[c244d04] | 1 | /*****************************************************************************\ |
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| 2 | * Computer Algebra System SINGULAR |
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| 3 | \*****************************************************************************/ |
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| 4 | /** @file fac_ezgcd.cc |
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| 5 | * |
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| 6 | * This file implements the GCD of two multivariate polynomials over Q using |
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| 7 | * EZ-GCD as described in "Algorithms for Computer Algebra" by Geddes, Czapor, |
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| 8 | * Labahnn |
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| 9 | * |
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| 10 | * @author Martin Lee |
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| 11 | * |
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| 12 | **/ |
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| 13 | /*****************************************************************************/ |
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[c1c3693] | 14 | |
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[e4fe2b] | 15 | #include "config.h" |
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[b973c0] | 16 | |
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[2a95b2] | 17 | #include "timing.h" |
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[650f2d8] | 18 | #include "cf_assert.h" |
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[0b61044] | 19 | #include "debug.h" |
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| 20 | |
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[c1c3693] | 21 | #include "cf_defs.h" |
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| 22 | #include "canonicalform.h" |
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[c244d04] | 23 | #include "fac_util.h" // HEADER for this file |
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[6746a4] | 24 | #include "cf_algorithm.h" |
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[c1c3693] | 25 | #include "cf_reval.h" |
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| 26 | #include "cf_random.h" |
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| 27 | #include "cf_primes.h" |
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[6db552] | 28 | #include "templates/ftmpl_functions.h" |
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[f7a4e9] | 29 | #include "cf_map.h" |
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| 30 | #include "facHensel.h" |
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| 31 | |
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[517530] | 32 | #ifdef HAVE_NTL |
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[2a95b2] | 33 | |
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| 34 | TIMING_DEFINE_PRINT(ez_eval) |
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| 35 | TIMING_DEFINE_PRINT(ez_compress) |
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| 36 | TIMING_DEFINE_PRINT(ez_hensel_lift) |
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| 37 | TIMING_DEFINE_PRINT(ez_content) |
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| 38 | TIMING_DEFINE_PRINT(ez_termination) |
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| 39 | |
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[f7a4e9] | 40 | static |
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| 41 | int compress4EZGCD (const CanonicalForm& F, const CanonicalForm& G, CFMap & M, |
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| 42 | CFMap & N, int& both_non_zero) |
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| 43 | { |
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| 44 | int n= tmax (F.level(), G.level()); |
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| 45 | int * degsf= new int [n + 1]; |
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| 46 | int * degsg= new int [n + 1]; |
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| 47 | |
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| 48 | for (int i = 0; i <= n; i++) |
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| 49 | degsf[i]= degsg[i]= 0; |
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| 50 | |
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| 51 | degsf= degrees (F, degsf); |
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| 52 | degsg= degrees (G, degsg); |
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| 53 | |
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| 54 | both_non_zero= 0; |
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| 55 | int f_zero= 0; |
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| 56 | int g_zero= 0; |
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| 57 | |
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| 58 | for (int i= 1; i <= n; i++) |
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| 59 | { |
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| 60 | if (degsf[i] != 0 && degsg[i] != 0) |
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| 61 | { |
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| 62 | both_non_zero++; |
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| 63 | continue; |
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| 64 | } |
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| 65 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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| 66 | { |
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| 67 | f_zero++; |
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| 68 | continue; |
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| 69 | } |
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| 70 | if (degsg[i] == 0 && degsf[i] && i <= F.level()) |
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| 71 | { |
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| 72 | g_zero++; |
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| 73 | continue; |
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| 74 | } |
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| 75 | } |
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| 76 | |
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| 77 | if (both_non_zero == 0) |
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| 78 | { |
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| 79 | delete [] degsf; |
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| 80 | delete [] degsg; |
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| 81 | return 0; |
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| 82 | } |
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| 83 | |
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| 84 | // map Variables which do not occur in both polynomials to higher levels |
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| 85 | int k= 1; |
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| 86 | int l= 1; |
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| 87 | for (int i= 1; i <= n; i++) |
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| 88 | { |
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| 89 | if (degsf[i] != 0 && degsg[i] == 0 && i <= F.level()) |
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| 90 | { |
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| 91 | if (k + both_non_zero != i) |
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| 92 | { |
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| 93 | M.newpair (Variable (i), Variable (k + both_non_zero)); |
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| 94 | N.newpair (Variable (k + both_non_zero), Variable (i)); |
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| 95 | } |
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| 96 | k++; |
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| 97 | } |
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| 98 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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| 99 | { |
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| 100 | if (l + g_zero + both_non_zero != i) |
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| 101 | { |
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| 102 | M.newpair (Variable (i), Variable (l + g_zero + both_non_zero)); |
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| 103 | N.newpair (Variable (l + g_zero + both_non_zero), Variable (i)); |
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| 104 | } |
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| 105 | l++; |
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| 106 | } |
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| 107 | } |
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| 108 | |
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| 109 | // sort Variables x_{i} in decreasing order of |
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| 110 | // min(deg_{x_{i}}(f),deg_{x_{i}}(g)) |
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| 111 | int m= tmin (F.level(), G.level()); |
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| 112 | int max_min_deg; |
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| 113 | k= both_non_zero; |
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| 114 | l= 0; |
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| 115 | int i= 1; |
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| 116 | while (k > 0) |
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| 117 | { |
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| 118 | max_min_deg= tmin (degsf[i], degsg[i]); |
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| 119 | while (max_min_deg == 0) |
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| 120 | { |
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| 121 | i++; |
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| 122 | max_min_deg= tmin (degsf[i], degsg[i]); |
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| 123 | } |
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| 124 | for (int j= i + 1; j <= m; j++) |
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| 125 | { |
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| 126 | if ((tmin (degsf[j],degsg[j]) < max_min_deg) && |
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| 127 | (tmin (degsf[j], degsg[j]) != 0)) |
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| 128 | { |
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| 129 | max_min_deg= tmin (degsf[j], degsg[j]); |
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| 130 | l= j; |
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| 131 | } |
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| 132 | } |
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| 133 | |
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| 134 | if (l != 0) |
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| 135 | { |
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| 136 | if (l != k) |
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| 137 | { |
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| 138 | M.newpair (Variable (l), Variable(k)); |
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| 139 | N.newpair (Variable (k), Variable(l)); |
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| 140 | degsf[l]= 0; |
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| 141 | degsg[l]= 0; |
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| 142 | l= 0; |
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| 143 | } |
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| 144 | else |
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| 145 | { |
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| 146 | degsf[l]= 0; |
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| 147 | degsg[l]= 0; |
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| 148 | l= 0; |
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| 149 | } |
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| 150 | } |
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| 151 | else if (l == 0) |
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| 152 | { |
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| 153 | if (i != k) |
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| 154 | { |
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| 155 | M.newpair (Variable (i), Variable (k)); |
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| 156 | N.newpair (Variable (k), Variable (i)); |
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| 157 | degsf[i]= 0; |
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| 158 | degsg[i]= 0; |
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| 159 | } |
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| 160 | else |
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| 161 | { |
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| 162 | degsf[i]= 0; |
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| 163 | degsg[i]= 0; |
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| 164 | } |
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| 165 | i++; |
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| 166 | } |
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| 167 | k--; |
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| 168 | } |
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| 169 | |
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| 170 | delete [] degsf; |
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| 171 | delete [] degsg; |
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| 172 | |
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| 173 | return both_non_zero; |
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| 174 | } |
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| 175 | |
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| 176 | static inline |
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| 177 | CanonicalForm myShift2Zero (const CanonicalForm& F, CFList& Feval, |
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| 178 | const CFList& evaluation) |
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| 179 | { |
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| 180 | CanonicalForm A= F; |
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| 181 | int k= 2; |
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| 182 | for (CFListIterator i= evaluation; i.hasItem(); i++, k++) |
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| 183 | A= A (Variable (k) + i.getItem(), k); |
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| 184 | |
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| 185 | CanonicalForm buf= A; |
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| 186 | Feval= CFList(); |
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| 187 | Feval.append (buf); |
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| 188 | for (k= evaluation.length() + 1; k > 2; k--) |
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| 189 | { |
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| 190 | buf= mod (buf, Variable (k)); |
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| 191 | Feval.insert (buf); |
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| 192 | } |
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| 193 | return A; |
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| 194 | } |
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| 195 | |
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| 196 | static inline |
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| 197 | CanonicalForm myReverseShift (const CanonicalForm& F, const CFList& evaluation) |
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| 198 | { |
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| 199 | int l= evaluation.length() + 1; |
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| 200 | CanonicalForm result= F; |
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| 201 | CFListIterator j= evaluation; |
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| 202 | for (int i= 2; i < l + 1; i++, j++) |
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| 203 | { |
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| 204 | if (F.level() < i) |
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| 205 | continue; |
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| 206 | result= result (Variable (i) - j.getItem(), i); |
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| 207 | } |
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| 208 | return result; |
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| 209 | } |
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| 210 | |
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| 211 | static inline |
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| 212 | Evaluation optimize4Lift (const CanonicalForm& F, CFMap & M, |
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| 213 | CFMap & N, const Evaluation& A) |
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| 214 | { |
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| 215 | int n= F.level(); |
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| 216 | int * degsf= new int [n + 1]; |
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| 217 | |
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| 218 | for (int i = 0; i <= n; i++) |
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| 219 | degsf[i]= 0; |
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| 220 | |
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| 221 | degsf= degrees (F, degsf); |
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| 222 | |
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| 223 | Evaluation result= Evaluation (A.min(), A.max()); |
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| 224 | ASSERT (A.min() == 2, "expected A.min() == 2"); |
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| 225 | int max_deg; |
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| 226 | int k= n; |
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| 227 | int l= 1; |
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| 228 | int i= 2; |
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| 229 | int pos= 2; |
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| 230 | while (k > 1) |
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| 231 | { |
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| 232 | max_deg= degsf [i]; |
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| 233 | while (max_deg == 0) |
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| 234 | { |
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| 235 | i++; |
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| 236 | max_deg= degsf [i]; |
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| 237 | } |
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| 238 | l= i; |
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| 239 | for (int j= i + 1; j <= n; j++) |
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| 240 | { |
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| 241 | if (degsf[j] > max_deg) |
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| 242 | { |
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| 243 | max_deg= degsf[j]; |
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| 244 | l= j; |
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| 245 | } |
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| 246 | } |
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| 247 | |
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| 248 | if (l <= n) |
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| 249 | { |
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| 250 | if (l != pos) |
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| 251 | { |
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| 252 | result.setValue (pos, A [l]); |
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| 253 | M.newpair (Variable (l), Variable (pos)); |
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| 254 | N.newpair (Variable (pos), Variable (l)); |
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| 255 | degsf[l]= 0; |
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| 256 | l= 2; |
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| 257 | if (k == 2 && n == 3) |
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| 258 | { |
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| 259 | result.setValue (l, A [pos]); |
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| 260 | M.newpair (Variable (pos), Variable (l)); |
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| 261 | N.newpair (Variable (l), Variable (pos)); |
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| 262 | degsf[pos]= 0; |
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| 263 | } |
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| 264 | } |
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| 265 | else |
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| 266 | { |
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| 267 | result.setValue (l, A [l]); |
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| 268 | degsf [l]= 0; |
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| 269 | } |
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| 270 | } |
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| 271 | pos++; |
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| 272 | k--; |
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| 273 | l= 2; |
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| 274 | } |
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| 275 | |
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| 276 | delete [] degsf; |
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| 277 | |
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| 278 | return result; |
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| 279 | } |
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| 280 | |
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| 281 | static inline |
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| 282 | int Hensel (const CanonicalForm & UU, CFArray & G, const Evaluation & AA, |
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| 283 | const CFArray& LeadCoeffs ) |
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| 284 | { |
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| 285 | CFList factors; |
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| 286 | factors.append (G[1]); |
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| 287 | factors.append (G[2]); |
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| 288 | |
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| 289 | CFMap NN, MM; |
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| 290 | Evaluation A= optimize4Lift (UU, MM, NN, AA); |
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| 291 | |
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| 292 | CanonicalForm U= MM (UU); |
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| 293 | CFArray LCs= CFArray (1,2); |
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| 294 | LCs [1]= MM (LeadCoeffs [1]); |
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| 295 | LCs [2]= MM (LeadCoeffs [2]); |
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| 296 | |
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| 297 | CFList evaluation; |
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| 298 | for (int i= A.min(); i <= A.max(); i++) |
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| 299 | evaluation.append (A [i]); |
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| 300 | CFList UEval; |
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| 301 | CanonicalForm shiftedU= myShift2Zero (U, UEval, evaluation); |
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| 302 | |
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| 303 | if (size (shiftedU)/getNumVars (U) > 500) |
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| 304 | return -1; |
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| 305 | |
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| 306 | CFArray shiftedLCs= CFArray (2); |
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| 307 | CFList shiftedLCsEval1, shiftedLCsEval2; |
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| 308 | shiftedLCs[0]= myShift2Zero (LCs[1], shiftedLCsEval1, evaluation); |
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| 309 | shiftedLCs[1]= myShift2Zero (LCs[2], shiftedLCsEval2, evaluation); |
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| 310 | factors.insert (1); |
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| 311 | int liftBound= degree (UEval.getLast(), 2) + 1; |
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| 312 | CFArray Pi; |
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| 313 | CFMatrix M= CFMatrix (liftBound, factors.length() - 1); |
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| 314 | CFList diophant; |
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| 315 | CFArray lcs= CFArray (2); |
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| 316 | lcs [0]= shiftedLCsEval1.getFirst(); |
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| 317 | lcs [1]= shiftedLCsEval2.getFirst(); |
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| 318 | nonMonicHenselLift12 (UEval.getFirst(), factors, liftBound, Pi, diophant, M, |
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| 319 | lcs, false); |
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| 320 | |
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| 321 | for (CFListIterator i= factors; i.hasItem(); i++) |
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| 322 | { |
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| 323 | if (!fdivides (i.getItem(), UEval.getFirst())) |
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| 324 | return 0; |
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| 325 | } |
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| 326 | |
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| 327 | int * liftBounds; |
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| 328 | bool noOneToOne= false; |
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| 329 | if (U.level() > 2) |
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| 330 | { |
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| 331 | liftBounds= new int [U.level() - 1]; /* index: 0.. U.level()-2 */ |
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| 332 | liftBounds[0]= liftBound; |
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| 333 | for (int i= 1; i < U.level() - 1; i++) |
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| 334 | liftBounds[i]= degree (shiftedU, Variable (i + 2)) + 1; |
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| 335 | factors= nonMonicHenselLift2 (UEval, factors, liftBounds, U.level() - 1, |
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| 336 | false, shiftedLCsEval1, shiftedLCsEval2, Pi, |
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| 337 | diophant, noOneToOne); |
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| 338 | delete [] liftBounds; |
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| 339 | if (noOneToOne) |
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| 340 | return 0; |
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| 341 | } |
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| 342 | G[1]= factors.getFirst(); |
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| 343 | G[2]= factors.getLast(); |
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| 344 | G[1]= myReverseShift (G[1], evaluation); |
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| 345 | G[2]= myReverseShift (G[2], evaluation); |
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| 346 | G[1]= NN (G[1]); |
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| 347 | G[2]= NN (G[2]); |
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| 348 | return 1; |
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| 349 | } |
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[c1c3693] | 350 | |
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[9f84ad] | 351 | static |
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| 352 | bool findeval (const CanonicalForm & F, const CanonicalForm & G, |
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| 353 | CanonicalForm & Fb, CanonicalForm & Gb, CanonicalForm & Db, |
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| 354 | REvaluation & b, int delta, int degF, int degG, int maxeval, |
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| 355 | int & count, int& k, int bound, int& l) |
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| 356 | { |
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| 357 | if( count == 0 && delta != 0) |
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| 358 | { |
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| 359 | if( count++ > maxeval ) |
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| 360 | return false; |
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| 361 | } |
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| 362 | if (count > 0) |
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| 363 | { |
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| 364 | b.nextpoint(k); |
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| 365 | if (k == 0) |
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| 366 | k++; |
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| 367 | l++; |
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| 368 | if (l > bound) |
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| 369 | { |
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| 370 | l= 1; |
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| 371 | k++; |
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| 372 | if (k > tmax (F.level(), G.level()) - 1) |
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| 373 | return false; |
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| 374 | b.nextpoint (k); |
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| 375 | } |
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| 376 | if (count++ > maxeval) |
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| 377 | return false; |
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| 378 | } |
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| 379 | while( true ) |
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| 380 | { |
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| 381 | Fb = b( F ); |
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| 382 | if( degree( Fb, 1 ) == degF ) |
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| 383 | { |
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| 384 | Gb = b( G ); |
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| 385 | if( degree( Gb, 1 ) == degG ) |
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| 386 | { |
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| 387 | Db = gcd( Fb, Gb ); |
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| 388 | if( delta > 0 ) |
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| 389 | { |
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| 390 | if( degree( Db, 1 ) <= delta ) |
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| 391 | return true; |
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| 392 | } |
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| 393 | else |
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| 394 | { |
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| 395 | k++; |
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| 396 | return true; |
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| 397 | } |
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| 398 | } |
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| 399 | } |
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| 400 | if (k == 0) |
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| 401 | k++; |
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| 402 | b.nextpoint(k); |
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| 403 | l++; |
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| 404 | if (l > bound) |
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| 405 | { |
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| 406 | l= 1; |
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| 407 | k++; |
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| 408 | if (k > tmax (F.level(), G.level()) - 1) |
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| 409 | return false; |
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| 410 | b.nextpoint (k); |
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| 411 | } |
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| 412 | if( count++ > maxeval ) |
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| 413 | return false; |
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| 414 | } |
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| 415 | } |
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| 416 | |
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[c244d04] | 417 | static CanonicalForm |
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| 418 | ezgcd ( const CanonicalForm & FF, const CanonicalForm & GG, REvaluation & b, |
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| 419 | bool internal ) |
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| 420 | { |
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| 421 | bool isRat= isOn (SW_RATIONAL); |
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| 422 | CanonicalForm F, G, f, g, d, Fb, Gb, Db, Fbt, Gbt, Dbt, B0, B, D0, lcF, lcG, |
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[e26667] | 423 | lcD, cand, contcand, result; |
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[c244d04] | 424 | CFArray DD( 1, 2 ), lcDD( 1, 2 ); |
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[9f84ad] | 425 | int degF, degG, delta, t, count, maxeval; |
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[c244d04] | 426 | REvaluation bt; |
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| 427 | bool gcdfound = false; |
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| 428 | Variable x = Variable(1); |
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[9f84ad] | 429 | count= 0; |
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| 430 | maxeval= 200; |
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| 431 | int o, l; |
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| 432 | o= 0; |
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| 433 | l= 1; |
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[c244d04] | 434 | |
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[9f84ad] | 435 | if (!isRat) |
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| 436 | On (SW_RATIONAL); |
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| 437 | F= FF*bCommonDen (FF); |
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| 438 | G= GG*bCommonDen (GG); |
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| 439 | if (!isRat) |
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| 440 | Off (SW_RATIONAL); |
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[c244d04] | 441 | |
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[2a95b2] | 442 | TIMING_START (ez_compress) |
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[c244d04] | 443 | CFMap M,N; |
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| 444 | int smallestDegLev; |
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| 445 | int best_level= compress4EZGCD (F, G, M, N, smallestDegLev); |
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| 446 | |
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| 447 | if (best_level == 0) |
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| 448 | { |
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[9f84ad] | 449 | DEBDECLEVEL( cerr, "ezgcd" ); |
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[c244d04] | 450 | return G.genOne(); |
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| 451 | } |
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[c1c3693] | 452 | |
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[c244d04] | 453 | F= M (F); |
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| 454 | G= M (G); |
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[2a95b2] | 455 | TIMING_END_AND_PRINT (ez_compress, "time for compression in EZ: ") |
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[c1c3693] | 456 | |
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[c244d04] | 457 | DEBINCLEVEL( cerr, "ezgcd" ); |
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| 458 | DEBOUTLN( cerr, "FF = " << FF ); |
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| 459 | DEBOUTLN( cerr, "GG = " << GG ); |
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[2a95b2] | 460 | TIMING_START (ez_content) |
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[c244d04] | 461 | f = content( F, x ); g = content( G, x ); d = gcd( f, g ); |
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[9f84ad] | 462 | d /= icontent (d); |
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[c244d04] | 463 | DEBOUTLN( cerr, "f = " << f ); |
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| 464 | DEBOUTLN( cerr, "g = " << g ); |
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| 465 | F /= f; G /= g; |
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[2a95b2] | 466 | TIMING_END_AND_PRINT (ez_content, "time to extract content in EZ: ") |
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[c244d04] | 467 | if ( F.isUnivariate() && G.isUnivariate() ) |
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| 468 | { |
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| 469 | DEBDECLEVEL( cerr, "ezgcd" ); |
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| 470 | if(F.mvar()==G.mvar()) |
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| 471 | d*=gcd(F,G); |
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| 472 | return N (d); |
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| 473 | } |
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[9f84ad] | 474 | |
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| 475 | int maxNumVars= tmax (getNumVars (F), getNumVars (G)); |
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| 476 | int sizeF= size (F); |
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| 477 | int sizeG= size (G); |
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| 478 | |
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| 479 | |
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| 480 | if (!isRat) |
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| 481 | On (SW_RATIONAL); |
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| 482 | if (sizeF/maxNumVars > 500 && sizeG/maxNumVars > 500) |
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| 483 | { |
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| 484 | Off(SW_USE_EZGCD); |
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| 485 | result=gcd( F, G ); |
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| 486 | On(SW_USE_EZGCD); |
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| 487 | if (!isRat) |
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| 488 | Off (SW_RATIONAL); |
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| 489 | result /= icontent (result); |
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| 490 | DEBDECLEVEL( cerr, "ezgcd" ); |
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| 491 | return N (d*result); |
---|
| 492 | } |
---|
| 493 | |
---|
| 494 | if ( gcd_test_one( F, G, false ) ) |
---|
[c244d04] | 495 | { |
---|
| 496 | DEBDECLEVEL( cerr, "ezgcd" ); |
---|
| 497 | if (!isRat) |
---|
| 498 | Off (SW_RATIONAL); |
---|
| 499 | return N (d); |
---|
| 500 | } |
---|
| 501 | lcF = LC( F, x ); lcG = LC( G, x ); |
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| 502 | lcD = gcd( lcF, lcG ); |
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| 503 | delta = 0; |
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| 504 | degF = degree( F, x ); degG = degree( G, x ); |
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| 505 | t = tmax( F.level(), G.level() ); |
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| 506 | if ( ! internal ) |
---|
| 507 | b = REvaluation( 2, t, IntRandom( 25 ) ); |
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| 508 | while ( ! gcdfound ) |
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| 509 | { |
---|
| 510 | /// ---> A2 |
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| 511 | DEBOUTLN( cerr, "search for evaluation, delta = " << delta ); |
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| 512 | DEBOUTLN( cerr, "F = " << F ); |
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| 513 | DEBOUTLN( cerr, "G = " << G ); |
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[2a95b2] | 514 | TIMING_START (ez_eval) |
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[9f84ad] | 515 | if (!findeval( F, G, Fb, Gb, Db, b, delta, degF, degG, maxeval, count, |
---|
| 516 | o, 25, l)) |
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| 517 | { |
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| 518 | Off(SW_USE_EZGCD); |
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| 519 | result=gcd( F, G ); |
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| 520 | On(SW_USE_EZGCD); |
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| 521 | if (!isRat) |
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| 522 | Off (SW_RATIONAL); |
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| 523 | DEBDECLEVEL( cerr, "ezgcd" ); |
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| 524 | result /= icontent (result); |
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| 525 | return N (d*result); |
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| 526 | } |
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[2a95b2] | 527 | TIMING_END_AND_PRINT (ez_eval, "time to find eval point in EZ1: ") |
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[c244d04] | 528 | DEBOUTLN( cerr, "found evaluation b = " << b ); |
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| 529 | DEBOUTLN( cerr, "F(b) = " << Fb ); |
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| 530 | DEBOUTLN( cerr, "G(b) = " << Gb ); |
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| 531 | DEBOUTLN( cerr, "D(b) = " << Db ); |
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| 532 | delta = degree( Db ); |
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| 533 | /// ---> A3 |
---|
| 534 | if ( delta == 0 ) |
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[e22ea7] | 535 | { |
---|
[c244d04] | 536 | DEBDECLEVEL( cerr, "ezgcd" ); |
---|
| 537 | if (!isRat) |
---|
| 538 | Off (SW_RATIONAL); |
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| 539 | return N (d); |
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[e22ea7] | 540 | } |
---|
[c244d04] | 541 | /// ---> A4 |
---|
| 542 | //deltaold = delta; |
---|
| 543 | while ( 1 ) |
---|
[e22ea7] | 544 | { |
---|
[c244d04] | 545 | bt = b; |
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[2a95b2] | 546 | TIMING_START (ez_eval) |
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[9f84ad] | 547 | if (!findeval( F, G, Fbt, Gbt, Dbt, bt, delta, degF, degG, maxeval, count, |
---|
| 548 | o, 25,l )) |
---|
| 549 | { |
---|
| 550 | Off(SW_USE_EZGCD); |
---|
| 551 | result=gcd( F, G ); |
---|
| 552 | On(SW_USE_EZGCD); |
---|
| 553 | if (!isRat) |
---|
| 554 | Off (SW_RATIONAL); |
---|
| 555 | DEBDECLEVEL( cerr, "ezgcd" ); |
---|
| 556 | result /= icontent (result); |
---|
| 557 | return N (d*result); |
---|
| 558 | } |
---|
[2a95b2] | 559 | TIMING_END_AND_PRINT (ez_eval, "time to find eval point in EZ2: ") |
---|
[c244d04] | 560 | int dd=degree( Dbt ); |
---|
| 561 | if ( dd /*degree( Dbt )*/ == 0 ) |
---|
| 562 | { |
---|
[e22ea7] | 563 | DEBDECLEVEL( cerr, "ezgcd" ); |
---|
[c244d04] | 564 | if (!isRat) |
---|
| 565 | Off (SW_RATIONAL); |
---|
[f7a4e9] | 566 | return N (d); |
---|
[c244d04] | 567 | } |
---|
| 568 | if ( dd /*degree( Dbt )*/ == delta ) |
---|
| 569 | break; |
---|
| 570 | else if ( dd /*degree( Dbt )*/ < delta ) |
---|
| 571 | { |
---|
| 572 | delta = dd /*degree( Dbt )*/; |
---|
| 573 | b = bt; |
---|
| 574 | Db = Dbt; Fb = Fbt; Gb = Gbt; |
---|
| 575 | } |
---|
[178abd] | 576 | DEBOUTLN( cerr, "now after A4, delta = " << delta ); |
---|
| 577 | /// ---> A5 |
---|
| 578 | if (delta == degF) |
---|
[c244d04] | 579 | { |
---|
[178abd] | 580 | if (degF <= degG && fdivides (F, G)) |
---|
| 581 | { |
---|
| 582 | DEBDECLEVEL( cerr, "ezgcd" ); |
---|
| 583 | if (!isRat) |
---|
| 584 | Off (SW_RATIONAL); |
---|
| 585 | return N (d*F); |
---|
| 586 | } |
---|
| 587 | else |
---|
| 588 | delta--; |
---|
[c244d04] | 589 | } |
---|
[178abd] | 590 | else if (delta == degG) |
---|
[c244d04] | 591 | { |
---|
[178abd] | 592 | if (degG <= degF && fdivides( G, F )) |
---|
| 593 | { |
---|
| 594 | DEBDECLEVEL( cerr, "ezgcd" ); |
---|
| 595 | if (!isRat) |
---|
| 596 | Off (SW_RATIONAL); |
---|
| 597 | return N (d*G); |
---|
| 598 | } |
---|
| 599 | else |
---|
| 600 | delta--; |
---|
[c244d04] | 601 | } |
---|
[6594d4] | 602 | } |
---|
[c244d04] | 603 | if ( delta != degF && delta != degG ) |
---|
| 604 | { |
---|
| 605 | /// ---> A6 |
---|
| 606 | bool B_is_F; |
---|
| 607 | CanonicalForm xxx1, xxx2; |
---|
| 608 | CanonicalForm buf; |
---|
| 609 | DD[1] = Fb / Db; |
---|
| 610 | buf= Gb/Db; |
---|
| 611 | xxx1 = gcd( DD[1], Db ); |
---|
| 612 | xxx2 = gcd( buf, Db ); |
---|
| 613 | if (((xxx1.inCoeffDomain() && xxx2.inCoeffDomain()) && |
---|
| 614 | (size (F) <= size (G))) |
---|
| 615 | || (xxx1.inCoeffDomain() && !xxx2.inCoeffDomain())) |
---|
| 616 | { |
---|
| 617 | B = F; |
---|
| 618 | DD[2] = Db; |
---|
| 619 | lcDD[1] = lcF; |
---|
| 620 | lcDD[2] = lcD; |
---|
| 621 | B_is_F = true; |
---|
| 622 | } |
---|
| 623 | else if (((xxx1.inCoeffDomain() && xxx2.inCoeffDomain()) && |
---|
| 624 | (size (G) < size (F))) |
---|
| 625 | || (!xxx1.inCoeffDomain() && xxx2.inCoeffDomain())) |
---|
| 626 | { |
---|
| 627 | DD[1] = buf; |
---|
| 628 | B = G; |
---|
| 629 | DD[2] = Db; |
---|
| 630 | lcDD[1] = lcG; |
---|
| 631 | lcDD[2] = lcD; |
---|
| 632 | B_is_F = false; |
---|
| 633 | } |
---|
| 634 | else |
---|
| 635 | { |
---|
| 636 | //special case |
---|
| 637 | Off(SW_USE_EZGCD); |
---|
| 638 | result=gcd( F, G ); |
---|
| 639 | On(SW_USE_EZGCD); |
---|
| 640 | if (!isRat) |
---|
| 641 | Off (SW_RATIONAL); |
---|
[9f84ad] | 642 | DEBDECLEVEL( cerr, "ezgcd" ); |
---|
| 643 | result /= icontent (result); |
---|
[c244d04] | 644 | return N (d*result); |
---|
| 645 | } |
---|
| 646 | /// ---> A7 |
---|
| 647 | DD[2] = DD[2] * ( b( lcDD[2] ) / lc( DD[2] ) ); |
---|
| 648 | DD[1] = DD[1] * ( b( lcDD[1] ) / lc( DD[1] ) ); |
---|
| 649 | DEBOUTLN( cerr, "(hensel) B = " << B ); |
---|
| 650 | DEBOUTLN( cerr, "(hensel) lcB = " << LC( B, Variable(1) ) ); |
---|
| 651 | DEBOUTLN( cerr, "(hensel) b(B) = " << b(B) ); |
---|
| 652 | DEBOUTLN( cerr, "(hensel) DD = " << DD ); |
---|
| 653 | DEBOUTLN( cerr, "(hensel) lcDD = " << lcDD ); |
---|
[2a95b2] | 654 | TIMING_START (ez_hensel_lift) |
---|
[c244d04] | 655 | gcdfound= Hensel (B*lcD, DD, b, lcDD); |
---|
[2a95b2] | 656 | TIMING_END_AND_PRINT (ez_hensel_lift, "time to hensel lift in EZ: ") |
---|
[c244d04] | 657 | DEBOUTLN( cerr, "(hensel finished) DD = " << DD ); |
---|
| 658 | |
---|
| 659 | if (gcdfound == -1) |
---|
| 660 | { |
---|
| 661 | Off (SW_USE_EZGCD); |
---|
| 662 | result= gcd (F,G); |
---|
| 663 | On (SW_USE_EZGCD); |
---|
| 664 | if (!isRat) |
---|
| 665 | Off (SW_RATIONAL); |
---|
[9f84ad] | 666 | DEBDECLEVEL( cerr, "ezgcd" ); |
---|
| 667 | result /= icontent (result); |
---|
[c244d04] | 668 | return N (d*result); |
---|
| 669 | } |
---|
[4e6908] | 670 | |
---|
[c244d04] | 671 | if (gcdfound) |
---|
| 672 | { |
---|
[2a95b2] | 673 | TIMING_START (ez_termination) |
---|
[e26667] | 674 | contcand= content (DD[2], Variable (1)); |
---|
| 675 | cand = DD[2] / contcand; |
---|
| 676 | if (B_is_F) |
---|
| 677 | gcdfound = fdivides( cand, G ) && cand*(DD[1]/(lcD/contcand)) == F; |
---|
| 678 | else |
---|
| 679 | gcdfound = fdivides( cand, F ) && cand*(DD[1]/(lcD/contcand)) == G; |
---|
[2a95b2] | 680 | TIMING_END_AND_PRINT (ez_termination, |
---|
| 681 | "time for termination test in EZ: ") |
---|
[c244d04] | 682 | } |
---|
| 683 | /// ---> A8 (gcdfound) |
---|
[c1c3693] | 684 | } |
---|
[c244d04] | 685 | delta--; |
---|
| 686 | } |
---|
| 687 | /// ---> A9 |
---|
| 688 | DEBDECLEVEL( cerr, "ezgcd" ); |
---|
[9f84ad] | 689 | cand *= bCommonDen (cand); |
---|
[c244d04] | 690 | if (!isRat) |
---|
| 691 | Off (SW_RATIONAL); |
---|
[9f84ad] | 692 | cand /= icontent (cand); |
---|
[c244d04] | 693 | return N (d*cand); |
---|
[c1c3693] | 694 | } |
---|
[517530] | 695 | #endif |
---|
[c1c3693] | 696 | |
---|
[c244d04] | 697 | CanonicalForm |
---|
| 698 | ezgcd ( const CanonicalForm & FF, const CanonicalForm & GG ) |
---|
[c1c3693] | 699 | { |
---|
[517530] | 700 | #ifdef HAVE_NTL |
---|
[c244d04] | 701 | REvaluation b; |
---|
| 702 | return ezgcd( FF, GG, b, false ); |
---|
[517530] | 703 | #else |
---|
| 704 | Off (SW_USE_EZGCD); |
---|
| 705 | return gcd (FF, GG); |
---|
| 706 | On (SW_USE_EZGCD); |
---|
| 707 | #endif |
---|
[c1c3693] | 708 | } |
---|
| 709 | |
---|