[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 | * ABSTRACT - dimension, multiplicity, HC, kbase |
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| 7 | */ |
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| 8 | |
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[599326] | 9 | #include <kernel/mod2.h> |
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[35aab3] | 10 | |
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| 11 | |
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[599326] | 12 | #include <kernel/structs.h> |
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| 13 | #include <kernel/febase.h> |
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[b1dfaf] | 14 | #include <omalloc/omalloc.h> |
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[599326] | 15 | #include <kernel/ideals.h> |
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[210e07] | 16 | #include <polys/polys.h> |
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| 17 | #include <misc/intvec.h> |
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[0f401f] | 18 | #include <coeffs/numbers.h> |
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[599326] | 19 | #include <kernel/hutil.h> |
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| 20 | #include <kernel/stairc.h> |
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[35aab3] | 21 | |
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| 22 | int hCo, hMu, hMu2; |
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[c5e0e1] | 23 | omBin indlist_bin = omGetSpecBin(sizeof(indlist)); |
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[35aab3] | 24 | |
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| 25 | /*0 implementation*/ |
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| 26 | |
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| 27 | // dimension |
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| 28 | |
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| 29 | void hDimSolve(scmon pure, int Npure, scfmon rad, int Nrad, |
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| 30 | varset var, int Nvar) |
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| 31 | { |
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| 32 | int dn, iv, rad0, b, c, x; |
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| 33 | scmon pn; |
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| 34 | scfmon rn; |
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| 35 | if (Nrad < 2) |
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| 36 | { |
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| 37 | dn = Npure + Nrad; |
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| 38 | if (dn < hCo) |
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| 39 | hCo = dn; |
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| 40 | return; |
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| 41 | } |
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| 42 | if (Npure+1 >= hCo) |
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| 43 | return; |
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| 44 | iv = Nvar; |
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| 45 | while(pure[var[iv]]) iv--; |
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| 46 | hStepR(rad, Nrad, var, iv, &rad0); |
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| 47 | if (rad0!=0) |
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| 48 | { |
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| 49 | iv--; |
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| 50 | if (rad0 < Nrad) |
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| 51 | { |
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| 52 | pn = hGetpure(pure); |
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| 53 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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| 54 | hDimSolve(pn, Npure + 1, rn, rad0, var, iv); |
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| 55 | b = rad0; |
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| 56 | c = Nrad; |
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| 57 | hElimR(rn, &rad0, b, c, var, iv); |
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| 58 | hPure(rn, b, &c, var, iv, pn, &x); |
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| 59 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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| 60 | rad0 += (c - b); |
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| 61 | hDimSolve(pn, Npure + x, rn, rad0, var, iv); |
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| 62 | } |
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| 63 | else |
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| 64 | { |
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| 65 | hDimSolve(pure, Npure, rad, Nrad, var, iv); |
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| 66 | } |
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| 67 | } |
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| 68 | else |
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| 69 | hCo = Npure + 1; |
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| 70 | } |
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| 71 | |
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| 72 | int scDimInt(ideal S, ideal Q) |
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| 73 | { |
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| 74 | int mc; |
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| 75 | hexist = hInit(S, Q, &hNexist); |
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| 76 | if (!hNexist) |
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[1f637e] | 77 | return (currRing->N); |
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[35aab3] | 78 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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[1f637e] | 79 | hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
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| 80 | hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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[35aab3] | 81 | mc = hisModule; |
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| 82 | if (!mc) |
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| 83 | { |
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| 84 | hrad = hexist; |
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| 85 | hNrad = hNexist; |
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| 86 | } |
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| 87 | else |
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| 88 | hrad = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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[1f637e] | 89 | radmem = hCreate((currRing->N) - 1); |
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| 90 | hCo = (currRing->N) + 1; |
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[35aab3] | 91 | loop |
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| 92 | { |
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| 93 | if (mc) |
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| 94 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
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| 95 | if (hNrad) |
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| 96 | { |
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[1f637e] | 97 | hNvar = (currRing->N); |
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[35aab3] | 98 | hRadical(hrad, &hNrad, hNvar); |
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| 99 | hSupp(hrad, hNrad, hvar, &hNvar); |
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| 100 | if (hNvar) |
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| 101 | { |
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[1f637e] | 102 | memset(hpure, 0, ((currRing->N) + 1) * sizeof(int)); |
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[35aab3] | 103 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
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| 104 | hLexR(hrad, hNrad, hvar, hNvar); |
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| 105 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
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| 106 | } |
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| 107 | } |
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| 108 | else |
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| 109 | { |
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| 110 | hCo = 0; |
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| 111 | break; |
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| 112 | } |
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| 113 | mc--; |
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| 114 | if (mc <= 0) |
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| 115 | break; |
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| 116 | } |
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[1f637e] | 117 | hKill(radmem, (currRing->N) - 1); |
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| 118 | omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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| 119 | omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int)); |
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[35aab3] | 120 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
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| 121 | hDelete(hexist, hNexist); |
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| 122 | if (hisModule) |
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| 123 | omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon)); |
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[1f637e] | 124 | return (currRing->N) - hCo; |
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[35aab3] | 125 | } |
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| 126 | |
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| 127 | // independent set |
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| 128 | static scmon hInd; |
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| 129 | |
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| 130 | static void hIndSolve(scmon pure, int Npure, scfmon rad, int Nrad, |
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| 131 | varset var, int Nvar) |
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| 132 | { |
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| 133 | int dn, iv, rad0, b, c, x; |
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| 134 | scmon pn; |
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| 135 | scfmon rn; |
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| 136 | if (Nrad < 2) |
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| 137 | { |
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| 138 | dn = Npure + Nrad; |
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| 139 | if (dn < hCo) |
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| 140 | { |
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| 141 | hCo = dn; |
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[1f637e] | 142 | for (iv=(currRing->N); iv; iv--) |
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[35aab3] | 143 | { |
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| 144 | if (pure[iv]) |
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| 145 | hInd[iv] = 0; |
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| 146 | else |
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| 147 | hInd[iv] = 1; |
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| 148 | } |
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| 149 | if (Nrad) |
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| 150 | { |
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| 151 | pn = *rad; |
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| 152 | iv = Nvar; |
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| 153 | loop |
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| 154 | { |
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| 155 | x = var[iv]; |
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| 156 | if (pn[x]) |
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| 157 | { |
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| 158 | hInd[x] = 0; |
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| 159 | break; |
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| 160 | } |
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| 161 | iv--; |
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| 162 | } |
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| 163 | } |
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| 164 | } |
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| 165 | return; |
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| 166 | } |
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| 167 | if (Npure+1 >= hCo) |
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| 168 | return; |
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| 169 | iv = Nvar; |
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| 170 | while(pure[var[iv]]) iv--; |
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| 171 | hStepR(rad, Nrad, var, iv, &rad0); |
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| 172 | if (rad0) |
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| 173 | { |
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| 174 | iv--; |
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| 175 | if (rad0 < Nrad) |
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| 176 | { |
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| 177 | pn = hGetpure(pure); |
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| 178 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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| 179 | pn[var[iv + 1]] = 1; |
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| 180 | hIndSolve(pn, Npure + 1, rn, rad0, var, iv); |
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| 181 | pn[var[iv + 1]] = 0; |
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| 182 | b = rad0; |
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| 183 | c = Nrad; |
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| 184 | hElimR(rn, &rad0, b, c, var, iv); |
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| 185 | hPure(rn, b, &c, var, iv, pn, &x); |
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| 186 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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| 187 | rad0 += (c - b); |
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| 188 | hIndSolve(pn, Npure + x, rn, rad0, var, iv); |
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| 189 | } |
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| 190 | else |
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| 191 | { |
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| 192 | hIndSolve(pure, Npure, rad, Nrad, var, iv); |
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| 193 | } |
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| 194 | } |
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| 195 | else |
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| 196 | { |
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| 197 | hCo = Npure + 1; |
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[1f637e] | 198 | for (x=(currRing->N); x; x--) |
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[35aab3] | 199 | { |
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| 200 | if (pure[x]) |
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| 201 | hInd[x] = 0; |
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| 202 | else |
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| 203 | hInd[x] = 1; |
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| 204 | } |
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| 205 | hInd[var[iv]] = 0; |
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| 206 | } |
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| 207 | } |
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| 208 | |
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| 209 | intvec * scIndIntvec(ideal S, ideal Q) |
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| 210 | { |
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[1f637e] | 211 | intvec *Set=new intvec((currRing->N)); |
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[35aab3] | 212 | int mc,i; |
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| 213 | hexist = hInit(S, Q, &hNexist); |
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| 214 | if (hNexist==0) |
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| 215 | { |
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[1f637e] | 216 | for(i=0; i<(currRing->N); i++) |
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[35aab3] | 217 | (*Set)[i]=1; |
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| 218 | return Set; |
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| 219 | } |
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| 220 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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[1f637e] | 221 | hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
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| 222 | hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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| 223 | hInd = (scmon)omAlloc((1 + (currRing->N)) * sizeof(int)); |
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[35aab3] | 224 | mc = hisModule; |
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| 225 | if (mc==0) |
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| 226 | { |
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| 227 | hrad = hexist; |
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| 228 | hNrad = hNexist; |
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| 229 | } |
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| 230 | else |
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| 231 | hrad = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
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[1f637e] | 232 | radmem = hCreate((currRing->N) - 1); |
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| 233 | hCo = (currRing->N) + 1; |
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[35aab3] | 234 | loop |
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| 235 | { |
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| 236 | if (mc!=0) |
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| 237 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
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| 238 | if (hNrad!=0) |
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| 239 | { |
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[1f637e] | 240 | hNvar = (currRing->N); |
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[35aab3] | 241 | hRadical(hrad, &hNrad, hNvar); |
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| 242 | hSupp(hrad, hNrad, hvar, &hNvar); |
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| 243 | if (hNvar!=0) |
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| 244 | { |
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[1f637e] | 245 | memset(hpure, 0, ((currRing->N) + 1) * sizeof(int)); |
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[35aab3] | 246 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
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| 247 | hLexR(hrad, hNrad, hvar, hNvar); |
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| 248 | hIndSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
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| 249 | } |
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| 250 | } |
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| 251 | else |
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| 252 | { |
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| 253 | hCo = 0; |
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| 254 | break; |
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| 255 | } |
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| 256 | mc--; |
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| 257 | if (mc <= 0) |
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| 258 | break; |
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| 259 | } |
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[1f637e] | 260 | for(i=0; i<(currRing->N); i++) |
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[35aab3] | 261 | (*Set)[i] = hInd[i+1]; |
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[1f637e] | 262 | hKill(radmem, (currRing->N) - 1); |
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| 263 | omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
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| 264 | omFreeSize((ADDRESS)hInd, (1 + (currRing->N)) * sizeof(int)); |
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| 265 | omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int)); |
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[35aab3] | 266 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
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| 267 | hDelete(hexist, hNexist); |
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| 268 | if (hisModule) |
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| 269 | omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon)); |
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| 270 | return Set; |
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| 271 | } |
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| 272 | |
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| 273 | indset ISet, JSet; |
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| 274 | |
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| 275 | static BOOLEAN hNotZero(scfmon rad, int Nrad, varset var, int Nvar) |
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| 276 | { |
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| 277 | int k1, i; |
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| 278 | k1 = var[Nvar]; |
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| 279 | i = 0; |
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| 280 | loop |
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| 281 | { |
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| 282 | if (rad[i][k1]==0) |
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| 283 | return FALSE; |
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| 284 | i++; |
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| 285 | if (i == Nrad) |
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| 286 | return TRUE; |
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| 287 | } |
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| 288 | } |
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| 289 | |
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| 290 | static void hIndep(scmon pure) |
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| 291 | { |
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| 292 | int iv; |
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| 293 | intvec *Set; |
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| 294 | |
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[1f637e] | 295 | Set = ISet->set = new intvec((currRing->N)); |
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| 296 | for (iv=(currRing->N); iv!=0 ; iv--) |
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[35aab3] | 297 | { |
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| 298 | if (pure[iv]) |
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| 299 | (*Set)[iv-1] = 0; |
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| 300 | else |
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| 301 | (*Set)[iv-1] = 1; |
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| 302 | } |
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| 303 | ISet = ISet->nx = (indset)omAlloc0Bin(indlist_bin); |
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| 304 | hMu++; |
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| 305 | } |
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| 306 | |
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| 307 | void hIndMult(scmon pure, int Npure, scfmon rad, int Nrad, |
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| 308 | varset var, int Nvar) |
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| 309 | { |
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| 310 | int dn, iv, rad0, b, c, x; |
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| 311 | scmon pn; |
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| 312 | scfmon rn; |
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| 313 | if (Nrad < 2) |
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| 314 | { |
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| 315 | dn = Npure + Nrad; |
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| 316 | if (dn == hCo) |
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| 317 | { |
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| 318 | if (Nrad==0) |
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| 319 | hIndep(pure); |
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| 320 | else |
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| 321 | { |
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| 322 | pn = *rad; |
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| 323 | for (iv = Nvar; iv!=0; iv--) |
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| 324 | { |
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| 325 | x = var[iv]; |
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| 326 | if (pn[x]) |
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| 327 | { |
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| 328 | pure[x] = 1; |
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| 329 | hIndep(pure); |
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| 330 | pure[x] = 0; |
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| 331 | } |
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| 332 | } |
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| 333 | } |
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| 334 | } |
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| 335 | return; |
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| 336 | } |
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| 337 | iv = Nvar; |
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| 338 | dn = Npure+1; |
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| 339 | if (dn >= hCo) |
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| 340 | { |
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| 341 | if (dn > hCo) |
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| 342 | return; |
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| 343 | loop |
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| 344 | { |
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| 345 | if(!pure[var[iv]]) |
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| 346 | { |
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| 347 | if(hNotZero(rad, Nrad, var, iv)) |
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| 348 | { |
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| 349 | pure[var[iv]] = 1; |
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| 350 | hIndep(pure); |
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| 351 | pure[var[iv]] = 0; |
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| 352 | } |
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| 353 | } |
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| 354 | iv--; |
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| 355 | if (!iv) |
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| 356 | return; |
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| 357 | } |
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| 358 | } |
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| 359 | while(pure[var[iv]]) iv--; |
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| 360 | hStepR(rad, Nrad, var, iv, &rad0); |
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| 361 | iv--; |
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| 362 | if (rad0 < Nrad) |
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| 363 | { |
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| 364 | pn = hGetpure(pure); |
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| 365 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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| 366 | pn[var[iv + 1]] = 1; |
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| 367 | hIndMult(pn, Npure + 1, rn, rad0, var, iv); |
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| 368 | pn[var[iv + 1]] = 0; |
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| 369 | b = rad0; |
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| 370 | c = Nrad; |
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| 371 | hElimR(rn, &rad0, b, c, var, iv); |
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| 372 | hPure(rn, b, &c, var, iv, pn, &x); |
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| 373 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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| 374 | rad0 += (c - b); |
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| 375 | hIndMult(pn, Npure + x, rn, rad0, var, iv); |
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| 376 | } |
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| 377 | else |
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| 378 | { |
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| 379 | hIndMult(pure, Npure, rad, Nrad, var, iv); |
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| 380 | } |
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| 381 | } |
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| 382 | |
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| 383 | /*3 |
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| 384 | * consider indset x := !pure |
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| 385 | * (for all i) (if(sm(i) > x) return FALSE) |
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| 386 | * else return TRUE |
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| 387 | */ |
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| 388 | static BOOLEAN hCheck1(indset sm, scmon pure) |
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| 389 | { |
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| 390 | int iv; |
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| 391 | intvec *Set; |
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| 392 | while (sm->nx != NULL) |
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| 393 | { |
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| 394 | Set = sm->set; |
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[1f637e] | 395 | iv=(currRing->N); |
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[35aab3] | 396 | loop |
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| 397 | { |
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| 398 | if (((*Set)[iv-1] == 0) && (pure[iv] == 0)) |
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| 399 | break; |
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| 400 | iv--; |
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| 401 | if (iv == 0) |
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| 402 | return FALSE; |
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| 403 | } |
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| 404 | sm = sm->nx; |
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| 405 | } |
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| 406 | return TRUE; |
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| 407 | } |
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| 408 | |
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| 409 | /*3 |
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| 410 | * consider indset x := !pure |
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| 411 | * (for all i) if(x > sm(i)) delete sm(i)) |
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| 412 | * return (place for x) |
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| 413 | */ |
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| 414 | static indset hCheck2(indset sm, scmon pure) |
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| 415 | { |
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| 416 | int iv; |
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| 417 | intvec *Set; |
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| 418 | indset be, a1 = NULL; |
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| 419 | while (sm->nx != NULL) |
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| 420 | { |
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| 421 | Set = sm->set; |
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[1f637e] | 422 | iv=(currRing->N); |
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[35aab3] | 423 | loop |
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| 424 | { |
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| 425 | if ((pure[iv] == 1) && ((*Set)[iv-1] == 1)) |
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| 426 | break; |
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| 427 | iv--; |
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| 428 | if (iv == 0) |
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| 429 | { |
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| 430 | if (a1 == NULL) |
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| 431 | { |
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| 432 | a1 = sm; |
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| 433 | } |
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| 434 | else |
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| 435 | { |
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| 436 | hMu2--; |
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| 437 | be->nx = sm->nx; |
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| 438 | delete Set; |
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| 439 | omFreeBin((ADDRESS)sm, indlist_bin); |
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| 440 | sm = be; |
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| 441 | } |
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| 442 | break; |
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| 443 | } |
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| 444 | } |
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| 445 | be = sm; |
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| 446 | sm = sm->nx; |
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| 447 | } |
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| 448 | if (a1 != NULL) |
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| 449 | { |
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| 450 | return a1; |
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| 451 | } |
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| 452 | else |
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| 453 | { |
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| 454 | hMu2++; |
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[1f637e] | 455 | sm->set = new intvec((currRing->N)); |
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[35aab3] | 456 | sm->nx = (indset)omAlloc0Bin(indlist_bin); |
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| 457 | return sm; |
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| 458 | } |
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| 459 | } |
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| 460 | |
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| 461 | /*2 |
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| 462 | * definition x >= y |
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| 463 | * x(i) == 0 => y(i) == 0 |
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| 464 | * > ex. j with x(j) == 1 and y(j) == 0 |
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| 465 | */ |
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| 466 | static void hCheckIndep(scmon pure) |
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| 467 | { |
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| 468 | intvec *Set; |
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| 469 | indset res; |
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| 470 | int iv; |
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| 471 | if (hCheck1(ISet, pure)) |
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| 472 | { |
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| 473 | if (hCheck1(JSet, pure)) |
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| 474 | { |
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| 475 | res = hCheck2(JSet,pure); |
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| 476 | if (res == NULL) |
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| 477 | return; |
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| 478 | Set = res->set; |
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[1f637e] | 479 | for (iv=(currRing->N); iv; iv--) |
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[35aab3] | 480 | { |
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| 481 | if (pure[iv]) |
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| 482 | (*Set)[iv-1] = 0; |
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| 483 | else |
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| 484 | (*Set)[iv-1] = 1; |
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| 485 | } |
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| 486 | } |
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| 487 | } |
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| 488 | } |
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| 489 | |
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| 490 | void hIndAllMult(scmon pure, int Npure, scfmon rad, int Nrad, |
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| 491 | varset var, int Nvar) |
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| 492 | { |
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| 493 | int dn, iv, rad0, b, c, x; |
---|
| 494 | scmon pn; |
---|
| 495 | scfmon rn; |
---|
| 496 | if (Nrad < 2) |
---|
| 497 | { |
---|
| 498 | dn = Npure + Nrad; |
---|
| 499 | if (dn > hCo) |
---|
| 500 | { |
---|
| 501 | if (!Nrad) |
---|
| 502 | hCheckIndep(pure); |
---|
| 503 | else |
---|
| 504 | { |
---|
| 505 | pn = *rad; |
---|
| 506 | for (iv = Nvar; iv; iv--) |
---|
| 507 | { |
---|
| 508 | x = var[iv]; |
---|
| 509 | if (pn[x]) |
---|
| 510 | { |
---|
| 511 | pure[x] = 1; |
---|
| 512 | hCheckIndep(pure); |
---|
| 513 | pure[x] = 0; |
---|
| 514 | } |
---|
| 515 | } |
---|
| 516 | } |
---|
| 517 | } |
---|
| 518 | return; |
---|
| 519 | } |
---|
| 520 | iv = Nvar; |
---|
| 521 | while(pure[var[iv]]) iv--; |
---|
| 522 | hStepR(rad, Nrad, var, iv, &rad0); |
---|
| 523 | iv--; |
---|
| 524 | if (rad0 < Nrad) |
---|
| 525 | { |
---|
| 526 | pn = hGetpure(pure); |
---|
| 527 | rn = hGetmem(Nrad, rad, radmem[iv]); |
---|
| 528 | pn[var[iv + 1]] = 1; |
---|
| 529 | hIndAllMult(pn, Npure + 1, rn, rad0, var, iv); |
---|
| 530 | pn[var[iv + 1]] = 0; |
---|
| 531 | b = rad0; |
---|
| 532 | c = Nrad; |
---|
| 533 | hElimR(rn, &rad0, b, c, var, iv); |
---|
| 534 | hPure(rn, b, &c, var, iv, pn, &x); |
---|
| 535 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
---|
| 536 | rad0 += (c - b); |
---|
| 537 | hIndAllMult(pn, Npure + x, rn, rad0, var, iv); |
---|
| 538 | } |
---|
| 539 | else |
---|
| 540 | { |
---|
| 541 | hIndAllMult(pure, Npure, rad, Nrad, var, iv); |
---|
| 542 | } |
---|
| 543 | } |
---|
| 544 | |
---|
| 545 | // multiplicity |
---|
| 546 | |
---|
| 547 | static int hZeroMult(scmon pure, scfmon stc, int Nstc, varset var, int Nvar) |
---|
| 548 | { |
---|
| 549 | int iv = Nvar -1, sum, a, a0, a1, b, i; |
---|
| 550 | int x, x0; |
---|
| 551 | scmon pn; |
---|
| 552 | scfmon sn; |
---|
| 553 | if (!iv) |
---|
| 554 | return pure[var[1]]; |
---|
| 555 | else if (!Nstc) |
---|
| 556 | { |
---|
| 557 | sum = 1; |
---|
| 558 | for (i = Nvar; i; i--) |
---|
| 559 | sum *= pure[var[i]]; |
---|
| 560 | return sum; |
---|
| 561 | } |
---|
| 562 | x = a = 0; |
---|
| 563 | pn = hGetpure(pure); |
---|
| 564 | sn = hGetmem(Nstc, stc, stcmem[iv]); |
---|
| 565 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
| 566 | if (a == Nstc) |
---|
| 567 | return pure[var[Nvar]] * hZeroMult(pn, sn, a, var, iv); |
---|
| 568 | else |
---|
| 569 | sum = x * hZeroMult(pn, sn, a, var, iv); |
---|
| 570 | b = a; |
---|
| 571 | loop |
---|
| 572 | { |
---|
| 573 | a0 = a; |
---|
| 574 | x0 = x; |
---|
| 575 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
| 576 | hElimS(sn, &b, a0, a, var, iv); |
---|
| 577 | a1 = a; |
---|
| 578 | hPure(sn, a0, &a1, var, iv, pn, &i); |
---|
| 579 | hLex2S(sn, b, a0, a1, var, iv, hwork); |
---|
| 580 | b += (a1 - a0); |
---|
| 581 | if (a < Nstc) |
---|
| 582 | { |
---|
| 583 | sum += (x - x0) * hZeroMult(pn, sn, b, var, iv); |
---|
| 584 | } |
---|
| 585 | else |
---|
| 586 | { |
---|
| 587 | sum += (pure[var[Nvar]] - x0) * hZeroMult(pn, sn, b, var, iv); |
---|
| 588 | return sum; |
---|
| 589 | } |
---|
| 590 | } |
---|
| 591 | } |
---|
| 592 | |
---|
| 593 | static void hProject(scmon pure, varset sel) |
---|
| 594 | { |
---|
| 595 | int i, i0, k; |
---|
| 596 | i0 = 0; |
---|
[1f637e] | 597 | for (i = 1; i <= (currRing->N); i++) |
---|
[35aab3] | 598 | { |
---|
| 599 | if (pure[i]) |
---|
| 600 | { |
---|
| 601 | i0++; |
---|
| 602 | sel[i0] = i; |
---|
| 603 | } |
---|
| 604 | } |
---|
| 605 | i = hNstc; |
---|
| 606 | memcpy(hwork, hstc, i * sizeof(scmon)); |
---|
| 607 | hStaircase(hwork, &i, sel, i0); |
---|
| 608 | if ((i0 > 2) && (i > 10)) |
---|
| 609 | hOrdSupp(hwork, i, sel, i0); |
---|
[1f637e] | 610 | memset(hpur0, 0, ((currRing->N) + 1) * sizeof(int)); |
---|
[35aab3] | 611 | hPure(hwork, 0, &i, sel, i0, hpur0, &k); |
---|
| 612 | hLexS(hwork, i, sel, i0); |
---|
| 613 | hMu += hZeroMult(hpur0, hwork, i, sel, i0); |
---|
| 614 | } |
---|
| 615 | |
---|
| 616 | static void hDimMult(scmon pure, int Npure, scfmon rad, int Nrad, |
---|
| 617 | varset var, int Nvar) |
---|
| 618 | { |
---|
| 619 | int dn, iv, rad0, b, c, x; |
---|
| 620 | scmon pn; |
---|
| 621 | scfmon rn; |
---|
| 622 | if (Nrad < 2) |
---|
| 623 | { |
---|
| 624 | dn = Npure + Nrad; |
---|
| 625 | if (dn == hCo) |
---|
| 626 | { |
---|
| 627 | if (!Nrad) |
---|
| 628 | hProject(pure, hsel); |
---|
| 629 | else |
---|
| 630 | { |
---|
| 631 | pn = *rad; |
---|
| 632 | for (iv = Nvar; iv; iv--) |
---|
| 633 | { |
---|
| 634 | x = var[iv]; |
---|
| 635 | if (pn[x]) |
---|
| 636 | { |
---|
| 637 | pure[x] = 1; |
---|
| 638 | hProject(pure, hsel); |
---|
| 639 | pure[x] = 0; |
---|
| 640 | } |
---|
| 641 | } |
---|
| 642 | } |
---|
| 643 | } |
---|
| 644 | return; |
---|
| 645 | } |
---|
| 646 | iv = Nvar; |
---|
| 647 | dn = Npure+1; |
---|
| 648 | if (dn >= hCo) |
---|
| 649 | { |
---|
| 650 | if (dn > hCo) |
---|
| 651 | return; |
---|
| 652 | loop |
---|
| 653 | { |
---|
| 654 | if(!pure[var[iv]]) |
---|
| 655 | { |
---|
| 656 | if(hNotZero(rad, Nrad, var, iv)) |
---|
| 657 | { |
---|
| 658 | pure[var[iv]] = 1; |
---|
| 659 | hProject(pure, hsel); |
---|
| 660 | pure[var[iv]] = 0; |
---|
| 661 | } |
---|
| 662 | } |
---|
| 663 | iv--; |
---|
| 664 | if (!iv) |
---|
| 665 | return; |
---|
| 666 | } |
---|
| 667 | } |
---|
| 668 | while(pure[var[iv]]) iv--; |
---|
| 669 | hStepR(rad, Nrad, var, iv, &rad0); |
---|
| 670 | iv--; |
---|
| 671 | if (rad0 < Nrad) |
---|
| 672 | { |
---|
| 673 | pn = hGetpure(pure); |
---|
| 674 | rn = hGetmem(Nrad, rad, radmem[iv]); |
---|
| 675 | pn[var[iv + 1]] = 1; |
---|
| 676 | hDimMult(pn, Npure + 1, rn, rad0, var, iv); |
---|
| 677 | pn[var[iv + 1]] = 0; |
---|
| 678 | b = rad0; |
---|
| 679 | c = Nrad; |
---|
| 680 | hElimR(rn, &rad0, b, c, var, iv); |
---|
| 681 | hPure(rn, b, &c, var, iv, pn, &x); |
---|
| 682 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
---|
| 683 | rad0 += (c - b); |
---|
| 684 | hDimMult(pn, Npure + x, rn, rad0, var, iv); |
---|
| 685 | } |
---|
| 686 | else |
---|
| 687 | { |
---|
| 688 | hDimMult(pure, Npure, rad, Nrad, var, iv); |
---|
| 689 | } |
---|
| 690 | } |
---|
| 691 | |
---|
| 692 | static void hDegree(ideal S, ideal Q) |
---|
| 693 | { |
---|
| 694 | int di; |
---|
| 695 | int mc; |
---|
| 696 | hexist = hInit(S, Q, &hNexist); |
---|
| 697 | if (!hNexist) |
---|
| 698 | { |
---|
| 699 | hCo = 0; |
---|
| 700 | hMu = 1; |
---|
| 701 | return; |
---|
| 702 | } |
---|
[b96d71] | 703 | //hWeight(); |
---|
[35aab3] | 704 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
[1f637e] | 705 | hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
| 706 | hsel = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
| 707 | hpure = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
| 708 | hpur0 = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
[35aab3] | 709 | mc = hisModule; |
---|
| 710 | hrad = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
| 711 | if (!mc) |
---|
| 712 | { |
---|
| 713 | memcpy(hrad, hexist, hNexist * sizeof(scmon)); |
---|
| 714 | hstc = hexist; |
---|
| 715 | hNrad = hNstc = hNexist; |
---|
| 716 | } |
---|
| 717 | else |
---|
| 718 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
[1f637e] | 719 | radmem = hCreate((currRing->N) - 1); |
---|
| 720 | stcmem = hCreate((currRing->N) - 1); |
---|
| 721 | hCo = (currRing->N) + 1; |
---|
[35aab3] | 722 | di = hCo + 1; |
---|
| 723 | loop |
---|
| 724 | { |
---|
| 725 | if (mc) |
---|
| 726 | { |
---|
| 727 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
---|
| 728 | hNstc = hNrad; |
---|
| 729 | memcpy(hstc, hrad, hNrad * sizeof(scmon)); |
---|
| 730 | } |
---|
| 731 | if (hNrad) |
---|
| 732 | { |
---|
[1f637e] | 733 | hNvar = (currRing->N); |
---|
[35aab3] | 734 | hRadical(hrad, &hNrad, hNvar); |
---|
| 735 | hSupp(hrad, hNrad, hvar, &hNvar); |
---|
| 736 | if (hNvar) |
---|
| 737 | { |
---|
| 738 | hCo = hNvar; |
---|
[1f637e] | 739 | memset(hpure, 0, ((currRing->N) + 1) * sizeof(int)); |
---|
[35aab3] | 740 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
---|
| 741 | hLexR(hrad, hNrad, hvar, hNvar); |
---|
| 742 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
| 743 | } |
---|
| 744 | } |
---|
| 745 | else |
---|
| 746 | { |
---|
| 747 | hNvar = 1; |
---|
| 748 | hCo = 0; |
---|
| 749 | } |
---|
| 750 | if (hCo < di) |
---|
| 751 | { |
---|
| 752 | di = hCo; |
---|
| 753 | hMu = 0; |
---|
| 754 | } |
---|
| 755 | if (hNvar && (hCo == di)) |
---|
| 756 | { |
---|
[1f637e] | 757 | if (di && (di < (currRing->N))) |
---|
[35aab3] | 758 | hDimMult(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
| 759 | else if (!di) |
---|
| 760 | hMu++; |
---|
| 761 | else |
---|
| 762 | { |
---|
| 763 | hStaircase(hstc, &hNstc, hvar, hNvar); |
---|
| 764 | if ((hNvar > 2) && (hNstc > 10)) |
---|
| 765 | hOrdSupp(hstc, hNstc, hvar, hNvar); |
---|
[1f637e] | 766 | memset(hpur0, 0, ((currRing->N) + 1) * sizeof(int)); |
---|
[35aab3] | 767 | hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure); |
---|
| 768 | hLexS(hstc, hNstc, hvar, hNvar); |
---|
| 769 | hMu += hZeroMult(hpur0, hstc, hNstc, hvar, hNvar); |
---|
| 770 | } |
---|
| 771 | } |
---|
| 772 | mc--; |
---|
| 773 | if (mc <= 0) |
---|
| 774 | break; |
---|
| 775 | } |
---|
| 776 | hCo = di; |
---|
[1f637e] | 777 | hKill(stcmem, (currRing->N) - 1); |
---|
| 778 | hKill(radmem, (currRing->N) - 1); |
---|
| 779 | omFreeSize((ADDRESS)hpur0, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
| 780 | omFreeSize((ADDRESS)hpure, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
| 781 | omFreeSize((ADDRESS)hsel, ((currRing->N) + 1) * sizeof(int)); |
---|
| 782 | omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int)); |
---|
[35aab3] | 783 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
| 784 | omFreeSize((ADDRESS)hrad, hNexist * sizeof(scmon)); |
---|
| 785 | hDelete(hexist, hNexist); |
---|
| 786 | if (hisModule) |
---|
| 787 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
| 788 | } |
---|
| 789 | |
---|
| 790 | int scMultInt(ideal S, ideal Q) |
---|
| 791 | { |
---|
| 792 | hDegree(S, Q); |
---|
| 793 | return hMu; |
---|
| 794 | } |
---|
| 795 | |
---|
| 796 | void scPrintDegree(int co, int mu) |
---|
| 797 | { |
---|
[1f637e] | 798 | int di = (currRing->N)-co; |
---|
[35aab3] | 799 | if (pOrdSgn == 1) |
---|
| 800 | { |
---|
[a4ceb4] | 801 | if (di>0) |
---|
[b2589b8] | 802 | Print("// dimension (proj.) = %d\n// degree (proj.) = %d\n", di-1, mu); |
---|
[35aab3] | 803 | else |
---|
[b2589b8] | 804 | Print("// dimension (affine) = 0\n// degree (affine) = %d\n", mu); |
---|
[35aab3] | 805 | } |
---|
| 806 | else |
---|
| 807 | Print("// dimension (local) = %d\n// multiplicity = %d\n", di, mu); |
---|
| 808 | } |
---|
| 809 | |
---|
[0f7ce1] | 810 | void scDegree(ideal S, intvec *modulweight, ideal Q) |
---|
[35aab3] | 811 | { |
---|
[0f7ce1] | 812 | int co, mu, l; |
---|
| 813 | intvec *hseries2; |
---|
| 814 | intvec *hseries1 = hFirstSeries(S, modulweight, Q); |
---|
| 815 | l = hseries1->length()-1; |
---|
| 816 | if (l > 1) |
---|
| 817 | hseries2 = hSecondSeries(hseries1); |
---|
| 818 | else |
---|
| 819 | hseries2 = hseries1; |
---|
| 820 | hDegreeSeries(hseries1, hseries2, &co, &mu); |
---|
| 821 | if ((l == 1) &&(mu == 0)) |
---|
[1f637e] | 822 | scPrintDegree((currRing->N)+1, 0); |
---|
[0f7ce1] | 823 | else |
---|
| 824 | scPrintDegree(co, mu); |
---|
| 825 | if (l>1) |
---|
| 826 | delete hseries1; |
---|
| 827 | delete hseries2; |
---|
[35aab3] | 828 | } |
---|
| 829 | |
---|
| 830 | static void hDegree0(ideal S, ideal Q) |
---|
| 831 | { |
---|
| 832 | int mc; |
---|
| 833 | hexist = hInit(S, Q, &hNexist); |
---|
| 834 | if (!hNexist) |
---|
| 835 | { |
---|
| 836 | hMu = -1; |
---|
| 837 | return; |
---|
| 838 | } |
---|
| 839 | else |
---|
| 840 | hMu = 0; |
---|
| 841 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
[1f637e] | 842 | hvar = (varset)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
| 843 | hpur0 = (scmon)omAlloc((1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
[35aab3] | 844 | mc = hisModule; |
---|
| 845 | if (!mc) |
---|
| 846 | { |
---|
| 847 | hstc = hexist; |
---|
| 848 | hNstc = hNexist; |
---|
| 849 | } |
---|
| 850 | else |
---|
| 851 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
[1f637e] | 852 | stcmem = hCreate((currRing->N) - 1); |
---|
[35aab3] | 853 | loop |
---|
| 854 | { |
---|
| 855 | if (mc) |
---|
| 856 | { |
---|
| 857 | hComp(hexist, hNexist, mc, hstc, &hNstc); |
---|
| 858 | if (!hNstc) |
---|
| 859 | { |
---|
| 860 | hMu = -1; |
---|
| 861 | break; |
---|
| 862 | } |
---|
| 863 | } |
---|
[1f637e] | 864 | hNvar = (currRing->N); |
---|
[35aab3] | 865 | for (int i = hNvar; i; i--) |
---|
| 866 | hvar[i] = i; |
---|
| 867 | hStaircase(hstc, &hNstc, hvar, hNvar); |
---|
| 868 | hSupp(hstc, hNstc, hvar, &hNvar); |
---|
[1f637e] | 869 | if ((hNvar == (currRing->N)) && (hNstc >= (currRing->N))) |
---|
[35aab3] | 870 | { |
---|
| 871 | if ((hNvar > 2) && (hNstc > 10)) |
---|
| 872 | hOrdSupp(hstc, hNstc, hvar, hNvar); |
---|
[1f637e] | 873 | memset(hpur0, 0, ((currRing->N) + 1) * sizeof(int)); |
---|
[35aab3] | 874 | hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure); |
---|
| 875 | if (hNpure == hNvar) |
---|
| 876 | { |
---|
| 877 | hLexS(hstc, hNstc, hvar, hNvar); |
---|
| 878 | hMu += hZeroMult(hpur0, hstc, hNstc, hvar, hNvar); |
---|
| 879 | } |
---|
| 880 | else |
---|
| 881 | hMu = -1; |
---|
| 882 | } |
---|
| 883 | else if (hNvar) |
---|
| 884 | hMu = -1; |
---|
| 885 | mc--; |
---|
| 886 | if (mc <= 0 || hMu < 0) |
---|
| 887 | break; |
---|
| 888 | } |
---|
[1f637e] | 889 | hKill(stcmem, (currRing->N) - 1); |
---|
| 890 | omFreeSize((ADDRESS)hpur0, (1 + ((currRing->N) * (currRing->N))) * sizeof(int)); |
---|
| 891 | omFreeSize((ADDRESS)hvar, ((currRing->N) + 1) * sizeof(int)); |
---|
[35aab3] | 892 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
| 893 | hDelete(hexist, hNexist); |
---|
| 894 | if (hisModule) |
---|
| 895 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
| 896 | } |
---|
| 897 | |
---|
| 898 | int scMult0Int(ideal S, ideal Q) |
---|
| 899 | { |
---|
| 900 | hDegree0(S, Q); |
---|
| 901 | return hMu; |
---|
| 902 | } |
---|
| 903 | |
---|
| 904 | |
---|
| 905 | // HC |
---|
| 906 | |
---|
| 907 | static poly pWork; |
---|
| 908 | |
---|
| 909 | static void hHedge(poly hEdge) |
---|
| 910 | { |
---|
| 911 | pSetm(pWork); |
---|
| 912 | if (pLmCmp(pWork, hEdge) == pOrdSgn) |
---|
| 913 | { |
---|
| 914 | for (int i = hNvar; i>0; i--) |
---|
| 915 | pSetExp(hEdge,i, pGetExp(pWork,i)); |
---|
| 916 | pSetm(hEdge); |
---|
| 917 | } |
---|
| 918 | } |
---|
| 919 | |
---|
| 920 | |
---|
| 921 | static void hHedgeStep(scmon pure, scfmon stc, |
---|
| 922 | int Nstc, varset var, int Nvar,poly hEdge) |
---|
| 923 | { |
---|
| 924 | int iv = Nvar -1, k = var[Nvar], a, a0, a1, b, i; |
---|
| 925 | int x, x0; |
---|
| 926 | scmon pn; |
---|
| 927 | scfmon sn; |
---|
| 928 | if (iv==0) |
---|
| 929 | { |
---|
| 930 | pSetExp(pWork, k, pure[k]); |
---|
| 931 | hHedge(hEdge); |
---|
| 932 | return; |
---|
| 933 | } |
---|
| 934 | else if (Nstc==0) |
---|
| 935 | { |
---|
| 936 | for (i = Nvar; i>0; i--) |
---|
| 937 | pSetExp(pWork, var[i], pure[var[i]]); |
---|
| 938 | hHedge(hEdge); |
---|
| 939 | return; |
---|
| 940 | } |
---|
| 941 | x = a = 0; |
---|
| 942 | pn = hGetpure(pure); |
---|
| 943 | sn = hGetmem(Nstc, stc, stcmem[iv]); |
---|
| 944 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
| 945 | if (a == Nstc) |
---|
| 946 | { |
---|
| 947 | pSetExp(pWork, k, pure[k]); |
---|
| 948 | hHedgeStep(pn, sn, a, var, iv,hEdge); |
---|
| 949 | return; |
---|
| 950 | } |
---|
| 951 | else |
---|
| 952 | { |
---|
| 953 | pSetExp(pWork, k, x); |
---|
| 954 | hHedgeStep(pn, sn, a, var, iv,hEdge); |
---|
| 955 | } |
---|
| 956 | b = a; |
---|
| 957 | loop |
---|
| 958 | { |
---|
| 959 | a0 = a; |
---|
| 960 | x0 = x; |
---|
| 961 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
| 962 | hElimS(sn, &b, a0, a, var, iv); |
---|
| 963 | a1 = a; |
---|
| 964 | hPure(sn, a0, &a1, var, iv, pn, &i); |
---|
| 965 | hLex2S(sn, b, a0, a1, var, iv, hwork); |
---|
| 966 | b += (a1 - a0); |
---|
| 967 | if (a < Nstc) |
---|
| 968 | { |
---|
| 969 | pSetExp(pWork, k, x); |
---|
| 970 | hHedgeStep(pn, sn, b, var, iv,hEdge); |
---|
| 971 | } |
---|
| 972 | else |
---|
| 973 | { |
---|
| 974 | pSetExp(pWork, k, pure[k]); |
---|
| 975 | hHedgeStep(pn, sn, b, var, iv,hEdge); |
---|
| 976 | return; |
---|
| 977 | } |
---|
| 978 | } |
---|
| 979 | } |
---|
| 980 | |
---|
| 981 | void scComputeHC(ideal S, ideal Q, int ak, poly &hEdge, ring tailRing) |
---|
| 982 | { |
---|
| 983 | int i; |
---|
| 984 | int k = ak; |
---|
[1f637e] | 985 | hNvar = (currRing->N); |
---|
[35aab3] | 986 | hexist = hInit(S, Q, &hNexist, tailRing); |
---|
| 987 | if (k!=0) |
---|
| 988 | hComp(hexist, hNexist, k, hexist, &hNstc); |
---|
| 989 | else |
---|
| 990 | hNstc = hNexist; |
---|
| 991 | hwork = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
| 992 | hvar = (varset)omAlloc((hNvar + 1) * sizeof(int)); |
---|
| 993 | hpure = (scmon)omAlloc((1 + (hNvar * hNvar)) * sizeof(int)); |
---|
| 994 | stcmem = hCreate(hNvar - 1); |
---|
| 995 | for (i = hNvar; i>0; i--) |
---|
| 996 | hvar[i] = i; |
---|
| 997 | hStaircase(hexist, &hNstc, hvar, hNvar); |
---|
| 998 | if ((hNvar > 2) && (hNstc > 10)) |
---|
| 999 | hOrdSupp(hexist, hNstc, hvar, hNvar); |
---|
| 1000 | memset(hpure, 0, (hNvar + 1) * sizeof(int)); |
---|
| 1001 | hPure(hexist, 0, &hNstc, hvar, hNvar, hpure, &hNpure); |
---|
| 1002 | hLexS(hexist, hNstc, hvar, hNvar); |
---|
| 1003 | if (hEdge!=NULL) |
---|
| 1004 | pLmFree(hEdge); |
---|
| 1005 | hEdge = pInit(); |
---|
| 1006 | pWork = pInit(); |
---|
| 1007 | hHedgeStep(hpure, hexist, hNstc, hvar, hNvar,hEdge); |
---|
| 1008 | pSetComp(hEdge,ak); |
---|
| 1009 | hKill(stcmem, hNvar - 1); |
---|
| 1010 | omFreeSize((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
| 1011 | omFreeSize((ADDRESS)hvar, (hNvar + 1) * sizeof(int)); |
---|
| 1012 | omFreeSize((ADDRESS)hpure, (1 + (hNvar * hNvar)) * sizeof(int)); |
---|
| 1013 | hDelete(hexist, hNexist); |
---|
| 1014 | pLmFree(pWork); |
---|
| 1015 | } |
---|
| 1016 | |
---|
| 1017 | |
---|
[894377] | 1018 | |
---|
[35aab3] | 1019 | // kbase |
---|
| 1020 | |
---|
| 1021 | static poly last; |
---|
| 1022 | static scmon act; |
---|
| 1023 | |
---|
| 1024 | static void scElKbase() |
---|
| 1025 | { |
---|
| 1026 | poly q = pInit(); |
---|
| 1027 | pSetCoeff0(q,nInit(1)); |
---|
| 1028 | pSetExpV(q,act); |
---|
| 1029 | pNext(q) = NULL; |
---|
| 1030 | last = pNext(last) = q; |
---|
| 1031 | } |
---|
| 1032 | |
---|
| 1033 | static int scMax( int i, scfmon stc, int Nvar) |
---|
| 1034 | { |
---|
| 1035 | int x, y=stc[0][Nvar]; |
---|
| 1036 | for (; i;) |
---|
| 1037 | { |
---|
| 1038 | i--; |
---|
| 1039 | x = stc[i][Nvar]; |
---|
| 1040 | if (x > y) y = x; |
---|
| 1041 | } |
---|
| 1042 | return y; |
---|
| 1043 | } |
---|
| 1044 | |
---|
| 1045 | static int scMin( int i, scfmon stc, int Nvar) |
---|
| 1046 | { |
---|
| 1047 | int x, y=stc[0][Nvar]; |
---|
| 1048 | for (; i;) |
---|
| 1049 | { |
---|
| 1050 | i--; |
---|
| 1051 | x = stc[i][Nvar]; |
---|
| 1052 | if (x < y) y = x; |
---|
| 1053 | } |
---|
| 1054 | return y; |
---|
| 1055 | } |
---|
| 1056 | |
---|
| 1057 | static int scRestrict( int &Nstc, scfmon stc, int Nvar) |
---|
| 1058 | { |
---|
| 1059 | int x, y; |
---|
| 1060 | int i, j, Istc = Nstc; |
---|
| 1061 | |
---|
[0d0ba9] | 1062 | y = INT_MAX; |
---|
[35aab3] | 1063 | for (i=Nstc-1; i>=0; i--) |
---|
| 1064 | { |
---|
| 1065 | j = Nvar-1; |
---|
| 1066 | loop |
---|
| 1067 | { |
---|
| 1068 | if(stc[i][j] != 0) break; |
---|
| 1069 | j--; |
---|
| 1070 | if (j == 0) |
---|
| 1071 | { |
---|
| 1072 | Istc--; |
---|
| 1073 | x = stc[i][Nvar]; |
---|
| 1074 | if (x < y) y = x; |
---|
| 1075 | stc[i] = NULL; |
---|
| 1076 | break; |
---|
| 1077 | } |
---|
| 1078 | } |
---|
| 1079 | } |
---|
| 1080 | if (Istc < Nstc) |
---|
| 1081 | { |
---|
| 1082 | for (i=Nstc-1; i>=0; i--) |
---|
| 1083 | { |
---|
| 1084 | if (stc[i] && (stc[i][Nvar] >= y)) |
---|
| 1085 | { |
---|
| 1086 | Istc--; |
---|
| 1087 | stc[i] = NULL; |
---|
| 1088 | } |
---|
| 1089 | } |
---|
| 1090 | j = 0; |
---|
| 1091 | while (stc[j]) j++; |
---|
| 1092 | i = j+1; |
---|
| 1093 | for(; i<Nstc; i++) |
---|
| 1094 | { |
---|
| 1095 | if (stc[i]) |
---|
| 1096 | { |
---|
| 1097 | stc[j] = stc[i]; |
---|
| 1098 | j++; |
---|
| 1099 | } |
---|
| 1100 | } |
---|
| 1101 | Nstc = Istc; |
---|
| 1102 | return y; |
---|
| 1103 | } |
---|
| 1104 | else |
---|
| 1105 | return -1; |
---|
| 1106 | } |
---|
| 1107 | |
---|
| 1108 | static void scAll( int Nvar, int deg) |
---|
| 1109 | { |
---|
| 1110 | int i; |
---|
| 1111 | int d = deg; |
---|
| 1112 | if (d == 0) |
---|
| 1113 | { |
---|
| 1114 | for (i=Nvar; i; i--) act[i] = 0; |
---|
| 1115 | scElKbase(); |
---|
| 1116 | return; |
---|
| 1117 | } |
---|
| 1118 | if (Nvar == 1) |
---|
| 1119 | { |
---|
| 1120 | act[1] = d; |
---|
| 1121 | scElKbase(); |
---|
| 1122 | return; |
---|
| 1123 | } |
---|
| 1124 | do |
---|
| 1125 | { |
---|
| 1126 | act[Nvar] = d; |
---|
| 1127 | scAll(Nvar-1, deg-d); |
---|
| 1128 | d--; |
---|
| 1129 | } while (d >= 0); |
---|
| 1130 | } |
---|
| 1131 | |
---|
| 1132 | static void scAllKbase( int Nvar, int ideg, int deg) |
---|
| 1133 | { |
---|
| 1134 | do |
---|
| 1135 | { |
---|
| 1136 | act[Nvar] = ideg; |
---|
| 1137 | scAll(Nvar-1, deg-ideg); |
---|
| 1138 | ideg--; |
---|
| 1139 | } while (ideg >= 0); |
---|
| 1140 | } |
---|
| 1141 | |
---|
| 1142 | static void scDegKbase( scfmon stc, int Nstc, int Nvar, int deg) |
---|
| 1143 | { |
---|
| 1144 | int Ivar, Istc, i, j; |
---|
| 1145 | scfmon sn; |
---|
| 1146 | int x, ideg; |
---|
| 1147 | |
---|
| 1148 | if (deg == 0) |
---|
| 1149 | { |
---|
[30d73e] | 1150 | for (i=Nstc-1; i>=0; i--) |
---|
| 1151 | { |
---|
| 1152 | for (j=Nvar;j;j--){ if(stc[i][j]) break; } |
---|
| 1153 | if (j==0){return;} |
---|
| 1154 | } |
---|
[35aab3] | 1155 | for (i=Nvar; i; i--) act[i] = 0; |
---|
| 1156 | scElKbase(); |
---|
| 1157 | return; |
---|
| 1158 | } |
---|
| 1159 | if (Nvar == 1) |
---|
| 1160 | { |
---|
| 1161 | for (i=Nstc-1; i>=0; i--) if(deg >= stc[i][1]) return; |
---|
| 1162 | act[1] = deg; |
---|
| 1163 | scElKbase(); |
---|
| 1164 | return; |
---|
| 1165 | } |
---|
| 1166 | Ivar = Nvar-1; |
---|
| 1167 | sn = hGetmem(Nstc, stc, stcmem[Ivar]); |
---|
| 1168 | x = scRestrict(Nstc, sn, Nvar); |
---|
| 1169 | if (x <= 0) |
---|
| 1170 | { |
---|
| 1171 | if (x == 0) return; |
---|
| 1172 | ideg = deg; |
---|
| 1173 | } |
---|
| 1174 | else |
---|
| 1175 | { |
---|
| 1176 | if (deg < x) ideg = deg; |
---|
| 1177 | else ideg = x-1; |
---|
| 1178 | if (Nstc == 0) |
---|
| 1179 | { |
---|
| 1180 | scAllKbase(Nvar, ideg, deg); |
---|
| 1181 | return; |
---|
| 1182 | } |
---|
| 1183 | } |
---|
| 1184 | loop |
---|
| 1185 | { |
---|
| 1186 | x = scMax(Nstc, sn, Nvar); |
---|
| 1187 | while (ideg >= x) |
---|
| 1188 | { |
---|
| 1189 | act[Nvar] = ideg; |
---|
| 1190 | scDegKbase(sn, Nstc, Ivar, deg-ideg); |
---|
| 1191 | ideg--; |
---|
| 1192 | } |
---|
| 1193 | if (ideg < 0) return; |
---|
| 1194 | Istc = Nstc; |
---|
| 1195 | for (i=Nstc-1; i>=0; i--) |
---|
| 1196 | { |
---|
| 1197 | if (ideg < sn[i][Nvar]) |
---|
| 1198 | { |
---|
| 1199 | Istc--; |
---|
| 1200 | sn[i] = NULL; |
---|
| 1201 | } |
---|
| 1202 | } |
---|
| 1203 | if (Istc == 0) |
---|
| 1204 | { |
---|
| 1205 | scAllKbase(Nvar, ideg, deg); |
---|
| 1206 | return; |
---|
| 1207 | } |
---|
| 1208 | j = 0; |
---|
| 1209 | while (sn[j]) j++; |
---|
| 1210 | i = j+1; |
---|
| 1211 | for (; i<Nstc; i++) |
---|
| 1212 | { |
---|
| 1213 | if (sn[i]) |
---|
| 1214 | { |
---|
| 1215 | sn[j] = sn[i]; |
---|
| 1216 | j++; |
---|
| 1217 | } |
---|
| 1218 | } |
---|
| 1219 | Nstc = Istc; |
---|
| 1220 | } |
---|
| 1221 | } |
---|
| 1222 | |
---|
| 1223 | static void scInKbase( scfmon stc, int Nstc, int Nvar) |
---|
| 1224 | { |
---|
| 1225 | int Ivar, Istc, i, j; |
---|
| 1226 | scfmon sn; |
---|
| 1227 | int x, ideg; |
---|
| 1228 | |
---|
| 1229 | if (Nvar == 1) |
---|
| 1230 | { |
---|
| 1231 | ideg = scMin(Nstc, stc, 1); |
---|
| 1232 | while (ideg > 0) |
---|
| 1233 | { |
---|
| 1234 | ideg--; |
---|
| 1235 | act[1] = ideg; |
---|
| 1236 | scElKbase(); |
---|
| 1237 | } |
---|
| 1238 | return; |
---|
| 1239 | } |
---|
| 1240 | Ivar = Nvar-1; |
---|
| 1241 | sn = hGetmem(Nstc, stc, stcmem[Ivar]); |
---|
| 1242 | x = scRestrict(Nstc, sn, Nvar); |
---|
| 1243 | if (x == 0) return; |
---|
| 1244 | ideg = x-1; |
---|
| 1245 | loop |
---|
| 1246 | { |
---|
| 1247 | x = scMax(Nstc, sn, Nvar); |
---|
| 1248 | while (ideg >= x) |
---|
| 1249 | { |
---|
| 1250 | act[Nvar] = ideg; |
---|
| 1251 | scInKbase(sn, Nstc, Ivar); |
---|
| 1252 | ideg--; |
---|
| 1253 | } |
---|
| 1254 | if (ideg < 0) return; |
---|
| 1255 | Istc = Nstc; |
---|
| 1256 | for (i=Nstc-1; i>=0; i--) |
---|
| 1257 | { |
---|
| 1258 | if (ideg < sn[i][Nvar]) |
---|
| 1259 | { |
---|
| 1260 | Istc--; |
---|
| 1261 | sn[i] = NULL; |
---|
| 1262 | } |
---|
| 1263 | } |
---|
| 1264 | j = 0; |
---|
| 1265 | while (sn[j]) j++; |
---|
| 1266 | i = j+1; |
---|
| 1267 | for (; i<Nstc; i++) |
---|
| 1268 | { |
---|
| 1269 | if (sn[i]) |
---|
| 1270 | { |
---|
| 1271 | sn[j] = sn[i]; |
---|
| 1272 | j++; |
---|
| 1273 | } |
---|
| 1274 | } |
---|
| 1275 | Nstc = Istc; |
---|
| 1276 | } |
---|
| 1277 | } |
---|
| 1278 | |
---|
| 1279 | static ideal scIdKbase() |
---|
| 1280 | { |
---|
| 1281 | polyset mm; |
---|
| 1282 | ideal res; |
---|
| 1283 | poly p, q = last; |
---|
| 1284 | int i = pLength(q); |
---|
| 1285 | res = idInit(i,1); |
---|
| 1286 | mm = res->m; |
---|
| 1287 | i = 0; |
---|
| 1288 | do |
---|
| 1289 | { |
---|
| 1290 | mm[i] = q; |
---|
| 1291 | i++; |
---|
| 1292 | p = pNext(q); |
---|
| 1293 | pNext(q) = NULL; |
---|
| 1294 | q = p; |
---|
| 1295 | } while (q!=NULL); |
---|
| 1296 | return res; |
---|
| 1297 | } |
---|
| 1298 | |
---|
[5563ba] | 1299 | ideal scKBase(int deg, ideal s, ideal Q, intvec * mv) |
---|
[35aab3] | 1300 | { |
---|
| 1301 | int i, di; |
---|
| 1302 | poly p; |
---|
| 1303 | |
---|
| 1304 | if (deg < 0) |
---|
| 1305 | { |
---|
| 1306 | di = scDimInt(s, Q); |
---|
| 1307 | if (di != 0) |
---|
| 1308 | { |
---|
| 1309 | //Werror("KBase not finite"); |
---|
| 1310 | return idInit(1,s->rank); |
---|
| 1311 | } |
---|
| 1312 | } |
---|
[1f637e] | 1313 | stcmem = hCreate((currRing->N) - 1); |
---|
[35aab3] | 1314 | hexist = hInit(s, Q, &hNexist); |
---|
| 1315 | p = last = pInit(); |
---|
| 1316 | /*pNext(p) = NULL;*/ |
---|
[1f637e] | 1317 | act = (scmon)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
[35aab3] | 1318 | *act = 0; |
---|
| 1319 | if (!hNexist) |
---|
| 1320 | { |
---|
[1f637e] | 1321 | scAll((currRing->N), deg); |
---|
[35aab3] | 1322 | goto ende; |
---|
| 1323 | } |
---|
| 1324 | if (!hisModule) |
---|
| 1325 | { |
---|
[1f637e] | 1326 | if (deg < 0) scInKbase(hexist, hNexist, (currRing->N)); |
---|
| 1327 | else scDegKbase(hexist, hNexist, (currRing->N), deg); |
---|
[35aab3] | 1328 | } |
---|
| 1329 | else |
---|
| 1330 | { |
---|
| 1331 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
| 1332 | for (i = 1; i <= hisModule; i++) |
---|
| 1333 | { |
---|
| 1334 | *act = i; |
---|
| 1335 | hComp(hexist, hNexist, i, hstc, &hNstc); |
---|
[5563ba] | 1336 | int deg_ei=deg; |
---|
| 1337 | if (mv!=NULL) deg_ei -= (*mv)[i-1]; |
---|
| 1338 | if ((deg < 0) || (deg_ei>=0)) |
---|
[35aab3] | 1339 | { |
---|
[5563ba] | 1340 | if (hNstc) |
---|
| 1341 | { |
---|
[1f637e] | 1342 | if (deg < 0) scInKbase(hstc, hNstc, (currRing->N)); |
---|
| 1343 | else scDegKbase(hstc, hNstc, (currRing->N), deg_ei); |
---|
[5563ba] | 1344 | } |
---|
| 1345 | else |
---|
[1f637e] | 1346 | scAll((currRing->N), deg_ei); |
---|
[35aab3] | 1347 | } |
---|
| 1348 | } |
---|
| 1349 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
| 1350 | } |
---|
| 1351 | ende: |
---|
| 1352 | hDelete(hexist, hNexist); |
---|
[1f637e] | 1353 | omFreeSize((ADDRESS)act, ((currRing->N) + 1) * sizeof(int)); |
---|
| 1354 | hKill(stcmem, (currRing->N) - 1); |
---|
[fb82895] | 1355 | pLmDelete(&p); |
---|
[35aab3] | 1356 | if (p == NULL) |
---|
| 1357 | return idInit(1,s->rank); |
---|
| 1358 | else |
---|
| 1359 | { |
---|
| 1360 | last = p; |
---|
| 1361 | ideal res=scIdKbase(); |
---|
| 1362 | res->rank=s->rank; |
---|
| 1363 | return res; |
---|
| 1364 | } |
---|
| 1365 | } |
---|
| 1366 | |
---|
[bdd0c97] | 1367 | #if 0 //-- alternative implementation of scComputeHC |
---|
[894377] | 1368 | void scComputeHCw(ideal ss, ideal Q, int ak, poly &hEdge, ring tailRing) |
---|
| 1369 | { |
---|
| 1370 | int i, di; |
---|
| 1371 | poly p; |
---|
| 1372 | |
---|
| 1373 | if (hEdge!=NULL) |
---|
| 1374 | pLmFree(hEdge); |
---|
[35aab3] | 1375 | |
---|
[894377] | 1376 | ideal s=idInit(IDELEMS(ss),ak); |
---|
| 1377 | for(i=IDELEMS(ss)-1;i>=0;i--) |
---|
| 1378 | { |
---|
| 1379 | if (ss->m[i]!=NULL) s->m[i]=pHead(ss->m[i]); |
---|
| 1380 | } |
---|
| 1381 | di = scDimInt(s, Q); |
---|
[1f637e] | 1382 | stcmem = hCreate((currRing->N) - 1); |
---|
[894377] | 1383 | hexist = hInit(s, Q, &hNexist); |
---|
| 1384 | p = last = pInit(); |
---|
| 1385 | /*pNext(p) = NULL;*/ |
---|
[1f637e] | 1386 | act = (scmon)omAlloc(((currRing->N) + 1) * sizeof(int)); |
---|
[894377] | 1387 | *act = 0; |
---|
| 1388 | if (!hNexist) |
---|
| 1389 | { |
---|
[1f637e] | 1390 | scAll((currRing->N), -1); |
---|
[894377] | 1391 | goto ende; |
---|
| 1392 | } |
---|
| 1393 | if (!hisModule) |
---|
| 1394 | { |
---|
[1f637e] | 1395 | scInKbase(hexist, hNexist, (currRing->N)); |
---|
[894377] | 1396 | } |
---|
| 1397 | else |
---|
| 1398 | { |
---|
| 1399 | hstc = (scfmon)omAlloc(hNexist * sizeof(scmon)); |
---|
| 1400 | for (i = 1; i <= hisModule; i++) |
---|
| 1401 | { |
---|
| 1402 | *act = i; |
---|
| 1403 | hComp(hexist, hNexist, i, hstc, &hNstc); |
---|
| 1404 | if (hNstc) |
---|
| 1405 | { |
---|
[1f637e] | 1406 | scInKbase(hstc, hNstc, (currRing->N)); |
---|
[894377] | 1407 | } |
---|
| 1408 | else |
---|
[1f637e] | 1409 | scAll((currRing->N), -1); |
---|
[894377] | 1410 | } |
---|
| 1411 | omFreeSize((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
| 1412 | } |
---|
| 1413 | ende: |
---|
| 1414 | hDelete(hexist, hNexist); |
---|
[1f637e] | 1415 | omFreeSize((ADDRESS)act, ((currRing->N) + 1) * sizeof(int)); |
---|
| 1416 | hKill(stcmem, (currRing->N) - 1); |
---|
[894377] | 1417 | pDeleteLm(&p); |
---|
| 1418 | idDelete(&s); |
---|
| 1419 | if (p == NULL) |
---|
| 1420 | { |
---|
| 1421 | return; // no HEdge |
---|
| 1422 | } |
---|
| 1423 | else |
---|
| 1424 | { |
---|
| 1425 | last = p; |
---|
| 1426 | ideal res=scIdKbase(); |
---|
| 1427 | res->rank=ss->rank; |
---|
[e4ca29b] | 1428 | poly p_ind=res->m[0]; int ind=0; |
---|
| 1429 | for(i=IDELEMS(res)-1;i>0;i--) |
---|
[894377] | 1430 | { |
---|
[e4ca29b] | 1431 | if (pCmp(res->m[i],p_ind)==-1) { p_ind=res->m[i]; ind=i; } |
---|
[894377] | 1432 | } |
---|
| 1433 | assume(p_ind!=NULL); |
---|
| 1434 | assume(res->m[ind]==p_ind); |
---|
| 1435 | hEdge=p_ind; |
---|
| 1436 | res->m[ind]=NULL; |
---|
| 1437 | nDelete(&pGetCoeff(hEdge)); |
---|
| 1438 | pGetCoeff(hEdge)=NULL; |
---|
[1f637e] | 1439 | for(i=(currRing->N);i>0;i--) |
---|
[894377] | 1440 | pIncrExp(hEdge,i); |
---|
| 1441 | pSetm(hEdge); |
---|
| 1442 | |
---|
| 1443 | idDelete(&res); |
---|
| 1444 | return; |
---|
| 1445 | } |
---|
| 1446 | } |
---|
[e4ca29b] | 1447 | #endif |
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