); |
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475 | bigmat->m[i] = pAdd(bigmat->m[i],p); |
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476 | } |
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477 | } |
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478 | /* enter given ideals ------------------------------------------*/ |
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479 | i = maxrk; |
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480 | k = 0; |
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481 | for (j=0;j<length;j++) |
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482 | { |
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483 | if (arg[j]!=NULL) |
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484 | { |
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485 | for (l=0;l<IDELEMS(arg[j]);l++) |
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486 | { |
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487 | if (arg[j]->m[l]!=NULL) |
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488 | { |
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489 | if (syz_ring==orig_ring) |
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490 | bigmat->m[i] = pCopy(arg[j]->m[l]); |
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491 | else |
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492 | bigmat->m[i] = prCopyR(arg[j]->m[l], orig_ring,currRing); |
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493 | p_Shift(&(bigmat->m[i]),k*maxrk+isIdeal,currRing); |
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494 | i++; |
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495 | } |
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496 | } |
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497 | k++; |
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498 | } |
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499 | } |
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500 | /* std computation --------------------------------------------*/ |
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501 | if (alg==GbDefault) alg=GbStd; |
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502 | if (alg==GbStd) |
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503 | { |
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504 | if (TEST_OPT_PROT) { PrintS("std:"); mflush(); } |
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505 | tempstd = kStd(bigmat,currRing->qideal,testHomog,&w,NULL,syzComp); |
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506 | if (w!=NULL) delete w; |
---|
507 | idDelete(&bigmat); |
---|
508 | } |
---|
509 | else if (alg==GbSlimgb) |
---|
510 | { |
---|
511 | if (TEST_OPT_PROT) { PrintS("slimgb:"); mflush(); } |
---|
512 | tempstd = t_rep_gb(currRing, bigmat, syzComp); |
---|
513 | idDelete(&bigmat); |
---|
514 | } |
---|
515 | else if (alg==GbGroebner) |
---|
516 | { |
---|
517 | if (TEST_OPT_PROT) { PrintS("groebner:"); mflush(); } |
---|
518 | BOOLEAN err; |
---|
519 | tempstd=(ideal)iiCallLibProc1("groebner",bigmat,MODUL_CMD,err); |
---|
520 | if (err) |
---|
521 | { |
---|
522 | Werror("error %d in >>groebner<<",err); |
---|
523 | tempstd=idInit(1,1); |
---|
524 | } |
---|
525 | } |
---|
526 | // else if (alg==GbModstd): requires ideal, not module |
---|
527 | // { |
---|
528 | // if (TEST_OPT_PROT) { PrintS("modstd:"); mflush(); } |
---|
529 | // BOOLEAN err; |
---|
530 | // tempstd=(ideal)iiCallLibProc1("modStd",bigmat,MODUL_CMD,err); |
---|
531 | // if (err) |
---|
532 | // { |
---|
533 | // Werror("error %d in >>modStd<<",err); |
---|
534 | // tempstd=idInit(1,1); |
---|
535 | // } |
---|
536 | // } |
---|
537 | //else if (alg==GbSba): requires order C,... |
---|
538 | //{ |
---|
539 | // if (TEST_OPT_PROT) { PrintS("sba:"); mflush(); } |
---|
540 | // tempstd = kSba(bigmat,currRing->qideal,hom,w,1,0,NULL,syzComp); |
---|
541 | // idDelete(&bigmat); |
---|
542 | //} |
---|
543 | else |
---|
544 | { |
---|
545 | tempstd=idInit(1,1); |
---|
546 | Werror("wrong algorith %d for SB",(int)alg); |
---|
547 | } |
---|
548 | |
---|
549 | if(syz_ring!=orig_ring) |
---|
550 | rChangeCurrRing(orig_ring); |
---|
551 | |
---|
552 | /* interprete result ----------------------------------------*/ |
---|
553 | result = idInit(IDELEMS(tempstd),maxrk); |
---|
554 | k = 0; |
---|
555 | for (j=0;j<IDELEMS(tempstd);j++) |
---|
556 | { |
---|
557 | if ((tempstd->m[j]!=NULL) && (__p_GetComp(tempstd->m[j],syz_ring)>syzComp)) |
---|
558 | { |
---|
559 | if (syz_ring==orig_ring) |
---|
560 | p = pCopy(tempstd->m[j]); |
---|
561 | else |
---|
562 | p = prCopyR(tempstd->m[j], syz_ring,currRing); |
---|
563 | p_Shift(&p,-syzComp-isIdeal,currRing); |
---|
564 | result->m[k] = p; |
---|
565 | k++; |
---|
566 | } |
---|
567 | } |
---|
568 | /* clean up ----------------------------------------------------*/ |
---|
569 | if(syz_ring!=orig_ring) |
---|
570 | rChangeCurrRing(syz_ring); |
---|
571 | idDelete(&tempstd); |
---|
572 | if(syz_ring!=orig_ring) |
---|
573 | { |
---|
574 | rChangeCurrRing(orig_ring); |
---|
575 | rDelete(syz_ring); |
---|
576 | } |
---|
577 | idSkipZeroes(result); |
---|
578 | return result; |
---|
579 | } |
---|
580 | |
---|
581 | /*2 |
---|
582 | *computes syzygies of h1, |
---|
583 | *if quot != NULL it computes in the quotient ring modulo "quot" |
---|
584 | *works always in a ring with ringorder_s |
---|
585 | */ |
---|
586 | static ideal idPrepare (ideal h1, tHomog hom, int syzcomp, intvec **w, GbVariant alg) |
---|
587 | { |
---|
588 | ideal h2, h3; |
---|
589 | int j,k; |
---|
590 | poly p,q; |
---|
591 | |
---|
592 | if (idIs0(h1)) return NULL; |
---|
593 | k = id_RankFreeModule(h1,currRing); |
---|
594 | h2=idCopy(h1); |
---|
595 | int i = IDELEMS(h2); |
---|
596 | if (k == 0) |
---|
597 | { |
---|
598 | id_Shift(h2,1,currRing); |
---|
599 | k = 1; |
---|
600 | } |
---|
601 | if (syzcomp<k) |
---|
602 | { |
---|
603 | Warn("syzcomp too low, should be %d instead of %d",k,syzcomp); |
---|
604 | syzcomp = k; |
---|
605 | rSetSyzComp(k,currRing); |
---|
606 | } |
---|
607 | h2->rank = syzcomp+i; |
---|
608 | |
---|
609 | //if (hom==testHomog) |
---|
610 | //{ |
---|
611 | // if(idHomIdeal(h1,currRing->qideal)) |
---|
612 | // { |
---|
613 | // hom=TRUE; |
---|
614 | // } |
---|
615 | //} |
---|
616 | |
---|
617 | for (j=0; j<i; j++) |
---|
618 | { |
---|
619 | p = h2->m[j]; |
---|
620 | q = pOne(); |
---|
621 | pSetComp(q,syzcomp+1+j); |
---|
622 | pSetmComp(q); |
---|
623 | if (p!=NULL) |
---|
624 | { |
---|
625 | while (pNext(p)) pIter(p); |
---|
626 | p->next = q; |
---|
627 | } |
---|
628 | else |
---|
629 | h2->m[j]=q; |
---|
630 | } |
---|
631 | |
---|
632 | idTest(h2); |
---|
633 | |
---|
634 | if (alg==GbDefault) alg=GbStd; |
---|
635 | if (alg==GbStd) |
---|
636 | { |
---|
637 | if (TEST_OPT_PROT) { PrintS("std:"); mflush(); } |
---|
638 | h3 = kStd(h2,currRing->qideal,hom,w,NULL,syzcomp); |
---|
639 | } |
---|
640 | else if (alg==GbSlimgb) |
---|
641 | { |
---|
642 | if (TEST_OPT_PROT) { PrintS("slimgb:"); mflush(); } |
---|
643 | h3 = t_rep_gb(currRing, h2, syzcomp); |
---|
644 | } |
---|
645 | else if (alg==GbGroebner) |
---|
646 | { |
---|
647 | if (TEST_OPT_PROT) { PrintS("groebner:"); mflush(); } |
---|
648 | BOOLEAN err; |
---|
649 | h3=(ideal)iiCallLibProc1("groebner",idCopy(h2),MODUL_CMD,err); |
---|
650 | if (err) |
---|
651 | { |
---|
652 | Werror("error %d in >>groebner<<",err); |
---|
653 | h3=idInit(1,1); |
---|
654 | } |
---|
655 | } |
---|
656 | else if (alg==GbModstd) |
---|
657 | { |
---|
658 | if (TEST_OPT_PROT) { PrintS("modstd:"); mflush(); } |
---|
659 | BOOLEAN err; |
---|
660 | void *args[]={idCopy(h2),(void*)1,NULL}; |
---|
661 | int arg_t[]={MODUL_CMD,INT_CMD,0}; |
---|
662 | h3=(ideal)iiCallLibProcM("modStd",args,arg_t,err); |
---|
663 | if (err) |
---|
664 | { |
---|
665 | Werror("error %d in >>modStd<<",err); |
---|
666 | h3=idInit(1,1); |
---|
667 | } |
---|
668 | } |
---|
669 | else if (alg==GbStdSat) |
---|
670 | { |
---|
671 | if (TEST_OPT_PROT) { PrintS("std:sat:"); mflush(); } |
---|
672 | BOOLEAN err; |
---|
673 | // search for 2nd block of vars |
---|
674 | int i=0; |
---|
675 | int block=-1; |
---|
676 | loop |
---|
677 | { |
---|
678 | if ((currRing->order[i]!=ringorder_c) |
---|
679 | && (currRing->order[i]!=ringorder_C) |
---|
680 | && (currRing->order[i]!=ringorder_s)) |
---|
681 | { |
---|
682 | if (currRing->order[i]==0) { err=TRUE;break;} |
---|
683 | block++; |
---|
684 | if (block==1) { block=i; break;} |
---|
685 | } |
---|
686 | i++; |
---|
687 | } |
---|
688 | if (block>0) |
---|
689 | { |
---|
690 | if (TEST_OPT_PROT) |
---|
691 | { |
---|
692 | Print("sat(%d..%d)\n",currRing->block0[block],currRing->block1[block]); |
---|
693 | mflush(); |
---|
694 | } |
---|
695 | ideal v=idInit(currRing->block1[block]-currRing->block0[block]+1,1); |
---|
696 | for(i=currRing->block0[block];i<=currRing->block1[block];i++) |
---|
697 | { |
---|
698 | v->m[i-currRing->block0[block]]=pOne(); |
---|
699 | pSetExp(v->m[i-currRing->block0[block]],i,1); |
---|
700 | pSetm(v->m[i-currRing->block0[block]]); |
---|
701 | } |
---|
702 | void *args[]={idCopy(h2),v,NULL}; |
---|
703 | int arg_t[]={MODUL_CMD,IDEAL_CMD,0}; |
---|
704 | h3=(ideal)iiCallLibProcM("satstd",args,arg_t,err); |
---|
705 | } |
---|
706 | if (err) |
---|
707 | { |
---|
708 | Werror("error %d in >>satstd<<",err); |
---|
709 | h3=idInit(1,1); |
---|
710 | } |
---|
711 | } |
---|
712 | //else if (alg==GbSba): requires order C,... |
---|
713 | //{ |
---|
714 | // if (TEST_OPT_PROT) { PrintS("sba:"); mflush(); } |
---|
715 | // h3 = kSba(h2,currRing->qideal,hom,w,1,0,NULL,syzcomp); |
---|
716 | //} |
---|
717 | else |
---|
718 | { |
---|
719 | h3=idInit(1,1); |
---|
720 | Werror("wrong algorith %d for SB",(int)alg); |
---|
721 | } |
---|
722 | |
---|
723 | idDelete(&h2); |
---|
724 | return h3; |
---|
725 | } |
---|
726 | |
---|
727 | /*2 |
---|
728 | * compute the syzygies of h1 in R/quot, |
---|
729 | * weights of components are in w |
---|
730 | * if setRegularity, return the regularity in deg |
---|
731 | * do not change h1, w |
---|
732 | */ |
---|
733 | ideal idSyzygies (ideal h1, tHomog h,intvec **w, BOOLEAN setSyzComp, |
---|
734 | BOOLEAN setRegularity, int *deg, GbVariant alg) |
---|
735 | { |
---|
736 | ideal s_h1; |
---|
737 | int j, k, length=0,reg; |
---|
738 | BOOLEAN isMonomial=TRUE; |
---|
739 | int ii, idElemens_h1; |
---|
740 | |
---|
741 | assume(h1 != NULL); |
---|
742 | |
---|
743 | idElemens_h1=IDELEMS(h1); |
---|
744 | #ifdef PDEBUG |
---|
745 | for(ii=0;ii<idElemens_h1 /*IDELEMS(h1)*/;ii++) pTest(h1->m[ii]); |
---|
746 | #endif |
---|
747 | if (idIs0(h1)) |
---|
748 | { |
---|
749 | ideal result=idFreeModule(idElemens_h1/*IDELEMS(h1)*/); |
---|
750 | return result; |
---|
751 | } |
---|
752 | int slength=(int)id_RankFreeModule(h1,currRing); |
---|
753 | k=si_max(1,slength /*id_RankFreeModule(h1)*/); |
---|
754 | |
---|
755 | assume(currRing != NULL); |
---|
756 | ring orig_ring=currRing; |
---|
757 | ring syz_ring=rAssure_SyzComp(orig_ring,TRUE); |
---|
758 | if (setSyzComp) rSetSyzComp(k,syz_ring); |
---|
759 | |
---|
760 | if (orig_ring != syz_ring) |
---|
761 | { |
---|
762 | rChangeCurrRing(syz_ring); |
---|
763 | s_h1=idrCopyR_NoSort(h1,orig_ring,syz_ring); |
---|
764 | } |
---|
765 | else |
---|
766 | { |
---|
767 | s_h1 = h1; |
---|
768 | } |
---|
769 | |
---|
770 | idTest(s_h1); |
---|
771 | |
---|
772 | ideal s_h3=idPrepare(s_h1,h,k,w,alg); // main (syz) GB computation |
---|
773 | |
---|
774 | if (s_h3==NULL) |
---|
775 | { |
---|
776 | if (orig_ring != syz_ring) |
---|
777 | { |
---|
778 | rChangeCurrRing(orig_ring); |
---|
779 | rDelete(syz_ring); |
---|
780 | } |
---|
781 | return idFreeModule( idElemens_h1 /*IDELEMS(h1)*/); |
---|
782 | } |
---|
783 | |
---|
784 | if (orig_ring != syz_ring) |
---|
785 | { |
---|
786 | idDelete(&s_h1); |
---|
787 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
788 | { |
---|
789 | if (s_h3->m[j] != NULL) |
---|
790 | { |
---|
791 | if (p_MinComp(s_h3->m[j],syz_ring) > k) |
---|
792 | p_Shift(&s_h3->m[j], -k,syz_ring); |
---|
793 | else |
---|
794 | p_Delete(&s_h3->m[j],syz_ring); |
---|
795 | } |
---|
796 | } |
---|
797 | idSkipZeroes(s_h3); |
---|
798 | s_h3->rank -= k; |
---|
799 | rChangeCurrRing(orig_ring); |
---|
800 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring); |
---|
801 | rDelete(syz_ring); |
---|
802 | #ifdef HAVE_PLURAL |
---|
803 | if (rIsPluralRing(orig_ring)) |
---|
804 | { |
---|
805 | id_DelMultiples(s_h3,orig_ring); |
---|
806 | idSkipZeroes(s_h3); |
---|
807 | } |
---|
808 | #endif |
---|
809 | idTest(s_h3); |
---|
810 | return s_h3; |
---|
811 | } |
---|
812 | |
---|
813 | ideal e = idInit(IDELEMS(s_h3), s_h3->rank); |
---|
814 | |
---|
815 | for (j=IDELEMS(s_h3)-1; j>=0; j--) |
---|
816 | { |
---|
817 | if (s_h3->m[j] != NULL) |
---|
818 | { |
---|
819 | if (p_MinComp(s_h3->m[j],syz_ring) <= k) |
---|
820 | { |
---|
821 | e->m[j] = s_h3->m[j]; |
---|
822 | isMonomial=isMonomial && (pNext(s_h3->m[j])==NULL); |
---|
823 | p_Delete(&pNext(s_h3->m[j]),syz_ring); |
---|
824 | s_h3->m[j] = NULL; |
---|
825 | } |
---|
826 | } |
---|
827 | } |
---|
828 | |
---|
829 | idSkipZeroes(s_h3); |
---|
830 | idSkipZeroes(e); |
---|
831 | |
---|
832 | if ((deg != NULL) |
---|
833 | && (!isMonomial) |
---|
834 | && (!TEST_OPT_NOTREGULARITY) |
---|
835 | && (setRegularity) |
---|
836 | && (h==isHomog) |
---|
837 | && (!rIsPluralRing(currRing)) |
---|
838 | && (!rField_is_Ring(currRing)) |
---|
839 | ) |
---|
840 | { |
---|
841 | assume(orig_ring==syz_ring); |
---|
842 | ring dp_C_ring = rAssure_dp_C(syz_ring); // will do rChangeCurrRing later |
---|
843 | if (dp_C_ring != syz_ring) |
---|
844 | { |
---|
845 | rChangeCurrRing(dp_C_ring); |
---|
846 | e = idrMoveR_NoSort(e, syz_ring, dp_C_ring); |
---|
847 | } |
---|
848 | resolvente res = sySchreyerResolvente(e,-1,&length,TRUE, TRUE); |
---|
849 | intvec * dummy = syBetti(res,length,®, *w); |
---|
850 | *deg = reg+2; |
---|
851 | delete dummy; |
---|
852 | for (j=0;j<length;j++) |
---|
853 | { |
---|
854 | if (res[j]!=NULL) idDelete(&(res[j])); |
---|
855 | } |
---|
856 | omFreeSize((ADDRESS)res,length*sizeof(ideal)); |
---|
857 | idDelete(&e); |
---|
858 | if (dp_C_ring != orig_ring) |
---|
859 | { |
---|
860 | rChangeCurrRing(orig_ring); |
---|
861 | rDelete(dp_C_ring); |
---|
862 | } |
---|
863 | } |
---|
864 | else |
---|
865 | { |
---|
866 | idDelete(&e); |
---|
867 | } |
---|
868 | assume(orig_ring==currRing); |
---|
869 | idTest(s_h3); |
---|
870 | if (currRing->qideal != NULL) |
---|
871 | { |
---|
872 | ideal ts_h3=kStd(s_h3,currRing->qideal,h,w); |
---|
873 | idDelete(&s_h3); |
---|
874 | s_h3 = ts_h3; |
---|
875 | } |
---|
876 | return s_h3; |
---|
877 | } |
---|
878 | |
---|
879 | /*2 |
---|
880 | */ |
---|
881 | ideal idXXX (ideal h1, int k) |
---|
882 | { |
---|
883 | ideal s_h1; |
---|
884 | intvec *w=NULL; |
---|
885 | |
---|
886 | assume(currRing != NULL); |
---|
887 | ring orig_ring=currRing; |
---|
888 | ring syz_ring=rAssure_SyzComp(orig_ring,TRUE); |
---|
889 | rSetSyzComp(k,syz_ring); |
---|
890 | rChangeCurrRing(syz_ring); |
---|
891 | |
---|
892 | if (orig_ring != syz_ring) |
---|
893 | { |
---|
894 | s_h1=idrCopyR_NoSort(h1,orig_ring, syz_ring); |
---|
895 | } |
---|
896 | else |
---|
897 | { |
---|
898 | s_h1 = h1; |
---|
899 | } |
---|
900 | |
---|
901 | ideal s_h3=kStd(s_h1,NULL,testHomog,&w,NULL,k); |
---|
902 | |
---|
903 | if (s_h3==NULL) |
---|
904 | { |
---|
905 | return idFreeModule(IDELEMS(h1)); |
---|
906 | } |
---|
907 | |
---|
908 | if (orig_ring != syz_ring) |
---|
909 | { |
---|
910 | idDelete(&s_h1); |
---|
911 | idSkipZeroes(s_h3); |
---|
912 | rChangeCurrRing(orig_ring); |
---|
913 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring); |
---|
914 | rDelete(syz_ring); |
---|
915 | idTest(s_h3); |
---|
916 | return s_h3; |
---|
917 | } |
---|
918 | |
---|
919 | idSkipZeroes(s_h3); |
---|
920 | idTest(s_h3); |
---|
921 | return s_h3; |
---|
922 | } |
---|
923 | |
---|
924 | /* |
---|
925 | *computes a standard basis for h1 and stores the transformation matrix |
---|
926 | * in ma |
---|
927 | */ |
---|
928 | ideal idLiftStd (ideal h1, matrix* ma, tHomog hi, ideal * syz, GbVariant alg) |
---|
929 | { |
---|
930 | int i, j, t, inputIsIdeal=id_RankFreeModule(h1,currRing); |
---|
931 | long k; |
---|
932 | poly p=NULL, q; |
---|
933 | intvec *w=NULL; |
---|
934 | |
---|
935 | idDelete((ideal*)ma); |
---|
936 | BOOLEAN lift3=FALSE; |
---|
937 | if (syz!=NULL) { lift3=TRUE; idDelete(syz); } |
---|
938 | if (idIs0(h1)) |
---|
939 | { |
---|
940 | *ma=mpNew(1,0); |
---|
941 | if (lift3) |
---|
942 | { |
---|
943 | *syz=idFreeModule(IDELEMS(h1)); |
---|
944 | } |
---|
945 | return idInit(1,h1->rank); |
---|
946 | } |
---|
947 | |
---|
948 | BITSET save2; |
---|
949 | SI_SAVE_OPT2(save2); |
---|
950 | |
---|
951 | k=si_max(1L,id_RankFreeModule(h1,currRing)); |
---|
952 | |
---|
953 | if ((k==1) && (!lift3)) si_opt_2 |=Sy_bit(V_IDLIFT); |
---|
954 | |
---|
955 | ring orig_ring = currRing; |
---|
956 | ring syz_ring = rAssure_SyzOrder(orig_ring,TRUE); |
---|
957 | rSetSyzComp(k,syz_ring); |
---|
958 | rChangeCurrRing(syz_ring); |
---|
959 | |
---|
960 | ideal s_h1=h1; |
---|
961 | |
---|
962 | if (orig_ring != syz_ring) |
---|
963 | s_h1 = idrCopyR_NoSort(h1,orig_ring,syz_ring); |
---|
964 | else |
---|
965 | s_h1 = h1; |
---|
966 | |
---|
967 | ideal s_h3=idPrepare(s_h1,hi,k,&w,alg); // main (syz) GB computation |
---|
968 | |
---|
969 | ideal s_h2 = idInit(IDELEMS(s_h3), s_h3->rank); |
---|
970 | |
---|
971 | if (lift3) (*syz)=idInit(IDELEMS(s_h3),IDELEMS(h1)); |
---|
972 | |
---|
973 | if (w!=NULL) delete w; |
---|
974 | i = 0; |
---|
975 | |
---|
976 | // now sort the result, SB : leave in s_h3 |
---|
977 | // T: put in s_h2 |
---|
978 | // syz: put in *syz |
---|
979 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
980 | { |
---|
981 | if (s_h3->m[j] != NULL) |
---|
982 | { |
---|
983 | //if (p_MinComp(s_h3->m[j],syz_ring) <= k) |
---|
984 | if (pGetComp(s_h3->m[j]) <= k) // syz_ring == currRing |
---|
985 | { |
---|
986 | i++; |
---|
987 | q = s_h3->m[j]; |
---|
988 | while (pNext(q) != NULL) |
---|
989 | { |
---|
990 | if (pGetComp(pNext(q)) > k) |
---|
991 | { |
---|
992 | s_h2->m[j] = pNext(q); |
---|
993 | pNext(q) = NULL; |
---|
994 | } |
---|
995 | else |
---|
996 | { |
---|
997 | pIter(q); |
---|
998 | } |
---|
999 | } |
---|
1000 | if (!inputIsIdeal) p_Shift(&(s_h3->m[j]), -1,currRing); |
---|
1001 | } |
---|
1002 | else |
---|
1003 | { |
---|
1004 | // we a syzygy here: |
---|
1005 | if (lift3) |
---|
1006 | { |
---|
1007 | p_Shift(&s_h3->m[j], -k,currRing); |
---|
1008 | (*syz)->m[j]=s_h3->m[j]; |
---|
1009 | s_h3->m[j]=NULL; |
---|
1010 | } |
---|
1011 | else |
---|
1012 | p_Delete(&(s_h3->m[j]),currRing); |
---|
1013 | } |
---|
1014 | } |
---|
1015 | } |
---|
1016 | idSkipZeroes(s_h3); |
---|
1017 | //extern char * iiStringMatrix(matrix im, int dim,char ch); |
---|
1018 | //PrintS("SB: ----------------------------------------\n"); |
---|
1019 | //PrintS(iiStringMatrix((matrix)s_h3,k,'\n')); |
---|
1020 | //PrintLn(); |
---|
1021 | //PrintS("T: ----------------------------------------\n"); |
---|
1022 | //PrintS(iiStringMatrix((matrix)s_h2,h1->rank,'\n')); |
---|
1023 | //PrintLn(); |
---|
1024 | |
---|
1025 | if (lift3) idSkipZeroes(*syz); |
---|
1026 | |
---|
1027 | j = IDELEMS(s_h1); |
---|
1028 | |
---|
1029 | |
---|
1030 | if (syz_ring!=orig_ring) |
---|
1031 | { |
---|
1032 | idDelete(&s_h1); |
---|
1033 | rChangeCurrRing(orig_ring); |
---|
1034 | } |
---|
1035 | |
---|
1036 | *ma = mpNew(j,i); |
---|
1037 | |
---|
1038 | i = 1; |
---|
1039 | for (j=0; j<IDELEMS(s_h2); j++) |
---|
1040 | { |
---|
1041 | if (s_h2->m[j] != NULL) |
---|
1042 | { |
---|
1043 | q = prMoveR( s_h2->m[j], syz_ring,orig_ring); |
---|
1044 | s_h2->m[j] = NULL; |
---|
1045 | |
---|
1046 | if (q!=NULL) |
---|
1047 | { |
---|
1048 | q=pReverse(q); |
---|
1049 | while (q != NULL) |
---|
1050 | { |
---|
1051 | p = q; |
---|
1052 | pIter(q); |
---|
1053 | pNext(p) = NULL; |
---|
1054 | t=pGetComp(p); |
---|
1055 | pSetComp(p,0); |
---|
1056 | pSetmComp(p); |
---|
1057 | MATELEM(*ma,t-k,i) = pAdd(MATELEM(*ma,t-k,i),p); |
---|
1058 | } |
---|
1059 | } |
---|
1060 | i++; |
---|
1061 | } |
---|
1062 | } |
---|
1063 | idDelete(&s_h2); |
---|
1064 | |
---|
1065 | for (i=0; i<IDELEMS(s_h3); i++) |
---|
1066 | { |
---|
1067 | s_h3->m[i] = prMoveR_NoSort(s_h3->m[i], syz_ring,orig_ring); |
---|
1068 | } |
---|
1069 | if (lift3) |
---|
1070 | { |
---|
1071 | for (i=0; i<IDELEMS(*syz); i++) |
---|
1072 | { |
---|
1073 | (*syz)->m[i] = prMoveR_NoSort((*syz)->m[i], syz_ring,orig_ring); |
---|
1074 | } |
---|
1075 | } |
---|
1076 | |
---|
1077 | if (syz_ring!=orig_ring) rDelete(syz_ring); |
---|
1078 | SI_RESTORE_OPT2(save2); |
---|
1079 | return s_h3; |
---|
1080 | } |
---|
1081 | |
---|
1082 | static void idPrepareStd(ideal s_temp, int k) |
---|
1083 | { |
---|
1084 | int j,rk=id_RankFreeModule(s_temp,currRing); |
---|
1085 | poly p,q; |
---|
1086 | |
---|
1087 | if (rk == 0) |
---|
1088 | { |
---|
1089 | for (j=0; j<IDELEMS(s_temp); j++) |
---|
1090 | { |
---|
1091 | if (s_temp->m[j]!=NULL) pSetCompP(s_temp->m[j],1); |
---|
1092 | } |
---|
1093 | k = si_max(k,1); |
---|
1094 | } |
---|
1095 | for (j=0; j<IDELEMS(s_temp); j++) |
---|
1096 | { |
---|
1097 | if (s_temp->m[j]!=NULL) |
---|
1098 | { |
---|
1099 | p = s_temp->m[j]; |
---|
1100 | q = pOne(); |
---|
1101 | //pGetCoeff(q)=nInpNeg(pGetCoeff(q)); //set q to -1 |
---|
1102 | pSetComp(q,k+1+j); |
---|
1103 | pSetmComp(q); |
---|
1104 | while (pNext(p)) pIter(p); |
---|
1105 | pNext(p) = q; |
---|
1106 | } |
---|
1107 | } |
---|
1108 | s_temp->rank = k+IDELEMS(s_temp); |
---|
1109 | } |
---|
1110 | |
---|
1111 | /*2 |
---|
1112 | *computes a representation of the generators of submod with respect to those |
---|
1113 | * of mod |
---|
1114 | */ |
---|
1115 | |
---|
1116 | ideal idLift(ideal mod, ideal submod,ideal *rest, BOOLEAN goodShape, |
---|
1117 | BOOLEAN isSB, BOOLEAN divide, matrix *unit, GbVariant alg) |
---|
1118 | { |
---|
1119 | int lsmod =id_RankFreeModule(submod,currRing), j, k; |
---|
1120 | int comps_to_add=0; |
---|
1121 | poly p; |
---|
1122 | |
---|
1123 | if (idIs0(submod)) |
---|
1124 | { |
---|
1125 | if (unit!=NULL) |
---|
1126 | { |
---|
1127 | *unit=mpNew(1,1); |
---|
1128 | MATELEM(*unit,1,1)=pOne(); |
---|
1129 | } |
---|
1130 | if (rest!=NULL) |
---|
1131 | { |
---|
1132 | *rest=idInit(1,mod->rank); |
---|
1133 | } |
---|
1134 | return idInit(1,mod->rank); |
---|
1135 | } |
---|
1136 | if (idIs0(mod)) /* and not idIs0(submod) */ |
---|
1137 | { |
---|
1138 | WerrorS("2nd module does not lie in the first"); |
---|
1139 | return NULL; |
---|
1140 | } |
---|
1141 | if (unit!=NULL) |
---|
1142 | { |
---|
1143 | comps_to_add = IDELEMS(submod); |
---|
1144 | while ((comps_to_add>0) && (submod->m[comps_to_add-1]==NULL)) |
---|
1145 | comps_to_add--; |
---|
1146 | } |
---|
1147 | k=si_max(id_RankFreeModule(mod,currRing),id_RankFreeModule(submod,currRing)); |
---|
1148 | if ((k!=0) && (lsmod==0)) lsmod=1; |
---|
1149 | k=si_max(k,(int)mod->rank); |
---|
1150 | if (k<submod->rank) { WarnS("rk(submod) > rk(mod) ?");k=submod->rank; } |
---|
1151 | |
---|
1152 | ring orig_ring=currRing; |
---|
1153 | ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE); |
---|
1154 | rSetSyzComp(k,syz_ring); |
---|
1155 | rChangeCurrRing(syz_ring); |
---|
1156 | |
---|
1157 | ideal s_mod, s_temp; |
---|
1158 | if (orig_ring != syz_ring) |
---|
1159 | { |
---|
1160 | s_mod = idrCopyR_NoSort(mod,orig_ring,syz_ring); |
---|
1161 | s_temp = idrCopyR_NoSort(submod,orig_ring,syz_ring); |
---|
1162 | } |
---|
1163 | else |
---|
1164 | { |
---|
1165 | s_mod = mod; |
---|
1166 | s_temp = idCopy(submod); |
---|
1167 | } |
---|
1168 | ideal s_h3; |
---|
1169 | if (isSB) |
---|
1170 | { |
---|
1171 | s_h3 = idCopy(s_mod); |
---|
1172 | idPrepareStd(s_h3, k+comps_to_add); |
---|
1173 | } |
---|
1174 | else |
---|
1175 | { |
---|
1176 | s_h3 = idPrepare(s_mod,(tHomog)FALSE,k+comps_to_add,NULL,alg); |
---|
1177 | } |
---|
1178 | if (!goodShape) |
---|
1179 | { |
---|
1180 | for (j=0;j<IDELEMS(s_h3);j++) |
---|
1181 | { |
---|
1182 | if ((s_h3->m[j] != NULL) && (pMinComp(s_h3->m[j]) > k)) |
---|
1183 | p_Delete(&(s_h3->m[j]),currRing); |
---|
1184 | } |
---|
1185 | } |
---|
1186 | idSkipZeroes(s_h3); |
---|
1187 | if (lsmod==0) |
---|
1188 | { |
---|
1189 | id_Shift(s_temp,1,currRing); |
---|
1190 | } |
---|
1191 | if (unit!=NULL) |
---|
1192 | { |
---|
1193 | for(j = 0;j<comps_to_add;j++) |
---|
1194 | { |
---|
1195 | p = s_temp->m[j]; |
---|
1196 | if (p!=NULL) |
---|
1197 | { |
---|
1198 | while (pNext(p)!=NULL) pIter(p); |
---|
1199 | pNext(p) = pOne(); |
---|
1200 | pIter(p); |
---|
1201 | pSetComp(p,1+j+k); |
---|
1202 | pSetmComp(p); |
---|
1203 | p = pNeg(p); |
---|
1204 | } |
---|
1205 | } |
---|
1206 | s_temp->rank += (k+comps_to_add); |
---|
1207 | } |
---|
1208 | ideal s_result = kNF(s_h3,currRing->qideal,s_temp,k); |
---|
1209 | s_result->rank = s_h3->rank; |
---|
1210 | ideal s_rest = idInit(IDELEMS(s_result),k); |
---|
1211 | idDelete(&s_h3); |
---|
1212 | idDelete(&s_temp); |
---|
1213 | |
---|
1214 | for (j=0;j<IDELEMS(s_result);j++) |
---|
1215 | { |
---|
1216 | if (s_result->m[j]!=NULL) |
---|
1217 | { |
---|
1218 | if (pGetComp(s_result->m[j])<=k) |
---|
1219 | { |
---|
1220 | if (!divide) |
---|
1221 | { |
---|
1222 | if (isSB) |
---|
1223 | { |
---|
1224 | WarnS("first module not a standardbasis\n" |
---|
1225 | "// ** or second not a proper submodule"); |
---|
1226 | } |
---|
1227 | else |
---|
1228 | WerrorS("2nd module does not lie in the first"); |
---|
1229 | idDelete(&s_result); |
---|
1230 | idDelete(&s_rest); |
---|
1231 | s_result=idInit(IDELEMS(submod),submod->rank); |
---|
1232 | break; |
---|
1233 | } |
---|
1234 | else |
---|
1235 | { |
---|
1236 | p = s_rest->m[j] = s_result->m[j]; |
---|
1237 | while ((pNext(p)!=NULL) && (pGetComp(pNext(p))<=k)) pIter(p); |
---|
1238 | s_result->m[j] = pNext(p); |
---|
1239 | pNext(p) = NULL; |
---|
1240 | } |
---|
1241 | } |
---|
1242 | p_Shift(&(s_result->m[j]),-k,currRing); |
---|
1243 | pNeg(s_result->m[j]); |
---|
1244 | } |
---|
1245 | } |
---|
1246 | if ((lsmod==0) && (s_rest!=NULL)) |
---|
1247 | { |
---|
1248 | for (j=IDELEMS(s_rest);j>0;j--) |
---|
1249 | { |
---|
1250 | if (s_rest->m[j-1]!=NULL) |
---|
1251 | { |
---|
1252 | p_Shift(&(s_rest->m[j-1]),-1,currRing); |
---|
1253 | s_rest->m[j-1] = s_rest->m[j-1]; |
---|
1254 | } |
---|
1255 | } |
---|
1256 | } |
---|
1257 | if(syz_ring!=orig_ring) |
---|
1258 | { |
---|
1259 | idDelete(&s_mod); |
---|
1260 | rChangeCurrRing(orig_ring); |
---|
1261 | s_result = idrMoveR_NoSort(s_result, syz_ring, orig_ring); |
---|
1262 | s_rest = idrMoveR_NoSort(s_rest, syz_ring, orig_ring); |
---|
1263 | rDelete(syz_ring); |
---|
1264 | } |
---|
1265 | if (rest!=NULL) |
---|
1266 | *rest = s_rest; |
---|
1267 | else |
---|
1268 | idDelete(&s_rest); |
---|
1269 | //idPrint(s_result); |
---|
1270 | if (unit!=NULL) |
---|
1271 | { |
---|
1272 | *unit=mpNew(comps_to_add,comps_to_add); |
---|
1273 | int i; |
---|
1274 | for(i=0;i<IDELEMS(s_result);i++) |
---|
1275 | { |
---|
1276 | poly p=s_result->m[i]; |
---|
1277 | poly q=NULL; |
---|
1278 | while(p!=NULL) |
---|
1279 | { |
---|
1280 | if(pGetComp(p)<=comps_to_add) |
---|
1281 | { |
---|
1282 | pSetComp(p,0); |
---|
1283 | if (q!=NULL) |
---|
1284 | { |
---|
1285 | pNext(q)=pNext(p); |
---|
1286 | } |
---|
1287 | else |
---|
1288 | { |
---|
1289 | pIter(s_result->m[i]); |
---|
1290 | } |
---|
1291 | pNext(p)=NULL; |
---|
1292 | MATELEM(*unit,i+1,i+1)=pAdd(MATELEM(*unit,i+1,i+1),p); |
---|
1293 | if(q!=NULL) p=pNext(q); |
---|
1294 | else p=s_result->m[i]; |
---|
1295 | } |
---|
1296 | else |
---|
1297 | { |
---|
1298 | q=p; |
---|
1299 | pIter(p); |
---|
1300 | } |
---|
1301 | } |
---|
1302 | p_Shift(&s_result->m[i],-comps_to_add,currRing); |
---|
1303 | } |
---|
1304 | } |
---|
1305 | return s_result; |
---|
1306 | } |
---|
1307 | |
---|
1308 | /*2 |
---|
1309 | *computes division of P by Q with remainder up to (w-weighted) degree n |
---|
1310 | *P, Q, and w are not changed |
---|
1311 | */ |
---|
1312 | void idLiftW(ideal P,ideal Q,int n,matrix &T, ideal &R,short *w) |
---|
1313 | { |
---|
1314 | long N=0; |
---|
1315 | int i; |
---|
1316 | for(i=IDELEMS(Q)-1;i>=0;i--) |
---|
1317 | if(w==NULL) |
---|
1318 | N=si_max(N,p_Deg(Q->m[i],currRing)); |
---|
1319 | else |
---|
1320 | N=si_max(N,p_DegW(Q->m[i],w,currRing)); |
---|
1321 | N+=n; |
---|
1322 | |
---|
1323 | T=mpNew(IDELEMS(Q),IDELEMS(P)); |
---|
1324 | R=idInit(IDELEMS(P),P->rank); |
---|
1325 | |
---|
1326 | for(i=IDELEMS(P)-1;i>=0;i--) |
---|
1327 | { |
---|
1328 | poly p; |
---|
1329 | if(w==NULL) |
---|
1330 | p=ppJet(P->m[i],N); |
---|
1331 | else |
---|
1332 | p=ppJetW(P->m[i],N,w); |
---|
1333 | |
---|
1334 | int j=IDELEMS(Q)-1; |
---|
1335 | while(p!=NULL) |
---|
1336 | { |
---|
1337 | if(pDivisibleBy(Q->m[j],p)) |
---|
1338 | { |
---|
1339 | poly p0=p_DivideM(pHead(p),pHead(Q->m[j]),currRing); |
---|
1340 | if(w==NULL) |
---|
1341 | p=pJet(pSub(p,ppMult_mm(Q->m[j],p0)),N); |
---|
1342 | else |
---|
1343 | p=pJetW(pSub(p,ppMult_mm(Q->m[j],p0)),N,w); |
---|
1344 | pNormalize(p); |
---|
1345 | if(((w==NULL)&&(p_Deg(p0,currRing)>n))||((w!=NULL)&&(p_DegW(p0,w,currRing)>n))) |
---|
1346 | p_Delete(&p0,currRing); |
---|
1347 | else |
---|
1348 | MATELEM(T,j+1,i+1)=pAdd(MATELEM(T,j+1,i+1),p0); |
---|
1349 | j=IDELEMS(Q)-1; |
---|
1350 | } |
---|
1351 | else |
---|
1352 | { |
---|
1353 | if(j==0) |
---|
1354 | { |
---|
1355 | poly p0=p; |
---|
1356 | pIter(p); |
---|
1357 | pNext(p0)=NULL; |
---|
1358 | if(((w==NULL)&&(p_Deg(p0,currRing)>n)) |
---|
1359 | ||((w!=NULL)&&(p_DegW(p0,w,currRing)>n))) |
---|
1360 | p_Delete(&p0,currRing); |
---|
1361 | else |
---|
1362 | R->m[i]=pAdd(R->m[i],p0); |
---|
1363 | j=IDELEMS(Q)-1; |
---|
1364 | } |
---|
1365 | else |
---|
1366 | j--; |
---|
1367 | } |
---|
1368 | } |
---|
1369 | } |
---|
1370 | } |
---|
1371 | |
---|
1372 | /*2 |
---|
1373 | *computes the quotient of h1,h2 : internal routine for idQuot |
---|
1374 | *BEWARE: the returned ideals may contain incorrectly ordered polys ! |
---|
1375 | * |
---|
1376 | */ |
---|
1377 | static ideal idInitializeQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN *addOnlyOne, int *kkmax) |
---|
1378 | { |
---|
1379 | idTest(h1); |
---|
1380 | idTest(h2); |
---|
1381 | |
---|
1382 | ideal temph1; |
---|
1383 | poly p,q = NULL; |
---|
1384 | int i,l,ll,k,kkk,kmax; |
---|
1385 | int j = 0; |
---|
1386 | int k1 = id_RankFreeModule(h1,currRing); |
---|
1387 | int k2 = id_RankFreeModule(h2,currRing); |
---|
1388 | tHomog hom=isNotHomog; |
---|
1389 | k=si_max(k1,k2); |
---|
1390 | if (k==0) |
---|
1391 | k = 1; |
---|
1392 | if ((k2==0) && (k>1)) *addOnlyOne = FALSE; |
---|
1393 | intvec * weights; |
---|
1394 | hom = (tHomog)idHomModule(h1,currRing->qideal,&weights); |
---|
1395 | if /**addOnlyOne &&*/ (/*(*/ !h1IsStb /*)*/) |
---|
1396 | temph1 = kStd(h1,currRing->qideal,hom,&weights,NULL); |
---|
1397 | else |
---|
1398 | temph1 = idCopy(h1); |
---|
1399 | if (weights!=NULL) delete weights; |
---|
1400 | idTest(temph1); |
---|
1401 | /*--- making a single vector from h2 ---------------------*/ |
---|
1402 | for (i=0; i<IDELEMS(h2); i++) |
---|
1403 | { |
---|
1404 | if (h2->m[i] != NULL) |
---|
1405 | { |
---|
1406 | p = pCopy(h2->m[i]); |
---|
1407 | if (k2 == 0) |
---|
1408 | p_Shift(&p,j*k+1,currRing); |
---|
1409 | else |
---|
1410 | p_Shift(&p,j*k,currRing); |
---|
1411 | q = pAdd(q,p); |
---|
1412 | j++; |
---|
1413 | } |
---|
1414 | } |
---|
1415 | *kkmax = kmax = j*k+1; |
---|
1416 | /*--- adding a monomial for the result (syzygy) ----------*/ |
---|
1417 | p = q; |
---|
1418 | while (pNext(p)!=NULL) pIter(p); |
---|
1419 | pNext(p) = pOne(); |
---|
1420 | pIter(p); |
---|
1421 | pSetComp(p,kmax); |
---|
1422 | pSetmComp(p); |
---|
1423 | /*--- constructing the big matrix ------------------------*/ |
---|
1424 | ideal h4 = idInit(k,kmax+k-1); |
---|
1425 | h4->m[0] = q; |
---|
1426 | if (k2 == 0) |
---|
1427 | { |
---|
1428 | for (i=1; i<k; i++) |
---|
1429 | { |
---|
1430 | if (h4->m[i-1]!=NULL) |
---|
1431 | { |
---|
1432 | p = p_Copy_noCheck(h4->m[i-1], currRing); |
---|
1433 | p_Shift(&p,1,currRing); |
---|
1434 | h4->m[i] = p; |
---|
1435 | } |
---|
1436 | else break; |
---|
1437 | } |
---|
1438 | } |
---|
1439 | idSkipZeroes(h4); |
---|
1440 | kkk = IDELEMS(h4); |
---|
1441 | i = IDELEMS(temph1); |
---|
1442 | for (l=0; l<i; l++) |
---|
1443 | { |
---|
1444 | if(temph1->m[l]!=NULL) |
---|
1445 | { |
---|
1446 | for (ll=0; ll<j; ll++) |
---|
1447 | { |
---|
1448 | p = pCopy(temph1->m[l]); |
---|
1449 | if (k1 == 0) |
---|
1450 | p_Shift(&p,ll*k+1,currRing); |
---|
1451 | else |
---|
1452 | p_Shift(&p,ll*k,currRing); |
---|
1453 | if (kkk >= IDELEMS(h4)) |
---|
1454 | { |
---|
1455 | pEnlargeSet(&(h4->m),IDELEMS(h4),16); |
---|
1456 | IDELEMS(h4) += 16; |
---|
1457 | } |
---|
1458 | h4->m[kkk] = p; |
---|
1459 | kkk++; |
---|
1460 | } |
---|
1461 | } |
---|
1462 | } |
---|
1463 | /*--- if h2 goes in as single vector - the h1-part is just SB ---*/ |
---|
1464 | if (*addOnlyOne) |
---|
1465 | { |
---|
1466 | idSkipZeroes(h4); |
---|
1467 | p = h4->m[0]; |
---|
1468 | for (i=0;i<IDELEMS(h4)-1;i++) |
---|
1469 | { |
---|
1470 | h4->m[i] = h4->m[i+1]; |
---|
1471 | } |
---|
1472 | h4->m[IDELEMS(h4)-1] = p; |
---|
1473 | } |
---|
1474 | idDelete(&temph1); |
---|
1475 | //idTest(h4);//see remark at the beginning |
---|
1476 | return h4; |
---|
1477 | } |
---|
1478 | |
---|
1479 | /*2 |
---|
1480 | *computes the quotient of h1,h2 |
---|
1481 | */ |
---|
1482 | ideal idQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN resultIsIdeal) |
---|
1483 | { |
---|
1484 | // first check for special case h1:(0) |
---|
1485 | if (idIs0(h2)) |
---|
1486 | { |
---|
1487 | ideal res; |
---|
1488 | if (resultIsIdeal) |
---|
1489 | { |
---|
1490 | res = idInit(1,1); |
---|
1491 | res->m[0] = pOne(); |
---|
1492 | } |
---|
1493 | else |
---|
1494 | res = idFreeModule(h1->rank); |
---|
1495 | return res; |
---|
1496 | } |
---|
1497 | int i, kmax; |
---|
1498 | BOOLEAN addOnlyOne=TRUE; |
---|
1499 | tHomog hom=isNotHomog; |
---|
1500 | intvec * weights1; |
---|
1501 | |
---|
1502 | ideal s_h4 = idInitializeQuot (h1,h2,h1IsStb,&addOnlyOne,&kmax); |
---|
1503 | |
---|
1504 | hom = (tHomog)idHomModule(s_h4,currRing->qideal,&weights1); |
---|
1505 | |
---|
1506 | ring orig_ring=currRing; |
---|
1507 | ring syz_ring=rAssure_SyzOrder(orig_ring,TRUE); |
---|
1508 | rSetSyzComp(kmax-1,syz_ring); |
---|
1509 | rChangeCurrRing(syz_ring); |
---|
1510 | if (orig_ring!=syz_ring) |
---|
1511 | // s_h4 = idrMoveR_NoSort(s_h4,orig_ring, syz_ring); |
---|
1512 | s_h4 = idrMoveR(s_h4,orig_ring, syz_ring); |
---|
1513 | idTest(s_h4); |
---|
1514 | #if 0 |
---|
1515 | void ipPrint_MA0(matrix m, const char *name); |
---|
1516 | matrix m=idModule2Matrix(idCopy(s_h4)); |
---|
1517 | PrintS("start:\n"); |
---|
1518 | ipPrint_MA0(m,"Q"); |
---|
1519 | idDelete((ideal *)&m); |
---|
1520 | PrintS("last elem:");wrp(s_h4->m[IDELEMS(s_h4)-1]);PrintLn(); |
---|
1521 | #endif |
---|
1522 | ideal s_h3; |
---|
1523 | if (addOnlyOne) |
---|
1524 | { |
---|
1525 | BITSET old_test1; |
---|
1526 | SI_SAVE_OPT1(old_test1); |
---|
1527 | if(!rField_is_Ring(currRing)) si_opt_1 |= Sy_bit(OPT_SB_1); |
---|
1528 | s_h3 = kStd(s_h4,currRing->qideal,hom,&weights1,NULL,0/*kmax-1*/,IDELEMS(s_h4)-1); |
---|
1529 | SI_RESTORE_OPT1(old_test1); |
---|
1530 | } |
---|
1531 | else |
---|
1532 | { |
---|
1533 | s_h3 = kStd(s_h4,currRing->qideal,hom,&weights1,NULL,kmax-1); |
---|
1534 | } |
---|
1535 | #if 0 |
---|
1536 | // only together with the above debug stuff |
---|
1537 | idSkipZeroes(s_h3); |
---|
1538 | m=idModule2Matrix(idCopy(s_h3)); |
---|
1539 | Print("result, kmax=%d:\n",kmax); |
---|
1540 | ipPrint_MA0(m,"S"); |
---|
1541 | idDelete((ideal *)&m); |
---|
1542 | #endif |
---|
1543 | idTest(s_h3); |
---|
1544 | if (weights1!=NULL) delete weights1; |
---|
1545 | idDelete(&s_h4); |
---|
1546 | |
---|
1547 | for (i=0;i<IDELEMS(s_h3);i++) |
---|
1548 | { |
---|
1549 | if ((s_h3->m[i]!=NULL) && (pGetComp(s_h3->m[i])>=kmax)) |
---|
1550 | { |
---|
1551 | if (resultIsIdeal) |
---|
1552 | p_Shift(&s_h3->m[i],-kmax,currRing); |
---|
1553 | else |
---|
1554 | p_Shift(&s_h3->m[i],-kmax+1,currRing); |
---|
1555 | } |
---|
1556 | else |
---|
1557 | p_Delete(&s_h3->m[i],currRing); |
---|
1558 | } |
---|
1559 | if (resultIsIdeal) |
---|
1560 | s_h3->rank = 1; |
---|
1561 | else |
---|
1562 | s_h3->rank = h1->rank; |
---|
1563 | if(syz_ring!=orig_ring) |
---|
1564 | { |
---|
1565 | rChangeCurrRing(orig_ring); |
---|
1566 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring, orig_ring); |
---|
1567 | rDelete(syz_ring); |
---|
1568 | } |
---|
1569 | idSkipZeroes(s_h3); |
---|
1570 | idTest(s_h3); |
---|
1571 | return s_h3; |
---|
1572 | } |
---|
1573 | |
---|
1574 | /*2 |
---|
1575 | * eliminate delVar (product of vars) in h1 |
---|
1576 | */ |
---|
1577 | ideal idElimination (ideal h1,poly delVar,intvec *hilb) |
---|
1578 | { |
---|
1579 | int i,j=0,k,l; |
---|
1580 | ideal h,hh, h3; |
---|
1581 | rRingOrder_t *ord; |
---|
1582 | int *block0,*block1; |
---|
1583 | int ordersize=2; |
---|
1584 | int **wv; |
---|
1585 | tHomog hom; |
---|
1586 | intvec * w; |
---|
1587 | ring tmpR; |
---|
1588 | ring origR = currRing; |
---|
1589 | |
---|
1590 | if (delVar==NULL) |
---|
1591 | { |
---|
1592 | return idCopy(h1); |
---|
1593 | } |
---|
1594 | if ((currRing->qideal!=NULL) && rIsPluralRing(origR)) |
---|
1595 | { |
---|
1596 | WerrorS("cannot eliminate in a qring"); |
---|
1597 | return NULL; |
---|
1598 | } |
---|
1599 | if (idIs0(h1)) return idInit(1,h1->rank); |
---|
1600 | #ifdef HAVE_PLURAL |
---|
1601 | if (rIsPluralRing(origR)) |
---|
1602 | /* in the NC case, we have to check the admissibility of */ |
---|
1603 | /* the subalgebra to be intersected with */ |
---|
1604 | { |
---|
1605 | if ((ncRingType(origR) != nc_skew) && (ncRingType(origR) != nc_exterior)) /* in (quasi)-commutative algebras every subalgebra is admissible */ |
---|
1606 | { |
---|
1607 | if (nc_CheckSubalgebra(delVar,origR)) |
---|
1608 | { |
---|
1609 | WerrorS("no elimination is possible: subalgebra is not admissible"); |
---|
1610 | return NULL; |
---|
1611 | } |
---|
1612 | } |
---|
1613 | } |
---|
1614 | #endif |
---|
1615 | hom=(tHomog)idHomModule(h1,NULL,&w); //sets w to weight vector or NULL |
---|
1616 | h3=idInit(16,h1->rank); |
---|
1617 | for (k=0;; k++) |
---|
1618 | { |
---|
1619 | if (origR->order[k]!=0) ordersize++; |
---|
1620 | else break; |
---|
1621 | } |
---|
1622 | #if 0 |
---|
1623 | if (rIsPluralRing(origR)) // we have too keep the odering: it may be needed |
---|
1624 | // for G-algebra |
---|
1625 | { |
---|
1626 | for (k=0;k<ordersize-1; k++) |
---|
1627 | { |
---|
1628 | block0[k+1] = origR->block0[k]; |
---|
1629 | block1[k+1] = origR->block1[k]; |
---|
1630 | ord[k+1] = origR->order[k]; |
---|
1631 | if (origR->wvhdl[k]!=NULL) wv[k+1] = (int*) omMemDup(origR->wvhdl[k]); |
---|
1632 | } |
---|
1633 | } |
---|
1634 | else |
---|
1635 | { |
---|
1636 | block0[1] = 1; |
---|
1637 | block1[1] = (currRing->N); |
---|
1638 | if (origR->OrdSgn==1) ord[1] = ringorder_wp; |
---|
1639 | else ord[1] = ringorder_ws; |
---|
1640 | wv[1]=(int*)omAlloc0((currRing->N)*sizeof(int)); |
---|
1641 | double wNsqr = (double)2.0 / (double)(currRing->N); |
---|
1642 | wFunctional = wFunctionalBuch; |
---|
1643 | int *x= (int * )omAlloc(2 * ((currRing->N) + 1) * sizeof(int)); |
---|
1644 | int sl=IDELEMS(h1) - 1; |
---|
1645 | wCall(h1->m, sl, x, wNsqr); |
---|
1646 | for (sl = (currRing->N); sl!=0; sl--) |
---|
1647 | wv[1][sl-1] = x[sl + (currRing->N) + 1]; |
---|
1648 | omFreeSize((ADDRESS)x, 2 * ((currRing->N) + 1) * sizeof(int)); |
---|
1649 | |
---|
1650 | ord[2]=ringorder_C; |
---|
1651 | ord[3]=0; |
---|
1652 | } |
---|
1653 | #else |
---|
1654 | #endif |
---|
1655 | if ((hom==TRUE) && (origR->OrdSgn==1) && (!rIsPluralRing(origR))) |
---|
1656 | { |
---|
1657 | #if 1 |
---|
1658 | // we change to an ordering: |
---|
1659 | // aa(1,1,1,...,0,0,0),wp(...),C |
---|
1660 | // this seems to be better than version 2 below, |
---|
1661 | // according to Tst/../elimiate_[3568].tat (- 17 %) |
---|
1662 | ord=(rRingOrder_t*)omAlloc0(4*sizeof(rRingOrder_t)); |
---|
1663 | block0=(int*)omAlloc0(4*sizeof(int)); |
---|
1664 | block1=(int*)omAlloc0(4*sizeof(int)); |
---|
1665 | wv=(int**) omAlloc0(4*sizeof(int**)); |
---|
1666 | block0[0] = block0[1] = 1; |
---|
1667 | block1[0] = block1[1] = rVar(origR); |
---|
1668 | wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
1669 | // use this special ordering: like ringorder_a, except that pFDeg, pWeights |
---|
1670 | // ignore it |
---|
1671 | ord[0] = ringorder_aa; |
---|
1672 | for (j=0;j<rVar(origR);j++) |
---|
1673 | if (pGetExp(delVar,j+1)!=0) wv[0][j]=1; |
---|
1674 | BOOLEAN wp=FALSE; |
---|
1675 | for (j=0;j<rVar(origR);j++) |
---|
1676 | if (p_Weight(j+1,origR)!=1) { wp=TRUE;break; } |
---|
1677 | if (wp) |
---|
1678 | { |
---|
1679 | wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
1680 | for (j=0;j<rVar(origR);j++) |
---|
1681 | wv[1][j]=p_Weight(j+1,origR); |
---|
1682 | ord[1] = ringorder_wp; |
---|
1683 | } |
---|
1684 | else |
---|
1685 | ord[1] = ringorder_dp; |
---|
1686 | #else |
---|
1687 | // we change to an ordering: |
---|
1688 | // a(w1,...wn),wp(1,...0.....),C |
---|
1689 | ord=(int*)omAlloc0(4*sizeof(int)); |
---|
1690 | block0=(int*)omAlloc0(4*sizeof(int)); |
---|
1691 | block1=(int*)omAlloc0(4*sizeof(int)); |
---|
1692 | wv=(int**) omAlloc0(4*sizeof(int**)); |
---|
1693 | block0[0] = block0[1] = 1; |
---|
1694 | block1[0] = block1[1] = rVar(origR); |
---|
1695 | wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
1696 | wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
1697 | ord[0] = ringorder_a; |
---|
1698 | for (j=0;j<rVar(origR);j++) |
---|
1699 | wv[0][j]=pWeight(j+1,origR); |
---|
1700 | ord[1] = ringorder_wp; |
---|
1701 | for (j=0;j<rVar(origR);j++) |
---|
1702 | if (pGetExp(delVar,j+1)!=0) wv[1][j]=1; |
---|
1703 | #endif |
---|
1704 | ord[2] = ringorder_C; |
---|
1705 | ord[3] = (rRingOrder_t)0; |
---|
1706 | } |
---|
1707 | else |
---|
1708 | { |
---|
1709 | // we change to an ordering: |
---|
1710 | // aa(....),orig_ordering |
---|
1711 | ord=(rRingOrder_t*)omAlloc0(ordersize*sizeof(rRingOrder_t)); |
---|
1712 | block0=(int*)omAlloc0(ordersize*sizeof(int)); |
---|
1713 | block1=(int*)omAlloc0(ordersize*sizeof(int)); |
---|
1714 | wv=(int**) omAlloc0(ordersize*sizeof(int**)); |
---|
1715 | for (k=0;k<ordersize-1; k++) |
---|
1716 | { |
---|
1717 | block0[k+1] = origR->block0[k]; |
---|
1718 | block1[k+1] = origR->block1[k]; |
---|
1719 | ord[k+1] = origR->order[k]; |
---|
1720 | if (origR->wvhdl[k]!=NULL) wv[k+1] = (int*) omMemDup(origR->wvhdl[k]); |
---|
1721 | } |
---|
1722 | block0[0] = 1; |
---|
1723 | block1[0] = rVar(origR); |
---|
1724 | wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
1725 | for (j=0;j<rVar(origR);j++) |
---|
1726 | if (pGetExp(delVar,j+1)!=0) wv[0][j]=1; |
---|
1727 | // use this special ordering: like ringorder_a, except that pFDeg, pWeights |
---|
1728 | // ignore it |
---|
1729 | ord[0] = ringorder_aa; |
---|
1730 | } |
---|
1731 | // fill in tmp ring to get back the data later on |
---|
1732 | tmpR = rCopy0(origR,FALSE,FALSE); // qring==NULL |
---|
1733 | //rUnComplete(tmpR); |
---|
1734 | tmpR->p_Procs=NULL; |
---|
1735 | tmpR->order = ord; |
---|
1736 | tmpR->block0 = block0; |
---|
1737 | tmpR->block1 = block1; |
---|
1738 | tmpR->wvhdl = wv; |
---|
1739 | rComplete(tmpR, 1); |
---|
1740 | |
---|
1741 | #ifdef HAVE_PLURAL |
---|
1742 | /* update nc structure on tmpR */ |
---|
1743 | if (rIsPluralRing(origR)) |
---|
1744 | { |
---|
1745 | if ( nc_rComplete(origR, tmpR, false) ) // no quotient ideal! |
---|
1746 | { |
---|
1747 | WerrorS("no elimination is possible: ordering condition is violated"); |
---|
1748 | // cleanup |
---|
1749 | rDelete(tmpR); |
---|
1750 | if (w!=NULL) |
---|
1751 | delete w; |
---|
1752 | return NULL; |
---|
1753 | } |
---|
1754 | } |
---|
1755 | #endif |
---|
1756 | // change into the new ring |
---|
1757 | //pChangeRing((currRing->N),currRing->OrdSgn,ord,block0,block1,wv); |
---|
1758 | rChangeCurrRing(tmpR); |
---|
1759 | |
---|
1760 | //h = idInit(IDELEMS(h1),h1->rank); |
---|
1761 | // fetch data from the old ring |
---|
1762 | //for (k=0;k<IDELEMS(h1);k++) h->m[k] = prCopyR( h1->m[k], origR); |
---|
1763 | h=idrCopyR(h1,origR,currRing); |
---|
1764 | if (origR->qideal!=NULL) |
---|
1765 | { |
---|
1766 | WarnS("eliminate in q-ring: experimental"); |
---|
1767 | ideal q=idrCopyR(origR->qideal,origR,currRing); |
---|
1768 | ideal s=idSimpleAdd(h,q); |
---|
1769 | idDelete(&h); |
---|
1770 | idDelete(&q); |
---|
1771 | h=s; |
---|
1772 | } |
---|
1773 | // compute kStd |
---|
1774 | #if 1 |
---|
1775 | //rWrite(tmpR);PrintLn(); |
---|
1776 | //BITSET save1; |
---|
1777 | //SI_SAVE_OPT1(save1); |
---|
1778 | //si_opt_1 |=1; |
---|
1779 | //Print("h: %d gen, rk=%d\n",IDELEMS(h),h->rank); |
---|
1780 | //extern char * showOption(); |
---|
1781 | //Print("%s\n",showOption()); |
---|
1782 | hh = kStd(h,NULL,hom,&w,hilb); |
---|
1783 | //SI_RESTORE_OPT1(save1); |
---|
1784 | idDelete(&h); |
---|
1785 | #else |
---|
1786 | extern ideal kGroebner(ideal F, ideal Q); |
---|
1787 | hh=kGroebner(h,NULL); |
---|
1788 | #endif |
---|
1789 | // go back to the original ring |
---|
1790 | rChangeCurrRing(origR); |
---|
1791 | i = IDELEMS(hh)-1; |
---|
1792 | while ((i >= 0) && (hh->m[i] == NULL)) i--; |
---|
1793 | j = -1; |
---|
1794 | // fetch data from temp ring |
---|
1795 | for (k=0; k<=i; k++) |
---|
1796 | { |
---|
1797 | l=(currRing->N); |
---|
1798 | while ((l>0) && (p_GetExp( hh->m[k],l,tmpR)*pGetExp(delVar,l)==0)) l--; |
---|
1799 | if (l==0) |
---|
1800 | { |
---|
1801 | j++; |
---|
1802 | if (j >= IDELEMS(h3)) |
---|
1803 | { |
---|
1804 | pEnlargeSet(&(h3->m),IDELEMS(h3),16); |
---|
1805 | IDELEMS(h3) += 16; |
---|
1806 | } |
---|
1807 | h3->m[j] = prMoveR( hh->m[k], tmpR,origR); |
---|
1808 | hh->m[k] = NULL; |
---|
1809 | } |
---|
1810 | } |
---|
1811 | id_Delete(&hh, tmpR); |
---|
1812 | idSkipZeroes(h3); |
---|
1813 | rDelete(tmpR); |
---|
1814 | if (w!=NULL) |
---|
1815 | delete w; |
---|
1816 | return h3; |
---|
1817 | } |
---|
1818 | |
---|
1819 | #ifdef WITH_OLD_MINOR |
---|
1820 | /*2 |
---|
1821 | * compute the which-th ar-minor of the matrix a |
---|
1822 | */ |
---|
1823 | poly idMinor(matrix a, int ar, unsigned long which, ideal R) |
---|
1824 | { |
---|
1825 | int i,j/*,k,size*/; |
---|
1826 | unsigned long curr; |
---|
1827 | int *rowchoise,*colchoise; |
---|
1828 | BOOLEAN rowch,colch; |
---|
1829 | // ideal result; |
---|
1830 | matrix tmp; |
---|
1831 | poly p,q; |
---|
1832 | |
---|
1833 | i = binom(a->rows(),ar); |
---|
1834 | j = binom(a->cols(),ar); |
---|
1835 | |
---|
1836 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
1837 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
1838 | // if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
1839 | // else size=i*j; |
---|
1840 | // result=idInit(size,1); |
---|
1841 | tmp=mpNew(ar,ar); |
---|
1842 | // k = 0; /* the index in result*/ |
---|
1843 | curr = 0; /* index of current minor */ |
---|
1844 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
1845 | while (!rowch) |
---|
1846 | { |
---|
1847 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
1848 | while (!colch) |
---|
1849 | { |
---|
1850 | if (curr == which) |
---|
1851 | { |
---|
1852 | for (i=1; i<=ar; i++) |
---|
1853 | { |
---|
1854 | for (j=1; j<=ar; j++) |
---|
1855 | { |
---|
1856 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
1857 | } |
---|
1858 | } |
---|
1859 | p = mp_DetBareiss(tmp,currRing); |
---|
1860 | if (p!=NULL) |
---|
1861 | { |
---|
1862 | if (R!=NULL) |
---|
1863 | { |
---|
1864 | q = p; |
---|
1865 | p = kNF(R,currRing->qideal,q); |
---|
1866 | p_Delete(&q,currRing); |
---|
1867 | } |
---|
1868 | /*delete the matrix tmp*/ |
---|
1869 | for (i=1; i<=ar; i++) |
---|
1870 | { |
---|
1871 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
1872 | } |
---|
1873 | idDelete((ideal*)&tmp); |
---|
1874 | omFreeSize((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
1875 | omFreeSize((ADDRESS)colchoise,ar*sizeof(int)); |
---|
1876 | return (p); |
---|
1877 | } |
---|
1878 | } |
---|
1879 | curr++; |
---|
1880 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
1881 | } |
---|
1882 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
1883 | } |
---|
1884 | return (poly) 1; |
---|
1885 | } |
---|
1886 | |
---|
1887 | /*2 |
---|
1888 | * compute all ar-minors of the matrix a |
---|
1889 | */ |
---|
1890 | ideal idMinors(matrix a, int ar, ideal R) |
---|
1891 | { |
---|
1892 | int i,j,/*k,*/size; |
---|
1893 | int *rowchoise,*colchoise; |
---|
1894 | BOOLEAN rowch,colch; |
---|
1895 | ideal result; |
---|
1896 | matrix tmp; |
---|
1897 | poly p,q; |
---|
1898 | |
---|
1899 | i = binom(a->rows(),ar); |
---|
1900 | j = binom(a->cols(),ar); |
---|
1901 | |
---|
1902 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
1903 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
1904 | if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
1905 | else size=i*j; |
---|
1906 | result=idInit(size,1); |
---|
1907 | tmp=mpNew(ar,ar); |
---|
1908 | // k = 0; /* the index in result*/ |
---|
1909 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
1910 | while (!rowch) |
---|
1911 | { |
---|
1912 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
1913 | while (!colch) |
---|
1914 | { |
---|
1915 | for (i=1; i<=ar; i++) |
---|
1916 | { |
---|
1917 | for (j=1; j<=ar; j++) |
---|
1918 | { |
---|
1919 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
1920 | } |
---|
1921 | } |
---|
1922 | p = mp_DetBareiss(tmp,currRing); |
---|
1923 | if (p!=NULL) |
---|
1924 | { |
---|
1925 | if (R!=NULL) |
---|
1926 | { |
---|
1927 | q = p; |
---|
1928 | p = kNF(R,currRing->qideal,q); |
---|
1929 | p_Delete(&q,currRing); |
---|
1930 | } |
---|
1931 | if (p!=NULL) |
---|
1932 | { |
---|
1933 | if (k>=size) |
---|
1934 | { |
---|
1935 | pEnlargeSet(&result->m,size,32); |
---|
1936 | size += 32; |
---|
1937 | } |
---|
1938 | result->m[k] = p; |
---|
1939 | k++; |
---|
1940 | } |
---|
1941 | } |
---|
1942 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
1943 | } |
---|
1944 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
1945 | } |
---|
1946 | /*delete the matrix tmp*/ |
---|
1947 | for (i=1; i<=ar; i++) |
---|
1948 | { |
---|
1949 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
1950 | } |
---|
1951 | idDelete((ideal*)&tmp); |
---|
1952 | if (k==0) |
---|
1953 | { |
---|
1954 | k=1; |
---|
1955 | result->m[0]=NULL; |
---|
1956 | } |
---|
1957 | omFreeSize((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
1958 | omFreeSize((ADDRESS)colchoise,ar*sizeof(int)); |
---|
1959 | pEnlargeSet(&result->m,size,k-size); |
---|
1960 | IDELEMS(result) = k; |
---|
1961 | return (result); |
---|
1962 | } |
---|
1963 | #else |
---|
1964 | |
---|
1965 | |
---|
1966 | /// compute all ar-minors of the matrix a |
---|
1967 | /// the caller of mpRecMin |
---|
1968 | /// the elements of the result are not in R (if R!=NULL) |
---|
1969 | ideal idMinors(matrix a, int ar, ideal R) |
---|
1970 | { |
---|
1971 | |
---|
1972 | const ring origR=currRing; |
---|
1973 | id_Test((ideal)a, origR); |
---|
1974 | |
---|
1975 | const int r = a->nrows; |
---|
1976 | const int c = a->ncols; |
---|
1977 | |
---|
1978 | if((ar<=0) || (ar>r) || (ar>c)) |
---|
1979 | { |
---|
1980 | Werror("%d-th minor, matrix is %dx%d",ar,r,c); |
---|
1981 | return NULL; |
---|
1982 | } |
---|
1983 | |
---|
1984 | ideal h = id_Matrix2Module(mp_Copy(a,origR),origR); |
---|
1985 | long bound = sm_ExpBound(h,c,r,ar,origR); |
---|
1986 | id_Delete(&h, origR); |
---|
1987 | |
---|
1988 | ring tmpR = sm_RingChange(origR,bound); |
---|
1989 | |
---|
1990 | matrix b = mpNew(r,c); |
---|
1991 | |
---|
1992 | for (int i=r*c-1;i>=0;i--) |
---|
1993 | if (a->m[i] != NULL) |
---|
1994 | b->m[i] = prCopyR(a->m[i],origR,tmpR); |
---|
1995 | |
---|
1996 | id_Test( (ideal)b, tmpR); |
---|
1997 | |
---|
1998 | if (R!=NULL) |
---|
1999 | { |
---|
2000 | R = idrCopyR(R,origR,tmpR); // TODO: overwrites R? memory leak? |
---|
2001 | //if (ar>1) // otherwise done in mpMinorToResult |
---|
2002 | //{ |
---|
2003 | // matrix bb=(matrix)kNF(R,currRing->qideal,(ideal)b); |
---|
2004 | // bb->rank=b->rank; bb->nrows=b->nrows; bb->ncols=b->ncols; |
---|
2005 | // idDelete((ideal*)&b); b=bb; |
---|
2006 | //} |
---|
2007 | id_Test( R, tmpR); |
---|
2008 | } |
---|
2009 | |
---|
2010 | |
---|
2011 | ideal result = idInit(32,1); |
---|
2012 | |
---|
2013 | int elems = 0; |
---|
2014 | |
---|
2015 | if(ar>1) |
---|
2016 | mp_RecMin(ar-1,result,elems,b,r,c,NULL,R,tmpR); |
---|
2017 | else |
---|
2018 | mp_MinorToResult(result,elems,b,r,c,R,tmpR); |
---|
2019 | |
---|
2020 | id_Test( (ideal)b, tmpR); |
---|
2021 | |
---|
2022 | id_Delete((ideal *)&b, tmpR); |
---|
2023 | |
---|
2024 | if (R!=NULL) id_Delete(&R,tmpR); |
---|
2025 | |
---|
2026 | idSkipZeroes(result); |
---|
2027 | rChangeCurrRing(origR); |
---|
2028 | result = idrMoveR(result,tmpR,origR); |
---|
2029 | sm_KillModifiedRing(tmpR); |
---|
2030 | idTest(result); |
---|
2031 | return result; |
---|
2032 | } |
---|
2033 | #endif |
---|
2034 | |
---|
2035 | /*2 |
---|
2036 | *returns TRUE if id1 is a submodule of id2 |
---|
2037 | */ |
---|
2038 | BOOLEAN idIsSubModule(ideal id1,ideal id2) |
---|
2039 | { |
---|
2040 | int i; |
---|
2041 | poly p; |
---|
2042 | |
---|
2043 | if (idIs0(id1)) return TRUE; |
---|
2044 | for (i=0;i<IDELEMS(id1);i++) |
---|
2045 | { |
---|
2046 | if (id1->m[i] != NULL) |
---|
2047 | { |
---|
2048 | p = kNF(id2,currRing->qideal,id1->m[i]); |
---|
2049 | if (p != NULL) |
---|
2050 | { |
---|
2051 | p_Delete(&p,currRing); |
---|
2052 | return FALSE; |
---|
2053 | } |
---|
2054 | } |
---|
2055 | } |
---|
2056 | return TRUE; |
---|
2057 | } |
---|
2058 | |
---|
2059 | BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w) |
---|
2060 | { |
---|
2061 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;} |
---|
2062 | if (idIs0(m)) return TRUE; |
---|
2063 | |
---|
2064 | int cmax=-1; |
---|
2065 | int i; |
---|
2066 | poly p=NULL; |
---|
2067 | int length=IDELEMS(m); |
---|
2068 | polyset P=m->m; |
---|
2069 | for (i=length-1;i>=0;i--) |
---|
2070 | { |
---|
2071 | p=P[i]; |
---|
2072 | if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1); |
---|
2073 | } |
---|
2074 | if (w != NULL) |
---|
2075 | if (w->length()+1 < cmax) |
---|
2076 | { |
---|
2077 | // Print("length: %d - %d \n", w->length(),cmax); |
---|
2078 | return FALSE; |
---|
2079 | } |
---|
2080 | |
---|
2081 | if(w!=NULL) |
---|
2082 | p_SetModDeg(w, currRing); |
---|
2083 | |
---|
2084 | for (i=length-1;i>=0;i--) |
---|
2085 | { |
---|
2086 | p=P[i]; |
---|
2087 | if (p!=NULL) |
---|
2088 | { |
---|
2089 | int d=currRing->pFDeg(p,currRing); |
---|
2090 | loop |
---|
2091 | { |
---|
2092 | pIter(p); |
---|
2093 | if (p==NULL) break; |
---|
2094 | if (d!=currRing->pFDeg(p,currRing)) |
---|
2095 | { |
---|
2096 | //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing)); |
---|
2097 | if(w!=NULL) |
---|
2098 | p_SetModDeg(NULL, currRing); |
---|
2099 | return FALSE; |
---|
2100 | } |
---|
2101 | } |
---|
2102 | } |
---|
2103 | } |
---|
2104 | |
---|
2105 | if(w!=NULL) |
---|
2106 | p_SetModDeg(NULL, currRing); |
---|
2107 | |
---|
2108 | return TRUE; |
---|
2109 | } |
---|
2110 | |
---|
2111 | ideal idSeries(int n,ideal M,matrix U,intvec *w) |
---|
2112 | { |
---|
2113 | for(int i=IDELEMS(M)-1;i>=0;i--) |
---|
2114 | { |
---|
2115 | if(U==NULL) |
---|
2116 | M->m[i]=pSeries(n,M->m[i],NULL,w); |
---|
2117 | else |
---|
2118 | { |
---|
2119 | M->m[i]=pSeries(n,M->m[i],MATELEM(U,i+1,i+1),w); |
---|
2120 | MATELEM(U,i+1,i+1)=NULL; |
---|
2121 | } |
---|
2122 | } |
---|
2123 | if(U!=NULL) |
---|
2124 | idDelete((ideal*)&U); |
---|
2125 | return M; |
---|
2126 | } |
---|
2127 | |
---|
2128 | matrix idDiff(matrix i, int k) |
---|
2129 | { |
---|
2130 | int e=MATCOLS(i)*MATROWS(i); |
---|
2131 | matrix r=mpNew(MATROWS(i),MATCOLS(i)); |
---|
2132 | r->rank=i->rank; |
---|
2133 | int j; |
---|
2134 | for(j=0; j<e; j++) |
---|
2135 | { |
---|
2136 | r->m[j]=pDiff(i->m[j],k); |
---|
2137 | } |
---|
2138 | return r; |
---|
2139 | } |
---|
2140 | |
---|
2141 | matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply) |
---|
2142 | { |
---|
2143 | matrix r=mpNew(IDELEMS(I),IDELEMS(J)); |
---|
2144 | int i,j; |
---|
2145 | for(i=0; i<IDELEMS(I); i++) |
---|
2146 | { |
---|
2147 | for(j=0; j<IDELEMS(J); j++) |
---|
2148 | { |
---|
2149 | MATELEM(r,i+1,j+1)=pDiffOp(I->m[i],J->m[j],multiply); |
---|
2150 | } |
---|
2151 | } |
---|
2152 | return r; |
---|
2153 | } |
---|
2154 | |
---|
2155 | /*3 |
---|
2156 | *handles for some ideal operations the ring/syzcomp managment |
---|
2157 | *returns all syzygies (componentwise-)shifted by -syzcomp |
---|
2158 | *or -syzcomp-1 (in case of ideals as input) |
---|
2159 | static ideal idHandleIdealOp(ideal arg,int syzcomp,int isIdeal=FALSE) |
---|
2160 | { |
---|
2161 | ring orig_ring=currRing; |
---|
2162 | ring syz_ring=rAssure_SyzOrder(orig_ring, TRUE); rChangeCurrRing(syz_ring); |
---|
2163 | rSetSyzComp(length, syz_ring); |
---|
2164 | |
---|
2165 | ideal s_temp; |
---|
2166 | if (orig_ring!=syz_ring) |
---|
2167 | s_temp=idrMoveR_NoSort(arg,orig_ring, syz_ring); |
---|
2168 | else |
---|
2169 | s_temp=arg; |
---|
2170 | |
---|
2171 | ideal s_temp1 = kStd(s_temp,currRing->qideal,testHomog,&w,NULL,length); |
---|
2172 | if (w!=NULL) delete w; |
---|
2173 | |
---|
2174 | if (syz_ring!=orig_ring) |
---|
2175 | { |
---|
2176 | idDelete(&s_temp); |
---|
2177 | rChangeCurrRing(orig_ring); |
---|
2178 | } |
---|
2179 | |
---|
2180 | idDelete(&temp); |
---|
2181 | ideal temp1=idRingCopy(s_temp1,syz_ring); |
---|
2182 | |
---|
2183 | if (syz_ring!=orig_ring) |
---|
2184 | { |
---|
2185 | rChangeCurrRing(syz_ring); |
---|
2186 | idDelete(&s_temp1); |
---|
2187 | rChangeCurrRing(orig_ring); |
---|
2188 | rDelete(syz_ring); |
---|
2189 | } |
---|
2190 | |
---|
2191 | for (i=0;i<IDELEMS(temp1);i++) |
---|
2192 | { |
---|
2193 | if ((temp1->m[i]!=NULL) |
---|
2194 | && (pGetComp(temp1->m[i])<=length)) |
---|
2195 | { |
---|
2196 | pDelete(&(temp1->m[i])); |
---|
2197 | } |
---|
2198 | else |
---|
2199 | { |
---|
2200 | p_Shift(&(temp1->m[i]),-length,currRing); |
---|
2201 | } |
---|
2202 | } |
---|
2203 | temp1->rank = rk; |
---|
2204 | idSkipZeroes(temp1); |
---|
2205 | |
---|
2206 | return temp1; |
---|
2207 | } |
---|
2208 | */ |
---|
2209 | /*2 |
---|
2210 | * represents (h1+h2)/h2=h1/(h1 intersect h2) |
---|
2211 | */ |
---|
2212 | //ideal idModulo (ideal h2,ideal h1) |
---|
2213 | ideal idModulo (ideal h2,ideal h1, tHomog hom, intvec ** w) |
---|
2214 | { |
---|
2215 | intvec *wtmp=NULL; |
---|
2216 | |
---|
2217 | int i,k,rk,flength=0,slength,length; |
---|
2218 | poly p,q; |
---|
2219 | |
---|
2220 | if (idIs0(h2)) |
---|
2221 | return idFreeModule(si_max(1,h2->ncols)); |
---|
2222 | if (!idIs0(h1)) |
---|
2223 | flength = id_RankFreeModule(h1,currRing); |
---|
2224 | slength = id_RankFreeModule(h2,currRing); |
---|
2225 | length = si_max(flength,slength); |
---|
2226 | if (length==0) |
---|
2227 | { |
---|
2228 | length = 1; |
---|
2229 | } |
---|
2230 | ideal temp = idInit(IDELEMS(h2),length+IDELEMS(h2)); |
---|
2231 | if ((w!=NULL)&&((*w)!=NULL)) |
---|
2232 | { |
---|
2233 | //Print("input weights:");(*w)->show(1);PrintLn(); |
---|
2234 | int d; |
---|
2235 | int k; |
---|
2236 | wtmp=new intvec(length+IDELEMS(h2)); |
---|
2237 | for (i=0;i<length;i++) |
---|
2238 | ((*wtmp)[i])=(**w)[i]; |
---|
2239 | for (i=0;i<IDELEMS(h2);i++) |
---|
2240 | { |
---|
2241 | poly p=h2->m[i]; |
---|
2242 | if (p!=NULL) |
---|
2243 | { |
---|
2244 | d = p_Deg(p,currRing); |
---|
2245 | k= pGetComp(p); |
---|
2246 | if (slength>0) k--; |
---|
2247 | d +=((**w)[k]); |
---|
2248 | ((*wtmp)[i+length]) = d; |
---|
2249 | } |
---|
2250 | } |
---|
2251 | //Print("weights:");wtmp->show(1);PrintLn(); |
---|
2252 | } |
---|
2253 | for (i=0;i<IDELEMS(h2);i++) |
---|
2254 | { |
---|
2255 | temp->m[i] = pCopy(h2->m[i]); |
---|
2256 | q = pOne(); |
---|
2257 | pSetComp(q,i+1+length); |
---|
2258 | pSetmComp(q); |
---|
2259 | if(temp->m[i]!=NULL) |
---|
2260 | { |
---|
2261 | if (slength==0) p_Shift(&(temp->m[i]),1,currRing); |
---|
2262 | p = temp->m[i]; |
---|
2263 | while (pNext(p)!=NULL) pIter(p); |
---|
2264 | pNext(p) = q; // will be sorted later correctly |
---|
2265 | } |
---|
2266 | else |
---|
2267 | temp->m[i]=q; |
---|
2268 | } |
---|
2269 | rk = k = IDELEMS(h2); |
---|
2270 | if (!idIs0(h1)) |
---|
2271 | { |
---|
2272 | pEnlargeSet(&(temp->m),IDELEMS(temp),IDELEMS(h1)); |
---|
2273 | IDELEMS(temp) += IDELEMS(h1); |
---|
2274 | for (i=0;i<IDELEMS(h1);i++) |
---|
2275 | { |
---|
2276 | if (h1->m[i]!=NULL) |
---|
2277 | { |
---|
2278 | temp->m[k] = pCopy(h1->m[i]); |
---|
2279 | if (flength==0) p_Shift(&(temp->m[k]),1,currRing); |
---|
2280 | k++; |
---|
2281 | } |
---|
2282 | } |
---|
2283 | } |
---|
2284 | |
---|
2285 | ring orig_ring=currRing; |
---|
2286 | ring syz_ring=rAssure_SyzOrder(orig_ring, TRUE); |
---|
2287 | rSetSyzComp(length,syz_ring); |
---|
2288 | rChangeCurrRing(syz_ring); |
---|
2289 | // we can use OPT_RETURN_SB only, if syz_ring==orig_ring, |
---|
2290 | // therefore we disable OPT_RETURN_SB for modulo: |
---|
2291 | // (see tr. #701) |
---|
2292 | //if (TEST_OPT_RETURN_SB) |
---|
2293 | // rSetSyzComp(IDELEMS(h2)+length, syz_ring); |
---|
2294 | //else |
---|
2295 | // rSetSyzComp(length, syz_ring); |
---|
2296 | ideal s_temp; |
---|
2297 | |
---|
2298 | if (syz_ring != orig_ring) |
---|
2299 | { |
---|
2300 | s_temp = idrMoveR_NoSort(temp, orig_ring, syz_ring); |
---|
2301 | } |
---|
2302 | else |
---|
2303 | { |
---|
2304 | s_temp = temp; |
---|
2305 | } |
---|
2306 | |
---|
2307 | idTest(s_temp); |
---|
2308 | ideal s_temp1 = kStd(s_temp,currRing->qideal,hom,&wtmp,NULL,length); |
---|
2309 | |
---|
2310 | //if (wtmp!=NULL) Print("output weights:");wtmp->show(1);PrintLn(); |
---|
2311 | if ((w!=NULL) && (*w !=NULL) && (wtmp!=NULL)) |
---|
2312 | { |
---|
2313 | delete *w; |
---|
2314 | *w=new intvec(IDELEMS(h2)); |
---|
2315 | for (i=0;i<IDELEMS(h2);i++) |
---|
2316 | ((**w)[i])=(*wtmp)[i+length]; |
---|
2317 | } |
---|
2318 | if (wtmp!=NULL) delete wtmp; |
---|
2319 | |
---|
2320 | for (i=0;i<IDELEMS(s_temp1);i++) |
---|
2321 | { |
---|
2322 | if ((s_temp1->m[i]!=NULL) |
---|
2323 | && (((int)pGetComp(s_temp1->m[i]))<=length)) |
---|
2324 | { |
---|
2325 | p_Delete(&(s_temp1->m[i]),currRing); |
---|
2326 | } |
---|
2327 | else |
---|
2328 | { |
---|
2329 | p_Shift(&(s_temp1->m[i]),-length,currRing); |
---|
2330 | } |
---|
2331 | } |
---|
2332 | s_temp1->rank = rk; |
---|
2333 | idSkipZeroes(s_temp1); |
---|
2334 | |
---|
2335 | if (syz_ring!=orig_ring) |
---|
2336 | { |
---|
2337 | rChangeCurrRing(orig_ring); |
---|
2338 | s_temp1 = idrMoveR_NoSort(s_temp1, syz_ring, orig_ring); |
---|
2339 | rDelete(syz_ring); |
---|
2340 | // Hmm ... here seems to be a memory leak |
---|
2341 | // However, simply deleting it causes memory trouble |
---|
2342 | // idDelete(&s_temp); |
---|
2343 | } |
---|
2344 | else |
---|
2345 | { |
---|
2346 | idDelete(&temp); |
---|
2347 | } |
---|
2348 | idTest(s_temp1); |
---|
2349 | return s_temp1; |
---|
2350 | } |
---|
2351 | |
---|
2352 | /* |
---|
2353 | *computes module-weights for liftings of homogeneous modules |
---|
2354 | */ |
---|
2355 | intvec * idMWLift(ideal mod,intvec * weights) |
---|
2356 | { |
---|
2357 | if (idIs0(mod)) return new intvec(2); |
---|
2358 | int i=IDELEMS(mod); |
---|
2359 | while ((i>0) && (mod->m[i-1]==NULL)) i--; |
---|
2360 | intvec *result = new intvec(i+1); |
---|
2361 | while (i>0) |
---|
2362 | { |
---|
2363 | (*result)[i]=currRing->pFDeg(mod->m[i],currRing)+(*weights)[pGetComp(mod->m[i])]; |
---|
2364 | } |
---|
2365 | return result; |
---|
2366 | } |
---|
2367 | |
---|
2368 | /*2 |
---|
2369 | *sorts the kbase for idCoef* in a special way (lexicographically |
---|
2370 | *with x_max,...,x_1) |
---|
2371 | */ |
---|
2372 | ideal idCreateSpecialKbase(ideal kBase,intvec ** convert) |
---|
2373 | { |
---|
2374 | int i; |
---|
2375 | ideal result; |
---|
2376 | |
---|
2377 | if (idIs0(kBase)) return NULL; |
---|
2378 | result = idInit(IDELEMS(kBase),kBase->rank); |
---|
2379 | *convert = idSort(kBase,FALSE); |
---|
2380 | for (i=0;i<(*convert)->length();i++) |
---|
2381 | { |
---|
2382 | result->m[i] = pCopy(kBase->m[(**convert)[i]-1]); |
---|
2383 | } |
---|
2384 | return result; |
---|
2385 | } |
---|
2386 | |
---|
2387 | /*2 |
---|
2388 | *returns the index of a given monom in the list of the special kbase |
---|
2389 | */ |
---|
2390 | int idIndexOfKBase(poly monom, ideal kbase) |
---|
2391 | { |
---|
2392 | int j=IDELEMS(kbase); |
---|
2393 | |
---|
2394 | while ((j>0) && (kbase->m[j-1]==NULL)) j--; |
---|
2395 | if (j==0) return -1; |
---|
2396 | int i=(currRing->N); |
---|
2397 | while (i>0) |
---|
2398 | { |
---|
2399 | loop |
---|
2400 | { |
---|
2401 | if (pGetExp(monom,i)>pGetExp(kbase->m[j-1],i)) return -1; |
---|
2402 | if (pGetExp(monom,i)==pGetExp(kbase->m[j-1],i)) break; |
---|
2403 | j--; |
---|
2404 | if (j==0) return -1; |
---|
2405 | } |
---|
2406 | if (i==1) |
---|
2407 | { |
---|
2408 | while(j>0) |
---|
2409 | { |
---|
2410 | if (pGetComp(monom)==pGetComp(kbase->m[j-1])) return j-1; |
---|
2411 | if (pGetComp(monom)>pGetComp(kbase->m[j-1])) return -1; |
---|
2412 | j--; |
---|
2413 | } |
---|
2414 | } |
---|
2415 | i--; |
---|
2416 | } |
---|
2417 | return -1; |
---|
2418 | } |
---|
2419 | |
---|
2420 | /*2 |
---|
2421 | *decomposes the monom in a part of coefficients described by the |
---|
2422 | *complement of how and a monom in variables occuring in how, the |
---|
2423 | *index of which in kbase is returned as integer pos (-1 if it don't |
---|
2424 | *exists) |
---|
2425 | */ |
---|
2426 | poly idDecompose(poly monom, poly how, ideal kbase, int * pos) |
---|
2427 | { |
---|
2428 | int i; |
---|
2429 | poly coeff=pOne(), base=pOne(); |
---|
2430 | |
---|
2431 | for (i=1;i<=(currRing->N);i++) |
---|
2432 | { |
---|
2433 | if (pGetExp(how,i)>0) |
---|
2434 | { |
---|
2435 | pSetExp(base,i,pGetExp(monom,i)); |
---|
2436 | } |
---|
2437 | else |
---|
2438 | { |
---|
2439 | pSetExp(coeff,i,pGetExp(monom,i)); |
---|
2440 | } |
---|
2441 | } |
---|
2442 | pSetComp(base,pGetComp(monom)); |
---|
2443 | pSetm(base); |
---|
2444 | pSetCoeff(coeff,nCopy(pGetCoeff(monom))); |
---|
2445 | pSetm(coeff); |
---|
2446 | *pos = idIndexOfKBase(base,kbase); |
---|
2447 | if (*pos<0) |
---|
2448 | p_Delete(&coeff,currRing); |
---|
2449 | p_Delete(&base,currRing); |
---|
2450 | return coeff; |
---|
2451 | } |
---|
2452 | |
---|
2453 | /*2 |
---|
2454 | *returns a matrix A of coefficients with kbase*A=arg |
---|
2455 | *if all monomials in variables of how occur in kbase |
---|
2456 | *the other are deleted |
---|
2457 | */ |
---|
2458 | matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how) |
---|
2459 | { |
---|
2460 | matrix result; |
---|
2461 | ideal tempKbase; |
---|
2462 | poly p,q; |
---|
2463 | intvec * convert; |
---|
2464 | int i=IDELEMS(kbase),j=IDELEMS(arg),k,pos; |
---|
2465 | #if 0 |
---|
2466 | while ((i>0) && (kbase->m[i-1]==NULL)) i--; |
---|
2467 | if (idIs0(arg)) |
---|
2468 | return mpNew(i,1); |
---|
2469 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
2470 | result = mpNew(i,j); |
---|
2471 | #else |
---|
2472 | result = mpNew(i, j); |
---|
2473 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
2474 | #endif |
---|
2475 | |
---|
2476 | tempKbase = idCreateSpecialKbase(kbase,&convert); |
---|
2477 | for (k=0;k<j;k++) |
---|
2478 | { |
---|
2479 | p = arg->m[k]; |
---|
2480 | while (p!=NULL) |
---|
2481 | { |
---|
2482 | q = idDecompose(p,how,tempKbase,&pos); |
---|
2483 | if (pos>=0) |
---|
2484 | { |
---|
2485 | MATELEM(result,(*convert)[pos],k+1) = |
---|
2486 | pAdd(MATELEM(result,(*convert)[pos],k+1),q); |
---|
2487 | } |
---|
2488 | else |
---|
2489 | p_Delete(&q,currRing); |
---|
2490 | pIter(p); |
---|
2491 | } |
---|
2492 | } |
---|
2493 | idDelete(&tempKbase); |
---|
2494 | return result; |
---|
2495 | } |
---|
2496 | |
---|
2497 | static void idDeleteComps(ideal arg,int* red_comp,int del) |
---|
2498 | // red_comp is an array [0..args->rank] |
---|
2499 | { |
---|
2500 | int i,j; |
---|
2501 | poly p; |
---|
2502 | |
---|
2503 | for (i=IDELEMS(arg)-1;i>=0;i--) |
---|
2504 | { |
---|
2505 | p = arg->m[i]; |
---|
2506 | while (p!=NULL) |
---|
2507 | { |
---|
2508 | j = pGetComp(p); |
---|
2509 | if (red_comp[j]!=j) |
---|
2510 | { |
---|
2511 | pSetComp(p,red_comp[j]); |
---|
2512 | pSetmComp(p); |
---|
2513 | } |
---|
2514 | pIter(p); |
---|
2515 | } |
---|
2516 | } |
---|
2517 | (arg->rank) -= del; |
---|
2518 | } |
---|
2519 | |
---|
2520 | /*2 |
---|
2521 | * returns the presentation of an isomorphic, minimally |
---|
2522 | * embedded module (arg represents the quotient!) |
---|
2523 | */ |
---|
2524 | ideal idMinEmbedding(ideal arg,BOOLEAN inPlace, intvec **w) |
---|
2525 | { |
---|
2526 | if (idIs0(arg)) return idInit(1,arg->rank); |
---|
2527 | int i,next_gen,next_comp; |
---|
2528 | ideal res=arg; |
---|
2529 | if (!inPlace) res = idCopy(arg); |
---|
2530 | res->rank=si_max(res->rank,id_RankFreeModule(res,currRing)); |
---|
2531 | int *red_comp=(int*)omAlloc((res->rank+1)*sizeof(int)); |
---|
2532 | for (i=res->rank;i>=0;i--) red_comp[i]=i; |
---|
2533 | |
---|
2534 | int del=0; |
---|
2535 | loop |
---|
2536 | { |
---|
2537 | next_gen = id_ReadOutPivot(res, &next_comp, currRing); |
---|
2538 | if (next_gen<0) break; |
---|
2539 | del++; |
---|
2540 | syGaussForOne(res,next_gen,next_comp,0,IDELEMS(res)); |
---|
2541 | for(i=next_comp+1;i<=arg->rank;i++) red_comp[i]--; |
---|
2542 | if ((w !=NULL)&&(*w!=NULL)) |
---|
2543 | { |
---|
2544 | for(i=next_comp;i<(*w)->length();i++) (**w)[i-1]=(**w)[i]; |
---|
2545 | } |
---|
2546 | } |
---|
2547 | |
---|
2548 | idDeleteComps(res,red_comp,del); |
---|
2549 | idSkipZeroes(res); |
---|
2550 | omFree(red_comp); |
---|
2551 | |
---|
2552 | if ((w !=NULL)&&(*w!=NULL) &&(del>0)) |
---|
2553 | { |
---|
2554 | int nl=si_max((*w)->length()-del,1); |
---|
2555 | intvec *wtmp=new intvec(nl); |
---|
2556 | for(i=0;i<res->rank;i++) (*wtmp)[i]=(**w)[i]; |
---|
2557 | delete *w; |
---|
2558 | *w=wtmp; |
---|
2559 | } |
---|
2560 | return res; |
---|
2561 | } |
---|
2562 | |
---|
2563 | #include "polys/clapsing.h" |
---|
2564 | |
---|
2565 | #if 0 |
---|
2566 | poly id_GCD(poly f, poly g, const ring r) |
---|
2567 | { |
---|
2568 | ring save_r=currRing; |
---|
2569 | rChangeCurrRing(r); |
---|
2570 | ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g; |
---|
2571 | intvec *w = NULL; |
---|
2572 | ideal S=idSyzygies(I,testHomog,&w); |
---|
2573 | if (w!=NULL) delete w; |
---|
2574 | poly gg=pTakeOutComp(&(S->m[0]),2); |
---|
2575 | idDelete(&S); |
---|
2576 | poly gcd_p=singclap_pdivide(f,gg,r); |
---|
2577 | p_Delete(&gg,r); |
---|
2578 | rChangeCurrRing(save_r); |
---|
2579 | return gcd_p; |
---|
2580 | } |
---|
2581 | #else |
---|
2582 | poly id_GCD(poly f, poly g, const ring r) |
---|
2583 | { |
---|
2584 | ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g; |
---|
2585 | intvec *w = NULL; |
---|
2586 | |
---|
2587 | ring save_r = currRing; |
---|
2588 | rChangeCurrRing(r); |
---|
2589 | ideal S=idSyzygies(I,testHomog,&w); |
---|
2590 | rChangeCurrRing(save_r); |
---|
2591 | |
---|
2592 | if (w!=NULL) delete w; |
---|
2593 | poly gg=p_TakeOutComp(&(S->m[0]), 2, r); |
---|
2594 | id_Delete(&S, r); |
---|
2595 | poly gcd_p=singclap_pdivide(f,gg, r); |
---|
2596 | p_Delete(&gg, r); |
---|
2597 | |
---|
2598 | return gcd_p; |
---|
2599 | } |
---|
2600 | #endif |
---|
2601 | |
---|
2602 | #if 0 |
---|
2603 | /*2 |
---|
2604 | * xx,q: arrays of length 0..rl-1 |
---|
2605 | * xx[i]: SB mod q[i] |
---|
2606 | * assume: char=0 |
---|
2607 | * assume: q[i]!=0 |
---|
2608 | * destroys xx |
---|
2609 | */ |
---|
2610 | ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring R) |
---|
2611 | { |
---|
2612 | int cnt=IDELEMS(xx[0])*xx[0]->nrows; |
---|
2613 | ideal result=idInit(cnt,xx[0]->rank); |
---|
2614 | result->nrows=xx[0]->nrows; // for lifting matrices |
---|
2615 | result->ncols=xx[0]->ncols; // for lifting matrices |
---|
2616 | int i,j; |
---|
2617 | poly r,h,hh,res_p; |
---|
2618 | number *x=(number *)omAlloc(rl*sizeof(number)); |
---|
2619 | for(i=cnt-1;i>=0;i--) |
---|
2620 | { |
---|
2621 | res_p=NULL; |
---|
2622 | loop |
---|
2623 | { |
---|
2624 | r=NULL; |
---|
2625 | for(j=rl-1;j>=0;j--) |
---|
2626 | { |
---|
2627 | h=xx[j]->m[i]; |
---|
2628 | if ((h!=NULL) |
---|
2629 | &&((r==NULL)||(p_LmCmp(r,h,R)==-1))) |
---|
2630 | r=h; |
---|
2631 | } |
---|
2632 | if (r==NULL) break; |
---|
2633 | h=p_Head(r, R); |
---|
2634 | for(j=rl-1;j>=0;j--) |
---|
2635 | { |
---|
2636 | hh=xx[j]->m[i]; |
---|
2637 | if ((hh!=NULL) && (p_LmCmp(r,hh, R)==0)) |
---|
2638 | { |
---|
2639 | x[j]=p_GetCoeff(hh, R); |
---|
2640 | hh=p_LmFreeAndNext(hh, R); |
---|
2641 | xx[j]->m[i]=hh; |
---|
2642 | } |
---|
2643 | else |
---|
2644 | x[j]=n_Init(0, R->cf); // is R->cf really n_Q???, yes! |
---|
2645 | } |
---|
2646 | |
---|
2647 | number n=n_ChineseRemainder(x,q,rl, R->cf); |
---|
2648 | |
---|
2649 | for(j=rl-1;j>=0;j--) |
---|
2650 | { |
---|
2651 | x[j]=NULL; // nlInit(0...) takes no memory |
---|
2652 | } |
---|
2653 | if (n_IsZero(n, R->cf)) p_Delete(&h, R); |
---|
2654 | else |
---|
2655 | { |
---|
2656 | p_SetCoeff(h,n, R); |
---|
2657 | //Print("new mon:");pWrite(h); |
---|
2658 | res_p=p_Add_q(res_p, h, R); |
---|
2659 | } |
---|
2660 | } |
---|
2661 | result->m[i]=res_p; |
---|
2662 | } |
---|
2663 | omFree(x); |
---|
2664 | for(i=rl-1;i>=0;i--) id_Delete(&(xx[i]), R); |
---|
2665 | omFree(xx); |
---|
2666 | return result; |
---|
2667 | } |
---|
2668 | #endif |
---|
2669 | /* currently unsed: |
---|
2670 | ideal idChineseRemainder(ideal *xx, intvec *iv) |
---|
2671 | { |
---|
2672 | int rl=iv->length(); |
---|
2673 | number *q=(number *)omAlloc(rl*sizeof(number)); |
---|
2674 | int i; |
---|
2675 | for(i=0; i<rl; i++) |
---|
2676 | { |
---|
2677 | q[i]=nInit((*iv)[i]); |
---|
2678 | } |
---|
2679 | return idChineseRemainder(xx,q,rl); |
---|
2680 | } |
---|
2681 | */ |
---|
2682 | /* |
---|
2683 | * lift ideal with coeffs over Z (mod N) to Q via Farey |
---|
2684 | */ |
---|
2685 | ideal id_Farey(ideal x, number N, const ring r) |
---|
2686 | { |
---|
2687 | int cnt=IDELEMS(x)*x->nrows; |
---|
2688 | ideal result=idInit(cnt,x->rank); |
---|
2689 | result->nrows=x->nrows; // for lifting matrices |
---|
2690 | result->ncols=x->ncols; // for lifting matrices |
---|
2691 | |
---|
2692 | int i; |
---|
2693 | for(i=cnt-1;i>=0;i--) |
---|
2694 | { |
---|
2695 | result->m[i]=p_Farey(x->m[i],N,r); |
---|
2696 | } |
---|
2697 | return result; |
---|
2698 | } |
---|
2699 | |
---|
2700 | |
---|
2701 | |
---|
2702 | |
---|
2703 | // uses glabl vars via pSetModDeg |
---|
2704 | /* |
---|
2705 | BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w) |
---|
2706 | { |
---|
2707 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;} |
---|
2708 | if (idIs0(m)) return TRUE; |
---|
2709 | |
---|
2710 | int cmax=-1; |
---|
2711 | int i; |
---|
2712 | poly p=NULL; |
---|
2713 | int length=IDELEMS(m); |
---|
2714 | poly* P=m->m; |
---|
2715 | for (i=length-1;i>=0;i--) |
---|
2716 | { |
---|
2717 | p=P[i]; |
---|
2718 | if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1); |
---|
2719 | } |
---|
2720 | if (w != NULL) |
---|
2721 | if (w->length()+1 < cmax) |
---|
2722 | { |
---|
2723 | // Print("length: %d - %d \n", w->length(),cmax); |
---|
2724 | return FALSE; |
---|
2725 | } |
---|
2726 | |
---|
2727 | if(w!=NULL) |
---|
2728 | p_SetModDeg(w, currRing); |
---|
2729 | |
---|
2730 | for (i=length-1;i>=0;i--) |
---|
2731 | { |
---|
2732 | p=P[i]; |
---|
2733 | poly q=p; |
---|
2734 | if (p!=NULL) |
---|
2735 | { |
---|
2736 | int d=p_FDeg(p,currRing); |
---|
2737 | loop |
---|
2738 | { |
---|
2739 | pIter(p); |
---|
2740 | if (p==NULL) break; |
---|
2741 | if (d!=p_FDeg(p,currRing)) |
---|
2742 | { |
---|
2743 | //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing)); |
---|
2744 | if(w!=NULL) |
---|
2745 | p_SetModDeg(NULL, currRing); |
---|
2746 | return FALSE; |
---|
2747 | } |
---|
2748 | } |
---|
2749 | } |
---|
2750 | } |
---|
2751 | |
---|
2752 | if(w!=NULL) |
---|
2753 | p_SetModDeg(NULL, currRing); |
---|
2754 | |
---|
2755 | return TRUE; |
---|
2756 | } |
---|
2757 | */ |
---|
2758 | |
---|
2759 | /// keeps the first k (>= 1) entries of the given ideal |
---|
2760 | /// (Note that the kept polynomials may be zero.) |
---|
2761 | void idKeepFirstK(ideal id, const int k) |
---|
2762 | { |
---|
2763 | for (int i = IDELEMS(id)-1; i >= k; i--) |
---|
2764 | { |
---|
2765 | if (id->m[i] != NULL) pDelete(&id->m[i]); |
---|
2766 | } |
---|
2767 | int kk=k; |
---|
2768 | if (k==0) kk=1; /* ideals must have at least one element(0)*/ |
---|
2769 | pEnlargeSet(&(id->m), IDELEMS(id), kk-IDELEMS(id)); |
---|
2770 | IDELEMS(id) = kk; |
---|
2771 | } |
---|
2772 | |
---|
2773 | typedef struct |
---|
2774 | { |
---|
2775 | poly p; |
---|
2776 | int index; |
---|
2777 | } poly_sort; |
---|
2778 | |
---|
2779 | int pCompare_qsort(const void *a, const void *b) |
---|
2780 | { |
---|
2781 | return (p_Compare(((poly_sort *)a)->p, ((poly_sort *)b)->p,currRing)); |
---|
2782 | } |
---|
2783 | |
---|
2784 | void idSort_qsort(poly_sort *id_sort, int idsize) |
---|
2785 | { |
---|
2786 | qsort(id_sort, idsize, sizeof(poly_sort), pCompare_qsort); |
---|
2787 | } |
---|
2788 | |
---|
2789 | /*2 |
---|
2790 | * ideal id = (id[i]) |
---|
2791 | * if id[i] = id[j] then id[j] is deleted for j > i |
---|
2792 | */ |
---|
2793 | void idDelEquals(ideal id) |
---|
2794 | { |
---|
2795 | int idsize = IDELEMS(id); |
---|
2796 | poly_sort *id_sort = (poly_sort *)omAlloc0(idsize*sizeof(poly_sort)); |
---|
2797 | for (int i = 0; i < idsize; i++) |
---|
2798 | { |
---|
2799 | id_sort[i].p = id->m[i]; |
---|
2800 | id_sort[i].index = i; |
---|
2801 | } |
---|
2802 | idSort_qsort(id_sort, idsize); |
---|
2803 | int index, index_i, index_j; |
---|
2804 | int i = 0; |
---|
2805 | for (int j = 1; j < idsize; j++) |
---|
2806 | { |
---|
2807 | if (id_sort[i].p != NULL && pEqualPolys(id_sort[i].p, id_sort[j].p)) |
---|
2808 | { |
---|
2809 | index_i = id_sort[i].index; |
---|
2810 | index_j = id_sort[j].index; |
---|
2811 | if (index_j > index_i) |
---|
2812 | { |
---|
2813 | index = index_j; |
---|
2814 | } |
---|
2815 | else |
---|
2816 | { |
---|
2817 | index = index_i; |
---|
2818 | i = j; |
---|
2819 | } |
---|
2820 | pDelete(&id->m[index]); |
---|
2821 | } |
---|
2822 | else |
---|
2823 | { |
---|
2824 | i = j; |
---|
2825 | } |
---|
2826 | } |
---|
2827 | omFreeSize((ADDRESS)(id_sort), idsize*sizeof(poly_sort)); |
---|
2828 | } |
---|
2829 | |
---|
2830 | static int * id_satstdSaturatingVariables=NULL; |
---|
2831 | |
---|
2832 | static BOOLEAN id_sat_vars_sp(kStrategy strat) |
---|
2833 | { |
---|
2834 | BOOLEAN b = FALSE; // set b to TRUE, if spoly was changed, |
---|
2835 | // let it remain FALSE otherwise |
---|
2836 | if (strat->P.t_p==NULL) |
---|
2837 | { |
---|
2838 | poly p=strat->P.p; |
---|
2839 | |
---|
2840 | // iterate over all terms of p and |
---|
2841 | // compute the minimum mm of all exponent vectors |
---|
2842 | int *mm=(int*)omAlloc((1+rVar(currRing))*sizeof(int)); |
---|
2843 | int *m0=(int*)omAlloc0((1+rVar(currRing))*sizeof(int)); |
---|
2844 | p_GetExpV(p,mm,currRing); |
---|
2845 | bool nonTrivialSaturationToBeDone=true; |
---|
2846 | for (p=pNext(p); p!=NULL; pIter(p)) |
---|
2847 | { |
---|
2848 | nonTrivialSaturationToBeDone=false; |
---|
2849 | p_GetExpV(p,m0,currRing); |
---|
2850 | for (int i=rVar(currRing); i>0; i--) |
---|
2851 | { |
---|
2852 | if (id_satstdSaturatingVariables[i]!=0) |
---|
2853 | { |
---|
2854 | mm[i]=si_min(mm[i],m0[i]); |
---|
2855 | if (mm[i]>0) nonTrivialSaturationToBeDone=true; |
---|
2856 | } |
---|
2857 | else mm[i]=0; |
---|
2858 | } |
---|
2859 | // abort if the minimum is zero in each component |
---|
2860 | if (!nonTrivialSaturationToBeDone) break; |
---|
2861 | } |
---|
2862 | if (nonTrivialSaturationToBeDone) |
---|
2863 | { |
---|
2864 | // std::cout << "simplifying!" << std::endl; |
---|
2865 | if (TEST_OPT_PROT) { PrintS("S"); mflush(); } |
---|
2866 | p=p_Copy(strat->P.p,currRing); |
---|
2867 | //pWrite(p); |
---|
2868 | // for (int i=rVar(currRing); i>0; i--) |
---|
2869 | // if (mm[i]!=0) Print("x_%d:%d ",i,mm[i]); |
---|
2870 | //PrintLn(); |
---|
2871 | memset(&strat->P,0,sizeof(strat->P)); |
---|
2872 | strat->P.tailRing = strat->tailRing; |
---|
2873 | strat->P.p=p; |
---|
2874 | while(p!=NULL) |
---|
2875 | { |
---|
2876 | for (int i=rVar(currRing); i>0; i--) |
---|
2877 | { |
---|
2878 | p_SubExp(p,i,mm[i],currRing); |
---|
2879 | } |
---|
2880 | p_Setm(p,currRing); |
---|
2881 | pIter(p); |
---|
2882 | } |
---|
2883 | b = TRUE; |
---|
2884 | } |
---|
2885 | omFree(mm); |
---|
2886 | omFree(m0); |
---|
2887 | } |
---|
2888 | else |
---|
2889 | { |
---|
2890 | poly p=strat->P.t_p; |
---|
2891 | |
---|
2892 | // iterate over all terms of p and |
---|
2893 | // compute the minimum mm of all exponent vectors |
---|
2894 | int *mm=(int*)omAlloc((1+rVar(currRing))*sizeof(int)); |
---|
2895 | int *m0=(int*)omAlloc0((1+rVar(currRing))*sizeof(int)); |
---|
2896 | p_GetExpV(p,mm,strat->tailRing); |
---|
2897 | bool nonTrivialSaturationToBeDone=true; |
---|
2898 | for (p = pNext(p); p!=NULL; pIter(p)) |
---|
2899 | { |
---|
2900 | nonTrivialSaturationToBeDone=false; |
---|
2901 | p_GetExpV(p,m0,strat->tailRing); |
---|
2902 | for(int i=rVar(currRing); i>0; i--) |
---|
2903 | { |
---|
2904 | if(id_satstdSaturatingVariables[i]!=0) |
---|
2905 | { |
---|
2906 | mm[i]=si_min(mm[i],m0[i]); |
---|
2907 | if (mm[i]>0) nonTrivialSaturationToBeDone = true; |
---|
2908 | } |
---|
2909 | else mm[i]=0; |
---|
2910 | } |
---|
2911 | // abort if the minimum is zero in each component |
---|
2912 | if (!nonTrivialSaturationToBeDone) break; |
---|
2913 | } |
---|
2914 | if (nonTrivialSaturationToBeDone) |
---|
2915 | { |
---|
2916 | if (TEST_OPT_PROT) { PrintS("S"); mflush(); } |
---|
2917 | p=p_Copy(strat->P.t_p,strat->tailRing); |
---|
2918 | //p_Write(p,strat->tailRing); |
---|
2919 | // for (int i=rVar(currRing); i>0; i--) |
---|
2920 | // if (mm[i]!=0) Print("x_%d:%d ",i,mm[i]); |
---|
2921 | //PrintLn(); |
---|
2922 | memset(&strat->P,0,sizeof(strat->P)); |
---|
2923 | strat->P.tailRing = strat->tailRing; |
---|
2924 | strat->P.t_p=p; |
---|
2925 | while(p!=NULL) |
---|
2926 | { |
---|
2927 | for(int i=rVar(currRing); i>0; i--) |
---|
2928 | { |
---|
2929 | p_SubExp(p,i,mm[i],strat->tailRing); |
---|
2930 | } |
---|
2931 | p_Setm(p,strat->tailRing); |
---|
2932 | pIter(p); |
---|
2933 | } |
---|
2934 | strat->P.GetP(); |
---|
2935 | b = TRUE; |
---|
2936 | } |
---|
2937 | omFree(mm); |
---|
2938 | omFree(m0); |
---|
2939 | } |
---|
2940 | return b; // return TRUE if sp was changed, FALSE if not |
---|
2941 | } |
---|
2942 | |
---|
2943 | ideal id_Satstd(const ideal I, ideal J, const ring r) |
---|
2944 | { |
---|
2945 | ring save=currRing; |
---|
2946 | if (currRing!=r) rChangeCurrRing(r); |
---|
2947 | idSkipZeroes(J); |
---|
2948 | id_satstdSaturatingVariables=(int*)omAlloc0((1+rVar(currRing))*sizeof(int)); |
---|
2949 | int k=IDELEMS(J); |
---|
2950 | if (k>1) |
---|
2951 | { |
---|
2952 | for (int i=0; i<k; i++) |
---|
2953 | { |
---|
2954 | poly x = J->m[i]; |
---|
2955 | int li = p_Var(x,r); |
---|
2956 | if (li>0) |
---|
2957 | id_satstdSaturatingVariables[li]=1; |
---|
2958 | else |
---|
2959 | { |
---|
2960 | if (currRing!=save) rChangeCurrRing(save); |
---|
2961 | WerrorS("ideal generators must be variables"); |
---|
2962 | return NULL; |
---|
2963 | } |
---|
2964 | } |
---|
2965 | } |
---|
2966 | else |
---|
2967 | { |
---|
2968 | poly x = J->m[0]; |
---|
2969 | for (int i=1; i<=r->N; i++) |
---|
2970 | { |
---|
2971 | int li = p_GetExp(x,i,r); |
---|
2972 | if (li==1) |
---|
2973 | id_satstdSaturatingVariables[i]=1; |
---|
2974 | else if (li>1) |
---|
2975 | { |
---|
2976 | if (currRing!=save) rChangeCurrRing(save); |
---|
2977 | Werror("exponent(x(%d)^%d) must be 0 or 1",i,li); |
---|
2978 | return NULL; |
---|
2979 | } |
---|
2980 | } |
---|
2981 | } |
---|
2982 | ideal res=kStd(I,r->qideal,testHomog,NULL,NULL,0,0,NULL,id_sat_vars_sp); |
---|
2983 | omFreeSize(id_satstdSaturatingVariables,(1+rVar(currRing))*sizeof(int)); |
---|
2984 | id_satstdSaturatingVariables=NULL; |
---|
2985 | if (currRing!=save) rChangeCurrRing(save); |
---|
2986 | return res; |
---|
2987 | } |
---|
2988 | |
---|
2989 | GbVariant syGetAlgorithm(char *n, const ring r, const ideal /*M*/) |
---|
2990 | { |
---|
2991 | GbVariant alg=GbDefault; |
---|
2992 | if (strcmp(n,"slimgb")==0) alg=GbSlimgb; |
---|
2993 | else if (strcmp(n,"std")==0) alg=GbStd; |
---|
2994 | else if (strcmp(n,"sba")==0) alg=GbSba; |
---|
2995 | else if (strcmp(n,"singmatic")==0) alg=GbSingmatic; |
---|
2996 | else if (strcmp(n,"groebner")==0) alg=GbGroebner; |
---|
2997 | else if (strcmp(n,"modstd")==0) alg=GbModstd; |
---|
2998 | else if (strcmp(n,"ffmod")==0) alg=GbFfmod; |
---|
2999 | else if (strcmp(n,"nfmod")==0) alg=GbNfmod; |
---|
3000 | else if (strcmp(n,"std:sat")==0) alg=GbStdSat; |
---|
3001 | else Warn(">>%s<< is an unknown algorithm",n); |
---|
3002 | |
---|
3003 | if (alg==GbSlimgb) // test conditions for slimgb |
---|
3004 | { |
---|
3005 | if(rHasGlobalOrdering(r) |
---|
3006 | &&(!rIsPluralRing(r)) |
---|
3007 | &&(r->qideal==NULL) |
---|
3008 | &&(!rField_is_Ring(r))) |
---|
3009 | { |
---|
3010 | return GbSlimgb; |
---|
3011 | } |
---|
3012 | if (TEST_OPT_PROT) |
---|
3013 | WarnS("requires: coef:field, commutative, global ordering, not qring"); |
---|
3014 | } |
---|
3015 | else if (alg==GbSba) // cond. for sba |
---|
3016 | { |
---|
3017 | if(rField_is_Domain(r) |
---|
3018 | &&(!rIsPluralRing(r)) |
---|
3019 | &&(rHasGlobalOrdering(r))) |
---|
3020 | { |
---|
3021 | return GbSba; |
---|
3022 | } |
---|
3023 | if (TEST_OPT_PROT) |
---|
3024 | WarnS("requires: coef:domain, commutative, global ordering"); |
---|
3025 | } |
---|
3026 | else if (alg==GbGroebner) // cond. for groebner |
---|
3027 | { |
---|
3028 | return GbGroebner; |
---|
3029 | } |
---|
3030 | else if(alg==GbModstd) // cond for modstd: Q or Q(a) |
---|
3031 | { |
---|
3032 | if(ggetid("modStd")==NULL) |
---|
3033 | { |
---|
3034 | WarnS(">>modStd<< not found"); |
---|
3035 | } |
---|
3036 | else if(rField_is_Q(r) |
---|
3037 | &&(!rIsPluralRing(r)) |
---|
3038 | &&(rHasGlobalOrdering(r))) |
---|
3039 | { |
---|
3040 | return GbModstd; |
---|
3041 | } |
---|
3042 | if (TEST_OPT_PROT) |
---|
3043 | WarnS("requires: coef:QQ, commutative, global ordering"); |
---|
3044 | } |
---|
3045 | else if(alg==GbStdSat) // cond for std:sat: 2 blocks of variables |
---|
3046 | { |
---|
3047 | if(ggetid("satstd")==NULL) |
---|
3048 | { |
---|
3049 | WarnS(">>satstd<< not found"); |
---|
3050 | } |
---|
3051 | else |
---|
3052 | { |
---|
3053 | return GbStdSat; |
---|
3054 | } |
---|
3055 | } |
---|
3056 | |
---|
3057 | return GbStd; // no conditions for std |
---|
3058 | } |
---|
3059 | //---------------------------------------------------------------------------- |
---|
3060 | // GB-algorithms and their pre-conditions |
---|
3061 | // std slimgb sba singmatic modstd ffmod nfmod groebner |
---|
3062 | // + + + - + - - + coeffs: QQ |
---|
3063 | // + + + + - - - + coeffs: ZZ/p |
---|
3064 | // + + + - ? - + + coeffs: K[a]/f |
---|
3065 | // + + + - ? + - + coeffs: K(a) |
---|
3066 | // + - + - - - - + coeffs: domain, not field |
---|
3067 | // + - - - - - - + coeffs: zero-divisors |
---|
3068 | // + + + + - ? ? + also for modules: C |
---|
3069 | // + + - + - ? ? + also for modules: all orderings |
---|
3070 | // + + - - - - - + exterior algebra |
---|
3071 | // + + - - - - - + G-algebra |
---|
3072 | // + + + + + + + + degree ordering |
---|
3073 | // + - + + + + + + non-degree ordering |
---|
3074 | // - - - + + + + + parallel |
---|