1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: ideals.cc,v 1.47 1999-05-19 11:41:46 Singular Exp $ */ |
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5 | /* |
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6 | * ABSTRACT - all basic methods to manipulate ideals |
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7 | */ |
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8 | |
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9 | /* includes */ |
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10 | #include "mod2.h" |
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11 | #include "tok.h" |
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12 | #include "mmemory.h" |
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13 | #include "febase.h" |
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14 | #include "numbers.h" |
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15 | #include "polys.h" |
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16 | #include "ipid.h" |
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17 | #include "ring.h" |
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18 | #include "kstd1.h" |
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19 | #include "matpol.h" |
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20 | #include "weight.h" |
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21 | #include "intvec.h" |
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22 | #include "syz.h" |
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23 | #include "ideals.h" |
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24 | #include "lists.h" |
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25 | |
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26 | |
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27 | // #define WITH_OLD_MINOR |
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28 | |
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29 | static poly * idpower; |
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30 | /*collects the monomials in makemonoms, must be allocated befor*/ |
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31 | static int idpowerpoint; |
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32 | /*index of the actual monomial in idpower*/ |
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33 | static poly * givenideal; |
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34 | /*the ideal from which a power is computed*/ |
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35 | |
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36 | /*0 implementation*/ |
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37 | |
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38 | /*2 |
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39 | * initialise an ideal |
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40 | */ |
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41 | #ifdef PDEBUG |
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42 | ideal idDBInit(int idsize, int rank, char *f, int l) |
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43 | #else |
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44 | ideal idInit(int idsize, int rank) |
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45 | #endif |
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46 | { |
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47 | /*- initialise an ideal -*/ |
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48 | #if defined(MDEBUG) && defined(PDEBUG) |
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49 | ideal hh = (ideal )mmDBAllocBlock(sizeof(*hh),f,l); |
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50 | #else |
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51 | ideal hh = (ideal )Alloc(sizeof(*hh)); |
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52 | #endif |
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53 | hh->nrows = 1; |
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54 | hh->rank = rank; |
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55 | IDELEMS(hh) = idsize; |
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56 | if (idsize>0) |
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57 | { |
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58 | #if defined(MDEBUG) && defined(PDEBUG) |
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59 | hh->m = (poly *)mmDBAllocBlock0(idsize*sizeof(poly),f,l); |
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60 | #else |
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61 | hh->m = (poly *)Alloc0(idsize*sizeof(poly)); |
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62 | #endif |
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63 | } |
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64 | else |
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65 | hh->m=NULL; |
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66 | return hh; |
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67 | } |
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68 | |
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69 | void idPrint(ideal id) |
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70 | { |
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71 | Print("Module of rank %d,real rank %d and %d generators.\n", |
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72 | id->rank,idRankFreeModule(id),IDELEMS(id)); |
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73 | for (int i=0;i<IDELEMS(id);i++) |
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74 | { |
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75 | if (id->m[i]!=NULL) |
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76 | { |
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77 | Print("generator %d: ",i);pWrite(id->m[i]); |
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78 | } |
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79 | } |
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80 | } |
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81 | |
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82 | /*2 |
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83 | * initialise the maximal ideal (at 0) |
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84 | */ |
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85 | ideal idMaxIdeal (void) |
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86 | { |
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87 | int l; |
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88 | ideal hh=NULL; |
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89 | |
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90 | hh=idInit(pVariables,1); |
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91 | for (l=0; l<pVariables; l++) |
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92 | { |
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93 | hh->m[l] = pOne(); |
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94 | pSetExp(hh->m[l],l+1,1); |
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95 | pSetm(hh->m[l]); |
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96 | } |
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97 | return hh; |
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98 | } |
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99 | |
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100 | /*2 |
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101 | * deletes an ideal/matrix |
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102 | */ |
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103 | #ifdef PDEBUG |
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104 | void idDBDelete (ideal* h, char *f, int l) |
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105 | #else |
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106 | void idDelete (ideal * h) |
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107 | #endif |
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108 | { |
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109 | int j,elems; |
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110 | if (*h == NULL) |
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111 | return; |
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112 | elems=j=(*h)->nrows*(*h)->ncols; |
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113 | if (j>0) |
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114 | { |
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115 | do |
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116 | { |
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117 | #ifdef PDEBUG |
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118 | pDBDelete(&((*h)->m[--j]),f,l); |
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119 | #else |
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120 | pDelete(&((*h)->m[--j])); |
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121 | #endif |
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122 | } |
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123 | while (j>0); |
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124 | #if defined(MDEBUG) && defined(PDEBUG) |
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125 | mmDBFreeBlock((ADDRESS)((*h)->m),sizeof(poly)*elems,f,l); |
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126 | #else |
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127 | Free((ADDRESS)((*h)->m),sizeof(poly)*elems); |
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128 | #endif |
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129 | } |
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130 | #if defined(MDEBUG) && defined(PDEBUG) |
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131 | mmDBFreeBlock((ADDRESS)(*h),sizeof(**h),f,l); |
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132 | #else |
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133 | Free((ADDRESS)*h,sizeof(**h)); |
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134 | #endif |
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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 | * ideal id = (id[i]) |
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177 | * result is leadcoeff(id[i]) = 1 |
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178 | */ |
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179 | void idNorm(ideal id) |
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180 | { |
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181 | for (int i=0; i<IDELEMS(id); i++) |
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182 | { |
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183 | if (id->m[i] != NULL) |
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184 | { |
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185 | pNorm(id->m[i]); |
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186 | } |
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187 | } |
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188 | } |
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189 | |
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190 | /*2 |
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191 | * ideal id = (id[i]), c any number |
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192 | * if id[i] = c*id[j] then id[j] is deleted for j > i |
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193 | */ |
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194 | void idDelMultiples(ideal id) |
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195 | { |
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196 | int i, j, t; |
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197 | int k = IDELEMS(id), l = k; |
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198 | for (i=k-2; i>=0; i--) |
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199 | { |
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200 | if (id->m[i]!=NULL) |
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201 | { |
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202 | for (j=l-1; j>i; j--) |
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203 | { |
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204 | if ((id->m[j]!=NULL) |
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205 | && (pComparePolys(id->m[i], id->m[j]))) |
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206 | { |
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207 | pDelete(&id->m[j]); |
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208 | l--; |
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209 | for(t=j; t<l; t++) |
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210 | { |
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211 | id->m[t] = id->m[t+1]; |
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212 | } |
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213 | } |
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214 | } |
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215 | } |
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216 | } |
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217 | if (l != k) |
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218 | { |
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219 | pEnlargeSet(&id->m, k, l-k); |
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220 | IDELEMS(id) = l; |
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221 | } |
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222 | } |
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223 | |
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224 | /*2 |
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225 | * ideal id = (id[i]) |
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226 | * if id[i] = id[j] then id[j] is deleted for j > i |
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227 | */ |
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228 | void idDelEquals(ideal id) |
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229 | { |
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230 | int i, j, t; |
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231 | int k = IDELEMS(id), l = k; |
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232 | for (i=k-2; i>=0; i--) |
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233 | { |
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234 | for (j=l-1; j>i; j--) |
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235 | { |
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236 | if (pEqualPolys(id->m[i], id->m[j])) |
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237 | { |
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238 | pDelete(&id->m[j]); |
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239 | l--; |
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240 | for(t=j; t<l; t++) |
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241 | { |
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242 | id->m[t] = id->m[t+1]; |
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243 | } |
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244 | } |
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245 | } |
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246 | } |
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247 | if (l != k) |
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248 | { |
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249 | pEnlargeSet(&id->m, k, l-k); |
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250 | IDELEMS(id) = l; |
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251 | } |
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252 | } |
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253 | |
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254 | // |
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255 | // Delete id[j], if Lm(j) == Lm(i) and j > i |
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256 | // |
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257 | void idDelLmEquals(ideal id) |
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258 | { |
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259 | int i, j, t; |
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260 | int k = IDELEMS(id), l = k; |
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261 | for (i=k-2; i>=0; i--) |
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262 | { |
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263 | for (j=l-1; j>i; j--) |
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264 | { |
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265 | if (pLmEqual(id->m[i], id->m[j])) |
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266 | { |
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267 | pDelete(&id->m[j]); |
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268 | l--; |
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269 | for(t=j; t<l; t++) |
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270 | { |
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271 | id->m[t] = id->m[t+1]; |
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272 | } |
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273 | } |
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274 | } |
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275 | } |
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276 | if (l != k) |
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277 | { |
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278 | pEnlargeSet(&id->m, k, l-k); |
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279 | IDELEMS(id) = l; |
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280 | } |
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281 | } |
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282 | |
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283 | void idDelDiv(ideal id) |
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284 | { |
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285 | int i, j, t; |
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286 | int k = IDELEMS(id), l = k; |
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287 | for (i=k-2; i>=0; i--) |
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288 | { |
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289 | for (j=l-1; j>i; j--) |
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290 | { |
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291 | |
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292 | if (((id->m[j] != NULL) && pDivisibleBy(id->m[i], id->m[j])) || |
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293 | (id->m[i] == NULL && id->m[j] == NULL)) |
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294 | { |
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295 | pDelete(&id->m[j]); |
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296 | l--; |
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297 | for(t=j; t<l; t++) |
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298 | { |
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299 | id->m[t] = id->m[t+1]; |
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300 | } |
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301 | } |
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302 | } |
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303 | } |
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304 | if (l != k) |
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305 | { |
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306 | pEnlargeSet(&id->m, k, l-k); |
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307 | IDELEMS(id) = l; |
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308 | } |
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309 | } |
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310 | |
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311 | |
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312 | /*2 |
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313 | * copy an ideal |
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314 | */ |
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315 | #ifdef PDEBUG |
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316 | ideal idDBCopy(ideal h1,char *f,int l) |
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317 | #else |
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318 | ideal idCopy (ideal h1) |
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319 | #endif |
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320 | { |
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321 | int i; |
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322 | ideal h2; |
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323 | |
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324 | //#ifdef TEST |
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325 | if (h1 == NULL) |
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326 | { |
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327 | #ifdef PDEBUG |
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328 | h2=idDBInit(1,1,f,l); |
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329 | #else |
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330 | h2=idInit(1,1); |
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331 | #endif |
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332 | } |
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333 | else |
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334 | //#endif |
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335 | { |
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336 | #ifdef PDEBUG |
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337 | h2=idDBInit(IDELEMS(h1),h1->rank,f,l); |
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338 | #else |
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339 | h2=idInit(IDELEMS(h1),h1->rank); |
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340 | #endif |
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341 | for (i=IDELEMS(h1)-1; i>=0; i--) |
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342 | #ifdef PDEBUG |
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343 | h2->m[i] = pDBCopy(h1->m[i],f,l); |
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344 | #else |
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345 | h2->m[i] = pCopy(h1->m[i]); |
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346 | #endif |
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347 | } |
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348 | return h2; |
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349 | } |
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350 | |
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351 | #ifdef PDEBUG |
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352 | void idDBTest(ideal h1,char *f,int l) |
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353 | { |
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354 | int i; |
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355 | |
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356 | if (h1 != NULL) |
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357 | { |
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358 | #ifdef MDEBUG |
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359 | mmDBTestBlock(h1,sizeof(*h1),f,l); |
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360 | #endif |
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361 | /* to be able to test matrices: */ |
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362 | for (i=(IDELEMS(h1)*h1->nrows)-1; i>=0; i--) |
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363 | pDBTest(h1->m[i],f,l); |
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364 | } |
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365 | } |
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366 | #endif |
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367 | |
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368 | /*3 |
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369 | * for idSort: compare a and b revlex inclusive module comp. |
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370 | */ |
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371 | static int pComp_RevLex(poly a, poly b) |
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372 | { |
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373 | int l=pVariables; |
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374 | while ((l>0) && (pGetExp(a,l)==pGetExp(b,l))) l--; |
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375 | if (l==0) |
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376 | { |
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377 | if (pGetComp(a)==pGetComp(b)) return 0; |
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378 | if (pGetComp(a)>pGetComp(b)) return 1; |
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379 | } |
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380 | else if (pGetExp(a,l)>pGetExp(b,l)) |
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381 | return 1; |
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382 | return -1; |
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383 | } |
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384 | |
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385 | /*2 |
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386 | *sorts the ideal w.r.t. the actual ringordering |
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387 | *uses lex-ordering when nolex = FALSE |
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388 | */ |
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389 | intvec *idSort(ideal id,BOOLEAN nolex) |
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390 | { |
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391 | poly p,q; |
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392 | intvec * result = new intvec(IDELEMS(id)); |
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393 | int i, j, actpos=0, newpos, l; |
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394 | int diff, olddiff, lastcomp, newcomp; |
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395 | BOOLEAN notFound; |
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396 | |
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397 | pCompProc oldComp=pComp0; |
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398 | |
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399 | if (!nolex) pComp0=pComp_RevLex; |
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400 | |
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401 | for (i=0;i<IDELEMS(id);i++) |
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402 | { |
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403 | if (id->m[i]!=NULL) |
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404 | { |
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405 | notFound = TRUE; |
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406 | newpos = actpos / 2; |
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407 | diff = (actpos+1) / 2; |
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408 | diff = (diff+1) / 2; |
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409 | lastcomp = pComp0(id->m[i],id->m[(*result)[newpos]]); |
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410 | if (lastcomp<0) |
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411 | { |
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412 | newpos -= diff; |
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413 | } |
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414 | else if (lastcomp>0) |
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415 | { |
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416 | newpos += diff; |
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417 | } |
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418 | else |
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419 | { |
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420 | notFound = FALSE; |
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421 | } |
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422 | while ((newpos>=0) && (newpos<actpos) && (notFound)) |
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423 | { |
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424 | newcomp = pComp0(id->m[i],id->m[(*result)[newpos]]); |
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425 | olddiff = diff; |
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426 | if (diff>1) |
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427 | { |
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428 | diff = (diff+1) / 2; |
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429 | if ((newcomp==1) |
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430 | && (actpos-newpos>1) |
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431 | && (diff>1) |
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432 | && (newpos+diff>=actpos)) |
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433 | { |
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434 | diff = actpos-newpos-1; |
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435 | } |
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436 | else if ((newcomp==-1) |
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437 | && (diff>1) |
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438 | && (newpos<diff)) |
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439 | { |
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440 | diff = newpos; |
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441 | } |
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442 | } |
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443 | if (newcomp<0) |
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444 | { |
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445 | if ((olddiff==1) && (lastcomp>0)) |
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446 | notFound = FALSE; |
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447 | else |
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448 | newpos -= diff; |
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449 | } |
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450 | else if (newcomp>0) |
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451 | { |
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452 | if ((olddiff==1) && (lastcomp<0)) |
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453 | { |
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454 | notFound = FALSE; |
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455 | newpos++; |
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456 | } |
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457 | else |
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458 | { |
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459 | newpos += diff; |
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460 | } |
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461 | } |
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462 | else |
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463 | { |
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464 | notFound = FALSE; |
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465 | } |
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466 | lastcomp = newcomp; |
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467 | if (diff==0) notFound=FALSE; /*hs*/ |
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468 | } |
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469 | if (newpos<0) newpos = 0; |
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470 | if (newpos>actpos) newpos = actpos; |
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471 | while ((newpos<actpos) && (pComp0(id->m[i],id->m[(*result)[newpos]])==0)) |
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472 | newpos++; |
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473 | for (j=actpos;j>newpos;j--) |
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474 | { |
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475 | (*result)[j] = (*result)[j-1]; |
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476 | } |
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477 | (*result)[newpos] = i; |
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478 | actpos++; |
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479 | } |
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480 | } |
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481 | for (j=0;j<actpos;j++) (*result)[j]++; |
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482 | pComp0=oldComp; |
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483 | return result; |
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484 | } |
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485 | |
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486 | /*2 |
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487 | * concat the lists h1 and h2 without zeros |
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488 | */ |
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489 | ideal idSimpleAdd (ideal h1,ideal h2) |
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490 | { |
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491 | int i,j,r,l; |
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492 | ideal result; |
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493 | |
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494 | if (h1==NULL) return idCopy(h2); |
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495 | if (h2==NULL) return idCopy(h1); |
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496 | j = IDELEMS(h1)-1; |
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497 | while ((j >= 0) && (h1->m[j] == NULL)) j--; |
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498 | i = IDELEMS(h2)-1; |
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499 | while ((i >= 0) && (h2->m[i] == NULL)) i--; |
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500 | r = max(h1->rank,h2->rank); |
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501 | if (i+j==(-2)) |
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502 | return idInit(1,r); |
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503 | else |
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504 | result=idInit(i+j+2,r); |
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505 | for (l=j; l>=0; l--) |
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506 | { |
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507 | result->m[l] = pCopy(h1->m[l]); |
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508 | } |
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509 | r = i+j+1; |
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510 | for (l=i; l>=0; l--, r--) |
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511 | { |
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512 | result->m[r] = pCopy(h2->m[l]); |
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513 | } |
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514 | return result; |
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515 | } |
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516 | |
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517 | /*2 |
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518 | * h1 + h2 |
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519 | */ |
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520 | ideal idAdd (ideal h1,ideal h2) |
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521 | { |
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522 | ideal result = idSimpleAdd(h1,h2); |
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523 | ideal tmp = idCompactify(result); |
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524 | |
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525 | idDelete(&result); |
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526 | return tmp; |
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527 | } |
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528 | |
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529 | /*2 |
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530 | * h1 * h2 |
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531 | */ |
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532 | ideal idMult (ideal h1,ideal h2) |
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533 | { |
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534 | int i,j,k; |
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535 | ideal hh; |
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536 | |
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537 | j = IDELEMS(h1); |
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538 | while ((j > 0) && (h1->m[j-1] == NULL)) j--; |
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539 | i = IDELEMS(h2); |
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540 | while ((i > 0) && (h2->m[i-1] == NULL)) i--; |
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541 | j = j * i; |
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542 | if (j == 0) |
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543 | hh = idInit(1,1); |
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544 | else |
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545 | hh=idInit(j,1); |
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546 | if (h1->rank<h2->rank) |
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547 | hh->rank = h2->rank; |
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548 | else |
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549 | hh->rank = h1->rank; |
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550 | if (j==0) return hh; |
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551 | k = 0; |
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552 | for (i=0; i<IDELEMS(h1); i++) |
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553 | { |
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554 | if (h1->m[i] != NULL) |
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555 | { |
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556 | for (j=0; j<IDELEMS(h2); j++) |
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557 | { |
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558 | if (h2->m[j] != NULL) |
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559 | { |
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560 | hh->m[k] = pMult(pCopy(h1->m[i]),pCopy(h2->m[j])); |
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561 | k++; |
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562 | } |
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563 | } |
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564 | } |
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565 | } |
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566 | { |
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567 | ideal tmp = idCompactify(hh); |
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568 | idDelete(&hh); |
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569 | return tmp; |
---|
570 | //return hh; |
---|
571 | } |
---|
572 | } |
---|
573 | |
---|
574 | /*2 |
---|
575 | *returns true if h is the zero ideal |
---|
576 | */ |
---|
577 | BOOLEAN idIs0 (ideal h) |
---|
578 | { |
---|
579 | int i; |
---|
580 | |
---|
581 | if (h == NULL) return TRUE; |
---|
582 | i = IDELEMS(h); |
---|
583 | while ((i > 0) && (h->m[i-1] == NULL)) |
---|
584 | { |
---|
585 | i--; |
---|
586 | } |
---|
587 | if (i == 0) |
---|
588 | return TRUE; |
---|
589 | else |
---|
590 | return FALSE; |
---|
591 | } |
---|
592 | |
---|
593 | /*2 |
---|
594 | * return the maximal component number found in any polynomial in s |
---|
595 | */ |
---|
596 | int idRankFreeModule (ideal s) |
---|
597 | { |
---|
598 | if (s!=NULL) |
---|
599 | { |
---|
600 | int j=0; |
---|
601 | int l=IDELEMS(s); |
---|
602 | poly *p=s->m; |
---|
603 | int k; |
---|
604 | |
---|
605 | for (; l != 0; l--) |
---|
606 | { |
---|
607 | if (*p!=NULL) |
---|
608 | { |
---|
609 | k = pMaxComp(*p); |
---|
610 | if (k>j) j = k; |
---|
611 | } |
---|
612 | p++; |
---|
613 | } |
---|
614 | return j; |
---|
615 | } |
---|
616 | return -1; |
---|
617 | } |
---|
618 | |
---|
619 | /*2 |
---|
620 | *returns true if id is homogenous with respect to the aktual weights |
---|
621 | */ |
---|
622 | BOOLEAN idHomIdeal (ideal id, ideal Q) |
---|
623 | { |
---|
624 | int i; |
---|
625 | BOOLEAN b; |
---|
626 | if ((id == NULL) || (IDELEMS(id) == 0)) return TRUE; |
---|
627 | i = 0; |
---|
628 | b = TRUE; |
---|
629 | while ((i < IDELEMS(id)) && b) |
---|
630 | { |
---|
631 | b = pIsHomogeneous(id->m[i]); |
---|
632 | i++; |
---|
633 | } |
---|
634 | if ((b) && (Q!=NULL) && (IDELEMS(Q)>0)) |
---|
635 | { |
---|
636 | i=0; |
---|
637 | while ((i < IDELEMS(Q)) && b) |
---|
638 | { |
---|
639 | b = pIsHomogeneous(Q->m[i]); |
---|
640 | i++; |
---|
641 | } |
---|
642 | } |
---|
643 | return b; |
---|
644 | } |
---|
645 | |
---|
646 | /*2 |
---|
647 | *returns a minimized set of generators of h1 |
---|
648 | */ |
---|
649 | ideal idMinBase (ideal h1) |
---|
650 | { |
---|
651 | ideal h2, h3,h4,e; |
---|
652 | int j,k; |
---|
653 | int i,l,ll; |
---|
654 | intvec * wth; |
---|
655 | BOOLEAN homog; |
---|
656 | |
---|
657 | homog = idHomModule(h1,currQuotient,&wth); |
---|
658 | if ((currRing->OrdSgn == 1) && (!homog)) |
---|
659 | { |
---|
660 | Warn("minbase applies only to the local or homogeneous case"); |
---|
661 | e=idCopy(h1); |
---|
662 | return e; |
---|
663 | } |
---|
664 | if ((currRing->OrdSgn == 1) && (homog)) |
---|
665 | { |
---|
666 | lists re=min_std(h1,currQuotient,(tHomog)homog,&wth,NULL,0,3); |
---|
667 | h2 = (ideal)re->m[1].data; |
---|
668 | re->m[1].data = NULL; |
---|
669 | re->m[1].rtyp = NONE; |
---|
670 | re->Clean(); |
---|
671 | return h2; |
---|
672 | } |
---|
673 | e=idInit(1,h1->rank); |
---|
674 | if (idIs0(h1)) |
---|
675 | { |
---|
676 | return e; |
---|
677 | } |
---|
678 | pEnlargeSet(&(e->m),IDELEMS(e),15); |
---|
679 | IDELEMS(e) = 16; |
---|
680 | h2 = kStd(h1,currQuotient,isNotHomog,NULL); |
---|
681 | h3 = idMaxIdeal(); |
---|
682 | h4=idMult(h2,h3); |
---|
683 | idDelete(&h3); |
---|
684 | h3=kStd(h4,currQuotient,isNotHomog,NULL); |
---|
685 | k = IDELEMS(h3); |
---|
686 | while ((k > 0) && (h3->m[k-1] == NULL)) k--; |
---|
687 | j = -1; |
---|
688 | l = IDELEMS(h2); |
---|
689 | while ((l > 0) && (h2->m[l-1] == NULL)) l--; |
---|
690 | for (i=l-1; i>=0; i--) |
---|
691 | { |
---|
692 | if (h2->m[i] != NULL) |
---|
693 | { |
---|
694 | ll = 0; |
---|
695 | while ((ll < k) && ((h3->m[ll] == NULL) |
---|
696 | || !pDivisibleBy(h3->m[ll],h2->m[i]))) |
---|
697 | ll++; |
---|
698 | if (ll >= k) |
---|
699 | { |
---|
700 | j++; |
---|
701 | if (j > IDELEMS(e)-1) |
---|
702 | { |
---|
703 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
---|
704 | IDELEMS(e) += 16; |
---|
705 | } |
---|
706 | e->m[j] = pCopy(h2->m[i]); |
---|
707 | } |
---|
708 | } |
---|
709 | } |
---|
710 | idDelete(&h2); |
---|
711 | idDelete(&h3); |
---|
712 | idDelete(&h4); |
---|
713 | if (currQuotient!=NULL) |
---|
714 | { |
---|
715 | h3=idInit(1,e->rank); |
---|
716 | h2=kNF(h3,currQuotient,e); |
---|
717 | idDelete(&h3); |
---|
718 | idDelete(&e); |
---|
719 | e=h2; |
---|
720 | } |
---|
721 | idSkipZeroes(e); |
---|
722 | return e; |
---|
723 | } |
---|
724 | |
---|
725 | /*2 |
---|
726 | *the minimal index of used variables - 1 |
---|
727 | */ |
---|
728 | int pLowVar (poly p) |
---|
729 | { |
---|
730 | int k,l,lex; |
---|
731 | |
---|
732 | if (p == NULL) return -1; |
---|
733 | |
---|
734 | k = 32000;/*a very large dummy value*/ |
---|
735 | while (p != NULL) |
---|
736 | { |
---|
737 | l = 1; |
---|
738 | lex = pGetExp(p,l); |
---|
739 | while ((l <= pVariables) && (lex == 0)) |
---|
740 | { |
---|
741 | l++; |
---|
742 | lex = pGetExp(p,l); |
---|
743 | } |
---|
744 | l--; |
---|
745 | if (l < k) k = l; |
---|
746 | pIter(p); |
---|
747 | } |
---|
748 | return k; |
---|
749 | } |
---|
750 | |
---|
751 | /*3 |
---|
752 | *multiplies p with t (!cas) or (t-1) |
---|
753 | *the index of t is:1, so we have to shift all variables |
---|
754 | *p is NOT in the actual ring, it has no t |
---|
755 | */ |
---|
756 | static poly pMultWithT (poly p,BOOLEAN cas) |
---|
757 | { |
---|
758 | /*qp is the working pointer in p*/ |
---|
759 | /*result is the result, qresult is the working pointer*/ |
---|
760 | /*pp is p in the actual ring(shifted), qpp the working pointer*/ |
---|
761 | poly result,qp,pp; |
---|
762 | poly qresult=NULL; |
---|
763 | poly qpp=NULL; |
---|
764 | int i,j,lex; |
---|
765 | number n; |
---|
766 | |
---|
767 | pp = NULL; |
---|
768 | result = NULL; |
---|
769 | qp = p; |
---|
770 | while (qp != NULL) |
---|
771 | { |
---|
772 | i = 0; |
---|
773 | if (result == NULL) |
---|
774 | {/*first monomial*/ |
---|
775 | result = pInit(); |
---|
776 | qresult = result; |
---|
777 | } |
---|
778 | else |
---|
779 | { |
---|
780 | qresult->next = pInit(); |
---|
781 | pIter(qresult); |
---|
782 | } |
---|
783 | for (j=pVariables-1; j>0; j--) |
---|
784 | { |
---|
785 | lex = pGetExp(qp,j); |
---|
786 | pSetExp(qresult,j+1,lex);/*copy all variables*/ |
---|
787 | } |
---|
788 | lex = pGetComp(qp); |
---|
789 | pSetComp(qresult,lex); |
---|
790 | n=nCopy(pGetCoeff(qp)); |
---|
791 | pSetCoeff0(qresult,n); |
---|
792 | qresult->next = NULL; |
---|
793 | pSetm(qresult); |
---|
794 | /*qresult is now qp brought into the actual ring*/ |
---|
795 | if (cas) |
---|
796 | { /*case: mult with t-1*/ |
---|
797 | pSetExp(qresult,1,0); |
---|
798 | pSetm(qresult); |
---|
799 | if (pp == NULL) |
---|
800 | { /*first monomial*/ |
---|
801 | pp = pCopy(qresult); |
---|
802 | qpp = pp; |
---|
803 | } |
---|
804 | else |
---|
805 | { |
---|
806 | qpp->next = pCopy(qresult); |
---|
807 | pIter(qpp); |
---|
808 | } |
---|
809 | pGetCoeff(qpp)=nNeg(pGetCoeff(qpp)); |
---|
810 | /*now qpp contains -1*qp*/ |
---|
811 | } |
---|
812 | pSetExp(qresult,1,1);/*this is mult. by t*/ |
---|
813 | pSetm(qresult); |
---|
814 | pIter(qp); |
---|
815 | } |
---|
816 | /* |
---|
817 | *now p is processed: |
---|
818 | *result contains t*p |
---|
819 | * if cas: pp contains -1*p (in the new ring) |
---|
820 | */ |
---|
821 | if (cas) qresult->next = pp; |
---|
822 | /* else qresult->next = NULL;*/ |
---|
823 | return result; |
---|
824 | } |
---|
825 | |
---|
826 | /*3 |
---|
827 | *deletes the place of t in p (t: variable with index 1) |
---|
828 | *p is NOT in the actual ring: it has pVariables+1 variables |
---|
829 | */ |
---|
830 | static poly pDivByT (poly * p,int size) |
---|
831 | { |
---|
832 | |
---|
833 | poly result=NULL, |
---|
834 | resultp=NULL , /** working pointer in result **/ |
---|
835 | pp; |
---|
836 | int i,j; |
---|
837 | |
---|
838 | while (*p != NULL) |
---|
839 | { |
---|
840 | i = 0; |
---|
841 | if (result == NULL) |
---|
842 | {/*the first monomial*/ |
---|
843 | result = pInit(); |
---|
844 | resultp = result; |
---|
845 | resultp->next = NULL; |
---|
846 | } |
---|
847 | else |
---|
848 | { |
---|
849 | resultp->next = pInit(); |
---|
850 | pIter(resultp); |
---|
851 | resultp->next = NULL; |
---|
852 | } |
---|
853 | for (j=1; j<=pVariables; j++) |
---|
854 | { |
---|
855 | pSetExp(resultp,j,pGetExp(*p,j+1)); |
---|
856 | } |
---|
857 | pSetComp(resultp,pGetComp(*p)); |
---|
858 | pSetCoeff0(resultp,pGetCoeff(*p)); |
---|
859 | pSetm(resultp); |
---|
860 | pp = (*p)->next; |
---|
861 | Free((ADDRESS)*p,size); |
---|
862 | *p = pp; |
---|
863 | } |
---|
864 | return result; |
---|
865 | } |
---|
866 | |
---|
867 | /*2 |
---|
868 | *dehomogenized the generators of the ideal id1 with the leading |
---|
869 | *monomial of p replaced by n |
---|
870 | */ |
---|
871 | ideal idDehomogen (ideal id1,poly p,number n) |
---|
872 | { |
---|
873 | int i; |
---|
874 | ideal result; |
---|
875 | |
---|
876 | if (idIs0(id1)) |
---|
877 | { |
---|
878 | return idInit(1,id1->rank); |
---|
879 | } |
---|
880 | result=idInit(IDELEMS(id1),id1->rank); |
---|
881 | for (i=0; i<IDELEMS(id1); i++) |
---|
882 | { |
---|
883 | result->m[i] = pDehomogen(id1->m[i],p,n); |
---|
884 | } |
---|
885 | return result; |
---|
886 | } |
---|
887 | |
---|
888 | /*2 |
---|
889 | * verschiebt die Indizees der Modulerzeugenden um i |
---|
890 | */ |
---|
891 | void pShift (poly * p,int i) |
---|
892 | { |
---|
893 | poly qp1 = *p,qp2 = *p;/*working pointers*/ |
---|
894 | int j = pMaxComp(*p),k = pMinComp(*p); |
---|
895 | |
---|
896 | if (j+i < 0) return ; |
---|
897 | while (qp1 != NULL) |
---|
898 | { |
---|
899 | if ((pGetComp(qp1)+i > 0) || ((j == -i) && (j == k))) |
---|
900 | { |
---|
901 | pSetComp(qp1,pGetComp(qp1)+i); |
---|
902 | qp2 = qp1; |
---|
903 | pIter(qp1); |
---|
904 | } |
---|
905 | else |
---|
906 | { |
---|
907 | if (qp2 == *p) |
---|
908 | { |
---|
909 | pIter(*p); |
---|
910 | qp2->next = NULL; |
---|
911 | pDelete(&qp2); |
---|
912 | qp2 = *p; |
---|
913 | qp1 = *p; |
---|
914 | } |
---|
915 | else |
---|
916 | { |
---|
917 | qp2->next = qp1->next; |
---|
918 | qp1->next = NULL; |
---|
919 | pDelete(&qp1); |
---|
920 | qp1 = qp2->next; |
---|
921 | } |
---|
922 | } |
---|
923 | } |
---|
924 | } |
---|
925 | |
---|
926 | /*2 |
---|
927 | *initialized a field with r numbers between beg and end for the |
---|
928 | *procedure idNextChoise |
---|
929 | */ |
---|
930 | void idInitChoise (int r,int beg,int end,BOOLEAN *endch,int * choise) |
---|
931 | { |
---|
932 | /*returns the first choise of r numbers between beg and end*/ |
---|
933 | int i; |
---|
934 | for (i=0; i<r; i++) |
---|
935 | { |
---|
936 | choise[i] = 0; |
---|
937 | } |
---|
938 | if (r <= end-beg+1) |
---|
939 | for (i=0; i<r; i++) |
---|
940 | { |
---|
941 | choise[i] = beg+i; |
---|
942 | } |
---|
943 | if (r > end-beg+1) |
---|
944 | *endch = TRUE; |
---|
945 | else |
---|
946 | *endch = FALSE; |
---|
947 | } |
---|
948 | |
---|
949 | /*2 |
---|
950 | *returns the next choise of r numbers between beg and end |
---|
951 | */ |
---|
952 | void idGetNextChoise (int r,int end,BOOLEAN *endch,int * choise) |
---|
953 | { |
---|
954 | int i = r-1,j; |
---|
955 | while ((i >= 0) && (choise[i] == end)) |
---|
956 | { |
---|
957 | i--; |
---|
958 | end--; |
---|
959 | } |
---|
960 | if (i == -1) |
---|
961 | *endch = TRUE; |
---|
962 | else |
---|
963 | { |
---|
964 | choise[i]++; |
---|
965 | for (j=i+1; j<r; j++) |
---|
966 | { |
---|
967 | choise[j] = choise[i]+j-i; |
---|
968 | } |
---|
969 | *endch = FALSE; |
---|
970 | } |
---|
971 | } |
---|
972 | |
---|
973 | /*2 |
---|
974 | *takes the field choise of d numbers between beg and end, cancels the t-th |
---|
975 | *entree and searches for the ordinal number of that d-1 dimensional field |
---|
976 | * w.r.t. the algorithm of construction |
---|
977 | */ |
---|
978 | int idGetNumberOfChoise(int t, int d, int begin, int end, int * choise) |
---|
979 | { |
---|
980 | int * localchoise,i,result=0; |
---|
981 | BOOLEAN b=FALSE; |
---|
982 | |
---|
983 | if (d<=1) return 1; |
---|
984 | localchoise=(int*)Alloc((d-1)*sizeof(int)); |
---|
985 | idInitChoise(d-1,begin,end,&b,localchoise); |
---|
986 | while (!b) |
---|
987 | { |
---|
988 | result++; |
---|
989 | i = 0; |
---|
990 | while ((i<t) && (localchoise[i]==choise[i])) i++; |
---|
991 | if (i>=t) |
---|
992 | { |
---|
993 | i = t+1; |
---|
994 | while ((i<d) && (localchoise[i-1]==choise[i])) i++; |
---|
995 | if (i>=d) |
---|
996 | { |
---|
997 | Free((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
998 | return result; |
---|
999 | } |
---|
1000 | } |
---|
1001 | idGetNextChoise(d-1,end,&b,localchoise); |
---|
1002 | } |
---|
1003 | Free((ADDRESS)localchoise,(d-1)*sizeof(int)); |
---|
1004 | return 0; |
---|
1005 | } |
---|
1006 | |
---|
1007 | /*2 |
---|
1008 | *computes the binomial coefficient |
---|
1009 | */ |
---|
1010 | int binom (int n,int r) |
---|
1011 | { |
---|
1012 | int i,result; |
---|
1013 | |
---|
1014 | if (r==0) return 1; |
---|
1015 | if (n-r<r) return binom(n,n-r); |
---|
1016 | result = n-r+1; |
---|
1017 | for (i=2;i<=r;i++) |
---|
1018 | { |
---|
1019 | result *= n-r+i; |
---|
1020 | result /= i; |
---|
1021 | } |
---|
1022 | return result; |
---|
1023 | } |
---|
1024 | |
---|
1025 | /*2 |
---|
1026 | *the free module of rank i |
---|
1027 | */ |
---|
1028 | ideal idFreeModule (int i) |
---|
1029 | { |
---|
1030 | int j; |
---|
1031 | ideal h; |
---|
1032 | |
---|
1033 | h=idInit(i,i); |
---|
1034 | for (j=0; j<i; j++) |
---|
1035 | { |
---|
1036 | h->m[j] = pOne(); |
---|
1037 | pSetComp(h->m[j],j+1); |
---|
1038 | } |
---|
1039 | return h; |
---|
1040 | } |
---|
1041 | |
---|
1042 | /*2 |
---|
1043 | * h3 := h1 intersect h2 |
---|
1044 | */ |
---|
1045 | ideal idSect (ideal h1,ideal h2) |
---|
1046 | { |
---|
1047 | ideal first=h2,second=h1,temp,temp1,result; |
---|
1048 | int i,j,k,flength,slength,length,rank=min(h1->rank,h2->rank); |
---|
1049 | intvec *w; |
---|
1050 | poly p,q; |
---|
1051 | |
---|
1052 | if ((idIs0(h1)) && (idIs0(h2))) return idInit(1,rank); |
---|
1053 | if (IDELEMS(h1)<IDELEMS(h2)) |
---|
1054 | { |
---|
1055 | first = h1; |
---|
1056 | second = h2; |
---|
1057 | } |
---|
1058 | flength = idRankFreeModule(first); |
---|
1059 | slength = idRankFreeModule(second); |
---|
1060 | length = max(flength,slength); |
---|
1061 | if (length==0) |
---|
1062 | { |
---|
1063 | length = 1; |
---|
1064 | } |
---|
1065 | temp = idInit(IDELEMS(first),1); |
---|
1066 | j = IDELEMS(temp); |
---|
1067 | while ((j>0) && (first->m[j-1]==NULL)) j--; |
---|
1068 | k = 0; |
---|
1069 | for (i=0;i<j;i++) |
---|
1070 | { |
---|
1071 | if (first->m[i]!=NULL) |
---|
1072 | { |
---|
1073 | temp->m[k] = pCopy(first->m[i]); |
---|
1074 | q = pOne(); |
---|
1075 | pSetComp(q,i+1+length); |
---|
1076 | if (flength==0) pShift(&(temp->m[k]),1); |
---|
1077 | p = temp->m[k]; |
---|
1078 | while (pNext(p)) pIter(p); |
---|
1079 | pNext(p) = q; |
---|
1080 | k++; |
---|
1081 | } |
---|
1082 | } |
---|
1083 | pEnlargeSet(&(temp->m),IDELEMS(temp),j+IDELEMS(second)-IDELEMS(temp)); |
---|
1084 | IDELEMS(temp) = j+IDELEMS(second); |
---|
1085 | for (i=0;i<IDELEMS(second);i++) |
---|
1086 | { |
---|
1087 | if (second->m[i]!=NULL) |
---|
1088 | { |
---|
1089 | temp->m[k] = pCopy(second->m[i]); |
---|
1090 | if (slength==0) pShift(&(temp->m[k]),1); |
---|
1091 | k++; |
---|
1092 | } |
---|
1093 | } |
---|
1094 | pSetSyzComp(length); |
---|
1095 | temp1 = kStd(temp,currQuotient,testHomog,&w,NULL,length); |
---|
1096 | if (w!=NULL) delete w; |
---|
1097 | pSetSyzComp(0); |
---|
1098 | idDelete(&temp); |
---|
1099 | result = idInit(IDELEMS(temp1),rank); |
---|
1100 | j = 0; |
---|
1101 | for (i=0;i<IDELEMS(temp1);i++) |
---|
1102 | { |
---|
1103 | if ((temp1->m[i]!=NULL) |
---|
1104 | && (pGetComp(temp1->m[i])>length)) |
---|
1105 | { |
---|
1106 | p = temp1->m[i]; |
---|
1107 | //PrintS("die Syzygie ist: ");pWrite(p); |
---|
1108 | temp1->m[i] = NULL; |
---|
1109 | while (p!=NULL) |
---|
1110 | { |
---|
1111 | q = pNext(p); |
---|
1112 | pNext(p) = NULL; |
---|
1113 | k = pGetComp(p)-1-length; |
---|
1114 | pSetComp(p,0); |
---|
1115 | //PrintS("das %d-te Element: ",k);pWrite(first->m[k]); |
---|
1116 | result->m[j] = pAdd(result->m[j],pMult(pCopy(first->m[k]),p)); |
---|
1117 | p = q; |
---|
1118 | } |
---|
1119 | //PrintS("Generator ist: ");pWrite(result->m[j]); |
---|
1120 | j++; |
---|
1121 | } |
---|
1122 | } |
---|
1123 | idSkipZeroes(result); |
---|
1124 | return result; |
---|
1125 | } |
---|
1126 | |
---|
1127 | /*2 |
---|
1128 | * ideal/module intersection for a list of objects |
---|
1129 | * given as 'resolvente' |
---|
1130 | */ |
---|
1131 | ideal idMultSect(resolvente arg, int length) |
---|
1132 | { |
---|
1133 | int i,j=0,k=0,syzComp,l,maxrk=-1,realrki; |
---|
1134 | ideal bigmat,tempstd,result; |
---|
1135 | poly p; |
---|
1136 | int isIdeal=0; |
---|
1137 | intvec * w=NULL; |
---|
1138 | |
---|
1139 | /* find 0-ideals and max rank -----------------------------------*/ |
---|
1140 | for (i=0;i<length;i++) |
---|
1141 | { |
---|
1142 | if (!idIs0(arg[i])) |
---|
1143 | { |
---|
1144 | realrki=idRankFreeModule(arg[i]); |
---|
1145 | k++; |
---|
1146 | j += IDELEMS(arg[i]); |
---|
1147 | if (realrki>maxrk) maxrk = realrki; |
---|
1148 | } |
---|
1149 | else |
---|
1150 | { |
---|
1151 | if (arg[i]!=NULL) |
---|
1152 | { |
---|
1153 | return idInit(1,arg[i]->rank); |
---|
1154 | } |
---|
1155 | } |
---|
1156 | } |
---|
1157 | if (maxrk == 0) |
---|
1158 | { |
---|
1159 | isIdeal = 1; |
---|
1160 | maxrk = 1; |
---|
1161 | } |
---|
1162 | /* init -----------------------------------------------------------*/ |
---|
1163 | j += maxrk; |
---|
1164 | bigmat = idInit(j,(k+1)*maxrk); |
---|
1165 | syzComp = k*maxrk; |
---|
1166 | pSetSyzComp(syzComp); |
---|
1167 | /* create unit matrices ------------------------------------------*/ |
---|
1168 | for (i=0;i<maxrk;i++) |
---|
1169 | { |
---|
1170 | for (j=0;j<=k;j++) |
---|
1171 | { |
---|
1172 | p = pOne(); |
---|
1173 | pSetComp(p,i+1+j*maxrk); |
---|
1174 | pSetm(p); |
---|
1175 | bigmat->m[i] = pAdd(bigmat->m[i],p); |
---|
1176 | } |
---|
1177 | } |
---|
1178 | /* enter given ideals ------------------------------------------*/ |
---|
1179 | i = maxrk; |
---|
1180 | k = 0; |
---|
1181 | for (j=0;j<length;j++) |
---|
1182 | { |
---|
1183 | if (arg[j]!=NULL) |
---|
1184 | { |
---|
1185 | for (l=0;l<IDELEMS(arg[j]);l++) |
---|
1186 | { |
---|
1187 | if (arg[j]->m[l]!=NULL) |
---|
1188 | { |
---|
1189 | bigmat->m[i] = pCopy(arg[j]->m[l]); |
---|
1190 | pShift(&(bigmat->m[i]),k*maxrk+isIdeal); |
---|
1191 | i++; |
---|
1192 | } |
---|
1193 | } |
---|
1194 | k++; |
---|
1195 | } |
---|
1196 | } |
---|
1197 | /* std computation --------------------------------------------*/ |
---|
1198 | tempstd = kStd(bigmat,currQuotient,testHomog,&w,NULL,syzComp); |
---|
1199 | if (w!=NULL) delete w; |
---|
1200 | idDelete(&bigmat); |
---|
1201 | pSetSyzComp(0); |
---|
1202 | /* interprete result ----------------------------------------*/ |
---|
1203 | result = idInit(8,maxrk); |
---|
1204 | k = 0; |
---|
1205 | for (j=0;j<IDELEMS(tempstd);j++) |
---|
1206 | { |
---|
1207 | if ((tempstd->m[j]!=NULL) && (pGetComp(tempstd->m[j])>syzComp)) |
---|
1208 | { |
---|
1209 | if (k>=IDELEMS(result)) |
---|
1210 | { |
---|
1211 | pEnlargeSet(&(result->m),IDELEMS(result),8); |
---|
1212 | IDELEMS(result) += 8; |
---|
1213 | } |
---|
1214 | p = tempstd->m[j]; |
---|
1215 | tempstd->m[j] = NULL; |
---|
1216 | pShift(&p,-syzComp-isIdeal); |
---|
1217 | result->m[k] = p; |
---|
1218 | k++; |
---|
1219 | } |
---|
1220 | } |
---|
1221 | /* clean up ----------------------------------------------------*/ |
---|
1222 | idDelete(&tempstd); |
---|
1223 | idSkipZeroes(result); |
---|
1224 | return result; |
---|
1225 | } |
---|
1226 | |
---|
1227 | /*2 |
---|
1228 | *computes the rank of the free module in which h1 embeds |
---|
1229 | */ |
---|
1230 | int lengthFreeModule (ideal h1) |
---|
1231 | { |
---|
1232 | int i,j,k; |
---|
1233 | |
---|
1234 | if (idIs0(h1)) return 0; |
---|
1235 | k = -1; |
---|
1236 | for (i=0; i<IDELEMS(h1); i++) |
---|
1237 | { |
---|
1238 | j = pMaxComp(h1->m[i]); |
---|
1239 | if (j>k) k = j; |
---|
1240 | } |
---|
1241 | return k; |
---|
1242 | } |
---|
1243 | |
---|
1244 | /*2 |
---|
1245 | *computes syzygies of h1, |
---|
1246 | *if quot != NULL it computes in the quotient ring modulo "quot" |
---|
1247 | */ |
---|
1248 | ideal idPrepare (ideal h1,ideal quot, tHomog h, |
---|
1249 | int* syzcomp, int *quotgen, int *quotdim, intvec **w) |
---|
1250 | { |
---|
1251 | ideal h2, h3; |
---|
1252 | int i; |
---|
1253 | int j,jj=0,k; |
---|
1254 | poly p,q; |
---|
1255 | BOOLEAN orderChanged=FALSE; |
---|
1256 | |
---|
1257 | if (idIs0(h1)) return NULL; |
---|
1258 | k = lengthFreeModule(h1); |
---|
1259 | if (*syzcomp<k) *syzcomp = k; |
---|
1260 | h2 = NULL; |
---|
1261 | h2=idCopy(h1); |
---|
1262 | i = IDELEMS(h2)-1; |
---|
1263 | //while ((i >= 0) && (h2->m[i] == NULL)) i--; |
---|
1264 | if (k == 0) |
---|
1265 | { |
---|
1266 | for (j=0; j<=i; j++) pShift(&(h2->m[j]),1); |
---|
1267 | *syzcomp = 1; |
---|
1268 | } |
---|
1269 | h2->rank = *syzcomp+i+1; |
---|
1270 | for (j=0; j<=i; j++) |
---|
1271 | { |
---|
1272 | p = h2->m[j]; |
---|
1273 | q = pOne(); |
---|
1274 | #ifdef DRING |
---|
1275 | if (pDRING) { pdSetDFlag(q,1); pSetm(q); } |
---|
1276 | #endif |
---|
1277 | pSetComp(q,*syzcomp+1+j); |
---|
1278 | if (p!=NULL) |
---|
1279 | { |
---|
1280 | while (pNext(p)) pIter(p); |
---|
1281 | p->next = q; |
---|
1282 | } |
---|
1283 | else |
---|
1284 | h2->m[j]=q; |
---|
1285 | } |
---|
1286 | if (currRing->order[0]!=ringorder_c) |
---|
1287 | { |
---|
1288 | while ((currRing->order[jj]!=0) && (currRing->order[jj]!=ringorder_c) |
---|
1289 | && (currRing->order[jj]!=ringorder_C)) |
---|
1290 | { |
---|
1291 | jj++; |
---|
1292 | } |
---|
1293 | if ((pOrdSgn==1) && (h==TRUE) && (*syzcomp==1) && (!pLexOrder) |
---|
1294 | && (currRing->order[jj]==ringorder_c)) |
---|
1295 | { |
---|
1296 | for(j=0;(j<IDELEMS(h2) && (!orderChanged));j++) |
---|
1297 | { |
---|
1298 | if (h2->m[j] != NULL) |
---|
1299 | { |
---|
1300 | p=h2->m[j]; |
---|
1301 | while ((p!=NULL) |
---|
1302 | && (pGetComp(p)<=*syzcomp)) |
---|
1303 | { |
---|
1304 | if (pIsConstantComp(p)) |
---|
1305 | { |
---|
1306 | pSetSyzComp(*syzcomp); |
---|
1307 | orderChanged=TRUE; |
---|
1308 | break; |
---|
1309 | } |
---|
1310 | pIter(p); |
---|
1311 | } |
---|
1312 | } |
---|
1313 | } |
---|
1314 | } |
---|
1315 | else |
---|
1316 | { |
---|
1317 | pSetSyzComp(*syzcomp); |
---|
1318 | orderChanged=TRUE; |
---|
1319 | } |
---|
1320 | } |
---|
1321 | |
---|
1322 | // if (orderChanged) PrintS("order changed\n"); |
---|
1323 | // else PrintS("order not changed\n"); |
---|
1324 | #ifdef PDEBUG |
---|
1325 | for(j=0;j<IDELEMS(h2);j++) pTest(h2->m[j]); |
---|
1326 | #endif |
---|
1327 | h3=kStd(h2,quot,h,w,NULL,*syzcomp); |
---|
1328 | //h3->rank = h2->rank; done by kStd -> initBuchMora -> initS |
---|
1329 | h3->rank-=*syzcomp; |
---|
1330 | idDelete(&h2); |
---|
1331 | if (orderChanged) pSetSyzComp(0); |
---|
1332 | return h3; |
---|
1333 | } |
---|
1334 | |
---|
1335 | ideal idSyzygies (ideal h1,ideal quot, tHomog h,intvec **w) |
---|
1336 | { |
---|
1337 | int d; |
---|
1338 | return idSyzygies(h1,quot,h,w,FALSE,d); |
---|
1339 | } |
---|
1340 | |
---|
1341 | ideal idSyzygies (ideal h1,ideal quot, tHomog h,intvec **w, |
---|
1342 | BOOLEAN setRegularity, int °) |
---|
1343 | { |
---|
1344 | ideal e, h3; |
---|
1345 | poly p; |
---|
1346 | int i, j, k=0, quotdim, quotgen,length=0,reg; |
---|
1347 | BOOLEAN isMonomial=TRUE; |
---|
1348 | |
---|
1349 | #ifdef PDEBUG |
---|
1350 | int ii; |
---|
1351 | for(ii=0;ii<IDELEMS(h1);ii++) pTest(h1->m[ii]); |
---|
1352 | if (quot!=NULL) |
---|
1353 | { |
---|
1354 | for(ii=0;ii<IDELEMS(quot);ii++) pTest(quot->m[ii]); |
---|
1355 | } |
---|
1356 | #endif |
---|
1357 | if (idIs0(h1)) |
---|
1358 | return idFreeModule(IDELEMS(h1)); |
---|
1359 | h3=idPrepare(h1,quot,h,&k,"gen,"dim,w); |
---|
1360 | if (h3==NULL) |
---|
1361 | return idFreeModule(IDELEMS(h1)); |
---|
1362 | i = -1; |
---|
1363 | e=idInit(16,h3->rank); |
---|
1364 | for (j=0; j<IDELEMS(h3); j++) |
---|
1365 | { |
---|
1366 | if (h3->m[j] != NULL) |
---|
1367 | { |
---|
1368 | if (pMinComp(h3->m[j]) > k) |
---|
1369 | { |
---|
1370 | p = h3->m[j]; |
---|
1371 | h3->m[j]=NULL; |
---|
1372 | pShift(&p,-k); |
---|
1373 | if (p!=NULL) |
---|
1374 | { |
---|
1375 | i++; |
---|
1376 | if (i+1 >= IDELEMS(e)) |
---|
1377 | { |
---|
1378 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
---|
1379 | IDELEMS(e) += 16; |
---|
1380 | } |
---|
1381 | e->m[i] = p; |
---|
1382 | } |
---|
1383 | } |
---|
1384 | else |
---|
1385 | { |
---|
1386 | isMonomial=isMonomial && (pNext(h3->m[j])==NULL); |
---|
1387 | pDelete(&pNext(h3->m[j])); |
---|
1388 | } |
---|
1389 | } |
---|
1390 | } |
---|
1391 | if ((!isMonomial) && (!TEST_OPT_NOTREGULARITY) && (setRegularity) && (h==isHomog)) |
---|
1392 | { |
---|
1393 | idSkipZeroes(h3); |
---|
1394 | resolvente res = sySchreyerResolvente(h3,-1,&length,TRUE); |
---|
1395 | intvec * dummy = syBetti(res,length,®, *w); |
---|
1396 | deg = reg+2; |
---|
1397 | delete dummy; |
---|
1398 | for (j=0;j<length;j++) |
---|
1399 | { |
---|
1400 | if (res[j]!=NULL) idDelete(&(res[j])); |
---|
1401 | } |
---|
1402 | Free((ADDRESS)res,length*sizeof(ideal)); |
---|
1403 | } |
---|
1404 | idDelete(&h3); |
---|
1405 | idSkipZeroes(e); |
---|
1406 | return e; |
---|
1407 | } |
---|
1408 | |
---|
1409 | /*2 |
---|
1410 | * computes syzygies and minimizes the input (h1) |
---|
1411 | * ONLY used in syMinRes |
---|
1412 | */ |
---|
1413 | ideal idSyzMin (ideal h1,ideal quot, tHomog h,intvec **w, |
---|
1414 | BOOLEAN setRegularity, int °) |
---|
1415 | { |
---|
1416 | ideal e, h3; |
---|
1417 | poly p; |
---|
1418 | intvec * reord; |
---|
1419 | int i, l=0, j, k=0, quotdim, quotgen,length=0,reg; |
---|
1420 | BOOLEAN isMonomial=TRUE; |
---|
1421 | |
---|
1422 | if (idIs0(h1)) |
---|
1423 | return idFreeModule(1); |
---|
1424 | //PrintS("h1 vorher\n"); |
---|
1425 | //for (i=0;i<IDELEMS(h1);i++) |
---|
1426 | //{ |
---|
1427 | //Print("Element %d: ",i);pWrite(h1->m[i]); |
---|
1428 | //} |
---|
1429 | idSkipZeroes(h1); |
---|
1430 | h3=idPrepare(h1,quot,h,&k,"gen,"dim,w); |
---|
1431 | //PrintS("h1 nachher\n"); |
---|
1432 | //for (i=0;i<IDELEMS(h3);i++) |
---|
1433 | //{ |
---|
1434 | //Print("Element %d: ",i);pWrite(h3->m[i]); |
---|
1435 | //} |
---|
1436 | if (h3==NULL) |
---|
1437 | return idFreeModule(1); |
---|
1438 | for (i=IDELEMS(h1);i!=0;i--) |
---|
1439 | pDelete(&(h1->m[i-1])); |
---|
1440 | reord = new intvec(IDELEMS(h1)+1); |
---|
1441 | i = -1; |
---|
1442 | e=idInit(16,h3->rank); |
---|
1443 | for (j=0; j<IDELEMS(h3); j++) |
---|
1444 | { |
---|
1445 | if (h3->m[j] != NULL) |
---|
1446 | { |
---|
1447 | p = h3->m[j]; |
---|
1448 | if (pGetComp(p) > k) |
---|
1449 | { |
---|
1450 | h3->m[j]=NULL; |
---|
1451 | pShift(&p,-k); |
---|
1452 | if (p!=NULL) |
---|
1453 | { |
---|
1454 | i++; |
---|
1455 | if (i+1 >= IDELEMS(e)) |
---|
1456 | { |
---|
1457 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
---|
1458 | IDELEMS(e) += 16; |
---|
1459 | } |
---|
1460 | e->m[i] = p; |
---|
1461 | } |
---|
1462 | } |
---|
1463 | else |
---|
1464 | { |
---|
1465 | while ((pNext(p)!=NULL) && (pGetComp(pNext(p))<=k)) pIter(p); |
---|
1466 | if (pIsConstantComp(pNext(p))) |
---|
1467 | { |
---|
1468 | (*reord)[pGetComp(pNext(p))-k] = l+1; |
---|
1469 | //Print("Element %d mit Comp %d: ",j,pGetComp(pNext(p))-k); |
---|
1470 | //pWrite(h3->m[j]); |
---|
1471 | h1->m[l] = h3->m[j]; |
---|
1472 | h3->m[j] = pCopy(h1->m[l]); |
---|
1473 | pDelete(&pNext(p)); |
---|
1474 | l++; |
---|
1475 | } |
---|
1476 | isMonomial=isMonomial && (pGetComp(pNext(h3->m[j]))>k); |
---|
1477 | pDelete(&pNext(h3->m[j])); |
---|
1478 | } |
---|
1479 | } |
---|
1480 | } |
---|
1481 | if ((!isMonomial) && (!TEST_OPT_NOTREGULARITY) && (setRegularity) && (h==isHomog)) |
---|
1482 | { |
---|
1483 | idSkipZeroes(h3); |
---|
1484 | resolvente res = sySchreyerResolvente(h3,0,&length); |
---|
1485 | intvec * dummy = syBetti(res,length,®, *w); |
---|
1486 | deg = reg+2; |
---|
1487 | delete dummy; |
---|
1488 | for (j=0;j<length;j++) |
---|
1489 | { |
---|
1490 | if (res[j]!=NULL) idDelete(&(res[j])); |
---|
1491 | } |
---|
1492 | Free((ADDRESS)res,length*sizeof(ideal)); |
---|
1493 | } |
---|
1494 | idDelete(&h3); |
---|
1495 | //PrintS("Komponententransformation: "); |
---|
1496 | //reord->show(); |
---|
1497 | //PrintLn(); |
---|
1498 | for (i=IDELEMS(e);i!=0;i--) |
---|
1499 | { |
---|
1500 | if (e->m[i-1]!=NULL) |
---|
1501 | { |
---|
1502 | p = e->m[i-1]; |
---|
1503 | while (p!=NULL) |
---|
1504 | { |
---|
1505 | j = pGetComp(p); |
---|
1506 | pSetComp(p,(*reord)[j]); |
---|
1507 | pIter(p); |
---|
1508 | } |
---|
1509 | e->m[i-1] = pOrdPolyMerge(e->m[i-1]); |
---|
1510 | } |
---|
1511 | } |
---|
1512 | idSkipZeroes(e); |
---|
1513 | delete reord; |
---|
1514 | return e; |
---|
1515 | } |
---|
1516 | |
---|
1517 | /* |
---|
1518 | *computes a standard basis for h1 and stores the transformation matrix |
---|
1519 | * in ma |
---|
1520 | */ |
---|
1521 | ideal idLiftStd (ideal h1,ideal quot, matrix* ma, tHomog h) |
---|
1522 | { |
---|
1523 | int i, j, k=0, t, quotgen, inputIsIdeal=lengthFreeModule(h1); |
---|
1524 | ideal e, h3; |
---|
1525 | poly p=NULL, q, qq; |
---|
1526 | intvec *w=NULL; |
---|
1527 | |
---|
1528 | idDelete((ideal*)ma); |
---|
1529 | *ma=mpNew(1,0); |
---|
1530 | if (idIs0(h1)) |
---|
1531 | return idInit(1,h1->rank); |
---|
1532 | h3=idPrepare(h1,quot,h,&k,"gen,&i,&w); |
---|
1533 | if (w!=NULL) delete w; |
---|
1534 | i = 0; |
---|
1535 | for (j=0;j<IDELEMS(h3);j++) |
---|
1536 | { |
---|
1537 | if ((h3->m[j] != NULL) && (pMinComp(h3->m[j]) <= k)) |
---|
1538 | i++; |
---|
1539 | } |
---|
1540 | j = IDELEMS(h1); |
---|
1541 | idDelete((ideal*)ma); |
---|
1542 | *ma = mpNew(j,i); |
---|
1543 | i = -1; |
---|
1544 | e=idInit(16,h1->rank); |
---|
1545 | for (j=0; j<IDELEMS(h3); j++) |
---|
1546 | { |
---|
1547 | if ((h3->m[j] != NULL) && (pMinComp(h3->m[j]) <= k)) |
---|
1548 | { |
---|
1549 | q = h3->m[j]; |
---|
1550 | qq=q; |
---|
1551 | h3->m[j]=NULL; |
---|
1552 | while (pNext(q) != NULL) |
---|
1553 | { |
---|
1554 | if (pGetComp(pNext(q)) > k) |
---|
1555 | { |
---|
1556 | p = pNext(q); |
---|
1557 | pNext(q) = pNext(pNext(q)); |
---|
1558 | pNext(p) = NULL; |
---|
1559 | t=pGetComp(p); |
---|
1560 | pSetComp(p,0); |
---|
1561 | MATELEM(*ma,t-k,i+2) = pAdd(MATELEM(*ma,t-k,i+2),p); |
---|
1562 | } |
---|
1563 | else |
---|
1564 | { |
---|
1565 | pIter(q); |
---|
1566 | } |
---|
1567 | } |
---|
1568 | if (!inputIsIdeal) pShift(&qq,-1); |
---|
1569 | //if (quotgen != 0) |
---|
1570 | //{ |
---|
1571 | // q = kNF(quot,qq); |
---|
1572 | // pDelete(&qq); |
---|
1573 | //} |
---|
1574 | //else |
---|
1575 | q = qq; |
---|
1576 | if (q !=NULL) |
---|
1577 | { |
---|
1578 | i++; |
---|
1579 | if (i+1 >= IDELEMS(e)) |
---|
1580 | { |
---|
1581 | pEnlargeSet(&(e->m),IDELEMS(e),16); |
---|
1582 | IDELEMS(e) += 16; |
---|
1583 | } |
---|
1584 | e->m[i] = q; |
---|
1585 | } |
---|
1586 | } |
---|
1587 | } |
---|
1588 | idDelete(&h3); |
---|
1589 | idSkipZeroes(e); |
---|
1590 | return e; |
---|
1591 | } |
---|
1592 | |
---|
1593 | /*2 |
---|
1594 | *computes a representation of the generators of submod with respect to those |
---|
1595 | * of mod |
---|
1596 | */ |
---|
1597 | ideal idLiftNonStB (ideal mod, ideal submod,BOOLEAN goodShape) |
---|
1598 | { |
---|
1599 | int lsmod =idRankFreeModule(submod), i, j, k, quotgen; |
---|
1600 | ideal result, h3, temp; |
---|
1601 | |
---|
1602 | if (idIs0(mod)) |
---|
1603 | return idInit(1,mod->rank); |
---|
1604 | |
---|
1605 | if ((idRankFreeModule(mod)!=0) && (lsmod==0)) lsmod=1; |
---|
1606 | k=lsmod; |
---|
1607 | //idSkipZeroes(mod); |
---|
1608 | h3=idPrepare(mod,currQuotient,(tHomog)FALSE,&k,"gen,&i,NULL); |
---|
1609 | if (!goodShape) |
---|
1610 | { |
---|
1611 | for (j=0;j<IDELEMS(h3);j++) |
---|
1612 | { |
---|
1613 | if ((h3->m[j] != NULL) && (pMinComp(h3->m[j]) > k)) |
---|
1614 | pDelete(&(h3->m[j])); |
---|
1615 | } |
---|
1616 | } |
---|
1617 | idSkipZeroes(h3); |
---|
1618 | if (lsmod==0) |
---|
1619 | { |
---|
1620 | temp = idCopy(submod); |
---|
1621 | for (j=IDELEMS(temp);j>0;j--) |
---|
1622 | { |
---|
1623 | if (temp->m[j-1]!=NULL) |
---|
1624 | pShift(&(temp->m[j-1]),1); |
---|
1625 | } |
---|
1626 | } |
---|
1627 | else |
---|
1628 | { |
---|
1629 | temp = submod; |
---|
1630 | } |
---|
1631 | pSetSyzComp(k); |
---|
1632 | result = kNF(h3,currQuotient,temp,k); |
---|
1633 | result->rank = h3->rank; |
---|
1634 | idDelete(&h3); |
---|
1635 | if (lsmod==0) |
---|
1636 | idDelete(&temp); |
---|
1637 | pSetSyzComp(0); |
---|
1638 | for (j=0;j<IDELEMS(result);j++) |
---|
1639 | { |
---|
1640 | if (result->m[j]!=NULL) |
---|
1641 | { |
---|
1642 | if (pGetComp(result->m[j])<=k) |
---|
1643 | { |
---|
1644 | WerrorS("2nd module lies not in the first"); |
---|
1645 | idDelete(&result); |
---|
1646 | return idInit(1,1); |
---|
1647 | } |
---|
1648 | else |
---|
1649 | { |
---|
1650 | pShift(&(result->m[j]),-k); |
---|
1651 | pNeg(result->m[j]); |
---|
1652 | } |
---|
1653 | } |
---|
1654 | } |
---|
1655 | return result; |
---|
1656 | } |
---|
1657 | |
---|
1658 | /*2 |
---|
1659 | *computes a representation of the generators of submod with respect to those |
---|
1660 | * of mod which is given as standardbasis, |
---|
1661 | * uses currQuotient as the quotient ideal (if not NULL) |
---|
1662 | */ |
---|
1663 | ideal idLift (ideal mod,ideal submod) |
---|
1664 | { |
---|
1665 | ideal temp, result; |
---|
1666 | int j,k; |
---|
1667 | poly p,q; |
---|
1668 | BOOLEAN reported=FALSE; |
---|
1669 | |
---|
1670 | if (idIs0(mod)) return idInit(1,mod->rank); |
---|
1671 | k = lengthFreeModule(mod); |
---|
1672 | temp=idCopy(mod); |
---|
1673 | if (k == 0) |
---|
1674 | { |
---|
1675 | for (j=0; j<IDELEMS(temp); j++) |
---|
1676 | { |
---|
1677 | if (temp->m[j]!=NULL) pSetCompP(temp->m[j],1); |
---|
1678 | } |
---|
1679 | k = 1; |
---|
1680 | } |
---|
1681 | for (j=0; j<IDELEMS(temp); j++) |
---|
1682 | { |
---|
1683 | if (temp->m[j]!=NULL) |
---|
1684 | { |
---|
1685 | p = temp->m[j]; |
---|
1686 | q = pOne(); |
---|
1687 | pGetCoeff(q)=nNeg(pGetCoeff(q)); //set q to -1 |
---|
1688 | pSetComp(q,k+1+j); |
---|
1689 | while (pNext(p)) pIter(p); |
---|
1690 | pNext(p) = q; |
---|
1691 | } |
---|
1692 | } |
---|
1693 | result=idInit(IDELEMS(submod),submod->rank); |
---|
1694 | pSetSyzComp(k); |
---|
1695 | for (j=0; j<IDELEMS(submod); j++) |
---|
1696 | { |
---|
1697 | if (submod->m[j]!=NULL) |
---|
1698 | { |
---|
1699 | p = pCopy(submod->m[j]); |
---|
1700 | if (pGetComp(p)==0) pSetCompP(p,1); |
---|
1701 | q = kNF(temp,currQuotient,p); |
---|
1702 | pDelete(&p); |
---|
1703 | if (q!=NULL) |
---|
1704 | { |
---|
1705 | if (pMinComp(q)<=k) |
---|
1706 | { |
---|
1707 | if (!reported) |
---|
1708 | { |
---|
1709 | WarnS("first module not a standardbasis\n" |
---|
1710 | "or second not a proper submodule"); |
---|
1711 | //Warn("first module not a standardbasis(comp=%d,k=%d), q=", |
---|
1712 | // pMinComp(q),k); |
---|
1713 | // pWrite(q); |
---|
1714 | //WarnS("or second not a proper submodule"); |
---|
1715 | reported=TRUE; |
---|
1716 | } |
---|
1717 | pDelete(&q); |
---|
1718 | } |
---|
1719 | else |
---|
1720 | { |
---|
1721 | pShift(&q,-k); |
---|
1722 | result->m[j] = q; |
---|
1723 | } |
---|
1724 | } |
---|
1725 | } |
---|
1726 | } |
---|
1727 | pSetSyzComp(0); |
---|
1728 | //idSkipZeroes(result); |
---|
1729 | idDelete(&temp); |
---|
1730 | return result; |
---|
1731 | } |
---|
1732 | |
---|
1733 | /*2 |
---|
1734 | *computes the quotient of h1,h2 |
---|
1735 | */ |
---|
1736 | #ifdef OLD_QUOT |
---|
1737 | ideal idQuot (ideal h1, ideal h2, BOOLEAN h1IsSB, BOOLEAN resultIsIdeal) |
---|
1738 | { |
---|
1739 | int i,j = 0,l,ll,k,kkk,k1,k2,kmax; |
---|
1740 | ideal h3,h4; |
---|
1741 | poly p,q = NULL; |
---|
1742 | BOOLEAN b = FALSE; |
---|
1743 | |
---|
1744 | k1 = lengthFreeModule(h1); |
---|
1745 | k2 = lengthFreeModule(h2); |
---|
1746 | k=max(k1,k2); |
---|
1747 | if (k==0) { k = 1; b=TRUE; } |
---|
1748 | h4 = idInit(1,1); |
---|
1749 | for (i=0; i<IDELEMS(h2); i++) |
---|
1750 | { |
---|
1751 | if (h2->m[i] != NULL) |
---|
1752 | { |
---|
1753 | p = pCopy(h2->m[i]); |
---|
1754 | if (k2 == 0) |
---|
1755 | pShift(&p,j*k+1); |
---|
1756 | else |
---|
1757 | pShift(&p,j*k); |
---|
1758 | q = pAdd(q,p); |
---|
1759 | j++; |
---|
1760 | } |
---|
1761 | } |
---|
1762 | kmax = j*k+1; |
---|
1763 | p = pOne(); |
---|
1764 | pSetComp(p,kmax); |
---|
1765 | pSetSyzComp(kmax-1); |
---|
1766 | q = pAdd(q,p); |
---|
1767 | h4->m[0] = q; |
---|
1768 | if (k2 == 0) |
---|
1769 | { |
---|
1770 | if (k > IDELEMS(h4)) |
---|
1771 | { |
---|
1772 | pEnlargeSet(&(h4->m),IDELEMS(h4),k-IDELEMS(h4)); |
---|
1773 | IDELEMS(h4) = k; |
---|
1774 | } |
---|
1775 | for (i=1; i<k; i++) |
---|
1776 | { |
---|
1777 | p = pCopy(h4->m[i-1]); |
---|
1778 | pShift(&p,1); |
---|
1779 | h4->m[i] = p; |
---|
1780 | } |
---|
1781 | } |
---|
1782 | kkk = IDELEMS(h4); |
---|
1783 | i = IDELEMS(h1); |
---|
1784 | while (h1->m[i-1] == NULL) i--; |
---|
1785 | for (l=0; l<i; l++) |
---|
1786 | { |
---|
1787 | if(h1->m[l]!=NULL) |
---|
1788 | { |
---|
1789 | for (ll=0; ll<j; ll++) |
---|
1790 | { |
---|
1791 | p = pCopy(h1->m[l]); |
---|
1792 | if (k1 == 0) |
---|
1793 | pShift(&p,ll*k+1); |
---|
1794 | else |
---|
1795 | pShift(&p,ll*k); |
---|
1796 | if (kkk >= IDELEMS(h4)) |
---|
1797 | { |
---|
1798 | pEnlargeSet(&(h4->m),IDELEMS(h4),16); |
---|
1799 | IDELEMS(h4) += 16; |
---|
1800 | } |
---|
1801 | h4->m[kkk] = p; |
---|
1802 | kkk++; |
---|
1803 | } |
---|
1804 | } |
---|
1805 | } |
---|
1806 | h3 = kStd(h4,currQuotient,(tHomog)FALSE,NULL,NULL,kmax-1); |
---|
1807 | pSetSyzComp(0); |
---|
1808 | idDelete(&h4); |
---|
1809 | for (i=0;i<IDELEMS(h3);i++) |
---|
1810 | { |
---|
1811 | if ((h3->m[i]!=NULL) && (pGetComp(h3->m[i])>=kmax)) |
---|
1812 | { |
---|
1813 | if (b) |
---|
1814 | pShift(&h3->m[i],-kmax); |
---|
1815 | else |
---|
1816 | pShift(&h3->m[i],-kmax+1); |
---|
1817 | } |
---|
1818 | else |
---|
1819 | pDelete(&h3->m[i]); |
---|
1820 | } |
---|
1821 | if (b) |
---|
1822 | h3->rank = 1; |
---|
1823 | else |
---|
1824 | h3->rank = h1->rank; |
---|
1825 | h4=idCompactify(h3); |
---|
1826 | idDelete(&h3); |
---|
1827 | return h4; |
---|
1828 | } |
---|
1829 | #else |
---|
1830 | ideal idQuot (ideal h1, ideal h2, BOOLEAN h1IsStb, BOOLEAN resultIsIdeal) |
---|
1831 | { |
---|
1832 | // first check for special case h1:(0) |
---|
1833 | ideal h3; |
---|
1834 | if (idIs0(h2)) |
---|
1835 | { |
---|
1836 | if (resultIsIdeal) |
---|
1837 | { |
---|
1838 | h3 = idInit(1,1); |
---|
1839 | h3->m[0] = pOne(); |
---|
1840 | } |
---|
1841 | else |
---|
1842 | h3 = idFreeModule(h1->rank); |
---|
1843 | return h3; |
---|
1844 | } |
---|
1845 | |
---|
1846 | // the usual part: |
---|
1847 | intvec * weights,* weights1; |
---|
1848 | ideal h4,temph1; |
---|
1849 | BITSET old_test=test; |
---|
1850 | poly p,q = NULL; |
---|
1851 | int i,l,ll,k,kkk,kmax; |
---|
1852 | int j = 0; |
---|
1853 | int k1 = lengthFreeModule(h1); |
---|
1854 | int k2 = lengthFreeModule(h2); |
---|
1855 | BOOLEAN addOnlyOne=TRUE; |
---|
1856 | tHomog hom=isNotHomog; |
---|
1857 | |
---|
1858 | k=max(k1,k2); |
---|
1859 | if (k==0) |
---|
1860 | { |
---|
1861 | k = 1; |
---|
1862 | //resultIsIdeal=TRUE; |
---|
1863 | } |
---|
1864 | //else if ((k1>0)&&(k2>0)) |
---|
1865 | //{ |
---|
1866 | // resultIsIdeal=TRUE; |
---|
1867 | //} |
---|
1868 | hom = (tHomog)idHomModule(h1,currQuotient,&weights) ; |
---|
1869 | h4 = idInit(1,1); |
---|
1870 | for (i=0; i<IDELEMS(h2); i++) |
---|
1871 | { |
---|
1872 | if (h2->m[i] != NULL) |
---|
1873 | { |
---|
1874 | p = pCopy(h2->m[i]); |
---|
1875 | if (k2 == 0) |
---|
1876 | pShift(&p,j*k+1); |
---|
1877 | else |
---|
1878 | pShift(&p,j*k); |
---|
1879 | q = pAdd(q,p); |
---|
1880 | j++; |
---|
1881 | } |
---|
1882 | } |
---|
1883 | kmax = j*k+1; |
---|
1884 | p = pOne(); |
---|
1885 | pSetComp(p,kmax); |
---|
1886 | pSetSyzComp(kmax-1); |
---|
1887 | q = pAdd(q,p); |
---|
1888 | h4->m[0] = q; |
---|
1889 | if (k2 == 0) |
---|
1890 | { |
---|
1891 | if (k > IDELEMS(h4)) |
---|
1892 | { |
---|
1893 | pEnlargeSet(&(h4->m),IDELEMS(h4),k-IDELEMS(h4)); |
---|
1894 | IDELEMS(h4) = k; |
---|
1895 | } |
---|
1896 | if (k>1) addOnlyOne = FALSE; |
---|
1897 | for (i=1; i<k; i++) |
---|
1898 | { |
---|
1899 | p = pCopy(h4->m[i-1]); |
---|
1900 | pShift(&p,1); |
---|
1901 | h4->m[i] = p; |
---|
1902 | } |
---|
1903 | } |
---|
1904 | kkk = IDELEMS(h4); |
---|
1905 | if (addOnlyOne && (!h1IsStb)) |
---|
1906 | temph1 = kStd(h1,currQuotient,hom,&weights,NULL); |
---|
1907 | else |
---|
1908 | temph1 = h1; |
---|
1909 | idTest(temph1); |
---|
1910 | i = IDELEMS(temph1); |
---|
1911 | while ((i>0) && (temph1->m[i-1]==NULL)) i--; |
---|
1912 | for (l=0; l<i; l++) |
---|
1913 | { |
---|
1914 | if(temph1->m[l]!=NULL) |
---|
1915 | { |
---|
1916 | for (ll=0; ll<j; ll++) |
---|
1917 | { |
---|
1918 | p = pCopy(temph1->m[l]); |
---|
1919 | if (k1 == 0) |
---|
1920 | pShift(&p,ll*k+1); |
---|
1921 | else |
---|
1922 | pShift(&p,ll*k); |
---|
1923 | if (kkk >= IDELEMS(h4)) |
---|
1924 | { |
---|
1925 | pEnlargeSet(&(h4->m),IDELEMS(h4),16); |
---|
1926 | IDELEMS(h4) += 16; |
---|
1927 | } |
---|
1928 | h4->m[kkk] = p; |
---|
1929 | kkk++; |
---|
1930 | } |
---|
1931 | } |
---|
1932 | } |
---|
1933 | idTest(h4); |
---|
1934 | if (addOnlyOne) |
---|
1935 | { |
---|
1936 | p = h4->m[0]; |
---|
1937 | for (i=0;i<IDELEMS(h4)-1;i++) |
---|
1938 | { |
---|
1939 | h4->m[i] = h4->m[i+1]; |
---|
1940 | } |
---|
1941 | h4->m[IDELEMS(h4)-1] = p; |
---|
1942 | idSkipZeroes(h4); |
---|
1943 | test |= Sy_bit(OPT_SB_1); |
---|
1944 | } |
---|
1945 | idTest(h4); |
---|
1946 | hom = (tHomog)idHomModule(h4,currQuotient,&weights1); |
---|
1947 | if (addOnlyOne) |
---|
1948 | { |
---|
1949 | h3 = kStd(h4,currQuotient,hom,&weights1,NULL,kmax-1,IDELEMS(h4)-1); |
---|
1950 | } |
---|
1951 | else |
---|
1952 | { |
---|
1953 | h3 = kStd(h4,currQuotient,hom,&weights1,NULL,kmax-1); |
---|
1954 | } |
---|
1955 | idTest(h3); |
---|
1956 | idDelete(&h4); |
---|
1957 | pSetSyzComp(0); |
---|
1958 | for (i=0;i<IDELEMS(h3);i++) |
---|
1959 | { |
---|
1960 | if ((h3->m[i]!=NULL) && (pGetComp(h3->m[i])>=kmax)) |
---|
1961 | { |
---|
1962 | if (resultIsIdeal) |
---|
1963 | pShift(&h3->m[i],-kmax); |
---|
1964 | else |
---|
1965 | pShift(&h3->m[i],-kmax+1); |
---|
1966 | } |
---|
1967 | else |
---|
1968 | pDelete(&h3->m[i]); |
---|
1969 | } |
---|
1970 | if (resultIsIdeal) |
---|
1971 | h3->rank = 1; |
---|
1972 | else |
---|
1973 | h3->rank = h1->rank; |
---|
1974 | idTest(h3); |
---|
1975 | idSkipZeroes(h3); |
---|
1976 | //h4=idCompactify(h3); |
---|
1977 | //idDelete(&h3); |
---|
1978 | if ((addOnlyOne) && (!h1IsStb)) |
---|
1979 | idDelete(&temph1); |
---|
1980 | if (weights!=NULL) delete weights; |
---|
1981 | if (weights1!=NULL) delete weights1; |
---|
1982 | test = old_test; |
---|
1983 | return h3; |
---|
1984 | } |
---|
1985 | #endif |
---|
1986 | |
---|
1987 | /*2 |
---|
1988 | *computes recursively all monomials of a certain degree |
---|
1989 | *in every step the actvar-th entry in the exponential |
---|
1990 | *vector is incremented and the other variables are |
---|
1991 | *computed by recursive calls of makemonoms |
---|
1992 | *if the last variable is reached, the difference to the |
---|
1993 | *degree is computed directly |
---|
1994 | *vars is the number variables |
---|
1995 | *actvar is the actual variable to handle |
---|
1996 | *deg is the degree of the monomials to compute |
---|
1997 | *monomdeg is the actual degree of the monomial in consideration |
---|
1998 | */ |
---|
1999 | static void makemonoms(int vars,int actvar,int deg,int monomdeg) |
---|
2000 | { |
---|
2001 | poly p; |
---|
2002 | int i=0; |
---|
2003 | |
---|
2004 | if ((idpowerpoint == 0) && (actvar ==1)) |
---|
2005 | { |
---|
2006 | idpower[idpowerpoint] = pOne(); |
---|
2007 | monomdeg = 0; |
---|
2008 | } |
---|
2009 | while (i<=deg) |
---|
2010 | { |
---|
2011 | if (deg == monomdeg) |
---|
2012 | { |
---|
2013 | pSetm(idpower[idpowerpoint]); |
---|
2014 | idpowerpoint++; |
---|
2015 | return; |
---|
2016 | } |
---|
2017 | if (actvar == vars) |
---|
2018 | { |
---|
2019 | pSetExp(idpower[idpowerpoint],actvar,deg-monomdeg); |
---|
2020 | pSetm(idpower[idpowerpoint]); |
---|
2021 | idpowerpoint++; |
---|
2022 | return; |
---|
2023 | } |
---|
2024 | else |
---|
2025 | { |
---|
2026 | p = pCopy(idpower[idpowerpoint]); |
---|
2027 | makemonoms(vars,actvar+1,deg,monomdeg); |
---|
2028 | idpower[idpowerpoint] = p; |
---|
2029 | } |
---|
2030 | monomdeg++; |
---|
2031 | pSetExp(idpower[idpowerpoint],actvar,pGetExp(idpower[idpowerpoint],actvar)+1); |
---|
2032 | pSetm(idpower[idpowerpoint]); |
---|
2033 | i++; |
---|
2034 | } |
---|
2035 | } |
---|
2036 | |
---|
2037 | /*2 |
---|
2038 | *returns the deg-th power of the maximal ideal of 0 |
---|
2039 | */ |
---|
2040 | ideal idMaxIdeal(int deg) |
---|
2041 | { |
---|
2042 | if (deg < 0) |
---|
2043 | { |
---|
2044 | WarnS("maxideal: power must be non-negative"); |
---|
2045 | } |
---|
2046 | if (deg < 1) |
---|
2047 | { |
---|
2048 | ideal I=idInit(1,1); |
---|
2049 | I->m[0]=pOne(); |
---|
2050 | return I; |
---|
2051 | } |
---|
2052 | if (deg == 1) |
---|
2053 | { |
---|
2054 | return idMaxIdeal(); |
---|
2055 | } |
---|
2056 | |
---|
2057 | int vars = currRing->N; |
---|
2058 | int i = binom(vars+deg-1,deg); |
---|
2059 | ideal id=idInit(i,1); |
---|
2060 | idpower = id->m; |
---|
2061 | idpowerpoint = 0; |
---|
2062 | makemonoms(vars,1,deg,0); |
---|
2063 | idpower = NULL; |
---|
2064 | idpowerpoint = 0; |
---|
2065 | return id; |
---|
2066 | } |
---|
2067 | |
---|
2068 | /*2 |
---|
2069 | *computes recursively all generators of a certain degree |
---|
2070 | *of the ideal "givenideal" |
---|
2071 | *elms is the number elements in the given ideal |
---|
2072 | *actelm is the actual element to handle |
---|
2073 | *deg is the degree of the power to compute |
---|
2074 | *gendeg is the actual degree of the generator in consideration |
---|
2075 | */ |
---|
2076 | static void makepotence(int elms,int actelm,int deg,int gendeg) |
---|
2077 | { |
---|
2078 | poly p; |
---|
2079 | int i=0; |
---|
2080 | |
---|
2081 | if ((idpowerpoint == 0) && (actelm ==1)) |
---|
2082 | { |
---|
2083 | idpower[idpowerpoint] = pOne(); |
---|
2084 | gendeg = 0; |
---|
2085 | } |
---|
2086 | while (i<=deg) |
---|
2087 | { |
---|
2088 | if (deg == gendeg) |
---|
2089 | { |
---|
2090 | idpowerpoint++; |
---|
2091 | return; |
---|
2092 | } |
---|
2093 | if (actelm == elms) |
---|
2094 | { |
---|
2095 | p=pPower(pCopy(givenideal[actelm-1]),deg-gendeg); |
---|
2096 | idpower[idpowerpoint]=pMult(idpower[idpowerpoint],p); |
---|
2097 | idpowerpoint++; |
---|
2098 | return; |
---|
2099 | } |
---|
2100 | else |
---|
2101 | { |
---|
2102 | p = pCopy(idpower[idpowerpoint]); |
---|
2103 | makepotence(elms,actelm+1,deg,gendeg); |
---|
2104 | idpower[idpowerpoint] = p; |
---|
2105 | } |
---|
2106 | gendeg++; |
---|
2107 | idpower[idpowerpoint]=pMult(idpower[idpowerpoint],pCopy(givenideal[actelm-1])); |
---|
2108 | i++; |
---|
2109 | } |
---|
2110 | } |
---|
2111 | |
---|
2112 | /*2 |
---|
2113 | *returns the deg-th power of the ideal gid |
---|
2114 | */ |
---|
2115 | //ideal idPower(ideal gid,int deg) |
---|
2116 | //{ |
---|
2117 | // int i; |
---|
2118 | // ideal id; |
---|
2119 | // |
---|
2120 | // if (deg < 1) deg = 1; |
---|
2121 | // i = binom(IDELEMS(gid)+deg-1,deg); |
---|
2122 | // id=idInit(i,1); |
---|
2123 | // idpower = id->m; |
---|
2124 | // givenideal = gid->m; |
---|
2125 | // idpowerpoint = 0; |
---|
2126 | // makepotence(IDELEMS(gid),1,deg,0); |
---|
2127 | // idpower = NULL; |
---|
2128 | // givenideal = NULL; |
---|
2129 | // idpowerpoint = 0; |
---|
2130 | // return id; |
---|
2131 | //} |
---|
2132 | static void idNextPotence(ideal given, ideal result, |
---|
2133 | int begin, int end, int deg, int restdeg, poly ap) |
---|
2134 | { |
---|
2135 | poly p; |
---|
2136 | int i; |
---|
2137 | |
---|
2138 | p = pPower(pCopy(given->m[begin]),restdeg); |
---|
2139 | i = result->nrows; |
---|
2140 | result->m[i] = pMult(pCopy(ap),p); |
---|
2141 | //PrintS("."); |
---|
2142 | (result->nrows)++; |
---|
2143 | if (result->nrows >= IDELEMS(result)) |
---|
2144 | { |
---|
2145 | pEnlargeSet(&(result->m),IDELEMS(result),16); |
---|
2146 | IDELEMS(result) += 16; |
---|
2147 | } |
---|
2148 | if (begin == end) return; |
---|
2149 | for (i=restdeg-1;i>=0;i--) |
---|
2150 | { |
---|
2151 | p = pPower(pCopy(given->m[begin]),i); |
---|
2152 | p = pMult(pCopy(ap),p); |
---|
2153 | idNextPotence(given, result, begin+1, end, deg, restdeg-i, p); |
---|
2154 | pDelete(&p); |
---|
2155 | } |
---|
2156 | } |
---|
2157 | |
---|
2158 | ideal idPower(ideal given,int exp) |
---|
2159 | { |
---|
2160 | ideal result,temp; |
---|
2161 | poly p1; |
---|
2162 | int i; |
---|
2163 | |
---|
2164 | if (idIs0(given)) return idInit(1,1); |
---|
2165 | temp = idCopy(given); |
---|
2166 | idSkipZeroes(temp); |
---|
2167 | i = binom(IDELEMS(temp)+exp-1,exp); |
---|
2168 | result = idInit(i,1); |
---|
2169 | result->nrows = 0; |
---|
2170 | //Print("ideal contains %d elements\n",i); |
---|
2171 | p1=pOne(); |
---|
2172 | idNextPotence(temp,result,0,IDELEMS(temp)-1,exp,exp,p1); |
---|
2173 | pDelete(&p1); |
---|
2174 | idDelete(&temp); |
---|
2175 | result->nrows = 1; |
---|
2176 | idSkipZeroes(result); |
---|
2177 | idDelEquals(result); |
---|
2178 | return result; |
---|
2179 | } |
---|
2180 | |
---|
2181 | /*2 |
---|
2182 | * eliminate delVar (product of vars) in h1 |
---|
2183 | */ |
---|
2184 | ideal idElimination (ideal h1,poly delVar,intvec *hilb) |
---|
2185 | { |
---|
2186 | int i,j=0,k,l; |
---|
2187 | ideal h,hh, h3; |
---|
2188 | int *ord,*block0,*block1; |
---|
2189 | int ordersize=2; |
---|
2190 | short **wv; |
---|
2191 | tHomog hom; |
---|
2192 | intvec * w; |
---|
2193 | sip_sring tmpR; |
---|
2194 | ring origR = currRing; |
---|
2195 | |
---|
2196 | if (delVar==NULL) |
---|
2197 | { |
---|
2198 | return idCopy(h1); |
---|
2199 | } |
---|
2200 | if (currQuotient!=NULL) |
---|
2201 | { |
---|
2202 | WerrorS("cannot eliminate in a qring"); |
---|
2203 | return idCopy(h1); |
---|
2204 | } |
---|
2205 | if (idIs0(h1)) return idInit(1,h1->rank); |
---|
2206 | hom=(tHomog)idHomModule(h1,NULL,&w); //sets w to weight vector or NULL |
---|
2207 | h3=idInit(16,h1->rank); |
---|
2208 | for (k=0;; k++) |
---|
2209 | { |
---|
2210 | if (currRing->order[k]!=0) ordersize++; |
---|
2211 | else break; |
---|
2212 | } |
---|
2213 | ord=(int*)Alloc0(ordersize*sizeof(int)); |
---|
2214 | block0=(int*)Alloc(ordersize*sizeof(int)); |
---|
2215 | block1=(int*)Alloc(ordersize*sizeof(int)); |
---|
2216 | for (k=0;; k++) |
---|
2217 | { |
---|
2218 | if (currRing->order[k]!=0) |
---|
2219 | { |
---|
2220 | block0[k+1] = currRing->block0[k]; |
---|
2221 | block1[k+1] = currRing->block1[k]; |
---|
2222 | ord[k+1] = currRing->order[k]; |
---|
2223 | } |
---|
2224 | else |
---|
2225 | break; |
---|
2226 | } |
---|
2227 | block0[0] = 1; |
---|
2228 | block1[0] = pVariables; |
---|
2229 | wv=(short**) Alloc0(ordersize*sizeof(short**)); |
---|
2230 | memcpy4(wv+1,currRing->wvhdl,(ordersize-1)*sizeof(short**)); |
---|
2231 | wv[0]=(short*)Alloc0((pVariables+1)*sizeof(short)); |
---|
2232 | for (j=0;j<pVariables;j++) |
---|
2233 | if (pGetExp(delVar,j+1)!=0) wv[0][j]=1; |
---|
2234 | ord[0] = ringorder_a; |
---|
2235 | |
---|
2236 | // fill in tmp ring to get back the data later on |
---|
2237 | tmpR = *origR; |
---|
2238 | tmpR.order = ord; |
---|
2239 | tmpR.block0 = block0; |
---|
2240 | tmpR.block1 = block1; |
---|
2241 | tmpR.wvhdl = wv; |
---|
2242 | rComplete(&tmpR); |
---|
2243 | |
---|
2244 | // change into the new ring |
---|
2245 | //pChangeRing(pVariables,currRing->OrdSgn,ord,block0,block1,wv); |
---|
2246 | rChangeCurrRing(&tmpR, TRUE); |
---|
2247 | currRing = &tmpR; |
---|
2248 | h = idInit(IDELEMS(h1),1); |
---|
2249 | // fetch data from the old ring |
---|
2250 | for (k=0;k<IDELEMS(h1);k++) h->m[k] = pFetchCopy(origR, h1->m[k]); |
---|
2251 | // compute kStd |
---|
2252 | hh = kStd(h,NULL,hom,&w,hilb); |
---|
2253 | idDelete(&h); |
---|
2254 | |
---|
2255 | // go back to the original ring |
---|
2256 | rChangeCurrRing(origR,TRUE); |
---|
2257 | i = IDELEMS(hh)-1; |
---|
2258 | while ((i >= 0) && (hh->m[i] == NULL)) i--; |
---|
2259 | j = -1; |
---|
2260 | // fetch data from temp ring |
---|
2261 | for (k=0; k<=i; k++) |
---|
2262 | { |
---|
2263 | l=pVariables; |
---|
2264 | while ((l>0) && (pRingGetExp(&tmpR, hh->m[k],l)*pGetExp(delVar,l)==0)) l--; |
---|
2265 | if (l==0) |
---|
2266 | { |
---|
2267 | j++; |
---|
2268 | if (j >= IDELEMS(h3)) |
---|
2269 | { |
---|
2270 | pEnlargeSet(&(h3->m),IDELEMS(h3),16); |
---|
2271 | IDELEMS(h3) += 16; |
---|
2272 | } |
---|
2273 | h3->m[j] = pFetchCopy(&tmpR, hh->m[k]); |
---|
2274 | } |
---|
2275 | } |
---|
2276 | idDelete(&hh); |
---|
2277 | idSkipZeroes(h3); |
---|
2278 | Free((ADDRESS)wv[0],(pVariables+1)*sizeof(short)); |
---|
2279 | Free((ADDRESS)wv,ordersize*sizeof(short**)); |
---|
2280 | Free((ADDRESS)ord,ordersize*sizeof(int)); |
---|
2281 | Free((ADDRESS)block0,ordersize*sizeof(int)); |
---|
2282 | Free((ADDRESS)block1,ordersize*sizeof(int)); |
---|
2283 | if (w!=NULL) |
---|
2284 | delete w; |
---|
2285 | return h3; |
---|
2286 | } |
---|
2287 | |
---|
2288 | //void idEnterSet (poly p,ideal r, int * next) |
---|
2289 | //{ |
---|
2290 | // |
---|
2291 | // if ((*next) == IDELEMS(r)-1) |
---|
2292 | // { |
---|
2293 | // pEnlargeSet(&(r->m),IDELEMS(r),16); |
---|
2294 | // IDELEMS(r)+=16; |
---|
2295 | // } |
---|
2296 | // int at; |
---|
2297 | // int i; |
---|
2298 | // if (*next==0) at=0; |
---|
2299 | // else |
---|
2300 | // { |
---|
2301 | // int an = 0; |
---|
2302 | // int en= *next-1; |
---|
2303 | // int c; |
---|
2304 | // if (pComp0(r->m[(*next)-1],p)!= 1) |
---|
2305 | // at=*next; |
---|
2306 | // else |
---|
2307 | // { |
---|
2308 | // loop |
---|
2309 | // { |
---|
2310 | // if (an >= en-1) |
---|
2311 | // { |
---|
2312 | // if (pComp0(r->m[an],p) == 1) |
---|
2313 | // { |
---|
2314 | // at=an; break; |
---|
2315 | // } |
---|
2316 | // else |
---|
2317 | // { |
---|
2318 | // at=en; break; |
---|
2319 | // } |
---|
2320 | // } |
---|
2321 | // i=(an+en) / 2; |
---|
2322 | // if (pComp0(r->m[i],p) == 1) en=i; |
---|
2323 | // else an=i; |
---|
2324 | // } |
---|
2325 | // } |
---|
2326 | // } |
---|
2327 | // if (pComp(r->m[at],p)==0) |
---|
2328 | // { |
---|
2329 | // pDelete(&p); |
---|
2330 | // } |
---|
2331 | // else |
---|
2332 | // { |
---|
2333 | // (*next)++; |
---|
2334 | // for (i=(*next); i>=at+1; i--) |
---|
2335 | // { |
---|
2336 | // r->m[i] = r->m[i-1]; |
---|
2337 | // } |
---|
2338 | // /*- save result -*/ |
---|
2339 | // r->m[at] = p; |
---|
2340 | // } |
---|
2341 | //} |
---|
2342 | /*3 |
---|
2343 | * produces recursively the ideal of all arxar-minors of a |
---|
2344 | */ |
---|
2345 | static void idRecMin(matrix a,int ar,poly *barDiv,ideal result, |
---|
2346 | int * nextPlace, int rowToChose=0) |
---|
2347 | { |
---|
2348 | //Print("Level: %d\n",ar); |
---|
2349 | /*--- there is no non-zero minor coming from a------------*/ |
---|
2350 | if((ar<0) || (ar>min(a->ncols,a->nrows)-1)) |
---|
2351 | { |
---|
2352 | idDelete((ideal *)&a); |
---|
2353 | pDelete(barDiv); |
---|
2354 | return; |
---|
2355 | } |
---|
2356 | |
---|
2357 | /*--- initializing temporary structures-------------------*/ |
---|
2358 | int i,j,r=rowToChose,c,newi,newp,k; |
---|
2359 | poly p=NULL; |
---|
2360 | |
---|
2361 | if (ar==0) |
---|
2362 | { |
---|
2363 | /*--- ar is 0, the matrix-entres are minors---------------*/ |
---|
2364 | for (i=a->nrows;i>0;i--) |
---|
2365 | { |
---|
2366 | for (j=a->ncols;j>0;j--) |
---|
2367 | { |
---|
2368 | p = MATELEM(a,i,j); |
---|
2369 | if (p!=NULL) |
---|
2370 | { |
---|
2371 | //idEnterSet(p,result,nextPlace); |
---|
2372 | if (*nextPlace>=IDELEMS(result)) |
---|
2373 | { |
---|
2374 | pEnlargeSet(&(result->m),IDELEMS(result),IDELEMS(result)); |
---|
2375 | IDELEMS(result) *=2; |
---|
2376 | } |
---|
2377 | result->m[*nextPlace] = p; |
---|
2378 | (*nextPlace)++; |
---|
2379 | MATELEM(a,i,j) = NULL; |
---|
2380 | } |
---|
2381 | } |
---|
2382 | } |
---|
2383 | idTest(result); |
---|
2384 | idDelete((ideal*)&a); |
---|
2385 | pDelete(barDiv); |
---|
2386 | return; |
---|
2387 | } |
---|
2388 | /*--- ar>0, we perform one step of the Bareiss algorithm--*/ |
---|
2389 | p = pCopy(*barDiv); //we had to store barDiv for the remaining loops |
---|
2390 | matrix nextStep = mpOneStepBareiss(a,barDiv,&r,&c); |
---|
2391 | //Print("next row is: %d, next col: %d\n",r,c); |
---|
2392 | /*--- there is no pivot - the det of matrix is zero -------------*/ |
---|
2393 | if ((r*c==0) || (MATELEM(nextStep,nextStep->nrows,nextStep->ncols)==NULL)) |
---|
2394 | { |
---|
2395 | idDelete((ideal*)&nextStep); |
---|
2396 | idDelete((ideal*)&a); |
---|
2397 | pDelete(&p); |
---|
2398 | // pDelete(barDiv); barDiv==NULL in this case |
---|
2399 | return; |
---|
2400 | } |
---|
2401 | /*--- we read out the r-1 x c-1 matrix for the next step--*/ |
---|
2402 | if ((a->nrows-1)*(a->ncols-1)>0) |
---|
2403 | { |
---|
2404 | matrix next = mpNew(a->nrows-1,a->ncols-1); |
---|
2405 | for (i=a->nrows-1;i>0;i--) |
---|
2406 | { |
---|
2407 | for (j=a->ncols-1;j>0;j--) |
---|
2408 | { |
---|
2409 | MATELEM(next,i,j) = MATELEM(nextStep,i,j); |
---|
2410 | MATELEM(nextStep,i,j) =NULL; |
---|
2411 | } |
---|
2412 | } |
---|
2413 | idDelete((ideal*)&nextStep); |
---|
2414 | /*--- we call the next Step------------------------------*/ |
---|
2415 | idRecMin(next,ar-1,barDiv,result,nextPlace); |
---|
2416 | next = NULL; |
---|
2417 | } |
---|
2418 | if ((*barDiv)!=NULL) pDelete(barDiv); |
---|
2419 | /*--- now we have to take out the r-th row...------------*/ |
---|
2420 | if (((a->nrows)>1) && (rowToChose==0)) |
---|
2421 | { |
---|
2422 | if (nextStep!=NULL) idDelete((ideal*)&nextStep); |
---|
2423 | nextStep = mpNew(a->nrows-1,a->ncols); |
---|
2424 | for (i=r-1;i>0;i--) |
---|
2425 | { |
---|
2426 | for (j=a->ncols;j>0;j--) |
---|
2427 | { |
---|
2428 | MATELEM(nextStep,i,j) = pCopy(MATELEM(a,i,j)); |
---|
2429 | } |
---|
2430 | } |
---|
2431 | for (i=a->nrows;i>r;i--) |
---|
2432 | { |
---|
2433 | for (j=a->ncols;j>0;j--) |
---|
2434 | { |
---|
2435 | MATELEM(nextStep,i-1,j) = pCopy(MATELEM(a,i,j)); |
---|
2436 | } |
---|
2437 | } |
---|
2438 | /*--- and to perform the algorithm with the rest---------*/ |
---|
2439 | poly q=pCopy(p); |
---|
2440 | idRecMin(nextStep,ar,&q,result,nextPlace); |
---|
2441 | assume(q==NULL); |
---|
2442 | nextStep = NULL; |
---|
2443 | } |
---|
2444 | /*--- now we have to take out the c-th col...------------*/ |
---|
2445 | if ((a->nrows)>1) |
---|
2446 | { |
---|
2447 | if (nextStep!=NULL) idDelete((ideal*)&nextStep); |
---|
2448 | nextStep = mpNew(a->nrows,a->ncols-1); |
---|
2449 | for (i=a->nrows;i>0;i--) |
---|
2450 | { |
---|
2451 | for (j=c-1;j>0;j--) |
---|
2452 | { |
---|
2453 | MATELEM(nextStep,i,j) = MATELEM(a,i,j); |
---|
2454 | MATELEM(a,i,j) = NULL; |
---|
2455 | } |
---|
2456 | } |
---|
2457 | for (i=a->nrows;i>0;i--) |
---|
2458 | { |
---|
2459 | for (j=a->ncols;j>c;j--) |
---|
2460 | { |
---|
2461 | MATELEM(nextStep,i,j-1) = MATELEM(a,i,j); |
---|
2462 | MATELEM(a,i,j) = NULL; |
---|
2463 | } |
---|
2464 | } |
---|
2465 | /*--- and to perform the algorithm with the rest---------*/ |
---|
2466 | idDelete((ideal*)&a); |
---|
2467 | idRecMin(nextStep,ar,&p,result,nextPlace,r); |
---|
2468 | //assume(p==NULL); |
---|
2469 | nextStep = NULL; |
---|
2470 | } |
---|
2471 | /*--- deleting temporary structures and returns----------*/ |
---|
2472 | pDelete(&p); |
---|
2473 | return; |
---|
2474 | } |
---|
2475 | |
---|
2476 | #ifdef WITH_OLD_MINOR |
---|
2477 | /*2 |
---|
2478 | * compute all ar-minors of the matrix a |
---|
2479 | */ |
---|
2480 | ideal idMinors(matrix a, int ar) |
---|
2481 | { |
---|
2482 | int i,j,k,size; |
---|
2483 | int *rowchoise,*colchoise; |
---|
2484 | BOOLEAN rowch,colch; |
---|
2485 | ideal result; |
---|
2486 | matrix tmp; |
---|
2487 | poly p; |
---|
2488 | |
---|
2489 | i = binom(a->rows(),ar); |
---|
2490 | j = binom(a->cols(),ar); |
---|
2491 | |
---|
2492 | rowchoise=(int *)Alloc(ar*sizeof(int)); |
---|
2493 | colchoise=(int *)Alloc(ar*sizeof(int)); |
---|
2494 | if ((i>512) || (j>512) || (i*j >512)) size=512; |
---|
2495 | else size=i*j; |
---|
2496 | result=idInit(size,1); |
---|
2497 | tmp=mpNew(ar,ar); |
---|
2498 | k = 0; /* the index in result*/ |
---|
2499 | idInitChoise(ar,1,a->rows(),&rowch,rowchoise); |
---|
2500 | while (!rowch) |
---|
2501 | { |
---|
2502 | idInitChoise(ar,1,a->cols(),&colch,colchoise); |
---|
2503 | while (!colch) |
---|
2504 | { |
---|
2505 | for (i=1; i<=ar; i++) |
---|
2506 | { |
---|
2507 | for (j=1; j<=ar; j++) |
---|
2508 | { |
---|
2509 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
2510 | } |
---|
2511 | } |
---|
2512 | p = mpDetBareiss(tmp); |
---|
2513 | if (p!=NULL) |
---|
2514 | { |
---|
2515 | if (k>=size) |
---|
2516 | { |
---|
2517 | pEnlargeSet(&result->m,size,32); |
---|
2518 | size += 32; |
---|
2519 | } |
---|
2520 | result->m[k] = p; |
---|
2521 | k++; |
---|
2522 | } |
---|
2523 | idGetNextChoise(ar,a->cols(),&colch,colchoise); |
---|
2524 | } |
---|
2525 | idGetNextChoise(ar,a->rows(),&rowch,rowchoise); |
---|
2526 | } |
---|
2527 | /*delete the matrix tmp*/ |
---|
2528 | for (i=1; i<=ar; i++) |
---|
2529 | { |
---|
2530 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
2531 | } |
---|
2532 | idDelete((ideal*)&tmp); |
---|
2533 | if (k==0) |
---|
2534 | { |
---|
2535 | k=1; |
---|
2536 | result->m[0]=NULL; |
---|
2537 | } |
---|
2538 | Free((ADDRESS)rowchoise,ar*sizeof(int)); |
---|
2539 | Free((ADDRESS)colchoise,ar*sizeof(int)); |
---|
2540 | pEnlargeSet(&result->m,size,k-size); |
---|
2541 | IDELEMS(result) = k; |
---|
2542 | return (result); |
---|
2543 | } |
---|
2544 | #else |
---|
2545 | /*2 |
---|
2546 | * compute all ar-minors of the matrix a |
---|
2547 | * the caller of idRecMin |
---|
2548 | */ |
---|
2549 | ideal idMinors(matrix a, int ar) |
---|
2550 | { |
---|
2551 | if((ar<=0) || (ar>min(a->ncols,a->nrows))) |
---|
2552 | { |
---|
2553 | Werror("%d-th minor, matrix is %dx%d",ar,a->ncols,a->nrows); |
---|
2554 | return NULL; |
---|
2555 | } |
---|
2556 | int i=0; |
---|
2557 | poly barDiv=NULL; |
---|
2558 | ideal result=idInit(16,1); |
---|
2559 | if (a->ncols>=a->nrows) |
---|
2560 | { |
---|
2561 | idRecMin(mpCopy(a),ar-1,&barDiv,result,&i); |
---|
2562 | } |
---|
2563 | else |
---|
2564 | { |
---|
2565 | idRecMin(mpTransp(a),ar-1,&barDiv,result,&i); |
---|
2566 | } |
---|
2567 | idSkipZeroes(result); |
---|
2568 | return result; |
---|
2569 | } |
---|
2570 | #endif |
---|
2571 | |
---|
2572 | |
---|
2573 | /*2 |
---|
2574 | *returns TRUE if p is a unit element in the current ring |
---|
2575 | */ |
---|
2576 | BOOLEAN pIsUnit(poly p) |
---|
2577 | { |
---|
2578 | int i; |
---|
2579 | |
---|
2580 | if (p == NULL) return FALSE; |
---|
2581 | i = 1; |
---|
2582 | while (i<=pVariables && pGetExp(p,i) == 0) i++; |
---|
2583 | if (i > pVariables && (pGetComp(p) == 0)) |
---|
2584 | { |
---|
2585 | if (currRing->OrdSgn == 1 && pNext(p) !=NULL) return FALSE; |
---|
2586 | return TRUE; |
---|
2587 | } |
---|
2588 | return FALSE; |
---|
2589 | } |
---|
2590 | |
---|
2591 | /*2 |
---|
2592 | *skips all zeroes and double elements, searches also for units |
---|
2593 | */ |
---|
2594 | ideal idCompactify(ideal id) |
---|
2595 | { |
---|
2596 | int i,j; |
---|
2597 | BOOLEAN b=FALSE; |
---|
2598 | |
---|
2599 | i = IDELEMS(id)-1; |
---|
2600 | while ((! b) && (i>=0)) |
---|
2601 | { |
---|
2602 | b=pIsUnit(id->m[i]); |
---|
2603 | i--; |
---|
2604 | } |
---|
2605 | if (b) |
---|
2606 | { |
---|
2607 | ideal result=idInit(1,id->rank); |
---|
2608 | result->m[0]=pOne(); |
---|
2609 | return result; |
---|
2610 | } |
---|
2611 | else |
---|
2612 | { |
---|
2613 | ideal result=idCopy(id); |
---|
2614 | for (i=1;i<IDELEMS(result);i++) |
---|
2615 | { |
---|
2616 | if (result->m[i]!=NULL) |
---|
2617 | { |
---|
2618 | for (j=0;j<i;j++) |
---|
2619 | { |
---|
2620 | if ((result->m[j]!=NULL) |
---|
2621 | && (pComparePolys(result->m[i],result->m[j]))) |
---|
2622 | { |
---|
2623 | pDelete(&(result->m[j])); |
---|
2624 | } |
---|
2625 | } |
---|
2626 | } |
---|
2627 | } |
---|
2628 | idSkipZeroes(result); |
---|
2629 | return result; |
---|
2630 | } |
---|
2631 | } |
---|
2632 | |
---|
2633 | /*2 |
---|
2634 | *returns TRUE if id1 is a submodule of id2 |
---|
2635 | */ |
---|
2636 | BOOLEAN idIsSubModule(ideal id1,ideal id2) |
---|
2637 | { |
---|
2638 | int i; |
---|
2639 | poly p; |
---|
2640 | |
---|
2641 | if (idIs0(id1)) return TRUE; |
---|
2642 | for (i=0;i<IDELEMS(id1);i++) |
---|
2643 | { |
---|
2644 | if (id1->m[i] != NULL) |
---|
2645 | { |
---|
2646 | p = kNF(id2,currQuotient,id1->m[i]); |
---|
2647 | if (p != NULL) |
---|
2648 | { |
---|
2649 | pDelete(&p); |
---|
2650 | return FALSE; |
---|
2651 | } |
---|
2652 | } |
---|
2653 | } |
---|
2654 | return TRUE; |
---|
2655 | } |
---|
2656 | |
---|
2657 | /*2 |
---|
2658 | * returns the ideals of initial terms |
---|
2659 | */ |
---|
2660 | ideal idHead(ideal h) |
---|
2661 | { |
---|
2662 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
2663 | int i; |
---|
2664 | |
---|
2665 | for (i=IDELEMS(h)-1;i>=0; i--) |
---|
2666 | { |
---|
2667 | if (h->m[i]!=NULL) m->m[i]=pHead(h->m[i]); |
---|
2668 | } |
---|
2669 | return m; |
---|
2670 | } |
---|
2671 | |
---|
2672 | ideal idHomogen(ideal h, int varnum) |
---|
2673 | { |
---|
2674 | ideal m = idInit(IDELEMS(h),h->rank); |
---|
2675 | int i; |
---|
2676 | |
---|
2677 | for (i=IDELEMS(h)-1;i>=0; i--) |
---|
2678 | { |
---|
2679 | m->m[i]=pHomogen(h->m[i],varnum); |
---|
2680 | } |
---|
2681 | return m; |
---|
2682 | } |
---|
2683 | |
---|
2684 | /*------------------type conversions----------------*/ |
---|
2685 | ideal idVec2Ideal(poly vec) |
---|
2686 | { |
---|
2687 | ideal result=idInit(1,1); |
---|
2688 | Free((ADDRESS)result->m,sizeof(poly)); |
---|
2689 | result->m=NULL; // remove later |
---|
2690 | pVec2Polys(vec, &(result->m), &(IDELEMS(result))); |
---|
2691 | return result; |
---|
2692 | } |
---|
2693 | |
---|
2694 | ideal idMatrix2Module(matrix mat) |
---|
2695 | { |
---|
2696 | ideal result = idInit(MATCOLS(mat),MATROWS(mat)); |
---|
2697 | int i,j; |
---|
2698 | poly h; |
---|
2699 | #ifdef DRING |
---|
2700 | poly p; |
---|
2701 | #endif |
---|
2702 | |
---|
2703 | for(j=0;j<MATCOLS(mat);j++) /* j is also index in result->m */ |
---|
2704 | { |
---|
2705 | for (i=1;i<=MATROWS(mat);i++) |
---|
2706 | { |
---|
2707 | h = MATELEM(mat,i,j+1); |
---|
2708 | if (h!=NULL) |
---|
2709 | { |
---|
2710 | MATELEM(mat,i,j+1)=NULL; |
---|
2711 | pSetCompP(h,i); |
---|
2712 | #ifdef DRING |
---|
2713 | pdSetDFlagP(h,0); |
---|
2714 | #endif |
---|
2715 | result->m[j] = pAdd(result->m[j],h); |
---|
2716 | } |
---|
2717 | } |
---|
2718 | } |
---|
2719 | return result; |
---|
2720 | } |
---|
2721 | |
---|
2722 | /*2 |
---|
2723 | * converts a module into a matrix, destroyes the input |
---|
2724 | */ |
---|
2725 | matrix idModule2Matrix(ideal mod) |
---|
2726 | { |
---|
2727 | matrix result = mpNew(mod->rank,IDELEMS(mod)); |
---|
2728 | int i,cp; |
---|
2729 | poly p,h; |
---|
2730 | |
---|
2731 | for(i=0;i<IDELEMS(mod);i++) |
---|
2732 | { |
---|
2733 | p=mod->m[i]; |
---|
2734 | mod->m[i]=NULL; |
---|
2735 | while (p!=NULL) |
---|
2736 | { |
---|
2737 | h=p; |
---|
2738 | pIter(p); |
---|
2739 | pNext(h)=NULL; |
---|
2740 | // cp = max(1,pGetComp(h)); // if used for ideals too |
---|
2741 | cp = pGetComp(h); |
---|
2742 | pSetComp(h,0); |
---|
2743 | #ifdef TEST |
---|
2744 | if (cp>mod->rank) |
---|
2745 | { |
---|
2746 | Print("## inv. rank %d -> %d\n",mod->rank,cp); |
---|
2747 | int k,l,o=mod->rank; |
---|
2748 | mod->rank=cp; |
---|
2749 | matrix d=mpNew(mod->rank,IDELEMS(mod)); |
---|
2750 | for (l=1; l<=o; l++) |
---|
2751 | { |
---|
2752 | for (k=1; k<=IDELEMS(mod); k++) |
---|
2753 | { |
---|
2754 | MATELEM(d,l,k)=MATELEM(result,l,k); |
---|
2755 | MATELEM(result,l,k)=NULL; |
---|
2756 | } |
---|
2757 | } |
---|
2758 | idDelete((ideal *)&result); |
---|
2759 | result=d; |
---|
2760 | } |
---|
2761 | #endif |
---|
2762 | MATELEM(result,cp,i+1) = pAdd(MATELEM(result,cp,i+1),h); |
---|
2763 | } |
---|
2764 | } |
---|
2765 | return result; |
---|
2766 | } |
---|
2767 | |
---|
2768 | matrix idModule2formatedMatrix(ideal mod,int rows, int cols) |
---|
2769 | { |
---|
2770 | matrix result = mpNew(rows,cols); |
---|
2771 | int i,cp,r=idRankFreeModule(mod),c=IDELEMS(mod); |
---|
2772 | poly p,h; |
---|
2773 | |
---|
2774 | if (r>rows) r = rows; |
---|
2775 | if (c>cols) c = cols; |
---|
2776 | for(i=0;i<c;i++) |
---|
2777 | { |
---|
2778 | p=mod->m[i]; |
---|
2779 | mod->m[i]=NULL; |
---|
2780 | while (p!=NULL) |
---|
2781 | { |
---|
2782 | h=p; |
---|
2783 | pIter(p); |
---|
2784 | pNext(h)=NULL; |
---|
2785 | cp = pGetComp(h); |
---|
2786 | if (cp<=r) |
---|
2787 | { |
---|
2788 | pSetComp(h,0); |
---|
2789 | MATELEM(result,cp,i+1) = pAdd(MATELEM(result,cp,i+1),h); |
---|
2790 | } |
---|
2791 | else |
---|
2792 | pDelete(&h); |
---|
2793 | } |
---|
2794 | } |
---|
2795 | idDelete(&mod); |
---|
2796 | return result; |
---|
2797 | } |
---|
2798 | |
---|
2799 | /*2 |
---|
2800 | * substitute the n-th variable by the monomial e in id |
---|
2801 | * destroy id |
---|
2802 | */ |
---|
2803 | ideal idSubst(ideal id, int n, poly e) |
---|
2804 | { |
---|
2805 | int k=MATROWS((matrix)id)*MATCOLS((matrix)id); |
---|
2806 | ideal res=(ideal)mpNew(MATROWS((matrix)id),MATCOLS((matrix)id)); |
---|
2807 | |
---|
2808 | res->rank = id->rank; |
---|
2809 | for(k--;k>=0;k--) |
---|
2810 | { |
---|
2811 | res->m[k]=pSubst(id->m[k],n,e); |
---|
2812 | id->m[k]=NULL; |
---|
2813 | } |
---|
2814 | idDelete(&id); |
---|
2815 | return res; |
---|
2816 | } |
---|
2817 | |
---|
2818 | BOOLEAN idHomModule(ideal m, ideal Q, intvec **w) |
---|
2819 | { |
---|
2820 | if (w!=NULL) *w=NULL; |
---|
2821 | if ((Q!=NULL) && (!idHomIdeal(Q,NULL))) return FALSE; |
---|
2822 | if (idIs0(m)) return TRUE; |
---|
2823 | |
---|
2824 | int i,j,cmax=2,order=0,ord,* diff,* iscom,diffmin=32000; |
---|
2825 | poly p=NULL; |
---|
2826 | int length=IDELEMS(m); |
---|
2827 | polyset P=m->m; |
---|
2828 | polyset F=(polyset)Alloc(length*sizeof(poly)); |
---|
2829 | for (i=length-1;i>=0;i--) |
---|
2830 | { |
---|
2831 | p=F[i]=P[i]; |
---|
2832 | cmax=max(cmax,pMaxComp(p)+1); |
---|
2833 | } |
---|
2834 | diff = (int *)Alloc0(cmax*sizeof(int)); |
---|
2835 | if (w!=NULL) *w=new intvec(cmax-1); |
---|
2836 | iscom = (int *)Alloc0(cmax*sizeof(int)); |
---|
2837 | i=0; |
---|
2838 | while (i<=length) |
---|
2839 | { |
---|
2840 | if (i<length) |
---|
2841 | { |
---|
2842 | p=F[i]; |
---|
2843 | while ((p!=NULL) && (!iscom[pGetComp(p)])) pIter(p); |
---|
2844 | } |
---|
2845 | if ((p==NULL) && (i<length)) |
---|
2846 | { |
---|
2847 | i++; |
---|
2848 | } |
---|
2849 | else |
---|
2850 | { |
---|
2851 | if (p==NULL) |
---|
2852 | { |
---|
2853 | i=0; |
---|
2854 | while ((i<length) && (F[i]==NULL)) i++; |
---|
2855 | if (i>=length) break; |
---|
2856 | p = F[i]; |
---|
2857 | } |
---|
2858 | if (pLexOrder) |
---|
2859 | order=pTotaldegree(p); |
---|
2860 | else |
---|
2861 | // order = p->order; |
---|
2862 | order = pFDeg(p); |
---|
2863 | order += diff[pGetComp(p)]; |
---|
2864 | p = F[i]; |
---|
2865 | //Print("Actual p=F[%d]: ",i);pWrite(p); |
---|
2866 | F[i] = NULL; |
---|
2867 | i=0; |
---|
2868 | } |
---|
2869 | while (p!=NULL) |
---|
2870 | { |
---|
2871 | //if (pLexOrder) |
---|
2872 | // ord=pTotaldegree(p); |
---|
2873 | //else |
---|
2874 | // ord = p->order; |
---|
2875 | ord = pFDeg(p); |
---|
2876 | if (!iscom[pGetComp(p)]) |
---|
2877 | { |
---|
2878 | diff[pGetComp(p)] = order-ord; |
---|
2879 | iscom[pGetComp(p)] = 1; |
---|
2880 | /* |
---|
2881 | *PrintS("new diff: "); |
---|
2882 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
2883 | *PrintLn(); |
---|
2884 | *PrintS("new iscom: "); |
---|
2885 | *for (j=0;j<cmax;j++) Print("%d ",iscom[j]); |
---|
2886 | *PrintLn(); |
---|
2887 | *Print("new set %d, order %d, ord %d, diff %d\n",pGetComp(p),order,ord,diff[pGetComp(p)]); |
---|
2888 | */ |
---|
2889 | } |
---|
2890 | else |
---|
2891 | { |
---|
2892 | /* |
---|
2893 | *PrintS("new diff: "); |
---|
2894 | *for (j=0;j<cmax;j++) Print("%d ",diff[j]); |
---|
2895 | *PrintLn(); |
---|
2896 | *Print("order %d, ord %d, diff %d\n",order,ord,diff[pGetComp(p)]); |
---|
2897 | */ |
---|
2898 | if (order != ord+diff[pGetComp(p)]) |
---|
2899 | { |
---|
2900 | Free((ADDRESS) iscom,cmax*sizeof(int)); |
---|
2901 | Free((ADDRESS) diff,cmax*sizeof(int)); |
---|
2902 | Free((ADDRESS) F,length*sizeof(poly)); |
---|
2903 | delete *w;*w=NULL; |
---|
2904 | return FALSE; |
---|
2905 | } |
---|
2906 | } |
---|
2907 | pIter(p); |
---|
2908 | } |
---|
2909 | } |
---|
2910 | Free((ADDRESS) iscom,cmax*sizeof(int)); |
---|
2911 | Free((ADDRESS) F,length*sizeof(poly)); |
---|
2912 | for (i=1;i<cmax;i++) (**w)[i-1]=diff[i]; |
---|
2913 | for (i=1;i<cmax;i++) |
---|
2914 | { |
---|
2915 | if (diff[i]<diffmin) diffmin=diff[i]; |
---|
2916 | } |
---|
2917 | for (i=1;i<cmax;i++) |
---|
2918 | { |
---|
2919 | (**w)[i-1]=diff[i]-diffmin; |
---|
2920 | } |
---|
2921 | Free((ADDRESS) diff,cmax*sizeof(int)); |
---|
2922 | return TRUE; |
---|
2923 | } |
---|
2924 | |
---|
2925 | ideal idJet(ideal i,int d) |
---|
2926 | { |
---|
2927 | ideal r=idInit((i->nrows)*(i->ncols),i->rank); |
---|
2928 | r->nrows = i-> nrows; |
---|
2929 | r->ncols = i-> ncols; |
---|
2930 | //r->rank = i-> rank; |
---|
2931 | int k; |
---|
2932 | for(k=(i->nrows)*(i->ncols)-1;k>=0; k--) |
---|
2933 | { |
---|
2934 | r->m[k]=pJet(i->m[k],d); |
---|
2935 | } |
---|
2936 | return r; |
---|
2937 | } |
---|
2938 | |
---|
2939 | ideal idJetW(ideal i,int d, intvec * iv) |
---|
2940 | { |
---|
2941 | ideal r=idInit(IDELEMS(i),i->rank); |
---|
2942 | if (ecartWeights!=NULL) |
---|
2943 | { |
---|
2944 | WerrorS("cannot compute weighted jets now"); |
---|
2945 | } |
---|
2946 | else |
---|
2947 | { |
---|
2948 | short *w=iv2array(iv); |
---|
2949 | int k; |
---|
2950 | for(k=0; k<IDELEMS(i); k++) |
---|
2951 | { |
---|
2952 | r->m[k]=pJetW(i->m[k],d,w); |
---|
2953 | } |
---|
2954 | Free((ADDRESS)w,(pVariables+1)*sizeof(short)); |
---|
2955 | } |
---|
2956 | return r; |
---|
2957 | } |
---|
2958 | |
---|
2959 | matrix idDiff(matrix i, int k) |
---|
2960 | { |
---|
2961 | int e=MATCOLS(i)*MATROWS(i); |
---|
2962 | matrix r=mpNew(MATROWS(i),MATCOLS(i)); |
---|
2963 | int j; |
---|
2964 | for(j=0; j<e; j++) |
---|
2965 | { |
---|
2966 | r->m[j]=pDiff(i->m[j],k); |
---|
2967 | } |
---|
2968 | return r; |
---|
2969 | } |
---|
2970 | |
---|
2971 | matrix idDiffOp(ideal I, ideal J,BOOLEAN multiply) |
---|
2972 | { |
---|
2973 | matrix r=mpNew(IDELEMS(I),IDELEMS(J)); |
---|
2974 | int i,j; |
---|
2975 | for(i=0; i<IDELEMS(I); i++) |
---|
2976 | { |
---|
2977 | for(j=0; j<IDELEMS(J); j++) |
---|
2978 | { |
---|
2979 | MATELEM(r,i+1,j+1)=pDiffOp(I->m[i],J->m[j],multiply); |
---|
2980 | } |
---|
2981 | } |
---|
2982 | return r; |
---|
2983 | } |
---|
2984 | |
---|
2985 | /*2 |
---|
2986 | * represents (h1+h2)/h2=h1/(h1 intersect h2) |
---|
2987 | */ |
---|
2988 | ideal idModulo (ideal h2,ideal h1) |
---|
2989 | { |
---|
2990 | ideal temp,temp1; |
---|
2991 | int i,j,k,rk,flength=0,slength,length; |
---|
2992 | intvec * w; |
---|
2993 | poly p,q; |
---|
2994 | |
---|
2995 | if (idIs0(h2)) |
---|
2996 | return idFreeModule(max(1,h2->ncols)); |
---|
2997 | if (!idIs0(h1)) |
---|
2998 | flength = idRankFreeModule(h1); |
---|
2999 | slength = idRankFreeModule(h2); |
---|
3000 | length = max(flength,slength); |
---|
3001 | if (length==0) |
---|
3002 | { |
---|
3003 | length = 1; |
---|
3004 | } |
---|
3005 | temp = idInit(IDELEMS(h2),1); |
---|
3006 | for (i=0;i<IDELEMS(h2);i++) |
---|
3007 | { |
---|
3008 | temp->m[i] = pCopy(h2->m[i]); |
---|
3009 | q = pOne(); |
---|
3010 | pSetComp(q,i+1+length); |
---|
3011 | if(temp->m[i]!=NULL) |
---|
3012 | { |
---|
3013 | if (slength==0) pShift(&(temp->m[i]),1); |
---|
3014 | p = temp->m[i]; |
---|
3015 | while (pNext(p)!=NULL) pIter(p); |
---|
3016 | pNext(p) = q; |
---|
3017 | } |
---|
3018 | else |
---|
3019 | temp->m[i]=q; |
---|
3020 | } |
---|
3021 | rk = k = IDELEMS(h2); |
---|
3022 | if (!idIs0(h1)) |
---|
3023 | { |
---|
3024 | pEnlargeSet(&(temp->m),IDELEMS(temp),IDELEMS(h1)); |
---|
3025 | IDELEMS(temp) += IDELEMS(h1); |
---|
3026 | for (i=0;i<IDELEMS(h1);i++) |
---|
3027 | { |
---|
3028 | if (h1->m[i]!=NULL) |
---|
3029 | { |
---|
3030 | temp->m[k] = pCopy(h1->m[i]); |
---|
3031 | if (flength==0) pShift(&(temp->m[k]),1); |
---|
3032 | k++; |
---|
3033 | } |
---|
3034 | } |
---|
3035 | } |
---|
3036 | pSetSyzComp(length); |
---|
3037 | temp1 = kStd(temp,currQuotient,testHomog,&w,NULL,length); |
---|
3038 | pSetSyzComp(0); |
---|
3039 | idDelete(&temp); |
---|
3040 | if (w!=NULL) delete w; |
---|
3041 | for (i=0;i<IDELEMS(temp1);i++) |
---|
3042 | { |
---|
3043 | if ((temp1->m[i]!=NULL) |
---|
3044 | && (pGetComp(temp1->m[i])<=length)) |
---|
3045 | { |
---|
3046 | pDelete(&(temp1->m[i])); |
---|
3047 | } |
---|
3048 | else |
---|
3049 | { |
---|
3050 | pShift(&(temp1->m[i]),-length); |
---|
3051 | } |
---|
3052 | } |
---|
3053 | idSkipZeroes(temp1); |
---|
3054 | temp1->rank = rk; |
---|
3055 | return temp1; |
---|
3056 | } |
---|
3057 | |
---|
3058 | int idElem(ideal F) |
---|
3059 | { |
---|
3060 | int i=0,j=0; |
---|
3061 | |
---|
3062 | while(j<IDELEMS(F)) |
---|
3063 | { |
---|
3064 | if ((F->m)[j]!=NULL) i++; |
---|
3065 | j++; |
---|
3066 | } |
---|
3067 | return i; |
---|
3068 | } |
---|
3069 | |
---|
3070 | /* |
---|
3071 | *computes module-weights for liftings of homogeneous modules |
---|
3072 | */ |
---|
3073 | intvec * idMWLift(ideal mod,intvec * weights) |
---|
3074 | { |
---|
3075 | if (idIs0(mod)) return new intvec(2); |
---|
3076 | int i=IDELEMS(mod); |
---|
3077 | while ((i>0) && (mod->m[i-1]==NULL)) i--; |
---|
3078 | intvec *result = new intvec(i+1); |
---|
3079 | while (i>0) |
---|
3080 | { |
---|
3081 | (*result)[i]=pFDeg(mod->m[i])+(*weights)[pGetComp(mod->m[i])]; |
---|
3082 | } |
---|
3083 | return result; |
---|
3084 | } |
---|
3085 | |
---|
3086 | /*2 |
---|
3087 | *sorts the kbase for idCoef* in a special way (lexicographically |
---|
3088 | *with x_max,...,x_1) |
---|
3089 | */ |
---|
3090 | ideal idCreateSpecialKbase(ideal kBase,intvec ** convert) |
---|
3091 | { |
---|
3092 | int i; |
---|
3093 | ideal result; |
---|
3094 | |
---|
3095 | if (idIs0(kBase)) return NULL; |
---|
3096 | result = idInit(IDELEMS(kBase),kBase->rank); |
---|
3097 | *convert = idSort(kBase,FALSE); |
---|
3098 | for (i=0;i<(*convert)->length();i++) |
---|
3099 | { |
---|
3100 | result->m[i] = pCopy(kBase->m[(**convert)[i]-1]); |
---|
3101 | } |
---|
3102 | return result; |
---|
3103 | } |
---|
3104 | |
---|
3105 | /*2 |
---|
3106 | *returns the index of a given monom in the list of the special kbase |
---|
3107 | */ |
---|
3108 | int idIndexOfKBase(poly monom, ideal kbase) |
---|
3109 | { |
---|
3110 | int j=IDELEMS(kbase); |
---|
3111 | |
---|
3112 | while ((j>0) && (kbase->m[j-1]==NULL)) j--; |
---|
3113 | if (j==0) return -1; |
---|
3114 | int i=pVariables; |
---|
3115 | while (i>0) |
---|
3116 | { |
---|
3117 | loop |
---|
3118 | { |
---|
3119 | if (pGetExp(monom,i)>pGetExp(kbase->m[j-1],i)) return -1; |
---|
3120 | if (pGetExp(monom,i)==pGetExp(kbase->m[j-1],i)) break; |
---|
3121 | j--; |
---|
3122 | if (j==0) return -1; |
---|
3123 | } |
---|
3124 | if (i==1) |
---|
3125 | { |
---|
3126 | while(j>0) |
---|
3127 | { |
---|
3128 | if (pGetComp(monom)==pGetComp(kbase->m[j-1])) return j-1; |
---|
3129 | if (pGetComp(monom)>pGetComp(kbase->m[j-1])) return -1; |
---|
3130 | j--; |
---|
3131 | } |
---|
3132 | } |
---|
3133 | i--; |
---|
3134 | } |
---|
3135 | return -1; |
---|
3136 | } |
---|
3137 | |
---|
3138 | /*2 |
---|
3139 | *decomposes the monom in a part of coefficients described by the |
---|
3140 | *complement of how and a monom in variables occuring in how, the |
---|
3141 | *index of which in kbase is returned as integer pos (-1 if it don't |
---|
3142 | *exists) |
---|
3143 | */ |
---|
3144 | poly idDecompose(poly monom, poly how, ideal kbase, int * pos) |
---|
3145 | { |
---|
3146 | int i; |
---|
3147 | poly coeff=pOne(), base=pOne(); |
---|
3148 | |
---|
3149 | for (i=1;i<=pVariables;i++) |
---|
3150 | { |
---|
3151 | if (pGetExp(how,i)>0) |
---|
3152 | { |
---|
3153 | pSetExp(base,i,pGetExp(monom,i)); |
---|
3154 | } |
---|
3155 | else |
---|
3156 | { |
---|
3157 | pSetExp(coeff,i,pGetExp(monom,i)); |
---|
3158 | } |
---|
3159 | } |
---|
3160 | pSetComp(base,pGetComp(monom)); |
---|
3161 | pSetm(base); |
---|
3162 | pSetCoeff(coeff,nCopy(pGetCoeff(monom))); |
---|
3163 | pSetm(coeff); |
---|
3164 | *pos = idIndexOfKBase(base,kbase); |
---|
3165 | if (*pos<0) |
---|
3166 | pDelete(&coeff); |
---|
3167 | pDelete(&base); |
---|
3168 | return coeff; |
---|
3169 | } |
---|
3170 | |
---|
3171 | /*2 |
---|
3172 | *returns a matrix A of coefficients with kbase*A=arg |
---|
3173 | *if all monomials in variables of how occur in kbase |
---|
3174 | *the other are deleted |
---|
3175 | */ |
---|
3176 | matrix idCoeffOfKBase(ideal arg, ideal kbase, poly how) |
---|
3177 | { |
---|
3178 | matrix result; |
---|
3179 | ideal tempKbase; |
---|
3180 | poly p,q; |
---|
3181 | intvec * convert; |
---|
3182 | int i=IDELEMS(kbase),j=IDELEMS(arg),k,pos; |
---|
3183 | #if 0 |
---|
3184 | while ((i>0) && (kbase->m[i-1]==NULL)) i--; |
---|
3185 | if (idIs0(arg)) |
---|
3186 | return mpNew(i,1); |
---|
3187 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
3188 | result = mpNew(i,j); |
---|
3189 | #else |
---|
3190 | result = mpNew(i, j); |
---|
3191 | while ((j>0) && (arg->m[j-1]==NULL)) j--; |
---|
3192 | #endif |
---|
3193 | |
---|
3194 | tempKbase = idCreateSpecialKbase(kbase,&convert); |
---|
3195 | for (k=0;k<j;k++) |
---|
3196 | { |
---|
3197 | p = arg->m[k]; |
---|
3198 | while (p!=NULL) |
---|
3199 | { |
---|
3200 | q = idDecompose(p,how,tempKbase,&pos); |
---|
3201 | if (pos>=0) |
---|
3202 | { |
---|
3203 | MATELEM(result,(*convert)[pos],k+1) = |
---|
3204 | pAdd(MATELEM(result,(*convert)[pos],k+1),q); |
---|
3205 | } |
---|
3206 | else |
---|
3207 | pDelete(&q); |
---|
3208 | pIter(p); |
---|
3209 | } |
---|
3210 | } |
---|
3211 | idDelete(&tempKbase); |
---|
3212 | return result; |
---|
3213 | } |
---|
3214 | |
---|
3215 | intvec * idQHomWeights(ideal id) |
---|
3216 | { |
---|
3217 | intvec * imat=new intvec(2*pVariables,pVariables,0); |
---|
3218 | poly actHead=NULL,wPoint=NULL; |
---|
3219 | int actIndex,i=-1,j=1,k; |
---|
3220 | BOOLEAN notReady=TRUE; |
---|
3221 | |
---|
3222 | while (notReady) |
---|
3223 | { |
---|
3224 | if (wPoint==NULL) |
---|
3225 | { |
---|
3226 | i++; |
---|
3227 | while ((i<IDELEMS(id)) |
---|
3228 | && ((id->m[i]==NULL) || (pNext(id->m[i])==NULL))) |
---|
3229 | i++; |
---|
3230 | if (i<IDELEMS(id)) |
---|
3231 | { |
---|
3232 | actHead = id->m[i]; |
---|
3233 | wPoint = pNext(actHead); |
---|
3234 | } |
---|
3235 | } |
---|
3236 | while ((wPoint!=NULL) && (j<=2*pVariables)) |
---|
3237 | { |
---|
3238 | for (k=1;k<=pVariables;k++) |
---|
3239 | IMATELEM(*imat,j,k) += pGetExp(actHead,k)-pGetExp(wPoint,k); |
---|
3240 | pIter(wPoint); |
---|
3241 | j++; |
---|
3242 | } |
---|
3243 | if ((i>=IDELEMS(id)) || (j>2*pVariables)) |
---|
3244 | { |
---|
3245 | ivTriangMat(imat,1,1); |
---|
3246 | j = ivFirstEmptyRow(imat); |
---|
3247 | if ((i>=IDELEMS(id)) || (j>pVariables)) notReady=FALSE; |
---|
3248 | } |
---|
3249 | } |
---|
3250 | intvec *result=NULL; |
---|
3251 | if (j<=pVariables) |
---|
3252 | { |
---|
3253 | result=ivSolveIntMat(imat); |
---|
3254 | } |
---|
3255 | //else |
---|
3256 | //{ |
---|
3257 | // WerrorS("not homogeneous"); |
---|
3258 | //} |
---|
3259 | delete imat; |
---|
3260 | return result; |
---|
3261 | } |
---|
3262 | |
---|
3263 | /*2 |
---|
3264 | * returns the presentation of an isomorphic, minimally |
---|
3265 | * embedded module |
---|
3266 | */ |
---|
3267 | ideal idMinEmbedding(ideal arg) |
---|
3268 | { |
---|
3269 | if (idIs0(arg)) return idInit(1,arg->rank); |
---|
3270 | |
---|
3271 | int i,j,k,pC; |
---|
3272 | poly p,q; |
---|
3273 | int rg=arg->rank; |
---|
3274 | ideal res = idCopy(arg); |
---|
3275 | intvec *indexMap=new intvec(rg+1); |
---|
3276 | intvec *toKill=new intvec(rg+1); |
---|
3277 | |
---|
3278 | loop |
---|
3279 | { |
---|
3280 | k = 0; |
---|
3281 | for (i=indexMap->length()-1;i>0;i--) |
---|
3282 | { |
---|
3283 | (*indexMap)[i] = i; |
---|
3284 | (*toKill)[i] = 0; |
---|
3285 | } |
---|
3286 | for (j=IDELEMS(res)-1;j>=0;j--) |
---|
3287 | { |
---|
3288 | if ((res->m[j]!=NULL) && (pIsConstantComp(res->m[j])) && |
---|
3289 | (pNext(res->m[j])==NULL)) |
---|
3290 | { |
---|
3291 | pC = pGetComp(res->m[j]); |
---|
3292 | if ((*toKill)[pC]==0) |
---|
3293 | { |
---|
3294 | rg--; |
---|
3295 | (*toKill)[pC] = 1; |
---|
3296 | for (i=indexMap->length()-1;i>=pC;i--) |
---|
3297 | (*indexMap)[i]--; |
---|
3298 | } |
---|
3299 | pDelete(&(res->m[j])); |
---|
3300 | k++; |
---|
3301 | } |
---|
3302 | } |
---|
3303 | idSkipZeroes(res); |
---|
3304 | if (k==0) break; |
---|
3305 | if (rg>0) |
---|
3306 | { |
---|
3307 | res->rank=rg; |
---|
3308 | for (j=IDELEMS(res)-1;j>=0;j--) |
---|
3309 | { |
---|
3310 | while ((res->m[j]!=NULL) && ((*toKill)[pGetComp(res->m[j])]==1)) |
---|
3311 | pDelete1(&res->m[j]); |
---|
3312 | p = res->m[j]; |
---|
3313 | while ((p!=NULL) && (pNext(p)!=NULL)) |
---|
3314 | { |
---|
3315 | pSetComp(p,(*indexMap)[pGetComp(p)]); |
---|
3316 | while ((pNext(p)!=NULL) && ((*toKill)[pGetComp(pNext(p))]==1)) |
---|
3317 | pDelete1(&pNext(p)); |
---|
3318 | pIter(p); |
---|
3319 | } |
---|
3320 | if (p!=NULL) pSetComp(p,(*indexMap)[pGetComp(p)]); |
---|
3321 | } |
---|
3322 | idSkipZeroes(res); |
---|
3323 | } |
---|
3324 | else |
---|
3325 | { |
---|
3326 | idDelete(&res); |
---|
3327 | res=idFreeModule(1); |
---|
3328 | break; |
---|
3329 | } |
---|
3330 | } |
---|
3331 | delete toKill; |
---|
3332 | delete indexMap; |
---|
3333 | return res; |
---|
3334 | } |
---|
3335 | |
---|
3336 | /*2 |
---|
3337 | * transpose a module |
---|
3338 | */ |
---|
3339 | ideal idTransp(ideal a) |
---|
3340 | { |
---|
3341 | int r = a->rank, c = IDELEMS(a); |
---|
3342 | ideal b = idInit(r,c); |
---|
3343 | |
---|
3344 | for (int i=c; i>0; i--) |
---|
3345 | { |
---|
3346 | poly p=a->m[i-1]; |
---|
3347 | while(p!=NULL) |
---|
3348 | { |
---|
3349 | poly h=pHead(p); |
---|
3350 | int co=pGetComp(h)-1; |
---|
3351 | pSetComp(h,i); |
---|
3352 | b->m[co]=pAdd(b->m[co],h); |
---|
3353 | pIter(p); |
---|
3354 | } |
---|
3355 | } |
---|
3356 | return b; |
---|
3357 | } |
---|
3358 | |
---|