[0e1846] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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[99cfcba] | 4 | /* $Id: hdegree.cc,v 1.12 1998-04-08 10:01:58 pohl Exp $ */ |
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[0e1846] | 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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| 9 | #include "mod2.h" |
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| 10 | #include "tok.h" |
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| 11 | #include "lists.h" |
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| 12 | #include "febase.h" |
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| 13 | #include "mmemory.h" |
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| 14 | #include "ipid.h" |
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| 15 | #include "ideals.h" |
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| 16 | #include "polys.h" |
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| 17 | #include "intvec.h" |
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[b5ae52] | 18 | #include "numbers.h" |
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[0e1846] | 19 | #include "hutil.h" |
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| 20 | #include "stairc.h" |
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| 21 | |
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| 22 | static int hCo, hMu, hMu2; |
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| 23 | |
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| 24 | /*0 implementation*/ |
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| 25 | |
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| 26 | // dimension |
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| 27 | |
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| 28 | static void hDimSolve(scmon pure, int Npure, scfmon rad, int Nrad, |
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| 29 | varset var, int Nvar) |
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| 30 | { |
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| 31 | int dn, iv, rad0, b, c, x; |
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| 32 | scmon pn; |
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| 33 | scfmon rn; |
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| 34 | if (Nrad < 2) |
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| 35 | { |
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| 36 | dn = Npure + Nrad; |
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| 37 | if (dn < hCo) |
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| 38 | hCo = dn; |
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| 39 | return; |
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| 40 | } |
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| 41 | if (Npure+1 >= hCo) |
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| 42 | return; |
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| 43 | iv = Nvar; |
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| 44 | while(pure[var[iv]]) iv--; |
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| 45 | hStepR(rad, Nrad, var, iv, &rad0); |
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[25f470] | 46 | if (rad0!=0) |
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[0e1846] | 47 | { |
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| 48 | iv--; |
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| 49 | if (rad0 < Nrad) |
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| 50 | { |
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| 51 | pn = hGetpure(pure); |
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| 52 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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| 53 | hDimSolve(pn, Npure + 1, rn, rad0, var, iv); |
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| 54 | b = rad0; |
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| 55 | c = Nrad; |
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| 56 | hElimR(rn, &rad0, b, c, var, iv); |
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| 57 | hPure(rn, b, &c, var, iv, pn, &x); |
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| 58 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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| 59 | rad0 += (c - b); |
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| 60 | hDimSolve(pn, Npure + x, rn, rad0, var, iv); |
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| 61 | } |
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| 62 | else |
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| 63 | { |
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| 64 | hDimSolve(pure, Npure, rad, Nrad, var, iv); |
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| 65 | } |
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| 66 | } |
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| 67 | else |
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| 68 | hCo = Npure + 1; |
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| 69 | } |
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| 70 | |
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| 71 | int scDimInt(ideal S, ideal Q) |
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| 72 | { |
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[e78cce] | 73 | Exponent_t mc; |
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[0e1846] | 74 | hexist = hInit(S, Q, &hNexist); |
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[99cfcba] | 75 | if (!hNexist) |
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[0e1846] | 76 | return pVariables; |
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| 77 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
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| 78 | hvar = (varset)Alloc((pVariables + 1) * sizeof(int)); |
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[e78cce] | 79 | hpure = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
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[0e1846] | 80 | mc = hisModule; |
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[99cfcba] | 81 | if (!mc) |
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[0e1846] | 82 | { |
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| 83 | hrad = hexist; |
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| 84 | hNrad = hNexist; |
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| 85 | } |
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| 86 | else |
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| 87 | hrad = (scfmon)Alloc(hNexist * sizeof(scmon)); |
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| 88 | radmem = hCreate(pVariables - 1); |
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| 89 | hCo = pVariables + 1; |
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| 90 | loop |
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| 91 | { |
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[99cfcba] | 92 | if (mc) |
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[0e1846] | 93 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
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[99cfcba] | 94 | if (hNrad) |
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[0e1846] | 95 | { |
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| 96 | hNvar = pVariables; |
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| 97 | hRadical(hrad, &hNrad, hNvar); |
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| 98 | hSupp(hrad, hNrad, hvar, &hNvar); |
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[99cfcba] | 99 | if (hNvar) |
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[0e1846] | 100 | { |
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[e78cce] | 101 | memset(hpure, 0, (pVariables + 1) * sizeof(Exponent_t)); |
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[0e1846] | 102 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
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| 103 | hLexR(hrad, hNrad, hvar, hNvar); |
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| 104 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
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| 105 | } |
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| 106 | } |
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| 107 | else |
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| 108 | { |
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| 109 | hCo = 0; |
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| 110 | break; |
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| 111 | } |
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| 112 | mc--; |
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| 113 | if (mc <= 0) |
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| 114 | break; |
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| 115 | } |
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| 116 | hKill(radmem, pVariables - 1); |
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[e78cce] | 117 | Free((ADDRESS)hpure, (1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
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[0e1846] | 118 | Free((ADDRESS)hvar, (pVariables + 1) * sizeof(int)); |
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| 119 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
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[e78cce] | 120 | hDelete(hexist, hNexist); |
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[99cfcba] | 121 | if (hisModule) |
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[0e1846] | 122 | Free((ADDRESS)hrad, hNexist * sizeof(scmon)); |
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| 123 | return pVariables - hCo; |
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| 124 | } |
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| 125 | |
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| 126 | // independent set |
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| 127 | static scmon hInd; |
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| 128 | |
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| 129 | static void hIndSolve(scmon pure, int Npure, scfmon rad, int Nrad, |
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| 130 | varset var, int Nvar) |
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| 131 | { |
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| 132 | int dn, iv, rad0, b, c, x; |
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| 133 | scmon pn; |
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| 134 | scfmon rn; |
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| 135 | if (Nrad < 2) |
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| 136 | { |
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| 137 | dn = Npure + Nrad; |
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| 138 | if (dn < hCo) |
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| 139 | { |
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| 140 | hCo = dn; |
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[99cfcba] | 141 | for (iv=pVariables; iv; iv--) |
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[0e1846] | 142 | { |
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[99cfcba] | 143 | if (pure[iv]) |
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[0e1846] | 144 | hInd[iv] = 0; |
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| 145 | else |
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| 146 | hInd[iv] = 1; |
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| 147 | } |
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[99cfcba] | 148 | if (Nrad) |
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[0e1846] | 149 | { |
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| 150 | pn = *rad; |
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| 151 | iv = Nvar; |
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| 152 | loop |
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| 153 | { |
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| 154 | x = var[iv]; |
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[99cfcba] | 155 | if (pn[x]) |
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[0e1846] | 156 | { |
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| 157 | hInd[x] = 0; |
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| 158 | break; |
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| 159 | } |
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| 160 | iv--; |
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| 161 | } |
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| 162 | } |
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| 163 | } |
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| 164 | return; |
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| 165 | } |
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| 166 | if (Npure+1 >= hCo) |
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| 167 | return; |
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| 168 | iv = Nvar; |
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| 169 | while(pure[var[iv]]) iv--; |
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| 170 | hStepR(rad, Nrad, var, iv, &rad0); |
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[99cfcba] | 171 | if (rad0) |
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[0e1846] | 172 | { |
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| 173 | iv--; |
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| 174 | if (rad0 < Nrad) |
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| 175 | { |
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| 176 | pn = hGetpure(pure); |
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| 177 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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| 178 | pn[var[iv + 1]] = 1; |
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| 179 | hIndSolve(pn, Npure + 1, rn, rad0, var, iv); |
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| 180 | pn[var[iv + 1]] = 0; |
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| 181 | b = rad0; |
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| 182 | c = Nrad; |
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| 183 | hElimR(rn, &rad0, b, c, var, iv); |
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| 184 | hPure(rn, b, &c, var, iv, pn, &x); |
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| 185 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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| 186 | rad0 += (c - b); |
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| 187 | hIndSolve(pn, Npure + x, rn, rad0, var, iv); |
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| 188 | } |
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| 189 | else |
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| 190 | { |
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| 191 | hIndSolve(pure, Npure, rad, Nrad, var, iv); |
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| 192 | } |
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| 193 | } |
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| 194 | else |
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| 195 | { |
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| 196 | hCo = Npure + 1; |
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[99cfcba] | 197 | for (x=pVariables; x; x--) |
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[0e1846] | 198 | { |
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[99cfcba] | 199 | if (pure[x]) |
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[0e1846] | 200 | hInd[x] = 0; |
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| 201 | else |
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| 202 | hInd[x] = 1; |
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| 203 | } |
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| 204 | hInd[var[iv]] = 0; |
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| 205 | } |
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| 206 | } |
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| 207 | |
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| 208 | intvec * scIndIntvec(ideal S, ideal Q) |
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| 209 | { |
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| 210 | intvec *Set=new intvec(pVariables); |
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[e78cce] | 211 | Exponent_t mc,i; |
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[0e1846] | 212 | hexist = hInit(S, Q, &hNexist); |
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[25f470] | 213 | if (hNexist==0) |
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[0e1846] | 214 | { |
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| 215 | for(i=0; i<pVariables; i++) |
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| 216 | (*Set)[i]=1; |
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| 217 | return Set; |
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| 218 | } |
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| 219 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
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| 220 | hvar = (varset)Alloc((pVariables + 1) * sizeof(int)); |
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[e78cce] | 221 | hpure = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
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| 222 | hInd = (scmon)Alloc((1 + pVariables) * sizeof(Exponent_t)); |
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[0e1846] | 223 | mc = hisModule; |
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[25f470] | 224 | if (mc==0) |
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[0e1846] | 225 | { |
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| 226 | hrad = hexist; |
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| 227 | hNrad = hNexist; |
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| 228 | } |
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| 229 | else |
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| 230 | hrad = (scfmon)Alloc(hNexist * sizeof(scmon)); |
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| 231 | radmem = hCreate(pVariables - 1); |
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| 232 | hCo = pVariables + 1; |
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| 233 | loop |
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| 234 | { |
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[25f470] | 235 | if (mc!=0) |
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[0e1846] | 236 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
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[25f470] | 237 | if (hNrad!=0) |
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[0e1846] | 238 | { |
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| 239 | hNvar = pVariables; |
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| 240 | hRadical(hrad, &hNrad, hNvar); |
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| 241 | hSupp(hrad, hNrad, hvar, &hNvar); |
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[25f470] | 242 | if (hNvar!=0) |
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[0e1846] | 243 | { |
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[e78cce] | 244 | memset(hpure, 0, (pVariables + 1) * sizeof(Exponent_t)); |
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[0e1846] | 245 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
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| 246 | hLexR(hrad, hNrad, hvar, hNvar); |
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| 247 | hIndSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
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| 248 | } |
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| 249 | } |
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| 250 | else |
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| 251 | { |
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| 252 | hCo = 0; |
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| 253 | break; |
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| 254 | } |
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| 255 | mc--; |
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| 256 | if (mc <= 0) |
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| 257 | break; |
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| 258 | } |
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| 259 | for(i=0; i<pVariables; i++) |
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| 260 | (*Set)[i] = hInd[i+1]; |
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| 261 | hKill(radmem, pVariables - 1); |
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[e78cce] | 262 | Free((ADDRESS)hpure, (1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
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| 263 | Free((ADDRESS)hInd, (1 + pVariables) * sizeof(Exponent_t)); |
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[0e1846] | 264 | Free((ADDRESS)hvar, (pVariables + 1) * sizeof(int)); |
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| 265 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
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[e78cce] | 266 | hDelete(hexist, hNexist); |
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[99cfcba] | 267 | if (hisModule) |
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[0e1846] | 268 | Free((ADDRESS)hrad, hNexist * sizeof(scmon)); |
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| 269 | return Set; |
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| 270 | } |
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| 271 | |
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| 272 | typedef struct sindlist indlist; |
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| 273 | typedef indlist * indset; |
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| 274 | |
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| 275 | struct sindlist |
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| 276 | { |
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| 277 | indset nx; |
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| 278 | intvec * set; |
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| 279 | }; |
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| 280 | indset ISet, JSet; |
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| 281 | |
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| 282 | static BOOLEAN hNotZero(scfmon rad, int Nrad, varset var, int Nvar) |
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| 283 | { |
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| 284 | int k1, i; |
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| 285 | k1 = var[Nvar]; |
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| 286 | i = 0; |
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| 287 | loop |
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| 288 | { |
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| 289 | if (rad[i][k1]==0) |
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| 290 | return FALSE; |
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| 291 | i++; |
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| 292 | if (i == Nrad) |
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| 293 | return TRUE; |
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| 294 | } |
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| 295 | } |
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| 296 | |
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| 297 | static void hIndep(scmon pure) |
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| 298 | { |
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| 299 | int iv; |
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| 300 | intvec *Set; |
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| 301 | |
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| 302 | Set = ISet->set = new intvec(pVariables); |
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[25f470] | 303 | for (iv=pVariables; iv!=0 ; iv--) |
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[0e1846] | 304 | { |
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[99cfcba] | 305 | if (pure[iv]) |
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[0e1846] | 306 | (*Set)[iv-1] = 0; |
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| 307 | else |
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| 308 | (*Set)[iv-1] = 1; |
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| 309 | } |
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| 310 | ISet = ISet->nx = (indset)Alloc0(sizeof(indlist)); |
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| 311 | hMu++; |
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| 312 | } |
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| 313 | |
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| 314 | static void hIndMult(scmon pure, int Npure, scfmon rad, int Nrad, |
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| 315 | varset var, int Nvar) |
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| 316 | { |
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| 317 | int dn, iv, rad0, b, c, x; |
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| 318 | scmon pn; |
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| 319 | scfmon rn; |
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| 320 | if (Nrad < 2) |
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| 321 | { |
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| 322 | dn = Npure + Nrad; |
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| 323 | if (dn == hCo) |
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| 324 | { |
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[25f470] | 325 | if (Nrad==0) |
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[0e1846] | 326 | hIndep(pure); |
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| 327 | else |
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| 328 | { |
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| 329 | pn = *rad; |
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[25f470] | 330 | for (iv = Nvar; iv!=0; iv--) |
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[0e1846] | 331 | { |
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| 332 | x = var[iv]; |
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[99cfcba] | 333 | if (pn[x]) |
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[0e1846] | 334 | { |
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| 335 | pure[x] = 1; |
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| 336 | hIndep(pure); |
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| 337 | pure[x] = 0; |
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| 338 | } |
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| 339 | } |
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| 340 | } |
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| 341 | } |
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| 342 | return; |
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| 343 | } |
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| 344 | iv = Nvar; |
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| 345 | dn = Npure+1; |
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| 346 | if (dn >= hCo) |
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| 347 | { |
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| 348 | if (dn > hCo) |
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| 349 | return; |
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| 350 | loop |
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| 351 | { |
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[99cfcba] | 352 | if(!pure[var[iv]]) |
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[0e1846] | 353 | { |
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| 354 | if(hNotZero(rad, Nrad, var, iv)) |
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| 355 | { |
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| 356 | pure[var[iv]] = 1; |
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| 357 | hIndep(pure); |
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| 358 | pure[var[iv]] = 0; |
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| 359 | } |
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| 360 | } |
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| 361 | iv--; |
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[99cfcba] | 362 | if (!iv) |
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[0e1846] | 363 | return; |
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| 364 | } |
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| 365 | } |
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[99cfcba] | 366 | while(pure[var[iv]]) iv--; |
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[0e1846] | 367 | hStepR(rad, Nrad, var, iv, &rad0); |
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| 368 | iv--; |
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| 369 | if (rad0 < Nrad) |
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| 370 | { |
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| 371 | pn = hGetpure(pure); |
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| 372 | rn = hGetmem(Nrad, rad, radmem[iv]); |
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| 373 | pn[var[iv + 1]] = 1; |
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| 374 | hIndMult(pn, Npure + 1, rn, rad0, var, iv); |
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| 375 | pn[var[iv + 1]] = 0; |
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| 376 | b = rad0; |
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| 377 | c = Nrad; |
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| 378 | hElimR(rn, &rad0, b, c, var, iv); |
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| 379 | hPure(rn, b, &c, var, iv, pn, &x); |
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| 380 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
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| 381 | rad0 += (c - b); |
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| 382 | hIndMult(pn, Npure + x, rn, rad0, var, iv); |
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| 383 | } |
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| 384 | else |
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| 385 | { |
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| 386 | hIndMult(pure, Npure, rad, Nrad, var, iv); |
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| 387 | } |
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| 388 | } |
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| 389 | |
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| 390 | /*3 |
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| 391 | * consider indset x := !pure |
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| 392 | * (for all i) (if(sm(i) > x) return FALSE) |
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| 393 | * else return TRUE |
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| 394 | */ |
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| 395 | static BOOLEAN hCheck1(indset sm, scmon pure) |
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| 396 | { |
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| 397 | int iv; |
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| 398 | intvec *Set; |
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| 399 | while (sm->nx != NULL) |
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| 400 | { |
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| 401 | Set = sm->set; |
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| 402 | iv=pVariables; |
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| 403 | loop |
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| 404 | { |
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| 405 | if (((*Set)[iv-1] == 0) && (pure[iv] == 0)) |
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| 406 | break; |
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| 407 | iv--; |
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| 408 | if (iv == 0) |
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| 409 | return FALSE; |
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| 410 | } |
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| 411 | sm = sm->nx; |
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| 412 | } |
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| 413 | return TRUE; |
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| 414 | } |
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| 415 | |
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| 416 | /*3 |
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| 417 | * consider indset x := !pure |
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| 418 | * (for all i) if(x > sm(i)) delete sm(i)) |
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| 419 | * return (place for x) |
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| 420 | */ |
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| 421 | static indset hCheck2(indset sm, scmon pure) |
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| 422 | { |
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| 423 | int iv; |
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| 424 | intvec *Set; |
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| 425 | indset be, a1 = NULL; |
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| 426 | while (sm->nx != NULL) |
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| 427 | { |
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| 428 | Set = sm->set; |
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| 429 | iv=pVariables; |
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| 430 | loop |
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| 431 | { |
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| 432 | if ((pure[iv] == 1) && ((*Set)[iv-1] == 1)) |
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| 433 | break; |
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| 434 | iv--; |
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| 435 | if (iv == 0) |
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| 436 | { |
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| 437 | if (a1 == NULL) |
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| 438 | { |
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| 439 | a1 = sm; |
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| 440 | } |
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| 441 | else |
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| 442 | { |
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| 443 | hMu2--; |
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| 444 | be->nx = sm->nx; |
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| 445 | delete Set; |
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| 446 | Free((ADDRESS)sm,sizeof(indlist)); |
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| 447 | sm = be; |
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| 448 | } |
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| 449 | break; |
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| 450 | } |
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| 451 | } |
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| 452 | be = sm; |
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| 453 | sm = sm->nx; |
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| 454 | } |
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| 455 | if (a1 != NULL) |
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| 456 | { |
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| 457 | return a1; |
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| 458 | } |
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| 459 | else |
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| 460 | { |
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| 461 | hMu2++; |
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| 462 | sm->set = new intvec(pVariables); |
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| 463 | sm->nx = (indset)Alloc0(sizeof(indlist)); |
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| 464 | return sm; |
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| 465 | } |
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| 466 | } |
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| 467 | |
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| 468 | /*2 |
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| 469 | * definition x >= y |
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| 470 | * x(i) == 0 => y(i) == 0 |
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| 471 | * > ex. j with x(j) == 1 and y(j) == 0 |
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| 472 | */ |
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| 473 | static void hCheckIndep(scmon pure) |
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| 474 | { |
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| 475 | intvec *Set; |
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| 476 | indset res; |
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| 477 | int iv; |
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| 478 | if (hCheck1(ISet, pure)) |
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| 479 | { |
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| 480 | if (hCheck1(JSet, pure)) |
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| 481 | { |
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| 482 | res = hCheck2(JSet,pure); |
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| 483 | if (res == NULL) |
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| 484 | return; |
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| 485 | Set = res->set; |
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| 486 | for (iv=pVariables; iv; iv--) |
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| 487 | { |
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[99cfcba] | 488 | if (pure[iv]) |
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[0e1846] | 489 | (*Set)[iv-1] = 0; |
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| 490 | else |
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| 491 | (*Set)[iv-1] = 1; |
---|
| 492 | } |
---|
| 493 | } |
---|
| 494 | } |
---|
| 495 | } |
---|
| 496 | |
---|
| 497 | static void hIndAllMult(scmon pure, int Npure, scfmon rad, int Nrad, |
---|
| 498 | varset var, int Nvar) |
---|
| 499 | { |
---|
| 500 | int dn, iv, rad0, b, c, x; |
---|
| 501 | scmon pn; |
---|
| 502 | scfmon rn; |
---|
| 503 | if (Nrad < 2) |
---|
| 504 | { |
---|
| 505 | dn = Npure + Nrad; |
---|
| 506 | if (dn > hCo) |
---|
| 507 | { |
---|
[99cfcba] | 508 | if (!Nrad) |
---|
[0e1846] | 509 | hCheckIndep(pure); |
---|
| 510 | else |
---|
| 511 | { |
---|
| 512 | pn = *rad; |
---|
[99cfcba] | 513 | for (iv = Nvar; iv; iv--) |
---|
[0e1846] | 514 | { |
---|
| 515 | x = var[iv]; |
---|
[99cfcba] | 516 | if (pn[x]) |
---|
[0e1846] | 517 | { |
---|
| 518 | pure[x] = 1; |
---|
| 519 | hCheckIndep(pure); |
---|
| 520 | pure[x] = 0; |
---|
| 521 | } |
---|
| 522 | } |
---|
| 523 | } |
---|
| 524 | } |
---|
| 525 | return; |
---|
| 526 | } |
---|
| 527 | iv = Nvar; |
---|
[99cfcba] | 528 | while(pure[var[iv]]) iv--; |
---|
[0e1846] | 529 | hStepR(rad, Nrad, var, iv, &rad0); |
---|
| 530 | iv--; |
---|
| 531 | if (rad0 < Nrad) |
---|
| 532 | { |
---|
| 533 | pn = hGetpure(pure); |
---|
| 534 | rn = hGetmem(Nrad, rad, radmem[iv]); |
---|
| 535 | pn[var[iv + 1]] = 1; |
---|
| 536 | hIndAllMult(pn, Npure + 1, rn, rad0, var, iv); |
---|
| 537 | pn[var[iv + 1]] = 0; |
---|
| 538 | b = rad0; |
---|
| 539 | c = Nrad; |
---|
| 540 | hElimR(rn, &rad0, b, c, var, iv); |
---|
| 541 | hPure(rn, b, &c, var, iv, pn, &x); |
---|
| 542 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
---|
| 543 | rad0 += (c - b); |
---|
| 544 | hIndAllMult(pn, Npure + x, rn, rad0, var, iv); |
---|
| 545 | } |
---|
| 546 | else |
---|
| 547 | { |
---|
| 548 | hIndAllMult(pure, Npure, rad, Nrad, var, iv); |
---|
| 549 | } |
---|
| 550 | } |
---|
| 551 | |
---|
| 552 | lists scIndIndset(ideal S, BOOLEAN all, ideal Q) |
---|
| 553 | { |
---|
| 554 | int i; |
---|
| 555 | indset save; |
---|
| 556 | lists res=(lists)Alloc0(sizeof(slists)); |
---|
| 557 | |
---|
| 558 | hexist = hInit(S, Q, &hNexist); |
---|
| 559 | if ((hNexist == 0) || (hisModule!=0)) |
---|
| 560 | { |
---|
| 561 | res->Init(0); |
---|
| 562 | return res; |
---|
| 563 | } |
---|
| 564 | save = ISet = (indset)Alloc0(sizeof(indlist)); |
---|
| 565 | hMu = 0; |
---|
| 566 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
| 567 | hvar = (varset)Alloc((pVariables + 1) * sizeof(int)); |
---|
[e78cce] | 568 | hpure = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
---|
[0e1846] | 569 | hrad = hexist; |
---|
| 570 | hNrad = hNexist; |
---|
| 571 | radmem = hCreate(pVariables - 1); |
---|
| 572 | hCo = pVariables + 1; |
---|
| 573 | hNvar = pVariables; |
---|
| 574 | hRadical(hrad, &hNrad, hNvar); |
---|
| 575 | hSupp(hrad, hNrad, hvar, &hNvar); |
---|
[99cfcba] | 576 | if (hNvar) |
---|
[0e1846] | 577 | { |
---|
| 578 | hCo = hNvar; |
---|
[e78cce] | 579 | memset(hpure, 0, (pVariables + 1) * sizeof(Exponent_t)); |
---|
[0e1846] | 580 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
---|
| 581 | hLexR(hrad, hNrad, hvar, hNvar); |
---|
| 582 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
| 583 | } |
---|
[99cfcba] | 584 | if (hCo && (hCo < pVariables)) |
---|
[0e1846] | 585 | { |
---|
| 586 | hIndMult(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
| 587 | } |
---|
| 588 | if (hMu!=0) |
---|
| 589 | { |
---|
| 590 | ISet = save; |
---|
| 591 | hMu2 = 0; |
---|
| 592 | if (all && (hCo+1 < pVariables)) |
---|
| 593 | { |
---|
| 594 | JSet = (indset)Alloc0(sizeof(indlist)); |
---|
| 595 | hIndAllMult(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
| 596 | i=hMu+hMu2; |
---|
| 597 | res->Init(i); |
---|
| 598 | if (hMu2 == 0) |
---|
| 599 | { |
---|
| 600 | Free((ADDRESS)JSet,sizeof(indlist)); |
---|
| 601 | } |
---|
| 602 | } |
---|
| 603 | else |
---|
| 604 | { |
---|
| 605 | res->Init(hMu); |
---|
| 606 | } |
---|
| 607 | for (i=0;i<hMu;i++) |
---|
| 608 | { |
---|
| 609 | res->m[i].data = (void *)save->set; |
---|
| 610 | res->m[i].rtyp = INTVEC_CMD; |
---|
| 611 | ISet = save; |
---|
| 612 | save = save->nx; |
---|
| 613 | Free((ADDRESS)ISet,sizeof(indlist)); |
---|
| 614 | } |
---|
| 615 | Free((ADDRESS)save,sizeof(indlist)); |
---|
| 616 | if (hMu2 != 0) |
---|
| 617 | { |
---|
| 618 | save = JSet; |
---|
| 619 | for (i=hMu;i<hMu+hMu2;i++) |
---|
| 620 | { |
---|
| 621 | res->m[i].data = (void *)save->set; |
---|
| 622 | res->m[i].rtyp = INTVEC_CMD; |
---|
| 623 | JSet = save; |
---|
| 624 | save = save->nx; |
---|
| 625 | Free((ADDRESS)JSet,sizeof(indlist)); |
---|
| 626 | } |
---|
| 627 | Free((ADDRESS)save,sizeof(indlist)); |
---|
| 628 | } |
---|
| 629 | } |
---|
| 630 | else |
---|
| 631 | { |
---|
| 632 | res->Init(0); |
---|
| 633 | Free((ADDRESS)ISet, sizeof(indlist)); |
---|
| 634 | } |
---|
| 635 | hKill(radmem, pVariables - 1); |
---|
[e78cce] | 636 | Free((ADDRESS)hpure, (1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
---|
[0e1846] | 637 | Free((ADDRESS)hvar, (pVariables + 1) * sizeof(int)); |
---|
| 638 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
[e78cce] | 639 | hDelete(hexist, hNexist); |
---|
[0e1846] | 640 | return res; |
---|
| 641 | } |
---|
| 642 | |
---|
| 643 | // multiplicity |
---|
| 644 | |
---|
| 645 | static int hZeroMult(scmon pure, scfmon stc, int Nstc, varset var, int Nvar) |
---|
| 646 | { |
---|
| 647 | int iv = Nvar -1, sum, a, a0, a1, b, i; |
---|
[e78cce] | 648 | Exponent_t x, x0; |
---|
[0e1846] | 649 | scmon pn; |
---|
| 650 | scfmon sn; |
---|
[99cfcba] | 651 | if (!iv) |
---|
[0e1846] | 652 | return pure[var[1]]; |
---|
[99cfcba] | 653 | else if (!Nstc) |
---|
[0e1846] | 654 | { |
---|
| 655 | sum = 1; |
---|
[99cfcba] | 656 | for (i = Nvar; i; i--) |
---|
[0e1846] | 657 | sum *= pure[var[i]]; |
---|
| 658 | return sum; |
---|
| 659 | } |
---|
| 660 | x = a = 0; |
---|
| 661 | pn = hGetpure(pure); |
---|
| 662 | sn = hGetmem(Nstc, stc, stcmem[iv]); |
---|
| 663 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
| 664 | if (a == Nstc) |
---|
| 665 | return pure[var[Nvar]] * hZeroMult(pn, sn, a, var, iv); |
---|
| 666 | else |
---|
| 667 | sum = x * hZeroMult(pn, sn, a, var, iv); |
---|
| 668 | b = a; |
---|
| 669 | loop |
---|
| 670 | { |
---|
| 671 | a0 = a; |
---|
| 672 | x0 = x; |
---|
| 673 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
| 674 | hElimS(sn, &b, a0, a, var, iv); |
---|
| 675 | a1 = a; |
---|
| 676 | hPure(sn, a0, &a1, var, iv, pn, &i); |
---|
| 677 | hLex2S(sn, b, a0, a1, var, iv, hwork); |
---|
| 678 | b += (a1 - a0); |
---|
| 679 | if (a < Nstc) |
---|
| 680 | { |
---|
| 681 | sum += (x - x0) * hZeroMult(pn, sn, b, var, iv); |
---|
| 682 | } |
---|
| 683 | else |
---|
| 684 | { |
---|
| 685 | sum += (pure[var[Nvar]] - x0) * hZeroMult(pn, sn, b, var, iv); |
---|
| 686 | return sum; |
---|
| 687 | } |
---|
| 688 | } |
---|
| 689 | } |
---|
| 690 | |
---|
| 691 | static void hProject(scmon pure, varset sel) |
---|
| 692 | { |
---|
| 693 | int i, i0, k; |
---|
| 694 | i0 = 0; |
---|
| 695 | for (i = 1; i <= pVariables; i++) |
---|
| 696 | { |
---|
[99cfcba] | 697 | if (pure[i]) |
---|
[0e1846] | 698 | { |
---|
| 699 | i0++; |
---|
| 700 | sel[i0] = i; |
---|
| 701 | } |
---|
| 702 | } |
---|
| 703 | i = hNstc; |
---|
| 704 | memcpy(hwork, hstc, i * sizeof(scmon)); |
---|
| 705 | hStaircase(hwork, &i, sel, i0); |
---|
| 706 | if ((i0 > 2) && (i > 10)) |
---|
| 707 | hOrdSupp(hwork, i, sel, i0); |
---|
[e78cce] | 708 | memset(hpur0, 0, (pVariables + 1) * sizeof(Exponent_t)); |
---|
[0e1846] | 709 | hPure(hwork, 0, &i, sel, i0, hpur0, &k); |
---|
| 710 | hLexS(hwork, i, sel, i0); |
---|
| 711 | hMu += hZeroMult(hpur0, hwork, i, sel, i0); |
---|
| 712 | } |
---|
| 713 | |
---|
| 714 | static void hDimMult(scmon pure, int Npure, scfmon rad, int Nrad, |
---|
| 715 | varset var, int Nvar) |
---|
| 716 | { |
---|
| 717 | int dn, iv, rad0, b, c, x; |
---|
| 718 | scmon pn; |
---|
| 719 | scfmon rn; |
---|
| 720 | if (Nrad < 2) |
---|
| 721 | { |
---|
| 722 | dn = Npure + Nrad; |
---|
| 723 | if (dn == hCo) |
---|
| 724 | { |
---|
[99cfcba] | 725 | if (!Nrad) |
---|
[0e1846] | 726 | hProject(pure, hsel); |
---|
| 727 | else |
---|
| 728 | { |
---|
| 729 | pn = *rad; |
---|
[99cfcba] | 730 | for (iv = Nvar; iv; iv--) |
---|
[0e1846] | 731 | { |
---|
| 732 | x = var[iv]; |
---|
[99cfcba] | 733 | if (pn[x]) |
---|
[0e1846] | 734 | { |
---|
| 735 | pure[x] = 1; |
---|
| 736 | hProject(pure, hsel); |
---|
| 737 | pure[x] = 0; |
---|
| 738 | } |
---|
| 739 | } |
---|
| 740 | } |
---|
| 741 | } |
---|
| 742 | return; |
---|
| 743 | } |
---|
| 744 | iv = Nvar; |
---|
| 745 | dn = Npure+1; |
---|
| 746 | if (dn >= hCo) |
---|
| 747 | { |
---|
| 748 | if (dn > hCo) |
---|
| 749 | return; |
---|
| 750 | loop |
---|
| 751 | { |
---|
[99cfcba] | 752 | if(!pure[var[iv]]) |
---|
[0e1846] | 753 | { |
---|
| 754 | if(hNotZero(rad, Nrad, var, iv)) |
---|
| 755 | { |
---|
| 756 | pure[var[iv]] = 1; |
---|
| 757 | hProject(pure, hsel); |
---|
| 758 | pure[var[iv]] = 0; |
---|
| 759 | } |
---|
| 760 | } |
---|
| 761 | iv--; |
---|
[99cfcba] | 762 | if (!iv) |
---|
[0e1846] | 763 | return; |
---|
| 764 | } |
---|
| 765 | } |
---|
| 766 | while(pure[var[iv]]) iv--; |
---|
| 767 | hStepR(rad, Nrad, var, iv, &rad0); |
---|
| 768 | iv--; |
---|
| 769 | if (rad0 < Nrad) |
---|
| 770 | { |
---|
| 771 | pn = hGetpure(pure); |
---|
| 772 | rn = hGetmem(Nrad, rad, radmem[iv]); |
---|
| 773 | pn[var[iv + 1]] = 1; |
---|
| 774 | hDimMult(pn, Npure + 1, rn, rad0, var, iv); |
---|
| 775 | pn[var[iv + 1]] = 0; |
---|
| 776 | b = rad0; |
---|
| 777 | c = Nrad; |
---|
| 778 | hElimR(rn, &rad0, b, c, var, iv); |
---|
| 779 | hPure(rn, b, &c, var, iv, pn, &x); |
---|
| 780 | hLex2R(rn, rad0, b, c, var, iv, hwork); |
---|
| 781 | rad0 += (c - b); |
---|
| 782 | hDimMult(pn, Npure + x, rn, rad0, var, iv); |
---|
| 783 | } |
---|
| 784 | else |
---|
| 785 | { |
---|
| 786 | hDimMult(pure, Npure, rad, Nrad, var, iv); |
---|
| 787 | } |
---|
| 788 | } |
---|
| 789 | |
---|
| 790 | static void hDegree(ideal S, ideal Q) |
---|
| 791 | { |
---|
| 792 | int di; |
---|
[e78cce] | 793 | Exponent_t mc; |
---|
[0e1846] | 794 | hexist = hInit(S, Q, &hNexist); |
---|
[99cfcba] | 795 | if (!hNexist) |
---|
[0e1846] | 796 | { |
---|
| 797 | hCo = 0; |
---|
| 798 | hMu = 1; |
---|
| 799 | return; |
---|
| 800 | } |
---|
| 801 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
| 802 | hvar = (varset)Alloc((pVariables + 1) * sizeof(int)); |
---|
| 803 | hsel = (varset)Alloc((pVariables + 1) * sizeof(int)); |
---|
[e78cce] | 804 | hpure = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
---|
| 805 | hpur0 = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
---|
[0e1846] | 806 | mc = hisModule; |
---|
| 807 | hrad = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
[99cfcba] | 808 | if (!mc) |
---|
[0e1846] | 809 | { |
---|
| 810 | memcpy(hrad, hexist, hNexist * sizeof(scmon)); |
---|
| 811 | hstc = hexist; |
---|
| 812 | hNrad = hNstc = hNexist; |
---|
| 813 | } |
---|
| 814 | else |
---|
| 815 | hstc = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
| 816 | radmem = hCreate(pVariables - 1); |
---|
| 817 | stcmem = hCreate(pVariables - 1); |
---|
| 818 | hCo = pVariables + 1; |
---|
| 819 | di = hCo + 1; |
---|
| 820 | loop |
---|
| 821 | { |
---|
[99cfcba] | 822 | if (mc) |
---|
[0e1846] | 823 | { |
---|
| 824 | hComp(hexist, hNexist, mc, hrad, &hNrad); |
---|
| 825 | hNstc = hNrad; |
---|
| 826 | memcpy(hstc, hrad, hNrad * sizeof(scmon)); |
---|
| 827 | } |
---|
[99cfcba] | 828 | if (hNrad) |
---|
[0e1846] | 829 | { |
---|
| 830 | hNvar = pVariables; |
---|
| 831 | hRadical(hrad, &hNrad, hNvar); |
---|
| 832 | hSupp(hrad, hNrad, hvar, &hNvar); |
---|
[99cfcba] | 833 | if (hNvar) |
---|
[0e1846] | 834 | { |
---|
| 835 | hCo = hNvar; |
---|
[e78cce] | 836 | memset(hpure, 0, (pVariables + 1) * sizeof(Exponent_t)); |
---|
[0e1846] | 837 | hPure(hrad, 0, &hNrad, hvar, hNvar, hpure, &hNpure); |
---|
| 838 | hLexR(hrad, hNrad, hvar, hNvar); |
---|
| 839 | hDimSolve(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
| 840 | } |
---|
| 841 | } |
---|
| 842 | else |
---|
| 843 | { |
---|
| 844 | hNvar = 1; |
---|
| 845 | hCo = 0; |
---|
| 846 | } |
---|
| 847 | if (hCo < di) |
---|
| 848 | { |
---|
| 849 | di = hCo; |
---|
| 850 | hMu = 0; |
---|
| 851 | } |
---|
[99cfcba] | 852 | if (hNvar && (hCo == di)) |
---|
[0e1846] | 853 | { |
---|
[99cfcba] | 854 | if (di && (di < pVariables)) |
---|
[0e1846] | 855 | hDimMult(hpure, hNpure, hrad, hNrad, hvar, hNvar); |
---|
[99cfcba] | 856 | else if (!di) |
---|
[0e1846] | 857 | hMu++; |
---|
| 858 | else |
---|
| 859 | { |
---|
| 860 | hStaircase(hstc, &hNstc, hvar, hNvar); |
---|
| 861 | if ((hNvar > 2) && (hNstc > 10)) |
---|
| 862 | hOrdSupp(hstc, hNstc, hvar, hNvar); |
---|
[e78cce] | 863 | memset(hpur0, 0, (pVariables + 1) * sizeof(Exponent_t)); |
---|
[0e1846] | 864 | hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure); |
---|
| 865 | hLexS(hstc, hNstc, hvar, hNvar); |
---|
| 866 | hMu += hZeroMult(hpur0, hstc, hNstc, hvar, hNvar); |
---|
| 867 | } |
---|
| 868 | } |
---|
| 869 | mc--; |
---|
| 870 | if (mc <= 0) |
---|
| 871 | break; |
---|
| 872 | } |
---|
| 873 | hCo = di; |
---|
| 874 | hKill(stcmem, pVariables - 1); |
---|
| 875 | hKill(radmem, pVariables - 1); |
---|
[e78cce] | 876 | Free((ADDRESS)hpur0, (1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
---|
| 877 | Free((ADDRESS)hpure, (1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
---|
[0e1846] | 878 | Free((ADDRESS)hsel, (pVariables + 1) * sizeof(int)); |
---|
| 879 | Free((ADDRESS)hvar, (pVariables + 1) * sizeof(int)); |
---|
| 880 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
| 881 | Free((ADDRESS)hrad, hNexist * sizeof(scmon)); |
---|
[e78cce] | 882 | hDelete(hexist, hNexist); |
---|
[0e1846] | 883 | if (hisModule) |
---|
| 884 | Free((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
| 885 | } |
---|
| 886 | |
---|
| 887 | int scMultInt(ideal S, ideal Q) |
---|
| 888 | { |
---|
| 889 | hDegree(S, Q); |
---|
| 890 | return hMu; |
---|
| 891 | } |
---|
| 892 | |
---|
| 893 | void scDegree(ideal S, ideal Q) |
---|
| 894 | { |
---|
| 895 | hDegree(S, Q); |
---|
| 896 | if (pOrdSgn == 1) |
---|
| 897 | Print("// codimension = %d\n// dimension = %d\n// degree = %d\n", |
---|
| 898 | hCo, pVariables - hCo, hMu); |
---|
| 899 | else |
---|
| 900 | Print("// codimension = %d\n// dimension = %d\n// multiplicity = %d\n", |
---|
| 901 | hCo, pVariables - hCo, hMu); |
---|
| 902 | } |
---|
| 903 | |
---|
| 904 | static void hDegree0(ideal S, ideal Q) |
---|
| 905 | { |
---|
[e78cce] | 906 | Exponent_t mc; |
---|
[0e1846] | 907 | hexist = hInit(S, Q, &hNexist); |
---|
| 908 | if (!hNexist) |
---|
| 909 | { |
---|
| 910 | hMu = -1; |
---|
| 911 | return; |
---|
| 912 | } |
---|
| 913 | else |
---|
| 914 | hMu = 0; |
---|
| 915 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
| 916 | hvar = (varset)Alloc((pVariables + 1) * sizeof(int)); |
---|
[e78cce] | 917 | hpur0 = (scmon)Alloc((1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
---|
[0e1846] | 918 | mc = hisModule; |
---|
| 919 | if (!mc) |
---|
| 920 | { |
---|
| 921 | hstc = hexist; |
---|
| 922 | hNstc = hNexist; |
---|
| 923 | } |
---|
| 924 | else |
---|
| 925 | hstc = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
| 926 | stcmem = hCreate(pVariables - 1); |
---|
| 927 | loop |
---|
| 928 | { |
---|
| 929 | if (mc) |
---|
| 930 | { |
---|
| 931 | hComp(hexist, hNexist, mc, hstc, &hNstc); |
---|
| 932 | if (!hNstc) |
---|
| 933 | { |
---|
| 934 | hMu = -1; |
---|
| 935 | break; |
---|
| 936 | } |
---|
| 937 | } |
---|
| 938 | hNvar = pVariables; |
---|
| 939 | for (int i = hNvar; i; i--) |
---|
| 940 | hvar[i] = i; |
---|
| 941 | hStaircase(hstc, &hNstc, hvar, hNvar); |
---|
| 942 | hSupp(hstc, hNstc, hvar, &hNvar); |
---|
| 943 | if ((hNvar == pVariables) && (hNstc >= pVariables)) |
---|
| 944 | { |
---|
| 945 | if ((hNvar > 2) && (hNstc > 10)) |
---|
| 946 | hOrdSupp(hstc, hNstc, hvar, hNvar); |
---|
[e78cce] | 947 | memset(hpur0, 0, (pVariables + 1) * sizeof(Exponent_t)); |
---|
[0e1846] | 948 | hPure(hstc, 0, &hNstc, hvar, hNvar, hpur0, &hNpure); |
---|
| 949 | if (hNpure == hNvar) |
---|
| 950 | { |
---|
| 951 | hLexS(hstc, hNstc, hvar, hNvar); |
---|
| 952 | hMu += hZeroMult(hpur0, hstc, hNstc, hvar, hNvar); |
---|
| 953 | } |
---|
| 954 | else |
---|
| 955 | hMu = -1; |
---|
| 956 | } |
---|
| 957 | else if (hNvar) |
---|
| 958 | hMu = -1; |
---|
| 959 | mc--; |
---|
| 960 | if (mc <= 0 || hMu < 0) |
---|
| 961 | break; |
---|
| 962 | } |
---|
| 963 | hKill(stcmem, pVariables - 1); |
---|
[e78cce] | 964 | Free((ADDRESS)hpur0, (1 + (pVariables * pVariables)) * sizeof(Exponent_t)); |
---|
[0e1846] | 965 | Free((ADDRESS)hvar, (pVariables + 1) * sizeof(int)); |
---|
| 966 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
[e78cce] | 967 | hDelete(hexist, hNexist); |
---|
[0e1846] | 968 | if (hisModule) |
---|
| 969 | Free((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
| 970 | } |
---|
| 971 | |
---|
| 972 | int scMult0Int(ideal S, ideal Q) |
---|
| 973 | { |
---|
| 974 | hDegree0(S, Q); |
---|
| 975 | return hMu; |
---|
| 976 | } |
---|
| 977 | |
---|
| 978 | |
---|
| 979 | // HC |
---|
| 980 | |
---|
| 981 | static poly pWork; |
---|
| 982 | |
---|
| 983 | static void hHedge(poly hEdge) |
---|
| 984 | { |
---|
| 985 | pSetm(pWork); |
---|
| 986 | if (pComp0(pWork, hEdge) == pOrdSgn) |
---|
| 987 | { |
---|
| 988 | for (int i = hNvar; i>0; i--) |
---|
[51c163] | 989 | pSetExp(hEdge,i, pGetExp(pWork,i)); |
---|
[0e1846] | 990 | pGetOrder(hEdge) = pGetOrder(pWork); |
---|
| 991 | } |
---|
| 992 | } |
---|
| 993 | |
---|
| 994 | |
---|
| 995 | static void hHedgeStep(scmon pure, scfmon stc, |
---|
| 996 | int Nstc, varset var, int Nvar,poly hEdge) |
---|
| 997 | { |
---|
| 998 | int iv = Nvar -1, k = var[Nvar], a, a0, a1, b, i; |
---|
[e78cce] | 999 | Exponent_t x, x0; |
---|
[0e1846] | 1000 | scmon pn; |
---|
| 1001 | scfmon sn; |
---|
| 1002 | if (iv==0) |
---|
| 1003 | { |
---|
| 1004 | pSetExp(pWork, k, pure[k]); |
---|
| 1005 | hHedge(hEdge); |
---|
| 1006 | return; |
---|
| 1007 | } |
---|
| 1008 | else if (Nstc==0) |
---|
| 1009 | { |
---|
| 1010 | for (i = Nvar; i>0; i--) |
---|
| 1011 | pSetExp(pWork, var[i], pure[var[i]]); |
---|
| 1012 | hHedge(hEdge); |
---|
| 1013 | return; |
---|
| 1014 | } |
---|
| 1015 | x = a = 0; |
---|
| 1016 | pn = hGetpure(pure); |
---|
| 1017 | sn = hGetmem(Nstc, stc, stcmem[iv]); |
---|
| 1018 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
| 1019 | if (a == Nstc) |
---|
| 1020 | { |
---|
| 1021 | pSetExp(pWork, k, pure[k]); |
---|
| 1022 | hHedgeStep(pn, sn, a, var, iv,hEdge); |
---|
| 1023 | return; |
---|
| 1024 | } |
---|
| 1025 | else |
---|
| 1026 | { |
---|
| 1027 | pSetExp(pWork, k, x); |
---|
| 1028 | hHedgeStep(pn, sn, a, var, iv,hEdge); |
---|
| 1029 | } |
---|
| 1030 | b = a; |
---|
| 1031 | loop |
---|
| 1032 | { |
---|
| 1033 | a0 = a; |
---|
| 1034 | x0 = x; |
---|
| 1035 | hStepS(sn, Nstc, var, Nvar, &a, &x); |
---|
| 1036 | hElimS(sn, &b, a0, a, var, iv); |
---|
| 1037 | a1 = a; |
---|
| 1038 | hPure(sn, a0, &a1, var, iv, pn, &i); |
---|
| 1039 | hLex2S(sn, b, a0, a1, var, iv, hwork); |
---|
| 1040 | b += (a1 - a0); |
---|
| 1041 | if (a < Nstc) |
---|
| 1042 | { |
---|
| 1043 | pSetExp(pWork, k, x); |
---|
| 1044 | hHedgeStep(pn, sn, b, var, iv,hEdge); |
---|
| 1045 | } |
---|
| 1046 | else |
---|
| 1047 | { |
---|
| 1048 | pSetExp(pWork, k, pure[k]); |
---|
| 1049 | hHedgeStep(pn, sn, b, var, iv,hEdge); |
---|
| 1050 | return; |
---|
| 1051 | } |
---|
| 1052 | } |
---|
| 1053 | } |
---|
| 1054 | |
---|
| 1055 | |
---|
| 1056 | void scComputeHC(ideal S, int ak, poly &hEdge) |
---|
| 1057 | { |
---|
| 1058 | int i; |
---|
[e78cce] | 1059 | Exponent_t k = ak; |
---|
[0e1846] | 1060 | hNvar = pVariables; |
---|
| 1061 | hexist = hInit(S, NULL, &hNexist); |
---|
| 1062 | if (k!=0) |
---|
| 1063 | hComp(hexist, hNexist, k, hexist, &hNstc); |
---|
| 1064 | else |
---|
| 1065 | hNstc = hNexist; |
---|
| 1066 | hwork = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
| 1067 | hvar = (varset)Alloc((hNvar + 1) * sizeof(int)); |
---|
[e78cce] | 1068 | hpure = (scmon)Alloc((1 + (hNvar * hNvar)) * sizeof(Exponent_t)); |
---|
[0e1846] | 1069 | stcmem = hCreate(hNvar - 1); |
---|
| 1070 | for (i = hNvar; i>0; i--) |
---|
| 1071 | hvar[i] = i; |
---|
| 1072 | hStaircase(hexist, &hNstc, hvar, hNvar); |
---|
| 1073 | if ((hNvar > 2) && (hNstc > 10)) |
---|
| 1074 | hOrdSupp(hexist, hNstc, hvar, hNvar); |
---|
[e78cce] | 1075 | memset(hpure, 0, (hNvar + 1) * sizeof(Exponent_t)); |
---|
[0e1846] | 1076 | hPure(hexist, 0, &hNstc, hvar, hNvar, hpure, &hNpure); |
---|
| 1077 | hLexS(hexist, hNstc, hvar, hNvar); |
---|
| 1078 | if (hEdge!=NULL) |
---|
| 1079 | pFree1(hEdge); |
---|
| 1080 | hEdge = pInit(); |
---|
| 1081 | pWork = pInit(); |
---|
| 1082 | hHedgeStep(hpure, hexist, hNstc, hvar, hNvar,hEdge); |
---|
| 1083 | pSetComp(hEdge,ak); |
---|
| 1084 | hKill(stcmem, hNvar - 1); |
---|
| 1085 | Free((ADDRESS)hwork, hNexist * sizeof(scmon)); |
---|
| 1086 | Free((ADDRESS)hvar, (hNvar + 1) * sizeof(int)); |
---|
[e78cce] | 1087 | Free((ADDRESS)hpure, (1 + (hNvar * hNvar)) * sizeof(Exponent_t)); |
---|
| 1088 | hDelete(hexist, hNexist); |
---|
[0e1846] | 1089 | pFree1(pWork); |
---|
| 1090 | } |
---|
| 1091 | |
---|
| 1092 | |
---|
| 1093 | // kbase |
---|
| 1094 | |
---|
[b5ae52] | 1095 | static poly last; |
---|
| 1096 | static scmon act; |
---|
[0e1846] | 1097 | |
---|
[b5ae52] | 1098 | static void scElKbase() |
---|
[0e1846] | 1099 | { |
---|
[e78cce] | 1100 | poly q = pInit(); |
---|
[b5ae52] | 1101 | pSetCoeff0(q,nInit(1)); |
---|
| 1102 | pSetExpV(q,act); |
---|
| 1103 | pNext(q) = NULL; |
---|
| 1104 | last = pNext(last) = q; |
---|
| 1105 | } |
---|
| 1106 | |
---|
[e78cce] | 1107 | static Exponent_t scMax( int i, scfmon stc, int Nvar) |
---|
[b5ae52] | 1108 | { |
---|
[e78cce] | 1109 | Exponent_t x, y=stc[0][Nvar]; |
---|
[b5ae52] | 1110 | for (; i;) |
---|
| 1111 | { |
---|
| 1112 | i--; |
---|
| 1113 | x = stc[i][Nvar]; |
---|
| 1114 | if (x > y) y = x; |
---|
| 1115 | } |
---|
| 1116 | return y; |
---|
| 1117 | } |
---|
| 1118 | |
---|
[e78cce] | 1119 | static Exponent_t scMin( int i, scfmon stc, int Nvar) |
---|
[b5ae52] | 1120 | { |
---|
[e78cce] | 1121 | Exponent_t x, y=stc[0][Nvar]; |
---|
[b5ae52] | 1122 | for (; i;) |
---|
[0e1846] | 1123 | { |
---|
[b5ae52] | 1124 | i--; |
---|
| 1125 | x = stc[i][Nvar]; |
---|
| 1126 | if (x < y) y = x; |
---|
| 1127 | } |
---|
| 1128 | return y; |
---|
| 1129 | } |
---|
| 1130 | |
---|
[e78cce] | 1131 | static Exponent_t scRestrict( int &Nstc, scfmon stc, int Nvar) |
---|
[b5ae52] | 1132 | { |
---|
[e78cce] | 1133 | Exponent_t x, y; |
---|
[b5ae52] | 1134 | int i, j, Istc = Nstc; |
---|
| 1135 | |
---|
[e78cce] | 1136 | y = MAX_EXPONENT; |
---|
[b5ae52] | 1137 | for (i=Nstc-1; i>=0; i--) |
---|
| 1138 | { |
---|
| 1139 | j = Nvar-1; |
---|
[0e1846] | 1140 | loop |
---|
| 1141 | { |
---|
[b5ae52] | 1142 | if(stc[i][j] != 0) break; |
---|
[0e1846] | 1143 | j--; |
---|
[b5ae52] | 1144 | if (j == 0) |
---|
[0e1846] | 1145 | { |
---|
[b5ae52] | 1146 | Istc--; |
---|
| 1147 | x = stc[i][Nvar]; |
---|
| 1148 | if (x < y) y = x; |
---|
| 1149 | stc[i] = NULL; |
---|
| 1150 | break; |
---|
| 1151 | } |
---|
| 1152 | } |
---|
| 1153 | } |
---|
| 1154 | if (Istc < Nstc) |
---|
| 1155 | { |
---|
[309f67] | 1156 | for (i=Nstc-1; i>=0; i--) |
---|
| 1157 | { |
---|
| 1158 | if (stc[i] && (stc[i][Nvar] >= y)) |
---|
| 1159 | { |
---|
| 1160 | Istc--; |
---|
| 1161 | stc[i] = NULL; |
---|
| 1162 | } |
---|
| 1163 | } |
---|
[b5ae52] | 1164 | j = 0; |
---|
| 1165 | while (stc[j]) j++; |
---|
| 1166 | i = j+1; |
---|
| 1167 | for(; i<Nstc; i++) |
---|
| 1168 | { |
---|
| 1169 | if (stc[i]) |
---|
| 1170 | { |
---|
| 1171 | stc[j] = stc[i]; |
---|
| 1172 | j++; |
---|
[0e1846] | 1173 | } |
---|
| 1174 | } |
---|
[b5ae52] | 1175 | Nstc = Istc; |
---|
| 1176 | return y; |
---|
| 1177 | } |
---|
| 1178 | else |
---|
| 1179 | return -1; |
---|
| 1180 | } |
---|
| 1181 | |
---|
[e78cce] | 1182 | static void scAll( int Nvar, Exponent_t deg) |
---|
[b5ae52] | 1183 | { |
---|
| 1184 | int i; |
---|
[e78cce] | 1185 | Exponent_t d = deg; |
---|
[b5ae52] | 1186 | if (d == 0) |
---|
| 1187 | { |
---|
| 1188 | for (i=Nvar; i; i--) act[i] = 0; |
---|
| 1189 | scElKbase(); |
---|
| 1190 | return; |
---|
[0e1846] | 1191 | } |
---|
[b5ae52] | 1192 | if (Nvar == 1) |
---|
[0e1846] | 1193 | { |
---|
[b5ae52] | 1194 | act[1] = d; |
---|
| 1195 | scElKbase(); |
---|
| 1196 | return; |
---|
[0e1846] | 1197 | } |
---|
[b5ae52] | 1198 | do |
---|
| 1199 | { |
---|
| 1200 | act[Nvar] = d; |
---|
| 1201 | scAll(Nvar-1, deg-d); |
---|
| 1202 | d--; |
---|
| 1203 | } while (d >= 0); |
---|
[0e1846] | 1204 | } |
---|
| 1205 | |
---|
[e78cce] | 1206 | static void scAllKbase( int Nvar, Exponent_t ideg, Exponent_t deg) |
---|
[b5ae52] | 1207 | { |
---|
| 1208 | do |
---|
| 1209 | { |
---|
| 1210 | act[Nvar] = ideg; |
---|
| 1211 | scAll(Nvar-1, deg-ideg); |
---|
| 1212 | ideg--; |
---|
| 1213 | } while (ideg >= 0); |
---|
| 1214 | } |
---|
[0e1846] | 1215 | |
---|
[e78cce] | 1216 | static void scDegKbase( scfmon stc, int Nstc, int Nvar, Exponent_t deg) |
---|
[0e1846] | 1217 | { |
---|
[b5ae52] | 1218 | int Ivar, Istc, i, j; |
---|
| 1219 | scfmon sn; |
---|
[e78cce] | 1220 | Exponent_t x, ideg; |
---|
[b5ae52] | 1221 | |
---|
| 1222 | if (deg == 0) |
---|
| 1223 | { |
---|
| 1224 | for (i=Nvar; i; i--) act[i] = 0; |
---|
| 1225 | scElKbase(); |
---|
| 1226 | return; |
---|
| 1227 | } |
---|
| 1228 | if (Nvar == 1) |
---|
| 1229 | { |
---|
| 1230 | for (i=Nstc-1; i>=0; i--) if(deg >= stc[i][1]) return; |
---|
| 1231 | act[1] = deg; |
---|
| 1232 | scElKbase(); |
---|
| 1233 | return; |
---|
| 1234 | } |
---|
| 1235 | Ivar = Nvar-1; |
---|
| 1236 | sn = hGetmem(Nstc, stc, stcmem[Ivar]); |
---|
| 1237 | x = scRestrict(Nstc, sn, Nvar); |
---|
[309f67] | 1238 | if (x <= 0) |
---|
| 1239 | { |
---|
| 1240 | if (x == 0) return; |
---|
| 1241 | ideg = deg; |
---|
| 1242 | } |
---|
[b5ae52] | 1243 | else |
---|
| 1244 | { |
---|
[309f67] | 1245 | if (deg < x) ideg = deg; |
---|
| 1246 | else ideg = x-1; |
---|
[b5ae52] | 1247 | if (Nstc == 0) |
---|
| 1248 | { |
---|
[309f67] | 1249 | scAllKbase(Nvar, ideg, deg); |
---|
[b5ae52] | 1250 | return; |
---|
| 1251 | } |
---|
| 1252 | } |
---|
| 1253 | loop |
---|
| 1254 | { |
---|
| 1255 | x = scMax(Nstc, sn, Nvar); |
---|
| 1256 | while (ideg >= x) |
---|
| 1257 | { |
---|
| 1258 | act[Nvar] = ideg; |
---|
| 1259 | scDegKbase(sn, Nstc, Ivar, deg-ideg); |
---|
| 1260 | ideg--; |
---|
| 1261 | } |
---|
| 1262 | if (ideg < 0) return; |
---|
| 1263 | Istc = Nstc; |
---|
| 1264 | for (i=Nstc-1; i>=0; i--) |
---|
| 1265 | { |
---|
| 1266 | if (ideg < sn[i][Nvar]) |
---|
| 1267 | { |
---|
| 1268 | Istc--; |
---|
| 1269 | sn[i] = NULL; |
---|
| 1270 | } |
---|
| 1271 | } |
---|
| 1272 | if (Istc == 0) |
---|
| 1273 | { |
---|
| 1274 | scAllKbase(Nvar, ideg, deg); |
---|
| 1275 | return; |
---|
| 1276 | } |
---|
| 1277 | j = 0; |
---|
| 1278 | while (sn[j]) j++; |
---|
| 1279 | i = j+1; |
---|
| 1280 | for (; i<Nstc; i++) |
---|
| 1281 | { |
---|
| 1282 | if (sn[i]) |
---|
| 1283 | { |
---|
| 1284 | sn[j] = sn[i]; |
---|
| 1285 | j++; |
---|
| 1286 | } |
---|
| 1287 | } |
---|
| 1288 | Nstc = Istc; |
---|
| 1289 | } |
---|
| 1290 | } |
---|
| 1291 | |
---|
| 1292 | static void scInKbase( scfmon stc, int Nstc, int Nvar) |
---|
| 1293 | { |
---|
| 1294 | int Ivar, Istc, i, j; |
---|
| 1295 | scfmon sn; |
---|
[e78cce] | 1296 | Exponent_t x, ideg; |
---|
[b5ae52] | 1297 | |
---|
| 1298 | if (Nvar == 1) |
---|
| 1299 | { |
---|
| 1300 | ideg = scMin(Nstc, stc, 1); |
---|
| 1301 | while (ideg > 0) |
---|
| 1302 | { |
---|
| 1303 | ideg--; |
---|
| 1304 | act[1] = ideg; |
---|
| 1305 | scElKbase(); |
---|
| 1306 | } |
---|
| 1307 | return; |
---|
| 1308 | } |
---|
| 1309 | Ivar = Nvar-1; |
---|
| 1310 | sn = hGetmem(Nstc, stc, stcmem[Ivar]); |
---|
| 1311 | x = scRestrict(Nstc, sn, Nvar); |
---|
[309f67] | 1312 | if (x == 0) return; |
---|
[b5ae52] | 1313 | ideg = x-1; |
---|
| 1314 | loop |
---|
| 1315 | { |
---|
| 1316 | x = scMax(Nstc, sn, Nvar); |
---|
| 1317 | while (ideg >= x) |
---|
| 1318 | { |
---|
| 1319 | act[Nvar] = ideg; |
---|
| 1320 | scInKbase(sn, Nstc, Ivar); |
---|
| 1321 | ideg--; |
---|
| 1322 | } |
---|
| 1323 | if (ideg < 0) return; |
---|
| 1324 | Istc = Nstc; |
---|
| 1325 | for (i=Nstc-1; i>=0; i--) |
---|
| 1326 | { |
---|
| 1327 | if (ideg < sn[i][Nvar]) |
---|
| 1328 | { |
---|
| 1329 | Istc--; |
---|
| 1330 | sn[i] = NULL; |
---|
| 1331 | } |
---|
| 1332 | } |
---|
| 1333 | j = 0; |
---|
| 1334 | while (sn[j]) j++; |
---|
| 1335 | i = j+1; |
---|
| 1336 | for (; i<Nstc; i++) |
---|
| 1337 | { |
---|
| 1338 | if (sn[i]) |
---|
| 1339 | { |
---|
| 1340 | sn[j] = sn[i]; |
---|
| 1341 | j++; |
---|
| 1342 | } |
---|
| 1343 | } |
---|
| 1344 | Nstc = Istc; |
---|
| 1345 | } |
---|
| 1346 | } |
---|
| 1347 | |
---|
| 1348 | static ideal scIdKbase() |
---|
| 1349 | { |
---|
| 1350 | polyset mm; |
---|
[0e1846] | 1351 | ideal res; |
---|
[b5ae52] | 1352 | poly p, q = last; |
---|
| 1353 | int i = pLength(q); |
---|
| 1354 | res = idInit(i,1); |
---|
| 1355 | mm = res->m; |
---|
| 1356 | i = 0; |
---|
| 1357 | do |
---|
| 1358 | { |
---|
| 1359 | mm[i] = q; |
---|
| 1360 | i++; |
---|
| 1361 | p = pNext(q); |
---|
| 1362 | pNext(q) = NULL; |
---|
| 1363 | q = p; |
---|
[25f470] | 1364 | } while (q!=NULL); |
---|
[b5ae52] | 1365 | return res; |
---|
| 1366 | } |
---|
| 1367 | |
---|
| 1368 | extern ideal scKBase(int deg, ideal s, ideal Q) |
---|
| 1369 | { |
---|
| 1370 | int i, di; |
---|
| 1371 | poly p; |
---|
| 1372 | |
---|
| 1373 | if (deg < 0) |
---|
| 1374 | { |
---|
| 1375 | di = scDimInt(s, Q); |
---|
| 1376 | if (di != 0) |
---|
| 1377 | { |
---|
[99cfcba] | 1378 | //Werror("KBase not finite"); |
---|
| 1379 | return idInit(1,s->rank); |
---|
[b5ae52] | 1380 | } |
---|
| 1381 | } |
---|
| 1382 | stcmem = hCreate(pVariables - 1); |
---|
[0e1846] | 1383 | hexist = hInit(s, Q, &hNexist); |
---|
[f3810e] | 1384 | p = last = pInit(); |
---|
| 1385 | /*pNext(p) = NULL;*/ |
---|
[e78cce] | 1386 | act = (scmon)Alloc((pVariables + 1) * sizeof(Exponent_t)); |
---|
[b5ae52] | 1387 | *act = 0; |
---|
| 1388 | if (!hNexist) |
---|
| 1389 | { |
---|
| 1390 | scAll(pVariables, deg); |
---|
| 1391 | goto ende; |
---|
| 1392 | } |
---|
[0e1846] | 1393 | if (!hisModule) |
---|
| 1394 | { |
---|
[b5ae52] | 1395 | if (deg < 0) scInKbase(hexist, hNexist, pVariables); |
---|
| 1396 | else scDegKbase(hexist, hNexist, pVariables, deg); |
---|
[0e1846] | 1397 | } |
---|
| 1398 | else |
---|
| 1399 | { |
---|
| 1400 | hstc = (scfmon)Alloc(hNexist * sizeof(scmon)); |
---|
| 1401 | for (i = 1; i <= hisModule; i++) |
---|
| 1402 | { |
---|
[b5ae52] | 1403 | *act = i; |
---|
[0e1846] | 1404 | hComp(hexist, hNexist, i, hstc, &hNstc); |
---|
| 1405 | if (hNstc) |
---|
| 1406 | { |
---|
[b5ae52] | 1407 | if (deg < 0) scInKbase(hstc, hNstc, pVariables); |
---|
| 1408 | else scDegKbase(hstc, hNstc, pVariables, deg); |
---|
[0e1846] | 1409 | } |
---|
[b5ae52] | 1410 | else |
---|
| 1411 | scAll(pVariables, deg); |
---|
[0e1846] | 1412 | } |
---|
| 1413 | Free((ADDRESS)hstc, hNexist * sizeof(scmon)); |
---|
| 1414 | } |
---|
[b5ae52] | 1415 | ende: |
---|
[e78cce] | 1416 | hDelete(hexist, hNexist); |
---|
| 1417 | Free((ADDRESS)act, (pVariables + 1) * sizeof(Exponent_t)); |
---|
[b5ae52] | 1418 | hKill(stcmem, pVariables - 1); |
---|
| 1419 | pDelete1(&p); |
---|
| 1420 | if (p == NULL) |
---|
[25f470] | 1421 | return idInit(1,s->rank); |
---|
[b5ae52] | 1422 | else |
---|
| 1423 | { |
---|
| 1424 | last = p; |
---|
[25f470] | 1425 | ideal res=scIdKbase(); |
---|
| 1426 | res->rank=s->rank; |
---|
| 1427 | return res; |
---|
[b5ae52] | 1428 | } |
---|
[0e1846] | 1429 | } |
---|
| 1430 | |
---|
| 1431 | |
---|