[35aab3] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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[341696] | 4 | /* $Id$ */ |
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[35aab3] | 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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[b78996] | 10 | #include "config.h" |
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| 11 | #include <misc/auxiliary.h> |
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| 12 | |
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| 13 | #include <omalloc/omalloc.h> |
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| 14 | #include <misc/mylimits.h> |
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| 15 | |
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| 16 | #include <misc/options.h> |
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| 17 | |
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| 18 | #include <reporter/reporter.h> |
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| 19 | #include <misc/intvec.h> |
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| 20 | |
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| 21 | #include <coeffs/numbers.h> |
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| 22 | #include "coeffrings.h" |
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| 23 | |
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| 24 | #include "monomials/ring.h" |
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| 25 | #include "monomials/p_polys.h" |
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| 26 | |
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| 27 | #include "simpleideals.h" |
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| 28 | |
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| 29 | |
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| 30 | #include "sparsmat.h" |
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| 31 | #include "prCopy.h" |
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| 32 | |
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| 33 | #include "templates/p_Procs.h" |
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| 34 | |
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| 35 | #include "kbuckets.h" |
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| 36 | #include "operations/p_Mult_q.h" |
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[35aab3] | 37 | |
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| 38 | // define SM_NO_BUCKETS, if sparsemat stuff should not use buckets |
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| 39 | // #define SM_NO_BUCKETS |
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| 40 | |
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| 41 | // this is also influenced by TEST_OPT_NOTBUCKETS |
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| 42 | #ifndef SM_NO_BUCKETS |
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| 43 | // buckets do carry a small additional overhead: only use them if |
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| 44 | // min-length of polys is >= SM_MIN_LENGTH_BUCKET |
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| 45 | #define SM_MIN_LENGTH_BUCKET MIN_LENGTH_BUCKET - 5 |
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| 46 | #else |
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[e554162] | 47 | #define SM_MIN_LENGTH_BUCKET MAX_INT_VAL |
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[35aab3] | 48 | #endif |
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| 49 | |
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[ed5c8d] | 50 | typedef struct smprec sm_prec; |
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| 51 | typedef sm_prec * smpoly; |
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| 52 | struct smprec |
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| 53 | { |
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| 54 | smpoly n; // the next element |
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| 55 | int pos; // position |
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| 56 | int e; // level |
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| 57 | poly m; // the element |
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| 58 | float f; // complexity of the element |
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| 59 | }; |
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| 60 | |
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[35aab3] | 61 | |
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[ebdaa1] | 62 | /* declare internal 'C' stuff */ |
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| 63 | static void sm_ExactPolyDiv(poly, poly, const ring); |
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| 64 | static BOOLEAN sm_IsNegQuot(poly, const poly, const poly, const ring); |
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| 65 | static void sm_ExpMultDiv(poly, const poly, const poly, const ring); |
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| 66 | static void sm_PolyDivN(poly, const number, const ring); |
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| 67 | static BOOLEAN smSmaller(poly, poly); |
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| 68 | static void sm_CombineChain(poly *, poly, const ring); |
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| 69 | static void sm_FindRef(poly *, poly *, poly, const ring); |
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| 70 | |
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| 71 | static void sm_ElemDelete(smpoly *, const ring); |
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| 72 | static smpoly smElemCopy(smpoly); |
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| 73 | static float sm_PolyWeight(smpoly, const ring); |
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| 74 | static smpoly sm_Poly2Smpoly(poly, const ring); |
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| 75 | static poly sm_Smpoly2Poly(smpoly, const ring); |
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| 76 | static BOOLEAN sm_HaveDenom(poly, const ring); |
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| 77 | static number sm_Cleardenom(ideal, const ring); |
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[a24e0a] | 78 | |
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[ebdaa1] | 79 | omBin smprec_bin = omGetSpecBin(sizeof(smprec)); |
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[a24e0a] | 80 | |
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[35aab3] | 81 | static poly pp_Mult_Coeff_mm_DivSelect_MultDiv(poly p, int &lp, poly m, |
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[b78996] | 82 | poly a, poly b, const ring currRing) |
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[35aab3] | 83 | { |
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| 84 | if (rOrd_is_Comp_dp(currRing) && currRing->ExpL_Size > 2) |
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| 85 | { |
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| 86 | // pp_Mult_Coeff_mm_DivSelectMult only works for (c/C,dp) and |
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| 87 | // ExpL_Size > 2 |
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| 88 | // should be generalized, at least to dp with ExpL_Size == 2 |
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| 89 | // (is the case for 1 variable) |
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| 90 | int shorter; |
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| 91 | p = currRing->p_Procs->pp_Mult_Coeff_mm_DivSelectMult(p, m, a, b, |
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| 92 | shorter, currRing); |
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| 93 | lp -= shorter; |
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| 94 | } |
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| 95 | else |
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| 96 | { |
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| 97 | p = pp_Mult_Coeff_mm_DivSelect(p, lp, m, currRing); |
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[b78996] | 98 | sm_ExpMultDiv(p, a, b, currRing); |
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[35aab3] | 99 | } |
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| 100 | return p; |
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| 101 | } |
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| 102 | |
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[b78996] | 103 | static poly sm_SelectCopy_ExpMultDiv(poly p, poly m, poly a, poly b, const ring currRing) |
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[35aab3] | 104 | { |
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| 105 | int lp = 0; |
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[b78996] | 106 | return pp_Mult_Coeff_mm_DivSelect_MultDiv(p, lp, m, a, b, currRing); |
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[35aab3] | 107 | } |
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| 108 | |
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| 109 | |
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| 110 | /* class for sparse matrix: |
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| 111 | * 3 parts of matrix during the algorithm |
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| 112 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
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| 113 | * input pivotcols as rows result |
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| 114 | * pivot like a stack from pivot and pivotcols |
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| 115 | * elimination rows reordered according |
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| 116 | * to pivot choise |
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| 117 | * stored in perm |
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| 118 | * a step is as follows |
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| 119 | * - search of pivot (smPivot) |
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| 120 | * - swap pivot column and last column (smSwapC) |
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| 121 | * select pivotrow to piv and red (smSelectPR) |
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| 122 | * consider sign |
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| 123 | * - elimination (smInitElim, sm0Elim, sm1Elim) |
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| 124 | * clear zero column as result of elimination (smZeroElim) |
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| 125 | * - tranfer from |
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| 126 | * piv and m_row to m_res (smRowToCol) |
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| 127 | * m_act to m_row (smColToRow) |
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| 128 | */ |
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| 129 | class sparse_mat{ |
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| 130 | private: |
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| 131 | int nrows, ncols; // dimension of the problem |
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| 132 | int sign; // for determinant (start: 1) |
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| 133 | int act; // number of unreduced columns (start: ncols) |
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| 134 | int crd; // number of reduced columns (start: 0) |
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| 135 | int tored; // border for rows to reduce |
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| 136 | int inred; // unreducable part |
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| 137 | int rpiv, cpiv; // position of the pivot |
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| 138 | int normalize; // Normalization flag |
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| 139 | int *perm; // permutation of rows |
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| 140 | float wpoints; // weight of all points |
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| 141 | float *wrw, *wcl; // weights of rows and columns |
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| 142 | smpoly * m_act; // unreduced columns |
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| 143 | smpoly * m_res; // reduced columns (result) |
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| 144 | smpoly * m_row; // reduced part of rows |
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| 145 | smpoly red; // row to reduce |
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| 146 | smpoly piv, oldpiv; // pivot and previous pivot |
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| 147 | smpoly dumm; // allocated dummy |
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[bf6a4d] | 148 | ring _R; |
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[b78996] | 149 | |
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[35aab3] | 150 | void smColToRow(); |
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| 151 | void smRowToCol(); |
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| 152 | void smFinalMult(); |
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| 153 | void smSparseHomog(); |
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| 154 | void smWeights(); |
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| 155 | void smPivot(); |
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| 156 | void smNewWeights(); |
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| 157 | void smNewPivot(); |
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| 158 | void smZeroElim(); |
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| 159 | void smToredElim(); |
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| 160 | void smCopToRes(); |
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| 161 | void smSelectPR(); |
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| 162 | void sm1Elim(); |
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| 163 | void smHElim(); |
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| 164 | void smMultCol(); |
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| 165 | poly smMultPoly(smpoly); |
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| 166 | void smActDel(); |
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| 167 | void smColDel(); |
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| 168 | void smPivDel(); |
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| 169 | void smSign(); |
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| 170 | void smInitPerm(); |
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| 171 | int smCheckNormalize(); |
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| 172 | void smNormalize(); |
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| 173 | public: |
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[b78996] | 174 | sparse_mat(ideal, const ring); |
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[35aab3] | 175 | ~sparse_mat(); |
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| 176 | int smGetSign() { return sign; } |
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| 177 | smpoly * smGetAct() { return m_act; } |
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| 178 | int smGetRed() { return tored; } |
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| 179 | ideal smRes2Mod(); |
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| 180 | poly smDet(); |
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| 181 | void smNewBareiss(int, int); |
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| 182 | void smToIntvec(intvec *); |
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| 183 | }; |
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| 184 | |
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| 185 | /* |
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| 186 | * estimate maximal exponent for det or minors, |
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| 187 | * the module m has di vectors and maximal rank ra, |
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| 188 | * estimate yields for the tXt minors, |
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| 189 | * we have di,ra >= t |
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| 190 | */ |
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[ed5c8d] | 191 | static void smMinSelect(long *, int, int); |
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[b78996] | 192 | |
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| 193 | long sm_ExpBound( ideal m, int di, int ra, int t, const ring currRing) |
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[35aab3] | 194 | { |
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| 195 | poly p; |
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[ed5c8d] | 196 | long kr, kc; |
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| 197 | long *r, *c; |
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[35aab3] | 198 | int al, bl, i, j, k; |
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| 199 | |
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| 200 | if (ra==0) ra=1; |
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[ed5c8d] | 201 | al = di*sizeof(long); |
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| 202 | c = (long *)omAlloc(al); |
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| 203 | bl = ra*sizeof(long); |
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| 204 | r = (long *)omAlloc0(bl); |
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[35aab3] | 205 | for (i=di-1;i>=0;i--) |
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| 206 | { |
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| 207 | kc = 0; |
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| 208 | p = m->m[i]; |
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| 209 | while(p!=NULL) |
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| 210 | { |
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[b78996] | 211 | k = p_GetComp(p, currRing)-1; |
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[35aab3] | 212 | kr = r[k]; |
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[b78996] | 213 | for (j=rVar(currRing);j>0;j--) |
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[35aab3] | 214 | { |
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[b78996] | 215 | if(p_GetExp(p,j, currRing)>kc) |
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| 216 | kc=p_GetExp(p,j, currRing); |
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| 217 | if(p_GetExp(p,j, currRing)>kr) |
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| 218 | kr=p_GetExp(p,j, currRing); |
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[35aab3] | 219 | } |
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| 220 | r[k] = kr; |
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| 221 | pIter(p); |
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| 222 | } |
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| 223 | c[i] = kc; |
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| 224 | } |
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| 225 | if (t<di) smMinSelect(c, t, di); |
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| 226 | if (t<ra) smMinSelect(r, t, ra); |
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| 227 | kr = kc = 0; |
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| 228 | for (j=t-1;j>=0;j--) |
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| 229 | { |
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| 230 | kr += r[j]; |
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| 231 | kc += c[j]; |
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| 232 | } |
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| 233 | omFreeSize((ADDRESS)c, al); |
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| 234 | omFreeSize((ADDRESS)r, bl); |
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| 235 | if (kr<kc) kc = kr; |
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| 236 | if (kr<1) kr = 1; |
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| 237 | return kr; |
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| 238 | } |
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| 239 | |
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[ed5c8d] | 240 | static void smMinSelect(long *c, int t, int d) |
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[35aab3] | 241 | { |
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[ed5c8d] | 242 | long m; |
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[35aab3] | 243 | int pos, i; |
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| 244 | do |
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| 245 | { |
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| 246 | d--; |
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| 247 | pos = d; |
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| 248 | m = c[pos]; |
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| 249 | for (i=d-1;i>=0;i--) |
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| 250 | { |
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| 251 | if(c[i]<m) |
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| 252 | { |
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| 253 | pos = i; |
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| 254 | m = c[i]; |
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| 255 | } |
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| 256 | } |
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| 257 | for (i=pos;i<d;i++) c[i] = c[i+1]; |
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| 258 | } while (d>t); |
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| 259 | } |
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| 260 | |
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| 261 | /* ----------------- ops with rings ------------------ */ |
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[bf6a4d] | 262 | ring sm_RingChange(const ring origR, long bound) |
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[35aab3] | 263 | { |
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[b78996] | 264 | // *origR =currRing; |
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[bf6a4d] | 265 | ring tmpR=rCopy0(origR,FALSE,FALSE); |
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[35aab3] | 266 | int *ord=(int*)omAlloc0(3*sizeof(int)); |
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| 267 | int *block0=(int*)omAlloc(3*sizeof(int)); |
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| 268 | int *block1=(int*)omAlloc(3*sizeof(int)); |
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| 269 | ord[0]=ringorder_c; |
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| 270 | ord[1]=ringorder_dp; |
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[ab453da] | 271 | tmpR->order=ord; |
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| 272 | tmpR->OrdSgn=1; |
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[35aab3] | 273 | block0[1]=1; |
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[ab453da] | 274 | tmpR->block0=block0; |
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| 275 | block1[1]=tmpR->N; |
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| 276 | tmpR->block1=block1; |
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| 277 | tmpR->bitmask = 2*bound; |
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[d39b74] | 278 | tmpR->wvhdl = (int **)omAlloc0((3) * sizeof(int*)); |
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[35aab3] | 279 | |
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| 280 | // ??? |
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[ab453da] | 281 | // if (tmpR->bitmask > currRing->bitmask) tmpR->bitmask = currRing->bitmask; |
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[35aab3] | 282 | |
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[ab453da] | 283 | rComplete(tmpR,1); |
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[bf6a4d] | 284 | if (origR->qideal!=NULL) |
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[4131d8] | 285 | { |
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[bf6a4d] | 286 | tmpR->qideal= idrCopyR_NoSort(origR->qideal, origR, tmpR); |
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[4131d8] | 287 | } |
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[35aab3] | 288 | if (TEST_OPT_PROT) |
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[ab453da] | 289 | Print("[%ld:%d]", (long) tmpR->bitmask, tmpR->ExpL_Size); |
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| 290 | return tmpR; |
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[35aab3] | 291 | } |
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| 292 | |
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[b78996] | 293 | void sm_KillModifiedRing(ring r) |
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[35aab3] | 294 | { |
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[ab453da] | 295 | if (r->qideal!=NULL) id_Delete(&(r->qideal),r); |
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| 296 | rKillModifiedRing(r); |
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[35aab3] | 297 | } |
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| 298 | |
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| 299 | /*2 |
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| 300 | * Bareiss or Chinese remainder ? |
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| 301 | * I is dXd |
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| 302 | * sw = TRUE -> I Matrix |
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| 303 | * FALSE -> I Module |
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| 304 | * return True -> change Type |
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| 305 | * FALSE -> same Type |
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| 306 | */ |
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[bf6a4d] | 307 | BOOLEAN sm_CheckDet(ideal I, int d, BOOLEAN sw, const ring r) |
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[35aab3] | 308 | { |
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| 309 | int s,t,i; |
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| 310 | poly p; |
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| 311 | |
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[bf6a4d] | 312 | if ((d>100) || (rIsExtension(r))) |
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[35aab3] | 313 | return sw; |
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[bf6a4d] | 314 | if (!rField_is_Q(r)) |
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[35aab3] | 315 | return sw; |
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| 316 | s = t = 0; |
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| 317 | if (sw) |
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| 318 | { |
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| 319 | for(i=IDELEMS(I)-1;i>=0;i--) |
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| 320 | { |
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| 321 | p=I->m[i]; |
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| 322 | if (p!=NULL) |
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| 323 | { |
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[bf6a4d] | 324 | if(!p_IsConstant(p,r)) |
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[35aab3] | 325 | return sw; |
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| 326 | s++; |
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[bf6a4d] | 327 | t+=n_Size(pGetCoeff(p),r->cf); |
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[35aab3] | 328 | } |
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| 329 | } |
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| 330 | } |
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| 331 | else |
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| 332 | { |
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| 333 | for(i=IDELEMS(I)-1;i>=0;i--) |
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| 334 | { |
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| 335 | p=I->m[i]; |
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[bf6a4d] | 336 | if (!p_IsConstantPoly(p,r)) |
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[35aab3] | 337 | return sw; |
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| 338 | while (p!=NULL) |
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| 339 | { |
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| 340 | s++; |
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[bf6a4d] | 341 | t+=n_Size(pGetCoeff(p),r->cf); |
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[35aab3] | 342 | pIter(p); |
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| 343 | } |
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| 344 | } |
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| 345 | } |
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| 346 | s*=15; |
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| 347 | if (t>s) |
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| 348 | return !sw; |
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| 349 | else |
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| 350 | return sw; |
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| 351 | } |
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| 352 | |
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| 353 | /* ----------------- basics (used from 'C') ------------------ */ |
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| 354 | /*2 |
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| 355 | *returns the determinant of the module I; |
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| 356 | *uses Bareiss algorithm |
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| 357 | */ |
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[bf6a4d] | 358 | poly sm_CallDet(ideal I,const ring R) |
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[35aab3] | 359 | { |
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| 360 | if (I->ncols != I->rank) |
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| 361 | { |
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[2132395] | 362 | Werror("det of %ld x %d module (matrix)",I->rank,I->ncols); |
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[35aab3] | 363 | return NULL; |
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| 364 | } |
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[bf6a4d] | 365 | int r=id_RankFreeModule(I,R); |
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[35aab3] | 366 | if (I->ncols != r) // some 0-lines at the end |
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| 367 | { |
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| 368 | return NULL; |
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| 369 | } |
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[bf6a4d] | 370 | long bound=sm_ExpBound(I,r,r,r,R); |
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| 371 | number diag,h=n_Init(1,R->cf); |
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[35aab3] | 372 | poly res; |
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[ab453da] | 373 | ring tmpR; |
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[35aab3] | 374 | sparse_mat *det; |
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| 375 | ideal II; |
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| 376 | |
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[bf6a4d] | 377 | tmpR=sm_RingChange(R,bound); |
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| 378 | II = idrCopyR(I, R, tmpR); |
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| 379 | diag = sm_Cleardenom(II,tmpR); |
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| 380 | det = new sparse_mat(II,tmpR); |
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| 381 | id_Delete(&II,tmpR); |
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[35aab3] | 382 | if (det->smGetAct() == NULL) |
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| 383 | { |
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| 384 | delete det; |
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[bf6a4d] | 385 | sm_KillModifiedRing(tmpR); |
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[35aab3] | 386 | return NULL; |
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| 387 | } |
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| 388 | res=det->smDet(); |
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[bf6a4d] | 389 | if(det->smGetSign()<0) res=p_Neg(res,tmpR); |
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[35aab3] | 390 | delete det; |
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[bf6a4d] | 391 | res = prMoveR(res, tmpR, R); |
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| 392 | sm_KillModifiedRing(tmpR); |
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| 393 | if (!n_Equal(diag,h,R->cf)) |
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[35aab3] | 394 | { |
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[bf6a4d] | 395 | p_Mult_nn(res,diag,R); |
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| 396 | p_Normalize(res,R); |
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[35aab3] | 397 | } |
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[bf6a4d] | 398 | n_Delete(&diag,R->cf); |
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| 399 | n_Delete(&h,R->cf); |
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[35aab3] | 400 | return res; |
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| 401 | } |
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| 402 | |
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[bf6a4d] | 403 | void sm_CallBareiss(ideal I, int x, int y, ideal & M, intvec **iv, const ring R) |
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[35aab3] | 404 | { |
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[bf6a4d] | 405 | int r=id_RankFreeModule(I,R),t=r; |
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[35aab3] | 406 | int c=IDELEMS(I),s=c; |
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[ed5c8d] | 407 | long bound; |
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[ab453da] | 408 | ring tmpR; |
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[35aab3] | 409 | sparse_mat *bareiss; |
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| 410 | |
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| 411 | if ((x>0) && (x<t)) |
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| 412 | t-=x; |
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| 413 | if ((y>1) && (y<s)) |
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| 414 | s-=y; |
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| 415 | if (t>s) t=s; |
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[bf6a4d] | 416 | bound=sm_ExpBound(I,c,r,t,R); |
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| 417 | tmpR=sm_RingChange(R,bound); |
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| 418 | ideal II = idrCopyR(I, R, tmpR); |
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| 419 | bareiss = new sparse_mat(II,tmpR); |
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[35aab3] | 420 | if (bareiss->smGetAct() == NULL) |
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| 421 | { |
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| 422 | delete bareiss; |
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[bf6a4d] | 423 | *iv=new intvec(1,rVar(tmpR)); |
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[35aab3] | 424 | } |
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| 425 | else |
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| 426 | { |
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[bf6a4d] | 427 | id_Delete(&II,tmpR); |
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[35aab3] | 428 | bareiss->smNewBareiss(x, y); |
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| 429 | II = bareiss->smRes2Mod(); |
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| 430 | *iv = new intvec(bareiss->smGetRed()); |
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| 431 | bareiss->smToIntvec(*iv); |
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| 432 | delete bareiss; |
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[bf6a4d] | 433 | II = idrMoveR(II,tmpR,R); |
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[35aab3] | 434 | } |
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[bf6a4d] | 435 | sm_KillModifiedRing(tmpR); |
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[35aab3] | 436 | M=II; |
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| 437 | } |
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| 438 | |
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| 439 | /* |
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| 440 | * constructor |
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| 441 | */ |
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[bf6a4d] | 442 | sparse_mat::sparse_mat(ideal smat, const ring RR) |
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[35aab3] | 443 | { |
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| 444 | int i; |
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[bf6a4d] | 445 | poly* pmat; |
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| 446 | _R=RR; |
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[35aab3] | 447 | |
---|
| 448 | ncols = smat->ncols; |
---|
[bf6a4d] | 449 | nrows = id_RankFreeModule(smat,RR); |
---|
[35aab3] | 450 | if (nrows <= 0) |
---|
| 451 | { |
---|
| 452 | m_act = NULL; |
---|
| 453 | return; |
---|
| 454 | } |
---|
| 455 | sign = 1; |
---|
| 456 | inred = act = ncols; |
---|
| 457 | crd = 0; |
---|
| 458 | tored = nrows; // without border |
---|
| 459 | i = tored+1; |
---|
| 460 | perm = (int *)omAlloc(sizeof(int)*(i+1)); |
---|
| 461 | perm[i] = 0; |
---|
| 462 | m_row = (smpoly *)omAlloc0(sizeof(smpoly)*i); |
---|
| 463 | wrw = (float *)omAlloc(sizeof(float)*i); |
---|
| 464 | i = ncols+1; |
---|
| 465 | wcl = (float *)omAlloc(sizeof(float)*i); |
---|
| 466 | m_act = (smpoly *)omAlloc(sizeof(smpoly)*i); |
---|
| 467 | m_res = (smpoly *)omAlloc0(sizeof(smpoly)*i); |
---|
| 468 | dumm = (smpoly)omAllocBin(smprec_bin); |
---|
| 469 | m_res[0] = (smpoly)omAllocBin(smprec_bin); |
---|
| 470 | m_res[0]->m = NULL; |
---|
| 471 | pmat = smat->m; |
---|
| 472 | for(i=ncols; i; i--) |
---|
| 473 | { |
---|
[bf6a4d] | 474 | m_act[i] = sm_Poly2Smpoly(pmat[i-1], RR); |
---|
[35aab3] | 475 | pmat[i-1] = NULL; |
---|
| 476 | } |
---|
| 477 | this->smZeroElim(); |
---|
| 478 | oldpiv = NULL; |
---|
| 479 | } |
---|
| 480 | |
---|
| 481 | /* |
---|
| 482 | * destructor |
---|
| 483 | */ |
---|
| 484 | sparse_mat::~sparse_mat() |
---|
| 485 | { |
---|
| 486 | int i; |
---|
| 487 | if (m_act == NULL) return; |
---|
| 488 | omFreeBin((ADDRESS)m_res[0], smprec_bin); |
---|
| 489 | omFreeBin((ADDRESS)dumm, smprec_bin); |
---|
| 490 | i = ncols+1; |
---|
| 491 | omFreeSize((ADDRESS)m_res, sizeof(smpoly)*i); |
---|
| 492 | omFreeSize((ADDRESS)m_act, sizeof(smpoly)*i); |
---|
| 493 | omFreeSize((ADDRESS)wcl, sizeof(float)*i); |
---|
| 494 | i = nrows+1; |
---|
| 495 | omFreeSize((ADDRESS)wrw, sizeof(float)*i); |
---|
| 496 | omFreeSize((ADDRESS)m_row, sizeof(smpoly)*i); |
---|
| 497 | omFreeSize((ADDRESS)perm, sizeof(int)*(i+1)); |
---|
| 498 | } |
---|
| 499 | |
---|
| 500 | /* |
---|
| 501 | * transform the result to a module |
---|
| 502 | */ |
---|
[bf6a4d] | 503 | |
---|
[35aab3] | 504 | ideal sparse_mat::smRes2Mod() |
---|
| 505 | { |
---|
| 506 | ideal res = idInit(crd, crd); |
---|
| 507 | int i; |
---|
| 508 | |
---|
[bf6a4d] | 509 | for (i=crd; i; i--) res->m[i-1] = sm_Smpoly2Poly(m_res[i],_R); |
---|
| 510 | res->rank = id_RankFreeModule(res,_R); |
---|
[35aab3] | 511 | return res; |
---|
| 512 | } |
---|
| 513 | |
---|
| 514 | /* |
---|
| 515 | * permutation of rows |
---|
| 516 | */ |
---|
| 517 | void sparse_mat::smToIntvec(intvec *v) |
---|
| 518 | { |
---|
| 519 | int i; |
---|
| 520 | |
---|
| 521 | for (i=v->rows()-1; i>=0; i--) |
---|
| 522 | (*v)[i] = perm[i+1]; |
---|
| 523 | } |
---|
| 524 | /* ---------------- the algorithm's ------------------ */ |
---|
| 525 | /* |
---|
| 526 | * the determinant (up to sign), uses new Bareiss elimination |
---|
| 527 | */ |
---|
| 528 | poly sparse_mat::smDet() |
---|
| 529 | { |
---|
| 530 | poly res = NULL; |
---|
| 531 | |
---|
| 532 | if (sign == 0) |
---|
| 533 | { |
---|
| 534 | this->smActDel(); |
---|
| 535 | return NULL; |
---|
| 536 | } |
---|
| 537 | if (act < 2) |
---|
| 538 | { |
---|
| 539 | if (act != 0) res = m_act[1]->m; |
---|
| 540 | omFreeBin((void *)m_act[1], smprec_bin); |
---|
| 541 | return res; |
---|
| 542 | } |
---|
| 543 | normalize = 0; |
---|
| 544 | this->smInitPerm(); |
---|
| 545 | this->smPivot(); |
---|
| 546 | this->smSign(); |
---|
| 547 | this->smSelectPR(); |
---|
| 548 | this->sm1Elim(); |
---|
| 549 | crd++; |
---|
| 550 | m_res[crd] = piv; |
---|
| 551 | this->smColDel(); |
---|
| 552 | act--; |
---|
| 553 | this->smZeroElim(); |
---|
| 554 | if (sign == 0) |
---|
| 555 | { |
---|
| 556 | this->smActDel(); |
---|
| 557 | return NULL; |
---|
| 558 | } |
---|
| 559 | if (act < 2) |
---|
| 560 | { |
---|
| 561 | this->smFinalMult(); |
---|
| 562 | this->smPivDel(); |
---|
| 563 | if (act != 0) res = m_act[1]->m; |
---|
| 564 | omFreeBin((void *)m_act[1], smprec_bin); |
---|
| 565 | return res; |
---|
| 566 | } |
---|
| 567 | loop |
---|
| 568 | { |
---|
| 569 | this->smNewPivot(); |
---|
| 570 | this->smSign(); |
---|
| 571 | this->smSelectPR(); |
---|
| 572 | this->smMultCol(); |
---|
| 573 | this->smHElim(); |
---|
| 574 | crd++; |
---|
| 575 | m_res[crd] = piv; |
---|
| 576 | this->smColDel(); |
---|
| 577 | act--; |
---|
| 578 | this->smZeroElim(); |
---|
| 579 | if (sign == 0) |
---|
| 580 | { |
---|
| 581 | this->smPivDel(); |
---|
| 582 | this->smActDel(); |
---|
| 583 | return NULL; |
---|
| 584 | } |
---|
| 585 | if (act < 2) |
---|
| 586 | { |
---|
| 587 | if (TEST_OPT_PROT) PrintS(".\n"); |
---|
| 588 | this->smFinalMult(); |
---|
| 589 | this->smPivDel(); |
---|
| 590 | if (act != 0) res = m_act[1]->m; |
---|
| 591 | omFreeBin((void *)m_act[1], smprec_bin); |
---|
| 592 | return res; |
---|
| 593 | } |
---|
| 594 | } |
---|
| 595 | } |
---|
| 596 | |
---|
| 597 | /* |
---|
| 598 | * the new Bareiss elimination: |
---|
| 599 | * - with x unreduced last rows, pivots from here are not allowed |
---|
| 600 | * - the method will finish for number of unreduced columns < y |
---|
| 601 | */ |
---|
| 602 | void sparse_mat::smNewBareiss(int x, int y) |
---|
| 603 | { |
---|
| 604 | if ((x > 0) && (x < nrows)) |
---|
| 605 | { |
---|
| 606 | tored -= x; |
---|
| 607 | this->smToredElim(); |
---|
| 608 | } |
---|
| 609 | if (y < 1) y = 1; |
---|
| 610 | if (act <= y) |
---|
| 611 | { |
---|
| 612 | this->smCopToRes(); |
---|
| 613 | return; |
---|
| 614 | } |
---|
| 615 | normalize = this->smCheckNormalize(); |
---|
| 616 | if (normalize) this->smNormalize(); |
---|
| 617 | this->smPivot(); |
---|
| 618 | this->smSelectPR(); |
---|
| 619 | this->sm1Elim(); |
---|
| 620 | crd++; |
---|
| 621 | this->smColToRow(); |
---|
| 622 | act--; |
---|
| 623 | this->smRowToCol(); |
---|
| 624 | this->smZeroElim(); |
---|
| 625 | if (tored != nrows) |
---|
| 626 | this->smToredElim(); |
---|
| 627 | if (act <= y) |
---|
| 628 | { |
---|
| 629 | this->smFinalMult(); |
---|
| 630 | this->smCopToRes(); |
---|
| 631 | return; |
---|
| 632 | } |
---|
| 633 | loop |
---|
| 634 | { |
---|
| 635 | if (normalize) this->smNormalize(); |
---|
| 636 | this->smNewPivot(); |
---|
| 637 | this->smSelectPR(); |
---|
| 638 | this->smMultCol(); |
---|
| 639 | this->smHElim(); |
---|
| 640 | crd++; |
---|
| 641 | this->smColToRow(); |
---|
| 642 | act--; |
---|
| 643 | this->smRowToCol(); |
---|
| 644 | this->smZeroElim(); |
---|
| 645 | if (tored != nrows) |
---|
| 646 | this->smToredElim(); |
---|
| 647 | if (act <= y) |
---|
| 648 | { |
---|
| 649 | if (TEST_OPT_PROT) PrintS(".\n"); |
---|
| 650 | this->smFinalMult(); |
---|
| 651 | this->smCopToRes(); |
---|
| 652 | return; |
---|
| 653 | } |
---|
| 654 | } |
---|
| 655 | } |
---|
| 656 | |
---|
| 657 | /* ----------------- pivot method ------------------ */ |
---|
| 658 | |
---|
| 659 | /* |
---|
| 660 | * prepare smPivot, compute weights for rows and columns |
---|
| 661 | * and the weight for all points |
---|
| 662 | */ |
---|
| 663 | void sparse_mat::smWeights() |
---|
| 664 | { |
---|
| 665 | float wc, wp, w; |
---|
| 666 | smpoly a; |
---|
| 667 | int i; |
---|
| 668 | |
---|
| 669 | wp = 0.0; |
---|
| 670 | for (i=tored; i; i--) wrw[i] = 0.0; // ??? |
---|
| 671 | for (i=act; i; i--) |
---|
| 672 | { |
---|
| 673 | wc = 0.0; |
---|
| 674 | a = m_act[i]; |
---|
| 675 | loop |
---|
| 676 | { |
---|
| 677 | if (a->pos > tored) |
---|
| 678 | break; |
---|
[bf6a4d] | 679 | w = a->f = sm_PolyWeight(a,_R); |
---|
[35aab3] | 680 | wc += w; |
---|
| 681 | wrw[a->pos] += w; |
---|
| 682 | a = a->n; |
---|
| 683 | if (a == NULL) |
---|
| 684 | break; |
---|
| 685 | } |
---|
| 686 | wp += wc; |
---|
| 687 | wcl[i] = wc; |
---|
| 688 | } |
---|
| 689 | wpoints = wp; |
---|
| 690 | } |
---|
| 691 | |
---|
| 692 | /* |
---|
| 693 | * compute pivot |
---|
| 694 | */ |
---|
| 695 | void sparse_mat::smPivot() |
---|
| 696 | { |
---|
| 697 | float wopt = 1.0e30; |
---|
| 698 | float wc, wr, wp, w; |
---|
| 699 | smpoly a; |
---|
| 700 | int i, copt, ropt; |
---|
| 701 | |
---|
| 702 | this->smWeights(); |
---|
| 703 | for (i=act; i; i--) |
---|
| 704 | { |
---|
| 705 | a = m_act[i]; |
---|
| 706 | loop |
---|
| 707 | { |
---|
| 708 | if (a->pos > tored) |
---|
| 709 | break; |
---|
| 710 | w = a->f; |
---|
| 711 | wc = wcl[i]-w; |
---|
| 712 | wr = wrw[a->pos]-w; |
---|
| 713 | if ((wr<0.25) || (wc<0.25)) // row or column with only one point |
---|
| 714 | { |
---|
| 715 | if (w<wopt) |
---|
| 716 | { |
---|
| 717 | wopt = w; |
---|
| 718 | copt = i; |
---|
| 719 | ropt = a->pos; |
---|
| 720 | } |
---|
| 721 | } |
---|
| 722 | else // elimination |
---|
| 723 | { |
---|
| 724 | wp = w*(wpoints-wcl[i]-wr); |
---|
| 725 | wp += wr*wc; |
---|
| 726 | if (wp < wopt) |
---|
| 727 | { |
---|
| 728 | wopt = wp; |
---|
| 729 | copt = i; |
---|
| 730 | ropt = a->pos; |
---|
| 731 | } |
---|
| 732 | } |
---|
| 733 | a = a->n; |
---|
| 734 | if (a == NULL) |
---|
| 735 | break; |
---|
| 736 | } |
---|
| 737 | } |
---|
| 738 | rpiv = ropt; |
---|
| 739 | cpiv = copt; |
---|
| 740 | if (cpiv != act) |
---|
| 741 | { |
---|
| 742 | a = m_act[act]; |
---|
| 743 | m_act[act] = m_act[cpiv]; |
---|
| 744 | m_act[cpiv] = a; |
---|
| 745 | } |
---|
| 746 | } |
---|
| 747 | |
---|
| 748 | /* |
---|
| 749 | * prepare smPivot, compute weights for rows and columns |
---|
| 750 | * and the weight for all points |
---|
| 751 | */ |
---|
| 752 | void sparse_mat::smNewWeights() |
---|
| 753 | { |
---|
| 754 | float wc, wp, w, hp = piv->f; |
---|
| 755 | smpoly a; |
---|
| 756 | int i, f, e = crd; |
---|
| 757 | |
---|
| 758 | wp = 0.0; |
---|
| 759 | for (i=tored; i; i--) wrw[i] = 0.0; // ??? |
---|
| 760 | for (i=act; i; i--) |
---|
| 761 | { |
---|
| 762 | wc = 0.0; |
---|
| 763 | a = m_act[i]; |
---|
| 764 | loop |
---|
| 765 | { |
---|
| 766 | if (a->pos > tored) |
---|
| 767 | break; |
---|
| 768 | w = a->f; |
---|
| 769 | f = a->e; |
---|
| 770 | if (f < e) |
---|
| 771 | { |
---|
| 772 | w *= hp; |
---|
| 773 | if (f) w /= m_res[f]->f; |
---|
| 774 | } |
---|
| 775 | wc += w; |
---|
| 776 | wrw[a->pos] += w; |
---|
| 777 | a = a->n; |
---|
| 778 | if (a == NULL) |
---|
| 779 | break; |
---|
| 780 | } |
---|
| 781 | wp += wc; |
---|
| 782 | wcl[i] = wc; |
---|
| 783 | } |
---|
| 784 | wpoints = wp; |
---|
| 785 | } |
---|
| 786 | |
---|
| 787 | /* |
---|
| 788 | * compute pivot |
---|
| 789 | */ |
---|
| 790 | void sparse_mat::smNewPivot() |
---|
| 791 | { |
---|
| 792 | float wopt = 1.0e30, hp = piv->f; |
---|
| 793 | float wc, wr, wp, w; |
---|
| 794 | smpoly a; |
---|
| 795 | int i, copt, ropt, f, e = crd; |
---|
| 796 | |
---|
| 797 | this->smNewWeights(); |
---|
| 798 | for (i=act; i; i--) |
---|
| 799 | { |
---|
| 800 | a = m_act[i]; |
---|
| 801 | loop |
---|
| 802 | { |
---|
| 803 | if (a->pos > tored) |
---|
| 804 | break; |
---|
| 805 | w = a->f; |
---|
| 806 | f = a->e; |
---|
| 807 | if (f < e) |
---|
| 808 | { |
---|
| 809 | w *= hp; |
---|
| 810 | if (f) w /= m_res[f]->f; |
---|
| 811 | } |
---|
| 812 | wc = wcl[i]-w; |
---|
| 813 | wr = wrw[a->pos]-w; |
---|
| 814 | if ((wr<0.25) || (wc<0.25)) // row or column with only one point |
---|
| 815 | { |
---|
| 816 | if (w<wopt) |
---|
| 817 | { |
---|
| 818 | wopt = w; |
---|
| 819 | copt = i; |
---|
| 820 | ropt = a->pos; |
---|
| 821 | } |
---|
| 822 | } |
---|
| 823 | else // elimination |
---|
| 824 | { |
---|
| 825 | wp = w*(wpoints-wcl[i]-wr); |
---|
| 826 | wp += wr*wc; |
---|
| 827 | if (wp < wopt) |
---|
| 828 | { |
---|
| 829 | wopt = wp; |
---|
| 830 | copt = i; |
---|
| 831 | ropt = a->pos; |
---|
| 832 | } |
---|
| 833 | } |
---|
| 834 | a = a->n; |
---|
| 835 | if (a == NULL) |
---|
| 836 | break; |
---|
| 837 | } |
---|
| 838 | } |
---|
| 839 | rpiv = ropt; |
---|
| 840 | cpiv = copt; |
---|
| 841 | if (cpiv != act) |
---|
| 842 | { |
---|
| 843 | a = m_act[act]; |
---|
| 844 | m_act[act] = m_act[cpiv]; |
---|
| 845 | m_act[cpiv] = a; |
---|
| 846 | } |
---|
| 847 | } |
---|
| 848 | |
---|
| 849 | /* ----------------- elimination ------------------ */ |
---|
| 850 | |
---|
| 851 | /* first step of elimination */ |
---|
| 852 | void sparse_mat::sm1Elim() |
---|
| 853 | { |
---|
| 854 | poly p = piv->m; // pivotelement |
---|
| 855 | smpoly c = m_act[act]; // pivotcolumn |
---|
| 856 | smpoly r = red; // row to reduce |
---|
| 857 | smpoly res, a, b; |
---|
| 858 | poly w, ha, hb; |
---|
| 859 | |
---|
| 860 | if ((c == NULL) || (r == NULL)) |
---|
| 861 | { |
---|
[bf6a4d] | 862 | while (r!=NULL) sm_ElemDelete(&r,_R); |
---|
[35aab3] | 863 | return; |
---|
| 864 | } |
---|
| 865 | do |
---|
| 866 | { |
---|
| 867 | a = m_act[r->pos]; |
---|
| 868 | res = dumm; |
---|
| 869 | res->n = NULL; |
---|
| 870 | b = c; |
---|
| 871 | w = r->m; |
---|
| 872 | loop // combine the chains a and b: p*a + w*b |
---|
| 873 | { |
---|
| 874 | if (a == NULL) |
---|
| 875 | { |
---|
| 876 | do |
---|
| 877 | { |
---|
| 878 | res = res->n = smElemCopy(b); |
---|
[bf6a4d] | 879 | res->m = pp_Mult_qq(b->m, w,_R); |
---|
[35aab3] | 880 | res->e = 1; |
---|
[bf6a4d] | 881 | res->f = sm_PolyWeight(res,_R); |
---|
[35aab3] | 882 | b = b->n; |
---|
| 883 | } while (b != NULL); |
---|
| 884 | break; |
---|
| 885 | } |
---|
| 886 | if (a->pos < b->pos) |
---|
| 887 | { |
---|
| 888 | res = res->n = a; |
---|
| 889 | a = a->n; |
---|
| 890 | } |
---|
| 891 | else if (a->pos > b->pos) |
---|
| 892 | { |
---|
| 893 | res = res->n = smElemCopy(b); |
---|
[bf6a4d] | 894 | res->m = pp_Mult_qq(b->m, w,_R); |
---|
[35aab3] | 895 | res->e = 1; |
---|
[bf6a4d] | 896 | res->f = sm_PolyWeight(res,_R); |
---|
[35aab3] | 897 | b = b->n; |
---|
| 898 | } |
---|
| 899 | else |
---|
| 900 | { |
---|
[bf6a4d] | 901 | ha = pp_Mult_qq(a->m, p,_R); |
---|
| 902 | p_Delete(&a->m,_R); |
---|
| 903 | hb = pp_Mult_qq(b->m, w,_R); |
---|
| 904 | ha = p_Add_q(ha, hb,_R); |
---|
[35aab3] | 905 | if (ha != NULL) |
---|
| 906 | { |
---|
| 907 | a->m = ha; |
---|
| 908 | a->e = 1; |
---|
[bf6a4d] | 909 | a->f = sm_PolyWeight(a,_R); |
---|
[35aab3] | 910 | res = res->n = a; |
---|
| 911 | a = a->n; |
---|
| 912 | } |
---|
| 913 | else |
---|
| 914 | { |
---|
[bf6a4d] | 915 | sm_ElemDelete(&a,_R); |
---|
[35aab3] | 916 | } |
---|
| 917 | b = b->n; |
---|
| 918 | } |
---|
| 919 | if (b == NULL) |
---|
| 920 | { |
---|
| 921 | res->n = a; |
---|
| 922 | break; |
---|
| 923 | } |
---|
| 924 | } |
---|
| 925 | m_act[r->pos] = dumm->n; |
---|
[bf6a4d] | 926 | sm_ElemDelete(&r,_R); |
---|
[35aab3] | 927 | } while (r != NULL); |
---|
| 928 | } |
---|
| 929 | |
---|
| 930 | /* higher steps of elimination */ |
---|
| 931 | void sparse_mat::smHElim() |
---|
| 932 | { |
---|
| 933 | poly hp = this->smMultPoly(piv); |
---|
| 934 | poly gp = piv->m; // pivotelement |
---|
| 935 | smpoly c = m_act[act]; // pivotcolumn |
---|
| 936 | smpoly r = red; // row to reduce |
---|
| 937 | smpoly res, a, b; |
---|
| 938 | poly ha, hr, x, y; |
---|
[2d2e40] | 939 | int e, ip, ir, ia; |
---|
[35aab3] | 940 | |
---|
| 941 | if ((c == NULL) || (r == NULL)) |
---|
| 942 | { |
---|
[bf6a4d] | 943 | while(r!=NULL) sm_ElemDelete(&r,_R); |
---|
| 944 | p_Delete(&hp,_R); |
---|
[35aab3] | 945 | return; |
---|
| 946 | } |
---|
| 947 | e = crd+1; |
---|
| 948 | ip = piv->e; |
---|
| 949 | do |
---|
| 950 | { |
---|
| 951 | a = m_act[r->pos]; |
---|
| 952 | res = dumm; |
---|
| 953 | res->n = NULL; |
---|
| 954 | b = c; |
---|
| 955 | hr = r->m; |
---|
| 956 | ir = r->e; |
---|
| 957 | loop // combine the chains a and b: (hp,gp)*a(l) + hr*b(h) |
---|
| 958 | { |
---|
| 959 | if (a == NULL) |
---|
| 960 | { |
---|
| 961 | do |
---|
| 962 | { |
---|
| 963 | res = res->n = smElemCopy(b); |
---|
[bf6a4d] | 964 | x = SM_MULT(b->m, hr, m_res[ir]->m,_R); |
---|
[35aab3] | 965 | b = b->n; |
---|
[bf6a4d] | 966 | if(ir) SM_DIV(x, m_res[ir]->m,_R); |
---|
[35aab3] | 967 | res->m = x; |
---|
| 968 | res->e = e; |
---|
[bf6a4d] | 969 | res->f = sm_PolyWeight(res,_R); |
---|
[35aab3] | 970 | } while (b != NULL); |
---|
| 971 | break; |
---|
| 972 | } |
---|
| 973 | if (a->pos < b->pos) |
---|
| 974 | { |
---|
| 975 | res = res->n = a; |
---|
| 976 | a = a->n; |
---|
| 977 | } |
---|
| 978 | else if (a->pos > b->pos) |
---|
| 979 | { |
---|
| 980 | res = res->n = smElemCopy(b); |
---|
[bf6a4d] | 981 | x = SM_MULT(b->m, hr, m_res[ir]->m,_R); |
---|
[35aab3] | 982 | b = b->n; |
---|
[bf6a4d] | 983 | if(ir) SM_DIV(x, m_res[ir]->m,_R); |
---|
[35aab3] | 984 | res->m = x; |
---|
| 985 | res->e = e; |
---|
[bf6a4d] | 986 | res->f = sm_PolyWeight(res,_R); |
---|
[35aab3] | 987 | } |
---|
| 988 | else |
---|
| 989 | { |
---|
| 990 | ha = a->m; |
---|
| 991 | ia = a->e; |
---|
| 992 | if (ir >= ia) |
---|
| 993 | { |
---|
| 994 | if (ir > ia) |
---|
| 995 | { |
---|
[bf6a4d] | 996 | x = SM_MULT(ha, m_res[ir]->m, m_res[ia]->m,_R); |
---|
| 997 | p_Delete(&ha,_R); |
---|
[35aab3] | 998 | ha = x; |
---|
[bf6a4d] | 999 | if (ia) SM_DIV(ha, m_res[ia]->m,_R); |
---|
[35aab3] | 1000 | ia = ir; |
---|
| 1001 | } |
---|
[bf6a4d] | 1002 | x = SM_MULT(ha, gp, m_res[ia]->m,_R); |
---|
| 1003 | p_Delete(&ha,_R); |
---|
| 1004 | y = SM_MULT(b->m, hr, m_res[ia]->m,_R); |
---|
[35aab3] | 1005 | } |
---|
| 1006 | else if (ir >= ip) |
---|
| 1007 | { |
---|
| 1008 | if (ia < crd) |
---|
| 1009 | { |
---|
[bf6a4d] | 1010 | x = SM_MULT(ha, m_res[crd]->m, m_res[ia]->m,_R); |
---|
| 1011 | p_Delete(&ha,_R); |
---|
[35aab3] | 1012 | ha = x; |
---|
[bf6a4d] | 1013 | SM_DIV(ha, m_res[ia]->m,_R); |
---|
[35aab3] | 1014 | } |
---|
| 1015 | y = hp; |
---|
| 1016 | if(ir > ip) |
---|
| 1017 | { |
---|
[bf6a4d] | 1018 | y = SM_MULT(y, m_res[ir]->m, m_res[ip]->m,_R); |
---|
| 1019 | if (ip) SM_DIV(y, m_res[ip]->m,_R); |
---|
[35aab3] | 1020 | } |
---|
| 1021 | ia = ir; |
---|
[bf6a4d] | 1022 | x = SM_MULT(ha, y, m_res[ia]->m,_R); |
---|
| 1023 | if (y != hp) p_Delete(&y,_R); |
---|
| 1024 | p_Delete(&ha,_R); |
---|
| 1025 | y = SM_MULT(b->m, hr, m_res[ia]->m,_R); |
---|
[35aab3] | 1026 | } |
---|
| 1027 | else |
---|
| 1028 | { |
---|
[bf6a4d] | 1029 | x = SM_MULT(hr, m_res[ia]->m, m_res[ir]->m,_R); |
---|
| 1030 | if (ir) SM_DIV(x, m_res[ir]->m,_R); |
---|
| 1031 | y = SM_MULT(b->m, x, m_res[ia]->m,_R); |
---|
| 1032 | p_Delete(&x,_R); |
---|
| 1033 | x = SM_MULT(ha, gp, m_res[ia]->m,_R); |
---|
| 1034 | p_Delete(&ha,_R); |
---|
[35aab3] | 1035 | } |
---|
[bf6a4d] | 1036 | ha = p_Add_q(x, y,_R); |
---|
[35aab3] | 1037 | if (ha != NULL) |
---|
| 1038 | { |
---|
[bf6a4d] | 1039 | if (ia) SM_DIV(ha, m_res[ia]->m,_R); |
---|
[35aab3] | 1040 | a->m = ha; |
---|
| 1041 | a->e = e; |
---|
[bf6a4d] | 1042 | a->f = sm_PolyWeight(a,_R); |
---|
[35aab3] | 1043 | res = res->n = a; |
---|
| 1044 | a = a->n; |
---|
| 1045 | } |
---|
| 1046 | else |
---|
| 1047 | { |
---|
| 1048 | a->m = NULL; |
---|
[bf6a4d] | 1049 | sm_ElemDelete(&a,_R); |
---|
[35aab3] | 1050 | } |
---|
| 1051 | b = b->n; |
---|
| 1052 | } |
---|
| 1053 | if (b == NULL) |
---|
| 1054 | { |
---|
| 1055 | res->n = a; |
---|
| 1056 | break; |
---|
| 1057 | } |
---|
| 1058 | } |
---|
| 1059 | m_act[r->pos] = dumm->n; |
---|
[bf6a4d] | 1060 | sm_ElemDelete(&r,_R); |
---|
[35aab3] | 1061 | } while (r != NULL); |
---|
[bf6a4d] | 1062 | p_Delete(&hp,_R); |
---|
[35aab3] | 1063 | } |
---|
| 1064 | |
---|
| 1065 | /* ----------------- transfer ------------------ */ |
---|
| 1066 | |
---|
| 1067 | /* |
---|
| 1068 | * select the pivotrow and store it to red and piv |
---|
| 1069 | */ |
---|
| 1070 | void sparse_mat::smSelectPR() |
---|
| 1071 | { |
---|
| 1072 | smpoly b = dumm; |
---|
| 1073 | smpoly a, ap; |
---|
| 1074 | int i; |
---|
| 1075 | |
---|
| 1076 | if (TEST_OPT_PROT) |
---|
| 1077 | { |
---|
| 1078 | if ((crd+1)%10) |
---|
| 1079 | PrintS("."); |
---|
| 1080 | else |
---|
| 1081 | PrintS(".\n"); |
---|
| 1082 | } |
---|
| 1083 | a = m_act[act]; |
---|
| 1084 | if (a->pos < rpiv) |
---|
| 1085 | { |
---|
| 1086 | do |
---|
| 1087 | { |
---|
| 1088 | ap = a; |
---|
| 1089 | a = a->n; |
---|
| 1090 | } while (a->pos < rpiv); |
---|
| 1091 | ap->n = a->n; |
---|
| 1092 | } |
---|
| 1093 | else |
---|
| 1094 | m_act[act] = a->n; |
---|
| 1095 | piv = a; |
---|
| 1096 | a->n = NULL; |
---|
| 1097 | for (i=1; i<act; i++) |
---|
| 1098 | { |
---|
| 1099 | a = m_act[i]; |
---|
| 1100 | if (a->pos < rpiv) |
---|
| 1101 | { |
---|
| 1102 | loop |
---|
| 1103 | { |
---|
| 1104 | ap = a; |
---|
| 1105 | a = a->n; |
---|
| 1106 | if ((a == NULL) || (a->pos > rpiv)) |
---|
| 1107 | break; |
---|
| 1108 | if (a->pos == rpiv) |
---|
| 1109 | { |
---|
| 1110 | ap->n = a->n; |
---|
[bf6a4d] | 1111 | a->m = p_Neg(a->m,_R); |
---|
[35aab3] | 1112 | b = b->n = a; |
---|
| 1113 | b->pos = i; |
---|
| 1114 | break; |
---|
| 1115 | } |
---|
| 1116 | } |
---|
| 1117 | } |
---|
| 1118 | else if (a->pos == rpiv) |
---|
| 1119 | { |
---|
| 1120 | m_act[i] = a->n; |
---|
[bf6a4d] | 1121 | a->m = p_Neg(a->m,_R); |
---|
[35aab3] | 1122 | b = b->n = a; |
---|
| 1123 | b->pos = i; |
---|
| 1124 | } |
---|
| 1125 | } |
---|
| 1126 | b->n = NULL; |
---|
| 1127 | red = dumm->n; |
---|
| 1128 | } |
---|
| 1129 | |
---|
| 1130 | /* |
---|
| 1131 | * store the pivotcol in m_row |
---|
| 1132 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] |
---|
| 1133 | */ |
---|
| 1134 | void sparse_mat::smColToRow() |
---|
| 1135 | { |
---|
| 1136 | smpoly c = m_act[act]; |
---|
| 1137 | smpoly h; |
---|
| 1138 | |
---|
| 1139 | while (c != NULL) |
---|
| 1140 | { |
---|
| 1141 | h = c; |
---|
| 1142 | c = c->n; |
---|
| 1143 | h->n = m_row[h->pos]; |
---|
| 1144 | m_row[h->pos] = h; |
---|
| 1145 | h->pos = crd; |
---|
| 1146 | } |
---|
| 1147 | } |
---|
| 1148 | |
---|
| 1149 | /* |
---|
| 1150 | * store the pivot and the assosiated row in m_row |
---|
| 1151 | * to m_res (result): |
---|
| 1152 | * piv + m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
---|
| 1153 | */ |
---|
| 1154 | void sparse_mat::smRowToCol() |
---|
| 1155 | { |
---|
| 1156 | smpoly r = m_row[rpiv]; |
---|
| 1157 | smpoly a, ap, h; |
---|
| 1158 | |
---|
| 1159 | m_row[rpiv] = NULL; |
---|
| 1160 | perm[crd] = rpiv; |
---|
| 1161 | piv->pos = crd; |
---|
| 1162 | m_res[crd] = piv; |
---|
| 1163 | while (r != NULL) |
---|
| 1164 | { |
---|
| 1165 | ap = m_res[r->pos]; |
---|
| 1166 | loop |
---|
| 1167 | { |
---|
| 1168 | a = ap->n; |
---|
| 1169 | if (a == NULL) |
---|
| 1170 | { |
---|
| 1171 | ap->n = h = r; |
---|
| 1172 | r = r->n; |
---|
| 1173 | h->n = a; |
---|
| 1174 | h->pos = crd; |
---|
| 1175 | break; |
---|
| 1176 | } |
---|
| 1177 | ap = a; |
---|
| 1178 | } |
---|
| 1179 | } |
---|
| 1180 | } |
---|
| 1181 | |
---|
| 1182 | /* ----------------- C++ stuff ------------------ */ |
---|
| 1183 | |
---|
| 1184 | /* |
---|
| 1185 | * clean m_act from zeros (after elim) |
---|
| 1186 | */ |
---|
| 1187 | void sparse_mat::smZeroElim() |
---|
| 1188 | { |
---|
| 1189 | int i = 0; |
---|
| 1190 | int j; |
---|
| 1191 | |
---|
| 1192 | loop |
---|
| 1193 | { |
---|
| 1194 | i++; |
---|
| 1195 | if (i > act) return; |
---|
| 1196 | if (m_act[i] == NULL) break; |
---|
| 1197 | } |
---|
| 1198 | j = i; |
---|
| 1199 | loop |
---|
| 1200 | { |
---|
| 1201 | j++; |
---|
| 1202 | if (j > act) break; |
---|
| 1203 | if (m_act[j] != NULL) |
---|
| 1204 | { |
---|
| 1205 | m_act[i] = m_act[j]; |
---|
| 1206 | i++; |
---|
| 1207 | } |
---|
| 1208 | } |
---|
| 1209 | act -= (j-i); |
---|
| 1210 | sign = 0; |
---|
| 1211 | } |
---|
| 1212 | |
---|
| 1213 | /* |
---|
| 1214 | * clean m_act from cols not to reduced (after elim) |
---|
| 1215 | * put them to m_res |
---|
| 1216 | */ |
---|
| 1217 | void sparse_mat::smToredElim() |
---|
| 1218 | { |
---|
| 1219 | int i = 0; |
---|
| 1220 | int j; |
---|
| 1221 | |
---|
| 1222 | loop |
---|
| 1223 | { |
---|
| 1224 | i++; |
---|
| 1225 | if (i > act) return; |
---|
| 1226 | if (m_act[i]->pos > tored) |
---|
| 1227 | { |
---|
| 1228 | m_res[inred] = m_act[i]; |
---|
| 1229 | inred--; |
---|
| 1230 | break; |
---|
| 1231 | } |
---|
| 1232 | } |
---|
| 1233 | j = i; |
---|
| 1234 | loop |
---|
| 1235 | { |
---|
| 1236 | j++; |
---|
| 1237 | if (j > act) break; |
---|
| 1238 | if (m_act[j]->pos > tored) |
---|
| 1239 | { |
---|
| 1240 | m_res[inred] = m_act[j]; |
---|
| 1241 | inred--; |
---|
| 1242 | } |
---|
| 1243 | else |
---|
| 1244 | { |
---|
| 1245 | m_act[i] = m_act[j]; |
---|
| 1246 | i++; |
---|
| 1247 | } |
---|
| 1248 | } |
---|
| 1249 | act -= (j-i); |
---|
| 1250 | sign = 0; |
---|
| 1251 | } |
---|
| 1252 | |
---|
| 1253 | /* |
---|
| 1254 | * copy m_act to m_res |
---|
| 1255 | */ |
---|
| 1256 | void sparse_mat::smCopToRes() |
---|
| 1257 | { |
---|
| 1258 | smpoly a,ap,r,h; |
---|
| 1259 | int i,j,k,l; |
---|
| 1260 | |
---|
| 1261 | i = 0; |
---|
| 1262 | if (act) |
---|
| 1263 | { |
---|
| 1264 | a = m_act[act]; // init perm |
---|
| 1265 | do |
---|
| 1266 | { |
---|
| 1267 | i++; |
---|
| 1268 | perm[crd+i] = a->pos; |
---|
| 1269 | a = a->n; |
---|
| 1270 | } while ((a != NULL) && (a->pos <= tored)); |
---|
| 1271 | for (j=act-1;j;j--) // load all positions of perm |
---|
| 1272 | { |
---|
| 1273 | a = m_act[j]; |
---|
| 1274 | k = 1; |
---|
| 1275 | loop |
---|
| 1276 | { |
---|
| 1277 | if (perm[crd+k] >= a->pos) |
---|
| 1278 | { |
---|
| 1279 | if (perm[crd+k] > a->pos) |
---|
| 1280 | { |
---|
| 1281 | for (l=i;l>=k;l--) perm[crd+l+1] = perm[crd+l]; |
---|
| 1282 | perm[crd+k] = a->pos; |
---|
| 1283 | i++; |
---|
| 1284 | } |
---|
| 1285 | a = a->n; |
---|
| 1286 | if ((a == NULL) || (a->pos > tored)) break; |
---|
| 1287 | } |
---|
| 1288 | k++; |
---|
| 1289 | if ((k > i) && (a->pos <= tored)) |
---|
| 1290 | { |
---|
| 1291 | do |
---|
| 1292 | { |
---|
| 1293 | i++; |
---|
| 1294 | perm[crd+i] = a->pos; |
---|
| 1295 | a = a->n; |
---|
| 1296 | } while ((a != NULL) && (a->pos <= tored)); |
---|
| 1297 | break; |
---|
| 1298 | } |
---|
| 1299 | } |
---|
| 1300 | } |
---|
| 1301 | } |
---|
| 1302 | for (j=act;j;j--) // renumber m_act |
---|
| 1303 | { |
---|
| 1304 | k = 1; |
---|
| 1305 | a = m_act[j]; |
---|
| 1306 | while ((a != NULL) && (a->pos <= tored)) |
---|
| 1307 | { |
---|
| 1308 | if (perm[crd+k] == a->pos) |
---|
| 1309 | { |
---|
| 1310 | a->pos = crd+k; |
---|
| 1311 | a = a->n; |
---|
| 1312 | } |
---|
| 1313 | k++; |
---|
| 1314 | } |
---|
| 1315 | } |
---|
| 1316 | tored = crd+i; |
---|
| 1317 | for(k=1;k<=i;k++) // clean this from m_row |
---|
| 1318 | { |
---|
| 1319 | j = perm[crd+k]; |
---|
| 1320 | if (m_row[j] != NULL) |
---|
| 1321 | { |
---|
| 1322 | r = m_row[j]; |
---|
| 1323 | m_row[j] = NULL; |
---|
| 1324 | do |
---|
| 1325 | { |
---|
| 1326 | ap = m_res[r->pos]; |
---|
| 1327 | loop |
---|
| 1328 | { |
---|
| 1329 | a = ap->n; |
---|
| 1330 | if (a == NULL) |
---|
| 1331 | { |
---|
| 1332 | h = ap->n = r; |
---|
| 1333 | r = r->n; |
---|
| 1334 | h->n = NULL; |
---|
| 1335 | h->pos = crd+k; |
---|
| 1336 | break; |
---|
| 1337 | } |
---|
| 1338 | ap = a; |
---|
| 1339 | } |
---|
| 1340 | } while (r!=NULL); |
---|
| 1341 | } |
---|
| 1342 | } |
---|
| 1343 | while(act) // clean m_act |
---|
| 1344 | { |
---|
| 1345 | crd++; |
---|
| 1346 | m_res[crd] = m_act[act]; |
---|
| 1347 | act--; |
---|
| 1348 | } |
---|
| 1349 | for (i=1;i<=tored;i++) // take the rest of m_row |
---|
| 1350 | { |
---|
| 1351 | if(m_row[i] != NULL) |
---|
| 1352 | { |
---|
| 1353 | tored++; |
---|
| 1354 | r = m_row[i]; |
---|
| 1355 | m_row[i] = NULL; |
---|
| 1356 | perm[tored] = i; |
---|
| 1357 | do |
---|
| 1358 | { |
---|
| 1359 | ap = m_res[r->pos]; |
---|
| 1360 | loop |
---|
| 1361 | { |
---|
| 1362 | a = ap->n; |
---|
| 1363 | if (a == NULL) |
---|
| 1364 | { |
---|
| 1365 | h = ap->n = r; |
---|
| 1366 | r = r->n; |
---|
| 1367 | h->n = NULL; |
---|
| 1368 | h->pos = tored; |
---|
| 1369 | break; |
---|
| 1370 | } |
---|
| 1371 | ap = a; |
---|
| 1372 | } |
---|
| 1373 | } while (r!=NULL); |
---|
| 1374 | } |
---|
| 1375 | } |
---|
| 1376 | for (i=tored+1;i<=nrows;i++) // take the rest of m_row |
---|
| 1377 | { |
---|
| 1378 | if(m_row[i] != NULL) |
---|
| 1379 | { |
---|
| 1380 | r = m_row[i]; |
---|
| 1381 | m_row[i] = NULL; |
---|
| 1382 | do |
---|
| 1383 | { |
---|
| 1384 | ap = m_res[r->pos]; |
---|
| 1385 | loop |
---|
| 1386 | { |
---|
| 1387 | a = ap->n; |
---|
| 1388 | if (a == NULL) |
---|
| 1389 | { |
---|
| 1390 | h = ap->n = r; |
---|
| 1391 | r = r->n; |
---|
| 1392 | h->n = NULL; |
---|
| 1393 | h->pos = i; |
---|
| 1394 | break; |
---|
| 1395 | } |
---|
| 1396 | ap = a; |
---|
| 1397 | } |
---|
| 1398 | } while (r!=NULL); |
---|
| 1399 | } |
---|
| 1400 | } |
---|
| 1401 | while (inred < ncols) // take unreducable |
---|
| 1402 | { |
---|
| 1403 | crd++; |
---|
| 1404 | inred++; |
---|
| 1405 | m_res[crd] = m_res[inred]; |
---|
| 1406 | } |
---|
| 1407 | } |
---|
| 1408 | |
---|
| 1409 | /* |
---|
| 1410 | * multiply and divide the column, that goes to result |
---|
| 1411 | */ |
---|
| 1412 | void sparse_mat::smMultCol() |
---|
| 1413 | { |
---|
| 1414 | smpoly a = m_act[act]; |
---|
| 1415 | int e = crd; |
---|
| 1416 | poly ha; |
---|
| 1417 | int f; |
---|
| 1418 | |
---|
| 1419 | while (a != NULL) |
---|
| 1420 | { |
---|
| 1421 | f = a->e; |
---|
| 1422 | if (f < e) |
---|
| 1423 | { |
---|
[bf6a4d] | 1424 | ha = SM_MULT(a->m, m_res[e]->m, m_res[f]->m,_R); |
---|
| 1425 | p_Delete(&a->m,_R); |
---|
| 1426 | if (f) SM_DIV(ha, m_res[f]->m,_R); |
---|
[35aab3] | 1427 | a->m = ha; |
---|
[bf6a4d] | 1428 | if (normalize) p_Normalize(a->m,_R); |
---|
[35aab3] | 1429 | } |
---|
| 1430 | a = a->n; |
---|
| 1431 | } |
---|
| 1432 | } |
---|
| 1433 | |
---|
| 1434 | /* |
---|
| 1435 | * multiply and divide the m_act finaly |
---|
| 1436 | */ |
---|
| 1437 | void sparse_mat::smFinalMult() |
---|
| 1438 | { |
---|
| 1439 | smpoly a; |
---|
| 1440 | poly ha; |
---|
| 1441 | int i, f; |
---|
| 1442 | int e = crd; |
---|
| 1443 | |
---|
| 1444 | for (i=act; i; i--) |
---|
| 1445 | { |
---|
| 1446 | a = m_act[i]; |
---|
| 1447 | do |
---|
| 1448 | { |
---|
| 1449 | f = a->e; |
---|
| 1450 | if (f < e) |
---|
| 1451 | { |
---|
[bf6a4d] | 1452 | ha = SM_MULT(a->m, m_res[e]->m, m_res[f]->m, _R); |
---|
| 1453 | p_Delete(&a->m,_R); |
---|
| 1454 | if (f) SM_DIV(ha, m_res[f]->m, _R); |
---|
[35aab3] | 1455 | a->m = ha; |
---|
| 1456 | } |
---|
[bf6a4d] | 1457 | if (normalize) p_Normalize(a->m, _R); |
---|
[35aab3] | 1458 | a = a->n; |
---|
| 1459 | } while (a != NULL); |
---|
| 1460 | } |
---|
| 1461 | } |
---|
| 1462 | |
---|
| 1463 | /* |
---|
| 1464 | * check for denominators |
---|
| 1465 | */ |
---|
| 1466 | int sparse_mat::smCheckNormalize() |
---|
| 1467 | { |
---|
| 1468 | int i; |
---|
| 1469 | smpoly a; |
---|
| 1470 | |
---|
| 1471 | for (i=act; i; i--) |
---|
| 1472 | { |
---|
| 1473 | a = m_act[i]; |
---|
| 1474 | do |
---|
| 1475 | { |
---|
[bf6a4d] | 1476 | if(sm_HaveDenom(a->m,_R)) return 1; |
---|
[35aab3] | 1477 | a = a->n; |
---|
| 1478 | } while (a != NULL); |
---|
| 1479 | } |
---|
| 1480 | return 0; |
---|
| 1481 | } |
---|
| 1482 | |
---|
| 1483 | /* |
---|
| 1484 | * normalize |
---|
| 1485 | */ |
---|
| 1486 | void sparse_mat::smNormalize() |
---|
| 1487 | { |
---|
| 1488 | smpoly a; |
---|
| 1489 | int i; |
---|
| 1490 | int e = crd; |
---|
| 1491 | |
---|
| 1492 | for (i=act; i; i--) |
---|
| 1493 | { |
---|
| 1494 | a = m_act[i]; |
---|
| 1495 | do |
---|
| 1496 | { |
---|
[bf6a4d] | 1497 | if (e == a->e) p_Normalize(a->m,_R); |
---|
[35aab3] | 1498 | a = a->n; |
---|
| 1499 | } while (a != NULL); |
---|
| 1500 | } |
---|
| 1501 | } |
---|
| 1502 | |
---|
| 1503 | /* |
---|
| 1504 | * multiply and divide the element, save poly |
---|
| 1505 | */ |
---|
| 1506 | poly sparse_mat::smMultPoly(smpoly a) |
---|
| 1507 | { |
---|
| 1508 | int f = a->e; |
---|
| 1509 | poly r, h; |
---|
| 1510 | |
---|
| 1511 | if (f < crd) |
---|
| 1512 | { |
---|
| 1513 | h = r = a->m; |
---|
[bf6a4d] | 1514 | h = SM_MULT(h, m_res[crd]->m, m_res[f]->m, _R); |
---|
| 1515 | if (f) SM_DIV(h, m_res[f]->m, _R); |
---|
[35aab3] | 1516 | a->m = h; |
---|
[bf6a4d] | 1517 | if (normalize) p_Normalize(a->m,_R); |
---|
| 1518 | a->f = sm_PolyWeight(a,_R); |
---|
[35aab3] | 1519 | return r; |
---|
| 1520 | } |
---|
| 1521 | else |
---|
| 1522 | return NULL; |
---|
| 1523 | } |
---|
| 1524 | |
---|
| 1525 | /* |
---|
| 1526 | * delete the m_act finaly |
---|
| 1527 | */ |
---|
| 1528 | void sparse_mat::smActDel() |
---|
| 1529 | { |
---|
| 1530 | smpoly a; |
---|
| 1531 | int i; |
---|
| 1532 | |
---|
| 1533 | for (i=act; i; i--) |
---|
| 1534 | { |
---|
| 1535 | a = m_act[i]; |
---|
| 1536 | do |
---|
| 1537 | { |
---|
[bf6a4d] | 1538 | sm_ElemDelete(&a,_R); |
---|
[35aab3] | 1539 | } while (a != NULL); |
---|
| 1540 | } |
---|
| 1541 | } |
---|
| 1542 | |
---|
| 1543 | /* |
---|
| 1544 | * delete the pivotcol |
---|
| 1545 | */ |
---|
| 1546 | void sparse_mat::smColDel() |
---|
| 1547 | { |
---|
| 1548 | smpoly a = m_act[act]; |
---|
| 1549 | |
---|
| 1550 | while (a != NULL) |
---|
| 1551 | { |
---|
[bf6a4d] | 1552 | sm_ElemDelete(&a,_R); |
---|
[35aab3] | 1553 | } |
---|
| 1554 | } |
---|
| 1555 | |
---|
| 1556 | /* |
---|
| 1557 | * delete pivot elements |
---|
| 1558 | */ |
---|
| 1559 | void sparse_mat::smPivDel() |
---|
| 1560 | { |
---|
| 1561 | int i=crd; |
---|
| 1562 | |
---|
| 1563 | while (i != 0) |
---|
| 1564 | { |
---|
[bf6a4d] | 1565 | sm_ElemDelete(&m_res[i],_R); |
---|
[35aab3] | 1566 | i--; |
---|
| 1567 | } |
---|
| 1568 | } |
---|
| 1569 | |
---|
| 1570 | /* |
---|
| 1571 | * the sign of the determinant |
---|
| 1572 | */ |
---|
| 1573 | void sparse_mat::smSign() |
---|
| 1574 | { |
---|
| 1575 | int j,i; |
---|
| 1576 | if (act > 2) |
---|
| 1577 | { |
---|
| 1578 | if (cpiv!=act) sign=-sign; |
---|
| 1579 | if ((act%2)==0) sign=-sign; |
---|
| 1580 | i=1; |
---|
| 1581 | j=perm[1]; |
---|
| 1582 | while(j<rpiv) |
---|
| 1583 | { |
---|
| 1584 | sign=-sign; |
---|
| 1585 | i++; |
---|
| 1586 | j=perm[i]; |
---|
| 1587 | } |
---|
| 1588 | while(perm[i]!=0) |
---|
| 1589 | { |
---|
| 1590 | perm[i]=perm[i+1]; |
---|
| 1591 | i++; |
---|
| 1592 | } |
---|
| 1593 | } |
---|
| 1594 | else |
---|
| 1595 | { |
---|
| 1596 | if (cpiv!=1) sign=-sign; |
---|
| 1597 | if (rpiv!=perm[1]) sign=-sign; |
---|
| 1598 | } |
---|
| 1599 | } |
---|
| 1600 | |
---|
| 1601 | void sparse_mat::smInitPerm() |
---|
| 1602 | { |
---|
| 1603 | int i; |
---|
| 1604 | for (i=act;i;i--) perm[i]=i; |
---|
| 1605 | } |
---|
| 1606 | |
---|
| 1607 | /* ----------------- arithmetic ------------------ */ |
---|
| 1608 | /*2 |
---|
| 1609 | * exact division a/b |
---|
| 1610 | * a destroyed, b NOT destroyed |
---|
| 1611 | */ |
---|
[bf6a4d] | 1612 | void sm_PolyDiv(poly a, poly b, const ring R) |
---|
[35aab3] | 1613 | { |
---|
| 1614 | const number x = pGetCoeff(b); |
---|
| 1615 | number y, yn; |
---|
| 1616 | poly t, h, dummy; |
---|
| 1617 | int i; |
---|
| 1618 | |
---|
| 1619 | if (pNext(b) == NULL) |
---|
| 1620 | { |
---|
| 1621 | do |
---|
| 1622 | { |
---|
[bf6a4d] | 1623 | if (!p_LmIsConstantComp(b,R)) |
---|
[35aab3] | 1624 | { |
---|
[bf6a4d] | 1625 | for (i=rVar(R); i; i--) |
---|
| 1626 | p_SubExp(a,i,p_GetExp(b,i,R),R); |
---|
| 1627 | p_Setm(a,R); |
---|
[35aab3] | 1628 | } |
---|
[bf6a4d] | 1629 | y = n_Div(pGetCoeff(a),x,R->cf); |
---|
| 1630 | n_Normalize(y,R->cf); |
---|
| 1631 | p_SetCoeff(a,y,R); |
---|
[35aab3] | 1632 | pIter(a); |
---|
| 1633 | } while (a != NULL); |
---|
| 1634 | return; |
---|
| 1635 | } |
---|
[bf6a4d] | 1636 | dummy = p_Init(R); |
---|
[35aab3] | 1637 | do |
---|
| 1638 | { |
---|
[bf6a4d] | 1639 | for (i=rVar(R); i; i--) |
---|
| 1640 | p_SubExp(a,i,p_GetExp(b,i,R),R); |
---|
| 1641 | p_Setm(a,R); |
---|
| 1642 | y = n_Div(pGetCoeff(a),x,R->cf); |
---|
| 1643 | n_Normalize(y,R->cf); |
---|
| 1644 | p_SetCoeff(a,y,R); |
---|
| 1645 | yn = n_Neg(n_Copy(y,R->cf),R->cf); |
---|
[35aab3] | 1646 | t = pNext(b); |
---|
| 1647 | h = dummy; |
---|
| 1648 | do |
---|
| 1649 | { |
---|
[bf6a4d] | 1650 | h = pNext(h) = p_Init(R); |
---|
[35aab3] | 1651 | //pSetComp(h,0); |
---|
[bf6a4d] | 1652 | for (i=rVar(R); i; i--) |
---|
| 1653 | p_SetExp(h,i,p_GetExp(a,i,R)+p_GetExp(t,i,R),R); |
---|
| 1654 | p_Setm(h,R); |
---|
| 1655 | pSetCoeff0(h,n_Mult(yn, pGetCoeff(t),R->cf)); |
---|
[35aab3] | 1656 | pIter(t); |
---|
| 1657 | } while (t != NULL); |
---|
[bf6a4d] | 1658 | n_Delete(&yn,R->cf); |
---|
[35aab3] | 1659 | pNext(h) = NULL; |
---|
[bf6a4d] | 1660 | a = pNext(a) = p_Add_q(pNext(a), pNext(dummy),R); |
---|
[35aab3] | 1661 | } while (a!=NULL); |
---|
[bf6a4d] | 1662 | p_LmFree(dummy, R); |
---|
[35aab3] | 1663 | } |
---|
| 1664 | |
---|
[4774ab] | 1665 | |
---|
[a24e0a] | 1666 | //disable that, as it fails with coef buckets |
---|
| 1667 | //#define X_MAS |
---|
| 1668 | #ifdef X_MAS |
---|
| 1669 | |
---|
| 1670 | /* |
---|
| 1671 | * returns the part of (a*b)/exp(lead(c)) with nonegative exponents |
---|
| 1672 | */ |
---|
| 1673 | poly smMultDiv(poly a, poly b, const poly c) |
---|
| 1674 | { |
---|
| 1675 | poly pa, e, res, r; |
---|
| 1676 | BOOLEAN lead;\ |
---|
| 1677 | int la, lb, lr; |
---|
| 1678 | |
---|
| 1679 | if ((c == NULL) || pLmIsConstantComp(c)) |
---|
| 1680 | { |
---|
[ebdaa1] | 1681 | return pp_Mult_qq(a, b); |
---|
[a24e0a] | 1682 | } |
---|
| 1683 | |
---|
| 1684 | pqLength(a, b, la, lb, SM_MIN_LENGTH_BUCKET); |
---|
| 1685 | |
---|
| 1686 | // we iter over b, so, make sure b is the shortest |
---|
| 1687 | // such that we minimize our iterations |
---|
| 1688 | if (lb > la) |
---|
| 1689 | { |
---|
| 1690 | r = a; |
---|
| 1691 | a = b; |
---|
| 1692 | b = r; |
---|
| 1693 | lr = la; |
---|
| 1694 | la = lb; |
---|
[35aab3] | 1695 | lb = lr; |
---|
| 1696 | } |
---|
| 1697 | res = NULL; |
---|
[bf6a4d] | 1698 | e = p_Init(); |
---|
[35aab3] | 1699 | lead = FALSE; |
---|
| 1700 | while (!lead) |
---|
| 1701 | { |
---|
| 1702 | pSetCoeff0(e,pGetCoeff(b)); |
---|
| 1703 | if (smIsNegQuot(e, b, c)) |
---|
| 1704 | { |
---|
| 1705 | lead = pLmDivisibleByNoComp(e, a); |
---|
| 1706 | r = smSelectCopy_ExpMultDiv(a, e, b, c); |
---|
| 1707 | } |
---|
| 1708 | else |
---|
| 1709 | { |
---|
| 1710 | lead = TRUE; |
---|
[bf6a4d] | 1711 | r = pp_Mult__mm(a, e); |
---|
[35aab3] | 1712 | } |
---|
| 1713 | if (lead) |
---|
| 1714 | { |
---|
| 1715 | if (res != NULL) |
---|
| 1716 | { |
---|
| 1717 | smFindRef(&pa, &res, r); |
---|
| 1718 | if (pa == NULL) |
---|
| 1719 | lead = FALSE; |
---|
| 1720 | } |
---|
| 1721 | else |
---|
| 1722 | { |
---|
| 1723 | pa = res = r; |
---|
| 1724 | } |
---|
| 1725 | } |
---|
| 1726 | else |
---|
[bf6a4d] | 1727 | res = p_Add_q(res, r); |
---|
[35aab3] | 1728 | pIter(b); |
---|
| 1729 | if (b == NULL) |
---|
| 1730 | { |
---|
| 1731 | pLmFree(e); |
---|
| 1732 | return res; |
---|
| 1733 | } |
---|
| 1734 | } |
---|
| 1735 | |
---|
| 1736 | if (!TEST_OPT_NOT_BUCKETS && lb >= SM_MIN_LENGTH_BUCKET) |
---|
| 1737 | { |
---|
| 1738 | // use buckets if minimum length is smaller than threshold |
---|
| 1739 | spolyrec rp; |
---|
| 1740 | poly append; |
---|
| 1741 | // find the last monomial before pa |
---|
| 1742 | if (res == pa) |
---|
| 1743 | { |
---|
| 1744 | append = &rp; |
---|
| 1745 | pNext(append) = res; |
---|
| 1746 | } |
---|
| 1747 | else |
---|
| 1748 | { |
---|
| 1749 | append = res; |
---|
| 1750 | while (pNext(append) != pa) |
---|
| 1751 | { |
---|
| 1752 | assume(pNext(append) != NULL); |
---|
| 1753 | pIter(append); |
---|
| 1754 | } |
---|
| 1755 | } |
---|
| 1756 | kBucket_pt bucket = kBucketCreate(currRing); |
---|
| 1757 | kBucketInit(bucket, pNext(append), 0); |
---|
| 1758 | do |
---|
| 1759 | { |
---|
| 1760 | pSetCoeff0(e,pGetCoeff(b)); |
---|
| 1761 | if (smIsNegQuot(e, b, c)) |
---|
| 1762 | { |
---|
| 1763 | lr = la; |
---|
| 1764 | r = pp_Mult_Coeff_mm_DivSelect_MultDiv(a, lr, e, b, c); |
---|
| 1765 | if (pLmDivisibleByNoComp(e, a)) |
---|
| 1766 | append = kBucket_ExtractLarger_Add_q(bucket, append, r, &lr); |
---|
| 1767 | else |
---|
| 1768 | kBucket_Add_q(bucket, r, &lr); |
---|
| 1769 | } |
---|
| 1770 | else |
---|
| 1771 | { |
---|
[bf6a4d] | 1772 | r = pp_Mult__mm(a, e); |
---|
[35aab3] | 1773 | append = kBucket_ExtractLarger_Add_q(bucket, append, r, &la); |
---|
| 1774 | } |
---|
| 1775 | pIter(b); |
---|
| 1776 | } while (b != NULL); |
---|
| 1777 | pNext(append) = kBucketClear(bucket); |
---|
| 1778 | kBucketDestroy(&bucket); |
---|
[4774ab] | 1779 | pTest(append); |
---|
[35aab3] | 1780 | } |
---|
| 1781 | else |
---|
| 1782 | { |
---|
| 1783 | // use old sm stuff |
---|
| 1784 | do |
---|
| 1785 | { |
---|
| 1786 | pSetCoeff0(e,pGetCoeff(b)); |
---|
| 1787 | if (smIsNegQuot(e, b, c)) |
---|
| 1788 | { |
---|
| 1789 | r = smSelectCopy_ExpMultDiv(a, e, b, c); |
---|
| 1790 | if (pLmDivisibleByNoComp(e, a)) |
---|
| 1791 | smCombineChain(&pa, r); |
---|
| 1792 | else |
---|
[bf6a4d] | 1793 | pa = p_Add_q(pa,r); |
---|
[35aab3] | 1794 | } |
---|
| 1795 | else |
---|
| 1796 | { |
---|
[bf6a4d] | 1797 | r = pp_Mult__mm(a, e); |
---|
[35aab3] | 1798 | smCombineChain(&pa, r); |
---|
| 1799 | } |
---|
| 1800 | pIter(b); |
---|
| 1801 | } while (b != NULL); |
---|
| 1802 | } |
---|
| 1803 | pLmFree(e); |
---|
| 1804 | return res; |
---|
| 1805 | } |
---|
| 1806 | |
---|
| 1807 | #else |
---|
| 1808 | |
---|
| 1809 | /* |
---|
| 1810 | * returns the part of (a*b)/exp(lead(c)) with nonegative exponents |
---|
| 1811 | */ |
---|
[bf6a4d] | 1812 | poly sm_MultDiv(poly a, poly b, const poly c, const ring R) |
---|
[35aab3] | 1813 | { |
---|
| 1814 | poly pa, e, res, r; |
---|
| 1815 | BOOLEAN lead; |
---|
| 1816 | |
---|
[bf6a4d] | 1817 | if ((c == NULL) || p_LmIsConstantComp(c,R)) |
---|
[35aab3] | 1818 | { |
---|
[bf6a4d] | 1819 | return pp_Mult_qq(a, b, R); |
---|
[35aab3] | 1820 | } |
---|
| 1821 | if (smSmaller(a, b)) |
---|
| 1822 | { |
---|
| 1823 | r = a; |
---|
| 1824 | a = b; |
---|
| 1825 | b = r; |
---|
| 1826 | } |
---|
| 1827 | res = NULL; |
---|
[bf6a4d] | 1828 | e = p_Init(R); |
---|
[35aab3] | 1829 | lead = FALSE; |
---|
| 1830 | while (!lead) |
---|
| 1831 | { |
---|
| 1832 | pSetCoeff0(e,pGetCoeff(b)); |
---|
[bf6a4d] | 1833 | if (sm_IsNegQuot(e, b, c, R)) |
---|
[35aab3] | 1834 | { |
---|
[bf6a4d] | 1835 | lead = p_LmDivisibleByNoComp(e, a, R); |
---|
| 1836 | r = sm_SelectCopy_ExpMultDiv(a, e, b, c, R); |
---|
[35aab3] | 1837 | } |
---|
| 1838 | else |
---|
| 1839 | { |
---|
| 1840 | lead = TRUE; |
---|
[bf6a4d] | 1841 | r = pp_Mult_mm(a, e,R); |
---|
[35aab3] | 1842 | } |
---|
| 1843 | if (lead) |
---|
| 1844 | { |
---|
| 1845 | if (res != NULL) |
---|
| 1846 | { |
---|
[bf6a4d] | 1847 | sm_FindRef(&pa, &res, r, R); |
---|
[35aab3] | 1848 | if (pa == NULL) |
---|
| 1849 | lead = FALSE; |
---|
| 1850 | } |
---|
| 1851 | else |
---|
| 1852 | { |
---|
| 1853 | pa = res = r; |
---|
| 1854 | } |
---|
| 1855 | } |
---|
| 1856 | else |
---|
[bf6a4d] | 1857 | res = p_Add_q(res, r, R); |
---|
[35aab3] | 1858 | pIter(b); |
---|
| 1859 | if (b == NULL) |
---|
| 1860 | { |
---|
[bf6a4d] | 1861 | p_LmFree(e, R); |
---|
[35aab3] | 1862 | return res; |
---|
| 1863 | } |
---|
| 1864 | } |
---|
| 1865 | do |
---|
| 1866 | { |
---|
| 1867 | pSetCoeff0(e,pGetCoeff(b)); |
---|
[bf6a4d] | 1868 | if (sm_IsNegQuot(e, b, c, R)) |
---|
[35aab3] | 1869 | { |
---|
[bf6a4d] | 1870 | r = sm_SelectCopy_ExpMultDiv(a, e, b, c, R); |
---|
| 1871 | if (p_LmDivisibleByNoComp(e, a,R)) |
---|
| 1872 | sm_CombineChain(&pa, r, R); |
---|
[35aab3] | 1873 | else |
---|
[bf6a4d] | 1874 | pa = p_Add_q(pa,r,R); |
---|
[35aab3] | 1875 | } |
---|
| 1876 | else |
---|
| 1877 | { |
---|
[bf6a4d] | 1878 | r = pp_Mult_mm(a, e, R); |
---|
| 1879 | sm_CombineChain(&pa, r, R); |
---|
[35aab3] | 1880 | } |
---|
| 1881 | pIter(b); |
---|
| 1882 | } while (b != NULL); |
---|
[bf6a4d] | 1883 | p_LmFree(e, R); |
---|
[35aab3] | 1884 | return res; |
---|
| 1885 | } |
---|
| 1886 | #endif |
---|
[bf6a4d] | 1887 | /*n |
---|
| 1888 | * exact division a/b |
---|
| 1889 | * a is a result of smMultDiv |
---|
| 1890 | * a destroyed, b NOT destroyed |
---|
| 1891 | */ |
---|
| 1892 | void sm_SpecialPolyDiv(poly a, poly b, const ring R) |
---|
| 1893 | { |
---|
| 1894 | if (pNext(b) == NULL) |
---|
| 1895 | { |
---|
| 1896 | sm_PolyDivN(a, pGetCoeff(b),R); |
---|
| 1897 | return; |
---|
| 1898 | } |
---|
| 1899 | sm_ExactPolyDiv(a, b, R); |
---|
| 1900 | } |
---|
| 1901 | |
---|
| 1902 | |
---|
[35aab3] | 1903 | /* ------------ internals arithmetic ------------- */ |
---|
[bf6a4d] | 1904 | static void sm_ExactPolyDiv(poly a, poly b, const ring R) |
---|
[35aab3] | 1905 | { |
---|
| 1906 | const number x = pGetCoeff(b); |
---|
[bf6a4d] | 1907 | poly tail = pNext(b), e = p_Init(R); |
---|
[35aab3] | 1908 | poly h; |
---|
| 1909 | number y, yn; |
---|
| 1910 | int lt = pLength(tail); |
---|
| 1911 | |
---|
| 1912 | if (lt + 1 >= SM_MIN_LENGTH_BUCKET && !TEST_OPT_NOT_BUCKETS) |
---|
| 1913 | { |
---|
[bf6a4d] | 1914 | kBucket_pt bucket = kBucketCreate(R); |
---|
[35aab3] | 1915 | kBucketInit(bucket, pNext(a), 0); |
---|
| 1916 | int lh = 0; |
---|
| 1917 | do |
---|
| 1918 | { |
---|
[bf6a4d] | 1919 | y = n_Div(pGetCoeff(a), x, R->cf); |
---|
| 1920 | n_Normalize(y, R->cf); |
---|
| 1921 | p_SetCoeff(a,y, R); |
---|
| 1922 | yn = n_Neg(n_Copy(y, R->cf), R->cf); |
---|
[35aab3] | 1923 | pSetCoeff0(e,yn); |
---|
| 1924 | lh = lt; |
---|
[bf6a4d] | 1925 | if (sm_IsNegQuot(e, a, b, R)) |
---|
[35aab3] | 1926 | { |
---|
[bf6a4d] | 1927 | h = pp_Mult_Coeff_mm_DivSelect_MultDiv(tail, lh, e, a, b, R); |
---|
[35aab3] | 1928 | } |
---|
| 1929 | else |
---|
[bf6a4d] | 1930 | h = pp_Mult_mm(tail, e, R); |
---|
| 1931 | n_Delete(&yn, R->cf); |
---|
[35aab3] | 1932 | kBucket_Add_q(bucket, h, &lh); |
---|
| 1933 | |
---|
| 1934 | a = pNext(a) = kBucketExtractLm(bucket); |
---|
| 1935 | } while (a!=NULL); |
---|
| 1936 | kBucketDestroy(&bucket); |
---|
| 1937 | } |
---|
| 1938 | else |
---|
| 1939 | { |
---|
| 1940 | do |
---|
| 1941 | { |
---|
[bf6a4d] | 1942 | y = n_Div(pGetCoeff(a), x, R->cf); |
---|
| 1943 | n_Normalize(y, R->cf); |
---|
| 1944 | p_SetCoeff(a,y, R); |
---|
| 1945 | yn = n_Neg(n_Copy(y, R->cf), R->cf); |
---|
[35aab3] | 1946 | pSetCoeff0(e,yn); |
---|
[bf6a4d] | 1947 | if (sm_IsNegQuot(e, a, b, R)) |
---|
| 1948 | h = sm_SelectCopy_ExpMultDiv(tail, e, a, b, R); |
---|
[35aab3] | 1949 | else |
---|
[bf6a4d] | 1950 | h = pp_Mult_mm(tail, e, R); |
---|
| 1951 | n_Delete(&yn, R->cf); |
---|
| 1952 | a = pNext(a) = p_Add_q(pNext(a), h, R); |
---|
[35aab3] | 1953 | } while (a!=NULL); |
---|
| 1954 | } |
---|
[bf6a4d] | 1955 | p_LmFree(e, R); |
---|
[35aab3] | 1956 | } |
---|
| 1957 | |
---|
[bf6a4d] | 1958 | // obachman --> Wilfried: check the following |
---|
| 1959 | static BOOLEAN sm_IsNegQuot(poly a, const poly b, const poly c, const ring R) |
---|
| 1960 | { |
---|
| 1961 | if (p_LmDivisibleByNoComp(c, b,R)) |
---|
| 1962 | { |
---|
| 1963 | p_ExpVectorDiff(a, b, c,R); |
---|
| 1964 | // Hmm: here used to be a p_Setm(a): but it is unnecessary, |
---|
| 1965 | // if b and c are correct |
---|
| 1966 | return FALSE; |
---|
| 1967 | } |
---|
| 1968 | else |
---|
| 1969 | { |
---|
| 1970 | int i; |
---|
| 1971 | for (i=rVar(R); i>0; i--) |
---|
| 1972 | { |
---|
| 1973 | if(p_GetExp(c,i,R) > p_GetExp(b,i,R)) |
---|
| 1974 | p_SetExp(a,i,p_GetExp(c,i,R)-p_GetExp(b,i,R),R); |
---|
| 1975 | else |
---|
| 1976 | p_SetExp(a,i,0,R); |
---|
| 1977 | } |
---|
| 1978 | // here we actually might need a p_Setm, if a is to be used in |
---|
| 1979 | // comparisons |
---|
| 1980 | return TRUE; |
---|
| 1981 | } |
---|
| 1982 | } |
---|
| 1983 | |
---|
| 1984 | static void sm_ExpMultDiv(poly t, const poly b, const poly c, const ring R) |
---|
| 1985 | { |
---|
| 1986 | p_Test(t,R); |
---|
| 1987 | p_LmTest(b,R); |
---|
| 1988 | p_LmTest(c,R); |
---|
| 1989 | poly bc = p_New(R); |
---|
| 1990 | |
---|
| 1991 | p_ExpVectorDiff(bc, b, c, R); |
---|
| 1992 | |
---|
| 1993 | while(t!=NULL) |
---|
| 1994 | { |
---|
| 1995 | p_ExpVectorAdd(t, bc, R); |
---|
| 1996 | pIter(t); |
---|
| 1997 | } |
---|
| 1998 | p_LmFree(bc, R); |
---|
| 1999 | } |
---|
| 2000 | |
---|
| 2001 | |
---|
| 2002 | static void sm_PolyDivN(poly a, const number x, const ring R) |
---|
[35aab3] | 2003 | { |
---|
| 2004 | number y; |
---|
| 2005 | |
---|
| 2006 | do |
---|
| 2007 | { |
---|
[bf6a4d] | 2008 | y = n_Div(pGetCoeff(a),x, R->cf); |
---|
| 2009 | n_Normalize(y, R->cf); |
---|
| 2010 | p_SetCoeff(a,y, R); |
---|
[35aab3] | 2011 | pIter(a); |
---|
| 2012 | } while (a != NULL); |
---|
| 2013 | } |
---|
| 2014 | |
---|
[bf6a4d] | 2015 | static BOOLEAN smSmaller(poly a, poly b) |
---|
| 2016 | { |
---|
| 2017 | loop |
---|
| 2018 | { |
---|
| 2019 | pIter(b); |
---|
| 2020 | if (b == NULL) return TRUE; |
---|
| 2021 | pIter(a); |
---|
| 2022 | if (a == NULL) return FALSE; |
---|
| 2023 | } |
---|
| 2024 | } |
---|
| 2025 | |
---|
| 2026 | static void sm_CombineChain(poly *px, poly r, const ring R) |
---|
| 2027 | { |
---|
| 2028 | poly pa = *px, pb; |
---|
| 2029 | number x; |
---|
| 2030 | int i; |
---|
| 2031 | |
---|
| 2032 | loop |
---|
| 2033 | { |
---|
| 2034 | pb = pNext(pa); |
---|
| 2035 | if (pb == NULL) |
---|
| 2036 | { |
---|
| 2037 | pa = pNext(pa) = r; |
---|
| 2038 | break; |
---|
| 2039 | } |
---|
| 2040 | i = p_LmCmp(pb, r,R); |
---|
| 2041 | if (i > 0) |
---|
| 2042 | pa = pb; |
---|
| 2043 | else |
---|
| 2044 | { |
---|
| 2045 | if (i == 0) |
---|
| 2046 | { |
---|
| 2047 | x = n_Add(pGetCoeff(pb), pGetCoeff(r),R->cf); |
---|
| 2048 | p_LmDelete(&r,R); |
---|
| 2049 | if (n_IsZero(x,R->cf)) |
---|
| 2050 | { |
---|
| 2051 | p_LmDelete(&pb,R); |
---|
| 2052 | pNext(pa) = p_Add_q(pb,r,R); |
---|
| 2053 | } |
---|
| 2054 | else |
---|
| 2055 | { |
---|
| 2056 | pa = pb; |
---|
| 2057 | p_SetCoeff(pa,x,R); |
---|
| 2058 | pNext(pa) = p_Add_q(pNext(pa), r, R); |
---|
| 2059 | } |
---|
| 2060 | } |
---|
| 2061 | else |
---|
| 2062 | { |
---|
| 2063 | pa = pNext(pa) = r; |
---|
| 2064 | pNext(pa) = p_Add_q(pb, pNext(pa),R); |
---|
| 2065 | } |
---|
| 2066 | break; |
---|
| 2067 | } |
---|
| 2068 | } |
---|
| 2069 | *px = pa; |
---|
| 2070 | } |
---|
| 2071 | |
---|
| 2072 | |
---|
| 2073 | static void sm_FindRef(poly *ref, poly *px, poly r, const ring R) |
---|
| 2074 | { |
---|
| 2075 | number x; |
---|
| 2076 | int i; |
---|
| 2077 | poly pa = *px, pp = NULL; |
---|
| 2078 | |
---|
| 2079 | loop |
---|
| 2080 | { |
---|
| 2081 | i = p_LmCmp(pa, r,R); |
---|
| 2082 | if (i > 0) |
---|
| 2083 | { |
---|
| 2084 | pp = pa; |
---|
| 2085 | pIter(pa); |
---|
| 2086 | if (pa==NULL) |
---|
| 2087 | { |
---|
| 2088 | pNext(pp) = r; |
---|
| 2089 | break; |
---|
| 2090 | } |
---|
| 2091 | } |
---|
| 2092 | else |
---|
| 2093 | { |
---|
| 2094 | if (i == 0) |
---|
| 2095 | { |
---|
| 2096 | x = n_Add(pGetCoeff(pa), pGetCoeff(r),R->cf); |
---|
| 2097 | p_LmDelete(&r,R); |
---|
| 2098 | if (n_IsZero(x,R->cf)) |
---|
| 2099 | { |
---|
| 2100 | p_LmDelete(&pa,R); |
---|
| 2101 | if (pp!=NULL) |
---|
| 2102 | pNext(pp) = p_Add_q(pa,r,R); |
---|
| 2103 | else |
---|
| 2104 | *px = p_Add_q(pa,r,R); |
---|
| 2105 | } |
---|
| 2106 | else |
---|
| 2107 | { |
---|
| 2108 | pp = pa; |
---|
| 2109 | p_SetCoeff(pp,x,R); |
---|
| 2110 | pNext(pp) = p_Add_q(pNext(pp), r, R); |
---|
| 2111 | } |
---|
| 2112 | } |
---|
| 2113 | else |
---|
| 2114 | { |
---|
| 2115 | if (pp!=NULL) |
---|
| 2116 | pp = pNext(pp) = r; |
---|
| 2117 | else |
---|
| 2118 | *px = pp = r; |
---|
| 2119 | pNext(pp) = p_Add_q(pa, pNext(r),R); |
---|
| 2120 | } |
---|
| 2121 | break; |
---|
| 2122 | } |
---|
| 2123 | } |
---|
| 2124 | *ref = pp; |
---|
| 2125 | } |
---|
| 2126 | |
---|
| 2127 | /* ----------------- internal 'C' stuff ------------------ */ |
---|
| 2128 | |
---|
| 2129 | static void sm_ElemDelete(smpoly *r, const ring R) |
---|
| 2130 | { |
---|
| 2131 | smpoly a = *r, b = a->n; |
---|
| 2132 | |
---|
| 2133 | p_Delete(&a->m, R); |
---|
| 2134 | omFreeBin((void *)a, smprec_bin); |
---|
| 2135 | *r = b; |
---|
| 2136 | } |
---|
| 2137 | |
---|
| 2138 | static smpoly smElemCopy(smpoly a) |
---|
| 2139 | { |
---|
| 2140 | smpoly r = (smpoly)omAllocBin(smprec_bin); |
---|
| 2141 | memcpy(r, a, sizeof(smprec)); |
---|
| 2142 | /* r->m = pCopy(r->m); */ |
---|
| 2143 | return r; |
---|
| 2144 | } |
---|
| 2145 | |
---|
| 2146 | /* |
---|
| 2147 | * from poly to smpoly |
---|
| 2148 | * do not destroy p |
---|
[35aab3] | 2149 | */ |
---|
[bf6a4d] | 2150 | static smpoly sm_Poly2Smpoly(poly q, const ring R) |
---|
[35aab3] | 2151 | { |
---|
[bf6a4d] | 2152 | poly pp; |
---|
| 2153 | smpoly res, a; |
---|
| 2154 | long x; |
---|
| 2155 | |
---|
| 2156 | if (q == NULL) |
---|
| 2157 | return NULL; |
---|
| 2158 | a = res = (smpoly)omAllocBin(smprec_bin); |
---|
| 2159 | a->pos = x = p_GetComp(q,R); |
---|
| 2160 | a->m = q; |
---|
| 2161 | a->e = 0; |
---|
| 2162 | loop |
---|
[35aab3] | 2163 | { |
---|
[bf6a4d] | 2164 | p_SetComp(q,0,R); |
---|
| 2165 | pp = q; |
---|
| 2166 | pIter(q); |
---|
| 2167 | if (q == NULL) |
---|
| 2168 | { |
---|
| 2169 | a->n = NULL; |
---|
| 2170 | return res; |
---|
| 2171 | } |
---|
| 2172 | if (p_GetComp(q,R) != x) |
---|
| 2173 | { |
---|
| 2174 | a = a->n = (smpoly)omAllocBin(smprec_bin); |
---|
| 2175 | pNext(pp) = NULL; |
---|
| 2176 | a->pos = x = p_GetComp(q,R); |
---|
| 2177 | a->m = q; |
---|
| 2178 | a->e = 0; |
---|
| 2179 | } |
---|
| 2180 | } |
---|
| 2181 | } |
---|
| 2182 | |
---|
| 2183 | /* |
---|
| 2184 | * from smpoly to poly |
---|
| 2185 | * destroy a |
---|
| 2186 | */ |
---|
| 2187 | static poly sm_Smpoly2Poly(smpoly a, const ring R) |
---|
| 2188 | { |
---|
| 2189 | smpoly b; |
---|
| 2190 | poly res, pp, q; |
---|
| 2191 | long x; |
---|
| 2192 | |
---|
| 2193 | if (a == NULL) |
---|
| 2194 | return NULL; |
---|
| 2195 | x = a->pos; |
---|
| 2196 | q = res = a->m; |
---|
| 2197 | loop |
---|
| 2198 | { |
---|
| 2199 | p_SetComp(q,x,R); |
---|
| 2200 | pp = q; |
---|
| 2201 | pIter(q); |
---|
| 2202 | if (q == NULL) |
---|
| 2203 | break; |
---|
| 2204 | } |
---|
| 2205 | loop |
---|
| 2206 | { |
---|
| 2207 | b = a; |
---|
| 2208 | a = a->n; |
---|
| 2209 | omFreeBin((void *)b, smprec_bin); |
---|
| 2210 | if (a == NULL) |
---|
| 2211 | return res; |
---|
| 2212 | x = a->pos; |
---|
| 2213 | q = pNext(pp) = a->m; |
---|
| 2214 | loop |
---|
| 2215 | { |
---|
| 2216 | p_SetComp(q,x,R); |
---|
| 2217 | pp = q; |
---|
| 2218 | pIter(q); |
---|
| 2219 | if (q == NULL) |
---|
| 2220 | break; |
---|
| 2221 | } |
---|
| 2222 | } |
---|
| 2223 | } |
---|
| 2224 | |
---|
| 2225 | /* |
---|
| 2226 | * weigth of a polynomial, for pivot strategy |
---|
| 2227 | */ |
---|
| 2228 | static float sm_PolyWeight(smpoly a, const ring R) |
---|
| 2229 | { |
---|
| 2230 | poly p = a->m; |
---|
| 2231 | int i; |
---|
| 2232 | float res = (float)n_Size(pGetCoeff(p),R->cf); |
---|
| 2233 | |
---|
| 2234 | if (pNext(p) == NULL) |
---|
| 2235 | { |
---|
| 2236 | for(i=rVar(R); i>0; i--) |
---|
| 2237 | { |
---|
| 2238 | if (p_GetExp(p,i,R) != 0) return res+1.0; |
---|
| 2239 | } |
---|
| 2240 | return res; |
---|
| 2241 | } |
---|
| 2242 | else |
---|
| 2243 | { |
---|
| 2244 | i = 0; |
---|
| 2245 | res = 0.0; |
---|
| 2246 | do |
---|
| 2247 | { |
---|
| 2248 | i++; |
---|
| 2249 | res += (float)n_Size(pGetCoeff(p),R->cf); |
---|
| 2250 | pIter(p); |
---|
| 2251 | } |
---|
| 2252 | while (p); |
---|
| 2253 | return res+(float)i; |
---|
| 2254 | } |
---|
| 2255 | } |
---|
| 2256 | |
---|
| 2257 | static BOOLEAN sm_HaveDenom(poly a, const ring R) |
---|
| 2258 | { |
---|
| 2259 | BOOLEAN sw; |
---|
| 2260 | number x; |
---|
| 2261 | |
---|
| 2262 | while (a != NULL) |
---|
| 2263 | { |
---|
| 2264 | x = n_GetDenom(pGetCoeff(a),R->cf); |
---|
| 2265 | sw = n_IsOne(x,R->cf); |
---|
| 2266 | n_Delete(&x,R->cf); |
---|
| 2267 | if (!sw) |
---|
| 2268 | { |
---|
| 2269 | return TRUE; |
---|
| 2270 | } |
---|
| 2271 | pIter(a); |
---|
| 2272 | } |
---|
| 2273 | return FALSE; |
---|
| 2274 | } |
---|
| 2275 | |
---|
| 2276 | static number sm_Cleardenom(ideal id, const ring R) |
---|
| 2277 | { |
---|
| 2278 | poly a; |
---|
| 2279 | number x,y,res=n_Init(1,R->cf); |
---|
| 2280 | BOOLEAN sw=FALSE; |
---|
| 2281 | |
---|
| 2282 | for (int i=0; i<IDELEMS(id); i++) |
---|
| 2283 | { |
---|
| 2284 | a = id->m[i]; |
---|
| 2285 | sw = sm_HaveDenom(a,R); |
---|
| 2286 | if (sw) break; |
---|
| 2287 | } |
---|
| 2288 | if (!sw) return res; |
---|
| 2289 | for (int i=0; i<IDELEMS(id); i++) |
---|
| 2290 | { |
---|
| 2291 | a = id->m[i]; |
---|
| 2292 | if (a!=NULL) |
---|
| 2293 | { |
---|
| 2294 | x = n_Copy(pGetCoeff(a),R->cf); |
---|
| 2295 | p_Cleardenom(a, R); |
---|
| 2296 | y = n_Div(x,pGetCoeff(a),R->cf); |
---|
| 2297 | n_Delete(&x,R->cf); |
---|
| 2298 | x = n_Mult(res,y,R->cf); |
---|
| 2299 | n_Normalize(x,R->cf); |
---|
| 2300 | n_Delete(&res,R->cf); |
---|
| 2301 | res = x; |
---|
| 2302 | } |
---|
[35aab3] | 2303 | } |
---|
[ebdaa1] | 2304 | return res; |
---|
[35aab3] | 2305 | } |
---|
| 2306 | |
---|
| 2307 | /* ----------------- gauss elimination ------------------ */ |
---|
| 2308 | /* in structs.h */ |
---|
| 2309 | typedef struct smnrec sm_nrec; |
---|
| 2310 | typedef sm_nrec * smnumber; |
---|
| 2311 | struct smnrec{ |
---|
| 2312 | smnumber n; // the next element |
---|
| 2313 | int pos; // position |
---|
| 2314 | number m; // the element |
---|
| 2315 | }; |
---|
| 2316 | |
---|
| 2317 | static omBin smnrec_bin = omGetSpecBin(sizeof(smnrec)); |
---|
| 2318 | |
---|
| 2319 | /* declare internal 'C' stuff */ |
---|
[bf6a4d] | 2320 | static void sm_NumberDelete(smnumber *, const ring R); |
---|
[35aab3] | 2321 | static smnumber smNumberCopy(smnumber); |
---|
[bf6a4d] | 2322 | static smnumber sm_Poly2Smnumber(poly, const ring); |
---|
| 2323 | static poly sm_Smnumber2Poly(number,const ring); |
---|
[35aab3] | 2324 | static BOOLEAN smCheckSolv(ideal); |
---|
| 2325 | |
---|
| 2326 | /* class for sparse number matrix: |
---|
| 2327 | */ |
---|
| 2328 | class sparse_number_mat{ |
---|
| 2329 | private: |
---|
| 2330 | int nrows, ncols; // dimension of the problem |
---|
| 2331 | int act; // number of unreduced columns (start: ncols) |
---|
| 2332 | int crd; // number of reduced columns (start: 0) |
---|
| 2333 | int tored; // border for rows to reduce |
---|
| 2334 | int sing; // indicator for singular problem |
---|
| 2335 | int rpiv; // row-position of the pivot |
---|
| 2336 | int *perm; // permutation of rows |
---|
| 2337 | number *sol; // field for solution |
---|
| 2338 | int *wrw, *wcl; // weights of rows and columns |
---|
| 2339 | smnumber * m_act; // unreduced columns |
---|
| 2340 | smnumber * m_res; // reduced columns (result) |
---|
| 2341 | smnumber * m_row; // reduced part of rows |
---|
| 2342 | smnumber red; // row to reduce |
---|
| 2343 | smnumber piv; // pivot |
---|
| 2344 | smnumber dumm; // allocated dummy |
---|
[bf6a4d] | 2345 | ring _R; |
---|
[35aab3] | 2346 | void smColToRow(); |
---|
| 2347 | void smRowToCol(); |
---|
| 2348 | void smSelectPR(); |
---|
| 2349 | void smRealPivot(); |
---|
| 2350 | void smZeroToredElim(); |
---|
| 2351 | void smGElim(); |
---|
| 2352 | void smAllDel(); |
---|
| 2353 | public: |
---|
[bf6a4d] | 2354 | sparse_number_mat(ideal, const ring); |
---|
[35aab3] | 2355 | ~sparse_number_mat(); |
---|
| 2356 | int smIsSing() { return sing; } |
---|
| 2357 | void smTriangular(); |
---|
| 2358 | void smSolv(); |
---|
| 2359 | ideal smRes2Ideal(); |
---|
| 2360 | }; |
---|
| 2361 | |
---|
| 2362 | /* ----------------- basics (used from 'C') ------------------ */ |
---|
| 2363 | /*2 |
---|
| 2364 | * returns the solution of a linear equation |
---|
| 2365 | * solution of M*x = r (M has dimension nXn) => |
---|
| 2366 | * I = module(transprose(M)) + r*gen(n+1) |
---|
| 2367 | * uses Gauss-elimination |
---|
| 2368 | */ |
---|
[bf6a4d] | 2369 | ideal sm_CallSolv(ideal I, const ring R) |
---|
[35aab3] | 2370 | { |
---|
| 2371 | sparse_number_mat *linsolv; |
---|
[ab453da] | 2372 | ring tmpR; |
---|
[35aab3] | 2373 | ideal rr; |
---|
| 2374 | |
---|
[bf6a4d] | 2375 | if (id_IsConstant(I,R)==FALSE) |
---|
[35aab3] | 2376 | { |
---|
| 2377 | WerrorS("symbol in equation"); |
---|
| 2378 | return NULL; |
---|
| 2379 | } |
---|
[bf6a4d] | 2380 | I->rank = id_RankFreeModule(I,R); |
---|
[35aab3] | 2381 | if (smCheckSolv(I)) return NULL; |
---|
[bf6a4d] | 2382 | tmpR=sm_RingChange(R,1); |
---|
| 2383 | rr=idrCopyR(I,R, tmpR); |
---|
| 2384 | linsolv = new sparse_number_mat(rr,tmpR); |
---|
[35aab3] | 2385 | rr=NULL; |
---|
| 2386 | linsolv->smTriangular(); |
---|
| 2387 | if (linsolv->smIsSing() == 0) |
---|
| 2388 | { |
---|
| 2389 | linsolv->smSolv(); |
---|
| 2390 | rr = linsolv->smRes2Ideal(); |
---|
| 2391 | } |
---|
| 2392 | else |
---|
| 2393 | WerrorS("singular problem for linsolv"); |
---|
| 2394 | delete linsolv; |
---|
| 2395 | if (rr!=NULL) |
---|
[bf6a4d] | 2396 | rr = idrMoveR(rr,tmpR,R); |
---|
| 2397 | sm_KillModifiedRing(tmpR); |
---|
[35aab3] | 2398 | return rr; |
---|
| 2399 | } |
---|
| 2400 | |
---|
| 2401 | /* |
---|
| 2402 | * constructor, destroy smat |
---|
| 2403 | */ |
---|
[bf6a4d] | 2404 | sparse_number_mat::sparse_number_mat(ideal smat, const ring R) |
---|
[35aab3] | 2405 | { |
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| 2406 | int i; |
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[bf6a4d] | 2407 | poly* pmat; |
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| 2408 | _R=R; |
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[35aab3] | 2409 | |
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| 2410 | crd = sing = 0; |
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| 2411 | act = ncols = smat->ncols; |
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| 2412 | tored = nrows = smat->rank; |
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| 2413 | i = tored+1; |
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| 2414 | perm = (int *)omAlloc(sizeof(int)*i); |
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| 2415 | m_row = (smnumber *)omAlloc0(sizeof(smnumber)*i); |
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| 2416 | wrw = (int *)omAlloc(sizeof(int)*i); |
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| 2417 | i = ncols+1; |
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| 2418 | wcl = (int *)omAlloc(sizeof(int)*i); |
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| 2419 | m_act = (smnumber *)omAlloc(sizeof(smnumber)*i); |
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| 2420 | m_res = (smnumber *)omAlloc0(sizeof(smnumber)*i); |
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| 2421 | dumm = (smnumber)omAllocBin(smnrec_bin); |
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| 2422 | pmat = smat->m; |
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| 2423 | for(i=ncols; i; i--) |
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| 2424 | { |
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[bf6a4d] | 2425 | m_act[i] = sm_Poly2Smnumber(pmat[i-1],_R); |
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[35aab3] | 2426 | } |
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| 2427 | omFreeSize((ADDRESS)pmat,smat->ncols*sizeof(poly)); |
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| 2428 | omFreeBin((ADDRESS)smat, sip_sideal_bin); |
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| 2429 | } |
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| 2430 | |
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| 2431 | /* |
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| 2432 | * destructor |
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| 2433 | */ |
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| 2434 | sparse_number_mat::~sparse_number_mat() |
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| 2435 | { |
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| 2436 | int i; |
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| 2437 | omFreeBin((ADDRESS)dumm, smnrec_bin); |
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| 2438 | i = ncols+1; |
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| 2439 | omFreeSize((ADDRESS)m_res, sizeof(smnumber)*i); |
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| 2440 | omFreeSize((ADDRESS)m_act, sizeof(smnumber)*i); |
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| 2441 | omFreeSize((ADDRESS)wcl, sizeof(int)*i); |
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| 2442 | i = nrows+1; |
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| 2443 | omFreeSize((ADDRESS)wrw, sizeof(int)*i); |
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| 2444 | omFreeSize((ADDRESS)m_row, sizeof(smnumber)*i); |
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| 2445 | omFreeSize((ADDRESS)perm, sizeof(int)*i); |
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| 2446 | } |
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| 2447 | |
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| 2448 | /* |
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| 2449 | * triangularization by Gauss-elimination |
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| 2450 | */ |
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| 2451 | void sparse_number_mat::smTriangular() |
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| 2452 | { |
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| 2453 | tored--; |
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| 2454 | this->smZeroToredElim(); |
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| 2455 | if (sing != 0) return; |
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| 2456 | while (act > 1) |
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| 2457 | { |
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| 2458 | this->smRealPivot(); |
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| 2459 | this->smSelectPR(); |
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| 2460 | this->smGElim(); |
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| 2461 | crd++; |
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| 2462 | this->smColToRow(); |
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| 2463 | act--; |
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| 2464 | this->smRowToCol(); |
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| 2465 | this->smZeroToredElim(); |
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| 2466 | if (sing != 0) return; |
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| 2467 | } |
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| 2468 | if (TEST_OPT_PROT) PrintS(".\n"); |
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| 2469 | piv = m_act[1]; |
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| 2470 | rpiv = piv->pos; |
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| 2471 | m_act[1] = piv->n; |
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| 2472 | piv->n = NULL; |
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| 2473 | crd++; |
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| 2474 | this->smColToRow(); |
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| 2475 | act--; |
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| 2476 | this->smRowToCol(); |
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| 2477 | } |
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| 2478 | |
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| 2479 | /* |
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| 2480 | * solve the triangular system |
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| 2481 | */ |
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| 2482 | void sparse_number_mat::smSolv() |
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| 2483 | { |
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| 2484 | int i, j; |
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| 2485 | number x, y, z; |
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| 2486 | smnumber s, d, r = m_row[nrows]; |
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| 2487 | |
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| 2488 | m_row[nrows] = NULL; |
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| 2489 | sol = (number *)omAlloc0(sizeof(number)*(crd+1)); |
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| 2490 | while (r != NULL) // expand the rigth hand side |
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| 2491 | { |
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| 2492 | sol[r->pos] = r->m; |
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| 2493 | s = r; |
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| 2494 | r = r->n; |
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| 2495 | omFreeBin((ADDRESS)s, smnrec_bin); |
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| 2496 | } |
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| 2497 | i = crd; // solve triangular system |
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| 2498 | if (sol[i] != NULL) |
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| 2499 | { |
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| 2500 | x = sol[i]; |
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[bf6a4d] | 2501 | sol[i] = n_Div(x, m_res[i]->m,_R->cf); |
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| 2502 | n_Delete(&x,_R->cf); |
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[35aab3] | 2503 | } |
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| 2504 | i--; |
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| 2505 | while (i > 0) |
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| 2506 | { |
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| 2507 | x = NULL; |
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| 2508 | d = m_res[i]; |
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| 2509 | s = d->n; |
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| 2510 | while (s != NULL) |
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| 2511 | { |
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| 2512 | j = s->pos; |
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| 2513 | if (sol[j] != NULL) |
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| 2514 | { |
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[bf6a4d] | 2515 | z = n_Mult(sol[j], s->m,_R->cf); |
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[35aab3] | 2516 | if (x != NULL) |
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| 2517 | { |
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| 2518 | y = x; |
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[bf6a4d] | 2519 | x = n_Sub(y, z,_R->cf); |
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| 2520 | n_Delete(&y,_R->cf); |
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| 2521 | n_Delete(&z,_R->cf); |
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[35aab3] | 2522 | } |
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| 2523 | else |
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[bf6a4d] | 2524 | x = n_Neg(z,_R->cf); |
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[35aab3] | 2525 | } |
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| 2526 | s = s->n; |
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| 2527 | } |
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| 2528 | if (sol[i] != NULL) |
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| 2529 | { |
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| 2530 | if (x != NULL) |
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| 2531 | { |
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[bf6a4d] | 2532 | y = n_Add(x, sol[i],_R->cf); |
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| 2533 | n_Delete(&x,_R->cf); |
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| 2534 | if (n_IsZero(y,_R->cf)) |
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[35aab3] | 2535 | { |
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[bf6a4d] | 2536 | n_Delete(&sol[i],_R->cf); |
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[35aab3] | 2537 | sol[i] = NULL; |
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| 2538 | } |
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| 2539 | else |
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| 2540 | sol[i] = y; |
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| 2541 | } |
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| 2542 | } |
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| 2543 | else |
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| 2544 | sol[i] = x; |
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| 2545 | if (sol[i] != NULL) |
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| 2546 | { |
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| 2547 | x = sol[i]; |
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[bf6a4d] | 2548 | sol[i] = n_Div(x, d->m,_R->cf); |
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| 2549 | n_Delete(&x,_R->cf); |
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[35aab3] | 2550 | } |
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| 2551 | i--; |
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| 2552 | } |
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| 2553 | this->smAllDel(); |
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| 2554 | } |
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| 2555 | |
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| 2556 | /* |
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| 2557 | * transform the result to an ideal |
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| 2558 | */ |
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| 2559 | ideal sparse_number_mat::smRes2Ideal() |
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| 2560 | { |
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| 2561 | int i, j; |
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| 2562 | ideal res = idInit(crd, 1); |
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| 2563 | |
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| 2564 | for (i=crd; i; i--) |
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| 2565 | { |
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| 2566 | j = perm[i]-1; |
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[bf6a4d] | 2567 | res->m[j] = sm_Smnumber2Poly(sol[i],_R); |
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[35aab3] | 2568 | } |
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| 2569 | omFreeSize((ADDRESS)sol, sizeof(number)*(crd+1)); |
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| 2570 | return res; |
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| 2571 | } |
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| 2572 | |
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| 2573 | /* ----------------- pivot method ------------------ */ |
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| 2574 | |
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| 2575 | /* |
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| 2576 | * compute pivot |
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| 2577 | */ |
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| 2578 | void sparse_number_mat::smRealPivot() |
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| 2579 | { |
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| 2580 | smnumber a; |
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| 2581 | number x, xo; |
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| 2582 | int i, copt, ropt; |
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| 2583 | |
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[bf6a4d] | 2584 | xo=n_Init(0,_R->cf); |
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[35aab3] | 2585 | for (i=act; i; i--) |
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| 2586 | { |
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| 2587 | a = m_act[i]; |
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| 2588 | while ((a!=NULL) && (a->pos<=tored)) |
---|
| 2589 | { |
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| 2590 | x = a->m; |
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[bf6a4d] | 2591 | if (n_GreaterZero(x,_R->cf)) |
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[35aab3] | 2592 | { |
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[bf6a4d] | 2593 | if (n_Greater(x,xo,_R->cf)) |
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[35aab3] | 2594 | { |
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[bf6a4d] | 2595 | n_Delete(&xo,_R->cf); |
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| 2596 | xo = n_Copy(x,_R->cf); |
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[35aab3] | 2597 | copt = i; |
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| 2598 | ropt = a->pos; |
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| 2599 | } |
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| 2600 | } |
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| 2601 | else |
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| 2602 | { |
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[bf6a4d] | 2603 | xo = n_Neg(xo,_R->cf); |
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| 2604 | if (n_Greater(xo,x,_R->cf)) |
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[35aab3] | 2605 | { |
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[bf6a4d] | 2606 | n_Delete(&xo,_R->cf); |
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| 2607 | xo = n_Copy(x,_R->cf); |
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[35aab3] | 2608 | copt = i; |
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| 2609 | ropt = a->pos; |
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| 2610 | } |
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[bf6a4d] | 2611 | xo = n_Neg(xo,_R->cf); |
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[35aab3] | 2612 | } |
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| 2613 | a = a->n; |
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| 2614 | } |
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| 2615 | } |
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| 2616 | rpiv = ropt; |
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| 2617 | if (copt != act) |
---|
| 2618 | { |
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| 2619 | a = m_act[act]; |
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| 2620 | m_act[act] = m_act[copt]; |
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| 2621 | m_act[copt] = a; |
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| 2622 | } |
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[bf6a4d] | 2623 | n_Delete(&xo,_R->cf); |
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[35aab3] | 2624 | } |
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| 2625 | |
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| 2626 | /* ----------------- elimination ------------------ */ |
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| 2627 | |
---|
| 2628 | /* one step of Gauss-elimination */ |
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| 2629 | void sparse_number_mat::smGElim() |
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| 2630 | { |
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[bf6a4d] | 2631 | number p = n_Invers(piv->m,_R->cf); // pivotelement |
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[35aab3] | 2632 | smnumber c = m_act[act]; // pivotcolumn |
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| 2633 | smnumber r = red; // row to reduce |
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| 2634 | smnumber res, a, b; |
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| 2635 | number w, ha, hb; |
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| 2636 | |
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| 2637 | if ((c == NULL) || (r == NULL)) |
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| 2638 | { |
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[bf6a4d] | 2639 | while (r!=NULL) sm_NumberDelete(&r,_R); |
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[35aab3] | 2640 | return; |
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| 2641 | } |
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| 2642 | do |
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| 2643 | { |
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| 2644 | a = m_act[r->pos]; |
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| 2645 | res = dumm; |
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| 2646 | res->n = NULL; |
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| 2647 | b = c; |
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[bf6a4d] | 2648 | w = n_Mult(r->m, p,_R->cf); |
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| 2649 | n_Delete(&r->m,_R->cf); |
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[35aab3] | 2650 | r->m = w; |
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| 2651 | loop // combine the chains a and b: a + w*b |
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| 2652 | { |
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| 2653 | if (a == NULL) |
---|
| 2654 | { |
---|
| 2655 | do |
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| 2656 | { |
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| 2657 | res = res->n = smNumberCopy(b); |
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[bf6a4d] | 2658 | res->m = n_Mult(b->m, w,_R->cf); |
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[35aab3] | 2659 | b = b->n; |
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| 2660 | } while (b != NULL); |
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| 2661 | break; |
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| 2662 | } |
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| 2663 | if (a->pos < b->pos) |
---|
| 2664 | { |
---|
| 2665 | res = res->n = a; |
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| 2666 | a = a->n; |
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| 2667 | } |
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| 2668 | else if (a->pos > b->pos) |
---|
| 2669 | { |
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| 2670 | res = res->n = smNumberCopy(b); |
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[bf6a4d] | 2671 | res->m = n_Mult(b->m, w,_R->cf); |
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[35aab3] | 2672 | b = b->n; |
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| 2673 | } |
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| 2674 | else |
---|
| 2675 | { |
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[bf6a4d] | 2676 | hb = n_Mult(b->m, w,_R->cf); |
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| 2677 | ha = n_Add(a->m, hb,_R->cf); |
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| 2678 | n_Delete(&hb,_R->cf); |
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| 2679 | n_Delete(&a->m,_R->cf); |
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| 2680 | if (n_IsZero(ha,_R->cf)) |
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[35aab3] | 2681 | { |
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[bf6a4d] | 2682 | sm_NumberDelete(&a,_R); |
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[35aab3] | 2683 | } |
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| 2684 | else |
---|
| 2685 | { |
---|
| 2686 | a->m = ha; |
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| 2687 | res = res->n = a; |
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| 2688 | a = a->n; |
---|
| 2689 | } |
---|
| 2690 | b = b->n; |
---|
| 2691 | } |
---|
| 2692 | if (b == NULL) |
---|
| 2693 | { |
---|
| 2694 | res->n = a; |
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| 2695 | break; |
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| 2696 | } |
---|
| 2697 | } |
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| 2698 | m_act[r->pos] = dumm->n; |
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[bf6a4d] | 2699 | sm_NumberDelete(&r,_R); |
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[35aab3] | 2700 | } while (r != NULL); |
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[bf6a4d] | 2701 | n_Delete(&p,_R->cf); |
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[35aab3] | 2702 | } |
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| 2703 | |
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| 2704 | /* ----------------- transfer ------------------ */ |
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| 2705 | |
---|
| 2706 | /* |
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| 2707 | * select the pivotrow and store it to red and piv |
---|
| 2708 | */ |
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| 2709 | void sparse_number_mat::smSelectPR() |
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| 2710 | { |
---|
| 2711 | smnumber b = dumm; |
---|
| 2712 | smnumber a, ap; |
---|
| 2713 | int i; |
---|
| 2714 | |
---|
| 2715 | if (TEST_OPT_PROT) |
---|
| 2716 | { |
---|
| 2717 | if ((crd+1)%10) |
---|
| 2718 | PrintS("."); |
---|
| 2719 | else |
---|
| 2720 | PrintS(".\n"); |
---|
| 2721 | } |
---|
| 2722 | a = m_act[act]; |
---|
| 2723 | if (a->pos < rpiv) |
---|
| 2724 | { |
---|
| 2725 | do |
---|
| 2726 | { |
---|
| 2727 | ap = a; |
---|
| 2728 | a = a->n; |
---|
| 2729 | } while (a->pos < rpiv); |
---|
| 2730 | ap->n = a->n; |
---|
| 2731 | } |
---|
| 2732 | else |
---|
| 2733 | m_act[act] = a->n; |
---|
| 2734 | piv = a; |
---|
| 2735 | a->n = NULL; |
---|
| 2736 | for (i=1; i<act; i++) |
---|
| 2737 | { |
---|
| 2738 | a = m_act[i]; |
---|
| 2739 | if (a->pos < rpiv) |
---|
| 2740 | { |
---|
| 2741 | loop |
---|
| 2742 | { |
---|
| 2743 | ap = a; |
---|
| 2744 | a = a->n; |
---|
| 2745 | if ((a == NULL) || (a->pos > rpiv)) |
---|
| 2746 | break; |
---|
| 2747 | if (a->pos == rpiv) |
---|
| 2748 | { |
---|
| 2749 | ap->n = a->n; |
---|
[bf6a4d] | 2750 | a->m = n_Neg(a->m,_R); |
---|
[35aab3] | 2751 | b = b->n = a; |
---|
| 2752 | b->pos = i; |
---|
| 2753 | break; |
---|
| 2754 | } |
---|
| 2755 | } |
---|
| 2756 | } |
---|
| 2757 | else if (a->pos == rpiv) |
---|
| 2758 | { |
---|
| 2759 | m_act[i] = a->n; |
---|
[bf6a4d] | 2760 | a->m = n_Neg(a->m,_R); |
---|
[35aab3] | 2761 | b = b->n = a; |
---|
| 2762 | b->pos = i; |
---|
| 2763 | } |
---|
| 2764 | } |
---|
| 2765 | b->n = NULL; |
---|
| 2766 | red = dumm->n; |
---|
| 2767 | } |
---|
| 2768 | |
---|
| 2769 | /* |
---|
| 2770 | * store the pivotcol in m_row |
---|
| 2771 | * m_act[cols][pos(rows)] => m_row[rows][pos(cols)] |
---|
| 2772 | */ |
---|
| 2773 | void sparse_number_mat::smColToRow() |
---|
| 2774 | { |
---|
| 2775 | smnumber c = m_act[act]; |
---|
| 2776 | smnumber h; |
---|
| 2777 | |
---|
| 2778 | while (c != NULL) |
---|
| 2779 | { |
---|
| 2780 | h = c; |
---|
| 2781 | c = c->n; |
---|
| 2782 | h->n = m_row[h->pos]; |
---|
| 2783 | m_row[h->pos] = h; |
---|
| 2784 | h->pos = crd; |
---|
| 2785 | } |
---|
| 2786 | } |
---|
| 2787 | |
---|
| 2788 | /* |
---|
| 2789 | * store the pivot and the assosiated row in m_row |
---|
| 2790 | * to m_res (result): |
---|
| 2791 | * piv + m_row[rows][pos(cols)] => m_res[cols][pos(rows)] |
---|
| 2792 | */ |
---|
| 2793 | void sparse_number_mat::smRowToCol() |
---|
| 2794 | { |
---|
| 2795 | smnumber r = m_row[rpiv]; |
---|
| 2796 | smnumber a, ap, h; |
---|
| 2797 | |
---|
| 2798 | m_row[rpiv] = NULL; |
---|
| 2799 | perm[crd] = rpiv; |
---|
| 2800 | piv->pos = crd; |
---|
| 2801 | m_res[crd] = piv; |
---|
| 2802 | while (r != NULL) |
---|
| 2803 | { |
---|
| 2804 | ap = m_res[r->pos]; |
---|
| 2805 | loop |
---|
| 2806 | { |
---|
| 2807 | a = ap->n; |
---|
| 2808 | if (a == NULL) |
---|
| 2809 | { |
---|
| 2810 | ap->n = h = r; |
---|
| 2811 | r = r->n; |
---|
| 2812 | h->n = a; |
---|
| 2813 | h->pos = crd; |
---|
| 2814 | break; |
---|
| 2815 | } |
---|
| 2816 | ap = a; |
---|
| 2817 | } |
---|
| 2818 | } |
---|
| 2819 | } |
---|
| 2820 | |
---|
| 2821 | /* ----------------- C++ stuff ------------------ */ |
---|
| 2822 | |
---|
| 2823 | /* |
---|
| 2824 | * check singularity |
---|
| 2825 | */ |
---|
| 2826 | void sparse_number_mat::smZeroToredElim() |
---|
| 2827 | { |
---|
| 2828 | smnumber a; |
---|
| 2829 | int i = act; |
---|
| 2830 | |
---|
| 2831 | loop |
---|
| 2832 | { |
---|
| 2833 | if (i == 0) return; |
---|
| 2834 | a = m_act[i]; |
---|
| 2835 | if ((a==NULL) || (a->pos>tored)) |
---|
| 2836 | { |
---|
| 2837 | sing = 1; |
---|
| 2838 | this->smAllDel(); |
---|
| 2839 | return; |
---|
| 2840 | } |
---|
| 2841 | i--; |
---|
| 2842 | } |
---|
| 2843 | } |
---|
| 2844 | |
---|
| 2845 | /* |
---|
| 2846 | * delete all smnumber's |
---|
| 2847 | */ |
---|
| 2848 | void sparse_number_mat::smAllDel() |
---|
| 2849 | { |
---|
| 2850 | smnumber a; |
---|
| 2851 | int i; |
---|
| 2852 | |
---|
| 2853 | for (i=act; i; i--) |
---|
| 2854 | { |
---|
| 2855 | a = m_act[i]; |
---|
| 2856 | while (a != NULL) |
---|
[bf6a4d] | 2857 | sm_NumberDelete(&a,_R); |
---|
[35aab3] | 2858 | } |
---|
| 2859 | for (i=crd; i; i--) |
---|
| 2860 | { |
---|
| 2861 | a = m_res[i]; |
---|
| 2862 | while (a != NULL) |
---|
[bf6a4d] | 2863 | sm_NumberDelete(&a,_R); |
---|
[35aab3] | 2864 | } |
---|
| 2865 | if (act) |
---|
| 2866 | { |
---|
| 2867 | for (i=nrows; i; i--) |
---|
| 2868 | { |
---|
| 2869 | a = m_row[i]; |
---|
| 2870 | while (a != NULL) |
---|
[bf6a4d] | 2871 | sm_NumberDelete(&a,_R); |
---|
[35aab3] | 2872 | } |
---|
| 2873 | } |
---|
| 2874 | } |
---|
| 2875 | |
---|
| 2876 | /* ----------------- internal 'C' stuff ------------------ */ |
---|
| 2877 | |
---|
[bf6a4d] | 2878 | static void sm_NumberDelete(smnumber *r, const ring R) |
---|
[35aab3] | 2879 | { |
---|
| 2880 | smnumber a = *r, b = a->n; |
---|
| 2881 | |
---|
[bf6a4d] | 2882 | n_Delete(&a->m,R->cf); |
---|
[35aab3] | 2883 | omFreeBin((ADDRESS)a, smnrec_bin); |
---|
| 2884 | *r = b; |
---|
| 2885 | } |
---|
| 2886 | |
---|
| 2887 | static smnumber smNumberCopy(smnumber a) |
---|
| 2888 | { |
---|
| 2889 | smnumber r = (smnumber)omAllocBin(smnrec_bin); |
---|
| 2890 | memcpy(r, a, sizeof(smnrec)); |
---|
| 2891 | return r; |
---|
| 2892 | } |
---|
| 2893 | |
---|
| 2894 | /* |
---|
| 2895 | * from poly to smnumber |
---|
| 2896 | * do not destroy p |
---|
| 2897 | */ |
---|
[bf6a4d] | 2898 | static smnumber sm_Poly2Smnumber(poly q, const ring R) |
---|
[35aab3] | 2899 | { |
---|
| 2900 | smnumber a, res; |
---|
| 2901 | poly p = q; |
---|
| 2902 | |
---|
| 2903 | if (p == NULL) |
---|
| 2904 | return NULL; |
---|
| 2905 | a = res = (smnumber)omAllocBin(smnrec_bin); |
---|
[bf6a4d] | 2906 | a->pos = p_GetComp(p,R); |
---|
[35aab3] | 2907 | a->m = pGetCoeff(p); |
---|
[bf6a4d] | 2908 | n_New(&pGetCoeff(p),R->cf); |
---|
[35aab3] | 2909 | loop |
---|
| 2910 | { |
---|
| 2911 | pIter(p); |
---|
| 2912 | if (p == NULL) |
---|
| 2913 | { |
---|
[bf6a4d] | 2914 | p_Delete(&q,R); |
---|
[35aab3] | 2915 | a->n = NULL; |
---|
| 2916 | return res; |
---|
| 2917 | } |
---|
| 2918 | a = a->n = (smnumber)omAllocBin(smnrec_bin); |
---|
[bf6a4d] | 2919 | a->pos = p_GetComp(p,R); |
---|
[35aab3] | 2920 | a->m = pGetCoeff(p); |
---|
[bf6a4d] | 2921 | n_New(&pGetCoeff(p),R->cf); |
---|
[35aab3] | 2922 | } |
---|
| 2923 | } |
---|
| 2924 | |
---|
| 2925 | /* |
---|
| 2926 | * from smnumber to poly |
---|
| 2927 | * destroy a |
---|
| 2928 | */ |
---|
[bf6a4d] | 2929 | static poly sm_Smnumber2Poly(number a, const ring R) |
---|
[35aab3] | 2930 | { |
---|
| 2931 | poly res; |
---|
| 2932 | |
---|
| 2933 | if (a == NULL) return NULL; |
---|
[bf6a4d] | 2934 | res = p_Init(R); |
---|
[35aab3] | 2935 | pSetCoeff0(res, a); |
---|
| 2936 | return res; |
---|
| 2937 | } |
---|
| 2938 | |
---|
| 2939 | /*2 |
---|
| 2940 | * check the input |
---|
| 2941 | */ |
---|
| 2942 | static BOOLEAN smCheckSolv(ideal I) |
---|
| 2943 | { int i = I->ncols; |
---|
| 2944 | if ((i == 0) || (i != I->rank-1)) |
---|
| 2945 | { |
---|
| 2946 | WerrorS("wrong dimensions for linsolv"); |
---|
| 2947 | return TRUE; |
---|
| 2948 | } |
---|
| 2949 | for(;i;i--) |
---|
| 2950 | { |
---|
| 2951 | if(I->m[i-1] == NULL) |
---|
| 2952 | { |
---|
| 2953 | WerrorS("singular input for linsolv"); |
---|
| 2954 | return TRUE; |
---|
| 2955 | } |
---|
| 2956 | } |
---|
| 2957 | return FALSE; |
---|
| 2958 | } |
---|