[9f7665] | 1 | |
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[0d5627] | 2 | #include "config.h" |
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[9f7665] | 3 | |
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[4dfcb1] | 4 | |
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[9c6887] | 5 | #ifndef NOSTREAMIO |
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[4dfcb1] | 6 | #ifdef HAVE_CSTDIO |
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| 7 | #include <cstdio> |
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| 8 | #else |
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[c99b6b] | 9 | #include <stdio.h> |
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[4dfcb1] | 10 | #endif |
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| 11 | #ifdef HAVE_IOSTREAM_H |
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[c99b6b] | 12 | #include <iostream.h> |
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[4dd2c4] | 13 | #elif defined(HAVE_IOSTREAM) |
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[4dfcb1] | 14 | #include <iostream> |
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| 15 | #endif |
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[4dd2c4] | 16 | #endif |
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[c99b6b] | 17 | |
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[517530] | 18 | #include "cf_assert.h" |
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[2a95b2] | 19 | #include "timing.h" |
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[517530] | 20 | |
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[fe2d4c] | 21 | #include "templates/ftmpl_functions.h" |
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[c99b6b] | 22 | #include "cf_defs.h" |
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| 23 | #include "canonicalform.h" |
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| 24 | #include "cf_iter.h" |
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| 25 | #include "cf_primes.h" |
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| 26 | #include "cf_algorithm.h" |
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[da6b0c] | 27 | #include "cfGcdAlgExt.h" |
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[1a82eb] | 28 | #include "cfUnivarGcd.h" |
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[359d742] | 29 | #include "cf_map.h" |
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| 30 | #include "cf_generator.h" |
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[1e5c50] | 31 | #include "facMul.h" |
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[d87069] | 32 | #include "cfNTLzzpEXGCD.h" |
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[c99b6b] | 33 | |
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[2156ec] | 34 | #ifdef HAVE_NTL |
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| 35 | #include "NTLconvert.h" |
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| 36 | #endif |
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| 37 | |
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[4782bc] | 38 | #ifdef HAVE_FLINT |
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| 39 | #include "FLINTconvert.h" |
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| 40 | #endif |
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| 41 | |
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[2a95b2] | 42 | TIMING_DEFINE_PRINT(alg_content_p) |
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| 43 | TIMING_DEFINE_PRINT(alg_content) |
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| 44 | TIMING_DEFINE_PRINT(alg_compress) |
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| 45 | TIMING_DEFINE_PRINT(alg_termination) |
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| 46 | TIMING_DEFINE_PRINT(alg_termination_p) |
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| 47 | TIMING_DEFINE_PRINT(alg_reconstruction) |
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| 48 | TIMING_DEFINE_PRINT(alg_newton_p) |
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| 49 | TIMING_DEFINE_PRINT(alg_recursion_p) |
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| 50 | TIMING_DEFINE_PRINT(alg_gcd_p) |
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| 51 | TIMING_DEFINE_PRINT(alg_euclid_p) |
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| 52 | |
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[fe2d4c] | 53 | /// compressing two polynomials F and G, M is used for compressing, |
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| 54 | /// N to reverse the compression |
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[c7afbd3] | 55 | static int myCompress (const CanonicalForm& F, const CanonicalForm& G, CFMap & M, |
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[fe2d4c] | 56 | CFMap & N, bool topLevel) |
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| 57 | { |
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| 58 | int n= tmax (F.level(), G.level()); |
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| 59 | int * degsf= new int [n + 1]; |
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| 60 | int * degsg= new int [n + 1]; |
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| 61 | |
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| 62 | for (int i = 0; i <= n; i++) |
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| 63 | degsf[i]= degsg[i]= 0; |
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| 64 | |
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| 65 | degsf= degrees (F, degsf); |
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| 66 | degsg= degrees (G, degsg); |
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| 67 | |
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| 68 | int both_non_zero= 0; |
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| 69 | int f_zero= 0; |
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| 70 | int g_zero= 0; |
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| 71 | int both_zero= 0; |
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| 72 | |
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| 73 | if (topLevel) |
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| 74 | { |
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| 75 | for (int i= 1; i <= n; i++) |
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| 76 | { |
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| 77 | if (degsf[i] != 0 && degsg[i] != 0) |
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| 78 | { |
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| 79 | both_non_zero++; |
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| 80 | continue; |
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| 81 | } |
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| 82 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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| 83 | { |
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| 84 | f_zero++; |
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| 85 | continue; |
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| 86 | } |
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| 87 | if (degsg[i] == 0 && degsf[i] && i <= F.level()) |
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| 88 | { |
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| 89 | g_zero++; |
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| 90 | continue; |
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| 91 | } |
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| 92 | } |
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| 93 | |
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| 94 | if (both_non_zero == 0) |
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| 95 | { |
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| 96 | delete [] degsf; |
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| 97 | delete [] degsg; |
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| 98 | return 0; |
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| 99 | } |
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| 100 | |
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| 101 | // map Variables which do not occur in both polynomials to higher levels |
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| 102 | int k= 1; |
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| 103 | int l= 1; |
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| 104 | for (int i= 1; i <= n; i++) |
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| 105 | { |
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| 106 | if (degsf[i] != 0 && degsg[i] == 0 && i <= F.level()) |
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| 107 | { |
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| 108 | if (k + both_non_zero != i) |
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| 109 | { |
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| 110 | M.newpair (Variable (i), Variable (k + both_non_zero)); |
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| 111 | N.newpair (Variable (k + both_non_zero), Variable (i)); |
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| 112 | } |
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| 113 | k++; |
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| 114 | } |
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| 115 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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| 116 | { |
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| 117 | if (l + g_zero + both_non_zero != i) |
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| 118 | { |
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| 119 | M.newpair (Variable (i), Variable (l + g_zero + both_non_zero)); |
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| 120 | N.newpair (Variable (l + g_zero + both_non_zero), Variable (i)); |
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| 121 | } |
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| 122 | l++; |
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| 123 | } |
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| 124 | } |
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| 125 | |
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| 126 | // sort Variables x_{i} in increasing order of |
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| 127 | // min(deg_{x_{i}}(f),deg_{x_{i}}(g)) |
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| 128 | int m= tmax (F.level(), G.level()); |
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| 129 | int min_max_deg; |
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| 130 | k= both_non_zero; |
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| 131 | l= 0; |
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| 132 | int i= 1; |
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| 133 | while (k > 0) |
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| 134 | { |
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| 135 | if (degsf [i] != 0 && degsg [i] != 0) |
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| 136 | min_max_deg= tmax (degsf[i], degsg[i]); |
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| 137 | else |
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| 138 | min_max_deg= 0; |
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| 139 | while (min_max_deg == 0) |
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| 140 | { |
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| 141 | i++; |
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| 142 | min_max_deg= tmax (degsf[i], degsg[i]); |
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| 143 | if (degsf [i] != 0 && degsg [i] != 0) |
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| 144 | min_max_deg= tmax (degsf[i], degsg[i]); |
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| 145 | else |
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| 146 | min_max_deg= 0; |
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| 147 | } |
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| 148 | for (int j= i + 1; j <= m; j++) |
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| 149 | { |
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| 150 | if (tmax (degsf[j],degsg[j]) <= min_max_deg && degsf[j] != 0 && degsg [j] != 0) |
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| 151 | { |
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| 152 | min_max_deg= tmax (degsf[j], degsg[j]); |
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| 153 | l= j; |
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| 154 | } |
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| 155 | } |
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| 156 | if (l != 0) |
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| 157 | { |
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| 158 | if (l != k) |
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| 159 | { |
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| 160 | M.newpair (Variable (l), Variable(k)); |
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| 161 | N.newpair (Variable (k), Variable(l)); |
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| 162 | degsf[l]= 0; |
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| 163 | degsg[l]= 0; |
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| 164 | l= 0; |
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| 165 | } |
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| 166 | else |
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| 167 | { |
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| 168 | degsf[l]= 0; |
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| 169 | degsg[l]= 0; |
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| 170 | l= 0; |
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| 171 | } |
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| 172 | } |
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| 173 | else if (l == 0) |
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| 174 | { |
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| 175 | if (i != k) |
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| 176 | { |
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| 177 | M.newpair (Variable (i), Variable (k)); |
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| 178 | N.newpair (Variable (k), Variable (i)); |
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| 179 | degsf[i]= 0; |
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| 180 | degsg[i]= 0; |
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| 181 | } |
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| 182 | else |
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| 183 | { |
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| 184 | degsf[i]= 0; |
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| 185 | degsg[i]= 0; |
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| 186 | } |
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| 187 | i++; |
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| 188 | } |
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| 189 | k--; |
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| 190 | } |
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| 191 | } |
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| 192 | else |
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| 193 | { |
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| 194 | //arrange Variables such that no gaps occur |
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| 195 | for (int i= 1; i <= n; i++) |
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| 196 | { |
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| 197 | if (degsf[i] == 0 && degsg[i] == 0) |
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| 198 | { |
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| 199 | both_zero++; |
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| 200 | continue; |
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| 201 | } |
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| 202 | else |
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| 203 | { |
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| 204 | if (both_zero != 0) |
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| 205 | { |
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| 206 | M.newpair (Variable (i), Variable (i - both_zero)); |
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| 207 | N.newpair (Variable (i - both_zero), Variable (i)); |
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| 208 | } |
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| 209 | } |
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| 210 | } |
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| 211 | } |
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| 212 | |
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| 213 | delete [] degsf; |
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| 214 | delete [] degsg; |
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| 215 | |
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| 216 | return 1; |
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| 217 | } |
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| 218 | |
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[ad8e1b] | 219 | void tryInvert( const CanonicalForm & F, const CanonicalForm & M, CanonicalForm & inv, bool & fail ) |
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| 220 | { // F, M are required to be "univariate" polynomials in an algebraic variable |
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| 221 | // we try to invert F modulo M |
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| 222 | if(F.inBaseDomain()) |
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| 223 | { |
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| 224 | if(F.isZero()) |
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| 225 | { |
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| 226 | fail = true; |
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| 227 | return; |
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| 228 | } |
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| 229 | inv = 1/F; |
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| 230 | return; |
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| 231 | } |
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| 232 | CanonicalForm b; |
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| 233 | Variable a = M.mvar(); |
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| 234 | Variable x = Variable(1); |
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| 235 | if(!extgcd( replacevar( F, a, x ), replacevar( M, a, x ), inv, b ).isOne()) |
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| 236 | fail = true; |
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| 237 | else |
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| 238 | inv = replacevar( inv, x, a ); // change back to alg var |
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| 239 | } |
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| 240 | |
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[9fd8d2] | 241 | #ifndef HAVE_NTL |
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[a8e8b9] | 242 | void tryDivrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
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| 243 | CanonicalForm& R, CanonicalForm& inv, const CanonicalForm& mipo, |
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| 244 | bool& fail) |
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| 245 | { |
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| 246 | if (F.inCoeffDomain()) |
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| 247 | { |
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| 248 | Q= 0; |
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| 249 | R= F; |
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| 250 | return; |
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| 251 | } |
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| 252 | |
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| 253 | CanonicalForm A, B; |
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| 254 | Variable x= F.mvar(); |
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| 255 | A= F; |
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| 256 | B= G; |
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| 257 | int degA= degree (A, x); |
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| 258 | int degB= degree (B, x); |
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| 259 | |
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| 260 | if (degA < degB) |
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| 261 | { |
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| 262 | R= A; |
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| 263 | Q= 0; |
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| 264 | return; |
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| 265 | } |
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| 266 | |
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| 267 | tryInvert (Lc (B), mipo, inv, fail); |
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| 268 | if (fail) |
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| 269 | return; |
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| 270 | |
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| 271 | R= A; |
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| 272 | Q= 0; |
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| 273 | CanonicalForm Qi; |
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| 274 | for (int i= degA -degB; i >= 0; i--) |
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| 275 | { |
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| 276 | if (degree (R, x) == i + degB) |
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| 277 | { |
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| 278 | Qi= Lc (R)*inv*power (x, i); |
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| 279 | Qi= reduce (Qi, mipo); |
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| 280 | R -= Qi*B; |
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| 281 | R= reduce (R, mipo); |
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| 282 | Q += Qi; |
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| 283 | } |
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| 284 | } |
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| 285 | } |
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| 286 | |
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[ad8e1b] | 287 | void tryEuclid( const CanonicalForm & A, const CanonicalForm & B, const CanonicalForm & M, CanonicalForm & result, bool & fail ) |
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[c99b6b] | 288 | { |
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| 289 | CanonicalForm P; |
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[ad8e1b] | 290 | if(A.inCoeffDomain()) |
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| 291 | { |
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| 292 | tryInvert( A, M, P, fail ); |
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| 293 | if(fail) |
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| 294 | return; |
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| 295 | result = 1; |
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| 296 | return; |
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| 297 | } |
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| 298 | if(B.inCoeffDomain()) |
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| 299 | { |
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| 300 | tryInvert( B, M, P, fail ); |
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| 301 | if(fail) |
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| 302 | return; |
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| 303 | result = 1; |
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| 304 | return; |
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| 305 | } |
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| 306 | // here: both not inCoeffDomain |
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| 307 | if( A.degree() > B.degree() ) |
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[c99b6b] | 308 | { |
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| 309 | P = A; result = B; |
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| 310 | } |
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| 311 | else |
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| 312 | { |
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| 313 | P = B; result = A; |
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| 314 | } |
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| 315 | CanonicalForm inv; |
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| 316 | if( result.isZero() ) |
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| 317 | { |
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| 318 | tryInvert( Lc(P), M, inv, fail ); |
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| 319 | if(fail) |
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| 320 | return; |
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[ad8e1b] | 321 | result = inv*P; // monify result (not reduced, yet) |
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[5df7d0] | 322 | result= reduce (result, M); |
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[c99b6b] | 323 | return; |
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| 324 | } |
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[ad8e1b] | 325 | Variable x = P.mvar(); |
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[a8e8b9] | 326 | CanonicalForm rem, Q; |
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[c99b6b] | 327 | // here: degree(P) >= degree(result) |
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| 328 | while(true) |
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| 329 | { |
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[a8e8b9] | 330 | tryDivrem (P, result, Q, rem, inv, M, fail); |
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| 331 | if (fail) |
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[c99b6b] | 332 | return; |
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| 333 | if( rem.isZero() ) |
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| 334 | { |
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[ad8e1b] | 335 | result *= inv; |
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[5df7d0] | 336 | result= reduce (result, M); |
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[c99b6b] | 337 | return; |
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| 338 | } |
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[ad8e1b] | 339 | if(result.degree(x) >= rem.degree(x)) |
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| 340 | { |
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| 341 | P = result; |
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| 342 | result = rem; |
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| 343 | } |
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| 344 | else |
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| 345 | P = rem; |
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[359d742] | 346 | } |
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[c99b6b] | 347 | } |
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[9fd8d2] | 348 | #endif |
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[c99b6b] | 349 | |
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[ad8e1b] | 350 | static CanonicalForm trycontent ( const CanonicalForm & f, const Variable & x, const CanonicalForm & M, bool & fail ); |
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| 351 | static CanonicalForm tryvcontent ( const CanonicalForm & f, const Variable & x, const CanonicalForm & M, bool & fail ); |
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| 352 | static CanonicalForm trycf_content ( const CanonicalForm & f, const CanonicalForm & g, const CanonicalForm & M, bool & fail ); |
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[359d742] | 353 | |
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[5df7d0] | 354 | static inline CanonicalForm |
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[d193e12] | 355 | tryNewtonInterp (const CanonicalForm & alpha, const CanonicalForm & u, |
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| 356 | const CanonicalForm & newtonPoly, const CanonicalForm & oldInterPoly, |
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[5df7d0] | 357 | const Variable & x, const CanonicalForm& M, bool& fail) |
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| 358 | { |
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| 359 | CanonicalForm interPoly; |
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| 360 | |
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| 361 | CanonicalForm inv; |
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| 362 | tryInvert (newtonPoly (alpha, x), M, inv, fail); |
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| 363 | if (fail) |
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| 364 | return 0; |
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| 365 | |
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| 366 | interPoly= oldInterPoly+reduce ((u - oldInterPoly (alpha, x))*inv*newtonPoly, M); |
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| 367 | return interPoly; |
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| 368 | } |
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[359d742] | 369 | |
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[fe2d4c] | 370 | void tryBrownGCD( const CanonicalForm & F, const CanonicalForm & G, const CanonicalForm & M, CanonicalForm & result, bool & fail, bool topLevel ) |
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[ad8e1b] | 371 | { // assume F,G are multivariate polys over Z/p(a) for big prime p, M "univariate" polynomial in an algebraic variable |
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| 372 | // M is assumed to be monic |
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[359d742] | 373 | if(F.isZero()) |
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| 374 | { |
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| 375 | if(G.isZero()) |
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| 376 | { |
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| 377 | result = G; // G is zero |
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| 378 | return; |
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| 379 | } |
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| 380 | if(G.inCoeffDomain()) |
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| 381 | { |
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| 382 | tryInvert(G,M,result,fail); |
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[ad8e1b] | 383 | if(fail) |
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| 384 | return; |
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| 385 | result = 1; |
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[359d742] | 386 | return; |
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| 387 | } |
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| 388 | // try to make G monic modulo M |
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| 389 | CanonicalForm inv; |
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| 390 | tryInvert(Lc(G),M,inv,fail); |
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| 391 | if(fail) |
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| 392 | return; |
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| 393 | result = inv*G; |
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[5df7d0] | 394 | result= reduce (result, M); |
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[359d742] | 395 | return; |
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| 396 | } |
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| 397 | if(G.isZero()) // F is non-zero |
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| 398 | { |
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| 399 | if(F.inCoeffDomain()) |
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| 400 | { |
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| 401 | tryInvert(F,M,result,fail); |
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[ad8e1b] | 402 | if(fail) |
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| 403 | return; |
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| 404 | result = 1; |
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[359d742] | 405 | return; |
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| 406 | } |
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| 407 | // try to make F monic modulo M |
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| 408 | CanonicalForm inv; |
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| 409 | tryInvert(Lc(F),M,inv,fail); |
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| 410 | if(fail) |
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| 411 | return; |
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| 412 | result = inv*F; |
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[5df7d0] | 413 | result= reduce (result, M); |
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[359d742] | 414 | return; |
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| 415 | } |
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[ad8e1b] | 416 | // here: F,G both nonzero |
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[359d742] | 417 | if(F.inCoeffDomain()) |
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| 418 | { |
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| 419 | tryInvert(F,M,result,fail); |
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[ad8e1b] | 420 | if(fail) |
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| 421 | return; |
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| 422 | result = 1; |
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[359d742] | 423 | return; |
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| 424 | } |
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| 425 | if(G.inCoeffDomain()) |
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| 426 | { |
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| 427 | tryInvert(G,M,result,fail); |
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[ad8e1b] | 428 | if(fail) |
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| 429 | return; |
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| 430 | result = 1; |
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[359d742] | 431 | return; |
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| 432 | } |
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[2a95b2] | 433 | TIMING_START (alg_compress) |
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[359d742] | 434 | CFMap MM,NN; |
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[fe2d4c] | 435 | int lev= myCompress (F, G, MM, NN, topLevel); |
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| 436 | if (lev == 0) |
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| 437 | { |
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| 438 | result= 1; |
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| 439 | return; |
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| 440 | } |
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[359d742] | 441 | CanonicalForm f=MM(F); |
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| 442 | CanonicalForm g=MM(G); |
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[2a95b2] | 443 | TIMING_END_AND_PRINT (alg_compress, "time to compress in alg gcd: ") |
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[ad8e1b] | 444 | // here: f,g are compressed |
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[359d742] | 445 | // compute largest variable in f or g (least one is Variable(1)) |
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| 446 | int mv = f.level(); |
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| 447 | if(g.level() > mv) |
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| 448 | mv = g.level(); |
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| 449 | // here: mv is level of the largest variable in f, g |
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[428b38e] | 450 | Variable v1= Variable (1); |
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| 451 | #ifdef HAVE_NTL |
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| 452 | Variable v= M.mvar(); |
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[bffe62d] | 453 | if (fac_NTL_char != getCharacteristic()) |
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| 454 | { |
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| 455 | fac_NTL_char= getCharacteristic(); |
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| 456 | zz_p::init (getCharacteristic()); |
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| 457 | } |
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[428b38e] | 458 | zz_pX NTLMipo= convertFacCF2NTLzzpX (M); |
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| 459 | zz_pE::init (NTLMipo); |
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| 460 | zz_pEX NTLResult; |
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| 461 | zz_pEX NTLF; |
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| 462 | zz_pEX NTLG; |
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| 463 | #endif |
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[359d742] | 464 | if(mv == 1) // f,g univariate |
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| 465 | { |
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[2a95b2] | 466 | TIMING_START (alg_euclid_p) |
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[428b38e] | 467 | #ifdef HAVE_NTL |
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| 468 | NTLF= convertFacCF2NTLzz_pEX (f, NTLMipo); |
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| 469 | NTLG= convertFacCF2NTLzz_pEX (g, NTLMipo); |
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| 470 | tryNTLGCD (NTLResult, NTLF, NTLG, fail); |
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| 471 | if (fail) |
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| 472 | return; |
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| 473 | result= convertNTLzz_pEX2CF (NTLResult, f.mvar(), v); |
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| 474 | #else |
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[359d742] | 475 | tryEuclid(f,g,M,result,fail); |
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| 476 | if(fail) |
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| 477 | return; |
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[428b38e] | 478 | #endif |
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| 479 | TIMING_END_AND_PRINT (alg_euclid_p, "time for euclidean alg mod p: ") |
---|
[5df7d0] | 480 | result= NN (reduce (result, M)); // do not forget to map back |
---|
[359d742] | 481 | return; |
---|
| 482 | } |
---|
[2a95b2] | 483 | TIMING_START (alg_content_p) |
---|
[359d742] | 484 | // here: mv > 1 |
---|
[ad8e1b] | 485 | CanonicalForm cf = tryvcontent(f, Variable(2), M, fail); // cf is univariate poly in var(1) |
---|
| 486 | if(fail) |
---|
| 487 | return; |
---|
| 488 | CanonicalForm cg = tryvcontent(g, Variable(2), M, fail); |
---|
| 489 | if(fail) |
---|
| 490 | return; |
---|
[359d742] | 491 | CanonicalForm c; |
---|
[428b38e] | 492 | #ifdef HAVE_NTL |
---|
| 493 | NTLF= convertFacCF2NTLzz_pEX (cf, NTLMipo); |
---|
| 494 | NTLG= convertFacCF2NTLzz_pEX (cg, NTLMipo); |
---|
| 495 | tryNTLGCD (NTLResult, NTLF, NTLG, fail); |
---|
| 496 | if (fail) |
---|
| 497 | return; |
---|
| 498 | c= convertNTLzz_pEX2CF (NTLResult, v1, v); |
---|
| 499 | #else |
---|
[359d742] | 500 | tryEuclid(cf,cg,M,c,fail); |
---|
| 501 | if(fail) |
---|
| 502 | return; |
---|
[428b38e] | 503 | #endif |
---|
[ad8e1b] | 504 | // f /= cf |
---|
[13f494] | 505 | f.tryDiv (cf, M, fail); |
---|
[ad8e1b] | 506 | if(fail) |
---|
| 507 | return; |
---|
| 508 | // g /= cg |
---|
[13f494] | 509 | g.tryDiv (cg, M, fail); |
---|
[ad8e1b] | 510 | if(fail) |
---|
| 511 | return; |
---|
[2a95b2] | 512 | TIMING_END_AND_PRINT (alg_content_p, "time for content in alg gcd mod p: ") |
---|
[359d742] | 513 | if(f.inCoeffDomain()) |
---|
| 514 | { |
---|
| 515 | tryInvert(f,M,result,fail); |
---|
| 516 | if(fail) |
---|
| 517 | return; |
---|
[ad8e1b] | 518 | result = NN(c); |
---|
[359d742] | 519 | return; |
---|
| 520 | } |
---|
| 521 | if(g.inCoeffDomain()) |
---|
| 522 | { |
---|
| 523 | tryInvert(g,M,result,fail); |
---|
| 524 | if(fail) |
---|
| 525 | return; |
---|
[ad8e1b] | 526 | result = NN(c); |
---|
[359d742] | 527 | return; |
---|
| 528 | } |
---|
| 529 | int *L = new int[mv+1]; // L is addressed by i from 2 to mv |
---|
| 530 | int *N = new int[mv+1]; |
---|
| 531 | for(int i=2; i<=mv; i++) |
---|
| 532 | L[i] = N[i] = 0; |
---|
| 533 | L = leadDeg(f, L); |
---|
| 534 | N = leadDeg(g, N); |
---|
| 535 | CanonicalForm gamma; |
---|
[2a95b2] | 536 | TIMING_START (alg_euclid_p) |
---|
[428b38e] | 537 | #ifdef HAVE_NTL |
---|
| 538 | NTLF= convertFacCF2NTLzz_pEX (firstLC (f), NTLMipo); |
---|
| 539 | NTLG= convertFacCF2NTLzz_pEX (firstLC (g), NTLMipo); |
---|
| 540 | tryNTLGCD (NTLResult, NTLF, NTLG, fail); |
---|
| 541 | if (fail) |
---|
| 542 | return; |
---|
| 543 | gamma= convertNTLzz_pEX2CF (NTLResult, v1, v); |
---|
| 544 | #else |
---|
[359d742] | 545 | tryEuclid( firstLC(f), firstLC(g), M, gamma, fail ); |
---|
| 546 | if(fail) |
---|
| 547 | return; |
---|
[428b38e] | 548 | #endif |
---|
| 549 | TIMING_END_AND_PRINT (alg_euclid_p, "time for gcd of lcs in alg mod p: ") |
---|
[ad8e1b] | 550 | for(int i=2; i<=mv; i++) // entries at i=0,1 not visited |
---|
[359d742] | 551 | if(N[i] < L[i]) |
---|
| 552 | L[i] = N[i]; |
---|
| 553 | // L is now upper bound for degrees of gcd |
---|
| 554 | int *dg_im = new int[mv+1]; // for the degree vector of the image we don't need any entry at i=1 |
---|
| 555 | for(int i=2; i<=mv; i++) |
---|
| 556 | dg_im[i] = 0; // initialize |
---|
| 557 | CanonicalForm gamma_image, m=1; |
---|
| 558 | CanonicalForm gm=0; |
---|
[5df7d0] | 559 | CanonicalForm g_image, alpha, gnew; |
---|
[359d742] | 560 | FFGenerator gen = FFGenerator(); |
---|
[6f08f3] | 561 | Variable x= Variable (1); |
---|
[13f494] | 562 | bool divides= true; |
---|
[359d742] | 563 | for(FFGenerator gen = FFGenerator(); gen.hasItems(); gen.next()) |
---|
| 564 | { |
---|
| 565 | alpha = gen.item(); |
---|
[6f08f3] | 566 | gamma_image = reduce(gamma(alpha, x),M); // plug in alpha for var(1) |
---|
[359d742] | 567 | if(gamma_image.isZero()) // skip lc-bad points var(1)-alpha |
---|
| 568 | continue; |
---|
[2a95b2] | 569 | TIMING_START (alg_recursion_p) |
---|
[6f08f3] | 570 | tryBrownGCD( f(alpha, x), g(alpha, x), M, g_image, fail, false ); // recursive call with one var less |
---|
[2a95b2] | 571 | TIMING_END_AND_PRINT (alg_recursion_p, |
---|
| 572 | "time for recursive calls in alg gcd mod p: ") |
---|
[359d742] | 573 | if(fail) |
---|
| 574 | return; |
---|
[ad8e1b] | 575 | g_image = reduce(g_image, M); |
---|
[359d742] | 576 | if(g_image.inCoeffDomain()) // early termination |
---|
| 577 | { |
---|
| 578 | tryInvert(g_image,M,result,fail); |
---|
| 579 | if(fail) |
---|
| 580 | return; |
---|
| 581 | result = NN(c); |
---|
| 582 | return; |
---|
| 583 | } |
---|
| 584 | for(int i=2; i<=mv; i++) |
---|
| 585 | dg_im[i] = 0; // reset (this is necessary, because some entries may not be updated by call to leadDeg) |
---|
| 586 | dg_im = leadDeg(g_image, dg_im); // dg_im cannot be NIL-pointer |
---|
| 587 | if(isEqual(dg_im, L, 2, mv)) |
---|
| 588 | { |
---|
[5df7d0] | 589 | CanonicalForm inv; |
---|
| 590 | tryInvert (firstLC (g_image), M, inv, fail); |
---|
| 591 | if (fail) |
---|
| 592 | return; |
---|
| 593 | g_image *= inv; |
---|
[359d742] | 594 | g_image *= gamma_image; // multiply by multiple of image lc(gcd) |
---|
[5df7d0] | 595 | g_image= reduce (g_image, M); |
---|
[2a95b2] | 596 | TIMING_START (alg_newton_p) |
---|
[5df7d0] | 597 | gnew= tryNewtonInterp (alpha, g_image, m, gm, x, M, fail); |
---|
[2a95b2] | 598 | TIMING_END_AND_PRINT (alg_newton_p, |
---|
| 599 | "time for Newton interpolation in alg gcd mod p: ") |
---|
[359d742] | 600 | // gnew = gm mod m |
---|
| 601 | // gnew = g_image mod var(1)-alpha |
---|
| 602 | // mnew = m * (var(1)-alpha) |
---|
| 603 | if(fail) |
---|
| 604 | return; |
---|
[5df7d0] | 605 | m *= (x - alpha); |
---|
[6bbe94] | 606 | if((firstLC(gnew) == gamma) || (gnew == gm)) // gnew did not change |
---|
[359d742] | 607 | { |
---|
[2a95b2] | 608 | TIMING_START (alg_termination_p) |
---|
[6bbe94] | 609 | cf = tryvcontent(gnew, Variable(2), M, fail); |
---|
[ad8e1b] | 610 | if(fail) |
---|
| 611 | return; |
---|
| 612 | divides = true; |
---|
[6bbe94] | 613 | g_image= gnew; |
---|
[13f494] | 614 | g_image.tryDiv (cf, M, fail); |
---|
[ad8e1b] | 615 | if(fail) |
---|
| 616 | return; |
---|
[13f494] | 617 | divides= tryFdivides (g_image,f, M, fail); // trial division (f) |
---|
[ad8e1b] | 618 | if(fail) |
---|
[359d742] | 619 | return; |
---|
[ad8e1b] | 620 | if(divides) |
---|
| 621 | { |
---|
[13f494] | 622 | bool divides2= tryFdivides (g_image,g, M, fail); // trial division (g) |
---|
[ad8e1b] | 623 | if(fail) |
---|
| 624 | return; |
---|
[13f494] | 625 | if(divides2) |
---|
[ad8e1b] | 626 | { |
---|
[5df7d0] | 627 | result = NN(reduce (c*g_image, M)); |
---|
[2a95b2] | 628 | TIMING_END_AND_PRINT (alg_termination_p, |
---|
| 629 | "time for successful termination test in alg gcd mod p: ") |
---|
[ad8e1b] | 630 | return; |
---|
| 631 | } |
---|
[359d742] | 632 | } |
---|
[2a95b2] | 633 | TIMING_END_AND_PRINT (alg_termination_p, |
---|
| 634 | "time for unsuccessful termination test in alg gcd mod p: ") |
---|
[359d742] | 635 | } |
---|
| 636 | gm = gnew; |
---|
| 637 | continue; |
---|
| 638 | } |
---|
| 639 | |
---|
| 640 | if(isLess(L, dg_im, 2, mv)) // dg_im > L --> current point unlucky |
---|
| 641 | continue; |
---|
| 642 | |
---|
[ad8e1b] | 643 | // here: isLess(dg_im, L, 2, mv) --> all previous points were unlucky |
---|
| 644 | m = CanonicalForm(1); // reset |
---|
| 645 | gm = 0; // reset |
---|
| 646 | for(int i=2; i<=mv; i++) // tighten bound |
---|
| 647 | L[i] = dg_im[i]; |
---|
[359d742] | 648 | } |
---|
| 649 | // we are out of evaluation points |
---|
| 650 | fail = true; |
---|
| 651 | } |
---|
| 652 | |
---|
[2156ec] | 653 | static CanonicalForm |
---|
| 654 | myicontent ( const CanonicalForm & f, const CanonicalForm & c ) |
---|
| 655 | { |
---|
[517530] | 656 | #ifdef HAVE_NTL |
---|
[2156ec] | 657 | if (f.isOne() || c.isOne()) |
---|
| 658 | return 1; |
---|
| 659 | if ( f.inBaseDomain() && c.inBaseDomain()) |
---|
| 660 | { |
---|
| 661 | if (c.isZero()) return abs(f); |
---|
| 662 | return bgcd( f, c ); |
---|
| 663 | } |
---|
| 664 | else if ( (f.inCoeffDomain() && c.inCoeffDomain()) || |
---|
| 665 | (f.inCoeffDomain() && c.inBaseDomain()) || |
---|
| 666 | (f.inBaseDomain() && c.inCoeffDomain())) |
---|
| 667 | { |
---|
| 668 | if (c.isZero()) return abs (f); |
---|
[4782bc] | 669 | #ifdef HAVE_FLINT |
---|
| 670 | fmpz_poly_t FLINTf, FLINTc; |
---|
| 671 | convertFacCF2Fmpz_poly_t (FLINTf, f); |
---|
| 672 | convertFacCF2Fmpz_poly_t (FLINTc, c); |
---|
| 673 | fmpz_poly_gcd (FLINTc, FLINTc, FLINTf); |
---|
| 674 | CanonicalForm result; |
---|
| 675 | if (f.inCoeffDomain()) |
---|
| 676 | result= convertFmpz_poly_t2FacCF (FLINTc, f.mvar()); |
---|
| 677 | else |
---|
| 678 | result= convertFmpz_poly_t2FacCF (FLINTc, c.mvar()); |
---|
| 679 | fmpz_poly_clear (FLINTc); |
---|
| 680 | fmpz_poly_clear (FLINTf); |
---|
| 681 | return result; |
---|
| 682 | #else |
---|
[2156ec] | 683 | ZZX NTLf= convertFacCF2NTLZZX (f); |
---|
| 684 | ZZX NTLc= convertFacCF2NTLZZX (c); |
---|
| 685 | NTLc= GCD (NTLc, NTLf); |
---|
| 686 | if (f.inCoeffDomain()) |
---|
| 687 | return convertNTLZZX2CF(NTLc,f.mvar()); |
---|
| 688 | else |
---|
| 689 | return convertNTLZZX2CF(NTLc,c.mvar()); |
---|
[4782bc] | 690 | #endif |
---|
[2156ec] | 691 | } |
---|
| 692 | else |
---|
| 693 | { |
---|
| 694 | CanonicalForm g = c; |
---|
| 695 | for ( CFIterator i = f; i.hasTerms() && ! g.isOne(); i++ ) |
---|
| 696 | g = myicontent( i.coeff(), g ); |
---|
| 697 | return g; |
---|
| 698 | } |
---|
[517530] | 699 | #else |
---|
| 700 | return 1; |
---|
[2156ec] | 701 | #endif |
---|
[517530] | 702 | } |
---|
[2156ec] | 703 | |
---|
[c7afbd3] | 704 | static CanonicalForm myicontent ( const CanonicalForm & f ) |
---|
[2156ec] | 705 | { |
---|
| 706 | #ifdef HAVE_NTL |
---|
| 707 | return myicontent( f, 0 ); |
---|
| 708 | #else |
---|
| 709 | return 1; |
---|
| 710 | #endif |
---|
| 711 | } |
---|
| 712 | |
---|
[ad8e1b] | 713 | CanonicalForm QGCD( const CanonicalForm & F, const CanonicalForm & G ) |
---|
| 714 | { // f,g in Q(a)[x1,...,xn] |
---|
| 715 | if(F.isZero()) |
---|
| 716 | { |
---|
| 717 | if(G.isZero()) |
---|
| 718 | return G; // G is zero |
---|
| 719 | if(G.inCoeffDomain()) |
---|
| 720 | return CanonicalForm(1); |
---|
[1682691] | 721 | CanonicalForm lcinv= 1/Lc (G); |
---|
| 722 | return G*lcinv; // return monic G |
---|
[ad8e1b] | 723 | } |
---|
| 724 | if(G.isZero()) // F is non-zero |
---|
| 725 | { |
---|
| 726 | if(F.inCoeffDomain()) |
---|
| 727 | return CanonicalForm(1); |
---|
[1682691] | 728 | CanonicalForm lcinv= 1/Lc (F); |
---|
| 729 | return F*lcinv; // return monic F |
---|
[ad8e1b] | 730 | } |
---|
| 731 | if(F.inCoeffDomain() || G.inCoeffDomain()) |
---|
| 732 | return CanonicalForm(1); |
---|
| 733 | // here: both NOT inCoeffDomain |
---|
| 734 | CanonicalForm f, g, tmp, M, q, D, Dp, cl, newq, mipo; |
---|
| 735 | int p, i; |
---|
| 736 | int *bound, *other; // degree vectors |
---|
| 737 | bool fail; |
---|
[713bdb] | 738 | bool off_rational=!isOn(SW_RATIONAL); |
---|
[ad8e1b] | 739 | On( SW_RATIONAL ); // needed by bCommonDen |
---|
| 740 | f = F * bCommonDen(F); |
---|
| 741 | g = G * bCommonDen(G); |
---|
[2a95b2] | 742 | TIMING_START (alg_content) |
---|
[2156ec] | 743 | CanonicalForm contf= myicontent (f); |
---|
| 744 | CanonicalForm contg= myicontent (g); |
---|
| 745 | f /= contf; |
---|
| 746 | g /= contg; |
---|
| 747 | CanonicalForm gcdcfcg= myicontent (contf, contg); |
---|
[2a95b2] | 748 | TIMING_END_AND_PRINT (alg_content, "time for content in alg gcd: ") |
---|
[ad8e1b] | 749 | Variable a, b; |
---|
| 750 | if(hasFirstAlgVar(f,a)) |
---|
| 751 | { |
---|
| 752 | if(hasFirstAlgVar(g,b)) |
---|
| 753 | { |
---|
| 754 | if(b.level() > a.level()) |
---|
| 755 | a = b; |
---|
| 756 | } |
---|
| 757 | } |
---|
| 758 | else |
---|
| 759 | { |
---|
| 760 | if(!hasFirstAlgVar(g,a))// both not in extension |
---|
| 761 | { |
---|
| 762 | Off( SW_RATIONAL ); |
---|
| 763 | Off( SW_USE_QGCD ); |
---|
[2156ec] | 764 | tmp = gcdcfcg*gcd( f, g ); |
---|
[ad8e1b] | 765 | On( SW_USE_QGCD ); |
---|
[713bdb] | 766 | if (off_rational) Off(SW_RATIONAL); |
---|
[ad8e1b] | 767 | return tmp; |
---|
| 768 | } |
---|
| 769 | } |
---|
| 770 | // here: a is the biggest alg. var in f and g AND some of f,g is in extension |
---|
| 771 | setReduce(a,false); // do not reduce expressions modulo mipo |
---|
| 772 | tmp = getMipo(a); |
---|
| 773 | M = tmp * bCommonDen(tmp); |
---|
| 774 | // here: f, g in Z[a][x1,...,xn], M in Z[a] not necessarily monic |
---|
| 775 | Off( SW_RATIONAL ); // needed by mod |
---|
| 776 | // calculate upper bound for degree vector of gcd |
---|
| 777 | int mv = f.level(); i = g.level(); |
---|
| 778 | if(i > mv) |
---|
| 779 | mv = i; |
---|
| 780 | // here: mv is level of the largest variable in f, g |
---|
| 781 | bound = new int[mv+1]; // 'bound' could be indexed from 0 to mv, but we will only use from 1 to mv |
---|
| 782 | other = new int[mv+1]; |
---|
| 783 | for(int i=1; i<=mv; i++) // initialize 'bound', 'other' with zeros |
---|
| 784 | bound[i] = other[i] = 0; |
---|
| 785 | bound = leadDeg(f,bound); // 'bound' is set the leading degree vector of f |
---|
| 786 | other = leadDeg(g,other); |
---|
| 787 | for(int i=1; i<=mv; i++) // entry at i=0 not visited |
---|
| 788 | if(other[i] < bound[i]) |
---|
| 789 | bound[i] = other[i]; |
---|
| 790 | // now 'bound' is the smaller vector |
---|
| 791 | cl = lc(M) * lc(f) * lc(g); |
---|
| 792 | q = 1; |
---|
| 793 | D = 0; |
---|
[fe2d4c] | 794 | CanonicalForm test= 0; |
---|
| 795 | bool equal= false; |
---|
[ad8e1b] | 796 | for( i=cf_getNumBigPrimes()-1; i>-1; i-- ) |
---|
| 797 | { |
---|
| 798 | p = cf_getBigPrime(i); |
---|
| 799 | if( mod( cl, p ).isZero() ) // skip lc-bad primes |
---|
| 800 | continue; |
---|
| 801 | fail = false; |
---|
| 802 | setCharacteristic(p); |
---|
| 803 | mipo = mapinto(M); |
---|
| 804 | mipo /= mipo.lc(); |
---|
| 805 | // here: mipo is monic |
---|
[2a95b2] | 806 | TIMING_START (alg_gcd_p) |
---|
[ad8e1b] | 807 | tryBrownGCD( mapinto(f), mapinto(g), mipo, Dp, fail ); |
---|
[2a95b2] | 808 | TIMING_END_AND_PRINT (alg_gcd_p, "time for alg gcd mod p: ") |
---|
[ad8e1b] | 809 | if( fail ) // mipo splits in char p |
---|
[3aa6878] | 810 | { |
---|
| 811 | setCharacteristic(0); |
---|
[ad8e1b] | 812 | continue; |
---|
[3aa6878] | 813 | } |
---|
[ad8e1b] | 814 | if( Dp.inCoeffDomain() ) // early termination |
---|
| 815 | { |
---|
| 816 | tryInvert(Dp,mipo,tmp,fail); // check if zero divisor |
---|
[3aa6878] | 817 | setCharacteristic(0); |
---|
[ad8e1b] | 818 | if(fail) |
---|
| 819 | continue; |
---|
| 820 | setReduce(a,true); |
---|
[713bdb] | 821 | if (off_rational) Off(SW_RATIONAL); else On(SW_RATIONAL); |
---|
[2156ec] | 822 | return gcdcfcg; |
---|
[ad8e1b] | 823 | } |
---|
[0a7d0ca] | 824 | setCharacteristic(0); |
---|
[ad8e1b] | 825 | // here: Dp NOT inCoeffDomain |
---|
| 826 | for(int i=1; i<=mv; i++) |
---|
| 827 | other[i] = 0; // reset (this is necessary, because some entries may not be updated by call to leadDeg) |
---|
| 828 | other = leadDeg(Dp,other); |
---|
[806c18] | 829 | |
---|
[ad8e1b] | 830 | if(isEqual(bound, other, 1, mv)) // equal |
---|
| 831 | { |
---|
[6bbe94] | 832 | chineseRemainder( D, q, mapinto(Dp), p, tmp, newq ); |
---|
[ad8e1b] | 833 | // tmp = Dp mod p |
---|
| 834 | // tmp = D mod q |
---|
| 835 | // newq = p*q |
---|
| 836 | q = newq; |
---|
| 837 | if( D != tmp ) |
---|
| 838 | D = tmp; |
---|
| 839 | On( SW_RATIONAL ); |
---|
[2a95b2] | 840 | TIMING_START (alg_reconstruction) |
---|
[6bbe94] | 841 | tmp = Farey( D, q ); // Farey |
---|
| 842 | tmp *= bCommonDen (tmp); |
---|
[2a95b2] | 843 | TIMING_END_AND_PRINT (alg_reconstruction, |
---|
| 844 | "time for rational reconstruction in alg gcd: ") |
---|
[ad8e1b] | 845 | setReduce(a,true); // reduce expressions modulo mipo |
---|
| 846 | On( SW_RATIONAL ); // needed by fdivides |
---|
[fe2d4c] | 847 | if (test != tmp) |
---|
| 848 | test= tmp; |
---|
| 849 | else |
---|
| 850 | equal= true; // modular image did not add any new information |
---|
[2a95b2] | 851 | TIMING_START (alg_termination) |
---|
[84299e] | 852 | #ifdef HAVE_NTL |
---|
[1e5c50] | 853 | #ifdef HAVE_FLINT |
---|
| 854 | if (equal && tmp.isUnivariate() && f.isUnivariate() && g.isUnivariate() |
---|
| 855 | && f.level() == tmp.level() && tmp.level() == g.level()) |
---|
| 856 | { |
---|
[88355eb] | 857 | CanonicalForm Q, R; |
---|
| 858 | newtonDivrem (f, tmp, Q, R); |
---|
[1e5c50] | 859 | if (R.isZero()) |
---|
| 860 | { |
---|
[88355eb] | 861 | newtonDivrem (g, tmp, Q, R); |
---|
[1e5c50] | 862 | if (R.isZero()) |
---|
| 863 | { |
---|
| 864 | Off (SW_RATIONAL); |
---|
| 865 | setReduce (a,true); |
---|
| 866 | if (off_rational) Off(SW_RATIONAL); else On(SW_RATIONAL); |
---|
| 867 | TIMING_END_AND_PRINT (alg_termination, |
---|
| 868 | "time for successful termination test in alg gcd: ") |
---|
| 869 | return tmp*gcdcfcg; |
---|
| 870 | } |
---|
| 871 | } |
---|
| 872 | } |
---|
| 873 | else |
---|
[84299e] | 874 | #endif |
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[1e5c50] | 875 | #endif |
---|
[fe2d4c] | 876 | if(equal && fdivides( tmp, f ) && fdivides( tmp, g )) // trial division |
---|
[ad8e1b] | 877 | { |
---|
| 878 | Off( SW_RATIONAL ); |
---|
| 879 | setReduce(a,true); |
---|
[713bdb] | 880 | if (off_rational) Off(SW_RATIONAL); else On(SW_RATIONAL); |
---|
[2a95b2] | 881 | TIMING_END_AND_PRINT (alg_termination, |
---|
| 882 | "time for successful termination test in alg gcd: ") |
---|
[2156ec] | 883 | return tmp*gcdcfcg; |
---|
[ad8e1b] | 884 | } |
---|
[2a95b2] | 885 | TIMING_END_AND_PRINT (alg_termination, |
---|
| 886 | "time for unsuccessful termination test in alg gcd: ") |
---|
[ad8e1b] | 887 | Off( SW_RATIONAL ); |
---|
| 888 | setReduce(a,false); // do not reduce expressions modulo mipo |
---|
| 889 | continue; |
---|
| 890 | } |
---|
| 891 | if( isLess(bound, other, 1, mv) ) // current prime unlucky |
---|
| 892 | continue; |
---|
| 893 | // here: isLess(other, bound, 1, mv) ) ==> all previous primes unlucky |
---|
| 894 | q = p; |
---|
[6bbe94] | 895 | D = mapinto(Dp); // shortcut CRA // shortcut CRA |
---|
[ad8e1b] | 896 | for(int i=1; i<=mv; i++) // tighten bound |
---|
| 897 | bound[i] = other[i]; |
---|
| 898 | } |
---|
| 899 | // hopefully, we never reach this point |
---|
| 900 | setReduce(a,true); |
---|
| 901 | Off( SW_USE_QGCD ); |
---|
[2156ec] | 902 | D = gcdcfcg*gcd( f, g ); |
---|
[ad8e1b] | 903 | On( SW_USE_QGCD ); |
---|
[713bdb] | 904 | if (off_rational) Off(SW_RATIONAL); else On(SW_RATIONAL); |
---|
[ad8e1b] | 905 | return D; |
---|
| 906 | } |
---|
| 907 | |
---|
| 908 | |
---|
| 909 | int * leadDeg(const CanonicalForm & f, int *degs) |
---|
| 910 | { // leading degree vector w.r.t. lex. monomial order x(i+1) > x(i) |
---|
| 911 | // if f is in a coeff domain, the zero pointer is returned |
---|
| 912 | // 'a' should point to an array of sufficient size level(f)+1 |
---|
| 913 | if(f.inCoeffDomain()) |
---|
| 914 | return 0; |
---|
| 915 | CanonicalForm tmp = f; |
---|
| 916 | do |
---|
| 917 | { |
---|
| 918 | degs[tmp.level()] = tmp.degree(); |
---|
| 919 | tmp = LC(tmp); |
---|
| 920 | } |
---|
| 921 | while(!tmp.inCoeffDomain()); |
---|
| 922 | return degs; |
---|
| 923 | } |
---|
| 924 | |
---|
| 925 | |
---|
| 926 | bool isLess(int *a, int *b, int lower, int upper) |
---|
| 927 | { // compares the degree vectors a,b on the specified part. Note: x(i+1) > x(i) |
---|
| 928 | for(int i=upper; i>=lower; i--) |
---|
| 929 | if(a[i] == b[i]) |
---|
| 930 | continue; |
---|
| 931 | else |
---|
| 932 | return a[i] < b[i]; |
---|
| 933 | return true; |
---|
| 934 | } |
---|
| 935 | |
---|
| 936 | |
---|
| 937 | bool isEqual(int *a, int *b, int lower, int upper) |
---|
| 938 | { // compares the degree vectors a,b on the specified part. Note: x(i+1) > x(i) |
---|
| 939 | for(int i=lower; i<=upper; i++) |
---|
| 940 | if(a[i] != b[i]) |
---|
| 941 | return false; |
---|
| 942 | return true; |
---|
| 943 | } |
---|
| 944 | |
---|
| 945 | |
---|
| 946 | CanonicalForm firstLC(const CanonicalForm & f) |
---|
| 947 | { // returns the leading coefficient (LC) of level <= 1 |
---|
| 948 | CanonicalForm ret = f; |
---|
| 949 | while(ret.level() > 1) |
---|
| 950 | ret = LC(ret); |
---|
| 951 | return ret; |
---|
| 952 | } |
---|
| 953 | |
---|
[9fd8d2] | 954 | #ifndef HAVE_NTL |
---|
[42f8ec] | 955 | void tryExtgcd( const CanonicalForm & F, const CanonicalForm & G, const CanonicalForm & M, CanonicalForm & result, CanonicalForm & s, CanonicalForm & t, bool & fail ) |
---|
[ad8e1b] | 956 | { // F, G are univariate polynomials (i.e. they have exactly one polynomial variable) |
---|
| 957 | // F and G must have the same level AND level > 0 |
---|
| 958 | // we try to calculate gcd(F,G) = s*F + t*G |
---|
[b52d27] | 959 | // if a zero divisor is encountered, 'fail' is set to one |
---|
[ad8e1b] | 960 | // M is assumed to be monic |
---|
| 961 | CanonicalForm P; |
---|
| 962 | if(F.inCoeffDomain()) |
---|
| 963 | { |
---|
| 964 | tryInvert( F, M, P, fail ); |
---|
| 965 | if(fail) |
---|
| 966 | return; |
---|
| 967 | result = 1; |
---|
| 968 | s = P; t = 0; |
---|
| 969 | return; |
---|
| 970 | } |
---|
| 971 | if(G.inCoeffDomain()) |
---|
| 972 | { |
---|
| 973 | tryInvert( G, M, P, fail ); |
---|
| 974 | if(fail) |
---|
| 975 | return; |
---|
| 976 | result = 1; |
---|
| 977 | s = 0; t = P; |
---|
| 978 | return; |
---|
| 979 | } |
---|
| 980 | // here: both not inCoeffDomain |
---|
| 981 | CanonicalForm inv, rem, tmp, u, v, q, sum=0; |
---|
| 982 | if( F.degree() > G.degree() ) |
---|
| 983 | { |
---|
| 984 | P = F; result = G; s=v=0; t=u=1; |
---|
| 985 | } |
---|
| 986 | else |
---|
| 987 | { |
---|
| 988 | P = G; result = F; s=v=1; t=u=0; |
---|
| 989 | } |
---|
| 990 | Variable x = P.mvar(); |
---|
| 991 | // here: degree(P) >= degree(result) |
---|
| 992 | while(true) |
---|
| 993 | { |
---|
[fe2d4c] | 994 | tryDivrem (P, result, q, rem, inv, M, fail); |
---|
[ad8e1b] | 995 | if(fail) |
---|
| 996 | return; |
---|
| 997 | if( rem.isZero() ) |
---|
| 998 | { |
---|
| 999 | s*=inv; |
---|
[4a05ed] | 1000 | s= reduce (s, M); |
---|
[ad8e1b] | 1001 | t*=inv; |
---|
[4a05ed] | 1002 | t= reduce (t, M); |
---|
[ad8e1b] | 1003 | result *= inv; // monify result |
---|
[4a05ed] | 1004 | result= reduce (result, M); |
---|
[ad8e1b] | 1005 | return; |
---|
| 1006 | } |
---|
| 1007 | sum += q; |
---|
| 1008 | if(result.degree(x) >= rem.degree(x)) |
---|
| 1009 | { |
---|
| 1010 | P=result; |
---|
| 1011 | result=rem; |
---|
| 1012 | tmp=u-sum*s; |
---|
| 1013 | u=s; |
---|
| 1014 | s=tmp; |
---|
| 1015 | tmp=v-sum*t; |
---|
| 1016 | v=t; |
---|
| 1017 | t=tmp; |
---|
| 1018 | sum = 0; // reset |
---|
| 1019 | } |
---|
| 1020 | else |
---|
| 1021 | P = rem; |
---|
| 1022 | } |
---|
| 1023 | } |
---|
[9fd8d2] | 1024 | #endif |
---|
[ad8e1b] | 1025 | |
---|
| 1026 | static CanonicalForm trycontent ( const CanonicalForm & f, const Variable & x, const CanonicalForm & M, bool & fail ) |
---|
| 1027 | { // as 'content', but takes care of zero divisors |
---|
| 1028 | ASSERT( x.level() > 0, "cannot calculate content with respect to algebraic variable" ); |
---|
| 1029 | Variable y = f.mvar(); |
---|
| 1030 | if ( y == x ) |
---|
| 1031 | return trycf_content( f, 0, M, fail ); |
---|
| 1032 | if ( y < x ) |
---|
| 1033 | return f; |
---|
| 1034 | return swapvar( trycontent( swapvar( f, y, x ), y, M, fail ), y, x ); |
---|
| 1035 | } |
---|
| 1036 | |
---|
| 1037 | |
---|
| 1038 | static CanonicalForm tryvcontent ( const CanonicalForm & f, const Variable & x, const CanonicalForm & M, bool & fail ) |
---|
| 1039 | { // as vcontent, but takes care of zero divisors |
---|
| 1040 | ASSERT( x.level() > 0, "cannot calculate vcontent with respect to algebraic variable" ); |
---|
| 1041 | if ( f.mvar() <= x ) |
---|
| 1042 | return trycontent( f, x, M, fail ); |
---|
| 1043 | CFIterator i; |
---|
| 1044 | CanonicalForm d = 0, e, ret; |
---|
| 1045 | for ( i = f; i.hasTerms() && ! d.isOne() && ! fail; i++ ) |
---|
| 1046 | { |
---|
| 1047 | e = tryvcontent( i.coeff(), x, M, fail ); |
---|
| 1048 | if(fail) |
---|
| 1049 | break; |
---|
| 1050 | tryBrownGCD( d, e, M, ret, fail ); |
---|
| 1051 | d = ret; |
---|
| 1052 | } |
---|
| 1053 | return d; |
---|
| 1054 | } |
---|
| 1055 | |
---|
| 1056 | |
---|
| 1057 | static CanonicalForm trycf_content ( const CanonicalForm & f, const CanonicalForm & g, const CanonicalForm & M, bool & fail ) |
---|
| 1058 | { // as cf_content, but takes care of zero divisors |
---|
| 1059 | if ( f.inPolyDomain() || ( f.inExtension() && ! getReduce( f.mvar() ) ) ) |
---|
| 1060 | { |
---|
| 1061 | CFIterator i = f; |
---|
| 1062 | CanonicalForm tmp = g, result; |
---|
| 1063 | while ( i.hasTerms() && ! tmp.isOne() && ! fail ) |
---|
| 1064 | { |
---|
| 1065 | tryBrownGCD( i.coeff(), tmp, M, result, fail ); |
---|
| 1066 | tmp = result; |
---|
| 1067 | i++; |
---|
| 1068 | } |
---|
| 1069 | return result; |
---|
| 1070 | } |
---|
| 1071 | return abs( f ); |
---|
| 1072 | } |
---|
| 1073 | |
---|