1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* |
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5 | * ABSTRACT - all basic methods to manipulate ideals |
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6 | */ |
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7 | |
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8 | |
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9 | /* includes */ |
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10 | |
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11 | |
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12 | |
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13 | #include <misc/auxiliary.h> |
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14 | |
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15 | #include <omalloc/omalloc.h> |
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16 | |
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17 | #include <misc/options.h> |
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18 | #include <misc/intvec.h> |
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19 | |
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20 | // #include <coeffs/longrat.h> |
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21 | #include "matpol.h" |
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22 | |
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23 | #include "monomials/p_polys.h" |
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24 | #include "weight.h" |
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25 | #include "sbuckets.h" |
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26 | #include "clapsing.h" |
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27 | |
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28 | #include "simpleideals.h" |
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29 | |
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30 | omBin sip_sideal_bin = omGetSpecBin(sizeof(sip_sideal)); |
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31 | |
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32 | static poly * idpower; |
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33 | /*collects the monomials in makemonoms, must be allocated befor*/ |
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34 | static int idpowerpoint; |
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35 | /*index of the actual monomial in idpower*/ |
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36 | |
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37 | /// initialise an ideal / module |
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38 | ideal idInit(int idsize, int rank) |
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39 | { |
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40 | assume( idsize >= 0 && rank >= 0 ); |
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41 | |
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42 | ideal hh = (ideal)omAllocBin(sip_sideal_bin); |
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43 | |
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44 | IDELEMS(hh) = idsize; // ncols |
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45 | hh->nrows = 1; // ideal/module! |
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46 | |
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47 | hh->rank = rank; // ideal: 1, module: >= 0! |
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48 | |
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49 | if (idsize>0) |
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50 | hh->m = (poly *)omAlloc0(idsize*sizeof(poly)); |
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51 | else |
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52 | hh->m = NULL; |
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53 | |
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54 | return hh; |
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55 | } |
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56 | |
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57 | #ifdef PDEBUG |
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58 | // this is only for outputting an ideal within the debugger |
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59 | // therefor it accept the otherwise illegal id==NULL |
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60 | void idShow(const ideal id, const ring lmRing, const ring tailRing, const int debugPrint) |
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61 | { |
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62 | assume( debugPrint >= 0 ); |
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63 | |
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64 | if( id == NULL ) |
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65 | PrintS("(NULL)"); |
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66 | else |
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67 | { |
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68 | Print("Module of rank %ld,real rank %ld and %d generators.\n", |
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69 | id->rank,id_RankFreeModule(id, lmRing, tailRing),IDELEMS(id)); |
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70 | |
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71 | int j = (id->ncols*id->nrows) - 1; |
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72 | while ((j > 0) && (id->m[j]==NULL)) j--; |
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73 | for (int i = 0; i <= j; i++) |
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74 | { |
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75 | Print("generator %d: ",i); p_wrp(id->m[i], lmRing, tailRing);PrintLn(); |
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76 | } |
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77 | } |
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78 | } |
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79 | #endif |
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80 | |
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81 | /// index of generator with leading term in ground ring (if any); |
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82 | /// otherwise -1 |
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83 | int id_PosConstant(ideal id, const ring r) |
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84 | { |
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85 | id_Test(id, r); |
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86 | const int N = IDELEMS(id) - 1; |
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87 | const poly * m = id->m + N; |
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88 | |
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89 | for (int k = N; k >= 0; --k, --m) |
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90 | { |
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91 | const poly p = *m; |
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92 | if (p!=NULL) |
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93 | if (p_LmIsConstantComp(p, r) == TRUE) |
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94 | return k; |
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95 | } |
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96 | |
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97 | return -1; |
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98 | } |
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99 | |
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100 | /// initialise the maximal ideal (at 0) |
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101 | ideal id_MaxIdeal (const ring r) |
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102 | { |
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103 | ideal hh = idInit(rVar(r), 1); |
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104 | for (int l=rVar(r)-1; l>=0; l--) |
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105 | { |
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106 | hh->m[l] = p_One(r); |
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107 | p_SetExp(hh->m[l],l+1,1,r); |
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108 | p_Setm(hh->m[l],r); |
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109 | } |
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110 | id_Test(hh, r); |
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111 | return hh; |
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112 | } |
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113 | |
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114 | /// deletes an ideal/module/matrix |
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115 | void id_Delete (ideal * h, ring r) |
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116 | { |
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117 | if (*h == NULL) |
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118 | return; |
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119 | |
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120 | id_Test(*h, r); |
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121 | |
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122 | const int elems = (*h)->nrows * (*h)->ncols; |
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123 | |
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124 | if ( elems > 0 ) |
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125 | { |
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126 | assume( (*h)->m != NULL ); |
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127 | |
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128 | int j = elems; |
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129 | do |
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130 | { |
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131 | j--; |
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132 | poly pp=((*h)->m[j]); |
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133 | if (pp!=NULL) p_Delete(&pp, r); |
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134 | } |
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135 | while (j>0); |
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136 | |
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137 | omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems); |
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138 | } |
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139 | |
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140 | omFreeBin((ADDRESS)*h, sip_sideal_bin); |
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141 | *h=NULL; |
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142 | } |
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143 | |
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144 | |
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145 | /// Shallowdeletes an ideal/matrix |
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146 | void id_ShallowDelete (ideal *h, ring r) |
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147 | { |
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148 | id_Test(*h, r); |
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149 | |
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150 | if (*h == NULL) |
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151 | return; |
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152 | |
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153 | int j,elems; |
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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 | assume( (*h)->m != NULL ); |
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158 | do |
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159 | { |
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160 | p_ShallowDelete(&((*h)->m[--j]), r); |
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161 | } |
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162 | while (j>0); |
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163 | omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems); |
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164 | } |
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165 | omFreeBin((ADDRESS)*h, sip_sideal_bin); |
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166 | *h=NULL; |
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167 | } |
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168 | |
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169 | /// gives an ideal/module the minimal possible size |
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170 | void idSkipZeroes (ideal ide) |
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171 | { |
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172 | assume (ide != NULL); |
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173 | |
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174 | int k; |
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175 | int j = -1; |
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176 | BOOLEAN change=FALSE; |
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177 | |
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178 | for (k=0; k<IDELEMS(ide); k++) |
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179 | { |
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180 | if (ide->m[k] != NULL) |
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181 | { |
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182 | j++; |
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183 | if (change) |
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184 | { |
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185 | ide->m[j] = ide->m[k]; |
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186 | } |
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187 | } |
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188 | else |
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189 | { |
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190 | change=TRUE; |
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191 | } |
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192 | } |
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193 | if (change) |
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194 | { |
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195 | if (j == -1) |
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196 | j = 0; |
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197 | else |
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198 | { |
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199 | for (k=j+1; k<IDELEMS(ide); k++) |
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200 | ide->m[k] = NULL; |
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201 | } |
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202 | pEnlargeSet(&(ide->m),IDELEMS(ide),j+1-IDELEMS(ide)); |
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203 | IDELEMS(ide) = j+1; |
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204 | } |
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205 | } |
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206 | |
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207 | /// count non-zero elements |
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208 | int idElem(const ideal F) |
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209 | { |
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210 | assume (F != NULL); |
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211 | |
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212 | int i=0,j=IDELEMS(F)-1; |
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213 | |
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214 | while(j>=0) |
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215 | { |
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216 | if ((F->m)[j]!=NULL) i++; |
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217 | j--; |
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218 | } |
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219 | return i; |
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220 | } |
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221 | |
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222 | /// copies the first k (>= 1) entries of the given ideal/module |
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223 | /// and returns these as a new ideal/module |
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224 | /// (Note that the copied entries may be zero.) |
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225 | ideal id_CopyFirstK (const ideal ide, const int k,const ring r) |
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226 | { |
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227 | id_Test(ide, r); |
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228 | |
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229 | assume( ide != NULL ); |
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230 | assume( k <= IDELEMS(ide) ); |
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231 | |
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232 | ideal newI = idInit(k, ide->rank); |
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233 | |
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234 | for (int i = 0; i < k; i++) |
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235 | newI->m[i] = p_Copy(ide->m[i],r); |
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236 | |
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237 | return newI; |
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238 | } |
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239 | |
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240 | /// ideal id = (id[i]), result is leadcoeff(id[i]) = 1 |
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241 | void id_Norm(ideal id, const ring r) |
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242 | { |
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243 | id_Test(id, r); |
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244 | for (int i=IDELEMS(id)-1; i>=0; i--) |
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245 | { |
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246 | if (id->m[i] != NULL) |
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247 | { |
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248 | p_Norm(id->m[i],r); |
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249 | } |
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250 | } |
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251 | } |
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252 | |
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253 | /// ideal id = (id[i]), c any unit |
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254 | /// if id[i] = c*id[j] then id[j] is deleted for j > i |
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255 | void id_DelMultiples(ideal id, const ring r) |
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256 | { |
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257 | id_Test(id, r); |
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258 | |
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259 | int i, j; |
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260 | int k = IDELEMS(id)-1; |
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261 | for (i=k; i>=0; i--) |
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262 | { |
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263 | if (id->m[i]!=NULL) |
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264 | { |
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265 | for (j=k; j>i; j--) |
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266 | { |
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267 | if (id->m[j]!=NULL) |
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268 | { |
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269 | if (rField_is_Ring(r)) |
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270 | { |
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271 | /* if id[j] = c*id[i] then delete id[j]. |
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272 | In the below cases of a ground field, we |
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273 | check whether id[i] = c*id[j] and, if so, |
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274 | delete id[j] for historical reasons (so |
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275 | that previous output does not change) */ |
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276 | if (p_ComparePolys(id->m[j], id->m[i],r)) p_Delete(&id->m[j],r); |
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277 | } |
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278 | else |
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279 | { |
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280 | if (p_ComparePolys(id->m[i], id->m[j],r)) p_Delete(&id->m[j],r); |
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281 | } |
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282 | } |
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283 | } |
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284 | } |
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285 | } |
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286 | } |
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287 | |
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288 | /// ideal id = (id[i]) |
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289 | /// if id[i] = id[j] then id[j] is deleted for j > i |
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290 | void id_DelEquals(ideal id, const ring r) |
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291 | { |
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292 | id_Test(id, r); |
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293 | |
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294 | int i, j; |
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295 | int k = IDELEMS(id)-1; |
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296 | for (i=k; i>=0; i--) |
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297 | { |
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298 | if (id->m[i]!=NULL) |
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299 | { |
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300 | for (j=k; j>i; j--) |
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301 | { |
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302 | if ((id->m[j]!=NULL) |
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303 | && (p_EqualPolys(id->m[i], id->m[j],r))) |
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304 | { |
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305 | p_Delete(&id->m[j],r); |
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306 | } |
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307 | } |
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308 | } |
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309 | } |
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310 | } |
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311 | |
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312 | /// Delete id[j], if Lm(j) == Lm(i) and both LC(j), LC(i) are units and j > i |
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313 | void id_DelLmEquals(ideal id, const ring r) |
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314 | { |
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315 | id_Test(id, r); |
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316 | |
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317 | int i, j; |
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318 | int k = IDELEMS(id)-1; |
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319 | for (i=k; i>=0; i--) |
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320 | { |
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321 | if (id->m[i] != NULL) |
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322 | { |
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323 | for (j=k; j>i; j--) |
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324 | { |
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325 | if ((id->m[j] != NULL) |
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326 | && p_LmEqual(id->m[i], id->m[j],r) |
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327 | #ifdef HAVE_RINGS |
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328 | && n_IsUnit(pGetCoeff(id->m[i]),r->cf) && n_IsUnit(pGetCoeff(id->m[j]),r->cf) |
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329 | #endif |
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330 | ) |
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331 | { |
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332 | p_Delete(&id->m[j],r); |
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333 | } |
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334 | } |
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335 | } |
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336 | } |
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337 | } |
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338 | |
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339 | /// delete id[j], if LT(j) == coeff*mon*LT(i) and vice versa, i.e., |
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340 | /// delete id[i], if LT(i) == coeff*mon*LT(j) |
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341 | void id_DelDiv(ideal id, const ring r) |
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342 | { |
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343 | id_Test(id, r); |
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344 | |
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345 | int i, j; |
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346 | int k = IDELEMS(id)-1; |
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347 | for (i=k; i>=0; i--) |
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348 | { |
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349 | if (id->m[i] != NULL) |
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350 | { |
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351 | for (j=k; j>i; j--) |
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352 | { |
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353 | if (id->m[j]!=NULL) |
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354 | { |
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355 | if (rField_is_Ring(r)) |
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356 | { |
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357 | if (p_DivisibleByRingCase(id->m[i], id->m[j],r)) |
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358 | { |
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359 | p_Delete(&id->m[j],r); |
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360 | } |
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361 | else if (p_DivisibleByRingCase(id->m[j], id->m[i],r)) |
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362 | { |
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363 | p_Delete(&id->m[i],r); |
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364 | break; |
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365 | } |
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366 | } |
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367 | else |
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368 | { |
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369 | /* the case of a ground field: */ |
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370 | if (p_DivisibleBy(id->m[i], id->m[j],r)) |
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371 | { |
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372 | p_Delete(&id->m[j],r); |
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373 | } |
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374 | else if (p_DivisibleBy(id->m[j], id->m[i],r)) |
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375 | { |
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376 | p_Delete(&id->m[i],r); |
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377 | break; |
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378 | } |
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379 | } |
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380 | } |
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381 | } |
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382 | } |
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383 | } |
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384 | } |
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385 | |
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386 | /// test if the ideal has only constant polynomials |
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387 | /// NOTE: zero ideal/module is also constant |
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388 | BOOLEAN id_IsConstant(ideal id, const ring r) |
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389 | { |
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390 | id_Test(id, r); |
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391 | |
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392 | for (int k = IDELEMS(id)-1; k>=0; k--) |
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393 | { |
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394 | if (!p_IsConstantPoly(id->m[k],r)) |
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395 | return FALSE; |
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396 | } |
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397 | return TRUE; |
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398 | } |
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399 | |
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400 | /// copy an ideal |
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401 | ideal id_Copy(ideal h1, const ring r) |
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402 | { |
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403 | id_Test(h1, r); |
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404 | |
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405 | ideal h2 = idInit(IDELEMS(h1), h1->rank); |
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406 | for (int 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 | return h2; |
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409 | } |
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410 | |
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411 | #ifdef PDEBUG |
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412 | /// Internal verification for ideals/modules and dense matrices! |
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413 | void id_DBTest(ideal h1, int level, const char *f,const int l, const ring r, const ring tailRing) |
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414 | { |
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415 | if (h1 != NULL) |
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416 | { |
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417 | // assume(IDELEMS(h1) > 0); for ideal/module, does not apply to matrix |
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418 | omCheckAddrSize(h1,sizeof(*h1)); |
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419 | |
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420 | assume( h1->ncols >= 0 ); |
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421 | assume( h1->nrows >= 0 ); // matrix case! |
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422 | |
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423 | assume( h1->rank >= 0 ); |
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424 | |
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425 | const int n = (h1->ncols * h1->nrows); |
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426 | |
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427 | assume( !( n > 0 && h1->m == NULL) ); |
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428 | |
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429 | if( h1->m != NULL && n > 0 ) |
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430 | omdebugAddrSize(h1->m, n * sizeof(poly)); |
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431 | |
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432 | long new_rk = 0; // inlining id_RankFreeModule(h1, r, tailRing); |
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433 | |
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434 | /* to be able to test matrices: */ |
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435 | for (int i=n - 1; i >= 0; i--) |
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436 | { |
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437 | _pp_Test(h1->m[i], r, tailRing, level); |
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438 | const long k = p_MaxComp(h1->m[i], r, tailRing); |
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439 | if (k > new_rk) new_rk = k; |
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440 | } |
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441 | |
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442 | // dense matrices only contain polynomials: |
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443 | // h1->nrows == h1->rank > 1 && new_rk == 0! |
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444 | assume( !( h1->nrows == h1->rank && h1->nrows > 1 && new_rk > 0 ) ); // |
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445 | |
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446 | if(new_rk > h1->rank) |
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447 | { |
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448 | dReportError("wrong rank %d (should be %d) in %s:%d\n", |
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449 | h1->rank, new_rk, f,l); |
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450 | omPrintAddrInfo(stderr, h1, " for ideal"); |
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451 | h1->rank = new_rk; |
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452 | } |
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453 | } |
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454 | else |
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455 | { |
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456 | Print("error: ideal==NULL in %s:%d\n",f,l); |
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457 | assume( h1 != NULL ); |
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458 | } |
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459 | } |
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460 | #endif |
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461 | |
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462 | /// for idSort: compare a and b revlex inclusive module comp. |
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463 | static int p_Comp_RevLex(poly a, poly b,BOOLEAN nolex, const ring R) |
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464 | { |
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465 | if (b==NULL) return 1; |
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466 | if (a==NULL) return -1; |
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467 | |
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468 | if (nolex) |
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469 | { |
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470 | int r=p_LmCmp(a,b,R); |
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471 | if (r!=0) return r; |
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472 | number h=n_Sub(pGetCoeff(a),pGetCoeff(b),R->cf); |
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473 | r = -1+n_IsZero(h,R->cf)+2*n_GreaterZero(h,R->cf); /* -1: <, 0:==, 1: > */ |
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474 | n_Delete(&h, R->cf); |
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475 | return r; |
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476 | } |
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477 | int l=rVar(R); |
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478 | while ((l>0) && (p_GetExp(a,l,R)==p_GetExp(b,l,R))) l--; |
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479 | if (l==0) |
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480 | { |
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481 | if (p_GetComp(a,R)==p_GetComp(b,R)) |
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482 | { |
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483 | number h=n_Sub(pGetCoeff(a),pGetCoeff(b),R->cf); |
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484 | int r = -1+n_IsZero(h,R->cf)+2*n_GreaterZero(h,R->cf); /* -1: <, 0:==, 1: > */ |
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485 | n_Delete(&h,R->cf); |
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486 | return r; |
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487 | } |
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488 | if (p_GetComp(a,R)>p_GetComp(b,R)) return 1; |
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489 | } |
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490 | else if (p_GetExp(a,l,R)>p_GetExp(b,l,R)) |
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491 | return 1; |
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492 | return -1; |
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493 | } |
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494 | |
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495 | // sorts the ideal w.r.t. the actual ringordering |
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496 | // uses lex-ordering when nolex = FALSE |
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497 | intvec *id_Sort(const ideal id, const BOOLEAN nolex, const ring r) |
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498 | { |
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499 | id_Test(id, r); |
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500 | |
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501 | intvec * result = new intvec(IDELEMS(id)); |
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502 | int i, j, actpos=0, newpos; |
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503 | int diff, olddiff, lastcomp, newcomp; |
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504 | BOOLEAN notFound; |
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505 | |
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506 | for (i=0;i<IDELEMS(id);i++) |
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507 | { |
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508 | if (id->m[i]!=NULL) |
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509 | { |
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510 | notFound = TRUE; |
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511 | newpos = actpos / 2; |
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512 | diff = (actpos+1) / 2; |
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513 | diff = (diff+1) / 2; |
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514 | lastcomp = p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r); |
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515 | if (lastcomp<0) |
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516 | { |
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517 | newpos -= diff; |
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518 | } |
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519 | else if (lastcomp>0) |
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520 | { |
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521 | newpos += diff; |
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522 | } |
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523 | else |
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524 | { |
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525 | notFound = FALSE; |
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526 | } |
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527 | //while ((newpos>=0) && (newpos<actpos) && (notFound)) |
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528 | while (notFound && (newpos>=0) && (newpos<actpos)) |
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529 | { |
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530 | newcomp = p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r); |
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531 | olddiff = diff; |
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532 | if (diff>1) |
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533 | { |
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534 | diff = (diff+1) / 2; |
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535 | if ((newcomp==1) |
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536 | && (actpos-newpos>1) |
---|
537 | && (diff>1) |
---|
538 | && (newpos+diff>=actpos)) |
---|
539 | { |
---|
540 | diff = actpos-newpos-1; |
---|
541 | } |
---|
542 | else if ((newcomp==-1) |
---|
543 | && (diff>1) |
---|
544 | && (newpos<diff)) |
---|
545 | { |
---|
546 | diff = newpos; |
---|
547 | } |
---|
548 | } |
---|
549 | if (newcomp<0) |
---|
550 | { |
---|
551 | if ((olddiff==1) && (lastcomp>0)) |
---|
552 | notFound = FALSE; |
---|
553 | else |
---|
554 | newpos -= diff; |
---|
555 | } |
---|
556 | else if (newcomp>0) |
---|
557 | { |
---|
558 | if ((olddiff==1) && (lastcomp<0)) |
---|
559 | { |
---|
560 | notFound = FALSE; |
---|
561 | newpos++; |
---|
562 | } |
---|
563 | else |
---|
564 | { |
---|
565 | newpos += diff; |
---|
566 | } |
---|
567 | } |
---|
568 | else |
---|
569 | { |
---|
570 | notFound = FALSE; |
---|
571 | } |
---|
572 | lastcomp = newcomp; |
---|
573 | if (diff==0) notFound=FALSE; /*hs*/ |
---|
574 | } |
---|
575 | if (newpos<0) newpos = 0; |
---|
576 | if (newpos>actpos) newpos = actpos; |
---|
577 | while ((newpos<actpos) && (p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r)==0)) |
---|
578 | newpos++; |
---|
579 | for (j=actpos;j>newpos;j--) |
---|
580 | { |
---|
581 | (*result)[j] = (*result)[j-1]; |
---|
582 | } |
---|
583 | (*result)[newpos] = i; |
---|
584 | actpos++; |
---|
585 | } |
---|
586 | } |
---|
587 | for (j=0;j<actpos;j++) (*result)[j]++; |
---|
588 | return result; |
---|
589 | } |
---|
590 | |
---|
591 | /// concat the lists h1 and h2 without zeros |
---|
592 | ideal id_SimpleAdd (ideal h1,ideal h2, const ring R) |
---|
593 | { |
---|
594 | id_Test(h1, R); |
---|
595 | id_Test(h2, R); |
---|
596 | |
---|
597 | if ( idIs0(h1) ) |
---|
598 | { |
---|
599 | ideal res=id_Copy(h2,R); |
---|
600 | if (res->rank<h1->rank) res->rank=h1->rank; |
---|
601 | return res; |
---|
602 | } |
---|
603 | if ( idIs0(h2) ) |
---|
604 | { |
---|
605 | ideal res=id_Copy(h1,R); |
---|
606 | if (res->rank<h2->rank) res->rank=h2->rank; |
---|
607 | return res; |
---|
608 | } |
---|
609 | |
---|
610 | int j = IDELEMS(h1)-1; |
---|
611 | while ((j >= 0) && (h1->m[j] == NULL)) j--; |
---|
612 | |
---|
613 | int i = IDELEMS(h2)-1; |
---|
614 | while ((i >= 0) && (h2->m[i] == NULL)) i--; |
---|
615 | |
---|
616 | const int r = si_max(h1->rank, h2->rank); |
---|
617 | |
---|
618 | ideal result = idInit(i+j+2,r); |
---|
619 | |
---|
620 | int l; |
---|
621 | |
---|
622 | for (l=j; l>=0; l--) |
---|
623 | result->m[l] = p_Copy(h1->m[l],R); |
---|
624 | |
---|
625 | j = i+j+1; |
---|
626 | for (l=i; l>=0; l--, j--) |
---|
627 | result->m[j] = p_Copy(h2->m[l],R); |
---|
628 | |
---|
629 | return result; |
---|
630 | } |
---|
631 | |
---|
632 | /// insert h2 into h1 (if h2 is not the zero polynomial) |
---|
633 | /// return TRUE iff h2 was indeed inserted |
---|
634 | BOOLEAN idInsertPoly (ideal h1, poly h2) |
---|
635 | { |
---|
636 | if (h2==NULL) return FALSE; |
---|
637 | assume (h1 != NULL); |
---|
638 | |
---|
639 | int j = IDELEMS(h1) - 1; |
---|
640 | |
---|
641 | while ((j >= 0) && (h1->m[j] == NULL)) j--; |
---|
642 | j++; |
---|
643 | if (j==IDELEMS(h1)) |
---|
644 | { |
---|
645 | pEnlargeSet(&(h1->m),IDELEMS(h1),16); |
---|
646 | IDELEMS(h1)+=16; |
---|
647 | } |
---|
648 | h1->m[j]=h2; |
---|
649 | return TRUE; |
---|
650 | } |
---|
651 | |
---|
652 | |
---|
653 | /*! insert h2 into h1 depending on the two boolean parameters: |
---|
654 | * - if zeroOk is true, then h2 will also be inserted when it is zero |
---|
655 | * - if duplicateOk is true, then h2 will also be inserted when it is |
---|
656 | * already present in h1 |
---|
657 | * return TRUE iff h2 was indeed inserted |
---|
658 | */ |
---|
659 | BOOLEAN id_InsertPolyWithTests (ideal h1, const int validEntries, |
---|
660 | const poly h2, const bool zeroOk, const bool duplicateOk, const ring r) |
---|
661 | { |
---|
662 | id_Test(h1, r); |
---|
663 | p_Test(h2, r); |
---|
664 | |
---|
665 | if ((!zeroOk) && (h2 == NULL)) return FALSE; |
---|
666 | if (!duplicateOk) |
---|
667 | { |
---|
668 | bool h2FoundInH1 = false; |
---|
669 | int i = 0; |
---|
670 | while ((i < validEntries) && (!h2FoundInH1)) |
---|
671 | { |
---|
672 | h2FoundInH1 = p_EqualPolys(h1->m[i], h2,r); |
---|
673 | i++; |
---|
674 | } |
---|
675 | if (h2FoundInH1) return FALSE; |
---|
676 | } |
---|
677 | if (validEntries == IDELEMS(h1)) |
---|
678 | { |
---|
679 | pEnlargeSet(&(h1->m), IDELEMS(h1), 16); |
---|
680 | IDELEMS(h1) += 16; |
---|
681 | } |
---|
682 | h1->m[validEntries] = h2; |
---|
683 | return TRUE; |
---|
684 | } |
---|
685 | |
---|
686 | /// h1 + h2 |
---|
687 | ideal id_Add (ideal h1,ideal h2, const ring r) |
---|
688 | { |
---|
689 | id_Test(h1, r); |
---|
690 | id_Test(h2, r); |
---|
691 | |
---|
692 | ideal result = id_SimpleAdd(h1,h2,r); |
---|
693 | id_Compactify(result,r); |
---|
694 | return result; |
---|
695 | } |
---|
696 | |
---|
697 | /// h1 * h2 |
---|
698 | /// one h_i must be an ideal (with at least one column) |
---|
699 | /// the other h_i may be a module (with no columns at all) |
---|
700 | ideal id_Mult (ideal h1,ideal h2, const ring R) |
---|
701 | { |
---|
702 | id_Test(h1, R); |
---|
703 | id_Test(h2, R); |
---|
704 | |
---|
705 | int j = IDELEMS(h1); |
---|
706 | while ((j > 0) && (h1->m[j-1] == NULL)) j--; |
---|
707 | |
---|
708 | int i = IDELEMS(h2); |
---|
709 | while ((i > 0) && (h2->m[i-1] == NULL)) i--; |
---|
710 | |
---|
711 | j *= i; |
---|
712 | int r = si_max( h2->rank, h1->rank ); |
---|
713 | if (j==0) |
---|
714 | { |
---|
715 | if ((IDELEMS(h1)>0) && (IDELEMS(h2)>0)) j=1; |
---|
716 | return idInit(j, r); |
---|
717 | } |
---|
718 | ideal hh = idInit(j, r); |
---|
719 | |
---|
720 | int k = 0; |
---|
721 | for (i=0; i<IDELEMS(h1); i++) |
---|
722 | { |
---|
723 | if (h1->m[i] != NULL) |
---|
724 | { |
---|
725 | for (j=0; j<IDELEMS(h2); j++) |
---|
726 | { |
---|
727 | if (h2->m[j] != NULL) |
---|
728 | { |
---|
729 | hh->m[k] = pp_Mult_qq(h1->m[i],h2->m[j],R); |
---|
730 | k++; |
---|
731 | } |
---|
732 | } |
---|
733 | } |
---|
734 | } |
---|
735 | |
---|
736 | id_Compactify(hh,R); |
---|
737 | return hh; |
---|
738 | } |
---|
739 | |
---|
740 | /// returns true if h is the zero ideal |
---|
741 | BOOLEAN idIs0 (ideal h) |
---|
742 | { |
---|
743 | assume (h != NULL); // will fail :( |
---|
744 | // if (h == NULL) return TRUE; |
---|
745 | |
---|
746 | for( int i = IDELEMS(h)-1; i >= 0; i-- ) |
---|
747 | if(h->m[i] != NULL) |
---|
748 | return FALSE; |
---|
749 | |
---|
750 | return TRUE; |
---|
751 | |
---|
752 | } |
---|
753 | |
---|
754 | /// return the maximal component number found in any polynomial in s |
---|
755 | long id_RankFreeModule (ideal s, ring lmRing, ring tailRing) |
---|
756 | { |
---|
757 | id_TestTail(s, lmRing, tailRing); |
---|
758 | |
---|
759 | long j = 0; |
---|
760 | |
---|
761 | if (rRing_has_Comp(tailRing) && rRing_has_Comp(lmRing)) |
---|
762 | { |
---|
763 | poly *p=s->m; |
---|
764 | for (unsigned int l=IDELEMS(s); l > 0; --l, ++p) |
---|
765 | if (*p != NULL) |
---|
766 | { |
---|
767 | pp_Test(*p, lmRing, tailRing); |
---|
768 | const long k = p_MaxComp(*p, lmRing, tailRing); |
---|
769 | if (k>j) j = k; |
---|
770 | } |
---|
771 | } |
---|
772 | |
---|
773 | return j; // return -1; |
---|
774 | } |
---|
775 | |
---|
776 | /*2 |
---|
777 | *returns true if id is homogenous with respect to the aktual weights |
---|
778 | */ |
---|
779 | BOOLEAN id_HomIdeal (ideal id, ideal Q, const ring r) |
---|
780 | { |
---|
781 | int i; |
---|
782 | BOOLEAN b; |
---|
783 | i = 0; |
---|
784 | b = TRUE; |
---|
785 | while ((i < IDELEMS(id)) && b) |
---|
786 | { |
---|
787 | b = p_IsHomogeneous(id->m[i],r); |
---|
788 | i++; |
---|
789 | } |
---|
790 | if ((b) && (Q!=NULL) && (IDELEMS(Q)>0)) |
---|
791 | { |
---|
792 | i=0; |
---|
793 | while ((i < IDELEMS(Q)) && b) |
---|
794 | { |
---|
795 | b = p_IsHomogeneous(Q->m[i],r); |
---|
796 | i++; |
---|
797 | } |
---|
798 | } |
---|
799 | return b; |
---|
800 | } |
---|
801 | |
---|
802 | /*2 |
---|
803 | *initialized a field with r numbers between beg and end for the |
---|
804 | *procedure idNextChoise |
---|
805 | */ |
---|
806 | void idInitChoise (int r,int beg,int end,BOOLEAN *endch,int * choise) |
---|
807 | { |
---|
808 | /*returns the first choise of r numbers between beg and end*/ |
---|
809 | int i; |
---|
810 | for (i=0; i<r; i++) |
---|
811 | { |
---|
812 | choise[i] = 0; |
---|
813 | } |
---|
814 | if (r <= end-beg+1) |
---|
815 | for (i=0; i<r; i++) |
---|
816 | { |
---|
817 | choise[i] = beg+i; |
---|
818 | } |
---|
819 | if (r > end-beg+1) |
---|
820 | *endch = TRUE; |
---|
821 | else |
---|
822 | *endch = FALSE; |
---|
823 | } |
---|
824 | |
---|
825 | /*2 |
---|
826 | *returns the next choise of r numbers between beg and end |
---|
827 | */ |
---|
828 | void idGetNextChoise (int r,int end,BOOLEAN *endch,int * choise) |
---|
829 | { |
---|
830 | int i = r-1,j; |
---|
831 | while ((i >= 0) && (choise[i] == end)) |
---|
832 | { |
---|
833 | i--; |
---|
834 | end--; |
---|
835 | } |
---|
836 | if (i == -1) |
---|
837 | *endch = TRUE; |
---|
838 | else |
---|
839 | { |
---|
840 | choise[i]++; |
---|
841 | for (j=i+1; j<r; j++) |
---|
842 | { |
---|
843 | choise[j] = choise[i]+j-i; |
---|
844 | } |
---|
845 | *endch = FALSE; |
---|
846 | } |
---|
847 | } |
---|
848 | |
---|
849 | /*2 |
---|
850 | *takes the field choise of d numbers between beg and end, cancels the t-th |
---|
851 | *entree and searches for the ordinal number of that d-1 dimensional field |
---|
852 | * w.r.t. the algorithm of construction |
---|
853 | */ |
---|
854 | int idGetNumberOfChoise(int t, int d, int begin, int end, int * choise) |
---|
855 | { |
---|
856 | int * localchoise,i,result=0; |
---|
857 | BOOLEAN b=FALSE; |
---|
858 | |
---|
859 | if (d<=1) return 1; |
---|
860 | localchoise=(int*)omAlloc((d-1)*sizeof(int)); |
---|
861 | idInitChoise(d-1,begin,end,&b,localchoise); |
---|
862 | while (!b) |
---|
863 | { |
---|
864 | result++; |
---|
865 | i = 0; |
---|
866 | while ((i<t) && (localchoise[i]==choise[i])) i++; |
---|
867 | if (i>=t) |
---|
868 | { |
---|
869 | i = t+1; |
---|
870 | while ((i<d) && (localchoise[i-1]==choise[i])) i++; |
---|
871 | if (i>=d) |
---|
872 | { |
---|
873 | omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
874 | return result; |
---|
875 | } |
---|
876 | } |
---|
877 | idGetNextChoise(d-1,end,&b,localchoise); |
---|
878 | } |
---|
879 | omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
880 | return 0; |
---|
881 | } |
---|
882 | |
---|
883 | /*2 |
---|
884 | *computes the binomial coefficient |
---|
885 | */ |
---|
886 | int binom (int n,int r) |
---|
887 | { |
---|
888 | int i,result; |
---|
889 | |
---|
890 | if (r==0) return 1; |
---|
891 | if (n-r<r) return binom(n,n-r); |
---|
892 | result = n-r+1; |
---|
893 | for (i=2;i<=r;i++) |
---|
894 | { |
---|
895 | result *= n-r+i; |
---|
896 | if (result<0) |
---|
897 | { |
---|
898 | WarnS("overflow in binomials"); |
---|
899 | return 0; |
---|
900 | } |
---|
901 | result /= i; |
---|
902 | } |
---|
903 | return result; |
---|
904 | } |
---|
905 | |
---|
906 | |
---|
907 | /// the free module of rank i |
---|
908 | ideal id_FreeModule (int i, const ring r) |
---|
909 | { |
---|
910 | assume(i >= 0); |
---|
911 | ideal h = idInit(i, i); |
---|
912 | |
---|
913 | for (int j=0; j<i; j++) |
---|
914 | { |
---|
915 | h->m[j] = p_One(r); |
---|
916 | p_SetComp(h->m[j],j+1,r); |
---|
917 | p_SetmComp(h->m[j],r); |
---|
918 | } |
---|
919 | |
---|
920 | return h; |
---|
921 | } |
---|
922 | |
---|
923 | /*2 |
---|
924 | *computes recursively all monomials of a certain degree |
---|
925 | *in every step the actvar-th entry in the exponential |
---|
926 | *vector is incremented and the other variables are |
---|
927 | *computed by recursive calls of makemonoms |
---|
928 | *if the last variable is reached, the difference to the |
---|
929 | *degree is computed directly |
---|
930 | *vars is the number variables |
---|
931 | *actvar is the actual variable to handle |
---|
932 | *deg is the degree of the monomials to compute |
---|
933 | *monomdeg is the actual degree of the monomial in consideration |
---|
934 | */ |
---|
935 | static void makemonoms(int vars,int actvar,int deg,int monomdeg, const ring r) |
---|
936 | { |
---|
937 | poly p; |
---|
938 | int i=0; |
---|
939 | |
---|
940 | if ((idpowerpoint == 0) && (actvar ==1)) |
---|
941 | { |
---|
942 | idpower[idpowerpoint] = p_One(r); |
---|
943 | monomdeg = 0; |
---|
944 | } |
---|
945 | while (i<=deg) |
---|
946 | { |
---|
947 | if (deg == monomdeg) |
---|
948 | { |
---|
949 | p_Setm(idpower[idpowerpoint],r); |
---|
950 | idpowerpoint++; |
---|
951 | return; |
---|
952 | } |
---|
953 | if (actvar == vars) |
---|
954 | { |
---|
955 | p_SetExp(idpower[idpowerpoint],actvar,deg-monomdeg,r); |
---|
956 | p_Setm(idpower[idpowerpoint],r); |
---|
957 | p_Test(idpower[idpowerpoint],r); |
---|
958 | idpowerpoint++; |
---|
959 | return; |
---|
960 | } |
---|
961 | else |
---|
962 | { |
---|
963 | p = p_Copy(idpower[idpowerpoint],r); |
---|
964 | makemonoms(vars,actvar+1,deg,monomdeg,r); |
---|
965 | idpower[idpowerpoint] = p; |
---|
966 | } |
---|
967 | monomdeg++; |
---|
968 | p_SetExp(idpower[idpowerpoint],actvar,p_GetExp(idpower[idpowerpoint],actvar,r)+1,r); |
---|
969 | p_Setm(idpower[idpowerpoint],r); |
---|
970 | p_Test(idpower[idpowerpoint],r); |
---|
971 | i++; |
---|
972 | } |
---|
973 | } |
---|
974 | |
---|
975 | /*2 |
---|
976 | *returns the deg-th power of the maximal ideal of 0 |
---|
977 | */ |
---|
978 | ideal id_MaxIdeal(int deg, const ring r) |
---|
979 | { |
---|
980 | if (deg < 0) |
---|
981 | { |
---|
982 | WarnS("maxideal: power must be non-negative"); |
---|
983 | } |
---|
984 | if (deg < 1) |
---|
985 | { |
---|
986 | ideal I=idInit(1,1); |
---|
987 | I->m[0]=p_One(r); |
---|
988 | return I; |
---|
989 | } |
---|
990 | if (deg == 1) |
---|
991 | { |
---|
992 | return id_MaxIdeal(r); |
---|
993 | } |
---|
994 | |
---|
995 | int vars = rVar(r); |
---|
996 | int i = binom(vars+deg-1,deg); |
---|
997 | if (i<=0) return idInit(1,1); |
---|
998 | ideal id=idInit(i,1); |
---|
999 | idpower = id->m; |
---|
1000 | idpowerpoint = 0; |
---|
1001 | makemonoms(vars,1,deg,0,r); |
---|
1002 | idpower = NULL; |
---|
1003 | idpowerpoint = 0; |
---|
1004 | return id; |
---|
1005 | } |
---|
1006 | |
---|
1007 | static void id_NextPotence(ideal given, ideal result, |
---|
1008 | int begin, int end, int deg, int restdeg, poly ap, const ring r) |
---|
1009 | { |
---|
1010 | poly p; |
---|
1011 | int i; |
---|
1012 | |
---|
1013 | p = p_Power(p_Copy(given->m[begin],r),restdeg,r); |
---|
1014 | i = result->nrows; |
---|
1015 | result->m[i] = p_Mult_q(p_Copy(ap,r),p,r); |
---|
1016 | //PrintS("."); |
---|
1017 | (result->nrows)++; |
---|
1018 | if (result->nrows >= IDELEMS(result)) |
---|
1019 | { |
---|
1020 | pEnlargeSet(&(result->m),IDELEMS(result),16); |
---|
1021 | IDELEMS(result) += 16; |
---|
1022 | } |
---|
1023 | if (begin == end) return; |
---|
1024 | for (i=restdeg-1;i>0;i--) |
---|
1025 | { |
---|
1026 | p = p_Power(p_Copy(given->m[begin],r),i,r); |
---|
1027 | p = p_Mult_q(p_Copy(ap,r),p,r); |
---|
1028 | id_NextPotence(given, result, begin+1, end, deg, restdeg-i, p,r); |
---|
1029 | p_Delete(&p,r); |
---|
1030 | } |
---|
1031 | id_NextPotence(given, result, begin+1, end, deg, restdeg, ap,r); |
---|
1032 | } |
---|
1033 | |
---|
1034 | ideal id_Power(ideal given,int exp, const ring r) |
---|
1035 | { |
---|
1036 | ideal result,temp; |
---|
1037 | poly p1; |
---|
1038 | int i; |
---|
1039 | |
---|
1040 | if (idIs0(given)) return idInit(1,1); |
---|
1041 | temp = id_Copy(given,r); |
---|
1042 | idSkipZeroes(temp); |
---|
1043 | i = binom(IDELEMS(temp)+exp-1,exp); |
---|
1044 | result = idInit(i,1); |
---|
1045 | result->nrows = 0; |
---|
1046 | //Print("ideal contains %d elements\n",i); |
---|
1047 | p1=p_One(r); |
---|
1048 | id_NextPotence(temp,result,0,IDELEMS(temp)-1,exp,exp,p1,r); |
---|
1049 | p_Delete(&p1,r); |
---|
1050 | id_Delete(&temp,r); |
---|
1051 | result->nrows = 1; |
---|
1052 | id_DelEquals(result,r); |
---|
1053 | idSkipZeroes(result); |
---|
1054 | return result; |
---|
1055 | } |
---|
1056 | |
---|
1057 | /*2 |
---|
1058 | *skips all zeroes and double elements, searches also for units |
---|
1059 | */ |
---|
1060 | void id_Compactify(ideal id, const ring r) |
---|
1061 | { |
---|
1062 | int i; |
---|
1063 | BOOLEAN b=FALSE; |
---|
1064 | |
---|
1065 | i = IDELEMS(id)-1; |
---|
1066 | while ((! b) && (i>=0)) |
---|
1067 | { |
---|
1068 | b=p_IsUnit(id->m[i],r); |
---|
1069 | i--; |
---|
1070 | } |
---|
1071 | if (b) |
---|
1072 | { |
---|
1073 | for(i=IDELEMS(id)-1;i>=0;i--) p_Delete(&id->m[i],r); |
---|
1074 | id->m[0]=p_One(r); |
---|
1075 | } |
---|
1076 | else |
---|
1077 | { |
---|
1078 | id_DelMultiples(id,r); |
---|
1079 | } |
---|
1080 | idSkipZeroes(id); |
---|
1081 | } |
---|
1082 | |
---|
1083 | /// returns the ideals of initial terms |
---|
1084 | ideal id_Head(ideal h,const ring r) |
---|
1085 | { |
---|
1086 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
1087 | |
---|
1088 | for (int i=IDELEMS(h)-1;i>=0; i--) |
---|
1089 | if (h->m[i]!=NULL) |
---|
1090 | m->m[i]=p_Head(h->m[i],r); |
---|
1091 | |
---|
1092 | return m; |
---|
1093 | } |
---|
1094 | |
---|
1095 | ideal id_Homogen(ideal h, int varnum,const ring r) |
---|
1096 | { |
---|
1097 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
1098 | int i; |
---|
1099 | |
---|
1100 | for (i=IDELEMS(h)-1;i>=0; i--) |
---|
1101 | { |
---|
1102 | m->m[i]=p_Homogen(h->m[i],varnum,r); |
---|
1103 | } |
---|
1104 | return m; |
---|
1105 | } |
---|
1106 | |
---|
1107 | /*------------------type conversions----------------*/ |
---|
1108 | ideal id_Vec2Ideal(poly vec, const ring R) |
---|
1109 | { |
---|
1110 | ideal result=idInit(1,1); |
---|
1111 | omFree((ADDRESS)result->m); |
---|
1112 | result->m=NULL; // remove later |
---|
1113 | p_Vec2Polys(vec, &(result->m), &(IDELEMS(result)),R); |
---|
1114 | return result; |
---|
1115 | } |
---|
1116 | |
---|
1117 | |
---|
1118 | // converts mat to module, destroys mat |
---|
1119 | ideal id_Matrix2Module(matrix mat, const ring R) |
---|
1120 | { |
---|
1121 | int mc=MATCOLS(mat); |
---|
1122 | int mr=MATROWS(mat); |
---|
1123 | ideal result = idInit(mc,mr); |
---|
1124 | int i,j,l; |
---|
1125 | poly h; |
---|
1126 | sBucket_pt bucket = sBucketCreate(R); |
---|
1127 | |
---|
1128 | for(j=0;j<mc /*MATCOLS(mat)*/;j++) /* j is also index in result->m */ |
---|
1129 | { |
---|
1130 | for (i=1;i<=mr /*MATROWS(mat)*/;i++) |
---|
1131 | { |
---|
1132 | h = MATELEM(mat,i,j+1); |
---|
1133 | if (h!=NULL) |
---|
1134 | { |
---|
1135 | l=pLength(h); |
---|
1136 | MATELEM(mat,i,j+1)=NULL; |
---|
1137 | p_SetCompP(h,i, R); |
---|
1138 | sBucket_Merge_p(bucket, h, l); |
---|
1139 | } |
---|
1140 | } |
---|
1141 | sBucketClearMerge(bucket, &(result->m[j]), &l); |
---|
1142 | } |
---|
1143 | sBucketDestroy(&bucket); |
---|
1144 | |
---|
1145 | // obachman: need to clean this up |
---|
1146 | id_Delete((ideal*) &mat,R); |
---|
1147 | return result; |
---|
1148 | } |
---|
1149 | |
---|
1150 | /*2 |
---|
1151 | * converts a module into a matrix, destroyes the input |
---|
1152 | */ |
---|
1153 | matrix id_Module2Matrix(ideal mod, const ring R) |
---|
1154 | { |
---|
1155 | matrix result = mpNew(mod->rank,IDELEMS(mod)); |
---|
1156 | long i; long cp; |
---|
1157 | poly p,h; |
---|
1158 | |
---|
1159 | for(i=0;i<IDELEMS(mod);i++) |
---|
1160 | { |
---|
1161 | p=pReverse(mod->m[i]); |
---|
1162 | mod->m[i]=NULL; |
---|
1163 | while (p!=NULL) |
---|
1164 | { |
---|
1165 | h=p; |
---|
1166 | pIter(p); |
---|
1167 | pNext(h)=NULL; |
---|
1168 | cp = si_max(1L,p_GetComp(h, R)); // if used for ideals too |
---|
1169 | //cp = p_GetComp(h,R); |
---|
1170 | p_SetComp(h,0,R); |
---|
1171 | p_SetmComp(h,R); |
---|
1172 | #ifdef TEST |
---|
1173 | if (cp>mod->rank) |
---|
1174 | { |
---|
1175 | Print("## inv. rank %ld -> %ld\n",mod->rank,cp); |
---|
1176 | int k,l,o=mod->rank; |
---|
1177 | mod->rank=cp; |
---|
1178 | matrix d=mpNew(mod->rank,IDELEMS(mod)); |
---|
1179 | for (l=1; l<=o; l++) |
---|
1180 | { |
---|
1181 | for (k=1; k<=IDELEMS(mod); k++) |
---|
1182 | { |
---|
1183 | MATELEM(d,l,k)=MATELEM(result,l,k); |
---|
1184 | MATELEM(result,l,k)=NULL; |
---|
1185 | } |
---|
1186 | } |
---|
1187 | id_Delete((ideal *)&result,R); |
---|
1188 | result=d; |
---|
1189 | } |
---|
1190 | #endif |
---|
1191 | MATELEM(result,cp,i+1) = p_Add_q(MATELEM(result,cp,i+1),h,R); |
---|
1192 | } |
---|
1193 | } |
---|
1194 | // obachman 10/99: added the following line, otherwise memory leack! |
---|
1195 | id_Delete(&mod,R); |
---|
1196 | return result; |
---|
1197 | } |
---|
1198 | |
---|
1199 | matrix id_Module2formatedMatrix(ideal mod,int rows, int cols, const ring R) |
---|
1200 | { |
---|
1201 | matrix result = mpNew(rows,cols); |
---|
1202 | int i,cp,r=id_RankFreeModule(mod,R),c=IDELEMS(mod); |
---|
1203 | poly p,h; |
---|
1204 | |
---|
1205 | if (r>rows) r = rows; |
---|
1206 | if (c>cols) c = cols; |
---|
1207 | for(i=0;i<c;i++) |
---|
1208 | { |
---|
1209 | p=pReverse(mod->m[i]); |
---|
1210 | mod->m[i]=NULL; |
---|
1211 | while (p!=NULL) |
---|
1212 | { |
---|
1213 | h=p; |
---|
1214 | pIter(p); |
---|
1215 | pNext(h)=NULL; |
---|
1216 | cp = p_GetComp(h,R); |
---|
1217 | if (cp<=r) |
---|
1218 | { |
---|
1219 | p_SetComp(h,0,R); |
---|
1220 | p_SetmComp(h,R); |
---|
1221 | MATELEM(result,cp,i+1) = p_Add_q(MATELEM(result,cp,i+1),h,R); |
---|
1222 | } |
---|
1223 | else |
---|
1224 | p_Delete(&h,R); |
---|
1225 | } |
---|
1226 | } |
---|
1227 | id_Delete(&mod,R); |
---|
1228 | return result; |
---|
1229 | } |
---|
1230 | |
---|
1231 | /*2 |
---|
1232 | * substitute the n-th variable by the monomial e in id |
---|
1233 | * destroy id |
---|
1234 | */ |
---|
1235 | ideal id_Subst(ideal id, int n, poly e, const ring r) |
---|
1236 | { |
---|
1237 | int k=MATROWS((matrix)id)*MATCOLS((matrix)id); |
---|
1238 | ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id)); |
---|
1239 | |
---|
1240 | res->rank = id->rank; |
---|
1241 | for(k--;k>=0;k--) |
---|
1242 | { |
---|
1243 | res->m[k]=p_Subst(id->m[k],n,e,r); |
---|
1244 | id->m[k]=NULL; |
---|
1245 | } |
---|
1246 | id_Delete(&id,r); |
---|
1247 | return res; |
---|
1248 | } |
---|
1249 | |
---|
1250 | BOOLEAN id_HomModule(ideal m, ideal Q, intvec **w, const ring R) |
---|
1251 | { |
---|
1252 | if (w!=NULL) *w=NULL; |
---|
1253 | if ((Q!=NULL) && (!id_HomIdeal(Q,NULL,R))) return FALSE; |
---|
1254 | if (idIs0(m)) |
---|
1255 | { |
---|
1256 | if (w!=NULL) (*w)=new intvec(m->rank); |
---|
1257 | return TRUE; |
---|
1258 | } |
---|
1259 | |
---|
1260 | long cmax=1,order=0,ord,* diff,diffmin=32000; |
---|
1261 | int *iscom; |
---|
1262 | int i; |
---|
1263 | poly p=NULL; |
---|
1264 | pFDegProc d; |
---|
1265 | if (R->pLexOrder && (R->order[0]==ringorder_lp)) |
---|
1266 | d=p_Totaldegree; |
---|
1267 | else |
---|
1268 | d=R->pFDeg; |
---|
1269 | int length=IDELEMS(m); |
---|
1270 | poly* P=m->m; |
---|
1271 | poly* F=(poly*)omAlloc(length*sizeof(poly)); |
---|
1272 | for (i=length-1;i>=0;i--) |
---|
1273 | { |
---|
1274 | p=F[i]=P[i]; |
---|
1275 | cmax=si_max(cmax,p_MaxComp(p,R)); |
---|
1276 | } |
---|
1277 | cmax++; |
---|
1278 | diff = (long *)omAlloc0(cmax*sizeof(long)); |
---|
1279 | if (w!=NULL) *w=new intvec(cmax-1); |
---|
1280 | iscom = (int *)omAlloc0(cmax*sizeof(int)); |
---|
1281 | i=0; |
---|
1282 | while (i<=length) |
---|
1283 | { |
---|
1284 | if (i<length) |
---|
1285 | { |
---|
1286 | p=F[i]; |
---|
1287 | while ((p!=NULL) && (iscom[p_GetComp(p,R)]==0)) pIter(p); |
---|
1288 | } |
---|
1289 | if ((p==NULL) && (i<length)) |
---|
1290 | { |
---|
1291 | i++; |
---|
1292 | } |
---|
1293 | else |
---|
1294 | { |
---|
1295 | if (p==NULL) /* && (i==length) */ |
---|
1296 | { |
---|
1297 | i=0; |
---|
1298 | while ((i<length) && (F[i]==NULL)) i++; |
---|
1299 | if (i>=length) break; |
---|
1300 | p = F[i]; |
---|
1301 | } |
---|
1302 | //if (pLexOrder && (currRing->order[0]==ringorder_lp)) |
---|
1303 | // order=pTotaldegree(p); |
---|
1304 | //else |
---|
1305 | // order = p->order; |
---|
1306 | // order = pFDeg(p,currRing); |
---|
1307 | order = d(p,R) +diff[p_GetComp(p,R)]; |
---|
1308 | //order += diff[pGetComp(p)]; |
---|
1309 | p = F[i]; |
---|
1310 | //Print("Actual p=F[%d]: ",i);pWrite(p); |
---|
1311 | F[i] = NULL; |
---|
1312 | i=0; |
---|
1313 | } |
---|
1314 | while (p!=NULL) |
---|
1315 | { |
---|
1316 | if (R->pLexOrder && (R->order[0]==ringorder_lp)) |
---|
1317 | ord=p_Totaldegree(p,R); |
---|
1318 | else |
---|
1319 | // ord = p->order; |
---|
1320 | ord = R->pFDeg(p,R); |
---|
1321 | if (iscom[p_GetComp(p,R)]==0) |
---|
1322 | { |
---|
1323 | diff[p_GetComp(p,R)] = order-ord; |
---|
1324 | iscom[p_GetComp(p,R)] = 1; |
---|
1325 | /* |
---|
1326 | *PrintS("new diff: "); |
---|
1327 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
1328 | *PrintLn(); |
---|
1329 | *PrintS("new iscom: "); |
---|
1330 | *for (j=0;j<cmax;j++) Print("%d ",iscom[j]); |
---|
1331 | *PrintLn(); |
---|
1332 | *Print("new set %d, order %d, ord %d, diff %d\n",pGetComp(p),order,ord,diff[pGetComp(p)]); |
---|
1333 | */ |
---|
1334 | } |
---|
1335 | else |
---|
1336 | { |
---|
1337 | /* |
---|
1338 | *PrintS("new diff: "); |
---|
1339 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
1340 | *PrintLn(); |
---|
1341 | *Print("order %d, ord %d, diff %d\n",order,ord,diff[pGetComp(p)]); |
---|
1342 | */ |
---|
1343 | if (order != (ord+diff[p_GetComp(p,R)])) |
---|
1344 | { |
---|
1345 | omFreeSize((ADDRESS) iscom,cmax*sizeof(int)); |
---|
1346 | omFreeSize((ADDRESS) diff,cmax*sizeof(long)); |
---|
1347 | omFreeSize((ADDRESS) F,length*sizeof(poly)); |
---|
1348 | delete *w;*w=NULL; |
---|
1349 | return FALSE; |
---|
1350 | } |
---|
1351 | } |
---|
1352 | pIter(p); |
---|
1353 | } |
---|
1354 | } |
---|
1355 | omFreeSize((ADDRESS) iscom,cmax*sizeof(int)); |
---|
1356 | omFreeSize((ADDRESS) F,length*sizeof(poly)); |
---|
1357 | for (i=1;i<cmax;i++) (**w)[i-1]=(int)(diff[i]); |
---|
1358 | for (i=1;i<cmax;i++) |
---|
1359 | { |
---|
1360 | if (diff[i]<diffmin) diffmin=diff[i]; |
---|
1361 | } |
---|
1362 | if (w!=NULL) |
---|
1363 | { |
---|
1364 | for (i=1;i<cmax;i++) |
---|
1365 | { |
---|
1366 | (**w)[i-1]=(int)(diff[i]-diffmin); |
---|
1367 | } |
---|
1368 | } |
---|
1369 | omFreeSize((ADDRESS) diff,cmax*sizeof(long)); |
---|
1370 | return TRUE; |
---|
1371 | } |
---|
1372 | |
---|
1373 | ideal id_Jet(ideal i,int d, const ring R) |
---|
1374 | { |
---|
1375 | ideal r=idInit((i->nrows)*(i->ncols),i->rank); |
---|
1376 | r->nrows = i-> nrows; |
---|
1377 | r->ncols = i-> ncols; |
---|
1378 | //r->rank = i-> rank; |
---|
1379 | |
---|
1380 | for(int k=(i->nrows)*(i->ncols)-1;k>=0; k--) |
---|
1381 | r->m[k]=pp_Jet(i->m[k],d,R); |
---|
1382 | |
---|
1383 | return r; |
---|
1384 | } |
---|
1385 | |
---|
1386 | ideal id_JetW(ideal i,int d, intvec * iv, const ring R) |
---|
1387 | { |
---|
1388 | ideal r=idInit(IDELEMS(i),i->rank); |
---|
1389 | if (ecartWeights!=NULL) |
---|
1390 | { |
---|
1391 | WerrorS("cannot compute weighted jets now"); |
---|
1392 | } |
---|
1393 | else |
---|
1394 | { |
---|
1395 | short *w=iv2array(iv,R); |
---|
1396 | int k; |
---|
1397 | for(k=0; k<IDELEMS(i); k++) |
---|
1398 | { |
---|
1399 | r->m[k]=pp_JetW(i->m[k],d,w,R); |
---|
1400 | } |
---|
1401 | omFreeSize((ADDRESS)w,(rVar(R)+1)*sizeof(short)); |
---|
1402 | } |
---|
1403 | return r; |
---|
1404 | } |
---|
1405 | |
---|
1406 | /*3 |
---|
1407 | * searches for the next unit in the components of the module arg and |
---|
1408 | * returns the first one; |
---|
1409 | */ |
---|
1410 | int id_ReadOutPivot(ideal arg,int* comp, const ring r) |
---|
1411 | { |
---|
1412 | if (idIs0(arg)) return -1; |
---|
1413 | int i=0,j, generator=-1; |
---|
1414 | int rk_arg=arg->rank; //idRankFreeModule(arg); |
---|
1415 | int * componentIsUsed =(int *)omAlloc((rk_arg+1)*sizeof(int)); |
---|
1416 | poly p; |
---|
1417 | |
---|
1418 | while ((generator<0) && (i<IDELEMS(arg))) |
---|
1419 | { |
---|
1420 | memset(componentIsUsed,0,(rk_arg+1)*sizeof(int)); |
---|
1421 | p = arg->m[i]; |
---|
1422 | while (p!=NULL) |
---|
1423 | { |
---|
1424 | j = p_GetComp(p,r); |
---|
1425 | if (componentIsUsed[j]==0) |
---|
1426 | { |
---|
1427 | if (p_LmIsConstantComp(p,r) && |
---|
1428 | (!rField_is_Ring(r) || n_IsUnit(pGetCoeff(p),r->cf))) |
---|
1429 | { |
---|
1430 | generator = i; |
---|
1431 | componentIsUsed[j] = 1; |
---|
1432 | } |
---|
1433 | else |
---|
1434 | { |
---|
1435 | componentIsUsed[j] = -1; |
---|
1436 | } |
---|
1437 | } |
---|
1438 | else if (componentIsUsed[j]>0) |
---|
1439 | { |
---|
1440 | (componentIsUsed[j])++; |
---|
1441 | } |
---|
1442 | pIter(p); |
---|
1443 | } |
---|
1444 | i++; |
---|
1445 | } |
---|
1446 | i = 0; |
---|
1447 | *comp = -1; |
---|
1448 | for (j=0;j<=rk_arg;j++) |
---|
1449 | { |
---|
1450 | if (componentIsUsed[j]>0) |
---|
1451 | { |
---|
1452 | if ((*comp==-1) || (componentIsUsed[j]<i)) |
---|
1453 | { |
---|
1454 | *comp = j; |
---|
1455 | i= componentIsUsed[j]; |
---|
1456 | } |
---|
1457 | } |
---|
1458 | } |
---|
1459 | omFree(componentIsUsed); |
---|
1460 | return generator; |
---|
1461 | } |
---|
1462 | |
---|
1463 | #if 0 |
---|
1464 | static void idDeleteComp(ideal arg,int red_comp) |
---|
1465 | { |
---|
1466 | int i,j; |
---|
1467 | poly p; |
---|
1468 | |
---|
1469 | for (i=IDELEMS(arg)-1;i>=0;i--) |
---|
1470 | { |
---|
1471 | p = arg->m[i]; |
---|
1472 | while (p!=NULL) |
---|
1473 | { |
---|
1474 | j = pGetComp(p); |
---|
1475 | if (j>red_comp) |
---|
1476 | { |
---|
1477 | pSetComp(p,j-1); |
---|
1478 | pSetm(p); |
---|
1479 | } |
---|
1480 | pIter(p); |
---|
1481 | } |
---|
1482 | } |
---|
1483 | (arg->rank)--; |
---|
1484 | } |
---|
1485 | #endif |
---|
1486 | |
---|
1487 | intvec * id_QHomWeight(ideal id, const ring r) |
---|
1488 | { |
---|
1489 | poly head, tail; |
---|
1490 | int k; |
---|
1491 | int in=IDELEMS(id)-1, ready=0, all=0, |
---|
1492 | coldim=rVar(r), rowmax=2*coldim; |
---|
1493 | if (in<0) return NULL; |
---|
1494 | intvec *imat=new intvec(rowmax+1,coldim,0); |
---|
1495 | |
---|
1496 | do |
---|
1497 | { |
---|
1498 | head = id->m[in--]; |
---|
1499 | if (head!=NULL) |
---|
1500 | { |
---|
1501 | tail = pNext(head); |
---|
1502 | while (tail!=NULL) |
---|
1503 | { |
---|
1504 | all++; |
---|
1505 | for (k=1;k<=coldim;k++) |
---|
1506 | IMATELEM(*imat,all,k) = p_GetExpDiff(head,tail,k,r); |
---|
1507 | if (all==rowmax) |
---|
1508 | { |
---|
1509 | ivTriangIntern(imat, ready, all); |
---|
1510 | if (ready==coldim) |
---|
1511 | { |
---|
1512 | delete imat; |
---|
1513 | return NULL; |
---|
1514 | } |
---|
1515 | } |
---|
1516 | pIter(tail); |
---|
1517 | } |
---|
1518 | } |
---|
1519 | } while (in>=0); |
---|
1520 | if (all>ready) |
---|
1521 | { |
---|
1522 | ivTriangIntern(imat, ready, all); |
---|
1523 | if (ready==coldim) |
---|
1524 | { |
---|
1525 | delete imat; |
---|
1526 | return NULL; |
---|
1527 | } |
---|
1528 | } |
---|
1529 | intvec *result = ivSolveKern(imat, ready); |
---|
1530 | delete imat; |
---|
1531 | return result; |
---|
1532 | } |
---|
1533 | |
---|
1534 | BOOLEAN id_IsZeroDim(ideal I, const ring r) |
---|
1535 | { |
---|
1536 | BOOLEAN *UsedAxis=(BOOLEAN *)omAlloc0(rVar(r)*sizeof(BOOLEAN)); |
---|
1537 | int i,n; |
---|
1538 | poly po; |
---|
1539 | BOOLEAN res=TRUE; |
---|
1540 | for(i=IDELEMS(I)-1;i>=0;i--) |
---|
1541 | { |
---|
1542 | po=I->m[i]; |
---|
1543 | if ((po!=NULL) &&((n=p_IsPurePower(po,r))!=0)) UsedAxis[n-1]=TRUE; |
---|
1544 | } |
---|
1545 | for(i=rVar(r)-1;i>=0;i--) |
---|
1546 | { |
---|
1547 | if(UsedAxis[i]==FALSE) {res=FALSE; break;} // not zero-dim. |
---|
1548 | } |
---|
1549 | omFreeSize(UsedAxis,rVar(r)*sizeof(BOOLEAN)); |
---|
1550 | return res; |
---|
1551 | } |
---|
1552 | |
---|
1553 | void id_Normalize(ideal I,const ring r) /* for ideal/matrix */ |
---|
1554 | { |
---|
1555 | if (rField_has_simple_inverse(r)) return; /* Z/p, GF(p,n), R, long R/C */ |
---|
1556 | int i; |
---|
1557 | for(i=I->nrows*I->ncols-1;i>=0;i--) |
---|
1558 | { |
---|
1559 | p_Normalize(I->m[i],r); |
---|
1560 | } |
---|
1561 | } |
---|
1562 | |
---|
1563 | int id_MinDegW(ideal M,intvec *w, const ring r) |
---|
1564 | { |
---|
1565 | int d=-1; |
---|
1566 | for(int i=0;i<IDELEMS(M);i++) |
---|
1567 | { |
---|
1568 | if (M->m[i]!=NULL) |
---|
1569 | { |
---|
1570 | int d0=p_MinDeg(M->m[i],w,r); |
---|
1571 | if(-1<d0&&((d0<d)||(d==-1))) |
---|
1572 | d=d0; |
---|
1573 | } |
---|
1574 | } |
---|
1575 | return d; |
---|
1576 | } |
---|
1577 | |
---|
1578 | // #include <kernel/clapsing.h> |
---|
1579 | |
---|
1580 | /*2 |
---|
1581 | * transpose a module |
---|
1582 | */ |
---|
1583 | ideal id_Transp(ideal a, const ring rRing) |
---|
1584 | { |
---|
1585 | int r = a->rank, c = IDELEMS(a); |
---|
1586 | ideal b = idInit(r,c); |
---|
1587 | |
---|
1588 | int i; |
---|
1589 | for (i=c; i>0; i--) |
---|
1590 | { |
---|
1591 | poly p=a->m[i-1]; |
---|
1592 | while(p!=NULL) |
---|
1593 | { |
---|
1594 | poly h=p_Head(p, rRing); |
---|
1595 | int co=p_GetComp(h, rRing)-1; |
---|
1596 | p_SetComp(h, i, rRing); |
---|
1597 | p_Setm(h, rRing); |
---|
1598 | h->next=b->m[co]; |
---|
1599 | b->m[co]=h; |
---|
1600 | pIter(p); |
---|
1601 | } |
---|
1602 | } |
---|
1603 | for (i=IDELEMS(b)-1; i>=0; i--) |
---|
1604 | { |
---|
1605 | poly p=b->m[i]; |
---|
1606 | if(p!=NULL) |
---|
1607 | { |
---|
1608 | b->m[i]=p_SortMerge(p,rRing,TRUE); |
---|
1609 | } |
---|
1610 | } |
---|
1611 | return b; |
---|
1612 | } |
---|
1613 | |
---|
1614 | /*2 |
---|
1615 | * The following is needed to compute the image of certain map used in |
---|
1616 | * the computation of cohomologies via BGG |
---|
1617 | * let M = { w_1, ..., w_k }, k = size(M) == ncols(M), n = nvars(currRing). |
---|
1618 | * assuming that nrows(M) <= m*n; the procedure computes: |
---|
1619 | * transpose(M) * transpose( var(1) I_m | ... | var(n) I_m ) :== transpose(module{f_1, ... f_k}), |
---|
1620 | * where f_i = \sum_{j=1}^{m} (w_i, v_j) gen(j), (w_i, v_j) is a `scalar` multiplication. |
---|
1621 | * that is, if w_i = (a^1_1, ... a^1_m) | (a^2_1, ..., a^2_m) | ... | (a^n_1, ..., a^n_m) then |
---|
1622 | |
---|
1623 | (a^1_1, ... a^1_m) | (a^2_1, ..., a^2_m) | ... | (a^n_1, ..., a^n_m) |
---|
1624 | * var_1 ... var_1 | var_2 ... var_2 | ... | var_n ... var(n) |
---|
1625 | * gen_1 ... gen_m | gen_1 ... gen_m | ... | gen_1 ... gen_m |
---|
1626 | + => |
---|
1627 | f_i = |
---|
1628 | |
---|
1629 | a^1_1 * var(1) * gen(1) + ... + a^1_m * var(1) * gen(m) + |
---|
1630 | a^2_1 * var(2) * gen(1) + ... + a^2_m * var(2) * gen(m) + |
---|
1631 | ... |
---|
1632 | a^n_1 * var(n) * gen(1) + ... + a^n_m * var(n) * gen(m); |
---|
1633 | |
---|
1634 | NOTE: for every f_i we run only ONCE along w_i saving partial sums into a temporary array of polys of size m |
---|
1635 | */ |
---|
1636 | ideal id_TensorModuleMult(const int m, const ideal M, const ring rRing) |
---|
1637 | { |
---|
1638 | // #ifdef DEBU |
---|
1639 | // WarnS("tensorModuleMult!!!!"); |
---|
1640 | |
---|
1641 | assume(m > 0); |
---|
1642 | assume(M != NULL); |
---|
1643 | |
---|
1644 | const int n = rRing->N; |
---|
1645 | |
---|
1646 | assume(M->rank <= m * n); |
---|
1647 | |
---|
1648 | const int k = IDELEMS(M); |
---|
1649 | |
---|
1650 | ideal idTemp = idInit(k,m); // = {f_1, ..., f_k } |
---|
1651 | |
---|
1652 | for( int i = 0; i < k; i++ ) // for every w \in M |
---|
1653 | { |
---|
1654 | poly pTempSum = NULL; |
---|
1655 | |
---|
1656 | poly w = M->m[i]; |
---|
1657 | |
---|
1658 | while(w != NULL) // for each term of w... |
---|
1659 | { |
---|
1660 | poly h = p_Head(w, rRing); |
---|
1661 | |
---|
1662 | const int gen = p_GetComp(h, rRing); // 1 ... |
---|
1663 | |
---|
1664 | assume(gen > 0); |
---|
1665 | assume(gen <= n*m); |
---|
1666 | |
---|
1667 | // TODO: write a formula with %, / instead of while! |
---|
1668 | /* |
---|
1669 | int c = gen; |
---|
1670 | int v = 1; |
---|
1671 | while(c > m) |
---|
1672 | { |
---|
1673 | c -= m; |
---|
1674 | v++; |
---|
1675 | } |
---|
1676 | */ |
---|
1677 | |
---|
1678 | int cc = gen % m; |
---|
1679 | if( cc == 0) cc = m; |
---|
1680 | int vv = 1 + (gen - cc) / m; |
---|
1681 | |
---|
1682 | // assume( cc == c ); |
---|
1683 | // assume( vv == v ); |
---|
1684 | |
---|
1685 | // 1<= c <= m |
---|
1686 | assume( cc > 0 ); |
---|
1687 | assume( cc <= m ); |
---|
1688 | |
---|
1689 | assume( vv > 0 ); |
---|
1690 | assume( vv <= n ); |
---|
1691 | |
---|
1692 | assume( (cc + (vv-1)*m) == gen ); |
---|
1693 | |
---|
1694 | p_IncrExp(h, vv, rRing); // h *= var(j) && // p_AddExp(h, vv, 1, rRing); |
---|
1695 | p_SetComp(h, cc, rRing); |
---|
1696 | |
---|
1697 | p_Setm(h, rRing); // addjust degree after the previous steps! |
---|
1698 | |
---|
1699 | pTempSum = p_Add_q(pTempSum, h, rRing); // it is slow since h will be usually put to the back of pTempSum!!! |
---|
1700 | |
---|
1701 | pIter(w); |
---|
1702 | } |
---|
1703 | |
---|
1704 | idTemp->m[i] = pTempSum; |
---|
1705 | } |
---|
1706 | |
---|
1707 | // simplify idTemp??? |
---|
1708 | |
---|
1709 | ideal idResult = id_Transp(idTemp, rRing); |
---|
1710 | |
---|
1711 | id_Delete(&idTemp, rRing); |
---|
1712 | |
---|
1713 | return(idResult); |
---|
1714 | } |
---|
1715 | |
---|
1716 | ideal id_ChineseRemainder(ideal *xx, number *q, int rl, const ring r) |
---|
1717 | { |
---|
1718 | int cnt=0;int rw=0; int cl=0; |
---|
1719 | int i,j; |
---|
1720 | // find max. size of xx[.]: |
---|
1721 | for(j=rl-1;j>=0;j--) |
---|
1722 | { |
---|
1723 | i=IDELEMS(xx[j])*xx[j]->nrows; |
---|
1724 | if (i>cnt) cnt=i; |
---|
1725 | if (xx[j]->nrows >rw) rw=xx[j]->nrows; // for lifting matrices |
---|
1726 | if (xx[j]->ncols >cl) cl=xx[j]->ncols; // for lifting matrices |
---|
1727 | } |
---|
1728 | if (rw*cl !=cnt) |
---|
1729 | { |
---|
1730 | WerrorS("format mismatch in CRT"); |
---|
1731 | return NULL; |
---|
1732 | } |
---|
1733 | ideal result=idInit(cnt,xx[0]->rank); |
---|
1734 | result->nrows=rw; // for lifting matrices |
---|
1735 | result->ncols=cl; // for lifting matrices |
---|
1736 | number *x=(number *)omAlloc(rl*sizeof(number)); |
---|
1737 | poly *p=(poly *)omAlloc(rl*sizeof(poly)); |
---|
1738 | CFArray inv_cache(rl); |
---|
1739 | for(i=cnt-1;i>=0;i--) |
---|
1740 | { |
---|
1741 | for(j=rl-1;j>=0;j--) |
---|
1742 | { |
---|
1743 | if(i>=IDELEMS(xx[j])*xx[j]->nrows) // out of range of this ideal |
---|
1744 | p[j]=NULL; |
---|
1745 | else |
---|
1746 | p[j]=xx[j]->m[i]; |
---|
1747 | } |
---|
1748 | result->m[i]=p_ChineseRemainder(p,x,q,rl,inv_cache,r); |
---|
1749 | for(j=rl-1;j>=0;j--) |
---|
1750 | { |
---|
1751 | if(i<IDELEMS(xx[j])*xx[j]->nrows) xx[j]->m[i]=p[j]; |
---|
1752 | } |
---|
1753 | } |
---|
1754 | omFreeSize(p,rl*sizeof(poly)); |
---|
1755 | omFreeSize(x,rl*sizeof(number)); |
---|
1756 | for(i=rl-1;i>=0;i--) id_Delete(&(xx[i]),r); |
---|
1757 | omFreeSize(xx,rl*sizeof(ideal)); |
---|
1758 | return result; |
---|
1759 | } |
---|
1760 | |
---|
1761 | void id_Shift(ideal M, int s, const ring r) |
---|
1762 | { |
---|
1763 | // id_Test( M, r ); |
---|
1764 | |
---|
1765 | // assume( s >= 0 ); // negative is also possible // TODO: verify input ideal in such a case!? |
---|
1766 | |
---|
1767 | for(int i=IDELEMS(M)-1; i>=0;i--) |
---|
1768 | p_Shift(&(M->m[i]),s,r); |
---|
1769 | |
---|
1770 | M->rank += s; |
---|
1771 | |
---|
1772 | // id_Test( M, r ); |
---|
1773 | } |
---|