[20118a] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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| 4 | /* $Id$ */ |
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| 5 | |
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| 6 | /* |
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| 7 | * ABSTRACT: |
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| 8 | */ |
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| 9 | |
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| 10 | #include <stdio.h> |
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| 11 | #include <math.h> |
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| 12 | |
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[2ad10e9] | 13 | #include "config.h" |
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| 14 | #include <misc/auxiliary.h> |
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| 15 | |
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[b1dfaf] | 16 | #include <omalloc/omalloc.h> |
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[2ad10e9] | 17 | #include <misc/mylimits.h> |
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| 18 | |
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| 19 | |
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| 20 | // #include <kernel/structs.h> |
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| 21 | // #include <kernel/kstd1.h> |
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| 22 | // #include <kernel/polys.h> |
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| 23 | |
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| 24 | #include <misc/intvec.h> |
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| 25 | #include <coeffs/numbers.h> |
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| 26 | |
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| 27 | #include <reporter/reporter.h> |
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| 28 | |
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| 29 | |
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| 30 | #include "monomials/ring.h" |
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| 31 | #include "monomials/p_polys.h" |
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| 32 | |
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| 33 | #include "coeffrings.h" |
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| 34 | #include "simpleideals.h" |
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| 35 | #include "matpol.h" |
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| 36 | #include "prCopy.h" |
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[20118a] | 37 | |
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[441a2e] | 38 | #include "sparsmat.h" |
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[73ad0c] | 39 | |
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| 40 | //omBin sip_sideal_bin = omGetSpecBin(sizeof(ip_smatrix)); |
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[20118a] | 41 | /*0 implementation*/ |
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| 42 | |
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[5d9aa6] | 43 | static poly mp_Exdiv ( poly m, poly d, poly vars, const ring); |
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| 44 | static poly mp_Select (poly fro, poly what, const ring); |
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| 45 | |
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| 46 | /// create a r x c zero-matrix |
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[20118a] | 47 | matrix mpNew(int r, int c) |
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| 48 | { |
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| 49 | if (r<=0) r=1; |
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[a2cdd62] | 50 | if ( (((int)(MAX_INT_VAL/sizeof(poly))) / r) <= c) |
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[20118a] | 51 | { |
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| 52 | Werror("internal error: creating matrix[%d][%d]",r,c); |
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| 53 | return NULL; |
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| 54 | } |
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[73ad0c] | 55 | matrix rc = (matrix)omAllocBin(sip_sideal_bin); |
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[20118a] | 56 | rc->nrows = r; |
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| 57 | rc->ncols = c; |
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| 58 | rc->rank = r; |
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| 59 | if (c != 0) |
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| 60 | { |
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| 61 | int s=r*c*sizeof(poly); |
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[5d9aa6] | 62 | rc->m = (poly*)omAlloc0(s); |
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[20118a] | 63 | //if (rc->m==NULL) |
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| 64 | //{ |
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| 65 | // Werror("internal error: creating matrix[%d][%d]",r,c); |
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| 66 | // return NULL; |
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| 67 | //} |
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| 68 | } |
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| 69 | return rc; |
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| 70 | } |
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| 71 | |
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[5d9aa6] | 72 | /// copies matrix a (from ring r to r) |
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| 73 | matrix mp_Copy (matrix a, const ring r) |
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[20118a] | 74 | { |
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[5d9aa6] | 75 | id_Test((ideal)a, r); |
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[20118a] | 76 | poly t; |
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| 77 | int i, m=MATROWS(a), n=MATCOLS(a); |
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| 78 | matrix b = mpNew(m, n); |
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| 79 | |
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| 80 | for (i=m*n-1; i>=0; i--) |
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| 81 | { |
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| 82 | t = a->m[i]; |
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| 83 | if (t!=NULL) |
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| 84 | { |
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[5d9aa6] | 85 | p_Normalize(t, r); |
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| 86 | b->m[i] = p_Copy(t, r); |
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[20118a] | 87 | } |
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| 88 | } |
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| 89 | b->rank=a->rank; |
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| 90 | return b; |
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| 91 | } |
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| 92 | |
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[5d9aa6] | 93 | /// copies matrix a from rSrc into rDst |
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| 94 | matrix mp_Copy(const matrix a, const ring rSrc, const ring rDst) |
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[20118a] | 95 | { |
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[5d9aa6] | 96 | id_Test((ideal)a, rSrc); |
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[20118a] | 97 | |
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| 98 | poly t; |
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| 99 | int i, m=MATROWS(a), n=MATCOLS(a); |
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| 100 | |
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| 101 | matrix b = mpNew(m, n); |
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| 102 | |
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| 103 | for (i=m*n-1; i>=0; i--) |
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| 104 | { |
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| 105 | t = a->m[i]; |
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| 106 | if (t!=NULL) |
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| 107 | { |
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| 108 | b->m[i] = prCopyR_NoSort(t, rSrc, rDst); |
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| 109 | p_Normalize(b->m[i], rDst); |
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| 110 | } |
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| 111 | } |
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| 112 | b->rank=a->rank; |
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| 113 | |
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[5d9aa6] | 114 | id_Test((ideal)b, rDst); |
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[20118a] | 115 | |
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| 116 | return b; |
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| 117 | } |
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| 118 | |
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| 119 | |
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| 120 | |
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[5d9aa6] | 121 | /// make it a p * unit matrix |
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[3d65be] | 122 | matrix mp_InitP(int r, int c, poly p, const ring R) |
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[20118a] | 123 | { |
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| 124 | matrix rc = mpNew(r,c); |
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| 125 | int i=si_min(r,c), n = c*(i-1)+i-1, inc = c+1; |
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| 126 | |
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[3d65be] | 127 | p_Normalize(p, R); |
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[20118a] | 128 | while (n>0) |
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| 129 | { |
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[3d65be] | 130 | rc->m[n] = p_Copy(p, R); |
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[20118a] | 131 | n -= inc; |
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| 132 | } |
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| 133 | rc->m[0]=p; |
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| 134 | return rc; |
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| 135 | } |
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| 136 | |
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[5d9aa6] | 137 | /// make it a v * unit matrix |
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| 138 | matrix mp_InitI(int r, int c, int v, const ring R) |
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[20118a] | 139 | { |
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[5d9aa6] | 140 | return mp_InitP(r, c, p_ISet(v, R), R); |
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[20118a] | 141 | } |
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| 142 | |
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[5d9aa6] | 143 | /// c = f*a |
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| 144 | matrix mp_MultI(matrix a, int f, const ring R) |
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[20118a] | 145 | { |
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| 146 | int k, n = a->nrows, m = a->ncols; |
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[5d9aa6] | 147 | poly p = p_ISet(f, R); |
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[20118a] | 148 | matrix c = mpNew(n,m); |
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| 149 | |
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| 150 | for (k=m*n-1; k>0; k--) |
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[5d9aa6] | 151 | c->m[k] = pp_Mult_qq(a->m[k], p, R); |
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| 152 | c->m[0] = p_Mult_q(p_Copy(a->m[0], R), p, R); |
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[20118a] | 153 | return c; |
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| 154 | } |
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| 155 | |
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[5d9aa6] | 156 | /// multiply a matrix 'a' by a poly 'p', destroy the args |
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| 157 | matrix mp_MultP(matrix a, poly p, const ring R) |
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[20118a] | 158 | { |
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| 159 | int k, n = a->nrows, m = a->ncols; |
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| 160 | |
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[5d9aa6] | 161 | p_Normalize(p, R); |
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[20118a] | 162 | for (k=m*n-1; k>0; k--) |
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| 163 | { |
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| 164 | if (a->m[k]!=NULL) |
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[5d9aa6] | 165 | a->m[k] = p_Mult_q(a->m[k], p_Copy(p, R), R); |
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[20118a] | 166 | } |
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[5d9aa6] | 167 | a->m[0] = p_Mult_q(a->m[0], p, R); |
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[20118a] | 168 | return a; |
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| 169 | } |
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| 170 | |
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[e14e1b0] | 171 | /*2 |
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| 172 | * multiply a poly 'p' by a matrix 'a', destroy the args |
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| 173 | */ |
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[5d9aa6] | 174 | matrix pMultMp(poly p, matrix a, const ring R) |
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[e14e1b0] | 175 | { |
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| 176 | int k, n = a->nrows, m = a->ncols; |
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| 177 | |
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[5d9aa6] | 178 | p_Normalize(p, R); |
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[e14e1b0] | 179 | for (k=m*n-1; k>0; k--) |
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| 180 | { |
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| 181 | if (a->m[k]!=NULL) |
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[5d9aa6] | 182 | a->m[k] = p_Mult_q(p_Copy(p, R), a->m[k], R); |
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[e14e1b0] | 183 | } |
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[5d9aa6] | 184 | a->m[0] = p_Mult_q(p, a->m[0], R); |
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[e14e1b0] | 185 | return a; |
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| 186 | } |
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| 187 | |
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[5d9aa6] | 188 | matrix mp_Add(matrix a, matrix b, const ring R) |
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[20118a] | 189 | { |
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| 190 | int k, n = a->nrows, m = a->ncols; |
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| 191 | if ((n != b->nrows) || (m != b->ncols)) |
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| 192 | { |
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| 193 | /* |
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| 194 | * Werror("cannot add %dx%d matrix and %dx%d matrix", |
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| 195 | * m,n,b->cols(),b->rows()); |
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| 196 | */ |
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| 197 | return NULL; |
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| 198 | } |
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| 199 | matrix c = mpNew(n,m); |
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| 200 | for (k=m*n-1; k>=0; k--) |
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[5d9aa6] | 201 | c->m[k] = p_Add_q(p_Copy(a->m[k], R), p_Copy(b->m[k], R), R); |
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[20118a] | 202 | return c; |
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| 203 | } |
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| 204 | |
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[5d9aa6] | 205 | matrix mp_Sub(matrix a, matrix b, const ring R) |
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[20118a] | 206 | { |
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| 207 | int k, n = a->nrows, m = a->ncols; |
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| 208 | if ((n != b->nrows) || (m != b->ncols)) |
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| 209 | { |
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| 210 | /* |
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| 211 | * Werror("cannot sub %dx%d matrix and %dx%d matrix", |
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| 212 | * m,n,b->cols(),b->rows()); |
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| 213 | */ |
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| 214 | return NULL; |
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| 215 | } |
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| 216 | matrix c = mpNew(n,m); |
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| 217 | for (k=m*n-1; k>=0; k--) |
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[5d9aa6] | 218 | c->m[k] = p_Sub(p_Copy(a->m[k], R), p_Copy(b->m[k], R), R); |
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[20118a] | 219 | return c; |
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| 220 | } |
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| 221 | |
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[5d9aa6] | 222 | matrix mp_Mult(matrix a, matrix b, const ring R) |
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[20118a] | 223 | { |
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| 224 | int i, j, k; |
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| 225 | int m = MATROWS(a); |
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| 226 | int p = MATCOLS(a); |
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| 227 | int q = MATCOLS(b); |
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| 228 | |
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| 229 | if (p!=MATROWS(b)) |
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| 230 | { |
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| 231 | /* |
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| 232 | * Werror("cannot multiply %dx%d matrix and %dx%d matrix", |
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| 233 | * m,p,b->rows(),q); |
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| 234 | */ |
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| 235 | return NULL; |
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| 236 | } |
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| 237 | matrix c = mpNew(m,q); |
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| 238 | |
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| 239 | for (i=1; i<=m; i++) |
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| 240 | { |
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| 241 | for (k=1; k<=p; k++) |
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| 242 | { |
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| 243 | poly aik; |
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| 244 | if ((aik=MATELEM(a,i,k))!=NULL) |
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| 245 | { |
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| 246 | for (j=1; j<=q; j++) |
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| 247 | { |
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| 248 | poly bkj; |
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| 249 | if ((bkj=MATELEM(b,k,j))!=NULL) |
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| 250 | { |
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[997e23] | 251 | poly *cij=&(MATELEM(c,i,j)); |
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[5d9aa6] | 252 | poly s = pp_Mult_qq(aik /*MATELEM(a,i,k)*/, bkj/*MATELEM(b,k,j)*/, R); |
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[20118a] | 253 | if (/*MATELEM(c,i,j)*/ (*cij)==NULL) (*cij)=s; |
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[5d9aa6] | 254 | else (*cij) = p_Add_q((*cij) /*MATELEM(c,i,j)*/ ,s, R); |
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[20118a] | 255 | } |
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| 256 | } |
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| 257 | } |
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| 258 | // pNormalize(t); |
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| 259 | // MATELEM(c,i,j) = t; |
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| 260 | } |
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| 261 | } |
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[5d9aa6] | 262 | for(i=m*q-1;i>=0;i--) p_Normalize(c->m[i], R); |
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[20118a] | 263 | return c; |
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| 264 | } |
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| 265 | |
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[5d9aa6] | 266 | matrix mp_Transp(matrix a, const ring R) |
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[20118a] | 267 | { |
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| 268 | int i, j, r = MATROWS(a), c = MATCOLS(a); |
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| 269 | poly *p; |
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| 270 | matrix b = mpNew(c,r); |
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| 271 | |
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| 272 | p = b->m; |
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| 273 | for (i=0; i<c; i++) |
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| 274 | { |
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| 275 | for (j=0; j<r; j++) |
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| 276 | { |
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[5d9aa6] | 277 | if (a->m[j*c+i]!=NULL) *p = p_Copy(a->m[j*c+i], R); |
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[20118a] | 278 | p++; |
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| 279 | } |
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| 280 | } |
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| 281 | return b; |
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| 282 | } |
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| 283 | |
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| 284 | /*2 |
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| 285 | *returns the trace of matrix a |
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| 286 | */ |
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[5d9aa6] | 287 | poly mp_Trace ( matrix a, const ring R) |
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[20118a] | 288 | { |
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| 289 | int i; |
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| 290 | int n = (MATCOLS(a)<MATROWS(a)) ? MATCOLS(a) : MATROWS(a); |
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| 291 | poly t = NULL; |
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| 292 | |
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| 293 | for (i=1; i<=n; i++) |
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[5d9aa6] | 294 | t = p_Add_q(t, p_Copy(MATELEM(a,i,i), R), R); |
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[20118a] | 295 | return t; |
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| 296 | } |
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| 297 | |
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| 298 | /*2 |
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| 299 | *returns the trace of the product of a and b |
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| 300 | */ |
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[3d65be] | 301 | poly TraceOfProd ( matrix a, matrix b, int n, const ring R) |
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[20118a] | 302 | { |
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| 303 | int i, j; |
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| 304 | poly p, t = NULL; |
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| 305 | |
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| 306 | for (i=1; i<=n; i++) |
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| 307 | { |
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| 308 | for (j=1; j<=n; j++) |
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| 309 | { |
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[3d65be] | 310 | p = pp_Mult_qq(MATELEM(a,i,j), MATELEM(b,j,i), R); |
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| 311 | t = p_Add_q(t, p, R); |
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[20118a] | 312 | } |
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| 313 | } |
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| 314 | return t; |
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| 315 | } |
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| 316 | |
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[845729b] | 317 | // #ifndef SIZE_OF_SYSTEM_PAGE |
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| 318 | // #define SIZE_OF_SYSTEM_PAGE 4096 |
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| 319 | // #endif |
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[20118a] | 320 | |
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| 321 | /*2 |
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| 322 | * corresponds to Maple's coeffs: |
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| 323 | * var has to be the number of a variable |
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| 324 | */ |
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[5d9aa6] | 325 | matrix mp_Coeffs (ideal I, int var, const ring R) |
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[20118a] | 326 | { |
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| 327 | poly h,f; |
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| 328 | int l, i, c, m=0; |
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| 329 | matrix co; |
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| 330 | /* look for maximal power m of x_var in I */ |
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| 331 | for (i=IDELEMS(I)-1; i>=0; i--) |
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| 332 | { |
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| 333 | f=I->m[i]; |
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| 334 | while (f!=NULL) |
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| 335 | { |
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[5d9aa6] | 336 | l=p_GetExp(f,var, R); |
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[20118a] | 337 | if (l>m) m=l; |
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| 338 | pIter(f); |
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| 339 | } |
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| 340 | } |
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| 341 | co=mpNew((m+1)*I->rank,IDELEMS(I)); |
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| 342 | /* divide each monomial by a power of x_var, |
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| 343 | * remember the power in l and the component in c*/ |
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| 344 | for (i=IDELEMS(I)-1; i>=0; i--) |
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| 345 | { |
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| 346 | f=I->m[i]; |
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[7d9253] | 347 | I->m[i]=NULL; |
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[20118a] | 348 | while (f!=NULL) |
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| 349 | { |
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[5d9aa6] | 350 | l=p_GetExp(f,var, R); |
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| 351 | p_SetExp(f,var,0, R); |
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| 352 | c=si_max((int)p_GetComp(f, R),1); |
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| 353 | p_SetComp(f,0, R); |
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| 354 | p_Setm(f, R); |
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[20118a] | 355 | /* now add the resulting monomial to co*/ |
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| 356 | h=pNext(f); |
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| 357 | pNext(f)=NULL; |
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| 358 | //MATELEM(co,c*(m+1)-l,i+1) |
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[5d9aa6] | 359 | // =p_Add_q(MATELEM(co,c*(m+1)-l,i+1),f, R); |
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[20118a] | 360 | MATELEM(co,(c-1)*(m+1)+l+1,i+1) |
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[5d9aa6] | 361 | =p_Add_q(MATELEM(co,(c-1)*(m+1)+l+1,i+1),f, R); |
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[20118a] | 362 | /* iterate f*/ |
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| 363 | f=h; |
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| 364 | } |
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| 365 | } |
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[5d9aa6] | 366 | id_Delete(&I, R); |
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[20118a] | 367 | return co; |
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| 368 | } |
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| 369 | |
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| 370 | /*2 |
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| 371 | * given the result c of mpCoeffs(ideal/module i, var) |
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| 372 | * i of rank r |
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| 373 | * build the matrix of the corresponding monomials in m |
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| 374 | */ |
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[5d9aa6] | 375 | void mp_Monomials(matrix c, int r, int var, matrix m, const ring R) |
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[20118a] | 376 | { |
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| 377 | /* clear contents of m*/ |
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| 378 | int k,l; |
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| 379 | for (k=MATROWS(m);k>0;k--) |
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| 380 | { |
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| 381 | for(l=MATCOLS(m);l>0;l--) |
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| 382 | { |
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[5d9aa6] | 383 | p_Delete(&MATELEM(m,k,l), R); |
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[20118a] | 384 | } |
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| 385 | } |
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| 386 | omfreeSize((ADDRESS)m->m,MATROWS(m)*MATCOLS(m)*sizeof(poly)); |
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| 387 | /* allocate monoms in the right size r x MATROWS(c)*/ |
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[503a31] | 388 | m->m=(poly*)omAlloc0(r*MATROWS(c)*sizeof(poly)); |
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[20118a] | 389 | MATROWS(m)=r; |
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| 390 | MATCOLS(m)=MATROWS(c); |
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| 391 | m->rank=r; |
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| 392 | /* the maximal power p of x_var: MATCOLS(m)=r*(p+1) */ |
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| 393 | int p=MATCOLS(m)/r-1; |
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| 394 | /* fill in the powers of x_var=h*/ |
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[5d9aa6] | 395 | poly h=p_One(R); |
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[20118a] | 396 | for(k=r;k>0; k--) |
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| 397 | { |
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[5d9aa6] | 398 | MATELEM(m,k,k*(p+1))=p_One(R); |
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[20118a] | 399 | } |
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| 400 | for(l=p;l>=0; l--) |
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| 401 | { |
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[503a31] | 402 | p_SetExp(h,var,p-l, R); |
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| 403 | p_Setm(h, R); |
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[20118a] | 404 | for(k=r;k>0; k--) |
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| 405 | { |
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[5d9aa6] | 406 | MATELEM(m,k,k*(p+1)-l)=p_Copy(h, R); |
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[20118a] | 407 | } |
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| 408 | } |
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[cf02b22] | 409 | p_Delete(&h, R); |
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[20118a] | 410 | } |
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| 411 | |
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[5d9aa6] | 412 | matrix mp_CoeffProc (poly f, poly vars, const ring R) |
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[20118a] | 413 | { |
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| 414 | assume(vars!=NULL); |
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| 415 | poly sel, h; |
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| 416 | int l, i; |
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| 417 | int pos_of_1 = -1; |
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| 418 | matrix co; |
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| 419 | |
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| 420 | if (f==NULL) |
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| 421 | { |
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| 422 | co = mpNew(2, 1); |
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[5d9aa6] | 423 | MATELEM(co,1,1) = p_One(R); |
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[20118a] | 424 | MATELEM(co,2,1) = NULL; |
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| 425 | return co; |
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| 426 | } |
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[cf02b22] | 427 | sel = mp_Select(f, vars, R); |
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[20118a] | 428 | l = pLength(sel); |
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| 429 | co = mpNew(2, l); |
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[73ad0c] | 430 | |
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[cf02b22] | 431 | if (rHasLocalOrMixedOrdering(R)) |
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[20118a] | 432 | { |
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| 433 | for (i=l; i>=1; i--) |
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| 434 | { |
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| 435 | h = sel; |
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| 436 | pIter(sel); |
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| 437 | pNext(h)=NULL; |
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| 438 | MATELEM(co,1,i) = h; |
---|
| 439 | MATELEM(co,2,i) = NULL; |
---|
[cf02b22] | 440 | if (p_IsConstant(h, R)) pos_of_1 = i; |
---|
[20118a] | 441 | } |
---|
| 442 | } |
---|
| 443 | else |
---|
| 444 | { |
---|
| 445 | for (i=1; i<=l; i++) |
---|
| 446 | { |
---|
| 447 | h = sel; |
---|
| 448 | pIter(sel); |
---|
| 449 | pNext(h)=NULL; |
---|
| 450 | MATELEM(co,1,i) = h; |
---|
| 451 | MATELEM(co,2,i) = NULL; |
---|
[cf02b22] | 452 | if (p_IsConstant(h, R)) pos_of_1 = i; |
---|
[20118a] | 453 | } |
---|
| 454 | } |
---|
| 455 | while (f!=NULL) |
---|
| 456 | { |
---|
| 457 | i = 1; |
---|
| 458 | loop |
---|
| 459 | { |
---|
| 460 | if (i!=pos_of_1) |
---|
| 461 | { |
---|
[cf02b22] | 462 | h = mp_Exdiv(f, MATELEM(co,1,i),vars, R); |
---|
[20118a] | 463 | if (h!=NULL) |
---|
| 464 | { |
---|
[5d9aa6] | 465 | MATELEM(co,2,i) = p_Add_q(MATELEM(co,2,i), h, R); |
---|
[20118a] | 466 | break; |
---|
| 467 | } |
---|
| 468 | } |
---|
| 469 | if (i == l) |
---|
| 470 | { |
---|
| 471 | // check monom 1 last: |
---|
| 472 | if (pos_of_1 != -1) |
---|
| 473 | { |
---|
[cf02b22] | 474 | h = mp_Exdiv(f, MATELEM(co,1,pos_of_1),vars, R); |
---|
[20118a] | 475 | if (h!=NULL) |
---|
| 476 | { |
---|
[5d9aa6] | 477 | MATELEM(co,2,pos_of_1) = p_Add_q(MATELEM(co,2,pos_of_1), h, R); |
---|
[20118a] | 478 | } |
---|
| 479 | } |
---|
| 480 | break; |
---|
| 481 | } |
---|
| 482 | i ++; |
---|
| 483 | } |
---|
| 484 | pIter(f); |
---|
| 485 | } |
---|
| 486 | return co; |
---|
| 487 | } |
---|
| 488 | |
---|
| 489 | /*2 |
---|
| 490 | *exact divisor: let d == x^i*y^j, m is thought to have only one term; |
---|
| 491 | * return m/d iff d divides m, and no x^k*y^l (k>i or l>j) divides m |
---|
| 492 | * consider all variables in vars |
---|
| 493 | */ |
---|
[3d65be] | 494 | static poly mp_Exdiv ( poly m, poly d, poly vars, const ring R) |
---|
[20118a] | 495 | { |
---|
| 496 | int i; |
---|
[3d65be] | 497 | poly h = p_Head(m, R); |
---|
| 498 | for (i=1; i<=rVar(R); i++) |
---|
[20118a] | 499 | { |
---|
[3d65be] | 500 | if (p_GetExp(vars,i, R) > 0) |
---|
[20118a] | 501 | { |
---|
[3d65be] | 502 | if (p_GetExp(d,i, R) != p_GetExp(h,i, R)) |
---|
[20118a] | 503 | { |
---|
[3d65be] | 504 | p_Delete(&h, R); |
---|
[20118a] | 505 | return NULL; |
---|
| 506 | } |
---|
[3d65be] | 507 | p_SetExp(h,i,0, R); |
---|
[20118a] | 508 | } |
---|
| 509 | } |
---|
[3d65be] | 510 | p_Setm(h, R); |
---|
[20118a] | 511 | return h; |
---|
| 512 | } |
---|
| 513 | |
---|
[3d65be] | 514 | void mp_Coef2(poly v, poly mon, matrix *c, matrix *m, const ring R) |
---|
[20118a] | 515 | { |
---|
[503a31] | 516 | poly* s; |
---|
[20118a] | 517 | poly p; |
---|
| 518 | int sl,i,j; |
---|
| 519 | int l=0; |
---|
[3d65be] | 520 | poly sel=mp_Select(v,mon, R); |
---|
[20118a] | 521 | |
---|
[3d65be] | 522 | p_Vec2Polys(sel,&s,&sl, R); |
---|
[20118a] | 523 | for (i=0; i<sl; i++) |
---|
| 524 | l=si_max(l,pLength(s[i])); |
---|
| 525 | *c=mpNew(sl,l); |
---|
| 526 | *m=mpNew(sl,l); |
---|
| 527 | poly h; |
---|
| 528 | int isConst; |
---|
| 529 | for (j=1; j<=sl;j++) |
---|
| 530 | { |
---|
| 531 | p=s[j-1]; |
---|
[3d65be] | 532 | if (p_IsConstant(p, R)) /*p != NULL */ |
---|
[20118a] | 533 | { |
---|
| 534 | isConst=-1; |
---|
| 535 | i=l; |
---|
| 536 | } |
---|
| 537 | else |
---|
| 538 | { |
---|
| 539 | isConst=1; |
---|
| 540 | i=1; |
---|
| 541 | } |
---|
| 542 | while(p!=NULL) |
---|
| 543 | { |
---|
[3d65be] | 544 | h = p_Head(p, R); |
---|
[20118a] | 545 | MATELEM(*m,j,i) = h; |
---|
| 546 | i+=isConst; |
---|
| 547 | p = p->next; |
---|
| 548 | } |
---|
| 549 | } |
---|
| 550 | while (v!=NULL) |
---|
| 551 | { |
---|
| 552 | i = 1; |
---|
[3d65be] | 553 | j = p_GetComp(v, R); |
---|
[20118a] | 554 | loop |
---|
| 555 | { |
---|
| 556 | poly mp=MATELEM(*m,j,i); |
---|
| 557 | if (mp!=NULL) |
---|
| 558 | { |
---|
[3d65be] | 559 | h = mp_Exdiv(v, mp /*MATELEM(*m,j,i)*/, mp, R); |
---|
[20118a] | 560 | if (h!=NULL) |
---|
| 561 | { |
---|
[3d65be] | 562 | p_SetComp(h,0, R); |
---|
| 563 | MATELEM(*c,j,i) = p_Add_q(MATELEM(*c,j,i), h, R); |
---|
[20118a] | 564 | break; |
---|
| 565 | } |
---|
| 566 | } |
---|
| 567 | if (i < l) |
---|
| 568 | i++; |
---|
| 569 | else |
---|
| 570 | break; |
---|
| 571 | } |
---|
| 572 | v = v->next; |
---|
| 573 | } |
---|
| 574 | } |
---|
| 575 | |
---|
| 576 | |
---|
[3d65be] | 577 | BOOLEAN mp_Equal(matrix a, matrix b, const ring R) |
---|
[20118a] | 578 | { |
---|
| 579 | if ((MATCOLS(a)!=MATCOLS(b)) || (MATROWS(a)!=MATROWS(b))) |
---|
| 580 | return FALSE; |
---|
| 581 | int i=MATCOLS(a)*MATROWS(b)-1; |
---|
| 582 | while (i>=0) |
---|
| 583 | { |
---|
| 584 | if (a->m[i]==NULL) |
---|
| 585 | { |
---|
| 586 | if (b->m[i]!=NULL) return FALSE; |
---|
| 587 | } |
---|
| 588 | else |
---|
| 589 | if (b->m[i]==NULL) return FALSE; |
---|
[3d65be] | 590 | else if (p_Cmp(a->m[i],b->m[i], R)!=0) return FALSE; |
---|
[20118a] | 591 | i--; |
---|
| 592 | } |
---|
| 593 | i=MATCOLS(a)*MATROWS(b)-1; |
---|
| 594 | while (i>=0) |
---|
| 595 | { |
---|
| 596 | #if 0 |
---|
[3d65be] | 597 | poly tt=p_Sub(p_Copy(a->m[i], R),p_Copy(b->m[i], R), R); |
---|
[20118a] | 598 | if (tt!=NULL) |
---|
| 599 | { |
---|
[3d65be] | 600 | p_Delete(&tt, R); |
---|
[20118a] | 601 | return FALSE; |
---|
| 602 | } |
---|
| 603 | #else |
---|
[3d65be] | 604 | if(!p_EqualPolys(a->m[i],b->m[i], R)) return FALSE; |
---|
[20118a] | 605 | #endif |
---|
| 606 | i--; |
---|
| 607 | } |
---|
| 608 | return TRUE; |
---|
| 609 | } |
---|
| 610 | |
---|
[5d9aa6] | 611 | static poly minuscopy (poly p, const ring R) |
---|
[20118a] | 612 | { |
---|
| 613 | poly w; |
---|
| 614 | number e; |
---|
[5d9aa6] | 615 | e = n_Init(-1, R); |
---|
| 616 | w = p_Copy(p, R); |
---|
| 617 | p_Mult_nn(w, e, R); |
---|
| 618 | n_Delete(&e, R); |
---|
[20118a] | 619 | return w; |
---|
| 620 | } |
---|
| 621 | |
---|
| 622 | /*2 |
---|
| 623 | * insert a monomial into a list, avoid duplicates |
---|
| 624 | * arguments are destroyed |
---|
| 625 | */ |
---|
[5d9aa6] | 626 | static poly p_Insert(poly p1, poly p2, const ring R) |
---|
[20118a] | 627 | { |
---|
| 628 | poly a1, p, a2, a; |
---|
| 629 | int c; |
---|
| 630 | |
---|
| 631 | if (p1==NULL) return p2; |
---|
| 632 | if (p2==NULL) return p1; |
---|
| 633 | a1 = p1; |
---|
| 634 | a2 = p2; |
---|
[5d9aa6] | 635 | a = p = p_One(R); |
---|
[20118a] | 636 | loop |
---|
| 637 | { |
---|
[cf02b22] | 638 | c = p_Cmp(a1, a2, R); |
---|
[20118a] | 639 | if (c == 1) |
---|
| 640 | { |
---|
| 641 | a = pNext(a) = a1; |
---|
| 642 | pIter(a1); |
---|
| 643 | if (a1==NULL) |
---|
| 644 | { |
---|
| 645 | pNext(a) = a2; |
---|
| 646 | break; |
---|
| 647 | } |
---|
| 648 | } |
---|
| 649 | else if (c == -1) |
---|
| 650 | { |
---|
| 651 | a = pNext(a) = a2; |
---|
| 652 | pIter(a2); |
---|
| 653 | if (a2==NULL) |
---|
| 654 | { |
---|
| 655 | pNext(a) = a1; |
---|
| 656 | break; |
---|
| 657 | } |
---|
| 658 | } |
---|
| 659 | else |
---|
| 660 | { |
---|
[cf02b22] | 661 | p_LmDelete(&a2, R); |
---|
[20118a] | 662 | a = pNext(a) = a1; |
---|
| 663 | pIter(a1); |
---|
| 664 | if (a1==NULL) |
---|
| 665 | { |
---|
| 666 | pNext(a) = a2; |
---|
| 667 | break; |
---|
| 668 | } |
---|
| 669 | else if (a2==NULL) |
---|
| 670 | { |
---|
| 671 | pNext(a) = a1; |
---|
| 672 | break; |
---|
| 673 | } |
---|
| 674 | } |
---|
| 675 | } |
---|
[cf02b22] | 676 | p_LmDelete(&p, R); |
---|
[20118a] | 677 | return p; |
---|
| 678 | } |
---|
| 679 | |
---|
| 680 | /*2 |
---|
| 681 | *if what == xy the result is the list of all different power products |
---|
| 682 | * x^i*y^j (i, j >= 0) that appear in fro |
---|
| 683 | */ |
---|
[3d65be] | 684 | static poly mp_Select (poly fro, poly what, const ring R) |
---|
[20118a] | 685 | { |
---|
| 686 | int i; |
---|
| 687 | poly h, res; |
---|
| 688 | res = NULL; |
---|
| 689 | while (fro!=NULL) |
---|
| 690 | { |
---|
[3d65be] | 691 | h = p_One(R); |
---|
| 692 | for (i=1; i<=rVar(R); i++) |
---|
| 693 | p_SetExp(h,i, p_GetExp(fro,i, R) * p_GetExp(what, i, R), R); |
---|
| 694 | p_SetComp(h, p_GetComp(fro, R), R); |
---|
| 695 | p_Setm(h, R); |
---|
| 696 | res = p_Insert(h, res, R); |
---|
[20118a] | 697 | fro = fro->next; |
---|
| 698 | } |
---|
| 699 | return res; |
---|
| 700 | } |
---|
| 701 | |
---|
| 702 | /* |
---|
| 703 | *static void ppp(matrix a) |
---|
| 704 | *{ |
---|
| 705 | * int j,i,r=a->nrows,c=a->ncols; |
---|
| 706 | * for(j=1;j<=r;j++) |
---|
| 707 | * { |
---|
| 708 | * for(i=1;i<=c;i++) |
---|
| 709 | * { |
---|
| 710 | * if(MATELEM(a,j,i)!=NULL) Print("X"); |
---|
| 711 | * else Print("0"); |
---|
| 712 | * } |
---|
| 713 | * Print("\n"); |
---|
| 714 | * } |
---|
| 715 | *} |
---|
| 716 | */ |
---|
| 717 | |
---|
[3d65be] | 718 | static void mp_PartClean(matrix a, int lr, int lc, const ring R) |
---|
[20118a] | 719 | { |
---|
| 720 | poly *q1; |
---|
| 721 | int i,j; |
---|
| 722 | |
---|
| 723 | for (i=lr-1;i>=0;i--) |
---|
| 724 | { |
---|
| 725 | q1 = &(a->m)[i*a->ncols]; |
---|
[3d65be] | 726 | for (j=lc-1;j>=0;j--) if(q1[j]) p_Delete(&q1[j], R); |
---|
[20118a] | 727 | } |
---|
| 728 | } |
---|
| 729 | |
---|
[2d2e40] | 730 | static void mp_FinalClean(matrix a, const ring) |
---|
[20118a] | 731 | { |
---|
| 732 | omFreeSize((ADDRESS)a->m,a->nrows*a->ncols*sizeof(poly)); |
---|
[73ad0c] | 733 | omFreeBin((ADDRESS)a, sip_sideal_bin); |
---|
[20118a] | 734 | } |
---|
| 735 | |
---|
[3d65be] | 736 | BOOLEAN mp_IsDiagUnit(matrix U, const ring R) |
---|
[20118a] | 737 | { |
---|
| 738 | if(MATROWS(U)!=MATCOLS(U)) |
---|
| 739 | return FALSE; |
---|
| 740 | for(int i=MATCOLS(U);i>=1;i--) |
---|
| 741 | { |
---|
| 742 | for(int j=MATCOLS(U); j>=1; j--) |
---|
| 743 | { |
---|
| 744 | if (i==j) |
---|
| 745 | { |
---|
[3d65be] | 746 | if (!p_IsUnit(MATELEM(U,i,i), R)) return FALSE; |
---|
[20118a] | 747 | } |
---|
| 748 | else if (MATELEM(U,i,j)!=NULL) return FALSE; |
---|
| 749 | } |
---|
| 750 | } |
---|
| 751 | return TRUE; |
---|
| 752 | } |
---|
| 753 | |
---|
[5d9aa6] | 754 | void iiWriteMatrix(matrix im, const char *n, int dim, const ring r, int spaces) |
---|
[20118a] | 755 | { |
---|
| 756 | int i,ii = MATROWS(im)-1; |
---|
| 757 | int j,jj = MATCOLS(im)-1; |
---|
| 758 | poly *pp = im->m; |
---|
| 759 | |
---|
| 760 | for (i=0; i<=ii; i++) |
---|
| 761 | { |
---|
| 762 | for (j=0; j<=jj; j++) |
---|
| 763 | { |
---|
| 764 | if (spaces>0) |
---|
| 765 | Print("%-*.*s",spaces,spaces," "); |
---|
| 766 | if (dim == 2) Print("%s[%u,%u]=",n,i+1,j+1); |
---|
| 767 | else if (dim == 1) Print("%s[%u]=",n,j+1); |
---|
| 768 | else if (dim == 0) Print("%s=",n); |
---|
[5d9aa6] | 769 | if ((i<ii)||(j<jj)) p_Write(*pp++, r); |
---|
| 770 | else p_Write0(*pp, r); |
---|
[20118a] | 771 | } |
---|
| 772 | } |
---|
| 773 | } |
---|
| 774 | |
---|
[cf02b22] | 775 | char * iiStringMatrix(matrix im, int dim, const ring r, char ch) |
---|
[20118a] | 776 | { |
---|
| 777 | int i,ii = MATROWS(im); |
---|
| 778 | int j,jj = MATCOLS(im); |
---|
| 779 | poly *pp = im->m; |
---|
| 780 | char *s=StringSetS(""); |
---|
| 781 | |
---|
| 782 | for (i=0; i<ii; i++) |
---|
| 783 | { |
---|
| 784 | for (j=0; j<jj; j++) |
---|
| 785 | { |
---|
[5d9aa6] | 786 | p_String0(*pp++, r); |
---|
[20118a] | 787 | s=StringAppend("%c",ch); |
---|
| 788 | if (dim > 1) s = StringAppendS("\n"); |
---|
| 789 | } |
---|
| 790 | } |
---|
| 791 | s[strlen(s)- (dim > 1 ? 2 : 1)]='\0'; |
---|
| 792 | return s; |
---|
| 793 | } |
---|
| 794 | |
---|
[5d9aa6] | 795 | void mp_Delete(matrix* a, const ring r) |
---|
[20118a] | 796 | { |
---|
| 797 | id_Delete((ideal *) a, r); |
---|
| 798 | } |
---|
[441a2e] | 799 | |
---|
| 800 | /* |
---|
| 801 | * C++ classes for Bareiss algorithm |
---|
| 802 | */ |
---|
| 803 | class row_col_weight |
---|
| 804 | { |
---|
| 805 | private: |
---|
| 806 | int ym, yn; |
---|
| 807 | public: |
---|
| 808 | float *wrow, *wcol; |
---|
| 809 | row_col_weight() : ym(0) {} |
---|
| 810 | row_col_weight(int, int); |
---|
| 811 | ~row_col_weight(); |
---|
| 812 | }; |
---|
| 813 | |
---|
[bf6a4d] | 814 | row_col_weight::row_col_weight(int i, int j) |
---|
| 815 | { |
---|
| 816 | ym = i; |
---|
| 817 | yn = j; |
---|
| 818 | wrow = (float *)omAlloc(i*sizeof(float)); |
---|
| 819 | wcol = (float *)omAlloc(j*sizeof(float)); |
---|
| 820 | } |
---|
| 821 | row_col_weight::~row_col_weight() |
---|
| 822 | { |
---|
| 823 | if (ym!=0) |
---|
| 824 | { |
---|
| 825 | omFreeSize((ADDRESS)wcol, yn*sizeof(float)); |
---|
| 826 | omFreeSize((ADDRESS)wrow, ym*sizeof(float)); |
---|
| 827 | } |
---|
| 828 | } |
---|
| 829 | |
---|
[441a2e] | 830 | /*2 |
---|
| 831 | * a submatrix M of a matrix X[m,n]: |
---|
| 832 | * 0 <= i < s_m <= a_m |
---|
| 833 | * 0 <= j < s_n <= a_n |
---|
| 834 | * M = ( Xarray[qrow[i],qcol[j]] ) |
---|
| 835 | * if a_m = a_n and s_m = s_n |
---|
| 836 | * det(X) = sign*div^(s_m-1)*det(M) |
---|
| 837 | * resticted pivot for elimination |
---|
| 838 | * 0 <= j < piv_s |
---|
| 839 | */ |
---|
| 840 | class mp_permmatrix |
---|
| 841 | { |
---|
| 842 | private: |
---|
| 843 | int a_m, a_n, s_m, s_n, sign, piv_s; |
---|
| 844 | int *qrow, *qcol; |
---|
| 845 | poly *Xarray; |
---|
[bf6a4d] | 846 | ring _R; |
---|
[441a2e] | 847 | void mpInitMat(); |
---|
[bf6a4d] | 848 | poly * mpRowAdr(int r) |
---|
| 849 | { return &(Xarray[a_n*qrow[r]]); } |
---|
| 850 | poly * mpColAdr(int c) |
---|
| 851 | { return &(Xarray[qcol[c]]); } |
---|
[441a2e] | 852 | void mpRowWeight(float *); |
---|
| 853 | void mpColWeight(float *); |
---|
| 854 | void mpRowSwap(int, int); |
---|
| 855 | void mpColSwap(int, int); |
---|
| 856 | public: |
---|
| 857 | mp_permmatrix() : a_m(0) {} |
---|
[bf6a4d] | 858 | mp_permmatrix(matrix, ring); |
---|
[441a2e] | 859 | mp_permmatrix(mp_permmatrix *); |
---|
| 860 | ~mp_permmatrix(); |
---|
| 861 | int mpGetRow(); |
---|
| 862 | int mpGetCol(); |
---|
[bf6a4d] | 863 | int mpGetRdim() { return s_m; } |
---|
| 864 | int mpGetCdim() { return s_n; } |
---|
| 865 | int mpGetSign() { return sign; } |
---|
[441a2e] | 866 | void mpSetSearch(int s); |
---|
[bf6a4d] | 867 | void mpSaveArray() { Xarray = NULL; } |
---|
[441a2e] | 868 | poly mpGetElem(int, int); |
---|
| 869 | void mpSetElem(poly, int, int); |
---|
| 870 | void mpDelElem(int, int); |
---|
| 871 | void mpElimBareiss(poly); |
---|
| 872 | int mpPivotBareiss(row_col_weight *); |
---|
| 873 | int mpPivotRow(row_col_weight *, int); |
---|
| 874 | void mpToIntvec(intvec *); |
---|
| 875 | void mpRowReorder(); |
---|
| 876 | void mpColReorder(); |
---|
| 877 | }; |
---|
[bf6a4d] | 878 | mp_permmatrix::mp_permmatrix(matrix A, ring R) : sign(1) |
---|
| 879 | { |
---|
| 880 | a_m = A->nrows; |
---|
| 881 | a_n = A->ncols; |
---|
| 882 | this->mpInitMat(); |
---|
| 883 | Xarray = A->m; |
---|
| 884 | _R=R; |
---|
| 885 | } |
---|
| 886 | |
---|
| 887 | mp_permmatrix::mp_permmatrix(mp_permmatrix *M) |
---|
| 888 | { |
---|
| 889 | poly p, *athis, *aM; |
---|
| 890 | int i, j; |
---|
| 891 | |
---|
| 892 | _R=M->_R; |
---|
| 893 | a_m = M->s_m; |
---|
| 894 | a_n = M->s_n; |
---|
| 895 | sign = M->sign; |
---|
| 896 | this->mpInitMat(); |
---|
| 897 | Xarray = (poly *)omAlloc0(a_m*a_n*sizeof(poly)); |
---|
| 898 | for (i=a_m-1; i>=0; i--) |
---|
| 899 | { |
---|
| 900 | athis = this->mpRowAdr(i); |
---|
| 901 | aM = M->mpRowAdr(i); |
---|
| 902 | for (j=a_n-1; j>=0; j--) |
---|
| 903 | { |
---|
| 904 | p = aM[M->qcol[j]]; |
---|
| 905 | if (p) |
---|
| 906 | { |
---|
| 907 | athis[j] = p_Copy(p,_R); |
---|
| 908 | } |
---|
| 909 | } |
---|
| 910 | } |
---|
| 911 | } |
---|
| 912 | |
---|
| 913 | mp_permmatrix::~mp_permmatrix() |
---|
| 914 | { |
---|
| 915 | int k; |
---|
| 916 | |
---|
| 917 | if (a_m != 0) |
---|
| 918 | { |
---|
| 919 | omFreeSize((ADDRESS)qrow,a_m*sizeof(int)); |
---|
| 920 | omFreeSize((ADDRESS)qcol,a_n*sizeof(int)); |
---|
| 921 | if (Xarray != NULL) |
---|
| 922 | { |
---|
| 923 | for (k=a_m*a_n-1; k>=0; k--) |
---|
| 924 | p_Delete(&Xarray[k],_R); |
---|
| 925 | omFreeSize((ADDRESS)Xarray,a_m*a_n*sizeof(poly)); |
---|
| 926 | } |
---|
| 927 | } |
---|
| 928 | } |
---|
| 929 | |
---|
| 930 | |
---|
| 931 | static float mp_PolyWeight(poly p, const ring r); |
---|
| 932 | void mp_permmatrix::mpColWeight(float *wcol) |
---|
| 933 | { |
---|
| 934 | poly p, *a; |
---|
| 935 | int i, j; |
---|
| 936 | float count; |
---|
| 937 | |
---|
| 938 | for (j=s_n; j>=0; j--) |
---|
| 939 | { |
---|
| 940 | a = this->mpColAdr(j); |
---|
| 941 | count = 0.0; |
---|
| 942 | for(i=s_m; i>=0; i--) |
---|
| 943 | { |
---|
| 944 | p = a[a_n*qrow[i]]; |
---|
| 945 | if (p) |
---|
| 946 | count += mp_PolyWeight(p,_R); |
---|
| 947 | } |
---|
| 948 | wcol[j] = count; |
---|
| 949 | } |
---|
| 950 | } |
---|
| 951 | void mp_permmatrix::mpRowWeight(float *wrow) |
---|
| 952 | { |
---|
| 953 | poly p, *a; |
---|
| 954 | int i, j; |
---|
| 955 | float count; |
---|
| 956 | |
---|
| 957 | for (i=s_m; i>=0; i--) |
---|
| 958 | { |
---|
| 959 | a = this->mpRowAdr(i); |
---|
| 960 | count = 0.0; |
---|
| 961 | for(j=s_n; j>=0; j--) |
---|
| 962 | { |
---|
| 963 | p = a[qcol[j]]; |
---|
| 964 | if (p) |
---|
| 965 | count += mp_PolyWeight(p,_R); |
---|
| 966 | } |
---|
| 967 | wrow[i] = count; |
---|
| 968 | } |
---|
| 969 | } |
---|
| 970 | |
---|
| 971 | void mp_permmatrix::mpRowSwap(int i1, int i2) |
---|
| 972 | { |
---|
| 973 | poly p, *a1, *a2; |
---|
| 974 | int j; |
---|
| 975 | |
---|
| 976 | a1 = &(Xarray[a_n*i1]); |
---|
| 977 | a2 = &(Xarray[a_n*i2]); |
---|
| 978 | for (j=a_n-1; j>= 0; j--) |
---|
| 979 | { |
---|
| 980 | p = a1[j]; |
---|
| 981 | a1[j] = a2[j]; |
---|
| 982 | a2[j] = p; |
---|
| 983 | } |
---|
| 984 | } |
---|
| 985 | |
---|
| 986 | void mp_permmatrix::mpColSwap(int j1, int j2) |
---|
| 987 | { |
---|
| 988 | poly p, *a1, *a2; |
---|
| 989 | int i, k = a_n*a_m; |
---|
| 990 | |
---|
| 991 | a1 = &(Xarray[j1]); |
---|
| 992 | a2 = &(Xarray[j2]); |
---|
| 993 | for (i=0; i< k; i+=a_n) |
---|
| 994 | { |
---|
| 995 | p = a1[i]; |
---|
| 996 | a1[i] = a2[i]; |
---|
| 997 | a2[i] = p; |
---|
| 998 | } |
---|
| 999 | } |
---|
| 1000 | void mp_permmatrix::mpInitMat() |
---|
| 1001 | { |
---|
| 1002 | int k; |
---|
| 1003 | |
---|
| 1004 | s_m = a_m; |
---|
| 1005 | s_n = a_n; |
---|
| 1006 | piv_s = 0; |
---|
| 1007 | qrow = (int *)omAlloc(a_m*sizeof(int)); |
---|
| 1008 | qcol = (int *)omAlloc(a_n*sizeof(int)); |
---|
| 1009 | for (k=a_m-1; k>=0; k--) qrow[k] = k; |
---|
| 1010 | for (k=a_n-1; k>=0; k--) qcol[k] = k; |
---|
| 1011 | } |
---|
| 1012 | |
---|
| 1013 | void mp_permmatrix::mpColReorder() |
---|
| 1014 | { |
---|
| 1015 | int k, j, j1, j2; |
---|
| 1016 | |
---|
| 1017 | if (a_n > a_m) |
---|
| 1018 | k = a_n - a_m; |
---|
| 1019 | else |
---|
| 1020 | k = 0; |
---|
| 1021 | for (j=a_n-1; j>=k; j--) |
---|
| 1022 | { |
---|
| 1023 | j1 = qcol[j]; |
---|
| 1024 | if (j1 != j) |
---|
| 1025 | { |
---|
| 1026 | this->mpColSwap(j1, j); |
---|
| 1027 | j2 = 0; |
---|
| 1028 | while (qcol[j2] != j) j2++; |
---|
| 1029 | qcol[j2] = j1; |
---|
| 1030 | } |
---|
| 1031 | } |
---|
| 1032 | } |
---|
| 1033 | |
---|
| 1034 | void mp_permmatrix::mpRowReorder() |
---|
| 1035 | { |
---|
| 1036 | int k, i, i1, i2; |
---|
[441a2e] | 1037 | |
---|
[bf6a4d] | 1038 | if (a_m > a_n) |
---|
| 1039 | k = a_m - a_n; |
---|
| 1040 | else |
---|
| 1041 | k = 0; |
---|
| 1042 | for (i=a_m-1; i>=k; i--) |
---|
| 1043 | { |
---|
| 1044 | i1 = qrow[i]; |
---|
| 1045 | if (i1 != i) |
---|
| 1046 | { |
---|
| 1047 | this->mpRowSwap(i1, i); |
---|
| 1048 | i2 = 0; |
---|
| 1049 | while (qrow[i2] != i) i2++; |
---|
| 1050 | qrow[i2] = i1; |
---|
| 1051 | } |
---|
| 1052 | } |
---|
| 1053 | } |
---|
| 1054 | |
---|
| 1055 | /* |
---|
| 1056 | * perform replacement for pivot strategy in Bareiss algorithm |
---|
| 1057 | * change sign of determinant |
---|
| 1058 | */ |
---|
| 1059 | static void mpReplace(int j, int n, int &sign, int *perm) |
---|
| 1060 | { |
---|
| 1061 | int k; |
---|
| 1062 | |
---|
| 1063 | if (j != n) |
---|
| 1064 | { |
---|
| 1065 | k = perm[n]; |
---|
| 1066 | perm[n] = perm[j]; |
---|
| 1067 | perm[j] = k; |
---|
| 1068 | sign = -sign; |
---|
| 1069 | } |
---|
| 1070 | } |
---|
| 1071 | /*2 |
---|
| 1072 | * pivot strategy for Bareiss algorithm |
---|
| 1073 | */ |
---|
| 1074 | int mp_permmatrix::mpPivotBareiss(row_col_weight *C) |
---|
| 1075 | { |
---|
| 1076 | poly p, *a; |
---|
| 1077 | int i, j, iopt, jopt; |
---|
| 1078 | float sum, f1, f2, fo, r, ro, lp; |
---|
| 1079 | float *dr = C->wrow, *dc = C->wcol; |
---|
| 1080 | |
---|
| 1081 | fo = 1.0e20; |
---|
| 1082 | ro = 0.0; |
---|
| 1083 | iopt = jopt = -1; |
---|
| 1084 | |
---|
| 1085 | s_n--; |
---|
| 1086 | s_m--; |
---|
| 1087 | if (s_m == 0) |
---|
| 1088 | return 0; |
---|
| 1089 | if (s_n == 0) |
---|
| 1090 | { |
---|
| 1091 | for(i=s_m; i>=0; i--) |
---|
| 1092 | { |
---|
| 1093 | p = this->mpRowAdr(i)[qcol[0]]; |
---|
| 1094 | if (p) |
---|
| 1095 | { |
---|
| 1096 | f1 = mp_PolyWeight(p,_R); |
---|
| 1097 | if (f1 < fo) |
---|
| 1098 | { |
---|
| 1099 | fo = f1; |
---|
| 1100 | if (iopt >= 0) |
---|
| 1101 | p_Delete(&(this->mpRowAdr(iopt)[qcol[0]]),_R); |
---|
| 1102 | iopt = i; |
---|
| 1103 | } |
---|
| 1104 | else |
---|
| 1105 | p_Delete(&(this->mpRowAdr(i)[qcol[0]]),_R); |
---|
| 1106 | } |
---|
| 1107 | } |
---|
| 1108 | if (iopt >= 0) |
---|
| 1109 | mpReplace(iopt, s_m, sign, qrow); |
---|
| 1110 | return 0; |
---|
| 1111 | } |
---|
| 1112 | this->mpRowWeight(dr); |
---|
| 1113 | this->mpColWeight(dc); |
---|
| 1114 | sum = 0.0; |
---|
| 1115 | for(i=s_m; i>=0; i--) |
---|
| 1116 | sum += dr[i]; |
---|
| 1117 | for(i=s_m; i>=0; i--) |
---|
| 1118 | { |
---|
| 1119 | r = dr[i]; |
---|
| 1120 | a = this->mpRowAdr(i); |
---|
| 1121 | for(j=s_n; j>=0; j--) |
---|
| 1122 | { |
---|
| 1123 | p = a[qcol[j]]; |
---|
| 1124 | if (p) |
---|
| 1125 | { |
---|
| 1126 | lp = mp_PolyWeight(p,_R); |
---|
| 1127 | ro = r - lp; |
---|
| 1128 | f1 = ro * (dc[j]-lp); |
---|
| 1129 | if (f1 != 0.0) |
---|
| 1130 | { |
---|
| 1131 | f2 = lp * (sum - ro - dc[j]); |
---|
| 1132 | f2 += f1; |
---|
| 1133 | } |
---|
| 1134 | else |
---|
| 1135 | f2 = lp-r-dc[j]; |
---|
| 1136 | if (f2 < fo) |
---|
| 1137 | { |
---|
| 1138 | fo = f2; |
---|
| 1139 | iopt = i; |
---|
| 1140 | jopt = j; |
---|
| 1141 | } |
---|
| 1142 | } |
---|
| 1143 | } |
---|
| 1144 | } |
---|
| 1145 | if (iopt < 0) |
---|
| 1146 | return 0; |
---|
| 1147 | mpReplace(iopt, s_m, sign, qrow); |
---|
| 1148 | mpReplace(jopt, s_n, sign, qcol); |
---|
| 1149 | return 1; |
---|
| 1150 | } |
---|
| 1151 | poly mp_permmatrix::mpGetElem(int r, int c) |
---|
| 1152 | { |
---|
| 1153 | return Xarray[a_n*qrow[r]+qcol[c]]; |
---|
| 1154 | } |
---|
| 1155 | |
---|
| 1156 | /* |
---|
| 1157 | * the Bareiss-type elimination with division by div (div != NULL) |
---|
| 1158 | */ |
---|
| 1159 | void mp_permmatrix::mpElimBareiss(poly div) |
---|
| 1160 | { |
---|
| 1161 | poly piv, elim, q1, q2, *ap, *a; |
---|
| 1162 | int i, j, jj; |
---|
| 1163 | |
---|
| 1164 | ap = this->mpRowAdr(s_m); |
---|
| 1165 | piv = ap[qcol[s_n]]; |
---|
| 1166 | for(i=s_m-1; i>=0; i--) |
---|
| 1167 | { |
---|
| 1168 | a = this->mpRowAdr(i); |
---|
| 1169 | elim = a[qcol[s_n]]; |
---|
| 1170 | if (elim != NULL) |
---|
| 1171 | { |
---|
| 1172 | elim = p_Neg(elim,_R); |
---|
| 1173 | for (j=s_n-1; j>=0; j--) |
---|
| 1174 | { |
---|
| 1175 | q2 = NULL; |
---|
| 1176 | jj = qcol[j]; |
---|
| 1177 | if (ap[jj] != NULL) |
---|
| 1178 | { |
---|
| 1179 | q2 = SM_MULT(ap[jj], elim, div,_R); |
---|
| 1180 | if (a[jj] != NULL) |
---|
| 1181 | { |
---|
| 1182 | q1 = SM_MULT(a[jj], piv, div,_R); |
---|
| 1183 | p_Delete(&a[jj],_R); |
---|
| 1184 | q2 = p_Add_q(q2, q1, _R); |
---|
| 1185 | } |
---|
| 1186 | } |
---|
| 1187 | else if (a[jj] != NULL) |
---|
| 1188 | { |
---|
| 1189 | q2 = SM_MULT(a[jj], piv, div, _R); |
---|
| 1190 | } |
---|
| 1191 | if ((q2!=NULL) && div) |
---|
| 1192 | SM_DIV(q2, div, _R); |
---|
| 1193 | a[jj] = q2; |
---|
| 1194 | } |
---|
| 1195 | p_Delete(&a[qcol[s_n]], _R); |
---|
| 1196 | } |
---|
| 1197 | else |
---|
| 1198 | { |
---|
| 1199 | for (j=s_n-1; j>=0; j--) |
---|
| 1200 | { |
---|
| 1201 | jj = qcol[j]; |
---|
| 1202 | if (a[jj] != NULL) |
---|
| 1203 | { |
---|
| 1204 | q2 = SM_MULT(a[jj], piv, div, _R); |
---|
| 1205 | p_Delete(&a[jj], _R); |
---|
| 1206 | if (div) |
---|
| 1207 | SM_DIV(q2, div, _R); |
---|
| 1208 | a[jj] = q2; |
---|
| 1209 | } |
---|
| 1210 | } |
---|
| 1211 | } |
---|
| 1212 | } |
---|
| 1213 | } |
---|
[441a2e] | 1214 | /* |
---|
| 1215 | * weigth of a polynomial, for pivot strategy |
---|
| 1216 | */ |
---|
| 1217 | static float mp_PolyWeight(poly p, const ring r) |
---|
| 1218 | { |
---|
| 1219 | int i; |
---|
| 1220 | float res; |
---|
| 1221 | |
---|
| 1222 | if (pNext(p) == NULL) |
---|
| 1223 | { |
---|
| 1224 | res = (float)n_Size(pGetCoeff(p),r->cf); |
---|
| 1225 | for (i=rVar(r);i>0;i--) |
---|
| 1226 | { |
---|
| 1227 | if(p_GetExp(p,i,r)!=0) |
---|
| 1228 | { |
---|
| 1229 | res += 2.0; |
---|
| 1230 | break; |
---|
| 1231 | } |
---|
| 1232 | } |
---|
| 1233 | } |
---|
| 1234 | else |
---|
| 1235 | { |
---|
| 1236 | res = 0.0; |
---|
| 1237 | do |
---|
| 1238 | { |
---|
| 1239 | res += (float)n_Size(pGetCoeff(p),r->cf)+2.0; |
---|
| 1240 | pIter(p); |
---|
| 1241 | } |
---|
| 1242 | while (p); |
---|
| 1243 | } |
---|
| 1244 | return res; |
---|
| 1245 | } |
---|
| 1246 | /* |
---|
| 1247 | * find best row |
---|
| 1248 | */ |
---|
| 1249 | static int mp_PivBar(matrix a, int lr, int lc, const ring r) |
---|
| 1250 | { |
---|
| 1251 | float f1, f2; |
---|
| 1252 | poly *q1; |
---|
| 1253 | int i,j,io; |
---|
| 1254 | |
---|
| 1255 | io = -1; |
---|
| 1256 | f1 = 1.0e30; |
---|
| 1257 | for (i=lr-1;i>=0;i--) |
---|
| 1258 | { |
---|
| 1259 | q1 = &(a->m)[i*a->ncols]; |
---|
| 1260 | f2 = 0.0; |
---|
| 1261 | for (j=lc-1;j>=0;j--) |
---|
| 1262 | { |
---|
| 1263 | if (q1[j]!=NULL) |
---|
| 1264 | f2 += mp_PolyWeight(q1[j],r); |
---|
| 1265 | } |
---|
| 1266 | if ((f2!=0.0) && (f2<f1)) |
---|
| 1267 | { |
---|
| 1268 | f1 = f2; |
---|
| 1269 | io = i; |
---|
| 1270 | } |
---|
| 1271 | } |
---|
| 1272 | if (io<0) return 0; |
---|
| 1273 | else return io+1; |
---|
| 1274 | } |
---|
| 1275 | |
---|
| 1276 | static void mpSwapRow(matrix a, int pos, int lr, int lc) |
---|
| 1277 | { |
---|
| 1278 | poly sw; |
---|
| 1279 | int j; |
---|
| 1280 | poly* a2 = a->m; |
---|
| 1281 | poly* a1 = &a2[a->ncols*(pos-1)]; |
---|
| 1282 | |
---|
| 1283 | a2 = &a2[a->ncols*(lr-1)]; |
---|
| 1284 | for (j=lc-1; j>=0; j--) |
---|
| 1285 | { |
---|
| 1286 | sw = a1[j]; |
---|
| 1287 | a1[j] = a2[j]; |
---|
| 1288 | a2[j] = sw; |
---|
| 1289 | } |
---|
| 1290 | } |
---|
| 1291 | |
---|
| 1292 | /*2 |
---|
| 1293 | * prepare one step of 'Bareiss' algorithm |
---|
| 1294 | * for application in minor |
---|
| 1295 | */ |
---|
| 1296 | static int mp_PrepareRow (matrix a, int lr, int lc, const ring R) |
---|
| 1297 | { |
---|
| 1298 | int r; |
---|
| 1299 | |
---|
| 1300 | r = mp_PivBar(a,lr,lc,R); |
---|
| 1301 | if(r==0) return 0; |
---|
| 1302 | if(r<lr) mpSwapRow(a, r, lr, lc); |
---|
| 1303 | return 1; |
---|
| 1304 | } |
---|
| 1305 | |
---|
| 1306 | /* |
---|
| 1307 | * find pivot in the last row |
---|
| 1308 | */ |
---|
| 1309 | static int mp_PivRow(matrix a, int lr, int lc, const ring r) |
---|
| 1310 | { |
---|
| 1311 | float f1, f2; |
---|
| 1312 | poly *q1; |
---|
| 1313 | int j,jo; |
---|
| 1314 | |
---|
| 1315 | jo = -1; |
---|
| 1316 | f1 = 1.0e30; |
---|
| 1317 | q1 = &(a->m)[(lr-1)*a->ncols]; |
---|
| 1318 | for (j=lc-1;j>=0;j--) |
---|
| 1319 | { |
---|
| 1320 | if (q1[j]!=NULL) |
---|
| 1321 | { |
---|
| 1322 | f2 = mp_PolyWeight(q1[j],r); |
---|
| 1323 | if (f2<f1) |
---|
| 1324 | { |
---|
| 1325 | f1 = f2; |
---|
| 1326 | jo = j; |
---|
| 1327 | } |
---|
| 1328 | } |
---|
| 1329 | } |
---|
| 1330 | if (jo<0) return 0; |
---|
| 1331 | else return jo+1; |
---|
| 1332 | } |
---|
| 1333 | |
---|
| 1334 | static void mpSwapCol(matrix a, int pos, int lr, int lc) |
---|
| 1335 | { |
---|
| 1336 | poly sw; |
---|
| 1337 | int j; |
---|
| 1338 | poly* a2 = a->m; |
---|
| 1339 | poly* a1 = &a2[pos-1]; |
---|
| 1340 | |
---|
| 1341 | a2 = &a2[lc-1]; |
---|
| 1342 | for (j=a->ncols*(lr-1); j>=0; j-=a->ncols) |
---|
| 1343 | { |
---|
| 1344 | sw = a1[j]; |
---|
| 1345 | a1[j] = a2[j]; |
---|
| 1346 | a2[j] = sw; |
---|
| 1347 | } |
---|
| 1348 | } |
---|
| 1349 | |
---|
| 1350 | /*2 |
---|
| 1351 | * prepare one step of 'Bareiss' algorithm |
---|
| 1352 | * for application in minor |
---|
| 1353 | */ |
---|
| 1354 | static int mp_PreparePiv (matrix a, int lr, int lc,const ring r) |
---|
| 1355 | { |
---|
| 1356 | int c; |
---|
| 1357 | |
---|
| 1358 | c = mp_PivRow(a, lr, lc,r); |
---|
| 1359 | if(c==0) return 0; |
---|
| 1360 | if(c<lc) mpSwapCol(a, c, lr, lc); |
---|
| 1361 | return 1; |
---|
| 1362 | } |
---|
| 1363 | |
---|
| 1364 | static inline BOOLEAN smSmaller(poly a, poly b) |
---|
| 1365 | { |
---|
| 1366 | loop |
---|
| 1367 | { |
---|
| 1368 | pIter(b); |
---|
| 1369 | if (b == NULL) return TRUE; |
---|
| 1370 | pIter(a); |
---|
| 1371 | if (a == NULL) return FALSE; |
---|
| 1372 | } |
---|
| 1373 | } |
---|
| 1374 | |
---|
| 1375 | static BOOLEAN sm_IsNegQuot(poly a, const poly b, const poly c, const ring R) |
---|
| 1376 | { |
---|
| 1377 | if (p_LmDivisibleByNoComp(c, b, R)) |
---|
| 1378 | { |
---|
| 1379 | p_ExpVectorDiff(a, b, c, R); |
---|
| 1380 | // Hmm: here used to be a pSetm(a): but it is unnecessary, |
---|
| 1381 | // if b and c are correct |
---|
| 1382 | return FALSE; |
---|
| 1383 | } |
---|
| 1384 | else |
---|
| 1385 | { |
---|
| 1386 | int i; |
---|
| 1387 | for (i=rVar(R); i>0; i--) |
---|
| 1388 | { |
---|
| 1389 | if(p_GetExp(c,i,R) > p_GetExp(b,i,R)) |
---|
| 1390 | p_SetExp(a,i,p_GetExp(c,i,R)-p_GetExp(b,i,R),R); |
---|
| 1391 | else |
---|
| 1392 | p_SetExp(a,i,0,R); |
---|
| 1393 | } |
---|
| 1394 | // here we actually might need a pSetm, if a is to be used in |
---|
| 1395 | // comparisons |
---|
| 1396 | return TRUE; |
---|
| 1397 | } |
---|
| 1398 | } |
---|
| 1399 | |
---|
| 1400 | static void mp_ElimBar(matrix a0, matrix re, poly div, int lr, int lc, const ring R) |
---|
| 1401 | { |
---|
| 1402 | int r=lr-1, c=lc-1; |
---|
| 1403 | poly *b = a0->m, *x = re->m; |
---|
| 1404 | poly piv, elim, q1, q2, *ap, *a, *q; |
---|
| 1405 | int i, j; |
---|
| 1406 | |
---|
| 1407 | ap = &b[r*a0->ncols]; |
---|
| 1408 | piv = ap[c]; |
---|
| 1409 | for(j=c-1; j>=0; j--) |
---|
| 1410 | if (ap[j] != NULL) ap[j] = p_Neg(ap[j],R); |
---|
| 1411 | for(i=r-1; i>=0; i--) |
---|
| 1412 | { |
---|
| 1413 | a = &b[i*a0->ncols]; |
---|
| 1414 | q = &x[i*re->ncols]; |
---|
| 1415 | if (a[c] != NULL) |
---|
| 1416 | { |
---|
| 1417 | elim = a[c]; |
---|
| 1418 | for (j=c-1; j>=0; j--) |
---|
| 1419 | { |
---|
| 1420 | q1 = NULL; |
---|
| 1421 | if (a[j] != NULL) |
---|
| 1422 | { |
---|
| 1423 | q1 = sm_MultDiv(a[j], piv, div,R); |
---|
| 1424 | if (ap[j] != NULL) |
---|
| 1425 | { |
---|
| 1426 | q2 = sm_MultDiv(ap[j], elim, div, R); |
---|
| 1427 | q1 = p_Add_q(q1,q2,R); |
---|
| 1428 | } |
---|
| 1429 | } |
---|
| 1430 | else if (ap[j] != NULL) |
---|
| 1431 | q1 = sm_MultDiv(ap[j], elim, div, R); |
---|
| 1432 | if (q1 != NULL) |
---|
| 1433 | { |
---|
| 1434 | if (div) |
---|
| 1435 | sm_SpecialPolyDiv(q1, div,R); |
---|
| 1436 | q[j] = q1; |
---|
| 1437 | } |
---|
| 1438 | } |
---|
| 1439 | } |
---|
| 1440 | else |
---|
| 1441 | { |
---|
| 1442 | for (j=c-1; j>=0; j--) |
---|
| 1443 | { |
---|
| 1444 | if (a[j] != NULL) |
---|
| 1445 | { |
---|
| 1446 | q1 = sm_MultDiv(a[j], piv, div, R); |
---|
| 1447 | if (div) |
---|
| 1448 | sm_SpecialPolyDiv(q1, div, R); |
---|
| 1449 | q[j] = q1; |
---|
| 1450 | } |
---|
| 1451 | } |
---|
| 1452 | } |
---|
| 1453 | } |
---|
| 1454 | } |
---|
| 1455 | |
---|
[2fce0e] | 1456 | /*2*/ |
---|
| 1457 | /// entries of a are minors and go to result (only if not in R) |
---|
[441a2e] | 1458 | void mp_MinorToResult(ideal result, int &elems, matrix a, int r, int c, |
---|
[2d2e40] | 1459 | ideal R, const ring) |
---|
[441a2e] | 1460 | { |
---|
| 1461 | poly *q1; |
---|
| 1462 | int e=IDELEMS(result); |
---|
| 1463 | int i,j; |
---|
| 1464 | |
---|
| 1465 | if (R != NULL) |
---|
| 1466 | { |
---|
| 1467 | for (i=r-1;i>=0;i--) |
---|
| 1468 | { |
---|
| 1469 | q1 = &(a->m)[i*a->ncols]; |
---|
| 1470 | //for (j=c-1;j>=0;j--) |
---|
| 1471 | //{ |
---|
| 1472 | // if (q1[j]!=NULL) q1[j] = kNF(R,currQuotient,q1[j]); |
---|
| 1473 | //} |
---|
| 1474 | } |
---|
| 1475 | } |
---|
| 1476 | for (i=r-1;i>=0;i--) |
---|
| 1477 | { |
---|
| 1478 | q1 = &(a->m)[i*a->ncols]; |
---|
| 1479 | for (j=c-1;j>=0;j--) |
---|
| 1480 | { |
---|
| 1481 | if (q1[j]!=NULL) |
---|
| 1482 | { |
---|
| 1483 | if (elems>=e) |
---|
| 1484 | { |
---|
| 1485 | pEnlargeSet(&(result->m),e,e); |
---|
| 1486 | e += e; |
---|
| 1487 | IDELEMS(result) =e; |
---|
| 1488 | } |
---|
| 1489 | result->m[elems] = q1[j]; |
---|
| 1490 | q1[j] = NULL; |
---|
| 1491 | elems++; |
---|
| 1492 | } |
---|
| 1493 | } |
---|
| 1494 | } |
---|
| 1495 | } |
---|
[2fce0e] | 1496 | /* |
---|
| 1497 | // from linalg_from_matpol.cc: TODO: compare with above & remove... |
---|
| 1498 | void mp_MinorToResult(ideal result, int &elems, matrix a, int r, int c, |
---|
| 1499 | ideal R, const ring R) |
---|
| 1500 | { |
---|
| 1501 | poly *q1; |
---|
| 1502 | int e=IDELEMS(result); |
---|
| 1503 | int i,j; |
---|
| 1504 | |
---|
| 1505 | if (R != NULL) |
---|
| 1506 | { |
---|
| 1507 | for (i=r-1;i>=0;i--) |
---|
| 1508 | { |
---|
| 1509 | q1 = &(a->m)[i*a->ncols]; |
---|
| 1510 | for (j=c-1;j>=0;j--) |
---|
| 1511 | { |
---|
| 1512 | if (q1[j]!=NULL) q1[j] = kNF(R,currQuotient,q1[j]); |
---|
| 1513 | } |
---|
| 1514 | } |
---|
| 1515 | } |
---|
| 1516 | for (i=r-1;i>=0;i--) |
---|
| 1517 | { |
---|
| 1518 | q1 = &(a->m)[i*a->ncols]; |
---|
| 1519 | for (j=c-1;j>=0;j--) |
---|
| 1520 | { |
---|
| 1521 | if (q1[j]!=NULL) |
---|
| 1522 | { |
---|
| 1523 | if (elems>=e) |
---|
| 1524 | { |
---|
| 1525 | if(e<SIZE_OF_SYSTEM_PAGE) |
---|
| 1526 | { |
---|
| 1527 | pEnlargeSet(&(result->m),e,e); |
---|
| 1528 | e += e; |
---|
| 1529 | } |
---|
| 1530 | else |
---|
| 1531 | { |
---|
| 1532 | pEnlargeSet(&(result->m),e,SIZE_OF_SYSTEM_PAGE); |
---|
| 1533 | e += SIZE_OF_SYSTEM_PAGE; |
---|
| 1534 | } |
---|
| 1535 | IDELEMS(result) =e; |
---|
| 1536 | } |
---|
| 1537 | result->m[elems] = q1[j]; |
---|
| 1538 | q1[j] = NULL; |
---|
| 1539 | elems++; |
---|
| 1540 | } |
---|
| 1541 | } |
---|
| 1542 | } |
---|
| 1543 | } |
---|
| 1544 | */ |
---|
[441a2e] | 1545 | |
---|
| 1546 | static void mpFinalClean(matrix a) |
---|
| 1547 | { |
---|
| 1548 | omFreeSize((ADDRESS)a->m,a->nrows*a->ncols*sizeof(poly)); |
---|
[73ad0c] | 1549 | omFreeBin((ADDRESS)a, sip_sideal_bin); |
---|
[441a2e] | 1550 | } |
---|
| 1551 | |
---|
[2fce0e] | 1552 | /*2*/ |
---|
| 1553 | /// produces recursively the ideal of all arxar-minors of a |
---|
[441a2e] | 1554 | void mp_RecMin(int ar,ideal result,int &elems,matrix a,int lr,int lc, |
---|
| 1555 | poly barDiv, ideal R, const ring r) |
---|
| 1556 | { |
---|
| 1557 | int k; |
---|
| 1558 | int kr=lr-1,kc=lc-1; |
---|
| 1559 | matrix nextLevel=mpNew(kr,kc); |
---|
| 1560 | |
---|
| 1561 | loop |
---|
| 1562 | { |
---|
| 1563 | /*--- look for an optimal row and bring it to last position ------------*/ |
---|
| 1564 | if(mp_PrepareRow(a,lr,lc,r)==0) break; |
---|
| 1565 | /*--- now take all pivots from the last row ------------*/ |
---|
| 1566 | k = lc; |
---|
| 1567 | loop |
---|
| 1568 | { |
---|
| 1569 | if(mp_PreparePiv(a,lr,k,r)==0) break; |
---|
| 1570 | mp_ElimBar(a,nextLevel,barDiv,lr,k,r); |
---|
| 1571 | k--; |
---|
| 1572 | if (ar>1) |
---|
| 1573 | { |
---|
| 1574 | mp_RecMin(ar-1,result,elems,nextLevel,kr,k,a->m[kr*a->ncols+k],R,r); |
---|
| 1575 | mp_PartClean(nextLevel,kr,k, r); |
---|
| 1576 | } |
---|
| 1577 | else mp_MinorToResult(result,elems,nextLevel,kr,k,R,r); |
---|
| 1578 | if (ar>k-1) break; |
---|
| 1579 | } |
---|
| 1580 | if (ar>=kr) break; |
---|
| 1581 | /*--- now we have to take out the last row...------------*/ |
---|
| 1582 | lr = kr; |
---|
| 1583 | kr--; |
---|
| 1584 | } |
---|
| 1585 | mpFinalClean(nextLevel); |
---|
| 1586 | } |
---|
[2fce0e] | 1587 | /* |
---|
| 1588 | // from linalg_from_matpol.cc: TODO: compare with above & remove... |
---|
| 1589 | void mp_RecMin(int ar,ideal result,int &elems,matrix a,int lr,int lc, |
---|
| 1590 | poly barDiv, ideal R, const ring R) |
---|
| 1591 | { |
---|
| 1592 | int k; |
---|
| 1593 | int kr=lr-1,kc=lc-1; |
---|
| 1594 | matrix nextLevel=mpNew(kr,kc); |
---|
[441a2e] | 1595 | |
---|
[2fce0e] | 1596 | loop |
---|
| 1597 | { |
---|
| 1598 | // --- look for an optimal row and bring it to last position ------------ |
---|
| 1599 | if(mpPrepareRow(a,lr,lc)==0) break; |
---|
| 1600 | // --- now take all pivots from the last row ------------ |
---|
| 1601 | k = lc; |
---|
| 1602 | loop |
---|
| 1603 | { |
---|
| 1604 | if(mpPreparePiv(a,lr,k)==0) break; |
---|
| 1605 | mpElimBar(a,nextLevel,barDiv,lr,k); |
---|
| 1606 | k--; |
---|
| 1607 | if (ar>1) |
---|
| 1608 | { |
---|
| 1609 | mpRecMin(ar-1,result,elems,nextLevel,kr,k,a->m[kr*a->ncols+k],R); |
---|
| 1610 | mpPartClean(nextLevel,kr,k); |
---|
| 1611 | } |
---|
| 1612 | else mpMinorToResult(result,elems,nextLevel,kr,k,R); |
---|
| 1613 | if (ar>k-1) break; |
---|
| 1614 | } |
---|
| 1615 | if (ar>=kr) break; |
---|
| 1616 | // --- now we have to take out the last row...------------ |
---|
| 1617 | lr = kr; |
---|
| 1618 | kr--; |
---|
| 1619 | } |
---|
| 1620 | mpFinalClean(nextLevel); |
---|
| 1621 | } |
---|
[441a2e] | 1622 | */ |
---|
[2fce0e] | 1623 | |
---|
| 1624 | /*2*/ |
---|
| 1625 | /// returns the determinant of the matrix m; |
---|
| 1626 | /// uses Bareiss algorithm |
---|
[441a2e] | 1627 | poly mp_DetBareiss (matrix a, const ring r) |
---|
| 1628 | { |
---|
| 1629 | int s; |
---|
| 1630 | poly div, res; |
---|
| 1631 | if (MATROWS(a) != MATCOLS(a)) |
---|
| 1632 | { |
---|
| 1633 | Werror("det of %d x %d matrix",MATROWS(a),MATCOLS(a)); |
---|
| 1634 | return NULL; |
---|
| 1635 | } |
---|
| 1636 | matrix c = mp_Copy(a,r); |
---|
[bf6a4d] | 1637 | mp_permmatrix *Bareiss = new mp_permmatrix(c,r); |
---|
[441a2e] | 1638 | row_col_weight w(Bareiss->mpGetRdim(), Bareiss->mpGetCdim()); |
---|
| 1639 | |
---|
| 1640 | /* Bareiss */ |
---|
| 1641 | div = NULL; |
---|
| 1642 | while(Bareiss->mpPivotBareiss(&w)) |
---|
| 1643 | { |
---|
| 1644 | Bareiss->mpElimBareiss(div); |
---|
| 1645 | div = Bareiss->mpGetElem(Bareiss->mpGetRdim(), Bareiss->mpGetCdim()); |
---|
| 1646 | } |
---|
| 1647 | Bareiss->mpRowReorder(); |
---|
| 1648 | Bareiss->mpColReorder(); |
---|
| 1649 | Bareiss->mpSaveArray(); |
---|
| 1650 | s = Bareiss->mpGetSign(); |
---|
| 1651 | delete Bareiss; |
---|
| 1652 | |
---|
| 1653 | /* result */ |
---|
| 1654 | res = MATELEM(c,1,1); |
---|
| 1655 | MATELEM(c,1,1) = NULL; |
---|
| 1656 | id_Delete((ideal *)&c,r); |
---|
| 1657 | if (s < 0) |
---|
| 1658 | res = p_Neg(res,r); |
---|
| 1659 | return res; |
---|
| 1660 | } |
---|
[2fce0e] | 1661 | /* |
---|
| 1662 | // from linalg_from_matpol.cc: TODO: compare with above & remove... |
---|
| 1663 | poly mp_DetBareiss (matrix a, const ring R) |
---|
| 1664 | { |
---|
| 1665 | int s; |
---|
| 1666 | poly div, res; |
---|
| 1667 | if (MATROWS(a) != MATCOLS(a)) |
---|
| 1668 | { |
---|
| 1669 | Werror("det of %d x %d matrix",MATROWS(a),MATCOLS(a)); |
---|
| 1670 | return NULL; |
---|
| 1671 | } |
---|
| 1672 | matrix c = mp_Copy(a, R); |
---|
| 1673 | mp_permmatrix *Bareiss = new mp_permmatrix(c, R); |
---|
| 1674 | row_col_weight w(Bareiss->mpGetRdim(), Bareiss->mpGetCdim()); |
---|
| 1675 | |
---|
| 1676 | // Bareiss |
---|
| 1677 | div = NULL; |
---|
| 1678 | while(Bareiss->mpPivotBareiss(&w)) |
---|
| 1679 | { |
---|
| 1680 | Bareiss->mpElimBareiss(div); |
---|
| 1681 | div = Bareiss->mpGetElem(Bareiss->mpGetRdim(), Bareiss->mpGetCdim()); |
---|
| 1682 | } |
---|
| 1683 | Bareiss->mpRowReorder(); |
---|
| 1684 | Bareiss->mpColReorder(); |
---|
| 1685 | Bareiss->mpSaveArray(); |
---|
| 1686 | s = Bareiss->mpGetSign(); |
---|
| 1687 | delete Bareiss; |
---|
| 1688 | |
---|
| 1689 | // result |
---|
| 1690 | res = MATELEM(c,1,1); |
---|
| 1691 | MATELEM(c,1,1) = NULL; |
---|
| 1692 | id_Delete((ideal *)&c, R); |
---|
| 1693 | if (s < 0) |
---|
| 1694 | res = p_Neg(res, R); |
---|
| 1695 | return res; |
---|
| 1696 | } |
---|
| 1697 | */ |
---|
| 1698 | |
---|
| 1699 | /*2 |
---|
| 1700 | * compute all ar-minors of the matrix a |
---|
| 1701 | */ |
---|
| 1702 | matrix mp_Wedge(matrix a, int ar, const ring R) |
---|
| 1703 | { |
---|
| 1704 | int i,j,k,l; |
---|
| 1705 | int *rowchoise,*colchoise; |
---|
| 1706 | BOOLEAN rowch,colch; |
---|
| 1707 | matrix result; |
---|
| 1708 | matrix tmp; |
---|
| 1709 | poly p; |
---|
| 1710 | |
---|
| 1711 | i = binom(a->nrows,ar); |
---|
| 1712 | j = binom(a->ncols,ar); |
---|
| 1713 | |
---|
| 1714 | rowchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
| 1715 | colchoise=(int *)omAlloc(ar*sizeof(int)); |
---|
| 1716 | result = mpNew(i,j); |
---|
| 1717 | tmp = mpNew(ar,ar); |
---|
| 1718 | l = 1; /* k,l:the index in result*/ |
---|
| 1719 | idInitChoise(ar,1,a->nrows,&rowch,rowchoise); |
---|
| 1720 | while (!rowch) |
---|
| 1721 | { |
---|
| 1722 | k=1; |
---|
| 1723 | idInitChoise(ar,1,a->ncols,&colch,colchoise); |
---|
| 1724 | while (!colch) |
---|
| 1725 | { |
---|
| 1726 | for (i=1; i<=ar; i++) |
---|
| 1727 | { |
---|
| 1728 | for (j=1; j<=ar; j++) |
---|
| 1729 | { |
---|
| 1730 | MATELEM(tmp,i,j) = MATELEM(a,rowchoise[i-1],colchoise[j-1]); |
---|
| 1731 | } |
---|
| 1732 | } |
---|
| 1733 | p = mp_DetBareiss(tmp, R); |
---|
| 1734 | if ((k+l) & 1) p=p_Neg(p, R); |
---|
| 1735 | MATELEM(result,l,k) = p; |
---|
| 1736 | k++; |
---|
| 1737 | idGetNextChoise(ar,a->ncols,&colch,colchoise); |
---|
| 1738 | } |
---|
| 1739 | idGetNextChoise(ar,a->nrows,&rowch,rowchoise); |
---|
| 1740 | l++; |
---|
| 1741 | } |
---|
| 1742 | |
---|
| 1743 | /*delete the matrix tmp*/ |
---|
| 1744 | for (i=1; i<=ar; i++) |
---|
| 1745 | { |
---|
| 1746 | for (j=1; j<=ar; j++) MATELEM(tmp,i,j) = NULL; |
---|
| 1747 | } |
---|
| 1748 | id_Delete((ideal *) &tmp, R); |
---|
| 1749 | return (result); |
---|
| 1750 | } |
---|