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