1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id$ */ |
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5 | /* |
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6 | * ABSTRACT - all basic methods to manipulate ideals |
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7 | */ |
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8 | |
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9 | /* includes */ |
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10 | #include <kernel/mod2.h> |
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11 | |
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12 | #ifndef NDEBUG |
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13 | # define MYTEST 0 |
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14 | #else /* ifndef NDEBUG */ |
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15 | # define MYTEST 1 |
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16 | #endif /* ifndef NDEBUG */ |
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17 | |
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18 | #include <kernel/options.h> |
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19 | #include <omalloc/omalloc.h> |
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20 | #include <kernel/febase.h> |
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21 | #include <kernel/numbers.h> |
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22 | #include <kernel/longrat.h> |
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23 | #include <kernel/polys.h> |
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24 | #include <kernel/ring.h> |
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25 | #include <kernel/kstd1.h> |
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26 | #include <kernel/matpol.h> |
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27 | #include <kernel/weight.h> |
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28 | #include <kernel/intvec.h> |
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29 | #include <kernel/syz.h> |
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30 | #include <kernel/sparsmat.h> |
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31 | #include <kernel/ideals.h> |
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32 | #include <kernel/prCopy.h> |
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33 | #include <kernel/gring.h> |
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34 | |
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35 | |
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36 | omBin sip_sideal_bin = omGetSpecBin(sizeof(sip_sideal)); |
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37 | |
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38 | /* #define WITH_OLD_MINOR */ |
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39 | #define pCopy_noCheck(p) pCopy(p) |
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40 | |
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41 | static poly * idpower; |
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42 | /*collects the monomials in makemonoms, must be allocated befor*/ |
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43 | static int idpowerpoint; |
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44 | /*index of the actual monomial in idpower*/ |
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45 | static poly * givenideal; |
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46 | /*the ideal from which a power is computed*/ |
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47 | |
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48 | /*0 implementation*/ |
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49 | |
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50 | /*2 |
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51 | * initialise an ideal |
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52 | */ |
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53 | ideal idInit(int idsize, int rank) |
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54 | { |
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55 | /*- initialise an ideal -*/ |
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56 | ideal hh = (ideal )omAllocBin(sip_sideal_bin); |
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57 | hh->nrows = 1; |
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58 | hh->rank = rank; |
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59 | IDELEMS(hh) = idsize; |
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60 | if (idsize>0) |
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61 | { |
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62 | hh->m = (poly *)omAlloc0(idsize*sizeof(poly)); |
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63 | } |
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64 | else |
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65 | hh->m=NULL; |
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66 | return hh; |
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67 | } |
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68 | |
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69 | #ifdef PDEBUG |
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70 | // this is only for outputting an ideal within the debugger |
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71 | void idShow(const ideal id, const ring lmRing, const ring tailRing, const int debugPrint) |
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72 | { |
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73 | assume( debugPrint >= 0 ); |
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74 | |
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75 | if( id == NULL ) |
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76 | PrintS("(NULL)"); |
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77 | else |
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78 | { |
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79 | Print("Module of rank %ld,real rank %ld and %d generators.\n", |
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80 | id->rank,idRankFreeModule(id, lmRing, tailRing),IDELEMS(id)); |
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81 | |
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82 | int j = (id->ncols*id->nrows) - 1; |
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83 | while ((j > 0) && (id->m[j]==NULL)) j--; |
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84 | for (int i = 0; i <= j; i++) |
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85 | { |
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86 | Print("generator %d: ",i); p_DebugPrint(id->m[i], lmRing, tailRing, debugPrint); |
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87 | } |
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88 | } |
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89 | } |
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90 | #endif |
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91 | |
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92 | /* index of generator with leading term in ground ring (if any); |
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93 | otherwise -1 */ |
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94 | int idPosConstant(ideal id) |
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95 | { |
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96 | int k; |
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97 | for (k = IDELEMS(id)-1; k>=0; k--) |
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98 | { |
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99 | if (p_LmIsConstantComp(id->m[k], currRing) == TRUE) |
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100 | return k; |
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101 | } |
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102 | return -1; |
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103 | } |
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104 | |
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105 | /*2 |
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106 | * initialise the maximal ideal (at 0) |
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107 | */ |
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108 | ideal idMaxIdeal (void) |
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109 | { |
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110 | int l; |
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111 | ideal hh=NULL; |
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112 | |
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113 | hh=idInit(pVariables,1); |
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114 | for (l=0; l<pVariables; l++) |
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115 | { |
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116 | hh->m[l] = pOne(); |
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117 | pSetExp(hh->m[l],l+1,1); |
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118 | pSetm(hh->m[l]); |
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119 | } |
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120 | return hh; |
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121 | } |
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122 | |
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123 | /*2 |
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124 | * deletes an ideal/matrix |
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125 | */ |
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126 | void id_Delete (ideal * h, ring r) |
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127 | { |
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128 | int j,elems; |
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129 | if (*h == NULL) |
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130 | return; |
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131 | elems=j=(*h)->nrows*(*h)->ncols; |
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132 | if (j>0) |
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133 | { |
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134 | do |
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135 | { |
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136 | p_Delete(&((*h)->m[--j]), r); |
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137 | } |
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138 | while (j>0); |
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139 | omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems); |
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140 | } |
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141 | omFreeBin((ADDRESS)*h, sip_sideal_bin); |
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142 | *h=NULL; |
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143 | } |
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144 | |
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145 | |
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146 | /*2 |
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147 | * Shallowdeletes an ideal/matrix |
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148 | */ |
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149 | void id_ShallowDelete (ideal *h, ring r) |
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150 | { |
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151 | int j,elems; |
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152 | if (*h == NULL) |
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153 | return; |
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154 | elems=j=(*h)->nrows*(*h)->ncols; |
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155 | if (j>0) |
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156 | { |
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157 | do |
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158 | { |
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159 | p_ShallowDelete(&((*h)->m[--j]), r); |
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160 | } |
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161 | while (j>0); |
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162 | omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems); |
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163 | } |
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164 | omFreeBin((ADDRESS)*h, sip_sideal_bin); |
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165 | *h=NULL; |
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166 | } |
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167 | |
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168 | /*2 |
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169 | *gives an ideal the minimal possible size |
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170 | */ |
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171 | void idSkipZeroes (ideal ide) |
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172 | { |
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173 | int k; |
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174 | int j = -1; |
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175 | BOOLEAN change=FALSE; |
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176 | for (k=0; k<IDELEMS(ide); k++) |
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177 | { |
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178 | if (ide->m[k] != NULL) |
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179 | { |
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180 | j++; |
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181 | if (change) |
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182 | { |
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183 | ide->m[j] = ide->m[k]; |
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184 | } |
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185 | } |
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186 | else |
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187 | { |
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188 | change=TRUE; |
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189 | } |
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190 | } |
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191 | if (change) |
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192 | { |
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193 | if (j == -1) |
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194 | j = 0; |
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195 | else |
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196 | { |
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197 | for (k=j+1; k<IDELEMS(ide); k++) |
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198 | ide->m[k] = NULL; |
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199 | } |
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200 | pEnlargeSet(&(ide->m),IDELEMS(ide),j+1-IDELEMS(ide)); |
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201 | IDELEMS(ide) = j+1; |
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202 | } |
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203 | } |
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204 | |
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205 | /*2 |
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206 | * copies the first k (>= 1) entries of the given ideal |
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207 | * and returns these as a new ideal |
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208 | * (Note that the copied polynomials may be zero.) |
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209 | */ |
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210 | ideal idCopyFirstK (const ideal ide, const int k) |
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211 | { |
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212 | ideal newI = idInit(k, 0); |
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213 | for (int i = 0; i < k; i++) |
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214 | newI->m[i] = pCopy(ide->m[i]); |
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215 | return newI; |
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216 | } |
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217 | |
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218 | /*2 |
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219 | * ideal id = (id[i]) |
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220 | * result is leadcoeff(id[i]) = 1 |
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221 | */ |
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222 | void idNorm(ideal id) |
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223 | { |
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224 | for (int i=IDELEMS(id)-1; i>=0; i--) |
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225 | { |
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226 | if (id->m[i] != NULL) |
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227 | { |
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228 | pNorm(id->m[i]); |
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229 | } |
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230 | } |
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231 | } |
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232 | |
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233 | /*2 |
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234 | * ideal id = (id[i]), c any unit |
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235 | * if id[i] = c*id[j] then id[j] is deleted for j > i |
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236 | */ |
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237 | void idDelMultiples(ideal id) |
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238 | { |
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239 | int i, j; |
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240 | int k = IDELEMS(id)-1; |
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241 | for (i=k; i>=0; i--) |
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242 | { |
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243 | if (id->m[i]!=NULL) |
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244 | { |
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245 | for (j=k; j>i; j--) |
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246 | { |
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247 | if (id->m[j]!=NULL) |
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248 | { |
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249 | #ifdef HAVE_RINGS |
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250 | if (rField_is_Ring(currRing)) |
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251 | { |
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252 | /* if id[j] = c*id[i] then delete id[j]. |
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253 | In the below cases of a ground field, we |
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254 | check whether id[i] = c*id[j] and, if so, |
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255 | delete id[j] for historical reasons (so |
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256 | that previous output does not change) */ |
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257 | if (pComparePolys(id->m[j], id->m[i])) pDelete(&id->m[j]); |
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258 | } |
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259 | else |
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260 | { |
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261 | if (pComparePolys(id->m[i], id->m[j])) pDelete(&id->m[j]); |
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262 | } |
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263 | #else |
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264 | if (pComparePolys(id->m[i], id->m[j])) pDelete(&id->m[j]); |
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265 | #endif |
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266 | } |
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267 | } |
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268 | } |
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269 | } |
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270 | } |
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271 | |
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272 | /*2 |
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273 | * ideal id = (id[i]) |
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274 | * if id[i] = id[j] then id[j] is deleted for j > i |
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275 | */ |
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276 | void idDelEquals(ideal id) |
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277 | { |
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278 | int i, j; |
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279 | int k = IDELEMS(id)-1; |
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280 | for (i=k; i>=0; i--) |
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281 | { |
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282 | if (id->m[i]!=NULL) |
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283 | { |
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284 | for (j=k; j>i; j--) |
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285 | { |
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286 | if ((id->m[j]!=NULL) |
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287 | && (pEqualPolys(id->m[i], id->m[j]))) |
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288 | { |
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289 | pDelete(&id->m[j]); |
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290 | } |
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291 | } |
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292 | } |
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293 | } |
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294 | } |
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295 | |
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296 | // |
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297 | // Delete id[j], if Lm(j) == Lm(i) and both LC(j), LC(i) are units and j > i |
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298 | // |
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299 | void idDelLmEquals(ideal id) |
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300 | { |
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301 | int i, j; |
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302 | int k = IDELEMS(id)-1; |
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303 | for (i=k; i>=0; i--) |
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304 | { |
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305 | if (id->m[i] != NULL) |
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306 | { |
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307 | for (j=k; j>i; j--) |
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308 | { |
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309 | if ((id->m[j] != NULL) |
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310 | && pLmEqual(id->m[i], id->m[j]) |
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311 | #ifdef HAVE_RINGS |
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312 | && nIsUnit(pGetCoeff(id->m[i])) && nIsUnit(pGetCoeff(id->m[j])) |
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313 | #endif |
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314 | ) |
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315 | { |
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316 | pDelete(&id->m[j]); |
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317 | } |
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318 | } |
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319 | } |
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320 | } |
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321 | } |
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322 | |
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323 | // |
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324 | // delete id[j], if LT(j) == coeff*mon*LT(i) and vice versa, i.e., |
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325 | // delete id[i], if LT(i) == coeff*mon*LT(j) |
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326 | // |
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327 | void idDelDiv(ideal id) |
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328 | { |
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329 | int i, j; |
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330 | int k = IDELEMS(id)-1; |
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331 | for (i=k; i>=0; i--) |
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332 | { |
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333 | if (id->m[i] != NULL) |
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334 | { |
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335 | for (j=k; j>i; j--) |
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336 | { |
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337 | if (id->m[j]!=NULL) |
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338 | { |
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339 | #ifdef HAVE_RINGS |
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340 | if (rField_is_Ring(currRing)) |
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341 | { |
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342 | if (pDivisibleByRingCase(id->m[i], id->m[j])) |
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343 | { |
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344 | pDelete(&id->m[j]); |
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345 | } |
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346 | else if (pDivisibleByRingCase(id->m[j], id->m[i])) |
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347 | { |
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348 | pDelete(&id->m[i]); |
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349 | break; |
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350 | } |
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351 | } |
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352 | else |
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353 | { |
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354 | #endif |
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355 | /* the case of a ground field: */ |
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356 | if (pDivisibleBy(id->m[i], id->m[j])) |
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357 | { |
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358 | pDelete(&id->m[j]); |
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359 | } |
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360 | else if (pDivisibleBy(id->m[j], id->m[i])) |
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361 | { |
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362 | pDelete(&id->m[i]); |
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363 | break; |
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364 | } |
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365 | #ifdef HAVE_RINGS |
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366 | } |
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367 | #endif |
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368 | } |
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369 | } |
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370 | } |
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371 | } |
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372 | } |
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373 | |
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374 | /*2 |
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375 | *test if the ideal has only constant polynomials |
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376 | */ |
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377 | BOOLEAN idIsConstant(ideal id) |
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378 | { |
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379 | int k; |
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380 | for (k = IDELEMS(id)-1; k>=0; k--) |
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381 | { |
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382 | if (pIsConstantPoly(id->m[k]) == FALSE) |
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383 | return FALSE; |
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384 | } |
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385 | return TRUE; |
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386 | } |
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387 | |
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388 | /*2 |
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389 | * copy an ideal |
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390 | */ |
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391 | |
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392 | ideal id_Copy (ideal h1, const ring r) |
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393 | { |
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394 | int i; |
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395 | ideal h2; |
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396 | |
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397 | //#ifdef TEST |
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398 | if (h1 == NULL) |
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399 | { |
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400 | h2=idInit(1,1); |
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401 | } |
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402 | else |
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403 | //#endif |
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404 | { |
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405 | h2=idInit(IDELEMS(h1),h1->rank); |
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406 | for (i=IDELEMS(h1)-1; i>=0; i--) |
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407 | h2->m[i] = p_Copy(h1->m[i],r); |
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408 | } |
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409 | return h2; |
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410 | } |
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411 | |
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412 | #ifdef PDEBUG |
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413 | void idDBTest(ideal h1, int level, const char *f,const int l) |
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414 | { |
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415 | int i; |
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416 | |
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417 | if (h1 != NULL) |
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418 | { |
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419 | // assume(IDELEMS(h1) > 0); for ideal/module, does not apply to matrix |
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420 | omCheckAddrSize(h1,sizeof(*h1)); |
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421 | omdebugAddrSize(h1->m,h1->ncols*h1->nrows*sizeof(poly)); |
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422 | /* to be able to test matrices: */ |
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423 | for (i=(h1->ncols*h1->nrows)-1; i>=0; i--) |
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424 | _p_Test(h1->m[i], currRing, level); |
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425 | int new_rk=idRankFreeModule(h1); |
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426 | if(new_rk > h1->rank) |
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427 | { |
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428 | dReportError("wrong rank %d (should be %d) in %s:%d\n", |
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429 | h1->rank, new_rk, f,l); |
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430 | omPrintAddrInfo(stderr, h1, " for ideal"); |
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431 | h1->rank=new_rk; |
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432 | } |
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433 | } |
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434 | } |
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435 | #endif |
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436 | |
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437 | /*3 |
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438 | * for idSort: compare a and b revlex inclusive module comp. |
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439 | */ |
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440 | static int pComp_RevLex(poly a, poly b,BOOLEAN nolex) |
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441 | { |
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442 | if (b==NULL) return 1; |
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443 | if (a==NULL) return -1; |
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444 | |
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445 | if (nolex) |
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446 | { |
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447 | int r=pLmCmp(a,b); |
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448 | if (r!=0) return r; |
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449 | number h=nSub(pGetCoeff(a),pGetCoeff(b)); |
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450 | r = -1+nIsZero(h)+2*nGreaterZero(h); /* -1: <, 0:==, 1: > */ |
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451 | nDelete(&h); |
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452 | return r; |
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453 | } |
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454 | int l=pVariables; |
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455 | while ((l>0) && (pGetExp(a,l)==pGetExp(b,l))) l--; |
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456 | if (l==0) |
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457 | { |
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458 | if (pGetComp(a)==pGetComp(b)) |
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459 | { |
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460 | number h=nSub(pGetCoeff(a),pGetCoeff(b)); |
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461 | int r = -1+nIsZero(h)+2*nGreaterZero(h); /* -1: <, 0:==, 1: > */ |
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462 | nDelete(&h); |
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463 | return r; |
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464 | } |
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465 | if (pGetComp(a)>pGetComp(b)) return 1; |
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466 | } |
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467 | else if (pGetExp(a,l)>pGetExp(b,l)) |
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468 | return 1; |
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469 | return -1; |
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470 | } |
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471 | |
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472 | /*2 |
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473 | *sorts the ideal w.r.t. the actual ringordering |
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474 | *uses lex-ordering when nolex = FALSE |
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475 | */ |
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476 | intvec *idSort(ideal id,BOOLEAN nolex) |
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477 | { |
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478 | poly p,q; |
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479 | intvec * result = new intvec(IDELEMS(id)); |
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480 | int i, j, actpos=0, newpos, l; |
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481 | int diff, olddiff, lastcomp, newcomp; |
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482 | BOOLEAN notFound; |
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483 | |
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484 | for (i=0;i<IDELEMS(id);i++) |
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485 | { |
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486 | if (id->m[i]!=NULL) |
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487 | { |
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488 | notFound = TRUE; |
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489 | newpos = actpos / 2; |
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490 | diff = (actpos+1) / 2; |
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491 | diff = (diff+1) / 2; |
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492 | lastcomp = pComp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex); |
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493 | if (lastcomp<0) |
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494 | { |
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495 | newpos -= diff; |
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496 | } |
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497 | else if (lastcomp>0) |
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498 | { |
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499 | newpos += diff; |
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500 | } |
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501 | else |
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502 | { |
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503 | notFound = FALSE; |
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504 | } |
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505 | //while ((newpos>=0) && (newpos<actpos) && (notFound)) |
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506 | while (notFound && (newpos>=0) && (newpos<actpos)) |
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507 | { |
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508 | newcomp = pComp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex); |
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509 | olddiff = diff; |
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510 | if (diff>1) |
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511 | { |
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512 | diff = (diff+1) / 2; |
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513 | if ((newcomp==1) |
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514 | && (actpos-newpos>1) |
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515 | && (diff>1) |
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516 | && (newpos+diff>=actpos)) |
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517 | { |
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518 | diff = actpos-newpos-1; |
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519 | } |
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520 | else if ((newcomp==-1) |
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521 | && (diff>1) |
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522 | && (newpos<diff)) |
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523 | { |
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524 | diff = newpos; |
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525 | } |
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526 | } |
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527 | if (newcomp<0) |
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528 | { |
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529 | if ((olddiff==1) && (lastcomp>0)) |
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530 | notFound = FALSE; |
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531 | else |
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532 | newpos -= diff; |
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533 | } |
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534 | else if (newcomp>0) |
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535 | { |
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536 | if ((olddiff==1) && (lastcomp<0)) |
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537 | { |
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538 | notFound = FALSE; |
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539 | newpos++; |
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540 | } |
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541 | else |
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542 | { |
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543 | newpos += diff; |
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544 | } |
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545 | } |
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546 | else |
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547 | { |
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548 | notFound = FALSE; |
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549 | } |
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550 | lastcomp = newcomp; |
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551 | if (diff==0) notFound=FALSE; /*hs*/ |
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552 | } |
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553 | if (newpos<0) newpos = 0; |
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554 | if (newpos>actpos) newpos = actpos; |
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555 | while ((newpos<actpos) && (pComp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex)==0)) |
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556 | newpos++; |
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557 | for (j=actpos;j>newpos;j--) |
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558 | { |
---|
559 | (*result)[j] = (*result)[j-1]; |
---|
560 | } |
---|
561 | (*result)[newpos] = i; |
---|
562 | actpos++; |
---|
563 | } |
---|
564 | } |
---|
565 | for (j=0;j<actpos;j++) (*result)[j]++; |
---|
566 | return result; |
---|
567 | } |
---|
568 | |
---|
569 | /*2 |
---|
570 | * concat the lists h1 and h2 without zeros |
---|
571 | */ |
---|
572 | ideal idSimpleAdd (ideal h1,ideal h2) |
---|
573 | { |
---|
574 | int i,j,r,l; |
---|
575 | ideal result; |
---|
576 | |
---|
577 | if (h1==NULL) return idCopy(h2); |
---|
578 | if (h2==NULL) return idCopy(h1); |
---|
579 | j = IDELEMS(h1)-1; |
---|
580 | while ((j >= 0) && (h1->m[j] == NULL)) j--; |
---|
581 | i = IDELEMS(h2)-1; |
---|
582 | while ((i >= 0) && (h2->m[i] == NULL)) i--; |
---|
583 | r = si_max(h1->rank,h2->rank); |
---|
584 | if (i+j==(-2)) |
---|
585 | return idInit(1,r); |
---|
586 | else |
---|
587 | result=idInit(i+j+2,r); |
---|
588 | for (l=j; l>=0; l--) |
---|
589 | { |
---|
590 | result->m[l] = pCopy(h1->m[l]); |
---|
591 | } |
---|
592 | r = i+j+1; |
---|
593 | for (l=i; l>=0; l--, r--) |
---|
594 | { |
---|
595 | result->m[r] = pCopy(h2->m[l]); |
---|
596 | } |
---|
597 | return result; |
---|
598 | } |
---|
599 | |
---|
600 | /*2 |
---|
601 | * insert h2 into h1 (if h2 is not the zero polynomial) |
---|
602 | * return TRUE iff h2 was indeed inserted |
---|
603 | */ |
---|
604 | BOOLEAN idInsertPoly (ideal h1, poly h2) |
---|
605 | { |
---|
606 | if (h2==NULL) return FALSE; |
---|
607 | int j = IDELEMS(h1)-1; |
---|
608 | while ((j >= 0) && (h1->m[j] == NULL)) j--; |
---|
609 | j++; |
---|
610 | if (j==IDELEMS(h1)) |
---|
611 | { |
---|
612 | pEnlargeSet(&(h1->m),IDELEMS(h1),16); |
---|
613 | IDELEMS(h1)+=16; |
---|
614 | } |
---|
615 | h1->m[j]=h2; |
---|
616 | return TRUE; |
---|
617 | } |
---|
618 | |
---|
619 | /*2 |
---|
620 | * insert h2 into h1 depending on the two boolean parameters: |
---|
621 | * - if zeroOk is true, then h2 will also be inserted when it is zero |
---|
622 | * - if duplicateOk is true, then h2 will also be inserted when it is |
---|
623 | * already present in h1 |
---|
624 | * return TRUE iff h2 was indeed inserted |
---|
625 | */ |
---|
626 | BOOLEAN idInsertPolyWithTests (ideal h1, const int validEntries, |
---|
627 | const poly h2, const bool zeroOk, const bool duplicateOk) |
---|
628 | { |
---|
629 | if ((!zeroOk) && (h2 == NULL)) return FALSE; |
---|
630 | if (!duplicateOk) |
---|
631 | { |
---|
632 | bool h2FoundInH1 = false; |
---|
633 | int i = 0; |
---|
634 | while ((i < validEntries) && (!h2FoundInH1)) |
---|
635 | { |
---|
636 | h2FoundInH1 = pEqualPolys(h1->m[i], h2); |
---|
637 | i++; |
---|
638 | } |
---|
639 | if (h2FoundInH1) return FALSE; |
---|
640 | } |
---|
641 | if (validEntries == IDELEMS(h1)) |
---|
642 | { |
---|
643 | pEnlargeSet(&(h1->m), IDELEMS(h1), 16); |
---|
644 | IDELEMS(h1) += 16; |
---|
645 | } |
---|
646 | h1->m[validEntries] = h2; |
---|
647 | return TRUE; |
---|
648 | } |
---|
649 | |
---|
650 | /*2 |
---|
651 | * h1 + h2 |
---|
652 | */ |
---|
653 | ideal idAdd (ideal h1,ideal h2) |
---|
654 | { |
---|
655 | ideal result = idSimpleAdd(h1,h2); |
---|
656 | idCompactify(result); |
---|
657 | return result; |
---|
658 | } |
---|
659 | |
---|
660 | /*2 |
---|
661 | * h1 * h2 |
---|
662 | */ |
---|
663 | ideal idMult (ideal h1,ideal h2) |
---|
664 | { |
---|
665 | int i,j,k; |
---|
666 | ideal hh; |
---|
667 | |
---|
668 | j = IDELEMS(h1); |
---|
669 | while ((j > 0) && (h1->m[j-1] == NULL)) j--; |
---|
670 | i = IDELEMS(h2); |
---|
671 | while ((i > 0) && (h2->m[i-1] == NULL)) i--; |
---|
672 | j = j * i; |
---|
673 | if (j == 0) |
---|
674 | hh = idInit(1,1); |
---|
675 | else |
---|
676 | hh=idInit(j,1); |
---|
677 | if (h1->rank<h2->rank) |
---|
678 | hh->rank = h2->rank; |
---|
679 | else |
---|
680 | hh->rank = h1->rank; |
---|
681 | if (j==0) return hh; |
---|
682 | k = 0; |
---|
683 | for (i=0; i<IDELEMS(h1); i++) |
---|
684 | { |
---|
685 | if (h1->m[i] != NULL) |
---|
686 | { |
---|
687 | for (j=0; j<IDELEMS(h2); j++) |
---|
688 | { |
---|
689 | if (h2->m[j] != NULL) |
---|
690 | { |
---|
691 | hh->m[k] = ppMult_qq(h1->m[i],h2->m[j]); |
---|
692 | k++; |
---|
693 | } |
---|
694 | } |
---|
695 | } |
---|
696 | } |
---|
697 | { |
---|
698 | idCompactify(hh); |
---|
699 | return hh; |
---|
700 | } |
---|
701 | } |
---|
702 | |
---|
703 | /*2 |
---|
704 | *returns true if h is the zero ideal |
---|
705 | */ |
---|
706 | BOOLEAN idIs0 (ideal h) |
---|
707 | { |
---|
708 | int i; |
---|
709 | |
---|
710 | if (h == NULL) return TRUE; |
---|
711 | i = IDELEMS(h)-1; |
---|
712 | while ((i >= 0) && (h->m[i] == NULL)) |
---|
713 | { |
---|
714 | i--; |
---|
715 | } |
---|
716 | if (i < 0) |
---|
717 | return TRUE; |
---|
718 | else |
---|
719 | return FALSE; |
---|
720 | } |
---|
721 | |
---|
722 | /*2 |
---|
723 | * return the maximal component number found in any polynomial in s |
---|
724 | */ |
---|
725 | long idRankFreeModule (ideal s, ring lmRing, ring tailRing) |
---|
726 | { |
---|
727 | if (s!=NULL) |
---|
728 | { |
---|
729 | int j=0; |
---|
730 | |
---|
731 | if (rRing_has_Comp(tailRing) && rRing_has_Comp(lmRing)) |
---|
732 | { |
---|
733 | int l=IDELEMS(s); |
---|
734 | poly *p=s->m; |
---|
735 | int k; |
---|
736 | for (; l != 0; l--) |
---|
737 | { |
---|
738 | if (*p!=NULL) |
---|
739 | { |
---|
740 | pp_Test(*p, lmRing, tailRing); |
---|
741 | k = p_MaxComp(*p, lmRing, tailRing); |
---|
742 | if (k>j) j = k; |
---|
743 | } |
---|
744 | p++; |
---|
745 | } |
---|
746 | } |
---|
747 | return j; |
---|
748 | } |
---|
749 | return -1; |
---|
750 | } |
---|
751 | |
---|
752 | BOOLEAN idIsModule(ideal id, ring r) |
---|
753 | { |
---|
754 | if (id != NULL && rRing_has_Comp(r)) |
---|
755 | { |
---|
756 | int j, l = IDELEMS(id); |
---|
757 | for (j=0; j<l; j++) |
---|
758 | { |
---|
759 | if (id->m[j] != NULL && p_GetComp(id->m[j], r) > 0) return TRUE; |
---|
760 | } |
---|
761 | } |
---|
762 | return FALSE; |
---|
763 | } |
---|
764 | |
---|
765 | |
---|
766 | /*2 |
---|
767 | *returns true if id is homogenous with respect to the aktual weights |
---|
768 | */ |
---|
769 | BOOLEAN idHomIdeal (ideal id, ideal Q) |
---|
770 | { |
---|
771 | int i; |
---|
772 | BOOLEAN b; |
---|
773 | if ((id == NULL) || (IDELEMS(id) == 0)) return TRUE; |
---|
774 | i = 0; |
---|
775 | b = TRUE; |
---|
776 | while ((i < IDELEMS(id)) && b) |
---|
777 | { |
---|
778 | b = pIsHomogeneous(id->m[i]); |
---|
779 | i++; |
---|
780 | } |
---|
781 | if ((b) && (Q!=NULL) && (IDELEMS(Q)>0)) |
---|
782 | { |
---|
783 | i=0; |
---|
784 | while ((i < IDELEMS(Q)) && b) |
---|
785 | { |
---|
786 | b = pIsHomogeneous(Q->m[i]); |
---|
787 | i++; |
---|
788 | } |
---|
789 | } |
---|
790 | return b; |
---|
791 | } |
---|
792 | |
---|
793 | /*2 |
---|
794 | *returns a minimized set of generators of h1 |
---|
795 | */ |
---|
796 | ideal idMinBase (ideal h1) |
---|
797 | { |
---|
798 | ideal h2, h3,h4,e; |
---|
799 | int j,k; |
---|
800 | int i,l,ll; |
---|
801 | intvec * wth; |
---|
802 | BOOLEAN homog; |
---|
803 | |
---|
804 | homog = idHomModule(h1,currQuotient,&wth); |
---|
805 | if (rHasGlobalOrdering_currRing()) |
---|
806 | { |
---|
807 | if(!homog) |
---|
808 | { |
---|
809 | WarnS("minbase applies only to the local or homogeneous case"); |
---|
810 | e=idCopy(h1); |
---|
811 | return e; |
---|
812 | } |
---|
813 | else |
---|
814 | { |
---|
815 | ideal re=kMin_std(h1,currQuotient,(tHomog)homog,&wth,h2,NULL,0,3); |
---|
816 | idDelete(&re); |
---|
817 | return h2; |
---|
818 | } |
---|
819 | } |
---|
820 | e=idInit(1,h1->rank); |
---|
821 | if (idIs0(h1)) |
---|
822 | { |
---|
823 | return e; |
---|
824 | } |
---|
825 | pEnlargeSet(&(e->m),IDELEMS(e),15); |
---|
826 | IDELEMS(e) = 16; |
---|
827 | h2 = kStd(h1,currQuotient,isNotHomog,NULL); |
---|
828 | h3 = idMaxIdeal(); |
---|
829 | h4=idMult(h2,h3); |
---|
830 | idDelete(&h3); |
---|
831 | h3=kStd(h4,currQuotient,isNotHomog,NULL); |
---|
832 | k = IDELEMS(h3); |
---|
833 | while ((k > 0) && (h3->m[k-1] == NULL)) k--; |
---|
834 | j = -1; |
---|
835 | l = IDELEMS(h2); |
---|
836 | while ((l > 0) && (h2->m[l-1] == NULL)) l--; |
---|
837 | for (i=l-1; i>=0; i--) |
---|
838 | { |
---|
839 | if (h2->m[i] != NULL) |
---|
840 | { |
---|
841 | ll = 0; |
---|
842 | while ((ll < k) && ((h3->m[ll] == NULL) |
---|
843 | || !pDivisibleBy(h3->m[ll],h2->m[i]))) |
---|
844 | ll++; |
---|
845 | if (ll >= k) |
---|
846 | { |
---|
847 | j++; |
---|
848 | if (j > IDELEMS(e)-1) |
---|
849 | { |
---|
850 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
---|
851 | IDELEMS(e) += 16; |
---|
852 | } |
---|
853 | e->m[j] = pCopy(h2->m[i]); |
---|
854 | } |
---|
855 | } |
---|
856 | } |
---|
857 | idDelete(&h2); |
---|
858 | idDelete(&h3); |
---|
859 | idDelete(&h4); |
---|
860 | if (currQuotient!=NULL) |
---|
861 | { |
---|
862 | h3=idInit(1,e->rank); |
---|
863 | h2=kNF(h3,currQuotient,e); |
---|
864 | idDelete(&h3); |
---|
865 | idDelete(&e); |
---|
866 | e=h2; |
---|
867 | } |
---|
868 | idSkipZeroes(e); |
---|
869 | return e; |
---|
870 | } |
---|
871 | |
---|
872 | /*2 |
---|
873 | *the minimal index of used variables - 1 |
---|
874 | */ |
---|
875 | int pLowVar (poly p) |
---|
876 | { |
---|
877 | int k,l,lex; |
---|
878 | |
---|
879 | if (p == NULL) return -1; |
---|
880 | |
---|
881 | k = 32000;/*a very large dummy value*/ |
---|
882 | while (p != NULL) |
---|
883 | { |
---|
884 | l = 1; |
---|
885 | lex = pGetExp(p,l); |
---|
886 | while ((l < pVariables) && (lex == 0)) |
---|
887 | { |
---|
888 | l++; |
---|
889 | lex = pGetExp(p,l); |
---|
890 | } |
---|
891 | l--; |
---|
892 | if (l < k) k = l; |
---|
893 | pIter(p); |
---|
894 | } |
---|
895 | return k; |
---|
896 | } |
---|
897 | |
---|
898 | /*3 |
---|
899 | *multiplies p with t (!cas) or (t-1) |
---|
900 | *the index of t is:1, so we have to shift all variables |
---|
901 | *p is NOT in the actual ring, it has no t |
---|
902 | */ |
---|
903 | static poly pMultWithT (poly p,BOOLEAN cas) |
---|
904 | { |
---|
905 | /*qp is the working pointer in p*/ |
---|
906 | /*result is the result, qresult is the working pointer*/ |
---|
907 | /*pp is p in the actual ring(shifted), qpp the working pointer*/ |
---|
908 | poly result,qp,pp; |
---|
909 | poly qresult=NULL; |
---|
910 | poly qpp=NULL; |
---|
911 | int i,j,lex; |
---|
912 | number n; |
---|
913 | |
---|
914 | pp = NULL; |
---|
915 | result = NULL; |
---|
916 | qp = p; |
---|
917 | while (qp != NULL) |
---|
918 | { |
---|
919 | i = 0; |
---|
920 | if (result == NULL) |
---|
921 | {/*first monomial*/ |
---|
922 | result = pInit(); |
---|
923 | qresult = result; |
---|
924 | } |
---|
925 | else |
---|
926 | { |
---|
927 | qresult->next = pInit(); |
---|
928 | pIter(qresult); |
---|
929 | } |
---|
930 | for (j=pVariables-1; j>0; j--) |
---|
931 | { |
---|
932 | lex = pGetExp(qp,j); |
---|
933 | pSetExp(qresult,j+1,lex);/*copy all variables*/ |
---|
934 | } |
---|
935 | lex = pGetComp(qp); |
---|
936 | pSetComp(qresult,lex); |
---|
937 | n=nCopy(pGetCoeff(qp)); |
---|
938 | pSetCoeff0(qresult,n); |
---|
939 | qresult->next = NULL; |
---|
940 | pSetm(qresult); |
---|
941 | /*qresult is now qp brought into the actual ring*/ |
---|
942 | if (cas) |
---|
943 | { /*case: mult with t-1*/ |
---|
944 | pSetExp(qresult,1,0); |
---|
945 | pSetm(qresult); |
---|
946 | if (pp == NULL) |
---|
947 | { /*first monomial*/ |
---|
948 | pp = pCopy(qresult); |
---|
949 | qpp = pp; |
---|
950 | } |
---|
951 | else |
---|
952 | { |
---|
953 | qpp->next = pCopy(qresult); |
---|
954 | pIter(qpp); |
---|
955 | } |
---|
956 | pGetCoeff(qpp)=nNeg(pGetCoeff(qpp)); |
---|
957 | /*now qpp contains -1*qp*/ |
---|
958 | } |
---|
959 | pSetExp(qresult,1,1);/*this is mult. by t*/ |
---|
960 | pSetm(qresult); |
---|
961 | pIter(qp); |
---|
962 | } |
---|
963 | /* |
---|
964 | *now p is processed: |
---|
965 | *result contains t*p |
---|
966 | * if cas: pp contains -1*p (in the new ring) |
---|
967 | */ |
---|
968 | if (cas) qresult->next = pp; |
---|
969 | /* else qresult->next = NULL;*/ |
---|
970 | return result; |
---|
971 | } |
---|
972 | |
---|
973 | /*2 |
---|
974 | * verschiebt die Indizees der Modulerzeugenden um i |
---|
975 | */ |
---|
976 | void pShift (poly * p,int i) |
---|
977 | { |
---|
978 | poly qp1 = *p,qp2 = *p;/*working pointers*/ |
---|
979 | int j = pMaxComp(*p),k = pMinComp(*p); |
---|
980 | |
---|
981 | if (j+i < 0) return ; |
---|
982 | while (qp1 != NULL) |
---|
983 | { |
---|
984 | if ((pGetComp(qp1)+i > 0) || ((j == -i) && (j == k))) |
---|
985 | { |
---|
986 | pAddComp(qp1,i); |
---|
987 | pSetmComp(qp1); |
---|
988 | qp2 = qp1; |
---|
989 | pIter(qp1); |
---|
990 | } |
---|
991 | else |
---|
992 | { |
---|
993 | if (qp2 == *p) |
---|
994 | { |
---|
995 | pIter(*p); |
---|
996 | pLmDelete(&qp2); |
---|
997 | qp2 = *p; |
---|
998 | qp1 = *p; |
---|
999 | } |
---|
1000 | else |
---|
1001 | { |
---|
1002 | qp2->next = qp1->next; |
---|
1003 | if (qp1!=NULL) pLmDelete(&qp1); |
---|
1004 | qp1 = qp2->next; |
---|
1005 | } |
---|
1006 | } |
---|
1007 | } |
---|
1008 | } |
---|
1009 | |
---|
1010 | /*2 |
---|
1011 | *initialized a field with r numbers between beg and end for the |
---|
1012 | *procedure idNextChoise |
---|
1013 | */ |
---|
1014 | void idInitChoise (int r,int beg,int end,BOOLEAN *endch,int * choise) |
---|
1015 | { |
---|
1016 | /*returns the first choise of r numbers between beg and end*/ |
---|
1017 | int i; |
---|
1018 | for (i=0; i<r; i++) |
---|
1019 | { |
---|
1020 | choise[i] = 0; |
---|
1021 | } |
---|
1022 | if (r <= end-beg+1) |
---|
1023 | for (i=0; i<r; i++) |
---|
1024 | { |
---|
1025 | choise[i] = beg+i; |
---|
1026 | } |
---|
1027 | if (r > end-beg+1) |
---|
1028 | *endch = TRUE; |
---|
1029 | else |
---|
1030 | *endch = FALSE; |
---|
1031 | } |
---|
1032 | |
---|
1033 | /*2 |
---|
1034 | *returns the next choise of r numbers between beg and end |
---|
1035 | */ |
---|
1036 | void idGetNextChoise (int r,int end,BOOLEAN *endch,int * choise) |
---|
1037 | { |
---|
1038 | int i = r-1,j; |
---|
1039 | while ((i >= 0) && (choise[i] == end)) |
---|
1040 | { |
---|
1041 | i--; |
---|
1042 | end--; |
---|
1043 | } |
---|
1044 | if (i == -1) |
---|
1045 | *endch = TRUE; |
---|
1046 | else |
---|
1047 | { |
---|
1048 | choise[i]++; |
---|
1049 | for (j=i+1; j<r; j++) |
---|
1050 | { |
---|
1051 | choise[j] = choise[i]+j-i; |
---|
1052 | } |
---|
1053 | *endch = FALSE; |
---|
1054 | } |
---|
1055 | } |
---|
1056 | |
---|
1057 | /*2 |
---|
1058 | *takes the field choise of d numbers between beg and end, cancels the t-th |
---|
1059 | *entree and searches for the ordinal number of that d-1 dimensional field |
---|
1060 | * w.r.t. the algorithm of construction |
---|
1061 | */ |
---|
1062 | int idGetNumberOfChoise(int t, int d, int begin, int end, int * choise) |
---|
1063 | { |
---|
1064 | int * localchoise,i,result=0; |
---|
1065 | BOOLEAN b=FALSE; |
---|
1066 | |
---|
1067 | if (d<=1) return 1; |
---|
1068 | localchoise=(int*)omAlloc((d-1)*sizeof(int)); |
---|
1069 | idInitChoise(d-1,begin,end,&b,localchoise); |
---|
1070 | while (!b) |
---|
1071 | { |
---|
1072 | result++; |
---|
1073 | i = 0; |
---|
1074 | while ((i<t) && (localchoise[i]==choise[i])) i++; |
---|
1075 | if (i>=t) |
---|
1076 | { |
---|
1077 | i = t+1; |
---|
1078 | while ((i<d) && (localchoise[i-1]==choise[i])) i++; |
---|
1079 | if (i>=d) |
---|
1080 | { |
---|
1081 | omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
1082 | return result; |
---|
1083 | } |
---|
1084 | } |
---|
1085 | idGetNextChoise(d-1,end,&b,localchoise); |
---|
1086 | } |
---|
1087 | omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
1088 | return 0; |
---|
1089 | } |
---|
1090 | |
---|
1091 | /*2 |
---|
1092 | *computes the binomial coefficient |
---|
1093 | */ |
---|
1094 | int binom (int n,int r) |
---|
1095 | { |
---|
1096 | int i,result; |
---|
1097 | |
---|
1098 | if (r==0) return 1; |
---|
1099 | if (n-r<r) return binom(n,n-r); |
---|
1100 | result = n-r+1; |
---|
1101 | for (i=2;i<=r;i++) |
---|
1102 | { |
---|
1103 | result *= n-r+i; |
---|
1104 | if (result<0) |
---|
1105 | { |
---|
1106 | WarnS("overflow in binomials"); |
---|
1107 | return 0; |
---|
1108 | } |
---|
1109 | result /= i; |
---|
1110 | } |
---|
1111 | return result; |
---|
1112 | } |
---|
1113 | |
---|
1114 | /*2 |
---|
1115 | *the free module of rank i |
---|
1116 | */ |
---|
1117 | ideal idFreeModule (int i) |
---|
1118 | { |
---|
1119 | int j; |
---|
1120 | ideal h; |
---|
1121 | |
---|
1122 | h=idInit(i,i); |
---|
1123 | for (j=0; j<i; j++) |
---|
1124 | { |
---|
1125 | h->m[j] = pOne(); |
---|
1126 | pSetComp(h->m[j],j+1); |
---|
1127 | pSetmComp(h->m[j]); |
---|
1128 | } |
---|
1129 | return h; |
---|
1130 | } |
---|
1131 | |
---|
1132 | ideal idSectWithElim (ideal h1,ideal h2) |
---|
1133 | // does not destroy h1,h2 |
---|
1134 | { |
---|
1135 | if (TEST_OPT_PROT) PrintS("intersect by elimination method\n"); |
---|
1136 | assume(!idIs0(h1)); |
---|
1137 | assume(!idIs0(h2)); |
---|
1138 | assume(IDELEMS(h1)<=IDELEMS(h2)); |
---|
1139 | assume(idRankFreeModule(h1)==0); |
---|
1140 | assume(idRankFreeModule(h2)==0); |
---|
1141 | // add a new variable: |
---|
1142 | int j; |
---|
1143 | ring origRing=currRing; |
---|
1144 | ring r=rCopy0(origRing); |
---|
1145 | r->N++; |
---|
1146 | r->block0[0]=1; |
---|
1147 | r->block1[0]= r->N; |
---|
1148 | omFree(r->order); |
---|
1149 | r->order=(int*)omAlloc0(3*sizeof(int*)); |
---|
1150 | r->order[0]=ringorder_dp; |
---|
1151 | r->order[1]=ringorder_C; |
---|
1152 | char **names=(char**)omAlloc0(rVar(r) * sizeof(char_ptr)); |
---|
1153 | for (j=0;j<r->N-1;j++) names[j]=r->names[j]; |
---|
1154 | names[r->N-1]=omStrDup("@"); |
---|
1155 | omFree(r->names); |
---|
1156 | r->names=names; |
---|
1157 | rComplete(r,TRUE); |
---|
1158 | // fetch h1, h2 |
---|
1159 | ideal h; |
---|
1160 | h1=idrCopyR(h1,origRing,r); |
---|
1161 | h2=idrCopyR(h2,origRing,r); |
---|
1162 | // switch to temp. ring r |
---|
1163 | rChangeCurrRing(r); |
---|
1164 | // create 1-t, t |
---|
1165 | poly omt=pOne(); |
---|
1166 | pSetExp(omt,r->N,1); |
---|
1167 | poly t=pCopy(omt); |
---|
1168 | pSetm(omt); |
---|
1169 | omt=pNeg(omt); |
---|
1170 | omt=pAdd(omt,pOne()); |
---|
1171 | // compute (1-t)*h1 |
---|
1172 | h1=(ideal)mpMultP((matrix)h1,omt); |
---|
1173 | // compute t*h2 |
---|
1174 | h2=(ideal)mpMultP((matrix)h2,pCopy(t)); |
---|
1175 | // (1-t)h1 + t*h2 |
---|
1176 | h=idInit(IDELEMS(h1)+IDELEMS(h2),1); |
---|
1177 | int l; |
---|
1178 | for (l=IDELEMS(h1)-1; l>=0; l--) |
---|
1179 | { |
---|
1180 | h->m[l] = h1->m[l]; h1->m[l]=NULL; |
---|
1181 | } |
---|
1182 | j=IDELEMS(h1); |
---|
1183 | for (l=IDELEMS(h2)-1; l>=0; l--) |
---|
1184 | { |
---|
1185 | h->m[l+j] = h2->m[l]; h2->m[l]=NULL; |
---|
1186 | } |
---|
1187 | idDelete(&h1); |
---|
1188 | idDelete(&h2); |
---|
1189 | // eliminate t: |
---|
1190 | |
---|
1191 | ideal res=idElimination(h,t); |
---|
1192 | // cleanup |
---|
1193 | idDelete(&h); |
---|
1194 | if (res!=NULL) res=idrMoveR(res,r,origRing); |
---|
1195 | rChangeCurrRing(origRing); |
---|
1196 | rKill(r); |
---|
1197 | return res; |
---|
1198 | } |
---|
1199 | /*2 |
---|
1200 | * h3 := h1 intersect h2 |
---|
1201 | */ |
---|
1202 | ideal idSect (ideal h1,ideal h2) |
---|
1203 | { |
---|
1204 | int i,j,k,length; |
---|
1205 | int flength = idRankFreeModule(h1); |
---|
1206 | int slength = idRankFreeModule(h2); |
---|
1207 | int rank=si_min(flength,slength); |
---|
1208 | if ((idIs0(h1)) || (idIs0(h2))) return idInit(1,rank); |
---|
1209 | |
---|
1210 | ideal first,second,temp,temp1,result; |
---|
1211 | poly p,q; |
---|
1212 | |
---|
1213 | if (IDELEMS(h1)<IDELEMS(h2)) |
---|
1214 | { |
---|
1215 | first = h1; |
---|
1216 | second = h2; |
---|
1217 | } |
---|
1218 | else |
---|
1219 | { |
---|
1220 | first = h2; |
---|
1221 | second = h1; |
---|
1222 | int t=flength; flength=slength; slength=t; |
---|
1223 | } |
---|
1224 | length = si_max(flength,slength); |
---|
1225 | if (length==0) |
---|
1226 | { |
---|
1227 | if ((currQuotient==NULL) |
---|
1228 | && (currRing->OrdSgn==1) |
---|
1229 | && (!rIsPluralRing(currRing)) |
---|
1230 | && ((TEST_V_INTERSECT_ELIM) || (!TEST_V_INTERSECT_SYZ))) |
---|
1231 | return idSectWithElim(first,second); |
---|
1232 | else length = 1; |
---|
1233 | } |
---|
1234 | if (TEST_OPT_PROT) PrintS("intersect by syzygy methods\n"); |
---|
1235 | j = IDELEMS(first); |
---|
1236 | |
---|
1237 | ring orig_ring=currRing; |
---|
1238 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
1239 | rSetSyzComp(length); |
---|
1240 | |
---|
1241 | while ((j>0) && (first->m[j-1]==NULL)) j--; |
---|
1242 | temp = idInit(j /*IDELEMS(first)*/+IDELEMS(second),length+j); |
---|
1243 | k = 0; |
---|
1244 | for (i=0;i<j;i++) |
---|
1245 | { |
---|
1246 | if (first->m[i]!=NULL) |
---|
1247 | { |
---|
1248 | if (syz_ring==orig_ring) |
---|
1249 | temp->m[k] = pCopy(first->m[i]); |
---|
1250 | else |
---|
1251 | temp->m[k] = prCopyR(first->m[i], orig_ring); |
---|
1252 | q = pOne(); |
---|
1253 | pSetComp(q,i+1+length); |
---|
1254 | pSetmComp(q); |
---|
1255 | if (flength==0) pShift(&(temp->m[k]),1); |
---|
1256 | p = temp->m[k]; |
---|
1257 | while (pNext(p)!=NULL) pIter(p); |
---|
1258 | pNext(p) = q; |
---|
1259 | k++; |
---|
1260 | } |
---|
1261 | } |
---|
1262 | for (i=0;i<IDELEMS(second);i++) |
---|
1263 | { |
---|
1264 | if (second->m[i]!=NULL) |
---|
1265 | { |
---|
1266 | if (syz_ring==orig_ring) |
---|
1267 | temp->m[k] = pCopy(second->m[i]); |
---|
1268 | else |
---|
1269 | temp->m[k] = prCopyR(second->m[i], orig_ring); |
---|
1270 | if (slength==0) pShift(&(temp->m[k]),1); |
---|
1271 | k++; |
---|
1272 | } |
---|
1273 | } |
---|
1274 | intvec *w=NULL; |
---|
1275 | temp1 = kStd(temp,currQuotient,testHomog,&w,NULL,length); |
---|
1276 | if (w!=NULL) delete w; |
---|
1277 | idDelete(&temp); |
---|
1278 | if(syz_ring!=orig_ring) |
---|
1279 | rChangeCurrRing(orig_ring); |
---|
1280 | |
---|
1281 | result = idInit(IDELEMS(temp1),rank); |
---|
1282 | j = 0; |
---|
1283 | for (i=0;i<IDELEMS(temp1);i++) |
---|
1284 | { |
---|
1285 | if ((temp1->m[i]!=NULL) |
---|
1286 | && (p_GetComp(temp1->m[i],syz_ring)>length)) |
---|
1287 | { |
---|
1288 | if(syz_ring==orig_ring) |
---|
1289 | { |
---|
1290 | p = temp1->m[i]; |
---|
1291 | } |
---|
1292 | else |
---|
1293 | { |
---|
1294 | p = prMoveR(temp1->m[i], syz_ring); |
---|
1295 | } |
---|
1296 | temp1->m[i]=NULL; |
---|
1297 | while (p!=NULL) |
---|
1298 | { |
---|
1299 | q = pNext(p); |
---|
1300 | pNext(p) = NULL; |
---|
1301 | k = pGetComp(p)-1-length; |
---|
1302 | pSetComp(p,0); |
---|
1303 | pSetmComp(p); |
---|
1304 | /* Warning! multiply only from the left! it's very important for Plural */ |
---|
1305 | result->m[j] = pAdd(result->m[j],pMult(p,pCopy(first->m[k]))); |
---|
1306 | p = q; |
---|
1307 | } |
---|
1308 | j++; |
---|
1309 | } |
---|
1310 | } |
---|
1311 | if(syz_ring!=orig_ring) |
---|
1312 | { |
---|
1313 | rChangeCurrRing(syz_ring); |
---|
1314 | idDelete(&temp1); |
---|
1315 | rChangeCurrRing(orig_ring); |
---|
1316 | rKill(syz_ring); |
---|
1317 | } |
---|
1318 | else |
---|
1319 | { |
---|
1320 | idDelete(&temp1); |
---|
1321 | } |
---|
1322 | |
---|
1323 | idSkipZeroes(result); |
---|
1324 | if (TEST_OPT_RETURN_SB) |
---|
1325 | { |
---|
1326 | w=NULL; |
---|
1327 | temp1=kStd(result,currQuotient,testHomog,&w); |
---|
1328 | if (w!=NULL) delete w; |
---|
1329 | idDelete(&result); |
---|
1330 | idSkipZeroes(temp1); |
---|
1331 | return temp1; |
---|
1332 | } |
---|
1333 | else //temp1=kInterRed(result,currQuotient); |
---|
1334 | return result; |
---|
1335 | } |
---|
1336 | |
---|
1337 | /*2 |
---|
1338 | * ideal/module intersection for a list of objects |
---|
1339 | * given as 'resolvente' |
---|
1340 | */ |
---|
1341 | ideal idMultSect(resolvente arg, int length) |
---|
1342 | { |
---|
1343 | int i,j=0,k=0,syzComp,l,maxrk=-1,realrki; |
---|
1344 | ideal bigmat,tempstd,result; |
---|
1345 | poly p; |
---|
1346 | int isIdeal=0; |
---|
1347 | intvec * w=NULL; |
---|
1348 | |
---|
1349 | /* find 0-ideals and max rank -----------------------------------*/ |
---|
1350 | for (i=0;i<length;i++) |
---|
1351 | { |
---|
1352 | if (!idIs0(arg[i])) |
---|
1353 | { |
---|
1354 | realrki=idRankFreeModule(arg[i]); |
---|
1355 | k++; |
---|
1356 | j += IDELEMS(arg[i]); |
---|
1357 | if (realrki>maxrk) maxrk = realrki; |
---|
1358 | } |
---|
1359 | else |
---|
1360 | { |
---|
1361 | if (arg[i]!=NULL) |
---|
1362 | { |
---|
1363 | return idInit(1,arg[i]->rank); |
---|
1364 | } |
---|
1365 | } |
---|
1366 | } |
---|
1367 | if (maxrk == 0) |
---|
1368 | { |
---|
1369 | isIdeal = 1; |
---|
1370 | maxrk = 1; |
---|
1371 | } |
---|
1372 | /* init -----------------------------------------------------------*/ |
---|
1373 | j += maxrk; |
---|
1374 | syzComp = k*maxrk; |
---|
1375 | |
---|
1376 | ring orig_ring=currRing; |
---|
1377 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
1378 | rSetSyzComp(syzComp); |
---|
1379 | |
---|
1380 | bigmat = idInit(j,(k+1)*maxrk); |
---|
1381 | /* create unit matrices ------------------------------------------*/ |
---|
1382 | for (i=0;i<maxrk;i++) |
---|
1383 | { |
---|
1384 | for (j=0;j<=k;j++) |
---|
1385 | { |
---|
1386 | p = pOne(); |
---|
1387 | pSetComp(p,i+1+j*maxrk); |
---|
1388 | pSetmComp(p); |
---|
1389 | bigmat->m[i] = pAdd(bigmat->m[i],p); |
---|
1390 | } |
---|
1391 | } |
---|
1392 | /* enter given ideals ------------------------------------------*/ |
---|
1393 | i = maxrk; |
---|
1394 | k = 0; |
---|
1395 | for (j=0;j<length;j++) |
---|
1396 | { |
---|
1397 | if (arg[j]!=NULL) |
---|
1398 | { |
---|
1399 | for (l=0;l<IDELEMS(arg[j]);l++) |
---|
1400 | { |
---|
1401 | if (arg[j]->m[l]!=NULL) |
---|
1402 | { |
---|
1403 | if (syz_ring==orig_ring) |
---|
1404 | bigmat->m[i] = pCopy(arg[j]->m[l]); |
---|
1405 | else |
---|
1406 | bigmat->m[i] = prCopyR(arg[j]->m[l], orig_ring); |
---|
1407 | pShift(&(bigmat->m[i]),k*maxrk+isIdeal); |
---|
1408 | i++; |
---|
1409 | } |
---|
1410 | } |
---|
1411 | k++; |
---|
1412 | } |
---|
1413 | } |
---|
1414 | /* std computation --------------------------------------------*/ |
---|
1415 | tempstd = kStd(bigmat,currQuotient,testHomog,&w,NULL,syzComp); |
---|
1416 | if (w!=NULL) delete w; |
---|
1417 | idDelete(&bigmat); |
---|
1418 | |
---|
1419 | if(syz_ring!=orig_ring) |
---|
1420 | rChangeCurrRing(orig_ring); |
---|
1421 | |
---|
1422 | /* interprete result ----------------------------------------*/ |
---|
1423 | result = idInit(IDELEMS(tempstd),maxrk); |
---|
1424 | k = 0; |
---|
1425 | for (j=0;j<IDELEMS(tempstd);j++) |
---|
1426 | { |
---|
1427 | if ((tempstd->m[j]!=NULL) && (p_GetComp(tempstd->m[j],syz_ring)>syzComp)) |
---|
1428 | { |
---|
1429 | if (syz_ring==orig_ring) |
---|
1430 | p = pCopy(tempstd->m[j]); |
---|
1431 | else |
---|
1432 | p = prCopyR(tempstd->m[j], syz_ring); |
---|
1433 | pShift(&p,-syzComp-isIdeal); |
---|
1434 | result->m[k] = p; |
---|
1435 | k++; |
---|
1436 | } |
---|
1437 | } |
---|
1438 | /* clean up ----------------------------------------------------*/ |
---|
1439 | if(syz_ring!=orig_ring) |
---|
1440 | rChangeCurrRing(syz_ring); |
---|
1441 | idDelete(&tempstd); |
---|
1442 | if(syz_ring!=orig_ring) |
---|
1443 | { |
---|
1444 | rChangeCurrRing(orig_ring); |
---|
1445 | rKill(syz_ring); |
---|
1446 | } |
---|
1447 | idSkipZeroes(result); |
---|
1448 | return result; |
---|
1449 | } |
---|
1450 | |
---|
1451 | /*2 |
---|
1452 | *computes syzygies of h1, |
---|
1453 | *if quot != NULL it computes in the quotient ring modulo "quot" |
---|
1454 | *works always in a ring with ringorder_s |
---|
1455 | */ |
---|
1456 | static ideal idPrepare (ideal h1, tHomog hom, int syzcomp, intvec **w) |
---|
1457 | { |
---|
1458 | ideal h2, h3; |
---|
1459 | int i; |
---|
1460 | int j,jj=0,k; |
---|
1461 | poly p,q; |
---|
1462 | |
---|
1463 | if (idIs0(h1)) return NULL; |
---|
1464 | k = idRankFreeModule(h1); |
---|
1465 | h2=idCopy(h1); |
---|
1466 | i = IDELEMS(h2)-1; |
---|
1467 | if (k == 0) |
---|
1468 | { |
---|
1469 | for (j=0; j<=i; j++) pShift(&(h2->m[j]),1); |
---|
1470 | k = 1; |
---|
1471 | } |
---|
1472 | if (syzcomp<k) |
---|
1473 | { |
---|
1474 | Warn("syzcomp too low, should be %d instead of %d",k,syzcomp); |
---|
1475 | syzcomp = k; |
---|
1476 | rSetSyzComp(k); |
---|
1477 | } |
---|
1478 | h2->rank = syzcomp+i+1; |
---|
1479 | |
---|
1480 | //if (hom==testHomog) |
---|
1481 | //{ |
---|
1482 | // if(idHomIdeal(h1,currQuotient)) |
---|
1483 | // { |
---|
1484 | // hom=TRUE; |
---|
1485 | // } |
---|
1486 | //} |
---|
1487 | |
---|
1488 | #if MYTEST |
---|
1489 | #ifdef RDEBUG |
---|
1490 | Print("Prepare::h2: "); |
---|
1491 | idPrint(h2); |
---|
1492 | |
---|
1493 | for(j=0;j<IDELEMS(h2);j++) pTest(h2->m[j]); |
---|
1494 | |
---|
1495 | #endif |
---|
1496 | #endif |
---|
1497 | |
---|
1498 | for (j=0; j<=i; j++) |
---|
1499 | { |
---|
1500 | p = h2->m[j]; |
---|
1501 | q = pOne(); |
---|
1502 | pSetComp(q,syzcomp+1+j); |
---|
1503 | pSetmComp(q); |
---|
1504 | if (p!=NULL) |
---|
1505 | { |
---|
1506 | while (pNext(p)) pIter(p); |
---|
1507 | p->next = q; |
---|
1508 | } |
---|
1509 | else |
---|
1510 | h2->m[j]=q; |
---|
1511 | } |
---|
1512 | |
---|
1513 | #ifdef PDEBUG |
---|
1514 | for(j=0;j<IDELEMS(h2);j++) pTest(h2->m[j]); |
---|
1515 | |
---|
1516 | #if MYTEST |
---|
1517 | #ifdef RDEBUG |
---|
1518 | Print("Prepare::Input: "); |
---|
1519 | idPrint(h2); |
---|
1520 | |
---|
1521 | Print("Prepare::currQuotient: "); |
---|
1522 | idPrint(currQuotient); |
---|
1523 | #endif |
---|
1524 | #endif |
---|
1525 | |
---|
1526 | #endif |
---|
1527 | |
---|
1528 | idTest(h2); |
---|
1529 | |
---|
1530 | h3 = kStd(h2,currQuotient,hom,w,NULL,syzcomp); |
---|
1531 | |
---|
1532 | #if MYTEST |
---|
1533 | #ifdef RDEBUG |
---|
1534 | Print("Prepare::Output: "); |
---|
1535 | idPrint(h3); |
---|
1536 | for(j=0;j<IDELEMS(h2);j++) pTest(h3->m[j]); |
---|
1537 | #endif |
---|
1538 | #endif |
---|
1539 | |
---|
1540 | |
---|
1541 | idDelete(&h2); |
---|
1542 | return h3; |
---|
1543 | } |
---|
1544 | |
---|
1545 | /*2 |
---|
1546 | * compute the syzygies of h1 in R/quot, |
---|
1547 | * weights of components are in w |
---|
1548 | * if setRegularity, return the regularity in deg |
---|
1549 | * do not change h1, w |
---|
1550 | */ |
---|
1551 | ideal idSyzygies (ideal h1, tHomog h,intvec **w, BOOLEAN setSyzComp, |
---|
1552 | BOOLEAN setRegularity, int *deg) |
---|
1553 | { |
---|
1554 | ideal s_h1; |
---|
1555 | poly p; |
---|
1556 | int j, k, length=0,reg; |
---|
1557 | BOOLEAN isMonomial=TRUE; |
---|
1558 | int ii, idElemens_h1; |
---|
1559 | |
---|
1560 | assume(h1 != NULL); |
---|
1561 | |
---|
1562 | idElemens_h1=IDELEMS(h1); |
---|
1563 | #ifdef PDEBUG |
---|
1564 | for(ii=0;ii<idElemens_h1 /*IDELEMS(h1)*/;ii++) pTest(h1->m[ii]); |
---|
1565 | #endif |
---|
1566 | if (idIs0(h1)) |
---|
1567 | { |
---|
1568 | ideal result=idFreeModule(idElemens_h1/*IDELEMS(h1)*/); |
---|
1569 | int curr_syz_limit=rGetCurrSyzLimit(); |
---|
1570 | if (curr_syz_limit>0) |
---|
1571 | for (ii=0;ii<idElemens_h1/*IDELEMS(h1)*/;ii++) |
---|
1572 | { |
---|
1573 | if (h1->m[ii]!=NULL) |
---|
1574 | pShift(&h1->m[ii],curr_syz_limit); |
---|
1575 | } |
---|
1576 | return result; |
---|
1577 | } |
---|
1578 | int slength=(int)idRankFreeModule(h1); |
---|
1579 | k=si_max(1,slength /*idRankFreeModule(h1)*/); |
---|
1580 | |
---|
1581 | assume(currRing != NULL); |
---|
1582 | ring orig_ring=currRing; |
---|
1583 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
1584 | |
---|
1585 | if (setSyzComp) |
---|
1586 | rSetSyzComp(k); |
---|
1587 | |
---|
1588 | if (orig_ring != syz_ring) |
---|
1589 | { |
---|
1590 | s_h1=idrCopyR_NoSort(h1,orig_ring); |
---|
1591 | } |
---|
1592 | else |
---|
1593 | { |
---|
1594 | s_h1 = h1; |
---|
1595 | } |
---|
1596 | |
---|
1597 | idTest(s_h1); |
---|
1598 | |
---|
1599 | ideal s_h3=idPrepare(s_h1,h,k,w); // main (syz) GB computation |
---|
1600 | |
---|
1601 | if (s_h3==NULL) |
---|
1602 | { |
---|
1603 | return idFreeModule( idElemens_h1 /*IDELEMS(h1)*/); |
---|
1604 | } |
---|
1605 | |
---|
1606 | if (orig_ring != syz_ring) |
---|
1607 | { |
---|
1608 | idDelete(&s_h1); |
---|
1609 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
1610 | { |
---|
1611 | if (s_h3->m[j] != NULL) |
---|
1612 | { |
---|
1613 | if (p_MinComp(s_h3->m[j],syz_ring) > k) |
---|
1614 | pShift(&s_h3->m[j], -k); |
---|
1615 | else |
---|
1616 | pDelete(&s_h3->m[j]); |
---|
1617 | } |
---|
1618 | } |
---|
1619 | idSkipZeroes(s_h3); |
---|
1620 | s_h3->rank -= k; |
---|
1621 | rChangeCurrRing(orig_ring); |
---|
1622 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
1623 | rKill(syz_ring); |
---|
1624 | #ifdef HAVE_PLURAL |
---|
1625 | if (rIsPluralRing(currRing)) |
---|
1626 | { |
---|
1627 | idDelMultiples(s_h3); |
---|
1628 | idSkipZeroes(s_h3); |
---|
1629 | } |
---|
1630 | #endif |
---|
1631 | idTest(s_h3); |
---|
1632 | return s_h3; |
---|
1633 | } |
---|
1634 | |
---|
1635 | ideal e = idInit(IDELEMS(s_h3), s_h3->rank); |
---|
1636 | |
---|
1637 | for (j=IDELEMS(s_h3)-1; j>=0; j--) |
---|
1638 | { |
---|
1639 | if (s_h3->m[j] != NULL) |
---|
1640 | { |
---|
1641 | if (p_MinComp(s_h3->m[j],syz_ring) <= k) |
---|
1642 | { |
---|
1643 | e->m[j] = s_h3->m[j]; |
---|
1644 | isMonomial=isMonomial && (pNext(s_h3->m[j])==NULL); |
---|
1645 | pDelete(&pNext(s_h3->m[j])); |
---|
1646 | s_h3->m[j] = NULL; |
---|
1647 | } |
---|
1648 | } |
---|
1649 | } |
---|
1650 | |
---|
1651 | idSkipZeroes(s_h3); |
---|
1652 | idSkipZeroes(e); |
---|
1653 | |
---|
1654 | if ((deg != NULL) |
---|
1655 | && (!isMonomial) |
---|
1656 | && (!TEST_OPT_NOTREGULARITY) |
---|
1657 | && (setRegularity) |
---|
1658 | && (h==isHomog) |
---|
1659 | && (!rIsPluralRing(currRing)) |
---|
1660 | ) |
---|
1661 | { |
---|
1662 | ring dp_C_ring = rCurrRingAssure_dp_C(); |
---|
1663 | if (dp_C_ring != syz_ring) |
---|
1664 | e = idrMoveR_NoSort(e, syz_ring); |
---|
1665 | resolvente res = sySchreyerResolvente(e,-1,&length,TRUE, TRUE); |
---|
1666 | intvec * dummy = syBetti(res,length,®, *w); |
---|
1667 | *deg = reg+2; |
---|
1668 | delete dummy; |
---|
1669 | for (j=0;j<length;j++) |
---|
1670 | { |
---|
1671 | if (res[j]!=NULL) idDelete(&(res[j])); |
---|
1672 | } |
---|
1673 | omFreeSize((ADDRESS)res,length*sizeof(ideal)); |
---|
1674 | idDelete(&e); |
---|
1675 | if (dp_C_ring != syz_ring) |
---|
1676 | { |
---|
1677 | rChangeCurrRing(syz_ring); |
---|
1678 | rKill(dp_C_ring); |
---|
1679 | } |
---|
1680 | } |
---|
1681 | else |
---|
1682 | { |
---|
1683 | idDelete(&e); |
---|
1684 | } |
---|
1685 | idTest(s_h3); |
---|
1686 | if (currQuotient != NULL) |
---|
1687 | { |
---|
1688 | ideal ts_h3=kStd(s_h3,currQuotient,h,w); |
---|
1689 | idDelete(&s_h3); |
---|
1690 | s_h3 = ts_h3; |
---|
1691 | } |
---|
1692 | return s_h3; |
---|
1693 | } |
---|
1694 | |
---|
1695 | /*2 |
---|
1696 | */ |
---|
1697 | ideal idXXX (ideal h1, int k) |
---|
1698 | { |
---|
1699 | ideal s_h1; |
---|
1700 | int j; |
---|
1701 | intvec *w=NULL; |
---|
1702 | |
---|
1703 | assume(currRing != NULL); |
---|
1704 | ring orig_ring=currRing; |
---|
1705 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
1706 | |
---|
1707 | rSetSyzComp(k); |
---|
1708 | |
---|
1709 | if (orig_ring != syz_ring) |
---|
1710 | { |
---|
1711 | s_h1=idrCopyR_NoSort(h1,orig_ring); |
---|
1712 | } |
---|
1713 | else |
---|
1714 | { |
---|
1715 | s_h1 = h1; |
---|
1716 | } |
---|
1717 | |
---|
1718 | ideal s_h3=kStd(s_h1,NULL,testHomog,&w,NULL,k); |
---|
1719 | |
---|
1720 | if (s_h3==NULL) |
---|
1721 | { |
---|
1722 | return idFreeModule(IDELEMS(h1)); |
---|
1723 | } |
---|
1724 | |
---|
1725 | if (orig_ring != syz_ring) |
---|
1726 | { |
---|
1727 | idDelete(&s_h1); |
---|
1728 | idSkipZeroes(s_h3); |
---|
1729 | rChangeCurrRing(orig_ring); |
---|
1730 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
1731 | rKill(syz_ring); |
---|
1732 | idTest(s_h3); |
---|
1733 | return s_h3; |
---|
1734 | } |
---|
1735 | |
---|
1736 | idSkipZeroes(s_h3); |
---|
1737 | idTest(s_h3); |
---|
1738 | return s_h3; |
---|
1739 | } |
---|
1740 | |
---|
1741 | /* |
---|
1742 | *computes a standard basis for h1 and stores the transformation matrix |
---|
1743 | * in ma |
---|
1744 | */ |
---|
1745 | ideal idLiftStd (ideal h1, matrix* ma, tHomog hi, ideal * syz) |
---|
1746 | { |
---|
1747 | int i, j, k, t, inputIsIdeal=idRankFreeModule(h1); |
---|
1748 | poly p=NULL, q, qq; |
---|
1749 | intvec *w=NULL; |
---|
1750 | |
---|
1751 | idDelete((ideal*)ma); |
---|
1752 | BOOLEAN lift3=FALSE; |
---|
1753 | if (syz!=NULL) { lift3=TRUE; idDelete(syz); } |
---|
1754 | if (idIs0(h1)) |
---|
1755 | { |
---|
1756 | *ma=mpNew(1,0); |
---|
1757 | if (lift3) |
---|
1758 | { |
---|
1759 | *syz=idFreeModule(IDELEMS(h1)); |
---|
1760 | int curr_syz_limit=rGetCurrSyzLimit(); |
---|
1761 | if (curr_syz_limit>0) |
---|
1762 | for (int ii=0;ii<IDELEMS(h1);ii++) |
---|
1763 | { |
---|
1764 | if (h1->m[ii]!=NULL) |
---|
1765 | pShift(&h1->m[ii],curr_syz_limit); |
---|
1766 | } |
---|
1767 | } |
---|
1768 | return idInit(1,h1->rank); |
---|
1769 | } |
---|
1770 | |
---|
1771 | BITSET save_verbose=verbose; |
---|
1772 | |
---|
1773 | k=si_max(1,(int)idRankFreeModule(h1)); |
---|
1774 | |
---|
1775 | if ((k==1) && (!lift3)) verbose |=Sy_bit(V_IDLIFT); |
---|
1776 | |
---|
1777 | ring orig_ring = currRing; |
---|
1778 | ring syz_ring = rCurrRingAssure_SyzComp(); |
---|
1779 | rSetSyzComp(k); |
---|
1780 | |
---|
1781 | ideal s_h1=h1; |
---|
1782 | |
---|
1783 | if (orig_ring != syz_ring) |
---|
1784 | s_h1 = idrCopyR_NoSort(h1,orig_ring); |
---|
1785 | else |
---|
1786 | s_h1 = h1; |
---|
1787 | |
---|
1788 | ideal s_h3=idPrepare(s_h1,hi,k,&w); // main (syz) GB computation |
---|
1789 | |
---|
1790 | ideal s_h2 = idInit(IDELEMS(s_h3), s_h3->rank); |
---|
1791 | |
---|
1792 | if (lift3) (*syz)=idInit(IDELEMS(s_h3),IDELEMS(h1)); |
---|
1793 | |
---|
1794 | if (w!=NULL) delete w; |
---|
1795 | i = 0; |
---|
1796 | |
---|
1797 | // now sort the result, SB : leave in s_h3 |
---|
1798 | // T: put in s_h2 |
---|
1799 | // syz: put in *syz |
---|
1800 | for (j=0; j<IDELEMS(s_h3); j++) |
---|
1801 | { |
---|
1802 | if (s_h3->m[j] != NULL) |
---|
1803 | { |
---|
1804 | //if (p_MinComp(s_h3->m[j],syz_ring) <= k) |
---|
1805 | if (pGetComp(s_h3->m[j]) <= k) // syz_ring == currRing |
---|
1806 | { |
---|
1807 | i++; |
---|
1808 | q = s_h3->m[j]; |
---|
1809 | while (pNext(q) != NULL) |
---|
1810 | { |
---|
1811 | if (pGetComp(pNext(q)) > k) |
---|
1812 | { |
---|
1813 | s_h2->m[j] = pNext(q); |
---|
1814 | pNext(q) = NULL; |
---|
1815 | } |
---|
1816 | else |
---|
1817 | { |
---|
1818 | pIter(q); |
---|
1819 | } |
---|
1820 | } |
---|
1821 | if (!inputIsIdeal) pShift(&(s_h3->m[j]), -1); |
---|
1822 | } |
---|
1823 | else |
---|
1824 | { |
---|
1825 | // we a syzygy here: |
---|
1826 | if (lift3) |
---|
1827 | { |
---|
1828 | pShift(&s_h3->m[j], -k); |
---|
1829 | (*syz)->m[j]=s_h3->m[j]; |
---|
1830 | s_h3->m[j]=NULL; |
---|
1831 | } |
---|
1832 | else |
---|
1833 | pDelete(&(s_h3->m[j])); |
---|
1834 | } |
---|
1835 | } |
---|
1836 | } |
---|
1837 | idSkipZeroes(s_h3); |
---|
1838 | //extern char * iiStringMatrix(matrix im, int dim,char ch); |
---|
1839 | //PrintS("SB: ----------------------------------------\n"); |
---|
1840 | //PrintS(iiStringMatrix((matrix)s_h3,k,'\n')); |
---|
1841 | //PrintLn(); |
---|
1842 | //PrintS("T: ----------------------------------------\n"); |
---|
1843 | //PrintS(iiStringMatrix((matrix)s_h2,h1->rank,'\n')); |
---|
1844 | //PrintLn(); |
---|
1845 | |
---|
1846 | if (lift3) idSkipZeroes(*syz); |
---|
1847 | |
---|
1848 | j = IDELEMS(s_h1); |
---|
1849 | |
---|
1850 | |
---|
1851 | if (syz_ring!=orig_ring) |
---|
1852 | { |
---|
1853 | idDelete(&s_h1); |
---|
1854 | rChangeCurrRing(orig_ring); |
---|
1855 | } |
---|
1856 | |
---|
1857 | *ma = mpNew(j,i); |
---|
1858 | |
---|
1859 | i = 1; |
---|
1860 | for (j=0; j<IDELEMS(s_h2); j++) |
---|
1861 | { |
---|
1862 | if (s_h2->m[j] != NULL) |
---|
1863 | { |
---|
1864 | q = prMoveR( s_h2->m[j], syz_ring); |
---|
1865 | s_h2->m[j] = NULL; |
---|
1866 | |
---|
1867 | while (q != NULL) |
---|
1868 | { |
---|
1869 | p = q; |
---|
1870 | pIter(q); |
---|
1871 | pNext(p) = NULL; |
---|
1872 | t=pGetComp(p); |
---|
1873 | pSetComp(p,0); |
---|
1874 | pSetmComp(p); |
---|
1875 | MATELEM(*ma,t-k,i) = pAdd(MATELEM(*ma,t-k,i),p); |
---|
1876 | } |
---|
1877 | i++; |
---|
1878 | } |
---|
1879 | } |
---|
1880 | idDelete(&s_h2); |
---|
1881 | |
---|
1882 | for (i=0; i<IDELEMS(s_h3); i++) |
---|
1883 | { |
---|
1884 | s_h3->m[i] = prMoveR_NoSort(s_h3->m[i], syz_ring); |
---|
1885 | } |
---|
1886 | if (lift3) |
---|
1887 | { |
---|
1888 | for (i=0; i<IDELEMS(*syz); i++) |
---|
1889 | { |
---|
1890 | (*syz)->m[i] = prMoveR_NoSort((*syz)->m[i], syz_ring); |
---|
1891 | } |
---|
1892 | } |
---|
1893 | |
---|
1894 | if (syz_ring!=orig_ring) rKill(syz_ring); |
---|
1895 | verbose = save_verbose; |
---|
1896 | return s_h3; |
---|
1897 | } |
---|
1898 | |
---|
1899 | static void idPrepareStd(ideal s_temp, int k) |
---|
1900 | { |
---|
1901 | int j,rk=idRankFreeModule(s_temp); |
---|
1902 | poly p,q; |
---|
1903 | |
---|
1904 | if (rk == 0) |
---|
1905 | { |
---|
1906 | for (j=0; j<IDELEMS(s_temp); j++) |
---|
1907 | { |
---|
1908 | if (s_temp->m[j]!=NULL) pSetCompP(s_temp->m[j],1); |
---|
1909 | } |
---|
1910 | k = si_max(k,1); |
---|
1911 | } |
---|
1912 | for (j=0; j<IDELEMS(s_temp); j++) |
---|
1913 | { |
---|
1914 | if (s_temp->m[j]!=NULL) |
---|
1915 | { |
---|
1916 | p = s_temp->m[j]; |
---|
1917 | q = pOne(); |
---|
1918 | //pGetCoeff(q)=nNeg(pGetCoeff(q)); //set q to -1 |
---|
1919 | pSetComp(q,k+1+j); |
---|
1920 | pSetmComp(q); |
---|
1921 | while (pNext(p)) pIter(p); |
---|
1922 | pNext(p) = q; |
---|
1923 | } |
---|
1924 | } |
---|
1925 | } |
---|
1926 | |
---|
1927 | /*2 |
---|
1928 | *computes a representation of the generators of submod with respect to those |
---|
1929 | * of mod |
---|
1930 | */ |
---|
1931 | |
---|
1932 | ideal idLift(ideal mod, ideal submod,ideal *rest, BOOLEAN goodShape, |
---|
1933 | BOOLEAN isSB, BOOLEAN divide, matrix *unit) |
---|
1934 | { |
---|
1935 | int lsmod =idRankFreeModule(submod), i, j, k; |
---|
1936 | int comps_to_add=0; |
---|
1937 | poly p; |
---|
1938 | |
---|
1939 | if (idIs0(submod)) |
---|
1940 | { |
---|
1941 | if (unit!=NULL) |
---|
1942 | { |
---|
1943 | *unit=mpNew(1,1); |
---|
1944 | MATELEM(*unit,1,1)=pOne(); |
---|
1945 | } |
---|
1946 | if (rest!=NULL) |
---|
1947 | { |
---|
1948 | *rest=idInit(1,mod->rank); |
---|
1949 | } |
---|
1950 | return idInit(1,mod->rank); |
---|
1951 | } |
---|
1952 | if (idIs0(mod)) /* and not idIs0(submod) */ |
---|
1953 | { |
---|
1954 | WerrorS("2nd module does not lie in the first"); |
---|
1955 | return NULL; |
---|
1956 | } |
---|
1957 | if (unit!=NULL) |
---|
1958 | { |
---|
1959 | comps_to_add = IDELEMS(submod); |
---|
1960 | while ((comps_to_add>0) && (submod->m[comps_to_add-1]==NULL)) |
---|
1961 | comps_to_add--; |
---|
1962 | } |
---|
1963 | k=si_max(idRankFreeModule(mod),idRankFreeModule(submod)); |
---|
1964 | if ((k!=0) && (lsmod==0)) lsmod=1; |
---|
1965 | k=si_max(k,(int)mod->rank); |
---|
1966 | if (k<submod->rank) { WarnS("rk(submod) > rk(mod) ?");k=submod->rank; } |
---|
1967 | |
---|
1968 | ring orig_ring=currRing; |
---|
1969 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
1970 | rSetSyzComp(k); |
---|
1971 | |
---|
1972 | ideal s_mod, s_temp; |
---|
1973 | if (orig_ring != syz_ring) |
---|
1974 | { |
---|
1975 | s_mod = idrCopyR_NoSort(mod,orig_ring); |
---|
1976 | s_temp = idrCopyR_NoSort(submod,orig_ring); |
---|
1977 | } |
---|
1978 | else |
---|
1979 | { |
---|
1980 | s_mod = mod; |
---|
1981 | s_temp = idCopy(submod); |
---|
1982 | } |
---|
1983 | ideal s_h3; |
---|
1984 | if (isSB) |
---|
1985 | { |
---|
1986 | s_h3 = idCopy(s_mod); |
---|
1987 | idPrepareStd(s_h3, k+comps_to_add); |
---|
1988 | } |
---|
1989 | else |
---|
1990 | { |
---|
1991 | s_h3 = idPrepare(s_mod,(tHomog)FALSE,k+comps_to_add,NULL); |
---|
1992 | } |
---|
1993 | if (!goodShape) |
---|
1994 | { |
---|
1995 | for (j=0;j<IDELEMS(s_h3);j++) |
---|
1996 | { |
---|
1997 | if ((s_h3->m[j] != NULL) && (pMinComp(s_h3->m[j]) > k)) |
---|
1998 | pDelete(&(s_h3->m[j])); |
---|
1999 | } |
---|
2000 | } |
---|
2001 | idSkipZeroes(s_h3); |
---|
2002 | if (lsmod==0) |
---|
2003 | { |
---|
2004 | for (j=IDELEMS(s_temp);j>0;j--) |
---|
2005 | { |
---|
2006 | if (s_temp->m[j-1]!=NULL) |
---|
2007 | pShift(&(s_temp->m[j-1]),1); |
---|
2008 | } |
---|
2009 | } |
---|
2010 | if (unit!=NULL) |
---|
2011 | { |
---|
2012 | for(j = 0;j<comps_to_add;j++) |
---|
2013 | { |
---|
2014 | p = s_temp->m[j]; |
---|
2015 | if (p!=NULL) |
---|
2016 | { |
---|
2017 | while (pNext(p)!=NULL) pIter(p); |
---|
2018 | pNext(p) = pOne(); |
---|
2019 | pIter(p); |
---|
2020 | pSetComp(p,1+j+k); |
---|
2021 | pSetmComp(p); |
---|
2022 | p = pNeg(p); |
---|
2023 | } |
---|
2024 | } |
---|
2025 | } |
---|
2026 | ideal s_result = kNF(s_h3,currQuotient,s_temp,k); |
---|
2027 | s_result->rank = s_h3->rank; |
---|
2028 | ideal s_rest = idInit(IDELEMS(s_result),k); |
---|
2029 | idDelete(&s_h3); |
---|
2030 | idDelete(&s_temp); |
---|
2031 | |
---|
2032 | for (j=0;j<IDELEMS(s_result);j++) |
---|
2033 | { |
---|
2034 | if (s_result->m[j]!=NULL) |
---|
2035 | { |
---|
2036 | if (pGetComp(s_result->m[j])<=k) |
---|
2037 | { |
---|
2038 | if (!divide) |
---|
2039 | { |
---|
2040 | if (isSB) |
---|
2041 | { |
---|
2042 | WarnS("first module not a standardbasis\n" |
---|
2043 | "// ** or second not a proper submodule"); |
---|
2044 | } |
---|
2045 | else |
---|
2046 | WerrorS("2nd module does not lie in the first"); |
---|
2047 | idDelete(&s_result); |
---|
2048 | idDelete(&s_rest); |
---|
2049 | s_result=idInit(IDELEMS(submod),submod->rank); |
---|
2050 | break; |
---|
2051 | } |
---|
2052 | else |
---|
2053 | { |
---|
2054 | p = s_rest->m[j] = s_result->m[j]; |
---|
2055 | while ((pNext(p)!=NULL) && (pGetComp(pNext(p))<=k)) pIter(p); |
---|
2056 | s_result->m[j] = pNext(p); |
---|
2057 | pNext(p) = NULL; |
---|
2058 | } |
---|
2059 | } |
---|
2060 | pShift(&(s_result->m[j]),-k); |
---|
2061 | pNeg(s_result->m[j]); |
---|
2062 | } |
---|
2063 | } |
---|
2064 | if ((lsmod==0) && (!idIs0(s_rest))) |
---|
2065 | { |
---|
2066 | for (j=IDELEMS(s_rest);j>0;j--) |
---|
2067 | { |
---|
2068 | if (s_rest->m[j-1]!=NULL) |
---|
2069 | { |
---|
2070 | pShift(&(s_rest->m[j-1]),-1); |
---|
2071 | s_rest->m[j-1] = s_rest->m[j-1]; |
---|
2072 | } |
---|
2073 | } |
---|
2074 | } |
---|
2075 | if(syz_ring!=orig_ring) |
---|
2076 | { |
---|
2077 | idDelete(&s_mod); |
---|
2078 | rChangeCurrRing(orig_ring); |
---|
2079 | s_result = idrMoveR_NoSort(s_result, syz_ring); |
---|
2080 | s_rest = idrMoveR_NoSort(s_rest, syz_ring); |
---|
2081 | rKill(syz_ring); |
---|
2082 | } |
---|
2083 | if (rest!=NULL) |
---|
2084 | *rest = s_rest; |
---|
2085 | else |
---|
2086 | idDelete(&s_rest); |
---|
2087 | //idPrint(s_result); |
---|
2088 | if (unit!=NULL) |
---|
2089 | { |
---|
2090 | *unit=mpNew(comps_to_add,comps_to_add); |
---|
2091 | int i; |
---|
2092 | for(i=0;i<IDELEMS(s_result);i++) |
---|
2093 | { |
---|
2094 | poly p=s_result->m[i]; |
---|
2095 | poly q=NULL; |
---|
2096 | while(p!=NULL) |
---|
2097 | { |
---|
2098 | if(pGetComp(p)<=comps_to_add) |
---|
2099 | { |
---|
2100 | pSetComp(p,0); |
---|
2101 | if (q!=NULL) |
---|
2102 | { |
---|
2103 | pNext(q)=pNext(p); |
---|
2104 | } |
---|
2105 | else |
---|
2106 | { |
---|
2107 | pIter(s_result->m[i]); |
---|
2108 | } |
---|
2109 | pNext(p)=NULL; |
---|
2110 | MATELEM(*unit,i+1,i+1)=pAdd(MATELEM(*unit,i+1,i+1),p); |
---|
2111 | if(q!=NULL) p=pNext(q); |
---|
2112 | else p=s_result->m[i]; |
---|
2113 | } |
---|
2114 | else |
---|
2115 | { |
---|
2116 | q=p; |
---|
2117 | pIter(p); |
---|
2118 | } |
---|
2119 | } |
---|
2120 | pShift(&s_result->m[i],-comps_to_add); |
---|
2121 | } |
---|
2122 | } |
---|
2123 | return s_result; |
---|
2124 | } |
---|
2125 | |
---|
2126 | /*2 |
---|
2127 | *computes division of P by Q with remainder up to (w-weighted) degree n |
---|
2128 | *P, Q, and w are not changed |
---|
2129 | */ |
---|
2130 | void idLiftW(ideal P,ideal Q,int n,matrix &T, ideal &R,short *w) |
---|
2131 | { |
---|
2132 | long N=0; |
---|
2133 | int i; |
---|
2134 | for(i=IDELEMS(Q)-1;i>=0;i--) |
---|
2135 | if(w==NULL) |
---|
2136 | N=si_max(N,pDeg(Q->m[i])); |
---|
2137 | else |
---|
2138 | N=si_max(N,pDegW(Q->m[i],w)); |
---|
2139 | N+=n; |
---|
2140 | |
---|
2141 | T=mpNew(IDELEMS(Q),IDELEMS(P)); |
---|
2142 | R=idInit(IDELEMS(P),P->rank); |
---|
2143 | |
---|
2144 | for(i=IDELEMS(P)-1;i>=0;i--) |
---|
2145 | { |
---|
2146 | poly p; |
---|
2147 | if(w==NULL) |
---|
2148 | p=ppJet(P->m[i],N); |
---|
2149 | else |
---|
2150 | p=ppJetW(P->m[i],N,w); |
---|
2151 | |
---|
2152 | int j=IDELEMS(Q)-1; |
---|
2153 | while(p!=NULL) |
---|
2154 | { |
---|
2155 | if(pDivisibleBy(Q->m[j],p)) |
---|
2156 | { |
---|
2157 | poly p0=pDivideM(pHead(p),pHead(Q->m[j])); |
---|
2158 | if(w==NULL) |
---|
2159 | p=pJet(pSub(p,ppMult_mm(Q->m[j],p0)),N); |
---|
2160 | else |
---|
2161 | p=pJetW(pSub(p,ppMult_mm(Q->m[j],p0)),N,w); |
---|
2162 | pNormalize(p); |
---|
2163 | if((w==NULL)&&(pDeg(p0)>n)||(w!=NULL)&&(pDegW(p0,w)>n)) |
---|
2164 | pDelete(&p0); |
---|
2165 | else |
---|
2166 | MATELEM(T,j+1,i+1)=pAdd(MATELEM(T,j+1,i+1),p0); |
---|
2167 | j=IDELEMS(Q)-1; |
---|
2168 | } |
---|
2169 | else |
---|
2170 | { |
---|
2171 | if(j==0) |
---|
2172 | { |
---|
2173 | poly p0=p; |
---|
2174 | pIter(p); |
---|
2175 | pNext(p0)=NULL; |
---|
2176 | if(((w==NULL)&&(pDeg(p0)>n)) |
---|
2177 | ||((w!=NULL)&&(pDegW(p0,w)>n))) |
---|
2178 | pDelete(&p0); |
---|
2179 | else |
---|
2180 | R->m[i]=pAdd(R->m[i],p0); |
---|
2181 | j=IDELEMS(Q)-1; |
---|
2182 | } |
---|
2183 | else |
---|
2184 | j--; |
---|
2185 | } |
---|
2186 | } |
---|
2187 | } |
---|
2188 | } |
---|
2189 | |
---|
2190 | /*2 |
---|
2191 | *computes the quotient of h1,h2 : internal routine for idQuot |
---|
2192 | *BEWARE: the returned ideals may contain incorrectly ordered polys ! |
---|
2193 | * |
---|
2194 | */ |
---|
2195 | static ideal idInitializeQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, |
---|
2196 | BOOLEAN *addOnlyOne, int *kkmax) |
---|
2197 | { |
---|
2198 | ideal temph1; |
---|
2199 | poly p,q = NULL; |
---|
2200 | int i,l,ll,k,kkk,kmax; |
---|
2201 | int j = 0; |
---|
2202 | int k1 = idRankFreeModule(h1); |
---|
2203 | int k2 = idRankFreeModule(h2); |
---|
2204 | tHomog hom=isNotHomog; |
---|
2205 | |
---|
2206 | k=si_max(k1,k2); |
---|
2207 | if (k==0) |
---|
2208 | k = 1; |
---|
2209 | if ((k2==0) && (k>1)) *addOnlyOne = FALSE; |
---|
2210 | |
---|
2211 | intvec * weights; |
---|
2212 | hom = (tHomog)idHomModule(h1,currQuotient,&weights); |
---|
2213 | if (/**addOnlyOne &&*/ (!h1IsStb)) |
---|
2214 | temph1 = kStd(h1,currQuotient,hom,&weights,NULL); |
---|
2215 | else |
---|
2216 | temph1 = idCopy(h1); |
---|
2217 | if (weights!=NULL) delete weights; |
---|
2218 | idTest(temph1); |
---|
2219 | /*--- making a single vector from h2 ---------------------*/ |
---|
2220 | for (i=0; i<IDELEMS(h2); i++) |
---|
2221 | { |
---|
2222 | if (h2->m[i] != NULL) |
---|
2223 | { |
---|
2224 | p = pCopy(h2->m[i]); |
---|
2225 | if (k2 == 0) |
---|
2226 | pShift(&p,j*k+1); |
---|
2227 | else |
---|
2228 | pShift(&p,j*k); |
---|
2229 | q = pAdd(q,p); |
---|
2230 | j++; |
---|
2231 | } |
---|
2232 | } |
---|
2233 | *kkmax = kmax = j*k+1; |
---|
2234 | /*--- adding a monomial for the result (syzygy) ----------*/ |
---|
2235 | p = q; |
---|
2236 | while (pNext(p)!=NULL) pIter(p); |
---|
2237 | pNext(p) = pOne(); |
---|
2238 | pIter(p); |
---|
2239 | pSetComp(p,kmax); |
---|
2240 | pSetmComp(p); |
---|
2241 | /*--- constructing the big matrix ------------------------*/ |
---|
2242 | ideal h4 = idInit(16,kmax+k-1); |
---|
2243 | h4->m[0] = q; |
---|
2244 | if (k2 == 0) |
---|
2245 | { |
---|
2246 | if (k > IDELEMS(h4)) |
---|
2247 | { |
---|
2248 | pEnlargeSet(&(h4->m),IDELEMS(h4),k-IDELEMS(h4)); |
---|
2249 | IDELEMS(h4) = k; |
---|
2250 | } |
---|
2251 | for (i=1; i<k; i++) |
---|
2252 | { |
---|
2253 | if (h4->m[i-1]!=NULL) |
---|
2254 | { |
---|
2255 | p = pCopy_noCheck(h4->m[i-1]); |
---|
2256 | pShift(&p,1); |
---|
2257 | h4->m[i] = p; |
---|
2258 | } |
---|
2259 | } |
---|
2260 | } |
---|
2261 | idSkipZeroes(h4); |
---|
2262 | kkk = IDELEMS(h4); |
---|
2263 | i = IDELEMS(temph1); |
---|
2264 | for (l=0; l<i; l++) |
---|
2265 | { |
---|
2266 | if(temph1->m[l]!=NULL) |
---|
2267 | { |
---|
2268 | for (ll=0; ll<j; ll++) |
---|
2269 | { |
---|
2270 | p = pCopy(temph1->m[l]); |
---|
2271 | if (k1 == 0) |
---|
2272 | pShift(&p,ll*k+1); |
---|
2273 | else |
---|
2274 | pShift(&p,ll*k); |
---|
2275 | if (kkk >= IDELEMS(h4)) |
---|
2276 | { |
---|
2277 | pEnlargeSet(&(h4->m),IDELEMS(h4),16); |
---|
2278 | IDELEMS(h4) += 16; |
---|
2279 | } |
---|
2280 | h4->m[kkk] = p; |
---|
2281 | kkk++; |
---|
2282 | } |
---|
2283 | } |
---|
2284 | } |
---|
2285 | /*--- if h2 goes in as single vector - the h1-part is just SB ---*/ |
---|
2286 | if (*addOnlyOne) |
---|
2287 | { |
---|
2288 | idSkipZeroes(h4); |
---|
2289 | p = h4->m[0]; |
---|
2290 | for (i=0;i<IDELEMS(h4)-1;i++) |
---|
2291 | { |
---|
2292 | h4->m[i] = h4->m[i+1]; |
---|
2293 | } |
---|
2294 | h4->m[IDELEMS(h4)-1] = p; |
---|
2295 | test |= Sy_bit(OPT_SB_1); |
---|
2296 | } |
---|
2297 | idDelete(&temph1); |
---|
2298 | return h4; |
---|
2299 | } |
---|
2300 | /*2 |
---|
2301 | *computes the quotient of h1,h2 |
---|
2302 | */ |
---|
2303 | ideal idQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN resultIsIdeal) |
---|
2304 | { |
---|
2305 | // first check for special case h1:(0) |
---|
2306 | if (idIs0(h2)) |
---|
2307 | { |
---|
2308 | ideal res; |
---|
2309 | if (resultIsIdeal) |
---|
2310 | { |
---|
2311 | res = idInit(1,1); |
---|
2312 | res->m[0] = pOne(); |
---|
2313 | } |
---|
2314 | else |
---|
2315 | res = idFreeModule(h1->rank); |
---|
2316 | return res; |
---|
2317 | } |
---|
2318 | BITSET old_test=test; |
---|
2319 | int i,l,ll,k,kkk,kmax; |
---|
2320 | BOOLEAN addOnlyOne=TRUE; |
---|
2321 | tHomog hom=isNotHomog; |
---|
2322 | intvec * weights1; |
---|
2323 | |
---|
2324 | ideal s_h4 = idInitializeQuot (h1,h2,h1IsStb,&addOnlyOne,&kmax); |
---|
2325 | |
---|
2326 | hom = (tHomog)idHomModule(s_h4,currQuotient,&weights1); |
---|
2327 | |
---|
2328 | ring orig_ring=currRing; |
---|
2329 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
2330 | rSetSyzComp(kmax-1); |
---|
2331 | if (orig_ring!=syz_ring) |
---|
2332 | // s_h4 = idrMoveR_NoSort(s_h4,orig_ring); |
---|
2333 | s_h4 = idrMoveR(s_h4,orig_ring); |
---|
2334 | idTest(s_h4); |
---|
2335 | #if 0 |
---|
2336 | void ipPrint_MA0(matrix m, const char *name); |
---|
2337 | matrix m=idModule2Matrix(idCopy(s_h4)); |
---|
2338 | PrintS("start:\n"); |
---|
2339 | ipPrint_MA0(m,"Q"); |
---|
2340 | idDelete((ideal *)&m); |
---|
2341 | PrintS("last elem:");wrp(s_h4->m[IDELEMS(s_h4)-1]);PrintLn(); |
---|
2342 | #endif |
---|
2343 | ideal s_h3; |
---|
2344 | if (addOnlyOne) |
---|
2345 | { |
---|
2346 | s_h3 = kStd(s_h4,currQuotient,hom,&weights1,NULL,0/*kmax-1*/,IDELEMS(s_h4)-1); |
---|
2347 | } |
---|
2348 | else |
---|
2349 | { |
---|
2350 | s_h3 = kStd(s_h4,currQuotient,hom,&weights1,NULL,kmax-1); |
---|
2351 | } |
---|
2352 | test = old_test; |
---|
2353 | #if 0 |
---|
2354 | // only together with the above debug stuff |
---|
2355 | idSkipZeroes(s_h3); |
---|
2356 | m=idModule2Matrix(idCopy(s_h3)); |
---|
2357 | Print("result, kmax=%d:\n",kmax); |
---|
2358 | ipPrint_MA0(m,"S"); |
---|
2359 | idDelete((ideal *)&m); |
---|
2360 | #endif |
---|
2361 | idTest(s_h3); |
---|
2362 | if (weights1!=NULL) delete weights1; |
---|
2363 | idDelete(&s_h4); |
---|
2364 | |
---|
2365 | for (i=0;i<IDELEMS(s_h3);i++) |
---|
2366 | { |
---|
2367 | if ((s_h3->m[i]!=NULL) && (pGetComp(s_h3->m[i])>=kmax)) |
---|
2368 | { |
---|
2369 | if (resultIsIdeal) |
---|
2370 | pShift(&s_h3->m[i],-kmax); |
---|
2371 | else |
---|
2372 | pShift(&s_h3->m[i],-kmax+1); |
---|
2373 | } |
---|
2374 | else |
---|
2375 | pDelete(&s_h3->m[i]); |
---|
2376 | } |
---|
2377 | if (resultIsIdeal) |
---|
2378 | s_h3->rank = 1; |
---|
2379 | else |
---|
2380 | s_h3->rank = h1->rank; |
---|
2381 | if(syz_ring!=orig_ring) |
---|
2382 | { |
---|
2383 | rChangeCurrRing(orig_ring); |
---|
2384 | s_h3 = idrMoveR_NoSort(s_h3, syz_ring); |
---|
2385 | rKill(syz_ring); |
---|
2386 | } |
---|
2387 | idSkipZeroes(s_h3); |
---|
2388 | idTest(s_h3); |
---|
2389 | return s_h3; |
---|
2390 | } |
---|
2391 | |
---|
2392 | /*2 |
---|
2393 | *computes recursively all monomials of a certain degree |
---|
2394 | *in every step the actvar-th entry in the exponential |
---|
2395 | *vector is incremented and the other variables are |
---|
2396 | *computed by recursive calls of makemonoms |
---|
2397 | *if the last variable is reached, the difference to the |
---|
2398 | *degree is computed directly |
---|
2399 | *vars is the number variables |
---|
2400 | *actvar is the actual variable to handle |
---|
2401 | *deg is the degree of the monomials to compute |
---|
2402 | *monomdeg is the actual degree of the monomial in consideration |
---|
2403 | */ |
---|
2404 | static void makemonoms(int vars,int actvar,int deg,int monomdeg) |
---|
2405 | { |
---|
2406 | poly p; |
---|
2407 | int i=0; |
---|
2408 | |
---|
2409 | if ((idpowerpoint == 0) && (actvar ==1)) |
---|
2410 | { |
---|
2411 | idpower[idpowerpoint] = pOne(); |
---|
2412 | monomdeg = 0; |
---|
2413 | } |
---|
2414 | while (i<=deg) |
---|
2415 | { |
---|
2416 | if (deg == monomdeg) |
---|
2417 | { |
---|
2418 | pSetm(idpower[idpowerpoint]); |
---|
2419 | idpowerpoint++; |
---|
2420 | return; |
---|
2421 | } |
---|
2422 | if (actvar == vars) |
---|
2423 | { |
---|
2424 | pSetExp(idpower[idpowerpoint],actvar,deg-monomdeg); |
---|
2425 | pSetm(idpower[idpowerpoint]); |
---|
2426 | pTest(idpower[idpowerpoint]); |
---|
2427 | idpowerpoint++; |
---|
2428 | return; |
---|
2429 | } |
---|
2430 | else |
---|
2431 | { |
---|
2432 | p = pCopy(idpower[idpowerpoint]); |
---|
2433 | makemonoms(vars,actvar+1,deg,monomdeg); |
---|
2434 | idpower[idpowerpoint] = p; |
---|
2435 | } |
---|
2436 | monomdeg++; |
---|
2437 | pSetExp(idpower[idpowerpoint],actvar,pGetExp(idpower[idpowerpoint],actvar)+1); |
---|
2438 | pSetm(idpower[idpowerpoint]); |
---|
2439 | pTest(idpower[idpowerpoint]); |
---|
2440 | i++; |
---|
2441 | } |
---|
2442 | } |
---|
2443 | |
---|
2444 | /*2 |
---|
2445 | *returns the deg-th power of the maximal ideal of 0 |
---|
2446 | */ |
---|
2447 | ideal idMaxIdeal(int deg) |
---|
2448 | { |
---|
2449 | if (deg < 0) |
---|
2450 | { |
---|
2451 | WarnS("maxideal: power must be non-negative"); |
---|
2452 | } |
---|
2453 | if (deg < 1) |
---|
2454 | { |
---|
2455 | ideal I=idInit(1,1); |
---|
2456 | I->m[0]=pOne(); |
---|
2457 | return I; |
---|
2458 | } |
---|
2459 | if (deg == 1) |
---|
2460 | { |
---|
2461 | return idMaxIdeal(); |
---|
2462 | } |
---|
2463 | |
---|
2464 | int vars = currRing->N; |
---|
2465 | int i = binom(vars+deg-1,deg); |
---|
2466 | if (i<=0) return idInit(1,1); |
---|
2467 | ideal id=idInit(i,1); |
---|
2468 | idpower = id->m; |
---|
2469 | idpowerpoint = 0; |
---|
2470 | makemonoms(vars,1,deg,0); |
---|
2471 | idpower = NULL; |
---|
2472 | idpowerpoint = 0; |
---|
2473 | return id; |
---|
2474 | } |
---|
2475 | |
---|
2476 | /*2 |
---|
2477 | *computes recursively all generators of a certain degree |
---|
2478 | *of the ideal "givenideal" |
---|
2479 | *elms is the number elements in the given ideal |
---|
2480 | *actelm is the actual element to handle |
---|
2481 | *deg is the degree of the power to compute |
---|
2482 | *gendeg is the actual degree of the generator in consideration |
---|
2483 | */ |
---|
2484 | static void makepotence(int elms,int actelm,int deg,int gendeg) |
---|
2485 | { |
---|
2486 | poly p; |
---|
2487 | int i=0; |
---|
2488 | |
---|
2489 | if ((idpowerpoint == 0) && (actelm ==1)) |
---|
2490 | { |
---|
2491 | idpower[idpowerpoint] = pOne(); |
---|
2492 | gendeg = 0; |
---|
2493 | } |
---|
2494 | while (i<=deg) |
---|
2495 | { |
---|
2496 | if (deg == gendeg) |
---|
2497 | { |
---|
2498 | idpowerpoint++; |
---|
2499 | return; |
---|
2500 | } |
---|
2501 | if (actelm == elms) |
---|
2502 | { |
---|
2503 | p=pPower(pCopy(givenideal[actelm-1]),deg-gendeg); |
---|
2504 | idpower[idpowerpoint]=pMult(idpower[idpowerpoint],p); |
---|
2505 | idpowerpoint++; |
---|
2506 | return; |
---|
2507 | } |
---|
2508 | else |
---|
2509 | { |
---|
2510 | p = pCopy(idpower[idpowerpoint]); |
---|
2511 | makepotence(elms,actelm+1,deg,gendeg); |
---|
2512 | idpower[idpowerpoint] = p; |
---|
2513 | } |
---|
2514 | gendeg++; |
---|
2515 | idpower[idpowerpoint]=pMult(idpower[idpowerpoint],pCopy(givenideal[actelm-1])); |
---|
2516 | i++; |
---|
2517 | } |
---|
2518 | } |
---|
2519 | |
---|
2520 | /*2 |
---|
2521 | *returns the deg-th power of the ideal gid |
---|
2522 | */ |
---|
2523 | //ideal idPower(ideal gid,int deg) |
---|
2524 | //{ |
---|
2525 | // int i; |
---|
2526 | // ideal id; |
---|
2527 | // |
---|
2528 | // if (deg < 1) deg = 1; |
---|
2529 | // i = binom(IDELEMS(gid)+deg-1,deg); |
---|
2530 | // id=idInit(i,1); |
---|
2531 | // idpower = id->m; |
---|
2532 | // givenideal = gid->m; |
---|
2533 | // idpowerpoint = 0; |
---|
2534 | // makepotence(IDELEMS(gid),1,deg,0); |
---|
2535 | // idpower = NULL; |
---|
2536 | // givenideal = NULL; |
---|
2537 | // idpowerpoint = 0; |
---|
2538 | // return id; |
---|
2539 | //} |
---|
2540 | static void idNextPotence(ideal given, ideal result, |
---|
2541 | int begin, int end, int deg, int restdeg, poly ap) |
---|
2542 | { |
---|
2543 | poly p; |
---|
2544 | int i; |
---|
2545 | |
---|
2546 | p = pPower(pCopy(given->m[begin]),restdeg); |
---|
2547 | i = result->nrows; |
---|
2548 | result->m[i] = pMult(pCopy(ap),p); |
---|
2549 | //PrintS("."); |
---|
2550 | (result->nrows)++; |
---|
2551 | if (result->nrows >= IDELEMS(result)) |
---|
2552 | { |
---|
2553 | pEnlargeSet(&(result->m),IDELEMS(result),16); |
---|
2554 | IDELEMS(result) += 16; |
---|
2555 | } |
---|
2556 | if (begin == end) return; |
---|
2557 | for (i=restdeg-1;i>0;i--) |
---|
2558 | { |
---|
2559 | p = pPower(pCopy(given->m[begin]),i); |
---|
2560 | p = pMult(pCopy(ap),p); |
---|
2561 | idNextPotence(given, result, begin+1, end, deg, restdeg-i, p); |
---|
2562 | pDelete(&p); |
---|
2563 | } |
---|
2564 | idNextPotence(given, result, begin+1, end, deg, restdeg, ap); |
---|
2565 | } |
---|
2566 | |
---|
2567 | ideal idPower(ideal given,int exp) |
---|
2568 | { |
---|
2569 | ideal result,temp; |
---|
2570 | poly p1; |
---|
2571 | int i; |
---|
2572 | |
---|
2573 | if (idIs0(given)) return idInit(1,1); |
---|
2574 | temp = idCopy(given); |
---|
2575 | idSkipZeroes(temp); |
---|
2576 | i = binom(IDELEMS(temp)+exp-1,exp); |
---|
2577 | result = idInit(i,1); |
---|
2578 | result->nrows = 0; |
---|
2579 | //Print("ideal contains %d elements\n",i); |
---|
2580 | p1=pOne(); |
---|
2581 | idNextPotence(temp,result,0,IDELEMS(temp)-1,exp,exp,p1); |
---|
2582 | pDelete(&p1); |
---|
2583 | idDelete(&temp); |
---|
2584 | result->nrows = 1; |
---|
2585 | idDelEquals(result); |
---|
2586 | idSkipZeroes(result); |
---|
2587 | return result; |
---|
2588 | } |
---|
2589 | |
---|
2590 | /*2 |
---|
2591 | * eliminate delVar (product of vars) in h1 |
---|
2592 | */ |
---|
2593 | ideal idElimination (ideal h1,poly delVar,intvec *hilb) |
---|
2594 | { |
---|
2595 | int i,j=0,k,l; |
---|
2596 | ideal h,hh, h3; |
---|
2597 | int *ord,*block0,*block1; |
---|
2598 | int ordersize=2; |
---|
2599 | int **wv; |
---|
2600 | tHomog hom; |
---|
2601 | intvec * w; |
---|
2602 | ring tmpR; |
---|
2603 | ring origR = currRing; |
---|
2604 | |
---|
2605 | if (delVar==NULL) |
---|
2606 | { |
---|
2607 | return idCopy(h1); |
---|
2608 | } |
---|
2609 | if ((currQuotient!=NULL) && rIsPluralRing(origR)) |
---|
2610 | { |
---|
2611 | WerrorS("cannot eliminate in a qring"); |
---|
2612 | return NULL; |
---|
2613 | } |
---|
2614 | if (idIs0(h1)) return idInit(1,h1->rank); |
---|
2615 | #ifdef HAVE_PLURAL |
---|
2616 | if (rIsPluralRing(origR)) |
---|
2617 | /* in the NC case, we have to check the admissibility of */ |
---|
2618 | /* the subalgebra to be intersected with */ |
---|
2619 | { |
---|
2620 | if ((ncRingType(origR) != nc_skew) && (ncRingType(origR) != nc_exterior)) /* in (quasi)-commutative algebras every subalgebra is admissible */ |
---|
2621 | { |
---|
2622 | if (nc_CheckSubalgebra(delVar,origR)) |
---|
2623 | { |
---|
2624 | WerrorS("no elimination is possible: subalgebra is not admissible"); |
---|
2625 | return NULL; |
---|
2626 | } |
---|
2627 | } |
---|
2628 | } |
---|
2629 | #endif |
---|
2630 | hom=(tHomog)idHomModule(h1,NULL,&w); //sets w to weight vector or NULL |
---|
2631 | h3=idInit(16,h1->rank); |
---|
2632 | for (k=0;; k++) |
---|
2633 | { |
---|
2634 | if (origR->order[k]!=0) ordersize++; |
---|
2635 | else break; |
---|
2636 | } |
---|
2637 | #if 0 |
---|
2638 | if (rIsPluralRing(origR)) // we have too keep the odering: it may be needed |
---|
2639 | // for G-algebra |
---|
2640 | { |
---|
2641 | for (k=0;k<ordersize-1; k++) |
---|
2642 | { |
---|
2643 | block0[k+1] = origR->block0[k]; |
---|
2644 | block1[k+1] = origR->block1[k]; |
---|
2645 | ord[k+1] = origR->order[k]; |
---|
2646 | if (origR->wvhdl[k]!=NULL) wv[k+1] = (int*) omMemDup(origR->wvhdl[k]); |
---|
2647 | } |
---|
2648 | } |
---|
2649 | else |
---|
2650 | { |
---|
2651 | block0[1] = 1; |
---|
2652 | block1[1] = pVariables; |
---|
2653 | if (origR->OrdSgn==1) ord[1] = ringorder_wp; |
---|
2654 | else ord[1] = ringorder_ws; |
---|
2655 | wv[1]=(int*)omAlloc0(pVariables*sizeof(int)); |
---|
2656 | double wNsqr = (double)2.0 / (double)pVariables; |
---|
2657 | wFunctional = wFunctionalBuch; |
---|
2658 | int *x= (int * )omAlloc(2 * (pVariables + 1) * sizeof(int)); |
---|
2659 | int sl=IDELEMS(h1) - 1; |
---|
2660 | wCall(h1->m, sl, x, wNsqr); |
---|
2661 | for (sl = pVariables; sl!=0; sl--) |
---|
2662 | wv[1][sl-1] = x[sl + pVariables + 1]; |
---|
2663 | omFreeSize((ADDRESS)x, 2 * (pVariables + 1) * sizeof(int)); |
---|
2664 | |
---|
2665 | ord[2]=ringorder_C; |
---|
2666 | ord[3]=0; |
---|
2667 | } |
---|
2668 | #else |
---|
2669 | #endif |
---|
2670 | if ((hom==TRUE) && (origR->OrdSgn==1) && (!rIsPluralRing(origR))) |
---|
2671 | { |
---|
2672 | #if 1 |
---|
2673 | // we change to an ordering: |
---|
2674 | // aa(1,1,1,...,0,0,0),wp(...),C |
---|
2675 | // this seems to be better than version 2 below, |
---|
2676 | // according to Tst/../elimiate_[3568].tat (- 17 %) |
---|
2677 | ord=(int*)omAlloc0(4*sizeof(int)); |
---|
2678 | block0=(int*)omAlloc0(4*sizeof(int)); |
---|
2679 | block1=(int*)omAlloc0(4*sizeof(int)); |
---|
2680 | wv=(int**) omAlloc0(4*sizeof(int**)); |
---|
2681 | block0[0] = block0[1] = 1; |
---|
2682 | block1[0] = block1[1] = rVar(origR); |
---|
2683 | wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
2684 | // use this special ordering: like ringorder_a, except that pFDeg, pWeights |
---|
2685 | // ignore it |
---|
2686 | ord[0] = ringorder_aa; |
---|
2687 | for (j=0;j<rVar(origR);j++) |
---|
2688 | if (pGetExp(delVar,j+1)!=0) wv[0][j]=1; |
---|
2689 | BOOLEAN wp=FALSE; |
---|
2690 | for (j=0;j<rVar(origR);j++) |
---|
2691 | if (pWeight(j+1,origR)!=1) { wp=TRUE;break; } |
---|
2692 | if (wp) |
---|
2693 | { |
---|
2694 | wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
2695 | for (j=0;j<rVar(origR);j++) |
---|
2696 | wv[1][j]=pWeight(j+1,origR); |
---|
2697 | ord[1] = ringorder_wp; |
---|
2698 | } |
---|
2699 | else |
---|
2700 | ord[1] = ringorder_dp; |
---|
2701 | #else |
---|
2702 | // we change to an ordering: |
---|
2703 | // a(w1,...wn),wp(1,...0.....),C |
---|
2704 | ord=(int*)omAlloc0(4*sizeof(int)); |
---|
2705 | block0=(int*)omAlloc0(4*sizeof(int)); |
---|
2706 | block1=(int*)omAlloc0(4*sizeof(int)); |
---|
2707 | wv=(int**) omAlloc0(4*sizeof(int**)); |
---|
2708 | block0[0] = block0[1] = 1; |
---|
2709 | block1[0] = block1[1] = rVar(origR); |
---|
2710 | wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
2711 | wv[1]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
2712 | ord[0] = ringorder_a; |
---|
2713 | for (j=0;j<rVar(origR);j++) |
---|
2714 | wv[0][j]=pWeight(j+1,origR); |
---|
2715 | ord[1] = ringorder_wp; |
---|
2716 | for (j=0;j<rVar(origR);j++) |
---|
2717 | if (pGetExp(delVar,j+1)!=0) wv[1][j]=1; |
---|
2718 | #endif |
---|
2719 | ord[2] = ringorder_C; |
---|
2720 | ord[3] = 0; |
---|
2721 | } |
---|
2722 | else |
---|
2723 | { |
---|
2724 | // we change to an ordering: |
---|
2725 | // aa(....),orig_ordering |
---|
2726 | ord=(int*)omAlloc0(ordersize*sizeof(int)); |
---|
2727 | block0=(int*)omAlloc0(ordersize*sizeof(int)); |
---|
2728 | block1=(int*)omAlloc0(ordersize*sizeof(int)); |
---|
2729 | wv=(int**) omAlloc0(ordersize*sizeof(int**)); |
---|
2730 | for (k=0;k<ordersize-1; k++) |
---|
2731 | { |
---|
2732 | block0[k+1] = origR->block0[k]; |
---|
2733 | block1[k+1] = origR->block1[k]; |
---|
2734 | ord[k+1] = origR->order[k]; |
---|
2735 | if (origR->wvhdl[k]!=NULL) wv[k+1] = (int*) omMemDup(origR->wvhdl[k]); |
---|
2736 | } |
---|
2737 | block0[0] = 1; |
---|
2738 | block1[0] = rVar(origR); |
---|
2739 | wv[0]=(int*)omAlloc0((rVar(origR) + 1)*sizeof(int)); |
---|
2740 | for (j=0;j<rVar(origR);j++) |
---|
2741 | if (pGetExp(delVar,j+1)!=0) wv[0][j]=1; |
---|
2742 | // use this special ordering: like ringorder_a, except that pFDeg, pWeights |
---|
2743 | // ignore it |
---|
2744 | ord[0] = ringorder_aa; |
---|
2745 | } |
---|
2746 | // fill in tmp ring to get back the data later on |
---|
2747 | tmpR = rCopy0(origR,FALSE,FALSE); // qring==NULL |
---|
2748 | //rUnComplete(tmpR); |
---|
2749 | tmpR->p_Procs=NULL; |
---|
2750 | tmpR->order = ord; |
---|
2751 | tmpR->block0 = block0; |
---|
2752 | tmpR->block1 = block1; |
---|
2753 | tmpR->wvhdl = wv; |
---|
2754 | rComplete(tmpR, 1); |
---|
2755 | |
---|
2756 | #ifdef HAVE_PLURAL |
---|
2757 | /* update nc structure on tmpR */ |
---|
2758 | if (rIsPluralRing(origR)) |
---|
2759 | { |
---|
2760 | if ( nc_rComplete(origR, tmpR, false) ) // no quotient ideal! |
---|
2761 | { |
---|
2762 | Werror("no elimination is possible: ordering condition is violated"); |
---|
2763 | // cleanup |
---|
2764 | rDelete(tmpR); |
---|
2765 | if (w!=NULL) |
---|
2766 | delete w; |
---|
2767 | return NULL; |
---|
2768 | } |
---|
2769 | } |
---|
2770 | #endif |
---|
2771 | // change into the new ring |
---|
2772 | //pChangeRing(pVariables,currRing->OrdSgn,ord,block0,block1,wv); |
---|
2773 | rChangeCurrRing(tmpR); |
---|
2774 | |
---|
2775 | //h = idInit(IDELEMS(h1),h1->rank); |
---|
2776 | // fetch data from the old ring |
---|
2777 | //for (k=0;k<IDELEMS(h1);k++) h->m[k] = prCopyR( h1->m[k], origR); |
---|
2778 | h=idrCopyR(h1,origR,currRing); |
---|
2779 | if (origR->qideal!=NULL) |
---|
2780 | { |
---|
2781 | WarnS("eliminate in q-ring: experimental"); |
---|
2782 | ideal q=idrCopyR(origR->qideal,origR,currRing); |
---|
2783 | ideal s=idSimpleAdd(h,q); |
---|
2784 | idDelete(&h); |
---|
2785 | idDelete(&q); |
---|
2786 | h=s; |
---|
2787 | } |
---|
2788 | // compute kStd |
---|
2789 | #if 1 |
---|
2790 | //rWrite(tmpR);PrintLn(); |
---|
2791 | BITSET save=test; |
---|
2792 | //test |=1; |
---|
2793 | //Print("h: %d gen, rk=%d\n",IDELEMS(h),h->rank); |
---|
2794 | //extern char * showOption(); |
---|
2795 | //Print("%s\n",showOption()); |
---|
2796 | hh = kStd(h,NULL,hom,&w,hilb); |
---|
2797 | test=save; |
---|
2798 | idDelete(&h); |
---|
2799 | #else |
---|
2800 | extern ideal kGroebner(ideal F, ideal Q); |
---|
2801 | hh=kGroebner(h,NULL); |
---|
2802 | #endif |
---|
2803 | // go back to the original ring |
---|
2804 | rChangeCurrRing(origR); |
---|
2805 | i = IDELEMS(hh)-1; |
---|
2806 | while ((i >= 0) && (hh->m[i] == NULL)) i--; |
---|
2807 | j = -1; |
---|
2808 | // fetch data from temp ring |
---|
2809 | for (k=0; k<=i; k++) |
---|
2810 | { |
---|
2811 | l=pVariables; |
---|
2812 | while ((l>0) && (p_GetExp( hh->m[k],l,tmpR)*pGetExp(delVar,l)==0)) l--; |
---|
2813 | if (l==0) |
---|
2814 | { |
---|
2815 | j++; |
---|
2816 | if (j >= IDELEMS(h3)) |
---|
2817 | { |
---|
2818 | pEnlargeSet(&(h3->m),IDELEMS(h3),16); |
---|
2819 | IDELEMS(h3) += 16; |
---|
2820 | } |
---|
2821 | h3->m[j] = prMoveR( hh->m[k], tmpR); |
---|
2822 | hh->m[k] = NULL; |
---|
2823 | } |
---|
2824 | } |
---|
2825 | id_Delete(&hh, tmpR); |
---|
2826 | idSkipZeroes(h3); |
---|
2827 | rDelete(tmpR); |
---|
2828 | if (w!=NULL) |
---|
2829 | delete w; |
---|
2830 | return h3; |
---|
2831 | } |
---|
2832 | |
---|
2833 | /*2 |
---|
2834 | * compute the which-th ar-minor of the matrix a |
---|
2835 | */ |
---|
2836 | poly idMinor(matrix a, int ar, unsigned long which, ideal R) |
---|
2837 | { |
---|
2838 | int i,j,k,size; |
---|
2839 | unsigned long curr; |
---|
2840 | int *rowchoise,*colchoise; |
---|
2841 | BOOLEAN rowch,colch; |
---|
2842 | ideal result; |
---|
2843 | matrix tmp; |
---|
2844 | poly p,q; |
---|
2845 | |
---|
2846 | i = binom(a->rows(),ar); |
---|
2847 | j = binom(a->cols(),ar); |
---|
2848 | |
---|
2849 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
2850 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
2851 | if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
2852 | else size=i*j; |
---|
2853 | result=idInit(size,1); |
---|
2854 | tmp=mpNew(ar,ar); |
---|
2855 | k = 0; /* the index in result*/ |
---|
2856 | curr = 0; /* index of current minor */ |
---|
2857 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
2858 | while (!rowch) |
---|
2859 | { |
---|
2860 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
2861 | while (!colch) |
---|
2862 | { |
---|
2863 | if (curr == which) |
---|
2864 | { |
---|
2865 | for (i=1; i<=ar; i++) |
---|
2866 | { |
---|
2867 | for (j=1; j<=ar; j++) |
---|
2868 | { |
---|
2869 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
2870 | } |
---|
2871 | } |
---|
2872 | p = mpDetBareiss(tmp); |
---|
2873 | if (p!=NULL) |
---|
2874 | { |
---|
2875 | if (R!=NULL) |
---|
2876 | { |
---|
2877 | q = p; |
---|
2878 | p = kNF(R,currQuotient,q); |
---|
2879 | pDelete(&q); |
---|
2880 | } |
---|
2881 | /*delete the matrix tmp*/ |
---|
2882 | for (i=1; i<=ar; i++) |
---|
2883 | { |
---|
2884 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
2885 | } |
---|
2886 | idDelete((ideal*)&tmp); |
---|
2887 | omFreeSize((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
2888 | omFreeSize((ADDRESS)colchoise,ar*sizeof(int)); |
---|
2889 | return (p); |
---|
2890 | } |
---|
2891 | } |
---|
2892 | curr++; |
---|
2893 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
2894 | } |
---|
2895 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
2896 | } |
---|
2897 | return (poly) 1; |
---|
2898 | } |
---|
2899 | |
---|
2900 | #ifdef WITH_OLD_MINOR |
---|
2901 | /*2 |
---|
2902 | * compute all ar-minors of the matrix a |
---|
2903 | */ |
---|
2904 | ideal idMinors(matrix a, int ar, ideal R) |
---|
2905 | { |
---|
2906 | int i,j,k,size; |
---|
2907 | int *rowchoise,*colchoise; |
---|
2908 | BOOLEAN rowch,colch; |
---|
2909 | ideal result; |
---|
2910 | matrix tmp; |
---|
2911 | poly p,q; |
---|
2912 | |
---|
2913 | i = binom(a->rows(),ar); |
---|
2914 | j = binom(a->cols(),ar); |
---|
2915 | |
---|
2916 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
2917 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
2918 | if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
2919 | else size=i*j; |
---|
2920 | result=idInit(size,1); |
---|
2921 | tmp=mpNew(ar,ar); |
---|
2922 | k = 0; /* the index in result*/ |
---|
2923 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
2924 | while (!rowch) |
---|
2925 | { |
---|
2926 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
2927 | while (!colch) |
---|
2928 | { |
---|
2929 | for (i=1; i<=ar; i++) |
---|
2930 | { |
---|
2931 | for (j=1; j<=ar; j++) |
---|
2932 | { |
---|
2933 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
2934 | } |
---|
2935 | } |
---|
2936 | p = mpDetBareiss(tmp); |
---|
2937 | if (p!=NULL) |
---|
2938 | { |
---|
2939 | if (R!=NULL) |
---|
2940 | { |
---|
2941 | q = p; |
---|
2942 | p = kNF(R,currQuotient,q); |
---|
2943 | pDelete(&q); |
---|
2944 | } |
---|
2945 | if (p!=NULL) |
---|
2946 | { |
---|
2947 | if (k>=size) |
---|
2948 | { |
---|
2949 | pEnlargeSet(&result->m,size,32); |
---|
2950 | size += 32; |
---|
2951 | } |
---|
2952 | result->m[k] = p; |
---|
2953 | k++; |
---|
2954 | } |
---|
2955 | } |
---|
2956 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
2957 | } |
---|
2958 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
2959 | } |
---|
2960 | /*delete the matrix tmp*/ |
---|
2961 | for (i=1; i<=ar; i++) |
---|
2962 | { |
---|
2963 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
2964 | } |
---|
2965 | idDelete((ideal*)&tmp); |
---|
2966 | if (k==0) |
---|
2967 | { |
---|
2968 | k=1; |
---|
2969 | result->m[0]=NULL; |
---|
2970 | } |
---|
2971 | omFreeSize((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
2972 | omFreeSize((ADDRESS)colchoise,ar*sizeof(int)); |
---|
2973 | pEnlargeSet(&result->m,size,k-size); |
---|
2974 | IDELEMS(result) = k; |
---|
2975 | return (result); |
---|
2976 | } |
---|
2977 | #else |
---|
2978 | /*2 |
---|
2979 | * compute all ar-minors of the matrix a |
---|
2980 | * the caller of mpRecMin |
---|
2981 | * the elements of the result are not in R (if R!=NULL) |
---|
2982 | */ |
---|
2983 | ideal idMinors(matrix a, int ar, ideal R) |
---|
2984 | { |
---|
2985 | int elems=0; |
---|
2986 | int r=a->nrows,c=a->ncols; |
---|
2987 | int i; |
---|
2988 | matrix b; |
---|
2989 | ideal result,h; |
---|
2990 | ring origR; |
---|
2991 | ring tmpR; |
---|
2992 | long bound; |
---|
2993 | |
---|
2994 | if((ar<=0) || (ar>r) || (ar>c)) |
---|
2995 | { |
---|
2996 | Werror("%d-th minor, matrix is %dx%d",ar,r,c); |
---|
2997 | return NULL; |
---|
2998 | } |
---|
2999 | h = idMatrix2Module(mpCopy(a)); |
---|
3000 | bound = smExpBound(h,c,r,ar); |
---|
3001 | idDelete(&h); |
---|
3002 | tmpR=smRingChange(&origR,bound); |
---|
3003 | b = mpNew(r,c); |
---|
3004 | for (i=r*c-1;i>=0;i--) |
---|
3005 | { |
---|
3006 | if (a->m[i]) |
---|
3007 | b->m[i] = prCopyR(a->m[i],origR); |
---|
3008 | } |
---|
3009 | if (R!=NULL) |
---|
3010 | { |
---|
3011 | R = idrCopyR(R,origR); |
---|
3012 | //if (ar>1) // otherwise done in mpMinorToResult |
---|
3013 | //{ |
---|
3014 | // matrix bb=(matrix)kNF(R,currQuotient,(ideal)b); |
---|
3015 | // bb->rank=b->rank; bb->nrows=b->nrows; bb->ncols=b->ncols; |
---|
3016 | // idDelete((ideal*)&b); b=bb; |
---|
3017 | //} |
---|
3018 | } |
---|
3019 | result=idInit(32,1); |
---|
3020 | if(ar>1) mpRecMin(ar-1,result,elems,b,r,c,NULL,R); |
---|
3021 | else mpMinorToResult(result,elems,b,r,c,R); |
---|
3022 | idDelete((ideal *)&b); |
---|
3023 | if (R!=NULL) idDelete(&R); |
---|
3024 | idSkipZeroes(result); |
---|
3025 | rChangeCurrRing(origR); |
---|
3026 | result = idrMoveR(result,tmpR); |
---|
3027 | smKillModifiedRing(tmpR); |
---|
3028 | idTest(result); |
---|
3029 | return result; |
---|
3030 | } |
---|
3031 | #endif |
---|
3032 | |
---|
3033 | /*2 |
---|
3034 | *skips all zeroes and double elements, searches also for units |
---|
3035 | */ |
---|
3036 | void idCompactify(ideal id) |
---|
3037 | { |
---|
3038 | int i,j; |
---|
3039 | BOOLEAN b=FALSE; |
---|
3040 | |
---|
3041 | i = IDELEMS(id)-1; |
---|
3042 | while ((! b) && (i>=0)) |
---|
3043 | { |
---|
3044 | b=pIsUnit(id->m[i]); |
---|
3045 | i--; |
---|
3046 | } |
---|
3047 | if (b) |
---|
3048 | { |
---|
3049 | for(i=IDELEMS(id)-1;i>=0;i--) pDelete(&id->m[i]); |
---|
3050 | id->m[0]=pOne(); |
---|
3051 | } |
---|
3052 | else |
---|
3053 | { |
---|
3054 | idDelMultiples(id); |
---|
3055 | } |
---|
3056 | idSkipZeroes(id); |
---|
3057 | } |
---|
3058 | |
---|
3059 | /*2 |
---|
3060 | *returns TRUE if id1 is a submodule of id2 |
---|
3061 | */ |
---|
3062 | BOOLEAN idIsSubModule(ideal id1,ideal id2) |
---|
3063 | { |
---|
3064 | int i; |
---|
3065 | poly p; |
---|
3066 | |
---|
3067 | if (idIs0(id1)) return TRUE; |
---|
3068 | for (i=0;i<IDELEMS(id1);i++) |
---|
3069 | { |
---|
3070 | if (id1->m[i] != NULL) |
---|
3071 | { |
---|
3072 | p = kNF(id2,currQuotient,id1->m[i]); |
---|
3073 | if (p != NULL) |
---|
3074 | { |
---|
3075 | pDelete(&p); |
---|
3076 | return FALSE; |
---|
3077 | } |
---|
3078 | } |
---|
3079 | } |
---|
3080 | return TRUE; |
---|
3081 | } |
---|
3082 | |
---|
3083 | /*2 |
---|
3084 | * returns the ideals of initial terms |
---|
3085 | */ |
---|
3086 | ideal idHead(ideal h) |
---|
3087 | { |
---|
3088 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
3089 | int i; |
---|
3090 | |
---|
3091 | for (i=IDELEMS(h)-1;i>=0; i--) |
---|
3092 | { |
---|
3093 | if (h->m[i]!=NULL) m->m[i]=pHead(h->m[i]); |
---|
3094 | } |
---|
3095 | return m; |
---|
3096 | } |
---|
3097 | |
---|
3098 | ideal idHomogen(ideal h, int varnum) |
---|
3099 | { |
---|
3100 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
3101 | int i; |
---|
3102 | |
---|
3103 | for (i=IDELEMS(h)-1;i>=0; i--) |
---|
3104 | { |
---|
3105 | m->m[i]=pHomogen(h->m[i],varnum); |
---|
3106 | } |
---|
3107 | return m; |
---|
3108 | } |
---|
3109 | |
---|
3110 | /*------------------type conversions----------------*/ |
---|
3111 | ideal idVec2Ideal(poly vec) |
---|
3112 | { |
---|
3113 | ideal result=idInit(1,1); |
---|
3114 | omFree((ADDRESS)result->m); |
---|
3115 | result->m=NULL; // remove later |
---|
3116 | pVec2Polys(vec, &(result->m), &(IDELEMS(result))); |
---|
3117 | return result; |
---|
3118 | } |
---|
3119 | |
---|
3120 | #define NEW_STUFF |
---|
3121 | #ifndef NEW_STUFF |
---|
3122 | // converts mat to module, destroys mat |
---|
3123 | ideal idMatrix2Module(matrix mat) |
---|
3124 | { |
---|
3125 | int mc=MATCOLS(mat); |
---|
3126 | int mr=MATROWS(mat); |
---|
3127 | ideal result = idInit(si_max(mc,1),si_max(mr,1)); |
---|
3128 | int i,j; |
---|
3129 | poly h; |
---|
3130 | |
---|
3131 | for(j=0;j<mc /*MATCOLS(mat)*/;j++) /* j is also index in result->m */ |
---|
3132 | { |
---|
3133 | for (i=1;i<=mr /*MATROWS(mat)*/;i++) |
---|
3134 | { |
---|
3135 | h = MATELEM(mat,i,j+1); |
---|
3136 | if (h!=NULL) |
---|
3137 | { |
---|
3138 | MATELEM(mat,i,j+1)=NULL; |
---|
3139 | pSetCompP(h,i); |
---|
3140 | result->m[j] = pAdd(result->m[j],h); |
---|
3141 | } |
---|
3142 | } |
---|
3143 | } |
---|
3144 | // obachman: need to clean this up |
---|
3145 | idDelete((ideal*) &mat); |
---|
3146 | return result; |
---|
3147 | } |
---|
3148 | #else |
---|
3149 | |
---|
3150 | #include <kernel/sbuckets.h> |
---|
3151 | |
---|
3152 | // converts mat to module, destroys mat |
---|
3153 | ideal idMatrix2Module(matrix mat) |
---|
3154 | { |
---|
3155 | int mc=MATCOLS(mat); |
---|
3156 | int mr=MATROWS(mat); |
---|
3157 | ideal result = idInit(si_max(mc,1),si_max(mr,1)); |
---|
3158 | int i,j, l; |
---|
3159 | poly h; |
---|
3160 | poly p; |
---|
3161 | sBucket_pt bucket = sBucketCreate(currRing); |
---|
3162 | |
---|
3163 | for(j=0;j<mc /*MATCOLS(mat)*/;j++) /* j is also index in result->m */ |
---|
3164 | { |
---|
3165 | for (i=1;i<=mr /*MATROWS(mat)*/;i++) |
---|
3166 | { |
---|
3167 | h = MATELEM(mat,i,j+1); |
---|
3168 | if (h!=NULL) |
---|
3169 | { |
---|
3170 | l=pLength(h); |
---|
3171 | MATELEM(mat,i,j+1)=NULL; |
---|
3172 | p_SetCompP(h,i, currRing); |
---|
3173 | sBucket_Merge_p(bucket, h, l); |
---|
3174 | } |
---|
3175 | } |
---|
3176 | sBucketClearMerge(bucket, &(result->m[j]), &l); |
---|
3177 | } |
---|
3178 | sBucketDestroy(&bucket); |
---|
3179 | |
---|
3180 | // obachman: need to clean this up |
---|
3181 | idDelete((ideal*) &mat); |
---|
3182 | return result; |
---|
3183 | } |
---|
3184 | #endif |
---|
3185 | |
---|
3186 | /*2 |
---|
3187 | * converts a module into a matrix, destroyes the input |
---|
3188 | */ |
---|
3189 | matrix idModule2Matrix(ideal mod) |
---|
3190 | { |
---|
3191 | matrix result = mpNew(mod->rank,IDELEMS(mod)); |
---|
3192 | int i,cp; |
---|
3193 | poly p,h; |
---|
3194 | |
---|
3195 | for(i=0;i<IDELEMS(mod);i++) |
---|
3196 | { |
---|
3197 | p=pReverse(mod->m[i]); |
---|
3198 | mod->m[i]=NULL; |
---|
3199 | while (p!=NULL) |
---|
3200 | { |
---|
3201 | h=p; |
---|
3202 | pIter(p); |
---|
3203 | pNext(h)=NULL; |
---|
3204 | // cp = si_max(1,pGetComp(h)); // if used for ideals too |
---|
3205 | cp = pGetComp(h); |
---|
3206 | pSetComp(h,0); |
---|
3207 | pSetmComp(h); |
---|
3208 | #ifdef TEST |
---|
3209 | if (cp>mod->rank) |
---|
3210 | { |
---|
3211 | Print("## inv. rank %ld -> %d\n",mod->rank,cp); |
---|
3212 | int k,l,o=mod->rank; |
---|
3213 | mod->rank=cp; |
---|
3214 | matrix d=mpNew(mod->rank,IDELEMS(mod)); |
---|
3215 | for (l=1; l<=o; l++) |
---|
3216 | { |
---|
3217 | for (k=1; k<=IDELEMS(mod); k++) |
---|
3218 | { |
---|
3219 | MATELEM(d,l,k)=MATELEM(result,l,k); |
---|
3220 | MATELEM(result,l,k)=NULL; |
---|
3221 | } |
---|
3222 | } |
---|
3223 | idDelete((ideal *)&result); |
---|
3224 | result=d; |
---|
3225 | } |
---|
3226 | #endif |
---|
3227 | MATELEM(result,cp,i+1) = pAdd(MATELEM(result,cp,i+1),h); |
---|
3228 | } |
---|
3229 | } |
---|
3230 | // obachman 10/99: added the following line, otherwise memory leack! |
---|
3231 | idDelete(&mod); |
---|
3232 | return result; |
---|
3233 | } |
---|
3234 | |
---|
3235 | matrix idModule2formatedMatrix(ideal mod,int rows, int cols) |
---|
3236 | { |
---|
3237 | matrix result = mpNew(rows,cols); |
---|
3238 | int i,cp,r=idRankFreeModule(mod),c=IDELEMS(mod); |
---|
3239 | poly p,h; |
---|
3240 | |
---|
3241 | if (r>rows) r = rows; |
---|
3242 | if (c>cols) c = cols; |
---|
3243 | for(i=0;i<c;i++) |
---|
3244 | { |
---|
3245 | p=pReverse(mod->m[i]); |
---|
3246 | mod->m[i]=NULL; |
---|
3247 | while (p!=NULL) |
---|
3248 | { |
---|
3249 | h=p; |
---|
3250 | pIter(p); |
---|
3251 | pNext(h)=NULL; |
---|
3252 | cp = pGetComp(h); |
---|
3253 | if (cp<=r) |
---|
3254 | { |
---|
3255 | pSetComp(h,0); |
---|
3256 | pSetmComp(h); |
---|
3257 | MATELEM(result,cp,i+1) = pAdd(MATELEM(result,cp,i+1),h); |
---|
3258 | } |
---|
3259 | else |
---|
3260 | pDelete(&h); |
---|
3261 | } |
---|
3262 | } |
---|
3263 | idDelete(&mod); |
---|
3264 | return result; |
---|
3265 | } |
---|
3266 | |
---|
3267 | /*2 |
---|
3268 | * substitute the n-th variable by the monomial e in id |
---|
3269 | * destroy id |
---|
3270 | */ |
---|
3271 | ideal idSubst(ideal id, int n, poly e) |
---|
3272 | { |
---|
3273 | int k=MATROWS((matrix)id)*MATCOLS((matrix)id); |
---|
3274 | ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id)); |
---|
3275 | |
---|
3276 | res->rank = id->rank; |
---|
3277 | for(k--;k>=0;k--) |
---|
3278 | { |
---|
3279 | res->m[k]=pSubst(id->m[k],n,e); |
---|
3280 | id->m[k]=NULL; |
---|
3281 | } |
---|
3282 | idDelete(&id); |
---|
3283 | return res; |
---|
3284 | } |
---|
3285 | |
---|
3286 | BOOLEAN idHomModule(ideal m, ideal Q, intvec **w) |
---|
3287 | { |
---|
3288 | if (w!=NULL) *w=NULL; |
---|
3289 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) return FALSE; |
---|
3290 | if (idIs0(m)) |
---|
3291 | { |
---|
3292 | if (w!=NULL) (*w)=new intvec(m->rank); |
---|
3293 | return TRUE; |
---|
3294 | } |
---|
3295 | |
---|
3296 | long cmax=1,order=0,ord,* diff,diffmin=32000; |
---|
3297 | int *iscom; |
---|
3298 | int i,j; |
---|
3299 | poly p=NULL; |
---|
3300 | pFDegProc d; |
---|
3301 | if (pLexOrder && (currRing->order[0]==ringorder_lp)) |
---|
3302 | d=p_Totaldegree; |
---|
3303 | else |
---|
3304 | d=pFDeg; |
---|
3305 | int length=IDELEMS(m); |
---|
3306 | polyset P=m->m; |
---|
3307 | polyset F=(polyset)omAlloc(length*sizeof(poly)); |
---|
3308 | for (i=length-1;i>=0;i--) |
---|
3309 | { |
---|
3310 | p=F[i]=P[i]; |
---|
3311 | cmax=si_max(cmax,(long)pMaxComp(p)); |
---|
3312 | } |
---|
3313 | cmax++; |
---|
3314 | diff = (long *)omAlloc0(cmax*sizeof(long)); |
---|
3315 | if (w!=NULL) *w=new intvec(cmax-1); |
---|
3316 | iscom = (int *)omAlloc0(cmax*sizeof(int)); |
---|
3317 | i=0; |
---|
3318 | while (i<=length) |
---|
3319 | { |
---|
3320 | if (i<length) |
---|
3321 | { |
---|
3322 | p=F[i]; |
---|
3323 | while ((p!=NULL) && (iscom[pGetComp(p)]==0)) pIter(p); |
---|
3324 | } |
---|
3325 | if ((p==NULL) && (i<length)) |
---|
3326 | { |
---|
3327 | i++; |
---|
3328 | } |
---|
3329 | else |
---|
3330 | { |
---|
3331 | if (p==NULL) /* && (i==length) */ |
---|
3332 | { |
---|
3333 | i=0; |
---|
3334 | while ((i<length) && (F[i]==NULL)) i++; |
---|
3335 | if (i>=length) break; |
---|
3336 | p = F[i]; |
---|
3337 | } |
---|
3338 | //if (pLexOrder && (currRing->order[0]==ringorder_lp)) |
---|
3339 | // order=pTotaldegree(p); |
---|
3340 | //else |
---|
3341 | // order = p->order; |
---|
3342 | // order = pFDeg(p,currRing); |
---|
3343 | order = d(p,currRing) +diff[pGetComp(p)]; |
---|
3344 | //order += diff[pGetComp(p)]; |
---|
3345 | p = F[i]; |
---|
3346 | //Print("Actual p=F[%d]: ",i);pWrite(p); |
---|
3347 | F[i] = NULL; |
---|
3348 | i=0; |
---|
3349 | } |
---|
3350 | while (p!=NULL) |
---|
3351 | { |
---|
3352 | if (pLexOrder && (currRing->order[0]==ringorder_lp)) |
---|
3353 | ord=pTotaldegree(p); |
---|
3354 | else |
---|
3355 | // ord = p->order; |
---|
3356 | ord = pFDeg(p,currRing); |
---|
3357 | if (iscom[pGetComp(p)]==0) |
---|
3358 | { |
---|
3359 | diff[pGetComp(p)] = order-ord; |
---|
3360 | iscom[pGetComp(p)] = 1; |
---|
3361 | /* |
---|
3362 | *PrintS("new diff: "); |
---|
3363 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
3364 | *PrintLn(); |
---|
3365 | *PrintS("new iscom: "); |
---|
3366 | *for (j=0;j<cmax;j++) Print("%d ",iscom[j]); |
---|
3367 | *PrintLn(); |
---|
3368 | *Print("new set %d, order %d, ord %d, diff %d\n",pGetComp(p),order,ord,diff[pGetComp(p)]); |
---|
3369 | */ |
---|
3370 | } |
---|
3371 | else |
---|
3372 | { |
---|
3373 | /* |
---|
3374 | *PrintS("new diff: "); |
---|
3375 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
3376 | *PrintLn(); |
---|
3377 | *Print("order %d, ord %d, diff %d\n",order,ord,diff[pGetComp(p)]); |
---|
3378 | */ |
---|
3379 | if (order != (ord+diff[pGetComp(p)])) |
---|
3380 | { |
---|
3381 | omFreeSize((ADDRESS) iscom,cmax*sizeof(int)); |
---|
3382 | omFreeSize((ADDRESS) diff,cmax*sizeof(long)); |
---|
3383 | omFreeSize((ADDRESS) F,length*sizeof(poly)); |
---|
3384 | delete *w;*w=NULL; |
---|
3385 | return FALSE; |
---|
3386 | } |
---|
3387 | } |
---|
3388 | pIter(p); |
---|
3389 | } |
---|
3390 | } |
---|
3391 | omFreeSize((ADDRESS) iscom,cmax*sizeof(int)); |
---|
3392 | omFreeSize((ADDRESS) F,length*sizeof(poly)); |
---|
3393 | for (i=1;i<cmax;i++) (**w)[i-1]=(int)(diff[i]); |
---|
3394 | for (i=1;i<cmax;i++) |
---|
3395 | { |
---|
3396 | if (diff[i]<diffmin) diffmin=diff[i]; |
---|
3397 | } |
---|
3398 | if (w!=NULL) |
---|
3399 | { |
---|
3400 | for (i=1;i<cmax;i++) |
---|
3401 | { |
---|
3402 | (**w)[i-1]=(int)(diff[i]-diffmin); |
---|
3403 | } |
---|
3404 | } |
---|
3405 | omFreeSize((ADDRESS) diff,cmax*sizeof(long)); |
---|
3406 | return TRUE; |
---|
3407 | } |
---|
3408 | |
---|
3409 | BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w) |
---|
3410 | { |
---|
3411 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;} |
---|
3412 | if (idIs0(m)) return TRUE; |
---|
3413 | |
---|
3414 | int cmax=-1; |
---|
3415 | int i; |
---|
3416 | poly p=NULL; |
---|
3417 | int length=IDELEMS(m); |
---|
3418 | polyset P=m->m; |
---|
3419 | for (i=length-1;i>=0;i--) |
---|
3420 | { |
---|
3421 | p=P[i]; |
---|
3422 | if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1); |
---|
3423 | } |
---|
3424 | if (w != NULL) |
---|
3425 | if (w->length()+1 < cmax) |
---|
3426 | { |
---|
3427 | // Print("length: %d - %d \n", w->length(),cmax); |
---|
3428 | return FALSE; |
---|
3429 | } |
---|
3430 | |
---|
3431 | if(w!=NULL) |
---|
3432 | pSetModDeg(w); |
---|
3433 | |
---|
3434 | for (i=length-1;i>=0;i--) |
---|
3435 | { |
---|
3436 | p=P[i]; |
---|
3437 | poly q=p; |
---|
3438 | if (p!=NULL) |
---|
3439 | { |
---|
3440 | int d=pFDeg(p,currRing); |
---|
3441 | loop |
---|
3442 | { |
---|
3443 | pIter(p); |
---|
3444 | if (p==NULL) break; |
---|
3445 | if (d!=pFDeg(p,currRing)) |
---|
3446 | { |
---|
3447 | //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing)); |
---|
3448 | if(w!=NULL) |
---|
3449 | pSetModDeg(NULL); |
---|
3450 | return FALSE; |
---|
3451 | } |
---|
3452 | } |
---|
3453 | } |
---|
3454 | } |
---|
3455 | |
---|
3456 | if(w!=NULL) |
---|
3457 | pSetModDeg(NULL); |
---|
3458 | |
---|
3459 | return TRUE; |
---|
3460 | } |
---|
3461 | |
---|
3462 | ideal idJet(ideal i,int d) |
---|
3463 | { |
---|
3464 | ideal r=idInit((i->nrows)*(i->ncols),i->rank); |
---|
3465 | r->nrows = i-> nrows; |
---|
3466 | r->ncols = i-> ncols; |
---|
3467 | //r->rank = i-> rank; |
---|
3468 | int k; |
---|
3469 | for(k=(i->nrows)*(i->ncols)-1;k>=0; k--) |
---|
3470 | { |
---|
3471 | r->m[k]=ppJet(i->m[k],d); |
---|
3472 | } |
---|
3473 | return r; |
---|
3474 | } |
---|
3475 | |
---|
3476 | ideal idJetW(ideal i,int d, intvec * iv) |
---|
3477 | { |
---|
3478 | ideal r=idInit(IDELEMS(i),i->rank); |
---|
3479 | if (ecartWeights!=NULL) |
---|
3480 | { |
---|
3481 | WerrorS("cannot compute weighted jets now"); |
---|
3482 | } |
---|
3483 | else |
---|
3484 | { |
---|
3485 | short *w=iv2array(iv); |
---|
3486 | int k; |
---|
3487 | for(k=0; k<IDELEMS(i); k++) |
---|
3488 | { |
---|
3489 | r->m[k]=ppJetW(i->m[k],d,w); |
---|
3490 | } |
---|
3491 | omFreeSize((ADDRESS)w,(pVariables+1)*sizeof(short)); |
---|
3492 | } |
---|
3493 | return r; |
---|
3494 | } |
---|
3495 | |
---|
3496 | int idMinDegW(ideal M,intvec *w) |
---|
3497 | { |
---|
3498 | int d=-1; |
---|
3499 | for(int i=0;i<IDELEMS(M);i++) |
---|
3500 | { |
---|
3501 | int d0=pMinDeg(M->m[i],w); |
---|
3502 | if(-1<d0&&(d0<d||d==-1)) |
---|
3503 | d=d0; |
---|
3504 | } |
---|
3505 | return d; |
---|
3506 | } |
---|
3507 | |
---|
3508 | ideal idSeries(int n,ideal M,matrix U,intvec *w) |
---|
3509 | { |
---|
3510 | for(int i=IDELEMS(M)-1;i>=0;i--) |
---|
3511 | { |
---|
3512 | if(U==NULL) |
---|
3513 | M->m[i]=pSeries(n,M->m[i],NULL,w); |
---|
3514 | else |
---|
3515 | { |
---|
3516 | M->m[i]=pSeries(n,M->m[i],MATELEM(U,i+1,i+1),w); |
---|
3517 | MATELEM(U,i+1,i+1)=NULL; |
---|
3518 | } |
---|
3519 | } |
---|
3520 | if(U!=NULL) |
---|
3521 | idDelete((ideal*)&U); |
---|
3522 | return M; |
---|
3523 | } |
---|
3524 | |
---|
3525 | matrix idDiff(matrix i, int k) |
---|
3526 | { |
---|
3527 | int e=MATCOLS(i)*MATROWS(i); |
---|
3528 | matrix r=mpNew(MATROWS(i),MATCOLS(i)); |
---|
3529 | r->rank=i->rank; |
---|
3530 | int j; |
---|
3531 | for(j=0; j<e; j++) |
---|
3532 | { |
---|
3533 | r->m[j]=pDiff(i->m[j],k); |
---|
3534 | } |
---|
3535 | return r; |
---|
3536 | } |
---|
3537 | |
---|
3538 | matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply) |
---|
3539 | { |
---|
3540 | matrix r=mpNew(IDELEMS(I),IDELEMS(J)); |
---|
3541 | int i,j; |
---|
3542 | for(i=0; i<IDELEMS(I); i++) |
---|
3543 | { |
---|
3544 | for(j=0; j<IDELEMS(J); j++) |
---|
3545 | { |
---|
3546 | MATELEM(r,i+1,j+1)=pDiffOp(I->m[i],J->m[j],multiply); |
---|
3547 | } |
---|
3548 | } |
---|
3549 | return r; |
---|
3550 | } |
---|
3551 | |
---|
3552 | /*3 |
---|
3553 | *handles for some ideal operations the ring/syzcomp managment |
---|
3554 | *returns all syzygies (componentwise-)shifted by -syzcomp |
---|
3555 | *or -syzcomp-1 (in case of ideals as input) |
---|
3556 | static ideal idHandleIdealOp(ideal arg,int syzcomp,int isIdeal=FALSE) |
---|
3557 | { |
---|
3558 | ring orig_ring=currRing; |
---|
3559 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
3560 | rSetSyzComp(length); |
---|
3561 | |
---|
3562 | ideal s_temp; |
---|
3563 | if (orig_ring!=syz_ring) |
---|
3564 | s_temp=idrMoveR_NoSort(arg,orig_ring); |
---|
3565 | else |
---|
3566 | s_temp=arg; |
---|
3567 | |
---|
3568 | ideal s_temp1 = kStd(s_temp,currQuotient,testHomog,&w,NULL,length); |
---|
3569 | if (w!=NULL) delete w; |
---|
3570 | |
---|
3571 | if (syz_ring!=orig_ring) |
---|
3572 | { |
---|
3573 | idDelete(&s_temp); |
---|
3574 | rChangeCurrRing(orig_ring); |
---|
3575 | } |
---|
3576 | |
---|
3577 | idDelete(&temp); |
---|
3578 | ideal temp1=idRingCopy(s_temp1,syz_ring); |
---|
3579 | |
---|
3580 | if (syz_ring!=orig_ring) |
---|
3581 | { |
---|
3582 | rChangeCurrRing(syz_ring); |
---|
3583 | idDelete(&s_temp1); |
---|
3584 | rChangeCurrRing(orig_ring); |
---|
3585 | rKill(syz_ring); |
---|
3586 | } |
---|
3587 | |
---|
3588 | for (i=0;i<IDELEMS(temp1);i++) |
---|
3589 | { |
---|
3590 | if ((temp1->m[i]!=NULL) |
---|
3591 | && (pGetComp(temp1->m[i])<=length)) |
---|
3592 | { |
---|
3593 | pDelete(&(temp1->m[i])); |
---|
3594 | } |
---|
3595 | else |
---|
3596 | { |
---|
3597 | pShift(&(temp1->m[i]),-length); |
---|
3598 | } |
---|
3599 | } |
---|
3600 | temp1->rank = rk; |
---|
3601 | idSkipZeroes(temp1); |
---|
3602 | |
---|
3603 | return temp1; |
---|
3604 | } |
---|
3605 | */ |
---|
3606 | /*2 |
---|
3607 | * represents (h1+h2)/h2=h1/(h1 intersect h2) |
---|
3608 | */ |
---|
3609 | //ideal idModulo (ideal h2,ideal h1) |
---|
3610 | ideal idModulo (ideal h2,ideal h1, tHomog hom, intvec ** w) |
---|
3611 | { |
---|
3612 | intvec *wtmp=NULL; |
---|
3613 | |
---|
3614 | int i,j,k,rk,flength=0,slength,length; |
---|
3615 | poly p,q; |
---|
3616 | |
---|
3617 | if (idIs0(h2)) |
---|
3618 | return idFreeModule(si_max(1,h2->ncols)); |
---|
3619 | if (!idIs0(h1)) |
---|
3620 | flength = idRankFreeModule(h1); |
---|
3621 | slength = idRankFreeModule(h2); |
---|
3622 | length = si_max(flength,slength); |
---|
3623 | if (length==0) |
---|
3624 | { |
---|
3625 | length = 1; |
---|
3626 | } |
---|
3627 | ideal temp = idInit(IDELEMS(h2),length+IDELEMS(h2)); |
---|
3628 | if ((w!=NULL)&&((*w)!=NULL)) |
---|
3629 | { |
---|
3630 | //Print("input weights:");(*w)->show(1);PrintLn(); |
---|
3631 | int d; |
---|
3632 | int k; |
---|
3633 | wtmp=new intvec(length+IDELEMS(h2)); |
---|
3634 | for (i=0;i<length;i++) |
---|
3635 | ((*wtmp)[i])=(**w)[i]; |
---|
3636 | for (i=0;i<IDELEMS(h2);i++) |
---|
3637 | { |
---|
3638 | poly p=h2->m[i]; |
---|
3639 | if (p!=NULL) |
---|
3640 | { |
---|
3641 | d = pDeg(p); |
---|
3642 | k= pGetComp(p); |
---|
3643 | if (slength>0) k--; |
---|
3644 | d +=((**w)[k]); |
---|
3645 | ((*wtmp)[i+length]) = d; |
---|
3646 | } |
---|
3647 | } |
---|
3648 | //Print("weights:");wtmp->show(1);PrintLn(); |
---|
3649 | } |
---|
3650 | for (i=0;i<IDELEMS(h2);i++) |
---|
3651 | { |
---|
3652 | temp->m[i] = pCopy(h2->m[i]); |
---|
3653 | q = pOne(); |
---|
3654 | pSetComp(q,i+1+length); |
---|
3655 | pSetmComp(q); |
---|
3656 | if(temp->m[i]!=NULL) |
---|
3657 | { |
---|
3658 | if (slength==0) pShift(&(temp->m[i]),1); |
---|
3659 | p = temp->m[i]; |
---|
3660 | while (pNext(p)!=NULL) pIter(p); |
---|
3661 | pNext(p) = q; |
---|
3662 | } |
---|
3663 | else |
---|
3664 | temp->m[i]=q; |
---|
3665 | } |
---|
3666 | rk = k = IDELEMS(h2); |
---|
3667 | if (!idIs0(h1)) |
---|
3668 | { |
---|
3669 | pEnlargeSet(&(temp->m),IDELEMS(temp),IDELEMS(h1)); |
---|
3670 | IDELEMS(temp) += IDELEMS(h1); |
---|
3671 | for (i=0;i<IDELEMS(h1);i++) |
---|
3672 | { |
---|
3673 | if (h1->m[i]!=NULL) |
---|
3674 | { |
---|
3675 | temp->m[k] = pCopy(h1->m[i]); |
---|
3676 | if (flength==0) pShift(&(temp->m[k]),1); |
---|
3677 | k++; |
---|
3678 | } |
---|
3679 | } |
---|
3680 | } |
---|
3681 | |
---|
3682 | ring orig_ring=currRing; |
---|
3683 | ring syz_ring=rCurrRingAssure_SyzComp(); |
---|
3684 | rSetSyzComp(length); |
---|
3685 | ideal s_temp; |
---|
3686 | |
---|
3687 | if (syz_ring != orig_ring) |
---|
3688 | { |
---|
3689 | s_temp = idrMoveR_NoSort(temp, orig_ring); |
---|
3690 | } |
---|
3691 | else |
---|
3692 | { |
---|
3693 | s_temp = temp; |
---|
3694 | } |
---|
3695 | |
---|
3696 | idTest(s_temp); |
---|
3697 | ideal s_temp1 = kStd(s_temp,currQuotient,hom,&wtmp,NULL,length); |
---|
3698 | |
---|
3699 | //if (wtmp!=NULL) Print("output weights:");wtmp->show(1);PrintLn(); |
---|
3700 | if ((w!=NULL) && (*w !=NULL) && (wtmp!=NULL)) |
---|
3701 | { |
---|
3702 | delete *w; |
---|
3703 | *w=new intvec(IDELEMS(h2)); |
---|
3704 | for (i=0;i<IDELEMS(h2);i++) |
---|
3705 | ((**w)[i])=(*wtmp)[i+length]; |
---|
3706 | } |
---|
3707 | if (wtmp!=NULL) delete wtmp; |
---|
3708 | |
---|
3709 | for (i=0;i<IDELEMS(s_temp1);i++) |
---|
3710 | { |
---|
3711 | if ((s_temp1->m[i]!=NULL) |
---|
3712 | && (pGetComp(s_temp1->m[i])<=length)) |
---|
3713 | { |
---|
3714 | pDelete(&(s_temp1->m[i])); |
---|
3715 | } |
---|
3716 | else |
---|
3717 | { |
---|
3718 | pShift(&(s_temp1->m[i]),-length); |
---|
3719 | } |
---|
3720 | } |
---|
3721 | s_temp1->rank = rk; |
---|
3722 | idSkipZeroes(s_temp1); |
---|
3723 | |
---|
3724 | if (syz_ring!=orig_ring) |
---|
3725 | { |
---|
3726 | rChangeCurrRing(orig_ring); |
---|
3727 | s_temp1 = idrMoveR_NoSort(s_temp1, syz_ring); |
---|
3728 | rKill(syz_ring); |
---|
3729 | // Hmm ... here seems to be a memory leak |
---|
3730 | // However, simply deleting it causes memory trouble |
---|
3731 | // idDelete(&s_temp); |
---|
3732 | } |
---|
3733 | else |
---|
3734 | { |
---|
3735 | idDelete(&temp); |
---|
3736 | } |
---|
3737 | idTest(s_temp1); |
---|
3738 | return s_temp1; |
---|
3739 | } |
---|
3740 | |
---|
3741 | int idElem(const ideal F) |
---|
3742 | { |
---|
3743 | int i=0,j=IDELEMS(F)-1; |
---|
3744 | |
---|
3745 | while(j>=0) |
---|
3746 | { |
---|
3747 | if ((F->m)[j]!=NULL) i++; |
---|
3748 | j--; |
---|
3749 | } |
---|
3750 | return i; |
---|
3751 | } |
---|
3752 | |
---|
3753 | /* |
---|
3754 | *computes module-weights for liftings of homogeneous modules |
---|
3755 | */ |
---|
3756 | intvec * idMWLift(ideal mod,intvec * weights) |
---|
3757 | { |
---|
3758 | if (idIs0(mod)) return new intvec(2); |
---|
3759 | int i=IDELEMS(mod); |
---|
3760 | while ((i>0) && (mod->m[i-1]==NULL)) i--; |
---|
3761 | intvec *result = new intvec(i+1); |
---|
3762 | while (i>0) |
---|
3763 | { |
---|
3764 | (*result)[i]=pFDeg(mod->m[i],currRing)+(*weights)[pGetComp(mod->m[i])]; |
---|
3765 | } |
---|
3766 | return result; |
---|
3767 | } |
---|
3768 | |
---|
3769 | /*2 |
---|
3770 | *sorts the kbase for idCoef* in a special way (lexicographically |
---|
3771 | *with x_max,...,x_1) |
---|
3772 | */ |
---|
3773 | ideal idCreateSpecialKbase(ideal kBase,intvec ** convert) |
---|
3774 | { |
---|
3775 | int i; |
---|
3776 | ideal result; |
---|
3777 | |
---|
3778 | if (idIs0(kBase)) return NULL; |
---|
3779 | result = idInit(IDELEMS(kBase),kBase->rank); |
---|
3780 | *convert = idSort(kBase,FALSE); |
---|
3781 | for (i=0;i<(*convert)->length();i++) |
---|
3782 | { |
---|
3783 | result->m[i] = pCopy(kBase->m[(**convert)[i]-1]); |
---|
3784 | } |
---|
3785 | return result; |
---|
3786 | } |
---|
3787 | |
---|
3788 | /*2 |
---|
3789 | *returns the index of a given monom in the list of the special kbase |
---|
3790 | */ |
---|
3791 | int idIndexOfKBase(poly monom, ideal kbase) |
---|
3792 | { |
---|
3793 | int j=IDELEMS(kbase); |
---|
3794 | |
---|
3795 | while ((j>0) && (kbase->m[j-1]==NULL)) j--; |
---|
3796 | if (j==0) return -1; |
---|
3797 | int i=pVariables; |
---|
3798 | while (i>0) |
---|
3799 | { |
---|
3800 | loop |
---|
3801 | { |
---|
3802 | if (pGetExp(monom,i)>pGetExp(kbase->m[j-1],i)) return -1; |
---|
3803 | if (pGetExp(monom,i)==pGetExp(kbase->m[j-1],i)) break; |
---|
3804 | j--; |
---|
3805 | if (j==0) return -1; |
---|
3806 | } |
---|
3807 | if (i==1) |
---|
3808 | { |
---|
3809 | while(j>0) |
---|
3810 | { |
---|
3811 | if (pGetComp(monom)==pGetComp(kbase->m[j-1])) return j-1; |
---|
3812 | if (pGetComp(monom)>pGetComp(kbase->m[j-1])) return -1; |
---|
3813 | j--; |
---|
3814 | } |
---|
3815 | } |
---|
3816 | i--; |
---|
3817 | } |
---|
3818 | return -1; |
---|
3819 | } |
---|
3820 | |
---|
3821 | /*2 |
---|
3822 | *decomposes the monom in a part of coefficients described by the |
---|
3823 | *complement of how and a monom in variables occuring in how, the |
---|
3824 | *index of which in kbase is returned as integer pos (-1 if it don't |
---|
3825 | *exists) |
---|
3826 | */ |
---|
3827 | poly idDecompose(poly monom, poly how, ideal kbase, int * pos) |
---|
3828 | { |
---|
3829 | int i; |
---|
3830 | poly coeff=pOne(), base=pOne(); |
---|
3831 | |
---|
3832 | for (i=1;i<=pVariables;i++) |
---|
3833 | { |
---|
3834 | if (pGetExp(how,i)>0) |
---|
3835 | { |
---|
3836 | pSetExp(base,i,pGetExp(monom,i)); |
---|
3837 | } |
---|
3838 | else |
---|
3839 | { |
---|
3840 | pSetExp(coeff,i,pGetExp(monom,i)); |
---|
3841 | } |
---|
3842 | } |
---|
3843 | pSetComp(base,pGetComp(monom)); |
---|
3844 | pSetm(base); |
---|
3845 | pSetCoeff(coeff,nCopy(pGetCoeff(monom))); |
---|
3846 | pSetm(coeff); |
---|
3847 | *pos = idIndexOfKBase(base,kbase); |
---|
3848 | if (*pos<0) |
---|
3849 | pDelete(&coeff); |
---|
3850 | pDelete(&base); |
---|
3851 | return coeff; |
---|
3852 | } |
---|
3853 | |
---|
3854 | /*2 |
---|
3855 | *returns a matrix A of coefficients with kbase*A=arg |
---|
3856 | *if all monomials in variables of how occur in kbase |
---|
3857 | *the other are deleted |
---|
3858 | */ |
---|
3859 | matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how) |
---|
3860 | { |
---|
3861 | matrix result; |
---|
3862 | ideal tempKbase; |
---|
3863 | poly p,q; |
---|
3864 | intvec * convert; |
---|
3865 | int i=IDELEMS(kbase),j=IDELEMS(arg),k,pos; |
---|
3866 | #if 0 |
---|
3867 | while ((i>0) && (kbase->m[i-1]==NULL)) i--; |
---|
3868 | if (idIs0(arg)) |
---|
3869 | return mpNew(i,1); |
---|
3870 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
3871 | result = mpNew(i,j); |
---|
3872 | #else |
---|
3873 | result = mpNew(i, j); |
---|
3874 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
3875 | #endif |
---|
3876 | |
---|
3877 | tempKbase = idCreateSpecialKbase(kbase,&convert); |
---|
3878 | for (k=0;k<j;k++) |
---|
3879 | { |
---|
3880 | p = arg->m[k]; |
---|
3881 | while (p!=NULL) |
---|
3882 | { |
---|
3883 | q = idDecompose(p,how,tempKbase,&pos); |
---|
3884 | if (pos>=0) |
---|
3885 | { |
---|
3886 | MATELEM(result,(*convert)[pos],k+1) = |
---|
3887 | pAdd(MATELEM(result,(*convert)[pos],k+1),q); |
---|
3888 | } |
---|
3889 | else |
---|
3890 | pDelete(&q); |
---|
3891 | pIter(p); |
---|
3892 | } |
---|
3893 | } |
---|
3894 | idDelete(&tempKbase); |
---|
3895 | return result; |
---|
3896 | } |
---|
3897 | |
---|
3898 | /*3 |
---|
3899 | * searches for the next unit in the components of the module arg and |
---|
3900 | * returns the first one; |
---|
3901 | */ |
---|
3902 | static int idReadOutPivot(ideal arg,int* comp) |
---|
3903 | { |
---|
3904 | if (idIs0(arg)) return -1; |
---|
3905 | int i=0,j, generator=-1; |
---|
3906 | int rk_arg=arg->rank; //idRankFreeModule(arg); |
---|
3907 | int * componentIsUsed =(int *)omAlloc((rk_arg+1)*sizeof(int)); |
---|
3908 | poly p; |
---|
3909 | |
---|
3910 | while ((generator<0) && (i<IDELEMS(arg))) |
---|
3911 | { |
---|
3912 | memset(componentIsUsed,0,(rk_arg+1)*sizeof(int)); |
---|
3913 | p = arg->m[i]; |
---|
3914 | while (p!=NULL) |
---|
3915 | { |
---|
3916 | j = pGetComp(p); |
---|
3917 | if (componentIsUsed[j]==0) |
---|
3918 | { |
---|
3919 | #ifdef HAVE_RINGS |
---|
3920 | if (pLmIsConstantComp(p) && |
---|
3921 | (!rField_is_Ring(currRing) || nIsUnit(pGetCoeff(p)))) |
---|
3922 | { |
---|
3923 | #else |
---|
3924 | if (pLmIsConstantComp(p)) |
---|
3925 | { |
---|
3926 | #endif |
---|
3927 | generator = i; |
---|
3928 | componentIsUsed[j] = 1; |
---|
3929 | } |
---|
3930 | else |
---|
3931 | { |
---|
3932 | componentIsUsed[j] = -1; |
---|
3933 | } |
---|
3934 | } |
---|
3935 | else if (componentIsUsed[j]>0) |
---|
3936 | { |
---|
3937 | (componentIsUsed[j])++; |
---|
3938 | } |
---|
3939 | pIter(p); |
---|
3940 | } |
---|
3941 | i++; |
---|
3942 | } |
---|
3943 | i = 0; |
---|
3944 | *comp = -1; |
---|
3945 | for (j=0;j<=rk_arg;j++) |
---|
3946 | { |
---|
3947 | if (componentIsUsed[j]>0) |
---|
3948 | { |
---|
3949 | if ((*comp==-1) || (componentIsUsed[j]<i)) |
---|
3950 | { |
---|
3951 | *comp = j; |
---|
3952 | i= componentIsUsed[j]; |
---|
3953 | } |
---|
3954 | } |
---|
3955 | } |
---|
3956 | omFree(componentIsUsed); |
---|
3957 | return generator; |
---|
3958 | } |
---|
3959 | |
---|
3960 | #if 0 |
---|
3961 | static void idDeleteComp(ideal arg,int red_comp) |
---|
3962 | { |
---|
3963 | int i,j; |
---|
3964 | poly p; |
---|
3965 | |
---|
3966 | for (i=IDELEMS(arg)-1;i>=0;i--) |
---|
3967 | { |
---|
3968 | p = arg->m[i]; |
---|
3969 | while (p!=NULL) |
---|
3970 | { |
---|
3971 | j = pGetComp(p); |
---|
3972 | if (j>red_comp) |
---|
3973 | { |
---|
3974 | pSetComp(p,j-1); |
---|
3975 | pSetm(p); |
---|
3976 | } |
---|
3977 | pIter(p); |
---|
3978 | } |
---|
3979 | } |
---|
3980 | (arg->rank)--; |
---|
3981 | } |
---|
3982 | #endif |
---|
3983 | |
---|
3984 | static void idDeleteComps(ideal arg,int* red_comp,int del) |
---|
3985 | // red_comp is an array [0..args->rank] |
---|
3986 | { |
---|
3987 | int i,j; |
---|
3988 | poly p; |
---|
3989 | |
---|
3990 | for (i=IDELEMS(arg)-1;i>=0;i--) |
---|
3991 | { |
---|
3992 | p = arg->m[i]; |
---|
3993 | while (p!=NULL) |
---|
3994 | { |
---|
3995 | j = pGetComp(p); |
---|
3996 | if (red_comp[j]!=j) |
---|
3997 | { |
---|
3998 | pSetComp(p,red_comp[j]); |
---|
3999 | pSetmComp(p); |
---|
4000 | } |
---|
4001 | pIter(p); |
---|
4002 | } |
---|
4003 | } |
---|
4004 | (arg->rank) -= del; |
---|
4005 | } |
---|
4006 | |
---|
4007 | /*2 |
---|
4008 | * returns the presentation of an isomorphic, minimally |
---|
4009 | * embedded module (arg represents the quotient!) |
---|
4010 | */ |
---|
4011 | ideal idMinEmbedding(ideal arg,BOOLEAN inPlace, intvec **w) |
---|
4012 | { |
---|
4013 | if (idIs0(arg)) return idInit(1,arg->rank); |
---|
4014 | int i,next_gen,next_comp; |
---|
4015 | ideal res=arg; |
---|
4016 | if (!inPlace) res = idCopy(arg); |
---|
4017 | res->rank=si_max(res->rank,idRankFreeModule(res)); |
---|
4018 | int *red_comp=(int*)omAlloc((res->rank+1)*sizeof(int)); |
---|
4019 | for (i=res->rank;i>=0;i--) red_comp[i]=i; |
---|
4020 | |
---|
4021 | int del=0; |
---|
4022 | loop |
---|
4023 | { |
---|
4024 | next_gen = idReadOutPivot(res,&next_comp); |
---|
4025 | if (next_gen<0) break; |
---|
4026 | del++; |
---|
4027 | syGaussForOne(res,next_gen,next_comp,0,IDELEMS(res)); |
---|
4028 | for(i=next_comp+1;i<=arg->rank;i++) red_comp[i]--; |
---|
4029 | if ((w !=NULL)&&(*w!=NULL)) |
---|
4030 | { |
---|
4031 | for(i=next_comp;i<(*w)->length();i++) (**w)[i-1]=(**w)[i]; |
---|
4032 | } |
---|
4033 | } |
---|
4034 | |
---|
4035 | idDeleteComps(res,red_comp,del); |
---|
4036 | idSkipZeroes(res); |
---|
4037 | omFree(red_comp); |
---|
4038 | |
---|
4039 | if ((w !=NULL)&&(*w!=NULL) &&(del>0)) |
---|
4040 | { |
---|
4041 | intvec *wtmp=new intvec((*w)->length()-del); |
---|
4042 | for(i=0;i<res->rank;i++) (*wtmp)[i]=(**w)[i]; |
---|
4043 | delete *w; |
---|
4044 | *w=wtmp; |
---|
4045 | } |
---|
4046 | return res; |
---|
4047 | } |
---|
4048 | |
---|
4049 | /*2 |
---|
4050 | * transpose a module |
---|
4051 | */ |
---|
4052 | ideal idTransp(ideal a) |
---|
4053 | { |
---|
4054 | int r = a->rank, c = IDELEMS(a); |
---|
4055 | ideal b = idInit(r,c); |
---|
4056 | |
---|
4057 | for (int i=c; i>0; i--) |
---|
4058 | { |
---|
4059 | poly p=a->m[i-1]; |
---|
4060 | while(p!=NULL) |
---|
4061 | { |
---|
4062 | poly h=pHead(p); |
---|
4063 | int co=pGetComp(h)-1; |
---|
4064 | pSetComp(h,i); |
---|
4065 | pSetmComp(h); |
---|
4066 | b->m[co]=pAdd(b->m[co],h); |
---|
4067 | pIter(p); |
---|
4068 | } |
---|
4069 | } |
---|
4070 | return b; |
---|
4071 | } |
---|
4072 | |
---|
4073 | intvec * idQHomWeight(ideal id) |
---|
4074 | { |
---|
4075 | poly head, tail; |
---|
4076 | int k; |
---|
4077 | int in=IDELEMS(id)-1, ready=0, all=0, |
---|
4078 | coldim=pVariables, rowmax=2*coldim; |
---|
4079 | if (in<0) return NULL; |
---|
4080 | intvec *imat=new intvec(rowmax+1,coldim,0); |
---|
4081 | |
---|
4082 | do |
---|
4083 | { |
---|
4084 | head = id->m[in--]; |
---|
4085 | if (head!=NULL) |
---|
4086 | { |
---|
4087 | tail = pNext(head); |
---|
4088 | while (tail!=NULL) |
---|
4089 | { |
---|
4090 | all++; |
---|
4091 | for (k=1;k<=coldim;k++) |
---|
4092 | IMATELEM(*imat,all,k) = pGetExpDiff(head,tail,k); |
---|
4093 | if (all==rowmax) |
---|
4094 | { |
---|
4095 | ivTriangIntern(imat, ready, all); |
---|
4096 | if (ready==coldim) |
---|
4097 | { |
---|
4098 | delete imat; |
---|
4099 | return NULL; |
---|
4100 | } |
---|
4101 | } |
---|
4102 | pIter(tail); |
---|
4103 | } |
---|
4104 | } |
---|
4105 | } while (in>=0); |
---|
4106 | if (all>ready) |
---|
4107 | { |
---|
4108 | ivTriangIntern(imat, ready, all); |
---|
4109 | if (ready==coldim) |
---|
4110 | { |
---|
4111 | delete imat; |
---|
4112 | return NULL; |
---|
4113 | } |
---|
4114 | } |
---|
4115 | intvec *result = ivSolveKern(imat, ready); |
---|
4116 | delete imat; |
---|
4117 | return result; |
---|
4118 | } |
---|
4119 | |
---|
4120 | BOOLEAN idIsZeroDim(ideal I) |
---|
4121 | { |
---|
4122 | BOOLEAN *UsedAxis=(BOOLEAN *)omAlloc0(pVariables*sizeof(BOOLEAN)); |
---|
4123 | int i,n; |
---|
4124 | poly po; |
---|
4125 | BOOLEAN res=TRUE; |
---|
4126 | for(i=IDELEMS(I)-1;i>=0;i--) |
---|
4127 | { |
---|
4128 | po=I->m[i]; |
---|
4129 | if ((po!=NULL) &&((n=pIsPurePower(po))!=0)) UsedAxis[n-1]=TRUE; |
---|
4130 | } |
---|
4131 | for(i=pVariables-1;i>=0;i--) |
---|
4132 | { |
---|
4133 | if(UsedAxis[i]==FALSE) {res=FALSE; break;} // not zero-dim. |
---|
4134 | } |
---|
4135 | omFreeSize(UsedAxis,pVariables*sizeof(BOOLEAN)); |
---|
4136 | return res; |
---|
4137 | } |
---|
4138 | |
---|
4139 | void idNormalize(ideal I) |
---|
4140 | { |
---|
4141 | if (rField_has_simple_inverse()) return; /* Z/p, GF(p,n), R, long R/C */ |
---|
4142 | int i; |
---|
4143 | for(i=IDELEMS(I)-1;i>=0;i--) |
---|
4144 | { |
---|
4145 | pNormalize(I->m[i]); |
---|
4146 | } |
---|
4147 | } |
---|
4148 | |
---|
4149 | #include <kernel/clapsing.h> |
---|
4150 | |
---|
4151 | #ifdef HAVE_FACTORY |
---|
4152 | poly id_GCD(poly f, poly g, const ring r) |
---|
4153 | { |
---|
4154 | ring save_r=currRing; |
---|
4155 | rChangeCurrRing(r); |
---|
4156 | ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g; |
---|
4157 | intvec *w = NULL; |
---|
4158 | ideal S=idSyzygies(I,testHomog,&w); |
---|
4159 | if (w!=NULL) delete w; |
---|
4160 | poly gg=pTakeOutComp(&(S->m[0]),2); |
---|
4161 | idDelete(&S); |
---|
4162 | poly gcd_p=singclap_pdivide(f,gg); |
---|
4163 | pDelete(&gg); |
---|
4164 | rChangeCurrRing(save_r); |
---|
4165 | return gcd_p; |
---|
4166 | } |
---|
4167 | #endif |
---|
4168 | |
---|
4169 | /*2 |
---|
4170 | * xx,q: arrays of length 0..rl-1 |
---|
4171 | * xx[i]: SB mod q[i] |
---|
4172 | * assume: char=0 |
---|
4173 | * assume: q[i]!=0 |
---|
4174 | * destroys xx |
---|
4175 | */ |
---|
4176 | #ifdef HAVE_FACTORY |
---|
4177 | ideal idChineseRemainder(ideal *xx, number *q, int rl) |
---|
4178 | { |
---|
4179 | int cnt=IDELEMS(xx[0])*xx[0]->nrows; |
---|
4180 | ideal result=idInit(cnt,xx[0]->rank); |
---|
4181 | result->nrows=xx[0]->nrows; // for lifting matrices |
---|
4182 | result->ncols=xx[0]->ncols; // for lifting matrices |
---|
4183 | int i,j; |
---|
4184 | poly r,h,hh,res_p; |
---|
4185 | number *x=(number *)omAlloc(rl*sizeof(number)); |
---|
4186 | for(i=cnt-1;i>=0;i--) |
---|
4187 | { |
---|
4188 | res_p=NULL; |
---|
4189 | loop |
---|
4190 | { |
---|
4191 | r=NULL; |
---|
4192 | for(j=rl-1;j>=0;j--) |
---|
4193 | { |
---|
4194 | h=xx[j]->m[i]; |
---|
4195 | if ((h!=NULL) |
---|
4196 | &&((r==NULL)||(pLmCmp(r,h)==-1))) |
---|
4197 | r=h; |
---|
4198 | } |
---|
4199 | if (r==NULL) break; |
---|
4200 | h=pHead(r); |
---|
4201 | for(j=rl-1;j>=0;j--) |
---|
4202 | { |
---|
4203 | hh=xx[j]->m[i]; |
---|
4204 | if ((hh!=NULL) && (pLmCmp(r,hh)==0)) |
---|
4205 | { |
---|
4206 | x[j]=pGetCoeff(hh); |
---|
4207 | hh=pLmFreeAndNext(hh); |
---|
4208 | xx[j]->m[i]=hh; |
---|
4209 | } |
---|
4210 | else |
---|
4211 | x[j]=nlInit(0, currRing); |
---|
4212 | } |
---|
4213 | number n=nlChineseRemainder(x,q,rl); |
---|
4214 | for(j=rl-1;j>=0;j--) |
---|
4215 | { |
---|
4216 | x[j]=NULL; // nlInit(0...) takes no memory |
---|
4217 | } |
---|
4218 | if (nlIsZero(n)) pDelete(&h); |
---|
4219 | else |
---|
4220 | { |
---|
4221 | pSetCoeff(h,n); |
---|
4222 | //Print("new mon:");pWrite(h); |
---|
4223 | res_p=pAdd(res_p,h); |
---|
4224 | } |
---|
4225 | } |
---|
4226 | result->m[i]=res_p; |
---|
4227 | } |
---|
4228 | omFree(x); |
---|
4229 | for(i=rl-1;i>=0;i--) idDelete(&(xx[i])); |
---|
4230 | omFree(xx); |
---|
4231 | return result; |
---|
4232 | } |
---|
4233 | #endif |
---|
4234 | /* currently unsed: |
---|
4235 | ideal idChineseRemainder(ideal *xx, intvec *iv) |
---|
4236 | { |
---|
4237 | int rl=iv->length(); |
---|
4238 | number *q=(number *)omAlloc(rl*sizeof(number)); |
---|
4239 | int i; |
---|
4240 | for(i=0; i<rl; i++) |
---|
4241 | { |
---|
4242 | q[i]=nInit((*iv)[i]); |
---|
4243 | } |
---|
4244 | return idChineseRemainder(xx,q,rl); |
---|
4245 | } |
---|
4246 | */ |
---|
4247 | /* |
---|
4248 | * lift ideal with coeffs over Z (mod N) to Q via Farey |
---|
4249 | */ |
---|
4250 | ideal idFarey(ideal x, number N) |
---|
4251 | { |
---|
4252 | int cnt=IDELEMS(x)*x->nrows; |
---|
4253 | ideal result=idInit(cnt,x->rank); |
---|
4254 | result->nrows=x->nrows; // for lifting matrices |
---|
4255 | result->ncols=x->ncols; // for lifting matrices |
---|
4256 | |
---|
4257 | int i; |
---|
4258 | for(i=cnt-1;i>=0;i--) |
---|
4259 | { |
---|
4260 | poly h=pCopy(x->m[i]); |
---|
4261 | result->m[i]=h; |
---|
4262 | while(h!=NULL) |
---|
4263 | { |
---|
4264 | number c=pGetCoeff(h); |
---|
4265 | pSetCoeff0(h,nlFarey(c,N)); |
---|
4266 | nDelete(&c); |
---|
4267 | pIter(h); |
---|
4268 | } |
---|
4269 | while((result->m[i]!=NULL)&&(nIsZero(pGetCoeff(result->m[i])))) |
---|
4270 | { |
---|
4271 | pLmDelete(&(result->m[i])); |
---|
4272 | } |
---|
4273 | h=result->m[i]; |
---|
4274 | while((h!=NULL) && (pNext(h)!=NULL)) |
---|
4275 | { |
---|
4276 | if(nIsZero(pGetCoeff(pNext(h)))) |
---|
4277 | { |
---|
4278 | pLmDelete(&pNext(h)); |
---|
4279 | } |
---|
4280 | else pIter(h); |
---|
4281 | } |
---|
4282 | } |
---|
4283 | return result; |
---|
4284 | } |
---|
4285 | |
---|
4286 | /*2 |
---|
4287 | * transpose a module |
---|
4288 | * NOTE: just a version of "ideal idTransp(ideal)" which works within specified ring. |
---|
4289 | */ |
---|
4290 | ideal id_Transp(ideal a, const ring rRing) |
---|
4291 | { |
---|
4292 | int r = a->rank, c = IDELEMS(a); |
---|
4293 | ideal b = idInit(r,c); |
---|
4294 | |
---|
4295 | for (int i=c; i>0; i--) |
---|
4296 | { |
---|
4297 | poly p=a->m[i-1]; |
---|
4298 | while(p!=NULL) |
---|
4299 | { |
---|
4300 | poly h=p_Head(p, rRing); |
---|
4301 | int co=p_GetComp(h, rRing)-1; |
---|
4302 | p_SetComp(h, i, rRing); |
---|
4303 | p_Setm(h, rRing); |
---|
4304 | b->m[co] = p_Add_q(b->m[co], h, rRing); |
---|
4305 | pIter(p); |
---|
4306 | } |
---|
4307 | } |
---|
4308 | return b; |
---|
4309 | } |
---|
4310 | |
---|
4311 | |
---|
4312 | |
---|
4313 | /*2 |
---|
4314 | * The following is needed to compute the image of certain map used in |
---|
4315 | * the computation of cohomologies via BGG |
---|
4316 | * let M = { w_1, ..., w_k }, k = size(M) == ncols(M), n = nvars(currRing). |
---|
4317 | * assuming that nrows(M) <= m*n; the procedure computes: |
---|
4318 | * transpose(M) * transpose( var(1) I_m | ... | var(n) I_m ) :== transpose(module{f_1, ... f_k}), |
---|
4319 | * where f_i = \sum_{j=1}^{m} (w_i, v_j) gen(j), (w_i, v_j) is a `scalar` multiplication. |
---|
4320 | * that is, if w_i = (a^1_1, ... a^1_m) | (a^2_1, ..., a^2_m) | ... | (a^n_1, ..., a^n_m) then |
---|
4321 | |
---|
4322 | (a^1_1, ... a^1_m) | (a^2_1, ..., a^2_m) | ... | (a^n_1, ..., a^n_m) |
---|
4323 | * var_1 ... var_1 | var_2 ... var_2 | ... | var_n ... var(n) |
---|
4324 | * gen_1 ... gen_m | gen_1 ... gen_m | ... | gen_1 ... gen_m |
---|
4325 | + => |
---|
4326 | f_i = |
---|
4327 | |
---|
4328 | a^1_1 * var(1) * gen(1) + ... + a^1_m * var(1) * gen(m) + |
---|
4329 | a^2_1 * var(2) * gen(1) + ... + a^2_m * var(2) * gen(m) + |
---|
4330 | ... |
---|
4331 | a^n_1 * var(n) * gen(1) + ... + a^n_m * var(n) * gen(m); |
---|
4332 | |
---|
4333 | NOTE: for every f_i we run only ONCE along w_i saving partial sums into a temporary array of polys of size m |
---|
4334 | */ |
---|
4335 | ideal id_TensorModuleMult(const int m, const ideal M, const ring rRing) |
---|
4336 | { |
---|
4337 | // #ifdef DEBU |
---|
4338 | // WarnS("tensorModuleMult!!!!"); |
---|
4339 | |
---|
4340 | assume(m > 0); |
---|
4341 | assume(M != NULL); |
---|
4342 | |
---|
4343 | const int n = rRing->N; |
---|
4344 | |
---|
4345 | assume(M->rank <= m * n); |
---|
4346 | |
---|
4347 | const int k = IDELEMS(M); |
---|
4348 | |
---|
4349 | ideal idTemp = idInit(k,m); // = {f_1, ..., f_k } |
---|
4350 | |
---|
4351 | for( int i = 0; i < k; i++ ) // for every w \in M |
---|
4352 | { |
---|
4353 | poly pTempSum = NULL; |
---|
4354 | |
---|
4355 | poly w = M->m[i]; |
---|
4356 | |
---|
4357 | while(w != NULL) // for each term of w... |
---|
4358 | { |
---|
4359 | poly h = p_Head(w, rRing); |
---|
4360 | |
---|
4361 | const int gen = p_GetComp(h, rRing); // 1 ... |
---|
4362 | |
---|
4363 | assume(gen > 0); |
---|
4364 | assume(gen <= n*m); |
---|
4365 | |
---|
4366 | // TODO: write a formula with %, / instead of while! |
---|
4367 | /* |
---|
4368 | int c = gen; |
---|
4369 | int v = 1; |
---|
4370 | while(c > m) |
---|
4371 | { |
---|
4372 | c -= m; |
---|
4373 | v++; |
---|
4374 | } |
---|
4375 | */ |
---|
4376 | |
---|
4377 | int cc = gen % m; |
---|
4378 | if( cc == 0) cc = m; |
---|
4379 | int vv = 1 + (gen - cc) / m; |
---|
4380 | |
---|
4381 | // assume( cc == c ); |
---|
4382 | // assume( vv == v ); |
---|
4383 | |
---|
4384 | // 1<= c <= m |
---|
4385 | assume( cc > 0 ); |
---|
4386 | assume( cc <= m ); |
---|
4387 | |
---|
4388 | assume( vv > 0 ); |
---|
4389 | assume( vv <= n ); |
---|
4390 | |
---|
4391 | assume( (cc + (vv-1)*m) == gen ); |
---|
4392 | |
---|
4393 | p_IncrExp(h, vv, rRing); // h *= var(j) && // p_AddExp(h, vv, 1, rRing); |
---|
4394 | p_SetComp(h, cc, rRing); |
---|
4395 | |
---|
4396 | p_Setm(h, rRing); // addjust degree after the previous steps! |
---|
4397 | |
---|
4398 | pTempSum = p_Add_q(pTempSum, h, rRing); // it is slow since h will be usually put to the back of pTempSum!!! |
---|
4399 | |
---|
4400 | pIter(w); |
---|
4401 | } |
---|
4402 | |
---|
4403 | idTemp->m[i] = pTempSum; |
---|
4404 | } |
---|
4405 | |
---|
4406 | // simplify idTemp??? |
---|
4407 | |
---|
4408 | ideal idResult = id_Transp(idTemp, rRing); |
---|
4409 | |
---|
4410 | id_Delete(&idTemp, rRing); |
---|
4411 | |
---|
4412 | return(idResult); |
---|
4413 | } |
---|