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 | |
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10 | /* includes */ |
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11 | #include "config.h" |
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12 | #include <misc/auxiliary.h> |
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13 | #include <misc/options.h> |
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14 | #include <omalloc/omalloc.h> |
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15 | #include <polys/monomials/p_polys.h> |
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16 | #include <misc/intvec.h> |
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17 | |
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18 | #include "simpleideals.h" |
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19 | |
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20 | /*2 |
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21 | * initialise an ideal |
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22 | */ |
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23 | ideal idInit(int idsize, int rank) |
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24 | { |
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25 | /*- initialise an ideal -*/ |
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26 | ideal hh = (ideal )omAllocBin(sip_sideal_bin); |
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27 | hh->nrows = 1; |
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28 | hh->rank = rank; |
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29 | IDELEMS(hh) = idsize; |
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30 | if (idsize>0) |
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31 | { |
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32 | hh->m = (poly *)omAlloc0(idsize*sizeof(poly)); |
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33 | } |
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34 | else |
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35 | hh->m=NULL; |
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36 | return hh; |
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37 | } |
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38 | |
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39 | #ifdef PDEBUG |
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40 | // this is only for outputting an ideal within the debugger |
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41 | void idShow(const ideal id, const ring lmRing, const ring tailRing, const int debugPrint) |
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42 | { |
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43 | assume( debugPrint >= 0 ); |
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44 | |
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45 | if( id == NULL ) |
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46 | PrintS("(NULL)"); |
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47 | else |
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48 | { |
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49 | Print("Module of rank %ld,real rank %ld and %d generators.\n", |
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50 | id->rank,id_RankFreeModule(id, lmRing, tailRing),IDELEMS(id)); |
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51 | |
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52 | int j = (id->ncols*id->nrows) - 1; |
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53 | while ((j > 0) && (id->m[j]==NULL)) j--; |
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54 | for (int i = 0; i <= j; i++) |
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55 | { |
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56 | Print("generator %d: ",i); p_DebugPrint(id->m[i], lmRing, tailRing, debugPrint); |
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57 | } |
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58 | } |
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59 | } |
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60 | #endif |
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61 | |
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62 | /* index of generator with leading term in ground ring (if any); |
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63 | otherwise -1 */ |
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64 | int id_PosConstant(ideal id, const ring r) |
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65 | { |
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66 | int k; |
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67 | for (k = IDELEMS(id)-1; k>=0; k--) |
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68 | { |
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69 | if (p_LmIsConstantComp(id->m[k], r) == TRUE) |
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70 | return k; |
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71 | } |
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72 | return -1; |
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73 | } |
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74 | |
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75 | /*2 |
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76 | * initialise the maximal ideal (at 0) |
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77 | */ |
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78 | ideal id_MaxIdeal (const ring r) |
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79 | { |
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80 | int l; |
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81 | ideal hh=NULL; |
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82 | |
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83 | hh=idInit(rVar(r),1); |
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84 | for (l=0; l<rVar(r); l++) |
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85 | { |
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86 | hh->m[l] = p_One(r); |
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87 | p_SetExp(hh->m[l],l+1,1,r); |
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88 | p_Setm(hh->m[l],r); |
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89 | } |
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90 | return hh; |
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91 | } |
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92 | |
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93 | /*2 |
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94 | * deletes an ideal/matrix |
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95 | */ |
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96 | void id_Delete (ideal * h, ring r) |
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97 | { |
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98 | int j,elems; |
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99 | if (*h == NULL) |
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100 | return; |
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101 | elems=j=(*h)->nrows*(*h)->ncols; |
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102 | if (j>0) |
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103 | { |
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104 | do |
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105 | { |
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106 | p_Delete(&((*h)->m[--j]), r); |
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107 | } |
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108 | while (j>0); |
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109 | omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems); |
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110 | } |
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111 | omFreeBin((ADDRESS)*h, sip_sideal_bin); |
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112 | *h=NULL; |
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113 | } |
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114 | |
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115 | |
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116 | /*2 |
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117 | * Shallowdeletes an ideal/matrix |
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118 | */ |
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119 | void id_ShallowDelete (ideal *h, ring r) |
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120 | { |
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121 | int j,elems; |
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122 | if (*h == NULL) |
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123 | return; |
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124 | elems=j=(*h)->nrows*(*h)->ncols; |
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125 | if (j>0) |
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126 | { |
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127 | do |
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128 | { |
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129 | p_ShallowDelete(&((*h)->m[--j]), r); |
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130 | } |
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131 | while (j>0); |
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132 | omFreeSize((ADDRESS)((*h)->m),sizeof(poly)*elems); |
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133 | } |
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134 | omFreeBin((ADDRESS)*h, sip_sideal_bin); |
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135 | *h=NULL; |
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136 | } |
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137 | |
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138 | /*2 |
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139 | *gives an ideal the minimal possible size |
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140 | */ |
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141 | void idSkipZeroes (ideal ide) |
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142 | { |
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143 | int k; |
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144 | int j = -1; |
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145 | BOOLEAN change=FALSE; |
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146 | for (k=0; k<IDELEMS(ide); k++) |
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147 | { |
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148 | if (ide->m[k] != NULL) |
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149 | { |
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150 | j++; |
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151 | if (change) |
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152 | { |
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153 | ide->m[j] = ide->m[k]; |
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154 | } |
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155 | } |
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156 | else |
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157 | { |
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158 | change=TRUE; |
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159 | } |
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160 | } |
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161 | if (change) |
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162 | { |
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163 | if (j == -1) |
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164 | j = 0; |
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165 | else |
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166 | { |
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167 | for (k=j+1; k<IDELEMS(ide); k++) |
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168 | ide->m[k] = NULL; |
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169 | } |
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170 | pEnlargeSet(&(ide->m),IDELEMS(ide),j+1-IDELEMS(ide)); |
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171 | IDELEMS(ide) = j+1; |
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172 | } |
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173 | } |
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174 | |
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175 | /*2 |
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176 | * copies the first k (>= 1) entries of the given ideal |
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177 | * and returns these as a new ideal |
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178 | * (Note that the copied polynomials may be zero.) |
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179 | */ |
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180 | ideal id_CopyFirstK (const ideal ide, const int k,const ring r) |
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181 | { |
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182 | ideal newI = idInit(k, 0); |
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183 | for (int i = 0; i < k; i++) |
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184 | newI->m[i] = p_Copy(ide->m[i],r); |
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185 | return newI; |
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186 | } |
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187 | |
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188 | /*2 |
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189 | * ideal id = (id[i]) |
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190 | * result is leadcoeff(id[i]) = 1 |
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191 | */ |
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192 | void id_Norm(ideal id, const ring r) |
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193 | { |
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194 | for (int i=IDELEMS(id)-1; i>=0; i--) |
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195 | { |
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196 | if (id->m[i] != NULL) |
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197 | { |
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198 | p_Norm(id->m[i],r); |
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199 | } |
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200 | } |
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201 | } |
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202 | |
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203 | /*2 |
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204 | * ideal id = (id[i]), c any unit |
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205 | * if id[i] = c*id[j] then id[j] is deleted for j > i |
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206 | */ |
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207 | void id_DelMultiples(ideal id, const ring r) |
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208 | { |
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209 | int i, j; |
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210 | int k = IDELEMS(id)-1; |
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211 | for (i=k; i>=0; i--) |
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212 | { |
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213 | if (id->m[i]!=NULL) |
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214 | { |
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215 | for (j=k; j>i; j--) |
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216 | { |
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217 | if (id->m[j]!=NULL) |
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218 | { |
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219 | #ifdef HAVE_RINGS |
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220 | if (rField_is_Ring(r)) |
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221 | { |
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222 | /* if id[j] = c*id[i] then delete id[j]. |
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223 | In the below cases of a ground field, we |
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224 | check whether id[i] = c*id[j] and, if so, |
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225 | delete id[j] for historical reasons (so |
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226 | that previous output does not change) */ |
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227 | if (p_ComparePolys(id->m[j], id->m[i],r)) p_Delete(&id->m[j],r); |
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228 | } |
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229 | else |
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230 | { |
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231 | if (p_ComparePolys(id->m[i], id->m[j],r)) p_Delete(&id->m[j],r); |
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232 | } |
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233 | #else |
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234 | if (p_ComparePolys(id->m[i], id->m[j],r)) p_Delete(&id->m[j],r); |
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235 | #endif |
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236 | } |
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237 | } |
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238 | } |
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239 | } |
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240 | } |
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241 | |
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242 | /*2 |
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243 | * ideal id = (id[i]) |
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244 | * if id[i] = id[j] then id[j] is deleted for j > i |
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245 | */ |
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246 | void id_DelEquals(ideal id, const ring r) |
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247 | { |
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248 | int i, j; |
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249 | int k = IDELEMS(id)-1; |
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250 | for (i=k; i>=0; i--) |
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251 | { |
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252 | if (id->m[i]!=NULL) |
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253 | { |
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254 | for (j=k; j>i; j--) |
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255 | { |
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256 | if ((id->m[j]!=NULL) |
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257 | && (p_EqualPolys(id->m[i], id->m[j],r))) |
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258 | { |
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259 | p_Delete(&id->m[j],r); |
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260 | } |
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261 | } |
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262 | } |
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263 | } |
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264 | } |
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265 | |
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266 | // |
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267 | // Delete id[j], if Lm(j) == Lm(i) and both LC(j), LC(i) are units and j > i |
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268 | // |
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269 | void id_DelLmEquals(ideal id, const ring r) |
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270 | { |
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271 | int i, j; |
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272 | int k = IDELEMS(id)-1; |
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273 | for (i=k; i>=0; i--) |
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274 | { |
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275 | if (id->m[i] != NULL) |
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276 | { |
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277 | for (j=k; j>i; j--) |
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278 | { |
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279 | if ((id->m[j] != NULL) |
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280 | && p_LmEqual(id->m[i], id->m[j],r) |
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281 | #ifdef HAVE_RINGS |
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282 | && n_IsUnit(pGetCoeff(id->m[i]),r->cf) && n_IsUnit(pGetCoeff(id->m[j]),r->cf) |
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283 | #endif |
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284 | ) |
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285 | { |
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286 | p_Delete(&id->m[j],r); |
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287 | } |
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288 | } |
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289 | } |
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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 | // delete id[j], if LT(j) == coeff*mon*LT(i) and vice versa, i.e., |
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295 | // delete id[i], if LT(i) == coeff*mon*LT(j) |
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296 | // |
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297 | void id_DelDiv(ideal id, const ring r) |
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298 | { |
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299 | int i, j; |
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300 | int k = IDELEMS(id)-1; |
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301 | for (i=k; i>=0; i--) |
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302 | { |
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303 | if (id->m[i] != NULL) |
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304 | { |
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305 | for (j=k; j>i; j--) |
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306 | { |
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307 | if (id->m[j]!=NULL) |
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308 | { |
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309 | #ifdef HAVE_RINGS |
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310 | if (rField_is_Ring(r)) |
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311 | { |
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312 | if (p_DivisibleByRingCase(id->m[i], id->m[j],r)) |
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313 | { |
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314 | p_Delete(&id->m[j],r); |
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315 | } |
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316 | else if (p_DivisibleByRingCase(id->m[j], id->m[i],r)) |
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317 | { |
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318 | p_Delete(&id->m[i],r); |
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319 | break; |
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320 | } |
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321 | } |
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322 | else |
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323 | { |
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324 | #endif |
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325 | /* the case of a ground field: */ |
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326 | if (p_DivisibleBy(id->m[i], id->m[j],r)) |
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327 | { |
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328 | p_Delete(&id->m[j],r); |
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329 | } |
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330 | else if (p_DivisibleBy(id->m[j], id->m[i],r)) |
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331 | { |
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332 | p_Delete(&id->m[i],r); |
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333 | break; |
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334 | } |
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335 | #ifdef HAVE_RINGS |
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336 | } |
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337 | #endif |
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338 | } |
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339 | } |
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340 | } |
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341 | } |
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342 | } |
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343 | |
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344 | /*2 |
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345 | *test if the ideal has only constant polynomials |
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346 | */ |
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347 | BOOLEAN id_IsConstant(ideal id, const ring r) |
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348 | { |
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349 | int k; |
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350 | for (k = IDELEMS(id)-1; k>=0; k--) |
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351 | { |
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352 | if (!p_IsConstantPoly(id->m[k],r)) |
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353 | return FALSE; |
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354 | } |
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355 | return TRUE; |
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356 | } |
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357 | |
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358 | /*2 |
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359 | * copy an ideal |
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360 | */ |
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361 | #ifdef PDEBUG |
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362 | ideal id_DBCopy(ideal h1,const char *f,int l, const ring r) |
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363 | { |
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364 | int i; |
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365 | ideal h2; |
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366 | |
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367 | id_DBTest(h1,PDEBUG,f,l,r); |
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368 | //#ifdef TEST |
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369 | if (h1 == NULL) |
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370 | { |
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371 | h2=idDBInit(1,1,f,l); |
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372 | } |
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373 | else |
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374 | //#endif |
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375 | { |
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376 | h2=idDBInit(IDELEMS(h1),h1->rank,f,l); |
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377 | for (i=IDELEMS(h1)-1; i>=0; i--) |
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378 | h2->m[i] = p_Copy(h1->m[i],r); |
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379 | } |
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380 | return h2; |
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381 | } |
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382 | #else |
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383 | ideal id_Copy(ideal h1, const ring r) |
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384 | { |
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385 | int i; |
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386 | ideal h2; |
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387 | |
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388 | //#ifdef TEST |
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389 | if (h1 == NULL) |
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390 | { |
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391 | h2=idInit(1,1); |
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392 | } |
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393 | else |
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394 | //#endif |
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395 | { |
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396 | h2=idInit(IDELEMS(h1),h1->rank); |
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397 | for (i=IDELEMS(h1)-1; i>=0; i--) |
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398 | h2->m[i] = p_Copy(h1->m[i],r); |
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399 | } |
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400 | return h2; |
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401 | } |
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402 | #endif |
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403 | |
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404 | #ifdef PDEBUG |
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405 | void id_DBTest(ideal h1, int level, const char *f,const int l, const ring r) |
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406 | { |
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407 | int i; |
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408 | |
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409 | if (h1 != NULL) |
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410 | { |
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411 | // assume(IDELEMS(h1) > 0); for ideal/module, does not apply to matrix |
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412 | omCheckAddrSize(h1,sizeof(*h1)); |
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413 | omdebugAddrSize(h1->m,h1->ncols*h1->nrows*sizeof(poly)); |
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414 | /* to be able to test matrices: */ |
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415 | for (i=(h1->ncols*h1->nrows)-1; i>=0; i--) |
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416 | _p_Test(h1->m[i], r, level); |
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417 | int new_rk=id_RankFreeModule(h1,r); |
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418 | if(new_rk > h1->rank) |
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419 | { |
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420 | dReportError("wrong rank %d (should be %d) in %s:%d\n", |
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421 | h1->rank, new_rk, f,l); |
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422 | omPrintAddrInfo(stderr, h1, " for ideal"); |
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423 | h1->rank=new_rk; |
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424 | } |
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425 | } |
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426 | } |
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427 | #endif |
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428 | |
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429 | /*3 |
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430 | * for idSort: compare a and b revlex inclusive module comp. |
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431 | */ |
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432 | static int p_Comp_RevLex(poly a, poly b,BOOLEAN nolex, const ring r) |
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433 | { |
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434 | if (b==NULL) return 1; |
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435 | if (a==NULL) return -1; |
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436 | |
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437 | if (nolex) |
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438 | { |
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439 | int r=p_LmCmp(a,b,r); |
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440 | if (r!=0) return r; |
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441 | number h=n_Sub(pGetCoeff(a),pGetCoeff(b),r->cf); |
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442 | r = -1+n_IsZero(h,r->cf)+2*n_GreaterZero(h,r->cf); /* -1: <, 0:==, 1: > */ |
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443 | n_Delete(&h, r->cf); |
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444 | return r; |
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445 | } |
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446 | int l=rVar(r); |
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447 | while ((l>0) && (p_GetExp(a,l,r)==pGetExp(b,l,r))) l--; |
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448 | if (l==0) |
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449 | { |
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450 | if (p_GetComp(a,r)==p_GetComp(b,r)) |
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451 | { |
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452 | number h=n_Sub(pGetCoeff(a),pGetCoeff(b),r->cf); |
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453 | int r = -1+n_IsZero(h,r->cf)+2*n_GreaterZero(h,r->cf); /* -1: <, 0:==, 1: > */ |
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454 | n_Delete(&h,r->cf); |
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455 | return r; |
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456 | } |
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457 | if (p_GetComp(a,r)>p_GetComp(b,r)) return 1; |
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458 | } |
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459 | else if (p_GetExp(a,l,r)>p_GetExp(b,l,r)) |
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460 | return 1; |
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461 | return -1; |
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462 | } |
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463 | |
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464 | /*2 |
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465 | *sorts the ideal w.r.t. the actual ringordering |
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466 | *uses lex-ordering when nolex = FALSE |
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467 | */ |
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468 | intvec *id_Sort(ideal id,BOOLEAN nolex, const ring r) |
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469 | { |
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470 | poly p,q; |
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471 | intvec * result = new intvec(IDELEMS(id)); |
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472 | int i, j, actpos=0, newpos, l; |
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473 | int diff, olddiff, lastcomp, newcomp; |
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474 | BOOLEAN notFound; |
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475 | |
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476 | for (i=0;i<IDELEMS(id);i++) |
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477 | { |
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478 | if (id->m[i]!=NULL) |
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479 | { |
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480 | notFound = TRUE; |
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481 | newpos = actpos / 2; |
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482 | diff = (actpos+1) / 2; |
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483 | diff = (diff+1) / 2; |
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484 | lastcomp = p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r); |
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485 | if (lastcomp<0) |
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486 | { |
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487 | newpos -= diff; |
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488 | } |
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489 | else if (lastcomp>0) |
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490 | { |
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491 | newpos += diff; |
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492 | } |
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493 | else |
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494 | { |
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495 | notFound = FALSE; |
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496 | } |
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497 | //while ((newpos>=0) && (newpos<actpos) && (notFound)) |
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498 | while (notFound && (newpos>=0) && (newpos<actpos)) |
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499 | { |
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500 | newcomp = p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r); |
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501 | olddiff = diff; |
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502 | if (diff>1) |
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503 | { |
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504 | diff = (diff+1) / 2; |
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505 | if ((newcomp==1) |
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506 | && (actpos-newpos>1) |
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507 | && (diff>1) |
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508 | && (newpos+diff>=actpos)) |
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509 | { |
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510 | diff = actpos-newpos-1; |
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511 | } |
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512 | else if ((newcomp==-1) |
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513 | && (diff>1) |
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514 | && (newpos<diff)) |
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515 | { |
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516 | diff = newpos; |
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517 | } |
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518 | } |
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519 | if (newcomp<0) |
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520 | { |
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521 | if ((olddiff==1) && (lastcomp>0)) |
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522 | notFound = FALSE; |
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523 | else |
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524 | newpos -= diff; |
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525 | } |
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526 | else if (newcomp>0) |
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527 | { |
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528 | if ((olddiff==1) && (lastcomp<0)) |
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529 | { |
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530 | notFound = FALSE; |
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531 | newpos++; |
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532 | } |
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533 | else |
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534 | { |
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535 | newpos += diff; |
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536 | } |
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537 | } |
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538 | else |
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539 | { |
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540 | notFound = FALSE; |
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541 | } |
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542 | lastcomp = newcomp; |
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543 | if (diff==0) notFound=FALSE; /*hs*/ |
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544 | } |
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545 | if (newpos<0) newpos = 0; |
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546 | if (newpos>actpos) newpos = actpos; |
---|
547 | while ((newpos<actpos) && (p_Comp_RevLex(id->m[i],id->m[(*result)[newpos]],nolex,r)==0)) |
---|
548 | newpos++; |
---|
549 | for (j=actpos;j>newpos;j--) |
---|
550 | { |
---|
551 | (*result)[j] = (*result)[j-1]; |
---|
552 | } |
---|
553 | (*result)[newpos] = i; |
---|
554 | actpos++; |
---|
555 | } |
---|
556 | } |
---|
557 | for (j=0;j<actpos;j++) (*result)[j]++; |
---|
558 | return result; |
---|
559 | } |
---|
560 | |
---|
561 | /*2 |
---|
562 | * concat the lists h1 and h2 without zeros |
---|
563 | */ |
---|
564 | ideal idSimpleAdd (ideal h1,ideal h2) |
---|
565 | { |
---|
566 | int i,j,r,l; |
---|
567 | ideal result; |
---|
568 | |
---|
569 | if (h1==NULL) return idCopy(h2); |
---|
570 | if (h2==NULL) return idCopy(h1); |
---|
571 | j = IDELEMS(h1)-1; |
---|
572 | while ((j >= 0) && (h1->m[j] == NULL)) j--; |
---|
573 | i = IDELEMS(h2)-1; |
---|
574 | while ((i >= 0) && (h2->m[i] == NULL)) i--; |
---|
575 | r = si_max(h1->rank,h2->rank); |
---|
576 | if (i+j==(-2)) |
---|
577 | return idInit(1,r); |
---|
578 | else |
---|
579 | result=idInit(i+j+2,r); |
---|
580 | for (l=j; l>=0; l--) |
---|
581 | { |
---|
582 | result->m[l] = pCopy(h1->m[l]); |
---|
583 | } |
---|
584 | r = i+j+1; |
---|
585 | for (l=i; l>=0; l--, r--) |
---|
586 | { |
---|
587 | result->m[r] = pCopy(h2->m[l]); |
---|
588 | } |
---|
589 | return result; |
---|
590 | } |
---|
591 | |
---|
592 | /*2 |
---|
593 | * insert h2 into h1 (if h2 is not the zero polynomial) |
---|
594 | * return TRUE iff h2 was indeed inserted |
---|
595 | */ |
---|
596 | BOOLEAN idInsertPoly (ideal h1, poly h2) |
---|
597 | { |
---|
598 | if (h2==NULL) return FALSE; |
---|
599 | int j = IDELEMS(h1)-1; |
---|
600 | while ((j >= 0) && (h1->m[j] == NULL)) j--; |
---|
601 | j++; |
---|
602 | if (j==IDELEMS(h1)) |
---|
603 | { |
---|
604 | pEnlargeSet(&(h1->m),IDELEMS(h1),16); |
---|
605 | IDELEMS(h1)+=16; |
---|
606 | } |
---|
607 | h1->m[j]=h2; |
---|
608 | return TRUE; |
---|
609 | } |
---|
610 | |
---|
611 | /*2 |
---|
612 | * insert h2 into h1 depending on the two boolean parameters: |
---|
613 | * - if zeroOk is true, then h2 will also be inserted when it is zero |
---|
614 | * - if duplicateOk is true, then h2 will also be inserted when it is |
---|
615 | * already present in h1 |
---|
616 | * return TRUE iff h2 was indeed inserted |
---|
617 | */ |
---|
618 | BOOLEAN idInsertPolyWithTests (ideal h1, const int validEntries, |
---|
619 | const poly h2, const bool zeroOk, const bool duplicateOk) |
---|
620 | { |
---|
621 | if ((!zeroOk) && (h2 == NULL)) return FALSE; |
---|
622 | if (!duplicateOk) |
---|
623 | { |
---|
624 | bool h2FoundInH1 = false; |
---|
625 | int i = 0; |
---|
626 | while ((i < validEntries) && (!h2FoundInH1)) |
---|
627 | { |
---|
628 | h2FoundInH1 = pEqualPolys(h1->m[i], h2); |
---|
629 | i++; |
---|
630 | } |
---|
631 | if (h2FoundInH1) return FALSE; |
---|
632 | } |
---|
633 | if (validEntries == IDELEMS(h1)) |
---|
634 | { |
---|
635 | pEnlargeSet(&(h1->m), IDELEMS(h1), 16); |
---|
636 | IDELEMS(h1) += 16; |
---|
637 | } |
---|
638 | h1->m[validEntries] = h2; |
---|
639 | return TRUE; |
---|
640 | } |
---|
641 | |
---|
642 | /*2 |
---|
643 | * h1 + h2 |
---|
644 | */ |
---|
645 | ideal idAdd (ideal h1,ideal h2) |
---|
646 | { |
---|
647 | ideal result = idSimpleAdd(h1,h2); |
---|
648 | idCompactify(result); |
---|
649 | return result; |
---|
650 | } |
---|
651 | |
---|
652 | /*2 |
---|
653 | * h1 * h2 |
---|
654 | */ |
---|
655 | ideal idMult (ideal h1,ideal h2) |
---|
656 | { |
---|
657 | int i,j,k; |
---|
658 | ideal hh; |
---|
659 | |
---|
660 | j = IDELEMS(h1); |
---|
661 | while ((j > 0) && (h1->m[j-1] == NULL)) j--; |
---|
662 | i = IDELEMS(h2); |
---|
663 | while ((i > 0) && (h2->m[i-1] == NULL)) i--; |
---|
664 | j = j * i; |
---|
665 | if (j == 0) |
---|
666 | hh = idInit(1,1); |
---|
667 | else |
---|
668 | hh=idInit(j,1); |
---|
669 | if (h1->rank<h2->rank) |
---|
670 | hh->rank = h2->rank; |
---|
671 | else |
---|
672 | hh->rank = h1->rank; |
---|
673 | if (j==0) return hh; |
---|
674 | k = 0; |
---|
675 | for (i=0; i<IDELEMS(h1); i++) |
---|
676 | { |
---|
677 | if (h1->m[i] != NULL) |
---|
678 | { |
---|
679 | for (j=0; j<IDELEMS(h2); j++) |
---|
680 | { |
---|
681 | if (h2->m[j] != NULL) |
---|
682 | { |
---|
683 | hh->m[k] = ppMult_qq(h1->m[i],h2->m[j]); |
---|
684 | k++; |
---|
685 | } |
---|
686 | } |
---|
687 | } |
---|
688 | } |
---|
689 | { |
---|
690 | idCompactify(hh); |
---|
691 | return hh; |
---|
692 | } |
---|
693 | } |
---|
694 | |
---|
695 | /*2 |
---|
696 | *returns true if h is the zero ideal |
---|
697 | */ |
---|
698 | BOOLEAN idIs0 (ideal h) |
---|
699 | { |
---|
700 | int i; |
---|
701 | |
---|
702 | if (h == NULL) return TRUE; |
---|
703 | i = IDELEMS(h)-1; |
---|
704 | while ((i >= 0) && (h->m[i] == NULL)) |
---|
705 | { |
---|
706 | i--; |
---|
707 | } |
---|
708 | if (i < 0) |
---|
709 | return TRUE; |
---|
710 | else |
---|
711 | return FALSE; |
---|
712 | } |
---|
713 | |
---|
714 | /*2 |
---|
715 | * return the maximal component number found in any polynomial in s |
---|
716 | */ |
---|
717 | long idRankFreeModule (ideal s, ring lmRing, ring tailRing) |
---|
718 | { |
---|
719 | if (s!=NULL) |
---|
720 | { |
---|
721 | int j=0; |
---|
722 | |
---|
723 | if (rRing_has_Comp(tailRing) && rRing_has_Comp(lmRing)) |
---|
724 | { |
---|
725 | int l=IDELEMS(s); |
---|
726 | poly *p=s->m; |
---|
727 | int k; |
---|
728 | for (; l != 0; l--) |
---|
729 | { |
---|
730 | if (*p!=NULL) |
---|
731 | { |
---|
732 | pp_Test(*p, lmRing, tailRing); |
---|
733 | k = p_MaxComp(*p, lmRing, tailRing); |
---|
734 | if (k>j) j = k; |
---|
735 | } |
---|
736 | p++; |
---|
737 | } |
---|
738 | } |
---|
739 | return j; |
---|
740 | } |
---|
741 | return -1; |
---|
742 | } |
---|
743 | |
---|
744 | BOOLEAN idIsModule(ideal id, ring r) |
---|
745 | { |
---|
746 | if (id != NULL && rRing_has_Comp(r)) |
---|
747 | { |
---|
748 | int j, l = IDELEMS(id); |
---|
749 | for (j=0; j<l; j++) |
---|
750 | { |
---|
751 | if (id->m[j] != NULL && p_GetComp(id->m[j], r) > 0) return TRUE; |
---|
752 | } |
---|
753 | } |
---|
754 | return FALSE; |
---|
755 | } |
---|
756 | |
---|
757 | |
---|
758 | /*2 |
---|
759 | *returns true if id is homogenous with respect to the aktual weights |
---|
760 | */ |
---|
761 | BOOLEAN idHomIdeal (ideal id, ideal Q) |
---|
762 | { |
---|
763 | int i; |
---|
764 | BOOLEAN b; |
---|
765 | if ((id == NULL) || (IDELEMS(id) == 0)) return TRUE; |
---|
766 | i = 0; |
---|
767 | b = TRUE; |
---|
768 | while ((i < IDELEMS(id)) && b) |
---|
769 | { |
---|
770 | b = pIsHomogeneous(id->m[i]); |
---|
771 | i++; |
---|
772 | } |
---|
773 | if ((b) && (Q!=NULL) && (IDELEMS(Q)>0)) |
---|
774 | { |
---|
775 | i=0; |
---|
776 | while ((i < IDELEMS(Q)) && b) |
---|
777 | { |
---|
778 | b = pIsHomogeneous(Q->m[i]); |
---|
779 | i++; |
---|
780 | } |
---|
781 | } |
---|
782 | return b; |
---|
783 | } |
---|
784 | |
---|
785 | /*2 |
---|
786 | *the minimal index of used variables - 1 |
---|
787 | */ |
---|
788 | int pLowVar (poly p) |
---|
789 | { |
---|
790 | int k,l,lex; |
---|
791 | |
---|
792 | if (p == NULL) return -1; |
---|
793 | |
---|
794 | k = 32000;/*a very large dummy value*/ |
---|
795 | while (p != NULL) |
---|
796 | { |
---|
797 | l = 1; |
---|
798 | lex = pGetExp(p,l); |
---|
799 | while ((l < pVariables) && (lex == 0)) |
---|
800 | { |
---|
801 | l++; |
---|
802 | lex = pGetExp(p,l); |
---|
803 | } |
---|
804 | l--; |
---|
805 | if (l < k) k = l; |
---|
806 | pIter(p); |
---|
807 | } |
---|
808 | return k; |
---|
809 | } |
---|
810 | |
---|
811 | /*3 |
---|
812 | *multiplies p with t (!cas) or (t-1) |
---|
813 | *the index of t is:1, so we have to shift all variables |
---|
814 | *p is NOT in the actual ring, it has no t |
---|
815 | */ |
---|
816 | static poly pMultWithT (poly p,BOOLEAN cas) |
---|
817 | { |
---|
818 | /*qp is the working pointer in p*/ |
---|
819 | /*result is the result, qresult is the working pointer*/ |
---|
820 | /*pp is p in the actual ring(shifted), qpp the working pointer*/ |
---|
821 | poly result,qp,pp; |
---|
822 | poly qresult=NULL; |
---|
823 | poly qpp=NULL; |
---|
824 | int i,j,lex; |
---|
825 | number n; |
---|
826 | |
---|
827 | pp = NULL; |
---|
828 | result = NULL; |
---|
829 | qp = p; |
---|
830 | while (qp != NULL) |
---|
831 | { |
---|
832 | i = 0; |
---|
833 | if (result == NULL) |
---|
834 | {/*first monomial*/ |
---|
835 | result = pInit(); |
---|
836 | qresult = result; |
---|
837 | } |
---|
838 | else |
---|
839 | { |
---|
840 | qresult->next = pInit(); |
---|
841 | pIter(qresult); |
---|
842 | } |
---|
843 | for (j=pVariables-1; j>0; j--) |
---|
844 | { |
---|
845 | lex = pGetExp(qp,j); |
---|
846 | pSetExp(qresult,j+1,lex);/*copy all variables*/ |
---|
847 | } |
---|
848 | lex = pGetComp(qp); |
---|
849 | pSetComp(qresult,lex); |
---|
850 | n=nCopy(pGetCoeff(qp)); |
---|
851 | pSetCoeff0(qresult,n); |
---|
852 | qresult->next = NULL; |
---|
853 | pSetm(qresult); |
---|
854 | /*qresult is now qp brought into the actual ring*/ |
---|
855 | if (cas) |
---|
856 | { /*case: mult with t-1*/ |
---|
857 | pSetExp(qresult,1,0); |
---|
858 | pSetm(qresult); |
---|
859 | if (pp == NULL) |
---|
860 | { /*first monomial*/ |
---|
861 | pp = pCopy(qresult); |
---|
862 | qpp = pp; |
---|
863 | } |
---|
864 | else |
---|
865 | { |
---|
866 | qpp->next = pCopy(qresult); |
---|
867 | pIter(qpp); |
---|
868 | } |
---|
869 | pGetCoeff(qpp)=nNeg(pGetCoeff(qpp)); |
---|
870 | /*now qpp contains -1*qp*/ |
---|
871 | } |
---|
872 | pSetExp(qresult,1,1);/*this is mult. by t*/ |
---|
873 | pSetm(qresult); |
---|
874 | pIter(qp); |
---|
875 | } |
---|
876 | /* |
---|
877 | *now p is processed: |
---|
878 | *result contains t*p |
---|
879 | * if cas: pp contains -1*p (in the new ring) |
---|
880 | */ |
---|
881 | if (cas) qresult->next = pp; |
---|
882 | /* else qresult->next = NULL;*/ |
---|
883 | return result; |
---|
884 | } |
---|
885 | |
---|
886 | /*2 |
---|
887 | * verschiebt die Indizees der Modulerzeugenden um i |
---|
888 | */ |
---|
889 | void pShift (poly * p,int i) |
---|
890 | { |
---|
891 | poly qp1 = *p,qp2 = *p;/*working pointers*/ |
---|
892 | int j = pMaxComp(*p),k = pMinComp(*p); |
---|
893 | |
---|
894 | if (j+i < 0) return ; |
---|
895 | while (qp1 != NULL) |
---|
896 | { |
---|
897 | if ((pGetComp(qp1)+i > 0) || ((j == -i) && (j == k))) |
---|
898 | { |
---|
899 | pAddComp(qp1,i); |
---|
900 | pSetmComp(qp1); |
---|
901 | qp2 = qp1; |
---|
902 | pIter(qp1); |
---|
903 | } |
---|
904 | else |
---|
905 | { |
---|
906 | if (qp2 == *p) |
---|
907 | { |
---|
908 | pIter(*p); |
---|
909 | pLmDelete(&qp2); |
---|
910 | qp2 = *p; |
---|
911 | qp1 = *p; |
---|
912 | } |
---|
913 | else |
---|
914 | { |
---|
915 | qp2->next = qp1->next; |
---|
916 | if (qp1!=NULL) pLmDelete(&qp1); |
---|
917 | qp1 = qp2->next; |
---|
918 | } |
---|
919 | } |
---|
920 | } |
---|
921 | } |
---|
922 | |
---|
923 | /*2 |
---|
924 | *initialized a field with r numbers between beg and end for the |
---|
925 | *procedure idNextChoise |
---|
926 | */ |
---|
927 | void idInitChoise (int r,int beg,int end,BOOLEAN *endch,int * choise) |
---|
928 | { |
---|
929 | /*returns the first choise of r numbers between beg and end*/ |
---|
930 | int i; |
---|
931 | for (i=0; i<r; i++) |
---|
932 | { |
---|
933 | choise[i] = 0; |
---|
934 | } |
---|
935 | if (r <= end-beg+1) |
---|
936 | for (i=0; i<r; i++) |
---|
937 | { |
---|
938 | choise[i] = beg+i; |
---|
939 | } |
---|
940 | if (r > end-beg+1) |
---|
941 | *endch = TRUE; |
---|
942 | else |
---|
943 | *endch = FALSE; |
---|
944 | } |
---|
945 | |
---|
946 | /*2 |
---|
947 | *returns the next choise of r numbers between beg and end |
---|
948 | */ |
---|
949 | void idGetNextChoise (int r,int end,BOOLEAN *endch,int * choise) |
---|
950 | { |
---|
951 | int i = r-1,j; |
---|
952 | while ((i >= 0) && (choise[i] == end)) |
---|
953 | { |
---|
954 | i--; |
---|
955 | end--; |
---|
956 | } |
---|
957 | if (i == -1) |
---|
958 | *endch = TRUE; |
---|
959 | else |
---|
960 | { |
---|
961 | choise[i]++; |
---|
962 | for (j=i+1; j<r; j++) |
---|
963 | { |
---|
964 | choise[j] = choise[i]+j-i; |
---|
965 | } |
---|
966 | *endch = FALSE; |
---|
967 | } |
---|
968 | } |
---|
969 | |
---|
970 | /*2 |
---|
971 | *takes the field choise of d numbers between beg and end, cancels the t-th |
---|
972 | *entree and searches for the ordinal number of that d-1 dimensional field |
---|
973 | * w.r.t. the algorithm of construction |
---|
974 | */ |
---|
975 | int idGetNumberOfChoise(int t, int d, int begin, int end, int * choise) |
---|
976 | { |
---|
977 | int * localchoise,i,result=0; |
---|
978 | BOOLEAN b=FALSE; |
---|
979 | |
---|
980 | if (d<=1) return 1; |
---|
981 | localchoise=(int*)omAlloc((d-1)*sizeof(int)); |
---|
982 | idInitChoise(d-1,begin,end,&b,localchoise); |
---|
983 | while (!b) |
---|
984 | { |
---|
985 | result++; |
---|
986 | i = 0; |
---|
987 | while ((i<t) && (localchoise[i]==choise[i])) i++; |
---|
988 | if (i>=t) |
---|
989 | { |
---|
990 | i = t+1; |
---|
991 | while ((i<d) && (localchoise[i-1]==choise[i])) i++; |
---|
992 | if (i>=d) |
---|
993 | { |
---|
994 | omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
995 | return result; |
---|
996 | } |
---|
997 | } |
---|
998 | idGetNextChoise(d-1,end,&b,localchoise); |
---|
999 | } |
---|
1000 | omFreeSize((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
1001 | return 0; |
---|
1002 | } |
---|
1003 | |
---|
1004 | /*2 |
---|
1005 | *computes the binomial coefficient |
---|
1006 | */ |
---|
1007 | int binom (int n,int r) |
---|
1008 | { |
---|
1009 | int i,result; |
---|
1010 | |
---|
1011 | if (r==0) return 1; |
---|
1012 | if (n-r<r) return binom(n,n-r); |
---|
1013 | result = n-r+1; |
---|
1014 | for (i=2;i<=r;i++) |
---|
1015 | { |
---|
1016 | result *= n-r+i; |
---|
1017 | if (result<0) |
---|
1018 | { |
---|
1019 | WarnS("overflow in binomials"); |
---|
1020 | return 0; |
---|
1021 | } |
---|
1022 | result /= i; |
---|
1023 | } |
---|
1024 | return result; |
---|
1025 | } |
---|
1026 | |
---|
1027 | /*2 |
---|
1028 | *the free module of rank i |
---|
1029 | */ |
---|
1030 | ideal idFreeModule (int i) |
---|
1031 | { |
---|
1032 | int j; |
---|
1033 | ideal h; |
---|
1034 | |
---|
1035 | h=idInit(i,i); |
---|
1036 | for (j=0; j<i; j++) |
---|
1037 | { |
---|
1038 | h->m[j] = pOne(); |
---|
1039 | pSetComp(h->m[j],j+1); |
---|
1040 | pSetmComp(h->m[j]); |
---|
1041 | } |
---|
1042 | return h; |
---|
1043 | } |
---|
1044 | |
---|
1045 | ideal idSectWithElim (ideal h1,ideal h2) |
---|
1046 | // does not destroy h1,h2 |
---|
1047 | { |
---|
1048 | if (TEST_OPT_PROT) PrintS("intersect by elimination method\n"); |
---|
1049 | assume(!idIs0(h1)); |
---|
1050 | assume(!idIs0(h2)); |
---|
1051 | assume(IDELEMS(h1)<=IDELEMS(h2)); |
---|
1052 | assume(idRankFreeModule(h1)==0); |
---|
1053 | assume(idRankFreeModule(h2)==0); |
---|
1054 | // add a new variable: |
---|
1055 | int j; |
---|
1056 | ring origRing=currRing; |
---|
1057 | ring r=rCopy0(origRing); |
---|
1058 | r->N++; |
---|
1059 | r->block0[0]=1; |
---|
1060 | r->block1[0]= r->N; |
---|
1061 | omFree(r->order); |
---|
1062 | r->order=(int*)omAlloc0(3*sizeof(int*)); |
---|
1063 | r->order[0]=ringorder_dp; |
---|
1064 | r->order[1]=ringorder_C; |
---|
1065 | char **names=(char**)omAlloc0(rVar(r) * sizeof(char_ptr)); |
---|
1066 | for (j=0;j<r->N-1;j++) names[j]=r->names[j]; |
---|
1067 | names[r->N-1]=omStrDup("@"); |
---|
1068 | omFree(r->names); |
---|
1069 | r->names=names; |
---|
1070 | rComplete(r,TRUE); |
---|
1071 | // fetch h1, h2 |
---|
1072 | ideal h; |
---|
1073 | h1=idrCopyR(h1,origRing,r); |
---|
1074 | h2=idrCopyR(h2,origRing,r); |
---|
1075 | // switch to temp. ring r |
---|
1076 | rChangeCurrRing(r); |
---|
1077 | // create 1-t, t |
---|
1078 | poly omt=pOne(); |
---|
1079 | pSetExp(omt,r->N,1); |
---|
1080 | poly t=pCopy(omt); |
---|
1081 | pSetm(omt); |
---|
1082 | omt=pNeg(omt); |
---|
1083 | omt=pAdd(omt,pOne()); |
---|
1084 | // compute (1-t)*h1 |
---|
1085 | h1=(ideal)mpMultP((matrix)h1,omt); |
---|
1086 | // compute t*h2 |
---|
1087 | h2=(ideal)mpMultP((matrix)h2,pCopy(t)); |
---|
1088 | // (1-t)h1 + t*h2 |
---|
1089 | h=idInit(IDELEMS(h1)+IDELEMS(h2),1); |
---|
1090 | int l; |
---|
1091 | for (l=IDELEMS(h1)-1; l>=0; l--) |
---|
1092 | { |
---|
1093 | h->m[l] = h1->m[l]; h1->m[l]=NULL; |
---|
1094 | } |
---|
1095 | j=IDELEMS(h1); |
---|
1096 | for (l=IDELEMS(h2)-1; l>=0; l--) |
---|
1097 | { |
---|
1098 | h->m[l+j] = h2->m[l]; h2->m[l]=NULL; |
---|
1099 | } |
---|
1100 | idDelete(&h1); |
---|
1101 | idDelete(&h2); |
---|
1102 | // eliminate t: |
---|
1103 | |
---|
1104 | ideal res=idElimination(h,t); |
---|
1105 | // cleanup |
---|
1106 | idDelete(&h); |
---|
1107 | res=idrMoveR(res,r,origRing); |
---|
1108 | rChangeCurrRing(origRing); |
---|
1109 | rKill(r); |
---|
1110 | return res; |
---|
1111 | } |
---|
1112 | |
---|
1113 | /*2 |
---|
1114 | *computes recursively all monomials of a certain degree |
---|
1115 | *in every step the actvar-th entry in the exponential |
---|
1116 | *vector is incremented and the other variables are |
---|
1117 | *computed by recursive calls of makemonoms |
---|
1118 | *if the last variable is reached, the difference to the |
---|
1119 | *degree is computed directly |
---|
1120 | *vars is the number variables |
---|
1121 | *actvar is the actual variable to handle |
---|
1122 | *deg is the degree of the monomials to compute |
---|
1123 | *monomdeg is the actual degree of the monomial in consideration |
---|
1124 | */ |
---|
1125 | static void makemonoms(int vars,int actvar,int deg,int monomdeg) |
---|
1126 | { |
---|
1127 | poly p; |
---|
1128 | int i=0; |
---|
1129 | |
---|
1130 | if ((idpowerpoint == 0) && (actvar ==1)) |
---|
1131 | { |
---|
1132 | idpower[idpowerpoint] = pOne(); |
---|
1133 | monomdeg = 0; |
---|
1134 | } |
---|
1135 | while (i<=deg) |
---|
1136 | { |
---|
1137 | if (deg == monomdeg) |
---|
1138 | { |
---|
1139 | pSetm(idpower[idpowerpoint]); |
---|
1140 | idpowerpoint++; |
---|
1141 | return; |
---|
1142 | } |
---|
1143 | if (actvar == vars) |
---|
1144 | { |
---|
1145 | pSetExp(idpower[idpowerpoint],actvar,deg-monomdeg); |
---|
1146 | pSetm(idpower[idpowerpoint]); |
---|
1147 | pTest(idpower[idpowerpoint]); |
---|
1148 | idpowerpoint++; |
---|
1149 | return; |
---|
1150 | } |
---|
1151 | else |
---|
1152 | { |
---|
1153 | p = pCopy(idpower[idpowerpoint]); |
---|
1154 | makemonoms(vars,actvar+1,deg,monomdeg); |
---|
1155 | idpower[idpowerpoint] = p; |
---|
1156 | } |
---|
1157 | monomdeg++; |
---|
1158 | pSetExp(idpower[idpowerpoint],actvar,pGetExp(idpower[idpowerpoint],actvar)+1); |
---|
1159 | pSetm(idpower[idpowerpoint]); |
---|
1160 | pTest(idpower[idpowerpoint]); |
---|
1161 | i++; |
---|
1162 | } |
---|
1163 | } |
---|
1164 | |
---|
1165 | /*2 |
---|
1166 | *returns the deg-th power of the maximal ideal of 0 |
---|
1167 | */ |
---|
1168 | ideal idMaxIdeal(int deg) |
---|
1169 | { |
---|
1170 | if (deg < 0) |
---|
1171 | { |
---|
1172 | WarnS("maxideal: power must be non-negative"); |
---|
1173 | } |
---|
1174 | if (deg < 1) |
---|
1175 | { |
---|
1176 | ideal I=idInit(1,1); |
---|
1177 | I->m[0]=pOne(); |
---|
1178 | return I; |
---|
1179 | } |
---|
1180 | if (deg == 1) |
---|
1181 | { |
---|
1182 | return idMaxIdeal(); |
---|
1183 | } |
---|
1184 | |
---|
1185 | int vars = currRing->N; |
---|
1186 | int i = binom(vars+deg-1,deg); |
---|
1187 | if (i<=0) return idInit(1,1); |
---|
1188 | ideal id=idInit(i,1); |
---|
1189 | idpower = id->m; |
---|
1190 | idpowerpoint = 0; |
---|
1191 | makemonoms(vars,1,deg,0); |
---|
1192 | idpower = NULL; |
---|
1193 | idpowerpoint = 0; |
---|
1194 | return id; |
---|
1195 | } |
---|
1196 | |
---|
1197 | /*2 |
---|
1198 | *computes recursively all generators of a certain degree |
---|
1199 | *of the ideal "givenideal" |
---|
1200 | *elms is the number elements in the given ideal |
---|
1201 | *actelm is the actual element to handle |
---|
1202 | *deg is the degree of the power to compute |
---|
1203 | *gendeg is the actual degree of the generator in consideration |
---|
1204 | */ |
---|
1205 | static void makepotence(int elms,int actelm,int deg,int gendeg) |
---|
1206 | { |
---|
1207 | poly p; |
---|
1208 | int i=0; |
---|
1209 | |
---|
1210 | if ((idpowerpoint == 0) && (actelm ==1)) |
---|
1211 | { |
---|
1212 | idpower[idpowerpoint] = pOne(); |
---|
1213 | gendeg = 0; |
---|
1214 | } |
---|
1215 | while (i<=deg) |
---|
1216 | { |
---|
1217 | if (deg == gendeg) |
---|
1218 | { |
---|
1219 | idpowerpoint++; |
---|
1220 | return; |
---|
1221 | } |
---|
1222 | if (actelm == elms) |
---|
1223 | { |
---|
1224 | p=pPower(pCopy(givenideal[actelm-1]),deg-gendeg); |
---|
1225 | idpower[idpowerpoint]=pMult(idpower[idpowerpoint],p); |
---|
1226 | idpowerpoint++; |
---|
1227 | return; |
---|
1228 | } |
---|
1229 | else |
---|
1230 | { |
---|
1231 | p = pCopy(idpower[idpowerpoint]); |
---|
1232 | makepotence(elms,actelm+1,deg,gendeg); |
---|
1233 | idpower[idpowerpoint] = p; |
---|
1234 | } |
---|
1235 | gendeg++; |
---|
1236 | idpower[idpowerpoint]=pMult(idpower[idpowerpoint],pCopy(givenideal[actelm-1])); |
---|
1237 | i++; |
---|
1238 | } |
---|
1239 | } |
---|
1240 | |
---|
1241 | /*2 |
---|
1242 | *returns the deg-th power of the ideal gid |
---|
1243 | */ |
---|
1244 | //ideal idPower(ideal gid,int deg) |
---|
1245 | //{ |
---|
1246 | // int i; |
---|
1247 | // ideal id; |
---|
1248 | // |
---|
1249 | // if (deg < 1) deg = 1; |
---|
1250 | // i = binom(IDELEMS(gid)+deg-1,deg); |
---|
1251 | // id=idInit(i,1); |
---|
1252 | // idpower = id->m; |
---|
1253 | // givenideal = gid->m; |
---|
1254 | // idpowerpoint = 0; |
---|
1255 | // makepotence(IDELEMS(gid),1,deg,0); |
---|
1256 | // idpower = NULL; |
---|
1257 | // givenideal = NULL; |
---|
1258 | // idpowerpoint = 0; |
---|
1259 | // return id; |
---|
1260 | //} |
---|
1261 | static void idNextPotence(ideal given, ideal result, |
---|
1262 | int begin, int end, int deg, int restdeg, poly ap) |
---|
1263 | { |
---|
1264 | poly p; |
---|
1265 | int i; |
---|
1266 | |
---|
1267 | p = pPower(pCopy(given->m[begin]),restdeg); |
---|
1268 | i = result->nrows; |
---|
1269 | result->m[i] = pMult(pCopy(ap),p); |
---|
1270 | //PrintS("."); |
---|
1271 | (result->nrows)++; |
---|
1272 | if (result->nrows >= IDELEMS(result)) |
---|
1273 | { |
---|
1274 | pEnlargeSet(&(result->m),IDELEMS(result),16); |
---|
1275 | IDELEMS(result) += 16; |
---|
1276 | } |
---|
1277 | if (begin == end) return; |
---|
1278 | for (i=restdeg-1;i>0;i--) |
---|
1279 | { |
---|
1280 | p = pPower(pCopy(given->m[begin]),i); |
---|
1281 | p = pMult(pCopy(ap),p); |
---|
1282 | idNextPotence(given, result, begin+1, end, deg, restdeg-i, p); |
---|
1283 | pDelete(&p); |
---|
1284 | } |
---|
1285 | idNextPotence(given, result, begin+1, end, deg, restdeg, ap); |
---|
1286 | } |
---|
1287 | |
---|
1288 | ideal idPower(ideal given,int exp) |
---|
1289 | { |
---|
1290 | ideal result,temp; |
---|
1291 | poly p1; |
---|
1292 | int i; |
---|
1293 | |
---|
1294 | if (idIs0(given)) return idInit(1,1); |
---|
1295 | temp = idCopy(given); |
---|
1296 | idSkipZeroes(temp); |
---|
1297 | i = binom(IDELEMS(temp)+exp-1,exp); |
---|
1298 | result = idInit(i,1); |
---|
1299 | result->nrows = 0; |
---|
1300 | //Print("ideal contains %d elements\n",i); |
---|
1301 | p1=pOne(); |
---|
1302 | idNextPotence(temp,result,0,IDELEMS(temp)-1,exp,exp,p1); |
---|
1303 | pDelete(&p1); |
---|
1304 | idDelete(&temp); |
---|
1305 | result->nrows = 1; |
---|
1306 | idDelEquals(result); |
---|
1307 | idSkipZeroes(result); |
---|
1308 | return result; |
---|
1309 | } |
---|
1310 | |
---|
1311 | /*2 |
---|
1312 | * compute the which-th ar-minor of the matrix a |
---|
1313 | */ |
---|
1314 | poly idMinor(matrix a, int ar, unsigned long which, ideal R) |
---|
1315 | { |
---|
1316 | int i,j,k,size; |
---|
1317 | unsigned long curr; |
---|
1318 | int *rowchoise,*colchoise; |
---|
1319 | BOOLEAN rowch,colch; |
---|
1320 | ideal result; |
---|
1321 | matrix tmp; |
---|
1322 | poly p,q; |
---|
1323 | |
---|
1324 | i = binom(a->rows(),ar); |
---|
1325 | j = binom(a->cols(),ar); |
---|
1326 | |
---|
1327 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
1328 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
1329 | if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
1330 | else size=i*j; |
---|
1331 | result=idInit(size,1); |
---|
1332 | tmp=mpNew(ar,ar); |
---|
1333 | k = 0; /* the index in result*/ |
---|
1334 | curr = 0; /* index of current minor */ |
---|
1335 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
1336 | while (!rowch) |
---|
1337 | { |
---|
1338 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
1339 | while (!colch) |
---|
1340 | { |
---|
1341 | if (curr == which) |
---|
1342 | { |
---|
1343 | for (i=1; i<=ar; i++) |
---|
1344 | { |
---|
1345 | for (j=1; j<=ar; j++) |
---|
1346 | { |
---|
1347 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
1348 | } |
---|
1349 | } |
---|
1350 | p = mpDetBareiss(tmp); |
---|
1351 | if (p!=NULL) |
---|
1352 | { |
---|
1353 | if (R!=NULL) |
---|
1354 | { |
---|
1355 | q = p; |
---|
1356 | p = kNF(R,currQuotient,q); |
---|
1357 | pDelete(&q); |
---|
1358 | } |
---|
1359 | /*delete the matrix tmp*/ |
---|
1360 | for (i=1; i<=ar; i++) |
---|
1361 | { |
---|
1362 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
1363 | } |
---|
1364 | idDelete((ideal*)&tmp); |
---|
1365 | omFreeSize((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
1366 | omFreeSize((ADDRESS)colchoise,ar*sizeof(int)); |
---|
1367 | return (p); |
---|
1368 | } |
---|
1369 | } |
---|
1370 | curr++; |
---|
1371 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
1372 | } |
---|
1373 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
1374 | } |
---|
1375 | return (poly) 1; |
---|
1376 | } |
---|
1377 | |
---|
1378 | #ifdef WITH_OLD_MINOR |
---|
1379 | /*2 |
---|
1380 | * compute all ar-minors of the matrix a |
---|
1381 | */ |
---|
1382 | ideal idMinors(matrix a, int ar, ideal R) |
---|
1383 | { |
---|
1384 | int i,j,k,size; |
---|
1385 | int *rowchoise,*colchoise; |
---|
1386 | BOOLEAN rowch,colch; |
---|
1387 | ideal result; |
---|
1388 | matrix tmp; |
---|
1389 | poly p,q; |
---|
1390 | |
---|
1391 | i = binom(a->rows(),ar); |
---|
1392 | j = binom(a->cols(),ar); |
---|
1393 | |
---|
1394 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
1395 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
1396 | if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
1397 | else size=i*j; |
---|
1398 | result=idInit(size,1); |
---|
1399 | tmp=mpNew(ar,ar); |
---|
1400 | k = 0; /* the index in result*/ |
---|
1401 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
1402 | while (!rowch) |
---|
1403 | { |
---|
1404 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
1405 | while (!colch) |
---|
1406 | { |
---|
1407 | for (i=1; i<=ar; i++) |
---|
1408 | { |
---|
1409 | for (j=1; j<=ar; j++) |
---|
1410 | { |
---|
1411 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
1412 | } |
---|
1413 | } |
---|
1414 | p = mpDetBareiss(tmp); |
---|
1415 | if (p!=NULL) |
---|
1416 | { |
---|
1417 | if (R!=NULL) |
---|
1418 | { |
---|
1419 | q = p; |
---|
1420 | p = kNF(R,currQuotient,q); |
---|
1421 | pDelete(&q); |
---|
1422 | } |
---|
1423 | if (p!=NULL) |
---|
1424 | { |
---|
1425 | if (k>=size) |
---|
1426 | { |
---|
1427 | pEnlargeSet(&result->m,size,32); |
---|
1428 | size += 32; |
---|
1429 | } |
---|
1430 | result->m[k] = p; |
---|
1431 | k++; |
---|
1432 | } |
---|
1433 | } |
---|
1434 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
1435 | } |
---|
1436 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
1437 | } |
---|
1438 | /*delete the matrix tmp*/ |
---|
1439 | for (i=1; i<=ar; i++) |
---|
1440 | { |
---|
1441 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
1442 | } |
---|
1443 | idDelete((ideal*)&tmp); |
---|
1444 | if (k==0) |
---|
1445 | { |
---|
1446 | k=1; |
---|
1447 | result->m[0]=NULL; |
---|
1448 | } |
---|
1449 | omFreeSize((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
1450 | omFreeSize((ADDRESS)colchoise,ar*sizeof(int)); |
---|
1451 | pEnlargeSet(&result->m,size,k-size); |
---|
1452 | IDELEMS(result) = k; |
---|
1453 | return (result); |
---|
1454 | } |
---|
1455 | #else |
---|
1456 | /*2 |
---|
1457 | * compute all ar-minors of the matrix a |
---|
1458 | * the caller of mpRecMin |
---|
1459 | * the elements of the result are not in R (if R!=NULL) |
---|
1460 | */ |
---|
1461 | ideal idMinors(matrix a, int ar, ideal R) |
---|
1462 | { |
---|
1463 | int elems=0; |
---|
1464 | int r=a->nrows,c=a->ncols; |
---|
1465 | int i; |
---|
1466 | matrix b; |
---|
1467 | ideal result,h; |
---|
1468 | ring origR; |
---|
1469 | ring tmpR; |
---|
1470 | long bound; |
---|
1471 | |
---|
1472 | if((ar<=0) || (ar>r) || (ar>c)) |
---|
1473 | { |
---|
1474 | Werror("%d-th minor, matrix is %dx%d",ar,r,c); |
---|
1475 | return NULL; |
---|
1476 | } |
---|
1477 | h = idMatrix2Module(mpCopy(a)); |
---|
1478 | bound = smExpBound(h,c,r,ar); |
---|
1479 | idDelete(&h); |
---|
1480 | tmpR=smRingChange(&origR,bound); |
---|
1481 | b = mpNew(r,c); |
---|
1482 | for (i=r*c-1;i>=0;i--) |
---|
1483 | { |
---|
1484 | if (a->m[i]) |
---|
1485 | b->m[i] = prCopyR(a->m[i],origR); |
---|
1486 | } |
---|
1487 | if (R!=NULL) |
---|
1488 | { |
---|
1489 | R = idrCopyR(R,origR); |
---|
1490 | //if (ar>1) // otherwise done in mpMinorToResult |
---|
1491 | //{ |
---|
1492 | // matrix bb=(matrix)kNF(R,currQuotient,(ideal)b); |
---|
1493 | // bb->rank=b->rank; bb->nrows=b->nrows; bb->ncols=b->ncols; |
---|
1494 | // idDelete((ideal*)&b); b=bb; |
---|
1495 | //} |
---|
1496 | } |
---|
1497 | result=idInit(32,1); |
---|
1498 | if(ar>1) mpRecMin(ar-1,result,elems,b,r,c,NULL,R); |
---|
1499 | else mpMinorToResult(result,elems,b,r,c,R); |
---|
1500 | idDelete((ideal *)&b); |
---|
1501 | if (R!=NULL) idDelete(&R); |
---|
1502 | idSkipZeroes(result); |
---|
1503 | rChangeCurrRing(origR); |
---|
1504 | result = idrMoveR(result,tmpR); |
---|
1505 | smKillModifiedRing(tmpR); |
---|
1506 | idTest(result); |
---|
1507 | return result; |
---|
1508 | } |
---|
1509 | #endif |
---|
1510 | |
---|
1511 | /*2 |
---|
1512 | *skips all zeroes and double elements, searches also for units |
---|
1513 | */ |
---|
1514 | void idCompactify(ideal id) |
---|
1515 | { |
---|
1516 | int i,j; |
---|
1517 | BOOLEAN b=FALSE; |
---|
1518 | |
---|
1519 | i = IDELEMS(id)-1; |
---|
1520 | while ((! b) && (i>=0)) |
---|
1521 | { |
---|
1522 | b=pIsUnit(id->m[i]); |
---|
1523 | i--; |
---|
1524 | } |
---|
1525 | if (b) |
---|
1526 | { |
---|
1527 | for(i=IDELEMS(id)-1;i>=0;i--) pDelete(&id->m[i]); |
---|
1528 | id->m[0]=pOne(); |
---|
1529 | } |
---|
1530 | else |
---|
1531 | { |
---|
1532 | idDelMultiples(id); |
---|
1533 | } |
---|
1534 | idSkipZeroes(id); |
---|
1535 | } |
---|
1536 | |
---|
1537 | /*2 |
---|
1538 | *returns TRUE if id1 is a submodule of id2 |
---|
1539 | */ |
---|
1540 | BOOLEAN idIsSubModule(ideal id1,ideal id2) |
---|
1541 | { |
---|
1542 | int i; |
---|
1543 | poly p; |
---|
1544 | |
---|
1545 | if (idIs0(id1)) return TRUE; |
---|
1546 | for (i=0;i<IDELEMS(id1);i++) |
---|
1547 | { |
---|
1548 | if (id1->m[i] != NULL) |
---|
1549 | { |
---|
1550 | p = kNF(id2,currQuotient,id1->m[i]); |
---|
1551 | if (p != NULL) |
---|
1552 | { |
---|
1553 | pDelete(&p); |
---|
1554 | return FALSE; |
---|
1555 | } |
---|
1556 | } |
---|
1557 | } |
---|
1558 | return TRUE; |
---|
1559 | } |
---|
1560 | |
---|
1561 | /*2 |
---|
1562 | * returns the ideals of initial terms |
---|
1563 | */ |
---|
1564 | ideal idHead(ideal h) |
---|
1565 | { |
---|
1566 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
1567 | int i; |
---|
1568 | |
---|
1569 | for (i=IDELEMS(h)-1;i>=0; i--) |
---|
1570 | { |
---|
1571 | if (h->m[i]!=NULL) m->m[i]=pHead(h->m[i]); |
---|
1572 | } |
---|
1573 | return m; |
---|
1574 | } |
---|
1575 | |
---|
1576 | ideal idHomogen(ideal h, int varnum) |
---|
1577 | { |
---|
1578 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
1579 | int i; |
---|
1580 | |
---|
1581 | for (i=IDELEMS(h)-1;i>=0; i--) |
---|
1582 | { |
---|
1583 | m->m[i]=pHomogen(h->m[i],varnum); |
---|
1584 | } |
---|
1585 | return m; |
---|
1586 | } |
---|
1587 | |
---|
1588 | /*------------------type conversions----------------*/ |
---|
1589 | ideal idVec2Ideal(poly vec) |
---|
1590 | { |
---|
1591 | ideal result=idInit(1,1); |
---|
1592 | omFree((ADDRESS)result->m); |
---|
1593 | result->m=NULL; // remove later |
---|
1594 | pVec2Polys(vec, &(result->m), &(IDELEMS(result))); |
---|
1595 | return result; |
---|
1596 | } |
---|
1597 | |
---|
1598 | #define NEW_STUFF |
---|
1599 | #ifndef NEW_STUFF |
---|
1600 | // converts mat to module, destroys mat |
---|
1601 | ideal idMatrix2Module(matrix mat) |
---|
1602 | { |
---|
1603 | int mc=MATCOLS(mat); |
---|
1604 | int mr=MATROWS(mat); |
---|
1605 | ideal result = idInit(si_max(mc,1),si_max(mr,1)); |
---|
1606 | int i,j; |
---|
1607 | poly h; |
---|
1608 | |
---|
1609 | for(j=0;j<mc /*MATCOLS(mat)*/;j++) /* j is also index in result->m */ |
---|
1610 | { |
---|
1611 | for (i=1;i<=mr /*MATROWS(mat)*/;i++) |
---|
1612 | { |
---|
1613 | h = MATELEM(mat,i,j+1); |
---|
1614 | if (h!=NULL) |
---|
1615 | { |
---|
1616 | MATELEM(mat,i,j+1)=NULL; |
---|
1617 | pSetCompP(h,i); |
---|
1618 | result->m[j] = pAdd(result->m[j],h); |
---|
1619 | } |
---|
1620 | } |
---|
1621 | } |
---|
1622 | // obachman: need to clean this up |
---|
1623 | idDelete((ideal*) &mat); |
---|
1624 | return result; |
---|
1625 | } |
---|
1626 | #else |
---|
1627 | |
---|
1628 | #include "sbuckets.h" |
---|
1629 | |
---|
1630 | // converts mat to module, destroys mat |
---|
1631 | ideal idMatrix2Module(matrix mat) |
---|
1632 | { |
---|
1633 | int mc=MATCOLS(mat); |
---|
1634 | int mr=MATROWS(mat); |
---|
1635 | ideal result = idInit(si_max(mc,1),si_max(mr,1)); |
---|
1636 | int i,j, l; |
---|
1637 | poly h; |
---|
1638 | poly p; |
---|
1639 | sBucket_pt bucket = sBucketCreate(currRing); |
---|
1640 | |
---|
1641 | for(j=0;j<mc /*MATCOLS(mat)*/;j++) /* j is also index in result->m */ |
---|
1642 | { |
---|
1643 | for (i=1;i<=mr /*MATROWS(mat)*/;i++) |
---|
1644 | { |
---|
1645 | h = MATELEM(mat,i,j+1); |
---|
1646 | if (h!=NULL) |
---|
1647 | { |
---|
1648 | l=pLength(h); |
---|
1649 | MATELEM(mat,i,j+1)=NULL; |
---|
1650 | p_SetCompP(h,i, currRing); |
---|
1651 | sBucket_Merge_p(bucket, h, l); |
---|
1652 | } |
---|
1653 | } |
---|
1654 | sBucketClearMerge(bucket, &(result->m[j]), &l); |
---|
1655 | } |
---|
1656 | sBucketDestroy(&bucket); |
---|
1657 | |
---|
1658 | // obachman: need to clean this up |
---|
1659 | idDelete((ideal*) &mat); |
---|
1660 | return result; |
---|
1661 | } |
---|
1662 | #endif |
---|
1663 | |
---|
1664 | /*2 |
---|
1665 | * converts a module into a matrix, destroyes the input |
---|
1666 | */ |
---|
1667 | matrix idModule2Matrix(ideal mod) |
---|
1668 | { |
---|
1669 | matrix result = mpNew(mod->rank,IDELEMS(mod)); |
---|
1670 | int i,cp; |
---|
1671 | poly p,h; |
---|
1672 | |
---|
1673 | for(i=0;i<IDELEMS(mod);i++) |
---|
1674 | { |
---|
1675 | p=pReverse(mod->m[i]); |
---|
1676 | mod->m[i]=NULL; |
---|
1677 | while (p!=NULL) |
---|
1678 | { |
---|
1679 | h=p; |
---|
1680 | pIter(p); |
---|
1681 | pNext(h)=NULL; |
---|
1682 | // cp = si_max(1,pGetComp(h)); // if used for ideals too |
---|
1683 | cp = pGetComp(h); |
---|
1684 | pSetComp(h,0); |
---|
1685 | pSetmComp(h); |
---|
1686 | #ifdef TEST |
---|
1687 | if (cp>mod->rank) |
---|
1688 | { |
---|
1689 | Print("## inv. rank %ld -> %d\n",mod->rank,cp); |
---|
1690 | int k,l,o=mod->rank; |
---|
1691 | mod->rank=cp; |
---|
1692 | matrix d=mpNew(mod->rank,IDELEMS(mod)); |
---|
1693 | for (l=1; l<=o; l++) |
---|
1694 | { |
---|
1695 | for (k=1; k<=IDELEMS(mod); k++) |
---|
1696 | { |
---|
1697 | MATELEM(d,l,k)=MATELEM(result,l,k); |
---|
1698 | MATELEM(result,l,k)=NULL; |
---|
1699 | } |
---|
1700 | } |
---|
1701 | idDelete((ideal *)&result); |
---|
1702 | result=d; |
---|
1703 | } |
---|
1704 | #endif |
---|
1705 | MATELEM(result,cp,i+1) = pAdd(MATELEM(result,cp,i+1),h); |
---|
1706 | } |
---|
1707 | } |
---|
1708 | // obachman 10/99: added the following line, otherwise memory leack! |
---|
1709 | idDelete(&mod); |
---|
1710 | return result; |
---|
1711 | } |
---|
1712 | |
---|
1713 | matrix idModule2formatedMatrix(ideal mod,int rows, int cols) |
---|
1714 | { |
---|
1715 | matrix result = mpNew(rows,cols); |
---|
1716 | int i,cp,r=idRankFreeModule(mod),c=IDELEMS(mod); |
---|
1717 | poly p,h; |
---|
1718 | |
---|
1719 | if (r>rows) r = rows; |
---|
1720 | if (c>cols) c = cols; |
---|
1721 | for(i=0;i<c;i++) |
---|
1722 | { |
---|
1723 | p=pReverse(mod->m[i]); |
---|
1724 | mod->m[i]=NULL; |
---|
1725 | while (p!=NULL) |
---|
1726 | { |
---|
1727 | h=p; |
---|
1728 | pIter(p); |
---|
1729 | pNext(h)=NULL; |
---|
1730 | cp = pGetComp(h); |
---|
1731 | if (cp<=r) |
---|
1732 | { |
---|
1733 | pSetComp(h,0); |
---|
1734 | pSetmComp(h); |
---|
1735 | MATELEM(result,cp,i+1) = pAdd(MATELEM(result,cp,i+1),h); |
---|
1736 | } |
---|
1737 | else |
---|
1738 | pDelete(&h); |
---|
1739 | } |
---|
1740 | } |
---|
1741 | idDelete(&mod); |
---|
1742 | return result; |
---|
1743 | } |
---|
1744 | |
---|
1745 | /*2 |
---|
1746 | * substitute the n-th variable by the monomial e in id |
---|
1747 | * destroy id |
---|
1748 | */ |
---|
1749 | ideal idSubst(ideal id, int n, poly e) |
---|
1750 | { |
---|
1751 | int k=MATROWS((matrix)id)*MATCOLS((matrix)id); |
---|
1752 | ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id)); |
---|
1753 | |
---|
1754 | res->rank = id->rank; |
---|
1755 | for(k--;k>=0;k--) |
---|
1756 | { |
---|
1757 | res->m[k]=pSubst(id->m[k],n,e); |
---|
1758 | id->m[k]=NULL; |
---|
1759 | } |
---|
1760 | idDelete(&id); |
---|
1761 | return res; |
---|
1762 | } |
---|
1763 | |
---|
1764 | BOOLEAN idHomModule(ideal m, ideal Q, intvec **w) |
---|
1765 | { |
---|
1766 | if (w!=NULL) *w=NULL; |
---|
1767 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) return FALSE; |
---|
1768 | if (idIs0(m)) |
---|
1769 | { |
---|
1770 | if (w!=NULL) (*w)=new intvec(m->rank); |
---|
1771 | return TRUE; |
---|
1772 | } |
---|
1773 | |
---|
1774 | long cmax=1,order=0,ord,* diff,diffmin=32000; |
---|
1775 | int *iscom; |
---|
1776 | int i,j; |
---|
1777 | poly p=NULL; |
---|
1778 | pFDegProc d; |
---|
1779 | if (pLexOrder && (currRing->order[0]==ringorder_lp)) |
---|
1780 | d=p_Totaldegree; |
---|
1781 | else |
---|
1782 | d=pFDeg; |
---|
1783 | int length=IDELEMS(m); |
---|
1784 | polyset P=m->m; |
---|
1785 | polyset F=(polyset)omAlloc(length*sizeof(poly)); |
---|
1786 | for (i=length-1;i>=0;i--) |
---|
1787 | { |
---|
1788 | p=F[i]=P[i]; |
---|
1789 | cmax=si_max(cmax,(long)pMaxComp(p)); |
---|
1790 | } |
---|
1791 | cmax++; |
---|
1792 | diff = (long *)omAlloc0(cmax*sizeof(long)); |
---|
1793 | if (w!=NULL) *w=new intvec(cmax-1); |
---|
1794 | iscom = (int *)omAlloc0(cmax*sizeof(int)); |
---|
1795 | i=0; |
---|
1796 | while (i<=length) |
---|
1797 | { |
---|
1798 | if (i<length) |
---|
1799 | { |
---|
1800 | p=F[i]; |
---|
1801 | while ((p!=NULL) && (iscom[pGetComp(p)]==0)) pIter(p); |
---|
1802 | } |
---|
1803 | if ((p==NULL) && (i<length)) |
---|
1804 | { |
---|
1805 | i++; |
---|
1806 | } |
---|
1807 | else |
---|
1808 | { |
---|
1809 | if (p==NULL) /* && (i==length) */ |
---|
1810 | { |
---|
1811 | i=0; |
---|
1812 | while ((i<length) && (F[i]==NULL)) i++; |
---|
1813 | if (i>=length) break; |
---|
1814 | p = F[i]; |
---|
1815 | } |
---|
1816 | //if (pLexOrder && (currRing->order[0]==ringorder_lp)) |
---|
1817 | // order=pTotaldegree(p); |
---|
1818 | //else |
---|
1819 | // order = p->order; |
---|
1820 | // order = pFDeg(p,currRing); |
---|
1821 | order = d(p,currRing) +diff[pGetComp(p)]; |
---|
1822 | //order += diff[pGetComp(p)]; |
---|
1823 | p = F[i]; |
---|
1824 | //Print("Actual p=F[%d]: ",i);pWrite(p); |
---|
1825 | F[i] = NULL; |
---|
1826 | i=0; |
---|
1827 | } |
---|
1828 | while (p!=NULL) |
---|
1829 | { |
---|
1830 | if (pLexOrder && (currRing->order[0]==ringorder_lp)) |
---|
1831 | ord=pTotaldegree(p); |
---|
1832 | else |
---|
1833 | // ord = p->order; |
---|
1834 | ord = pFDeg(p,currRing); |
---|
1835 | if (iscom[pGetComp(p)]==0) |
---|
1836 | { |
---|
1837 | diff[pGetComp(p)] = order-ord; |
---|
1838 | iscom[pGetComp(p)] = 1; |
---|
1839 | /* |
---|
1840 | *PrintS("new diff: "); |
---|
1841 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
1842 | *PrintLn(); |
---|
1843 | *PrintS("new iscom: "); |
---|
1844 | *for (j=0;j<cmax;j++) Print("%d ",iscom[j]); |
---|
1845 | *PrintLn(); |
---|
1846 | *Print("new set %d, order %d, ord %d, diff %d\n",pGetComp(p),order,ord,diff[pGetComp(p)]); |
---|
1847 | */ |
---|
1848 | } |
---|
1849 | else |
---|
1850 | { |
---|
1851 | /* |
---|
1852 | *PrintS("new diff: "); |
---|
1853 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
1854 | *PrintLn(); |
---|
1855 | *Print("order %d, ord %d, diff %d\n",order,ord,diff[pGetComp(p)]); |
---|
1856 | */ |
---|
1857 | if (order != (ord+diff[pGetComp(p)])) |
---|
1858 | { |
---|
1859 | omFreeSize((ADDRESS) iscom,cmax*sizeof(int)); |
---|
1860 | omFreeSize((ADDRESS) diff,cmax*sizeof(long)); |
---|
1861 | omFreeSize((ADDRESS) F,length*sizeof(poly)); |
---|
1862 | delete *w;*w=NULL; |
---|
1863 | return FALSE; |
---|
1864 | } |
---|
1865 | } |
---|
1866 | pIter(p); |
---|
1867 | } |
---|
1868 | } |
---|
1869 | omFreeSize((ADDRESS) iscom,cmax*sizeof(int)); |
---|
1870 | omFreeSize((ADDRESS) F,length*sizeof(poly)); |
---|
1871 | for (i=1;i<cmax;i++) (**w)[i-1]=(int)(diff[i]); |
---|
1872 | for (i=1;i<cmax;i++) |
---|
1873 | { |
---|
1874 | if (diff[i]<diffmin) diffmin=diff[i]; |
---|
1875 | } |
---|
1876 | if (w!=NULL) |
---|
1877 | { |
---|
1878 | for (i=1;i<cmax;i++) |
---|
1879 | { |
---|
1880 | (**w)[i-1]=(int)(diff[i]-diffmin); |
---|
1881 | } |
---|
1882 | } |
---|
1883 | omFreeSize((ADDRESS) diff,cmax*sizeof(long)); |
---|
1884 | return TRUE; |
---|
1885 | } |
---|
1886 | |
---|
1887 | BOOLEAN idTestHomModule(ideal m, ideal Q, intvec *w) |
---|
1888 | { |
---|
1889 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) { PrintS(" Q not hom\n"); return FALSE;} |
---|
1890 | if (idIs0(m)) return TRUE; |
---|
1891 | |
---|
1892 | int cmax=-1; |
---|
1893 | int i; |
---|
1894 | poly p=NULL; |
---|
1895 | int length=IDELEMS(m); |
---|
1896 | polyset P=m->m; |
---|
1897 | for (i=length-1;i>=0;i--) |
---|
1898 | { |
---|
1899 | p=P[i]; |
---|
1900 | if (p!=NULL) cmax=si_max(cmax,(int)pMaxComp(p)+1); |
---|
1901 | } |
---|
1902 | if (w != NULL) |
---|
1903 | if (w->length()+1 < cmax) |
---|
1904 | { |
---|
1905 | // Print("length: %d - %d \n", w->length(),cmax); |
---|
1906 | return FALSE; |
---|
1907 | } |
---|
1908 | |
---|
1909 | if(w!=NULL) |
---|
1910 | pSetModDeg(w); |
---|
1911 | |
---|
1912 | for (i=length-1;i>=0;i--) |
---|
1913 | { |
---|
1914 | p=P[i]; |
---|
1915 | poly q=p; |
---|
1916 | if (p!=NULL) |
---|
1917 | { |
---|
1918 | int d=pFDeg(p,currRing); |
---|
1919 | loop |
---|
1920 | { |
---|
1921 | pIter(p); |
---|
1922 | if (p==NULL) break; |
---|
1923 | if (d!=pFDeg(p,currRing)) |
---|
1924 | { |
---|
1925 | //pWrite(q); wrp(p); Print(" -> %d - %d\n",d,pFDeg(p,currRing)); |
---|
1926 | if(w!=NULL) |
---|
1927 | pSetModDeg(NULL); |
---|
1928 | return FALSE; |
---|
1929 | } |
---|
1930 | } |
---|
1931 | } |
---|
1932 | } |
---|
1933 | |
---|
1934 | if(w!=NULL) |
---|
1935 | pSetModDeg(NULL); |
---|
1936 | |
---|
1937 | return TRUE; |
---|
1938 | } |
---|
1939 | |
---|
1940 | ideal idJet(ideal i,int d) |
---|
1941 | { |
---|
1942 | ideal r=idInit((i->nrows)*(i->ncols),i->rank); |
---|
1943 | r->nrows = i-> nrows; |
---|
1944 | r->ncols = i-> ncols; |
---|
1945 | //r->rank = i-> rank; |
---|
1946 | int k; |
---|
1947 | for(k=(i->nrows)*(i->ncols)-1;k>=0; k--) |
---|
1948 | { |
---|
1949 | r->m[k]=ppJet(i->m[k],d); |
---|
1950 | } |
---|
1951 | return r; |
---|
1952 | } |
---|
1953 | |
---|
1954 | ideal idJetW(ideal i,int d, intvec * iv) |
---|
1955 | { |
---|
1956 | ideal r=idInit(IDELEMS(i),i->rank); |
---|
1957 | if (ecartWeights!=NULL) |
---|
1958 | { |
---|
1959 | WerrorS("cannot compute weighted jets now"); |
---|
1960 | } |
---|
1961 | else |
---|
1962 | { |
---|
1963 | short *w=iv2array(iv); |
---|
1964 | int k; |
---|
1965 | for(k=0; k<IDELEMS(i); k++) |
---|
1966 | { |
---|
1967 | r->m[k]=ppJetW(i->m[k],d,w); |
---|
1968 | } |
---|
1969 | omFreeSize((ADDRESS)w,(pVariables+1)*sizeof(short)); |
---|
1970 | } |
---|
1971 | return r; |
---|
1972 | } |
---|
1973 | |
---|
1974 | int idMinDegW(ideal M,intvec *w) |
---|
1975 | { |
---|
1976 | int d=-1; |
---|
1977 | for(int i=0;i<IDELEMS(M);i++) |
---|
1978 | { |
---|
1979 | int d0=pMinDeg(M->m[i],w); |
---|
1980 | if(-1<d0&&(d0<d||d==-1)) |
---|
1981 | d=d0; |
---|
1982 | } |
---|
1983 | return d; |
---|
1984 | } |
---|
1985 | |
---|
1986 | ideal idSeries(int n,ideal M,matrix U,intvec *w) |
---|
1987 | { |
---|
1988 | for(int i=IDELEMS(M)-1;i>=0;i--) |
---|
1989 | { |
---|
1990 | if(U==NULL) |
---|
1991 | M->m[i]=pSeries(n,M->m[i],NULL,w); |
---|
1992 | else |
---|
1993 | { |
---|
1994 | M->m[i]=pSeries(n,M->m[i],MATELEM(U,i+1,i+1),w); |
---|
1995 | MATELEM(U,i+1,i+1)=NULL; |
---|
1996 | } |
---|
1997 | } |
---|
1998 | if(U!=NULL) |
---|
1999 | idDelete((ideal*)&U); |
---|
2000 | return M; |
---|
2001 | } |
---|
2002 | |
---|
2003 | matrix idDiff(matrix i, int k) |
---|
2004 | { |
---|
2005 | int e=MATCOLS(i)*MATROWS(i); |
---|
2006 | matrix r=mpNew(MATROWS(i),MATCOLS(i)); |
---|
2007 | r->rank=i->rank; |
---|
2008 | int j; |
---|
2009 | for(j=0; j<e; j++) |
---|
2010 | { |
---|
2011 | r->m[j]=pDiff(i->m[j],k); |
---|
2012 | } |
---|
2013 | return r; |
---|
2014 | } |
---|
2015 | |
---|
2016 | matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply) |
---|
2017 | { |
---|
2018 | matrix r=mpNew(IDELEMS(I),IDELEMS(J)); |
---|
2019 | int i,j; |
---|
2020 | for(i=0; i<IDELEMS(I); i++) |
---|
2021 | { |
---|
2022 | for(j=0; j<IDELEMS(J); j++) |
---|
2023 | { |
---|
2024 | MATELEM(r,i+1,j+1)=pDiffOp(I->m[i],J->m[j],multiply); |
---|
2025 | } |
---|
2026 | } |
---|
2027 | return r; |
---|
2028 | } |
---|
2029 | |
---|
2030 | int idElem(const ideal F) |
---|
2031 | { |
---|
2032 | int i=0,j=IDELEMS(F)-1; |
---|
2033 | |
---|
2034 | while(j>=0) |
---|
2035 | { |
---|
2036 | if ((F->m)[j]!=NULL) i++; |
---|
2037 | j--; |
---|
2038 | } |
---|
2039 | return i; |
---|
2040 | } |
---|
2041 | |
---|
2042 | /* |
---|
2043 | *computes module-weights for liftings of homogeneous modules |
---|
2044 | */ |
---|
2045 | intvec * idMWLift(ideal mod,intvec * weights) |
---|
2046 | { |
---|
2047 | if (idIs0(mod)) return new intvec(2); |
---|
2048 | int i=IDELEMS(mod); |
---|
2049 | while ((i>0) && (mod->m[i-1]==NULL)) i--; |
---|
2050 | intvec *result = new intvec(i+1); |
---|
2051 | while (i>0) |
---|
2052 | { |
---|
2053 | (*result)[i]=pFDeg(mod->m[i],currRing)+(*weights)[pGetComp(mod->m[i])]; |
---|
2054 | } |
---|
2055 | return result; |
---|
2056 | } |
---|
2057 | |
---|
2058 | /*2 |
---|
2059 | *sorts the kbase for idCoef* in a special way (lexicographically |
---|
2060 | *with x_max,...,x_1) |
---|
2061 | */ |
---|
2062 | ideal idCreateSpecialKbase(ideal kBase,intvec ** convert) |
---|
2063 | { |
---|
2064 | int i; |
---|
2065 | ideal result; |
---|
2066 | |
---|
2067 | if (idIs0(kBase)) return NULL; |
---|
2068 | result = idInit(IDELEMS(kBase),kBase->rank); |
---|
2069 | *convert = idSort(kBase,FALSE); |
---|
2070 | for (i=0;i<(*convert)->length();i++) |
---|
2071 | { |
---|
2072 | result->m[i] = pCopy(kBase->m[(**convert)[i]-1]); |
---|
2073 | } |
---|
2074 | return result; |
---|
2075 | } |
---|
2076 | |
---|
2077 | /*2 |
---|
2078 | *returns the index of a given monom in the list of the special kbase |
---|
2079 | */ |
---|
2080 | int idIndexOfKBase(poly monom, ideal kbase) |
---|
2081 | { |
---|
2082 | int j=IDELEMS(kbase); |
---|
2083 | |
---|
2084 | while ((j>0) && (kbase->m[j-1]==NULL)) j--; |
---|
2085 | if (j==0) return -1; |
---|
2086 | int i=pVariables; |
---|
2087 | while (i>0) |
---|
2088 | { |
---|
2089 | loop |
---|
2090 | { |
---|
2091 | if (pGetExp(monom,i)>pGetExp(kbase->m[j-1],i)) return -1; |
---|
2092 | if (pGetExp(monom,i)==pGetExp(kbase->m[j-1],i)) break; |
---|
2093 | j--; |
---|
2094 | if (j==0) return -1; |
---|
2095 | } |
---|
2096 | if (i==1) |
---|
2097 | { |
---|
2098 | while(j>0) |
---|
2099 | { |
---|
2100 | if (pGetComp(monom)==pGetComp(kbase->m[j-1])) return j-1; |
---|
2101 | if (pGetComp(monom)>pGetComp(kbase->m[j-1])) return -1; |
---|
2102 | j--; |
---|
2103 | } |
---|
2104 | } |
---|
2105 | i--; |
---|
2106 | } |
---|
2107 | return -1; |
---|
2108 | } |
---|
2109 | |
---|
2110 | /*2 |
---|
2111 | *decomposes the monom in a part of coefficients described by the |
---|
2112 | *complement of how and a monom in variables occuring in how, the |
---|
2113 | *index of which in kbase is returned as integer pos (-1 if it don't |
---|
2114 | *exists) |
---|
2115 | */ |
---|
2116 | poly idDecompose(poly monom, poly how, ideal kbase, int * pos) |
---|
2117 | { |
---|
2118 | int i; |
---|
2119 | poly coeff=pOne(), base=pOne(); |
---|
2120 | |
---|
2121 | for (i=1;i<=pVariables;i++) |
---|
2122 | { |
---|
2123 | if (pGetExp(how,i)>0) |
---|
2124 | { |
---|
2125 | pSetExp(base,i,pGetExp(monom,i)); |
---|
2126 | } |
---|
2127 | else |
---|
2128 | { |
---|
2129 | pSetExp(coeff,i,pGetExp(monom,i)); |
---|
2130 | } |
---|
2131 | } |
---|
2132 | pSetComp(base,pGetComp(monom)); |
---|
2133 | pSetm(base); |
---|
2134 | pSetCoeff(coeff,nCopy(pGetCoeff(monom))); |
---|
2135 | pSetm(coeff); |
---|
2136 | *pos = idIndexOfKBase(base,kbase); |
---|
2137 | if (*pos<0) |
---|
2138 | pDelete(&coeff); |
---|
2139 | pDelete(&base); |
---|
2140 | return coeff; |
---|
2141 | } |
---|
2142 | |
---|
2143 | /*2 |
---|
2144 | *returns a matrix A of coefficients with kbase*A=arg |
---|
2145 | *if all monomials in variables of how occur in kbase |
---|
2146 | *the other are deleted |
---|
2147 | */ |
---|
2148 | matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how) |
---|
2149 | { |
---|
2150 | matrix result; |
---|
2151 | ideal tempKbase; |
---|
2152 | poly p,q; |
---|
2153 | intvec * convert; |
---|
2154 | int i=IDELEMS(kbase),j=IDELEMS(arg),k,pos; |
---|
2155 | #if 0 |
---|
2156 | while ((i>0) && (kbase->m[i-1]==NULL)) i--; |
---|
2157 | if (idIs0(arg)) |
---|
2158 | return mpNew(i,1); |
---|
2159 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
2160 | result = mpNew(i,j); |
---|
2161 | #else |
---|
2162 | result = mpNew(i, j); |
---|
2163 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
2164 | #endif |
---|
2165 | |
---|
2166 | tempKbase = idCreateSpecialKbase(kbase,&convert); |
---|
2167 | for (k=0;k<j;k++) |
---|
2168 | { |
---|
2169 | p = arg->m[k]; |
---|
2170 | while (p!=NULL) |
---|
2171 | { |
---|
2172 | q = idDecompose(p,how,tempKbase,&pos); |
---|
2173 | if (pos>=0) |
---|
2174 | { |
---|
2175 | MATELEM(result,(*convert)[pos],k+1) = |
---|
2176 | pAdd(MATELEM(result,(*convert)[pos],k+1),q); |
---|
2177 | } |
---|
2178 | else |
---|
2179 | pDelete(&q); |
---|
2180 | pIter(p); |
---|
2181 | } |
---|
2182 | } |
---|
2183 | idDelete(&tempKbase); |
---|
2184 | return result; |
---|
2185 | } |
---|
2186 | |
---|
2187 | /*3 |
---|
2188 | * searches for the next unit in the components of the module arg and |
---|
2189 | * returns the first one; |
---|
2190 | */ |
---|
2191 | static int idReadOutPivot(ideal arg,int* comp) |
---|
2192 | { |
---|
2193 | if (idIs0(arg)) return -1; |
---|
2194 | int i=0,j, generator=-1; |
---|
2195 | int rk_arg=arg->rank; //idRankFreeModule(arg); |
---|
2196 | int * componentIsUsed =(int *)omAlloc((rk_arg+1)*sizeof(int)); |
---|
2197 | poly p; |
---|
2198 | |
---|
2199 | while ((generator<0) && (i<IDELEMS(arg))) |
---|
2200 | { |
---|
2201 | memset(componentIsUsed,0,(rk_arg+1)*sizeof(int)); |
---|
2202 | p = arg->m[i]; |
---|
2203 | while (p!=NULL) |
---|
2204 | { |
---|
2205 | j = pGetComp(p); |
---|
2206 | if (componentIsUsed[j]==0) |
---|
2207 | { |
---|
2208 | #ifdef HAVE_RINGS |
---|
2209 | if (pLmIsConstantComp(p) && |
---|
2210 | (!rField_is_Ring(currRing) || nIsUnit(pGetCoeff(p)))) |
---|
2211 | { |
---|
2212 | #else |
---|
2213 | if (pLmIsConstantComp(p)) |
---|
2214 | { |
---|
2215 | #endif |
---|
2216 | generator = i; |
---|
2217 | componentIsUsed[j] = 1; |
---|
2218 | } |
---|
2219 | else |
---|
2220 | { |
---|
2221 | componentIsUsed[j] = -1; |
---|
2222 | } |
---|
2223 | } |
---|
2224 | else if (componentIsUsed[j]>0) |
---|
2225 | { |
---|
2226 | (componentIsUsed[j])++; |
---|
2227 | } |
---|
2228 | pIter(p); |
---|
2229 | } |
---|
2230 | i++; |
---|
2231 | } |
---|
2232 | i = 0; |
---|
2233 | *comp = -1; |
---|
2234 | for (j=0;j<=rk_arg;j++) |
---|
2235 | { |
---|
2236 | if (componentIsUsed[j]>0) |
---|
2237 | { |
---|
2238 | if ((*comp==-1) || (componentIsUsed[j]<i)) |
---|
2239 | { |
---|
2240 | *comp = j; |
---|
2241 | i= componentIsUsed[j]; |
---|
2242 | } |
---|
2243 | } |
---|
2244 | } |
---|
2245 | omFree(componentIsUsed); |
---|
2246 | return generator; |
---|
2247 | } |
---|
2248 | |
---|
2249 | #if 0 |
---|
2250 | static void idDeleteComp(ideal arg,int red_comp) |
---|
2251 | { |
---|
2252 | int i,j; |
---|
2253 | poly p; |
---|
2254 | |
---|
2255 | for (i=IDELEMS(arg)-1;i>=0;i--) |
---|
2256 | { |
---|
2257 | p = arg->m[i]; |
---|
2258 | while (p!=NULL) |
---|
2259 | { |
---|
2260 | j = pGetComp(p); |
---|
2261 | if (j>red_comp) |
---|
2262 | { |
---|
2263 | pSetComp(p,j-1); |
---|
2264 | pSetm(p); |
---|
2265 | } |
---|
2266 | pIter(p); |
---|
2267 | } |
---|
2268 | } |
---|
2269 | (arg->rank)--; |
---|
2270 | } |
---|
2271 | #endif |
---|
2272 | |
---|
2273 | static void idDeleteComps(ideal arg,int* red_comp,int del) |
---|
2274 | // red_comp is an array [0..args->rank] |
---|
2275 | { |
---|
2276 | int i,j; |
---|
2277 | poly p; |
---|
2278 | |
---|
2279 | for (i=IDELEMS(arg)-1;i>=0;i--) |
---|
2280 | { |
---|
2281 | p = arg->m[i]; |
---|
2282 | while (p!=NULL) |
---|
2283 | { |
---|
2284 | j = pGetComp(p); |
---|
2285 | if (red_comp[j]!=j) |
---|
2286 | { |
---|
2287 | pSetComp(p,red_comp[j]); |
---|
2288 | pSetmComp(p); |
---|
2289 | } |
---|
2290 | pIter(p); |
---|
2291 | } |
---|
2292 | } |
---|
2293 | (arg->rank) -= del; |
---|
2294 | } |
---|
2295 | |
---|
2296 | /*2 |
---|
2297 | * returns the presentation of an isomorphic, minimally |
---|
2298 | * embedded module (arg represents the quotient!) |
---|
2299 | */ |
---|
2300 | ideal idMinEmbedding(ideal arg,BOOLEAN inPlace, intvec **w) |
---|
2301 | { |
---|
2302 | if (idIs0(arg)) return idInit(1,arg->rank); |
---|
2303 | int i,next_gen,next_comp; |
---|
2304 | ideal res=arg; |
---|
2305 | if (!inPlace) res = idCopy(arg); |
---|
2306 | res->rank=si_max(res->rank,idRankFreeModule(res)); |
---|
2307 | int *red_comp=(int*)omAlloc((res->rank+1)*sizeof(int)); |
---|
2308 | for (i=res->rank;i>=0;i--) red_comp[i]=i; |
---|
2309 | |
---|
2310 | int del=0; |
---|
2311 | loop |
---|
2312 | { |
---|
2313 | next_gen = idReadOutPivot(res,&next_comp); |
---|
2314 | if (next_gen<0) break; |
---|
2315 | del++; |
---|
2316 | syGaussForOne(res,next_gen,next_comp,0,IDELEMS(res)); |
---|
2317 | for(i=next_comp+1;i<=arg->rank;i++) red_comp[i]--; |
---|
2318 | if ((w !=NULL)&&(*w!=NULL)) |
---|
2319 | { |
---|
2320 | for(i=next_comp;i<(*w)->length();i++) (**w)[i-1]=(**w)[i]; |
---|
2321 | } |
---|
2322 | } |
---|
2323 | |
---|
2324 | idDeleteComps(res,red_comp,del); |
---|
2325 | idSkipZeroes(res); |
---|
2326 | omFree(red_comp); |
---|
2327 | |
---|
2328 | if ((w !=NULL)&&(*w!=NULL) &&(del>0)) |
---|
2329 | { |
---|
2330 | intvec *wtmp=new intvec((*w)->length()-del); |
---|
2331 | for(i=0;i<res->rank;i++) (*wtmp)[i]=(**w)[i]; |
---|
2332 | delete *w; |
---|
2333 | *w=wtmp; |
---|
2334 | } |
---|
2335 | return res; |
---|
2336 | } |
---|
2337 | |
---|
2338 | /*2 |
---|
2339 | * transpose a module |
---|
2340 | */ |
---|
2341 | ideal idTransp(ideal a) |
---|
2342 | { |
---|
2343 | int r = a->rank, c = IDELEMS(a); |
---|
2344 | ideal b = idInit(r,c); |
---|
2345 | |
---|
2346 | for (int i=c; i>0; i--) |
---|
2347 | { |
---|
2348 | poly p=a->m[i-1]; |
---|
2349 | while(p!=NULL) |
---|
2350 | { |
---|
2351 | poly h=pHead(p); |
---|
2352 | int co=pGetComp(h)-1; |
---|
2353 | pSetComp(h,i); |
---|
2354 | pSetmComp(h); |
---|
2355 | b->m[co]=pAdd(b->m[co],h); |
---|
2356 | pIter(p); |
---|
2357 | } |
---|
2358 | } |
---|
2359 | return b; |
---|
2360 | } |
---|
2361 | |
---|
2362 | intvec * idQHomWeight(ideal id) |
---|
2363 | { |
---|
2364 | poly head, tail; |
---|
2365 | int k; |
---|
2366 | int in=IDELEMS(id)-1, ready=0, all=0, |
---|
2367 | coldim=pVariables, rowmax=2*coldim; |
---|
2368 | if (in<0) return NULL; |
---|
2369 | intvec *imat=new intvec(rowmax+1,coldim,0); |
---|
2370 | |
---|
2371 | do |
---|
2372 | { |
---|
2373 | head = id->m[in--]; |
---|
2374 | if (head!=NULL) |
---|
2375 | { |
---|
2376 | tail = pNext(head); |
---|
2377 | while (tail!=NULL) |
---|
2378 | { |
---|
2379 | all++; |
---|
2380 | for (k=1;k<=coldim;k++) |
---|
2381 | IMATELEM(*imat,all,k) = pGetExpDiff(head,tail,k); |
---|
2382 | if (all==rowmax) |
---|
2383 | { |
---|
2384 | ivTriangIntern(imat, ready, all); |
---|
2385 | if (ready==coldim) |
---|
2386 | { |
---|
2387 | delete imat; |
---|
2388 | return NULL; |
---|
2389 | } |
---|
2390 | } |
---|
2391 | pIter(tail); |
---|
2392 | } |
---|
2393 | } |
---|
2394 | } while (in>=0); |
---|
2395 | if (all>ready) |
---|
2396 | { |
---|
2397 | ivTriangIntern(imat, ready, all); |
---|
2398 | if (ready==coldim) |
---|
2399 | { |
---|
2400 | delete imat; |
---|
2401 | return NULL; |
---|
2402 | } |
---|
2403 | } |
---|
2404 | intvec *result = ivSolveKern(imat, ready); |
---|
2405 | delete imat; |
---|
2406 | return result; |
---|
2407 | } |
---|
2408 | |
---|
2409 | BOOLEAN idIsZeroDim(ideal I) |
---|
2410 | { |
---|
2411 | BOOLEAN *UsedAxis=(BOOLEAN *)omAlloc0(pVariables*sizeof(BOOLEAN)); |
---|
2412 | int i,n; |
---|
2413 | poly po; |
---|
2414 | BOOLEAN res=TRUE; |
---|
2415 | for(i=IDELEMS(I)-1;i>=0;i--) |
---|
2416 | { |
---|
2417 | po=I->m[i]; |
---|
2418 | if ((po!=NULL) &&((n=pIsPurePower(po))!=0)) UsedAxis[n-1]=TRUE; |
---|
2419 | } |
---|
2420 | for(i=pVariables-1;i>=0;i--) |
---|
2421 | { |
---|
2422 | if(UsedAxis[i]==FALSE) {res=FALSE; break;} // not zero-dim. |
---|
2423 | } |
---|
2424 | omFreeSize(UsedAxis,pVariables*sizeof(BOOLEAN)); |
---|
2425 | return res; |
---|
2426 | } |
---|
2427 | |
---|
2428 | void idNormalize(ideal I) |
---|
2429 | { |
---|
2430 | if (rField_has_simple_inverse()) return; /* Z/p, GF(p,n), R, long R/C */ |
---|
2431 | int i; |
---|
2432 | for(i=IDELEMS(I)-1;i>=0;i--) |
---|
2433 | { |
---|
2434 | pNormalize(I->m[i]); |
---|
2435 | } |
---|
2436 | } |
---|
2437 | |
---|
2438 | // #include <kernel/clapsing.h> |
---|
2439 | |
---|
2440 | #ifdef HAVE_FACTORY |
---|
2441 | poly id_GCD(poly f, poly g, const ring r) |
---|
2442 | { |
---|
2443 | ring save_r=currRing; |
---|
2444 | rChangeCurrRing(r); |
---|
2445 | ideal I=idInit(2,1); I->m[0]=f; I->m[1]=g; |
---|
2446 | intvec *w = NULL; |
---|
2447 | ideal S=idSyzygies(I,testHomog,&w); |
---|
2448 | if (w!=NULL) delete w; |
---|
2449 | poly gg=pTakeOutComp(&(S->m[0]),2); |
---|
2450 | idDelete(&S); |
---|
2451 | poly gcd_p=singclap_pdivide(f,gg); |
---|
2452 | pDelete(&gg); |
---|
2453 | rChangeCurrRing(save_r); |
---|
2454 | return gcd_p; |
---|
2455 | } |
---|
2456 | #endif |
---|
2457 | |
---|
2458 | /*2 |
---|
2459 | * xx,q: arrays of length 0..rl-1 |
---|
2460 | * xx[i]: SB mod q[i] |
---|
2461 | * assume: char=0 |
---|
2462 | * assume: q[i]!=0 |
---|
2463 | * destroys xx |
---|
2464 | */ |
---|
2465 | #ifdef HAVE_FACTORY |
---|
2466 | ideal idChineseRemainder(ideal *xx, number *q, int rl) |
---|
2467 | { |
---|
2468 | int cnt=IDELEMS(xx[0])*xx[0]->nrows; |
---|
2469 | ideal result=idInit(cnt,xx[0]->rank); |
---|
2470 | result->nrows=xx[0]->nrows; // for lifting matrices |
---|
2471 | result->ncols=xx[0]->ncols; // for lifting matrices |
---|
2472 | int i,j; |
---|
2473 | poly r,h,hh,res_p; |
---|
2474 | number *x=(number *)omAlloc(rl*sizeof(number)); |
---|
2475 | for(i=cnt-1;i>=0;i--) |
---|
2476 | { |
---|
2477 | res_p=NULL; |
---|
2478 | loop |
---|
2479 | { |
---|
2480 | r=NULL; |
---|
2481 | for(j=rl-1;j>=0;j--) |
---|
2482 | { |
---|
2483 | h=xx[j]->m[i]; |
---|
2484 | if ((h!=NULL) |
---|
2485 | &&((r==NULL)||(pLmCmp(r,h)==-1))) |
---|
2486 | r=h; |
---|
2487 | } |
---|
2488 | if (r==NULL) break; |
---|
2489 | h=pHead(r); |
---|
2490 | for(j=rl-1;j>=0;j--) |
---|
2491 | { |
---|
2492 | hh=xx[j]->m[i]; |
---|
2493 | if ((hh!=NULL) && (pLmCmp(r,hh)==0)) |
---|
2494 | { |
---|
2495 | x[j]=pGetCoeff(hh); |
---|
2496 | hh=pLmFreeAndNext(hh); |
---|
2497 | xx[j]->m[i]=hh; |
---|
2498 | } |
---|
2499 | else |
---|
2500 | x[j]=nlInit(0, currRing); |
---|
2501 | } |
---|
2502 | number n=nlChineseRemainder(x,q,rl); |
---|
2503 | for(j=rl-1;j>=0;j--) |
---|
2504 | { |
---|
2505 | x[j]=NULL; // nlInit(0...) takes no memory |
---|
2506 | } |
---|
2507 | if (nlIsZero(n)) pDelete(&h); |
---|
2508 | else |
---|
2509 | { |
---|
2510 | pSetCoeff(h,n); |
---|
2511 | //Print("new mon:");pWrite(h); |
---|
2512 | res_p=pAdd(res_p,h); |
---|
2513 | } |
---|
2514 | } |
---|
2515 | result->m[i]=res_p; |
---|
2516 | } |
---|
2517 | omFree(x); |
---|
2518 | for(i=rl-1;i>=0;i--) idDelete(&(xx[i])); |
---|
2519 | omFree(xx); |
---|
2520 | return result; |
---|
2521 | } |
---|
2522 | #endif |
---|
2523 | /* currently unsed: |
---|
2524 | ideal idChineseRemainder(ideal *xx, intvec *iv) |
---|
2525 | { |
---|
2526 | int rl=iv->length(); |
---|
2527 | number *q=(number *)omAlloc(rl*sizeof(number)); |
---|
2528 | int i; |
---|
2529 | for(i=0; i<rl; i++) |
---|
2530 | { |
---|
2531 | q[i]=nInit((*iv)[i]); |
---|
2532 | } |
---|
2533 | return idChineseRemainder(xx,q,rl); |
---|
2534 | } |
---|
2535 | */ |
---|
2536 | /* |
---|
2537 | * lift ideal with coeffs over Z (mod N) to Q via Farey |
---|
2538 | */ |
---|
2539 | ideal idFarey(ideal x, number N) |
---|
2540 | { |
---|
2541 | int cnt=IDELEMS(x)*x->nrows; |
---|
2542 | ideal result=idInit(cnt,x->rank); |
---|
2543 | result->nrows=x->nrows; // for lifting matrices |
---|
2544 | result->ncols=x->ncols; // for lifting matrices |
---|
2545 | |
---|
2546 | int i; |
---|
2547 | for(i=cnt-1;i>=0;i--) |
---|
2548 | { |
---|
2549 | poly h=pCopy(x->m[i]); |
---|
2550 | result->m[i]=h; |
---|
2551 | while(h!=NULL) |
---|
2552 | { |
---|
2553 | number c=pGetCoeff(h); |
---|
2554 | pSetCoeff0(h,nlFarey(c,N)); |
---|
2555 | nDelete(&c); |
---|
2556 | pIter(h); |
---|
2557 | } |
---|
2558 | while((result->m[i]!=NULL)&&(nIsZero(pGetCoeff(result->m[i])))) |
---|
2559 | { |
---|
2560 | pLmDelete(&(result->m[i])); |
---|
2561 | } |
---|
2562 | h=result->m[i]; |
---|
2563 | while((h!=NULL) && (pNext(h)!=NULL)) |
---|
2564 | { |
---|
2565 | if(nIsZero(pGetCoeff(pNext(h)))) |
---|
2566 | { |
---|
2567 | pLmDelete(&pNext(h)); |
---|
2568 | } |
---|
2569 | else pIter(h); |
---|
2570 | } |
---|
2571 | } |
---|
2572 | return result; |
---|
2573 | } |
---|
2574 | |
---|
2575 | /*2 |
---|
2576 | * transpose a module |
---|
2577 | * NOTE: just a version of "ideal idTransp(ideal)" which works within specified ring. |
---|
2578 | */ |
---|
2579 | ideal id_Transp(ideal a, const ring rRing) |
---|
2580 | { |
---|
2581 | int r = a->rank, c = IDELEMS(a); |
---|
2582 | ideal b = idInit(r,c); |
---|
2583 | |
---|
2584 | for (int i=c; i>0; i--) |
---|
2585 | { |
---|
2586 | poly p=a->m[i-1]; |
---|
2587 | while(p!=NULL) |
---|
2588 | { |
---|
2589 | poly h=p_Head(p, rRing); |
---|
2590 | int co=p_GetComp(h, rRing)-1; |
---|
2591 | p_SetComp(h, i, rRing); |
---|
2592 | p_Setm(h, rRing); |
---|
2593 | b->m[co] = p_Add_q(b->m[co], h, rRing); |
---|
2594 | pIter(p); |
---|
2595 | } |
---|
2596 | } |
---|
2597 | return b; |
---|
2598 | } |
---|
2599 | |
---|
2600 | |
---|
2601 | |
---|
2602 | /*2 |
---|
2603 | * The following is needed to compute the image of certain map used in |
---|
2604 | * the computation of cohomologies via BGG |
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2605 | * let M = { w_1, ..., w_k }, k = size(M) == ncols(M), n = nvars(currRing). |
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2606 | * assuming that nrows(M) <= m*n; the procedure computes: |
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2607 | * transpose(M) * transpose( var(1) I_m | ... | var(n) I_m ) :== transpose(module{f_1, ... f_k}), |
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2608 | * where f_i = \sum_{j=1}^{m} (w_i, v_j) gen(j), (w_i, v_j) is a `scalar` multiplication. |
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2609 | * that is, if w_i = (a^1_1, ... a^1_m) | (a^2_1, ..., a^2_m) | ... | (a^n_1, ..., a^n_m) then |
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2610 | |
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2611 | (a^1_1, ... a^1_m) | (a^2_1, ..., a^2_m) | ... | (a^n_1, ..., a^n_m) |
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2612 | * var_1 ... var_1 | var_2 ... var_2 | ... | var_n ... var(n) |
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2613 | * gen_1 ... gen_m | gen_1 ... gen_m | ... | gen_1 ... gen_m |
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2614 | + => |
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2615 | f_i = |
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2616 | |
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2617 | a^1_1 * var(1) * gen(1) + ... + a^1_m * var(1) * gen(m) + |
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2618 | a^2_1 * var(2) * gen(1) + ... + a^2_m * var(2) * gen(m) + |
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2619 | ... |
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2620 | a^n_1 * var(n) * gen(1) + ... + a^n_m * var(n) * gen(m); |
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2621 | |
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2622 | NOTE: for every f_i we run only ONCE along w_i saving partial sums into a temporary array of polys of size m |
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2623 | */ |
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2624 | ideal id_TensorModuleMult(const int m, const ideal M, const ring rRing) |
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2625 | { |
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2626 | // #ifdef DEBU |
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2627 | // WarnS("tensorModuleMult!!!!"); |
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2628 | |
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2629 | assume(m > 0); |
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2630 | assume(M != NULL); |
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2631 | |
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2632 | const int n = rRing->N; |
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2633 | |
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2634 | assume(M->rank <= m * n); |
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2635 | |
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2636 | const int k = IDELEMS(M); |
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2637 | |
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2638 | ideal idTemp = idInit(k,m); // = {f_1, ..., f_k } |
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2639 | |
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2640 | for( int i = 0; i < k; i++ ) // for every w \in M |
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2641 | { |
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2642 | poly pTempSum = NULL; |
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2643 | |
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2644 | poly w = M->m[i]; |
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2645 | |
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2646 | while(w != NULL) // for each term of w... |
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2647 | { |
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2648 | poly h = p_Head(w, rRing); |
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2649 | |
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2650 | const int gen = p_GetComp(h, rRing); // 1 ... |
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2651 | |
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2652 | assume(gen > 0); |
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2653 | assume(gen <= n*m); |
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2654 | |
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2655 | // TODO: write a formula with %, / instead of while! |
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2656 | /* |
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2657 | int c = gen; |
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2658 | int v = 1; |
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2659 | while(c > m) |
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2660 | { |
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2661 | c -= m; |
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2662 | v++; |
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2663 | } |
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2664 | */ |
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2665 | |
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2666 | int cc = gen % m; |
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2667 | if( cc == 0) cc = m; |
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2668 | int vv = 1 + (gen - cc) / m; |
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2669 | |
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2670 | // assume( cc == c ); |
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2671 | // assume( vv == v ); |
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2672 | |
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2673 | // 1<= c <= m |
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2674 | assume( cc > 0 ); |
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2675 | assume( cc <= m ); |
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2676 | |
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2677 | assume( vv > 0 ); |
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2678 | assume( vv <= n ); |
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2679 | |
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2680 | assume( (cc + (vv-1)*m) == gen ); |
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2681 | |
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2682 | p_IncrExp(h, vv, rRing); // h *= var(j) && // p_AddExp(h, vv, 1, rRing); |
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2683 | p_SetComp(h, cc, rRing); |
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2684 | |
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2685 | p_Setm(h, rRing); // addjust degree after the previous steps! |
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2686 | |
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2687 | pTempSum = p_Add_q(pTempSum, h, rRing); // it is slow since h will be usually put to the back of pTempSum!!! |
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2688 | |
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2689 | pIter(w); |
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2690 | } |
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2691 | |
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2692 | idTemp->m[i] = pTempSum; |
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2693 | } |
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2694 | |
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2695 | // simplify idTemp??? |
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2696 | |
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2697 | ideal idResult = id_Transp(idTemp, rRing); |
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2698 | |
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2699 | id_Delete(&idTemp, rRing); |
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2700 | |
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2701 | return(idResult); |
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2702 | } |
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