1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | |
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5 | /* |
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6 | * ABSTRACT: operations with sparse matrices (bareiss, ...) |
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7 | */ |
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8 | |
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9 | #include <misc/auxiliary.h> |
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10 | |
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11 | #include <omalloc/omalloc.h> |
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12 | #include <misc/mylimits.h> |
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13 | |
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14 | #include <misc/options.h> |
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15 | |
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16 | #include <reporter/reporter.h> |
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17 | #include <misc/intvec.h> |
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18 | |
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19 | #include <coeffs/numbers.h> |
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20 | |
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21 | #include "monomials/ring.h" |
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22 | #include "monomials/p_polys.h" |
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23 | |
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24 | #include "simpleideals.h" |
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25 | |
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26 | #include "sparsmat.h" |
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27 | #include "prCopy.h" |
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28 | |
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29 | #include "templates/p_Procs.h" |
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30 | |
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31 | #include "kbuckets.h" |
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32 | #include "operations/p_Mult_q.h" |
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33 | |
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34 | // define SM_NO_BUCKETS, if sparsemat stuff should not use buckets |
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35 | // #define SM_NO_BUCKETS |
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36 | |
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37 | // this is also influenced by TEST_OPT_NOTBUCKETS |
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38 | #ifndef SM_NO_BUCKETS |
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39 | // buckets do carry a small additional overhead: only use them if |
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40 | // min-length of polys is >= SM_MIN_LENGTH_BUCKET |
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41 | #define SM_MIN_LENGTH_BUCKET MIN_LENGTH_BUCKET - 5 |
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42 | #else |
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43 | #define SM_MIN_LENGTH_BUCKET MAX_INT_VAL |
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44 | #endif |
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45 | |
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46 | typedef struct smprec sm_prec; |
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47 | typedef sm_prec * smpoly; |
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48 | struct smprec |
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49 | { |
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50 | smpoly n; // the next element |
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51 | int pos; // position |
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52 | int e; // level |
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53 | poly m; // the element |
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54 | float f; // complexity of the element |
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55 | }; |
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56 | |
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57 | |
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58 | /* declare internal 'C' stuff */ |
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59 | static void sm_ExactPolyDiv(poly, poly, const ring); |
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60 | static BOOLEAN sm_IsNegQuot(poly, const poly, const poly, const ring); |
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61 | static void sm_ExpMultDiv(poly, const poly, const poly, const ring); |
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62 | static void sm_PolyDivN(poly, const number, const ring); |
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63 | static BOOLEAN smSmaller(poly, poly); |
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64 | static void sm_CombineChain(poly *, poly, const ring); |
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65 | static void sm_FindRef(poly *, poly *, poly, const ring); |
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66 | |
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67 | static void sm_ElemDelete(smpoly *, const ring); |
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68 | static smpoly smElemCopy(smpoly); |
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69 | static float sm_PolyWeight(smpoly, const ring); |
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70 | static smpoly sm_Poly2Smpoly(poly, const ring); |
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71 | static poly sm_Smpoly2Poly(smpoly, const ring); |
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72 | static BOOLEAN sm_HaveDenom(poly, const ring); |
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73 | static number sm_Cleardenom(ideal, const ring); |
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74 | |
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75 | omBin smprec_bin = omGetSpecBin(sizeof(smprec)); |
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76 | |
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77 | static poly pp_Mult_Coeff_mm_DivSelect_MultDiv(poly p, int &lp, poly m, |
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78 | poly a, poly b, const ring currRing) |
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79 | { |
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80 | if (rOrd_is_Comp_dp(currRing) && currRing->ExpL_Size > 2) |
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81 | { |
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82 | // pp_Mult_Coeff_mm_DivSelectMult only works for (c/C,dp) and |
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83 | // ExpL_Size > 2 |
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84 | // should be generalized, at least to dp with ExpL_Size == 2 |
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85 | // (is the case for 1 variable) |
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86 | int shorter; |
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87 | p = currRing->p_Procs->pp_Mult_Coeff_mm_DivSelectMult(p, m, a, b, |
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88 | shorter, currRing); |
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89 | lp -= shorter; |
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90 | } |
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91 | else |
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92 | { |
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93 | p = pp_Mult_Coeff_mm_DivSelect(p, lp, m, currRing); |
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94 | sm_ExpMultDiv(p, a, b, currRing); |
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95 | } |
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96 | return p; |
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97 | } |
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98 | |
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99 | static poly sm_SelectCopy_ExpMultDiv(poly p, poly m, poly a, poly b, const ring currRing) |
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100 | { |
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101 | int lp = 0; |
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102 | return pp_Mult_Coeff_mm_DivSelect_MultDiv(p, lp, m, a, b, currRing); |
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103 | } |
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104 | |
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105 | |
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106 | /* class for sparse matrix: |
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107 | * 3 parts of matrix during the algorithm |
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108 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
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109 | * input pivotcols as rows result |
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110 | * pivot like a stack from pivot and pivotcols |
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111 | * elimination rows reordered according |
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112 | * to pivot choise |
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113 | * stored in perm |
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114 | * a step is as follows |
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115 | * - search of pivot (smPivot) |
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116 | * - swap pivot column and last column (smSwapC) |
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117 | * select pivotrow to piv and red (smSelectPR) |
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118 | * consider sign |
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119 | * - elimination (smInitElim, sm0Elim, sm1Elim) |
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120 | * clear zero column as result of elimination (smZeroElim) |
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121 | * - tranfer from |
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122 | * piv and m_row to m_res (smRowToCol) |
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123 | * m_act to m_row (smColToRow) |
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124 | */ |
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125 | class sparse_mat{ |
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126 | private: |
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127 | int nrows, ncols; // dimension of the problem |
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128 | int sign; // for determinant (start: 1) |
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129 | int act; // number of unreduced columns (start: ncols) |
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130 | int crd; // number of reduced columns (start: 0) |
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131 | int tored; // border for rows to reduce |
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132 | int inred; // unreducable part |
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133 | int rpiv, cpiv; // position of the pivot |
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134 | int normalize; // Normalization flag |
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135 | int *perm; // permutation of rows |
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136 | float wpoints; // weight of all points |
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137 | float *wrw, *wcl; // weights of rows and columns |
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138 | smpoly * m_act; // unreduced columns |
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139 | smpoly * m_res; // reduced columns (result) |
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140 | smpoly * m_row; // reduced part of rows |
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141 | smpoly red; // row to reduce |
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142 | smpoly piv, oldpiv; // pivot and previous pivot |
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143 | smpoly dumm; // allocated dummy |
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144 | ring _R; |
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145 | |
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146 | void smColToRow(); |
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147 | void smRowToCol(); |
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148 | void smFinalMult(); |
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149 | void smSparseHomog(); |
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150 | void smWeights(); |
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151 | void smPivot(); |
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152 | void smNewWeights(); |
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153 | void smNewPivot(); |
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154 | void smZeroElim(); |
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155 | void smToredElim(); |
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156 | void smCopToRes(); |
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157 | void smSelectPR(); |
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158 | void sm1Elim(); |
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159 | void smHElim(); |
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160 | void smMultCol(); |
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161 | poly smMultPoly(smpoly); |
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162 | void smActDel(); |
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163 | void smColDel(); |
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164 | void smPivDel(); |
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165 | void smSign(); |
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166 | void smInitPerm(); |
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167 | int smCheckNormalize(); |
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168 | void smNormalize(); |
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169 | public: |
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170 | sparse_mat(ideal, const ring); |
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171 | ~sparse_mat(); |
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172 | int smGetSign() { return sign; } |
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173 | smpoly * smGetAct() { return m_act; } |
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174 | int smGetRed() { return tored; } |
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175 | ideal smRes2Mod(); |
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176 | poly smDet(); |
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177 | void smNewBareiss(int, int); |
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178 | void smToIntvec(intvec *); |
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179 | }; |
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180 | |
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181 | /* |
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182 | * estimate maximal exponent for det or minors, |
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183 | * the module m has di vectors and maximal rank ra, |
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184 | * estimate yields for the tXt minors, |
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185 | * we have di,ra >= t |
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186 | */ |
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187 | static void smMinSelect(long *, int, int); |
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188 | |
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189 | long sm_ExpBound( ideal m, int di, int ra, int t, const ring currRing) |
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190 | { |
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191 | poly p; |
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192 | long kr, kc; |
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193 | long *r, *c; |
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194 | int al, bl, i, j, k; |
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195 | |
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196 | if (ra==0) ra=1; |
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197 | al = di*sizeof(long); |
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198 | c = (long *)omAlloc(al); |
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199 | bl = ra*sizeof(long); |
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200 | r = (long *)omAlloc0(bl); |
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201 | for (i=di-1;i>=0;i--) |
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202 | { |
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203 | kc = 0; |
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204 | p = m->m[i]; |
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205 | while(p!=NULL) |
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206 | { |
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207 | k = p_GetComp(p, currRing)-1; |
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208 | kr = r[k]; |
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209 | for (j=currRing->N;j>0;j--) |
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210 | { |
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211 | long t=p_GetExp(p,j, currRing); |
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212 | if(t /*p_GetExp(p,j, currRing)*/ >kc) |
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213 | kc=t; /*p_GetExp(p,j, currRing);*/ |
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214 | if(t /*p_GetExp(p,j, currRing)s*/ >kr) |
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215 | kr=t; /*p_GetExp(p,j, currRing);*/ |
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216 | } |
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217 | r[k] = kr; |
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218 | pIter(p); |
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219 | } |
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220 | c[i] = kc; |
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221 | } |
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222 | if (t<di) smMinSelect(c, t, di); |
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223 | if (t<ra) smMinSelect(r, t, ra); |
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224 | kr = kc = 0; |
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225 | for (j=t-1;j>=0;j--) |
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226 | { |
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227 | kr += r[j]; |
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228 | kc += c[j]; |
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229 | } |
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230 | omFreeSize((ADDRESS)c, al); |
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231 | omFreeSize((ADDRESS)r, bl); |
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232 | if (kr<kc) kc = kr; |
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233 | if (kr<1) kr = 1; |
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234 | return kr; |
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235 | } |
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236 | |
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237 | static void smMinSelect(long *c, int t, int d) |
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238 | { |
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239 | long m; |
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240 | int pos, i; |
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241 | do |
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242 | { |
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243 | d--; |
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244 | pos = d; |
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245 | m = c[pos]; |
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246 | for (i=d-1;i>=0;i--) |
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247 | { |
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248 | if(c[i]<m) |
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249 | { |
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250 | pos = i; |
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251 | m = c[i]; |
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252 | } |
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253 | } |
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254 | for (i=pos;i<d;i++) c[i] = c[i+1]; |
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255 | } while (d>t); |
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256 | } |
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257 | |
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258 | /* ----------------- ops with rings ------------------ */ |
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259 | ring sm_RingChange(const ring origR, long bound) |
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260 | { |
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261 | // *origR =currRing; |
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262 | ring tmpR=rCopy0(origR,FALSE,FALSE); |
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263 | rRingOrder_t *ord=(rRingOrder_t*)omAlloc0(3*sizeof(rRingOrder_t)); |
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264 | int *block0=(int*)omAlloc(3*sizeof(int)); |
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265 | int *block1=(int*)omAlloc(3*sizeof(int)); |
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266 | ord[0]=ringorder_c; |
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267 | ord[1]=ringorder_dp; |
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268 | tmpR->order=ord; |
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269 | tmpR->OrdSgn=1; |
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270 | block0[1]=1; |
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271 | tmpR->block0=block0; |
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272 | block1[1]=tmpR->N; |
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273 | tmpR->block1=block1; |
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274 | tmpR->bitmask = 2*bound; |
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275 | tmpR->wvhdl = (int **)omAlloc0((3) * sizeof(int*)); |
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276 | |
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277 | // ??? |
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278 | // if (tmpR->bitmask > currRing->bitmask) tmpR->bitmask = currRing->bitmask; |
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279 | |
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280 | rComplete(tmpR,1); |
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281 | if (origR->qideal!=NULL) |
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282 | { |
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283 | tmpR->qideal= idrCopyR_NoSort(origR->qideal, origR, tmpR); |
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284 | } |
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285 | if (TEST_OPT_PROT) |
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286 | Print("[%ld:%d]", (long) tmpR->bitmask, tmpR->ExpL_Size); |
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287 | return tmpR; |
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288 | } |
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289 | |
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290 | void sm_KillModifiedRing(ring r) |
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291 | { |
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292 | if (r->qideal!=NULL) id_Delete(&(r->qideal),r); |
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293 | rKillModifiedRing(r); |
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294 | } |
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295 | |
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296 | /*2 |
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297 | * Bareiss or Chinese remainder ? |
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298 | * I is dXd |
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299 | * sw = TRUE -> I Matrix |
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300 | * FALSE -> I Module |
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301 | * return True -> change Type |
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302 | * FALSE -> same Type |
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303 | */ |
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304 | BOOLEAN sm_CheckDet(ideal I, int d, BOOLEAN sw, const ring r) |
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305 | { |
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306 | int s,t,i; |
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307 | poly p; |
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308 | |
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309 | if (d>100) |
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310 | return sw; |
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311 | if (!rField_is_Q(r)) |
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312 | return sw; |
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313 | s = t = 0; |
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314 | if (sw) |
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315 | { |
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316 | for(i=IDELEMS(I)-1;i>=0;i--) |
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317 | { |
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318 | p=I->m[i]; |
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319 | if (p!=NULL) |
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320 | { |
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321 | if(!p_IsConstant(p,r)) |
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322 | return sw; |
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323 | s++; |
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324 | t+=n_Size(pGetCoeff(p),r->cf); |
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325 | } |
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326 | } |
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327 | } |
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328 | else |
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329 | { |
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330 | for(i=IDELEMS(I)-1;i>=0;i--) |
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331 | { |
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332 | p=I->m[i]; |
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333 | if (!p_IsConstantPoly(p,r)) |
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334 | return sw; |
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335 | while (p!=NULL) |
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336 | { |
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337 | s++; |
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338 | t+=n_Size(pGetCoeff(p),r->cf); |
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339 | pIter(p); |
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340 | } |
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341 | } |
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342 | } |
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343 | s*=15; |
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344 | if (t>s) |
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345 | return !sw; |
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346 | else |
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347 | return sw; |
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348 | } |
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349 | |
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350 | /* ----------------- basics (used from 'C') ------------------ */ |
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351 | /*2 |
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352 | *returns the determinant of the module I; |
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353 | *uses Bareiss algorithm |
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354 | */ |
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355 | poly sm_CallDet(ideal I,const ring R) |
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356 | { |
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357 | if (I->ncols != I->rank) |
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358 | { |
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359 | Werror("det of %ld x %d module (matrix)",I->rank,I->ncols); |
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360 | return NULL; |
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361 | } |
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362 | int r=id_RankFreeModule(I,R); |
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363 | if (I->ncols != r) // some 0-lines at the end |
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364 | { |
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365 | return NULL; |
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366 | } |
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367 | long bound=sm_ExpBound(I,r,r,r,R); |
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368 | number diag,h=n_Init(1,R->cf); |
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369 | poly res; |
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370 | ring tmpR; |
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371 | sparse_mat *det; |
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372 | ideal II; |
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373 | |
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374 | tmpR=sm_RingChange(R,bound); |
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375 | II = idrCopyR(I, R, tmpR); |
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376 | diag = sm_Cleardenom(II,tmpR); |
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377 | det = new sparse_mat(II,tmpR); |
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378 | id_Delete(&II,tmpR); |
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379 | if (det->smGetAct() == NULL) |
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380 | { |
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381 | delete det; |
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382 | sm_KillModifiedRing(tmpR); |
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383 | return NULL; |
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384 | } |
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385 | res=det->smDet(); |
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386 | if(det->smGetSign()<0) res=p_Neg(res,tmpR); |
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387 | delete det; |
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388 | res = prMoveR(res, tmpR, R); |
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389 | sm_KillModifiedRing(tmpR); |
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390 | if (!n_Equal(diag,h,R->cf)) |
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391 | { |
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392 | p_Mult_nn(res,diag,R); |
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393 | p_Normalize(res,R); |
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394 | } |
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395 | n_Delete(&diag,R->cf); |
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396 | n_Delete(&h,R->cf); |
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397 | return res; |
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398 | } |
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399 | |
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400 | void sm_CallBareiss(ideal I, int x, int y, ideal & M, intvec **iv, const ring R) |
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401 | { |
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402 | int r=id_RankFreeModule(I,R),t=r; |
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403 | int c=IDELEMS(I),s=c; |
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404 | long bound; |
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405 | ring tmpR; |
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406 | sparse_mat *bareiss; |
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407 | |
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408 | if ((x>0) && (x<t)) |
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409 | t-=x; |
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410 | if ((y>1) && (y<s)) |
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411 | s-=y; |
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412 | if (t>s) t=s; |
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413 | bound=sm_ExpBound(I,c,r,t,R); |
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414 | tmpR=sm_RingChange(R,bound); |
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415 | ideal II = idrCopyR(I, R, tmpR); |
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416 | bareiss = new sparse_mat(II,tmpR); |
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417 | if (bareiss->smGetAct() == NULL) |
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418 | { |
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419 | delete bareiss; |
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420 | *iv=new intvec(1,rVar(tmpR)); |
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421 | } |
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422 | else |
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423 | { |
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424 | id_Delete(&II,tmpR); |
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425 | bareiss->smNewBareiss(x, y); |
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426 | II = bareiss->smRes2Mod(); |
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427 | *iv = new intvec(bareiss->smGetRed()); |
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428 | bareiss->smToIntvec(*iv); |
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429 | delete bareiss; |
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430 | II = idrMoveR(II,tmpR,R); |
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431 | } |
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432 | sm_KillModifiedRing(tmpR); |
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433 | M=II; |
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434 | } |
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435 | |
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436 | /* |
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437 | * constructor |
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438 | */ |
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439 | sparse_mat::sparse_mat(ideal smat, const ring RR) |
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440 | { |
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441 | int i; |
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442 | poly* pmat; |
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443 | _R=RR; |
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444 | |
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445 | ncols = smat->ncols; |
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446 | nrows = id_RankFreeModule(smat,RR); |
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447 | if (nrows <= 0) |
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448 | { |
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449 | m_act = NULL; |
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450 | return; |
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451 | } |
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452 | sign = 1; |
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453 | inred = act = ncols; |
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454 | crd = 0; |
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455 | tored = nrows; // without border |
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456 | i = tored+1; |
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457 | perm = (int *)omAlloc(sizeof(int)*(i+1)); |
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458 | perm[i] = 0; |
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459 | m_row = (smpoly *)omAlloc0(sizeof(smpoly)*i); |
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460 | wrw = (float *)omAlloc(sizeof(float)*i); |
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461 | i = ncols+1; |
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462 | wcl = (float *)omAlloc(sizeof(float)*i); |
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463 | m_act = (smpoly *)omAlloc(sizeof(smpoly)*i); |
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464 | m_res = (smpoly *)omAlloc0(sizeof(smpoly)*i); |
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465 | dumm = (smpoly)omAllocBin(smprec_bin); |
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466 | m_res[0] = (smpoly)omAllocBin(smprec_bin); |
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467 | m_res[0]->m = NULL; |
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468 | pmat = smat->m; |
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469 | for(i=ncols; i; i--) |
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470 | { |
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471 | m_act[i] = sm_Poly2Smpoly(pmat[i-1], RR); |
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472 | pmat[i-1] = NULL; |
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473 | } |
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474 | this->smZeroElim(); |
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475 | oldpiv = NULL; |
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476 | } |
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477 | |
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478 | /* |
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479 | * destructor |
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480 | */ |
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481 | sparse_mat::~sparse_mat() |
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482 | { |
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483 | int i; |
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484 | if (m_act == NULL) return; |
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485 | omFreeBin((ADDRESS)m_res[0], smprec_bin); |
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486 | omFreeBin((ADDRESS)dumm, smprec_bin); |
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487 | i = ncols+1; |
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488 | omFreeSize((ADDRESS)m_res, sizeof(smpoly)*i); |
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489 | omFreeSize((ADDRESS)m_act, sizeof(smpoly)*i); |
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490 | omFreeSize((ADDRESS)wcl, sizeof(float)*i); |
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491 | i = nrows+1; |
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492 | omFreeSize((ADDRESS)wrw, sizeof(float)*i); |
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493 | omFreeSize((ADDRESS)m_row, sizeof(smpoly)*i); |
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494 | omFreeSize((ADDRESS)perm, sizeof(int)*(i+1)); |
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495 | } |
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496 | |
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497 | /* |
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498 | * transform the result to a module |
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499 | */ |
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500 | |
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501 | ideal sparse_mat::smRes2Mod() |
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502 | { |
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503 | ideal res = idInit(crd, crd); |
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504 | int i; |
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505 | |
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506 | for (i=crd; i; i--) |
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507 | { |
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508 | res->m[i-1] = sm_Smpoly2Poly(m_res[i],_R); |
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509 | res->rank=si_max(res->rank, p_MaxComp(res->m[i-1],_R)); |
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510 | } |
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511 | return res; |
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512 | } |
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513 | |
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514 | /* |
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515 | * permutation of rows |
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516 | */ |
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517 | void sparse_mat::smToIntvec(intvec *v) |
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518 | { |
---|
519 | int i; |
---|
520 | |
---|
521 | for (i=v->rows()-1; i>=0; i--) |
---|
522 | (*v)[i] = perm[i+1]; |
---|
523 | } |
---|
524 | /* ---------------- the algorithm's ------------------ */ |
---|
525 | /* |
---|
526 | * the determinant (up to sign), uses new Bareiss elimination |
---|
527 | */ |
---|
528 | poly sparse_mat::smDet() |
---|
529 | { |
---|
530 | poly res = NULL; |
---|
531 | |
---|
532 | if (sign == 0) |
---|
533 | { |
---|
534 | this->smActDel(); |
---|
535 | return NULL; |
---|
536 | } |
---|
537 | if (act < 2) |
---|
538 | { |
---|
539 | if (act != 0) res = m_act[1]->m; |
---|
540 | omFreeBin((void *)m_act[1], smprec_bin); |
---|
541 | return res; |
---|
542 | } |
---|
543 | normalize = 0; |
---|
544 | this->smInitPerm(); |
---|
545 | this->smPivot(); |
---|
546 | this->smSign(); |
---|
547 | this->smSelectPR(); |
---|
548 | this->sm1Elim(); |
---|
549 | crd++; |
---|
550 | m_res[crd] = piv; |
---|
551 | this->smColDel(); |
---|
552 | act--; |
---|
553 | this->smZeroElim(); |
---|
554 | if (sign == 0) |
---|
555 | { |
---|
556 | this->smActDel(); |
---|
557 | return NULL; |
---|
558 | } |
---|
559 | if (act < 2) |
---|
560 | { |
---|
561 | this->smFinalMult(); |
---|
562 | this->smPivDel(); |
---|
563 | if (act != 0) res = m_act[1]->m; |
---|
564 | omFreeBin((void *)m_act[1], smprec_bin); |
---|
565 | return res; |
---|
566 | } |
---|
567 | loop |
---|
568 | { |
---|
569 | this->smNewPivot(); |
---|
570 | this->smSign(); |
---|
571 | this->smSelectPR(); |
---|
572 | this->smMultCol(); |
---|
573 | this->smHElim(); |
---|
574 | crd++; |
---|
575 | m_res[crd] = piv; |
---|
576 | this->smColDel(); |
---|
577 | act--; |
---|
578 | this->smZeroElim(); |
---|
579 | if (sign == 0) |
---|
580 | { |
---|
581 | this->smPivDel(); |
---|
582 | this->smActDel(); |
---|
583 | return NULL; |
---|
584 | } |
---|
585 | if (act < 2) |
---|
586 | { |
---|
587 | if (TEST_OPT_PROT) PrintS(".\n"); |
---|
588 | this->smFinalMult(); |
---|
589 | this->smPivDel(); |
---|
590 | if (act != 0) res = m_act[1]->m; |
---|
591 | omFreeBin((void *)m_act[1], smprec_bin); |
---|
592 | return res; |
---|
593 | } |
---|
594 | } |
---|
595 | } |
---|
596 | |
---|
597 | /* |
---|
598 | * the new Bareiss elimination: |
---|
599 | * - with x unreduced last rows, pivots from here are not allowed |
---|
600 | * - the method will finish for number of unreduced columns < y |
---|
601 | */ |
---|
602 | void sparse_mat::smNewBareiss(int x, int y) |
---|
603 | { |
---|
604 | if ((x > 0) && (x < nrows)) |
---|
605 | { |
---|
606 | tored -= x; |
---|
607 | this->smToredElim(); |
---|
608 | } |
---|
609 | if (y < 1) y = 1; |
---|
610 | if (act <= y) |
---|
611 | { |
---|
612 | this->smCopToRes(); |
---|
613 | return; |
---|
614 | } |
---|
615 | normalize = this->smCheckNormalize(); |
---|
616 | if (normalize) this->smNormalize(); |
---|
617 | this->smPivot(); |
---|
618 | this->smSelectPR(); |
---|
619 | this->sm1Elim(); |
---|
620 | crd++; |
---|
621 | this->smColToRow(); |
---|
622 | act--; |
---|
623 | this->smRowToCol(); |
---|
624 | this->smZeroElim(); |
---|
625 | if (tored != nrows) |
---|
626 | this->smToredElim(); |
---|
627 | if (act <= y) |
---|
628 | { |
---|
629 | this->smFinalMult(); |
---|
630 | this->smCopToRes(); |
---|
631 | return; |
---|
632 | } |
---|
633 | loop |
---|
634 | { |
---|
635 | if (normalize) this->smNormalize(); |
---|
636 | this->smNewPivot(); |
---|
637 | this->smSelectPR(); |
---|
638 | this->smMultCol(); |
---|
639 | this->smHElim(); |
---|
640 | crd++; |
---|
641 | this->smColToRow(); |
---|
642 | act--; |
---|
643 | this->smRowToCol(); |
---|
644 | this->smZeroElim(); |
---|
645 | if (tored != nrows) |
---|
646 | this->smToredElim(); |
---|
647 | if (act <= y) |
---|
648 | { |
---|
649 | if (TEST_OPT_PROT) PrintS(".\n"); |
---|
650 | this->smFinalMult(); |
---|
651 | this->smCopToRes(); |
---|
652 | return; |
---|
653 | } |
---|
654 | } |
---|
655 | } |
---|
656 | |
---|
657 | /* ----------------- pivot method ------------------ */ |
---|
658 | |
---|
659 | /* |
---|
660 | * prepare smPivot, compute weights for rows and columns |
---|
661 | * and the weight for all points |
---|
662 | */ |
---|
663 | void sparse_mat::smWeights() |
---|
664 | { |
---|
665 | float wc, wp, w; |
---|
666 | smpoly a; |
---|
667 | int i; |
---|
668 | |
---|
669 | wp = 0.0; |
---|
670 | for (i=tored; i; i--) wrw[i] = 0.0; // ??? |
---|
671 | for (i=act; i; i--) |
---|
672 | { |
---|
673 | wc = 0.0; |
---|
674 | a = m_act[i]; |
---|
675 | loop |
---|
676 | { |
---|
677 | if (a->pos > tored) |
---|
678 | break; |
---|
679 | w = a->f = sm_PolyWeight(a,_R); |
---|
680 | wc += w; |
---|
681 | wrw[a->pos] += w; |
---|
682 | a = a->n; |
---|
683 | if (a == NULL) |
---|
684 | break; |
---|
685 | } |
---|
686 | wp += wc; |
---|
687 | wcl[i] = wc; |
---|
688 | } |
---|
689 | wpoints = wp; |
---|
690 | } |
---|
691 | |
---|
692 | /* |
---|
693 | * compute pivot |
---|
694 | */ |
---|
695 | void sparse_mat::smPivot() |
---|
696 | { |
---|
697 | float wopt = 1.0e30; |
---|
698 | float wc, wr, wp, w; |
---|
699 | smpoly a; |
---|
700 | int i, copt, ropt; |
---|
701 | |
---|
702 | this->smWeights(); |
---|
703 | for (i=act; i; i--) |
---|
704 | { |
---|
705 | a = m_act[i]; |
---|
706 | loop |
---|
707 | { |
---|
708 | if (a->pos > tored) |
---|
709 | break; |
---|
710 | w = a->f; |
---|
711 | wc = wcl[i]-w; |
---|
712 | wr = wrw[a->pos]-w; |
---|
713 | if ((wr<0.25) || (wc<0.25)) // row or column with only one point |
---|
714 | { |
---|
715 | if (w<wopt) |
---|
716 | { |
---|
717 | wopt = w; |
---|
718 | copt = i; |
---|
719 | ropt = a->pos; |
---|
720 | } |
---|
721 | } |
---|
722 | else // elimination |
---|
723 | { |
---|
724 | wp = w*(wpoints-wcl[i]-wr); |
---|
725 | wp += wr*wc; |
---|
726 | if (wp < wopt) |
---|
727 | { |
---|
728 | wopt = wp; |
---|
729 | copt = i; |
---|
730 | ropt = a->pos; |
---|
731 | } |
---|
732 | } |
---|
733 | a = a->n; |
---|
734 | if (a == NULL) |
---|
735 | break; |
---|
736 | } |
---|
737 | } |
---|
738 | rpiv = ropt; |
---|
739 | cpiv = copt; |
---|
740 | if (cpiv != act) |
---|
741 | { |
---|
742 | a = m_act[act]; |
---|
743 | m_act[act] = m_act[cpiv]; |
---|
744 | m_act[cpiv] = a; |
---|
745 | } |
---|
746 | } |
---|
747 | |
---|
748 | /* |
---|
749 | * prepare smPivot, compute weights for rows and columns |
---|
750 | * and the weight for all points |
---|
751 | */ |
---|
752 | void sparse_mat::smNewWeights() |
---|
753 | { |
---|
754 | float wc, wp, w, hp = piv->f; |
---|
755 | smpoly a; |
---|
756 | int i, f, e = crd; |
---|
757 | |
---|
758 | wp = 0.0; |
---|
759 | for (i=tored; i; i--) wrw[i] = 0.0; // ??? |
---|
760 | for (i=act; i; i--) |
---|
761 | { |
---|
762 | wc = 0.0; |
---|
763 | a = m_act[i]; |
---|
764 | loop |
---|
765 | { |
---|
766 | if (a->pos > tored) |
---|
767 | break; |
---|
768 | w = a->f; |
---|
769 | f = a->e; |
---|
770 | if (f < e) |
---|
771 | { |
---|
772 | w *= hp; |
---|
773 | if (f) w /= m_res[f]->f; |
---|
774 | } |
---|
775 | wc += w; |
---|
776 | wrw[a->pos] += w; |
---|
777 | a = a->n; |
---|
778 | if (a == NULL) |
---|
779 | break; |
---|
780 | } |
---|
781 | wp += wc; |
---|
782 | wcl[i] = wc; |
---|
783 | } |
---|
784 | wpoints = wp; |
---|
785 | } |
---|
786 | |
---|
787 | /* |
---|
788 | * compute pivot |
---|
789 | */ |
---|
790 | void sparse_mat::smNewPivot() |
---|
791 | { |
---|
792 | float wopt = 1.0e30, hp = piv->f; |
---|
793 | float wc, wr, wp, w; |
---|
794 | smpoly a; |
---|
795 | int i, copt, ropt, f, e = crd; |
---|
796 | |
---|
797 | this->smNewWeights(); |
---|
798 | for (i=act; i; i--) |
---|
799 | { |
---|
800 | a = m_act[i]; |
---|
801 | loop |
---|
802 | { |
---|
803 | if (a->pos > tored) |
---|
804 | break; |
---|
805 | w = a->f; |
---|
806 | f = a->e; |
---|
807 | if (f < e) |
---|
808 | { |
---|
809 | w *= hp; |
---|
810 | if (f) w /= m_res[f]->f; |
---|
811 | } |
---|
812 | wc = wcl[i]-w; |
---|
813 | wr = wrw[a->pos]-w; |
---|
814 | if ((wr<0.25) || (wc<0.25)) // row or column with only one point |
---|
815 | { |
---|
816 | if (w<wopt) |
---|
817 | { |
---|
818 | wopt = w; |
---|
819 | copt = i; |
---|
820 | ropt = a->pos; |
---|
821 | } |
---|
822 | } |
---|
823 | else // elimination |
---|
824 | { |
---|
825 | wp = w*(wpoints-wcl[i]-wr); |
---|
826 | wp += wr*wc; |
---|
827 | if (wp < wopt) |
---|
828 | { |
---|
829 | wopt = wp; |
---|
830 | copt = i; |
---|
831 | ropt = a->pos; |
---|
832 | } |
---|
833 | } |
---|
834 | a = a->n; |
---|
835 | if (a == NULL) |
---|
836 | break; |
---|
837 | } |
---|
838 | } |
---|
839 | rpiv = ropt; |
---|
840 | cpiv = copt; |
---|
841 | if (cpiv != act) |
---|
842 | { |
---|
843 | a = m_act[act]; |
---|
844 | m_act[act] = m_act[cpiv]; |
---|
845 | m_act[cpiv] = a; |
---|
846 | } |
---|
847 | } |
---|
848 | |
---|
849 | /* ----------------- elimination ------------------ */ |
---|
850 | |
---|
851 | /* first step of elimination */ |
---|
852 | void sparse_mat::sm1Elim() |
---|
853 | { |
---|
854 | poly p = piv->m; // pivotelement |
---|
855 | smpoly c = m_act[act]; // pivotcolumn |
---|
856 | smpoly r = red; // row to reduce |
---|
857 | smpoly res, a, b; |
---|
858 | poly w, ha, hb; |
---|
859 | |
---|
860 | if ((c == NULL) || (r == NULL)) |
---|
861 | { |
---|
862 | while (r!=NULL) sm_ElemDelete(&r,_R); |
---|
863 | return; |
---|
864 | } |
---|
865 | do |
---|
866 | { |
---|
867 | a = m_act[r->pos]; |
---|
868 | res = dumm; |
---|
869 | res->n = NULL; |
---|
870 | b = c; |
---|
871 | w = r->m; |
---|
872 | loop // combine the chains a and b: p*a + w*b |
---|
873 | { |
---|
874 | if (a == NULL) |
---|
875 | { |
---|
876 | do |
---|
877 | { |
---|
878 | res = res->n = smElemCopy(b); |
---|
879 | res->m = pp_Mult_qq(b->m, w,_R); |
---|
880 | res->e = 1; |
---|
881 | res->f = sm_PolyWeight(res,_R); |
---|
882 | b = b->n; |
---|
883 | } while (b != NULL); |
---|
884 | break; |
---|
885 | } |
---|
886 | if (a->pos < b->pos) |
---|
887 | { |
---|
888 | res = res->n = a; |
---|
889 | a = a->n; |
---|
890 | } |
---|
891 | else if (a->pos > b->pos) |
---|
892 | { |
---|
893 | res = res->n = smElemCopy(b); |
---|
894 | res->m = pp_Mult_qq(b->m, w,_R); |
---|
895 | res->e = 1; |
---|
896 | res->f = sm_PolyWeight(res,_R); |
---|
897 | b = b->n; |
---|
898 | } |
---|
899 | else |
---|
900 | { |
---|
901 | ha = pp_Mult_qq(a->m, p,_R); |
---|
902 | p_Delete(&a->m,_R); |
---|
903 | hb = pp_Mult_qq(b->m, w,_R); |
---|
904 | ha = p_Add_q(ha, hb,_R); |
---|
905 | if (ha != NULL) |
---|
906 | { |
---|
907 | a->m = ha; |
---|
908 | a->e = 1; |
---|
909 | a->f = sm_PolyWeight(a,_R); |
---|
910 | res = res->n = a; |
---|
911 | a = a->n; |
---|
912 | } |
---|
913 | else |
---|
914 | { |
---|
915 | sm_ElemDelete(&a,_R); |
---|
916 | } |
---|
917 | b = b->n; |
---|
918 | } |
---|
919 | if (b == NULL) |
---|
920 | { |
---|
921 | res->n = a; |
---|
922 | break; |
---|
923 | } |
---|
924 | } |
---|
925 | m_act[r->pos] = dumm->n; |
---|
926 | sm_ElemDelete(&r,_R); |
---|
927 | } while (r != NULL); |
---|
928 | } |
---|
929 | |
---|
930 | /* higher steps of elimination */ |
---|
931 | void sparse_mat::smHElim() |
---|
932 | { |
---|
933 | poly hp = this->smMultPoly(piv); |
---|
934 | poly gp = piv->m; // pivotelement |
---|
935 | smpoly c = m_act[act]; // pivotcolumn |
---|
936 | smpoly r = red; // row to reduce |
---|
937 | smpoly res, a, b; |
---|
938 | poly ha, hr, x, y; |
---|
939 | int e, ip, ir, ia; |
---|
940 | |
---|
941 | if ((c == NULL) || (r == NULL)) |
---|
942 | { |
---|
943 | while(r!=NULL) sm_ElemDelete(&r,_R); |
---|
944 | p_Delete(&hp,_R); |
---|
945 | return; |
---|
946 | } |
---|
947 | e = crd+1; |
---|
948 | ip = piv->e; |
---|
949 | do |
---|
950 | { |
---|
951 | a = m_act[r->pos]; |
---|
952 | res = dumm; |
---|
953 | res->n = NULL; |
---|
954 | b = c; |
---|
955 | hr = r->m; |
---|
956 | ir = r->e; |
---|
957 | loop // combine the chains a and b: (hp,gp)*a(l) + hr*b(h) |
---|
958 | { |
---|
959 | if (a == NULL) |
---|
960 | { |
---|
961 | do |
---|
962 | { |
---|
963 | res = res->n = smElemCopy(b); |
---|
964 | x = SM_MULT(b->m, hr, m_res[ir]->m,_R); |
---|
965 | b = b->n; |
---|
966 | if(ir) SM_DIV(x, m_res[ir]->m,_R); |
---|
967 | res->m = x; |
---|
968 | res->e = e; |
---|
969 | res->f = sm_PolyWeight(res,_R); |
---|
970 | } while (b != NULL); |
---|
971 | break; |
---|
972 | } |
---|
973 | if (a->pos < b->pos) |
---|
974 | { |
---|
975 | res = res->n = a; |
---|
976 | a = a->n; |
---|
977 | } |
---|
978 | else if (a->pos > b->pos) |
---|
979 | { |
---|
980 | res = res->n = smElemCopy(b); |
---|
981 | x = SM_MULT(b->m, hr, m_res[ir]->m,_R); |
---|
982 | b = b->n; |
---|
983 | if(ir) SM_DIV(x, m_res[ir]->m,_R); |
---|
984 | res->m = x; |
---|
985 | res->e = e; |
---|
986 | res->f = sm_PolyWeight(res,_R); |
---|
987 | } |
---|
988 | else |
---|
989 | { |
---|
990 | ha = a->m; |
---|
991 | ia = a->e; |
---|
992 | if (ir >= ia) |
---|
993 | { |
---|
994 | if (ir > ia) |
---|
995 | { |
---|
996 | x = SM_MULT(ha, m_res[ir]->m, m_res[ia]->m,_R); |
---|
997 | p_Delete(&ha,_R); |
---|
998 | ha = x; |
---|
999 | if (ia) SM_DIV(ha, m_res[ia]->m,_R); |
---|
1000 | ia = ir; |
---|
1001 | } |
---|
1002 | x = SM_MULT(ha, gp, m_res[ia]->m,_R); |
---|
1003 | p_Delete(&ha,_R); |
---|
1004 | y = SM_MULT(b->m, hr, m_res[ia]->m,_R); |
---|
1005 | } |
---|
1006 | else if (ir >= ip) |
---|
1007 | { |
---|
1008 | if (ia < crd) |
---|
1009 | { |
---|
1010 | x = SM_MULT(ha, m_res[crd]->m, m_res[ia]->m,_R); |
---|
1011 | p_Delete(&ha,_R); |
---|
1012 | ha = x; |
---|
1013 | SM_DIV(ha, m_res[ia]->m,_R); |
---|
1014 | } |
---|
1015 | y = hp; |
---|
1016 | if(ir > ip) |
---|
1017 | { |
---|
1018 | y = SM_MULT(y, m_res[ir]->m, m_res[ip]->m,_R); |
---|
1019 | if (ip) SM_DIV(y, m_res[ip]->m,_R); |
---|
1020 | } |
---|
1021 | ia = ir; |
---|
1022 | x = SM_MULT(ha, y, m_res[ia]->m,_R); |
---|
1023 | if (y != hp) p_Delete(&y,_R); |
---|
1024 | p_Delete(&ha,_R); |
---|
1025 | y = SM_MULT(b->m, hr, m_res[ia]->m,_R); |
---|
1026 | } |
---|
1027 | else |
---|
1028 | { |
---|
1029 | x = SM_MULT(hr, m_res[ia]->m, m_res[ir]->m,_R); |
---|
1030 | if (ir) SM_DIV(x, m_res[ir]->m,_R); |
---|
1031 | y = SM_MULT(b->m, x, m_res[ia]->m,_R); |
---|
1032 | p_Delete(&x,_R); |
---|
1033 | x = SM_MULT(ha, gp, m_res[ia]->m,_R); |
---|
1034 | p_Delete(&ha,_R); |
---|
1035 | } |
---|
1036 | ha = p_Add_q(x, y,_R); |
---|
1037 | if (ha != NULL) |
---|
1038 | { |
---|
1039 | if (ia) SM_DIV(ha, m_res[ia]->m,_R); |
---|
1040 | a->m = ha; |
---|
1041 | a->e = e; |
---|
1042 | a->f = sm_PolyWeight(a,_R); |
---|
1043 | res = res->n = a; |
---|
1044 | a = a->n; |
---|
1045 | } |
---|
1046 | else |
---|
1047 | { |
---|
1048 | a->m = NULL; |
---|
1049 | sm_ElemDelete(&a,_R); |
---|
1050 | } |
---|
1051 | b = b->n; |
---|
1052 | } |
---|
1053 | if (b == NULL) |
---|
1054 | { |
---|
1055 | res->n = a; |
---|
1056 | break; |
---|
1057 | } |
---|
1058 | } |
---|
1059 | m_act[r->pos] = dumm->n; |
---|
1060 | sm_ElemDelete(&r,_R); |
---|
1061 | } while (r != NULL); |
---|
1062 | p_Delete(&hp,_R); |
---|
1063 | } |
---|
1064 | |
---|
1065 | /* ----------------- transfer ------------------ */ |
---|
1066 | |
---|
1067 | /* |
---|
1068 | * select the pivotrow and store it to red and piv |
---|
1069 | */ |
---|
1070 | void sparse_mat::smSelectPR() |
---|
1071 | { |
---|
1072 | smpoly b = dumm; |
---|
1073 | smpoly a, ap; |
---|
1074 | int i; |
---|
1075 | |
---|
1076 | if (TEST_OPT_PROT) |
---|
1077 | { |
---|
1078 | if ((crd+1)%10) |
---|
1079 | PrintS("."); |
---|
1080 | else |
---|
1081 | PrintS(".\n"); |
---|
1082 | } |
---|
1083 | a = m_act[act]; |
---|
1084 | if (a->pos < rpiv) |
---|
1085 | { |
---|
1086 | do |
---|
1087 | { |
---|
1088 | ap = a; |
---|
1089 | a = a->n; |
---|
1090 | } while (a->pos < rpiv); |
---|
1091 | ap->n = a->n; |
---|
1092 | } |
---|
1093 | else |
---|
1094 | m_act[act] = a->n; |
---|
1095 | piv = a; |
---|
1096 | a->n = NULL; |
---|
1097 | for (i=1; i<act; i++) |
---|
1098 | { |
---|
1099 | a = m_act[i]; |
---|
1100 | if (a->pos < rpiv) |
---|
1101 | { |
---|
1102 | loop |
---|
1103 | { |
---|
1104 | ap = a; |
---|
1105 | a = a->n; |
---|
1106 | if ((a == NULL) || (a->pos > rpiv)) |
---|
1107 | break; |
---|
1108 | if (a->pos == rpiv) |
---|
1109 | { |
---|
1110 | ap->n = a->n; |
---|
1111 | a->m = p_Neg(a->m,_R); |
---|
1112 | b = b->n = a; |
---|
1113 | b->pos = i; |
---|
1114 | break; |
---|
1115 | } |
---|
1116 | } |
---|
1117 | } |
---|
1118 | else if (a->pos == rpiv) |
---|
1119 | { |
---|
1120 | m_act[i] = a->n; |
---|
1121 | a->m = p_Neg(a->m,_R); |
---|
1122 | b = b->n = a; |
---|
1123 | b->pos = i; |
---|
1124 | } |
---|
1125 | } |
---|
1126 | b->n = NULL; |
---|
1127 | red = dumm->n; |
---|
1128 | } |
---|
1129 | |
---|
1130 | /* |
---|
1131 | * store the pivotcol in m_row |
---|
1132 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] |
---|
1133 | */ |
---|
1134 | void sparse_mat::smColToRow() |
---|
1135 | { |
---|
1136 | smpoly c = m_act[act]; |
---|
1137 | smpoly h; |
---|
1138 | |
---|
1139 | while (c != NULL) |
---|
1140 | { |
---|
1141 | h = c; |
---|
1142 | c = c->n; |
---|
1143 | h->n = m_row[h->pos]; |
---|
1144 | m_row[h->pos] = h; |
---|
1145 | h->pos = crd; |
---|
1146 | } |
---|
1147 | } |
---|
1148 | |
---|
1149 | /* |
---|
1150 | * store the pivot and the assosiated row in m_row |
---|
1151 | * to m_res (result): |
---|
1152 | * piv + m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
---|
1153 | */ |
---|
1154 | void sparse_mat::smRowToCol() |
---|
1155 | { |
---|
1156 | smpoly r = m_row[rpiv]; |
---|
1157 | smpoly a, ap, h; |
---|
1158 | |
---|
1159 | m_row[rpiv] = NULL; |
---|
1160 | perm[crd] = rpiv; |
---|
1161 | piv->pos = crd; |
---|
1162 | m_res[crd] = piv; |
---|
1163 | while (r != NULL) |
---|
1164 | { |
---|
1165 | ap = m_res[r->pos]; |
---|
1166 | loop |
---|
1167 | { |
---|
1168 | a = ap->n; |
---|
1169 | if (a == NULL) |
---|
1170 | { |
---|
1171 | ap->n = h = r; |
---|
1172 | r = r->n; |
---|
1173 | h->n = a; |
---|
1174 | h->pos = crd; |
---|
1175 | break; |
---|
1176 | } |
---|
1177 | ap = a; |
---|
1178 | } |
---|
1179 | } |
---|
1180 | } |
---|
1181 | |
---|
1182 | /* ----------------- C++ stuff ------------------ */ |
---|
1183 | |
---|
1184 | /* |
---|
1185 | * clean m_act from zeros (after elim) |
---|
1186 | */ |
---|
1187 | void sparse_mat::smZeroElim() |
---|
1188 | { |
---|
1189 | int i = 0; |
---|
1190 | int j; |
---|
1191 | |
---|
1192 | loop |
---|
1193 | { |
---|
1194 | i++; |
---|
1195 | if (i > act) return; |
---|
1196 | if (m_act[i] == NULL) break; |
---|
1197 | } |
---|
1198 | j = i; |
---|
1199 | loop |
---|
1200 | { |
---|
1201 | j++; |
---|
1202 | if (j > act) break; |
---|
1203 | if (m_act[j] != NULL) |
---|
1204 | { |
---|
1205 | m_act[i] = m_act[j]; |
---|
1206 | i++; |
---|
1207 | } |
---|
1208 | } |
---|
1209 | act -= (j-i); |
---|
1210 | sign = 0; |
---|
1211 | } |
---|
1212 | |
---|
1213 | /* |
---|
1214 | * clean m_act from cols not to reduced (after elim) |
---|
1215 | * put them to m_res |
---|
1216 | */ |
---|
1217 | void sparse_mat::smToredElim() |
---|
1218 | { |
---|
1219 | int i = 0; |
---|
1220 | int j; |
---|
1221 | |
---|
1222 | loop |
---|
1223 | { |
---|
1224 | i++; |
---|
1225 | if (i > act) return; |
---|
1226 | if (m_act[i]->pos > tored) |
---|
1227 | { |
---|
1228 | m_res[inred] = m_act[i]; |
---|
1229 | inred--; |
---|
1230 | break; |
---|
1231 | } |
---|
1232 | } |
---|
1233 | j = i; |
---|
1234 | loop |
---|
1235 | { |
---|
1236 | j++; |
---|
1237 | if (j > act) break; |
---|
1238 | if (m_act[j]->pos > tored) |
---|
1239 | { |
---|
1240 | m_res[inred] = m_act[j]; |
---|
1241 | inred--; |
---|
1242 | } |
---|
1243 | else |
---|
1244 | { |
---|
1245 | m_act[i] = m_act[j]; |
---|
1246 | i++; |
---|
1247 | } |
---|
1248 | } |
---|
1249 | act -= (j-i); |
---|
1250 | sign = 0; |
---|
1251 | } |
---|
1252 | |
---|
1253 | /* |
---|
1254 | * copy m_act to m_res |
---|
1255 | */ |
---|
1256 | void sparse_mat::smCopToRes() |
---|
1257 | { |
---|
1258 | smpoly a,ap,r,h; |
---|
1259 | int i,j,k,l; |
---|
1260 | |
---|
1261 | i = 0; |
---|
1262 | if (act) |
---|
1263 | { |
---|
1264 | a = m_act[act]; // init perm |
---|
1265 | do |
---|
1266 | { |
---|
1267 | i++; |
---|
1268 | perm[crd+i] = a->pos; |
---|
1269 | a = a->n; |
---|
1270 | } while ((a != NULL) && (a->pos <= tored)); |
---|
1271 | for (j=act-1;j;j--) // load all positions of perm |
---|
1272 | { |
---|
1273 | a = m_act[j]; |
---|
1274 | k = 1; |
---|
1275 | loop |
---|
1276 | { |
---|
1277 | if (perm[crd+k] >= a->pos) |
---|
1278 | { |
---|
1279 | if (perm[crd+k] > a->pos) |
---|
1280 | { |
---|
1281 | for (l=i;l>=k;l--) perm[crd+l+1] = perm[crd+l]; |
---|
1282 | perm[crd+k] = a->pos; |
---|
1283 | i++; |
---|
1284 | } |
---|
1285 | a = a->n; |
---|
1286 | if ((a == NULL) || (a->pos > tored)) break; |
---|
1287 | } |
---|
1288 | k++; |
---|
1289 | if ((k > i) && (a->pos <= tored)) |
---|
1290 | { |
---|
1291 | do |
---|
1292 | { |
---|
1293 | i++; |
---|
1294 | perm[crd+i] = a->pos; |
---|
1295 | a = a->n; |
---|
1296 | } while ((a != NULL) && (a->pos <= tored)); |
---|
1297 | break; |
---|
1298 | } |
---|
1299 | } |
---|
1300 | } |
---|
1301 | } |
---|
1302 | for (j=act;j;j--) // renumber m_act |
---|
1303 | { |
---|
1304 | k = 1; |
---|
1305 | a = m_act[j]; |
---|
1306 | while ((a != NULL) && (a->pos <= tored)) |
---|
1307 | { |
---|
1308 | if (perm[crd+k] == a->pos) |
---|
1309 | { |
---|
1310 | a->pos = crd+k; |
---|
1311 | a = a->n; |
---|
1312 | } |
---|
1313 | k++; |
---|
1314 | } |
---|
1315 | } |
---|
1316 | tored = crd+i; |
---|
1317 | for(k=1;k<=i;k++) // clean this from m_row |
---|
1318 | { |
---|
1319 | j = perm[crd+k]; |
---|
1320 | if (m_row[j] != NULL) |
---|
1321 | { |
---|
1322 | r = m_row[j]; |
---|
1323 | m_row[j] = NULL; |
---|
1324 | do |
---|
1325 | { |
---|
1326 | ap = m_res[r->pos]; |
---|
1327 | loop |
---|
1328 | { |
---|
1329 | a = ap->n; |
---|
1330 | if (a == NULL) |
---|
1331 | { |
---|
1332 | h = ap->n = r; |
---|
1333 | r = r->n; |
---|
1334 | h->n = NULL; |
---|
1335 | h->pos = crd+k; |
---|
1336 | break; |
---|
1337 | } |
---|
1338 | ap = a; |
---|
1339 | } |
---|
1340 | } while (r!=NULL); |
---|
1341 | } |
---|
1342 | } |
---|
1343 | while(act) // clean m_act |
---|
1344 | { |
---|
1345 | crd++; |
---|
1346 | m_res[crd] = m_act[act]; |
---|
1347 | act--; |
---|
1348 | } |
---|
1349 | for (i=1;i<=tored;i++) // take the rest of m_row |
---|
1350 | { |
---|
1351 | if(m_row[i] != NULL) |
---|
1352 | { |
---|
1353 | tored++; |
---|
1354 | r = m_row[i]; |
---|
1355 | m_row[i] = NULL; |
---|
1356 | perm[tored] = i; |
---|
1357 | do |
---|
1358 | { |
---|
1359 | ap = m_res[r->pos]; |
---|
1360 | loop |
---|
1361 | { |
---|
1362 | a = ap->n; |
---|
1363 | if (a == NULL) |
---|
1364 | { |
---|
1365 | h = ap->n = r; |
---|
1366 | r = r->n; |
---|
1367 | h->n = NULL; |
---|
1368 | h->pos = tored; |
---|
1369 | break; |
---|
1370 | } |
---|
1371 | ap = a; |
---|
1372 | } |
---|
1373 | } while (r!=NULL); |
---|
1374 | } |
---|
1375 | } |
---|
1376 | for (i=tored+1;i<=nrows;i++) // take the rest of m_row |
---|
1377 | { |
---|
1378 | if(m_row[i] != NULL) |
---|
1379 | { |
---|
1380 | r = m_row[i]; |
---|
1381 | m_row[i] = NULL; |
---|
1382 | do |
---|
1383 | { |
---|
1384 | ap = m_res[r->pos]; |
---|
1385 | loop |
---|
1386 | { |
---|
1387 | a = ap->n; |
---|
1388 | if (a == NULL) |
---|
1389 | { |
---|
1390 | h = ap->n = r; |
---|
1391 | r = r->n; |
---|
1392 | h->n = NULL; |
---|
1393 | h->pos = i; |
---|
1394 | break; |
---|
1395 | } |
---|
1396 | ap = a; |
---|
1397 | } |
---|
1398 | } while (r!=NULL); |
---|
1399 | } |
---|
1400 | } |
---|
1401 | while (inred < ncols) // take unreducable |
---|
1402 | { |
---|
1403 | crd++; |
---|
1404 | inred++; |
---|
1405 | m_res[crd] = m_res[inred]; |
---|
1406 | } |
---|
1407 | } |
---|
1408 | |
---|
1409 | /* |
---|
1410 | * multiply and divide the column, that goes to result |
---|
1411 | */ |
---|
1412 | void sparse_mat::smMultCol() |
---|
1413 | { |
---|
1414 | smpoly a = m_act[act]; |
---|
1415 | int e = crd; |
---|
1416 | poly ha; |
---|
1417 | int f; |
---|
1418 | |
---|
1419 | while (a != NULL) |
---|
1420 | { |
---|
1421 | f = a->e; |
---|
1422 | if (f < e) |
---|
1423 | { |
---|
1424 | ha = SM_MULT(a->m, m_res[e]->m, m_res[f]->m,_R); |
---|
1425 | p_Delete(&a->m,_R); |
---|
1426 | if (f) SM_DIV(ha, m_res[f]->m,_R); |
---|
1427 | a->m = ha; |
---|
1428 | if (normalize) p_Normalize(a->m,_R); |
---|
1429 | } |
---|
1430 | a = a->n; |
---|
1431 | } |
---|
1432 | } |
---|
1433 | |
---|
1434 | /* |
---|
1435 | * multiply and divide the m_act finaly |
---|
1436 | */ |
---|
1437 | void sparse_mat::smFinalMult() |
---|
1438 | { |
---|
1439 | smpoly a; |
---|
1440 | poly ha; |
---|
1441 | int i, f; |
---|
1442 | int e = crd; |
---|
1443 | |
---|
1444 | for (i=act; i; i--) |
---|
1445 | { |
---|
1446 | a = m_act[i]; |
---|
1447 | do |
---|
1448 | { |
---|
1449 | f = a->e; |
---|
1450 | if (f < e) |
---|
1451 | { |
---|
1452 | ha = SM_MULT(a->m, m_res[e]->m, m_res[f]->m, _R); |
---|
1453 | p_Delete(&a->m,_R); |
---|
1454 | if (f) SM_DIV(ha, m_res[f]->m, _R); |
---|
1455 | a->m = ha; |
---|
1456 | } |
---|
1457 | if (normalize) p_Normalize(a->m, _R); |
---|
1458 | a = a->n; |
---|
1459 | } while (a != NULL); |
---|
1460 | } |
---|
1461 | } |
---|
1462 | |
---|
1463 | /* |
---|
1464 | * check for denominators |
---|
1465 | */ |
---|
1466 | int sparse_mat::smCheckNormalize() |
---|
1467 | { |
---|
1468 | int i; |
---|
1469 | smpoly a; |
---|
1470 | |
---|
1471 | for (i=act; i; i--) |
---|
1472 | { |
---|
1473 | a = m_act[i]; |
---|
1474 | do |
---|
1475 | { |
---|
1476 | if(sm_HaveDenom(a->m,_R)) return 1; |
---|
1477 | a = a->n; |
---|
1478 | } while (a != NULL); |
---|
1479 | } |
---|
1480 | return 0; |
---|
1481 | } |
---|
1482 | |
---|
1483 | /* |
---|
1484 | * normalize |
---|
1485 | */ |
---|
1486 | void sparse_mat::smNormalize() |
---|
1487 | { |
---|
1488 | smpoly a; |
---|
1489 | int i; |
---|
1490 | int e = crd; |
---|
1491 | |
---|
1492 | for (i=act; i; i--) |
---|
1493 | { |
---|
1494 | a = m_act[i]; |
---|
1495 | do |
---|
1496 | { |
---|
1497 | if (e == a->e) p_Normalize(a->m,_R); |
---|
1498 | a = a->n; |
---|
1499 | } while (a != NULL); |
---|
1500 | } |
---|
1501 | } |
---|
1502 | |
---|
1503 | /* |
---|
1504 | * multiply and divide the element, save poly |
---|
1505 | */ |
---|
1506 | poly sparse_mat::smMultPoly(smpoly a) |
---|
1507 | { |
---|
1508 | int f = a->e; |
---|
1509 | poly r, h; |
---|
1510 | |
---|
1511 | if (f < crd) |
---|
1512 | { |
---|
1513 | h = r = a->m; |
---|
1514 | h = SM_MULT(h, m_res[crd]->m, m_res[f]->m, _R); |
---|
1515 | if (f) SM_DIV(h, m_res[f]->m, _R); |
---|
1516 | a->m = h; |
---|
1517 | if (normalize) p_Normalize(a->m,_R); |
---|
1518 | a->f = sm_PolyWeight(a,_R); |
---|
1519 | return r; |
---|
1520 | } |
---|
1521 | else |
---|
1522 | return NULL; |
---|
1523 | } |
---|
1524 | |
---|
1525 | /* |
---|
1526 | * delete the m_act finaly |
---|
1527 | */ |
---|
1528 | void sparse_mat::smActDel() |
---|
1529 | { |
---|
1530 | smpoly a; |
---|
1531 | int i; |
---|
1532 | |
---|
1533 | for (i=act; i; i--) |
---|
1534 | { |
---|
1535 | a = m_act[i]; |
---|
1536 | do |
---|
1537 | { |
---|
1538 | sm_ElemDelete(&a,_R); |
---|
1539 | } while (a != NULL); |
---|
1540 | } |
---|
1541 | } |
---|
1542 | |
---|
1543 | /* |
---|
1544 | * delete the pivotcol |
---|
1545 | */ |
---|
1546 | void sparse_mat::smColDel() |
---|
1547 | { |
---|
1548 | smpoly a = m_act[act]; |
---|
1549 | |
---|
1550 | while (a != NULL) |
---|
1551 | { |
---|
1552 | sm_ElemDelete(&a,_R); |
---|
1553 | } |
---|
1554 | } |
---|
1555 | |
---|
1556 | /* |
---|
1557 | * delete pivot elements |
---|
1558 | */ |
---|
1559 | void sparse_mat::smPivDel() |
---|
1560 | { |
---|
1561 | int i=crd; |
---|
1562 | |
---|
1563 | while (i != 0) |
---|
1564 | { |
---|
1565 | sm_ElemDelete(&m_res[i],_R); |
---|
1566 | i--; |
---|
1567 | } |
---|
1568 | } |
---|
1569 | |
---|
1570 | /* |
---|
1571 | * the sign of the determinant |
---|
1572 | */ |
---|
1573 | void sparse_mat::smSign() |
---|
1574 | { |
---|
1575 | int j,i; |
---|
1576 | if (act > 2) |
---|
1577 | { |
---|
1578 | if (cpiv!=act) sign=-sign; |
---|
1579 | if ((act%2)==0) sign=-sign; |
---|
1580 | i=1; |
---|
1581 | j=perm[1]; |
---|
1582 | while(j<rpiv) |
---|
1583 | { |
---|
1584 | sign=-sign; |
---|
1585 | i++; |
---|
1586 | j=perm[i]; |
---|
1587 | } |
---|
1588 | while(perm[i]!=0) |
---|
1589 | { |
---|
1590 | perm[i]=perm[i+1]; |
---|
1591 | i++; |
---|
1592 | } |
---|
1593 | } |
---|
1594 | else |
---|
1595 | { |
---|
1596 | if (cpiv!=1) sign=-sign; |
---|
1597 | if (rpiv!=perm[1]) sign=-sign; |
---|
1598 | } |
---|
1599 | } |
---|
1600 | |
---|
1601 | void sparse_mat::smInitPerm() |
---|
1602 | { |
---|
1603 | int i; |
---|
1604 | for (i=act;i;i--) perm[i]=i; |
---|
1605 | } |
---|
1606 | |
---|
1607 | /* ----------------- arithmetic ------------------ */ |
---|
1608 | #ifdef OLD_DIV |
---|
1609 | /*2 |
---|
1610 | * exact division a/b |
---|
1611 | * a destroyed, b NOT destroyed |
---|
1612 | */ |
---|
1613 | void sm_PolyDiv(poly a, poly b, const ring R) |
---|
1614 | { |
---|
1615 | const number x = pGetCoeff(b); |
---|
1616 | number y, yn; |
---|
1617 | poly t, h, dummy; |
---|
1618 | int i; |
---|
1619 | |
---|
1620 | if (pNext(b) == NULL) |
---|
1621 | { |
---|
1622 | do |
---|
1623 | { |
---|
1624 | if (!p_LmIsConstantComp(b,R)) |
---|
1625 | { |
---|
1626 | for (i=rVar(R); i; i--) |
---|
1627 | p_SubExp(a,i,p_GetExp(b,i,R),R); |
---|
1628 | p_Setm(a,R); |
---|
1629 | } |
---|
1630 | y = n_Div(pGetCoeff(a),x,R->cf); |
---|
1631 | n_Normalize(y,R->cf); |
---|
1632 | p_SetCoeff(a,y,R); |
---|
1633 | pIter(a); |
---|
1634 | } while (a != NULL); |
---|
1635 | return; |
---|
1636 | } |
---|
1637 | dummy = p_Init(R); |
---|
1638 | do |
---|
1639 | { |
---|
1640 | for (i=rVar(R); i; i--) |
---|
1641 | p_SubExp(a,i,p_GetExp(b,i,R),R); |
---|
1642 | p_Setm(a,R); |
---|
1643 | y = n_Div(pGetCoeff(a),x,R->cf); |
---|
1644 | n_Normalize(y,R->cf); |
---|
1645 | p_SetCoeff(a,y,R); |
---|
1646 | yn = n_InpNeg(n_Copy(y,R->cf),R->cf); |
---|
1647 | t = pNext(b); |
---|
1648 | h = dummy; |
---|
1649 | do |
---|
1650 | { |
---|
1651 | h = pNext(h) = p_Init(R); |
---|
1652 | //pSetComp(h,0); |
---|
1653 | for (i=rVar(R); i; i--) |
---|
1654 | p_SetExp(h,i,p_GetExp(a,i,R)+p_GetExp(t,i,R),R); |
---|
1655 | p_Setm(h,R); |
---|
1656 | pSetCoeff0(h,n_Mult(yn, pGetCoeff(t),R->cf)); |
---|
1657 | pIter(t); |
---|
1658 | } while (t != NULL); |
---|
1659 | n_Delete(&yn,R->cf); |
---|
1660 | pNext(h) = NULL; |
---|
1661 | a = pNext(a) = p_Add_q(pNext(a), pNext(dummy),R); |
---|
1662 | } while (a!=NULL); |
---|
1663 | p_LmFree(dummy, R); |
---|
1664 | } |
---|
1665 | #endif |
---|
1666 | |
---|
1667 | //disable that, as it fails with coef buckets |
---|
1668 | //#define X_MAS |
---|
1669 | #ifdef X_MAS |
---|
1670 | // Note: the following in not addapted to SW :( |
---|
1671 | /* |
---|
1672 | /// returns the part of (a*b)/exp(lead(c)) with nonegative exponents |
---|
1673 | poly smMultDiv(poly a, poly b, const poly c) |
---|
1674 | { |
---|
1675 | poly pa, e, res, r; |
---|
1676 | BOOLEAN lead; |
---|
1677 | int la, lb, lr; |
---|
1678 | |
---|
1679 | if ((c == NULL) || pLmIsConstantComp(c)) |
---|
1680 | { |
---|
1681 | return pp_Mult_qq(a, b); |
---|
1682 | } |
---|
1683 | |
---|
1684 | pqLength(a, b, la, lb, SM_MIN_LENGTH_BUCKET); |
---|
1685 | |
---|
1686 | // we iter over b, so, make sure b is the shortest |
---|
1687 | // such that we minimize our iterations |
---|
1688 | if (lb > la) |
---|
1689 | { |
---|
1690 | r = a; |
---|
1691 | a = b; |
---|
1692 | b = r; |
---|
1693 | lr = la; |
---|
1694 | la = lb; |
---|
1695 | lb = lr; |
---|
1696 | } |
---|
1697 | res = NULL; |
---|
1698 | e = p_Init(); |
---|
1699 | lead = FALSE; |
---|
1700 | while (!lead) |
---|
1701 | { |
---|
1702 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1703 | if (smIsNegQuot(e, b, c)) |
---|
1704 | { |
---|
1705 | lead = pLmDivisibleByNoComp(e, a); |
---|
1706 | r = smSelectCopy_ExpMultDiv(a, e, b, c); |
---|
1707 | } |
---|
1708 | else |
---|
1709 | { |
---|
1710 | lead = TRUE; |
---|
1711 | r = pp_Mult__mm(a, e); |
---|
1712 | } |
---|
1713 | if (lead) |
---|
1714 | { |
---|
1715 | if (res != NULL) |
---|
1716 | { |
---|
1717 | smFindRef(&pa, &res, r); |
---|
1718 | if (pa == NULL) |
---|
1719 | lead = FALSE; |
---|
1720 | } |
---|
1721 | else |
---|
1722 | { |
---|
1723 | pa = res = r; |
---|
1724 | } |
---|
1725 | } |
---|
1726 | else |
---|
1727 | res = p_Add_q(res, r); |
---|
1728 | pIter(b); |
---|
1729 | if (b == NULL) |
---|
1730 | { |
---|
1731 | pLmFree(e); |
---|
1732 | return res; |
---|
1733 | } |
---|
1734 | } |
---|
1735 | |
---|
1736 | if (!TEST_OPT_NOT_BUCKETS && lb >= SM_MIN_LENGTH_BUCKET) |
---|
1737 | { |
---|
1738 | // use buckets if minimum length is smaller than threshold |
---|
1739 | spolyrec rp; |
---|
1740 | poly append; |
---|
1741 | // find the last monomial before pa |
---|
1742 | if (res == pa) |
---|
1743 | { |
---|
1744 | append = &rp; |
---|
1745 | pNext(append) = res; |
---|
1746 | } |
---|
1747 | else |
---|
1748 | { |
---|
1749 | append = res; |
---|
1750 | while (pNext(append) != pa) |
---|
1751 | { |
---|
1752 | assume(pNext(append) != NULL); |
---|
1753 | pIter(append); |
---|
1754 | } |
---|
1755 | } |
---|
1756 | kBucket_pt bucket = kBucketCreate(currRing); |
---|
1757 | kBucketInit(bucket, pNext(append), 0); |
---|
1758 | do |
---|
1759 | { |
---|
1760 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1761 | if (smIsNegQuot(e, b, c)) |
---|
1762 | { |
---|
1763 | lr = la; |
---|
1764 | r = pp_Mult_Coeff_mm_DivSelect_MultDiv(a, lr, e, b, c); |
---|
1765 | if (pLmDivisibleByNoComp(e, a)) |
---|
1766 | append = kBucket_ExtractLarger_Add_q(bucket, append, r, &lr); |
---|
1767 | else |
---|
1768 | kBucket_Add_q(bucket, r, &lr); |
---|
1769 | } |
---|
1770 | else |
---|
1771 | { |
---|
1772 | r = pp_Mult__mm(a, e); |
---|
1773 | append = kBucket_ExtractLarger_Add_q(bucket, append, r, &la); |
---|
1774 | } |
---|
1775 | pIter(b); |
---|
1776 | } while (b != NULL); |
---|
1777 | pNext(append) = kBucketClear(bucket); |
---|
1778 | kBucketDestroy(&bucket); |
---|
1779 | pTest(append); |
---|
1780 | } |
---|
1781 | else |
---|
1782 | { |
---|
1783 | // use old sm stuff |
---|
1784 | do |
---|
1785 | { |
---|
1786 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1787 | if (smIsNegQuot(e, b, c)) |
---|
1788 | { |
---|
1789 | r = smSelectCopy_ExpMultDiv(a, e, b, c); |
---|
1790 | if (pLmDivisibleByNoComp(e, a)) |
---|
1791 | smCombineChain(&pa, r); |
---|
1792 | else |
---|
1793 | pa = p_Add_q(pa,r); |
---|
1794 | } |
---|
1795 | else |
---|
1796 | { |
---|
1797 | r = pp_Mult__mm(a, e); |
---|
1798 | smCombineChain(&pa, r); |
---|
1799 | } |
---|
1800 | pIter(b); |
---|
1801 | } while (b != NULL); |
---|
1802 | } |
---|
1803 | pLmFree(e); |
---|
1804 | return res; |
---|
1805 | } |
---|
1806 | */ |
---|
1807 | #else |
---|
1808 | |
---|
1809 | /* |
---|
1810 | * returns the part of (a*b)/exp(lead(c)) with nonegative exponents |
---|
1811 | */ |
---|
1812 | poly sm_MultDiv(poly a, poly b, const poly c, const ring R) |
---|
1813 | { |
---|
1814 | poly pa, e, res, r; |
---|
1815 | BOOLEAN lead; |
---|
1816 | |
---|
1817 | if ((c == NULL) || p_LmIsConstantComp(c,R)) |
---|
1818 | { |
---|
1819 | return pp_Mult_qq(a, b, R); |
---|
1820 | } |
---|
1821 | if (smSmaller(a, b)) |
---|
1822 | { |
---|
1823 | r = a; |
---|
1824 | a = b; |
---|
1825 | b = r; |
---|
1826 | } |
---|
1827 | res = NULL; |
---|
1828 | e = p_Init(R); |
---|
1829 | lead = FALSE; |
---|
1830 | while (!lead) |
---|
1831 | { |
---|
1832 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1833 | if (sm_IsNegQuot(e, b, c, R)) |
---|
1834 | { |
---|
1835 | lead = p_LmDivisibleByNoComp(e, a, R); |
---|
1836 | r = sm_SelectCopy_ExpMultDiv(a, e, b, c, R); |
---|
1837 | } |
---|
1838 | else |
---|
1839 | { |
---|
1840 | lead = TRUE; |
---|
1841 | r = pp_Mult_mm(a, e,R); |
---|
1842 | } |
---|
1843 | if (lead) |
---|
1844 | { |
---|
1845 | if (res != NULL) |
---|
1846 | { |
---|
1847 | sm_FindRef(&pa, &res, r, R); |
---|
1848 | if (pa == NULL) |
---|
1849 | lead = FALSE; |
---|
1850 | } |
---|
1851 | else |
---|
1852 | { |
---|
1853 | pa = res = r; |
---|
1854 | } |
---|
1855 | } |
---|
1856 | else |
---|
1857 | res = p_Add_q(res, r, R); |
---|
1858 | pIter(b); |
---|
1859 | if (b == NULL) |
---|
1860 | { |
---|
1861 | p_LmFree(e, R); |
---|
1862 | return res; |
---|
1863 | } |
---|
1864 | } |
---|
1865 | do |
---|
1866 | { |
---|
1867 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1868 | if (sm_IsNegQuot(e, b, c, R)) |
---|
1869 | { |
---|
1870 | r = sm_SelectCopy_ExpMultDiv(a, e, b, c, R); |
---|
1871 | if (p_LmDivisibleByNoComp(e, a,R)) |
---|
1872 | sm_CombineChain(&pa, r, R); |
---|
1873 | else |
---|
1874 | pa = p_Add_q(pa,r,R); |
---|
1875 | } |
---|
1876 | else |
---|
1877 | { |
---|
1878 | r = pp_Mult_mm(a, e, R); |
---|
1879 | sm_CombineChain(&pa, r, R); |
---|
1880 | } |
---|
1881 | pIter(b); |
---|
1882 | } while (b != NULL); |
---|
1883 | p_LmFree(e, R); |
---|
1884 | return res; |
---|
1885 | } |
---|
1886 | #endif /*else X_MAS*/ |
---|
1887 | |
---|
1888 | /*n |
---|
1889 | * exact division a/b |
---|
1890 | * a is a result of smMultDiv |
---|
1891 | * a destroyed, b NOT destroyed |
---|
1892 | */ |
---|
1893 | void sm_SpecialPolyDiv(poly a, poly b, const ring R) |
---|
1894 | { |
---|
1895 | if (pNext(b) == NULL) |
---|
1896 | { |
---|
1897 | sm_PolyDivN(a, pGetCoeff(b),R); |
---|
1898 | return; |
---|
1899 | } |
---|
1900 | sm_ExactPolyDiv(a, b, R); |
---|
1901 | } |
---|
1902 | |
---|
1903 | /* ------------ internals arithmetic ------------- */ |
---|
1904 | static void sm_ExactPolyDiv(poly a, poly b, const ring R) |
---|
1905 | { |
---|
1906 | const number x = pGetCoeff(b); |
---|
1907 | poly tail = pNext(b), e = p_Init(R); |
---|
1908 | poly h; |
---|
1909 | number y, yn; |
---|
1910 | int lt = pLength(tail); |
---|
1911 | |
---|
1912 | if (lt + 1 >= SM_MIN_LENGTH_BUCKET && !TEST_OPT_NOT_BUCKETS) |
---|
1913 | { |
---|
1914 | kBucket_pt bucket = kBucketCreate(R); |
---|
1915 | kBucketInit(bucket, pNext(a), 0); |
---|
1916 | int lh = 0; |
---|
1917 | do |
---|
1918 | { |
---|
1919 | y = n_Div(pGetCoeff(a), x, R->cf); |
---|
1920 | n_Normalize(y, R->cf); |
---|
1921 | p_SetCoeff(a,y, R); |
---|
1922 | yn = n_InpNeg(n_Copy(y, R->cf), R->cf); |
---|
1923 | pSetCoeff0(e,yn); |
---|
1924 | lh = lt; |
---|
1925 | if (sm_IsNegQuot(e, a, b, R)) |
---|
1926 | { |
---|
1927 | h = pp_Mult_Coeff_mm_DivSelect_MultDiv(tail, lh, e, a, b, R); |
---|
1928 | } |
---|
1929 | else |
---|
1930 | h = pp_Mult_mm(tail, e, R); |
---|
1931 | n_Delete(&yn, R->cf); |
---|
1932 | kBucket_Add_q(bucket, h, &lh); |
---|
1933 | |
---|
1934 | a = pNext(a) = kBucketExtractLm(bucket); |
---|
1935 | } while (a!=NULL); |
---|
1936 | kBucketDestroy(&bucket); |
---|
1937 | } |
---|
1938 | else |
---|
1939 | { |
---|
1940 | do |
---|
1941 | { |
---|
1942 | y = n_Div(pGetCoeff(a), x, R->cf); |
---|
1943 | n_Normalize(y, R->cf); |
---|
1944 | p_SetCoeff(a,y, R); |
---|
1945 | yn = n_InpNeg(n_Copy(y, R->cf), R->cf); |
---|
1946 | pSetCoeff0(e,yn); |
---|
1947 | if (sm_IsNegQuot(e, a, b, R)) |
---|
1948 | h = sm_SelectCopy_ExpMultDiv(tail, e, a, b, R); |
---|
1949 | else |
---|
1950 | h = pp_Mult_mm(tail, e, R); |
---|
1951 | n_Delete(&yn, R->cf); |
---|
1952 | a = pNext(a) = p_Add_q(pNext(a), h, R); |
---|
1953 | } while (a!=NULL); |
---|
1954 | } |
---|
1955 | p_LmFree(e, R); |
---|
1956 | } |
---|
1957 | |
---|
1958 | // obachman --> Wilfried: check the following |
---|
1959 | static BOOLEAN sm_IsNegQuot(poly a, const poly b, const poly c, const ring R) |
---|
1960 | { |
---|
1961 | if (p_LmDivisibleByNoComp(c, b,R)) |
---|
1962 | { |
---|
1963 | p_ExpVectorDiff(a, b, c,R); |
---|
1964 | // Hmm: here used to be a p_Setm(a): but it is unnecessary, |
---|
1965 | // if b and c are correct |
---|
1966 | return FALSE; |
---|
1967 | } |
---|
1968 | else |
---|
1969 | { |
---|
1970 | int i; |
---|
1971 | for (i=rVar(R); i>0; i--) |
---|
1972 | { |
---|
1973 | if(p_GetExp(c,i,R) > p_GetExp(b,i,R)) |
---|
1974 | p_SetExp(a,i,p_GetExp(c,i,R)-p_GetExp(b,i,R),R); |
---|
1975 | else |
---|
1976 | p_SetExp(a,i,0,R); |
---|
1977 | } |
---|
1978 | // here we actually might need a p_Setm, if a is to be used in |
---|
1979 | // comparisons |
---|
1980 | return TRUE; |
---|
1981 | } |
---|
1982 | } |
---|
1983 | |
---|
1984 | static void sm_ExpMultDiv(poly t, const poly b, const poly c, const ring R) |
---|
1985 | { |
---|
1986 | p_Test(t,R); |
---|
1987 | p_LmTest(b,R); |
---|
1988 | p_LmTest(c,R); |
---|
1989 | poly bc = p_New(R); |
---|
1990 | |
---|
1991 | p_ExpVectorDiff(bc, b, c, R); |
---|
1992 | |
---|
1993 | while(t!=NULL) |
---|
1994 | { |
---|
1995 | p_ExpVectorAdd(t, bc, R); |
---|
1996 | pIter(t); |
---|
1997 | } |
---|
1998 | p_LmFree(bc, R); |
---|
1999 | } |
---|
2000 | |
---|
2001 | |
---|
2002 | static void sm_PolyDivN(poly a, const number x, const ring R) |
---|
2003 | { |
---|
2004 | number y; |
---|
2005 | |
---|
2006 | do |
---|
2007 | { |
---|
2008 | y = n_Div(pGetCoeff(a),x, R->cf); |
---|
2009 | n_Normalize(y, R->cf); |
---|
2010 | p_SetCoeff(a,y, R); |
---|
2011 | pIter(a); |
---|
2012 | } while (a != NULL); |
---|
2013 | } |
---|
2014 | |
---|
2015 | static BOOLEAN smSmaller(poly a, poly b) |
---|
2016 | { |
---|
2017 | loop |
---|
2018 | { |
---|
2019 | pIter(b); |
---|
2020 | if (b == NULL) return TRUE; |
---|
2021 | pIter(a); |
---|
2022 | if (a == NULL) return FALSE; |
---|
2023 | } |
---|
2024 | } |
---|
2025 | |
---|
2026 | static void sm_CombineChain(poly *px, poly r, const ring R) |
---|
2027 | { |
---|
2028 | poly pa = *px, pb; |
---|
2029 | number x; |
---|
2030 | int i; |
---|
2031 | |
---|
2032 | loop |
---|
2033 | { |
---|
2034 | pb = pNext(pa); |
---|
2035 | if (pb == NULL) |
---|
2036 | { |
---|
2037 | pa = pNext(pa) = r; |
---|
2038 | break; |
---|
2039 | } |
---|
2040 | i = p_LmCmp(pb, r,R); |
---|
2041 | if (i > 0) |
---|
2042 | pa = pb; |
---|
2043 | else |
---|
2044 | { |
---|
2045 | if (i == 0) |
---|
2046 | { |
---|
2047 | x = n_Add(pGetCoeff(pb), pGetCoeff(r),R->cf); |
---|
2048 | p_LmDelete(&r,R); |
---|
2049 | if (n_IsZero(x,R->cf)) |
---|
2050 | { |
---|
2051 | p_LmDelete(&pb,R); |
---|
2052 | pNext(pa) = p_Add_q(pb,r,R); |
---|
2053 | } |
---|
2054 | else |
---|
2055 | { |
---|
2056 | pa = pb; |
---|
2057 | p_SetCoeff(pa,x,R); |
---|
2058 | pNext(pa) = p_Add_q(pNext(pa), r, R); |
---|
2059 | } |
---|
2060 | } |
---|
2061 | else |
---|
2062 | { |
---|
2063 | pa = pNext(pa) = r; |
---|
2064 | pNext(pa) = p_Add_q(pb, pNext(pa),R); |
---|
2065 | } |
---|
2066 | break; |
---|
2067 | } |
---|
2068 | } |
---|
2069 | *px = pa; |
---|
2070 | } |
---|
2071 | |
---|
2072 | |
---|
2073 | static void sm_FindRef(poly *ref, poly *px, poly r, const ring R) |
---|
2074 | { |
---|
2075 | number x; |
---|
2076 | int i; |
---|
2077 | poly pa = *px, pp = NULL; |
---|
2078 | |
---|
2079 | loop |
---|
2080 | { |
---|
2081 | i = p_LmCmp(pa, r,R); |
---|
2082 | if (i > 0) |
---|
2083 | { |
---|
2084 | pp = pa; |
---|
2085 | pIter(pa); |
---|
2086 | if (pa==NULL) |
---|
2087 | { |
---|
2088 | pNext(pp) = r; |
---|
2089 | break; |
---|
2090 | } |
---|
2091 | } |
---|
2092 | else |
---|
2093 | { |
---|
2094 | if (i == 0) |
---|
2095 | { |
---|
2096 | x = n_Add(pGetCoeff(pa), pGetCoeff(r),R->cf); |
---|
2097 | p_LmDelete(&r,R); |
---|
2098 | if (n_IsZero(x,R->cf)) |
---|
2099 | { |
---|
2100 | p_LmDelete(&pa,R); |
---|
2101 | if (pp!=NULL) |
---|
2102 | pNext(pp) = p_Add_q(pa,r,R); |
---|
2103 | else |
---|
2104 | *px = p_Add_q(pa,r,R); |
---|
2105 | } |
---|
2106 | else |
---|
2107 | { |
---|
2108 | pp = pa; |
---|
2109 | p_SetCoeff(pp,x,R); |
---|
2110 | pNext(pp) = p_Add_q(pNext(pp), r, R); |
---|
2111 | } |
---|
2112 | } |
---|
2113 | else |
---|
2114 | { |
---|
2115 | if (pp!=NULL) |
---|
2116 | pp = pNext(pp) = r; |
---|
2117 | else |
---|
2118 | *px = pp = r; |
---|
2119 | pNext(pp) = p_Add_q(pa, pNext(r),R); |
---|
2120 | } |
---|
2121 | break; |
---|
2122 | } |
---|
2123 | } |
---|
2124 | *ref = pp; |
---|
2125 | } |
---|
2126 | |
---|
2127 | /* ----------------- internal 'C' stuff ------------------ */ |
---|
2128 | |
---|
2129 | static void sm_ElemDelete(smpoly *r, const ring R) |
---|
2130 | { |
---|
2131 | smpoly a = *r, b = a->n; |
---|
2132 | |
---|
2133 | p_Delete(&a->m, R); |
---|
2134 | omFreeBin((void *)a, smprec_bin); |
---|
2135 | *r = b; |
---|
2136 | } |
---|
2137 | |
---|
2138 | static smpoly smElemCopy(smpoly a) |
---|
2139 | { |
---|
2140 | smpoly r = (smpoly)omAllocBin(smprec_bin); |
---|
2141 | memcpy(r, a, sizeof(smprec)); |
---|
2142 | /* r->m = pCopy(r->m); */ |
---|
2143 | return r; |
---|
2144 | } |
---|
2145 | |
---|
2146 | /* |
---|
2147 | * from poly to smpoly |
---|
2148 | * do not destroy p |
---|
2149 | */ |
---|
2150 | static smpoly sm_Poly2Smpoly(poly q, const ring R) |
---|
2151 | { |
---|
2152 | poly pp; |
---|
2153 | smpoly res, a; |
---|
2154 | long x; |
---|
2155 | |
---|
2156 | if (q == NULL) |
---|
2157 | return NULL; |
---|
2158 | a = res = (smpoly)omAllocBin(smprec_bin); |
---|
2159 | a->pos = x = p_GetComp(q,R); |
---|
2160 | a->m = q; |
---|
2161 | a->e = 0; |
---|
2162 | loop |
---|
2163 | { |
---|
2164 | p_SetComp(q,0,R); |
---|
2165 | pp = q; |
---|
2166 | pIter(q); |
---|
2167 | if (q == NULL) |
---|
2168 | { |
---|
2169 | a->n = NULL; |
---|
2170 | return res; |
---|
2171 | } |
---|
2172 | if (p_GetComp(q,R) != x) |
---|
2173 | { |
---|
2174 | a = a->n = (smpoly)omAllocBin(smprec_bin); |
---|
2175 | pNext(pp) = NULL; |
---|
2176 | a->pos = x = p_GetComp(q,R); |
---|
2177 | a->m = q; |
---|
2178 | a->e = 0; |
---|
2179 | } |
---|
2180 | } |
---|
2181 | } |
---|
2182 | |
---|
2183 | /* |
---|
2184 | * from smpoly to poly |
---|
2185 | * destroy a |
---|
2186 | */ |
---|
2187 | static poly sm_Smpoly2Poly(smpoly a, const ring R) |
---|
2188 | { |
---|
2189 | smpoly b; |
---|
2190 | poly res, pp, q; |
---|
2191 | long x; |
---|
2192 | |
---|
2193 | if (a == NULL) |
---|
2194 | return NULL; |
---|
2195 | x = a->pos; |
---|
2196 | q = res = a->m; |
---|
2197 | loop |
---|
2198 | { |
---|
2199 | p_SetComp(q,x,R); |
---|
2200 | pp = q; |
---|
2201 | pIter(q); |
---|
2202 | if (q == NULL) |
---|
2203 | break; |
---|
2204 | } |
---|
2205 | loop |
---|
2206 | { |
---|
2207 | b = a; |
---|
2208 | a = a->n; |
---|
2209 | omFreeBin((void *)b, smprec_bin); |
---|
2210 | if (a == NULL) |
---|
2211 | return res; |
---|
2212 | x = a->pos; |
---|
2213 | q = pNext(pp) = a->m; |
---|
2214 | loop |
---|
2215 | { |
---|
2216 | p_SetComp(q,x,R); |
---|
2217 | pp = q; |
---|
2218 | pIter(q); |
---|
2219 | if (q == NULL) |
---|
2220 | break; |
---|
2221 | } |
---|
2222 | } |
---|
2223 | } |
---|
2224 | |
---|
2225 | /* |
---|
2226 | * weigth of a polynomial, for pivot strategy |
---|
2227 | */ |
---|
2228 | static float sm_PolyWeight(smpoly a, const ring R) |
---|
2229 | { |
---|
2230 | poly p = a->m; |
---|
2231 | int i; |
---|
2232 | float res = (float)n_Size(pGetCoeff(p),R->cf); |
---|
2233 | |
---|
2234 | if (pNext(p) == NULL) |
---|
2235 | { |
---|
2236 | for(i=rVar(R); i>0; i--) |
---|
2237 | { |
---|
2238 | if (p_GetExp(p,i,R) != 0) return res+1.0; |
---|
2239 | } |
---|
2240 | return res; |
---|
2241 | } |
---|
2242 | else |
---|
2243 | { |
---|
2244 | i = 0; |
---|
2245 | res = 0.0; |
---|
2246 | do |
---|
2247 | { |
---|
2248 | i++; |
---|
2249 | res += (float)n_Size(pGetCoeff(p),R->cf); |
---|
2250 | pIter(p); |
---|
2251 | } |
---|
2252 | while (p); |
---|
2253 | return res+(float)i; |
---|
2254 | } |
---|
2255 | } |
---|
2256 | |
---|
2257 | static BOOLEAN sm_HaveDenom(poly a, const ring R) |
---|
2258 | { |
---|
2259 | BOOLEAN sw; |
---|
2260 | number x; |
---|
2261 | |
---|
2262 | while (a != NULL) |
---|
2263 | { |
---|
2264 | x = n_GetDenom(pGetCoeff(a),R->cf); |
---|
2265 | sw = n_IsOne(x,R->cf); |
---|
2266 | n_Delete(&x,R->cf); |
---|
2267 | if (!sw) |
---|
2268 | { |
---|
2269 | return TRUE; |
---|
2270 | } |
---|
2271 | pIter(a); |
---|
2272 | } |
---|
2273 | return FALSE; |
---|
2274 | } |
---|
2275 | |
---|
2276 | static number sm_Cleardenom(ideal id, const ring R) |
---|
2277 | { |
---|
2278 | poly a; |
---|
2279 | number x,y,res=n_Init(1,R->cf); |
---|
2280 | BOOLEAN sw=FALSE; |
---|
2281 | |
---|
2282 | for (int i=0; i<IDELEMS(id); i++) |
---|
2283 | { |
---|
2284 | a = id->m[i]; |
---|
2285 | sw = sm_HaveDenom(a,R); |
---|
2286 | if (sw) break; |
---|
2287 | } |
---|
2288 | if (!sw) return res; |
---|
2289 | for (int i=0; i<IDELEMS(id); i++) |
---|
2290 | { |
---|
2291 | a = id->m[i]; |
---|
2292 | if (a!=NULL) |
---|
2293 | { |
---|
2294 | x = n_Copy(pGetCoeff(a),R->cf); |
---|
2295 | p_Cleardenom(a, R); |
---|
2296 | y = n_Div(x,pGetCoeff(a),R->cf); |
---|
2297 | n_Delete(&x,R->cf); |
---|
2298 | x = n_Mult(res,y,R->cf); |
---|
2299 | n_Normalize(x,R->cf); |
---|
2300 | n_Delete(&res,R->cf); |
---|
2301 | res = x; |
---|
2302 | } |
---|
2303 | } |
---|
2304 | return res; |
---|
2305 | } |
---|
2306 | |
---|
2307 | /* ----------------- gauss elimination ------------------ */ |
---|
2308 | /* in structs.h */ |
---|
2309 | typedef struct smnrec sm_nrec; |
---|
2310 | typedef sm_nrec * smnumber; |
---|
2311 | struct smnrec{ |
---|
2312 | smnumber n; // the next element |
---|
2313 | int pos; // position |
---|
2314 | number m; // the element |
---|
2315 | }; |
---|
2316 | |
---|
2317 | static omBin smnrec_bin = omGetSpecBin(sizeof(smnrec)); |
---|
2318 | |
---|
2319 | /* declare internal 'C' stuff */ |
---|
2320 | static void sm_NumberDelete(smnumber *, const ring R); |
---|
2321 | static smnumber smNumberCopy(smnumber); |
---|
2322 | static smnumber sm_Poly2Smnumber(poly, const ring); |
---|
2323 | static poly sm_Smnumber2Poly(number,const ring); |
---|
2324 | static BOOLEAN smCheckSolv(ideal); |
---|
2325 | |
---|
2326 | /* class for sparse number matrix: |
---|
2327 | */ |
---|
2328 | class sparse_number_mat{ |
---|
2329 | private: |
---|
2330 | int nrows, ncols; // dimension of the problem |
---|
2331 | int act; // number of unreduced columns (start: ncols) |
---|
2332 | int crd; // number of reduced columns (start: 0) |
---|
2333 | int tored; // border for rows to reduce |
---|
2334 | int sing; // indicator for singular problem |
---|
2335 | int rpiv; // row-position of the pivot |
---|
2336 | int *perm; // permutation of rows |
---|
2337 | number *sol; // field for solution |
---|
2338 | int *wrw, *wcl; // weights of rows and columns |
---|
2339 | smnumber * m_act; // unreduced columns |
---|
2340 | smnumber * m_res; // reduced columns (result) |
---|
2341 | smnumber * m_row; // reduced part of rows |
---|
2342 | smnumber red; // row to reduce |
---|
2343 | smnumber piv; // pivot |
---|
2344 | smnumber dumm; // allocated dummy |
---|
2345 | ring _R; |
---|
2346 | void smColToRow(); |
---|
2347 | void smRowToCol(); |
---|
2348 | void smSelectPR(); |
---|
2349 | void smRealPivot(); |
---|
2350 | void smZeroToredElim(); |
---|
2351 | void smGElim(); |
---|
2352 | void smAllDel(); |
---|
2353 | public: |
---|
2354 | sparse_number_mat(ideal, const ring); |
---|
2355 | ~sparse_number_mat(); |
---|
2356 | int smIsSing() { return sing; } |
---|
2357 | void smTriangular(); |
---|
2358 | void smSolv(); |
---|
2359 | ideal smRes2Ideal(); |
---|
2360 | }; |
---|
2361 | |
---|
2362 | /* ----------------- basics (used from 'C') ------------------ */ |
---|
2363 | /*2 |
---|
2364 | * returns the solution of a linear equation |
---|
2365 | * solution of M*x = r (M has dimension nXn) => |
---|
2366 | * I = module(transprose(M)) + r*gen(n+1) |
---|
2367 | * uses Gauss-elimination |
---|
2368 | */ |
---|
2369 | ideal sm_CallSolv(ideal I, const ring R) |
---|
2370 | { |
---|
2371 | sparse_number_mat *linsolv; |
---|
2372 | ring tmpR; |
---|
2373 | ideal rr; |
---|
2374 | |
---|
2375 | if (id_IsConstant(I,R)==FALSE) |
---|
2376 | { |
---|
2377 | WerrorS("symbol in equation"); |
---|
2378 | return NULL; |
---|
2379 | } |
---|
2380 | I->rank = id_RankFreeModule(I,R); |
---|
2381 | if (smCheckSolv(I)) return NULL; |
---|
2382 | tmpR=sm_RingChange(R,1); |
---|
2383 | rr=idrCopyR(I,R, tmpR); |
---|
2384 | linsolv = new sparse_number_mat(rr,tmpR); |
---|
2385 | rr=NULL; |
---|
2386 | linsolv->smTriangular(); |
---|
2387 | if (linsolv->smIsSing() == 0) |
---|
2388 | { |
---|
2389 | linsolv->smSolv(); |
---|
2390 | rr = linsolv->smRes2Ideal(); |
---|
2391 | } |
---|
2392 | else |
---|
2393 | WerrorS("singular problem for linsolv"); |
---|
2394 | delete linsolv; |
---|
2395 | if (rr!=NULL) |
---|
2396 | rr = idrMoveR(rr,tmpR,R); |
---|
2397 | sm_KillModifiedRing(tmpR); |
---|
2398 | return rr; |
---|
2399 | } |
---|
2400 | |
---|
2401 | /* |
---|
2402 | * constructor, destroy smat |
---|
2403 | */ |
---|
2404 | sparse_number_mat::sparse_number_mat(ideal smat, const ring R) |
---|
2405 | { |
---|
2406 | int i; |
---|
2407 | poly* pmat; |
---|
2408 | _R=R; |
---|
2409 | |
---|
2410 | crd = sing = 0; |
---|
2411 | act = ncols = smat->ncols; |
---|
2412 | tored = nrows = smat->rank; |
---|
2413 | i = tored+1; |
---|
2414 | perm = (int *)omAlloc(sizeof(int)*i); |
---|
2415 | m_row = (smnumber *)omAlloc0(sizeof(smnumber)*i); |
---|
2416 | wrw = (int *)omAlloc(sizeof(int)*i); |
---|
2417 | i = ncols+1; |
---|
2418 | wcl = (int *)omAlloc(sizeof(int)*i); |
---|
2419 | m_act = (smnumber *)omAlloc(sizeof(smnumber)*i); |
---|
2420 | m_res = (smnumber *)omAlloc0(sizeof(smnumber)*i); |
---|
2421 | dumm = (smnumber)omAllocBin(smnrec_bin); |
---|
2422 | pmat = smat->m; |
---|
2423 | for(i=ncols; i; i--) |
---|
2424 | { |
---|
2425 | m_act[i] = sm_Poly2Smnumber(pmat[i-1],_R); |
---|
2426 | } |
---|
2427 | omFreeSize((ADDRESS)pmat,smat->ncols*sizeof(poly)); |
---|
2428 | omFreeBin((ADDRESS)smat, sip_sideal_bin); |
---|
2429 | } |
---|
2430 | |
---|
2431 | /* |
---|
2432 | * destructor |
---|
2433 | */ |
---|
2434 | sparse_number_mat::~sparse_number_mat() |
---|
2435 | { |
---|
2436 | int i; |
---|
2437 | omFreeBin((ADDRESS)dumm, smnrec_bin); |
---|
2438 | i = ncols+1; |
---|
2439 | omFreeSize((ADDRESS)m_res, sizeof(smnumber)*i); |
---|
2440 | omFreeSize((ADDRESS)m_act, sizeof(smnumber)*i); |
---|
2441 | omFreeSize((ADDRESS)wcl, sizeof(int)*i); |
---|
2442 | i = nrows+1; |
---|
2443 | omFreeSize((ADDRESS)wrw, sizeof(int)*i); |
---|
2444 | omFreeSize((ADDRESS)m_row, sizeof(smnumber)*i); |
---|
2445 | omFreeSize((ADDRESS)perm, sizeof(int)*i); |
---|
2446 | } |
---|
2447 | |
---|
2448 | /* |
---|
2449 | * triangularization by Gauss-elimination |
---|
2450 | */ |
---|
2451 | void sparse_number_mat::smTriangular() |
---|
2452 | { |
---|
2453 | tored--; |
---|
2454 | this->smZeroToredElim(); |
---|
2455 | if (sing != 0) return; |
---|
2456 | while (act > 1) |
---|
2457 | { |
---|
2458 | this->smRealPivot(); |
---|
2459 | this->smSelectPR(); |
---|
2460 | this->smGElim(); |
---|
2461 | crd++; |
---|
2462 | this->smColToRow(); |
---|
2463 | act--; |
---|
2464 | this->smRowToCol(); |
---|
2465 | this->smZeroToredElim(); |
---|
2466 | if (sing != 0) return; |
---|
2467 | } |
---|
2468 | if (TEST_OPT_PROT) PrintS(".\n"); |
---|
2469 | piv = m_act[1]; |
---|
2470 | rpiv = piv->pos; |
---|
2471 | m_act[1] = piv->n; |
---|
2472 | piv->n = NULL; |
---|
2473 | crd++; |
---|
2474 | this->smColToRow(); |
---|
2475 | act--; |
---|
2476 | this->smRowToCol(); |
---|
2477 | } |
---|
2478 | |
---|
2479 | /* |
---|
2480 | * solve the triangular system |
---|
2481 | */ |
---|
2482 | void sparse_number_mat::smSolv() |
---|
2483 | { |
---|
2484 | int i, j; |
---|
2485 | number x, y, z; |
---|
2486 | smnumber s, d, r = m_row[nrows]; |
---|
2487 | |
---|
2488 | m_row[nrows] = NULL; |
---|
2489 | sol = (number *)omAlloc0(sizeof(number)*(crd+1)); |
---|
2490 | while (r != NULL) // expand the rigth hand side |
---|
2491 | { |
---|
2492 | sol[r->pos] = r->m; |
---|
2493 | s = r; |
---|
2494 | r = r->n; |
---|
2495 | omFreeBin((ADDRESS)s, smnrec_bin); |
---|
2496 | } |
---|
2497 | i = crd; // solve triangular system |
---|
2498 | if (sol[i] != NULL) |
---|
2499 | { |
---|
2500 | x = sol[i]; |
---|
2501 | sol[i] = n_Div(x, m_res[i]->m,_R->cf); |
---|
2502 | n_Delete(&x,_R->cf); |
---|
2503 | } |
---|
2504 | i--; |
---|
2505 | while (i > 0) |
---|
2506 | { |
---|
2507 | x = NULL; |
---|
2508 | d = m_res[i]; |
---|
2509 | s = d->n; |
---|
2510 | while (s != NULL) |
---|
2511 | { |
---|
2512 | j = s->pos; |
---|
2513 | if (sol[j] != NULL) |
---|
2514 | { |
---|
2515 | z = n_Mult(sol[j], s->m,_R->cf); |
---|
2516 | if (x != NULL) |
---|
2517 | { |
---|
2518 | y = x; |
---|
2519 | x = n_Sub(y, z,_R->cf); |
---|
2520 | n_Delete(&y,_R->cf); |
---|
2521 | n_Delete(&z,_R->cf); |
---|
2522 | } |
---|
2523 | else |
---|
2524 | x = n_InpNeg(z,_R->cf); |
---|
2525 | } |
---|
2526 | s = s->n; |
---|
2527 | } |
---|
2528 | if (sol[i] != NULL) |
---|
2529 | { |
---|
2530 | if (x != NULL) |
---|
2531 | { |
---|
2532 | y = n_Add(x, sol[i],_R->cf); |
---|
2533 | n_Delete(&x,_R->cf); |
---|
2534 | if (n_IsZero(y,_R->cf)) |
---|
2535 | { |
---|
2536 | n_Delete(&sol[i],_R->cf); |
---|
2537 | sol[i] = NULL; |
---|
2538 | } |
---|
2539 | else |
---|
2540 | sol[i] = y; |
---|
2541 | } |
---|
2542 | } |
---|
2543 | else |
---|
2544 | sol[i] = x; |
---|
2545 | if (sol[i] != NULL) |
---|
2546 | { |
---|
2547 | x = sol[i]; |
---|
2548 | sol[i] = n_Div(x, d->m,_R->cf); |
---|
2549 | n_Delete(&x,_R->cf); |
---|
2550 | } |
---|
2551 | i--; |
---|
2552 | } |
---|
2553 | this->smAllDel(); |
---|
2554 | } |
---|
2555 | |
---|
2556 | /* |
---|
2557 | * transform the result to an ideal |
---|
2558 | */ |
---|
2559 | ideal sparse_number_mat::smRes2Ideal() |
---|
2560 | { |
---|
2561 | int i, j; |
---|
2562 | ideal res = idInit(crd, 1); |
---|
2563 | |
---|
2564 | for (i=crd; i; i--) |
---|
2565 | { |
---|
2566 | j = perm[i]-1; |
---|
2567 | res->m[j] = sm_Smnumber2Poly(sol[i],_R); |
---|
2568 | } |
---|
2569 | omFreeSize((ADDRESS)sol, sizeof(number)*(crd+1)); |
---|
2570 | return res; |
---|
2571 | } |
---|
2572 | |
---|
2573 | /* ----------------- pivot method ------------------ */ |
---|
2574 | |
---|
2575 | /* |
---|
2576 | * compute pivot |
---|
2577 | */ |
---|
2578 | void sparse_number_mat::smRealPivot() |
---|
2579 | { |
---|
2580 | smnumber a; |
---|
2581 | number x, xo; |
---|
2582 | int i, copt, ropt; |
---|
2583 | |
---|
2584 | xo=n_Init(0,_R->cf); |
---|
2585 | for (i=act; i; i--) |
---|
2586 | { |
---|
2587 | a = m_act[i]; |
---|
2588 | while ((a!=NULL) && (a->pos<=tored)) |
---|
2589 | { |
---|
2590 | x = a->m; |
---|
2591 | if (n_GreaterZero(x,_R->cf)) |
---|
2592 | { |
---|
2593 | if (n_Greater(x,xo,_R->cf)) |
---|
2594 | { |
---|
2595 | n_Delete(&xo,_R->cf); |
---|
2596 | xo = n_Copy(x,_R->cf); |
---|
2597 | copt = i; |
---|
2598 | ropt = a->pos; |
---|
2599 | } |
---|
2600 | } |
---|
2601 | else |
---|
2602 | { |
---|
2603 | xo = n_InpNeg(xo,_R->cf); |
---|
2604 | if (n_Greater(xo,x,_R->cf)) |
---|
2605 | { |
---|
2606 | n_Delete(&xo,_R->cf); |
---|
2607 | xo = n_Copy(x,_R->cf); |
---|
2608 | copt = i; |
---|
2609 | ropt = a->pos; |
---|
2610 | } |
---|
2611 | xo = n_InpNeg(xo,_R->cf); |
---|
2612 | } |
---|
2613 | a = a->n; |
---|
2614 | } |
---|
2615 | } |
---|
2616 | rpiv = ropt; |
---|
2617 | if (copt != act) |
---|
2618 | { |
---|
2619 | a = m_act[act]; |
---|
2620 | m_act[act] = m_act[copt]; |
---|
2621 | m_act[copt] = a; |
---|
2622 | } |
---|
2623 | n_Delete(&xo,_R->cf); |
---|
2624 | } |
---|
2625 | |
---|
2626 | /* ----------------- elimination ------------------ */ |
---|
2627 | |
---|
2628 | /* one step of Gauss-elimination */ |
---|
2629 | void sparse_number_mat::smGElim() |
---|
2630 | { |
---|
2631 | number p = n_Invers(piv->m,_R->cf); // pivotelement |
---|
2632 | smnumber c = m_act[act]; // pivotcolumn |
---|
2633 | smnumber r = red; // row to reduce |
---|
2634 | smnumber res, a, b; |
---|
2635 | number w, ha, hb; |
---|
2636 | |
---|
2637 | if ((c == NULL) || (r == NULL)) |
---|
2638 | { |
---|
2639 | while (r!=NULL) sm_NumberDelete(&r,_R); |
---|
2640 | return; |
---|
2641 | } |
---|
2642 | do |
---|
2643 | { |
---|
2644 | a = m_act[r->pos]; |
---|
2645 | res = dumm; |
---|
2646 | res->n = NULL; |
---|
2647 | b = c; |
---|
2648 | w = n_Mult(r->m, p,_R->cf); |
---|
2649 | n_Delete(&r->m,_R->cf); |
---|
2650 | r->m = w; |
---|
2651 | loop // combine the chains a and b: a + w*b |
---|
2652 | { |
---|
2653 | if (a == NULL) |
---|
2654 | { |
---|
2655 | do |
---|
2656 | { |
---|
2657 | res = res->n = smNumberCopy(b); |
---|
2658 | res->m = n_Mult(b->m, w,_R->cf); |
---|
2659 | b = b->n; |
---|
2660 | } while (b != NULL); |
---|
2661 | break; |
---|
2662 | } |
---|
2663 | if (a->pos < b->pos) |
---|
2664 | { |
---|
2665 | res = res->n = a; |
---|
2666 | a = a->n; |
---|
2667 | } |
---|
2668 | else if (a->pos > b->pos) |
---|
2669 | { |
---|
2670 | res = res->n = smNumberCopy(b); |
---|
2671 | res->m = n_Mult(b->m, w,_R->cf); |
---|
2672 | b = b->n; |
---|
2673 | } |
---|
2674 | else |
---|
2675 | { |
---|
2676 | hb = n_Mult(b->m, w,_R->cf); |
---|
2677 | ha = n_Add(a->m, hb,_R->cf); |
---|
2678 | n_Delete(&hb,_R->cf); |
---|
2679 | n_Delete(&a->m,_R->cf); |
---|
2680 | if (n_IsZero(ha,_R->cf)) |
---|
2681 | { |
---|
2682 | sm_NumberDelete(&a,_R); |
---|
2683 | } |
---|
2684 | else |
---|
2685 | { |
---|
2686 | a->m = ha; |
---|
2687 | res = res->n = a; |
---|
2688 | a = a->n; |
---|
2689 | } |
---|
2690 | b = b->n; |
---|
2691 | } |
---|
2692 | if (b == NULL) |
---|
2693 | { |
---|
2694 | res->n = a; |
---|
2695 | break; |
---|
2696 | } |
---|
2697 | } |
---|
2698 | m_act[r->pos] = dumm->n; |
---|
2699 | sm_NumberDelete(&r,_R); |
---|
2700 | } while (r != NULL); |
---|
2701 | n_Delete(&p,_R->cf); |
---|
2702 | } |
---|
2703 | |
---|
2704 | /* ----------------- transfer ------------------ */ |
---|
2705 | |
---|
2706 | /* |
---|
2707 | * select the pivotrow and store it to red and piv |
---|
2708 | */ |
---|
2709 | void sparse_number_mat::smSelectPR() |
---|
2710 | { |
---|
2711 | smnumber b = dumm; |
---|
2712 | smnumber a, ap; |
---|
2713 | int i; |
---|
2714 | |
---|
2715 | if (TEST_OPT_PROT) |
---|
2716 | { |
---|
2717 | if ((crd+1)%10) |
---|
2718 | PrintS("."); |
---|
2719 | else |
---|
2720 | PrintS(".\n"); |
---|
2721 | } |
---|
2722 | a = m_act[act]; |
---|
2723 | if (a->pos < rpiv) |
---|
2724 | { |
---|
2725 | do |
---|
2726 | { |
---|
2727 | ap = a; |
---|
2728 | a = a->n; |
---|
2729 | } while (a->pos < rpiv); |
---|
2730 | ap->n = a->n; |
---|
2731 | } |
---|
2732 | else |
---|
2733 | m_act[act] = a->n; |
---|
2734 | piv = a; |
---|
2735 | a->n = NULL; |
---|
2736 | for (i=1; i<act; i++) |
---|
2737 | { |
---|
2738 | a = m_act[i]; |
---|
2739 | if (a->pos < rpiv) |
---|
2740 | { |
---|
2741 | loop |
---|
2742 | { |
---|
2743 | ap = a; |
---|
2744 | a = a->n; |
---|
2745 | if ((a == NULL) || (a->pos > rpiv)) |
---|
2746 | break; |
---|
2747 | if (a->pos == rpiv) |
---|
2748 | { |
---|
2749 | ap->n = a->n; |
---|
2750 | a->m = n_InpNeg(a->m,_R->cf); |
---|
2751 | b = b->n = a; |
---|
2752 | b->pos = i; |
---|
2753 | break; |
---|
2754 | } |
---|
2755 | } |
---|
2756 | } |
---|
2757 | else if (a->pos == rpiv) |
---|
2758 | { |
---|
2759 | m_act[i] = a->n; |
---|
2760 | a->m = n_InpNeg(a->m,_R->cf); |
---|
2761 | b = b->n = a; |
---|
2762 | b->pos = i; |
---|
2763 | } |
---|
2764 | } |
---|
2765 | b->n = NULL; |
---|
2766 | red = dumm->n; |
---|
2767 | } |
---|
2768 | |
---|
2769 | /* |
---|
2770 | * store the pivotcol in m_row |
---|
2771 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] |
---|
2772 | */ |
---|
2773 | void sparse_number_mat::smColToRow() |
---|
2774 | { |
---|
2775 | smnumber c = m_act[act]; |
---|
2776 | smnumber h; |
---|
2777 | |
---|
2778 | while (c != NULL) |
---|
2779 | { |
---|
2780 | h = c; |
---|
2781 | c = c->n; |
---|
2782 | h->n = m_row[h->pos]; |
---|
2783 | m_row[h->pos] = h; |
---|
2784 | h->pos = crd; |
---|
2785 | } |
---|
2786 | } |
---|
2787 | |
---|
2788 | /* |
---|
2789 | * store the pivot and the assosiated row in m_row |
---|
2790 | * to m_res (result): |
---|
2791 | * piv + m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
---|
2792 | */ |
---|
2793 | void sparse_number_mat::smRowToCol() |
---|
2794 | { |
---|
2795 | smnumber r = m_row[rpiv]; |
---|
2796 | smnumber a, ap, h; |
---|
2797 | |
---|
2798 | m_row[rpiv] = NULL; |
---|
2799 | perm[crd] = rpiv; |
---|
2800 | piv->pos = crd; |
---|
2801 | m_res[crd] = piv; |
---|
2802 | while (r != NULL) |
---|
2803 | { |
---|
2804 | ap = m_res[r->pos]; |
---|
2805 | loop |
---|
2806 | { |
---|
2807 | a = ap->n; |
---|
2808 | if (a == NULL) |
---|
2809 | { |
---|
2810 | ap->n = h = r; |
---|
2811 | r = r->n; |
---|
2812 | h->n = a; |
---|
2813 | h->pos = crd; |
---|
2814 | break; |
---|
2815 | } |
---|
2816 | ap = a; |
---|
2817 | } |
---|
2818 | } |
---|
2819 | } |
---|
2820 | |
---|
2821 | /* ----------------- C++ stuff ------------------ */ |
---|
2822 | |
---|
2823 | /* |
---|
2824 | * check singularity |
---|
2825 | */ |
---|
2826 | void sparse_number_mat::smZeroToredElim() |
---|
2827 | { |
---|
2828 | smnumber a; |
---|
2829 | int i = act; |
---|
2830 | |
---|
2831 | loop |
---|
2832 | { |
---|
2833 | if (i == 0) return; |
---|
2834 | a = m_act[i]; |
---|
2835 | if ((a==NULL) || (a->pos>tored)) |
---|
2836 | { |
---|
2837 | sing = 1; |
---|
2838 | this->smAllDel(); |
---|
2839 | return; |
---|
2840 | } |
---|
2841 | i--; |
---|
2842 | } |
---|
2843 | } |
---|
2844 | |
---|
2845 | /* |
---|
2846 | * delete all smnumber's |
---|
2847 | */ |
---|
2848 | void sparse_number_mat::smAllDel() |
---|
2849 | { |
---|
2850 | smnumber a; |
---|
2851 | int i; |
---|
2852 | |
---|
2853 | for (i=act; i; i--) |
---|
2854 | { |
---|
2855 | a = m_act[i]; |
---|
2856 | while (a != NULL) |
---|
2857 | sm_NumberDelete(&a,_R); |
---|
2858 | } |
---|
2859 | for (i=crd; i; i--) |
---|
2860 | { |
---|
2861 | a = m_res[i]; |
---|
2862 | while (a != NULL) |
---|
2863 | sm_NumberDelete(&a,_R); |
---|
2864 | } |
---|
2865 | if (act) |
---|
2866 | { |
---|
2867 | for (i=nrows; i; i--) |
---|
2868 | { |
---|
2869 | a = m_row[i]; |
---|
2870 | while (a != NULL) |
---|
2871 | sm_NumberDelete(&a,_R); |
---|
2872 | } |
---|
2873 | } |
---|
2874 | } |
---|
2875 | |
---|
2876 | /* ----------------- internal 'C' stuff ------------------ */ |
---|
2877 | |
---|
2878 | static void sm_NumberDelete(smnumber *r, const ring R) |
---|
2879 | { |
---|
2880 | smnumber a = *r, b = a->n; |
---|
2881 | |
---|
2882 | n_Delete(&a->m,R->cf); |
---|
2883 | omFreeBin((ADDRESS)a, smnrec_bin); |
---|
2884 | *r = b; |
---|
2885 | } |
---|
2886 | |
---|
2887 | static smnumber smNumberCopy(smnumber a) |
---|
2888 | { |
---|
2889 | smnumber r = (smnumber)omAllocBin(smnrec_bin); |
---|
2890 | memcpy(r, a, sizeof(smnrec)); |
---|
2891 | return r; |
---|
2892 | } |
---|
2893 | |
---|
2894 | /* |
---|
2895 | * from poly to smnumber |
---|
2896 | * do not destroy p |
---|
2897 | */ |
---|
2898 | static smnumber sm_Poly2Smnumber(poly q, const ring R) |
---|
2899 | { |
---|
2900 | smnumber a, res; |
---|
2901 | poly p = q; |
---|
2902 | |
---|
2903 | if (p == NULL) |
---|
2904 | return NULL; |
---|
2905 | a = res = (smnumber)omAllocBin(smnrec_bin); |
---|
2906 | a->pos = p_GetComp(p,R); |
---|
2907 | a->m = pGetCoeff(p); |
---|
2908 | n_New(&pGetCoeff(p),R->cf); |
---|
2909 | loop |
---|
2910 | { |
---|
2911 | pIter(p); |
---|
2912 | if (p == NULL) |
---|
2913 | { |
---|
2914 | p_Delete(&q,R); |
---|
2915 | a->n = NULL; |
---|
2916 | return res; |
---|
2917 | } |
---|
2918 | a = a->n = (smnumber)omAllocBin(smnrec_bin); |
---|
2919 | a->pos = p_GetComp(p,R); |
---|
2920 | a->m = pGetCoeff(p); |
---|
2921 | n_New(&pGetCoeff(p),R->cf); |
---|
2922 | } |
---|
2923 | } |
---|
2924 | |
---|
2925 | /* |
---|
2926 | * from smnumber to poly |
---|
2927 | * destroy a |
---|
2928 | */ |
---|
2929 | static poly sm_Smnumber2Poly(number a, const ring R) |
---|
2930 | { |
---|
2931 | poly res; |
---|
2932 | |
---|
2933 | if (a == NULL) return NULL; |
---|
2934 | res = p_Init(R); |
---|
2935 | pSetCoeff0(res, a); |
---|
2936 | return res; |
---|
2937 | } |
---|
2938 | |
---|
2939 | /*2 |
---|
2940 | * check the input |
---|
2941 | */ |
---|
2942 | static BOOLEAN smCheckSolv(ideal I) |
---|
2943 | { int i = I->ncols; |
---|
2944 | if ((i == 0) || (i != I->rank-1)) |
---|
2945 | { |
---|
2946 | WerrorS("wrong dimensions for linsolv"); |
---|
2947 | return TRUE; |
---|
2948 | } |
---|
2949 | for(;i;i--) |
---|
2950 | { |
---|
2951 | if(I->m[i-1] == NULL) |
---|
2952 | { |
---|
2953 | WerrorS("singular input for linsolv"); |
---|
2954 | return TRUE; |
---|
2955 | } |
---|
2956 | } |
---|
2957 | return FALSE; |
---|
2958 | } |
---|