1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: sparsmat.cc,v 1.48 2000-12-31 15:54:47 obachman Exp $ */ |
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5 | |
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6 | /* |
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7 | * ABSTRACT: operations with sparse matrices (bareiss, ...) |
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8 | */ |
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9 | |
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10 | #include "mod2.h" |
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11 | #include "structs.h" |
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12 | #include "tok.h" |
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13 | #include "febase.h" |
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14 | #include "structs.h" |
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15 | #include "intvec.h" |
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16 | #include "lists.h" |
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17 | #include "ring.h" |
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18 | #include "polys.h" |
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19 | #include "ipid.h" |
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20 | #include "ideals.h" |
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21 | #include "numbers.h" |
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22 | #include "sparsmat.h" |
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23 | #include "prCopy.h" |
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24 | #include "p_Procs.h" |
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25 | #include "kbuckets.h" |
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26 | #include "p_Mult_q.h" |
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27 | |
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28 | // define SM_NO_BUCKETS, if sparsemat stuff should not use buckets |
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29 | // #define SM_NO_BUCKETS |
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30 | |
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31 | // this is also influenced by TEST_OPT_NOTBUCKETS |
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32 | #ifndef SM_NO_BUCKETS |
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33 | // buckets do carry a small additional overhead: only use them if |
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34 | // min-length of polys is >= SM_MIN_LENGTH_BUCKET |
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35 | #define SM_MIN_LENGTH_BUCKET MIN_LENGTH_BUCKET - 5 |
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36 | #else |
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37 | #define SM_MIN_LENGTH_BUCKET INT_MAX |
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38 | #endif |
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39 | |
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40 | |
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41 | /* declare internal 'C' stuff */ |
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42 | static void smExactPolyDiv(poly, poly); |
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43 | static BOOLEAN smIsNegQuot(poly, const poly, const poly); |
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44 | static void smExpMultDiv(poly, const poly, const poly); |
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45 | static void smPolyDivN(poly, const number); |
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46 | static BOOLEAN smSmaller(poly, poly); |
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47 | static void smCombineChain(poly *, poly); |
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48 | static void smFindRef(poly *, poly *, poly); |
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49 | |
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50 | static void smElemDelete(smpoly *); |
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51 | static smpoly smElemCopy(smpoly); |
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52 | static float smPolyWeight(smpoly); |
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53 | static smpoly smPoly2Smpoly(poly); |
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54 | static poly smSmpoly2Poly(smpoly); |
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55 | static BOOLEAN smHaveDenom(poly); |
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56 | static number smCleardenom(ideal); |
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57 | |
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58 | static poly pp_Mult_Coeff_mm_DivSelect_MultDiv(poly p, int &lp, poly m, |
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59 | poly a, poly b) |
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60 | { |
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61 | if (rOrd_is_Comp_dp(currRing) && currRing->ExpL_Size > 2) |
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62 | { |
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63 | // pp_Mult_Coeff_mm_DivSelectMult only works for (c/C,dp) and |
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64 | // ExpL_Size > 2 |
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65 | // should be generalized, at least to dp with ExpL_Size == 2 |
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66 | // (is the case for 1 variable) |
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67 | int shorter; |
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68 | p = currRing->p_Procs->pp_Mult_Coeff_mm_DivSelectMult(p, m, a, b, |
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69 | shorter, currRing); |
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70 | lp -= shorter; |
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71 | } |
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72 | else |
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73 | { |
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74 | p = pp_Mult_Coeff_mm_DivSelect(p, lp, m, currRing); |
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75 | smExpMultDiv(p, a, b); |
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76 | } |
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77 | return p; |
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78 | } |
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79 | |
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80 | static poly smSelectCopy_ExpMultDiv(poly p, poly m, poly a, poly b) |
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81 | { |
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82 | int lp = 0; |
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83 | return pp_Mult_Coeff_mm_DivSelect_MultDiv(p, lp, m, a, b); |
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84 | } |
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85 | |
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86 | |
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87 | /* class for sparse matrix: |
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88 | * 3 parts of matrix during the algorithm |
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89 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
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90 | * input pivotcols as rows result |
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91 | * pivot like a stack from pivot and pivotcols |
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92 | * elimination rows reordered according |
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93 | * to pivot choise |
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94 | * stored in perm |
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95 | * a step is as follows |
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96 | * - search of pivot (smPivot) |
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97 | * - swap pivot column and last column (smSwapC) |
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98 | * select pivotrow to piv and red (smSelectPR) |
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99 | * consider sign |
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100 | * - elimination (smInitElim, sm0Elim, sm1Elim) |
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101 | * clear zero column as result of elimination (smZeroElim) |
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102 | * - tranfer from |
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103 | * piv and m_row to m_res (smRowToCol) |
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104 | * m_act to m_row (smColToRow) |
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105 | */ |
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106 | class sparse_mat{ |
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107 | private: |
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108 | int nrows, ncols; // dimension of the problem |
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109 | int sign; // for determinant (start: 1) |
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110 | int act; // number of unreduced columns (start: ncols) |
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111 | int crd; // number of reduced columns (start: 0) |
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112 | int tored; // border for rows to reduce |
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113 | int inred; // unreducable part |
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114 | int rpiv, cpiv; // position of the pivot |
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115 | int normalize; // Normalization flag |
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116 | int *perm; // permutation of rows |
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117 | float wpoints; // weight of all points |
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118 | float *wrw, *wcl; // weights of rows and columns |
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119 | smpoly * m_act; // unreduced columns |
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120 | smpoly * m_res; // reduced columns (result) |
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121 | smpoly * m_row; // reduced part of rows |
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122 | smpoly red; // row to reduce |
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123 | smpoly piv, oldpiv; // pivot and previous pivot |
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124 | smpoly dumm; // allocated dummy |
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125 | void smColToRow(); |
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126 | void smRowToCol(); |
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127 | void smFinalMult(); |
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128 | void smSparseHomog(); |
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129 | void smWeights(); |
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130 | void smPivot(); |
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131 | void smNewWeights(); |
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132 | void smNewPivot(); |
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133 | void smZeroElim(); |
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134 | void smToredElim(); |
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135 | void smCopToRes(); |
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136 | void smSelectPR(); |
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137 | void smElim(); |
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138 | void sm1Elim(); |
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139 | void smHElim(); |
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140 | void smMultCol(); |
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141 | poly smMultPoly(smpoly); |
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142 | void smActDel(); |
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143 | void smColDel(); |
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144 | void smPivDel(); |
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145 | void smSign(); |
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146 | void smInitPerm(); |
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147 | int smCheckNormalize(); |
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148 | void smNormalize(); |
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149 | public: |
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150 | sparse_mat(ideal); |
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151 | ~sparse_mat(); |
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152 | int smGetSign() { return sign; } |
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153 | smpoly * smGetAct() { return m_act; } |
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154 | int smGetRed() { return tored; } |
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155 | ideal smRes2Mod(); |
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156 | poly smDet(); |
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157 | void smBareiss(int, int); |
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158 | void smNewBareiss(int, int); |
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159 | void smToIntvec(intvec *); |
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160 | }; |
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161 | |
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162 | Exponent_t smExpBound(ideal Id) |
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163 | { |
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164 | Exponent_t max = 0; |
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165 | long ldeg; |
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166 | int dummy, i, n = IDELEMS(Id); |
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167 | |
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168 | for (i=0; i<n; i++) |
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169 | { |
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170 | if (Id->m[i] != NULL) |
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171 | { |
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172 | ldeg = pLDeg(Id->m[i], &dummy); |
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173 | if (ldeg > max) max = ldeg; |
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174 | } |
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175 | } |
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176 | return max*2*n; |
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177 | } |
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178 | |
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179 | // #define HOMOG_LP |
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180 | /* ----------------- ops with rings ------------------ */ |
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181 | ideal smRingCopy(ideal I, ring *ri, sip_sring &tmpR) |
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182 | { |
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183 | ring origR =NULL; |
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184 | ideal II; |
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185 | origR =currRing; |
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186 | tmpR=*origR; |
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187 | int *ord=(int*)omAlloc0(3*sizeof(int)); |
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188 | int *block0=(int*)omAlloc(3*sizeof(int)); |
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189 | int *block1=(int*)omAlloc(3*sizeof(int)); |
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190 | ord[0]=ringorder_c; |
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191 | #ifdef HOMOG_LP |
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192 | if (idHomIdeal(I)) |
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193 | ord[1] = ringorder_lp; |
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194 | else |
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195 | #endif |
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196 | ord[1]=ringorder_dp; |
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197 | tmpR.order=ord; |
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198 | tmpR.OrdSgn=1; |
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199 | block0[1]=1; |
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200 | tmpR.block0=block0; |
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201 | block1[1]=tmpR.N; |
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202 | tmpR.block1=block1; |
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203 | |
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204 | tmpR.bitmask = smExpBound(I); |
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205 | |
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206 | // unfortunately, we can not work (yet) with r->N == 0 |
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207 | if (tmpR.bitmask < 1) tmpR.bitmask = 1; |
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208 | if (tmpR.bitmask > currRing->bitmask) tmpR.bitmask = currRing->bitmask; |
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209 | |
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210 | rComplete(&tmpR,1); |
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211 | rChangeCurrRing(&tmpR); |
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212 | if (TEST_OPT_PROT) |
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213 | Print("[%d:%d]", (long) tmpR.bitmask, tmpR.ExpL_Size); |
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214 | // fetch data from the old ring |
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215 | II = idrCopyR(I, origR); |
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216 | idTest(II); |
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217 | *ri = origR; |
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218 | return II; |
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219 | } |
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220 | |
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221 | void smRingClean(ring origR, ip_sring &tmpR) |
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222 | { |
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223 | rChangeCurrRing(origR); |
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224 | rUnComplete(&tmpR); |
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225 | omFreeSize((ADDRESS)tmpR.order,3*sizeof(int)); |
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226 | omFreeSize((ADDRESS)tmpR.block0,3*sizeof(int)); |
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227 | omFreeSize((ADDRESS)tmpR.block1,3*sizeof(int)); |
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228 | } |
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229 | |
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230 | /* ----------------- basics (used from 'C') ------------------ */ |
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231 | /*2 |
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232 | *returns the determinant of the module I; |
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233 | *uses Bareiss algorithm |
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234 | */ |
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235 | poly smCallDet(ideal I) |
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236 | { |
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237 | if (I->ncols != I->rank) |
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238 | { |
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239 | Werror("det of %d x %d module (matrix)",I->rank,I->ncols); |
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240 | return NULL; |
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241 | } |
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242 | int r=idRankFreeModule(I); |
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243 | if (I->ncols != r) // some 0-lines at the end |
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244 | { |
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245 | return NULL; |
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246 | } |
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247 | number diag,h=nInit(1); |
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248 | poly res,save; |
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249 | ring origR; |
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250 | sip_sring tmpR; |
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251 | sparse_mat *det; |
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252 | ideal II=smRingCopy(I,&origR,tmpR); |
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253 | |
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254 | diag = smCleardenom(II); |
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255 | det = new sparse_mat(II); |
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256 | idDelete(&II); |
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257 | if (det->smGetAct() == NULL) |
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258 | { |
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259 | delete det; |
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260 | if (origR!=NULL) smRingClean(origR,tmpR); |
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261 | return NULL; |
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262 | } |
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263 | res=det->smDet(); |
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264 | if(det->smGetSign()<0) res=pNeg(res); |
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265 | delete det; |
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266 | if (origR!=NULL) |
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267 | { |
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268 | rChangeCurrRing(origR); |
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269 | save = res; |
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270 | res = prCopyR( save, &tmpR); |
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271 | rChangeCurrRing(&tmpR); |
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272 | pDelete(&save); |
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273 | smRingClean(origR,tmpR); |
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274 | } |
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275 | if (nEqual(diag,h) == FALSE) |
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276 | { |
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277 | pMult_nn(res,diag); |
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278 | pNormalize(res); |
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279 | } |
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280 | nDelete(&diag); |
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281 | nDelete(&h); |
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282 | return res; |
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283 | } |
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284 | |
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285 | lists smCallBareiss(ideal I, int x, int y) |
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286 | { |
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287 | ring origR; |
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288 | sip_sring tmpR; |
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289 | lists res=(lists)omAllocBin(slists_bin); |
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290 | ideal II = smRingCopy(I,&origR,tmpR); |
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291 | sparse_mat *bareiss = new sparse_mat(II); |
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292 | ideal mm=II; |
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293 | intvec *v; |
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294 | ideal m; |
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295 | |
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296 | if (bareiss->smGetAct() == NULL) |
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297 | { |
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298 | delete bareiss; |
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299 | if (origR!=NULL) smRingClean(origR,tmpR); |
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300 | v=new intvec(1,pVariables); |
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301 | } |
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302 | else |
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303 | { |
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304 | idDelete(&II); |
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305 | bareiss->smBareiss(x, y); |
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306 | m = bareiss->smRes2Mod(); |
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307 | v = new intvec(bareiss->smGetRed()); |
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308 | bareiss->smToIntvec(v); |
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309 | delete bareiss; |
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310 | if (origR!=NULL) |
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311 | { |
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312 | rChangeCurrRing(origR); |
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313 | mm=idInit(IDELEMS(m),m->rank); |
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314 | int k; |
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315 | for (k=0;k<IDELEMS(m);k++) mm->m[k] = prCopyR( m->m[k], &tmpR); |
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316 | rChangeCurrRing(&tmpR); |
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317 | idDelete(&m); |
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318 | smRingClean(origR,tmpR); |
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319 | } |
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320 | else |
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321 | { |
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322 | mm=m; |
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323 | } |
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324 | } |
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325 | res->Init(2); |
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326 | res->m[0].rtyp=MODUL_CMD; |
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327 | res->m[0].data=(void *)mm; |
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328 | res->m[1].rtyp=INTVEC_CMD; |
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329 | res->m[1].data=(void *)v; |
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330 | return res; |
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331 | } |
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332 | |
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333 | lists smCallNewBareiss(ideal I, int x, int y) |
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334 | { |
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335 | ring origR; |
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336 | sip_sring tmpR; |
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337 | lists res=(lists)omAllocBin(slists_bin); |
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338 | ideal II=smRingCopy(I,&origR,tmpR); |
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339 | sparse_mat *bareiss = new sparse_mat(II); |
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340 | ideal mm=II; |
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341 | intvec *v; |
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342 | ideal m; |
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343 | |
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344 | if (bareiss->smGetAct() == NULL) |
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345 | { |
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346 | delete bareiss; |
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347 | if (origR!=NULL) smRingClean(origR,tmpR); |
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348 | v=new intvec(1,pVariables); |
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349 | } |
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350 | else |
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351 | { |
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352 | idDelete(&II); |
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353 | bareiss->smNewBareiss(x, y); |
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354 | m = bareiss->smRes2Mod(); |
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355 | v = new intvec(bareiss->smGetRed()); |
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356 | bareiss->smToIntvec(v); |
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357 | delete bareiss; |
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358 | if (origR!=NULL) |
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359 | { |
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360 | rChangeCurrRing(origR); |
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361 | mm=idInit(IDELEMS(m),m->rank); |
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362 | int k; |
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363 | for (k=0;k<IDELEMS(m);k++) mm->m[k] = prCopyR( m->m[k], &tmpR); |
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364 | rChangeCurrRing(&tmpR); |
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365 | idDelete(&m); |
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366 | smRingClean(origR,tmpR); |
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367 | } |
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368 | else |
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369 | { |
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370 | mm=m; |
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371 | } |
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372 | } |
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373 | res->Init(2); |
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374 | res->m[0].rtyp=MODUL_CMD; |
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375 | res->m[0].data=(void *)mm; |
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376 | res->m[1].rtyp=INTVEC_CMD; |
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377 | res->m[1].data=(void *)v; |
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378 | return res; |
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379 | } |
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380 | |
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381 | /* |
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382 | * constructor |
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383 | */ |
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384 | sparse_mat::sparse_mat(ideal smat) |
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385 | { |
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386 | int i; |
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387 | polyset pmat; |
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388 | |
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389 | ncols = smat->ncols; |
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390 | nrows = idRankFreeModule(smat); |
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391 | if (nrows <= 0) |
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392 | { |
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393 | m_act = NULL; |
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394 | return; |
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395 | } |
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396 | sign = 1; |
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397 | inred = act = ncols; |
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398 | crd = 0; |
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399 | tored = nrows; // without border |
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400 | i = tored+1; |
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401 | perm = (int *)omAlloc(sizeof(int)*(i+1)); |
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402 | perm[i] = 0; |
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403 | m_row = (smpoly *)omAlloc0(sizeof(smpoly)*i); |
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404 | wrw = (float *)omAlloc(sizeof(float)*i); |
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405 | i = ncols+1; |
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406 | wcl = (float *)omAlloc(sizeof(float)*i); |
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407 | m_act = (smpoly *)omAlloc(sizeof(smpoly)*i); |
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408 | m_res = (smpoly *)omAlloc0(sizeof(smpoly)*i); |
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409 | dumm = (smpoly)omAllocBin(smprec_bin); |
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410 | m_res[0] = (smpoly)omAllocBin(smprec_bin); |
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411 | m_res[0]->m = NULL; |
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412 | pmat = smat->m; |
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413 | for(i=ncols; i; i--) |
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414 | { |
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415 | m_act[i] = smPoly2Smpoly(pmat[i-1]); |
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416 | pmat[i-1] = NULL; |
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417 | } |
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418 | this->smZeroElim(); |
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419 | oldpiv = NULL; |
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420 | } |
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421 | |
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422 | /* |
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423 | * destructor |
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424 | */ |
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425 | sparse_mat::~sparse_mat() |
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426 | { |
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427 | int i; |
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428 | if (m_act == NULL) return; |
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429 | omFreeBin((ADDRESS)m_res[0], smprec_bin); |
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430 | omFreeBin((ADDRESS)dumm, smprec_bin); |
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431 | i = ncols+1; |
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432 | omFreeSize((ADDRESS)m_res, sizeof(smpoly)*i); |
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433 | omFreeSize((ADDRESS)m_act, sizeof(smpoly)*i); |
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434 | omFreeSize((ADDRESS)wcl, sizeof(float)*i); |
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435 | i = nrows+1; |
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436 | omFreeSize((ADDRESS)wrw, sizeof(float)*i); |
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437 | omFreeSize((ADDRESS)m_row, sizeof(smpoly)*i); |
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438 | omFreeSize((ADDRESS)perm, sizeof(int)*(i+1)); |
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439 | } |
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440 | |
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441 | /* |
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442 | * transform the result to a module |
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443 | */ |
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444 | ideal sparse_mat::smRes2Mod() |
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445 | { |
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446 | ideal res = idInit(crd, crd); |
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447 | int i; |
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448 | |
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449 | for (i=crd; i; i--) res->m[i-1] = smSmpoly2Poly(m_res[i]); |
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450 | res->rank = idRankFreeModule(res); |
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451 | return res; |
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452 | } |
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453 | |
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454 | /* |
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455 | * permutation of rows |
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456 | */ |
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457 | void sparse_mat::smToIntvec(intvec *v) |
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458 | { |
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459 | int i; |
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460 | |
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461 | for (i=v->rows()-1; i>=0; i--) |
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462 | (*v)[i] = perm[i+1]; |
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463 | } |
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464 | /* ---------------- the algorithm's ------------------ */ |
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465 | /* |
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466 | * the determinant (up to sign), uses new Bareiss elimination |
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467 | */ |
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468 | poly sparse_mat::smDet() |
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469 | { |
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470 | int y; |
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471 | poly res = NULL; |
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472 | |
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473 | if (sign == 0) |
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474 | { |
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475 | this->smActDel(); |
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476 | return NULL; |
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477 | } |
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478 | if (act < 2) |
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479 | { |
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480 | if (act != 0) res = m_act[1]->m; |
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481 | omFreeBin((void *)m_act[1], smprec_bin); |
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482 | return res; |
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483 | } |
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484 | normalize = 0; |
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485 | this->smInitPerm(); |
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486 | this->smPivot(); |
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487 | this->smSign(); |
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488 | this->smSelectPR(); |
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489 | this->sm1Elim(); |
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490 | crd++; |
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491 | m_res[crd] = piv; |
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492 | this->smColDel(); |
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493 | act--; |
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494 | this->smZeroElim(); |
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495 | if (sign == 0) |
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496 | { |
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497 | this->smActDel(); |
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498 | return NULL; |
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499 | } |
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500 | if (act < 2) |
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501 | { |
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502 | this->smFinalMult(); |
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503 | this->smPivDel(); |
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504 | if (act != 0) res = m_act[1]->m; |
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505 | omFreeBin((void *)m_act[1], smprec_bin); |
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506 | return res; |
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507 | } |
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508 | loop |
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509 | { |
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510 | this->smNewPivot(); |
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511 | this->smSign(); |
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512 | this->smSelectPR(); |
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513 | this->smMultCol(); |
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514 | this->smHElim(); |
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515 | crd++; |
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516 | m_res[crd] = piv; |
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517 | this->smColDel(); |
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518 | act--; |
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519 | this->smZeroElim(); |
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520 | if (sign == 0) |
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521 | { |
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522 | this->smPivDel(); |
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523 | this->smActDel(); |
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524 | return NULL; |
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525 | } |
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526 | if (act < 2) |
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527 | { |
---|
528 | if (TEST_OPT_PROT) PrintS(".\n"); |
---|
529 | this->smFinalMult(); |
---|
530 | this->smPivDel(); |
---|
531 | if (act != 0) res = m_act[1]->m; |
---|
532 | omFreeBin((void *)m_act[1], smprec_bin); |
---|
533 | return res; |
---|
534 | } |
---|
535 | } |
---|
536 | } |
---|
537 | |
---|
538 | /* |
---|
539 | * the Bareiss elimination: |
---|
540 | * - with x unreduced last rows, pivots from here are not allowed |
---|
541 | * - the method will finish for number of unreduced columns < y |
---|
542 | */ |
---|
543 | void sparse_mat::smBareiss(int x, int y) |
---|
544 | { |
---|
545 | if ((x > 0) && (x < nrows)) |
---|
546 | { |
---|
547 | tored -= x; |
---|
548 | this->smToredElim(); |
---|
549 | } |
---|
550 | if (y < 1) y = 1; |
---|
551 | if (act <= y) |
---|
552 | { |
---|
553 | this->smCopToRes(); |
---|
554 | return; |
---|
555 | } |
---|
556 | normalize = this->smCheckNormalize(); |
---|
557 | if (normalize) this->smNormalize(); |
---|
558 | this->smPivot(); |
---|
559 | this->smSelectPR(); |
---|
560 | this->smElim(); |
---|
561 | crd++; |
---|
562 | this->smColToRow(); |
---|
563 | act--; |
---|
564 | this->smRowToCol(); |
---|
565 | this->smZeroElim(); |
---|
566 | if (tored != nrows) |
---|
567 | this->smToredElim(); |
---|
568 | if (act < y) |
---|
569 | { |
---|
570 | this->smCopToRes(); |
---|
571 | return; |
---|
572 | } |
---|
573 | loop |
---|
574 | { |
---|
575 | if (normalize) this->smNormalize(); |
---|
576 | this->smPivot(); |
---|
577 | oldpiv = piv; |
---|
578 | this->smSelectPR(); |
---|
579 | this->smElim(); |
---|
580 | crd++; |
---|
581 | this->smColToRow(); |
---|
582 | act--; |
---|
583 | this->smRowToCol(); |
---|
584 | this->smZeroElim(); |
---|
585 | if (tored != nrows) |
---|
586 | this->smToredElim(); |
---|
587 | if (act < y) |
---|
588 | { |
---|
589 | if (TEST_OPT_PROT) PrintS(".\n"); |
---|
590 | this->smCopToRes(); |
---|
591 | return; |
---|
592 | } |
---|
593 | } |
---|
594 | } |
---|
595 | |
---|
596 | /* |
---|
597 | * the new Bareiss elimination: |
---|
598 | * - with x unreduced last rows, pivots from here are not allowed |
---|
599 | * - the method will finish for number of unreduced columns < y |
---|
600 | */ |
---|
601 | void sparse_mat::smNewBareiss(int x, int y) |
---|
602 | { |
---|
603 | if ((x > 0) && (x < nrows)) |
---|
604 | { |
---|
605 | tored -= x; |
---|
606 | this->smToredElim(); |
---|
607 | } |
---|
608 | if (y < 1) y = 1; |
---|
609 | if (act <= y) |
---|
610 | { |
---|
611 | this->smCopToRes(); |
---|
612 | return; |
---|
613 | } |
---|
614 | normalize = this->smCheckNormalize(); |
---|
615 | if (normalize) this->smNormalize(); |
---|
616 | this->smPivot(); |
---|
617 | this->smSelectPR(); |
---|
618 | this->sm1Elim(); |
---|
619 | crd++; |
---|
620 | this->smColToRow(); |
---|
621 | act--; |
---|
622 | this->smRowToCol(); |
---|
623 | this->smZeroElim(); |
---|
624 | if (tored != nrows) |
---|
625 | this->smToredElim(); |
---|
626 | if (act <= y) |
---|
627 | { |
---|
628 | this->smFinalMult(); |
---|
629 | this->smCopToRes(); |
---|
630 | return; |
---|
631 | } |
---|
632 | loop |
---|
633 | { |
---|
634 | if (normalize) this->smNormalize(); |
---|
635 | this->smNewPivot(); |
---|
636 | this->smSelectPR(); |
---|
637 | this->smMultCol(); |
---|
638 | this->smHElim(); |
---|
639 | crd++; |
---|
640 | this->smColToRow(); |
---|
641 | act--; |
---|
642 | this->smRowToCol(); |
---|
643 | this->smZeroElim(); |
---|
644 | if (tored != nrows) |
---|
645 | this->smToredElim(); |
---|
646 | if (act <= y) |
---|
647 | { |
---|
648 | if (TEST_OPT_PROT) PrintS(".\n"); |
---|
649 | this->smFinalMult(); |
---|
650 | this->smCopToRes(); |
---|
651 | return; |
---|
652 | } |
---|
653 | } |
---|
654 | } |
---|
655 | |
---|
656 | /* ----------------- pivot method ------------------ */ |
---|
657 | |
---|
658 | /* |
---|
659 | * prepare smPivot, compute weights for rows and columns |
---|
660 | * and the weight for all points |
---|
661 | */ |
---|
662 | void sparse_mat::smWeights() |
---|
663 | { |
---|
664 | float wc, wp, w; |
---|
665 | smpoly a; |
---|
666 | int i; |
---|
667 | |
---|
668 | wp = 0.0; |
---|
669 | for (i=tored; i; i--) wrw[i] = 0.0; // ??? |
---|
670 | for (i=act; i; i--) |
---|
671 | { |
---|
672 | wc = 0.0; |
---|
673 | a = m_act[i]; |
---|
674 | loop |
---|
675 | { |
---|
676 | if (a->pos > tored) |
---|
677 | break; |
---|
678 | w = a->f = smPolyWeight(a); |
---|
679 | wc += w; |
---|
680 | wrw[a->pos] += w; |
---|
681 | a = a->n; |
---|
682 | if (a == NULL) |
---|
683 | break; |
---|
684 | } |
---|
685 | wp += wc; |
---|
686 | wcl[i] = wc; |
---|
687 | } |
---|
688 | wpoints = wp; |
---|
689 | } |
---|
690 | |
---|
691 | /* |
---|
692 | * compute pivot |
---|
693 | */ |
---|
694 | void sparse_mat::smPivot() |
---|
695 | { |
---|
696 | float wopt = 1.0e30; |
---|
697 | float wc, wr, wp, w; |
---|
698 | smpoly a; |
---|
699 | int i, copt, ropt; |
---|
700 | |
---|
701 | this->smWeights(); |
---|
702 | for (i=act; i; i--) |
---|
703 | { |
---|
704 | a = m_act[i]; |
---|
705 | loop |
---|
706 | { |
---|
707 | if (a->pos > tored) |
---|
708 | break; |
---|
709 | w = a->f; |
---|
710 | wc = wcl[i]-w; |
---|
711 | wr = wrw[a->pos]-w; |
---|
712 | if ((wr<0.25) || (wc<0.25)) // row or column with only one point |
---|
713 | { |
---|
714 | if (w<wopt) |
---|
715 | { |
---|
716 | wopt = w; |
---|
717 | copt = i; |
---|
718 | ropt = a->pos; |
---|
719 | } |
---|
720 | } |
---|
721 | else // elimination |
---|
722 | { |
---|
723 | wp = w*(wpoints-wcl[i]-wr); |
---|
724 | wp += wr*wc; |
---|
725 | if (wp < wopt) |
---|
726 | { |
---|
727 | wopt = wp; |
---|
728 | copt = i; |
---|
729 | ropt = a->pos; |
---|
730 | } |
---|
731 | } |
---|
732 | a = a->n; |
---|
733 | if (a == NULL) |
---|
734 | break; |
---|
735 | } |
---|
736 | } |
---|
737 | rpiv = ropt; |
---|
738 | cpiv = copt; |
---|
739 | if (cpiv != act) |
---|
740 | { |
---|
741 | a = m_act[act]; |
---|
742 | m_act[act] = m_act[cpiv]; |
---|
743 | m_act[cpiv] = a; |
---|
744 | } |
---|
745 | } |
---|
746 | |
---|
747 | /* |
---|
748 | * prepare smPivot, compute weights for rows and columns |
---|
749 | * and the weight for all points |
---|
750 | */ |
---|
751 | void sparse_mat::smNewWeights() |
---|
752 | { |
---|
753 | float wc, wp, w, hp = piv->f; |
---|
754 | smpoly a; |
---|
755 | int i, f, e = crd; |
---|
756 | |
---|
757 | wp = 0.0; |
---|
758 | for (i=tored; i; i--) wrw[i] = 0.0; // ??? |
---|
759 | for (i=act; i; i--) |
---|
760 | { |
---|
761 | wc = 0.0; |
---|
762 | a = m_act[i]; |
---|
763 | loop |
---|
764 | { |
---|
765 | if (a->pos > tored) |
---|
766 | break; |
---|
767 | w = a->f; |
---|
768 | f = a->e; |
---|
769 | if (f < e) |
---|
770 | { |
---|
771 | w *= hp; |
---|
772 | if (f) w /= m_res[f]->f; |
---|
773 | } |
---|
774 | wc += w; |
---|
775 | wrw[a->pos] += w; |
---|
776 | a = a->n; |
---|
777 | if (a == NULL) |
---|
778 | break; |
---|
779 | } |
---|
780 | wp += wc; |
---|
781 | wcl[i] = wc; |
---|
782 | } |
---|
783 | wpoints = wp; |
---|
784 | } |
---|
785 | |
---|
786 | /* |
---|
787 | * compute pivot |
---|
788 | */ |
---|
789 | void sparse_mat::smNewPivot() |
---|
790 | { |
---|
791 | float wopt = 1.0e30, hp = piv->f; |
---|
792 | float wc, wr, wp, w; |
---|
793 | smpoly a; |
---|
794 | int i, copt, ropt, f, e = crd; |
---|
795 | |
---|
796 | this->smNewWeights(); |
---|
797 | for (i=act; i; i--) |
---|
798 | { |
---|
799 | a = m_act[i]; |
---|
800 | loop |
---|
801 | { |
---|
802 | if (a->pos > tored) |
---|
803 | break; |
---|
804 | w = a->f; |
---|
805 | f = a->e; |
---|
806 | if (f < e) |
---|
807 | { |
---|
808 | w *= hp; |
---|
809 | if (f) w /= m_res[f]->f; |
---|
810 | } |
---|
811 | wc = wcl[i]-w; |
---|
812 | wr = wrw[a->pos]-w; |
---|
813 | if ((wr<0.25) || (wc<0.25)) // row or column with only one point |
---|
814 | { |
---|
815 | if (w<wopt) |
---|
816 | { |
---|
817 | wopt = w; |
---|
818 | copt = i; |
---|
819 | ropt = a->pos; |
---|
820 | } |
---|
821 | } |
---|
822 | else // elimination |
---|
823 | { |
---|
824 | wp = w*(wpoints-wcl[i]-wr); |
---|
825 | wp += wr*wc; |
---|
826 | if (wp < wopt) |
---|
827 | { |
---|
828 | wopt = wp; |
---|
829 | copt = i; |
---|
830 | ropt = a->pos; |
---|
831 | } |
---|
832 | } |
---|
833 | a = a->n; |
---|
834 | if (a == NULL) |
---|
835 | break; |
---|
836 | } |
---|
837 | } |
---|
838 | rpiv = ropt; |
---|
839 | cpiv = copt; |
---|
840 | if (cpiv != act) |
---|
841 | { |
---|
842 | a = m_act[act]; |
---|
843 | m_act[act] = m_act[cpiv]; |
---|
844 | m_act[cpiv] = a; |
---|
845 | } |
---|
846 | } |
---|
847 | |
---|
848 | /* ----------------- elimination ------------------ */ |
---|
849 | |
---|
850 | /* steps of elimination */ |
---|
851 | void sparse_mat::smElim() |
---|
852 | { |
---|
853 | poly p = piv->m; // pivotelement |
---|
854 | smpoly c = m_act[act]; // pivotcolumn |
---|
855 | smpoly r = red; // row to reduce |
---|
856 | poly q; |
---|
857 | smpoly res, a, b; |
---|
858 | poly w, ha, hb; |
---|
859 | int i; |
---|
860 | |
---|
861 | if (oldpiv != NULL) q = oldpiv->m; // previous pivot |
---|
862 | else q = NULL; |
---|
863 | if ((c == NULL) || (r == NULL)) |
---|
864 | { |
---|
865 | while (r) smElemDelete(&r); |
---|
866 | for (i=1; i<act; i++) |
---|
867 | { |
---|
868 | a = m_act[i]; |
---|
869 | while (a != NULL) |
---|
870 | { |
---|
871 | ha = SM_MULT(a->m, p, q); |
---|
872 | pDelete(&a->m); |
---|
873 | if (q) SM_DIV(ha, q); |
---|
874 | a->m = ha; |
---|
875 | a = a->n; |
---|
876 | } |
---|
877 | } |
---|
878 | return; |
---|
879 | } |
---|
880 | for (i=1; i<act; i++) |
---|
881 | { |
---|
882 | a = m_act[i]; |
---|
883 | if ((r == NULL) || (i != r->pos)) // cols without elimination |
---|
884 | { |
---|
885 | while (a != NULL) |
---|
886 | { |
---|
887 | ha = SM_MULT(a->m, p, q); |
---|
888 | pDelete(&a->m); |
---|
889 | if (q) SM_DIV(ha, q); |
---|
890 | a->m = ha; |
---|
891 | a = a->n; |
---|
892 | } |
---|
893 | } |
---|
894 | else // cols with elimination |
---|
895 | { |
---|
896 | res = dumm; |
---|
897 | res->n = NULL; |
---|
898 | b = c; |
---|
899 | w = r->m; |
---|
900 | loop // combine the chains a and b: p*a + w*b |
---|
901 | { |
---|
902 | if (a == NULL) |
---|
903 | { |
---|
904 | if (b != NULL) |
---|
905 | { |
---|
906 | do |
---|
907 | { |
---|
908 | res = res->n = smElemCopy(b); |
---|
909 | hb = SM_MULT(b->m, w, q); |
---|
910 | if (q) SM_DIV(hb, q); |
---|
911 | res->m = hb; |
---|
912 | b = b->n; |
---|
913 | } while (b != NULL); |
---|
914 | } |
---|
915 | else |
---|
916 | res->n = NULL; |
---|
917 | break; |
---|
918 | } |
---|
919 | if (b == NULL) |
---|
920 | { |
---|
921 | do |
---|
922 | { |
---|
923 | ha = SM_MULT(a->m, p, q); |
---|
924 | pDelete(&a->m); |
---|
925 | if (q) SM_DIV(ha, q); |
---|
926 | a->m = ha; |
---|
927 | res = res->n = a; |
---|
928 | a = a->n; |
---|
929 | } while (a != NULL); |
---|
930 | break; |
---|
931 | } |
---|
932 | if (a->pos < b->pos) |
---|
933 | { |
---|
934 | ha = SM_MULT(a->m, p, q); |
---|
935 | pDelete(&a->m); |
---|
936 | if (q) SM_DIV(ha, q); |
---|
937 | a->m = ha; |
---|
938 | res = res->n = a; |
---|
939 | a = a->n; |
---|
940 | } |
---|
941 | else if (a->pos > b->pos) |
---|
942 | { |
---|
943 | res = res->n = smElemCopy(b); |
---|
944 | hb = SM_MULT(b->m, w, q); |
---|
945 | b = b->n; |
---|
946 | if (q) SM_DIV(hb, q); |
---|
947 | res->m = hb; |
---|
948 | } |
---|
949 | else |
---|
950 | { |
---|
951 | ha = SM_MULT(a->m, p, q); |
---|
952 | pDelete(&a->m); |
---|
953 | hb = SM_MULT(b->m, w, q); |
---|
954 | ha = pAdd(ha, hb); |
---|
955 | if (ha != NULL) |
---|
956 | { |
---|
957 | if (q) SM_DIV(ha, q); |
---|
958 | a->m = ha; |
---|
959 | res = res->n = a; |
---|
960 | a = a->n; |
---|
961 | } |
---|
962 | else |
---|
963 | { |
---|
964 | smElemDelete(&a); |
---|
965 | } |
---|
966 | b = b->n; |
---|
967 | } |
---|
968 | } |
---|
969 | m_act[i] = dumm->n; |
---|
970 | if (r) smElemDelete(&r); |
---|
971 | } |
---|
972 | } |
---|
973 | } |
---|
974 | |
---|
975 | /* first step of elimination */ |
---|
976 | void sparse_mat::sm1Elim() |
---|
977 | { |
---|
978 | poly p = piv->m; // pivotelement |
---|
979 | smpoly c = m_act[act]; // pivotcolumn |
---|
980 | smpoly r = red; // row to reduce |
---|
981 | smpoly res, a, b; |
---|
982 | poly w, ha, hb; |
---|
983 | |
---|
984 | if ((c == NULL) || (r == NULL)) |
---|
985 | { |
---|
986 | while (r!=NULL) smElemDelete(&r); |
---|
987 | return; |
---|
988 | } |
---|
989 | do |
---|
990 | { |
---|
991 | a = m_act[r->pos]; |
---|
992 | res = dumm; |
---|
993 | res->n = NULL; |
---|
994 | b = c; |
---|
995 | w = r->m; |
---|
996 | loop // combine the chains a and b: p*a + w*b |
---|
997 | { |
---|
998 | if (a == NULL) |
---|
999 | { |
---|
1000 | do |
---|
1001 | { |
---|
1002 | res = res->n = smElemCopy(b); |
---|
1003 | res->m = ppMult_qq(b->m, w); |
---|
1004 | res->e = 1; |
---|
1005 | res->f = smPolyWeight(res); |
---|
1006 | b = b->n; |
---|
1007 | } while (b != NULL); |
---|
1008 | break; |
---|
1009 | } |
---|
1010 | if (a->pos < b->pos) |
---|
1011 | { |
---|
1012 | res = res->n = a; |
---|
1013 | a = a->n; |
---|
1014 | } |
---|
1015 | else if (a->pos > b->pos) |
---|
1016 | { |
---|
1017 | res = res->n = smElemCopy(b); |
---|
1018 | res->m = ppMult_qq(b->m, w); |
---|
1019 | res->e = 1; |
---|
1020 | res->f = smPolyWeight(res); |
---|
1021 | b = b->n; |
---|
1022 | } |
---|
1023 | else |
---|
1024 | { |
---|
1025 | ha = ppMult_qq(a->m, p); |
---|
1026 | pDelete(&a->m); |
---|
1027 | hb = ppMult_qq(b->m, w); |
---|
1028 | ha = pAdd(ha, hb); |
---|
1029 | if (ha != NULL) |
---|
1030 | { |
---|
1031 | a->m = ha; |
---|
1032 | a->e = 1; |
---|
1033 | a->f = smPolyWeight(a); |
---|
1034 | res = res->n = a; |
---|
1035 | a = a->n; |
---|
1036 | } |
---|
1037 | else |
---|
1038 | { |
---|
1039 | smElemDelete(&a); |
---|
1040 | } |
---|
1041 | b = b->n; |
---|
1042 | } |
---|
1043 | if (b == NULL) |
---|
1044 | { |
---|
1045 | res->n = a; |
---|
1046 | break; |
---|
1047 | } |
---|
1048 | } |
---|
1049 | m_act[r->pos] = dumm->n; |
---|
1050 | smElemDelete(&r); |
---|
1051 | } while (r != NULL); |
---|
1052 | } |
---|
1053 | |
---|
1054 | /* higher steps of elimination */ |
---|
1055 | void sparse_mat::smHElim() |
---|
1056 | { |
---|
1057 | poly hp = this->smMultPoly(piv); |
---|
1058 | poly gp = piv->m; // pivotelement |
---|
1059 | smpoly c = m_act[act]; // pivotcolumn |
---|
1060 | smpoly r = red; // row to reduce |
---|
1061 | smpoly res, a, b; |
---|
1062 | poly ha, hr, x, y; |
---|
1063 | int e, ip, ir, ia, lev; |
---|
1064 | |
---|
1065 | if ((c == NULL) || (r == NULL)) |
---|
1066 | { |
---|
1067 | while(r!=NULL) smElemDelete(&r); |
---|
1068 | pDelete(&hp); |
---|
1069 | return; |
---|
1070 | } |
---|
1071 | e = crd+1; |
---|
1072 | ip = piv->e; |
---|
1073 | do |
---|
1074 | { |
---|
1075 | a = m_act[r->pos]; |
---|
1076 | res = dumm; |
---|
1077 | res->n = NULL; |
---|
1078 | b = c; |
---|
1079 | hr = r->m; |
---|
1080 | ir = r->e; |
---|
1081 | loop // combine the chains a and b: (hp,gp)*a(l) + hr*b(h) |
---|
1082 | { |
---|
1083 | if (a == NULL) |
---|
1084 | { |
---|
1085 | do |
---|
1086 | { |
---|
1087 | res = res->n = smElemCopy(b); |
---|
1088 | x = SM_MULT(b->m, hr, m_res[ir]->m); |
---|
1089 | b = b->n; |
---|
1090 | if(ir) SM_DIV(x, m_res[ir]->m); |
---|
1091 | res->m = x; |
---|
1092 | res->e = e; |
---|
1093 | res->f = smPolyWeight(res); |
---|
1094 | } while (b != NULL); |
---|
1095 | break; |
---|
1096 | } |
---|
1097 | if (a->pos < b->pos) |
---|
1098 | { |
---|
1099 | res = res->n = a; |
---|
1100 | a = a->n; |
---|
1101 | } |
---|
1102 | else if (a->pos > b->pos) |
---|
1103 | { |
---|
1104 | res = res->n = smElemCopy(b); |
---|
1105 | x = SM_MULT(b->m, hr, m_res[ir]->m); |
---|
1106 | b = b->n; |
---|
1107 | if(ir) SM_DIV(x, m_res[ir]->m); |
---|
1108 | res->m = x; |
---|
1109 | res->e = e; |
---|
1110 | res->f = smPolyWeight(res); |
---|
1111 | } |
---|
1112 | else |
---|
1113 | { |
---|
1114 | ha = a->m; |
---|
1115 | ia = a->e; |
---|
1116 | if (ir >= ia) |
---|
1117 | { |
---|
1118 | if (ir > ia) |
---|
1119 | { |
---|
1120 | x = SM_MULT(ha, m_res[ir]->m, m_res[ia]->m); |
---|
1121 | pDelete(&ha); |
---|
1122 | ha = x; |
---|
1123 | if (ia) SM_DIV(ha, m_res[ia]->m); |
---|
1124 | ia = ir; |
---|
1125 | } |
---|
1126 | x = SM_MULT(ha, gp, m_res[ia]->m); |
---|
1127 | pDelete(&ha); |
---|
1128 | y = SM_MULT(b->m, hr, m_res[ia]->m); |
---|
1129 | } |
---|
1130 | else if (ir >= ip) |
---|
1131 | { |
---|
1132 | if (ia < crd) |
---|
1133 | { |
---|
1134 | x = SM_MULT(ha, m_res[crd]->m, m_res[ia]->m); |
---|
1135 | pDelete(&ha); |
---|
1136 | ha = x; |
---|
1137 | SM_DIV(ha, m_res[ia]->m); |
---|
1138 | } |
---|
1139 | y = hp; |
---|
1140 | if(ir > ip) |
---|
1141 | { |
---|
1142 | y = SM_MULT(y, m_res[ir]->m, m_res[ip]->m); |
---|
1143 | if (ip) SM_DIV(y, m_res[ip]->m); |
---|
1144 | } |
---|
1145 | ia = ir; |
---|
1146 | x = SM_MULT(ha, y, m_res[ia]->m); |
---|
1147 | if (y != hp) pDelete(&y); |
---|
1148 | pDelete(&ha); |
---|
1149 | y = SM_MULT(b->m, hr, m_res[ia]->m); |
---|
1150 | } |
---|
1151 | else |
---|
1152 | { |
---|
1153 | x = SM_MULT(hr, m_res[ia]->m, m_res[ir]->m); |
---|
1154 | if (ir) SM_DIV(x, m_res[ir]->m); |
---|
1155 | y = SM_MULT(b->m, x, m_res[ia]->m); |
---|
1156 | pDelete(&x); |
---|
1157 | x = SM_MULT(ha, gp, m_res[ia]->m); |
---|
1158 | pDelete(&ha); |
---|
1159 | } |
---|
1160 | ha = pAdd(x, y); |
---|
1161 | if (ha != NULL) |
---|
1162 | { |
---|
1163 | if (ia) SM_DIV(ha, m_res[ia]->m); |
---|
1164 | a->m = ha; |
---|
1165 | a->e = e; |
---|
1166 | a->f = smPolyWeight(a); |
---|
1167 | res = res->n = a; |
---|
1168 | a = a->n; |
---|
1169 | } |
---|
1170 | else |
---|
1171 | { |
---|
1172 | a->m = NULL; |
---|
1173 | smElemDelete(&a); |
---|
1174 | } |
---|
1175 | b = b->n; |
---|
1176 | } |
---|
1177 | if (b == NULL) |
---|
1178 | { |
---|
1179 | res->n = a; |
---|
1180 | break; |
---|
1181 | } |
---|
1182 | } |
---|
1183 | m_act[r->pos] = dumm->n; |
---|
1184 | smElemDelete(&r); |
---|
1185 | } while (r != NULL); |
---|
1186 | pDelete(&hp); |
---|
1187 | } |
---|
1188 | |
---|
1189 | /* ----------------- transfer ------------------ */ |
---|
1190 | |
---|
1191 | /* |
---|
1192 | * select the pivotrow and store it to red and piv |
---|
1193 | */ |
---|
1194 | void sparse_mat::smSelectPR() |
---|
1195 | { |
---|
1196 | smpoly b = dumm; |
---|
1197 | smpoly a, ap; |
---|
1198 | int i; |
---|
1199 | |
---|
1200 | if (TEST_OPT_PROT) |
---|
1201 | { |
---|
1202 | if ((crd+1)%10) |
---|
1203 | PrintS("."); |
---|
1204 | else |
---|
1205 | PrintS(".\n"); |
---|
1206 | } |
---|
1207 | a = m_act[act]; |
---|
1208 | if (a->pos < rpiv) |
---|
1209 | { |
---|
1210 | do |
---|
1211 | { |
---|
1212 | ap = a; |
---|
1213 | a = a->n; |
---|
1214 | } while (a->pos < rpiv); |
---|
1215 | ap->n = a->n; |
---|
1216 | } |
---|
1217 | else |
---|
1218 | m_act[act] = a->n; |
---|
1219 | piv = a; |
---|
1220 | a->n = NULL; |
---|
1221 | for (i=1; i<act; i++) |
---|
1222 | { |
---|
1223 | a = m_act[i]; |
---|
1224 | if (a->pos < rpiv) |
---|
1225 | { |
---|
1226 | loop |
---|
1227 | { |
---|
1228 | ap = a; |
---|
1229 | a = a->n; |
---|
1230 | if ((a == NULL) || (a->pos > rpiv)) |
---|
1231 | break; |
---|
1232 | if (a->pos == rpiv) |
---|
1233 | { |
---|
1234 | ap->n = a->n; |
---|
1235 | a->m = pNeg(a->m); |
---|
1236 | b = b->n = a; |
---|
1237 | b->pos = i; |
---|
1238 | break; |
---|
1239 | } |
---|
1240 | } |
---|
1241 | } |
---|
1242 | else if (a->pos == rpiv) |
---|
1243 | { |
---|
1244 | m_act[i] = a->n; |
---|
1245 | a->m = pNeg(a->m); |
---|
1246 | b = b->n = a; |
---|
1247 | b->pos = i; |
---|
1248 | } |
---|
1249 | } |
---|
1250 | b->n = NULL; |
---|
1251 | red = dumm->n; |
---|
1252 | } |
---|
1253 | |
---|
1254 | /* |
---|
1255 | * store the pivotcol in m_row |
---|
1256 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] |
---|
1257 | */ |
---|
1258 | void sparse_mat::smColToRow() |
---|
1259 | { |
---|
1260 | smpoly c = m_act[act]; |
---|
1261 | smpoly h; |
---|
1262 | |
---|
1263 | while (c != NULL) |
---|
1264 | { |
---|
1265 | h = c; |
---|
1266 | c = c->n; |
---|
1267 | h->n = m_row[h->pos]; |
---|
1268 | m_row[h->pos] = h; |
---|
1269 | h->pos = crd; |
---|
1270 | } |
---|
1271 | } |
---|
1272 | |
---|
1273 | /* |
---|
1274 | * store the pivot and the assosiated row in m_row |
---|
1275 | * to m_res (result): |
---|
1276 | * piv + m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
---|
1277 | */ |
---|
1278 | void sparse_mat::smRowToCol() |
---|
1279 | { |
---|
1280 | smpoly r = m_row[rpiv]; |
---|
1281 | smpoly a, ap, h; |
---|
1282 | |
---|
1283 | m_row[rpiv] = NULL; |
---|
1284 | perm[crd] = rpiv; |
---|
1285 | piv->pos = crd; |
---|
1286 | m_res[crd] = piv; |
---|
1287 | while (r != NULL) |
---|
1288 | { |
---|
1289 | ap = m_res[r->pos]; |
---|
1290 | loop |
---|
1291 | { |
---|
1292 | a = ap->n; |
---|
1293 | if (a == NULL) |
---|
1294 | { |
---|
1295 | ap->n = h = r; |
---|
1296 | r = r->n; |
---|
1297 | h->n = a; |
---|
1298 | h->pos = crd; |
---|
1299 | break; |
---|
1300 | } |
---|
1301 | ap = a; |
---|
1302 | } |
---|
1303 | } |
---|
1304 | } |
---|
1305 | |
---|
1306 | /* ----------------- C++ stuff ------------------ */ |
---|
1307 | |
---|
1308 | /* |
---|
1309 | * clean m_act from zeros (after elim) |
---|
1310 | */ |
---|
1311 | void sparse_mat::smZeroElim() |
---|
1312 | { |
---|
1313 | int i = 0; |
---|
1314 | int j; |
---|
1315 | |
---|
1316 | loop |
---|
1317 | { |
---|
1318 | i++; |
---|
1319 | if (i > act) return; |
---|
1320 | if (m_act[i] == NULL) break; |
---|
1321 | } |
---|
1322 | j = i; |
---|
1323 | loop |
---|
1324 | { |
---|
1325 | j++; |
---|
1326 | if (j > act) break; |
---|
1327 | if (m_act[j] != NULL) |
---|
1328 | { |
---|
1329 | m_act[i] = m_act[j]; |
---|
1330 | i++; |
---|
1331 | } |
---|
1332 | } |
---|
1333 | act -= (j-i); |
---|
1334 | sign = 0; |
---|
1335 | } |
---|
1336 | |
---|
1337 | /* |
---|
1338 | * clean m_act from cols not to reduced (after elim) |
---|
1339 | * put them to m_res |
---|
1340 | */ |
---|
1341 | void sparse_mat::smToredElim() |
---|
1342 | { |
---|
1343 | int i = 0; |
---|
1344 | int j; |
---|
1345 | |
---|
1346 | loop |
---|
1347 | { |
---|
1348 | i++; |
---|
1349 | if (i > act) return; |
---|
1350 | if (m_act[i]->pos > tored) |
---|
1351 | { |
---|
1352 | m_res[inred] = m_act[i]; |
---|
1353 | inred--; |
---|
1354 | break; |
---|
1355 | } |
---|
1356 | } |
---|
1357 | j = i; |
---|
1358 | loop |
---|
1359 | { |
---|
1360 | j++; |
---|
1361 | if (j > act) break; |
---|
1362 | if (m_act[j]->pos > tored) |
---|
1363 | { |
---|
1364 | m_res[inred] = m_act[j]; |
---|
1365 | inred--; |
---|
1366 | } |
---|
1367 | else |
---|
1368 | { |
---|
1369 | m_act[i] = m_act[j]; |
---|
1370 | i++; |
---|
1371 | } |
---|
1372 | } |
---|
1373 | act -= (j-i); |
---|
1374 | sign = 0; |
---|
1375 | } |
---|
1376 | |
---|
1377 | /* |
---|
1378 | * copy m_act to m_res |
---|
1379 | */ |
---|
1380 | void sparse_mat::smCopToRes() |
---|
1381 | { |
---|
1382 | smpoly a,ap,r,h; |
---|
1383 | int i,j,k,l; |
---|
1384 | |
---|
1385 | i = 0; |
---|
1386 | if (act) |
---|
1387 | { |
---|
1388 | a = m_act[act]; // init perm |
---|
1389 | do |
---|
1390 | { |
---|
1391 | i++; |
---|
1392 | perm[crd+i] = a->pos; |
---|
1393 | a = a->n; |
---|
1394 | } while ((a != NULL) && (a->pos <= tored)); |
---|
1395 | for (j=act-1;j;j--) // load all positions of perm |
---|
1396 | { |
---|
1397 | a = m_act[j]; |
---|
1398 | k = 1; |
---|
1399 | loop |
---|
1400 | { |
---|
1401 | if (perm[crd+k] >= a->pos) |
---|
1402 | { |
---|
1403 | if (perm[crd+k] > a->pos) |
---|
1404 | { |
---|
1405 | for (l=i;l>=k;l--) perm[crd+l+1] = perm[crd+l]; |
---|
1406 | perm[crd+k] = a->pos; |
---|
1407 | i++; |
---|
1408 | } |
---|
1409 | a = a->n; |
---|
1410 | if ((a == NULL) || (a->pos > tored)) break; |
---|
1411 | } |
---|
1412 | k++; |
---|
1413 | if ((k > i) && (a->pos <= tored)) |
---|
1414 | { |
---|
1415 | do |
---|
1416 | { |
---|
1417 | i++; |
---|
1418 | perm[crd+i] = a->pos; |
---|
1419 | a = a->n; |
---|
1420 | } while ((a != NULL) && (a->pos <= tored)); |
---|
1421 | break; |
---|
1422 | } |
---|
1423 | } |
---|
1424 | } |
---|
1425 | } |
---|
1426 | for (j=act;j;j--) // renumber m_act |
---|
1427 | { |
---|
1428 | k = 1; |
---|
1429 | a = m_act[j]; |
---|
1430 | while ((a != NULL) && (a->pos <= tored)) |
---|
1431 | { |
---|
1432 | if (perm[crd+k] == a->pos) |
---|
1433 | { |
---|
1434 | a->pos = crd+k; |
---|
1435 | a = a->n; |
---|
1436 | } |
---|
1437 | k++; |
---|
1438 | } |
---|
1439 | } |
---|
1440 | tored = crd+i; |
---|
1441 | for(k=1;k<=i;k++) // clean this from m_row |
---|
1442 | { |
---|
1443 | j = perm[crd+k]; |
---|
1444 | if (m_row[j] != NULL) |
---|
1445 | { |
---|
1446 | r = m_row[j]; |
---|
1447 | m_row[j] = NULL; |
---|
1448 | do |
---|
1449 | { |
---|
1450 | ap = m_res[r->pos]; |
---|
1451 | loop |
---|
1452 | { |
---|
1453 | a = ap->n; |
---|
1454 | if (a == NULL) |
---|
1455 | { |
---|
1456 | h = ap->n = r; |
---|
1457 | r = r->n; |
---|
1458 | h->n = NULL; |
---|
1459 | h->pos = crd+k; |
---|
1460 | break; |
---|
1461 | } |
---|
1462 | ap = a; |
---|
1463 | } |
---|
1464 | } while (r!=NULL); |
---|
1465 | } |
---|
1466 | } |
---|
1467 | while(act) // clean m_act |
---|
1468 | { |
---|
1469 | crd++; |
---|
1470 | m_res[crd] = m_act[act]; |
---|
1471 | act--; |
---|
1472 | } |
---|
1473 | for (i=1;i<=tored;i++) // take the rest of m_row |
---|
1474 | { |
---|
1475 | if(m_row[i] != NULL) |
---|
1476 | { |
---|
1477 | tored++; |
---|
1478 | r = m_row[i]; |
---|
1479 | m_row[i] = NULL; |
---|
1480 | perm[tored] = i; |
---|
1481 | do |
---|
1482 | { |
---|
1483 | ap = m_res[r->pos]; |
---|
1484 | loop |
---|
1485 | { |
---|
1486 | a = ap->n; |
---|
1487 | if (a == NULL) |
---|
1488 | { |
---|
1489 | h = ap->n = r; |
---|
1490 | r = r->n; |
---|
1491 | h->n = NULL; |
---|
1492 | h->pos = tored; |
---|
1493 | break; |
---|
1494 | } |
---|
1495 | ap = a; |
---|
1496 | } |
---|
1497 | } while (r!=NULL); |
---|
1498 | } |
---|
1499 | } |
---|
1500 | for (i=tored+1;i<=nrows;i++) // take the rest of m_row |
---|
1501 | { |
---|
1502 | if(m_row[i] != NULL) |
---|
1503 | { |
---|
1504 | r = m_row[i]; |
---|
1505 | m_row[i] = NULL; |
---|
1506 | do |
---|
1507 | { |
---|
1508 | ap = m_res[r->pos]; |
---|
1509 | loop |
---|
1510 | { |
---|
1511 | a = ap->n; |
---|
1512 | if (a == NULL) |
---|
1513 | { |
---|
1514 | h = ap->n = r; |
---|
1515 | r = r->n; |
---|
1516 | h->n = NULL; |
---|
1517 | h->pos = i; |
---|
1518 | break; |
---|
1519 | } |
---|
1520 | ap = a; |
---|
1521 | } |
---|
1522 | } while (r!=NULL); |
---|
1523 | } |
---|
1524 | } |
---|
1525 | while (inred < ncols) // take unreducable |
---|
1526 | { |
---|
1527 | crd++; |
---|
1528 | inred++; |
---|
1529 | m_res[crd] = m_res[inred]; |
---|
1530 | } |
---|
1531 | } |
---|
1532 | |
---|
1533 | /* |
---|
1534 | * multiply and divide the column, that goes to result |
---|
1535 | */ |
---|
1536 | void sparse_mat::smMultCol() |
---|
1537 | { |
---|
1538 | smpoly a = m_act[act]; |
---|
1539 | int e = crd; |
---|
1540 | poly ha; |
---|
1541 | int f; |
---|
1542 | |
---|
1543 | while (a != NULL) |
---|
1544 | { |
---|
1545 | f = a->e; |
---|
1546 | if (f < e) |
---|
1547 | { |
---|
1548 | ha = SM_MULT(a->m, m_res[e]->m, m_res[f]->m); |
---|
1549 | pDelete(&a->m); |
---|
1550 | if (f) SM_DIV(ha, m_res[f]->m); |
---|
1551 | a->m = ha; |
---|
1552 | if (normalize) pNormalize(a->m); |
---|
1553 | } |
---|
1554 | a = a->n; |
---|
1555 | } |
---|
1556 | } |
---|
1557 | |
---|
1558 | /* |
---|
1559 | * multiply and divide the m_act finaly |
---|
1560 | */ |
---|
1561 | void sparse_mat::smFinalMult() |
---|
1562 | { |
---|
1563 | smpoly a; |
---|
1564 | poly ha; |
---|
1565 | int i, f; |
---|
1566 | int e = crd; |
---|
1567 | |
---|
1568 | for (i=act; i; i--) |
---|
1569 | { |
---|
1570 | a = m_act[i]; |
---|
1571 | do |
---|
1572 | { |
---|
1573 | f = a->e; |
---|
1574 | if (f < e) |
---|
1575 | { |
---|
1576 | ha = SM_MULT(a->m, m_res[e]->m, m_res[f]->m); |
---|
1577 | pDelete(&a->m); |
---|
1578 | if (f) SM_DIV(ha, m_res[f]->m); |
---|
1579 | a->m = ha; |
---|
1580 | } |
---|
1581 | if (normalize) pNormalize(a->m); |
---|
1582 | a = a->n; |
---|
1583 | } while (a != NULL); |
---|
1584 | } |
---|
1585 | } |
---|
1586 | |
---|
1587 | /* |
---|
1588 | * check for denominators |
---|
1589 | */ |
---|
1590 | int sparse_mat::smCheckNormalize() |
---|
1591 | { |
---|
1592 | int i; |
---|
1593 | smpoly a; |
---|
1594 | |
---|
1595 | for (i=act; i; i--) |
---|
1596 | { |
---|
1597 | a = m_act[i]; |
---|
1598 | do |
---|
1599 | { |
---|
1600 | if(smHaveDenom(a->m)) return 1; |
---|
1601 | a = a->n; |
---|
1602 | } while (a != NULL); |
---|
1603 | } |
---|
1604 | return 0; |
---|
1605 | } |
---|
1606 | |
---|
1607 | /* |
---|
1608 | * normalize |
---|
1609 | */ |
---|
1610 | void sparse_mat::smNormalize() |
---|
1611 | { |
---|
1612 | smpoly a; |
---|
1613 | int i; |
---|
1614 | int e = crd; |
---|
1615 | |
---|
1616 | for (i=act; i; i--) |
---|
1617 | { |
---|
1618 | a = m_act[i]; |
---|
1619 | do |
---|
1620 | { |
---|
1621 | if (e == a->e) pNormalize(a->m); |
---|
1622 | a = a->n; |
---|
1623 | } while (a != NULL); |
---|
1624 | } |
---|
1625 | } |
---|
1626 | |
---|
1627 | /* |
---|
1628 | * multiply and divide the element, save poly |
---|
1629 | */ |
---|
1630 | poly sparse_mat::smMultPoly(smpoly a) |
---|
1631 | { |
---|
1632 | int f = a->e; |
---|
1633 | poly r, h; |
---|
1634 | |
---|
1635 | if (f < crd) |
---|
1636 | { |
---|
1637 | h = r = a->m; |
---|
1638 | h = SM_MULT(h, m_res[crd]->m, m_res[f]->m); |
---|
1639 | if (f) SM_DIV(h, m_res[f]->m); |
---|
1640 | a->m = h; |
---|
1641 | if (normalize) pNormalize(a->m); |
---|
1642 | a->f = smPolyWeight(a); |
---|
1643 | return r; |
---|
1644 | } |
---|
1645 | else |
---|
1646 | return NULL; |
---|
1647 | } |
---|
1648 | |
---|
1649 | /* |
---|
1650 | * delete the m_act finaly |
---|
1651 | */ |
---|
1652 | void sparse_mat::smActDel() |
---|
1653 | { |
---|
1654 | smpoly a; |
---|
1655 | int i; |
---|
1656 | |
---|
1657 | for (i=act; i; i--) |
---|
1658 | { |
---|
1659 | a = m_act[i]; |
---|
1660 | do |
---|
1661 | { |
---|
1662 | smElemDelete(&a); |
---|
1663 | } while (a != NULL); |
---|
1664 | } |
---|
1665 | } |
---|
1666 | |
---|
1667 | /* |
---|
1668 | * delete the pivotcol |
---|
1669 | */ |
---|
1670 | void sparse_mat::smColDel() |
---|
1671 | { |
---|
1672 | smpoly a = m_act[act]; |
---|
1673 | |
---|
1674 | while (a != NULL) |
---|
1675 | { |
---|
1676 | smElemDelete(&a); |
---|
1677 | } |
---|
1678 | } |
---|
1679 | |
---|
1680 | /* |
---|
1681 | * delete pivot elements |
---|
1682 | */ |
---|
1683 | void sparse_mat::smPivDel() |
---|
1684 | { |
---|
1685 | int i=crd; |
---|
1686 | |
---|
1687 | while (i != 0) |
---|
1688 | { |
---|
1689 | smElemDelete(&m_res[i]); |
---|
1690 | i--; |
---|
1691 | } |
---|
1692 | } |
---|
1693 | |
---|
1694 | /* |
---|
1695 | * the sign of the determinant |
---|
1696 | */ |
---|
1697 | void sparse_mat::smSign() |
---|
1698 | { |
---|
1699 | int j,i; |
---|
1700 | if (act > 2) |
---|
1701 | { |
---|
1702 | if (cpiv!=act) sign=-sign; |
---|
1703 | if ((act%2)==0) sign=-sign; |
---|
1704 | i=1; |
---|
1705 | j=perm[1]; |
---|
1706 | while(j<rpiv) |
---|
1707 | { |
---|
1708 | sign=-sign; |
---|
1709 | i++; |
---|
1710 | j=perm[i]; |
---|
1711 | } |
---|
1712 | while(perm[i]!=0) |
---|
1713 | { |
---|
1714 | perm[i]=perm[i+1]; |
---|
1715 | i++; |
---|
1716 | } |
---|
1717 | } |
---|
1718 | else |
---|
1719 | { |
---|
1720 | if (cpiv!=1) sign=-sign; |
---|
1721 | if (rpiv!=perm[1]) sign=-sign; |
---|
1722 | } |
---|
1723 | } |
---|
1724 | |
---|
1725 | void sparse_mat::smInitPerm() |
---|
1726 | { |
---|
1727 | int i; |
---|
1728 | for (i=act;i;i--) perm[i]=i; |
---|
1729 | } |
---|
1730 | |
---|
1731 | /* ----------------- arithmetic ------------------ */ |
---|
1732 | /*2 |
---|
1733 | * exact division a/b |
---|
1734 | * a destroyed, b NOT destroyed |
---|
1735 | */ |
---|
1736 | void smPolyDiv(poly a, poly b) |
---|
1737 | { |
---|
1738 | const number x = pGetCoeff(b); |
---|
1739 | number y, yn; |
---|
1740 | poly t, h, dummy; |
---|
1741 | int i; |
---|
1742 | |
---|
1743 | if (pNext(b) == NULL) |
---|
1744 | { |
---|
1745 | do |
---|
1746 | { |
---|
1747 | if (!pLmIsConstantComp(b)) |
---|
1748 | { |
---|
1749 | for (i=pVariables; i; i--) |
---|
1750 | pSubExp(a,i,pGetExp(b,i)); |
---|
1751 | pSetm(a); |
---|
1752 | } |
---|
1753 | y = nDiv(pGetCoeff(a),x); |
---|
1754 | nNormalize(y); |
---|
1755 | pSetCoeff(a,y); |
---|
1756 | pIter(a); |
---|
1757 | } while (a != NULL); |
---|
1758 | return; |
---|
1759 | } |
---|
1760 | dummy = pInit(); |
---|
1761 | do |
---|
1762 | { |
---|
1763 | for (i=pVariables; i; i--) |
---|
1764 | pSubExp(a,i,pGetExp(b,i)); |
---|
1765 | pSetm(a); |
---|
1766 | y = nDiv(pGetCoeff(a),x); |
---|
1767 | nNormalize(y); |
---|
1768 | pSetCoeff(a,y); |
---|
1769 | yn = nNeg(nCopy(y)); |
---|
1770 | t = pNext(b); |
---|
1771 | h = dummy; |
---|
1772 | do |
---|
1773 | { |
---|
1774 | h = pNext(h) = pInit(); |
---|
1775 | //pSetComp(h,0); |
---|
1776 | for (i=pVariables; i; i--) |
---|
1777 | pSetExp(h,i,pGetExp(a,i)+pGetExp(t,i)); |
---|
1778 | pSetm(h); |
---|
1779 | pSetCoeff0(h,nMult(yn, pGetCoeff(t))); |
---|
1780 | pIter(t); |
---|
1781 | } while (t != NULL); |
---|
1782 | nDelete(&yn); |
---|
1783 | pNext(h) = NULL; |
---|
1784 | a = pNext(a) = pAdd(pNext(a), pNext(dummy)); |
---|
1785 | } while (a!=NULL); |
---|
1786 | pLmFree(dummy); |
---|
1787 | } |
---|
1788 | |
---|
1789 | #define X_MAS |
---|
1790 | #ifdef X_MAS |
---|
1791 | |
---|
1792 | /* |
---|
1793 | * returns the part of (a*b)/exp(lead(c)) with nonegative exponents |
---|
1794 | */ |
---|
1795 | poly smMultDiv(poly a, poly b, const poly c) |
---|
1796 | { |
---|
1797 | poly pa, e, res, r; |
---|
1798 | BOOLEAN lead;\ |
---|
1799 | int la, lb, lr; |
---|
1800 | |
---|
1801 | if ((c == NULL) || pLmIsConstantComp(c)) |
---|
1802 | { |
---|
1803 | return ppMult_qq(a, b); |
---|
1804 | } |
---|
1805 | |
---|
1806 | pqLength(a, b, la, lb, SM_MIN_LENGTH_BUCKET); |
---|
1807 | |
---|
1808 | // we iter over b, so, make sure b is the shortest |
---|
1809 | // such that we minimize our iterations |
---|
1810 | if (lb > la) |
---|
1811 | { |
---|
1812 | r = a; |
---|
1813 | a = b; |
---|
1814 | b = r; |
---|
1815 | lr = la; |
---|
1816 | la = lb; |
---|
1817 | lb = lr; |
---|
1818 | } |
---|
1819 | res = NULL; |
---|
1820 | e = pInit(); |
---|
1821 | lead = FALSE; |
---|
1822 | while (!lead) |
---|
1823 | { |
---|
1824 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1825 | if (smIsNegQuot(e, b, c)) |
---|
1826 | { |
---|
1827 | lead = pLmDivisibleByNoComp(e, a); |
---|
1828 | r = smSelectCopy_ExpMultDiv(a, e, b, c); |
---|
1829 | } |
---|
1830 | else |
---|
1831 | { |
---|
1832 | lead = TRUE; |
---|
1833 | r = ppMult_mm(a, e); |
---|
1834 | } |
---|
1835 | if (lead) |
---|
1836 | { |
---|
1837 | if (res != NULL) |
---|
1838 | { |
---|
1839 | smFindRef(&pa, &res, r); |
---|
1840 | if (pa == NULL) |
---|
1841 | lead = FALSE; |
---|
1842 | } |
---|
1843 | else |
---|
1844 | { |
---|
1845 | pa = res = r; |
---|
1846 | } |
---|
1847 | } |
---|
1848 | else |
---|
1849 | res = pAdd(res, r); |
---|
1850 | pIter(b); |
---|
1851 | if (b == NULL) |
---|
1852 | { |
---|
1853 | pLmFree(e); |
---|
1854 | return res; |
---|
1855 | } |
---|
1856 | } |
---|
1857 | |
---|
1858 | if (!TEST_OPT_NOT_BUCKETS && lb >= SM_MIN_LENGTH_BUCKET) |
---|
1859 | { |
---|
1860 | // use buckets if minimum length is smaller than threshold |
---|
1861 | spolyrec rp; |
---|
1862 | poly append; |
---|
1863 | // find the last monomial before pa |
---|
1864 | if (res == pa) |
---|
1865 | { |
---|
1866 | append = &rp; |
---|
1867 | pNext(append) = res; |
---|
1868 | } |
---|
1869 | else |
---|
1870 | { |
---|
1871 | append = res; |
---|
1872 | while (pNext(append) != pa) |
---|
1873 | { |
---|
1874 | assume(pNext(append) != NULL); |
---|
1875 | pIter(append); |
---|
1876 | } |
---|
1877 | } |
---|
1878 | kBucket_pt bucket = kBucketCreate(currRing); |
---|
1879 | kBucketInit(bucket, pNext(append), 0); |
---|
1880 | do |
---|
1881 | { |
---|
1882 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1883 | if (smIsNegQuot(e, b, c)) |
---|
1884 | { |
---|
1885 | lr = la; |
---|
1886 | r = pp_Mult_Coeff_mm_DivSelect_MultDiv(a, lr, e, b, c); |
---|
1887 | if (pLmDivisibleByNoComp(e, a)) |
---|
1888 | append = kBucket_ExtractLarger_Add_q(bucket, append, r, &lr); |
---|
1889 | else |
---|
1890 | kBucket_Add_q(bucket, r, &lr); |
---|
1891 | } |
---|
1892 | else |
---|
1893 | { |
---|
1894 | r = ppMult_mm(a, e); |
---|
1895 | append = kBucket_ExtractLarger_Add_q(bucket, append, r, &la); |
---|
1896 | } |
---|
1897 | pIter(b); |
---|
1898 | } while (b != NULL); |
---|
1899 | pNext(append) = kBucketClear(bucket); |
---|
1900 | kBucketDestroy(&bucket); |
---|
1901 | } |
---|
1902 | else |
---|
1903 | { |
---|
1904 | // use old sm stuff |
---|
1905 | do |
---|
1906 | { |
---|
1907 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1908 | if (smIsNegQuot(e, b, c)) |
---|
1909 | { |
---|
1910 | r = smSelectCopy_ExpMultDiv(a, e, b, c); |
---|
1911 | if (pLmDivisibleByNoComp(e, a)) |
---|
1912 | smCombineChain(&pa, r); |
---|
1913 | else |
---|
1914 | pa = pAdd(pa,r); |
---|
1915 | } |
---|
1916 | else |
---|
1917 | { |
---|
1918 | r = ppMult_mm(a, e); |
---|
1919 | smCombineChain(&pa, r); |
---|
1920 | } |
---|
1921 | pIter(b); |
---|
1922 | } while (b != NULL); |
---|
1923 | } |
---|
1924 | pLmFree(e); |
---|
1925 | return res; |
---|
1926 | } |
---|
1927 | |
---|
1928 | #else |
---|
1929 | |
---|
1930 | /* |
---|
1931 | * returns the part of (a*b)/exp(lead(c)) with nonegative exponents |
---|
1932 | */ |
---|
1933 | poly smMultDiv(poly a, poly b, const poly c) |
---|
1934 | { |
---|
1935 | poly pa, e, res, r; |
---|
1936 | BOOLEAN lead; |
---|
1937 | |
---|
1938 | if ((c == NULL) || pLmIsConstantComp(c)) |
---|
1939 | { |
---|
1940 | return ppMult_qq(a, b); |
---|
1941 | } |
---|
1942 | if (smSmaller(a, b)) |
---|
1943 | { |
---|
1944 | r = a; |
---|
1945 | a = b; |
---|
1946 | b = r; |
---|
1947 | } |
---|
1948 | res = NULL; |
---|
1949 | e = pInit(); |
---|
1950 | lead = FALSE; |
---|
1951 | while (!lead) |
---|
1952 | { |
---|
1953 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1954 | if (smIsNegQuot(e, b, c)) |
---|
1955 | { |
---|
1956 | lead = pLmDivisibleByNoComp(e, a); |
---|
1957 | r = smSelectCopy_ExpMultDiv(a, e, b, c); |
---|
1958 | } |
---|
1959 | else |
---|
1960 | { |
---|
1961 | lead = TRUE; |
---|
1962 | r = ppMult_mm(a, e); |
---|
1963 | } |
---|
1964 | if (lead) |
---|
1965 | { |
---|
1966 | if (res != NULL) |
---|
1967 | { |
---|
1968 | smFindRef(&pa, &res, r); |
---|
1969 | if (pa == NULL) |
---|
1970 | lead = FALSE; |
---|
1971 | } |
---|
1972 | else |
---|
1973 | { |
---|
1974 | pa = res = r; |
---|
1975 | } |
---|
1976 | } |
---|
1977 | else |
---|
1978 | res = pAdd(res, r); |
---|
1979 | pIter(b); |
---|
1980 | if (b == NULL) |
---|
1981 | { |
---|
1982 | pLmFree(e); |
---|
1983 | return res; |
---|
1984 | } |
---|
1985 | } |
---|
1986 | do |
---|
1987 | { |
---|
1988 | pSetCoeff0(e,pGetCoeff(b)); |
---|
1989 | if (smIsNegQuot(e, b, c)) |
---|
1990 | { |
---|
1991 | r = smSelectCopy_ExpMultDiv(a, e, b, c); |
---|
1992 | if (pLmDivisibleByNoComp(e, a)) |
---|
1993 | smCombineChain(&pa, r); |
---|
1994 | else |
---|
1995 | pa = pAdd(pa,r); |
---|
1996 | } |
---|
1997 | else |
---|
1998 | { |
---|
1999 | r = ppMult_mm(a, e); |
---|
2000 | smCombineChain(&pa, r); |
---|
2001 | } |
---|
2002 | pIter(b); |
---|
2003 | } while (b != NULL); |
---|
2004 | pLmFree(e); |
---|
2005 | return res; |
---|
2006 | } |
---|
2007 | #endif |
---|
2008 | /*n |
---|
2009 | * exact division a/b |
---|
2010 | * a is a result of smMultDiv |
---|
2011 | * a destroyed, b NOT destroyed |
---|
2012 | */ |
---|
2013 | void smSpecialPolyDiv(poly a, poly b) |
---|
2014 | { |
---|
2015 | if (pNext(b) == NULL) |
---|
2016 | { |
---|
2017 | smPolyDivN(a, pGetCoeff(b)); |
---|
2018 | return; |
---|
2019 | } |
---|
2020 | smExactPolyDiv(a, b); |
---|
2021 | } |
---|
2022 | |
---|
2023 | |
---|
2024 | /* ------------ internals arithmetic ------------- */ |
---|
2025 | static void smExactPolyDiv(poly a, poly b) |
---|
2026 | { |
---|
2027 | const number x = pGetCoeff(b); |
---|
2028 | poly tail = pNext(b), e = pInit(); |
---|
2029 | poly h; |
---|
2030 | number y, yn; |
---|
2031 | int lt = pLength(tail); |
---|
2032 | |
---|
2033 | if (lt + 1 >= SM_MIN_LENGTH_BUCKET && !TEST_OPT_NOT_BUCKETS) |
---|
2034 | { |
---|
2035 | kBucket_pt bucket = kBucketCreate(currRing); |
---|
2036 | kBucketInit(bucket, pNext(a), 0); |
---|
2037 | int lh = 0; |
---|
2038 | do |
---|
2039 | { |
---|
2040 | y = nDiv(pGetCoeff(a), x); |
---|
2041 | nNormalize(y); |
---|
2042 | pSetCoeff(a,y); |
---|
2043 | yn = nNeg(nCopy(y)); |
---|
2044 | pSetCoeff0(e,yn); |
---|
2045 | lh = lt; |
---|
2046 | if (smIsNegQuot(e, a, b)) |
---|
2047 | { |
---|
2048 | h = pp_Mult_Coeff_mm_DivSelect_MultDiv(tail, lh, e, a, b); |
---|
2049 | } |
---|
2050 | else |
---|
2051 | h = ppMult_mm(tail, e); |
---|
2052 | nDelete(&yn); |
---|
2053 | kBucket_Add_q(bucket, h, &lh); |
---|
2054 | |
---|
2055 | a = pNext(a) = kBucketExtractLm(bucket); |
---|
2056 | } while (a!=NULL); |
---|
2057 | kBucketDestroy(&bucket); |
---|
2058 | } |
---|
2059 | else |
---|
2060 | { |
---|
2061 | do |
---|
2062 | { |
---|
2063 | y = nDiv(pGetCoeff(a), x); |
---|
2064 | nNormalize(y); |
---|
2065 | pSetCoeff(a,y); |
---|
2066 | yn = nNeg(nCopy(y)); |
---|
2067 | pSetCoeff0(e,yn); |
---|
2068 | if (smIsNegQuot(e, a, b)) |
---|
2069 | h = smSelectCopy_ExpMultDiv(tail, e, a, b); |
---|
2070 | else |
---|
2071 | h = ppMult_mm(tail, e); |
---|
2072 | nDelete(&yn); |
---|
2073 | a = pNext(a) = pAdd(pNext(a), h); |
---|
2074 | } while (a!=NULL); |
---|
2075 | } |
---|
2076 | pLmFree(e); |
---|
2077 | } |
---|
2078 | |
---|
2079 | // obachman --> Wilfried: check the following |
---|
2080 | static BOOLEAN smIsNegQuot(poly a, const poly b, const poly c) |
---|
2081 | { |
---|
2082 | if (pLmDivisibleByNoComp(c, b)) |
---|
2083 | { |
---|
2084 | pExpVectorDiff(a, b, c); |
---|
2085 | // Hmm: here used to be a pSetm(a): but it is unnecessary, |
---|
2086 | // if b and c are correct |
---|
2087 | return FALSE; |
---|
2088 | } |
---|
2089 | else |
---|
2090 | { |
---|
2091 | int i; |
---|
2092 | for (i=pVariables; i>0; i--) |
---|
2093 | { |
---|
2094 | if(pGetExp(c,i) > pGetExp(b,i)) |
---|
2095 | pSetExp(a,i,pGetExp(c,i)-pGetExp(b,i)); |
---|
2096 | else |
---|
2097 | pSetExp(a,i,0); |
---|
2098 | } |
---|
2099 | // here we actually might need a pSetm, if a is to be used in |
---|
2100 | // comparisons |
---|
2101 | return TRUE; |
---|
2102 | } |
---|
2103 | } |
---|
2104 | |
---|
2105 | static void smExpMultDiv(poly t, const poly b, const poly c) |
---|
2106 | { |
---|
2107 | int i; |
---|
2108 | pTest(t); |
---|
2109 | pLmTest(b); |
---|
2110 | pLmTest(c); |
---|
2111 | poly bc = p_New(currRing); |
---|
2112 | |
---|
2113 | p_ExpVectorDiff(bc, b, c, currRing); |
---|
2114 | |
---|
2115 | while(t!=NULL) |
---|
2116 | { |
---|
2117 | pExpVectorAdd(t, bc); |
---|
2118 | pIter(t); |
---|
2119 | } |
---|
2120 | p_LmFree(bc, currRing); |
---|
2121 | } |
---|
2122 | |
---|
2123 | |
---|
2124 | static void smPolyDivN(poly a, const number x) |
---|
2125 | { |
---|
2126 | number y; |
---|
2127 | |
---|
2128 | do |
---|
2129 | { |
---|
2130 | y = nDiv(pGetCoeff(a),x); |
---|
2131 | nNormalize(y); |
---|
2132 | pSetCoeff(a,y); |
---|
2133 | pIter(a); |
---|
2134 | } while (a != NULL); |
---|
2135 | } |
---|
2136 | |
---|
2137 | static BOOLEAN smSmaller(poly a, poly b) |
---|
2138 | { |
---|
2139 | loop |
---|
2140 | { |
---|
2141 | pIter(b); |
---|
2142 | if (b == NULL) return TRUE; |
---|
2143 | pIter(a); |
---|
2144 | if (a == NULL) return FALSE; |
---|
2145 | } |
---|
2146 | } |
---|
2147 | |
---|
2148 | static void smCombineChain(poly *px, poly r) |
---|
2149 | { |
---|
2150 | poly pa = *px, pb; |
---|
2151 | number x; |
---|
2152 | int i; |
---|
2153 | |
---|
2154 | loop |
---|
2155 | { |
---|
2156 | pb = pNext(pa); |
---|
2157 | if (pb == NULL) |
---|
2158 | { |
---|
2159 | pa = pNext(pa) = r; |
---|
2160 | break; |
---|
2161 | } |
---|
2162 | i = pLmCmp(pb, r); |
---|
2163 | if (i > 0) |
---|
2164 | pa = pb; |
---|
2165 | else |
---|
2166 | { |
---|
2167 | if (i == 0) |
---|
2168 | { |
---|
2169 | x = nAdd(pGetCoeff(pb), pGetCoeff(r)); |
---|
2170 | pDeleteLm(&r); |
---|
2171 | if (nIsZero(x)) |
---|
2172 | { |
---|
2173 | pDeleteLm(&pb); |
---|
2174 | pNext(pa) = pAdd(pb,r); |
---|
2175 | } |
---|
2176 | else |
---|
2177 | { |
---|
2178 | pa = pb; |
---|
2179 | pSetCoeff(pa,x); |
---|
2180 | pNext(pa) = pAdd(pNext(pa), r); |
---|
2181 | } |
---|
2182 | } |
---|
2183 | else |
---|
2184 | { |
---|
2185 | pa = pNext(pa) = r; |
---|
2186 | pNext(pa) = pAdd(pb, pNext(pa)); |
---|
2187 | } |
---|
2188 | break; |
---|
2189 | } |
---|
2190 | } |
---|
2191 | *px = pa; |
---|
2192 | } |
---|
2193 | |
---|
2194 | |
---|
2195 | static void smFindRef(poly *ref, poly *px, poly r) |
---|
2196 | { |
---|
2197 | number x; |
---|
2198 | int i; |
---|
2199 | poly pa = *px, pp = NULL; |
---|
2200 | |
---|
2201 | loop |
---|
2202 | { |
---|
2203 | i = pLmCmp(pa, r); |
---|
2204 | if (i > 0) |
---|
2205 | { |
---|
2206 | pp = pa; |
---|
2207 | pIter(pa); |
---|
2208 | if (pa==NULL) |
---|
2209 | { |
---|
2210 | pNext(pp) = r; |
---|
2211 | break; |
---|
2212 | } |
---|
2213 | } |
---|
2214 | else |
---|
2215 | { |
---|
2216 | if (i == 0) |
---|
2217 | { |
---|
2218 | x = nAdd(pGetCoeff(pa), pGetCoeff(r)); |
---|
2219 | pDeleteLm(&r); |
---|
2220 | if (nIsZero(x)) |
---|
2221 | { |
---|
2222 | pDeleteLm(&pa); |
---|
2223 | if (pp!=NULL) |
---|
2224 | pNext(pp) = pAdd(pa,r); |
---|
2225 | else |
---|
2226 | *px = pAdd(pa,r); |
---|
2227 | } |
---|
2228 | else |
---|
2229 | { |
---|
2230 | pp = pa; |
---|
2231 | pSetCoeff(pp,x); |
---|
2232 | pNext(pp) = pAdd(pNext(pp), r); |
---|
2233 | } |
---|
2234 | } |
---|
2235 | else |
---|
2236 | { |
---|
2237 | if (pp!=NULL) |
---|
2238 | pp = pNext(pp) = r; |
---|
2239 | else |
---|
2240 | *px = pp = r; |
---|
2241 | pNext(pp) = pAdd(pa, pNext(r)); |
---|
2242 | } |
---|
2243 | break; |
---|
2244 | } |
---|
2245 | } |
---|
2246 | *ref = pp; |
---|
2247 | } |
---|
2248 | |
---|
2249 | /* ----------------- internal 'C' stuff ------------------ */ |
---|
2250 | |
---|
2251 | static void smElemDelete(smpoly *r) |
---|
2252 | { |
---|
2253 | smpoly a = *r, b = a->n; |
---|
2254 | |
---|
2255 | pDelete(&a->m); |
---|
2256 | omFreeBin((void *)a, smprec_bin); |
---|
2257 | *r = b; |
---|
2258 | } |
---|
2259 | |
---|
2260 | static smpoly smElemCopy(smpoly a) |
---|
2261 | { |
---|
2262 | smpoly r = (smpoly)omAllocBin(smprec_bin); |
---|
2263 | memcpy(r, a, sizeof(smprec)); |
---|
2264 | /* r->m = pCopy(r->m); */ |
---|
2265 | return r; |
---|
2266 | } |
---|
2267 | |
---|
2268 | /* |
---|
2269 | * from poly to smpoly |
---|
2270 | * do not destroy p |
---|
2271 | */ |
---|
2272 | static smpoly smPoly2Smpoly(poly q) |
---|
2273 | { |
---|
2274 | poly pp; |
---|
2275 | smpoly res, a; |
---|
2276 | Exponent_t x; |
---|
2277 | |
---|
2278 | if (q == NULL) |
---|
2279 | return NULL; |
---|
2280 | a = res = (smpoly)omAllocBin(smprec_bin); |
---|
2281 | a->pos = x = pGetComp(q); |
---|
2282 | a->m = q; |
---|
2283 | a->e = 0; |
---|
2284 | loop |
---|
2285 | { |
---|
2286 | pSetComp(q,0); |
---|
2287 | pp = q; |
---|
2288 | pIter(q); |
---|
2289 | if (q == NULL) |
---|
2290 | { |
---|
2291 | a->n = NULL; |
---|
2292 | return res; |
---|
2293 | } |
---|
2294 | if (pGetComp(q) != x) |
---|
2295 | { |
---|
2296 | a = a->n = (smpoly)omAllocBin(smprec_bin); |
---|
2297 | pNext(pp) = NULL; |
---|
2298 | a->pos = x = pGetComp(q); |
---|
2299 | a->m = q; |
---|
2300 | a->e = 0; |
---|
2301 | } |
---|
2302 | } |
---|
2303 | } |
---|
2304 | |
---|
2305 | /* |
---|
2306 | * from smpoly to poly |
---|
2307 | * destroy a |
---|
2308 | */ |
---|
2309 | static poly smSmpoly2Poly(smpoly a) |
---|
2310 | { |
---|
2311 | smpoly b; |
---|
2312 | poly res, pp, q; |
---|
2313 | Exponent_t x; |
---|
2314 | |
---|
2315 | if (a == NULL) |
---|
2316 | return NULL; |
---|
2317 | x = a->pos; |
---|
2318 | q = res = a->m; |
---|
2319 | loop |
---|
2320 | { |
---|
2321 | pSetComp(q,x); |
---|
2322 | pp = q; |
---|
2323 | pIter(q); |
---|
2324 | if (q == NULL) |
---|
2325 | break; |
---|
2326 | } |
---|
2327 | loop |
---|
2328 | { |
---|
2329 | b = a; |
---|
2330 | a = a->n; |
---|
2331 | omFreeBin((void *)b, smprec_bin); |
---|
2332 | if (a == NULL) |
---|
2333 | return res; |
---|
2334 | x = a->pos; |
---|
2335 | q = pNext(pp) = a->m; |
---|
2336 | loop |
---|
2337 | { |
---|
2338 | pSetComp(q,x); |
---|
2339 | pp = q; |
---|
2340 | pIter(q); |
---|
2341 | if (q == NULL) |
---|
2342 | break; |
---|
2343 | } |
---|
2344 | } |
---|
2345 | } |
---|
2346 | |
---|
2347 | /* |
---|
2348 | * weigth of a polynomial, for pivot strategy |
---|
2349 | */ |
---|
2350 | static float smPolyWeight(smpoly a) |
---|
2351 | { |
---|
2352 | poly p = a->m; |
---|
2353 | int i; |
---|
2354 | float res = (float)nSize(pGetCoeff(p)); |
---|
2355 | |
---|
2356 | if (pNext(p) == NULL) |
---|
2357 | { |
---|
2358 | for(i=pVariables; i>0; i--) |
---|
2359 | { |
---|
2360 | if (pGetExp(p,i) != 0) return res+1.0; |
---|
2361 | } |
---|
2362 | return res; |
---|
2363 | } |
---|
2364 | else |
---|
2365 | { |
---|
2366 | i = 0; |
---|
2367 | res = 0.0; |
---|
2368 | do |
---|
2369 | { |
---|
2370 | i++; |
---|
2371 | res += (float)nSize(pGetCoeff(p)); |
---|
2372 | pIter(p); |
---|
2373 | } |
---|
2374 | while (p); |
---|
2375 | return res+(float)i; |
---|
2376 | } |
---|
2377 | } |
---|
2378 | |
---|
2379 | static BOOLEAN smHaveDenom(poly a) |
---|
2380 | { |
---|
2381 | BOOLEAN sw; |
---|
2382 | number x,o=nInit(1); |
---|
2383 | |
---|
2384 | while (a != NULL) |
---|
2385 | { |
---|
2386 | x = nGetDenom(pGetCoeff(a)); |
---|
2387 | sw = nEqual(x,o); |
---|
2388 | nDelete(&x); |
---|
2389 | if (!sw) |
---|
2390 | { |
---|
2391 | nDelete(&o); |
---|
2392 | return TRUE; |
---|
2393 | } |
---|
2394 | pIter(a); |
---|
2395 | } |
---|
2396 | nDelete(&o); |
---|
2397 | return FALSE; |
---|
2398 | } |
---|
2399 | |
---|
2400 | static number smCleardenom(ideal id) |
---|
2401 | { |
---|
2402 | poly a; |
---|
2403 | number x,y,res=nInit(1); |
---|
2404 | BOOLEAN sw=FALSE; |
---|
2405 | |
---|
2406 | for (int i=0; i<IDELEMS(id); i++) |
---|
2407 | { |
---|
2408 | a = id->m[i]; |
---|
2409 | sw = smHaveDenom(a); |
---|
2410 | if (sw) break; |
---|
2411 | } |
---|
2412 | if (!sw) return res; |
---|
2413 | for (int i=0; i<IDELEMS(id); i++) |
---|
2414 | { |
---|
2415 | a = id->m[i]; |
---|
2416 | x = nCopy(pGetCoeff(a)); |
---|
2417 | pCleardenom(a); |
---|
2418 | y = nDiv(x,pGetCoeff(a)); |
---|
2419 | nDelete(&x); |
---|
2420 | x = nMult(res,y); |
---|
2421 | nNormalize(x); |
---|
2422 | nDelete(&res); |
---|
2423 | res = x; |
---|
2424 | } |
---|
2425 | return res; |
---|
2426 | } |
---|
2427 | |
---|
2428 | /* ----------------- gauss elimination ------------------ */ |
---|
2429 | /* in structs.h */ |
---|
2430 | typedef struct smnrec sm_nrec; |
---|
2431 | typedef sm_nrec * smnumber; |
---|
2432 | struct smnrec{ |
---|
2433 | smnumber n; // the next element |
---|
2434 | int pos; // position |
---|
2435 | number m; // the element |
---|
2436 | }; |
---|
2437 | |
---|
2438 | static omBin smnrec_bin = omGetSpecBin(sizeof(smnrec)); |
---|
2439 | |
---|
2440 | /* declare internal 'C' stuff */ |
---|
2441 | static void smNumberDelete(smnumber *); |
---|
2442 | static smnumber smNumberCopy(smnumber); |
---|
2443 | static smnumber smPoly2Smnumber(poly); |
---|
2444 | static poly smSmnumber2Poly(number); |
---|
2445 | static BOOLEAN smCheckSolv(ideal); |
---|
2446 | |
---|
2447 | /* class for sparse number matrix: |
---|
2448 | */ |
---|
2449 | class sparse_number_mat{ |
---|
2450 | private: |
---|
2451 | int nrows, ncols; // dimension of the problem |
---|
2452 | int act; // number of unreduced columns (start: ncols) |
---|
2453 | int crd; // number of reduced columns (start: 0) |
---|
2454 | int tored; // border for rows to reduce |
---|
2455 | int sing; // indicator for singular problem |
---|
2456 | int rpiv; // row-position of the pivot |
---|
2457 | int *perm; // permutation of rows |
---|
2458 | number one; // the "1" |
---|
2459 | number *sol; // field for solution |
---|
2460 | int *wrw, *wcl; // weights of rows and columns |
---|
2461 | smnumber * m_act; // unreduced columns |
---|
2462 | smnumber * m_res; // reduced columns (result) |
---|
2463 | smnumber * m_row; // reduced part of rows |
---|
2464 | smnumber red; // row to reduce |
---|
2465 | smnumber piv; // pivot |
---|
2466 | smnumber dumm; // allocated dummy |
---|
2467 | void smColToRow(); |
---|
2468 | void smRowToCol(); |
---|
2469 | void smSelectPR(); |
---|
2470 | void smRealPivot(); |
---|
2471 | void smZeroToredElim(); |
---|
2472 | void smGElim(); |
---|
2473 | void smAllDel(); |
---|
2474 | public: |
---|
2475 | sparse_number_mat(ideal); |
---|
2476 | ~sparse_number_mat(); |
---|
2477 | int smIsSing() { return sing; } |
---|
2478 | void smTriangular(); |
---|
2479 | void smSolv(); |
---|
2480 | ideal smRes2Ideal(); |
---|
2481 | }; |
---|
2482 | |
---|
2483 | /* ----------------- basics (used from 'C') ------------------ */ |
---|
2484 | /*2 |
---|
2485 | * returns the solution of a linear equation |
---|
2486 | * solution of M*x = r (M has dimension nXn) => |
---|
2487 | * I = module(transprose(M)) + r*gen(n+1) |
---|
2488 | * uses Gauss-elimination |
---|
2489 | */ |
---|
2490 | lists smCallSolv(ideal I) |
---|
2491 | { |
---|
2492 | sparse_number_mat *linsolv; |
---|
2493 | int k; |
---|
2494 | ring origR; |
---|
2495 | sip_sring tmpR; |
---|
2496 | ideal rr, ss; |
---|
2497 | lists res; |
---|
2498 | |
---|
2499 | if (idIsConstant(I)==FALSE) |
---|
2500 | { |
---|
2501 | WerrorS("symbol in equation"); |
---|
2502 | return NULL; |
---|
2503 | } |
---|
2504 | I->rank = idRankFreeModule(I); |
---|
2505 | if (smCheckSolv(I)) return NULL; |
---|
2506 | res=(lists)omAllocBin(slists_bin); |
---|
2507 | rr=smRingCopy(I,&origR,tmpR); |
---|
2508 | ss = NULL; |
---|
2509 | linsolv = new sparse_number_mat(rr); |
---|
2510 | linsolv->smTriangular(); |
---|
2511 | if (linsolv->smIsSing() == 0) |
---|
2512 | { |
---|
2513 | linsolv->smSolv(); |
---|
2514 | ss = linsolv->smRes2Ideal(); |
---|
2515 | } |
---|
2516 | else |
---|
2517 | WerrorS("singular problem for linsolv"); |
---|
2518 | delete linsolv; |
---|
2519 | if ((origR!=NULL) && (ss!=NULL)) |
---|
2520 | { |
---|
2521 | rChangeCurrRing(origR); |
---|
2522 | rr = idInit(IDELEMS(ss), 1); |
---|
2523 | for (k=0;k<IDELEMS(ss);k++) |
---|
2524 | rr->m[k] = prCopyR(ss->m[k], &tmpR); |
---|
2525 | rChangeCurrRing(&tmpR); |
---|
2526 | idDelete(&ss); |
---|
2527 | ss = rr; |
---|
2528 | } |
---|
2529 | if(origR!=NULL) |
---|
2530 | smRingClean(origR,tmpR); |
---|
2531 | res->Init(1); |
---|
2532 | res->m[0].rtyp=IDEAL_CMD; |
---|
2533 | res->m[0].data=(void *)ss; |
---|
2534 | return res; |
---|
2535 | } |
---|
2536 | |
---|
2537 | /* |
---|
2538 | * constructor, destroy smat |
---|
2539 | */ |
---|
2540 | sparse_number_mat::sparse_number_mat(ideal smat) |
---|
2541 | { |
---|
2542 | int i; |
---|
2543 | polyset pmat; |
---|
2544 | |
---|
2545 | crd = sing = 0; |
---|
2546 | act = ncols = smat->ncols; |
---|
2547 | tored = nrows = smat->rank; |
---|
2548 | i = tored+1; |
---|
2549 | perm = (int *)omAlloc(sizeof(int)*i); |
---|
2550 | m_row = (smnumber *)omAlloc0(sizeof(smnumber)*i); |
---|
2551 | wrw = (int *)omAlloc(sizeof(int)*i); |
---|
2552 | i = ncols+1; |
---|
2553 | wcl = (int *)omAlloc(sizeof(int)*i); |
---|
2554 | m_act = (smnumber *)omAlloc(sizeof(smnumber)*i); |
---|
2555 | m_res = (smnumber *)omAlloc0(sizeof(smnumber)*i); |
---|
2556 | dumm = (smnumber)omAllocBin(smnrec_bin); |
---|
2557 | pmat = smat->m; |
---|
2558 | for(i=ncols; i; i--) |
---|
2559 | { |
---|
2560 | m_act[i] = smPoly2Smnumber(pmat[i-1]); |
---|
2561 | } |
---|
2562 | omFreeSize((ADDRESS)pmat,smat->ncols*sizeof(poly)); |
---|
2563 | omFreeBin((ADDRESS)smat, sip_sideal_bin); |
---|
2564 | one = nInit(1); |
---|
2565 | } |
---|
2566 | |
---|
2567 | /* |
---|
2568 | * destructor |
---|
2569 | */ |
---|
2570 | sparse_number_mat::~sparse_number_mat() |
---|
2571 | { |
---|
2572 | int i; |
---|
2573 | omFreeBin((ADDRESS)dumm, smnrec_bin); |
---|
2574 | i = ncols+1; |
---|
2575 | omFreeSize((ADDRESS)m_res, sizeof(smnumber)*i); |
---|
2576 | omFreeSize((ADDRESS)m_act, sizeof(smnumber)*i); |
---|
2577 | omFreeSize((ADDRESS)wcl, sizeof(int)*i); |
---|
2578 | i = nrows+1; |
---|
2579 | omFreeSize((ADDRESS)wrw, sizeof(int)*i); |
---|
2580 | omFreeSize((ADDRESS)m_row, sizeof(smnumber)*i); |
---|
2581 | omFreeSize((ADDRESS)perm, sizeof(int)*i); |
---|
2582 | nDelete(&one); |
---|
2583 | } |
---|
2584 | |
---|
2585 | /* |
---|
2586 | * triangularization by Gauss-elimination |
---|
2587 | */ |
---|
2588 | void sparse_number_mat::smTriangular() |
---|
2589 | { |
---|
2590 | tored--; |
---|
2591 | this->smZeroToredElim(); |
---|
2592 | if (sing != 0) return; |
---|
2593 | while (act > 1) |
---|
2594 | { |
---|
2595 | this->smRealPivot(); |
---|
2596 | this->smSelectPR(); |
---|
2597 | this->smGElim(); |
---|
2598 | crd++; |
---|
2599 | this->smColToRow(); |
---|
2600 | act--; |
---|
2601 | this->smRowToCol(); |
---|
2602 | this->smZeroToredElim(); |
---|
2603 | if (sing != 0) return; |
---|
2604 | } |
---|
2605 | if (TEST_OPT_PROT) PrintS(".\n"); |
---|
2606 | piv = m_act[1]; |
---|
2607 | rpiv = piv->pos; |
---|
2608 | m_act[1] = piv->n; |
---|
2609 | piv->n = NULL; |
---|
2610 | crd++; |
---|
2611 | this->smColToRow(); |
---|
2612 | act--; |
---|
2613 | this->smRowToCol(); |
---|
2614 | } |
---|
2615 | |
---|
2616 | /* |
---|
2617 | * solve the triangular system |
---|
2618 | */ |
---|
2619 | void sparse_number_mat::smSolv() |
---|
2620 | { |
---|
2621 | int i, j; |
---|
2622 | number x, y, z; |
---|
2623 | smnumber s, d, r = m_row[nrows]; |
---|
2624 | |
---|
2625 | m_row[nrows] = NULL; |
---|
2626 | sol = (number *)omAlloc0(sizeof(number)*(crd+1)); |
---|
2627 | while (r != NULL) // expand the rigth hand side |
---|
2628 | { |
---|
2629 | sol[r->pos] = r->m; |
---|
2630 | s = r; |
---|
2631 | r = r->n; |
---|
2632 | omFreeBin((ADDRESS)s, smnrec_bin); |
---|
2633 | } |
---|
2634 | i = crd; // solve triangular system |
---|
2635 | if (sol[i] != NULL) |
---|
2636 | { |
---|
2637 | x = sol[i]; |
---|
2638 | sol[i] = nDiv(x, m_res[i]->m); |
---|
2639 | nDelete(&x); |
---|
2640 | } |
---|
2641 | i--; |
---|
2642 | while (i > 0) |
---|
2643 | { |
---|
2644 | x = NULL; |
---|
2645 | d = m_res[i]; |
---|
2646 | s = d->n; |
---|
2647 | while (s != NULL) |
---|
2648 | { |
---|
2649 | j = s->pos; |
---|
2650 | if (sol[j] != NULL) |
---|
2651 | { |
---|
2652 | z = nMult(sol[j], s->m); |
---|
2653 | if (x != NULL) |
---|
2654 | { |
---|
2655 | y = x; |
---|
2656 | x = nSub(y, z); |
---|
2657 | nDelete(&y); |
---|
2658 | nDelete(&z); |
---|
2659 | } |
---|
2660 | else |
---|
2661 | x = nNeg(z); |
---|
2662 | } |
---|
2663 | s = s->n; |
---|
2664 | } |
---|
2665 | if (sol[i] != NULL) |
---|
2666 | { |
---|
2667 | if (x != NULL) |
---|
2668 | { |
---|
2669 | y = nAdd(x, sol[i]); |
---|
2670 | nDelete(&x); |
---|
2671 | if (nIsZero(y)) |
---|
2672 | { |
---|
2673 | nDelete(&sol[i]); |
---|
2674 | sol[i] = NULL; |
---|
2675 | } |
---|
2676 | else |
---|
2677 | sol[i] = y; |
---|
2678 | } |
---|
2679 | } |
---|
2680 | else |
---|
2681 | sol[i] = x; |
---|
2682 | if (sol[i] != NULL) |
---|
2683 | { |
---|
2684 | x = sol[i]; |
---|
2685 | sol[i] = nDiv(x, d->m); |
---|
2686 | nDelete(&x); |
---|
2687 | } |
---|
2688 | i--; |
---|
2689 | } |
---|
2690 | this->smAllDel(); |
---|
2691 | } |
---|
2692 | |
---|
2693 | /* |
---|
2694 | * transform the result to an ideal |
---|
2695 | */ |
---|
2696 | ideal sparse_number_mat::smRes2Ideal() |
---|
2697 | { |
---|
2698 | int i, j; |
---|
2699 | ideal res = idInit(crd, 1); |
---|
2700 | |
---|
2701 | for (i=crd; i; i--) |
---|
2702 | { |
---|
2703 | j = perm[i]-1; |
---|
2704 | res->m[j] = smSmnumber2Poly(sol[i]); |
---|
2705 | } |
---|
2706 | omFreeSize((ADDRESS)sol, sizeof(number)*(crd+1)); |
---|
2707 | return res; |
---|
2708 | } |
---|
2709 | |
---|
2710 | /* ----------------- pivot method ------------------ */ |
---|
2711 | |
---|
2712 | /* |
---|
2713 | * compute pivot |
---|
2714 | */ |
---|
2715 | void sparse_number_mat::smRealPivot() |
---|
2716 | { |
---|
2717 | smnumber a; |
---|
2718 | number x, xo; |
---|
2719 | int i, copt, ropt; |
---|
2720 | |
---|
2721 | xo=nInit(0); |
---|
2722 | for (i=act; i; i--) |
---|
2723 | { |
---|
2724 | a = m_act[i]; |
---|
2725 | while ((a!=NULL) && (a->pos<=tored)) |
---|
2726 | { |
---|
2727 | x = a->m; |
---|
2728 | if (nGreaterZero(x)) |
---|
2729 | { |
---|
2730 | if (nGreater(x,xo)) |
---|
2731 | { |
---|
2732 | nDelete(&xo); |
---|
2733 | xo = nCopy(x); |
---|
2734 | copt = i; |
---|
2735 | ropt = a->pos; |
---|
2736 | } |
---|
2737 | } |
---|
2738 | else |
---|
2739 | { |
---|
2740 | xo = nNeg(xo); |
---|
2741 | if (nGreater(xo,x)) |
---|
2742 | { |
---|
2743 | nDelete(&xo); |
---|
2744 | xo = nCopy(x); |
---|
2745 | copt = i; |
---|
2746 | ropt = a->pos; |
---|
2747 | } |
---|
2748 | xo = nNeg(xo); |
---|
2749 | } |
---|
2750 | a = a->n; |
---|
2751 | } |
---|
2752 | } |
---|
2753 | rpiv = ropt; |
---|
2754 | if (copt != act) |
---|
2755 | { |
---|
2756 | a = m_act[act]; |
---|
2757 | m_act[act] = m_act[copt]; |
---|
2758 | m_act[copt] = a; |
---|
2759 | } |
---|
2760 | nDelete(&xo); |
---|
2761 | } |
---|
2762 | |
---|
2763 | /* ----------------- elimination ------------------ */ |
---|
2764 | |
---|
2765 | /* one step of Gauss-elimination */ |
---|
2766 | void sparse_number_mat::smGElim() |
---|
2767 | { |
---|
2768 | number p = nDiv(one,piv->m); // pivotelement |
---|
2769 | smnumber c = m_act[act]; // pivotcolumn |
---|
2770 | smnumber r = red; // row to reduce |
---|
2771 | smnumber res, a, b; |
---|
2772 | number w, ha, hb; |
---|
2773 | |
---|
2774 | if ((c == NULL) || (r == NULL)) |
---|
2775 | { |
---|
2776 | while (r!=NULL) smNumberDelete(&r); |
---|
2777 | return; |
---|
2778 | } |
---|
2779 | do |
---|
2780 | { |
---|
2781 | a = m_act[r->pos]; |
---|
2782 | res = dumm; |
---|
2783 | res->n = NULL; |
---|
2784 | b = c; |
---|
2785 | w = nMult(r->m, p); |
---|
2786 | nDelete(&r->m); |
---|
2787 | r->m = w; |
---|
2788 | loop // combine the chains a and b: a + w*b |
---|
2789 | { |
---|
2790 | if (a == NULL) |
---|
2791 | { |
---|
2792 | do |
---|
2793 | { |
---|
2794 | res = res->n = smNumberCopy(b); |
---|
2795 | res->m = nMult(b->m, w); |
---|
2796 | b = b->n; |
---|
2797 | } while (b != NULL); |
---|
2798 | break; |
---|
2799 | } |
---|
2800 | if (a->pos < b->pos) |
---|
2801 | { |
---|
2802 | res = res->n = a; |
---|
2803 | a = a->n; |
---|
2804 | } |
---|
2805 | else if (a->pos > b->pos) |
---|
2806 | { |
---|
2807 | res = res->n = smNumberCopy(b); |
---|
2808 | res->m = nMult(b->m, w); |
---|
2809 | b = b->n; |
---|
2810 | } |
---|
2811 | else |
---|
2812 | { |
---|
2813 | hb = nMult(b->m, w); |
---|
2814 | ha = nAdd(a->m, hb); |
---|
2815 | nDelete(&hb); |
---|
2816 | nDelete(&a->m); |
---|
2817 | if (nIsZero(ha)) |
---|
2818 | { |
---|
2819 | smNumberDelete(&a); |
---|
2820 | } |
---|
2821 | else |
---|
2822 | { |
---|
2823 | a->m = ha; |
---|
2824 | res = res->n = a; |
---|
2825 | a = a->n; |
---|
2826 | } |
---|
2827 | b = b->n; |
---|
2828 | } |
---|
2829 | if (b == NULL) |
---|
2830 | { |
---|
2831 | res->n = a; |
---|
2832 | break; |
---|
2833 | } |
---|
2834 | } |
---|
2835 | m_act[r->pos] = dumm->n; |
---|
2836 | smNumberDelete(&r); |
---|
2837 | } while (r != NULL); |
---|
2838 | nDelete(&p); |
---|
2839 | } |
---|
2840 | |
---|
2841 | /* ----------------- transfer ------------------ */ |
---|
2842 | |
---|
2843 | /* |
---|
2844 | * select the pivotrow and store it to red and piv |
---|
2845 | */ |
---|
2846 | void sparse_number_mat::smSelectPR() |
---|
2847 | { |
---|
2848 | smnumber b = dumm; |
---|
2849 | smnumber a, ap; |
---|
2850 | int i; |
---|
2851 | |
---|
2852 | if (TEST_OPT_PROT) |
---|
2853 | { |
---|
2854 | if ((crd+1)%10) |
---|
2855 | PrintS("."); |
---|
2856 | else |
---|
2857 | PrintS(".\n"); |
---|
2858 | } |
---|
2859 | a = m_act[act]; |
---|
2860 | if (a->pos < rpiv) |
---|
2861 | { |
---|
2862 | do |
---|
2863 | { |
---|
2864 | ap = a; |
---|
2865 | a = a->n; |
---|
2866 | } while (a->pos < rpiv); |
---|
2867 | ap->n = a->n; |
---|
2868 | } |
---|
2869 | else |
---|
2870 | m_act[act] = a->n; |
---|
2871 | piv = a; |
---|
2872 | a->n = NULL; |
---|
2873 | for (i=1; i<act; i++) |
---|
2874 | { |
---|
2875 | a = m_act[i]; |
---|
2876 | if (a->pos < rpiv) |
---|
2877 | { |
---|
2878 | loop |
---|
2879 | { |
---|
2880 | ap = a; |
---|
2881 | a = a->n; |
---|
2882 | if ((a == NULL) || (a->pos > rpiv)) |
---|
2883 | break; |
---|
2884 | if (a->pos == rpiv) |
---|
2885 | { |
---|
2886 | ap->n = a->n; |
---|
2887 | a->m = nNeg(a->m); |
---|
2888 | b = b->n = a; |
---|
2889 | b->pos = i; |
---|
2890 | break; |
---|
2891 | } |
---|
2892 | } |
---|
2893 | } |
---|
2894 | else if (a->pos == rpiv) |
---|
2895 | { |
---|
2896 | m_act[i] = a->n; |
---|
2897 | a->m = nNeg(a->m); |
---|
2898 | b = b->n = a; |
---|
2899 | b->pos = i; |
---|
2900 | } |
---|
2901 | } |
---|
2902 | b->n = NULL; |
---|
2903 | red = dumm->n; |
---|
2904 | } |
---|
2905 | |
---|
2906 | /* |
---|
2907 | * store the pivotcol in m_row |
---|
2908 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] |
---|
2909 | */ |
---|
2910 | void sparse_number_mat::smColToRow() |
---|
2911 | { |
---|
2912 | smnumber c = m_act[act]; |
---|
2913 | smnumber h; |
---|
2914 | |
---|
2915 | while (c != NULL) |
---|
2916 | { |
---|
2917 | h = c; |
---|
2918 | c = c->n; |
---|
2919 | h->n = m_row[h->pos]; |
---|
2920 | m_row[h->pos] = h; |
---|
2921 | h->pos = crd; |
---|
2922 | } |
---|
2923 | } |
---|
2924 | |
---|
2925 | /* |
---|
2926 | * store the pivot and the assosiated row in m_row |
---|
2927 | * to m_res (result): |
---|
2928 | * piv + m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
---|
2929 | */ |
---|
2930 | void sparse_number_mat::smRowToCol() |
---|
2931 | { |
---|
2932 | smnumber r = m_row[rpiv]; |
---|
2933 | smnumber a, ap, h; |
---|
2934 | |
---|
2935 | m_row[rpiv] = NULL; |
---|
2936 | perm[crd] = rpiv; |
---|
2937 | piv->pos = crd; |
---|
2938 | m_res[crd] = piv; |
---|
2939 | while (r != NULL) |
---|
2940 | { |
---|
2941 | ap = m_res[r->pos]; |
---|
2942 | loop |
---|
2943 | { |
---|
2944 | a = ap->n; |
---|
2945 | if (a == NULL) |
---|
2946 | { |
---|
2947 | ap->n = h = r; |
---|
2948 | r = r->n; |
---|
2949 | h->n = a; |
---|
2950 | h->pos = crd; |
---|
2951 | break; |
---|
2952 | } |
---|
2953 | ap = a; |
---|
2954 | } |
---|
2955 | } |
---|
2956 | } |
---|
2957 | |
---|
2958 | /* ----------------- C++ stuff ------------------ */ |
---|
2959 | |
---|
2960 | /* |
---|
2961 | * check singularity |
---|
2962 | */ |
---|
2963 | void sparse_number_mat::smZeroToredElim() |
---|
2964 | { |
---|
2965 | smnumber a; |
---|
2966 | int i = act; |
---|
2967 | |
---|
2968 | loop |
---|
2969 | { |
---|
2970 | if (i == 0) return; |
---|
2971 | a = m_act[i]; |
---|
2972 | if ((a==NULL) || (a->pos>tored)) |
---|
2973 | { |
---|
2974 | sing = 1; |
---|
2975 | this->smAllDel(); |
---|
2976 | return; |
---|
2977 | } |
---|
2978 | i--; |
---|
2979 | } |
---|
2980 | } |
---|
2981 | |
---|
2982 | /* |
---|
2983 | * delete all smnumber's |
---|
2984 | */ |
---|
2985 | void sparse_number_mat::smAllDel() |
---|
2986 | { |
---|
2987 | smnumber a; |
---|
2988 | int i; |
---|
2989 | |
---|
2990 | for (i=act; i; i--) |
---|
2991 | { |
---|
2992 | a = m_act[i]; |
---|
2993 | while (a != NULL) |
---|
2994 | smNumberDelete(&a); |
---|
2995 | } |
---|
2996 | for (i=crd; i; i--) |
---|
2997 | { |
---|
2998 | a = m_res[i]; |
---|
2999 | while (a != NULL) |
---|
3000 | smNumberDelete(&a); |
---|
3001 | } |
---|
3002 | if (act) |
---|
3003 | { |
---|
3004 | for (i=nrows; i; i--) |
---|
3005 | { |
---|
3006 | a = m_row[i]; |
---|
3007 | while (a != NULL) |
---|
3008 | smNumberDelete(&a); |
---|
3009 | } |
---|
3010 | } |
---|
3011 | } |
---|
3012 | |
---|
3013 | /* ----------------- internal 'C' stuff ------------------ */ |
---|
3014 | |
---|
3015 | static void smNumberDelete(smnumber *r) |
---|
3016 | { |
---|
3017 | smnumber a = *r, b = a->n; |
---|
3018 | |
---|
3019 | nDelete(&a->m); |
---|
3020 | omFreeBin((ADDRESS)a, smnrec_bin); |
---|
3021 | *r = b; |
---|
3022 | } |
---|
3023 | |
---|
3024 | static smnumber smNumberCopy(smnumber a) |
---|
3025 | { |
---|
3026 | smnumber r = (smnumber)omAllocBin(smnrec_bin); |
---|
3027 | memcpy(r, a, sizeof(smnrec)); |
---|
3028 | return r; |
---|
3029 | } |
---|
3030 | |
---|
3031 | /* |
---|
3032 | * from poly to smnumber |
---|
3033 | * do not destroy p |
---|
3034 | */ |
---|
3035 | static smnumber smPoly2Smnumber(poly q) |
---|
3036 | { |
---|
3037 | smnumber a, res; |
---|
3038 | poly p = q; |
---|
3039 | |
---|
3040 | if (p == NULL) |
---|
3041 | return NULL; |
---|
3042 | a = res = (smnumber)omAllocBin(smnrec_bin); |
---|
3043 | a->pos = pGetComp(p); |
---|
3044 | a->m = pGetCoeff(p); |
---|
3045 | nNew(&pGetCoeff(p)); |
---|
3046 | loop |
---|
3047 | { |
---|
3048 | pIter(p); |
---|
3049 | if (p == NULL) |
---|
3050 | { |
---|
3051 | pDelete(&q); |
---|
3052 | a->n = NULL; |
---|
3053 | return res; |
---|
3054 | } |
---|
3055 | a = a->n = (smnumber)omAllocBin(smnrec_bin); |
---|
3056 | a->pos = pGetComp(p); |
---|
3057 | a->m = pGetCoeff(p); |
---|
3058 | nNew(&pGetCoeff(p)); |
---|
3059 | } |
---|
3060 | } |
---|
3061 | |
---|
3062 | /* |
---|
3063 | * from smnumber to poly |
---|
3064 | * destroy a |
---|
3065 | */ |
---|
3066 | static poly smSmnumber2Poly(number a) |
---|
3067 | { |
---|
3068 | poly res; |
---|
3069 | |
---|
3070 | if (a == NULL) return NULL; |
---|
3071 | res = pInit(); |
---|
3072 | pSetCoeff0(res, a); |
---|
3073 | return res; |
---|
3074 | } |
---|
3075 | |
---|
3076 | /*2 |
---|
3077 | * check the input |
---|
3078 | */ |
---|
3079 | static BOOLEAN smCheckSolv(ideal I) |
---|
3080 | { int i = I->ncols; |
---|
3081 | if ((i == 0) || (i != I->rank-1)) |
---|
3082 | { |
---|
3083 | WerrorS("wrong dimensions for linsolv"); |
---|
3084 | return TRUE; |
---|
3085 | } |
---|
3086 | for(;i;i--) |
---|
3087 | { |
---|
3088 | if(I->m[i-1] == NULL) |
---|
3089 | { |
---|
3090 | WerrorS("singular input for linsolv"); |
---|
3091 | return TRUE; |
---|
3092 | } |
---|
3093 | } |
---|
3094 | return FALSE; |
---|
3095 | } |
---|