[10af64] | 1 | // -*- c++ -*- |
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| 2 | //***************************************************************************** |
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| 3 | /** @file cf_gcd_smallp.cc |
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| 4 | * |
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| 5 | * @author Martin Lee |
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| 6 | * @date 22.10.2009 |
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| 7 | * |
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[806c18] | 8 | * This file implements the GCD of two polynomials over \f$ F_{p} \f$ , |
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| 9 | * \f$ F_{p}(\alpha ) \f$ or GF based on Alg. 7.2. as described in "Algorithms |
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[10af64] | 10 | * for Computer Algebra" by Geddes, Czapor, Labahnn |
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| 11 | * |
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| 12 | * @par Copyright: |
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| 13 | * (c) by The SINGULAR Team, see LICENSE file |
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| 14 | * |
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| 15 | **/ |
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| 16 | //***************************************************************************** |
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| 17 | |
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[e4fe2b] | 18 | #include "config.h" |
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[10af64] | 19 | |
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[650f2d8] | 20 | #include "cf_assert.h" |
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[10af64] | 21 | #include "debug.h" |
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| 22 | #include "timing.h" |
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| 23 | |
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| 24 | #include "canonicalform.h" |
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[81d96c] | 25 | #include "algext.h" |
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[10af64] | 26 | #include "cf_map.h" |
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[88f3644] | 27 | #include "cf_util.h" |
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[6db552] | 28 | #include "templates/ftmpl_functions.h" |
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[10af64] | 29 | #include "cf_random.h" |
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[0349c20] | 30 | #include "cf_reval.h" |
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[08daea] | 31 | #include "facHensel.h" |
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[015711] | 32 | #include "cf_iter.h" |
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[e243418] | 33 | #include "cfNewtonPolygon.h" |
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[517530] | 34 | #include "cf_algorithm.h" |
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[10af64] | 35 | |
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[c4f4fd] | 36 | // iinline helper functions: |
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[51615d6] | 37 | #include "cf_map_ext.h" |
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[9c115e1] | 38 | |
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[10af64] | 39 | #ifdef HAVE_NTL |
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[04dd0c] | 40 | #include <NTLconvert.h> |
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[10af64] | 41 | #endif |
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| 42 | |
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[8fa570] | 43 | #ifdef HAVE_FLINT |
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| 44 | #include "FLINTconvert.h" |
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| 45 | #endif |
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| 46 | |
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[911444] | 47 | #include "cf_gcd_smallp.h" |
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| 48 | |
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[e76d7a6] | 49 | TIMING_DEFINE_PRINT(gcd_recursion) |
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| 50 | TIMING_DEFINE_PRINT(newton_interpolation) |
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[2a95b2] | 51 | TIMING_DEFINE_PRINT(termination_test) |
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| 52 | TIMING_DEFINE_PRINT(ez_p_compress) |
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| 53 | TIMING_DEFINE_PRINT(ez_p_hensel_lift) |
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| 54 | TIMING_DEFINE_PRINT(ez_p_eval) |
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| 55 | TIMING_DEFINE_PRINT(ez_p_content) |
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[10af64] | 56 | |
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[1e4b53] | 57 | bool |
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| 58 | terminationTest (const CanonicalForm& F, const CanonicalForm& G, |
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| 59 | const CanonicalForm& coF, const CanonicalForm& coG, |
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| 60 | const CanonicalForm& cand) |
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| 61 | { |
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| 62 | CanonicalForm LCCand= abs (LC (cand)); |
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| 63 | if (LCCand*abs (LC (coF)) == abs (LC (F))) |
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| 64 | { |
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| 65 | if (LCCand*abs (LC (coG)) == abs (LC (G))) |
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| 66 | { |
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| 67 | if (abs (cand)*abs (coF) == abs (F)) |
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| 68 | { |
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| 69 | if (abs (cand)*abs (coG) == abs (G)) |
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| 70 | return true; |
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| 71 | } |
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| 72 | return false; |
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| 73 | } |
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| 74 | return false; |
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| 75 | } |
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| 76 | return false; |
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| 77 | } |
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| 78 | |
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[517530] | 79 | #ifdef HAVE_NTL |
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| 80 | |
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[08daea] | 81 | static const double log2exp= 1.442695041; |
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| 82 | |
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[806c18] | 83 | /// compressing two polynomials F and G, M is used for compressing, |
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[10af64] | 84 | /// N to reverse the compression |
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| 85 | int myCompress (const CanonicalForm& F, const CanonicalForm& G, CFMap & M, |
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[08daea] | 86 | CFMap & N, bool topLevel) |
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[806c18] | 87 | { |
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[10af64] | 88 | int n= tmax (F.level(), G.level()); |
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| 89 | int * degsf= new int [n + 1]; |
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| 90 | int * degsg= new int [n + 1]; |
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| 91 | |
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| 92 | for (int i = 0; i <= n; i++) |
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| 93 | degsf[i]= degsg[i]= 0; |
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[806c18] | 94 | |
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[10af64] | 95 | degsf= degrees (F, degsf); |
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| 96 | degsg= degrees (G, degsg); |
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[806c18] | 97 | |
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[10af64] | 98 | int both_non_zero= 0; |
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| 99 | int f_zero= 0; |
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| 100 | int g_zero= 0; |
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| 101 | int both_zero= 0; |
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| 102 | |
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[806c18] | 103 | if (topLevel) |
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[10af64] | 104 | { |
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[806c18] | 105 | for (int i= 1; i <= n; i++) |
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[10af64] | 106 | { |
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[806c18] | 107 | if (degsf[i] != 0 && degsg[i] != 0) |
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[10af64] | 108 | { |
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| 109 | both_non_zero++; |
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| 110 | continue; |
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| 111 | } |
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[806c18] | 112 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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[10af64] | 113 | { |
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| 114 | f_zero++; |
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| 115 | continue; |
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| 116 | } |
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[806c18] | 117 | if (degsg[i] == 0 && degsf[i] && i <= F.level()) |
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[10af64] | 118 | { |
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| 119 | g_zero++; |
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| 120 | continue; |
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| 121 | } |
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| 122 | } |
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| 123 | |
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[806c18] | 124 | if (both_non_zero == 0) |
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[dec1024] | 125 | { |
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| 126 | delete [] degsf; |
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| 127 | delete [] degsg; |
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| 128 | return 0; |
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| 129 | } |
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[10af64] | 130 | |
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| 131 | // map Variables which do not occur in both polynomials to higher levels |
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| 132 | int k= 1; |
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| 133 | int l= 1; |
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[806c18] | 134 | for (int i= 1; i <= n; i++) |
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| 135 | { |
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| 136 | if (degsf[i] != 0 && degsg[i] == 0 && i <= F.level()) |
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[10af64] | 137 | { |
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[806c18] | 138 | if (k + both_non_zero != i) |
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[10af64] | 139 | { |
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| 140 | M.newpair (Variable (i), Variable (k + both_non_zero)); |
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| 141 | N.newpair (Variable (k + both_non_zero), Variable (i)); |
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| 142 | } |
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| 143 | k++; |
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| 144 | } |
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[806c18] | 145 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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[10af64] | 146 | { |
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[806c18] | 147 | if (l + g_zero + both_non_zero != i) |
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[10af64] | 148 | { |
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| 149 | M.newpair (Variable (i), Variable (l + g_zero + both_non_zero)); |
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| 150 | N.newpair (Variable (l + g_zero + both_non_zero), Variable (i)); |
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| 151 | } |
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| 152 | l++; |
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| 153 | } |
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| 154 | } |
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[806c18] | 155 | |
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[10af64] | 156 | // sort Variables x_{i} in increasing order of |
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[806c18] | 157 | // min(deg_{x_{i}}(f),deg_{x_{i}}(g)) |
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[9ff686] | 158 | int m= tmax (F.level(), G.level()); |
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| 159 | int min_max_deg; |
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[10af64] | 160 | k= both_non_zero; |
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| 161 | l= 0; |
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| 162 | int i= 1; |
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[806c18] | 163 | while (k > 0) |
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[10af64] | 164 | { |
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[9ff686] | 165 | if (degsf [i] != 0 && degsg [i] != 0) |
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| 166 | min_max_deg= tmax (degsf[i], degsg[i]); |
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| 167 | else |
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| 168 | min_max_deg= 0; |
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| 169 | while (min_max_deg == 0) |
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[10af64] | 170 | { |
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| 171 | i++; |
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[9ff686] | 172 | if (degsf [i] != 0 && degsg [i] != 0) |
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| 173 | min_max_deg= tmax (degsf[i], degsg[i]); |
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| 174 | else |
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| 175 | min_max_deg= 0; |
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[10af64] | 176 | } |
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[806c18] | 177 | for (int j= i + 1; j <= m; j++) |
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[10af64] | 178 | { |
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[9ff686] | 179 | if (degsf[j] != 0 && degsg [j] != 0 && |
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| 180 | tmax (degsf[j],degsg[j]) <= min_max_deg) |
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[10af64] | 181 | { |
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[9ff686] | 182 | min_max_deg= tmax (degsf[j], degsg[j]); |
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[806c18] | 183 | l= j; |
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[10af64] | 184 | } |
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| 185 | } |
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[806c18] | 186 | if (l != 0) |
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[10af64] | 187 | { |
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[806c18] | 188 | if (l != k) |
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[10af64] | 189 | { |
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| 190 | M.newpair (Variable (l), Variable(k)); |
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| 191 | N.newpair (Variable (k), Variable(l)); |
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| 192 | degsf[l]= 0; |
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| 193 | degsg[l]= 0; |
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| 194 | l= 0; |
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| 195 | } |
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[806c18] | 196 | else |
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[10af64] | 197 | { |
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| 198 | degsf[l]= 0; |
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| 199 | degsg[l]= 0; |
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| 200 | l= 0; |
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| 201 | } |
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[806c18] | 202 | } |
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| 203 | else if (l == 0) |
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[10af64] | 204 | { |
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[806c18] | 205 | if (i != k) |
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[10af64] | 206 | { |
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| 207 | M.newpair (Variable (i), Variable (k)); |
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| 208 | N.newpair (Variable (k), Variable (i)); |
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| 209 | degsf[i]= 0; |
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| 210 | degsg[i]= 0; |
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| 211 | } |
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[806c18] | 212 | else |
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[10af64] | 213 | { |
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| 214 | degsf[i]= 0; |
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| 215 | degsg[i]= 0; |
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| 216 | } |
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| 217 | i++; |
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[806c18] | 218 | } |
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[10af64] | 219 | k--; |
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| 220 | } |
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| 221 | } |
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[806c18] | 222 | else |
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[10af64] | 223 | { |
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| 224 | //arrange Variables such that no gaps occur |
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[806c18] | 225 | for (int i= 1; i <= n; i++) |
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[10af64] | 226 | { |
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[806c18] | 227 | if (degsf[i] == 0 && degsg[i] == 0) |
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[10af64] | 228 | { |
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| 229 | both_zero++; |
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| 230 | continue; |
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| 231 | } |
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[806c18] | 232 | else |
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[10af64] | 233 | { |
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[806c18] | 234 | if (both_zero != 0) |
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[10af64] | 235 | { |
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| 236 | M.newpair (Variable (i), Variable (i - both_zero)); |
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| 237 | N.newpair (Variable (i - both_zero), Variable (i)); |
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| 238 | } |
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| 239 | } |
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| 240 | } |
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| 241 | } |
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| 242 | |
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| 243 | delete [] degsf; |
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| 244 | delete [] degsg; |
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| 245 | |
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[c4f4fd] | 246 | return 1; |
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[10af64] | 247 | } |
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| 248 | |
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[806c18] | 249 | static inline CanonicalForm |
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[dec1024] | 250 | uni_content (const CanonicalForm & F); |
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| 251 | |
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| 252 | CanonicalForm |
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| 253 | uni_content (const CanonicalForm& F, const Variable& x) |
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| 254 | { |
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| 255 | if (F.inCoeffDomain()) |
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| 256 | return F.genOne(); |
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| 257 | if (F.level() == x.level() && F.isUnivariate()) |
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| 258 | return F; |
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| 259 | if (F.level() != x.level() && F.isUnivariate()) |
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| 260 | return F.genOne(); |
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[806c18] | 261 | |
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[dec1024] | 262 | if (x.level() != 1) |
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| 263 | { |
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| 264 | CanonicalForm f= swapvar (F, x, Variable (1)); |
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| 265 | CanonicalForm result= uni_content (f); |
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| 266 | return swapvar (result, x, Variable (1)); |
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| 267 | } |
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| 268 | else |
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| 269 | return uni_content (F); |
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[806c18] | 270 | } |
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[dec1024] | 271 | |
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[806c18] | 272 | /// compute the content of F, where F is considered as an element of |
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| 273 | /// \f$ R[x_{1}][x_{2},\ldots ,x_{n}] \f$ |
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| 274 | static inline CanonicalForm |
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| 275 | uni_content (const CanonicalForm & F) |
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| 276 | { |
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[10af64] | 277 | if (F.inBaseDomain()) |
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| 278 | return F.genOne(); |
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| 279 | if (F.level() == 1 && F.isUnivariate()) |
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| 280 | return F; |
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| 281 | if (F.level() != 1 && F.isUnivariate()) |
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| 282 | return F.genOne(); |
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[c4f4fd] | 283 | if (degree (F,1) == 0) return F.genOne(); |
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[10af64] | 284 | |
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| 285 | int l= F.level(); |
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[806c18] | 286 | if (l == 2) |
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[10af64] | 287 | return content(F); |
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[806c18] | 288 | else |
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[10af64] | 289 | { |
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| 290 | CanonicalForm pol, c = 0; |
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| 291 | CFIterator i = F; |
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[806c18] | 292 | for (; i.hasTerms(); i++) |
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[10af64] | 293 | { |
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[806c18] | 294 | pol= i.coeff(); |
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[10af64] | 295 | pol= uni_content (pol); |
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| 296 | c= gcd (c, pol); |
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| 297 | if (c.isOne()) |
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| 298 | return c; |
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| 299 | } |
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| 300 | return c; |
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| 301 | } |
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| 302 | } |
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| 303 | |
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[806c18] | 304 | CanonicalForm |
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| 305 | extractContents (const CanonicalForm& F, const CanonicalForm& G, |
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| 306 | CanonicalForm& contentF, CanonicalForm& contentG, |
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[dec1024] | 307 | CanonicalForm& ppF, CanonicalForm& ppG, const int d) |
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| 308 | { |
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| 309 | CanonicalForm uniContentF, uniContentG, gcdcFcG; |
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| 310 | contentF= 1; |
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| 311 | contentG= 1; |
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| 312 | ppF= F; |
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| 313 | ppG= G; |
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| 314 | CanonicalForm result= 1; |
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| 315 | for (int i= 1; i <= d; i++) |
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| 316 | { |
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| 317 | uniContentF= uni_content (F, Variable (i)); |
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| 318 | uniContentG= uni_content (G, Variable (i)); |
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| 319 | gcdcFcG= gcd (uniContentF, uniContentG); |
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| 320 | contentF *= uniContentF; |
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| 321 | contentG *= uniContentG; |
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| 322 | ppF /= uniContentF; |
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| 323 | ppG /= uniContentG; |
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| 324 | result *= gcdcFcG; |
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| 325 | } |
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| 326 | return result; |
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| 327 | } |
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| 328 | |
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[10af64] | 329 | /// compute the leading coefficient of F, where F is considered as an element |
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| 330 | /// of \f$ R[x_{1}][x_{2},\ldots ,x_{n}] \f$, order on Mon (x_{2},\ldots ,x_{n}) |
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[c4f4fd] | 331 | /// is dp. |
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[10af64] | 332 | static inline |
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[806c18] | 333 | CanonicalForm uni_lcoeff (const CanonicalForm& F) |
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[10af64] | 334 | { |
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[c1b9927] | 335 | if (F.level() > 1) |
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[10af64] | 336 | { |
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| 337 | Variable x= Variable (2); |
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| 338 | int deg= totaldegree (F, x, F.mvar()); |
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| 339 | for (CFIterator i= F; i.hasTerms(); i++) |
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| 340 | { |
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| 341 | if (i.exp() + totaldegree (i.coeff(), x, i.coeff().mvar()) == deg) |
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[806c18] | 342 | return uni_lcoeff (i.coeff()); |
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[10af64] | 343 | } |
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| 344 | } |
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[c1b9927] | 345 | return F; |
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[10af64] | 346 | } |
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| 347 | |
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| 348 | /// Newton interpolation - Incremental algorithm. |
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| 349 | /// Given a list of values alpha_i and a list of polynomials u_i, 1 <= i <= n, |
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| 350 | /// computes the interpolation polynomial assuming that |
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| 351 | /// the polynomials in u are the results of evaluating the variabe x |
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| 352 | /// of the unknown polynomial at the alpha values. |
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| 353 | /// This incremental version receives only the values of alpha_n and u_n and |
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| 354 | /// the previous interpolation polynomial for points 1 <= i <= n-1, and computes |
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| 355 | /// the polynomial interpolating in all the points. |
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| 356 | /// newtonPoly must be equal to (x - alpha_1) * ... * (x - alpha_{n-1}) |
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| 357 | static inline CanonicalForm |
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[9ff686] | 358 | newtonInterp(const CanonicalForm alpha, const CanonicalForm u, |
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| 359 | const CanonicalForm newtonPoly, const CanonicalForm oldInterPoly, |
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| 360 | const Variable & x) |
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[10af64] | 361 | { |
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| 362 | CanonicalForm interPoly; |
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| 363 | |
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[9ff686] | 364 | interPoly= oldInterPoly + ((u - oldInterPoly(alpha, x))/newtonPoly(alpha, x)) |
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| 365 | *newtonPoly; |
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[10af64] | 366 | return interPoly; |
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| 367 | } |
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| 368 | |
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[806c18] | 369 | /// compute a random element a of \f$ F_{p}(\alpha ) \f$ , |
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[10af64] | 370 | /// s.t. F(a) \f$ \neq 0 \f$ , F is a univariate polynomial, returns |
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[806c18] | 371 | /// fail if there are no field elements left which have not been used before |
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| 372 | static inline CanonicalForm |
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[10af64] | 373 | randomElement (const CanonicalForm & F, const Variable & alpha, CFList & list, |
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[806c18] | 374 | bool & fail) |
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[10af64] | 375 | { |
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| 376 | fail= false; |
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| 377 | Variable x= F.mvar(); |
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| 378 | AlgExtRandomF genAlgExt (alpha); |
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| 379 | FFRandom genFF; |
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| 380 | CanonicalForm random, mipo; |
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| 381 | mipo= getMipo (alpha); |
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| 382 | int p= getCharacteristic (); |
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| 383 | int d= degree (mipo); |
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[c4f4fd] | 384 | int bound= ipower (p, d); |
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[806c18] | 385 | do |
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[10af64] | 386 | { |
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| 387 | if (list.length() == bound) |
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| 388 | { |
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| 389 | fail= true; |
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| 390 | break; |
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| 391 | } |
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[806c18] | 392 | if (list.length() < p) |
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[10af64] | 393 | { |
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| 394 | random= genFF.generate(); |
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| 395 | while (find (list, random)) |
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| 396 | random= genFF.generate(); |
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| 397 | } |
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[806c18] | 398 | else |
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[10af64] | 399 | { |
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| 400 | random= genAlgExt.generate(); |
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| 401 | while (find (list, random)) |
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| 402 | random= genAlgExt.generate(); |
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| 403 | } |
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[806c18] | 404 | if (F (random, x) == 0) |
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[10af64] | 405 | { |
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| 406 | list.append (random); |
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| 407 | continue; |
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| 408 | } |
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| 409 | } while (find (list, random)); |
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| 410 | return random; |
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| 411 | } |
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| 412 | |
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[9ff686] | 413 | static inline |
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| 414 | Variable chooseExtension (const Variable & alpha) |
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| 415 | { |
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[bffe62d] | 416 | if (fac_NTL_char != getCharacteristic()) |
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| 417 | { |
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| 418 | fac_NTL_char= getCharacteristic(); |
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| 419 | zz_p::init (getCharacteristic()); |
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| 420 | } |
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[9ff686] | 421 | zz_pX NTLIrredpoly; |
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| 422 | int i, m; |
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| 423 | // extension of F_p needed |
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| 424 | if (alpha.level() == 1) |
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| 425 | { |
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| 426 | i= 1; |
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| 427 | m= 2; |
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| 428 | } //extension of F_p(alpha) |
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| 429 | if (alpha.level() != 1) |
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| 430 | { |
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| 431 | i= 4; |
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| 432 | m= degree (getMipo (alpha)); |
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| 433 | } |
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| 434 | BuildIrred (NTLIrredpoly, i*m); |
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| 435 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
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| 436 | return rootOf (newMipo); |
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| 437 | } |
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| 438 | |
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[806c18] | 439 | /// chooses a suitable extension of \f$ F_{p}(\alpha ) \f$ |
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[10af64] | 440 | /// we do not extend \f$ F_{p}(\alpha ) \f$ itself but extend \f$ F_{p} \f$ , |
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[806c18] | 441 | /// s.t. \f$ F_{p}(\alpha ) \subset F_{p}(\beta ) \f$ |
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[10af64] | 442 | static inline |
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[806c18] | 443 | void choose_extension (const int& d, const int& num_vars, Variable& beta) |
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[10af64] | 444 | { |
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| 445 | int p= getCharacteristic(); |
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[bffe62d] | 446 | if (p != fac_NTL_char) |
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| 447 | { |
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| 448 | fac_NTL_char= p; |
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| 449 | zz_p::init (p); |
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| 450 | } |
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[9a12097] | 451 | zz_pX NTLirredpoly; |
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[10af64] | 452 | //TODO: replace d by max_{i} (deg_x{i}(f)) |
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[806c18] | 453 | int i= (int) (log ((double) ipower (d + 1, num_vars))/log ((double) p)); |
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[10af64] | 454 | int m= degree (getMipo (beta)); |
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| 455 | if (i <= 1) |
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| 456 | i= 2; |
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[806c18] | 457 | BuildIrred (NTLirredpoly, i*m); |
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[9a12097] | 458 | CanonicalForm mipo= convertNTLzzpX2CF (NTLirredpoly, Variable(1)); |
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[806c18] | 459 | beta= rootOf (mipo); |
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[10af64] | 460 | } |
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| 461 | |
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[597783] | 462 | CanonicalForm |
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| 463 | GCD_Fp_extension (const CanonicalForm& F, const CanonicalForm& G, |
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| 464 | CanonicalForm& coF, CanonicalForm& coG, |
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| 465 | Variable & alpha, CFList& l, bool& topLevel); |
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| 466 | |
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| 467 | CanonicalForm |
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| 468 | GCD_Fp_extension (const CanonicalForm& F, const CanonicalForm& G, |
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| 469 | Variable & alpha, CFList& l, bool& topLevel) |
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| 470 | { |
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| 471 | CanonicalForm dummy1, dummy2; |
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| 472 | CanonicalForm result= GCD_Fp_extension (F, G, dummy1, dummy2, alpha, l, |
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| 473 | topLevel); |
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| 474 | return result; |
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| 475 | } |
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| 476 | |
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[806c18] | 477 | /// GCD of F and G over \f$ F_{p}(\alpha ) \f$ , |
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[dec1024] | 478 | /// l and topLevel are only used internally, output is monic |
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[10af64] | 479 | /// based on Alg. 7.2. as described in "Algorithms for |
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| 480 | /// Computer Algebra" by Geddes, Czapor, Labahn |
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[806c18] | 481 | CanonicalForm |
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| 482 | GCD_Fp_extension (const CanonicalForm& F, const CanonicalForm& G, |
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[597783] | 483 | CanonicalForm& coF, CanonicalForm& coG, |
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[806c18] | 484 | Variable & alpha, CFList& l, bool& topLevel) |
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| 485 | { |
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[10af64] | 486 | CanonicalForm A= F; |
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| 487 | CanonicalForm B= G; |
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[597783] | 488 | if (F.isZero() && degree(G) > 0) |
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| 489 | { |
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| 490 | coF= 0; |
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| 491 | coG= Lc (G); |
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| 492 | return G/Lc(G); |
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| 493 | } |
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| 494 | else if (G.isZero() && degree (F) > 0) |
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| 495 | { |
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| 496 | coF= Lc (F); |
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| 497 | coG= 0; |
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| 498 | return F/Lc(F); |
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| 499 | } |
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| 500 | else if (F.isZero() && G.isZero()) |
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| 501 | { |
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| 502 | coF= coG= 0; |
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| 503 | return F.genOne(); |
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| 504 | } |
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| 505 | if (F.inBaseDomain() || G.inBaseDomain()) |
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| 506 | { |
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| 507 | coF= F; |
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| 508 | coG= G; |
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| 509 | return F.genOne(); |
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| 510 | } |
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| 511 | if (F.isUnivariate() && fdivides(F, G, coG)) |
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| 512 | { |
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| 513 | coF= Lc (F); |
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| 514 | return F/Lc(F); |
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| 515 | } |
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| 516 | if (G.isUnivariate() && fdivides(G, F, coF)) |
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| 517 | { |
---|
| 518 | coG= Lc (G); |
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| 519 | return G/Lc(G); |
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| 520 | } |
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| 521 | if (F == G) |
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| 522 | { |
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| 523 | coF= coG= Lc (F); |
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| 524 | return F/Lc(F); |
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| 525 | } |
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[806c18] | 526 | |
---|
[10af64] | 527 | CFMap M,N; |
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[dec1024] | 528 | int best_level= myCompress (A, B, M, N, topLevel); |
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[10af64] | 529 | |
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[597783] | 530 | if (best_level == 0) |
---|
| 531 | { |
---|
| 532 | coF= F; |
---|
| 533 | coG= G; |
---|
| 534 | return B.genOne(); |
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| 535 | } |
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[10af64] | 536 | |
---|
| 537 | A= M(A); |
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| 538 | B= M(B); |
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| 539 | |
---|
| 540 | Variable x= Variable(1); |
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| 541 | |
---|
[806c18] | 542 | //univariate case |
---|
| 543 | if (A.isUnivariate() && B.isUnivariate()) |
---|
[597783] | 544 | { |
---|
| 545 | CanonicalForm result= gcd (A, B); |
---|
| 546 | coF= N (A/result); |
---|
| 547 | coG= N (B/result); |
---|
| 548 | return N (result); |
---|
| 549 | } |
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[806c18] | 550 | |
---|
[10af64] | 551 | CanonicalForm cA, cB; // content of A and B |
---|
| 552 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
| 553 | CanonicalForm gcdcAcB; |
---|
[c4f4fd] | 554 | |
---|
[ea5ff1d] | 555 | cA = uni_content (A); |
---|
| 556 | cB = uni_content (B); |
---|
| 557 | gcdcAcB= gcd (cA, cB); |
---|
| 558 | ppA= A/cA; |
---|
| 559 | ppB= B/cB; |
---|
[10af64] | 560 | |
---|
[e243418] | 561 | int sizeNewtonPolyg; |
---|
| 562 | int ** newtonPolyg= NULL; |
---|
| 563 | mat_ZZ MM; |
---|
| 564 | vec_ZZ V; |
---|
[ea095d] | 565 | bool compressConvexDense= false; //(ppA.level() == 2 && ppB.level() == 2); |
---|
[e243418] | 566 | if (compressConvexDense) |
---|
| 567 | { |
---|
[597783] | 568 | CanonicalForm bufcA= cA; |
---|
| 569 | CanonicalForm bufcB= cB; |
---|
[e243418] | 570 | cA= content (ppA, 1); |
---|
| 571 | cB= content (ppB, 1); |
---|
| 572 | ppA /= cA; |
---|
| 573 | ppB /= cB; |
---|
| 574 | gcdcAcB *= gcd (cA, cB); |
---|
[597783] | 575 | cA *= bufcA; |
---|
| 576 | cB *= bufcB; |
---|
[e243418] | 577 | if (ppA.isUnivariate() || ppB.isUnivariate()) |
---|
| 578 | { |
---|
| 579 | if (ppA.level() == ppB.level()) |
---|
[597783] | 580 | { |
---|
| 581 | CanonicalForm result= gcd (ppA, ppB); |
---|
| 582 | coF= N ((ppA/result)*(cA/gcdcAcB)); |
---|
| 583 | coG= N ((ppB/result)*(cB/gcdcAcB)); |
---|
| 584 | return N (result*gcdcAcB); |
---|
| 585 | } |
---|
[e243418] | 586 | else |
---|
[597783] | 587 | { |
---|
| 588 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 589 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 590 | return N (gcdcAcB); |
---|
[597783] | 591 | } |
---|
[e243418] | 592 | } |
---|
| 593 | |
---|
| 594 | newtonPolyg= newtonPolygon (ppA,ppB, sizeNewtonPolyg); |
---|
| 595 | convexDense (newtonPolyg, sizeNewtonPolyg, MM, V); |
---|
| 596 | |
---|
| 597 | for (int i= 0; i < sizeNewtonPolyg; i++) |
---|
| 598 | delete [] newtonPolyg[i]; |
---|
| 599 | delete [] newtonPolyg; |
---|
| 600 | |
---|
| 601 | ppA= compress (ppA, MM, V, false); |
---|
| 602 | ppB= compress (ppB, MM, V, false); |
---|
| 603 | MM= inv (MM); |
---|
| 604 | |
---|
| 605 | if (ppA.isUnivariate() && ppB.isUnivariate()) |
---|
| 606 | { |
---|
| 607 | if (ppA.level() == ppB.level()) |
---|
[597783] | 608 | { |
---|
| 609 | CanonicalForm result= gcd (ppA, ppB); |
---|
| 610 | coF= N (decompress ((ppA/result), MM, V)*(cA/gcdcAcB)); |
---|
| 611 | coG= N (decompress ((ppB/result), MM, V)*(cB/gcdcAcB)); |
---|
| 612 | return N (decompress (result, MM, V)*gcdcAcB); |
---|
| 613 | } |
---|
[e243418] | 614 | else |
---|
[597783] | 615 | { |
---|
| 616 | coF= N (decompress (ppA, MM, V)); |
---|
| 617 | coG= N (decompress (ppB, MM, V)); |
---|
[a9a6dcb] | 618 | return N (gcdcAcB); |
---|
[597783] | 619 | } |
---|
[e243418] | 620 | } |
---|
| 621 | } |
---|
| 622 | |
---|
[10af64] | 623 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
[806c18] | 624 | CanonicalForm gcdlcAlcB; |
---|
[10af64] | 625 | |
---|
| 626 | lcA= uni_lcoeff (ppA); |
---|
| 627 | lcB= uni_lcoeff (ppB); |
---|
[806c18] | 628 | |
---|
[597783] | 629 | /*if (fdivides (lcA, lcB)) |
---|
[806c18] | 630 | { |
---|
[10af64] | 631 | if (fdivides (A, B)) |
---|
[806c18] | 632 | return F/Lc(F); |
---|
[10af64] | 633 | } |
---|
| 634 | if (fdivides (lcB, lcA)) |
---|
[806c18] | 635 | { |
---|
| 636 | if (fdivides (B, A)) |
---|
[10af64] | 637 | return G/Lc(G); |
---|
[597783] | 638 | }*/ |
---|
[10af64] | 639 | |
---|
| 640 | gcdlcAlcB= gcd (lcA, lcB); |
---|
| 641 | |
---|
| 642 | int d= totaldegree (ppA, Variable(2), Variable (ppA.level())); |
---|
| 643 | |
---|
[dec1024] | 644 | if (d == 0) |
---|
[597783] | 645 | { |
---|
| 646 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 647 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 648 | return N(gcdcAcB); |
---|
[597783] | 649 | } |
---|
[a9a6dcb] | 650 | |
---|
[10af64] | 651 | int d0= totaldegree (ppB, Variable(2), Variable (ppB.level())); |
---|
[806c18] | 652 | if (d0 < d) |
---|
| 653 | d= d0; |
---|
[dec1024] | 654 | if (d == 0) |
---|
[597783] | 655 | { |
---|
| 656 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 657 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 658 | return N(gcdcAcB); |
---|
[597783] | 659 | } |
---|
[10af64] | 660 | |
---|
| 661 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
[597783] | 662 | CanonicalForm newtonPoly, coF_random_element, coG_random_element, coF_m, |
---|
| 663 | coG_m, ppCoF, ppCoG; |
---|
[10af64] | 664 | |
---|
| 665 | newtonPoly= 1; |
---|
| 666 | m= gcdlcAlcB; |
---|
| 667 | G_m= 0; |
---|
[597783] | 668 | coF= 0; |
---|
| 669 | coG= 0; |
---|
[10af64] | 670 | H= 0; |
---|
| 671 | bool fail= false; |
---|
[dec1024] | 672 | topLevel= false; |
---|
[10af64] | 673 | bool inextension= false; |
---|
| 674 | Variable V_buf= alpha; |
---|
| 675 | CanonicalForm prim_elem, im_prim_elem; |
---|
| 676 | CFList source, dest; |
---|
[597783] | 677 | int bound1= degree (ppA, 1); |
---|
| 678 | int bound2= degree (ppB, 1); |
---|
[806c18] | 679 | do |
---|
[10af64] | 680 | { |
---|
[597783] | 681 | random_element= randomElement (m*lcA*lcB, V_buf, l, fail); |
---|
[806c18] | 682 | if (fail) |
---|
[10af64] | 683 | { |
---|
| 684 | source= CFList(); |
---|
| 685 | dest= CFList(); |
---|
[c4f4fd] | 686 | |
---|
[9ff686] | 687 | Variable V_buf3= V_buf; |
---|
| 688 | V_buf= chooseExtension (V_buf); |
---|
[10af64] | 689 | bool prim_fail= false; |
---|
| 690 | Variable V_buf2; |
---|
| 691 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
[c4f4fd] | 692 | |
---|
[9ff686] | 693 | if (V_buf3 != alpha) |
---|
| 694 | { |
---|
| 695 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
[597783] | 696 | G_m= mapDown (G_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 697 | coF_m= mapDown (coF_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 698 | coG_m= mapDown (coG_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
[9ff686] | 699 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
| 700 | source, dest); |
---|
| 701 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 702 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 703 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, |
---|
| 704 | source, dest); |
---|
[597783] | 705 | lcA= mapDown (lcA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 706 | lcB= mapDown (lcB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
[9ff686] | 707 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 708 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
| 709 | source, dest); |
---|
| 710 | } |
---|
| 711 | |
---|
[10af64] | 712 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
| 713 | if (prim_fail) |
---|
| 714 | ; //ERROR |
---|
| 715 | else |
---|
| 716 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
[c4f4fd] | 717 | |
---|
[10af64] | 718 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
[04dd0c] | 719 | DEBOUTLN (cerr, "getMipo (V_buf2)= " << getMipo (V_buf2)); |
---|
[10af64] | 720 | inextension= true; |
---|
[806c18] | 721 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 722 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
[10af64] | 723 | im_prim_elem, source, dest); |
---|
| 724 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 725 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
[597783] | 726 | coF_m= mapUp (coF_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 727 | coG_m= mapUp (coG_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
[806c18] | 728 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
[10af64] | 729 | source, dest); |
---|
| 730 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 731 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
[806c18] | 732 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
[10af64] | 733 | source, dest); |
---|
[597783] | 734 | lcA= mapUp (lcA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 735 | lcB= mapUp (lcB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
[10af64] | 736 | |
---|
| 737 | fail= false; |
---|
[597783] | 738 | random_element= randomElement (m*lcA*lcB, V_buf, l, fail ); |
---|
[a5cc7b3] | 739 | DEBOUTLN (cerr, "fail= " << fail); |
---|
[10af64] | 740 | CFList list; |
---|
| 741 | TIMING_START (gcd_recursion); |
---|
[806c18] | 742 | G_random_element= |
---|
[597783] | 743 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), |
---|
| 744 | coF_random_element, coG_random_element, V_buf, |
---|
[dec1024] | 745 | list, topLevel); |
---|
[806c18] | 746 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
[10af64] | 747 | "time for recursive call: "); |
---|
| 748 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 749 | } |
---|
[806c18] | 750 | else |
---|
[10af64] | 751 | { |
---|
| 752 | CFList list; |
---|
| 753 | TIMING_START (gcd_recursion); |
---|
[806c18] | 754 | G_random_element= |
---|
[597783] | 755 | GCD_Fp_extension (ppA(random_element, x), ppB(random_element, x), |
---|
| 756 | coF_random_element, coG_random_element, V_buf, |
---|
[dec1024] | 757 | list, topLevel); |
---|
[806c18] | 758 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
[10af64] | 759 | "time for recursive call: "); |
---|
| 760 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 761 | } |
---|
| 762 | |
---|
[a76d6fe] | 763 | if (!G_random_element.inCoeffDomain()) |
---|
| 764 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 765 | Variable (G_random_element.level())); |
---|
| 766 | else |
---|
| 767 | d0= 0; |
---|
| 768 | |
---|
[dec1024] | 769 | if (d0 == 0) |
---|
[597783] | 770 | { |
---|
| 771 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 772 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 773 | return N(gcdcAcB); |
---|
[597783] | 774 | } |
---|
[806c18] | 775 | if (d0 > d) |
---|
[10af64] | 776 | { |
---|
| 777 | if (!find (l, random_element)) |
---|
| 778 | l.append (random_element); |
---|
| 779 | continue; |
---|
| 780 | } |
---|
| 781 | |
---|
[806c18] | 782 | G_random_element= |
---|
[10af64] | 783 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
| 784 | * G_random_element; |
---|
[597783] | 785 | coF_random_element= (lcA(random_element,x)/uni_lcoeff(coF_random_element)) |
---|
| 786 | *coF_random_element; |
---|
| 787 | coG_random_element= (lcB(random_element,x)/uni_lcoeff(coG_random_element)) |
---|
| 788 | *coG_random_element; |
---|
[10af64] | 789 | |
---|
[a76d6fe] | 790 | if (!G_random_element.inCoeffDomain()) |
---|
| 791 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 792 | Variable (G_random_element.level())); |
---|
| 793 | else |
---|
| 794 | d0= 0; |
---|
| 795 | |
---|
[806c18] | 796 | if (d0 < d) |
---|
[10af64] | 797 | { |
---|
| 798 | m= gcdlcAlcB; |
---|
| 799 | newtonPoly= 1; |
---|
| 800 | G_m= 0; |
---|
| 801 | d= d0; |
---|
[597783] | 802 | coF_m= 0; |
---|
| 803 | coG_m= 0; |
---|
[10af64] | 804 | } |
---|
| 805 | |
---|
| 806 | TIMING_START (newton_interpolation); |
---|
| 807 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
[597783] | 808 | coF= newtonInterp (random_element, coF_random_element, newtonPoly, coF_m,x); |
---|
| 809 | coG= newtonInterp (random_element, coG_random_element, newtonPoly, coG_m,x); |
---|
[806c18] | 810 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
[10af64] | 811 | "time for newton interpolation: "); |
---|
| 812 | |
---|
[806c18] | 813 | //termination test |
---|
[597783] | 814 | if ((uni_lcoeff (H) == gcdlcAlcB) || (G_m == H)) |
---|
[10af64] | 815 | { |
---|
[2a95b2] | 816 | TIMING_START (termination_test); |
---|
[597783] | 817 | if (gcdlcAlcB.isOne()) |
---|
| 818 | cH= 1; |
---|
| 819 | else |
---|
| 820 | cH= uni_content (H); |
---|
[10af64] | 821 | ppH= H/cH; |
---|
[597783] | 822 | CanonicalForm lcppH= gcdlcAlcB/cH; |
---|
| 823 | CanonicalForm ccoF= lcA/lcppH; |
---|
| 824 | ccoF /= Lc (ccoF); |
---|
| 825 | CanonicalForm ccoG= lcB/lcppH; |
---|
| 826 | ccoG /= Lc (ccoG); |
---|
| 827 | ppCoF= coF/ccoF; |
---|
| 828 | ppCoG= coG/ccoG; |
---|
[806c18] | 829 | if (inextension) |
---|
[10af64] | 830 | { |
---|
[597783] | 831 | if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
| 832 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
[1e4b53] | 833 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
[597783] | 834 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
[dec1024] | 835 | { |
---|
[597783] | 836 | CFList u, v; |
---|
[c723d80] | 837 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
[621271b] | 838 | ppH /= Lc(ppH); |
---|
[c723d80] | 839 | ppH= mapDown (ppH, prim_elem, im_prim_elem, alpha, u, v); |
---|
[597783] | 840 | ppCoF= mapDown (ppCoF, prim_elem, im_prim_elem, alpha, u, v); |
---|
| 841 | ppCoF= mapDown (ppCoG, prim_elem, im_prim_elem, alpha, u, v); |
---|
[c723d80] | 842 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
[e243418] | 843 | if (compressConvexDense) |
---|
[597783] | 844 | { |
---|
[e243418] | 845 | ppH= decompress (ppH, MM, V); |
---|
[597783] | 846 | ppCoF= decompress (ppCoF, MM, V); |
---|
| 847 | ppCoG= decompress (ppCoG, MM, V); |
---|
| 848 | } |
---|
| 849 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
| 850 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
[2a95b2] | 851 | TIMING_END_AND_PRINT (termination_test, |
---|
| 852 | "time for successful termination test Fq: "); |
---|
[10af64] | 853 | return N(gcdcAcB*ppH); |
---|
[dec1024] | 854 | } |
---|
[10af64] | 855 | } |
---|
[597783] | 856 | else if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
| 857 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
[1e4b53] | 858 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
[597783] | 859 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
[dec1024] | 860 | { |
---|
[e243418] | 861 | if (compressConvexDense) |
---|
[597783] | 862 | { |
---|
[e243418] | 863 | ppH= decompress (ppH, MM, V); |
---|
[597783] | 864 | ppCoF= decompress (ppCoF, MM, V); |
---|
| 865 | ppCoG= decompress (ppCoG, MM, V); |
---|
| 866 | } |
---|
| 867 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
[2a95b2] | 868 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
| 869 | TIMING_END_AND_PRINT (termination_test, |
---|
| 870 | "time for successful termination test Fq: "); |
---|
[dec1024] | 871 | return N(gcdcAcB*ppH); |
---|
| 872 | } |
---|
[2a95b2] | 873 | TIMING_END_AND_PRINT (termination_test, |
---|
| 874 | "time for unsuccessful termination test Fq: "); |
---|
[10af64] | 875 | } |
---|
| 876 | |
---|
| 877 | G_m= H; |
---|
[597783] | 878 | coF_m= coF; |
---|
| 879 | coG_m= coG; |
---|
[10af64] | 880 | newtonPoly= newtonPoly*(x - random_element); |
---|
| 881 | m= m*(x - random_element); |
---|
| 882 | if (!find (l, random_element)) |
---|
| 883 | l.append (random_element); |
---|
| 884 | } while (1); |
---|
| 885 | } |
---|
| 886 | |
---|
[806c18] | 887 | /// compute a random element a of GF, s.t. F(a) \f$ \neq 0 \f$ , F is a |
---|
[10af64] | 888 | /// univariate polynomial, returns fail if there are no field elements left |
---|
| 889 | /// which have not been used before |
---|
[04dd0c] | 890 | static inline |
---|
[10af64] | 891 | CanonicalForm |
---|
| 892 | GFRandomElement (const CanonicalForm& F, CFList& list, bool& fail) |
---|
| 893 | { |
---|
| 894 | fail= false; |
---|
| 895 | Variable x= F.mvar(); |
---|
| 896 | GFRandom genGF; |
---|
| 897 | CanonicalForm random; |
---|
| 898 | int p= getCharacteristic(); |
---|
| 899 | int d= getGFDegree(); |
---|
[c4f4fd] | 900 | int bound= ipower (p, d); |
---|
[806c18] | 901 | do |
---|
[10af64] | 902 | { |
---|
| 903 | if (list.length() == bound) |
---|
| 904 | { |
---|
| 905 | fail= true; |
---|
| 906 | break; |
---|
| 907 | } |
---|
| 908 | if (list.length() < 1) |
---|
| 909 | random= 0; |
---|
[806c18] | 910 | else |
---|
[10af64] | 911 | { |
---|
| 912 | random= genGF.generate(); |
---|
| 913 | while (find (list, random)) |
---|
| 914 | random= genGF.generate(); |
---|
| 915 | } |
---|
[806c18] | 916 | if (F (random, x) == 0) |
---|
[10af64] | 917 | { |
---|
| 918 | list.append (random); |
---|
| 919 | continue; |
---|
| 920 | } |
---|
| 921 | } while (find (list, random)); |
---|
| 922 | return random; |
---|
| 923 | } |
---|
| 924 | |
---|
[597783] | 925 | CanonicalForm |
---|
| 926 | GCD_GF (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 927 | CanonicalForm& coF, CanonicalForm& coG, |
---|
| 928 | CFList& l, bool& topLevel); |
---|
| 929 | |
---|
| 930 | CanonicalForm |
---|
| 931 | GCD_GF (const CanonicalForm& F, const CanonicalForm& G, CFList& l, |
---|
| 932 | bool& topLevel) |
---|
| 933 | { |
---|
| 934 | CanonicalForm dummy1, dummy2; |
---|
| 935 | CanonicalForm result= GCD_GF (F, G, dummy1, dummy2, l, topLevel); |
---|
| 936 | return result; |
---|
| 937 | } |
---|
| 938 | |
---|
[10af64] | 939 | /// GCD of F and G over GF, based on Alg. 7.2. as described in "Algorithms for |
---|
| 940 | /// Computer Algebra" by Geddes, Czapor, Labahn |
---|
| 941 | /// Usually this algorithm will be faster than GCD_Fp_extension since GF has |
---|
| 942 | /// faster field arithmetics, however it might fail if the input is large since |
---|
| 943 | /// the size of the base field is bounded by 2^16, output is monic |
---|
[597783] | 944 | CanonicalForm |
---|
| 945 | GCD_GF (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 946 | CanonicalForm& coF, CanonicalForm& coG, |
---|
[806c18] | 947 | CFList& l, bool& topLevel) |
---|
| 948 | { |
---|
[10af64] | 949 | CanonicalForm A= F; |
---|
| 950 | CanonicalForm B= G; |
---|
[597783] | 951 | if (F.isZero() && degree(G) > 0) |
---|
| 952 | { |
---|
| 953 | coF= 0; |
---|
| 954 | coG= Lc (G); |
---|
| 955 | return G/Lc(G); |
---|
| 956 | } |
---|
| 957 | else if (G.isZero() && degree (F) > 0) |
---|
| 958 | { |
---|
| 959 | coF= Lc (F); |
---|
| 960 | coG= 0; |
---|
| 961 | return F/Lc(F); |
---|
| 962 | } |
---|
| 963 | else if (F.isZero() && G.isZero()) |
---|
| 964 | { |
---|
| 965 | coF= coG= 0; |
---|
| 966 | return F.genOne(); |
---|
| 967 | } |
---|
| 968 | if (F.inBaseDomain() || G.inBaseDomain()) |
---|
| 969 | { |
---|
| 970 | coF= F; |
---|
| 971 | coG= G; |
---|
| 972 | return F.genOne(); |
---|
| 973 | } |
---|
| 974 | if (F.isUnivariate() && fdivides(F, G, coG)) |
---|
| 975 | { |
---|
| 976 | coF= Lc (F); |
---|
| 977 | return F/Lc(F); |
---|
| 978 | } |
---|
| 979 | if (G.isUnivariate() && fdivides(G, F, coF)) |
---|
| 980 | { |
---|
| 981 | coG= Lc (G); |
---|
| 982 | return G/Lc(G); |
---|
| 983 | } |
---|
| 984 | if (F == G) |
---|
| 985 | { |
---|
| 986 | coF= coG= Lc (F); |
---|
| 987 | return F/Lc(F); |
---|
| 988 | } |
---|
[806c18] | 989 | |
---|
[10af64] | 990 | CFMap M,N; |
---|
[dec1024] | 991 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
[10af64] | 992 | |
---|
[597783] | 993 | if (best_level == 0) |
---|
| 994 | { |
---|
| 995 | coF= F; |
---|
| 996 | coG= G; |
---|
| 997 | return B.genOne(); |
---|
| 998 | } |
---|
[10af64] | 999 | |
---|
| 1000 | A= M(A); |
---|
| 1001 | B= M(B); |
---|
| 1002 | |
---|
| 1003 | Variable x= Variable(1); |
---|
| 1004 | |
---|
[806c18] | 1005 | //univariate case |
---|
| 1006 | if (A.isUnivariate() && B.isUnivariate()) |
---|
[597783] | 1007 | { |
---|
| 1008 | CanonicalForm result= gcd (A, B); |
---|
| 1009 | coF= N (A/result); |
---|
| 1010 | coG= N (B/result); |
---|
| 1011 | return N (result); |
---|
| 1012 | } |
---|
[10af64] | 1013 | |
---|
| 1014 | CanonicalForm cA, cB; // content of A and B |
---|
| 1015 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
| 1016 | CanonicalForm gcdcAcB; |
---|
| 1017 | |
---|
[ea5ff1d] | 1018 | cA = uni_content (A); |
---|
| 1019 | cB = uni_content (B); |
---|
| 1020 | gcdcAcB= gcd (cA, cB); |
---|
| 1021 | ppA= A/cA; |
---|
| 1022 | ppB= B/cB; |
---|
[10af64] | 1023 | |
---|
[e243418] | 1024 | int sizeNewtonPolyg; |
---|
| 1025 | int ** newtonPolyg= NULL; |
---|
| 1026 | mat_ZZ MM; |
---|
| 1027 | vec_ZZ V; |
---|
[ea095d] | 1028 | bool compressConvexDense= false; //(ppA.level() == 2 && ppB.level() == 2); |
---|
[e243418] | 1029 | if (compressConvexDense) |
---|
| 1030 | { |
---|
[597783] | 1031 | CanonicalForm bufcA= cA; |
---|
| 1032 | CanonicalForm bufcB= cB; |
---|
[e243418] | 1033 | cA= content (ppA, 1); |
---|
| 1034 | cB= content (ppB, 1); |
---|
| 1035 | ppA /= cA; |
---|
| 1036 | ppB /= cB; |
---|
| 1037 | gcdcAcB *= gcd (cA, cB); |
---|
[597783] | 1038 | cA *= bufcA; |
---|
| 1039 | cB *= bufcB; |
---|
[e243418] | 1040 | if (ppA.isUnivariate() || ppB.isUnivariate()) |
---|
| 1041 | { |
---|
| 1042 | if (ppA.level() == ppB.level()) |
---|
[597783] | 1043 | { |
---|
| 1044 | CanonicalForm result= gcd (ppA, ppB); |
---|
| 1045 | coF= N ((ppA/result)*(cA/gcdcAcB)); |
---|
| 1046 | coG= N ((ppB/result)*(cB/gcdcAcB)); |
---|
| 1047 | return N (result*gcdcAcB); |
---|
| 1048 | } |
---|
[e243418] | 1049 | else |
---|
[597783] | 1050 | { |
---|
| 1051 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 1052 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 1053 | return N (gcdcAcB); |
---|
[597783] | 1054 | } |
---|
[e243418] | 1055 | } |
---|
| 1056 | |
---|
| 1057 | newtonPolyg= newtonPolygon (ppA,ppB, sizeNewtonPolyg); |
---|
| 1058 | convexDense (newtonPolyg, sizeNewtonPolyg, MM, V); |
---|
| 1059 | |
---|
| 1060 | for (int i= 0; i < sizeNewtonPolyg; i++) |
---|
| 1061 | delete [] newtonPolyg[i]; |
---|
| 1062 | delete [] newtonPolyg; |
---|
| 1063 | |
---|
| 1064 | ppA= compress (ppA, MM, V, false); |
---|
| 1065 | ppB= compress (ppB, MM, V, false); |
---|
| 1066 | MM= inv (MM); |
---|
| 1067 | |
---|
| 1068 | if (ppA.isUnivariate() && ppB.isUnivariate()) |
---|
| 1069 | { |
---|
| 1070 | if (ppA.level() == ppB.level()) |
---|
[597783] | 1071 | { |
---|
| 1072 | CanonicalForm result= gcd (ppA, ppB); |
---|
| 1073 | coF= N (decompress ((ppA/result), MM, V)*(cA/gcdcAcB)); |
---|
| 1074 | coG= N (decompress ((ppB/result), MM, V)*(cB/gcdcAcB)); |
---|
| 1075 | return N (decompress (result, MM, V)*gcdcAcB); |
---|
| 1076 | } |
---|
[e243418] | 1077 | else |
---|
[597783] | 1078 | { |
---|
| 1079 | coF= N (decompress (ppA, MM, V)); |
---|
| 1080 | coG= N (decompress (ppB, MM, V)); |
---|
[a9a6dcb] | 1081 | return N (gcdcAcB); |
---|
[597783] | 1082 | } |
---|
[e243418] | 1083 | } |
---|
| 1084 | } |
---|
| 1085 | |
---|
[10af64] | 1086 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
[806c18] | 1087 | CanonicalForm gcdlcAlcB; |
---|
[10af64] | 1088 | |
---|
| 1089 | lcA= uni_lcoeff (ppA); |
---|
| 1090 | lcB= uni_lcoeff (ppB); |
---|
| 1091 | |
---|
[597783] | 1092 | /*if (fdivides (lcA, lcB)) |
---|
[806c18] | 1093 | { |
---|
[597783] | 1094 | if (fdivides (ppA, ppB, coG)) |
---|
| 1095 | { |
---|
| 1096 | coF= 1; |
---|
| 1097 | if (compressConvexDense) |
---|
| 1098 | coG= decompress (coG, MM, V); |
---|
| 1099 | coG= N (coG*(cB/gcdcAcB)); |
---|
[806c18] | 1100 | return F; |
---|
[597783] | 1101 | } |
---|
[806c18] | 1102 | } |
---|
| 1103 | if (fdivides (lcB, lcA)) |
---|
| 1104 | { |
---|
[597783] | 1105 | if (fdivides (ppB, ppA, coF)) |
---|
| 1106 | { |
---|
| 1107 | coG= 1; |
---|
| 1108 | if (compressConvexDense) |
---|
| 1109 | coF= decompress (coF, MM, V); |
---|
| 1110 | coF= N (coF*(cA/gcdcAcB)); |
---|
[10af64] | 1111 | return G; |
---|
[597783] | 1112 | } |
---|
| 1113 | }*/ |
---|
[10af64] | 1114 | |
---|
| 1115 | gcdlcAlcB= gcd (lcA, lcB); |
---|
| 1116 | |
---|
| 1117 | int d= totaldegree (ppA, Variable(2), Variable (ppA.level())); |
---|
[dec1024] | 1118 | if (d == 0) |
---|
[597783] | 1119 | { |
---|
| 1120 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 1121 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 1122 | return N(gcdcAcB); |
---|
[597783] | 1123 | } |
---|
[10af64] | 1124 | int d0= totaldegree (ppB, Variable(2), Variable (ppB.level())); |
---|
[806c18] | 1125 | if (d0 < d) |
---|
| 1126 | d= d0; |
---|
[dec1024] | 1127 | if (d == 0) |
---|
[597783] | 1128 | { |
---|
| 1129 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 1130 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 1131 | return N(gcdcAcB); |
---|
[597783] | 1132 | } |
---|
[10af64] | 1133 | |
---|
| 1134 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
[597783] | 1135 | CanonicalForm newtonPoly, coF_random_element, coG_random_element, coF_m, |
---|
| 1136 | coG_m, ppCoF, ppCoG; |
---|
[10af64] | 1137 | |
---|
| 1138 | newtonPoly= 1; |
---|
| 1139 | m= gcdlcAlcB; |
---|
| 1140 | G_m= 0; |
---|
[597783] | 1141 | coF= 0; |
---|
| 1142 | coG= 0; |
---|
[10af64] | 1143 | H= 0; |
---|
| 1144 | bool fail= false; |
---|
[597783] | 1145 | //topLevel= false; |
---|
[10af64] | 1146 | bool inextension= false; |
---|
[c1b9927] | 1147 | int p=-1; |
---|
[10af64] | 1148 | int k= getGFDegree(); |
---|
| 1149 | int kk; |
---|
[88f3644] | 1150 | int expon; |
---|
[10af64] | 1151 | char gf_name_buf= gf_name; |
---|
[597783] | 1152 | int bound1= degree (ppA, 1); |
---|
| 1153 | int bound2= degree (ppB, 1); |
---|
[806c18] | 1154 | do |
---|
[10af64] | 1155 | { |
---|
[597783] | 1156 | random_element= GFRandomElement (m*lcA*lcB, l, fail); |
---|
[806c18] | 1157 | if (fail) |
---|
| 1158 | { |
---|
[10af64] | 1159 | p= getCharacteristic(); |
---|
[9ff686] | 1160 | expon= 2; |
---|
[806c18] | 1161 | kk= getGFDegree(); |
---|
| 1162 | if (ipower (p, kk*expon) < (1 << 16)) |
---|
[10af64] | 1163 | setCharacteristic (p, kk*(int)expon, 'b'); |
---|
[806c18] | 1164 | else |
---|
[10af64] | 1165 | { |
---|
[04dd0c] | 1166 | expon= (int) floor((log ((double)((1<<16) - 1)))/(log((double)p)*kk)); |
---|
[10af64] | 1167 | ASSERT (expon >= 2, "not enough points in GCD_GF"); |
---|
| 1168 | setCharacteristic (p, (int)(kk*expon), 'b'); |
---|
| 1169 | } |
---|
| 1170 | inextension= true; |
---|
| 1171 | fail= false; |
---|
[806c18] | 1172 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
[10af64] | 1173 | i.getItem()= GFMapUp (i.getItem(), kk); |
---|
| 1174 | m= GFMapUp (m, kk); |
---|
| 1175 | G_m= GFMapUp (G_m, kk); |
---|
| 1176 | newtonPoly= GFMapUp (newtonPoly, kk); |
---|
[597783] | 1177 | coF_m= GFMapUp (coF_m, kk); |
---|
| 1178 | coG_m= GFMapUp (coG_m, kk); |
---|
[10af64] | 1179 | ppA= GFMapUp (ppA, kk); |
---|
| 1180 | ppB= GFMapUp (ppB, kk); |
---|
| 1181 | gcdlcAlcB= GFMapUp (gcdlcAlcB, kk); |
---|
[597783] | 1182 | lcA= GFMapUp (lcA, kk); |
---|
| 1183 | lcB= GFMapUp (lcB, kk); |
---|
| 1184 | random_element= GFRandomElement (m*lcA*lcB, l, fail); |
---|
[a5cc7b3] | 1185 | DEBOUTLN (cerr, "fail= " << fail); |
---|
[10af64] | 1186 | CFList list; |
---|
| 1187 | TIMING_START (gcd_recursion); |
---|
[806c18] | 1188 | G_random_element= GCD_GF (ppA(random_element, x), ppB(random_element, x), |
---|
[597783] | 1189 | coF_random_element, coG_random_element, |
---|
[dec1024] | 1190 | list, topLevel); |
---|
[806c18] | 1191 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
[10af64] | 1192 | "time for recursive call: "); |
---|
| 1193 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 1194 | } |
---|
[806c18] | 1195 | else |
---|
[10af64] | 1196 | { |
---|
| 1197 | CFList list; |
---|
| 1198 | TIMING_START (gcd_recursion); |
---|
[806c18] | 1199 | G_random_element= GCD_GF (ppA(random_element, x), ppB(random_element, x), |
---|
[597783] | 1200 | coF_random_element, coG_random_element, |
---|
[dec1024] | 1201 | list, topLevel); |
---|
[806c18] | 1202 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
[10af64] | 1203 | "time for recursive call: "); |
---|
| 1204 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 1205 | } |
---|
| 1206 | |
---|
[a76d6fe] | 1207 | if (!G_random_element.inCoeffDomain()) |
---|
| 1208 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 1209 | Variable (G_random_element.level())); |
---|
| 1210 | else |
---|
| 1211 | d0= 0; |
---|
| 1212 | |
---|
[806c18] | 1213 | if (d0 == 0) |
---|
[10af64] | 1214 | { |
---|
[806c18] | 1215 | if (inextension) |
---|
[10af64] | 1216 | setCharacteristic (p, k, gf_name_buf); |
---|
[597783] | 1217 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 1218 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 1219 | return N(gcdcAcB); |
---|
[806c18] | 1220 | } |
---|
| 1221 | if (d0 > d) |
---|
[10af64] | 1222 | { |
---|
| 1223 | if (!find (l, random_element)) |
---|
| 1224 | l.append (random_element); |
---|
| 1225 | continue; |
---|
| 1226 | } |
---|
| 1227 | |
---|
[806c18] | 1228 | G_random_element= |
---|
[10af64] | 1229 | (gcdlcAlcB(random_element, x)/uni_lcoeff(G_random_element)) * |
---|
| 1230 | G_random_element; |
---|
[597783] | 1231 | |
---|
| 1232 | coF_random_element= (lcA(random_element,x)/uni_lcoeff(coF_random_element)) |
---|
| 1233 | *coF_random_element; |
---|
| 1234 | coG_random_element= (lcB(random_element,x)/uni_lcoeff(coG_random_element)) |
---|
| 1235 | *coG_random_element; |
---|
| 1236 | |
---|
[a76d6fe] | 1237 | if (!G_random_element.inCoeffDomain()) |
---|
| 1238 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 1239 | Variable (G_random_element.level())); |
---|
| 1240 | else |
---|
| 1241 | d0= 0; |
---|
[10af64] | 1242 | |
---|
[806c18] | 1243 | if (d0 < d) |
---|
[10af64] | 1244 | { |
---|
| 1245 | m= gcdlcAlcB; |
---|
| 1246 | newtonPoly= 1; |
---|
| 1247 | G_m= 0; |
---|
| 1248 | d= d0; |
---|
[597783] | 1249 | coF_m= 0; |
---|
| 1250 | coG_m= 0; |
---|
[10af64] | 1251 | } |
---|
| 1252 | |
---|
| 1253 | TIMING_START (newton_interpolation); |
---|
| 1254 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
[597783] | 1255 | coF= newtonInterp (random_element, coF_random_element, newtonPoly, coF_m,x); |
---|
| 1256 | coG= newtonInterp (random_element, coG_random_element, newtonPoly, coG_m,x); |
---|
| 1257 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
| 1258 | "time for newton interpolation: "); |
---|
[10af64] | 1259 | |
---|
[806c18] | 1260 | //termination test |
---|
[597783] | 1261 | if ((uni_lcoeff (H) == gcdlcAlcB) || (G_m == H)) |
---|
[10af64] | 1262 | { |
---|
[2a95b2] | 1263 | TIMING_START (termination_test); |
---|
[597783] | 1264 | if (gcdlcAlcB.isOne()) |
---|
| 1265 | cH= 1; |
---|
| 1266 | else |
---|
| 1267 | cH= uni_content (H); |
---|
[10af64] | 1268 | ppH= H/cH; |
---|
[597783] | 1269 | CanonicalForm lcppH= gcdlcAlcB/cH; |
---|
| 1270 | CanonicalForm ccoF= lcA/lcppH; |
---|
| 1271 | ccoF /= Lc (ccoF); |
---|
| 1272 | CanonicalForm ccoG= lcB/lcppH; |
---|
| 1273 | ccoG /= Lc (ccoG); |
---|
| 1274 | ppCoF= coF/ccoF; |
---|
| 1275 | ppCoG= coG/ccoG; |
---|
[806c18] | 1276 | if (inextension) |
---|
[10af64] | 1277 | { |
---|
[597783] | 1278 | if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
| 1279 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
[1e4b53] | 1280 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
[597783] | 1281 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
[10af64] | 1282 | { |
---|
| 1283 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
| 1284 | ppH= GFMapDown (ppH, k); |
---|
[597783] | 1285 | ppCoF= GFMapDown (ppCoF, k); |
---|
| 1286 | ppCoG= GFMapDown (ppCoG, k); |
---|
[10af64] | 1287 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
[e243418] | 1288 | if (compressConvexDense) |
---|
[597783] | 1289 | { |
---|
[e243418] | 1290 | ppH= decompress (ppH, MM, V); |
---|
[597783] | 1291 | ppCoF= decompress (ppCoF, MM, V); |
---|
| 1292 | ppCoG= decompress (ppCoG, MM, V); |
---|
| 1293 | } |
---|
| 1294 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
| 1295 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
[10af64] | 1296 | setCharacteristic (p, k, gf_name_buf); |
---|
[2a95b2] | 1297 | TIMING_END_AND_PRINT (termination_test, |
---|
| 1298 | "time for successful termination GF: "); |
---|
[10af64] | 1299 | return N(gcdcAcB*ppH); |
---|
| 1300 | } |
---|
| 1301 | } |
---|
[806c18] | 1302 | else |
---|
[10af64] | 1303 | { |
---|
[597783] | 1304 | if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
| 1305 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
[1e4b53] | 1306 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
[597783] | 1307 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
[dec1024] | 1308 | { |
---|
[e243418] | 1309 | if (compressConvexDense) |
---|
[597783] | 1310 | { |
---|
[e243418] | 1311 | ppH= decompress (ppH, MM, V); |
---|
[597783] | 1312 | ppCoF= decompress (ppCoF, MM, V); |
---|
| 1313 | ppCoG= decompress (ppCoG, MM, V); |
---|
| 1314 | } |
---|
| 1315 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
| 1316 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
[2a95b2] | 1317 | TIMING_END_AND_PRINT (termination_test, |
---|
| 1318 | "time for successful termination GF: "); |
---|
[10af64] | 1319 | return N(gcdcAcB*ppH); |
---|
[dec1024] | 1320 | } |
---|
[10af64] | 1321 | } |
---|
[2a95b2] | 1322 | TIMING_END_AND_PRINT (termination_test, |
---|
| 1323 | "time for unsuccessful termination GF: "); |
---|
[10af64] | 1324 | } |
---|
| 1325 | |
---|
| 1326 | G_m= H; |
---|
[597783] | 1327 | coF_m= coF; |
---|
| 1328 | coG_m= coG; |
---|
[10af64] | 1329 | newtonPoly= newtonPoly*(x - random_element); |
---|
| 1330 | m= m*(x - random_element); |
---|
| 1331 | if (!find (l, random_element)) |
---|
| 1332 | l.append (random_element); |
---|
| 1333 | } while (1); |
---|
| 1334 | } |
---|
| 1335 | |
---|
| 1336 | /// F is assumed to be an univariate polynomial in x, |
---|
[806c18] | 1337 | /// computes a random monic irreducible univariate polynomial of random |
---|
[10af64] | 1338 | /// degree < i in x which does not divide F |
---|
[806c18] | 1339 | CanonicalForm |
---|
| 1340 | randomIrredpoly (int i, const Variable & x) |
---|
[10af64] | 1341 | { |
---|
| 1342 | int p= getCharacteristic(); |
---|
[bffe62d] | 1343 | if (fac_NTL_char != p) |
---|
| 1344 | { |
---|
| 1345 | fac_NTL_char= p; |
---|
| 1346 | zz_p::init (p); |
---|
| 1347 | } |
---|
[9a12097] | 1348 | zz_pX NTLirredpoly; |
---|
[10af64] | 1349 | CanonicalForm CFirredpoly; |
---|
[04dd0c] | 1350 | BuildIrred (NTLirredpoly, i + 1); |
---|
[9a12097] | 1351 | CFirredpoly= convertNTLzzpX2CF (NTLirredpoly, x); |
---|
[10af64] | 1352 | return CFirredpoly; |
---|
[806c18] | 1353 | } |
---|
[10af64] | 1354 | |
---|
[04dd0c] | 1355 | static inline |
---|
[10af64] | 1356 | CanonicalForm |
---|
| 1357 | FpRandomElement (const CanonicalForm& F, CFList& list, bool& fail) |
---|
| 1358 | { |
---|
| 1359 | fail= false; |
---|
| 1360 | Variable x= F.mvar(); |
---|
| 1361 | FFRandom genFF; |
---|
| 1362 | CanonicalForm random; |
---|
| 1363 | int p= getCharacteristic(); |
---|
[88f3644] | 1364 | int bound= p; |
---|
[806c18] | 1365 | do |
---|
[10af64] | 1366 | { |
---|
| 1367 | if (list.length() == bound) |
---|
| 1368 | { |
---|
| 1369 | fail= true; |
---|
| 1370 | break; |
---|
| 1371 | } |
---|
| 1372 | if (list.length() < 1) |
---|
| 1373 | random= 0; |
---|
[806c18] | 1374 | else |
---|
[10af64] | 1375 | { |
---|
| 1376 | random= genFF.generate(); |
---|
| 1377 | while (find (list, random)) |
---|
| 1378 | random= genFF.generate(); |
---|
| 1379 | } |
---|
[806c18] | 1380 | if (F (random, x) == 0) |
---|
[10af64] | 1381 | { |
---|
| 1382 | list.append (random); |
---|
| 1383 | continue; |
---|
| 1384 | } |
---|
| 1385 | } while (find (list, random)); |
---|
| 1386 | return random; |
---|
| 1387 | } |
---|
| 1388 | |
---|
[597783] | 1389 | CanonicalForm |
---|
| 1390 | GCD_small_p (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 1391 | CanonicalForm& coF, CanonicalForm& coG, |
---|
| 1392 | bool& topLevel, CFList& l); |
---|
| 1393 | |
---|
| 1394 | CanonicalForm |
---|
| 1395 | GCD_small_p (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 1396 | bool& topLevel, CFList& l) |
---|
| 1397 | { |
---|
| 1398 | CanonicalForm dummy1, dummy2; |
---|
| 1399 | CanonicalForm result= GCD_small_p (F, G, dummy1, dummy2, topLevel, l); |
---|
| 1400 | return result; |
---|
| 1401 | } |
---|
| 1402 | |
---|
| 1403 | CanonicalForm |
---|
| 1404 | GCD_small_p (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 1405 | CanonicalForm& coF, CanonicalForm& coG, |
---|
| 1406 | bool& topLevel, CFList& l) |
---|
[10af64] | 1407 | { |
---|
| 1408 | CanonicalForm A= F; |
---|
| 1409 | CanonicalForm B= G; |
---|
[597783] | 1410 | if (F.isZero() && degree(G) > 0) |
---|
| 1411 | { |
---|
| 1412 | coF= 0; |
---|
| 1413 | coG= Lc (G); |
---|
| 1414 | return G/Lc(G); |
---|
| 1415 | } |
---|
| 1416 | else if (G.isZero() && degree (F) > 0) |
---|
| 1417 | { |
---|
| 1418 | coF= Lc (F); |
---|
| 1419 | coG= 0; |
---|
| 1420 | return F/Lc(F); |
---|
| 1421 | } |
---|
| 1422 | else if (F.isZero() && G.isZero()) |
---|
| 1423 | { |
---|
| 1424 | coF= coG= 0; |
---|
| 1425 | return F.genOne(); |
---|
| 1426 | } |
---|
| 1427 | if (F.inBaseDomain() || G.inBaseDomain()) |
---|
| 1428 | { |
---|
| 1429 | coF= F; |
---|
| 1430 | coG= G; |
---|
| 1431 | return F.genOne(); |
---|
| 1432 | } |
---|
| 1433 | if (F.isUnivariate() && fdivides(F, G, coG)) |
---|
| 1434 | { |
---|
| 1435 | coF= Lc (F); |
---|
| 1436 | return F/Lc(F); |
---|
| 1437 | } |
---|
| 1438 | if (G.isUnivariate() && fdivides(G, F, coF)) |
---|
| 1439 | { |
---|
| 1440 | coG= Lc (G); |
---|
| 1441 | return G/Lc(G); |
---|
| 1442 | } |
---|
| 1443 | if (F == G) |
---|
| 1444 | { |
---|
| 1445 | coF= coG= Lc (F); |
---|
| 1446 | return F/Lc(F); |
---|
| 1447 | } |
---|
[10af64] | 1448 | CFMap M,N; |
---|
[dec1024] | 1449 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
[10af64] | 1450 | |
---|
[597783] | 1451 | if (best_level == 0) |
---|
| 1452 | { |
---|
| 1453 | coF= F; |
---|
| 1454 | coG= G; |
---|
| 1455 | return B.genOne(); |
---|
| 1456 | } |
---|
[10af64] | 1457 | |
---|
| 1458 | A= M(A); |
---|
| 1459 | B= M(B); |
---|
| 1460 | |
---|
[c4f4fd] | 1461 | Variable x= Variable (1); |
---|
| 1462 | |
---|
[806c18] | 1463 | //univariate case |
---|
| 1464 | if (A.isUnivariate() && B.isUnivariate()) |
---|
[597783] | 1465 | { |
---|
| 1466 | CanonicalForm result= gcd (A, B); |
---|
| 1467 | coF= N (A/result); |
---|
| 1468 | coG= N (B/result); |
---|
| 1469 | return N (result); |
---|
| 1470 | } |
---|
[10af64] | 1471 | |
---|
| 1472 | CanonicalForm cA, cB; // content of A and B |
---|
| 1473 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
| 1474 | CanonicalForm gcdcAcB; |
---|
[dec1024] | 1475 | |
---|
[ea5ff1d] | 1476 | cA = uni_content (A); |
---|
| 1477 | cB = uni_content (B); |
---|
| 1478 | gcdcAcB= gcd (cA, cB); |
---|
| 1479 | ppA= A/cA; |
---|
| 1480 | ppB= B/cB; |
---|
[10af64] | 1481 | |
---|
[e243418] | 1482 | int sizeNewtonPolyg; |
---|
| 1483 | int ** newtonPolyg= NULL; |
---|
| 1484 | mat_ZZ MM; |
---|
| 1485 | vec_ZZ V; |
---|
[ea095d] | 1486 | bool compressConvexDense= false; //(ppA.level() == 2 && ppB.level() == 2); |
---|
[e243418] | 1487 | if (compressConvexDense) |
---|
| 1488 | { |
---|
[597783] | 1489 | CanonicalForm bufcA= cA; |
---|
| 1490 | CanonicalForm bufcB= cB; |
---|
[e243418] | 1491 | cA= content (ppA, 1); |
---|
| 1492 | cB= content (ppB, 1); |
---|
| 1493 | ppA /= cA; |
---|
| 1494 | ppB /= cB; |
---|
| 1495 | gcdcAcB *= gcd (cA, cB); |
---|
[597783] | 1496 | cA *= bufcA; |
---|
| 1497 | cB *= bufcB; |
---|
[e243418] | 1498 | if (ppA.isUnivariate() || ppB.isUnivariate()) |
---|
| 1499 | { |
---|
| 1500 | if (ppA.level() == ppB.level()) |
---|
[597783] | 1501 | { |
---|
| 1502 | CanonicalForm result= gcd (ppA, ppB); |
---|
| 1503 | coF= N ((ppA/result)*(cA/gcdcAcB)); |
---|
| 1504 | coG= N ((ppB/result)*(cB/gcdcAcB)); |
---|
| 1505 | return N (result*gcdcAcB); |
---|
| 1506 | } |
---|
[e243418] | 1507 | else |
---|
[597783] | 1508 | { |
---|
| 1509 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 1510 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 1511 | return N (gcdcAcB); |
---|
[597783] | 1512 | } |
---|
[e243418] | 1513 | } |
---|
| 1514 | |
---|
| 1515 | newtonPolyg= newtonPolygon (ppA,ppB, sizeNewtonPolyg); |
---|
| 1516 | convexDense (newtonPolyg, sizeNewtonPolyg, MM, V); |
---|
| 1517 | |
---|
| 1518 | for (int i= 0; i < sizeNewtonPolyg; i++) |
---|
| 1519 | delete [] newtonPolyg[i]; |
---|
| 1520 | delete [] newtonPolyg; |
---|
| 1521 | |
---|
| 1522 | ppA= compress (ppA, MM, V, false); |
---|
| 1523 | ppB= compress (ppB, MM, V, false); |
---|
| 1524 | MM= inv (MM); |
---|
| 1525 | |
---|
| 1526 | if (ppA.isUnivariate() && ppB.isUnivariate()) |
---|
| 1527 | { |
---|
| 1528 | if (ppA.level() == ppB.level()) |
---|
[597783] | 1529 | { |
---|
| 1530 | CanonicalForm result= gcd (ppA, ppB); |
---|
| 1531 | coF= N (decompress ((ppA/result), MM, V)*(cA/gcdcAcB)); |
---|
| 1532 | coG= N (decompress ((ppB/result), MM, V)*(cB/gcdcAcB)); |
---|
| 1533 | return N (decompress (result, MM, V)*gcdcAcB); |
---|
| 1534 | } |
---|
[e243418] | 1535 | else |
---|
[597783] | 1536 | { |
---|
| 1537 | coF= N (decompress (ppA, MM, V)); |
---|
| 1538 | coG= N (decompress (ppB, MM, V)); |
---|
[a9a6dcb] | 1539 | return N (gcdcAcB); |
---|
[597783] | 1540 | } |
---|
[e243418] | 1541 | } |
---|
| 1542 | } |
---|
| 1543 | |
---|
[10af64] | 1544 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
[806c18] | 1545 | CanonicalForm gcdlcAlcB; |
---|
[10af64] | 1546 | lcA= uni_lcoeff (ppA); |
---|
| 1547 | lcB= uni_lcoeff (ppB); |
---|
| 1548 | |
---|
[597783] | 1549 | /*if (fdivides (lcA, lcB)) |
---|
[806c18] | 1550 | { |
---|
[10af64] | 1551 | if (fdivides (A, B)) |
---|
| 1552 | return F/Lc(F); |
---|
[806c18] | 1553 | } |
---|
[10af64] | 1554 | if (fdivides (lcB, lcA)) |
---|
[806c18] | 1555 | { |
---|
| 1556 | if (fdivides (B, A)) |
---|
[10af64] | 1557 | return G/Lc(G); |
---|
[597783] | 1558 | }*/ |
---|
[c4f4fd] | 1559 | |
---|
[806c18] | 1560 | gcdlcAlcB= gcd (lcA, lcB); |
---|
| 1561 | |
---|
[10af64] | 1562 | int d= totaldegree (ppA, Variable (2), Variable (ppA.level())); |
---|
| 1563 | int d0; |
---|
| 1564 | |
---|
[dec1024] | 1565 | if (d == 0) |
---|
[597783] | 1566 | { |
---|
| 1567 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 1568 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 1569 | return N(gcdcAcB); |
---|
[597783] | 1570 | } |
---|
[a9a6dcb] | 1571 | |
---|
[10af64] | 1572 | d0= totaldegree (ppB, Variable (2), Variable (ppB.level())); |
---|
| 1573 | |
---|
[806c18] | 1574 | if (d0 < d) |
---|
[10af64] | 1575 | d= d0; |
---|
| 1576 | |
---|
[806c18] | 1577 | if (d == 0) |
---|
[597783] | 1578 | { |
---|
| 1579 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 1580 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 1581 | return N(gcdcAcB); |
---|
[597783] | 1582 | } |
---|
[10af64] | 1583 | |
---|
| 1584 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
[597783] | 1585 | CanonicalForm newtonPoly, coF_random_element, coG_random_element, |
---|
| 1586 | coF_m, coG_m, ppCoF, ppCoG; |
---|
| 1587 | |
---|
| 1588 | newtonPoly= 1; |
---|
[10af64] | 1589 | m= gcdlcAlcB; |
---|
| 1590 | H= 0; |
---|
[597783] | 1591 | coF= 0; |
---|
| 1592 | coG= 0; |
---|
[10af64] | 1593 | G_m= 0; |
---|
| 1594 | Variable alpha, V_buf; |
---|
| 1595 | bool fail= false; |
---|
| 1596 | bool inextension= false; |
---|
[d1dc39] | 1597 | topLevel= false; |
---|
[10af64] | 1598 | CFList source, dest; |
---|
[597783] | 1599 | int bound1= degree (ppA, 1); |
---|
| 1600 | int bound2= degree (ppB, 1); |
---|
[806c18] | 1601 | do |
---|
[10af64] | 1602 | { |
---|
| 1603 | if (inextension) |
---|
[597783] | 1604 | random_element= randomElement (m*lcA*lcB, V_buf, l, fail); |
---|
[10af64] | 1605 | else |
---|
[597783] | 1606 | random_element= FpRandomElement (m*lcA*lcB, l, fail); |
---|
[10af64] | 1607 | |
---|
| 1608 | if (!fail && !inextension) |
---|
| 1609 | { |
---|
| 1610 | CFList list; |
---|
| 1611 | TIMING_START (gcd_recursion); |
---|
[806c18] | 1612 | G_random_element= |
---|
[597783] | 1613 | GCD_small_p (ppA (random_element,x), ppB (random_element,x), |
---|
[d1dc39] | 1614 | coF_random_element, coG_random_element, topLevel, |
---|
[597783] | 1615 | list); |
---|
[806c18] | 1616 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
[10af64] | 1617 | "time for recursive call: "); |
---|
| 1618 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 1619 | } |
---|
| 1620 | else if (!fail && inextension) |
---|
| 1621 | { |
---|
[806c18] | 1622 | CFList list; |
---|
[10af64] | 1623 | TIMING_START (gcd_recursion); |
---|
[806c18] | 1624 | G_random_element= |
---|
[597783] | 1625 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), |
---|
| 1626 | coF_random_element, coG_random_element, alpha, |
---|
[d1dc39] | 1627 | list, topLevel); |
---|
[806c18] | 1628 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
[10af64] | 1629 | "time for recursive call: "); |
---|
[806c18] | 1630 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
[10af64] | 1631 | } |
---|
| 1632 | else if (fail && !inextension) |
---|
| 1633 | { |
---|
| 1634 | source= CFList(); |
---|
| 1635 | dest= CFList(); |
---|
| 1636 | CFList list; |
---|
[a5cc7b3] | 1637 | CanonicalForm mipo; |
---|
[dec1024] | 1638 | int deg= 2; |
---|
[a5cc7b3] | 1639 | do { |
---|
[806c18] | 1640 | mipo= randomIrredpoly (deg, x); |
---|
[a5cc7b3] | 1641 | alpha= rootOf (mipo); |
---|
| 1642 | inextension= true; |
---|
| 1643 | fail= false; |
---|
[597783] | 1644 | random_element= randomElement (m*lcA*lcB, alpha, l, fail); |
---|
[a5cc7b3] | 1645 | deg++; |
---|
[806c18] | 1646 | } while (fail); |
---|
[10af64] | 1647 | list= CFList(); |
---|
[9ff686] | 1648 | V_buf= alpha; |
---|
[10af64] | 1649 | TIMING_START (gcd_recursion); |
---|
[806c18] | 1650 | G_random_element= |
---|
[597783] | 1651 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), |
---|
| 1652 | coF_random_element, coG_random_element, alpha, |
---|
[d1dc39] | 1653 | list, topLevel); |
---|
[806c18] | 1654 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
[10af64] | 1655 | "time for recursive call: "); |
---|
| 1656 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 1657 | } |
---|
| 1658 | else if (fail && inextension) |
---|
| 1659 | { |
---|
| 1660 | source= CFList(); |
---|
| 1661 | dest= CFList(); |
---|
[9ff686] | 1662 | |
---|
| 1663 | Variable V_buf3= V_buf; |
---|
| 1664 | V_buf= chooseExtension (V_buf); |
---|
[10af64] | 1665 | bool prim_fail= false; |
---|
| 1666 | Variable V_buf2; |
---|
| 1667 | CanonicalForm prim_elem, im_prim_elem; |
---|
| 1668 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
[806c18] | 1669 | |
---|
[9ff686] | 1670 | if (V_buf3 != alpha) |
---|
| 1671 | { |
---|
| 1672 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
[597783] | 1673 | G_m= mapDown (G_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 1674 | coF_m= mapDown (coF_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 1675 | coG_m= mapDown (coG_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
[9ff686] | 1676 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
| 1677 | source, dest); |
---|
| 1678 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 1679 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 1680 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, source, |
---|
| 1681 | dest); |
---|
[597783] | 1682 | lcA= mapDown (lcA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 1683 | lcB= mapDown (lcB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
[9ff686] | 1684 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 1685 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
| 1686 | source, dest); |
---|
| 1687 | } |
---|
| 1688 | |
---|
[10af64] | 1689 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
| 1690 | if (prim_fail) |
---|
| 1691 | ; //ERROR |
---|
| 1692 | else |
---|
| 1693 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
| 1694 | |
---|
| 1695 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
| 1696 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
| 1697 | |
---|
[806c18] | 1698 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 1699 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
[10af64] | 1700 | im_prim_elem, source, dest); |
---|
| 1701 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 1702 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
[597783] | 1703 | coF_m= mapUp (coF_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 1704 | coG_m= mapUp (coG_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
[806c18] | 1705 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
[10af64] | 1706 | source, dest); |
---|
| 1707 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 1708 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
[806c18] | 1709 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
[10af64] | 1710 | source, dest); |
---|
[597783] | 1711 | lcA= mapUp (lcA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 1712 | lcB= mapUp (lcB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
[10af64] | 1713 | fail= false; |
---|
[597783] | 1714 | random_element= randomElement (m*lcA*lcB, V_buf, l, fail ); |
---|
[a5cc7b3] | 1715 | DEBOUTLN (cerr, "fail= " << fail); |
---|
[10af64] | 1716 | CFList list; |
---|
| 1717 | TIMING_START (gcd_recursion); |
---|
[806c18] | 1718 | G_random_element= |
---|
[597783] | 1719 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), |
---|
| 1720 | coF_random_element, coG_random_element, V_buf, |
---|
[d1dc39] | 1721 | list, topLevel); |
---|
[806c18] | 1722 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
[10af64] | 1723 | "time for recursive call: "); |
---|
| 1724 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
[806c18] | 1725 | } |
---|
[10af64] | 1726 | |
---|
[a76d6fe] | 1727 | if (!G_random_element.inCoeffDomain()) |
---|
| 1728 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 1729 | Variable (G_random_element.level())); |
---|
| 1730 | else |
---|
| 1731 | d0= 0; |
---|
[10af64] | 1732 | |
---|
| 1733 | if (d0 == 0) |
---|
[597783] | 1734 | { |
---|
| 1735 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 1736 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 1737 | return N(gcdcAcB); |
---|
[597783] | 1738 | } |
---|
| 1739 | |
---|
[806c18] | 1740 | if (d0 > d) |
---|
| 1741 | { |
---|
[10af64] | 1742 | if (!find (l, random_element)) |
---|
| 1743 | l.append (random_element); |
---|
| 1744 | continue; |
---|
| 1745 | } |
---|
| 1746 | |
---|
| 1747 | G_random_element= (gcdlcAlcB(random_element,x)/uni_lcoeff(G_random_element)) |
---|
[806c18] | 1748 | *G_random_element; |
---|
[10af64] | 1749 | |
---|
[597783] | 1750 | coF_random_element= (lcA(random_element,x)/uni_lcoeff(coF_random_element)) |
---|
| 1751 | *coF_random_element; |
---|
| 1752 | coG_random_element= (lcB(random_element,x)/uni_lcoeff(coG_random_element)) |
---|
| 1753 | *coG_random_element; |
---|
[806c18] | 1754 | |
---|
[a76d6fe] | 1755 | if (!G_random_element.inCoeffDomain()) |
---|
| 1756 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 1757 | Variable (G_random_element.level())); |
---|
| 1758 | else |
---|
| 1759 | d0= 0; |
---|
[10af64] | 1760 | |
---|
[806c18] | 1761 | if (d0 < d) |
---|
[10af64] | 1762 | { |
---|
| 1763 | m= gcdlcAlcB; |
---|
| 1764 | newtonPoly= 1; |
---|
| 1765 | G_m= 0; |
---|
| 1766 | d= d0; |
---|
[597783] | 1767 | coF_m= 0; |
---|
| 1768 | coG_m= 0; |
---|
[10af64] | 1769 | } |
---|
[806c18] | 1770 | |
---|
[10af64] | 1771 | TIMING_START (newton_interpolation); |
---|
| 1772 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
[597783] | 1773 | coF= newtonInterp (random_element, coF_random_element, newtonPoly, coF_m,x); |
---|
| 1774 | coG= newtonInterp (random_element, coG_random_element, newtonPoly, coG_m,x); |
---|
[806c18] | 1775 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
[10af64] | 1776 | "time for newton_interpolation: "); |
---|
| 1777 | |
---|
| 1778 | //termination test |
---|
[597783] | 1779 | if ((uni_lcoeff (H) == gcdlcAlcB) || (G_m == H)) |
---|
[10af64] | 1780 | { |
---|
[2a95b2] | 1781 | TIMING_START (termination_test); |
---|
[597783] | 1782 | if (gcdlcAlcB.isOne()) |
---|
| 1783 | cH= 1; |
---|
| 1784 | else |
---|
| 1785 | cH= uni_content (H); |
---|
[10af64] | 1786 | ppH= H/cH; |
---|
| 1787 | ppH /= Lc (ppH); |
---|
[597783] | 1788 | CanonicalForm lcppH= gcdlcAlcB/cH; |
---|
| 1789 | CanonicalForm ccoF= lcppH/Lc (lcppH); |
---|
| 1790 | CanonicalForm ccoG= lcppH/Lc (lcppH); |
---|
| 1791 | ppCoF= coF/ccoF; |
---|
| 1792 | ppCoG= coG/ccoG; |
---|
[10af64] | 1793 | DEBOUTLN (cerr, "ppH= " << ppH); |
---|
[597783] | 1794 | if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
| 1795 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
[1e4b53] | 1796 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
[597783] | 1797 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
[dec1024] | 1798 | { |
---|
[e243418] | 1799 | if (compressConvexDense) |
---|
[597783] | 1800 | { |
---|
[e243418] | 1801 | ppH= decompress (ppH, MM, V); |
---|
[597783] | 1802 | ppCoF= decompress (ppCoF, MM, V); |
---|
| 1803 | ppCoG= decompress (ppCoG, MM, V); |
---|
| 1804 | } |
---|
| 1805 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
| 1806 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
[2a95b2] | 1807 | TIMING_END_AND_PRINT (termination_test, |
---|
| 1808 | "time for successful termination Fp: "); |
---|
[10af64] | 1809 | return N(gcdcAcB*ppH); |
---|
[dec1024] | 1810 | } |
---|
[2a95b2] | 1811 | TIMING_END_AND_PRINT (termination_test, |
---|
| 1812 | "time for unsuccessful termination Fp: "); |
---|
[10af64] | 1813 | } |
---|
| 1814 | |
---|
| 1815 | G_m= H; |
---|
[597783] | 1816 | coF_m= coF; |
---|
| 1817 | coG_m= coG; |
---|
[10af64] | 1818 | newtonPoly= newtonPoly*(x - random_element); |
---|
| 1819 | m= m*(x - random_element); |
---|
| 1820 | if (!find (l, random_element)) |
---|
| 1821 | l.append (random_element); |
---|
| 1822 | } while (1); |
---|
| 1823 | } |
---|
| 1824 | |
---|
[08daea] | 1825 | CFArray |
---|
| 1826 | solveVandermonde (const CFArray& M, const CFArray& A) |
---|
| 1827 | { |
---|
| 1828 | int r= M.size(); |
---|
| 1829 | ASSERT (A.size() == r, "vector does not have right size"); |
---|
| 1830 | |
---|
| 1831 | if (r == 1) |
---|
| 1832 | { |
---|
| 1833 | CFArray result= CFArray (1); |
---|
| 1834 | result [0]= A [0] / M [0]; |
---|
| 1835 | return result; |
---|
| 1836 | } |
---|
| 1837 | // check solvability |
---|
| 1838 | bool notDistinct= false; |
---|
| 1839 | for (int i= 0; i < r - 1; i++) |
---|
| 1840 | { |
---|
| 1841 | for (int j= i + 1; j < r; j++) |
---|
| 1842 | { |
---|
| 1843 | if (M [i] == M [j]) |
---|
| 1844 | { |
---|
| 1845 | notDistinct= true; |
---|
| 1846 | break; |
---|
| 1847 | } |
---|
| 1848 | } |
---|
| 1849 | } |
---|
| 1850 | if (notDistinct) |
---|
| 1851 | return CFArray(); |
---|
| 1852 | |
---|
| 1853 | CanonicalForm master= 1; |
---|
| 1854 | Variable x= Variable (1); |
---|
| 1855 | for (int i= 0; i < r; i++) |
---|
| 1856 | master *= x - M [i]; |
---|
| 1857 | CFList Pj; |
---|
| 1858 | CanonicalForm tmp; |
---|
| 1859 | for (int i= 0; i < r; i++) |
---|
| 1860 | { |
---|
| 1861 | tmp= master/(x - M [i]); |
---|
| 1862 | tmp /= tmp (M [i], 1); |
---|
| 1863 | Pj.append (tmp); |
---|
| 1864 | } |
---|
| 1865 | CFArray result= CFArray (r); |
---|
| 1866 | |
---|
| 1867 | CFListIterator j= Pj; |
---|
| 1868 | for (int i= 1; i <= r; i++, j++) |
---|
| 1869 | { |
---|
| 1870 | tmp= 0; |
---|
| 1871 | for (int l= 0; l < A.size(); l++) |
---|
| 1872 | tmp += A[l]*j.getItem()[l]; |
---|
| 1873 | result[i - 1]= tmp; |
---|
| 1874 | } |
---|
| 1875 | return result; |
---|
| 1876 | } |
---|
| 1877 | |
---|
| 1878 | CFArray |
---|
| 1879 | solveGeneralVandermonde (const CFArray& M, const CFArray& A) |
---|
| 1880 | { |
---|
| 1881 | int r= M.size(); |
---|
| 1882 | ASSERT (A.size() == r, "vector does not have right size"); |
---|
| 1883 | if (r == 1) |
---|
| 1884 | { |
---|
| 1885 | CFArray result= CFArray (1); |
---|
| 1886 | result [0]= A[0] / M [0]; |
---|
| 1887 | return result; |
---|
| 1888 | } |
---|
| 1889 | // check solvability |
---|
| 1890 | bool notDistinct= false; |
---|
| 1891 | for (int i= 0; i < r - 1; i++) |
---|
| 1892 | { |
---|
| 1893 | for (int j= i + 1; j < r; j++) |
---|
| 1894 | { |
---|
| 1895 | if (M [i] == M [j]) |
---|
| 1896 | { |
---|
| 1897 | notDistinct= true; |
---|
| 1898 | break; |
---|
| 1899 | } |
---|
| 1900 | } |
---|
| 1901 | } |
---|
| 1902 | if (notDistinct) |
---|
| 1903 | return CFArray(); |
---|
| 1904 | |
---|
| 1905 | CanonicalForm master= 1; |
---|
| 1906 | Variable x= Variable (1); |
---|
| 1907 | for (int i= 0; i < r; i++) |
---|
| 1908 | master *= x - M [i]; |
---|
| 1909 | master *= x; |
---|
| 1910 | CFList Pj; |
---|
| 1911 | CanonicalForm tmp; |
---|
| 1912 | for (int i= 0; i < r; i++) |
---|
| 1913 | { |
---|
| 1914 | tmp= master/(x - M [i]); |
---|
| 1915 | tmp /= tmp (M [i], 1); |
---|
| 1916 | Pj.append (tmp); |
---|
| 1917 | } |
---|
| 1918 | |
---|
| 1919 | CFArray result= CFArray (r); |
---|
| 1920 | |
---|
| 1921 | CFListIterator j= Pj; |
---|
| 1922 | for (int i= 1; i <= r; i++, j++) |
---|
| 1923 | { |
---|
| 1924 | tmp= 0; |
---|
| 1925 | |
---|
| 1926 | for (int l= 1; l <= A.size(); l++) |
---|
| 1927 | tmp += A[l - 1]*j.getItem()[l]; |
---|
| 1928 | result[i - 1]= tmp; |
---|
| 1929 | } |
---|
| 1930 | return result; |
---|
| 1931 | } |
---|
| 1932 | |
---|
| 1933 | /// M in row echolon form, rk rank of M |
---|
| 1934 | CFArray |
---|
| 1935 | readOffSolution (const CFMatrix& M, const long rk) |
---|
| 1936 | { |
---|
| 1937 | CFArray result= CFArray (rk); |
---|
| 1938 | CanonicalForm tmp1, tmp2, tmp3; |
---|
| 1939 | for (int i= rk; i >= 1; i--) |
---|
| 1940 | { |
---|
| 1941 | tmp3= 0; |
---|
| 1942 | tmp1= M (i, M.columns()); |
---|
| 1943 | for (int j= M.columns() - 1; j >= 1; j--) |
---|
| 1944 | { |
---|
| 1945 | tmp2= M (i, j); |
---|
| 1946 | if (j == i) |
---|
| 1947 | break; |
---|
| 1948 | else |
---|
| 1949 | tmp3 += tmp2*result[j - 1]; |
---|
| 1950 | } |
---|
| 1951 | result[i - 1]= (tmp1 - tmp3)/tmp2; |
---|
| 1952 | } |
---|
| 1953 | return result; |
---|
| 1954 | } |
---|
| 1955 | |
---|
| 1956 | CFArray |
---|
| 1957 | readOffSolution (const CFMatrix& M, const CFArray& L, const CFArray& partialSol) |
---|
| 1958 | { |
---|
| 1959 | CFArray result= CFArray (M.rows()); |
---|
| 1960 | CanonicalForm tmp1, tmp2, tmp3; |
---|
| 1961 | int k; |
---|
| 1962 | for (int i= M.rows(); i >= 1; i--) |
---|
| 1963 | { |
---|
| 1964 | tmp3= 0; |
---|
| 1965 | tmp1= L[i - 1]; |
---|
| 1966 | k= 0; |
---|
| 1967 | for (int j= M.columns(); j >= 1; j--, k++) |
---|
| 1968 | { |
---|
| 1969 | tmp2= M (i, j); |
---|
| 1970 | if (j == i) |
---|
| 1971 | break; |
---|
| 1972 | else |
---|
| 1973 | { |
---|
| 1974 | if (k > partialSol.size() - 1) |
---|
| 1975 | tmp3 += tmp2*result[j - 1]; |
---|
| 1976 | else |
---|
| 1977 | tmp3 += tmp2*partialSol[partialSol.size() - k - 1]; |
---|
| 1978 | } |
---|
| 1979 | } |
---|
| 1980 | result [i - 1]= (tmp1 - tmp3)/tmp2; |
---|
| 1981 | } |
---|
| 1982 | return result; |
---|
| 1983 | } |
---|
| 1984 | |
---|
| 1985 | long |
---|
| 1986 | gaussianElimFp (CFMatrix& M, CFArray& L) |
---|
| 1987 | { |
---|
| 1988 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
| 1989 | CFMatrix *N; |
---|
| 1990 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
| 1991 | |
---|
| 1992 | for (int i= 1; i <= M.rows(); i++) |
---|
| 1993 | for (int j= 1; j <= M.columns(); j++) |
---|
| 1994 | (*N) (i, j)= M (i, j); |
---|
| 1995 | |
---|
| 1996 | int j= 1; |
---|
| 1997 | for (int i= 0; i < L.size(); i++, j++) |
---|
| 1998 | (*N) (j, M.columns() + 1)= L[i]; |
---|
[8fa570] | 1999 | #ifdef HAVE_FLINT |
---|
| 2000 | nmod_mat_t FLINTN; |
---|
| 2001 | convertFacCFMatrix2nmod_mat_t (FLINTN, *N); |
---|
| 2002 | long* dummy= new long [M.rows()]; |
---|
| 2003 | for (int i= 0; i < M.rows(); i++) |
---|
| 2004 | dummy[i]= 0; |
---|
| 2005 | long rk= nmod_mat_rref (dummy, FLINTN); |
---|
| 2006 | |
---|
| 2007 | N= convertNmod_mat_t2FacCFMatrix (FLINTN); |
---|
| 2008 | nmod_mat_clear (FLINTN); |
---|
| 2009 | delete dummy; |
---|
| 2010 | #else |
---|
[08daea] | 2011 | int p= getCharacteristic (); |
---|
[bffe62d] | 2012 | if (fac_NTL_char != p) |
---|
| 2013 | { |
---|
| 2014 | fac_NTL_char= p; |
---|
| 2015 | zz_p::init (p); |
---|
| 2016 | } |
---|
[08daea] | 2017 | mat_zz_p *NTLN= convertFacCFMatrix2NTLmat_zz_p(*N); |
---|
| 2018 | long rk= gauss (*NTLN); |
---|
| 2019 | |
---|
| 2020 | N= convertNTLmat_zz_p2FacCFMatrix (*NTLN); |
---|
[8fa570] | 2021 | #endif |
---|
[08daea] | 2022 | |
---|
| 2023 | L= CFArray (M.rows()); |
---|
| 2024 | for (int i= 0; i < M.rows(); i++) |
---|
| 2025 | L[i]= (*N) (i + 1, M.columns() + 1); |
---|
| 2026 | M= (*N) (1, M.rows(), 1, M.columns()); |
---|
[618da5] | 2027 | delete N; |
---|
[08daea] | 2028 | return rk; |
---|
| 2029 | } |
---|
| 2030 | |
---|
| 2031 | long |
---|
| 2032 | gaussianElimFq (CFMatrix& M, CFArray& L, const Variable& alpha) |
---|
| 2033 | { |
---|
| 2034 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
| 2035 | CFMatrix *N; |
---|
| 2036 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
| 2037 | |
---|
| 2038 | for (int i= 1; i <= M.rows(); i++) |
---|
| 2039 | for (int j= 1; j <= M.columns(); j++) |
---|
| 2040 | (*N) (i, j)= M (i, j); |
---|
| 2041 | |
---|
| 2042 | int j= 1; |
---|
| 2043 | for (int i= 0; i < L.size(); i++, j++) |
---|
| 2044 | (*N) (j, M.columns() + 1)= L[i]; |
---|
| 2045 | int p= getCharacteristic (); |
---|
[bffe62d] | 2046 | if (fac_NTL_char != p) |
---|
| 2047 | { |
---|
| 2048 | fac_NTL_char= p; |
---|
| 2049 | zz_p::init (p); |
---|
| 2050 | } |
---|
[08daea] | 2051 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 2052 | zz_pE::init (NTLMipo); |
---|
| 2053 | mat_zz_pE *NTLN= convertFacCFMatrix2NTLmat_zz_pE(*N); |
---|
| 2054 | long rk= gauss (*NTLN); |
---|
| 2055 | |
---|
| 2056 | N= convertNTLmat_zz_pE2FacCFMatrix (*NTLN, alpha); |
---|
| 2057 | |
---|
| 2058 | M= (*N) (1, M.rows(), 1, M.columns()); |
---|
| 2059 | L= CFArray (M.rows()); |
---|
| 2060 | for (int i= 0; i < M.rows(); i++) |
---|
| 2061 | L[i]= (*N) (i + 1, M.columns() + 1); |
---|
[618da5] | 2062 | |
---|
| 2063 | delete N; |
---|
[08daea] | 2064 | return rk; |
---|
| 2065 | } |
---|
| 2066 | |
---|
| 2067 | CFArray |
---|
| 2068 | solveSystemFp (const CFMatrix& M, const CFArray& L) |
---|
| 2069 | { |
---|
| 2070 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
| 2071 | CFMatrix *N; |
---|
| 2072 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
| 2073 | |
---|
| 2074 | for (int i= 1; i <= M.rows(); i++) |
---|
| 2075 | for (int j= 1; j <= M.columns(); j++) |
---|
| 2076 | (*N) (i, j)= M (i, j); |
---|
| 2077 | |
---|
| 2078 | int j= 1; |
---|
| 2079 | for (int i= 0; i < L.size(); i++, j++) |
---|
| 2080 | (*N) (j, M.columns() + 1)= L[i]; |
---|
[8fa570] | 2081 | |
---|
| 2082 | #ifdef HAVE_FLINT |
---|
| 2083 | nmod_mat_t FLINTN; |
---|
| 2084 | convertFacCFMatrix2nmod_mat_t (FLINTN, *N); |
---|
| 2085 | long* dummy= new long [M.rows()]; |
---|
| 2086 | for (int i= 0; i < M.rows(); i++) |
---|
| 2087 | dummy[i]= 0; |
---|
| 2088 | long rk= nmod_mat_rref (dummy, FLINTN); |
---|
| 2089 | #else |
---|
[08daea] | 2090 | int p= getCharacteristic (); |
---|
[bffe62d] | 2091 | if (fac_NTL_char != p) |
---|
| 2092 | { |
---|
| 2093 | fac_NTL_char= p; |
---|
| 2094 | zz_p::init (p); |
---|
| 2095 | } |
---|
[08daea] | 2096 | mat_zz_p *NTLN= convertFacCFMatrix2NTLmat_zz_p(*N); |
---|
| 2097 | long rk= gauss (*NTLN); |
---|
[8fa570] | 2098 | #endif |
---|
[08daea] | 2099 | if (rk != M.columns()) |
---|
[618da5] | 2100 | { |
---|
[8fa570] | 2101 | #ifdef HAVE_FLINT |
---|
| 2102 | nmod_mat_clear (FLINTN); |
---|
| 2103 | delete dummy; |
---|
| 2104 | #endif |
---|
[618da5] | 2105 | delete N; |
---|
[08daea] | 2106 | return CFArray(); |
---|
[618da5] | 2107 | } |
---|
[8fa570] | 2108 | #ifdef HAVE_FLINT |
---|
| 2109 | N= convertNmod_mat_t2FacCFMatrix (FLINTN); |
---|
| 2110 | nmod_mat_clear (FLINTN); |
---|
| 2111 | delete dummy; |
---|
| 2112 | #else |
---|
[08daea] | 2113 | N= convertNTLmat_zz_p2FacCFMatrix (*NTLN); |
---|
[8fa570] | 2114 | #endif |
---|
[08daea] | 2115 | CFArray A= readOffSolution (*N, rk); |
---|
| 2116 | |
---|
[618da5] | 2117 | delete N; |
---|
[08daea] | 2118 | return A; |
---|
| 2119 | } |
---|
| 2120 | |
---|
| 2121 | CFArray |
---|
| 2122 | solveSystemFq (const CFMatrix& M, const CFArray& L, const Variable& alpha) |
---|
| 2123 | { |
---|
| 2124 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
| 2125 | CFMatrix *N; |
---|
| 2126 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
| 2127 | |
---|
| 2128 | for (int i= 1; i <= M.rows(); i++) |
---|
| 2129 | for (int j= 1; j <= M.columns(); j++) |
---|
| 2130 | (*N) (i, j)= M (i, j); |
---|
| 2131 | int j= 1; |
---|
| 2132 | for (int i= 0; i < L.size(); i++, j++) |
---|
| 2133 | (*N) (j, M.columns() + 1)= L[i]; |
---|
| 2134 | int p= getCharacteristic (); |
---|
[bffe62d] | 2135 | if (fac_NTL_char != p) |
---|
| 2136 | { |
---|
| 2137 | fac_NTL_char= p; |
---|
| 2138 | zz_p::init (p); |
---|
| 2139 | } |
---|
[08daea] | 2140 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 2141 | zz_pE::init (NTLMipo); |
---|
| 2142 | mat_zz_pE *NTLN= convertFacCFMatrix2NTLmat_zz_pE(*N); |
---|
| 2143 | long rk= gauss (*NTLN); |
---|
| 2144 | if (rk != M.columns()) |
---|
[618da5] | 2145 | { |
---|
| 2146 | delete N; |
---|
[08daea] | 2147 | return CFArray(); |
---|
[618da5] | 2148 | } |
---|
[08daea] | 2149 | N= convertNTLmat_zz_pE2FacCFMatrix (*NTLN, alpha); |
---|
| 2150 | |
---|
| 2151 | CFArray A= readOffSolution (*N, rk); |
---|
| 2152 | |
---|
[618da5] | 2153 | delete N; |
---|
[08daea] | 2154 | return A; |
---|
| 2155 | } |
---|
[6f6320] | 2156 | #endif |
---|
[08daea] | 2157 | |
---|
| 2158 | CFArray |
---|
| 2159 | getMonoms (const CanonicalForm& F) |
---|
| 2160 | { |
---|
| 2161 | if (F.inCoeffDomain()) |
---|
| 2162 | { |
---|
| 2163 | CFArray result= CFArray (1); |
---|
| 2164 | result [0]= 1; |
---|
| 2165 | return result; |
---|
| 2166 | } |
---|
| 2167 | if (F.isUnivariate()) |
---|
| 2168 | { |
---|
| 2169 | CFArray result= CFArray (size(F)); |
---|
| 2170 | int j= 0; |
---|
| 2171 | for (CFIterator i= F; i.hasTerms(); i++, j++) |
---|
| 2172 | result[j]= power (F.mvar(), i.exp()); |
---|
| 2173 | return result; |
---|
| 2174 | } |
---|
| 2175 | int numMon= size (F); |
---|
| 2176 | CFArray result= CFArray (numMon); |
---|
| 2177 | int j= 0; |
---|
| 2178 | CFArray recResult; |
---|
| 2179 | Variable x= F.mvar(); |
---|
| 2180 | CanonicalForm powX; |
---|
| 2181 | for (CFIterator i= F; i.hasTerms(); i++) |
---|
| 2182 | { |
---|
| 2183 | powX= power (x, i.exp()); |
---|
| 2184 | recResult= getMonoms (i.coeff()); |
---|
| 2185 | for (int k= 0; k < recResult.size(); k++) |
---|
| 2186 | result[j+k]= powX*recResult[k]; |
---|
| 2187 | j += recResult.size(); |
---|
| 2188 | } |
---|
| 2189 | return result; |
---|
| 2190 | } |
---|
| 2191 | |
---|
[6f6320] | 2192 | #ifdef HAVE_NTL |
---|
[08daea] | 2193 | CFArray |
---|
| 2194 | evaluateMonom (const CanonicalForm& F, const CFList& evalPoints) |
---|
| 2195 | { |
---|
| 2196 | if (F.inCoeffDomain()) |
---|
| 2197 | { |
---|
| 2198 | CFArray result= CFArray (1); |
---|
| 2199 | result [0]= F; |
---|
| 2200 | return result; |
---|
| 2201 | } |
---|
| 2202 | if (F.isUnivariate()) |
---|
| 2203 | { |
---|
| 2204 | ASSERT (evalPoints.length() == 1, |
---|
| 2205 | "expected an eval point with only one component"); |
---|
| 2206 | CFArray result= CFArray (size(F)); |
---|
| 2207 | int j= 0; |
---|
| 2208 | CanonicalForm evalPoint= evalPoints.getLast(); |
---|
| 2209 | for (CFIterator i= F; i.hasTerms(); i++, j++) |
---|
| 2210 | result[j]= power (evalPoint, i.exp()); |
---|
| 2211 | return result; |
---|
| 2212 | } |
---|
| 2213 | int numMon= size (F); |
---|
| 2214 | CFArray result= CFArray (numMon); |
---|
| 2215 | int j= 0; |
---|
| 2216 | CanonicalForm evalPoint= evalPoints.getLast(); |
---|
| 2217 | CFList buf= evalPoints; |
---|
| 2218 | buf.removeLast(); |
---|
| 2219 | CFArray recResult; |
---|
| 2220 | CanonicalForm powEvalPoint; |
---|
| 2221 | for (CFIterator i= F; i.hasTerms(); i++) |
---|
| 2222 | { |
---|
| 2223 | powEvalPoint= power (evalPoint, i.exp()); |
---|
| 2224 | recResult= evaluateMonom (i.coeff(), buf); |
---|
| 2225 | for (int k= 0; k < recResult.size(); k++) |
---|
| 2226 | result[j+k]= powEvalPoint*recResult[k]; |
---|
| 2227 | j += recResult.size(); |
---|
| 2228 | } |
---|
| 2229 | return result; |
---|
| 2230 | } |
---|
| 2231 | |
---|
| 2232 | CFArray |
---|
| 2233 | evaluate (const CFArray& A, const CFList& evalPoints) |
---|
| 2234 | { |
---|
| 2235 | CFArray result= A.size(); |
---|
| 2236 | CanonicalForm tmp; |
---|
| 2237 | int k; |
---|
| 2238 | for (int i= 0; i < A.size(); i++) |
---|
| 2239 | { |
---|
| 2240 | tmp= A[i]; |
---|
| 2241 | k= 1; |
---|
| 2242 | for (CFListIterator j= evalPoints; j.hasItem(); j++, k++) |
---|
| 2243 | tmp= tmp (j.getItem(), k); |
---|
| 2244 | result[i]= tmp; |
---|
| 2245 | } |
---|
| 2246 | return result; |
---|
| 2247 | } |
---|
| 2248 | |
---|
| 2249 | CFList |
---|
| 2250 | evaluationPoints (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 2251 | CanonicalForm& Feval, CanonicalForm& Geval, |
---|
| 2252 | const CanonicalForm& LCF, const bool& GF, |
---|
| 2253 | const Variable& alpha, bool& fail, CFList& list |
---|
| 2254 | ) |
---|
| 2255 | { |
---|
| 2256 | int k= tmax (F.level(), G.level()) - 1; |
---|
| 2257 | Variable x= Variable (1); |
---|
| 2258 | CFList result; |
---|
| 2259 | FFRandom genFF; |
---|
| 2260 | GFRandom genGF; |
---|
| 2261 | int p= getCharacteristic (); |
---|
| 2262 | int bound; |
---|
| 2263 | if (alpha != Variable (1)) |
---|
| 2264 | { |
---|
| 2265 | bound= ipower (p, degree (getMipo(alpha))); |
---|
| 2266 | bound= ipower (bound, k); |
---|
| 2267 | } |
---|
| 2268 | else if (GF) |
---|
| 2269 | { |
---|
| 2270 | bound= ipower (p, getGFDegree()); |
---|
| 2271 | bound= ipower (bound, k); |
---|
| 2272 | } |
---|
| 2273 | else |
---|
| 2274 | bound= ipower (p, k); |
---|
| 2275 | |
---|
| 2276 | CanonicalForm random; |
---|
| 2277 | int j; |
---|
| 2278 | bool zeroOneOccured= false; |
---|
| 2279 | bool allEqual= false; |
---|
| 2280 | CanonicalForm buf; |
---|
| 2281 | do |
---|
| 2282 | { |
---|
| 2283 | random= 0; |
---|
| 2284 | // possible overflow if list.length() does not fit into a int |
---|
| 2285 | if (list.length() >= bound) |
---|
| 2286 | { |
---|
| 2287 | fail= true; |
---|
| 2288 | break; |
---|
| 2289 | } |
---|
| 2290 | for (int i= 0; i < k; i++) |
---|
| 2291 | { |
---|
| 2292 | if (GF) |
---|
| 2293 | { |
---|
| 2294 | result.append (genGF.generate()); |
---|
| 2295 | random += result.getLast()*power (x, i); |
---|
| 2296 | } |
---|
[1372ae] | 2297 | else if (alpha.level() != 1) |
---|
[08daea] | 2298 | { |
---|
| 2299 | AlgExtRandomF genAlgExt (alpha); |
---|
| 2300 | result.append (genAlgExt.generate()); |
---|
| 2301 | random += result.getLast()*power (x, i); |
---|
| 2302 | } |
---|
| 2303 | else |
---|
| 2304 | { |
---|
| 2305 | result.append (genFF.generate()); |
---|
| 2306 | random += result.getLast()*power (x, i); |
---|
| 2307 | } |
---|
| 2308 | if (result.getLast().isOne() || result.getLast().isZero()) |
---|
| 2309 | zeroOneOccured= true; |
---|
| 2310 | } |
---|
| 2311 | if (find (list, random)) |
---|
| 2312 | { |
---|
| 2313 | zeroOneOccured= false; |
---|
| 2314 | allEqual= false; |
---|
| 2315 | result= CFList(); |
---|
| 2316 | continue; |
---|
| 2317 | } |
---|
| 2318 | if (zeroOneOccured) |
---|
| 2319 | { |
---|
| 2320 | list.append (random); |
---|
| 2321 | zeroOneOccured= false; |
---|
| 2322 | allEqual= false; |
---|
| 2323 | result= CFList(); |
---|
| 2324 | continue; |
---|
| 2325 | } |
---|
| 2326 | // no zero at this point |
---|
| 2327 | if (k > 1) |
---|
| 2328 | { |
---|
| 2329 | allEqual= true; |
---|
| 2330 | CFIterator iter= random; |
---|
| 2331 | buf= iter.coeff(); |
---|
| 2332 | iter++; |
---|
| 2333 | for (; iter.hasTerms(); iter++) |
---|
| 2334 | if (buf != iter.coeff()) |
---|
| 2335 | allEqual= false; |
---|
| 2336 | } |
---|
| 2337 | if (allEqual) |
---|
| 2338 | { |
---|
| 2339 | list.append (random); |
---|
| 2340 | allEqual= false; |
---|
| 2341 | zeroOneOccured= false; |
---|
| 2342 | result= CFList(); |
---|
| 2343 | continue; |
---|
| 2344 | } |
---|
| 2345 | |
---|
| 2346 | Feval= F; |
---|
| 2347 | Geval= G; |
---|
| 2348 | CanonicalForm LCeval= LCF; |
---|
| 2349 | j= 1; |
---|
| 2350 | for (CFListIterator i= result; i.hasItem(); i++, j++) |
---|
| 2351 | { |
---|
| 2352 | Feval= Feval (i.getItem(), j); |
---|
| 2353 | Geval= Geval (i.getItem(), j); |
---|
| 2354 | LCeval= LCeval (i.getItem(), j); |
---|
| 2355 | } |
---|
| 2356 | |
---|
| 2357 | if (LCeval.isZero()) |
---|
| 2358 | { |
---|
| 2359 | if (!find (list, random)) |
---|
| 2360 | list.append (random); |
---|
| 2361 | zeroOneOccured= false; |
---|
| 2362 | allEqual= false; |
---|
| 2363 | result= CFList(); |
---|
| 2364 | continue; |
---|
| 2365 | } |
---|
| 2366 | |
---|
| 2367 | if (list.length() >= bound) |
---|
| 2368 | { |
---|
| 2369 | fail= true; |
---|
| 2370 | break; |
---|
| 2371 | } |
---|
| 2372 | } while (find (list, random)); |
---|
| 2373 | |
---|
| 2374 | return result; |
---|
| 2375 | } |
---|
| 2376 | |
---|
| 2377 | /// multiply two lists componentwise |
---|
| 2378 | void mult (CFList& L1, const CFList& L2) |
---|
| 2379 | { |
---|
| 2380 | ASSERT (L1.length() == L2.length(), "lists of the same size expected"); |
---|
| 2381 | |
---|
| 2382 | CFListIterator j= L2; |
---|
| 2383 | for (CFListIterator i= L1; i.hasItem(); i++, j++) |
---|
| 2384 | i.getItem() *= j.getItem(); |
---|
| 2385 | } |
---|
| 2386 | |
---|
| 2387 | void eval (const CanonicalForm& A, const CanonicalForm& B, CanonicalForm& Aeval, |
---|
| 2388 | CanonicalForm& Beval, const CFList& L) |
---|
| 2389 | { |
---|
| 2390 | Aeval= A; |
---|
| 2391 | Beval= B; |
---|
| 2392 | int j= 1; |
---|
| 2393 | for (CFListIterator i= L; i.hasItem(); i++, j++) |
---|
| 2394 | { |
---|
| 2395 | Aeval= Aeval (i.getItem(), j); |
---|
| 2396 | Beval= Beval (i.getItem(), j); |
---|
| 2397 | } |
---|
| 2398 | } |
---|
| 2399 | |
---|
[c1b9927] | 2400 | CanonicalForm |
---|
[08daea] | 2401 | monicSparseInterpol (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 2402 | const CanonicalForm& skeleton, const Variable& alpha, |
---|
| 2403 | bool& fail, CFArray*& coeffMonoms, CFArray& Monoms |
---|
| 2404 | ) |
---|
| 2405 | { |
---|
| 2406 | CanonicalForm A= F; |
---|
| 2407 | CanonicalForm B= G; |
---|
| 2408 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
| 2409 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
| 2410 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
| 2411 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
| 2412 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
| 2413 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
| 2414 | if (F == G) return F/Lc(F); |
---|
| 2415 | |
---|
| 2416 | CFMap M,N; |
---|
| 2417 | int best_level= myCompress (A, B, M, N, false); |
---|
| 2418 | |
---|
| 2419 | if (best_level == 0) |
---|
| 2420 | return B.genOne(); |
---|
| 2421 | |
---|
| 2422 | A= M(A); |
---|
| 2423 | B= M(B); |
---|
| 2424 | |
---|
| 2425 | Variable x= Variable (1); |
---|
[f71453] | 2426 | ASSERT (degree (A, x) == 0, "expected degree (F, 1) == 0"); |
---|
| 2427 | ASSERT (degree (B, x) == 0, "expected degree (G, 1) == 0"); |
---|
[08daea] | 2428 | |
---|
[c1b9927] | 2429 | //univariate case |
---|
[08daea] | 2430 | if (A.isUnivariate() && B.isUnivariate()) |
---|
| 2431 | return N (gcd (A, B)); |
---|
| 2432 | |
---|
| 2433 | CanonicalForm skel= M(skeleton); |
---|
| 2434 | CanonicalForm cA, cB; // content of A and B |
---|
| 2435 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
| 2436 | CanonicalForm gcdcAcB; |
---|
| 2437 | cA = uni_content (A); |
---|
| 2438 | cB = uni_content (B); |
---|
| 2439 | gcdcAcB= gcd (cA, cB); |
---|
| 2440 | ppA= A/cA; |
---|
| 2441 | ppB= B/cB; |
---|
| 2442 | |
---|
| 2443 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
| 2444 | CanonicalForm gcdlcAlcB; |
---|
| 2445 | lcA= uni_lcoeff (ppA); |
---|
| 2446 | lcB= uni_lcoeff (ppB); |
---|
| 2447 | |
---|
| 2448 | if (fdivides (lcA, lcB)) |
---|
| 2449 | { |
---|
| 2450 | if (fdivides (A, B)) |
---|
| 2451 | return F/Lc(F); |
---|
| 2452 | } |
---|
| 2453 | if (fdivides (lcB, lcA)) |
---|
| 2454 | { |
---|
| 2455 | if (fdivides (B, A)) |
---|
| 2456 | return G/Lc(G); |
---|
| 2457 | } |
---|
| 2458 | |
---|
| 2459 | gcdlcAlcB= gcd (lcA, lcB); |
---|
| 2460 | int skelSize= size (skel, skel.mvar()); |
---|
| 2461 | |
---|
| 2462 | int j= 0; |
---|
| 2463 | int biggestSize= 0; |
---|
| 2464 | |
---|
| 2465 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
| 2466 | biggestSize= tmax (biggestSize, size (i.coeff())); |
---|
| 2467 | |
---|
| 2468 | CanonicalForm g, Aeval, Beval; |
---|
| 2469 | |
---|
| 2470 | CFList evalPoints; |
---|
| 2471 | bool evalFail= false; |
---|
| 2472 | CFList list; |
---|
| 2473 | bool GF= false; |
---|
| 2474 | CanonicalForm LCA= LC (A); |
---|
| 2475 | CanonicalForm tmp; |
---|
| 2476 | CFArray gcds= CFArray (biggestSize); |
---|
| 2477 | CFList * pEvalPoints= new CFList [biggestSize]; |
---|
| 2478 | Variable V_buf= alpha; |
---|
| 2479 | CFList source, dest; |
---|
| 2480 | CanonicalForm prim_elem, im_prim_elem; |
---|
| 2481 | for (int i= 0; i < biggestSize; i++) |
---|
| 2482 | { |
---|
| 2483 | if (i == 0) |
---|
| 2484 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, evalFail, |
---|
| 2485 | list); |
---|
| 2486 | else |
---|
| 2487 | { |
---|
| 2488 | mult (evalPoints, pEvalPoints [0]); |
---|
| 2489 | eval (A, B, Aeval, Beval, evalPoints); |
---|
| 2490 | } |
---|
| 2491 | |
---|
| 2492 | if (evalFail) |
---|
| 2493 | { |
---|
[9ff686] | 2494 | if (V_buf.level() != 1) |
---|
[08daea] | 2495 | { |
---|
| 2496 | do |
---|
| 2497 | { |
---|
[9ff686] | 2498 | Variable V_buf2= chooseExtension (V_buf); |
---|
[08daea] | 2499 | source= CFList(); |
---|
| 2500 | dest= CFList(); |
---|
| 2501 | |
---|
| 2502 | bool prim_fail= false; |
---|
| 2503 | Variable V_buf3; |
---|
| 2504 | prim_elem= primitiveElement (V_buf, V_buf3, prim_fail); |
---|
| 2505 | |
---|
| 2506 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
| 2507 | if (prim_fail) |
---|
| 2508 | ; //ERROR |
---|
| 2509 | else |
---|
| 2510 | im_prim_elem= mapPrimElem (prim_elem, V_buf, V_buf2); |
---|
| 2511 | |
---|
| 2512 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf)); |
---|
| 2513 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
| 2514 | |
---|
| 2515 | for (CFListIterator j= list; j.hasItem(); j++) |
---|
| 2516 | j.getItem()= mapUp (j.getItem(), V_buf, V_buf2, prim_elem, |
---|
| 2517 | im_prim_elem, source, dest); |
---|
| 2518 | for (int k= 0; k < i; k++) |
---|
| 2519 | { |
---|
| 2520 | for (CFListIterator j= pEvalPoints[k]; j.hasItem(); j++) |
---|
| 2521 | j.getItem()= mapUp (j.getItem(), V_buf, V_buf2, prim_elem, |
---|
| 2522 | im_prim_elem, source, dest); |
---|
| 2523 | gcds[k]= mapUp (gcds[k], V_buf, V_buf2, prim_elem, im_prim_elem, |
---|
| 2524 | source, dest); |
---|
| 2525 | } |
---|
| 2526 | |
---|
[9ff686] | 2527 | if (alpha.level() != 1) |
---|
[08daea] | 2528 | { |
---|
| 2529 | A= mapUp (A, V_buf, V_buf2, prim_elem, im_prim_elem, source,dest); |
---|
| 2530 | B= mapUp (B, V_buf, V_buf2, prim_elem, im_prim_elem, source,dest); |
---|
| 2531 | } |
---|
| 2532 | evalFail= false; |
---|
| 2533 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
| 2534 | evalFail, list); |
---|
| 2535 | } while (evalFail); |
---|
| 2536 | } |
---|
| 2537 | else |
---|
| 2538 | { |
---|
| 2539 | CanonicalForm mipo; |
---|
| 2540 | int deg= 2; |
---|
| 2541 | do { |
---|
| 2542 | mipo= randomIrredpoly (deg, x); |
---|
| 2543 | V_buf= rootOf (mipo); |
---|
| 2544 | evalFail= false; |
---|
| 2545 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
[c1b9927] | 2546 | evalFail, list); |
---|
[08daea] | 2547 | deg++; |
---|
| 2548 | } while (evalFail); |
---|
| 2549 | } |
---|
| 2550 | } |
---|
| 2551 | |
---|
| 2552 | g= gcd (Aeval, Beval); |
---|
| 2553 | g /= Lc (g); |
---|
| 2554 | |
---|
| 2555 | if (degree (g) != degree (skel) || (skelSize != size (g))) |
---|
| 2556 | { |
---|
| 2557 | delete[] pEvalPoints; |
---|
| 2558 | fail= true; |
---|
| 2559 | return 0; |
---|
| 2560 | } |
---|
| 2561 | CFIterator l= skel; |
---|
| 2562 | for (CFIterator k= g; k.hasTerms(); k++, l++) |
---|
| 2563 | { |
---|
| 2564 | if (k.exp() != l.exp()) |
---|
| 2565 | { |
---|
| 2566 | delete[] pEvalPoints; |
---|
| 2567 | fail= true; |
---|
| 2568 | return 0; |
---|
| 2569 | } |
---|
| 2570 | } |
---|
| 2571 | pEvalPoints[i]= evalPoints; |
---|
| 2572 | gcds[i]= g; |
---|
| 2573 | |
---|
| 2574 | tmp= 0; |
---|
| 2575 | int j= 0; |
---|
| 2576 | for (CFListIterator k= evalPoints; k.hasItem(); k++, j++) |
---|
| 2577 | tmp += k.getItem()*power (x, j); |
---|
| 2578 | list.append (tmp); |
---|
| 2579 | } |
---|
| 2580 | |
---|
| 2581 | if (Monoms.size() == 0) |
---|
| 2582 | Monoms= getMonoms (skel); |
---|
| 2583 | if (coeffMonoms == NULL) |
---|
| 2584 | coeffMonoms= new CFArray [skelSize]; |
---|
| 2585 | j= 0; |
---|
| 2586 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
| 2587 | coeffMonoms[j]= getMonoms (i.coeff()); |
---|
| 2588 | |
---|
| 2589 | CFArray* pL= new CFArray [skelSize]; |
---|
| 2590 | CFArray* pM= new CFArray [skelSize]; |
---|
| 2591 | for (int i= 0; i < biggestSize; i++) |
---|
| 2592 | { |
---|
| 2593 | CFIterator l= gcds [i]; |
---|
| 2594 | evalPoints= pEvalPoints [i]; |
---|
| 2595 | for (int k= 0; k < skelSize; k++, l++) |
---|
| 2596 | { |
---|
| 2597 | if (i == 0) |
---|
| 2598 | pL[k]= CFArray (biggestSize); |
---|
| 2599 | pL[k] [i]= l.coeff(); |
---|
| 2600 | |
---|
| 2601 | if (i == 0) |
---|
| 2602 | pM[k]= evaluate (coeffMonoms [k], evalPoints); |
---|
| 2603 | } |
---|
| 2604 | } |
---|
| 2605 | |
---|
| 2606 | CFArray solution; |
---|
| 2607 | CanonicalForm result= 0; |
---|
| 2608 | int ind= 0; |
---|
| 2609 | CFArray bufArray; |
---|
| 2610 | CFMatrix Mat; |
---|
| 2611 | for (int k= 0; k < skelSize; k++) |
---|
| 2612 | { |
---|
| 2613 | if (biggestSize != coeffMonoms[k].size()) |
---|
| 2614 | { |
---|
| 2615 | bufArray= CFArray (coeffMonoms[k].size()); |
---|
| 2616 | for (int i= 0; i < coeffMonoms[k].size(); i++) |
---|
| 2617 | bufArray [i]= pL[k] [i]; |
---|
| 2618 | solution= solveGeneralVandermonde (pM [k], bufArray); |
---|
| 2619 | } |
---|
| 2620 | else |
---|
| 2621 | solution= solveGeneralVandermonde (pM [k], pL[k]); |
---|
| 2622 | |
---|
| 2623 | if (solution.size() == 0) |
---|
| 2624 | { |
---|
| 2625 | delete[] pEvalPoints; |
---|
| 2626 | delete[] pM; |
---|
| 2627 | delete[] pL; |
---|
| 2628 | delete[] coeffMonoms; |
---|
| 2629 | fail= true; |
---|
| 2630 | return 0; |
---|
| 2631 | } |
---|
| 2632 | for (int l= 0; l < solution.size(); l++) |
---|
| 2633 | result += solution[l]*Monoms [ind + l]; |
---|
| 2634 | ind += solution.size(); |
---|
| 2635 | } |
---|
| 2636 | |
---|
| 2637 | delete[] pEvalPoints; |
---|
| 2638 | delete[] pM; |
---|
| 2639 | delete[] pL; |
---|
| 2640 | |
---|
[9ff686] | 2641 | if (alpha.level() != 1 && V_buf != alpha) |
---|
[08daea] | 2642 | { |
---|
| 2643 | CFList u, v; |
---|
| 2644 | result= mapDown (result, prim_elem, im_prim_elem, alpha, u, v); |
---|
| 2645 | } |
---|
| 2646 | |
---|
| 2647 | result= N(result); |
---|
| 2648 | if (fdivides (result, F) && fdivides (result, G)) |
---|
| 2649 | return result; |
---|
| 2650 | else |
---|
| 2651 | { |
---|
| 2652 | delete[] coeffMonoms; |
---|
| 2653 | fail= true; |
---|
| 2654 | return 0; |
---|
| 2655 | } |
---|
| 2656 | } |
---|
| 2657 | |
---|
| 2658 | CanonicalForm |
---|
| 2659 | nonMonicSparseInterpol (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 2660 | const CanonicalForm& skeleton, const Variable& alpha, |
---|
| 2661 | bool& fail, CFArray*& coeffMonoms, CFArray& Monoms |
---|
| 2662 | ) |
---|
| 2663 | { |
---|
| 2664 | CanonicalForm A= F; |
---|
| 2665 | CanonicalForm B= G; |
---|
| 2666 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
| 2667 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
| 2668 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
| 2669 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
| 2670 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
| 2671 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
| 2672 | if (F == G) return F/Lc(F); |
---|
| 2673 | |
---|
| 2674 | CFMap M,N; |
---|
| 2675 | int best_level= myCompress (A, B, M, N, false); |
---|
| 2676 | |
---|
| 2677 | if (best_level == 0) |
---|
| 2678 | return B.genOne(); |
---|
| 2679 | |
---|
| 2680 | A= M(A); |
---|
| 2681 | B= M(B); |
---|
| 2682 | |
---|
| 2683 | Variable x= Variable (1); |
---|
[f71453] | 2684 | ASSERT (degree (A, x) == 0, "expected degree (F, 1) == 0"); |
---|
| 2685 | ASSERT (degree (B, x) == 0, "expected degree (G, 1) == 0"); |
---|
[08daea] | 2686 | |
---|
[c1b9927] | 2687 | //univariate case |
---|
[08daea] | 2688 | if (A.isUnivariate() && B.isUnivariate()) |
---|
| 2689 | return N (gcd (A, B)); |
---|
| 2690 | |
---|
| 2691 | CanonicalForm skel= M(skeleton); |
---|
| 2692 | |
---|
| 2693 | CanonicalForm cA, cB; // content of A and B |
---|
| 2694 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
| 2695 | CanonicalForm gcdcAcB; |
---|
| 2696 | cA = uni_content (A); |
---|
| 2697 | cB = uni_content (B); |
---|
| 2698 | gcdcAcB= gcd (cA, cB); |
---|
| 2699 | ppA= A/cA; |
---|
| 2700 | ppB= B/cB; |
---|
| 2701 | |
---|
| 2702 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
| 2703 | CanonicalForm gcdlcAlcB; |
---|
| 2704 | lcA= uni_lcoeff (ppA); |
---|
| 2705 | lcB= uni_lcoeff (ppB); |
---|
| 2706 | |
---|
| 2707 | if (fdivides (lcA, lcB)) |
---|
| 2708 | { |
---|
| 2709 | if (fdivides (A, B)) |
---|
| 2710 | return F/Lc(F); |
---|
| 2711 | } |
---|
| 2712 | if (fdivides (lcB, lcA)) |
---|
| 2713 | { |
---|
| 2714 | if (fdivides (B, A)) |
---|
| 2715 | return G/Lc(G); |
---|
| 2716 | } |
---|
| 2717 | |
---|
| 2718 | gcdlcAlcB= gcd (lcA, lcB); |
---|
| 2719 | int skelSize= size (skel, skel.mvar()); |
---|
| 2720 | |
---|
| 2721 | int j= 0; |
---|
| 2722 | int biggestSize= 0; |
---|
| 2723 | int bufSize; |
---|
| 2724 | int numberUni= 0; |
---|
| 2725 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
| 2726 | { |
---|
| 2727 | bufSize= size (i.coeff()); |
---|
| 2728 | biggestSize= tmax (biggestSize, bufSize); |
---|
| 2729 | numberUni += bufSize; |
---|
| 2730 | } |
---|
| 2731 | numberUni--; |
---|
| 2732 | numberUni= (int) ceil ( (double) numberUni / (skelSize - 1)); |
---|
| 2733 | biggestSize= tmax (biggestSize , numberUni); |
---|
| 2734 | |
---|
| 2735 | numberUni= biggestSize + size (LC(skel)) - 1; |
---|
| 2736 | int biggestSize2= tmax (numberUni, biggestSize); |
---|
| 2737 | |
---|
| 2738 | CanonicalForm g, Aeval, Beval; |
---|
| 2739 | |
---|
| 2740 | CFList evalPoints; |
---|
| 2741 | CFArray coeffEval; |
---|
| 2742 | bool evalFail= false; |
---|
| 2743 | CFList list; |
---|
| 2744 | bool GF= false; |
---|
| 2745 | CanonicalForm LCA= LC (A); |
---|
| 2746 | CanonicalForm tmp; |
---|
| 2747 | CFArray gcds= CFArray (biggestSize); |
---|
| 2748 | CFList * pEvalPoints= new CFList [biggestSize]; |
---|
| 2749 | Variable V_buf= alpha; |
---|
| 2750 | CFList source, dest; |
---|
| 2751 | CanonicalForm prim_elem, im_prim_elem; |
---|
| 2752 | for (int i= 0; i < biggestSize; i++) |
---|
| 2753 | { |
---|
| 2754 | if (i == 0) |
---|
| 2755 | { |
---|
| 2756 | if (getCharacteristic() > 3) |
---|
| 2757 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
| 2758 | evalFail, list); |
---|
| 2759 | else |
---|
| 2760 | evalFail= true; |
---|
| 2761 | |
---|
| 2762 | if (evalFail) |
---|
| 2763 | { |
---|
[9ff686] | 2764 | if (V_buf.level() != 1) |
---|
[08daea] | 2765 | { |
---|
| 2766 | do |
---|
| 2767 | { |
---|
[9ff686] | 2768 | Variable V_buf2= chooseExtension (V_buf); |
---|
[08daea] | 2769 | source= CFList(); |
---|
| 2770 | dest= CFList(); |
---|
| 2771 | |
---|
| 2772 | bool prim_fail= false; |
---|
| 2773 | Variable V_buf3; |
---|
| 2774 | prim_elem= primitiveElement (V_buf, V_buf3, prim_fail); |
---|
| 2775 | |
---|
| 2776 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
| 2777 | if (prim_fail) |
---|
| 2778 | ; //ERROR |
---|
| 2779 | else |
---|
| 2780 | im_prim_elem= mapPrimElem (prim_elem, V_buf, V_buf2); |
---|
| 2781 | |
---|
| 2782 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf)); |
---|
| 2783 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
| 2784 | |
---|
[c1b9927] | 2785 | for (CFListIterator i= list; i.hasItem(); i++) |
---|
[08daea] | 2786 | i.getItem()= mapUp (i.getItem(), V_buf, V_buf2, prim_elem, |
---|
| 2787 | im_prim_elem, source, dest); |
---|
| 2788 | evalFail= false; |
---|
| 2789 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
| 2790 | evalFail, list); |
---|
| 2791 | } while (evalFail); |
---|
| 2792 | } |
---|
| 2793 | else |
---|
| 2794 | { |
---|
| 2795 | CanonicalForm mipo; |
---|
| 2796 | int deg= 2; |
---|
| 2797 | do { |
---|
| 2798 | mipo= randomIrredpoly (deg, x); |
---|
| 2799 | V_buf= rootOf (mipo); |
---|
| 2800 | evalFail= false; |
---|
| 2801 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
| 2802 | evalFail, list); |
---|
| 2803 | deg++; |
---|
| 2804 | } while (evalFail); |
---|
| 2805 | } |
---|
| 2806 | } |
---|
| 2807 | } |
---|
| 2808 | else |
---|
| 2809 | { |
---|
| 2810 | mult (evalPoints, pEvalPoints[0]); |
---|
| 2811 | eval (A, B, Aeval, Beval, evalPoints); |
---|
| 2812 | } |
---|
| 2813 | |
---|
| 2814 | g= gcd (Aeval, Beval); |
---|
| 2815 | g /= Lc (g); |
---|
| 2816 | |
---|
| 2817 | if (degree (g) != degree (skel) || (skelSize != size (g))) |
---|
| 2818 | { |
---|
| 2819 | delete[] pEvalPoints; |
---|
| 2820 | fail= true; |
---|
| 2821 | return 0; |
---|
| 2822 | } |
---|
| 2823 | CFIterator l= skel; |
---|
| 2824 | for (CFIterator k= g; k.hasTerms(); k++, l++) |
---|
| 2825 | { |
---|
| 2826 | if (k.exp() != l.exp()) |
---|
| 2827 | { |
---|
| 2828 | delete[] pEvalPoints; |
---|
| 2829 | fail= true; |
---|
| 2830 | return 0; |
---|
| 2831 | } |
---|
| 2832 | } |
---|
| 2833 | pEvalPoints[i]= evalPoints; |
---|
| 2834 | gcds[i]= g; |
---|
| 2835 | |
---|
| 2836 | tmp= 0; |
---|
| 2837 | int j= 0; |
---|
| 2838 | for (CFListIterator k= evalPoints; k.hasItem(); k++, j++) |
---|
| 2839 | tmp += k.getItem()*power (x, j); |
---|
| 2840 | list.append (tmp); |
---|
| 2841 | } |
---|
| 2842 | |
---|
| 2843 | if (Monoms.size() == 0) |
---|
| 2844 | Monoms= getMonoms (skel); |
---|
| 2845 | |
---|
| 2846 | if (coeffMonoms == NULL) |
---|
| 2847 | coeffMonoms= new CFArray [skelSize]; |
---|
| 2848 | |
---|
| 2849 | j= 0; |
---|
| 2850 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
| 2851 | coeffMonoms[j]= getMonoms (i.coeff()); |
---|
| 2852 | |
---|
| 2853 | int minimalColumnsIndex; |
---|
| 2854 | if (skelSize > 1) |
---|
| 2855 | minimalColumnsIndex= 1; |
---|
| 2856 | else |
---|
| 2857 | minimalColumnsIndex= 0; |
---|
[c1b9927] | 2858 | int minimalColumns=-1; |
---|
[08daea] | 2859 | |
---|
| 2860 | CFArray* pM= new CFArray [skelSize]; |
---|
| 2861 | CFMatrix Mat; |
---|
[c1b9927] | 2862 | // find the Matrix with minimal number of columns |
---|
[08daea] | 2863 | for (int i= 0; i < skelSize; i++) |
---|
| 2864 | { |
---|
| 2865 | pM[i]= CFArray (coeffMonoms[i].size()); |
---|
| 2866 | if (i == 1) |
---|
| 2867 | minimalColumns= coeffMonoms[i].size(); |
---|
| 2868 | if (i > 1) |
---|
| 2869 | { |
---|
| 2870 | if (minimalColumns > coeffMonoms[i].size()) |
---|
| 2871 | { |
---|
| 2872 | minimalColumns= coeffMonoms[i].size(); |
---|
| 2873 | minimalColumnsIndex= i; |
---|
| 2874 | } |
---|
| 2875 | } |
---|
| 2876 | } |
---|
| 2877 | CFMatrix* pMat= new CFMatrix [2]; |
---|
| 2878 | pMat[0]= CFMatrix (biggestSize, coeffMonoms[0].size()); |
---|
| 2879 | pMat[1]= CFMatrix (biggestSize, coeffMonoms[minimalColumnsIndex].size()); |
---|
| 2880 | CFArray* pL= new CFArray [skelSize]; |
---|
| 2881 | for (int i= 0; i < biggestSize; i++) |
---|
| 2882 | { |
---|
| 2883 | CFIterator l= gcds [i]; |
---|
| 2884 | evalPoints= pEvalPoints [i]; |
---|
| 2885 | for (int k= 0; k < skelSize; k++, l++) |
---|
| 2886 | { |
---|
| 2887 | if (i == 0) |
---|
| 2888 | pL[k]= CFArray (biggestSize); |
---|
[c1b9927] | 2889 | pL[k] [i]= l.coeff(); |
---|
[08daea] | 2890 | |
---|
| 2891 | if (i == 0 && k != 0 && k != minimalColumnsIndex) |
---|
| 2892 | pM[k]= evaluate (coeffMonoms[k], evalPoints); |
---|
| 2893 | else if (i == 0 && (k == 0 || k == minimalColumnsIndex)) |
---|
| 2894 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
| 2895 | if (i > 0 && (k == 0 || k == minimalColumnsIndex)) |
---|
| 2896 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
| 2897 | |
---|
| 2898 | if (k == 0) |
---|
| 2899 | { |
---|
| 2900 | if (pMat[k].rows() >= i + 1) |
---|
| 2901 | { |
---|
| 2902 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
| 2903 | pMat[k] (i + 1, ind)= coeffEval[ind - 1]; |
---|
| 2904 | } |
---|
| 2905 | } |
---|
| 2906 | if (k == minimalColumnsIndex) |
---|
| 2907 | { |
---|
| 2908 | if (pMat[1].rows() >= i + 1) |
---|
| 2909 | { |
---|
| 2910 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
| 2911 | pMat[1] (i + 1, ind)= coeffEval[ind - 1]; |
---|
| 2912 | } |
---|
| 2913 | } |
---|
| 2914 | } |
---|
| 2915 | } |
---|
| 2916 | |
---|
| 2917 | CFArray solution; |
---|
| 2918 | CanonicalForm result= 0; |
---|
| 2919 | int ind= 1; |
---|
| 2920 | int matRows, matColumns; |
---|
| 2921 | matRows= pMat[1].rows(); |
---|
[c1b9927] | 2922 | matColumns= pMat[0].columns() - 1; |
---|
[08daea] | 2923 | matColumns += pMat[1].columns(); |
---|
| 2924 | |
---|
| 2925 | Mat= CFMatrix (matRows, matColumns); |
---|
| 2926 | for (int i= 1; i <= matRows; i++) |
---|
| 2927 | for (int j= 1; j <= pMat[1].columns(); j++) |
---|
| 2928 | Mat (i, j)= pMat[1] (i, j); |
---|
| 2929 | |
---|
[c1b9927] | 2930 | for (int j= pMat[1].columns() + 1; j <= matColumns; |
---|
[08daea] | 2931 | j++, ind++) |
---|
| 2932 | { |
---|
[c1b9927] | 2933 | for (int i= 1; i <= matRows; i++) |
---|
[08daea] | 2934 | Mat (i, j)= (-pMat [0] (i, ind + 1))*pL[minimalColumnsIndex] [i - 1]; |
---|
| 2935 | } |
---|
| 2936 | |
---|
| 2937 | CFArray firstColumn= CFArray (pMat[0].rows()); |
---|
| 2938 | for (int i= 0; i < pMat[0].rows(); i++) |
---|
[c1b9927] | 2939 | firstColumn [i]= pMat[0] (i + 1, 1); |
---|
[08daea] | 2940 | |
---|
| 2941 | CFArray bufArray= pL[minimalColumnsIndex]; |
---|
| 2942 | |
---|
| 2943 | for (int i= 0; i < biggestSize; i++) |
---|
| 2944 | pL[minimalColumnsIndex] [i] *= firstColumn[i]; |
---|
| 2945 | |
---|
| 2946 | CFMatrix bufMat= pMat[1]; |
---|
| 2947 | pMat[1]= Mat; |
---|
| 2948 | |
---|
[9ff686] | 2949 | if (V_buf.level() != 1) |
---|
[c1b9927] | 2950 | solution= solveSystemFq (pMat[1], |
---|
[08daea] | 2951 | pL[minimalColumnsIndex], V_buf); |
---|
| 2952 | else |
---|
[c1b9927] | 2953 | solution= solveSystemFp (pMat[1], |
---|
[08daea] | 2954 | pL[minimalColumnsIndex]); |
---|
| 2955 | |
---|
| 2956 | if (solution.size() == 0) |
---|
| 2957 | { //Javadi's method failed, try deKleine, Monagan, Wittkopf instead |
---|
| 2958 | CFMatrix bufMat0= pMat[0]; |
---|
| 2959 | delete [] pMat; |
---|
| 2960 | pMat= new CFMatrix [skelSize]; |
---|
[c1b9927] | 2961 | pL[minimalColumnsIndex]= bufArray; |
---|
[618da5] | 2962 | CFList* bufpEvalPoints= NULL; |
---|
[08daea] | 2963 | CFArray bufGcds; |
---|
| 2964 | if (biggestSize != biggestSize2) |
---|
| 2965 | { |
---|
| 2966 | bufpEvalPoints= pEvalPoints; |
---|
| 2967 | pEvalPoints= new CFList [biggestSize2]; |
---|
| 2968 | bufGcds= gcds; |
---|
| 2969 | gcds= CFArray (biggestSize2); |
---|
| 2970 | for (int i= 0; i < biggestSize; i++) |
---|
| 2971 | { |
---|
| 2972 | pEvalPoints[i]= bufpEvalPoints [i]; |
---|
| 2973 | gcds[i]= bufGcds[i]; |
---|
| 2974 | } |
---|
| 2975 | for (int i= 0; i < biggestSize2 - biggestSize; i++) |
---|
| 2976 | { |
---|
| 2977 | mult (evalPoints, pEvalPoints[0]); |
---|
| 2978 | eval (A, B, Aeval, Beval, evalPoints); |
---|
| 2979 | g= gcd (Aeval, Beval); |
---|
| 2980 | g /= Lc (g); |
---|
| 2981 | if (degree (g) != degree (skel) || (skelSize != size (g))) |
---|
| 2982 | { |
---|
| 2983 | delete[] pEvalPoints; |
---|
| 2984 | delete[] pMat; |
---|
| 2985 | delete[] pL; |
---|
| 2986 | delete[] coeffMonoms; |
---|
| 2987 | delete[] pM; |
---|
[618da5] | 2988 | if (bufpEvalPoints != NULL) |
---|
| 2989 | delete [] bufpEvalPoints; |
---|
[08daea] | 2990 | fail= true; |
---|
| 2991 | return 0; |
---|
| 2992 | } |
---|
| 2993 | CFIterator l= skel; |
---|
| 2994 | for (CFIterator k= g; k.hasTerms(); k++, l++) |
---|
| 2995 | { |
---|
| 2996 | if (k.exp() != l.exp()) |
---|
| 2997 | { |
---|
| 2998 | delete[] pEvalPoints; |
---|
| 2999 | delete[] pMat; |
---|
| 3000 | delete[] pL; |
---|
| 3001 | delete[] coeffMonoms; |
---|
| 3002 | delete[] pM; |
---|
[618da5] | 3003 | if (bufpEvalPoints != NULL) |
---|
| 3004 | delete [] bufpEvalPoints; |
---|
[08daea] | 3005 | fail= true; |
---|
| 3006 | return 0; |
---|
| 3007 | } |
---|
| 3008 | } |
---|
| 3009 | pEvalPoints[i + biggestSize]= evalPoints; |
---|
| 3010 | gcds[i + biggestSize]= g; |
---|
| 3011 | } |
---|
| 3012 | } |
---|
| 3013 | for (int i= 0; i < biggestSize; i++) |
---|
| 3014 | { |
---|
| 3015 | CFIterator l= gcds [i]; |
---|
| 3016 | evalPoints= pEvalPoints [i]; |
---|
| 3017 | for (int k= 1; k < skelSize; k++, l++) |
---|
| 3018 | { |
---|
| 3019 | if (i == 0) |
---|
| 3020 | pMat[k]= CFMatrix (biggestSize2,coeffMonoms[k].size()+biggestSize2-1); |
---|
| 3021 | if (k == minimalColumnsIndex) |
---|
| 3022 | continue; |
---|
| 3023 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
[c1b9927] | 3024 | if (pMat[k].rows() >= i + 1) |
---|
[08daea] | 3025 | { |
---|
| 3026 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
| 3027 | pMat[k] (i + 1, ind)= coeffEval[ind - 1]; |
---|
| 3028 | } |
---|
| 3029 | } |
---|
| 3030 | } |
---|
| 3031 | Mat= bufMat0; |
---|
| 3032 | pMat[0]= CFMatrix (biggestSize2, coeffMonoms[0].size() + biggestSize2 - 1); |
---|
| 3033 | for (int j= 1; j <= Mat.rows(); j++) |
---|
| 3034 | for (int k= 1; k <= Mat.columns(); k++) |
---|
| 3035 | pMat [0] (j,k)= Mat (j,k); |
---|
| 3036 | Mat= bufMat; |
---|
| 3037 | for (int j= 1; j <= Mat.rows(); j++) |
---|
| 3038 | for (int k= 1; k <= Mat.columns(); k++) |
---|
| 3039 | pMat [minimalColumnsIndex] (j,k)= Mat (j,k); |
---|
| 3040 | // write old matrix entries into new matrices |
---|
| 3041 | for (int i= 0; i < skelSize; i++) |
---|
| 3042 | { |
---|
| 3043 | bufArray= pL[i]; |
---|
| 3044 | pL[i]= CFArray (biggestSize2); |
---|
| 3045 | for (int j= 0; j < bufArray.size(); j++) |
---|
| 3046 | pL[i] [j]= bufArray [j]; |
---|
| 3047 | } |
---|
| 3048 | //write old vector entries into new and add new entries to old matrices |
---|
| 3049 | for (int i= 0; i < biggestSize2 - biggestSize; i++) |
---|
| 3050 | { |
---|
| 3051 | CFIterator l= gcds [i + biggestSize]; |
---|
| 3052 | evalPoints= pEvalPoints [i + biggestSize]; |
---|
| 3053 | for (int k= 0; k < skelSize; k++, l++) |
---|
| 3054 | { |
---|
[c1b9927] | 3055 | pL[k] [i + biggestSize]= l.coeff(); |
---|
[08daea] | 3056 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
[c1b9927] | 3057 | if (pMat[k].rows() >= i + biggestSize + 1) |
---|
| 3058 | { |
---|
[08daea] | 3059 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
| 3060 | pMat[k] (i + biggestSize + 1, ind)= coeffEval[ind - 1]; |
---|
| 3061 | } |
---|
| 3062 | } |
---|
| 3063 | } |
---|
| 3064 | // begin new |
---|
| 3065 | for (int i= 0; i < skelSize; i++) |
---|
| 3066 | { |
---|
| 3067 | if (pL[i].size() > 1) |
---|
| 3068 | { |
---|
[c1b9927] | 3069 | for (int j= 2; j <= pMat[i].rows(); j++) |
---|
| 3070 | pMat[i] (j, coeffMonoms[i].size() + j - 1)= |
---|
[08daea] | 3071 | -pL[i] [j - 1]; |
---|
| 3072 | } |
---|
| 3073 | } |
---|
| 3074 | |
---|
| 3075 | matColumns= biggestSize2 - 1; |
---|
| 3076 | matRows= 0; |
---|
| 3077 | for (int i= 0; i < skelSize; i++) |
---|
| 3078 | { |
---|
[9ff686] | 3079 | if (V_buf.level() == 1) |
---|
[d1dc39] | 3080 | (void) gaussianElimFp (pMat[i], pL[i]); |
---|
[08daea] | 3081 | else |
---|
[d1dc39] | 3082 | (void) gaussianElimFq (pMat[i], pL[i], V_buf); |
---|
[08daea] | 3083 | |
---|
| 3084 | if (pMat[i] (coeffMonoms[i].size(), coeffMonoms[i].size()) == 0) |
---|
| 3085 | { |
---|
| 3086 | delete[] pEvalPoints; |
---|
| 3087 | delete[] pMat; |
---|
| 3088 | delete[] pL; |
---|
| 3089 | delete[] coeffMonoms; |
---|
| 3090 | delete[] pM; |
---|
[618da5] | 3091 | if (bufpEvalPoints != NULL) |
---|
| 3092 | delete [] bufpEvalPoints; |
---|
[08daea] | 3093 | fail= true; |
---|
| 3094 | return 0; |
---|
| 3095 | } |
---|
| 3096 | matRows += pMat[i].rows() - coeffMonoms[i].size(); |
---|
| 3097 | } |
---|
| 3098 | |
---|
| 3099 | CFMatrix bufMat; |
---|
| 3100 | Mat= CFMatrix (matRows, matColumns); |
---|
| 3101 | ind= 0; |
---|
| 3102 | bufArray= CFArray (matRows); |
---|
| 3103 | CFArray bufArray2; |
---|
| 3104 | for (int i= 0; i < skelSize; i++) |
---|
| 3105 | { |
---|
| 3106 | bufMat= pMat[i] (coeffMonoms[i].size() + 1, pMat[i].rows(), |
---|
| 3107 | coeffMonoms[i].size() + 1, pMat[i].columns()); |
---|
| 3108 | |
---|
| 3109 | for (int j= 1; j <= bufMat.rows(); j++) |
---|
| 3110 | for (int k= 1; k <= bufMat.columns(); k++) |
---|
| 3111 | Mat (j + ind, k)= bufMat(j, k); |
---|
| 3112 | bufArray2= coeffMonoms[i].size(); |
---|
| 3113 | for (int j= 1; j <= pMat[i].rows(); j++) |
---|
| 3114 | { |
---|
| 3115 | if (j > coeffMonoms[i].size()) |
---|
| 3116 | bufArray [j-coeffMonoms[i].size() + ind - 1]= pL[i] [j - 1]; |
---|
[c1b9927] | 3117 | else |
---|
[08daea] | 3118 | bufArray2 [j - 1]= pL[i] [j - 1]; |
---|
| 3119 | } |
---|
| 3120 | pL[i]= bufArray2; |
---|
| 3121 | ind += bufMat.rows(); |
---|
| 3122 | pMat[i]= pMat[i] (1, coeffMonoms[i].size(), 1, pMat[i].columns()); |
---|
| 3123 | } |
---|
| 3124 | |
---|
[9ff686] | 3125 | if (V_buf.level() != 1) |
---|
[08daea] | 3126 | solution= solveSystemFq (Mat, bufArray, V_buf); |
---|
| 3127 | else |
---|
| 3128 | solution= solveSystemFp (Mat, bufArray); |
---|
| 3129 | |
---|
| 3130 | if (solution.size() == 0) |
---|
| 3131 | { |
---|
| 3132 | delete[] pEvalPoints; |
---|
| 3133 | delete[] pMat; |
---|
| 3134 | delete[] pL; |
---|
| 3135 | delete[] coeffMonoms; |
---|
| 3136 | delete[] pM; |
---|
[618da5] | 3137 | if (bufpEvalPoints != NULL) |
---|
| 3138 | delete [] bufpEvalPoints; |
---|
[08daea] | 3139 | fail= true; |
---|
| 3140 | return 0; |
---|
| 3141 | } |
---|
| 3142 | |
---|
| 3143 | ind= 0; |
---|
| 3144 | result= 0; |
---|
| 3145 | CFArray bufSolution; |
---|
| 3146 | for (int i= 0; i < skelSize; i++) |
---|
| 3147 | { |
---|
| 3148 | bufSolution= readOffSolution (pMat[i], pL[i], solution); |
---|
| 3149 | for (int i= 0; i < bufSolution.size(); i++, ind++) |
---|
| 3150 | result += Monoms [ind]*bufSolution[i]; |
---|
| 3151 | } |
---|
[9ff686] | 3152 | if (alpha.level() != 1 && V_buf != alpha) |
---|
[08daea] | 3153 | { |
---|
| 3154 | CFList u, v; |
---|
| 3155 | result= mapDown (result, prim_elem, im_prim_elem, alpha, u, v); |
---|
| 3156 | } |
---|
| 3157 | result= N(result); |
---|
| 3158 | if (fdivides (result, F) && fdivides (result, G)) |
---|
[618da5] | 3159 | { |
---|
| 3160 | delete[] pEvalPoints; |
---|
| 3161 | delete[] pMat; |
---|
| 3162 | delete[] pL; |
---|
| 3163 | delete[] pM; |
---|
| 3164 | if (bufpEvalPoints != NULL) |
---|
| 3165 | delete [] bufpEvalPoints; |
---|
[08daea] | 3166 | return result; |
---|
[618da5] | 3167 | } |
---|
[08daea] | 3168 | else |
---|
| 3169 | { |
---|
[618da5] | 3170 | delete[] pEvalPoints; |
---|
| 3171 | delete[] pMat; |
---|
| 3172 | delete[] pL; |
---|
| 3173 | delete[] coeffMonoms; |
---|
| 3174 | delete[] pM; |
---|
| 3175 | if (bufpEvalPoints != NULL) |
---|
| 3176 | delete [] bufpEvalPoints; |
---|
[08daea] | 3177 | fail= true; |
---|
| 3178 | return 0; |
---|
| 3179 | } |
---|
| 3180 | } // end of deKleine, Monagan & Wittkopf |
---|
| 3181 | |
---|
| 3182 | result += Monoms[0]; |
---|
| 3183 | int ind2= 0, ind3= 2; |
---|
| 3184 | ind= 0; |
---|
| 3185 | for (int l= 0; l < minimalColumnsIndex; l++) |
---|
| 3186 | ind += coeffMonoms[l].size(); |
---|
| 3187 | for (int l= solution.size() - pMat[0].columns() + 1; l < solution.size(); |
---|
| 3188 | l++, ind2++, ind3++) |
---|
| 3189 | { |
---|
| 3190 | result += solution[l]*Monoms [1 + ind2]; |
---|
[c1b9927] | 3191 | for (int i= 0; i < pMat[0].rows(); i++) |
---|
[08daea] | 3192 | firstColumn[i] += solution[l]*pMat[0] (i + 1, ind3); |
---|
| 3193 | } |
---|
| 3194 | for (int l= 0; l < solution.size() + 1 - pMat[0].columns(); l++) |
---|
| 3195 | result += solution[l]*Monoms [ind + l]; |
---|
| 3196 | ind= coeffMonoms[0].size(); |
---|
| 3197 | for (int k= 1; k < skelSize; k++) |
---|
| 3198 | { |
---|
| 3199 | if (k == minimalColumnsIndex) |
---|
| 3200 | { |
---|
| 3201 | ind += coeffMonoms[k].size(); |
---|
| 3202 | continue; |
---|
| 3203 | } |
---|
| 3204 | if (k != minimalColumnsIndex) |
---|
| 3205 | { |
---|
| 3206 | for (int i= 0; i < biggestSize; i++) |
---|
| 3207 | pL[k] [i] *= firstColumn [i]; |
---|
| 3208 | } |
---|
| 3209 | |
---|
| 3210 | if (biggestSize != coeffMonoms[k].size() && k != minimalColumnsIndex) |
---|
| 3211 | { |
---|
| 3212 | bufArray= CFArray (coeffMonoms[k].size()); |
---|
| 3213 | for (int i= 0; i < bufArray.size(); i++) |
---|
| 3214 | bufArray [i]= pL[k] [i]; |
---|
| 3215 | solution= solveGeneralVandermonde (pM[k], bufArray); |
---|
| 3216 | } |
---|
| 3217 | else |
---|
| 3218 | solution= solveGeneralVandermonde (pM[k], pL[k]); |
---|
| 3219 | |
---|
| 3220 | if (solution.size() == 0) |
---|
| 3221 | { |
---|
| 3222 | delete[] pEvalPoints; |
---|
| 3223 | delete[] pMat; |
---|
| 3224 | delete[] pL; |
---|
| 3225 | delete[] coeffMonoms; |
---|
| 3226 | delete[] pM; |
---|
| 3227 | fail= true; |
---|
| 3228 | return 0; |
---|
| 3229 | } |
---|
| 3230 | if (k != minimalColumnsIndex) |
---|
| 3231 | { |
---|
| 3232 | for (int l= 0; l < solution.size(); l++) |
---|
| 3233 | result += solution[l]*Monoms [ind + l]; |
---|
| 3234 | ind += solution.size(); |
---|
| 3235 | } |
---|
| 3236 | } |
---|
| 3237 | |
---|
| 3238 | delete[] pEvalPoints; |
---|
| 3239 | delete[] pMat; |
---|
| 3240 | delete[] pL; |
---|
| 3241 | delete[] pM; |
---|
| 3242 | |
---|
[9ff686] | 3243 | if (alpha.level() != 1 && V_buf != alpha) |
---|
[08daea] | 3244 | { |
---|
| 3245 | CFList u, v; |
---|
| 3246 | result= mapDown (result, prim_elem, im_prim_elem, alpha, u, v); |
---|
| 3247 | } |
---|
| 3248 | result= N(result); |
---|
| 3249 | |
---|
| 3250 | if (fdivides (result, F) && fdivides (result, G)) |
---|
| 3251 | return result; |
---|
| 3252 | else |
---|
| 3253 | { |
---|
| 3254 | delete[] coeffMonoms; |
---|
| 3255 | fail= true; |
---|
| 3256 | return 0; |
---|
| 3257 | } |
---|
| 3258 | } |
---|
| 3259 | |
---|
| 3260 | CanonicalForm sparseGCDFq (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 3261 | const Variable & alpha, CFList& l, bool& topLevel) |
---|
| 3262 | { |
---|
| 3263 | CanonicalForm A= F; |
---|
| 3264 | CanonicalForm B= G; |
---|
| 3265 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
| 3266 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
| 3267 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
| 3268 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
| 3269 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
| 3270 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
| 3271 | if (F == G) return F/Lc(F); |
---|
| 3272 | |
---|
| 3273 | CFMap M,N; |
---|
| 3274 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
| 3275 | |
---|
| 3276 | if (best_level == 0) return B.genOne(); |
---|
| 3277 | |
---|
| 3278 | A= M(A); |
---|
| 3279 | B= M(B); |
---|
| 3280 | |
---|
| 3281 | Variable x= Variable (1); |
---|
| 3282 | |
---|
[c1b9927] | 3283 | //univariate case |
---|
[08daea] | 3284 | if (A.isUnivariate() && B.isUnivariate()) |
---|
| 3285 | return N (gcd (A, B)); |
---|
| 3286 | |
---|
| 3287 | CanonicalForm cA, cB; // content of A and B |
---|
| 3288 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
| 3289 | CanonicalForm gcdcAcB; |
---|
[ea5ff1d] | 3290 | |
---|
| 3291 | cA = uni_content (A); |
---|
| 3292 | cB = uni_content (B); |
---|
| 3293 | gcdcAcB= gcd (cA, cB); |
---|
| 3294 | ppA= A/cA; |
---|
| 3295 | ppB= B/cB; |
---|
[08daea] | 3296 | |
---|
| 3297 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
| 3298 | CanonicalForm gcdlcAlcB; |
---|
| 3299 | lcA= uni_lcoeff (ppA); |
---|
| 3300 | lcB= uni_lcoeff (ppB); |
---|
| 3301 | |
---|
| 3302 | if (fdivides (lcA, lcB)) |
---|
| 3303 | { |
---|
| 3304 | if (fdivides (A, B)) |
---|
| 3305 | return F/Lc(F); |
---|
| 3306 | } |
---|
| 3307 | if (fdivides (lcB, lcA)) |
---|
| 3308 | { |
---|
| 3309 | if (fdivides (B, A)) |
---|
| 3310 | return G/Lc(G); |
---|
| 3311 | } |
---|
| 3312 | |
---|
| 3313 | gcdlcAlcB= gcd (lcA, lcB); |
---|
| 3314 | |
---|
| 3315 | int d= totaldegree (ppA, Variable (2), Variable (ppA.level())); |
---|
| 3316 | int d0; |
---|
| 3317 | |
---|
[c1b9927] | 3318 | if (d == 0) |
---|
[a9a6dcb] | 3319 | return N(gcdcAcB); |
---|
[08daea] | 3320 | d0= totaldegree (ppB, Variable (2), Variable (ppB.level())); |
---|
| 3321 | |
---|
| 3322 | if (d0 < d) |
---|
| 3323 | d= d0; |
---|
| 3324 | |
---|
| 3325 | if (d == 0) |
---|
[a9a6dcb] | 3326 | return N(gcdcAcB); |
---|
[08daea] | 3327 | |
---|
| 3328 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH, skeleton; |
---|
| 3329 | CanonicalForm newtonPoly= 1; |
---|
| 3330 | m= gcdlcAlcB; |
---|
| 3331 | G_m= 0; |
---|
| 3332 | H= 0; |
---|
| 3333 | bool fail= false; |
---|
| 3334 | topLevel= false; |
---|
| 3335 | bool inextension= false; |
---|
| 3336 | Variable V_buf= alpha; |
---|
| 3337 | CanonicalForm prim_elem, im_prim_elem; |
---|
| 3338 | CFList source, dest; |
---|
| 3339 | do // first do |
---|
| 3340 | { |
---|
| 3341 | random_element= randomElement (m, V_buf, l, fail); |
---|
| 3342 | if (random_element == 0 && !fail) |
---|
| 3343 | { |
---|
| 3344 | if (!find (l, random_element)) |
---|
| 3345 | l.append (random_element); |
---|
| 3346 | continue; |
---|
| 3347 | } |
---|
| 3348 | if (fail) |
---|
| 3349 | { |
---|
| 3350 | source= CFList(); |
---|
| 3351 | dest= CFList(); |
---|
| 3352 | |
---|
[9ff686] | 3353 | Variable V_buf3= V_buf; |
---|
| 3354 | V_buf= chooseExtension (V_buf); |
---|
[08daea] | 3355 | bool prim_fail= false; |
---|
| 3356 | Variable V_buf2; |
---|
| 3357 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
| 3358 | |
---|
[9ff686] | 3359 | if (V_buf3 != alpha) |
---|
| 3360 | { |
---|
| 3361 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3362 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3363 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
| 3364 | source, dest); |
---|
| 3365 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3366 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3367 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, source, |
---|
| 3368 | dest); |
---|
| 3369 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 3370 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
| 3371 | source, dest); |
---|
| 3372 | } |
---|
| 3373 | |
---|
[08daea] | 3374 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
| 3375 | if (prim_fail) |
---|
| 3376 | ; //ERROR |
---|
| 3377 | else |
---|
| 3378 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
| 3379 | |
---|
| 3380 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
| 3381 | DEBOUTLN (cerr, "getMipo (V_buf2)= " << getMipo (V_buf2)); |
---|
| 3382 | inextension= true; |
---|
[c1b9927] | 3383 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
[08daea] | 3384 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
| 3385 | im_prim_elem, source, dest); |
---|
| 3386 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3387 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3388 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
| 3389 | source, dest); |
---|
| 3390 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3391 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3392 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
| 3393 | source, dest); |
---|
| 3394 | |
---|
| 3395 | fail= false; |
---|
| 3396 | random_element= randomElement (m, V_buf, l, fail ); |
---|
| 3397 | DEBOUTLN (cerr, "fail= " << fail); |
---|
| 3398 | CFList list; |
---|
| 3399 | TIMING_START (gcd_recursion); |
---|
| 3400 | G_random_element= |
---|
| 3401 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), V_buf, |
---|
| 3402 | list, topLevel); |
---|
| 3403 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3404 | "time for recursive call: "); |
---|
| 3405 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3406 | } |
---|
| 3407 | else |
---|
| 3408 | { |
---|
| 3409 | CFList list; |
---|
| 3410 | TIMING_START (gcd_recursion); |
---|
| 3411 | G_random_element= |
---|
| 3412 | sparseGCDFq (ppA(random_element, x), ppB(random_element, x), V_buf, |
---|
| 3413 | list, topLevel); |
---|
| 3414 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3415 | "time for recursive call: "); |
---|
| 3416 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3417 | } |
---|
| 3418 | |
---|
[a76d6fe] | 3419 | if (!G_random_element.inCoeffDomain()) |
---|
| 3420 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 3421 | Variable (G_random_element.level())); |
---|
| 3422 | else |
---|
| 3423 | d0= 0; |
---|
| 3424 | |
---|
[08daea] | 3425 | if (d0 == 0) |
---|
[a9a6dcb] | 3426 | return N(gcdcAcB); |
---|
[08daea] | 3427 | if (d0 > d) |
---|
| 3428 | { |
---|
| 3429 | if (!find (l, random_element)) |
---|
| 3430 | l.append (random_element); |
---|
| 3431 | continue; |
---|
| 3432 | } |
---|
| 3433 | |
---|
| 3434 | G_random_element= |
---|
| 3435 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
| 3436 | * G_random_element; |
---|
| 3437 | |
---|
| 3438 | skeleton= G_random_element; |
---|
[a76d6fe] | 3439 | if (!G_random_element.inCoeffDomain()) |
---|
| 3440 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 3441 | Variable (G_random_element.level())); |
---|
| 3442 | else |
---|
| 3443 | d0= 0; |
---|
| 3444 | |
---|
[08daea] | 3445 | if (d0 < d) |
---|
| 3446 | { |
---|
| 3447 | m= gcdlcAlcB; |
---|
| 3448 | newtonPoly= 1; |
---|
| 3449 | G_m= 0; |
---|
| 3450 | d= d0; |
---|
| 3451 | } |
---|
| 3452 | |
---|
| 3453 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
| 3454 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
| 3455 | { |
---|
| 3456 | cH= uni_content (H); |
---|
| 3457 | ppH= H/cH; |
---|
| 3458 | if (inextension) |
---|
| 3459 | { |
---|
| 3460 | CFList u, v; |
---|
| 3461 | //maybe it's better to test if ppH is an element of F(\alpha) before |
---|
| 3462 | //mapping down |
---|
[c723d80] | 3463 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
[08daea] | 3464 | { |
---|
[c723d80] | 3465 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
| 3466 | ppH= mapDown (ppH, prim_elem, im_prim_elem, alpha, u, v); |
---|
| 3467 | ppH /= Lc(ppH); |
---|
| 3468 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
[08daea] | 3469 | return N(gcdcAcB*ppH); |
---|
| 3470 | } |
---|
| 3471 | } |
---|
[c723d80] | 3472 | else if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
[08daea] | 3473 | return N(gcdcAcB*ppH); |
---|
| 3474 | } |
---|
| 3475 | G_m= H; |
---|
| 3476 | newtonPoly= newtonPoly*(x - random_element); |
---|
| 3477 | m= m*(x - random_element); |
---|
| 3478 | if (!find (l, random_element)) |
---|
| 3479 | l.append (random_element); |
---|
| 3480 | |
---|
[d08ed8] | 3481 | if (getCharacteristic () > 3 && size (skeleton) < 100) |
---|
[08daea] | 3482 | { |
---|
| 3483 | CFArray Monoms; |
---|
| 3484 | CFArray *coeffMonoms= NULL; |
---|
| 3485 | do //second do |
---|
| 3486 | { |
---|
| 3487 | random_element= randomElement (m, V_buf, l, fail); |
---|
| 3488 | if (random_element == 0 && !fail) |
---|
| 3489 | { |
---|
| 3490 | if (!find (l, random_element)) |
---|
| 3491 | l.append (random_element); |
---|
| 3492 | continue; |
---|
| 3493 | } |
---|
| 3494 | if (fail) |
---|
| 3495 | { |
---|
| 3496 | source= CFList(); |
---|
| 3497 | dest= CFList(); |
---|
| 3498 | |
---|
[9ff686] | 3499 | Variable V_buf3= V_buf; |
---|
| 3500 | V_buf= chooseExtension (V_buf); |
---|
[08daea] | 3501 | bool prim_fail= false; |
---|
| 3502 | Variable V_buf2; |
---|
| 3503 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
| 3504 | |
---|
[9ff686] | 3505 | if (V_buf3 != alpha) |
---|
| 3506 | { |
---|
| 3507 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3508 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3509 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
| 3510 | source, dest); |
---|
| 3511 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3512 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3513 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, |
---|
| 3514 | source, dest); |
---|
| 3515 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 3516 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
| 3517 | source, dest); |
---|
| 3518 | } |
---|
| 3519 | |
---|
[08daea] | 3520 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
| 3521 | if (prim_fail) |
---|
| 3522 | ; //ERROR |
---|
| 3523 | else |
---|
| 3524 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
| 3525 | |
---|
| 3526 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
| 3527 | DEBOUTLN (cerr, "getMipo (V_buf2)= " << getMipo (V_buf2)); |
---|
| 3528 | inextension= true; |
---|
[c1b9927] | 3529 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
[08daea] | 3530 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
| 3531 | im_prim_elem, source, dest); |
---|
| 3532 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3533 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3534 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
| 3535 | source, dest); |
---|
| 3536 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3537 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3538 | |
---|
| 3539 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
| 3540 | source, dest); |
---|
| 3541 | |
---|
| 3542 | fail= false; |
---|
| 3543 | random_element= randomElement (m, V_buf, l, fail); |
---|
| 3544 | DEBOUTLN (cerr, "fail= " << fail); |
---|
| 3545 | CFList list; |
---|
| 3546 | TIMING_START (gcd_recursion); |
---|
| 3547 | |
---|
| 3548 | //sparseInterpolation |
---|
| 3549 | bool sparseFail= false; |
---|
| 3550 | if (LC (skeleton).inCoeffDomain()) |
---|
[c1b9927] | 3551 | G_random_element= |
---|
[08daea] | 3552 | monicSparseInterpol (ppA (random_element, x), ppB(random_element,x), |
---|
| 3553 | skeleton,V_buf, sparseFail, coeffMonoms,Monoms); |
---|
| 3554 | else |
---|
| 3555 | G_random_element= |
---|
| 3556 | nonMonicSparseInterpol (ppA(random_element,x),ppB(random_element,x), |
---|
| 3557 | skeleton, V_buf, sparseFail, coeffMonoms, |
---|
| 3558 | Monoms); |
---|
| 3559 | if (sparseFail) |
---|
| 3560 | break; |
---|
| 3561 | |
---|
| 3562 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3563 | "time for recursive call: "); |
---|
| 3564 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3565 | } |
---|
| 3566 | else |
---|
| 3567 | { |
---|
| 3568 | CFList list; |
---|
| 3569 | TIMING_START (gcd_recursion); |
---|
| 3570 | bool sparseFail= false; |
---|
| 3571 | if (LC (skeleton).inCoeffDomain()) |
---|
[c1b9927] | 3572 | G_random_element= |
---|
[08daea] | 3573 | monicSparseInterpol (ppA (random_element, x),ppB(random_element, x), |
---|
| 3574 | skeleton,V_buf, sparseFail,coeffMonoms, Monoms); |
---|
| 3575 | else |
---|
| 3576 | G_random_element= |
---|
| 3577 | nonMonicSparseInterpol (ppA(random_element,x),ppB(random_element,x), |
---|
[c1b9927] | 3578 | skeleton, V_buf, sparseFail, coeffMonoms, |
---|
[08daea] | 3579 | Monoms); |
---|
| 3580 | if (sparseFail) |
---|
| 3581 | break; |
---|
| 3582 | |
---|
| 3583 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3584 | "time for recursive call: "); |
---|
| 3585 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3586 | } |
---|
| 3587 | |
---|
[a76d6fe] | 3588 | if (!G_random_element.inCoeffDomain()) |
---|
| 3589 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 3590 | Variable (G_random_element.level())); |
---|
| 3591 | else |
---|
| 3592 | d0= 0; |
---|
| 3593 | |
---|
[08daea] | 3594 | if (d0 == 0) |
---|
[a9a6dcb] | 3595 | return N(gcdcAcB); |
---|
[08daea] | 3596 | if (d0 > d) |
---|
| 3597 | { |
---|
| 3598 | if (!find (l, random_element)) |
---|
| 3599 | l.append (random_element); |
---|
| 3600 | continue; |
---|
| 3601 | } |
---|
| 3602 | |
---|
| 3603 | G_random_element= |
---|
| 3604 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
| 3605 | * G_random_element; |
---|
| 3606 | |
---|
[a76d6fe] | 3607 | if (!G_random_element.inCoeffDomain()) |
---|
| 3608 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 3609 | Variable (G_random_element.level())); |
---|
| 3610 | else |
---|
| 3611 | d0= 0; |
---|
| 3612 | |
---|
[08daea] | 3613 | if (d0 < d) |
---|
| 3614 | { |
---|
| 3615 | m= gcdlcAlcB; |
---|
| 3616 | newtonPoly= 1; |
---|
| 3617 | G_m= 0; |
---|
| 3618 | d= d0; |
---|
| 3619 | } |
---|
| 3620 | |
---|
| 3621 | TIMING_START (newton_interpolation); |
---|
| 3622 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
| 3623 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
| 3624 | "time for newton interpolation: "); |
---|
| 3625 | |
---|
| 3626 | //termination test |
---|
| 3627 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
| 3628 | { |
---|
| 3629 | cH= uni_content (H); |
---|
| 3630 | ppH= H/cH; |
---|
| 3631 | if (inextension) |
---|
| 3632 | { |
---|
| 3633 | CFList u, v; |
---|
| 3634 | //maybe it's better to test if ppH is an element of F(\alpha) before |
---|
| 3635 | //mapping down |
---|
[c723d80] | 3636 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
[08daea] | 3637 | { |
---|
[c723d80] | 3638 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
| 3639 | ppH= mapDown (ppH, prim_elem, im_prim_elem, alpha, u, v); |
---|
| 3640 | ppH /= Lc(ppH); |
---|
| 3641 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
[08daea] | 3642 | return N(gcdcAcB*ppH); |
---|
| 3643 | } |
---|
| 3644 | } |
---|
[c723d80] | 3645 | else if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
[08daea] | 3646 | { |
---|
| 3647 | return N(gcdcAcB*ppH); |
---|
| 3648 | } |
---|
| 3649 | } |
---|
| 3650 | |
---|
| 3651 | G_m= H; |
---|
| 3652 | newtonPoly= newtonPoly*(x - random_element); |
---|
| 3653 | m= m*(x - random_element); |
---|
| 3654 | if (!find (l, random_element)) |
---|
| 3655 | l.append (random_element); |
---|
| 3656 | |
---|
| 3657 | } while (1); |
---|
| 3658 | } |
---|
| 3659 | } while (1); |
---|
| 3660 | } |
---|
| 3661 | |
---|
| 3662 | CanonicalForm sparseGCDFp (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 3663 | bool& topLevel, CFList& l) |
---|
| 3664 | { |
---|
| 3665 | CanonicalForm A= F; |
---|
| 3666 | CanonicalForm B= G; |
---|
| 3667 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
| 3668 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
| 3669 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
| 3670 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
| 3671 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
| 3672 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
| 3673 | if (F == G) return F/Lc(F); |
---|
| 3674 | |
---|
| 3675 | CFMap M,N; |
---|
| 3676 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
| 3677 | |
---|
| 3678 | if (best_level == 0) return B.genOne(); |
---|
| 3679 | |
---|
| 3680 | A= M(A); |
---|
| 3681 | B= M(B); |
---|
| 3682 | |
---|
| 3683 | Variable x= Variable (1); |
---|
| 3684 | |
---|
[c1b9927] | 3685 | //univariate case |
---|
[08daea] | 3686 | if (A.isUnivariate() && B.isUnivariate()) |
---|
| 3687 | return N (gcd (A, B)); |
---|
| 3688 | |
---|
| 3689 | CanonicalForm cA, cB; // content of A and B |
---|
| 3690 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
| 3691 | CanonicalForm gcdcAcB; |
---|
[ea5ff1d] | 3692 | |
---|
| 3693 | cA = uni_content (A); |
---|
| 3694 | cB = uni_content (B); |
---|
| 3695 | gcdcAcB= gcd (cA, cB); |
---|
| 3696 | ppA= A/cA; |
---|
| 3697 | ppB= B/cB; |
---|
[08daea] | 3698 | |
---|
| 3699 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
| 3700 | CanonicalForm gcdlcAlcB; |
---|
| 3701 | lcA= uni_lcoeff (ppA); |
---|
| 3702 | lcB= uni_lcoeff (ppB); |
---|
| 3703 | |
---|
| 3704 | if (fdivides (lcA, lcB)) |
---|
| 3705 | { |
---|
| 3706 | if (fdivides (A, B)) |
---|
| 3707 | return F/Lc(F); |
---|
| 3708 | } |
---|
| 3709 | if (fdivides (lcB, lcA)) |
---|
| 3710 | { |
---|
| 3711 | if (fdivides (B, A)) |
---|
| 3712 | return G/Lc(G); |
---|
| 3713 | } |
---|
| 3714 | |
---|
| 3715 | gcdlcAlcB= gcd (lcA, lcB); |
---|
| 3716 | |
---|
| 3717 | int d= totaldegree (ppA, Variable (2), Variable (ppA.level())); |
---|
| 3718 | int d0; |
---|
| 3719 | |
---|
| 3720 | if (d == 0) |
---|
[a9a6dcb] | 3721 | return N(gcdcAcB); |
---|
| 3722 | |
---|
[08daea] | 3723 | d0= totaldegree (ppB, Variable (2), Variable (ppB.level())); |
---|
| 3724 | |
---|
| 3725 | if (d0 < d) |
---|
| 3726 | d= d0; |
---|
| 3727 | |
---|
| 3728 | if (d == 0) |
---|
[a9a6dcb] | 3729 | return N(gcdcAcB); |
---|
[08daea] | 3730 | |
---|
| 3731 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH, skeleton; |
---|
| 3732 | CanonicalForm newtonPoly= 1; |
---|
| 3733 | m= gcdlcAlcB; |
---|
| 3734 | G_m= 0; |
---|
| 3735 | H= 0; |
---|
| 3736 | bool fail= false; |
---|
| 3737 | topLevel= false; |
---|
| 3738 | bool inextension= false; |
---|
| 3739 | Variable V_buf, alpha; |
---|
| 3740 | CanonicalForm prim_elem, im_prim_elem; |
---|
| 3741 | CFList source, dest; |
---|
| 3742 | do //first do |
---|
| 3743 | { |
---|
| 3744 | if (inextension) |
---|
[9ff686] | 3745 | random_element= randomElement (m, V_buf, l, fail); |
---|
[08daea] | 3746 | else |
---|
| 3747 | random_element= FpRandomElement (m, l, fail); |
---|
| 3748 | if (random_element == 0 && !fail) |
---|
| 3749 | { |
---|
| 3750 | if (!find (l, random_element)) |
---|
| 3751 | l.append (random_element); |
---|
| 3752 | continue; |
---|
| 3753 | } |
---|
| 3754 | |
---|
| 3755 | if (!fail && !inextension) |
---|
| 3756 | { |
---|
| 3757 | CFList list; |
---|
| 3758 | TIMING_START (gcd_recursion); |
---|
| 3759 | G_random_element= |
---|
| 3760 | sparseGCDFp (ppA (random_element,x), ppB (random_element,x), topLevel, |
---|
| 3761 | list); |
---|
| 3762 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3763 | "time for recursive call: "); |
---|
| 3764 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3765 | } |
---|
| 3766 | else if (!fail && inextension) |
---|
| 3767 | { |
---|
| 3768 | CFList list; |
---|
| 3769 | TIMING_START (gcd_recursion); |
---|
| 3770 | G_random_element= |
---|
| 3771 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), alpha, |
---|
| 3772 | list, topLevel); |
---|
| 3773 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3774 | "time for recursive call: "); |
---|
| 3775 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3776 | } |
---|
| 3777 | else if (fail && !inextension) |
---|
| 3778 | { |
---|
| 3779 | source= CFList(); |
---|
| 3780 | dest= CFList(); |
---|
| 3781 | CFList list; |
---|
| 3782 | CanonicalForm mipo; |
---|
| 3783 | int deg= 2; |
---|
| 3784 | do |
---|
| 3785 | { |
---|
| 3786 | mipo= randomIrredpoly (deg, x); |
---|
| 3787 | alpha= rootOf (mipo); |
---|
| 3788 | inextension= true; |
---|
| 3789 | fail= false; |
---|
[c1b9927] | 3790 | random_element= randomElement (m, alpha, l, fail); |
---|
[08daea] | 3791 | deg++; |
---|
| 3792 | } while (fail); |
---|
[9ff686] | 3793 | V_buf= alpha; |
---|
[08daea] | 3794 | list= CFList(); |
---|
| 3795 | TIMING_START (gcd_recursion); |
---|
| 3796 | G_random_element= |
---|
| 3797 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), alpha, |
---|
| 3798 | list, topLevel); |
---|
| 3799 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3800 | "time for recursive call: "); |
---|
| 3801 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3802 | } |
---|
| 3803 | else if (fail && inextension) |
---|
| 3804 | { |
---|
| 3805 | source= CFList(); |
---|
| 3806 | dest= CFList(); |
---|
[9ff686] | 3807 | |
---|
| 3808 | Variable V_buf3= V_buf; |
---|
| 3809 | V_buf= chooseExtension (V_buf); |
---|
[08daea] | 3810 | bool prim_fail= false; |
---|
| 3811 | Variable V_buf2; |
---|
| 3812 | CanonicalForm prim_elem, im_prim_elem; |
---|
| 3813 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
| 3814 | |
---|
[9ff686] | 3815 | if (V_buf3 != alpha) |
---|
| 3816 | { |
---|
| 3817 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3818 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3819 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, source, |
---|
| 3820 | dest); |
---|
| 3821 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3822 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3823 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, source, |
---|
| 3824 | dest); |
---|
| 3825 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 3826 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
| 3827 | source, dest); |
---|
| 3828 | } |
---|
| 3829 | |
---|
[08daea] | 3830 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
| 3831 | if (prim_fail) |
---|
| 3832 | ; //ERROR |
---|
| 3833 | else |
---|
| 3834 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
| 3835 | |
---|
| 3836 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
| 3837 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
| 3838 | |
---|
| 3839 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 3840 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
| 3841 | im_prim_elem, source, dest); |
---|
| 3842 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3843 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3844 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
| 3845 | source, dest); |
---|
| 3846 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3847 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3848 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
| 3849 | source, dest); |
---|
| 3850 | fail= false; |
---|
| 3851 | random_element= randomElement (m, V_buf, l, fail ); |
---|
| 3852 | DEBOUTLN (cerr, "fail= " << fail); |
---|
| 3853 | CFList list; |
---|
| 3854 | TIMING_START (gcd_recursion); |
---|
| 3855 | G_random_element= |
---|
| 3856 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), V_buf, |
---|
| 3857 | list, topLevel); |
---|
| 3858 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3859 | "time for recursive call: "); |
---|
| 3860 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3861 | } |
---|
| 3862 | |
---|
[a76d6fe] | 3863 | if (!G_random_element.inCoeffDomain()) |
---|
| 3864 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 3865 | Variable (G_random_element.level())); |
---|
| 3866 | else |
---|
| 3867 | d0= 0; |
---|
| 3868 | |
---|
[08daea] | 3869 | if (d0 == 0) |
---|
[a9a6dcb] | 3870 | return N(gcdcAcB); |
---|
[08daea] | 3871 | if (d0 > d) |
---|
| 3872 | { |
---|
| 3873 | if (!find (l, random_element)) |
---|
| 3874 | l.append (random_element); |
---|
| 3875 | continue; |
---|
| 3876 | } |
---|
| 3877 | |
---|
| 3878 | G_random_element= |
---|
| 3879 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
| 3880 | * G_random_element; |
---|
| 3881 | |
---|
| 3882 | skeleton= G_random_element; |
---|
| 3883 | |
---|
[a76d6fe] | 3884 | if (!G_random_element.inCoeffDomain()) |
---|
| 3885 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 3886 | Variable (G_random_element.level())); |
---|
| 3887 | else |
---|
| 3888 | d0= 0; |
---|
| 3889 | |
---|
[08daea] | 3890 | if (d0 < d) |
---|
| 3891 | { |
---|
| 3892 | m= gcdlcAlcB; |
---|
| 3893 | newtonPoly= 1; |
---|
| 3894 | G_m= 0; |
---|
| 3895 | d= d0; |
---|
| 3896 | } |
---|
| 3897 | |
---|
| 3898 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
| 3899 | |
---|
| 3900 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
| 3901 | { |
---|
| 3902 | cH= uni_content (H); |
---|
| 3903 | ppH= H/cH; |
---|
| 3904 | ppH /= Lc (ppH); |
---|
| 3905 | DEBOUTLN (cerr, "ppH= " << ppH); |
---|
| 3906 | |
---|
[c723d80] | 3907 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
[08daea] | 3908 | return N(gcdcAcB*ppH); |
---|
| 3909 | } |
---|
| 3910 | G_m= H; |
---|
| 3911 | newtonPoly= newtonPoly*(x - random_element); |
---|
| 3912 | m= m*(x - random_element); |
---|
| 3913 | if (!find (l, random_element)) |
---|
| 3914 | l.append (random_element); |
---|
| 3915 | |
---|
[d08ed8] | 3916 | if ((getCharacteristic() > 3 && size (skeleton) < 100)) |
---|
[08daea] | 3917 | { |
---|
| 3918 | CFArray Monoms; |
---|
| 3919 | CFArray* coeffMonoms= NULL; |
---|
| 3920 | |
---|
| 3921 | do //second do |
---|
| 3922 | { |
---|
| 3923 | if (inextension) |
---|
| 3924 | random_element= randomElement (m, alpha, l, fail); |
---|
| 3925 | else |
---|
| 3926 | random_element= FpRandomElement (m, l, fail); |
---|
| 3927 | if (random_element == 0 && !fail) |
---|
| 3928 | { |
---|
| 3929 | if (!find (l, random_element)) |
---|
| 3930 | l.append (random_element); |
---|
| 3931 | continue; |
---|
| 3932 | } |
---|
| 3933 | |
---|
| 3934 | bool sparseFail= false; |
---|
| 3935 | if (!fail && !inextension) |
---|
| 3936 | { |
---|
| 3937 | CFList list; |
---|
| 3938 | TIMING_START (gcd_recursion); |
---|
| 3939 | if (LC (skeleton).inCoeffDomain()) |
---|
| 3940 | G_random_element= |
---|
| 3941 | monicSparseInterpol(ppA(random_element, x), ppB (random_element, x), |
---|
| 3942 | skeleton, Variable(1), sparseFail, coeffMonoms, |
---|
| 3943 | Monoms); |
---|
| 3944 | else |
---|
| 3945 | G_random_element= |
---|
| 3946 | nonMonicSparseInterpol(ppA(random_element,x), ppB(random_element,x), |
---|
| 3947 | skeleton, Variable (1), sparseFail, |
---|
| 3948 | coeffMonoms, Monoms); |
---|
| 3949 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3950 | "time for recursive call: "); |
---|
| 3951 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3952 | } |
---|
| 3953 | else if (!fail && inextension) |
---|
| 3954 | { |
---|
| 3955 | CFList list; |
---|
| 3956 | TIMING_START (gcd_recursion); |
---|
| 3957 | if (LC (skeleton).inCoeffDomain()) |
---|
| 3958 | G_random_element= |
---|
| 3959 | monicSparseInterpol(ppA (random_element,x), ppB (random_element, x), |
---|
| 3960 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
| 3961 | Monoms); |
---|
| 3962 | else |
---|
| 3963 | G_random_element= |
---|
| 3964 | nonMonicSparseInterpol(ppA(random_element,x), ppB(random_element,x), |
---|
| 3965 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
| 3966 | Monoms); |
---|
| 3967 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3968 | "time for recursive call: "); |
---|
| 3969 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3970 | } |
---|
| 3971 | else if (fail && !inextension) |
---|
| 3972 | { |
---|
| 3973 | source= CFList(); |
---|
| 3974 | dest= CFList(); |
---|
| 3975 | CFList list; |
---|
| 3976 | CanonicalForm mipo; |
---|
| 3977 | int deg= 2; |
---|
[c1b9927] | 3978 | do |
---|
[08daea] | 3979 | { |
---|
| 3980 | mipo= randomIrredpoly (deg, x); |
---|
| 3981 | alpha= rootOf (mipo); |
---|
| 3982 | inextension= true; |
---|
| 3983 | fail= false; |
---|
| 3984 | random_element= randomElement (m, alpha, l, fail); |
---|
| 3985 | deg++; |
---|
| 3986 | } while (fail); |
---|
[9ff686] | 3987 | V_buf= alpha; |
---|
[08daea] | 3988 | list= CFList(); |
---|
| 3989 | TIMING_START (gcd_recursion); |
---|
| 3990 | if (LC (skeleton).inCoeffDomain()) |
---|
| 3991 | G_random_element= |
---|
| 3992 | monicSparseInterpol (ppA (random_element,x), ppB (random_element,x), |
---|
| 3993 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
| 3994 | Monoms); |
---|
| 3995 | else |
---|
| 3996 | G_random_element= |
---|
| 3997 | nonMonicSparseInterpol(ppA(random_element,x), ppB(random_element,x), |
---|
| 3998 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
| 3999 | Monoms); |
---|
| 4000 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 4001 | "time for recursive call: "); |
---|
| 4002 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 4003 | } |
---|
| 4004 | else if (fail && inextension) |
---|
| 4005 | { |
---|
| 4006 | source= CFList(); |
---|
| 4007 | dest= CFList(); |
---|
[9ff686] | 4008 | |
---|
| 4009 | Variable V_buf3= V_buf; |
---|
| 4010 | V_buf= chooseExtension (V_buf); |
---|
[08daea] | 4011 | bool prim_fail= false; |
---|
| 4012 | Variable V_buf2; |
---|
| 4013 | CanonicalForm prim_elem, im_prim_elem; |
---|
| 4014 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
| 4015 | |
---|
[9ff686] | 4016 | if (V_buf3 != alpha) |
---|
| 4017 | { |
---|
| 4018 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 4019 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 4020 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
| 4021 | source, dest); |
---|
| 4022 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 4023 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 4024 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, |
---|
| 4025 | source, dest); |
---|
| 4026 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 4027 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
| 4028 | source, dest); |
---|
| 4029 | } |
---|
| 4030 | |
---|
[08daea] | 4031 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
| 4032 | if (prim_fail) |
---|
| 4033 | ; //ERROR |
---|
| 4034 | else |
---|
| 4035 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
| 4036 | |
---|
| 4037 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
| 4038 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
| 4039 | |
---|
| 4040 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 4041 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
| 4042 | im_prim_elem, source, dest); |
---|
| 4043 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 4044 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 4045 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
| 4046 | source, dest); |
---|
| 4047 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 4048 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 4049 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
| 4050 | source, dest); |
---|
| 4051 | fail= false; |
---|
| 4052 | random_element= randomElement (m, V_buf, l, fail ); |
---|
| 4053 | DEBOUTLN (cerr, "fail= " << fail); |
---|
| 4054 | CFList list; |
---|
| 4055 | TIMING_START (gcd_recursion); |
---|
| 4056 | if (LC (skeleton).inCoeffDomain()) |
---|
| 4057 | G_random_element= |
---|
| 4058 | monicSparseInterpol (ppA (random_element, x), ppB (random_element, x), |
---|
| 4059 | skeleton, V_buf, sparseFail, coeffMonoms, |
---|
| 4060 | Monoms); |
---|
| 4061 | else |
---|
| 4062 | G_random_element= |
---|
| 4063 | nonMonicSparseInterpol (ppA(random_element,x), ppB(random_element,x), |
---|
| 4064 | skeleton, V_buf, sparseFail, |
---|
| 4065 | coeffMonoms, Monoms); |
---|
| 4066 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 4067 | "time for recursive call: "); |
---|
| 4068 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 4069 | } |
---|
| 4070 | |
---|
| 4071 | if (sparseFail) |
---|
| 4072 | break; |
---|
| 4073 | |
---|
[a76d6fe] | 4074 | if (!G_random_element.inCoeffDomain()) |
---|
| 4075 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 4076 | Variable (G_random_element.level())); |
---|
| 4077 | else |
---|
| 4078 | d0= 0; |
---|
| 4079 | |
---|
[08daea] | 4080 | if (d0 == 0) |
---|
[a9a6dcb] | 4081 | return N(gcdcAcB); |
---|
[08daea] | 4082 | if (d0 > d) |
---|
| 4083 | { |
---|
| 4084 | if (!find (l, random_element)) |
---|
| 4085 | l.append (random_element); |
---|
| 4086 | continue; |
---|
| 4087 | } |
---|
| 4088 | |
---|
| 4089 | G_random_element= |
---|
| 4090 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
| 4091 | * G_random_element; |
---|
| 4092 | |
---|
[a76d6fe] | 4093 | if (!G_random_element.inCoeffDomain()) |
---|
| 4094 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 4095 | Variable (G_random_element.level())); |
---|
| 4096 | else |
---|
| 4097 | d0= 0; |
---|
| 4098 | |
---|
[08daea] | 4099 | if (d0 < d) |
---|
| 4100 | { |
---|
| 4101 | m= gcdlcAlcB; |
---|
| 4102 | newtonPoly= 1; |
---|
| 4103 | G_m= 0; |
---|
| 4104 | d= d0; |
---|
| 4105 | } |
---|
| 4106 | |
---|
| 4107 | TIMING_START (newton_interpolation); |
---|
| 4108 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
| 4109 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
| 4110 | "time for newton interpolation: "); |
---|
| 4111 | |
---|
| 4112 | //termination test |
---|
| 4113 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
| 4114 | { |
---|
| 4115 | cH= uni_content (H); |
---|
| 4116 | ppH= H/cH; |
---|
| 4117 | ppH /= Lc (ppH); |
---|
| 4118 | DEBOUTLN (cerr, "ppH= " << ppH); |
---|
[c723d80] | 4119 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
[08daea] | 4120 | return N(gcdcAcB*ppH); |
---|
| 4121 | } |
---|
| 4122 | |
---|
| 4123 | G_m= H; |
---|
| 4124 | newtonPoly= newtonPoly*(x - random_element); |
---|
| 4125 | m= m*(x - random_element); |
---|
| 4126 | if (!find (l, random_element)) |
---|
| 4127 | l.append (random_element); |
---|
| 4128 | |
---|
| 4129 | } while (1); //end of second do |
---|
| 4130 | } |
---|
| 4131 | } while (1); //end of first do |
---|
| 4132 | } |
---|
| 4133 | |
---|
| 4134 | static inline |
---|
| 4135 | int compress4EZGCD (const CanonicalForm& F, const CanonicalForm& G, CFMap & M, |
---|
| 4136 | CFMap & N, int& both_non_zero) |
---|
| 4137 | { |
---|
| 4138 | int n= tmax (F.level(), G.level()); |
---|
| 4139 | int * degsf= new int [n + 1]; |
---|
| 4140 | int * degsg= new int [n + 1]; |
---|
| 4141 | |
---|
| 4142 | for (int i = 0; i <= n; i++) |
---|
| 4143 | degsf[i]= degsg[i]= 0; |
---|
| 4144 | |
---|
| 4145 | degsf= degrees (F, degsf); |
---|
| 4146 | degsg= degrees (G, degsg); |
---|
| 4147 | |
---|
| 4148 | both_non_zero= 0; |
---|
| 4149 | int f_zero= 0; |
---|
| 4150 | int g_zero= 0; |
---|
| 4151 | |
---|
| 4152 | for (int i= 1; i <= n; i++) |
---|
| 4153 | { |
---|
| 4154 | if (degsf[i] != 0 && degsg[i] != 0) |
---|
| 4155 | { |
---|
| 4156 | both_non_zero++; |
---|
| 4157 | continue; |
---|
| 4158 | } |
---|
| 4159 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
---|
| 4160 | { |
---|
| 4161 | f_zero++; |
---|
| 4162 | continue; |
---|
| 4163 | } |
---|
| 4164 | if (degsg[i] == 0 && degsf[i] && i <= F.level()) |
---|
| 4165 | { |
---|
| 4166 | g_zero++; |
---|
| 4167 | continue; |
---|
| 4168 | } |
---|
| 4169 | } |
---|
| 4170 | |
---|
[618da5] | 4171 | if (both_non_zero == 0) |
---|
| 4172 | { |
---|
| 4173 | delete [] degsf; |
---|
| 4174 | delete [] degsg; |
---|
| 4175 | return 0; |
---|
| 4176 | } |
---|
[08daea] | 4177 | |
---|
| 4178 | // map Variables which do not occur in both polynomials to higher levels |
---|
| 4179 | int k= 1; |
---|
| 4180 | int l= 1; |
---|
| 4181 | for (int i= 1; i <= n; i++) |
---|
| 4182 | { |
---|
| 4183 | if (degsf[i] != 0 && degsg[i] == 0 && i <= F.level()) |
---|
| 4184 | { |
---|
| 4185 | if (k + both_non_zero != i) |
---|
| 4186 | { |
---|
| 4187 | M.newpair (Variable (i), Variable (k + both_non_zero)); |
---|
| 4188 | N.newpair (Variable (k + both_non_zero), Variable (i)); |
---|
| 4189 | } |
---|
| 4190 | k++; |
---|
| 4191 | } |
---|
| 4192 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
---|
| 4193 | { |
---|
| 4194 | if (l + g_zero + both_non_zero != i) |
---|
| 4195 | { |
---|
| 4196 | M.newpair (Variable (i), Variable (l + g_zero + both_non_zero)); |
---|
| 4197 | N.newpair (Variable (l + g_zero + both_non_zero), Variable (i)); |
---|
| 4198 | } |
---|
| 4199 | l++; |
---|
| 4200 | } |
---|
| 4201 | } |
---|
| 4202 | |
---|
| 4203 | // sort Variables x_{i} in decreasing order of |
---|
| 4204 | // min(deg_{x_{i}}(f),deg_{x_{i}}(g)) |
---|
| 4205 | int m= tmin (F.level(), G.level()); |
---|
| 4206 | int max_min_deg; |
---|
| 4207 | k= both_non_zero; |
---|
| 4208 | l= 0; |
---|
| 4209 | int i= 1; |
---|
| 4210 | while (k > 0) |
---|
| 4211 | { |
---|
| 4212 | max_min_deg= tmin (degsf[i], degsg[i]); |
---|
| 4213 | while (max_min_deg == 0) |
---|
| 4214 | { |
---|
| 4215 | i++; |
---|
| 4216 | max_min_deg= tmin (degsf[i], degsg[i]); |
---|
| 4217 | } |
---|
| 4218 | for (int j= i + 1; j <= m; j++) |
---|
| 4219 | { |
---|
| 4220 | if ((tmin (degsf[j],degsg[j]) < max_min_deg) && |
---|
| 4221 | (tmin (degsf[j], degsg[j]) != 0)) |
---|
| 4222 | { |
---|
| 4223 | max_min_deg= tmin (degsf[j], degsg[j]); |
---|
| 4224 | l= j; |
---|
| 4225 | } |
---|
| 4226 | } |
---|
| 4227 | |
---|
| 4228 | if (l != 0) |
---|
| 4229 | { |
---|
| 4230 | if (l != k) |
---|
| 4231 | { |
---|
| 4232 | M.newpair (Variable (l), Variable(k)); |
---|
| 4233 | N.newpair (Variable (k), Variable(l)); |
---|
| 4234 | degsf[l]= 0; |
---|
| 4235 | degsg[l]= 0; |
---|
| 4236 | l= 0; |
---|
| 4237 | } |
---|
| 4238 | else |
---|
| 4239 | { |
---|
| 4240 | degsf[l]= 0; |
---|
| 4241 | degsg[l]= 0; |
---|
| 4242 | l= 0; |
---|
| 4243 | } |
---|
| 4244 | } |
---|
| 4245 | else if (l == 0) |
---|
| 4246 | { |
---|
| 4247 | if (i != k) |
---|
| 4248 | { |
---|
| 4249 | M.newpair (Variable (i), Variable (k)); |
---|
| 4250 | N.newpair (Variable (k), Variable (i)); |
---|
| 4251 | degsf[i]= 0; |
---|
| 4252 | degsg[i]= 0; |
---|
| 4253 | } |
---|
| 4254 | else |
---|
| 4255 | { |
---|
| 4256 | degsf[i]= 0; |
---|
| 4257 | degsg[i]= 0; |
---|
| 4258 | } |
---|
| 4259 | i++; |
---|
| 4260 | } |
---|
| 4261 | k--; |
---|
| 4262 | } |
---|
| 4263 | |
---|
| 4264 | delete [] degsf; |
---|
| 4265 | delete [] degsg; |
---|
| 4266 | |
---|
| 4267 | return both_non_zero; |
---|
| 4268 | } |
---|
| 4269 | |
---|
| 4270 | static inline |
---|
| 4271 | CanonicalForm myShift2Zero (const CanonicalForm& F, CFList& Feval, |
---|
| 4272 | const CFList& evaluation) |
---|
| 4273 | { |
---|
| 4274 | CanonicalForm A= F; |
---|
| 4275 | int k= 2; |
---|
| 4276 | for (CFListIterator i= evaluation; i.hasItem(); i++, k++) |
---|
| 4277 | A= A (Variable (k) + i.getItem(), k); |
---|
| 4278 | |
---|
| 4279 | CanonicalForm buf= A; |
---|
| 4280 | Feval= CFList(); |
---|
| 4281 | Feval.append (buf); |
---|
| 4282 | for (k= evaluation.length() + 1; k > 2; k--) |
---|
| 4283 | { |
---|
| 4284 | buf= mod (buf, Variable (k)); |
---|
| 4285 | Feval.insert (buf); |
---|
| 4286 | } |
---|
| 4287 | return A; |
---|
| 4288 | } |
---|
| 4289 | |
---|
| 4290 | static inline |
---|
| 4291 | CanonicalForm myReverseShift (const CanonicalForm& F, const CFList& evaluation) |
---|
| 4292 | { |
---|
| 4293 | int l= evaluation.length() + 1; |
---|
| 4294 | CanonicalForm result= F; |
---|
| 4295 | CFListIterator j= evaluation; |
---|
| 4296 | for (int i= 2; i < l + 1; i++, j++) |
---|
| 4297 | { |
---|
| 4298 | if (F.level() < i) |
---|
| 4299 | continue; |
---|
| 4300 | result= result (Variable (i) - j.getItem(), i); |
---|
| 4301 | } |
---|
| 4302 | return result; |
---|
| 4303 | } |
---|
| 4304 | |
---|
| 4305 | static inline |
---|
[9ff686] | 4306 | Evaluation optimize4Lift (const CanonicalForm& F, CFMap & M, |
---|
| 4307 | CFMap & N, const Evaluation& A) |
---|
| 4308 | { |
---|
| 4309 | int n= F.level(); |
---|
| 4310 | int * degsf= new int [n + 1]; |
---|
| 4311 | |
---|
| 4312 | for (int i = 0; i <= n; i++) |
---|
| 4313 | degsf[i]= 0; |
---|
| 4314 | |
---|
| 4315 | degsf= degrees (F, degsf); |
---|
| 4316 | |
---|
| 4317 | Evaluation result= Evaluation (A.min(), A.max()); |
---|
| 4318 | ASSERT (A.min() == 2, "expected A.min() == 2"); |
---|
| 4319 | int max_deg; |
---|
| 4320 | int k= n; |
---|
| 4321 | int l= 1; |
---|
| 4322 | int i= 2; |
---|
| 4323 | int pos= 2; |
---|
| 4324 | while (k > 1) |
---|
| 4325 | { |
---|
| 4326 | max_deg= degsf [i]; |
---|
| 4327 | while (max_deg == 0) |
---|
| 4328 | { |
---|
| 4329 | i++; |
---|
| 4330 | max_deg= degsf [i]; |
---|
| 4331 | } |
---|
| 4332 | l= i; |
---|
| 4333 | for (int j= i + 1; j <= n; j++) |
---|
| 4334 | { |
---|
| 4335 | if (degsf[j] > max_deg) |
---|
| 4336 | { |
---|
| 4337 | max_deg= degsf[j]; |
---|
| 4338 | l= j; |
---|
| 4339 | } |
---|
| 4340 | } |
---|
| 4341 | |
---|
| 4342 | if (l <= n) |
---|
| 4343 | { |
---|
| 4344 | if (l != pos) |
---|
| 4345 | { |
---|
| 4346 | result.setValue (pos, A [l]); |
---|
| 4347 | M.newpair (Variable (l), Variable (pos)); |
---|
| 4348 | N.newpair (Variable (pos), Variable (l)); |
---|
| 4349 | degsf[l]= 0; |
---|
| 4350 | l= 2; |
---|
| 4351 | if (k == 2 && n == 3) |
---|
| 4352 | { |
---|
| 4353 | result.setValue (l, A [pos]); |
---|
| 4354 | M.newpair (Variable (pos), Variable (l)); |
---|
| 4355 | N.newpair (Variable (l), Variable (pos)); |
---|
| 4356 | degsf[pos]= 0; |
---|
| 4357 | } |
---|
| 4358 | } |
---|
| 4359 | else |
---|
| 4360 | { |
---|
| 4361 | result.setValue (l, A [l]); |
---|
| 4362 | degsf [l]= 0; |
---|
| 4363 | } |
---|
| 4364 | } |
---|
| 4365 | pos++; |
---|
| 4366 | k--; |
---|
| 4367 | l= 2; |
---|
| 4368 | } |
---|
| 4369 | |
---|
| 4370 | delete [] degsf; |
---|
| 4371 | |
---|
| 4372 | return result; |
---|
| 4373 | } |
---|
| 4374 | |
---|
| 4375 | static inline |
---|
| 4376 | int Hensel_P (const CanonicalForm & UU, CFArray & G, const Evaluation & AA, |
---|
[0349c20] | 4377 | const CFArray& LeadCoeffs ) |
---|
[08daea] | 4378 | { |
---|
| 4379 | CFList factors; |
---|
| 4380 | factors.append (G[1]); |
---|
| 4381 | factors.append (G[2]); |
---|
[9ff686] | 4382 | |
---|
| 4383 | CFMap NN, MM; |
---|
| 4384 | Evaluation A= optimize4Lift (UU, MM, NN, AA); |
---|
| 4385 | |
---|
| 4386 | CanonicalForm U= MM (UU); |
---|
| 4387 | CFArray LCs= CFArray (1,2); |
---|
| 4388 | LCs [1]= MM (LeadCoeffs [1]); |
---|
| 4389 | LCs [2]= MM (LeadCoeffs [2]); |
---|
| 4390 | |
---|
[08daea] | 4391 | CFList evaluation; |
---|
| 4392 | for (int i= A.min(); i <= A.max(); i++) |
---|
| 4393 | evaluation.append (A [i]); |
---|
| 4394 | CFList UEval; |
---|
| 4395 | CanonicalForm shiftedU= myShift2Zero (U, UEval, evaluation); |
---|
[9ff686] | 4396 | |
---|
| 4397 | if (size (shiftedU)/getNumVars (U) > 500) |
---|
| 4398 | return -1; |
---|
| 4399 | |
---|
[08daea] | 4400 | CFArray shiftedLCs= CFArray (2); |
---|
| 4401 | CFList shiftedLCsEval1, shiftedLCsEval2; |
---|
| 4402 | shiftedLCs[0]= myShift2Zero (LCs[1], shiftedLCsEval1, evaluation); |
---|
| 4403 | shiftedLCs[1]= myShift2Zero (LCs[2], shiftedLCsEval2, evaluation); |
---|
| 4404 | factors.insert (1); |
---|
| 4405 | int liftBound= degree (UEval.getLast(), 2) + 1; |
---|
| 4406 | CFArray Pi; |
---|
| 4407 | CFMatrix M= CFMatrix (liftBound, factors.length() - 1); |
---|
| 4408 | CFList diophant; |
---|
| 4409 | CFArray lcs= CFArray (2); |
---|
| 4410 | lcs [0]= shiftedLCsEval1.getFirst(); |
---|
| 4411 | lcs [1]= shiftedLCsEval2.getFirst(); |
---|
[81d96c] | 4412 | nonMonicHenselLift12 (UEval.getFirst(), factors, liftBound, Pi, diophant, M, |
---|
| 4413 | lcs, false); |
---|
[08daea] | 4414 | |
---|
| 4415 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
| 4416 | { |
---|
[9ff686] | 4417 | if (!fdivides (i.getItem(), UEval.getFirst())) |
---|
| 4418 | return 0; |
---|
[08daea] | 4419 | } |
---|
[9ff686] | 4420 | |
---|
[08daea] | 4421 | int * liftBounds; |
---|
[9189e93] | 4422 | bool noOneToOne= false; |
---|
[08daea] | 4423 | if (U.level() > 2) |
---|
| 4424 | { |
---|
[ea88e0] | 4425 | liftBounds= new int [U.level() - 1]; /* index: 0.. U.level()-2 */ |
---|
[08daea] | 4426 | liftBounds[0]= liftBound; |
---|
[ea88e0] | 4427 | for (int i= 1; i < U.level() - 1; i++) |
---|
[08daea] | 4428 | liftBounds[i]= degree (shiftedU, Variable (i + 2)) + 1; |
---|
[81d96c] | 4429 | factors= nonMonicHenselLift2 (UEval, factors, liftBounds, U.level() - 1, |
---|
| 4430 | false, shiftedLCsEval1, shiftedLCsEval2, Pi, |
---|
| 4431 | diophant, noOneToOne); |
---|
[9ff686] | 4432 | delete [] liftBounds; |
---|
| 4433 | if (noOneToOne) |
---|
| 4434 | return 0; |
---|
[08daea] | 4435 | } |
---|
| 4436 | G[1]= factors.getFirst(); |
---|
| 4437 | G[2]= factors.getLast(); |
---|
| 4438 | G[1]= myReverseShift (G[1], evaluation); |
---|
| 4439 | G[2]= myReverseShift (G[2], evaluation); |
---|
[9ff686] | 4440 | G[1]= NN (G[1]); |
---|
| 4441 | G[2]= NN (G[2]); |
---|
| 4442 | return 1; |
---|
[08daea] | 4443 | } |
---|
| 4444 | |
---|
| 4445 | static inline |
---|
| 4446 | bool findeval_P (const CanonicalForm & F, const CanonicalForm & G, |
---|
| 4447 | CanonicalForm & Fb, CanonicalForm & Gb, CanonicalForm & Db, |
---|
[9ff686] | 4448 | REvaluation & b, int delta, int degF, int degG, int maxeval, |
---|
| 4449 | int & count, int& k, int bound, int& l) |
---|
[08daea] | 4450 | { |
---|
| 4451 | if( count == 0 && delta != 0) |
---|
| 4452 | { |
---|
| 4453 | if( count++ > maxeval ) |
---|
| 4454 | return false; |
---|
| 4455 | } |
---|
| 4456 | if (count > 0) |
---|
| 4457 | { |
---|
[9ff686] | 4458 | b.nextpoint(k); |
---|
[b5c084] | 4459 | if (k == 0) |
---|
| 4460 | k++; |
---|
[9ff686] | 4461 | l++; |
---|
| 4462 | if (l > bound) |
---|
| 4463 | { |
---|
| 4464 | l= 1; |
---|
| 4465 | k++; |
---|
| 4466 | if (k > tmax (F.level(), G.level()) - 1) |
---|
| 4467 | return false; |
---|
| 4468 | b.nextpoint (k); |
---|
| 4469 | } |
---|
[08daea] | 4470 | if (count++ > maxeval) |
---|
| 4471 | return false; |
---|
| 4472 | } |
---|
| 4473 | while( true ) |
---|
| 4474 | { |
---|
| 4475 | Fb = b( F ); |
---|
| 4476 | if( degree( Fb, 1 ) == degF ) |
---|
| 4477 | { |
---|
| 4478 | Gb = b( G ); |
---|
| 4479 | if( degree( Gb, 1 ) == degG ) |
---|
| 4480 | { |
---|
| 4481 | Db = gcd( Fb, Gb ); |
---|
| 4482 | if( delta > 0 ) |
---|
| 4483 | { |
---|
| 4484 | if( degree( Db, 1 ) <= delta ) |
---|
| 4485 | return true; |
---|
| 4486 | } |
---|
| 4487 | else |
---|
| 4488 | return true; |
---|
| 4489 | } |
---|
| 4490 | } |
---|
[9ff686] | 4491 | if (k == 0) |
---|
| 4492 | k++; |
---|
| 4493 | b.nextpoint(k); |
---|
| 4494 | l++; |
---|
| 4495 | if (l > bound) |
---|
| 4496 | { |
---|
| 4497 | l= 1; |
---|
| 4498 | k++; |
---|
| 4499 | if (k > tmax (F.level(), G.level()) - 1) |
---|
| 4500 | return false; |
---|
| 4501 | b.nextpoint (k); |
---|
| 4502 | } |
---|
[08daea] | 4503 | if( count++ > maxeval ) |
---|
| 4504 | return false; |
---|
| 4505 | } |
---|
| 4506 | } |
---|
| 4507 | |
---|
| 4508 | // parameters for heuristic |
---|
| 4509 | static int maxNumEval= 200; |
---|
| 4510 | static int sizePerVars1= 500; //try dense gcd if size/#variables is bigger |
---|
| 4511 | |
---|
| 4512 | /// Extended Zassenhaus GCD for finite fields |
---|
| 4513 | CanonicalForm EZGCD_P( const CanonicalForm & FF, const CanonicalForm & GG ) |
---|
| 4514 | { |
---|
| 4515 | if (FF.isZero() && degree(GG) > 0) return GG/Lc(GG); |
---|
| 4516 | else if (GG.isZero() && degree (FF) > 0) return FF/Lc(FF); |
---|
| 4517 | else if (FF.isZero() && GG.isZero()) return FF.genOne(); |
---|
| 4518 | if (FF.inBaseDomain() || GG.inBaseDomain()) return FF.genOne(); |
---|
| 4519 | if (FF.isUnivariate() && fdivides(FF, GG)) return FF/Lc(FF); |
---|
| 4520 | if (GG.isUnivariate() && fdivides(GG, FF)) return GG/Lc(GG); |
---|
| 4521 | if (FF == GG) return FF/Lc(FF); |
---|
| 4522 | |
---|
| 4523 | CanonicalForm F, G, f, g, d, Fb, Gb, Db, Fbt, Gbt, Dbt, B0, B, D0, lcF, lcG, |
---|
| 4524 | lcD; |
---|
| 4525 | CFArray DD( 1, 2 ), lcDD( 1, 2 ); |
---|
| 4526 | int degF, degG, delta, count; |
---|
| 4527 | int maxeval; |
---|
| 4528 | maxeval= tmin((getCharacteristic()/ |
---|
| 4529 | (int)(ilog2(getCharacteristic())*log2exp))*2, maxNumEval); |
---|
| 4530 | count= 0; // number of eval. used |
---|
[9ff686] | 4531 | REvaluation b, bt; |
---|
| 4532 | int gcdfound = 0; |
---|
[08daea] | 4533 | Variable x = Variable(1); |
---|
| 4534 | |
---|
| 4535 | F= FF; |
---|
| 4536 | G= GG; |
---|
| 4537 | |
---|
| 4538 | CFMap M,N; |
---|
| 4539 | int smallestDegLev; |
---|
[2a95b2] | 4540 | TIMING_START (ez_p_compress) |
---|
[08daea] | 4541 | int best_level= compress4EZGCD (F, G, M, N, smallestDegLev); |
---|
| 4542 | |
---|
| 4543 | if (best_level == 0) return G.genOne(); |
---|
| 4544 | |
---|
| 4545 | F= M (F); |
---|
| 4546 | G= M (G); |
---|
[2a95b2] | 4547 | TIMING_END_AND_PRINT (ez_p_compress, "time for compression in EZ_P: ") |
---|
[08daea] | 4548 | |
---|
[2a95b2] | 4549 | TIMING_START (ez_p_content) |
---|
[08daea] | 4550 | f = content( F, x ); g = content( G, x ); |
---|
| 4551 | d = gcd( f, g ); |
---|
| 4552 | F /= f; G /= g; |
---|
[2a95b2] | 4553 | TIMING_END_AND_PRINT (ez_p_content, "time to extract content in EZ_P: ") |
---|
[08daea] | 4554 | |
---|
| 4555 | if( F.isUnivariate() && G.isUnivariate() ) |
---|
| 4556 | { |
---|
| 4557 | if( F.mvar() == G.mvar() ) |
---|
| 4558 | d *= gcd( F, G ); |
---|
| 4559 | return N (d); |
---|
| 4560 | } |
---|
| 4561 | |
---|
| 4562 | int maxNumVars= tmax (getNumVars (F), getNumVars (G)); |
---|
[9ff686] | 4563 | Variable a, oldA; |
---|
[08daea] | 4564 | int sizeF= size (F); |
---|
| 4565 | int sizeG= size (G); |
---|
| 4566 | |
---|
| 4567 | if (sizeF/maxNumVars > sizePerVars1 && sizeG/maxNumVars > sizePerVars1) |
---|
| 4568 | { |
---|
| 4569 | if (hasFirstAlgVar (F, a) || hasFirstAlgVar (G, a)) |
---|
| 4570 | return N (d*GCD_Fp_extension (F, G, a)); |
---|
| 4571 | else if (CFFactory::gettype() == GaloisFieldDomain) |
---|
| 4572 | return N (d*GCD_GF (F, G)); |
---|
| 4573 | else |
---|
| 4574 | return N (d*GCD_small_p (F, G)); |
---|
| 4575 | } |
---|
| 4576 | |
---|
[5b2d2b] | 4577 | int dummy= 0; |
---|
| 4578 | if( gcd_test_one( F, G, false, dummy ) ) |
---|
[08daea] | 4579 | { |
---|
| 4580 | return N (d); |
---|
| 4581 | } |
---|
| 4582 | |
---|
[9ff686] | 4583 | bool passToGF= false; |
---|
| 4584 | bool extOfExt= false; |
---|
| 4585 | int p= getCharacteristic(); |
---|
| 4586 | bool algExtension= (hasFirstAlgVar(F,a) || hasFirstAlgVar(G,a)); |
---|
| 4587 | int k= 1; |
---|
| 4588 | CanonicalForm primElem, imPrimElem; |
---|
| 4589 | CFList source, dest; |
---|
| 4590 | if (p < 50 && CFFactory::gettype() != GaloisFieldDomain && !algExtension) |
---|
[08daea] | 4591 | { |
---|
[9ff686] | 4592 | if (p == 2) |
---|
[6e8834] | 4593 | setCharacteristic (2, 12, 'Z'); |
---|
[9ff686] | 4594 | else if (p == 3) |
---|
| 4595 | setCharacteristic (3, 4, 'Z'); |
---|
| 4596 | else if (p == 5 || p == 7) |
---|
| 4597 | setCharacteristic (p, 3, 'Z'); |
---|
| 4598 | else |
---|
| 4599 | setCharacteristic (p, 2, 'Z'); |
---|
| 4600 | passToGF= true; |
---|
| 4601 | F= F.mapinto(); |
---|
| 4602 | G= G.mapinto(); |
---|
| 4603 | maxeval= 2*ipower (p, getGFDegree()); |
---|
[08daea] | 4604 | } |
---|
[9ff686] | 4605 | else if (CFFactory::gettype() == GaloisFieldDomain && |
---|
| 4606 | ipower (p , getGFDegree()) < 50) |
---|
[08daea] | 4607 | { |
---|
[9ff686] | 4608 | k= getGFDegree(); |
---|
| 4609 | if (ipower (p, 2*k) > 50) |
---|
| 4610 | setCharacteristic (p, 2*k, gf_name); |
---|
[08daea] | 4611 | else |
---|
[9ff686] | 4612 | setCharacteristic (p, 3*k, gf_name); |
---|
| 4613 | F= GFMapUp (F, k); |
---|
| 4614 | G= GFMapUp (G, k); |
---|
| 4615 | maxeval= tmin (2*ipower (p, getGFDegree()), maxNumEval); |
---|
| 4616 | } |
---|
| 4617 | else if (p < 50 && algExtension && !CFFactory::gettype() == GaloisFieldDomain) |
---|
| 4618 | { |
---|
| 4619 | int d= degree (getMipo (a)); |
---|
| 4620 | oldA= a; |
---|
| 4621 | Variable v2; |
---|
| 4622 | if (p == 2 && d < 6) |
---|
| 4623 | { |
---|
[bffe62d] | 4624 | if (fac_NTL_char != p) |
---|
| 4625 | { |
---|
| 4626 | fac_NTL_char= p; |
---|
| 4627 | zz_p::init (p); |
---|
| 4628 | } |
---|
[9ff686] | 4629 | bool primFail= false; |
---|
| 4630 | Variable vBuf; |
---|
| 4631 | primElem= primitiveElement (a, vBuf, primFail); |
---|
| 4632 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
| 4633 | if (d < 3) |
---|
| 4634 | { |
---|
| 4635 | zz_pX NTLIrredpoly; |
---|
| 4636 | BuildIrred (NTLIrredpoly, d*3); |
---|
| 4637 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
| 4638 | v2= rootOf (newMipo); |
---|
| 4639 | } |
---|
[08daea] | 4640 | else |
---|
[9ff686] | 4641 | { |
---|
| 4642 | zz_pX NTLIrredpoly; |
---|
| 4643 | BuildIrred (NTLIrredpoly, d*2); |
---|
| 4644 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
| 4645 | v2= rootOf (newMipo); |
---|
| 4646 | } |
---|
| 4647 | imPrimElem= mapPrimElem (primElem, a, v2); |
---|
| 4648 | extOfExt= true; |
---|
| 4649 | } |
---|
| 4650 | else if ((p == 3 && d < 4) || ((p == 5 || p == 7) && d < 3)) |
---|
| 4651 | { |
---|
[bffe62d] | 4652 | if (fac_NTL_char != p) |
---|
| 4653 | { |
---|
| 4654 | fac_NTL_char= p; |
---|
| 4655 | zz_p::init (p); |
---|
| 4656 | } |
---|
[9ff686] | 4657 | bool primFail= false; |
---|
| 4658 | Variable vBuf; |
---|
| 4659 | primElem= primitiveElement (a, vBuf, primFail); |
---|
| 4660 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
| 4661 | zz_pX NTLIrredpoly; |
---|
| 4662 | BuildIrred (NTLIrredpoly, d*2); |
---|
| 4663 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
| 4664 | v2= rootOf (newMipo); |
---|
| 4665 | imPrimElem= mapPrimElem (primElem, a, v2); |
---|
| 4666 | extOfExt= true; |
---|
| 4667 | } |
---|
| 4668 | if (extOfExt) |
---|
| 4669 | { |
---|
| 4670 | maxeval= tmin (2*ipower (p, degree (getMipo (v2))), maxNumEval); |
---|
| 4671 | F= mapUp (F, a, v2, primElem, imPrimElem, source, dest); |
---|
| 4672 | G= mapUp (G, a, v2, primElem, imPrimElem, source, dest); |
---|
| 4673 | a= v2; |
---|
[08daea] | 4674 | } |
---|
| 4675 | } |
---|
[9ff686] | 4676 | |
---|
| 4677 | lcF = LC( F, x ); lcG = LC( G, x ); |
---|
| 4678 | lcD = gcd( lcF, lcG ); |
---|
| 4679 | |
---|
| 4680 | delta = 0; |
---|
| 4681 | degF = degree( F, x ); degG = degree( G, x ); |
---|
| 4682 | |
---|
| 4683 | if(hasFirstAlgVar(G,a)) |
---|
| 4684 | b = REvaluation( 2, tmax(F.level(), G.level()), AlgExtRandomF( a ) ); |
---|
| 4685 | else |
---|
| 4686 | { // both not in extension given by algebraic variable |
---|
| 4687 | if (CFFactory::gettype() != GaloisFieldDomain) |
---|
| 4688 | b = REvaluation( 2, tmax(F.level(), G.level()), FFRandom() ); |
---|
| 4689 | else |
---|
| 4690 | b = REvaluation( 2, tmax(F.level(), G.level()), GFRandom() ); |
---|
| 4691 | } |
---|
| 4692 | |
---|
[e26667] | 4693 | CanonicalForm cand, contcand; |
---|
[9ff686] | 4694 | CanonicalForm result; |
---|
| 4695 | int o, t; |
---|
| 4696 | o= 0; |
---|
| 4697 | t= 1; |
---|
| 4698 | int goodPointCount= 0; |
---|
[08daea] | 4699 | while( !gcdfound ) |
---|
| 4700 | { |
---|
[2a95b2] | 4701 | TIMING_START (ez_p_eval); |
---|
[9ff686] | 4702 | if( !findeval_P( F, G, Fb, Gb, Db, b, delta, degF, degG, maxeval, count, o, |
---|
| 4703 | maxeval/maxNumVars, t )) |
---|
[08daea] | 4704 | { // too many eval. used --> try another method |
---|
[9ff686] | 4705 | Off (SW_USE_EZGCD_P); |
---|
| 4706 | result= gcd (F,G); |
---|
| 4707 | On (SW_USE_EZGCD_P); |
---|
| 4708 | if (passToGF) |
---|
[08daea] | 4709 | { |
---|
[0a7d0ca] | 4710 | CanonicalForm mipo= gf_mipo; |
---|
[9ff686] | 4711 | setCharacteristic (p); |
---|
[0a7d0ca] | 4712 | Variable alpha= rootOf (mipo.mapinto()); |
---|
[9ff686] | 4713 | result= GF2FalphaRep (result, alpha); |
---|
[08daea] | 4714 | } |
---|
[9ff686] | 4715 | if (k > 1) |
---|
| 4716 | { |
---|
| 4717 | result= GFMapDown (result, k); |
---|
| 4718 | setCharacteristic (p, k, gf_name); |
---|
| 4719 | } |
---|
| 4720 | if (extOfExt) |
---|
| 4721 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
| 4722 | return N (d*result); |
---|
[08daea] | 4723 | } |
---|
[2a95b2] | 4724 | TIMING_END_AND_PRINT (ez_p_eval, "time for eval point search in EZ_P1: "); |
---|
[08daea] | 4725 | delta = degree( Db ); |
---|
| 4726 | if( delta == 0 ) |
---|
[9ff686] | 4727 | { |
---|
| 4728 | if (passToGF) |
---|
| 4729 | setCharacteristic (p); |
---|
| 4730 | if (k > 1) |
---|
| 4731 | setCharacteristic (p, k, gf_name); |
---|
[08daea] | 4732 | return N (d); |
---|
[9ff686] | 4733 | } |
---|
[08daea] | 4734 | while( true ) |
---|
| 4735 | { |
---|
| 4736 | bt = b; |
---|
[2a95b2] | 4737 | TIMING_START (ez_p_eval); |
---|
[9ff686] | 4738 | if( !findeval_P(F,G,Fbt,Gbt,Dbt, bt, delta, degF, degG, maxeval, count, o, |
---|
| 4739 | maxeval/maxNumVars, t )) |
---|
[08daea] | 4740 | { // too many eval. used --> try another method |
---|
[9ff686] | 4741 | Off (SW_USE_EZGCD_P); |
---|
| 4742 | result= gcd (F,G); |
---|
| 4743 | On (SW_USE_EZGCD_P); |
---|
| 4744 | if (passToGF) |
---|
[08daea] | 4745 | { |
---|
[0a7d0ca] | 4746 | CanonicalForm mipo= gf_mipo; |
---|
[9ff686] | 4747 | setCharacteristic (p); |
---|
[0a7d0ca] | 4748 | Variable alpha= rootOf (mipo.mapinto()); |
---|
[9ff686] | 4749 | result= GF2FalphaRep (result, alpha); |
---|
[08daea] | 4750 | } |
---|
[9ff686] | 4751 | if (k > 1) |
---|
| 4752 | { |
---|
| 4753 | result= GFMapDown (result, k); |
---|
| 4754 | setCharacteristic (p, k, gf_name); |
---|
| 4755 | } |
---|
| 4756 | if (extOfExt) |
---|
| 4757 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
| 4758 | return N (d*result); |
---|
[08daea] | 4759 | } |
---|
[2a95b2] | 4760 | TIMING_END_AND_PRINT (ez_p_eval, "time for eval point search in EZ_P2: "); |
---|
[08daea] | 4761 | int dd = degree( Dbt ); |
---|
| 4762 | if( dd == 0 ) |
---|
[9ff686] | 4763 | { |
---|
| 4764 | if (passToGF) |
---|
| 4765 | setCharacteristic (p); |
---|
| 4766 | if (k > 1) |
---|
| 4767 | setCharacteristic (p, k, gf_name); |
---|
[08daea] | 4768 | return N (d); |
---|
[9ff686] | 4769 | } |
---|
[08daea] | 4770 | if( dd == delta ) |
---|
[9ff686] | 4771 | { |
---|
| 4772 | goodPointCount++; |
---|
| 4773 | if (goodPointCount == 5) |
---|
| 4774 | break; |
---|
| 4775 | } |
---|
[08daea] | 4776 | if( dd < delta ) |
---|
| 4777 | { |
---|
[9ff686] | 4778 | goodPointCount= 0; |
---|
[08daea] | 4779 | delta = dd; |
---|
| 4780 | b = bt; |
---|
| 4781 | Db = Dbt; Fb = Fbt; Gb = Gbt; |
---|
| 4782 | } |
---|
[9ff686] | 4783 | if (delta == degF) |
---|
| 4784 | { |
---|
| 4785 | if (degF <= degG && fdivides (F, G)) |
---|
| 4786 | { |
---|
| 4787 | if (passToGF) |
---|
| 4788 | { |
---|
[0a7d0ca] | 4789 | CanonicalForm mipo= gf_mipo; |
---|
[9ff686] | 4790 | setCharacteristic (p); |
---|
[0a7d0ca] | 4791 | Variable alpha= rootOf (mipo.mapinto()); |
---|
[9ff686] | 4792 | F= GF2FalphaRep (F, alpha); |
---|
| 4793 | } |
---|
| 4794 | if (k > 1) |
---|
| 4795 | { |
---|
| 4796 | F= GFMapDown (F, k); |
---|
| 4797 | setCharacteristic (p, k, gf_name); |
---|
| 4798 | } |
---|
| 4799 | if (extOfExt) |
---|
| 4800 | F= mapDown (F, primElem, imPrimElem, oldA, dest, source); |
---|
| 4801 | return N (d*F); |
---|
| 4802 | } |
---|
| 4803 | else |
---|
| 4804 | delta--; |
---|
| 4805 | } |
---|
| 4806 | else if (delta == degG) |
---|
| 4807 | { |
---|
| 4808 | if (degG <= degF && fdivides (G, F)) |
---|
| 4809 | { |
---|
| 4810 | if (passToGF) |
---|
| 4811 | { |
---|
[0a7d0ca] | 4812 | CanonicalForm mipo= gf_mipo; |
---|
[9ff686] | 4813 | setCharacteristic (p); |
---|
[0a7d0ca] | 4814 | Variable alpha= rootOf (mipo.mapinto()); |
---|
[9ff686] | 4815 | G= GF2FalphaRep (G, alpha); |
---|
| 4816 | } |
---|
| 4817 | if (k > 1) |
---|
| 4818 | { |
---|
| 4819 | G= GFMapDown (G, k); |
---|
| 4820 | setCharacteristic (p, k, gf_name); |
---|
| 4821 | } |
---|
| 4822 | if (extOfExt) |
---|
| 4823 | G= mapDown (G, primElem, imPrimElem, oldA, dest, source); |
---|
| 4824 | return N (d*G); |
---|
| 4825 | } |
---|
| 4826 | else |
---|
| 4827 | delta--; |
---|
| 4828 | } |
---|
[08daea] | 4829 | } |
---|
| 4830 | if( delta != degF && delta != degG ) |
---|
| 4831 | { |
---|
| 4832 | bool B_is_F; |
---|
| 4833 | CanonicalForm xxx1, xxx2; |
---|
| 4834 | CanonicalForm buf; |
---|
| 4835 | DD[1] = Fb / Db; |
---|
| 4836 | buf= Gb/Db; |
---|
| 4837 | xxx1 = gcd( DD[1], Db ); |
---|
| 4838 | xxx2 = gcd( buf, Db ); |
---|
| 4839 | if (((xxx1.inCoeffDomain() && xxx2.inCoeffDomain()) && |
---|
[c1b9927] | 4840 | (size (F) <= size (G))) |
---|
[08daea] | 4841 | || (xxx1.inCoeffDomain() && !xxx2.inCoeffDomain())) |
---|
| 4842 | { |
---|
| 4843 | B = F; |
---|
| 4844 | DD[2] = Db; |
---|
| 4845 | lcDD[1] = lcF; |
---|
| 4846 | lcDD[2] = lcD; |
---|
| 4847 | B_is_F = true; |
---|
| 4848 | } |
---|
| 4849 | else if (((xxx1.inCoeffDomain() && xxx2.inCoeffDomain()) && |
---|
[c1b9927] | 4850 | (size (G) < size (F))) |
---|
[08daea] | 4851 | || (!xxx1.inCoeffDomain() && xxx2.inCoeffDomain())) |
---|
| 4852 | { |
---|
| 4853 | DD[1] = buf; |
---|
| 4854 | B = G; |
---|
| 4855 | DD[2] = Db; |
---|
| 4856 | lcDD[1] = lcG; |
---|
| 4857 | lcDD[2] = lcD; |
---|
| 4858 | B_is_F = false; |
---|
| 4859 | } |
---|
| 4860 | else // special case handling |
---|
| 4861 | { |
---|
[9ff686] | 4862 | Off (SW_USE_EZGCD_P); |
---|
| 4863 | result= gcd (F,G); |
---|
| 4864 | On (SW_USE_EZGCD_P); |
---|
| 4865 | if (passToGF) |
---|
| 4866 | { |
---|
[0a7d0ca] | 4867 | CanonicalForm mipo= gf_mipo; |
---|
[9ff686] | 4868 | setCharacteristic (p); |
---|
[0a7d0ca] | 4869 | Variable alpha= rootOf (mipo.mapinto()); |
---|
[9ff686] | 4870 | result= GF2FalphaRep (result, alpha); |
---|
| 4871 | } |
---|
| 4872 | if (k > 1) |
---|
[08daea] | 4873 | { |
---|
[9ff686] | 4874 | result= GFMapDown (result, k); |
---|
| 4875 | setCharacteristic (p, k, gf_name); |
---|
| 4876 | } |
---|
| 4877 | if (extOfExt) |
---|
| 4878 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
| 4879 | return N (d*result); |
---|
| 4880 | } |
---|
| 4881 | DD[2] = DD[2] * ( b( lcDD[2] ) / lc( DD[2] ) ); |
---|
| 4882 | DD[1] = DD[1] * ( b( lcDD[1] ) / lc( DD[1] ) ); |
---|
| 4883 | |
---|
| 4884 | if (size (B*lcDD[2])/maxNumVars > sizePerVars1) |
---|
| 4885 | { |
---|
| 4886 | if (algExtension) |
---|
| 4887 | { |
---|
| 4888 | result= GCD_Fp_extension (F, G, a); |
---|
| 4889 | if (extOfExt) |
---|
| 4890 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
| 4891 | return N (d*result); |
---|
| 4892 | } |
---|
| 4893 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
| 4894 | { |
---|
| 4895 | result= GCD_GF (F, G); |
---|
| 4896 | if (passToGF) |
---|
| 4897 | { |
---|
[0a7d0ca] | 4898 | CanonicalForm mipo= gf_mipo; |
---|
[9ff686] | 4899 | setCharacteristic (p); |
---|
[0a7d0ca] | 4900 | Variable alpha= rootOf (mipo.mapinto()); |
---|
[9ff686] | 4901 | result= GF2FalphaRep (result, alpha); |
---|
| 4902 | } |
---|
| 4903 | if (k > 1) |
---|
[08daea] | 4904 | { |
---|
[9ff686] | 4905 | result= GFMapDown (result, k); |
---|
| 4906 | setCharacteristic (p, k, gf_name); |
---|
[08daea] | 4907 | } |
---|
[9ff686] | 4908 | return N (d*result); |
---|
[08daea] | 4909 | } |
---|
| 4910 | else |
---|
[9ff686] | 4911 | return N (d*GCD_small_p (F,G)); |
---|
[08daea] | 4912 | } |
---|
| 4913 | |
---|
[2a95b2] | 4914 | TIMING_START (ez_p_hensel_lift); |
---|
[0349c20] | 4915 | gcdfound= Hensel_P (B*lcD, DD, b, lcDD); |
---|
[2a95b2] | 4916 | TIMING_END_AND_PRINT (ez_p_hensel_lift, "time for Hensel lift in EZ_P: "); |
---|
[08daea] | 4917 | |
---|
[7964658] | 4918 | if (gcdfound == -1) //things became dense |
---|
[9ff686] | 4919 | { |
---|
[7964658] | 4920 | if (algExtension) |
---|
[9ff686] | 4921 | { |
---|
[7964658] | 4922 | result= GCD_Fp_extension (F, G, a); |
---|
| 4923 | if (extOfExt) |
---|
| 4924 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
| 4925 | return N (d*result); |
---|
[9ff686] | 4926 | } |
---|
[7964658] | 4927 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
[9ff686] | 4928 | { |
---|
[7964658] | 4929 | result= GCD_GF (F, G); |
---|
| 4930 | if (passToGF) |
---|
| 4931 | { |
---|
| 4932 | CanonicalForm mipo= gf_mipo; |
---|
| 4933 | setCharacteristic (p); |
---|
| 4934 | Variable alpha= rootOf (mipo.mapinto()); |
---|
| 4935 | result= GF2FalphaRep (result, alpha); |
---|
| 4936 | } |
---|
| 4937 | if (k > 1) |
---|
| 4938 | { |
---|
| 4939 | result= GFMapDown (result, k); |
---|
| 4940 | setCharacteristic (p, k, gf_name); |
---|
| 4941 | } |
---|
| 4942 | return N (d*result); |
---|
[9ff686] | 4943 | } |
---|
[7964658] | 4944 | else |
---|
| 4945 | return N (d*GCD_small_p (F,G)); |
---|
[9ff686] | 4946 | } |
---|
| 4947 | |
---|
| 4948 | if (gcdfound == 1) |
---|
[08daea] | 4949 | { |
---|
[2a95b2] | 4950 | TIMING_START (termination_test); |
---|
[e26667] | 4951 | contcand= content (DD[2], Variable (1)); |
---|
| 4952 | cand = DD[2] / contcand; |
---|
| 4953 | if (B_is_F) |
---|
| 4954 | gcdfound = fdivides( cand, G ) && cand*(DD[1]/(lcD/contcand)) == F; |
---|
| 4955 | else |
---|
| 4956 | gcdfound = fdivides( cand, F ) && cand*(DD[1]/(lcD/contcand)) == G; |
---|
[2a95b2] | 4957 | TIMING_END_AND_PRINT (termination_test, |
---|
| 4958 | "time for termination test EZ_P: "); |
---|
[9ff686] | 4959 | |
---|
| 4960 | if (passToGF && gcdfound) |
---|
| 4961 | { |
---|
[0a7d0ca] | 4962 | CanonicalForm mipo= gf_mipo; |
---|
[9ff686] | 4963 | setCharacteristic (p); |
---|
[0a7d0ca] | 4964 | Variable alpha= rootOf (mipo.mapinto()); |
---|
[9ff686] | 4965 | cand= GF2FalphaRep (cand, alpha); |
---|
| 4966 | } |
---|
| 4967 | if (k > 1 && gcdfound) |
---|
| 4968 | { |
---|
| 4969 | cand= GFMapDown (cand, k); |
---|
| 4970 | setCharacteristic (p, k, gf_name); |
---|
| 4971 | } |
---|
| 4972 | if (extOfExt && gcdfound) |
---|
| 4973 | cand= mapDown (cand, primElem, imPrimElem, oldA, dest, source); |
---|
[08daea] | 4974 | } |
---|
| 4975 | } |
---|
[9ff686] | 4976 | delta--; |
---|
| 4977 | goodPointCount= 0; |
---|
[08daea] | 4978 | } |
---|
| 4979 | return N (d*cand); |
---|
| 4980 | } |
---|
| 4981 | |
---|
| 4982 | |
---|
[10af64] | 4983 | #endif |
---|