[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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[911444] | 43 | #include "cf_gcd_smallp.h" |
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| 44 | |
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[e76d7a6] | 45 | TIMING_DEFINE_PRINT(gcd_recursion) |
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| 46 | TIMING_DEFINE_PRINT(newton_interpolation) |
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[10af64] | 47 | |
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[1e4b53] | 48 | bool |
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| 49 | terminationTest (const CanonicalForm& F, const CanonicalForm& G, |
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| 50 | const CanonicalForm& coF, const CanonicalForm& coG, |
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| 51 | const CanonicalForm& cand) |
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| 52 | { |
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| 53 | CanonicalForm LCCand= abs (LC (cand)); |
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| 54 | if (LCCand*abs (LC (coF)) == abs (LC (F))) |
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| 55 | { |
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| 56 | if (LCCand*abs (LC (coG)) == abs (LC (G))) |
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| 57 | { |
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| 58 | if (abs (cand)*abs (coF) == abs (F)) |
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| 59 | { |
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| 60 | if (abs (cand)*abs (coG) == abs (G)) |
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| 61 | return true; |
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| 62 | } |
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| 63 | return false; |
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| 64 | } |
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| 65 | return false; |
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| 66 | } |
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| 67 | return false; |
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| 68 | } |
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| 69 | |
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[517530] | 70 | #ifdef HAVE_NTL |
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| 71 | |
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[08daea] | 72 | static const double log2exp= 1.442695041; |
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| 73 | |
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[806c18] | 74 | /// compressing two polynomials F and G, M is used for compressing, |
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[10af64] | 75 | /// N to reverse the compression |
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| 76 | int myCompress (const CanonicalForm& F, const CanonicalForm& G, CFMap & M, |
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[08daea] | 77 | CFMap & N, bool topLevel) |
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[806c18] | 78 | { |
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[10af64] | 79 | int n= tmax (F.level(), G.level()); |
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| 80 | int * degsf= new int [n + 1]; |
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| 81 | int * degsg= new int [n + 1]; |
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| 82 | |
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| 83 | for (int i = 0; i <= n; i++) |
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| 84 | degsf[i]= degsg[i]= 0; |
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[806c18] | 85 | |
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[10af64] | 86 | degsf= degrees (F, degsf); |
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| 87 | degsg= degrees (G, degsg); |
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[806c18] | 88 | |
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[10af64] | 89 | int both_non_zero= 0; |
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| 90 | int f_zero= 0; |
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| 91 | int g_zero= 0; |
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| 92 | int both_zero= 0; |
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| 93 | |
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[806c18] | 94 | if (topLevel) |
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[10af64] | 95 | { |
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[806c18] | 96 | for (int i= 1; i <= n; i++) |
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[10af64] | 97 | { |
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[806c18] | 98 | if (degsf[i] != 0 && degsg[i] != 0) |
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[10af64] | 99 | { |
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| 100 | both_non_zero++; |
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| 101 | continue; |
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| 102 | } |
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[806c18] | 103 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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[10af64] | 104 | { |
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| 105 | f_zero++; |
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| 106 | continue; |
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| 107 | } |
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[806c18] | 108 | if (degsg[i] == 0 && degsf[i] && i <= F.level()) |
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[10af64] | 109 | { |
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| 110 | g_zero++; |
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| 111 | continue; |
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| 112 | } |
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| 113 | } |
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| 114 | |
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[806c18] | 115 | if (both_non_zero == 0) |
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[dec1024] | 116 | { |
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| 117 | delete [] degsf; |
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| 118 | delete [] degsg; |
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| 119 | return 0; |
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| 120 | } |
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[10af64] | 121 | |
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| 122 | // map Variables which do not occur in both polynomials to higher levels |
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| 123 | int k= 1; |
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| 124 | int l= 1; |
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[806c18] | 125 | for (int i= 1; i <= n; i++) |
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| 126 | { |
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| 127 | if (degsf[i] != 0 && degsg[i] == 0 && i <= F.level()) |
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[10af64] | 128 | { |
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[806c18] | 129 | if (k + both_non_zero != i) |
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[10af64] | 130 | { |
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| 131 | M.newpair (Variable (i), Variable (k + both_non_zero)); |
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| 132 | N.newpair (Variable (k + both_non_zero), Variable (i)); |
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| 133 | } |
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| 134 | k++; |
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| 135 | } |
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[806c18] | 136 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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[10af64] | 137 | { |
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[806c18] | 138 | if (l + g_zero + both_non_zero != i) |
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[10af64] | 139 | { |
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| 140 | M.newpair (Variable (i), Variable (l + g_zero + both_non_zero)); |
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| 141 | N.newpair (Variable (l + g_zero + both_non_zero), Variable (i)); |
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| 142 | } |
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| 143 | l++; |
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| 144 | } |
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| 145 | } |
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[806c18] | 146 | |
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[10af64] | 147 | // sort Variables x_{i} in increasing order of |
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[806c18] | 148 | // min(deg_{x_{i}}(f),deg_{x_{i}}(g)) |
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[9ff686] | 149 | int m= tmax (F.level(), G.level()); |
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| 150 | int min_max_deg; |
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[10af64] | 151 | k= both_non_zero; |
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| 152 | l= 0; |
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| 153 | int i= 1; |
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[806c18] | 154 | while (k > 0) |
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[10af64] | 155 | { |
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[9ff686] | 156 | if (degsf [i] != 0 && degsg [i] != 0) |
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| 157 | min_max_deg= tmax (degsf[i], degsg[i]); |
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| 158 | else |
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| 159 | min_max_deg= 0; |
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| 160 | while (min_max_deg == 0) |
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[10af64] | 161 | { |
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| 162 | i++; |
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[9ff686] | 163 | if (degsf [i] != 0 && degsg [i] != 0) |
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| 164 | min_max_deg= tmax (degsf[i], degsg[i]); |
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| 165 | else |
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| 166 | min_max_deg= 0; |
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[10af64] | 167 | } |
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[806c18] | 168 | for (int j= i + 1; j <= m; j++) |
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[10af64] | 169 | { |
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[9ff686] | 170 | if (degsf[j] != 0 && degsg [j] != 0 && |
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| 171 | tmax (degsf[j],degsg[j]) <= min_max_deg) |
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[10af64] | 172 | { |
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[9ff686] | 173 | min_max_deg= tmax (degsf[j], degsg[j]); |
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[806c18] | 174 | l= j; |
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[10af64] | 175 | } |
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| 176 | } |
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[806c18] | 177 | if (l != 0) |
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[10af64] | 178 | { |
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[806c18] | 179 | if (l != k) |
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[10af64] | 180 | { |
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| 181 | M.newpair (Variable (l), Variable(k)); |
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| 182 | N.newpair (Variable (k), Variable(l)); |
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| 183 | degsf[l]= 0; |
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| 184 | degsg[l]= 0; |
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| 185 | l= 0; |
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| 186 | } |
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[806c18] | 187 | else |
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[10af64] | 188 | { |
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| 189 | degsf[l]= 0; |
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| 190 | degsg[l]= 0; |
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| 191 | l= 0; |
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| 192 | } |
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[806c18] | 193 | } |
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| 194 | else if (l == 0) |
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[10af64] | 195 | { |
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[806c18] | 196 | if (i != k) |
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[10af64] | 197 | { |
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| 198 | M.newpair (Variable (i), Variable (k)); |
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| 199 | N.newpair (Variable (k), Variable (i)); |
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| 200 | degsf[i]= 0; |
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| 201 | degsg[i]= 0; |
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| 202 | } |
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[806c18] | 203 | else |
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[10af64] | 204 | { |
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| 205 | degsf[i]= 0; |
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| 206 | degsg[i]= 0; |
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| 207 | } |
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| 208 | i++; |
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[806c18] | 209 | } |
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[10af64] | 210 | k--; |
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| 211 | } |
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| 212 | } |
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[806c18] | 213 | else |
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[10af64] | 214 | { |
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| 215 | //arrange Variables such that no gaps occur |
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[806c18] | 216 | for (int i= 1; i <= n; i++) |
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[10af64] | 217 | { |
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[806c18] | 218 | if (degsf[i] == 0 && degsg[i] == 0) |
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[10af64] | 219 | { |
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| 220 | both_zero++; |
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| 221 | continue; |
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| 222 | } |
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[806c18] | 223 | else |
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[10af64] | 224 | { |
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[806c18] | 225 | if (both_zero != 0) |
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[10af64] | 226 | { |
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| 227 | M.newpair (Variable (i), Variable (i - both_zero)); |
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| 228 | N.newpair (Variable (i - both_zero), Variable (i)); |
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| 229 | } |
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| 230 | } |
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| 231 | } |
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| 232 | } |
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| 233 | |
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| 234 | delete [] degsf; |
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| 235 | delete [] degsg; |
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| 236 | |
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[c4f4fd] | 237 | return 1; |
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[10af64] | 238 | } |
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| 239 | |
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[806c18] | 240 | static inline CanonicalForm |
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[dec1024] | 241 | uni_content (const CanonicalForm & F); |
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| 242 | |
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| 243 | CanonicalForm |
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| 244 | uni_content (const CanonicalForm& F, const Variable& x) |
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| 245 | { |
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| 246 | if (F.inCoeffDomain()) |
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| 247 | return F.genOne(); |
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| 248 | if (F.level() == x.level() && F.isUnivariate()) |
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| 249 | return F; |
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| 250 | if (F.level() != x.level() && F.isUnivariate()) |
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| 251 | return F.genOne(); |
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[806c18] | 252 | |
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[dec1024] | 253 | if (x.level() != 1) |
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| 254 | { |
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| 255 | CanonicalForm f= swapvar (F, x, Variable (1)); |
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| 256 | CanonicalForm result= uni_content (f); |
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| 257 | return swapvar (result, x, Variable (1)); |
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| 258 | } |
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| 259 | else |
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| 260 | return uni_content (F); |
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[806c18] | 261 | } |
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[dec1024] | 262 | |
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[806c18] | 263 | /// compute the content of F, where F is considered as an element of |
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| 264 | /// \f$ R[x_{1}][x_{2},\ldots ,x_{n}] \f$ |
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| 265 | static inline CanonicalForm |
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| 266 | uni_content (const CanonicalForm & F) |
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| 267 | { |
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[10af64] | 268 | if (F.inBaseDomain()) |
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| 269 | return F.genOne(); |
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| 270 | if (F.level() == 1 && F.isUnivariate()) |
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| 271 | return F; |
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| 272 | if (F.level() != 1 && F.isUnivariate()) |
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| 273 | return F.genOne(); |
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[c4f4fd] | 274 | if (degree (F,1) == 0) return F.genOne(); |
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[10af64] | 275 | |
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| 276 | int l= F.level(); |
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[806c18] | 277 | if (l == 2) |
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[10af64] | 278 | return content(F); |
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[806c18] | 279 | else |
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[10af64] | 280 | { |
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| 281 | CanonicalForm pol, c = 0; |
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| 282 | CFIterator i = F; |
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[806c18] | 283 | for (; i.hasTerms(); i++) |
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[10af64] | 284 | { |
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[806c18] | 285 | pol= i.coeff(); |
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[10af64] | 286 | pol= uni_content (pol); |
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| 287 | c= gcd (c, pol); |
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| 288 | if (c.isOne()) |
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| 289 | return c; |
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| 290 | } |
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| 291 | return c; |
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| 292 | } |
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| 293 | } |
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| 294 | |
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[806c18] | 295 | CanonicalForm |
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| 296 | extractContents (const CanonicalForm& F, const CanonicalForm& G, |
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| 297 | CanonicalForm& contentF, CanonicalForm& contentG, |
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[dec1024] | 298 | CanonicalForm& ppF, CanonicalForm& ppG, const int d) |
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| 299 | { |
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| 300 | CanonicalForm uniContentF, uniContentG, gcdcFcG; |
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| 301 | contentF= 1; |
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| 302 | contentG= 1; |
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| 303 | ppF= F; |
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| 304 | ppG= G; |
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| 305 | CanonicalForm result= 1; |
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| 306 | for (int i= 1; i <= d; i++) |
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| 307 | { |
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| 308 | uniContentF= uni_content (F, Variable (i)); |
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| 309 | uniContentG= uni_content (G, Variable (i)); |
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| 310 | gcdcFcG= gcd (uniContentF, uniContentG); |
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| 311 | contentF *= uniContentF; |
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| 312 | contentG *= uniContentG; |
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| 313 | ppF /= uniContentF; |
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| 314 | ppG /= uniContentG; |
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| 315 | result *= gcdcFcG; |
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| 316 | } |
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| 317 | return result; |
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| 318 | } |
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| 319 | |
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[10af64] | 320 | /// compute the leading coefficient of F, where F is considered as an element |
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| 321 | /// of \f$ R[x_{1}][x_{2},\ldots ,x_{n}] \f$, order on Mon (x_{2},\ldots ,x_{n}) |
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[c4f4fd] | 322 | /// is dp. |
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[10af64] | 323 | static inline |
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[806c18] | 324 | CanonicalForm uni_lcoeff (const CanonicalForm& F) |
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[10af64] | 325 | { |
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[c1b9927] | 326 | if (F.level() > 1) |
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[10af64] | 327 | { |
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| 328 | Variable x= Variable (2); |
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| 329 | int deg= totaldegree (F, x, F.mvar()); |
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| 330 | for (CFIterator i= F; i.hasTerms(); i++) |
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| 331 | { |
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| 332 | if (i.exp() + totaldegree (i.coeff(), x, i.coeff().mvar()) == deg) |
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[806c18] | 333 | return uni_lcoeff (i.coeff()); |
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[10af64] | 334 | } |
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| 335 | } |
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[c1b9927] | 336 | return F; |
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[10af64] | 337 | } |
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| 338 | |
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| 339 | /// Newton interpolation - Incremental algorithm. |
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| 340 | /// Given a list of values alpha_i and a list of polynomials u_i, 1 <= i <= n, |
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| 341 | /// computes the interpolation polynomial assuming that |
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| 342 | /// the polynomials in u are the results of evaluating the variabe x |
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| 343 | /// of the unknown polynomial at the alpha values. |
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| 344 | /// This incremental version receives only the values of alpha_n and u_n and |
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| 345 | /// the previous interpolation polynomial for points 1 <= i <= n-1, and computes |
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| 346 | /// the polynomial interpolating in all the points. |
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| 347 | /// newtonPoly must be equal to (x - alpha_1) * ... * (x - alpha_{n-1}) |
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| 348 | static inline CanonicalForm |
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[9ff686] | 349 | newtonInterp(const CanonicalForm alpha, const CanonicalForm u, |
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| 350 | const CanonicalForm newtonPoly, const CanonicalForm oldInterPoly, |
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| 351 | const Variable & x) |
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[10af64] | 352 | { |
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| 353 | CanonicalForm interPoly; |
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| 354 | |
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[9ff686] | 355 | interPoly= oldInterPoly + ((u - oldInterPoly(alpha, x))/newtonPoly(alpha, x)) |
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| 356 | *newtonPoly; |
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[10af64] | 357 | return interPoly; |
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| 358 | } |
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| 359 | |
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[806c18] | 360 | /// compute a random element a of \f$ F_{p}(\alpha ) \f$ , |
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[10af64] | 361 | /// s.t. F(a) \f$ \neq 0 \f$ , F is a univariate polynomial, returns |
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[806c18] | 362 | /// fail if there are no field elements left which have not been used before |
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| 363 | static inline CanonicalForm |
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[10af64] | 364 | randomElement (const CanonicalForm & F, const Variable & alpha, CFList & list, |
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[806c18] | 365 | bool & fail) |
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[10af64] | 366 | { |
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| 367 | fail= false; |
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| 368 | Variable x= F.mvar(); |
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| 369 | AlgExtRandomF genAlgExt (alpha); |
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| 370 | FFRandom genFF; |
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| 371 | CanonicalForm random, mipo; |
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| 372 | mipo= getMipo (alpha); |
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| 373 | int p= getCharacteristic (); |
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| 374 | int d= degree (mipo); |
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[c4f4fd] | 375 | int bound= ipower (p, d); |
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[806c18] | 376 | do |
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[10af64] | 377 | { |
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| 378 | if (list.length() == bound) |
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| 379 | { |
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| 380 | fail= true; |
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| 381 | break; |
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| 382 | } |
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[806c18] | 383 | if (list.length() < p) |
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[10af64] | 384 | { |
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| 385 | random= genFF.generate(); |
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| 386 | while (find (list, random)) |
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| 387 | random= genFF.generate(); |
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| 388 | } |
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[806c18] | 389 | else |
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[10af64] | 390 | { |
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| 391 | random= genAlgExt.generate(); |
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| 392 | while (find (list, random)) |
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| 393 | random= genAlgExt.generate(); |
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| 394 | } |
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[806c18] | 395 | if (F (random, x) == 0) |
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[10af64] | 396 | { |
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| 397 | list.append (random); |
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| 398 | continue; |
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| 399 | } |
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| 400 | } while (find (list, random)); |
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| 401 | return random; |
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| 402 | } |
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| 403 | |
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[9ff686] | 404 | static inline |
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| 405 | Variable chooseExtension (const Variable & alpha) |
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| 406 | { |
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| 407 | zz_p::init (getCharacteristic()); |
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| 408 | zz_pX NTLIrredpoly; |
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| 409 | int i, m; |
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| 410 | // extension of F_p needed |
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| 411 | if (alpha.level() == 1) |
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| 412 | { |
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| 413 | i= 1; |
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| 414 | m= 2; |
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| 415 | } //extension of F_p(alpha) |
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| 416 | if (alpha.level() != 1) |
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| 417 | { |
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| 418 | i= 4; |
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| 419 | m= degree (getMipo (alpha)); |
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| 420 | } |
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| 421 | BuildIrred (NTLIrredpoly, i*m); |
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| 422 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
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| 423 | return rootOf (newMipo); |
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| 424 | } |
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| 425 | |
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[806c18] | 426 | /// chooses a suitable extension of \f$ F_{p}(\alpha ) \f$ |
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[10af64] | 427 | /// we do not extend \f$ F_{p}(\alpha ) \f$ itself but extend \f$ F_{p} \f$ , |
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[806c18] | 428 | /// s.t. \f$ F_{p}(\alpha ) \subset F_{p}(\beta ) \f$ |
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[10af64] | 429 | static inline |
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[806c18] | 430 | void choose_extension (const int& d, const int& num_vars, Variable& beta) |
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[10af64] | 431 | { |
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| 432 | int p= getCharacteristic(); |
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[9a12097] | 433 | zz_p::init (p); |
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| 434 | zz_pX NTLirredpoly; |
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[10af64] | 435 | //TODO: replace d by max_{i} (deg_x{i}(f)) |
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[806c18] | 436 | int i= (int) (log ((double) ipower (d + 1, num_vars))/log ((double) p)); |
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[10af64] | 437 | int m= degree (getMipo (beta)); |
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| 438 | if (i <= 1) |
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| 439 | i= 2; |
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[806c18] | 440 | BuildIrred (NTLirredpoly, i*m); |
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[9a12097] | 441 | CanonicalForm mipo= convertNTLzzpX2CF (NTLirredpoly, Variable(1)); |
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[806c18] | 442 | beta= rootOf (mipo); |
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[10af64] | 443 | } |
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| 444 | |
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[597783] | 445 | CanonicalForm |
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| 446 | GCD_Fp_extension (const CanonicalForm& F, const CanonicalForm& G, |
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| 447 | CanonicalForm& coF, CanonicalForm& coG, |
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| 448 | Variable & alpha, CFList& l, bool& topLevel); |
---|
| 449 | |
---|
| 450 | CanonicalForm |
---|
| 451 | GCD_Fp_extension (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 452 | Variable & alpha, CFList& l, bool& topLevel) |
---|
| 453 | { |
---|
| 454 | CanonicalForm dummy1, dummy2; |
---|
| 455 | CanonicalForm result= GCD_Fp_extension (F, G, dummy1, dummy2, alpha, l, |
---|
| 456 | topLevel); |
---|
| 457 | return result; |
---|
| 458 | } |
---|
| 459 | |
---|
[806c18] | 460 | /// GCD of F and G over \f$ F_{p}(\alpha ) \f$ , |
---|
[dec1024] | 461 | /// l and topLevel are only used internally, output is monic |
---|
[10af64] | 462 | /// based on Alg. 7.2. as described in "Algorithms for |
---|
| 463 | /// Computer Algebra" by Geddes, Czapor, Labahn |
---|
[806c18] | 464 | CanonicalForm |
---|
| 465 | GCD_Fp_extension (const CanonicalForm& F, const CanonicalForm& G, |
---|
[597783] | 466 | CanonicalForm& coF, CanonicalForm& coG, |
---|
[806c18] | 467 | Variable & alpha, CFList& l, bool& topLevel) |
---|
| 468 | { |
---|
[10af64] | 469 | CanonicalForm A= F; |
---|
| 470 | CanonicalForm B= G; |
---|
[597783] | 471 | if (F.isZero() && degree(G) > 0) |
---|
| 472 | { |
---|
| 473 | coF= 0; |
---|
| 474 | coG= Lc (G); |
---|
| 475 | return G/Lc(G); |
---|
| 476 | } |
---|
| 477 | else if (G.isZero() && degree (F) > 0) |
---|
| 478 | { |
---|
| 479 | coF= Lc (F); |
---|
| 480 | coG= 0; |
---|
| 481 | return F/Lc(F); |
---|
| 482 | } |
---|
| 483 | else if (F.isZero() && G.isZero()) |
---|
| 484 | { |
---|
| 485 | coF= coG= 0; |
---|
| 486 | return F.genOne(); |
---|
| 487 | } |
---|
| 488 | if (F.inBaseDomain() || G.inBaseDomain()) |
---|
| 489 | { |
---|
| 490 | coF= F; |
---|
| 491 | coG= G; |
---|
| 492 | return F.genOne(); |
---|
| 493 | } |
---|
| 494 | if (F.isUnivariate() && fdivides(F, G, coG)) |
---|
| 495 | { |
---|
| 496 | coF= Lc (F); |
---|
| 497 | return F/Lc(F); |
---|
| 498 | } |
---|
| 499 | if (G.isUnivariate() && fdivides(G, F, coF)) |
---|
| 500 | { |
---|
| 501 | coG= Lc (G); |
---|
| 502 | return G/Lc(G); |
---|
| 503 | } |
---|
| 504 | if (F == G) |
---|
| 505 | { |
---|
| 506 | coF= coG= Lc (F); |
---|
| 507 | return F/Lc(F); |
---|
| 508 | } |
---|
[806c18] | 509 | |
---|
[10af64] | 510 | CFMap M,N; |
---|
[dec1024] | 511 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
[10af64] | 512 | |
---|
[597783] | 513 | if (best_level == 0) |
---|
| 514 | { |
---|
| 515 | coF= F; |
---|
| 516 | coG= G; |
---|
| 517 | return B.genOne(); |
---|
| 518 | } |
---|
[10af64] | 519 | |
---|
| 520 | A= M(A); |
---|
| 521 | B= M(B); |
---|
| 522 | |
---|
| 523 | Variable x= Variable(1); |
---|
| 524 | |
---|
[806c18] | 525 | //univariate case |
---|
| 526 | if (A.isUnivariate() && B.isUnivariate()) |
---|
[597783] | 527 | { |
---|
| 528 | CanonicalForm result= gcd (A, B); |
---|
| 529 | coF= N (A/result); |
---|
| 530 | coG= N (B/result); |
---|
| 531 | return N (result); |
---|
| 532 | } |
---|
[806c18] | 533 | |
---|
[10af64] | 534 | CanonicalForm cA, cB; // content of A and B |
---|
| 535 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
| 536 | CanonicalForm gcdcAcB; |
---|
[c4f4fd] | 537 | |
---|
[ea5ff1d] | 538 | cA = uni_content (A); |
---|
| 539 | cB = uni_content (B); |
---|
| 540 | gcdcAcB= gcd (cA, cB); |
---|
| 541 | ppA= A/cA; |
---|
| 542 | ppB= B/cB; |
---|
[10af64] | 543 | |
---|
[e243418] | 544 | int sizeNewtonPolyg; |
---|
| 545 | int ** newtonPolyg= NULL; |
---|
| 546 | mat_ZZ MM; |
---|
| 547 | vec_ZZ V; |
---|
[ea095d] | 548 | bool compressConvexDense= false; //(ppA.level() == 2 && ppB.level() == 2); |
---|
[e243418] | 549 | if (compressConvexDense) |
---|
| 550 | { |
---|
[597783] | 551 | CanonicalForm bufcA= cA; |
---|
| 552 | CanonicalForm bufcB= cB; |
---|
[e243418] | 553 | cA= content (ppA, 1); |
---|
| 554 | cB= content (ppB, 1); |
---|
| 555 | ppA /= cA; |
---|
| 556 | ppB /= cB; |
---|
| 557 | gcdcAcB *= gcd (cA, cB); |
---|
[597783] | 558 | cA *= bufcA; |
---|
| 559 | cB *= bufcB; |
---|
[e243418] | 560 | if (ppA.isUnivariate() || ppB.isUnivariate()) |
---|
| 561 | { |
---|
| 562 | if (ppA.level() == ppB.level()) |
---|
[597783] | 563 | { |
---|
| 564 | CanonicalForm result= gcd (ppA, ppB); |
---|
| 565 | coF= N ((ppA/result)*(cA/gcdcAcB)); |
---|
| 566 | coG= N ((ppB/result)*(cB/gcdcAcB)); |
---|
| 567 | return N (result*gcdcAcB); |
---|
| 568 | } |
---|
[e243418] | 569 | else |
---|
[597783] | 570 | { |
---|
| 571 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 572 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 573 | return N (gcdcAcB); |
---|
[597783] | 574 | } |
---|
[e243418] | 575 | } |
---|
| 576 | |
---|
| 577 | newtonPolyg= newtonPolygon (ppA,ppB, sizeNewtonPolyg); |
---|
| 578 | convexDense (newtonPolyg, sizeNewtonPolyg, MM, V); |
---|
| 579 | |
---|
| 580 | for (int i= 0; i < sizeNewtonPolyg; i++) |
---|
| 581 | delete [] newtonPolyg[i]; |
---|
| 582 | delete [] newtonPolyg; |
---|
| 583 | |
---|
| 584 | ppA= compress (ppA, MM, V, false); |
---|
| 585 | ppB= compress (ppB, MM, V, false); |
---|
| 586 | MM= inv (MM); |
---|
| 587 | |
---|
| 588 | if (ppA.isUnivariate() && ppB.isUnivariate()) |
---|
| 589 | { |
---|
| 590 | if (ppA.level() == ppB.level()) |
---|
[597783] | 591 | { |
---|
| 592 | CanonicalForm result= gcd (ppA, ppB); |
---|
| 593 | coF= N (decompress ((ppA/result), MM, V)*(cA/gcdcAcB)); |
---|
| 594 | coG= N (decompress ((ppB/result), MM, V)*(cB/gcdcAcB)); |
---|
| 595 | return N (decompress (result, MM, V)*gcdcAcB); |
---|
| 596 | } |
---|
[e243418] | 597 | else |
---|
[597783] | 598 | { |
---|
| 599 | coF= N (decompress (ppA, MM, V)); |
---|
| 600 | coG= N (decompress (ppB, MM, V)); |
---|
[a9a6dcb] | 601 | return N (gcdcAcB); |
---|
[597783] | 602 | } |
---|
[e243418] | 603 | } |
---|
| 604 | } |
---|
| 605 | |
---|
[10af64] | 606 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
[806c18] | 607 | CanonicalForm gcdlcAlcB; |
---|
[10af64] | 608 | |
---|
| 609 | lcA= uni_lcoeff (ppA); |
---|
| 610 | lcB= uni_lcoeff (ppB); |
---|
[806c18] | 611 | |
---|
[597783] | 612 | /*if (fdivides (lcA, lcB)) |
---|
[806c18] | 613 | { |
---|
[10af64] | 614 | if (fdivides (A, B)) |
---|
[806c18] | 615 | return F/Lc(F); |
---|
[10af64] | 616 | } |
---|
| 617 | if (fdivides (lcB, lcA)) |
---|
[806c18] | 618 | { |
---|
| 619 | if (fdivides (B, A)) |
---|
[10af64] | 620 | return G/Lc(G); |
---|
[597783] | 621 | }*/ |
---|
[10af64] | 622 | |
---|
| 623 | gcdlcAlcB= gcd (lcA, lcB); |
---|
| 624 | |
---|
| 625 | int d= totaldegree (ppA, Variable(2), Variable (ppA.level())); |
---|
| 626 | |
---|
[dec1024] | 627 | if (d == 0) |
---|
[597783] | 628 | { |
---|
| 629 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 630 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 631 | return N(gcdcAcB); |
---|
[597783] | 632 | } |
---|
[a9a6dcb] | 633 | |
---|
[10af64] | 634 | int d0= totaldegree (ppB, Variable(2), Variable (ppB.level())); |
---|
[806c18] | 635 | if (d0 < d) |
---|
| 636 | d= d0; |
---|
[dec1024] | 637 | if (d == 0) |
---|
[597783] | 638 | { |
---|
| 639 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 640 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 641 | return N(gcdcAcB); |
---|
[597783] | 642 | } |
---|
[10af64] | 643 | |
---|
| 644 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
[597783] | 645 | CanonicalForm newtonPoly, coF_random_element, coG_random_element, coF_m, |
---|
| 646 | coG_m, ppCoF, ppCoG; |
---|
[10af64] | 647 | |
---|
| 648 | newtonPoly= 1; |
---|
| 649 | m= gcdlcAlcB; |
---|
| 650 | G_m= 0; |
---|
[597783] | 651 | coF= 0; |
---|
| 652 | coG= 0; |
---|
[10af64] | 653 | H= 0; |
---|
| 654 | bool fail= false; |
---|
[dec1024] | 655 | topLevel= false; |
---|
[10af64] | 656 | bool inextension= false; |
---|
| 657 | Variable V_buf= alpha; |
---|
| 658 | CanonicalForm prim_elem, im_prim_elem; |
---|
| 659 | CFList source, dest; |
---|
[597783] | 660 | int bound1= degree (ppA, 1); |
---|
| 661 | int bound2= degree (ppB, 1); |
---|
[806c18] | 662 | do |
---|
[10af64] | 663 | { |
---|
[597783] | 664 | random_element= randomElement (m*lcA*lcB, V_buf, l, fail); |
---|
[806c18] | 665 | if (fail) |
---|
[10af64] | 666 | { |
---|
| 667 | source= CFList(); |
---|
| 668 | dest= CFList(); |
---|
[c4f4fd] | 669 | |
---|
[9ff686] | 670 | Variable V_buf3= V_buf; |
---|
| 671 | V_buf= chooseExtension (V_buf); |
---|
[10af64] | 672 | bool prim_fail= false; |
---|
| 673 | Variable V_buf2; |
---|
| 674 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
[c4f4fd] | 675 | |
---|
[9ff686] | 676 | if (V_buf3 != alpha) |
---|
| 677 | { |
---|
| 678 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
[597783] | 679 | G_m= mapDown (G_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 680 | coF_m= mapDown (coF_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 681 | coG_m= mapDown (coG_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
[9ff686] | 682 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
| 683 | source, dest); |
---|
| 684 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 685 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 686 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, |
---|
| 687 | source, dest); |
---|
[597783] | 688 | lcA= mapDown (lcA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 689 | lcB= mapDown (lcB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
[9ff686] | 690 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 691 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
| 692 | source, dest); |
---|
| 693 | } |
---|
| 694 | |
---|
[10af64] | 695 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
| 696 | if (prim_fail) |
---|
| 697 | ; //ERROR |
---|
| 698 | else |
---|
| 699 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
[c4f4fd] | 700 | |
---|
[10af64] | 701 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
[04dd0c] | 702 | DEBOUTLN (cerr, "getMipo (V_buf2)= " << getMipo (V_buf2)); |
---|
[10af64] | 703 | inextension= true; |
---|
[806c18] | 704 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 705 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
[10af64] | 706 | im_prim_elem, source, dest); |
---|
| 707 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 708 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
[597783] | 709 | coF_m= mapUp (coF_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 710 | coG_m= mapUp (coG_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
[806c18] | 711 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
[10af64] | 712 | source, dest); |
---|
| 713 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 714 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
[806c18] | 715 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
[10af64] | 716 | source, dest); |
---|
[597783] | 717 | lcA= mapUp (lcA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 718 | lcB= mapUp (lcB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
[10af64] | 719 | |
---|
| 720 | fail= false; |
---|
[597783] | 721 | random_element= randomElement (m*lcA*lcB, V_buf, l, fail ); |
---|
[a5cc7b3] | 722 | DEBOUTLN (cerr, "fail= " << fail); |
---|
[10af64] | 723 | CFList list; |
---|
| 724 | TIMING_START (gcd_recursion); |
---|
[806c18] | 725 | G_random_element= |
---|
[597783] | 726 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), |
---|
| 727 | coF_random_element, coG_random_element, V_buf, |
---|
[dec1024] | 728 | list, topLevel); |
---|
[806c18] | 729 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
[10af64] | 730 | "time for recursive call: "); |
---|
| 731 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 732 | } |
---|
[806c18] | 733 | else |
---|
[10af64] | 734 | { |
---|
| 735 | CFList list; |
---|
| 736 | TIMING_START (gcd_recursion); |
---|
[806c18] | 737 | G_random_element= |
---|
[597783] | 738 | GCD_Fp_extension (ppA(random_element, x), ppB(random_element, x), |
---|
| 739 | coF_random_element, coG_random_element, V_buf, |
---|
[dec1024] | 740 | list, topLevel); |
---|
[806c18] | 741 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
[10af64] | 742 | "time for recursive call: "); |
---|
| 743 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 744 | } |
---|
| 745 | |
---|
[a76d6fe] | 746 | if (!G_random_element.inCoeffDomain()) |
---|
| 747 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 748 | Variable (G_random_element.level())); |
---|
| 749 | else |
---|
| 750 | d0= 0; |
---|
| 751 | |
---|
[dec1024] | 752 | if (d0 == 0) |
---|
[597783] | 753 | { |
---|
| 754 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 755 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 756 | return N(gcdcAcB); |
---|
[597783] | 757 | } |
---|
[806c18] | 758 | if (d0 > d) |
---|
[10af64] | 759 | { |
---|
| 760 | if (!find (l, random_element)) |
---|
| 761 | l.append (random_element); |
---|
| 762 | continue; |
---|
| 763 | } |
---|
| 764 | |
---|
[806c18] | 765 | G_random_element= |
---|
[10af64] | 766 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
| 767 | * G_random_element; |
---|
[597783] | 768 | coF_random_element= (lcA(random_element,x)/uni_lcoeff(coF_random_element)) |
---|
| 769 | *coF_random_element; |
---|
| 770 | coG_random_element= (lcB(random_element,x)/uni_lcoeff(coG_random_element)) |
---|
| 771 | *coG_random_element; |
---|
[10af64] | 772 | |
---|
[a76d6fe] | 773 | if (!G_random_element.inCoeffDomain()) |
---|
| 774 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 775 | Variable (G_random_element.level())); |
---|
| 776 | else |
---|
| 777 | d0= 0; |
---|
| 778 | |
---|
[806c18] | 779 | if (d0 < d) |
---|
[10af64] | 780 | { |
---|
| 781 | m= gcdlcAlcB; |
---|
| 782 | newtonPoly= 1; |
---|
| 783 | G_m= 0; |
---|
| 784 | d= d0; |
---|
[597783] | 785 | coF_m= 0; |
---|
| 786 | coG_m= 0; |
---|
[10af64] | 787 | } |
---|
| 788 | |
---|
| 789 | TIMING_START (newton_interpolation); |
---|
| 790 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
[597783] | 791 | coF= newtonInterp (random_element, coF_random_element, newtonPoly, coF_m,x); |
---|
| 792 | coG= newtonInterp (random_element, coG_random_element, newtonPoly, coG_m,x); |
---|
[806c18] | 793 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
[10af64] | 794 | "time for newton interpolation: "); |
---|
| 795 | |
---|
[806c18] | 796 | //termination test |
---|
[597783] | 797 | if ((uni_lcoeff (H) == gcdlcAlcB) || (G_m == H)) |
---|
[10af64] | 798 | { |
---|
[597783] | 799 | if (gcdlcAlcB.isOne()) |
---|
| 800 | cH= 1; |
---|
| 801 | else |
---|
| 802 | cH= uni_content (H); |
---|
[10af64] | 803 | ppH= H/cH; |
---|
[597783] | 804 | CanonicalForm lcppH= gcdlcAlcB/cH; |
---|
| 805 | CanonicalForm ccoF= lcA/lcppH; |
---|
| 806 | ccoF /= Lc (ccoF); |
---|
| 807 | CanonicalForm ccoG= lcB/lcppH; |
---|
| 808 | ccoG /= Lc (ccoG); |
---|
| 809 | ppCoF= coF/ccoF; |
---|
| 810 | ppCoG= coG/ccoG; |
---|
[806c18] | 811 | if (inextension) |
---|
[10af64] | 812 | { |
---|
[597783] | 813 | if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
| 814 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
[1e4b53] | 815 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
[597783] | 816 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
[dec1024] | 817 | { |
---|
[597783] | 818 | CFList u, v; |
---|
[c723d80] | 819 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
| 820 | ppH= mapDown (ppH, prim_elem, im_prim_elem, alpha, u, v); |
---|
[597783] | 821 | ppCoF= mapDown (ppCoF, prim_elem, im_prim_elem, alpha, u, v); |
---|
| 822 | ppCoF= mapDown (ppCoG, prim_elem, im_prim_elem, alpha, u, v); |
---|
[c723d80] | 823 | ppH /= Lc(ppH); |
---|
| 824 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
[e243418] | 825 | if (compressConvexDense) |
---|
[597783] | 826 | { |
---|
[e243418] | 827 | ppH= decompress (ppH, MM, V); |
---|
[597783] | 828 | ppCoF= decompress (ppCoF, MM, V); |
---|
| 829 | ppCoG= decompress (ppCoG, MM, V); |
---|
| 830 | } |
---|
| 831 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
| 832 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
[10af64] | 833 | return N(gcdcAcB*ppH); |
---|
[dec1024] | 834 | } |
---|
[10af64] | 835 | } |
---|
[597783] | 836 | else if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
| 837 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
[1e4b53] | 838 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
[597783] | 839 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
[dec1024] | 840 | { |
---|
[e243418] | 841 | if (compressConvexDense) |
---|
[597783] | 842 | { |
---|
[e243418] | 843 | ppH= decompress (ppH, MM, V); |
---|
[597783] | 844 | ppCoF= decompress (ppCoF, MM, V); |
---|
| 845 | ppCoG= decompress (ppCoG, MM, V); |
---|
| 846 | } |
---|
| 847 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
| 848 | coG= N ((cB/gcdcAcB)*ppCoG);; |
---|
[dec1024] | 849 | return N(gcdcAcB*ppH); |
---|
| 850 | } |
---|
[10af64] | 851 | } |
---|
| 852 | |
---|
| 853 | G_m= H; |
---|
[597783] | 854 | coF_m= coF; |
---|
| 855 | coG_m= coG; |
---|
[10af64] | 856 | newtonPoly= newtonPoly*(x - random_element); |
---|
| 857 | m= m*(x - random_element); |
---|
| 858 | if (!find (l, random_element)) |
---|
| 859 | l.append (random_element); |
---|
| 860 | } while (1); |
---|
| 861 | } |
---|
| 862 | |
---|
[806c18] | 863 | /// compute a random element a of GF, s.t. F(a) \f$ \neq 0 \f$ , F is a |
---|
[10af64] | 864 | /// univariate polynomial, returns fail if there are no field elements left |
---|
| 865 | /// which have not been used before |
---|
[04dd0c] | 866 | static inline |
---|
[10af64] | 867 | CanonicalForm |
---|
| 868 | GFRandomElement (const CanonicalForm& F, CFList& list, bool& fail) |
---|
| 869 | { |
---|
| 870 | fail= false; |
---|
| 871 | Variable x= F.mvar(); |
---|
| 872 | GFRandom genGF; |
---|
| 873 | CanonicalForm random; |
---|
| 874 | int p= getCharacteristic(); |
---|
| 875 | int d= getGFDegree(); |
---|
[c4f4fd] | 876 | int bound= ipower (p, d); |
---|
[806c18] | 877 | do |
---|
[10af64] | 878 | { |
---|
| 879 | if (list.length() == bound) |
---|
| 880 | { |
---|
| 881 | fail= true; |
---|
| 882 | break; |
---|
| 883 | } |
---|
| 884 | if (list.length() < 1) |
---|
| 885 | random= 0; |
---|
[806c18] | 886 | else |
---|
[10af64] | 887 | { |
---|
| 888 | random= genGF.generate(); |
---|
| 889 | while (find (list, random)) |
---|
| 890 | random= genGF.generate(); |
---|
| 891 | } |
---|
[806c18] | 892 | if (F (random, x) == 0) |
---|
[10af64] | 893 | { |
---|
| 894 | list.append (random); |
---|
| 895 | continue; |
---|
| 896 | } |
---|
| 897 | } while (find (list, random)); |
---|
| 898 | return random; |
---|
| 899 | } |
---|
| 900 | |
---|
[597783] | 901 | CanonicalForm |
---|
| 902 | GCD_GF (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 903 | CanonicalForm& coF, CanonicalForm& coG, |
---|
| 904 | CFList& l, bool& topLevel); |
---|
| 905 | |
---|
| 906 | CanonicalForm |
---|
| 907 | GCD_GF (const CanonicalForm& F, const CanonicalForm& G, CFList& l, |
---|
| 908 | bool& topLevel) |
---|
| 909 | { |
---|
| 910 | CanonicalForm dummy1, dummy2; |
---|
| 911 | CanonicalForm result= GCD_GF (F, G, dummy1, dummy2, l, topLevel); |
---|
| 912 | return result; |
---|
| 913 | } |
---|
| 914 | |
---|
[10af64] | 915 | /// GCD of F and G over GF, based on Alg. 7.2. as described in "Algorithms for |
---|
| 916 | /// Computer Algebra" by Geddes, Czapor, Labahn |
---|
| 917 | /// Usually this algorithm will be faster than GCD_Fp_extension since GF has |
---|
| 918 | /// faster field arithmetics, however it might fail if the input is large since |
---|
| 919 | /// the size of the base field is bounded by 2^16, output is monic |
---|
[597783] | 920 | CanonicalForm |
---|
| 921 | GCD_GF (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 922 | CanonicalForm& coF, CanonicalForm& coG, |
---|
[806c18] | 923 | CFList& l, bool& topLevel) |
---|
| 924 | { |
---|
[10af64] | 925 | CanonicalForm A= F; |
---|
| 926 | CanonicalForm B= G; |
---|
[597783] | 927 | if (F.isZero() && degree(G) > 0) |
---|
| 928 | { |
---|
| 929 | coF= 0; |
---|
| 930 | coG= Lc (G); |
---|
| 931 | return G/Lc(G); |
---|
| 932 | } |
---|
| 933 | else if (G.isZero() && degree (F) > 0) |
---|
| 934 | { |
---|
| 935 | coF= Lc (F); |
---|
| 936 | coG= 0; |
---|
| 937 | return F/Lc(F); |
---|
| 938 | } |
---|
| 939 | else if (F.isZero() && G.isZero()) |
---|
| 940 | { |
---|
| 941 | coF= coG= 0; |
---|
| 942 | return F.genOne(); |
---|
| 943 | } |
---|
| 944 | if (F.inBaseDomain() || G.inBaseDomain()) |
---|
| 945 | { |
---|
| 946 | coF= F; |
---|
| 947 | coG= G; |
---|
| 948 | return F.genOne(); |
---|
| 949 | } |
---|
| 950 | if (F.isUnivariate() && fdivides(F, G, coG)) |
---|
| 951 | { |
---|
| 952 | coF= Lc (F); |
---|
| 953 | return F/Lc(F); |
---|
| 954 | } |
---|
| 955 | if (G.isUnivariate() && fdivides(G, F, coF)) |
---|
| 956 | { |
---|
| 957 | coG= Lc (G); |
---|
| 958 | return G/Lc(G); |
---|
| 959 | } |
---|
| 960 | if (F == G) |
---|
| 961 | { |
---|
| 962 | coF= coG= Lc (F); |
---|
| 963 | return F/Lc(F); |
---|
| 964 | } |
---|
[806c18] | 965 | |
---|
[10af64] | 966 | CFMap M,N; |
---|
[dec1024] | 967 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
[10af64] | 968 | |
---|
[597783] | 969 | if (best_level == 0) |
---|
| 970 | { |
---|
| 971 | coF= F; |
---|
| 972 | coG= G; |
---|
| 973 | return B.genOne(); |
---|
| 974 | } |
---|
[10af64] | 975 | |
---|
| 976 | A= M(A); |
---|
| 977 | B= M(B); |
---|
| 978 | |
---|
| 979 | Variable x= Variable(1); |
---|
| 980 | |
---|
[806c18] | 981 | //univariate case |
---|
| 982 | if (A.isUnivariate() && B.isUnivariate()) |
---|
[597783] | 983 | { |
---|
| 984 | CanonicalForm result= gcd (A, B); |
---|
| 985 | coF= N (A/result); |
---|
| 986 | coG= N (B/result); |
---|
| 987 | return N (result); |
---|
| 988 | } |
---|
[10af64] | 989 | |
---|
| 990 | CanonicalForm cA, cB; // content of A and B |
---|
| 991 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
| 992 | CanonicalForm gcdcAcB; |
---|
| 993 | |
---|
[ea5ff1d] | 994 | cA = uni_content (A); |
---|
| 995 | cB = uni_content (B); |
---|
| 996 | gcdcAcB= gcd (cA, cB); |
---|
| 997 | ppA= A/cA; |
---|
| 998 | ppB= B/cB; |
---|
[10af64] | 999 | |
---|
[e243418] | 1000 | int sizeNewtonPolyg; |
---|
| 1001 | int ** newtonPolyg= NULL; |
---|
| 1002 | mat_ZZ MM; |
---|
| 1003 | vec_ZZ V; |
---|
[ea095d] | 1004 | bool compressConvexDense= false; //(ppA.level() == 2 && ppB.level() == 2); |
---|
[e243418] | 1005 | if (compressConvexDense) |
---|
| 1006 | { |
---|
[597783] | 1007 | CanonicalForm bufcA= cA; |
---|
| 1008 | CanonicalForm bufcB= cB; |
---|
[e243418] | 1009 | cA= content (ppA, 1); |
---|
| 1010 | cB= content (ppB, 1); |
---|
| 1011 | ppA /= cA; |
---|
| 1012 | ppB /= cB; |
---|
| 1013 | gcdcAcB *= gcd (cA, cB); |
---|
[597783] | 1014 | cA *= bufcA; |
---|
| 1015 | cB *= bufcB; |
---|
[e243418] | 1016 | if (ppA.isUnivariate() || ppB.isUnivariate()) |
---|
| 1017 | { |
---|
| 1018 | if (ppA.level() == ppB.level()) |
---|
[597783] | 1019 | { |
---|
| 1020 | CanonicalForm result= gcd (ppA, ppB); |
---|
| 1021 | coF= N ((ppA/result)*(cA/gcdcAcB)); |
---|
| 1022 | coG= N ((ppB/result)*(cB/gcdcAcB)); |
---|
| 1023 | return N (result*gcdcAcB); |
---|
| 1024 | } |
---|
[e243418] | 1025 | else |
---|
[597783] | 1026 | { |
---|
| 1027 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 1028 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 1029 | return N (gcdcAcB); |
---|
[597783] | 1030 | } |
---|
[e243418] | 1031 | } |
---|
| 1032 | |
---|
| 1033 | newtonPolyg= newtonPolygon (ppA,ppB, sizeNewtonPolyg); |
---|
| 1034 | convexDense (newtonPolyg, sizeNewtonPolyg, MM, V); |
---|
| 1035 | |
---|
| 1036 | for (int i= 0; i < sizeNewtonPolyg; i++) |
---|
| 1037 | delete [] newtonPolyg[i]; |
---|
| 1038 | delete [] newtonPolyg; |
---|
| 1039 | |
---|
| 1040 | ppA= compress (ppA, MM, V, false); |
---|
| 1041 | ppB= compress (ppB, MM, V, false); |
---|
| 1042 | MM= inv (MM); |
---|
| 1043 | |
---|
| 1044 | if (ppA.isUnivariate() && ppB.isUnivariate()) |
---|
| 1045 | { |
---|
| 1046 | if (ppA.level() == ppB.level()) |
---|
[597783] | 1047 | { |
---|
| 1048 | CanonicalForm result= gcd (ppA, ppB); |
---|
| 1049 | coF= N (decompress ((ppA/result), MM, V)*(cA/gcdcAcB)); |
---|
| 1050 | coG= N (decompress ((ppB/result), MM, V)*(cB/gcdcAcB)); |
---|
| 1051 | return N (decompress (result, MM, V)*gcdcAcB); |
---|
| 1052 | } |
---|
[e243418] | 1053 | else |
---|
[597783] | 1054 | { |
---|
| 1055 | coF= N (decompress (ppA, MM, V)); |
---|
| 1056 | coG= N (decompress (ppB, MM, V)); |
---|
[a9a6dcb] | 1057 | return N (gcdcAcB); |
---|
[597783] | 1058 | } |
---|
[e243418] | 1059 | } |
---|
| 1060 | } |
---|
| 1061 | |
---|
[10af64] | 1062 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
[806c18] | 1063 | CanonicalForm gcdlcAlcB; |
---|
[10af64] | 1064 | |
---|
| 1065 | lcA= uni_lcoeff (ppA); |
---|
| 1066 | lcB= uni_lcoeff (ppB); |
---|
| 1067 | |
---|
[597783] | 1068 | /*if (fdivides (lcA, lcB)) |
---|
[806c18] | 1069 | { |
---|
[597783] | 1070 | if (fdivides (ppA, ppB, coG)) |
---|
| 1071 | { |
---|
| 1072 | coF= 1; |
---|
| 1073 | if (compressConvexDense) |
---|
| 1074 | coG= decompress (coG, MM, V); |
---|
| 1075 | coG= N (coG*(cB/gcdcAcB)); |
---|
[806c18] | 1076 | return F; |
---|
[597783] | 1077 | } |
---|
[806c18] | 1078 | } |
---|
| 1079 | if (fdivides (lcB, lcA)) |
---|
| 1080 | { |
---|
[597783] | 1081 | if (fdivides (ppB, ppA, coF)) |
---|
| 1082 | { |
---|
| 1083 | coG= 1; |
---|
| 1084 | if (compressConvexDense) |
---|
| 1085 | coF= decompress (coF, MM, V); |
---|
| 1086 | coF= N (coF*(cA/gcdcAcB)); |
---|
[10af64] | 1087 | return G; |
---|
[597783] | 1088 | } |
---|
| 1089 | }*/ |
---|
[10af64] | 1090 | |
---|
| 1091 | gcdlcAlcB= gcd (lcA, lcB); |
---|
| 1092 | |
---|
| 1093 | int d= totaldegree (ppA, Variable(2), Variable (ppA.level())); |
---|
[dec1024] | 1094 | if (d == 0) |
---|
[597783] | 1095 | { |
---|
| 1096 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 1097 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 1098 | return N(gcdcAcB); |
---|
[597783] | 1099 | } |
---|
[10af64] | 1100 | int d0= totaldegree (ppB, Variable(2), Variable (ppB.level())); |
---|
[806c18] | 1101 | if (d0 < d) |
---|
| 1102 | d= d0; |
---|
[dec1024] | 1103 | if (d == 0) |
---|
[597783] | 1104 | { |
---|
| 1105 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 1106 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 1107 | return N(gcdcAcB); |
---|
[597783] | 1108 | } |
---|
[10af64] | 1109 | |
---|
| 1110 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
[597783] | 1111 | CanonicalForm newtonPoly, coF_random_element, coG_random_element, coF_m, |
---|
| 1112 | coG_m, ppCoF, ppCoG; |
---|
[10af64] | 1113 | |
---|
| 1114 | newtonPoly= 1; |
---|
| 1115 | m= gcdlcAlcB; |
---|
| 1116 | G_m= 0; |
---|
[597783] | 1117 | coF= 0; |
---|
| 1118 | coG= 0; |
---|
[10af64] | 1119 | H= 0; |
---|
| 1120 | bool fail= false; |
---|
[597783] | 1121 | //topLevel= false; |
---|
[10af64] | 1122 | bool inextension= false; |
---|
[c1b9927] | 1123 | int p=-1; |
---|
[10af64] | 1124 | int k= getGFDegree(); |
---|
| 1125 | int kk; |
---|
[88f3644] | 1126 | int expon; |
---|
[10af64] | 1127 | char gf_name_buf= gf_name; |
---|
[597783] | 1128 | int bound1= degree (ppA, 1); |
---|
| 1129 | int bound2= degree (ppB, 1); |
---|
[806c18] | 1130 | do |
---|
[10af64] | 1131 | { |
---|
[597783] | 1132 | random_element= GFRandomElement (m*lcA*lcB, l, fail); |
---|
[806c18] | 1133 | if (fail) |
---|
| 1134 | { |
---|
[10af64] | 1135 | p= getCharacteristic(); |
---|
[9ff686] | 1136 | expon= 2; |
---|
[806c18] | 1137 | kk= getGFDegree(); |
---|
| 1138 | if (ipower (p, kk*expon) < (1 << 16)) |
---|
[10af64] | 1139 | setCharacteristic (p, kk*(int)expon, 'b'); |
---|
[806c18] | 1140 | else |
---|
[10af64] | 1141 | { |
---|
[04dd0c] | 1142 | expon= (int) floor((log ((double)((1<<16) - 1)))/(log((double)p)*kk)); |
---|
[10af64] | 1143 | ASSERT (expon >= 2, "not enough points in GCD_GF"); |
---|
| 1144 | setCharacteristic (p, (int)(kk*expon), 'b'); |
---|
| 1145 | } |
---|
| 1146 | inextension= true; |
---|
| 1147 | fail= false; |
---|
[806c18] | 1148 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
[10af64] | 1149 | i.getItem()= GFMapUp (i.getItem(), kk); |
---|
| 1150 | m= GFMapUp (m, kk); |
---|
| 1151 | G_m= GFMapUp (G_m, kk); |
---|
| 1152 | newtonPoly= GFMapUp (newtonPoly, kk); |
---|
[597783] | 1153 | coF_m= GFMapUp (coF_m, kk); |
---|
| 1154 | coG_m= GFMapUp (coG_m, kk); |
---|
[10af64] | 1155 | ppA= GFMapUp (ppA, kk); |
---|
| 1156 | ppB= GFMapUp (ppB, kk); |
---|
| 1157 | gcdlcAlcB= GFMapUp (gcdlcAlcB, kk); |
---|
[597783] | 1158 | lcA= GFMapUp (lcA, kk); |
---|
| 1159 | lcB= GFMapUp (lcB, kk); |
---|
| 1160 | random_element= GFRandomElement (m*lcA*lcB, l, fail); |
---|
[a5cc7b3] | 1161 | DEBOUTLN (cerr, "fail= " << fail); |
---|
[10af64] | 1162 | CFList list; |
---|
| 1163 | TIMING_START (gcd_recursion); |
---|
[806c18] | 1164 | G_random_element= GCD_GF (ppA(random_element, x), ppB(random_element, x), |
---|
[597783] | 1165 | coF_random_element, coG_random_element, |
---|
[dec1024] | 1166 | list, topLevel); |
---|
[806c18] | 1167 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
[10af64] | 1168 | "time for recursive call: "); |
---|
| 1169 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 1170 | } |
---|
[806c18] | 1171 | else |
---|
[10af64] | 1172 | { |
---|
| 1173 | CFList list; |
---|
| 1174 | TIMING_START (gcd_recursion); |
---|
[806c18] | 1175 | G_random_element= GCD_GF (ppA(random_element, x), ppB(random_element, x), |
---|
[597783] | 1176 | coF_random_element, coG_random_element, |
---|
[dec1024] | 1177 | list, topLevel); |
---|
[806c18] | 1178 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
[10af64] | 1179 | "time for recursive call: "); |
---|
| 1180 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 1181 | } |
---|
| 1182 | |
---|
[a76d6fe] | 1183 | if (!G_random_element.inCoeffDomain()) |
---|
| 1184 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 1185 | Variable (G_random_element.level())); |
---|
| 1186 | else |
---|
| 1187 | d0= 0; |
---|
| 1188 | |
---|
[806c18] | 1189 | if (d0 == 0) |
---|
[10af64] | 1190 | { |
---|
[806c18] | 1191 | if (inextension) |
---|
[10af64] | 1192 | setCharacteristic (p, k, gf_name_buf); |
---|
[597783] | 1193 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 1194 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 1195 | return N(gcdcAcB); |
---|
[806c18] | 1196 | } |
---|
| 1197 | if (d0 > d) |
---|
[10af64] | 1198 | { |
---|
| 1199 | if (!find (l, random_element)) |
---|
| 1200 | l.append (random_element); |
---|
| 1201 | continue; |
---|
| 1202 | } |
---|
| 1203 | |
---|
[806c18] | 1204 | G_random_element= |
---|
[10af64] | 1205 | (gcdlcAlcB(random_element, x)/uni_lcoeff(G_random_element)) * |
---|
| 1206 | G_random_element; |
---|
[597783] | 1207 | |
---|
| 1208 | coF_random_element= (lcA(random_element,x)/uni_lcoeff(coF_random_element)) |
---|
| 1209 | *coF_random_element; |
---|
| 1210 | coG_random_element= (lcB(random_element,x)/uni_lcoeff(coG_random_element)) |
---|
| 1211 | *coG_random_element; |
---|
| 1212 | |
---|
[a76d6fe] | 1213 | if (!G_random_element.inCoeffDomain()) |
---|
| 1214 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 1215 | Variable (G_random_element.level())); |
---|
| 1216 | else |
---|
| 1217 | d0= 0; |
---|
[10af64] | 1218 | |
---|
[806c18] | 1219 | if (d0 < d) |
---|
[10af64] | 1220 | { |
---|
| 1221 | m= gcdlcAlcB; |
---|
| 1222 | newtonPoly= 1; |
---|
| 1223 | G_m= 0; |
---|
| 1224 | d= d0; |
---|
[597783] | 1225 | coF_m= 0; |
---|
| 1226 | coG_m= 0; |
---|
[10af64] | 1227 | } |
---|
| 1228 | |
---|
| 1229 | TIMING_START (newton_interpolation); |
---|
| 1230 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
[597783] | 1231 | coF= newtonInterp (random_element, coF_random_element, newtonPoly, coF_m,x); |
---|
| 1232 | coG= newtonInterp (random_element, coG_random_element, newtonPoly, coG_m,x); |
---|
| 1233 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
| 1234 | "time for newton interpolation: "); |
---|
[10af64] | 1235 | |
---|
[806c18] | 1236 | //termination test |
---|
[597783] | 1237 | if ((uni_lcoeff (H) == gcdlcAlcB) || (G_m == H)) |
---|
[10af64] | 1238 | { |
---|
[597783] | 1239 | if (gcdlcAlcB.isOne()) |
---|
| 1240 | cH= 1; |
---|
| 1241 | else |
---|
| 1242 | cH= uni_content (H); |
---|
[10af64] | 1243 | ppH= H/cH; |
---|
[597783] | 1244 | CanonicalForm lcppH= gcdlcAlcB/cH; |
---|
| 1245 | CanonicalForm ccoF= lcA/lcppH; |
---|
| 1246 | ccoF /= Lc (ccoF); |
---|
| 1247 | CanonicalForm ccoG= lcB/lcppH; |
---|
| 1248 | ccoG /= Lc (ccoG); |
---|
| 1249 | ppCoF= coF/ccoF; |
---|
| 1250 | ppCoG= coG/ccoG; |
---|
[806c18] | 1251 | if (inextension) |
---|
[10af64] | 1252 | { |
---|
[597783] | 1253 | if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
| 1254 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
[1e4b53] | 1255 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
[597783] | 1256 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
[10af64] | 1257 | { |
---|
| 1258 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
| 1259 | ppH= GFMapDown (ppH, k); |
---|
[597783] | 1260 | ppCoF= GFMapDown (ppCoF, k); |
---|
| 1261 | ppCoG= GFMapDown (ppCoG, k); |
---|
[10af64] | 1262 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
[e243418] | 1263 | if (compressConvexDense) |
---|
[597783] | 1264 | { |
---|
[e243418] | 1265 | ppH= decompress (ppH, MM, V); |
---|
[597783] | 1266 | ppCoF= decompress (ppCoF, MM, V); |
---|
| 1267 | ppCoG= decompress (ppCoG, MM, V); |
---|
| 1268 | } |
---|
| 1269 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
| 1270 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
[10af64] | 1271 | setCharacteristic (p, k, gf_name_buf); |
---|
| 1272 | return N(gcdcAcB*ppH); |
---|
| 1273 | } |
---|
| 1274 | } |
---|
[806c18] | 1275 | else |
---|
[10af64] | 1276 | { |
---|
[597783] | 1277 | if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
| 1278 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
[1e4b53] | 1279 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
[597783] | 1280 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
[dec1024] | 1281 | { |
---|
[e243418] | 1282 | if (compressConvexDense) |
---|
[597783] | 1283 | { |
---|
[e243418] | 1284 | ppH= decompress (ppH, MM, V); |
---|
[597783] | 1285 | ppCoF= decompress (ppCoF, MM, V); |
---|
| 1286 | ppCoG= decompress (ppCoG, MM, V); |
---|
| 1287 | } |
---|
| 1288 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
| 1289 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
[10af64] | 1290 | return N(gcdcAcB*ppH); |
---|
[dec1024] | 1291 | } |
---|
[10af64] | 1292 | } |
---|
| 1293 | } |
---|
| 1294 | |
---|
| 1295 | G_m= H; |
---|
[597783] | 1296 | coF_m= coF; |
---|
| 1297 | coG_m= coG; |
---|
[10af64] | 1298 | newtonPoly= newtonPoly*(x - random_element); |
---|
| 1299 | m= m*(x - random_element); |
---|
| 1300 | if (!find (l, random_element)) |
---|
| 1301 | l.append (random_element); |
---|
| 1302 | } while (1); |
---|
| 1303 | } |
---|
| 1304 | |
---|
| 1305 | /// F is assumed to be an univariate polynomial in x, |
---|
[806c18] | 1306 | /// computes a random monic irreducible univariate polynomial of random |
---|
[10af64] | 1307 | /// degree < i in x which does not divide F |
---|
[806c18] | 1308 | CanonicalForm |
---|
| 1309 | randomIrredpoly (int i, const Variable & x) |
---|
[10af64] | 1310 | { |
---|
| 1311 | int p= getCharacteristic(); |
---|
[9a12097] | 1312 | zz_p::init (p); |
---|
| 1313 | zz_pX NTLirredpoly; |
---|
[10af64] | 1314 | CanonicalForm CFirredpoly; |
---|
[04dd0c] | 1315 | BuildIrred (NTLirredpoly, i + 1); |
---|
[9a12097] | 1316 | CFirredpoly= convertNTLzzpX2CF (NTLirredpoly, x); |
---|
[10af64] | 1317 | return CFirredpoly; |
---|
[806c18] | 1318 | } |
---|
[10af64] | 1319 | |
---|
[04dd0c] | 1320 | static inline |
---|
[10af64] | 1321 | CanonicalForm |
---|
| 1322 | FpRandomElement (const CanonicalForm& F, CFList& list, bool& fail) |
---|
| 1323 | { |
---|
| 1324 | fail= false; |
---|
| 1325 | Variable x= F.mvar(); |
---|
| 1326 | FFRandom genFF; |
---|
| 1327 | CanonicalForm random; |
---|
| 1328 | int p= getCharacteristic(); |
---|
[88f3644] | 1329 | int bound= p; |
---|
[806c18] | 1330 | do |
---|
[10af64] | 1331 | { |
---|
| 1332 | if (list.length() == bound) |
---|
| 1333 | { |
---|
| 1334 | fail= true; |
---|
| 1335 | break; |
---|
| 1336 | } |
---|
| 1337 | if (list.length() < 1) |
---|
| 1338 | random= 0; |
---|
[806c18] | 1339 | else |
---|
[10af64] | 1340 | { |
---|
| 1341 | random= genFF.generate(); |
---|
| 1342 | while (find (list, random)) |
---|
| 1343 | random= genFF.generate(); |
---|
| 1344 | } |
---|
[806c18] | 1345 | if (F (random, x) == 0) |
---|
[10af64] | 1346 | { |
---|
| 1347 | list.append (random); |
---|
| 1348 | continue; |
---|
| 1349 | } |
---|
| 1350 | } while (find (list, random)); |
---|
| 1351 | return random; |
---|
| 1352 | } |
---|
| 1353 | |
---|
[597783] | 1354 | CanonicalForm |
---|
| 1355 | GCD_small_p (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 1356 | CanonicalForm& coF, CanonicalForm& coG, |
---|
| 1357 | bool& topLevel, CFList& l); |
---|
| 1358 | |
---|
| 1359 | CanonicalForm |
---|
| 1360 | GCD_small_p (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 1361 | bool& topLevel, CFList& l) |
---|
| 1362 | { |
---|
| 1363 | CanonicalForm dummy1, dummy2; |
---|
| 1364 | CanonicalForm result= GCD_small_p (F, G, dummy1, dummy2, topLevel, l); |
---|
| 1365 | return result; |
---|
| 1366 | } |
---|
| 1367 | |
---|
| 1368 | CanonicalForm |
---|
| 1369 | GCD_small_p (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 1370 | CanonicalForm& coF, CanonicalForm& coG, |
---|
| 1371 | bool& topLevel, CFList& l) |
---|
[10af64] | 1372 | { |
---|
| 1373 | CanonicalForm A= F; |
---|
| 1374 | CanonicalForm B= G; |
---|
[597783] | 1375 | if (F.isZero() && degree(G) > 0) |
---|
| 1376 | { |
---|
| 1377 | coF= 0; |
---|
| 1378 | coG= Lc (G); |
---|
| 1379 | return G/Lc(G); |
---|
| 1380 | } |
---|
| 1381 | else if (G.isZero() && degree (F) > 0) |
---|
| 1382 | { |
---|
| 1383 | coF= Lc (F); |
---|
| 1384 | coG= 0; |
---|
| 1385 | return F/Lc(F); |
---|
| 1386 | } |
---|
| 1387 | else if (F.isZero() && G.isZero()) |
---|
| 1388 | { |
---|
| 1389 | coF= coG= 0; |
---|
| 1390 | return F.genOne(); |
---|
| 1391 | } |
---|
| 1392 | if (F.inBaseDomain() || G.inBaseDomain()) |
---|
| 1393 | { |
---|
| 1394 | coF= F; |
---|
| 1395 | coG= G; |
---|
| 1396 | return F.genOne(); |
---|
| 1397 | } |
---|
| 1398 | if (F.isUnivariate() && fdivides(F, G, coG)) |
---|
| 1399 | { |
---|
| 1400 | coF= Lc (F); |
---|
| 1401 | return F/Lc(F); |
---|
| 1402 | } |
---|
| 1403 | if (G.isUnivariate() && fdivides(G, F, coF)) |
---|
| 1404 | { |
---|
| 1405 | coG= Lc (G); |
---|
| 1406 | return G/Lc(G); |
---|
| 1407 | } |
---|
| 1408 | if (F == G) |
---|
| 1409 | { |
---|
| 1410 | coF= coG= Lc (F); |
---|
| 1411 | return F/Lc(F); |
---|
| 1412 | } |
---|
[10af64] | 1413 | CFMap M,N; |
---|
[dec1024] | 1414 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
[10af64] | 1415 | |
---|
[597783] | 1416 | if (best_level == 0) |
---|
| 1417 | { |
---|
| 1418 | coF= F; |
---|
| 1419 | coG= G; |
---|
| 1420 | return B.genOne(); |
---|
| 1421 | } |
---|
[10af64] | 1422 | |
---|
| 1423 | A= M(A); |
---|
| 1424 | B= M(B); |
---|
| 1425 | |
---|
[c4f4fd] | 1426 | Variable x= Variable (1); |
---|
| 1427 | |
---|
[806c18] | 1428 | //univariate case |
---|
| 1429 | if (A.isUnivariate() && B.isUnivariate()) |
---|
[597783] | 1430 | { |
---|
| 1431 | CanonicalForm result= gcd (A, B); |
---|
| 1432 | coF= N (A/result); |
---|
| 1433 | coG= N (B/result); |
---|
| 1434 | return N (result); |
---|
| 1435 | } |
---|
[10af64] | 1436 | |
---|
| 1437 | CanonicalForm cA, cB; // content of A and B |
---|
| 1438 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
| 1439 | CanonicalForm gcdcAcB; |
---|
[dec1024] | 1440 | |
---|
[ea5ff1d] | 1441 | cA = uni_content (A); |
---|
| 1442 | cB = uni_content (B); |
---|
| 1443 | gcdcAcB= gcd (cA, cB); |
---|
| 1444 | ppA= A/cA; |
---|
| 1445 | ppB= B/cB; |
---|
[10af64] | 1446 | |
---|
[e243418] | 1447 | int sizeNewtonPolyg; |
---|
| 1448 | int ** newtonPolyg= NULL; |
---|
| 1449 | mat_ZZ MM; |
---|
| 1450 | vec_ZZ V; |
---|
[ea095d] | 1451 | bool compressConvexDense= false; //(ppA.level() == 2 && ppB.level() == 2); |
---|
[e243418] | 1452 | if (compressConvexDense) |
---|
| 1453 | { |
---|
[597783] | 1454 | CanonicalForm bufcA= cA; |
---|
| 1455 | CanonicalForm bufcB= cB; |
---|
[e243418] | 1456 | cA= content (ppA, 1); |
---|
| 1457 | cB= content (ppB, 1); |
---|
| 1458 | ppA /= cA; |
---|
| 1459 | ppB /= cB; |
---|
| 1460 | gcdcAcB *= gcd (cA, cB); |
---|
[597783] | 1461 | cA *= bufcA; |
---|
| 1462 | cB *= bufcB; |
---|
[e243418] | 1463 | if (ppA.isUnivariate() || ppB.isUnivariate()) |
---|
| 1464 | { |
---|
| 1465 | if (ppA.level() == ppB.level()) |
---|
[597783] | 1466 | { |
---|
| 1467 | CanonicalForm result= gcd (ppA, ppB); |
---|
| 1468 | coF= N ((ppA/result)*(cA/gcdcAcB)); |
---|
| 1469 | coG= N ((ppB/result)*(cB/gcdcAcB)); |
---|
| 1470 | return N (result*gcdcAcB); |
---|
| 1471 | } |
---|
[e243418] | 1472 | else |
---|
[597783] | 1473 | { |
---|
| 1474 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 1475 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 1476 | return N (gcdcAcB); |
---|
[597783] | 1477 | } |
---|
[e243418] | 1478 | } |
---|
| 1479 | |
---|
| 1480 | newtonPolyg= newtonPolygon (ppA,ppB, sizeNewtonPolyg); |
---|
| 1481 | convexDense (newtonPolyg, sizeNewtonPolyg, MM, V); |
---|
| 1482 | |
---|
| 1483 | for (int i= 0; i < sizeNewtonPolyg; i++) |
---|
| 1484 | delete [] newtonPolyg[i]; |
---|
| 1485 | delete [] newtonPolyg; |
---|
| 1486 | |
---|
| 1487 | ppA= compress (ppA, MM, V, false); |
---|
| 1488 | ppB= compress (ppB, MM, V, false); |
---|
| 1489 | MM= inv (MM); |
---|
| 1490 | |
---|
| 1491 | if (ppA.isUnivariate() && ppB.isUnivariate()) |
---|
| 1492 | { |
---|
| 1493 | if (ppA.level() == ppB.level()) |
---|
[597783] | 1494 | { |
---|
| 1495 | CanonicalForm result= gcd (ppA, ppB); |
---|
| 1496 | coF= N (decompress ((ppA/result), MM, V)*(cA/gcdcAcB)); |
---|
| 1497 | coG= N (decompress ((ppB/result), MM, V)*(cB/gcdcAcB)); |
---|
| 1498 | return N (decompress (result, MM, V)*gcdcAcB); |
---|
| 1499 | } |
---|
[e243418] | 1500 | else |
---|
[597783] | 1501 | { |
---|
| 1502 | coF= N (decompress (ppA, MM, V)); |
---|
| 1503 | coG= N (decompress (ppB, MM, V)); |
---|
[a9a6dcb] | 1504 | return N (gcdcAcB); |
---|
[597783] | 1505 | } |
---|
[e243418] | 1506 | } |
---|
| 1507 | } |
---|
| 1508 | |
---|
[10af64] | 1509 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
[806c18] | 1510 | CanonicalForm gcdlcAlcB; |
---|
[10af64] | 1511 | lcA= uni_lcoeff (ppA); |
---|
| 1512 | lcB= uni_lcoeff (ppB); |
---|
| 1513 | |
---|
[597783] | 1514 | /*if (fdivides (lcA, lcB)) |
---|
[806c18] | 1515 | { |
---|
[10af64] | 1516 | if (fdivides (A, B)) |
---|
| 1517 | return F/Lc(F); |
---|
[806c18] | 1518 | } |
---|
[10af64] | 1519 | if (fdivides (lcB, lcA)) |
---|
[806c18] | 1520 | { |
---|
| 1521 | if (fdivides (B, A)) |
---|
[10af64] | 1522 | return G/Lc(G); |
---|
[597783] | 1523 | }*/ |
---|
[c4f4fd] | 1524 | |
---|
[806c18] | 1525 | gcdlcAlcB= gcd (lcA, lcB); |
---|
| 1526 | |
---|
[10af64] | 1527 | int d= totaldegree (ppA, Variable (2), Variable (ppA.level())); |
---|
| 1528 | int d0; |
---|
| 1529 | |
---|
[dec1024] | 1530 | if (d == 0) |
---|
[597783] | 1531 | { |
---|
| 1532 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 1533 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 1534 | return N(gcdcAcB); |
---|
[597783] | 1535 | } |
---|
[a9a6dcb] | 1536 | |
---|
[10af64] | 1537 | d0= totaldegree (ppB, Variable (2), Variable (ppB.level())); |
---|
| 1538 | |
---|
[806c18] | 1539 | if (d0 < d) |
---|
[10af64] | 1540 | d= d0; |
---|
| 1541 | |
---|
[806c18] | 1542 | if (d == 0) |
---|
[597783] | 1543 | { |
---|
| 1544 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 1545 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 1546 | return N(gcdcAcB); |
---|
[597783] | 1547 | } |
---|
[10af64] | 1548 | |
---|
| 1549 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
[597783] | 1550 | CanonicalForm newtonPoly, coF_random_element, coG_random_element, |
---|
| 1551 | coF_m, coG_m, ppCoF, ppCoG; |
---|
| 1552 | |
---|
| 1553 | newtonPoly= 1; |
---|
[10af64] | 1554 | m= gcdlcAlcB; |
---|
| 1555 | H= 0; |
---|
[597783] | 1556 | coF= 0; |
---|
| 1557 | coG= 0; |
---|
[10af64] | 1558 | G_m= 0; |
---|
| 1559 | Variable alpha, V_buf; |
---|
| 1560 | bool fail= false; |
---|
| 1561 | bool inextension= false; |
---|
[d1dc39] | 1562 | topLevel= false; |
---|
[10af64] | 1563 | CFList source, dest; |
---|
[597783] | 1564 | int bound1= degree (ppA, 1); |
---|
| 1565 | int bound2= degree (ppB, 1); |
---|
[806c18] | 1566 | do |
---|
[10af64] | 1567 | { |
---|
| 1568 | if (inextension) |
---|
[597783] | 1569 | random_element= randomElement (m*lcA*lcB, V_buf, l, fail); |
---|
[10af64] | 1570 | else |
---|
[597783] | 1571 | random_element= FpRandomElement (m*lcA*lcB, l, fail); |
---|
[10af64] | 1572 | |
---|
| 1573 | if (!fail && !inextension) |
---|
| 1574 | { |
---|
| 1575 | CFList list; |
---|
| 1576 | TIMING_START (gcd_recursion); |
---|
[806c18] | 1577 | G_random_element= |
---|
[597783] | 1578 | GCD_small_p (ppA (random_element,x), ppB (random_element,x), |
---|
[d1dc39] | 1579 | coF_random_element, coG_random_element, topLevel, |
---|
[597783] | 1580 | list); |
---|
[806c18] | 1581 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
[10af64] | 1582 | "time for recursive call: "); |
---|
| 1583 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 1584 | } |
---|
| 1585 | else if (!fail && inextension) |
---|
| 1586 | { |
---|
[806c18] | 1587 | CFList list; |
---|
[10af64] | 1588 | TIMING_START (gcd_recursion); |
---|
[806c18] | 1589 | G_random_element= |
---|
[597783] | 1590 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), |
---|
| 1591 | coF_random_element, coG_random_element, alpha, |
---|
[d1dc39] | 1592 | list, topLevel); |
---|
[806c18] | 1593 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
[10af64] | 1594 | "time for recursive call: "); |
---|
[806c18] | 1595 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
[10af64] | 1596 | } |
---|
| 1597 | else if (fail && !inextension) |
---|
| 1598 | { |
---|
| 1599 | source= CFList(); |
---|
| 1600 | dest= CFList(); |
---|
| 1601 | CFList list; |
---|
[a5cc7b3] | 1602 | CanonicalForm mipo; |
---|
[dec1024] | 1603 | int deg= 2; |
---|
[a5cc7b3] | 1604 | do { |
---|
[806c18] | 1605 | mipo= randomIrredpoly (deg, x); |
---|
[a5cc7b3] | 1606 | alpha= rootOf (mipo); |
---|
| 1607 | inextension= true; |
---|
| 1608 | fail= false; |
---|
[597783] | 1609 | random_element= randomElement (m*lcA*lcB, alpha, l, fail); |
---|
[a5cc7b3] | 1610 | deg++; |
---|
[806c18] | 1611 | } while (fail); |
---|
[10af64] | 1612 | list= CFList(); |
---|
[9ff686] | 1613 | V_buf= alpha; |
---|
[10af64] | 1614 | TIMING_START (gcd_recursion); |
---|
[806c18] | 1615 | G_random_element= |
---|
[597783] | 1616 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), |
---|
| 1617 | coF_random_element, coG_random_element, alpha, |
---|
[d1dc39] | 1618 | list, topLevel); |
---|
[806c18] | 1619 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
[10af64] | 1620 | "time for recursive call: "); |
---|
| 1621 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 1622 | } |
---|
| 1623 | else if (fail && inextension) |
---|
| 1624 | { |
---|
| 1625 | source= CFList(); |
---|
| 1626 | dest= CFList(); |
---|
[9ff686] | 1627 | |
---|
| 1628 | Variable V_buf3= V_buf; |
---|
| 1629 | V_buf= chooseExtension (V_buf); |
---|
[10af64] | 1630 | bool prim_fail= false; |
---|
| 1631 | Variable V_buf2; |
---|
| 1632 | CanonicalForm prim_elem, im_prim_elem; |
---|
| 1633 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
[806c18] | 1634 | |
---|
[9ff686] | 1635 | if (V_buf3 != alpha) |
---|
| 1636 | { |
---|
| 1637 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
[597783] | 1638 | G_m= mapDown (G_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 1639 | coF_m= mapDown (coF_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 1640 | coG_m= mapDown (coG_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
[9ff686] | 1641 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
| 1642 | source, dest); |
---|
| 1643 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 1644 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 1645 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, source, |
---|
| 1646 | dest); |
---|
[597783] | 1647 | lcA= mapDown (lcA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 1648 | lcB= mapDown (lcB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
[9ff686] | 1649 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 1650 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
| 1651 | source, dest); |
---|
| 1652 | } |
---|
| 1653 | |
---|
[10af64] | 1654 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
| 1655 | if (prim_fail) |
---|
| 1656 | ; //ERROR |
---|
| 1657 | else |
---|
| 1658 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
| 1659 | |
---|
| 1660 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
| 1661 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
| 1662 | |
---|
[806c18] | 1663 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 1664 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
[10af64] | 1665 | im_prim_elem, source, dest); |
---|
| 1666 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 1667 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
[597783] | 1668 | coF_m= mapUp (coF_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 1669 | coG_m= mapUp (coG_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
[806c18] | 1670 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
[10af64] | 1671 | source, dest); |
---|
| 1672 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 1673 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
[806c18] | 1674 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
[10af64] | 1675 | source, dest); |
---|
[597783] | 1676 | lcA= mapUp (lcA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 1677 | lcB= mapUp (lcB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
[10af64] | 1678 | fail= false; |
---|
[597783] | 1679 | random_element= randomElement (m*lcA*lcB, V_buf, l, fail ); |
---|
[a5cc7b3] | 1680 | DEBOUTLN (cerr, "fail= " << fail); |
---|
[10af64] | 1681 | CFList list; |
---|
| 1682 | TIMING_START (gcd_recursion); |
---|
[806c18] | 1683 | G_random_element= |
---|
[597783] | 1684 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), |
---|
| 1685 | coF_random_element, coG_random_element, V_buf, |
---|
[d1dc39] | 1686 | list, topLevel); |
---|
[806c18] | 1687 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
[10af64] | 1688 | "time for recursive call: "); |
---|
| 1689 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
[806c18] | 1690 | } |
---|
[10af64] | 1691 | |
---|
[a76d6fe] | 1692 | if (!G_random_element.inCoeffDomain()) |
---|
| 1693 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 1694 | Variable (G_random_element.level())); |
---|
| 1695 | else |
---|
| 1696 | d0= 0; |
---|
[10af64] | 1697 | |
---|
| 1698 | if (d0 == 0) |
---|
[597783] | 1699 | { |
---|
| 1700 | coF= N (ppA*(cA/gcdcAcB)); |
---|
| 1701 | coG= N (ppB*(cB/gcdcAcB)); |
---|
[a9a6dcb] | 1702 | return N(gcdcAcB); |
---|
[597783] | 1703 | } |
---|
| 1704 | |
---|
[806c18] | 1705 | if (d0 > d) |
---|
| 1706 | { |
---|
[10af64] | 1707 | if (!find (l, random_element)) |
---|
| 1708 | l.append (random_element); |
---|
| 1709 | continue; |
---|
| 1710 | } |
---|
| 1711 | |
---|
| 1712 | G_random_element= (gcdlcAlcB(random_element,x)/uni_lcoeff(G_random_element)) |
---|
[806c18] | 1713 | *G_random_element; |
---|
[10af64] | 1714 | |
---|
[597783] | 1715 | coF_random_element= (lcA(random_element,x)/uni_lcoeff(coF_random_element)) |
---|
| 1716 | *coF_random_element; |
---|
| 1717 | coG_random_element= (lcB(random_element,x)/uni_lcoeff(coG_random_element)) |
---|
| 1718 | *coG_random_element; |
---|
[806c18] | 1719 | |
---|
[a76d6fe] | 1720 | if (!G_random_element.inCoeffDomain()) |
---|
| 1721 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 1722 | Variable (G_random_element.level())); |
---|
| 1723 | else |
---|
| 1724 | d0= 0; |
---|
[10af64] | 1725 | |
---|
[806c18] | 1726 | if (d0 < d) |
---|
[10af64] | 1727 | { |
---|
| 1728 | m= gcdlcAlcB; |
---|
| 1729 | newtonPoly= 1; |
---|
| 1730 | G_m= 0; |
---|
| 1731 | d= d0; |
---|
[597783] | 1732 | coF_m= 0; |
---|
| 1733 | coG_m= 0; |
---|
[10af64] | 1734 | } |
---|
[806c18] | 1735 | |
---|
[10af64] | 1736 | TIMING_START (newton_interpolation); |
---|
| 1737 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
[597783] | 1738 | coF= newtonInterp (random_element, coF_random_element, newtonPoly, coF_m,x); |
---|
| 1739 | coG= newtonInterp (random_element, coG_random_element, newtonPoly, coG_m,x); |
---|
[806c18] | 1740 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
[10af64] | 1741 | "time for newton_interpolation: "); |
---|
| 1742 | |
---|
| 1743 | //termination test |
---|
[597783] | 1744 | if ((uni_lcoeff (H) == gcdlcAlcB) || (G_m == H)) |
---|
[10af64] | 1745 | { |
---|
[597783] | 1746 | if (gcdlcAlcB.isOne()) |
---|
| 1747 | cH= 1; |
---|
| 1748 | else |
---|
| 1749 | cH= uni_content (H); |
---|
[10af64] | 1750 | ppH= H/cH; |
---|
| 1751 | ppH /= Lc (ppH); |
---|
[597783] | 1752 | CanonicalForm lcppH= gcdlcAlcB/cH; |
---|
| 1753 | CanonicalForm ccoF= lcppH/Lc (lcppH); |
---|
| 1754 | CanonicalForm ccoG= lcppH/Lc (lcppH); |
---|
| 1755 | ppCoF= coF/ccoF; |
---|
| 1756 | ppCoG= coG/ccoG; |
---|
[10af64] | 1757 | DEBOUTLN (cerr, "ppH= " << ppH); |
---|
[597783] | 1758 | if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
| 1759 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
[1e4b53] | 1760 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
[597783] | 1761 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
[dec1024] | 1762 | { |
---|
[e243418] | 1763 | if (compressConvexDense) |
---|
[597783] | 1764 | { |
---|
[e243418] | 1765 | ppH= decompress (ppH, MM, V); |
---|
[597783] | 1766 | ppCoF= decompress (ppCoF, MM, V); |
---|
| 1767 | ppCoG= decompress (ppCoG, MM, V); |
---|
| 1768 | } |
---|
| 1769 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
| 1770 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
[10af64] | 1771 | return N(gcdcAcB*ppH); |
---|
[dec1024] | 1772 | } |
---|
[10af64] | 1773 | } |
---|
| 1774 | |
---|
| 1775 | G_m= H; |
---|
[597783] | 1776 | coF_m= coF; |
---|
| 1777 | coG_m= coG; |
---|
[10af64] | 1778 | newtonPoly= newtonPoly*(x - random_element); |
---|
| 1779 | m= m*(x - random_element); |
---|
| 1780 | if (!find (l, random_element)) |
---|
| 1781 | l.append (random_element); |
---|
| 1782 | } while (1); |
---|
| 1783 | } |
---|
| 1784 | |
---|
[08daea] | 1785 | CFArray |
---|
| 1786 | solveVandermonde (const CFArray& M, const CFArray& A) |
---|
| 1787 | { |
---|
| 1788 | int r= M.size(); |
---|
| 1789 | ASSERT (A.size() == r, "vector does not have right size"); |
---|
| 1790 | |
---|
| 1791 | if (r == 1) |
---|
| 1792 | { |
---|
| 1793 | CFArray result= CFArray (1); |
---|
| 1794 | result [0]= A [0] / M [0]; |
---|
| 1795 | return result; |
---|
| 1796 | } |
---|
| 1797 | // check solvability |
---|
| 1798 | bool notDistinct= false; |
---|
| 1799 | for (int i= 0; i < r - 1; i++) |
---|
| 1800 | { |
---|
| 1801 | for (int j= i + 1; j < r; j++) |
---|
| 1802 | { |
---|
| 1803 | if (M [i] == M [j]) |
---|
| 1804 | { |
---|
| 1805 | notDistinct= true; |
---|
| 1806 | break; |
---|
| 1807 | } |
---|
| 1808 | } |
---|
| 1809 | } |
---|
| 1810 | if (notDistinct) |
---|
| 1811 | return CFArray(); |
---|
| 1812 | |
---|
| 1813 | CanonicalForm master= 1; |
---|
| 1814 | Variable x= Variable (1); |
---|
| 1815 | for (int i= 0; i < r; i++) |
---|
| 1816 | master *= x - M [i]; |
---|
| 1817 | CFList Pj; |
---|
| 1818 | CanonicalForm tmp; |
---|
| 1819 | for (int i= 0; i < r; i++) |
---|
| 1820 | { |
---|
| 1821 | tmp= master/(x - M [i]); |
---|
| 1822 | tmp /= tmp (M [i], 1); |
---|
| 1823 | Pj.append (tmp); |
---|
| 1824 | } |
---|
| 1825 | CFArray result= CFArray (r); |
---|
| 1826 | |
---|
| 1827 | CFListIterator j= Pj; |
---|
| 1828 | for (int i= 1; i <= r; i++, j++) |
---|
| 1829 | { |
---|
| 1830 | tmp= 0; |
---|
| 1831 | for (int l= 0; l < A.size(); l++) |
---|
| 1832 | tmp += A[l]*j.getItem()[l]; |
---|
| 1833 | result[i - 1]= tmp; |
---|
| 1834 | } |
---|
| 1835 | return result; |
---|
| 1836 | } |
---|
| 1837 | |
---|
| 1838 | CFArray |
---|
| 1839 | solveGeneralVandermonde (const CFArray& M, const CFArray& A) |
---|
| 1840 | { |
---|
| 1841 | int r= M.size(); |
---|
| 1842 | ASSERT (A.size() == r, "vector does not have right size"); |
---|
| 1843 | if (r == 1) |
---|
| 1844 | { |
---|
| 1845 | CFArray result= CFArray (1); |
---|
| 1846 | result [0]= A[0] / M [0]; |
---|
| 1847 | return result; |
---|
| 1848 | } |
---|
| 1849 | // check solvability |
---|
| 1850 | bool notDistinct= false; |
---|
| 1851 | for (int i= 0; i < r - 1; i++) |
---|
| 1852 | { |
---|
| 1853 | for (int j= i + 1; j < r; j++) |
---|
| 1854 | { |
---|
| 1855 | if (M [i] == M [j]) |
---|
| 1856 | { |
---|
| 1857 | notDistinct= true; |
---|
| 1858 | break; |
---|
| 1859 | } |
---|
| 1860 | } |
---|
| 1861 | } |
---|
| 1862 | if (notDistinct) |
---|
| 1863 | return CFArray(); |
---|
| 1864 | |
---|
| 1865 | CanonicalForm master= 1; |
---|
| 1866 | Variable x= Variable (1); |
---|
| 1867 | for (int i= 0; i < r; i++) |
---|
| 1868 | master *= x - M [i]; |
---|
| 1869 | master *= x; |
---|
| 1870 | CFList Pj; |
---|
| 1871 | CanonicalForm tmp; |
---|
| 1872 | for (int i= 0; i < r; i++) |
---|
| 1873 | { |
---|
| 1874 | tmp= master/(x - M [i]); |
---|
| 1875 | tmp /= tmp (M [i], 1); |
---|
| 1876 | Pj.append (tmp); |
---|
| 1877 | } |
---|
| 1878 | |
---|
| 1879 | CFArray result= CFArray (r); |
---|
| 1880 | |
---|
| 1881 | CFListIterator j= Pj; |
---|
| 1882 | for (int i= 1; i <= r; i++, j++) |
---|
| 1883 | { |
---|
| 1884 | tmp= 0; |
---|
| 1885 | |
---|
| 1886 | for (int l= 1; l <= A.size(); l++) |
---|
| 1887 | tmp += A[l - 1]*j.getItem()[l]; |
---|
| 1888 | result[i - 1]= tmp; |
---|
| 1889 | } |
---|
| 1890 | return result; |
---|
| 1891 | } |
---|
| 1892 | |
---|
| 1893 | /// M in row echolon form, rk rank of M |
---|
| 1894 | CFArray |
---|
| 1895 | readOffSolution (const CFMatrix& M, const long rk) |
---|
| 1896 | { |
---|
| 1897 | CFArray result= CFArray (rk); |
---|
| 1898 | CanonicalForm tmp1, tmp2, tmp3; |
---|
| 1899 | for (int i= rk; i >= 1; i--) |
---|
| 1900 | { |
---|
| 1901 | tmp3= 0; |
---|
| 1902 | tmp1= M (i, M.columns()); |
---|
| 1903 | for (int j= M.columns() - 1; j >= 1; j--) |
---|
| 1904 | { |
---|
| 1905 | tmp2= M (i, j); |
---|
| 1906 | if (j == i) |
---|
| 1907 | break; |
---|
| 1908 | else |
---|
| 1909 | tmp3 += tmp2*result[j - 1]; |
---|
| 1910 | } |
---|
| 1911 | result[i - 1]= (tmp1 - tmp3)/tmp2; |
---|
| 1912 | } |
---|
| 1913 | return result; |
---|
| 1914 | } |
---|
| 1915 | |
---|
| 1916 | CFArray |
---|
| 1917 | readOffSolution (const CFMatrix& M, const CFArray& L, const CFArray& partialSol) |
---|
| 1918 | { |
---|
| 1919 | CFArray result= CFArray (M.rows()); |
---|
| 1920 | CanonicalForm tmp1, tmp2, tmp3; |
---|
| 1921 | int k; |
---|
| 1922 | for (int i= M.rows(); i >= 1; i--) |
---|
| 1923 | { |
---|
| 1924 | tmp3= 0; |
---|
| 1925 | tmp1= L[i - 1]; |
---|
| 1926 | k= 0; |
---|
| 1927 | for (int j= M.columns(); j >= 1; j--, k++) |
---|
| 1928 | { |
---|
| 1929 | tmp2= M (i, j); |
---|
| 1930 | if (j == i) |
---|
| 1931 | break; |
---|
| 1932 | else |
---|
| 1933 | { |
---|
| 1934 | if (k > partialSol.size() - 1) |
---|
| 1935 | tmp3 += tmp2*result[j - 1]; |
---|
| 1936 | else |
---|
| 1937 | tmp3 += tmp2*partialSol[partialSol.size() - k - 1]; |
---|
| 1938 | } |
---|
| 1939 | } |
---|
| 1940 | result [i - 1]= (tmp1 - tmp3)/tmp2; |
---|
| 1941 | } |
---|
| 1942 | return result; |
---|
| 1943 | } |
---|
| 1944 | |
---|
| 1945 | long |
---|
| 1946 | gaussianElimFp (CFMatrix& M, CFArray& L) |
---|
| 1947 | { |
---|
| 1948 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
| 1949 | CFMatrix *N; |
---|
| 1950 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
| 1951 | |
---|
| 1952 | for (int i= 1; i <= M.rows(); i++) |
---|
| 1953 | for (int j= 1; j <= M.columns(); j++) |
---|
| 1954 | (*N) (i, j)= M (i, j); |
---|
| 1955 | |
---|
| 1956 | int j= 1; |
---|
| 1957 | for (int i= 0; i < L.size(); i++, j++) |
---|
| 1958 | (*N) (j, M.columns() + 1)= L[i]; |
---|
| 1959 | int p= getCharacteristic (); |
---|
| 1960 | zz_p::init (p); |
---|
| 1961 | mat_zz_p *NTLN= convertFacCFMatrix2NTLmat_zz_p(*N); |
---|
| 1962 | long rk= gauss (*NTLN); |
---|
| 1963 | |
---|
| 1964 | N= convertNTLmat_zz_p2FacCFMatrix (*NTLN); |
---|
| 1965 | |
---|
| 1966 | L= CFArray (M.rows()); |
---|
| 1967 | for (int i= 0; i < M.rows(); i++) |
---|
| 1968 | L[i]= (*N) (i + 1, M.columns() + 1); |
---|
| 1969 | M= (*N) (1, M.rows(), 1, M.columns()); |
---|
[618da5] | 1970 | delete N; |
---|
[08daea] | 1971 | return rk; |
---|
| 1972 | } |
---|
| 1973 | |
---|
| 1974 | long |
---|
| 1975 | gaussianElimFq (CFMatrix& M, CFArray& L, const Variable& alpha) |
---|
| 1976 | { |
---|
| 1977 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
| 1978 | CFMatrix *N; |
---|
| 1979 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
| 1980 | |
---|
| 1981 | for (int i= 1; i <= M.rows(); i++) |
---|
| 1982 | for (int j= 1; j <= M.columns(); j++) |
---|
| 1983 | (*N) (i, j)= M (i, j); |
---|
| 1984 | |
---|
| 1985 | int j= 1; |
---|
| 1986 | for (int i= 0; i < L.size(); i++, j++) |
---|
| 1987 | (*N) (j, M.columns() + 1)= L[i]; |
---|
| 1988 | int p= getCharacteristic (); |
---|
| 1989 | zz_p::init (p); |
---|
| 1990 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 1991 | zz_pE::init (NTLMipo); |
---|
| 1992 | mat_zz_pE *NTLN= convertFacCFMatrix2NTLmat_zz_pE(*N); |
---|
| 1993 | long rk= gauss (*NTLN); |
---|
| 1994 | |
---|
| 1995 | N= convertNTLmat_zz_pE2FacCFMatrix (*NTLN, alpha); |
---|
| 1996 | |
---|
| 1997 | M= (*N) (1, M.rows(), 1, M.columns()); |
---|
| 1998 | L= CFArray (M.rows()); |
---|
| 1999 | for (int i= 0; i < M.rows(); i++) |
---|
| 2000 | L[i]= (*N) (i + 1, M.columns() + 1); |
---|
[618da5] | 2001 | |
---|
| 2002 | delete N; |
---|
[08daea] | 2003 | return rk; |
---|
| 2004 | } |
---|
| 2005 | |
---|
| 2006 | CFArray |
---|
| 2007 | solveSystemFp (const CFMatrix& M, const CFArray& L) |
---|
| 2008 | { |
---|
| 2009 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
| 2010 | CFMatrix *N; |
---|
| 2011 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
| 2012 | |
---|
| 2013 | for (int i= 1; i <= M.rows(); i++) |
---|
| 2014 | for (int j= 1; j <= M.columns(); j++) |
---|
| 2015 | (*N) (i, j)= M (i, j); |
---|
| 2016 | |
---|
| 2017 | int j= 1; |
---|
| 2018 | for (int i= 0; i < L.size(); i++, j++) |
---|
| 2019 | (*N) (j, M.columns() + 1)= L[i]; |
---|
| 2020 | int p= getCharacteristic (); |
---|
| 2021 | zz_p::init (p); |
---|
| 2022 | mat_zz_p *NTLN= convertFacCFMatrix2NTLmat_zz_p(*N); |
---|
| 2023 | long rk= gauss (*NTLN); |
---|
| 2024 | if (rk != M.columns()) |
---|
[618da5] | 2025 | { |
---|
| 2026 | delete N; |
---|
[08daea] | 2027 | return CFArray(); |
---|
[618da5] | 2028 | } |
---|
[08daea] | 2029 | N= convertNTLmat_zz_p2FacCFMatrix (*NTLN); |
---|
| 2030 | |
---|
| 2031 | CFArray A= readOffSolution (*N, rk); |
---|
| 2032 | |
---|
[618da5] | 2033 | delete N; |
---|
[08daea] | 2034 | return A; |
---|
| 2035 | } |
---|
| 2036 | |
---|
| 2037 | CFArray |
---|
| 2038 | solveSystemFq (const CFMatrix& M, const CFArray& L, const Variable& alpha) |
---|
| 2039 | { |
---|
| 2040 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
| 2041 | CFMatrix *N; |
---|
| 2042 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
| 2043 | |
---|
| 2044 | for (int i= 1; i <= M.rows(); i++) |
---|
| 2045 | for (int j= 1; j <= M.columns(); j++) |
---|
| 2046 | (*N) (i, j)= M (i, j); |
---|
| 2047 | int j= 1; |
---|
| 2048 | for (int i= 0; i < L.size(); i++, j++) |
---|
| 2049 | (*N) (j, M.columns() + 1)= L[i]; |
---|
| 2050 | int p= getCharacteristic (); |
---|
| 2051 | zz_p::init (p); |
---|
| 2052 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 2053 | zz_pE::init (NTLMipo); |
---|
| 2054 | mat_zz_pE *NTLN= convertFacCFMatrix2NTLmat_zz_pE(*N); |
---|
| 2055 | long rk= gauss (*NTLN); |
---|
| 2056 | if (rk != M.columns()) |
---|
[618da5] | 2057 | { |
---|
| 2058 | delete N; |
---|
[08daea] | 2059 | return CFArray(); |
---|
[618da5] | 2060 | } |
---|
[08daea] | 2061 | N= convertNTLmat_zz_pE2FacCFMatrix (*NTLN, alpha); |
---|
| 2062 | |
---|
| 2063 | CFArray A= readOffSolution (*N, rk); |
---|
| 2064 | |
---|
[618da5] | 2065 | delete N; |
---|
[08daea] | 2066 | return A; |
---|
| 2067 | } |
---|
[6f6320] | 2068 | #endif |
---|
[08daea] | 2069 | |
---|
| 2070 | CFArray |
---|
| 2071 | getMonoms (const CanonicalForm& F) |
---|
| 2072 | { |
---|
| 2073 | if (F.inCoeffDomain()) |
---|
| 2074 | { |
---|
| 2075 | CFArray result= CFArray (1); |
---|
| 2076 | result [0]= 1; |
---|
| 2077 | return result; |
---|
| 2078 | } |
---|
| 2079 | if (F.isUnivariate()) |
---|
| 2080 | { |
---|
| 2081 | CFArray result= CFArray (size(F)); |
---|
| 2082 | int j= 0; |
---|
| 2083 | for (CFIterator i= F; i.hasTerms(); i++, j++) |
---|
| 2084 | result[j]= power (F.mvar(), i.exp()); |
---|
| 2085 | return result; |
---|
| 2086 | } |
---|
| 2087 | int numMon= size (F); |
---|
| 2088 | CFArray result= CFArray (numMon); |
---|
| 2089 | int j= 0; |
---|
| 2090 | CFArray recResult; |
---|
| 2091 | Variable x= F.mvar(); |
---|
| 2092 | CanonicalForm powX; |
---|
| 2093 | for (CFIterator i= F; i.hasTerms(); i++) |
---|
| 2094 | { |
---|
| 2095 | powX= power (x, i.exp()); |
---|
| 2096 | recResult= getMonoms (i.coeff()); |
---|
| 2097 | for (int k= 0; k < recResult.size(); k++) |
---|
| 2098 | result[j+k]= powX*recResult[k]; |
---|
| 2099 | j += recResult.size(); |
---|
| 2100 | } |
---|
| 2101 | return result; |
---|
| 2102 | } |
---|
| 2103 | |
---|
[6f6320] | 2104 | #ifdef HAVE_NTL |
---|
[08daea] | 2105 | CFArray |
---|
| 2106 | evaluateMonom (const CanonicalForm& F, const CFList& evalPoints) |
---|
| 2107 | { |
---|
| 2108 | if (F.inCoeffDomain()) |
---|
| 2109 | { |
---|
| 2110 | CFArray result= CFArray (1); |
---|
| 2111 | result [0]= F; |
---|
| 2112 | return result; |
---|
| 2113 | } |
---|
| 2114 | if (F.isUnivariate()) |
---|
| 2115 | { |
---|
| 2116 | ASSERT (evalPoints.length() == 1, |
---|
| 2117 | "expected an eval point with only one component"); |
---|
| 2118 | CFArray result= CFArray (size(F)); |
---|
| 2119 | int j= 0; |
---|
| 2120 | CanonicalForm evalPoint= evalPoints.getLast(); |
---|
| 2121 | for (CFIterator i= F; i.hasTerms(); i++, j++) |
---|
| 2122 | result[j]= power (evalPoint, i.exp()); |
---|
| 2123 | return result; |
---|
| 2124 | } |
---|
| 2125 | int numMon= size (F); |
---|
| 2126 | CFArray result= CFArray (numMon); |
---|
| 2127 | int j= 0; |
---|
| 2128 | CanonicalForm evalPoint= evalPoints.getLast(); |
---|
| 2129 | CFList buf= evalPoints; |
---|
| 2130 | buf.removeLast(); |
---|
| 2131 | CFArray recResult; |
---|
| 2132 | CanonicalForm powEvalPoint; |
---|
| 2133 | for (CFIterator i= F; i.hasTerms(); i++) |
---|
| 2134 | { |
---|
| 2135 | powEvalPoint= power (evalPoint, i.exp()); |
---|
| 2136 | recResult= evaluateMonom (i.coeff(), buf); |
---|
| 2137 | for (int k= 0; k < recResult.size(); k++) |
---|
| 2138 | result[j+k]= powEvalPoint*recResult[k]; |
---|
| 2139 | j += recResult.size(); |
---|
| 2140 | } |
---|
| 2141 | return result; |
---|
| 2142 | } |
---|
| 2143 | |
---|
| 2144 | CFArray |
---|
| 2145 | evaluate (const CFArray& A, const CFList& evalPoints) |
---|
| 2146 | { |
---|
| 2147 | CFArray result= A.size(); |
---|
| 2148 | CanonicalForm tmp; |
---|
| 2149 | int k; |
---|
| 2150 | for (int i= 0; i < A.size(); i++) |
---|
| 2151 | { |
---|
| 2152 | tmp= A[i]; |
---|
| 2153 | k= 1; |
---|
| 2154 | for (CFListIterator j= evalPoints; j.hasItem(); j++, k++) |
---|
| 2155 | tmp= tmp (j.getItem(), k); |
---|
| 2156 | result[i]= tmp; |
---|
| 2157 | } |
---|
| 2158 | return result; |
---|
| 2159 | } |
---|
| 2160 | |
---|
| 2161 | CFList |
---|
| 2162 | evaluationPoints (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 2163 | CanonicalForm& Feval, CanonicalForm& Geval, |
---|
| 2164 | const CanonicalForm& LCF, const bool& GF, |
---|
| 2165 | const Variable& alpha, bool& fail, CFList& list |
---|
| 2166 | ) |
---|
| 2167 | { |
---|
| 2168 | int k= tmax (F.level(), G.level()) - 1; |
---|
| 2169 | Variable x= Variable (1); |
---|
| 2170 | CFList result; |
---|
| 2171 | FFRandom genFF; |
---|
| 2172 | GFRandom genGF; |
---|
| 2173 | int p= getCharacteristic (); |
---|
| 2174 | int bound; |
---|
| 2175 | if (alpha != Variable (1)) |
---|
| 2176 | { |
---|
| 2177 | bound= ipower (p, degree (getMipo(alpha))); |
---|
| 2178 | bound= ipower (bound, k); |
---|
| 2179 | } |
---|
| 2180 | else if (GF) |
---|
| 2181 | { |
---|
| 2182 | bound= ipower (p, getGFDegree()); |
---|
| 2183 | bound= ipower (bound, k); |
---|
| 2184 | } |
---|
| 2185 | else |
---|
| 2186 | bound= ipower (p, k); |
---|
| 2187 | |
---|
| 2188 | CanonicalForm random; |
---|
| 2189 | int j; |
---|
| 2190 | bool zeroOneOccured= false; |
---|
| 2191 | bool allEqual= false; |
---|
| 2192 | CanonicalForm buf; |
---|
| 2193 | do |
---|
| 2194 | { |
---|
| 2195 | random= 0; |
---|
| 2196 | // possible overflow if list.length() does not fit into a int |
---|
| 2197 | if (list.length() >= bound) |
---|
| 2198 | { |
---|
| 2199 | fail= true; |
---|
| 2200 | break; |
---|
| 2201 | } |
---|
| 2202 | for (int i= 0; i < k; i++) |
---|
| 2203 | { |
---|
| 2204 | if (GF) |
---|
| 2205 | { |
---|
| 2206 | result.append (genGF.generate()); |
---|
| 2207 | random += result.getLast()*power (x, i); |
---|
| 2208 | } |
---|
[1372ae] | 2209 | else if (alpha.level() != 1) |
---|
[08daea] | 2210 | { |
---|
| 2211 | AlgExtRandomF genAlgExt (alpha); |
---|
| 2212 | result.append (genAlgExt.generate()); |
---|
| 2213 | random += result.getLast()*power (x, i); |
---|
| 2214 | } |
---|
| 2215 | else |
---|
| 2216 | { |
---|
| 2217 | result.append (genFF.generate()); |
---|
| 2218 | random += result.getLast()*power (x, i); |
---|
| 2219 | } |
---|
| 2220 | if (result.getLast().isOne() || result.getLast().isZero()) |
---|
| 2221 | zeroOneOccured= true; |
---|
| 2222 | } |
---|
| 2223 | if (find (list, random)) |
---|
| 2224 | { |
---|
| 2225 | zeroOneOccured= false; |
---|
| 2226 | allEqual= false; |
---|
| 2227 | result= CFList(); |
---|
| 2228 | continue; |
---|
| 2229 | } |
---|
| 2230 | if (zeroOneOccured) |
---|
| 2231 | { |
---|
| 2232 | list.append (random); |
---|
| 2233 | zeroOneOccured= false; |
---|
| 2234 | allEqual= false; |
---|
| 2235 | result= CFList(); |
---|
| 2236 | continue; |
---|
| 2237 | } |
---|
| 2238 | // no zero at this point |
---|
| 2239 | if (k > 1) |
---|
| 2240 | { |
---|
| 2241 | allEqual= true; |
---|
| 2242 | CFIterator iter= random; |
---|
| 2243 | buf= iter.coeff(); |
---|
| 2244 | iter++; |
---|
| 2245 | for (; iter.hasTerms(); iter++) |
---|
| 2246 | if (buf != iter.coeff()) |
---|
| 2247 | allEqual= false; |
---|
| 2248 | } |
---|
| 2249 | if (allEqual) |
---|
| 2250 | { |
---|
| 2251 | list.append (random); |
---|
| 2252 | allEqual= false; |
---|
| 2253 | zeroOneOccured= false; |
---|
| 2254 | result= CFList(); |
---|
| 2255 | continue; |
---|
| 2256 | } |
---|
| 2257 | |
---|
| 2258 | Feval= F; |
---|
| 2259 | Geval= G; |
---|
| 2260 | CanonicalForm LCeval= LCF; |
---|
| 2261 | j= 1; |
---|
| 2262 | for (CFListIterator i= result; i.hasItem(); i++, j++) |
---|
| 2263 | { |
---|
| 2264 | Feval= Feval (i.getItem(), j); |
---|
| 2265 | Geval= Geval (i.getItem(), j); |
---|
| 2266 | LCeval= LCeval (i.getItem(), j); |
---|
| 2267 | } |
---|
| 2268 | |
---|
| 2269 | if (LCeval.isZero()) |
---|
| 2270 | { |
---|
| 2271 | if (!find (list, random)) |
---|
| 2272 | list.append (random); |
---|
| 2273 | zeroOneOccured= false; |
---|
| 2274 | allEqual= false; |
---|
| 2275 | result= CFList(); |
---|
| 2276 | continue; |
---|
| 2277 | } |
---|
| 2278 | |
---|
| 2279 | if (list.length() >= bound) |
---|
| 2280 | { |
---|
| 2281 | fail= true; |
---|
| 2282 | break; |
---|
| 2283 | } |
---|
| 2284 | } while (find (list, random)); |
---|
| 2285 | |
---|
| 2286 | return result; |
---|
| 2287 | } |
---|
| 2288 | |
---|
| 2289 | /// multiply two lists componentwise |
---|
| 2290 | void mult (CFList& L1, const CFList& L2) |
---|
| 2291 | { |
---|
| 2292 | ASSERT (L1.length() == L2.length(), "lists of the same size expected"); |
---|
| 2293 | |
---|
| 2294 | CFListIterator j= L2; |
---|
| 2295 | for (CFListIterator i= L1; i.hasItem(); i++, j++) |
---|
| 2296 | i.getItem() *= j.getItem(); |
---|
| 2297 | } |
---|
| 2298 | |
---|
| 2299 | void eval (const CanonicalForm& A, const CanonicalForm& B, CanonicalForm& Aeval, |
---|
| 2300 | CanonicalForm& Beval, const CFList& L) |
---|
| 2301 | { |
---|
| 2302 | Aeval= A; |
---|
| 2303 | Beval= B; |
---|
| 2304 | int j= 1; |
---|
| 2305 | for (CFListIterator i= L; i.hasItem(); i++, j++) |
---|
| 2306 | { |
---|
| 2307 | Aeval= Aeval (i.getItem(), j); |
---|
| 2308 | Beval= Beval (i.getItem(), j); |
---|
| 2309 | } |
---|
| 2310 | } |
---|
| 2311 | |
---|
[c1b9927] | 2312 | CanonicalForm |
---|
[08daea] | 2313 | monicSparseInterpol (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 2314 | const CanonicalForm& skeleton, const Variable& alpha, |
---|
| 2315 | bool& fail, CFArray*& coeffMonoms, CFArray& Monoms |
---|
| 2316 | ) |
---|
| 2317 | { |
---|
| 2318 | CanonicalForm A= F; |
---|
| 2319 | CanonicalForm B= G; |
---|
| 2320 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
| 2321 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
| 2322 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
| 2323 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
| 2324 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
| 2325 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
| 2326 | if (F == G) return F/Lc(F); |
---|
| 2327 | |
---|
| 2328 | CFMap M,N; |
---|
| 2329 | int best_level= myCompress (A, B, M, N, false); |
---|
| 2330 | |
---|
| 2331 | if (best_level == 0) |
---|
| 2332 | return B.genOne(); |
---|
| 2333 | |
---|
| 2334 | A= M(A); |
---|
| 2335 | B= M(B); |
---|
| 2336 | |
---|
| 2337 | Variable x= Variable (1); |
---|
[f71453] | 2338 | ASSERT (degree (A, x) == 0, "expected degree (F, 1) == 0"); |
---|
| 2339 | ASSERT (degree (B, x) == 0, "expected degree (G, 1) == 0"); |
---|
[08daea] | 2340 | |
---|
[c1b9927] | 2341 | //univariate case |
---|
[08daea] | 2342 | if (A.isUnivariate() && B.isUnivariate()) |
---|
| 2343 | return N (gcd (A, B)); |
---|
| 2344 | |
---|
| 2345 | CanonicalForm skel= M(skeleton); |
---|
| 2346 | CanonicalForm cA, cB; // content of A and B |
---|
| 2347 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
| 2348 | CanonicalForm gcdcAcB; |
---|
| 2349 | cA = uni_content (A); |
---|
| 2350 | cB = uni_content (B); |
---|
| 2351 | gcdcAcB= gcd (cA, cB); |
---|
| 2352 | ppA= A/cA; |
---|
| 2353 | ppB= B/cB; |
---|
| 2354 | |
---|
| 2355 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
| 2356 | CanonicalForm gcdlcAlcB; |
---|
| 2357 | lcA= uni_lcoeff (ppA); |
---|
| 2358 | lcB= uni_lcoeff (ppB); |
---|
| 2359 | |
---|
| 2360 | if (fdivides (lcA, lcB)) |
---|
| 2361 | { |
---|
| 2362 | if (fdivides (A, B)) |
---|
| 2363 | return F/Lc(F); |
---|
| 2364 | } |
---|
| 2365 | if (fdivides (lcB, lcA)) |
---|
| 2366 | { |
---|
| 2367 | if (fdivides (B, A)) |
---|
| 2368 | return G/Lc(G); |
---|
| 2369 | } |
---|
| 2370 | |
---|
| 2371 | gcdlcAlcB= gcd (lcA, lcB); |
---|
| 2372 | int skelSize= size (skel, skel.mvar()); |
---|
| 2373 | |
---|
| 2374 | int j= 0; |
---|
| 2375 | int biggestSize= 0; |
---|
| 2376 | |
---|
| 2377 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
| 2378 | biggestSize= tmax (biggestSize, size (i.coeff())); |
---|
| 2379 | |
---|
| 2380 | CanonicalForm g, Aeval, Beval; |
---|
| 2381 | |
---|
| 2382 | CFList evalPoints; |
---|
| 2383 | bool evalFail= false; |
---|
| 2384 | CFList list; |
---|
| 2385 | bool GF= false; |
---|
| 2386 | CanonicalForm LCA= LC (A); |
---|
| 2387 | CanonicalForm tmp; |
---|
| 2388 | CFArray gcds= CFArray (biggestSize); |
---|
| 2389 | CFList * pEvalPoints= new CFList [biggestSize]; |
---|
| 2390 | Variable V_buf= alpha; |
---|
| 2391 | CFList source, dest; |
---|
| 2392 | CanonicalForm prim_elem, im_prim_elem; |
---|
| 2393 | for (int i= 0; i < biggestSize; i++) |
---|
| 2394 | { |
---|
| 2395 | if (i == 0) |
---|
| 2396 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, evalFail, |
---|
| 2397 | list); |
---|
| 2398 | else |
---|
| 2399 | { |
---|
| 2400 | mult (evalPoints, pEvalPoints [0]); |
---|
| 2401 | eval (A, B, Aeval, Beval, evalPoints); |
---|
| 2402 | } |
---|
| 2403 | |
---|
| 2404 | if (evalFail) |
---|
| 2405 | { |
---|
[9ff686] | 2406 | if (V_buf.level() != 1) |
---|
[08daea] | 2407 | { |
---|
| 2408 | do |
---|
| 2409 | { |
---|
[9ff686] | 2410 | Variable V_buf2= chooseExtension (V_buf); |
---|
[08daea] | 2411 | source= CFList(); |
---|
| 2412 | dest= CFList(); |
---|
| 2413 | |
---|
| 2414 | bool prim_fail= false; |
---|
| 2415 | Variable V_buf3; |
---|
| 2416 | prim_elem= primitiveElement (V_buf, V_buf3, prim_fail); |
---|
| 2417 | |
---|
| 2418 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
| 2419 | if (prim_fail) |
---|
| 2420 | ; //ERROR |
---|
| 2421 | else |
---|
| 2422 | im_prim_elem= mapPrimElem (prim_elem, V_buf, V_buf2); |
---|
| 2423 | |
---|
| 2424 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf)); |
---|
| 2425 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
| 2426 | |
---|
| 2427 | for (CFListIterator j= list; j.hasItem(); j++) |
---|
| 2428 | j.getItem()= mapUp (j.getItem(), V_buf, V_buf2, prim_elem, |
---|
| 2429 | im_prim_elem, source, dest); |
---|
| 2430 | for (int k= 0; k < i; k++) |
---|
| 2431 | { |
---|
| 2432 | for (CFListIterator j= pEvalPoints[k]; j.hasItem(); j++) |
---|
| 2433 | j.getItem()= mapUp (j.getItem(), V_buf, V_buf2, prim_elem, |
---|
| 2434 | im_prim_elem, source, dest); |
---|
| 2435 | gcds[k]= mapUp (gcds[k], V_buf, V_buf2, prim_elem, im_prim_elem, |
---|
| 2436 | source, dest); |
---|
| 2437 | } |
---|
| 2438 | |
---|
[9ff686] | 2439 | if (alpha.level() != 1) |
---|
[08daea] | 2440 | { |
---|
| 2441 | A= mapUp (A, V_buf, V_buf2, prim_elem, im_prim_elem, source,dest); |
---|
| 2442 | B= mapUp (B, V_buf, V_buf2, prim_elem, im_prim_elem, source,dest); |
---|
| 2443 | } |
---|
| 2444 | evalFail= false; |
---|
| 2445 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
| 2446 | evalFail, list); |
---|
| 2447 | } while (evalFail); |
---|
| 2448 | } |
---|
| 2449 | else |
---|
| 2450 | { |
---|
| 2451 | CanonicalForm mipo; |
---|
| 2452 | int deg= 2; |
---|
| 2453 | do { |
---|
| 2454 | mipo= randomIrredpoly (deg, x); |
---|
| 2455 | V_buf= rootOf (mipo); |
---|
| 2456 | evalFail= false; |
---|
| 2457 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
[c1b9927] | 2458 | evalFail, list); |
---|
[08daea] | 2459 | deg++; |
---|
| 2460 | } while (evalFail); |
---|
| 2461 | } |
---|
| 2462 | } |
---|
| 2463 | |
---|
| 2464 | g= gcd (Aeval, Beval); |
---|
| 2465 | g /= Lc (g); |
---|
| 2466 | |
---|
| 2467 | if (degree (g) != degree (skel) || (skelSize != size (g))) |
---|
| 2468 | { |
---|
| 2469 | delete[] pEvalPoints; |
---|
| 2470 | fail= true; |
---|
| 2471 | return 0; |
---|
| 2472 | } |
---|
| 2473 | CFIterator l= skel; |
---|
| 2474 | for (CFIterator k= g; k.hasTerms(); k++, l++) |
---|
| 2475 | { |
---|
| 2476 | if (k.exp() != l.exp()) |
---|
| 2477 | { |
---|
| 2478 | delete[] pEvalPoints; |
---|
| 2479 | fail= true; |
---|
| 2480 | return 0; |
---|
| 2481 | } |
---|
| 2482 | } |
---|
| 2483 | pEvalPoints[i]= evalPoints; |
---|
| 2484 | gcds[i]= g; |
---|
| 2485 | |
---|
| 2486 | tmp= 0; |
---|
| 2487 | int j= 0; |
---|
| 2488 | for (CFListIterator k= evalPoints; k.hasItem(); k++, j++) |
---|
| 2489 | tmp += k.getItem()*power (x, j); |
---|
| 2490 | list.append (tmp); |
---|
| 2491 | } |
---|
| 2492 | |
---|
| 2493 | if (Monoms.size() == 0) |
---|
| 2494 | Monoms= getMonoms (skel); |
---|
| 2495 | if (coeffMonoms == NULL) |
---|
| 2496 | coeffMonoms= new CFArray [skelSize]; |
---|
| 2497 | j= 0; |
---|
| 2498 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
| 2499 | coeffMonoms[j]= getMonoms (i.coeff()); |
---|
| 2500 | |
---|
| 2501 | CFArray* pL= new CFArray [skelSize]; |
---|
| 2502 | CFArray* pM= new CFArray [skelSize]; |
---|
| 2503 | for (int i= 0; i < biggestSize; i++) |
---|
| 2504 | { |
---|
| 2505 | CFIterator l= gcds [i]; |
---|
| 2506 | evalPoints= pEvalPoints [i]; |
---|
| 2507 | for (int k= 0; k < skelSize; k++, l++) |
---|
| 2508 | { |
---|
| 2509 | if (i == 0) |
---|
| 2510 | pL[k]= CFArray (biggestSize); |
---|
| 2511 | pL[k] [i]= l.coeff(); |
---|
| 2512 | |
---|
| 2513 | if (i == 0) |
---|
| 2514 | pM[k]= evaluate (coeffMonoms [k], evalPoints); |
---|
| 2515 | } |
---|
| 2516 | } |
---|
| 2517 | |
---|
| 2518 | CFArray solution; |
---|
| 2519 | CanonicalForm result= 0; |
---|
| 2520 | int ind= 0; |
---|
| 2521 | CFArray bufArray; |
---|
| 2522 | CFMatrix Mat; |
---|
| 2523 | for (int k= 0; k < skelSize; k++) |
---|
| 2524 | { |
---|
| 2525 | if (biggestSize != coeffMonoms[k].size()) |
---|
| 2526 | { |
---|
| 2527 | bufArray= CFArray (coeffMonoms[k].size()); |
---|
| 2528 | for (int i= 0; i < coeffMonoms[k].size(); i++) |
---|
| 2529 | bufArray [i]= pL[k] [i]; |
---|
| 2530 | solution= solveGeneralVandermonde (pM [k], bufArray); |
---|
| 2531 | } |
---|
| 2532 | else |
---|
| 2533 | solution= solveGeneralVandermonde (pM [k], pL[k]); |
---|
| 2534 | |
---|
| 2535 | if (solution.size() == 0) |
---|
| 2536 | { |
---|
| 2537 | delete[] pEvalPoints; |
---|
| 2538 | delete[] pM; |
---|
| 2539 | delete[] pL; |
---|
| 2540 | delete[] coeffMonoms; |
---|
| 2541 | fail= true; |
---|
| 2542 | return 0; |
---|
| 2543 | } |
---|
| 2544 | for (int l= 0; l < solution.size(); l++) |
---|
| 2545 | result += solution[l]*Monoms [ind + l]; |
---|
| 2546 | ind += solution.size(); |
---|
| 2547 | } |
---|
| 2548 | |
---|
| 2549 | delete[] pEvalPoints; |
---|
| 2550 | delete[] pM; |
---|
| 2551 | delete[] pL; |
---|
| 2552 | |
---|
[9ff686] | 2553 | if (alpha.level() != 1 && V_buf != alpha) |
---|
[08daea] | 2554 | { |
---|
| 2555 | CFList u, v; |
---|
| 2556 | result= mapDown (result, prim_elem, im_prim_elem, alpha, u, v); |
---|
| 2557 | } |
---|
| 2558 | |
---|
| 2559 | result= N(result); |
---|
| 2560 | if (fdivides (result, F) && fdivides (result, G)) |
---|
| 2561 | return result; |
---|
| 2562 | else |
---|
| 2563 | { |
---|
| 2564 | delete[] coeffMonoms; |
---|
| 2565 | fail= true; |
---|
| 2566 | return 0; |
---|
| 2567 | } |
---|
| 2568 | } |
---|
| 2569 | |
---|
| 2570 | CanonicalForm |
---|
| 2571 | nonMonicSparseInterpol (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 2572 | const CanonicalForm& skeleton, const Variable& alpha, |
---|
| 2573 | bool& fail, CFArray*& coeffMonoms, CFArray& Monoms |
---|
| 2574 | ) |
---|
| 2575 | { |
---|
| 2576 | CanonicalForm A= F; |
---|
| 2577 | CanonicalForm B= G; |
---|
| 2578 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
| 2579 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
| 2580 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
| 2581 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
| 2582 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
| 2583 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
| 2584 | if (F == G) return F/Lc(F); |
---|
| 2585 | |
---|
| 2586 | CFMap M,N; |
---|
| 2587 | int best_level= myCompress (A, B, M, N, false); |
---|
| 2588 | |
---|
| 2589 | if (best_level == 0) |
---|
| 2590 | return B.genOne(); |
---|
| 2591 | |
---|
| 2592 | A= M(A); |
---|
| 2593 | B= M(B); |
---|
| 2594 | |
---|
| 2595 | Variable x= Variable (1); |
---|
[f71453] | 2596 | ASSERT (degree (A, x) == 0, "expected degree (F, 1) == 0"); |
---|
| 2597 | ASSERT (degree (B, x) == 0, "expected degree (G, 1) == 0"); |
---|
[08daea] | 2598 | |
---|
[c1b9927] | 2599 | //univariate case |
---|
[08daea] | 2600 | if (A.isUnivariate() && B.isUnivariate()) |
---|
| 2601 | return N (gcd (A, B)); |
---|
| 2602 | |
---|
| 2603 | CanonicalForm skel= M(skeleton); |
---|
| 2604 | |
---|
| 2605 | CanonicalForm cA, cB; // content of A and B |
---|
| 2606 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
| 2607 | CanonicalForm gcdcAcB; |
---|
| 2608 | cA = uni_content (A); |
---|
| 2609 | cB = uni_content (B); |
---|
| 2610 | gcdcAcB= gcd (cA, cB); |
---|
| 2611 | ppA= A/cA; |
---|
| 2612 | ppB= B/cB; |
---|
| 2613 | |
---|
| 2614 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
| 2615 | CanonicalForm gcdlcAlcB; |
---|
| 2616 | lcA= uni_lcoeff (ppA); |
---|
| 2617 | lcB= uni_lcoeff (ppB); |
---|
| 2618 | |
---|
| 2619 | if (fdivides (lcA, lcB)) |
---|
| 2620 | { |
---|
| 2621 | if (fdivides (A, B)) |
---|
| 2622 | return F/Lc(F); |
---|
| 2623 | } |
---|
| 2624 | if (fdivides (lcB, lcA)) |
---|
| 2625 | { |
---|
| 2626 | if (fdivides (B, A)) |
---|
| 2627 | return G/Lc(G); |
---|
| 2628 | } |
---|
| 2629 | |
---|
| 2630 | gcdlcAlcB= gcd (lcA, lcB); |
---|
| 2631 | int skelSize= size (skel, skel.mvar()); |
---|
| 2632 | |
---|
| 2633 | int j= 0; |
---|
| 2634 | int biggestSize= 0; |
---|
| 2635 | int bufSize; |
---|
| 2636 | int numberUni= 0; |
---|
| 2637 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
| 2638 | { |
---|
| 2639 | bufSize= size (i.coeff()); |
---|
| 2640 | biggestSize= tmax (biggestSize, bufSize); |
---|
| 2641 | numberUni += bufSize; |
---|
| 2642 | } |
---|
| 2643 | numberUni--; |
---|
| 2644 | numberUni= (int) ceil ( (double) numberUni / (skelSize - 1)); |
---|
| 2645 | biggestSize= tmax (biggestSize , numberUni); |
---|
| 2646 | |
---|
| 2647 | numberUni= biggestSize + size (LC(skel)) - 1; |
---|
| 2648 | int biggestSize2= tmax (numberUni, biggestSize); |
---|
| 2649 | |
---|
| 2650 | CanonicalForm g, Aeval, Beval; |
---|
| 2651 | |
---|
| 2652 | CFList evalPoints; |
---|
| 2653 | CFArray coeffEval; |
---|
| 2654 | bool evalFail= false; |
---|
| 2655 | CFList list; |
---|
| 2656 | bool GF= false; |
---|
| 2657 | CanonicalForm LCA= LC (A); |
---|
| 2658 | CanonicalForm tmp; |
---|
| 2659 | CFArray gcds= CFArray (biggestSize); |
---|
| 2660 | CFList * pEvalPoints= new CFList [biggestSize]; |
---|
| 2661 | Variable V_buf= alpha; |
---|
| 2662 | CFList source, dest; |
---|
| 2663 | CanonicalForm prim_elem, im_prim_elem; |
---|
| 2664 | for (int i= 0; i < biggestSize; i++) |
---|
| 2665 | { |
---|
| 2666 | if (i == 0) |
---|
| 2667 | { |
---|
| 2668 | if (getCharacteristic() > 3) |
---|
| 2669 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
| 2670 | evalFail, list); |
---|
| 2671 | else |
---|
| 2672 | evalFail= true; |
---|
| 2673 | |
---|
| 2674 | if (evalFail) |
---|
| 2675 | { |
---|
[9ff686] | 2676 | if (V_buf.level() != 1) |
---|
[08daea] | 2677 | { |
---|
| 2678 | do |
---|
| 2679 | { |
---|
[9ff686] | 2680 | Variable V_buf2= chooseExtension (V_buf); |
---|
[08daea] | 2681 | source= CFList(); |
---|
| 2682 | dest= CFList(); |
---|
| 2683 | |
---|
| 2684 | bool prim_fail= false; |
---|
| 2685 | Variable V_buf3; |
---|
| 2686 | prim_elem= primitiveElement (V_buf, V_buf3, prim_fail); |
---|
| 2687 | |
---|
| 2688 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
| 2689 | if (prim_fail) |
---|
| 2690 | ; //ERROR |
---|
| 2691 | else |
---|
| 2692 | im_prim_elem= mapPrimElem (prim_elem, V_buf, V_buf2); |
---|
| 2693 | |
---|
| 2694 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf)); |
---|
| 2695 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
| 2696 | |
---|
[c1b9927] | 2697 | for (CFListIterator i= list; i.hasItem(); i++) |
---|
[08daea] | 2698 | i.getItem()= mapUp (i.getItem(), V_buf, V_buf2, prim_elem, |
---|
| 2699 | im_prim_elem, source, dest); |
---|
| 2700 | evalFail= false; |
---|
| 2701 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
| 2702 | evalFail, list); |
---|
| 2703 | } while (evalFail); |
---|
| 2704 | } |
---|
| 2705 | else |
---|
| 2706 | { |
---|
| 2707 | CanonicalForm mipo; |
---|
| 2708 | int deg= 2; |
---|
| 2709 | do { |
---|
| 2710 | mipo= randomIrredpoly (deg, x); |
---|
| 2711 | V_buf= rootOf (mipo); |
---|
| 2712 | evalFail= false; |
---|
| 2713 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
| 2714 | evalFail, list); |
---|
| 2715 | deg++; |
---|
| 2716 | } while (evalFail); |
---|
| 2717 | } |
---|
| 2718 | } |
---|
| 2719 | } |
---|
| 2720 | else |
---|
| 2721 | { |
---|
| 2722 | mult (evalPoints, pEvalPoints[0]); |
---|
| 2723 | eval (A, B, Aeval, Beval, evalPoints); |
---|
| 2724 | } |
---|
| 2725 | |
---|
| 2726 | g= gcd (Aeval, Beval); |
---|
| 2727 | g /= Lc (g); |
---|
| 2728 | |
---|
| 2729 | if (degree (g) != degree (skel) || (skelSize != size (g))) |
---|
| 2730 | { |
---|
| 2731 | delete[] pEvalPoints; |
---|
| 2732 | fail= true; |
---|
| 2733 | return 0; |
---|
| 2734 | } |
---|
| 2735 | CFIterator l= skel; |
---|
| 2736 | for (CFIterator k= g; k.hasTerms(); k++, l++) |
---|
| 2737 | { |
---|
| 2738 | if (k.exp() != l.exp()) |
---|
| 2739 | { |
---|
| 2740 | delete[] pEvalPoints; |
---|
| 2741 | fail= true; |
---|
| 2742 | return 0; |
---|
| 2743 | } |
---|
| 2744 | } |
---|
| 2745 | pEvalPoints[i]= evalPoints; |
---|
| 2746 | gcds[i]= g; |
---|
| 2747 | |
---|
| 2748 | tmp= 0; |
---|
| 2749 | int j= 0; |
---|
| 2750 | for (CFListIterator k= evalPoints; k.hasItem(); k++, j++) |
---|
| 2751 | tmp += k.getItem()*power (x, j); |
---|
| 2752 | list.append (tmp); |
---|
| 2753 | } |
---|
| 2754 | |
---|
| 2755 | if (Monoms.size() == 0) |
---|
| 2756 | Monoms= getMonoms (skel); |
---|
| 2757 | |
---|
| 2758 | if (coeffMonoms == NULL) |
---|
| 2759 | coeffMonoms= new CFArray [skelSize]; |
---|
| 2760 | |
---|
| 2761 | j= 0; |
---|
| 2762 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
| 2763 | coeffMonoms[j]= getMonoms (i.coeff()); |
---|
| 2764 | |
---|
| 2765 | int minimalColumnsIndex; |
---|
| 2766 | if (skelSize > 1) |
---|
| 2767 | minimalColumnsIndex= 1; |
---|
| 2768 | else |
---|
| 2769 | minimalColumnsIndex= 0; |
---|
[c1b9927] | 2770 | int minimalColumns=-1; |
---|
[08daea] | 2771 | |
---|
| 2772 | CFArray* pM= new CFArray [skelSize]; |
---|
| 2773 | CFMatrix Mat; |
---|
[c1b9927] | 2774 | // find the Matrix with minimal number of columns |
---|
[08daea] | 2775 | for (int i= 0; i < skelSize; i++) |
---|
| 2776 | { |
---|
| 2777 | pM[i]= CFArray (coeffMonoms[i].size()); |
---|
| 2778 | if (i == 1) |
---|
| 2779 | minimalColumns= coeffMonoms[i].size(); |
---|
| 2780 | if (i > 1) |
---|
| 2781 | { |
---|
| 2782 | if (minimalColumns > coeffMonoms[i].size()) |
---|
| 2783 | { |
---|
| 2784 | minimalColumns= coeffMonoms[i].size(); |
---|
| 2785 | minimalColumnsIndex= i; |
---|
| 2786 | } |
---|
| 2787 | } |
---|
| 2788 | } |
---|
| 2789 | CFMatrix* pMat= new CFMatrix [2]; |
---|
| 2790 | pMat[0]= CFMatrix (biggestSize, coeffMonoms[0].size()); |
---|
| 2791 | pMat[1]= CFMatrix (biggestSize, coeffMonoms[minimalColumnsIndex].size()); |
---|
| 2792 | CFArray* pL= new CFArray [skelSize]; |
---|
| 2793 | for (int i= 0; i < biggestSize; i++) |
---|
| 2794 | { |
---|
| 2795 | CFIterator l= gcds [i]; |
---|
| 2796 | evalPoints= pEvalPoints [i]; |
---|
| 2797 | for (int k= 0; k < skelSize; k++, l++) |
---|
| 2798 | { |
---|
| 2799 | if (i == 0) |
---|
| 2800 | pL[k]= CFArray (biggestSize); |
---|
[c1b9927] | 2801 | pL[k] [i]= l.coeff(); |
---|
[08daea] | 2802 | |
---|
| 2803 | if (i == 0 && k != 0 && k != minimalColumnsIndex) |
---|
| 2804 | pM[k]= evaluate (coeffMonoms[k], evalPoints); |
---|
| 2805 | else if (i == 0 && (k == 0 || k == minimalColumnsIndex)) |
---|
| 2806 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
| 2807 | if (i > 0 && (k == 0 || k == minimalColumnsIndex)) |
---|
| 2808 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
| 2809 | |
---|
| 2810 | if (k == 0) |
---|
| 2811 | { |
---|
| 2812 | if (pMat[k].rows() >= i + 1) |
---|
| 2813 | { |
---|
| 2814 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
| 2815 | pMat[k] (i + 1, ind)= coeffEval[ind - 1]; |
---|
| 2816 | } |
---|
| 2817 | } |
---|
| 2818 | if (k == minimalColumnsIndex) |
---|
| 2819 | { |
---|
| 2820 | if (pMat[1].rows() >= i + 1) |
---|
| 2821 | { |
---|
| 2822 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
| 2823 | pMat[1] (i + 1, ind)= coeffEval[ind - 1]; |
---|
| 2824 | } |
---|
| 2825 | } |
---|
| 2826 | } |
---|
| 2827 | } |
---|
| 2828 | |
---|
| 2829 | CFArray solution; |
---|
| 2830 | CanonicalForm result= 0; |
---|
| 2831 | int ind= 1; |
---|
| 2832 | int matRows, matColumns; |
---|
| 2833 | matRows= pMat[1].rows(); |
---|
[c1b9927] | 2834 | matColumns= pMat[0].columns() - 1; |
---|
[08daea] | 2835 | matColumns += pMat[1].columns(); |
---|
| 2836 | |
---|
| 2837 | Mat= CFMatrix (matRows, matColumns); |
---|
| 2838 | for (int i= 1; i <= matRows; i++) |
---|
| 2839 | for (int j= 1; j <= pMat[1].columns(); j++) |
---|
| 2840 | Mat (i, j)= pMat[1] (i, j); |
---|
| 2841 | |
---|
[c1b9927] | 2842 | for (int j= pMat[1].columns() + 1; j <= matColumns; |
---|
[08daea] | 2843 | j++, ind++) |
---|
| 2844 | { |
---|
[c1b9927] | 2845 | for (int i= 1; i <= matRows; i++) |
---|
[08daea] | 2846 | Mat (i, j)= (-pMat [0] (i, ind + 1))*pL[minimalColumnsIndex] [i - 1]; |
---|
| 2847 | } |
---|
| 2848 | |
---|
| 2849 | CFArray firstColumn= CFArray (pMat[0].rows()); |
---|
| 2850 | for (int i= 0; i < pMat[0].rows(); i++) |
---|
[c1b9927] | 2851 | firstColumn [i]= pMat[0] (i + 1, 1); |
---|
[08daea] | 2852 | |
---|
| 2853 | CFArray bufArray= pL[minimalColumnsIndex]; |
---|
| 2854 | |
---|
| 2855 | for (int i= 0; i < biggestSize; i++) |
---|
| 2856 | pL[minimalColumnsIndex] [i] *= firstColumn[i]; |
---|
| 2857 | |
---|
| 2858 | CFMatrix bufMat= pMat[1]; |
---|
| 2859 | pMat[1]= Mat; |
---|
| 2860 | |
---|
[9ff686] | 2861 | if (V_buf.level() != 1) |
---|
[c1b9927] | 2862 | solution= solveSystemFq (pMat[1], |
---|
[08daea] | 2863 | pL[minimalColumnsIndex], V_buf); |
---|
| 2864 | else |
---|
[c1b9927] | 2865 | solution= solveSystemFp (pMat[1], |
---|
[08daea] | 2866 | pL[minimalColumnsIndex]); |
---|
| 2867 | |
---|
| 2868 | if (solution.size() == 0) |
---|
| 2869 | { //Javadi's method failed, try deKleine, Monagan, Wittkopf instead |
---|
| 2870 | CFMatrix bufMat0= pMat[0]; |
---|
| 2871 | delete [] pMat; |
---|
| 2872 | pMat= new CFMatrix [skelSize]; |
---|
[c1b9927] | 2873 | pL[minimalColumnsIndex]= bufArray; |
---|
[618da5] | 2874 | CFList* bufpEvalPoints= NULL; |
---|
[08daea] | 2875 | CFArray bufGcds; |
---|
| 2876 | if (biggestSize != biggestSize2) |
---|
| 2877 | { |
---|
| 2878 | bufpEvalPoints= pEvalPoints; |
---|
| 2879 | pEvalPoints= new CFList [biggestSize2]; |
---|
| 2880 | bufGcds= gcds; |
---|
| 2881 | gcds= CFArray (biggestSize2); |
---|
| 2882 | for (int i= 0; i < biggestSize; i++) |
---|
| 2883 | { |
---|
| 2884 | pEvalPoints[i]= bufpEvalPoints [i]; |
---|
| 2885 | gcds[i]= bufGcds[i]; |
---|
| 2886 | } |
---|
| 2887 | for (int i= 0; i < biggestSize2 - biggestSize; i++) |
---|
| 2888 | { |
---|
| 2889 | mult (evalPoints, pEvalPoints[0]); |
---|
| 2890 | eval (A, B, Aeval, Beval, evalPoints); |
---|
| 2891 | g= gcd (Aeval, Beval); |
---|
| 2892 | g /= Lc (g); |
---|
| 2893 | if (degree (g) != degree (skel) || (skelSize != size (g))) |
---|
| 2894 | { |
---|
| 2895 | delete[] pEvalPoints; |
---|
| 2896 | delete[] pMat; |
---|
| 2897 | delete[] pL; |
---|
| 2898 | delete[] coeffMonoms; |
---|
| 2899 | delete[] pM; |
---|
[618da5] | 2900 | if (bufpEvalPoints != NULL) |
---|
| 2901 | delete [] bufpEvalPoints; |
---|
[08daea] | 2902 | fail= true; |
---|
| 2903 | return 0; |
---|
| 2904 | } |
---|
| 2905 | CFIterator l= skel; |
---|
| 2906 | for (CFIterator k= g; k.hasTerms(); k++, l++) |
---|
| 2907 | { |
---|
| 2908 | if (k.exp() != l.exp()) |
---|
| 2909 | { |
---|
| 2910 | delete[] pEvalPoints; |
---|
| 2911 | delete[] pMat; |
---|
| 2912 | delete[] pL; |
---|
| 2913 | delete[] coeffMonoms; |
---|
| 2914 | delete[] pM; |
---|
[618da5] | 2915 | if (bufpEvalPoints != NULL) |
---|
| 2916 | delete [] bufpEvalPoints; |
---|
[08daea] | 2917 | fail= true; |
---|
| 2918 | return 0; |
---|
| 2919 | } |
---|
| 2920 | } |
---|
| 2921 | pEvalPoints[i + biggestSize]= evalPoints; |
---|
| 2922 | gcds[i + biggestSize]= g; |
---|
| 2923 | } |
---|
| 2924 | } |
---|
| 2925 | for (int i= 0; i < biggestSize; i++) |
---|
| 2926 | { |
---|
| 2927 | CFIterator l= gcds [i]; |
---|
| 2928 | evalPoints= pEvalPoints [i]; |
---|
| 2929 | for (int k= 1; k < skelSize; k++, l++) |
---|
| 2930 | { |
---|
| 2931 | if (i == 0) |
---|
| 2932 | pMat[k]= CFMatrix (biggestSize2,coeffMonoms[k].size()+biggestSize2-1); |
---|
| 2933 | if (k == minimalColumnsIndex) |
---|
| 2934 | continue; |
---|
| 2935 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
[c1b9927] | 2936 | if (pMat[k].rows() >= i + 1) |
---|
[08daea] | 2937 | { |
---|
| 2938 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
| 2939 | pMat[k] (i + 1, ind)= coeffEval[ind - 1]; |
---|
| 2940 | } |
---|
| 2941 | } |
---|
| 2942 | } |
---|
| 2943 | Mat= bufMat0; |
---|
| 2944 | pMat[0]= CFMatrix (biggestSize2, coeffMonoms[0].size() + biggestSize2 - 1); |
---|
| 2945 | for (int j= 1; j <= Mat.rows(); j++) |
---|
| 2946 | for (int k= 1; k <= Mat.columns(); k++) |
---|
| 2947 | pMat [0] (j,k)= Mat (j,k); |
---|
| 2948 | Mat= bufMat; |
---|
| 2949 | for (int j= 1; j <= Mat.rows(); j++) |
---|
| 2950 | for (int k= 1; k <= Mat.columns(); k++) |
---|
| 2951 | pMat [minimalColumnsIndex] (j,k)= Mat (j,k); |
---|
| 2952 | // write old matrix entries into new matrices |
---|
| 2953 | for (int i= 0; i < skelSize; i++) |
---|
| 2954 | { |
---|
| 2955 | bufArray= pL[i]; |
---|
| 2956 | pL[i]= CFArray (biggestSize2); |
---|
| 2957 | for (int j= 0; j < bufArray.size(); j++) |
---|
| 2958 | pL[i] [j]= bufArray [j]; |
---|
| 2959 | } |
---|
| 2960 | //write old vector entries into new and add new entries to old matrices |
---|
| 2961 | for (int i= 0; i < biggestSize2 - biggestSize; i++) |
---|
| 2962 | { |
---|
| 2963 | CFIterator l= gcds [i + biggestSize]; |
---|
| 2964 | evalPoints= pEvalPoints [i + biggestSize]; |
---|
| 2965 | for (int k= 0; k < skelSize; k++, l++) |
---|
| 2966 | { |
---|
[c1b9927] | 2967 | pL[k] [i + biggestSize]= l.coeff(); |
---|
[08daea] | 2968 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
[c1b9927] | 2969 | if (pMat[k].rows() >= i + biggestSize + 1) |
---|
| 2970 | { |
---|
[08daea] | 2971 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
| 2972 | pMat[k] (i + biggestSize + 1, ind)= coeffEval[ind - 1]; |
---|
| 2973 | } |
---|
| 2974 | } |
---|
| 2975 | } |
---|
| 2976 | // begin new |
---|
| 2977 | for (int i= 0; i < skelSize; i++) |
---|
| 2978 | { |
---|
| 2979 | if (pL[i].size() > 1) |
---|
| 2980 | { |
---|
[c1b9927] | 2981 | for (int j= 2; j <= pMat[i].rows(); j++) |
---|
| 2982 | pMat[i] (j, coeffMonoms[i].size() + j - 1)= |
---|
[08daea] | 2983 | -pL[i] [j - 1]; |
---|
| 2984 | } |
---|
| 2985 | } |
---|
| 2986 | |
---|
| 2987 | matColumns= biggestSize2 - 1; |
---|
| 2988 | matRows= 0; |
---|
| 2989 | for (int i= 0; i < skelSize; i++) |
---|
| 2990 | { |
---|
[9ff686] | 2991 | if (V_buf.level() == 1) |
---|
[d1dc39] | 2992 | (void) gaussianElimFp (pMat[i], pL[i]); |
---|
[08daea] | 2993 | else |
---|
[d1dc39] | 2994 | (void) gaussianElimFq (pMat[i], pL[i], V_buf); |
---|
[08daea] | 2995 | |
---|
| 2996 | if (pMat[i] (coeffMonoms[i].size(), coeffMonoms[i].size()) == 0) |
---|
| 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 | matRows += pMat[i].rows() - coeffMonoms[i].size(); |
---|
| 3009 | } |
---|
| 3010 | |
---|
| 3011 | CFMatrix bufMat; |
---|
| 3012 | Mat= CFMatrix (matRows, matColumns); |
---|
| 3013 | ind= 0; |
---|
| 3014 | bufArray= CFArray (matRows); |
---|
| 3015 | CFArray bufArray2; |
---|
| 3016 | for (int i= 0; i < skelSize; i++) |
---|
| 3017 | { |
---|
| 3018 | bufMat= pMat[i] (coeffMonoms[i].size() + 1, pMat[i].rows(), |
---|
| 3019 | coeffMonoms[i].size() + 1, pMat[i].columns()); |
---|
| 3020 | |
---|
| 3021 | for (int j= 1; j <= bufMat.rows(); j++) |
---|
| 3022 | for (int k= 1; k <= bufMat.columns(); k++) |
---|
| 3023 | Mat (j + ind, k)= bufMat(j, k); |
---|
| 3024 | bufArray2= coeffMonoms[i].size(); |
---|
| 3025 | for (int j= 1; j <= pMat[i].rows(); j++) |
---|
| 3026 | { |
---|
| 3027 | if (j > coeffMonoms[i].size()) |
---|
| 3028 | bufArray [j-coeffMonoms[i].size() + ind - 1]= pL[i] [j - 1]; |
---|
[c1b9927] | 3029 | else |
---|
[08daea] | 3030 | bufArray2 [j - 1]= pL[i] [j - 1]; |
---|
| 3031 | } |
---|
| 3032 | pL[i]= bufArray2; |
---|
| 3033 | ind += bufMat.rows(); |
---|
| 3034 | pMat[i]= pMat[i] (1, coeffMonoms[i].size(), 1, pMat[i].columns()); |
---|
| 3035 | } |
---|
| 3036 | |
---|
[9ff686] | 3037 | if (V_buf.level() != 1) |
---|
[08daea] | 3038 | solution= solveSystemFq (Mat, bufArray, V_buf); |
---|
| 3039 | else |
---|
| 3040 | solution= solveSystemFp (Mat, bufArray); |
---|
| 3041 | |
---|
| 3042 | if (solution.size() == 0) |
---|
| 3043 | { |
---|
| 3044 | delete[] pEvalPoints; |
---|
| 3045 | delete[] pMat; |
---|
| 3046 | delete[] pL; |
---|
| 3047 | delete[] coeffMonoms; |
---|
| 3048 | delete[] pM; |
---|
[618da5] | 3049 | if (bufpEvalPoints != NULL) |
---|
| 3050 | delete [] bufpEvalPoints; |
---|
[08daea] | 3051 | fail= true; |
---|
| 3052 | return 0; |
---|
| 3053 | } |
---|
| 3054 | |
---|
| 3055 | ind= 0; |
---|
| 3056 | result= 0; |
---|
| 3057 | CFArray bufSolution; |
---|
| 3058 | for (int i= 0; i < skelSize; i++) |
---|
| 3059 | { |
---|
| 3060 | bufSolution= readOffSolution (pMat[i], pL[i], solution); |
---|
| 3061 | for (int i= 0; i < bufSolution.size(); i++, ind++) |
---|
| 3062 | result += Monoms [ind]*bufSolution[i]; |
---|
| 3063 | } |
---|
[9ff686] | 3064 | if (alpha.level() != 1 && V_buf != alpha) |
---|
[08daea] | 3065 | { |
---|
| 3066 | CFList u, v; |
---|
| 3067 | result= mapDown (result, prim_elem, im_prim_elem, alpha, u, v); |
---|
| 3068 | } |
---|
| 3069 | result= N(result); |
---|
| 3070 | if (fdivides (result, F) && fdivides (result, G)) |
---|
[618da5] | 3071 | { |
---|
| 3072 | delete[] pEvalPoints; |
---|
| 3073 | delete[] pMat; |
---|
| 3074 | delete[] pL; |
---|
| 3075 | delete[] pM; |
---|
| 3076 | if (bufpEvalPoints != NULL) |
---|
| 3077 | delete [] bufpEvalPoints; |
---|
[08daea] | 3078 | return result; |
---|
[618da5] | 3079 | } |
---|
[08daea] | 3080 | else |
---|
| 3081 | { |
---|
[618da5] | 3082 | delete[] pEvalPoints; |
---|
| 3083 | delete[] pMat; |
---|
| 3084 | delete[] pL; |
---|
| 3085 | delete[] coeffMonoms; |
---|
| 3086 | delete[] pM; |
---|
| 3087 | if (bufpEvalPoints != NULL) |
---|
| 3088 | delete [] bufpEvalPoints; |
---|
[08daea] | 3089 | fail= true; |
---|
| 3090 | return 0; |
---|
| 3091 | } |
---|
| 3092 | } // end of deKleine, Monagan & Wittkopf |
---|
| 3093 | |
---|
| 3094 | result += Monoms[0]; |
---|
| 3095 | int ind2= 0, ind3= 2; |
---|
| 3096 | ind= 0; |
---|
| 3097 | for (int l= 0; l < minimalColumnsIndex; l++) |
---|
| 3098 | ind += coeffMonoms[l].size(); |
---|
| 3099 | for (int l= solution.size() - pMat[0].columns() + 1; l < solution.size(); |
---|
| 3100 | l++, ind2++, ind3++) |
---|
| 3101 | { |
---|
| 3102 | result += solution[l]*Monoms [1 + ind2]; |
---|
[c1b9927] | 3103 | for (int i= 0; i < pMat[0].rows(); i++) |
---|
[08daea] | 3104 | firstColumn[i] += solution[l]*pMat[0] (i + 1, ind3); |
---|
| 3105 | } |
---|
| 3106 | for (int l= 0; l < solution.size() + 1 - pMat[0].columns(); l++) |
---|
| 3107 | result += solution[l]*Monoms [ind + l]; |
---|
| 3108 | ind= coeffMonoms[0].size(); |
---|
| 3109 | for (int k= 1; k < skelSize; k++) |
---|
| 3110 | { |
---|
| 3111 | if (k == minimalColumnsIndex) |
---|
| 3112 | { |
---|
| 3113 | ind += coeffMonoms[k].size(); |
---|
| 3114 | continue; |
---|
| 3115 | } |
---|
| 3116 | if (k != minimalColumnsIndex) |
---|
| 3117 | { |
---|
| 3118 | for (int i= 0; i < biggestSize; i++) |
---|
| 3119 | pL[k] [i] *= firstColumn [i]; |
---|
| 3120 | } |
---|
| 3121 | |
---|
| 3122 | if (biggestSize != coeffMonoms[k].size() && k != minimalColumnsIndex) |
---|
| 3123 | { |
---|
| 3124 | bufArray= CFArray (coeffMonoms[k].size()); |
---|
| 3125 | for (int i= 0; i < bufArray.size(); i++) |
---|
| 3126 | bufArray [i]= pL[k] [i]; |
---|
| 3127 | solution= solveGeneralVandermonde (pM[k], bufArray); |
---|
| 3128 | } |
---|
| 3129 | else |
---|
| 3130 | solution= solveGeneralVandermonde (pM[k], pL[k]); |
---|
| 3131 | |
---|
| 3132 | if (solution.size() == 0) |
---|
| 3133 | { |
---|
| 3134 | delete[] pEvalPoints; |
---|
| 3135 | delete[] pMat; |
---|
| 3136 | delete[] pL; |
---|
| 3137 | delete[] coeffMonoms; |
---|
| 3138 | delete[] pM; |
---|
| 3139 | fail= true; |
---|
| 3140 | return 0; |
---|
| 3141 | } |
---|
| 3142 | if (k != minimalColumnsIndex) |
---|
| 3143 | { |
---|
| 3144 | for (int l= 0; l < solution.size(); l++) |
---|
| 3145 | result += solution[l]*Monoms [ind + l]; |
---|
| 3146 | ind += solution.size(); |
---|
| 3147 | } |
---|
| 3148 | } |
---|
| 3149 | |
---|
| 3150 | delete[] pEvalPoints; |
---|
| 3151 | delete[] pMat; |
---|
| 3152 | delete[] pL; |
---|
| 3153 | delete[] pM; |
---|
| 3154 | |
---|
[9ff686] | 3155 | if (alpha.level() != 1 && V_buf != alpha) |
---|
[08daea] | 3156 | { |
---|
| 3157 | CFList u, v; |
---|
| 3158 | result= mapDown (result, prim_elem, im_prim_elem, alpha, u, v); |
---|
| 3159 | } |
---|
| 3160 | result= N(result); |
---|
| 3161 | |
---|
| 3162 | if (fdivides (result, F) && fdivides (result, G)) |
---|
| 3163 | return result; |
---|
| 3164 | else |
---|
| 3165 | { |
---|
| 3166 | delete[] coeffMonoms; |
---|
| 3167 | fail= true; |
---|
| 3168 | return 0; |
---|
| 3169 | } |
---|
| 3170 | } |
---|
| 3171 | |
---|
| 3172 | CanonicalForm sparseGCDFq (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 3173 | const Variable & alpha, CFList& l, bool& topLevel) |
---|
| 3174 | { |
---|
| 3175 | CanonicalForm A= F; |
---|
| 3176 | CanonicalForm B= G; |
---|
| 3177 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
| 3178 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
| 3179 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
| 3180 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
| 3181 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
| 3182 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
| 3183 | if (F == G) return F/Lc(F); |
---|
| 3184 | |
---|
| 3185 | CFMap M,N; |
---|
| 3186 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
| 3187 | |
---|
| 3188 | if (best_level == 0) return B.genOne(); |
---|
| 3189 | |
---|
| 3190 | A= M(A); |
---|
| 3191 | B= M(B); |
---|
| 3192 | |
---|
| 3193 | Variable x= Variable (1); |
---|
| 3194 | |
---|
[c1b9927] | 3195 | //univariate case |
---|
[08daea] | 3196 | if (A.isUnivariate() && B.isUnivariate()) |
---|
| 3197 | return N (gcd (A, B)); |
---|
| 3198 | |
---|
| 3199 | CanonicalForm cA, cB; // content of A and B |
---|
| 3200 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
| 3201 | CanonicalForm gcdcAcB; |
---|
[ea5ff1d] | 3202 | |
---|
| 3203 | cA = uni_content (A); |
---|
| 3204 | cB = uni_content (B); |
---|
| 3205 | gcdcAcB= gcd (cA, cB); |
---|
| 3206 | ppA= A/cA; |
---|
| 3207 | ppB= B/cB; |
---|
[08daea] | 3208 | |
---|
| 3209 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
| 3210 | CanonicalForm gcdlcAlcB; |
---|
| 3211 | lcA= uni_lcoeff (ppA); |
---|
| 3212 | lcB= uni_lcoeff (ppB); |
---|
| 3213 | |
---|
| 3214 | if (fdivides (lcA, lcB)) |
---|
| 3215 | { |
---|
| 3216 | if (fdivides (A, B)) |
---|
| 3217 | return F/Lc(F); |
---|
| 3218 | } |
---|
| 3219 | if (fdivides (lcB, lcA)) |
---|
| 3220 | { |
---|
| 3221 | if (fdivides (B, A)) |
---|
| 3222 | return G/Lc(G); |
---|
| 3223 | } |
---|
| 3224 | |
---|
| 3225 | gcdlcAlcB= gcd (lcA, lcB); |
---|
| 3226 | |
---|
| 3227 | int d= totaldegree (ppA, Variable (2), Variable (ppA.level())); |
---|
| 3228 | int d0; |
---|
| 3229 | |
---|
[c1b9927] | 3230 | if (d == 0) |
---|
[a9a6dcb] | 3231 | return N(gcdcAcB); |
---|
[08daea] | 3232 | d0= totaldegree (ppB, Variable (2), Variable (ppB.level())); |
---|
| 3233 | |
---|
| 3234 | if (d0 < d) |
---|
| 3235 | d= d0; |
---|
| 3236 | |
---|
| 3237 | if (d == 0) |
---|
[a9a6dcb] | 3238 | return N(gcdcAcB); |
---|
[08daea] | 3239 | |
---|
| 3240 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH, skeleton; |
---|
| 3241 | CanonicalForm newtonPoly= 1; |
---|
| 3242 | m= gcdlcAlcB; |
---|
| 3243 | G_m= 0; |
---|
| 3244 | H= 0; |
---|
| 3245 | bool fail= false; |
---|
| 3246 | topLevel= false; |
---|
| 3247 | bool inextension= false; |
---|
| 3248 | Variable V_buf= alpha; |
---|
| 3249 | CanonicalForm prim_elem, im_prim_elem; |
---|
| 3250 | CFList source, dest; |
---|
| 3251 | do // first do |
---|
| 3252 | { |
---|
| 3253 | random_element= randomElement (m, V_buf, l, fail); |
---|
| 3254 | if (random_element == 0 && !fail) |
---|
| 3255 | { |
---|
| 3256 | if (!find (l, random_element)) |
---|
| 3257 | l.append (random_element); |
---|
| 3258 | continue; |
---|
| 3259 | } |
---|
| 3260 | if (fail) |
---|
| 3261 | { |
---|
| 3262 | source= CFList(); |
---|
| 3263 | dest= CFList(); |
---|
| 3264 | |
---|
[9ff686] | 3265 | Variable V_buf3= V_buf; |
---|
| 3266 | V_buf= chooseExtension (V_buf); |
---|
[08daea] | 3267 | bool prim_fail= false; |
---|
| 3268 | Variable V_buf2; |
---|
| 3269 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
| 3270 | |
---|
[9ff686] | 3271 | if (V_buf3 != alpha) |
---|
| 3272 | { |
---|
| 3273 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3274 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3275 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
| 3276 | source, dest); |
---|
| 3277 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3278 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3279 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, source, |
---|
| 3280 | dest); |
---|
| 3281 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 3282 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
| 3283 | source, dest); |
---|
| 3284 | } |
---|
| 3285 | |
---|
[08daea] | 3286 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
| 3287 | if (prim_fail) |
---|
| 3288 | ; //ERROR |
---|
| 3289 | else |
---|
| 3290 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
| 3291 | |
---|
| 3292 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
| 3293 | DEBOUTLN (cerr, "getMipo (V_buf2)= " << getMipo (V_buf2)); |
---|
| 3294 | inextension= true; |
---|
[c1b9927] | 3295 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
[08daea] | 3296 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
| 3297 | im_prim_elem, source, dest); |
---|
| 3298 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3299 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3300 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
| 3301 | source, dest); |
---|
| 3302 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3303 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3304 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
| 3305 | source, dest); |
---|
| 3306 | |
---|
| 3307 | fail= false; |
---|
| 3308 | random_element= randomElement (m, V_buf, l, fail ); |
---|
| 3309 | DEBOUTLN (cerr, "fail= " << fail); |
---|
| 3310 | CFList list; |
---|
| 3311 | TIMING_START (gcd_recursion); |
---|
| 3312 | G_random_element= |
---|
| 3313 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), V_buf, |
---|
| 3314 | list, topLevel); |
---|
| 3315 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3316 | "time for recursive call: "); |
---|
| 3317 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3318 | } |
---|
| 3319 | else |
---|
| 3320 | { |
---|
| 3321 | CFList list; |
---|
| 3322 | TIMING_START (gcd_recursion); |
---|
| 3323 | G_random_element= |
---|
| 3324 | sparseGCDFq (ppA(random_element, x), ppB(random_element, x), V_buf, |
---|
| 3325 | list, topLevel); |
---|
| 3326 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3327 | "time for recursive call: "); |
---|
| 3328 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3329 | } |
---|
| 3330 | |
---|
[a76d6fe] | 3331 | if (!G_random_element.inCoeffDomain()) |
---|
| 3332 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 3333 | Variable (G_random_element.level())); |
---|
| 3334 | else |
---|
| 3335 | d0= 0; |
---|
| 3336 | |
---|
[08daea] | 3337 | if (d0 == 0) |
---|
[a9a6dcb] | 3338 | return N(gcdcAcB); |
---|
[08daea] | 3339 | if (d0 > d) |
---|
| 3340 | { |
---|
| 3341 | if (!find (l, random_element)) |
---|
| 3342 | l.append (random_element); |
---|
| 3343 | continue; |
---|
| 3344 | } |
---|
| 3345 | |
---|
| 3346 | G_random_element= |
---|
| 3347 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
| 3348 | * G_random_element; |
---|
| 3349 | |
---|
| 3350 | skeleton= G_random_element; |
---|
[a76d6fe] | 3351 | if (!G_random_element.inCoeffDomain()) |
---|
| 3352 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 3353 | Variable (G_random_element.level())); |
---|
| 3354 | else |
---|
| 3355 | d0= 0; |
---|
| 3356 | |
---|
[08daea] | 3357 | if (d0 < d) |
---|
| 3358 | { |
---|
| 3359 | m= gcdlcAlcB; |
---|
| 3360 | newtonPoly= 1; |
---|
| 3361 | G_m= 0; |
---|
| 3362 | d= d0; |
---|
| 3363 | } |
---|
| 3364 | |
---|
| 3365 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
| 3366 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
| 3367 | { |
---|
| 3368 | cH= uni_content (H); |
---|
| 3369 | ppH= H/cH; |
---|
| 3370 | if (inextension) |
---|
| 3371 | { |
---|
| 3372 | CFList u, v; |
---|
| 3373 | //maybe it's better to test if ppH is an element of F(\alpha) before |
---|
| 3374 | //mapping down |
---|
[c723d80] | 3375 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
[08daea] | 3376 | { |
---|
[c723d80] | 3377 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
| 3378 | ppH= mapDown (ppH, prim_elem, im_prim_elem, alpha, u, v); |
---|
| 3379 | ppH /= Lc(ppH); |
---|
| 3380 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
[08daea] | 3381 | return N(gcdcAcB*ppH); |
---|
| 3382 | } |
---|
| 3383 | } |
---|
[c723d80] | 3384 | else if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
[08daea] | 3385 | return N(gcdcAcB*ppH); |
---|
| 3386 | } |
---|
| 3387 | G_m= H; |
---|
| 3388 | newtonPoly= newtonPoly*(x - random_element); |
---|
| 3389 | m= m*(x - random_element); |
---|
| 3390 | if (!find (l, random_element)) |
---|
| 3391 | l.append (random_element); |
---|
| 3392 | |
---|
[d08ed8] | 3393 | if (getCharacteristic () > 3 && size (skeleton) < 100) |
---|
[08daea] | 3394 | { |
---|
| 3395 | CFArray Monoms; |
---|
| 3396 | CFArray *coeffMonoms= NULL; |
---|
| 3397 | do //second do |
---|
| 3398 | { |
---|
| 3399 | random_element= randomElement (m, V_buf, l, fail); |
---|
| 3400 | if (random_element == 0 && !fail) |
---|
| 3401 | { |
---|
| 3402 | if (!find (l, random_element)) |
---|
| 3403 | l.append (random_element); |
---|
| 3404 | continue; |
---|
| 3405 | } |
---|
| 3406 | if (fail) |
---|
| 3407 | { |
---|
| 3408 | source= CFList(); |
---|
| 3409 | dest= CFList(); |
---|
| 3410 | |
---|
[9ff686] | 3411 | Variable V_buf3= V_buf; |
---|
| 3412 | V_buf= chooseExtension (V_buf); |
---|
[08daea] | 3413 | bool prim_fail= false; |
---|
| 3414 | Variable V_buf2; |
---|
| 3415 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
| 3416 | |
---|
[9ff686] | 3417 | if (V_buf3 != alpha) |
---|
| 3418 | { |
---|
| 3419 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3420 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3421 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
| 3422 | source, dest); |
---|
| 3423 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3424 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3425 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, |
---|
| 3426 | source, dest); |
---|
| 3427 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 3428 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
| 3429 | source, dest); |
---|
| 3430 | } |
---|
| 3431 | |
---|
[08daea] | 3432 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
| 3433 | if (prim_fail) |
---|
| 3434 | ; //ERROR |
---|
| 3435 | else |
---|
| 3436 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
| 3437 | |
---|
| 3438 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
| 3439 | DEBOUTLN (cerr, "getMipo (V_buf2)= " << getMipo (V_buf2)); |
---|
| 3440 | inextension= true; |
---|
[c1b9927] | 3441 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
[08daea] | 3442 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
| 3443 | im_prim_elem, source, dest); |
---|
| 3444 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3445 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3446 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
| 3447 | source, dest); |
---|
| 3448 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3449 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3450 | |
---|
| 3451 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
| 3452 | source, dest); |
---|
| 3453 | |
---|
| 3454 | fail= false; |
---|
| 3455 | random_element= randomElement (m, V_buf, l, fail); |
---|
| 3456 | DEBOUTLN (cerr, "fail= " << fail); |
---|
| 3457 | CFList list; |
---|
| 3458 | TIMING_START (gcd_recursion); |
---|
| 3459 | |
---|
| 3460 | //sparseInterpolation |
---|
| 3461 | bool sparseFail= false; |
---|
| 3462 | if (LC (skeleton).inCoeffDomain()) |
---|
[c1b9927] | 3463 | G_random_element= |
---|
[08daea] | 3464 | monicSparseInterpol (ppA (random_element, x), ppB(random_element,x), |
---|
| 3465 | skeleton,V_buf, sparseFail, coeffMonoms,Monoms); |
---|
| 3466 | else |
---|
| 3467 | G_random_element= |
---|
| 3468 | nonMonicSparseInterpol (ppA(random_element,x),ppB(random_element,x), |
---|
| 3469 | skeleton, V_buf, sparseFail, coeffMonoms, |
---|
| 3470 | Monoms); |
---|
| 3471 | if (sparseFail) |
---|
| 3472 | break; |
---|
| 3473 | |
---|
| 3474 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3475 | "time for recursive call: "); |
---|
| 3476 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3477 | } |
---|
| 3478 | else |
---|
| 3479 | { |
---|
| 3480 | CFList list; |
---|
| 3481 | TIMING_START (gcd_recursion); |
---|
| 3482 | bool sparseFail= false; |
---|
| 3483 | if (LC (skeleton).inCoeffDomain()) |
---|
[c1b9927] | 3484 | G_random_element= |
---|
[08daea] | 3485 | monicSparseInterpol (ppA (random_element, x),ppB(random_element, x), |
---|
| 3486 | skeleton,V_buf, sparseFail,coeffMonoms, Monoms); |
---|
| 3487 | else |
---|
| 3488 | G_random_element= |
---|
| 3489 | nonMonicSparseInterpol (ppA(random_element,x),ppB(random_element,x), |
---|
[c1b9927] | 3490 | skeleton, V_buf, sparseFail, coeffMonoms, |
---|
[08daea] | 3491 | Monoms); |
---|
| 3492 | if (sparseFail) |
---|
| 3493 | break; |
---|
| 3494 | |
---|
| 3495 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3496 | "time for recursive call: "); |
---|
| 3497 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3498 | } |
---|
| 3499 | |
---|
[a76d6fe] | 3500 | if (!G_random_element.inCoeffDomain()) |
---|
| 3501 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 3502 | Variable (G_random_element.level())); |
---|
| 3503 | else |
---|
| 3504 | d0= 0; |
---|
| 3505 | |
---|
[08daea] | 3506 | if (d0 == 0) |
---|
[a9a6dcb] | 3507 | return N(gcdcAcB); |
---|
[08daea] | 3508 | if (d0 > d) |
---|
| 3509 | { |
---|
| 3510 | if (!find (l, random_element)) |
---|
| 3511 | l.append (random_element); |
---|
| 3512 | continue; |
---|
| 3513 | } |
---|
| 3514 | |
---|
| 3515 | G_random_element= |
---|
| 3516 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
| 3517 | * G_random_element; |
---|
| 3518 | |
---|
[a76d6fe] | 3519 | if (!G_random_element.inCoeffDomain()) |
---|
| 3520 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 3521 | Variable (G_random_element.level())); |
---|
| 3522 | else |
---|
| 3523 | d0= 0; |
---|
| 3524 | |
---|
[08daea] | 3525 | if (d0 < d) |
---|
| 3526 | { |
---|
| 3527 | m= gcdlcAlcB; |
---|
| 3528 | newtonPoly= 1; |
---|
| 3529 | G_m= 0; |
---|
| 3530 | d= d0; |
---|
| 3531 | } |
---|
| 3532 | |
---|
| 3533 | TIMING_START (newton_interpolation); |
---|
| 3534 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
| 3535 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
| 3536 | "time for newton interpolation: "); |
---|
| 3537 | |
---|
| 3538 | //termination test |
---|
| 3539 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
| 3540 | { |
---|
| 3541 | cH= uni_content (H); |
---|
| 3542 | ppH= H/cH; |
---|
| 3543 | if (inextension) |
---|
| 3544 | { |
---|
| 3545 | CFList u, v; |
---|
| 3546 | //maybe it's better to test if ppH is an element of F(\alpha) before |
---|
| 3547 | //mapping down |
---|
[c723d80] | 3548 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
[08daea] | 3549 | { |
---|
[c723d80] | 3550 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
| 3551 | ppH= mapDown (ppH, prim_elem, im_prim_elem, alpha, u, v); |
---|
| 3552 | ppH /= Lc(ppH); |
---|
| 3553 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
[08daea] | 3554 | return N(gcdcAcB*ppH); |
---|
| 3555 | } |
---|
| 3556 | } |
---|
[c723d80] | 3557 | else if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
[08daea] | 3558 | { |
---|
| 3559 | return N(gcdcAcB*ppH); |
---|
| 3560 | } |
---|
| 3561 | } |
---|
| 3562 | |
---|
| 3563 | G_m= H; |
---|
| 3564 | newtonPoly= newtonPoly*(x - random_element); |
---|
| 3565 | m= m*(x - random_element); |
---|
| 3566 | if (!find (l, random_element)) |
---|
| 3567 | l.append (random_element); |
---|
| 3568 | |
---|
| 3569 | } while (1); |
---|
| 3570 | } |
---|
| 3571 | } while (1); |
---|
| 3572 | } |
---|
| 3573 | |
---|
| 3574 | CanonicalForm sparseGCDFp (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 3575 | bool& topLevel, CFList& l) |
---|
| 3576 | { |
---|
| 3577 | CanonicalForm A= F; |
---|
| 3578 | CanonicalForm B= G; |
---|
| 3579 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
| 3580 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
| 3581 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
| 3582 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
| 3583 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
| 3584 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
| 3585 | if (F == G) return F/Lc(F); |
---|
| 3586 | |
---|
| 3587 | CFMap M,N; |
---|
| 3588 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
| 3589 | |
---|
| 3590 | if (best_level == 0) return B.genOne(); |
---|
| 3591 | |
---|
| 3592 | A= M(A); |
---|
| 3593 | B= M(B); |
---|
| 3594 | |
---|
| 3595 | Variable x= Variable (1); |
---|
| 3596 | |
---|
[c1b9927] | 3597 | //univariate case |
---|
[08daea] | 3598 | if (A.isUnivariate() && B.isUnivariate()) |
---|
| 3599 | return N (gcd (A, B)); |
---|
| 3600 | |
---|
| 3601 | CanonicalForm cA, cB; // content of A and B |
---|
| 3602 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
| 3603 | CanonicalForm gcdcAcB; |
---|
[ea5ff1d] | 3604 | |
---|
| 3605 | cA = uni_content (A); |
---|
| 3606 | cB = uni_content (B); |
---|
| 3607 | gcdcAcB= gcd (cA, cB); |
---|
| 3608 | ppA= A/cA; |
---|
| 3609 | ppB= B/cB; |
---|
[08daea] | 3610 | |
---|
| 3611 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
| 3612 | CanonicalForm gcdlcAlcB; |
---|
| 3613 | lcA= uni_lcoeff (ppA); |
---|
| 3614 | lcB= uni_lcoeff (ppB); |
---|
| 3615 | |
---|
| 3616 | if (fdivides (lcA, lcB)) |
---|
| 3617 | { |
---|
| 3618 | if (fdivides (A, B)) |
---|
| 3619 | return F/Lc(F); |
---|
| 3620 | } |
---|
| 3621 | if (fdivides (lcB, lcA)) |
---|
| 3622 | { |
---|
| 3623 | if (fdivides (B, A)) |
---|
| 3624 | return G/Lc(G); |
---|
| 3625 | } |
---|
| 3626 | |
---|
| 3627 | gcdlcAlcB= gcd (lcA, lcB); |
---|
| 3628 | |
---|
| 3629 | int d= totaldegree (ppA, Variable (2), Variable (ppA.level())); |
---|
| 3630 | int d0; |
---|
| 3631 | |
---|
| 3632 | if (d == 0) |
---|
[a9a6dcb] | 3633 | return N(gcdcAcB); |
---|
| 3634 | |
---|
[08daea] | 3635 | d0= totaldegree (ppB, Variable (2), Variable (ppB.level())); |
---|
| 3636 | |
---|
| 3637 | if (d0 < d) |
---|
| 3638 | d= d0; |
---|
| 3639 | |
---|
| 3640 | if (d == 0) |
---|
[a9a6dcb] | 3641 | return N(gcdcAcB); |
---|
[08daea] | 3642 | |
---|
| 3643 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH, skeleton; |
---|
| 3644 | CanonicalForm newtonPoly= 1; |
---|
| 3645 | m= gcdlcAlcB; |
---|
| 3646 | G_m= 0; |
---|
| 3647 | H= 0; |
---|
| 3648 | bool fail= false; |
---|
| 3649 | topLevel= false; |
---|
| 3650 | bool inextension= false; |
---|
| 3651 | Variable V_buf, alpha; |
---|
| 3652 | CanonicalForm prim_elem, im_prim_elem; |
---|
| 3653 | CFList source, dest; |
---|
| 3654 | do //first do |
---|
| 3655 | { |
---|
| 3656 | if (inextension) |
---|
[9ff686] | 3657 | random_element= randomElement (m, V_buf, l, fail); |
---|
[08daea] | 3658 | else |
---|
| 3659 | random_element= FpRandomElement (m, l, fail); |
---|
| 3660 | if (random_element == 0 && !fail) |
---|
| 3661 | { |
---|
| 3662 | if (!find (l, random_element)) |
---|
| 3663 | l.append (random_element); |
---|
| 3664 | continue; |
---|
| 3665 | } |
---|
| 3666 | |
---|
| 3667 | if (!fail && !inextension) |
---|
| 3668 | { |
---|
| 3669 | CFList list; |
---|
| 3670 | TIMING_START (gcd_recursion); |
---|
| 3671 | G_random_element= |
---|
| 3672 | sparseGCDFp (ppA (random_element,x), ppB (random_element,x), topLevel, |
---|
| 3673 | list); |
---|
| 3674 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3675 | "time for recursive call: "); |
---|
| 3676 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3677 | } |
---|
| 3678 | else if (!fail && inextension) |
---|
| 3679 | { |
---|
| 3680 | CFList list; |
---|
| 3681 | TIMING_START (gcd_recursion); |
---|
| 3682 | G_random_element= |
---|
| 3683 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), alpha, |
---|
| 3684 | list, topLevel); |
---|
| 3685 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3686 | "time for recursive call: "); |
---|
| 3687 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3688 | } |
---|
| 3689 | else if (fail && !inextension) |
---|
| 3690 | { |
---|
| 3691 | source= CFList(); |
---|
| 3692 | dest= CFList(); |
---|
| 3693 | CFList list; |
---|
| 3694 | CanonicalForm mipo; |
---|
| 3695 | int deg= 2; |
---|
| 3696 | do |
---|
| 3697 | { |
---|
| 3698 | mipo= randomIrredpoly (deg, x); |
---|
| 3699 | alpha= rootOf (mipo); |
---|
| 3700 | inextension= true; |
---|
| 3701 | fail= false; |
---|
[c1b9927] | 3702 | random_element= randomElement (m, alpha, l, fail); |
---|
[08daea] | 3703 | deg++; |
---|
| 3704 | } while (fail); |
---|
[9ff686] | 3705 | V_buf= alpha; |
---|
[08daea] | 3706 | list= CFList(); |
---|
| 3707 | TIMING_START (gcd_recursion); |
---|
| 3708 | G_random_element= |
---|
| 3709 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), alpha, |
---|
| 3710 | list, topLevel); |
---|
| 3711 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3712 | "time for recursive call: "); |
---|
| 3713 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3714 | } |
---|
| 3715 | else if (fail && inextension) |
---|
| 3716 | { |
---|
| 3717 | source= CFList(); |
---|
| 3718 | dest= CFList(); |
---|
[9ff686] | 3719 | |
---|
| 3720 | Variable V_buf3= V_buf; |
---|
| 3721 | V_buf= chooseExtension (V_buf); |
---|
[08daea] | 3722 | bool prim_fail= false; |
---|
| 3723 | Variable V_buf2; |
---|
| 3724 | CanonicalForm prim_elem, im_prim_elem; |
---|
| 3725 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
| 3726 | |
---|
[9ff686] | 3727 | if (V_buf3 != alpha) |
---|
| 3728 | { |
---|
| 3729 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3730 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3731 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, source, |
---|
| 3732 | dest); |
---|
| 3733 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3734 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3735 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, source, |
---|
| 3736 | dest); |
---|
| 3737 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 3738 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
| 3739 | source, dest); |
---|
| 3740 | } |
---|
| 3741 | |
---|
[08daea] | 3742 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
| 3743 | if (prim_fail) |
---|
| 3744 | ; //ERROR |
---|
| 3745 | else |
---|
| 3746 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
| 3747 | |
---|
| 3748 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
| 3749 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
| 3750 | |
---|
| 3751 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 3752 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
| 3753 | im_prim_elem, source, dest); |
---|
| 3754 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3755 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3756 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
| 3757 | source, dest); |
---|
| 3758 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3759 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3760 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
| 3761 | source, dest); |
---|
| 3762 | fail= false; |
---|
| 3763 | random_element= randomElement (m, V_buf, l, fail ); |
---|
| 3764 | DEBOUTLN (cerr, "fail= " << fail); |
---|
| 3765 | CFList list; |
---|
| 3766 | TIMING_START (gcd_recursion); |
---|
| 3767 | G_random_element= |
---|
| 3768 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), V_buf, |
---|
| 3769 | list, topLevel); |
---|
| 3770 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3771 | "time for recursive call: "); |
---|
| 3772 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3773 | } |
---|
| 3774 | |
---|
[a76d6fe] | 3775 | if (!G_random_element.inCoeffDomain()) |
---|
| 3776 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 3777 | Variable (G_random_element.level())); |
---|
| 3778 | else |
---|
| 3779 | d0= 0; |
---|
| 3780 | |
---|
[08daea] | 3781 | if (d0 == 0) |
---|
[a9a6dcb] | 3782 | return N(gcdcAcB); |
---|
[08daea] | 3783 | if (d0 > d) |
---|
| 3784 | { |
---|
| 3785 | if (!find (l, random_element)) |
---|
| 3786 | l.append (random_element); |
---|
| 3787 | continue; |
---|
| 3788 | } |
---|
| 3789 | |
---|
| 3790 | G_random_element= |
---|
| 3791 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
| 3792 | * G_random_element; |
---|
| 3793 | |
---|
| 3794 | skeleton= G_random_element; |
---|
| 3795 | |
---|
[a76d6fe] | 3796 | if (!G_random_element.inCoeffDomain()) |
---|
| 3797 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 3798 | Variable (G_random_element.level())); |
---|
| 3799 | else |
---|
| 3800 | d0= 0; |
---|
| 3801 | |
---|
[08daea] | 3802 | if (d0 < d) |
---|
| 3803 | { |
---|
| 3804 | m= gcdlcAlcB; |
---|
| 3805 | newtonPoly= 1; |
---|
| 3806 | G_m= 0; |
---|
| 3807 | d= d0; |
---|
| 3808 | } |
---|
| 3809 | |
---|
| 3810 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
| 3811 | |
---|
| 3812 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
| 3813 | { |
---|
| 3814 | cH= uni_content (H); |
---|
| 3815 | ppH= H/cH; |
---|
| 3816 | ppH /= Lc (ppH); |
---|
| 3817 | DEBOUTLN (cerr, "ppH= " << ppH); |
---|
| 3818 | |
---|
[c723d80] | 3819 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
[08daea] | 3820 | return N(gcdcAcB*ppH); |
---|
| 3821 | } |
---|
| 3822 | G_m= H; |
---|
| 3823 | newtonPoly= newtonPoly*(x - random_element); |
---|
| 3824 | m= m*(x - random_element); |
---|
| 3825 | if (!find (l, random_element)) |
---|
| 3826 | l.append (random_element); |
---|
| 3827 | |
---|
[d08ed8] | 3828 | if ((getCharacteristic() > 3 && size (skeleton) < 100)) |
---|
[08daea] | 3829 | { |
---|
| 3830 | CFArray Monoms; |
---|
| 3831 | CFArray* coeffMonoms= NULL; |
---|
| 3832 | |
---|
| 3833 | do //second do |
---|
| 3834 | { |
---|
| 3835 | if (inextension) |
---|
| 3836 | random_element= randomElement (m, alpha, l, fail); |
---|
| 3837 | else |
---|
| 3838 | random_element= FpRandomElement (m, l, fail); |
---|
| 3839 | if (random_element == 0 && !fail) |
---|
| 3840 | { |
---|
| 3841 | if (!find (l, random_element)) |
---|
| 3842 | l.append (random_element); |
---|
| 3843 | continue; |
---|
| 3844 | } |
---|
| 3845 | |
---|
| 3846 | bool sparseFail= false; |
---|
| 3847 | if (!fail && !inextension) |
---|
| 3848 | { |
---|
| 3849 | CFList list; |
---|
| 3850 | TIMING_START (gcd_recursion); |
---|
| 3851 | if (LC (skeleton).inCoeffDomain()) |
---|
| 3852 | G_random_element= |
---|
| 3853 | monicSparseInterpol(ppA(random_element, x), ppB (random_element, x), |
---|
| 3854 | skeleton, Variable(1), sparseFail, coeffMonoms, |
---|
| 3855 | Monoms); |
---|
| 3856 | else |
---|
| 3857 | G_random_element= |
---|
| 3858 | nonMonicSparseInterpol(ppA(random_element,x), ppB(random_element,x), |
---|
| 3859 | skeleton, Variable (1), sparseFail, |
---|
| 3860 | coeffMonoms, Monoms); |
---|
| 3861 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3862 | "time for recursive call: "); |
---|
| 3863 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3864 | } |
---|
| 3865 | else if (!fail && inextension) |
---|
| 3866 | { |
---|
| 3867 | CFList list; |
---|
| 3868 | TIMING_START (gcd_recursion); |
---|
| 3869 | if (LC (skeleton).inCoeffDomain()) |
---|
| 3870 | G_random_element= |
---|
| 3871 | monicSparseInterpol(ppA (random_element,x), ppB (random_element, x), |
---|
| 3872 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
| 3873 | Monoms); |
---|
| 3874 | else |
---|
| 3875 | G_random_element= |
---|
| 3876 | nonMonicSparseInterpol(ppA(random_element,x), ppB(random_element,x), |
---|
| 3877 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
| 3878 | Monoms); |
---|
| 3879 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3880 | "time for recursive call: "); |
---|
| 3881 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3882 | } |
---|
| 3883 | else if (fail && !inextension) |
---|
| 3884 | { |
---|
| 3885 | source= CFList(); |
---|
| 3886 | dest= CFList(); |
---|
| 3887 | CFList list; |
---|
| 3888 | CanonicalForm mipo; |
---|
| 3889 | int deg= 2; |
---|
[c1b9927] | 3890 | do |
---|
[08daea] | 3891 | { |
---|
| 3892 | mipo= randomIrredpoly (deg, x); |
---|
| 3893 | alpha= rootOf (mipo); |
---|
| 3894 | inextension= true; |
---|
| 3895 | fail= false; |
---|
| 3896 | random_element= randomElement (m, alpha, l, fail); |
---|
| 3897 | deg++; |
---|
| 3898 | } while (fail); |
---|
[9ff686] | 3899 | V_buf= alpha; |
---|
[08daea] | 3900 | list= CFList(); |
---|
| 3901 | TIMING_START (gcd_recursion); |
---|
| 3902 | if (LC (skeleton).inCoeffDomain()) |
---|
| 3903 | G_random_element= |
---|
| 3904 | monicSparseInterpol (ppA (random_element,x), ppB (random_element,x), |
---|
| 3905 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
| 3906 | Monoms); |
---|
| 3907 | else |
---|
| 3908 | G_random_element= |
---|
| 3909 | nonMonicSparseInterpol(ppA(random_element,x), ppB(random_element,x), |
---|
| 3910 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
| 3911 | Monoms); |
---|
| 3912 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3913 | "time for recursive call: "); |
---|
| 3914 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3915 | } |
---|
| 3916 | else if (fail && inextension) |
---|
| 3917 | { |
---|
| 3918 | source= CFList(); |
---|
| 3919 | dest= CFList(); |
---|
[9ff686] | 3920 | |
---|
| 3921 | Variable V_buf3= V_buf; |
---|
| 3922 | V_buf= chooseExtension (V_buf); |
---|
[08daea] | 3923 | bool prim_fail= false; |
---|
| 3924 | Variable V_buf2; |
---|
| 3925 | CanonicalForm prim_elem, im_prim_elem; |
---|
| 3926 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
| 3927 | |
---|
[9ff686] | 3928 | if (V_buf3 != alpha) |
---|
| 3929 | { |
---|
| 3930 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3931 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3932 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
| 3933 | source, dest); |
---|
| 3934 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3935 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
| 3936 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, |
---|
| 3937 | source, dest); |
---|
| 3938 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 3939 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
| 3940 | source, dest); |
---|
| 3941 | } |
---|
| 3942 | |
---|
[08daea] | 3943 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
| 3944 | if (prim_fail) |
---|
| 3945 | ; //ERROR |
---|
| 3946 | else |
---|
| 3947 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
| 3948 | |
---|
| 3949 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
| 3950 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
| 3951 | |
---|
| 3952 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 3953 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
| 3954 | im_prim_elem, source, dest); |
---|
| 3955 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3956 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3957 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
| 3958 | source, dest); |
---|
| 3959 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3960 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
| 3961 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
| 3962 | source, dest); |
---|
| 3963 | fail= false; |
---|
| 3964 | random_element= randomElement (m, V_buf, l, fail ); |
---|
| 3965 | DEBOUTLN (cerr, "fail= " << fail); |
---|
| 3966 | CFList list; |
---|
| 3967 | TIMING_START (gcd_recursion); |
---|
| 3968 | if (LC (skeleton).inCoeffDomain()) |
---|
| 3969 | G_random_element= |
---|
| 3970 | monicSparseInterpol (ppA (random_element, x), ppB (random_element, x), |
---|
| 3971 | skeleton, V_buf, sparseFail, coeffMonoms, |
---|
| 3972 | Monoms); |
---|
| 3973 | else |
---|
| 3974 | G_random_element= |
---|
| 3975 | nonMonicSparseInterpol (ppA(random_element,x), ppB(random_element,x), |
---|
| 3976 | skeleton, V_buf, sparseFail, |
---|
| 3977 | coeffMonoms, Monoms); |
---|
| 3978 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
| 3979 | "time for recursive call: "); |
---|
| 3980 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
| 3981 | } |
---|
| 3982 | |
---|
| 3983 | if (sparseFail) |
---|
| 3984 | break; |
---|
| 3985 | |
---|
[a76d6fe] | 3986 | if (!G_random_element.inCoeffDomain()) |
---|
| 3987 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 3988 | Variable (G_random_element.level())); |
---|
| 3989 | else |
---|
| 3990 | d0= 0; |
---|
| 3991 | |
---|
[08daea] | 3992 | if (d0 == 0) |
---|
[a9a6dcb] | 3993 | return N(gcdcAcB); |
---|
[08daea] | 3994 | if (d0 > d) |
---|
| 3995 | { |
---|
| 3996 | if (!find (l, random_element)) |
---|
| 3997 | l.append (random_element); |
---|
| 3998 | continue; |
---|
| 3999 | } |
---|
| 4000 | |
---|
| 4001 | G_random_element= |
---|
| 4002 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
| 4003 | * G_random_element; |
---|
| 4004 | |
---|
[a76d6fe] | 4005 | if (!G_random_element.inCoeffDomain()) |
---|
| 4006 | d0= totaldegree (G_random_element, Variable(2), |
---|
| 4007 | Variable (G_random_element.level())); |
---|
| 4008 | else |
---|
| 4009 | d0= 0; |
---|
| 4010 | |
---|
[08daea] | 4011 | if (d0 < d) |
---|
| 4012 | { |
---|
| 4013 | m= gcdlcAlcB; |
---|
| 4014 | newtonPoly= 1; |
---|
| 4015 | G_m= 0; |
---|
| 4016 | d= d0; |
---|
| 4017 | } |
---|
| 4018 | |
---|
| 4019 | TIMING_START (newton_interpolation); |
---|
| 4020 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
| 4021 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
| 4022 | "time for newton interpolation: "); |
---|
| 4023 | |
---|
| 4024 | //termination test |
---|
| 4025 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
| 4026 | { |
---|
| 4027 | cH= uni_content (H); |
---|
| 4028 | ppH= H/cH; |
---|
| 4029 | ppH /= Lc (ppH); |
---|
| 4030 | DEBOUTLN (cerr, "ppH= " << ppH); |
---|
[c723d80] | 4031 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
[08daea] | 4032 | return N(gcdcAcB*ppH); |
---|
| 4033 | } |
---|
| 4034 | |
---|
| 4035 | G_m= H; |
---|
| 4036 | newtonPoly= newtonPoly*(x - random_element); |
---|
| 4037 | m= m*(x - random_element); |
---|
| 4038 | if (!find (l, random_element)) |
---|
| 4039 | l.append (random_element); |
---|
| 4040 | |
---|
| 4041 | } while (1); //end of second do |
---|
| 4042 | } |
---|
| 4043 | } while (1); //end of first do |
---|
| 4044 | } |
---|
| 4045 | |
---|
| 4046 | static inline |
---|
| 4047 | int compress4EZGCD (const CanonicalForm& F, const CanonicalForm& G, CFMap & M, |
---|
| 4048 | CFMap & N, int& both_non_zero) |
---|
| 4049 | { |
---|
| 4050 | int n= tmax (F.level(), G.level()); |
---|
| 4051 | int * degsf= new int [n + 1]; |
---|
| 4052 | int * degsg= new int [n + 1]; |
---|
| 4053 | |
---|
| 4054 | for (int i = 0; i <= n; i++) |
---|
| 4055 | degsf[i]= degsg[i]= 0; |
---|
| 4056 | |
---|
| 4057 | degsf= degrees (F, degsf); |
---|
| 4058 | degsg= degrees (G, degsg); |
---|
| 4059 | |
---|
| 4060 | both_non_zero= 0; |
---|
| 4061 | int f_zero= 0; |
---|
| 4062 | int g_zero= 0; |
---|
| 4063 | |
---|
| 4064 | for (int i= 1; i <= n; i++) |
---|
| 4065 | { |
---|
| 4066 | if (degsf[i] != 0 && degsg[i] != 0) |
---|
| 4067 | { |
---|
| 4068 | both_non_zero++; |
---|
| 4069 | continue; |
---|
| 4070 | } |
---|
| 4071 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
---|
| 4072 | { |
---|
| 4073 | f_zero++; |
---|
| 4074 | continue; |
---|
| 4075 | } |
---|
| 4076 | if (degsg[i] == 0 && degsf[i] && i <= F.level()) |
---|
| 4077 | { |
---|
| 4078 | g_zero++; |
---|
| 4079 | continue; |
---|
| 4080 | } |
---|
| 4081 | } |
---|
| 4082 | |
---|
[618da5] | 4083 | if (both_non_zero == 0) |
---|
| 4084 | { |
---|
| 4085 | delete [] degsf; |
---|
| 4086 | delete [] degsg; |
---|
| 4087 | return 0; |
---|
| 4088 | } |
---|
[08daea] | 4089 | |
---|
| 4090 | // map Variables which do not occur in both polynomials to higher levels |
---|
| 4091 | int k= 1; |
---|
| 4092 | int l= 1; |
---|
| 4093 | for (int i= 1; i <= n; i++) |
---|
| 4094 | { |
---|
| 4095 | if (degsf[i] != 0 && degsg[i] == 0 && i <= F.level()) |
---|
| 4096 | { |
---|
| 4097 | if (k + both_non_zero != i) |
---|
| 4098 | { |
---|
| 4099 | M.newpair (Variable (i), Variable (k + both_non_zero)); |
---|
| 4100 | N.newpair (Variable (k + both_non_zero), Variable (i)); |
---|
| 4101 | } |
---|
| 4102 | k++; |
---|
| 4103 | } |
---|
| 4104 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
---|
| 4105 | { |
---|
| 4106 | if (l + g_zero + both_non_zero != i) |
---|
| 4107 | { |
---|
| 4108 | M.newpair (Variable (i), Variable (l + g_zero + both_non_zero)); |
---|
| 4109 | N.newpair (Variable (l + g_zero + both_non_zero), Variable (i)); |
---|
| 4110 | } |
---|
| 4111 | l++; |
---|
| 4112 | } |
---|
| 4113 | } |
---|
| 4114 | |
---|
| 4115 | // sort Variables x_{i} in decreasing order of |
---|
| 4116 | // min(deg_{x_{i}}(f),deg_{x_{i}}(g)) |
---|
| 4117 | int m= tmin (F.level(), G.level()); |
---|
| 4118 | int max_min_deg; |
---|
| 4119 | k= both_non_zero; |
---|
| 4120 | l= 0; |
---|
| 4121 | int i= 1; |
---|
| 4122 | while (k > 0) |
---|
| 4123 | { |
---|
| 4124 | max_min_deg= tmin (degsf[i], degsg[i]); |
---|
| 4125 | while (max_min_deg == 0) |
---|
| 4126 | { |
---|
| 4127 | i++; |
---|
| 4128 | max_min_deg= tmin (degsf[i], degsg[i]); |
---|
| 4129 | } |
---|
| 4130 | for (int j= i + 1; j <= m; j++) |
---|
| 4131 | { |
---|
| 4132 | if ((tmin (degsf[j],degsg[j]) < max_min_deg) && |
---|
| 4133 | (tmin (degsf[j], degsg[j]) != 0)) |
---|
| 4134 | { |
---|
| 4135 | max_min_deg= tmin (degsf[j], degsg[j]); |
---|
| 4136 | l= j; |
---|
| 4137 | } |
---|
| 4138 | } |
---|
| 4139 | |
---|
| 4140 | if (l != 0) |
---|
| 4141 | { |
---|
| 4142 | if (l != k) |
---|
| 4143 | { |
---|
| 4144 | M.newpair (Variable (l), Variable(k)); |
---|
| 4145 | N.newpair (Variable (k), Variable(l)); |
---|
| 4146 | degsf[l]= 0; |
---|
| 4147 | degsg[l]= 0; |
---|
| 4148 | l= 0; |
---|
| 4149 | } |
---|
| 4150 | else |
---|
| 4151 | { |
---|
| 4152 | degsf[l]= 0; |
---|
| 4153 | degsg[l]= 0; |
---|
| 4154 | l= 0; |
---|
| 4155 | } |
---|
| 4156 | } |
---|
| 4157 | else if (l == 0) |
---|
| 4158 | { |
---|
| 4159 | if (i != k) |
---|
| 4160 | { |
---|
| 4161 | M.newpair (Variable (i), Variable (k)); |
---|
| 4162 | N.newpair (Variable (k), Variable (i)); |
---|
| 4163 | degsf[i]= 0; |
---|
| 4164 | degsg[i]= 0; |
---|
| 4165 | } |
---|
| 4166 | else |
---|
| 4167 | { |
---|
| 4168 | degsf[i]= 0; |
---|
| 4169 | degsg[i]= 0; |
---|
| 4170 | } |
---|
| 4171 | i++; |
---|
| 4172 | } |
---|
| 4173 | k--; |
---|
| 4174 | } |
---|
| 4175 | |
---|
| 4176 | delete [] degsf; |
---|
| 4177 | delete [] degsg; |
---|
| 4178 | |
---|
| 4179 | return both_non_zero; |
---|
| 4180 | } |
---|
| 4181 | |
---|
| 4182 | static inline |
---|
| 4183 | CanonicalForm myShift2Zero (const CanonicalForm& F, CFList& Feval, |
---|
| 4184 | const CFList& evaluation) |
---|
| 4185 | { |
---|
| 4186 | CanonicalForm A= F; |
---|
| 4187 | int k= 2; |
---|
| 4188 | for (CFListIterator i= evaluation; i.hasItem(); i++, k++) |
---|
| 4189 | A= A (Variable (k) + i.getItem(), k); |
---|
| 4190 | |
---|
| 4191 | CanonicalForm buf= A; |
---|
| 4192 | Feval= CFList(); |
---|
| 4193 | Feval.append (buf); |
---|
| 4194 | for (k= evaluation.length() + 1; k > 2; k--) |
---|
| 4195 | { |
---|
| 4196 | buf= mod (buf, Variable (k)); |
---|
| 4197 | Feval.insert (buf); |
---|
| 4198 | } |
---|
| 4199 | return A; |
---|
| 4200 | } |
---|
| 4201 | |
---|
| 4202 | static inline |
---|
| 4203 | CanonicalForm myReverseShift (const CanonicalForm& F, const CFList& evaluation) |
---|
| 4204 | { |
---|
| 4205 | int l= evaluation.length() + 1; |
---|
| 4206 | CanonicalForm result= F; |
---|
| 4207 | CFListIterator j= evaluation; |
---|
| 4208 | for (int i= 2; i < l + 1; i++, j++) |
---|
| 4209 | { |
---|
| 4210 | if (F.level() < i) |
---|
| 4211 | continue; |
---|
| 4212 | result= result (Variable (i) - j.getItem(), i); |
---|
| 4213 | } |
---|
| 4214 | return result; |
---|
| 4215 | } |
---|
| 4216 | |
---|
| 4217 | static inline |
---|
[9ff686] | 4218 | Evaluation optimize4Lift (const CanonicalForm& F, CFMap & M, |
---|
| 4219 | CFMap & N, const Evaluation& A) |
---|
| 4220 | { |
---|
| 4221 | int n= F.level(); |
---|
| 4222 | int * degsf= new int [n + 1]; |
---|
| 4223 | |
---|
| 4224 | for (int i = 0; i <= n; i++) |
---|
| 4225 | degsf[i]= 0; |
---|
| 4226 | |
---|
| 4227 | degsf= degrees (F, degsf); |
---|
| 4228 | |
---|
| 4229 | Evaluation result= Evaluation (A.min(), A.max()); |
---|
| 4230 | ASSERT (A.min() == 2, "expected A.min() == 2"); |
---|
[050d1b] | 4231 | ASSERT (A.max() >= n, "expected A.max() >= n"); |
---|
[9ff686] | 4232 | int max_deg; |
---|
| 4233 | int k= n; |
---|
| 4234 | int l= 1; |
---|
| 4235 | int i= 2; |
---|
| 4236 | int pos= 2; |
---|
| 4237 | while (k > 1) |
---|
| 4238 | { |
---|
| 4239 | max_deg= degsf [i]; |
---|
| 4240 | while (max_deg == 0) |
---|
| 4241 | { |
---|
| 4242 | i++; |
---|
| 4243 | max_deg= degsf [i]; |
---|
| 4244 | } |
---|
| 4245 | l= i; |
---|
| 4246 | for (int j= i + 1; j <= n; j++) |
---|
| 4247 | { |
---|
| 4248 | if (degsf[j] > max_deg) |
---|
| 4249 | { |
---|
| 4250 | max_deg= degsf[j]; |
---|
| 4251 | l= j; |
---|
| 4252 | } |
---|
| 4253 | } |
---|
| 4254 | |
---|
| 4255 | if (l <= n) |
---|
| 4256 | { |
---|
| 4257 | if (l != pos) |
---|
| 4258 | { |
---|
| 4259 | result.setValue (pos, A [l]); |
---|
| 4260 | M.newpair (Variable (l), Variable (pos)); |
---|
| 4261 | N.newpair (Variable (pos), Variable (l)); |
---|
| 4262 | degsf[l]= 0; |
---|
| 4263 | l= 2; |
---|
| 4264 | if (k == 2 && n == 3) |
---|
| 4265 | { |
---|
| 4266 | result.setValue (l, A [pos]); |
---|
| 4267 | M.newpair (Variable (pos), Variable (l)); |
---|
| 4268 | N.newpair (Variable (l), Variable (pos)); |
---|
| 4269 | degsf[pos]= 0; |
---|
| 4270 | } |
---|
| 4271 | } |
---|
| 4272 | else |
---|
| 4273 | { |
---|
| 4274 | result.setValue (l, A [l]); |
---|
| 4275 | degsf [l]= 0; |
---|
| 4276 | } |
---|
| 4277 | } |
---|
| 4278 | pos++; |
---|
| 4279 | k--; |
---|
| 4280 | l= 2; |
---|
| 4281 | } |
---|
| 4282 | |
---|
| 4283 | delete [] degsf; |
---|
| 4284 | |
---|
| 4285 | return result; |
---|
| 4286 | } |
---|
| 4287 | |
---|
| 4288 | static inline |
---|
| 4289 | int Hensel_P (const CanonicalForm & UU, CFArray & G, const Evaluation & AA, |
---|
[0349c20] | 4290 | const CFArray& LeadCoeffs ) |
---|
[08daea] | 4291 | { |
---|
| 4292 | CFList factors; |
---|
| 4293 | factors.append (G[1]); |
---|
| 4294 | factors.append (G[2]); |
---|
[9ff686] | 4295 | |
---|
| 4296 | CFMap NN, MM; |
---|
| 4297 | Evaluation A= optimize4Lift (UU, MM, NN, AA); |
---|
| 4298 | |
---|
| 4299 | CanonicalForm U= MM (UU); |
---|
| 4300 | CFArray LCs= CFArray (1,2); |
---|
| 4301 | LCs [1]= MM (LeadCoeffs [1]); |
---|
| 4302 | LCs [2]= MM (LeadCoeffs [2]); |
---|
| 4303 | |
---|
[08daea] | 4304 | CFList evaluation; |
---|
| 4305 | for (int i= A.min(); i <= A.max(); i++) |
---|
| 4306 | evaluation.append (A [i]); |
---|
| 4307 | CFList UEval; |
---|
| 4308 | CanonicalForm shiftedU= myShift2Zero (U, UEval, evaluation); |
---|
[9ff686] | 4309 | |
---|
| 4310 | if (size (shiftedU)/getNumVars (U) > 500) |
---|
| 4311 | return -1; |
---|
| 4312 | |
---|
[08daea] | 4313 | CFArray shiftedLCs= CFArray (2); |
---|
| 4314 | CFList shiftedLCsEval1, shiftedLCsEval2; |
---|
| 4315 | shiftedLCs[0]= myShift2Zero (LCs[1], shiftedLCsEval1, evaluation); |
---|
| 4316 | shiftedLCs[1]= myShift2Zero (LCs[2], shiftedLCsEval2, evaluation); |
---|
| 4317 | factors.insert (1); |
---|
| 4318 | int liftBound= degree (UEval.getLast(), 2) + 1; |
---|
| 4319 | CFArray Pi; |
---|
| 4320 | CFMatrix M= CFMatrix (liftBound, factors.length() - 1); |
---|
| 4321 | CFList diophant; |
---|
| 4322 | CFArray lcs= CFArray (2); |
---|
| 4323 | lcs [0]= shiftedLCsEval1.getFirst(); |
---|
| 4324 | lcs [1]= shiftedLCsEval2.getFirst(); |
---|
[81d96c] | 4325 | nonMonicHenselLift12 (UEval.getFirst(), factors, liftBound, Pi, diophant, M, |
---|
| 4326 | lcs, false); |
---|
[08daea] | 4327 | |
---|
| 4328 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
| 4329 | { |
---|
[9ff686] | 4330 | if (!fdivides (i.getItem(), UEval.getFirst())) |
---|
| 4331 | return 0; |
---|
[08daea] | 4332 | } |
---|
[9ff686] | 4333 | |
---|
[08daea] | 4334 | int * liftBounds; |
---|
[9189e93] | 4335 | bool noOneToOne= false; |
---|
[08daea] | 4336 | if (U.level() > 2) |
---|
| 4337 | { |
---|
[ea88e0] | 4338 | liftBounds= new int [U.level() - 1]; /* index: 0.. U.level()-2 */ |
---|
[08daea] | 4339 | liftBounds[0]= liftBound; |
---|
[ea88e0] | 4340 | for (int i= 1; i < U.level() - 1; i++) |
---|
[08daea] | 4341 | liftBounds[i]= degree (shiftedU, Variable (i + 2)) + 1; |
---|
[81d96c] | 4342 | factors= nonMonicHenselLift2 (UEval, factors, liftBounds, U.level() - 1, |
---|
| 4343 | false, shiftedLCsEval1, shiftedLCsEval2, Pi, |
---|
| 4344 | diophant, noOneToOne); |
---|
[9ff686] | 4345 | delete [] liftBounds; |
---|
| 4346 | if (noOneToOne) |
---|
| 4347 | return 0; |
---|
[08daea] | 4348 | } |
---|
| 4349 | G[1]= factors.getFirst(); |
---|
| 4350 | G[2]= factors.getLast(); |
---|
| 4351 | G[1]= myReverseShift (G[1], evaluation); |
---|
| 4352 | G[2]= myReverseShift (G[2], evaluation); |
---|
[9ff686] | 4353 | G[1]= NN (G[1]); |
---|
| 4354 | G[2]= NN (G[2]); |
---|
| 4355 | return 1; |
---|
[08daea] | 4356 | } |
---|
| 4357 | |
---|
| 4358 | static inline |
---|
| 4359 | bool findeval_P (const CanonicalForm & F, const CanonicalForm & G, |
---|
| 4360 | CanonicalForm & Fb, CanonicalForm & Gb, CanonicalForm & Db, |
---|
[9ff686] | 4361 | REvaluation & b, int delta, int degF, int degG, int maxeval, |
---|
| 4362 | int & count, int& k, int bound, int& l) |
---|
[08daea] | 4363 | { |
---|
| 4364 | if( count == 0 && delta != 0) |
---|
| 4365 | { |
---|
| 4366 | if( count++ > maxeval ) |
---|
| 4367 | return false; |
---|
| 4368 | } |
---|
| 4369 | if (count > 0) |
---|
| 4370 | { |
---|
[9ff686] | 4371 | b.nextpoint(k); |
---|
[b5c084] | 4372 | if (k == 0) |
---|
| 4373 | k++; |
---|
[9ff686] | 4374 | l++; |
---|
| 4375 | if (l > bound) |
---|
| 4376 | { |
---|
| 4377 | l= 1; |
---|
| 4378 | k++; |
---|
| 4379 | if (k > tmax (F.level(), G.level()) - 1) |
---|
| 4380 | return false; |
---|
| 4381 | b.nextpoint (k); |
---|
| 4382 | } |
---|
[08daea] | 4383 | if (count++ > maxeval) |
---|
| 4384 | return false; |
---|
| 4385 | } |
---|
| 4386 | while( true ) |
---|
| 4387 | { |
---|
| 4388 | Fb = b( F ); |
---|
| 4389 | if( degree( Fb, 1 ) == degF ) |
---|
| 4390 | { |
---|
| 4391 | Gb = b( G ); |
---|
| 4392 | if( degree( Gb, 1 ) == degG ) |
---|
| 4393 | { |
---|
| 4394 | Db = gcd( Fb, Gb ); |
---|
| 4395 | if( delta > 0 ) |
---|
| 4396 | { |
---|
| 4397 | if( degree( Db, 1 ) <= delta ) |
---|
| 4398 | return true; |
---|
| 4399 | } |
---|
| 4400 | else |
---|
| 4401 | return true; |
---|
| 4402 | } |
---|
| 4403 | } |
---|
[9ff686] | 4404 | if (k == 0) |
---|
| 4405 | k++; |
---|
| 4406 | b.nextpoint(k); |
---|
| 4407 | l++; |
---|
| 4408 | if (l > bound) |
---|
| 4409 | { |
---|
| 4410 | l= 1; |
---|
| 4411 | k++; |
---|
| 4412 | if (k > tmax (F.level(), G.level()) - 1) |
---|
| 4413 | return false; |
---|
| 4414 | b.nextpoint (k); |
---|
| 4415 | } |
---|
[08daea] | 4416 | if( count++ > maxeval ) |
---|
| 4417 | return false; |
---|
| 4418 | } |
---|
| 4419 | } |
---|
| 4420 | |
---|
| 4421 | // parameters for heuristic |
---|
| 4422 | static int maxNumEval= 200; |
---|
| 4423 | static int sizePerVars1= 500; //try dense gcd if size/#variables is bigger |
---|
| 4424 | |
---|
| 4425 | /// Extended Zassenhaus GCD for finite fields |
---|
| 4426 | CanonicalForm EZGCD_P( const CanonicalForm & FF, const CanonicalForm & GG ) |
---|
| 4427 | { |
---|
| 4428 | if (FF.isZero() && degree(GG) > 0) return GG/Lc(GG); |
---|
| 4429 | else if (GG.isZero() && degree (FF) > 0) return FF/Lc(FF); |
---|
| 4430 | else if (FF.isZero() && GG.isZero()) return FF.genOne(); |
---|
| 4431 | if (FF.inBaseDomain() || GG.inBaseDomain()) return FF.genOne(); |
---|
| 4432 | if (FF.isUnivariate() && fdivides(FF, GG)) return FF/Lc(FF); |
---|
| 4433 | if (GG.isUnivariate() && fdivides(GG, FF)) return GG/Lc(GG); |
---|
| 4434 | if (FF == GG) return FF/Lc(FF); |
---|
| 4435 | |
---|
| 4436 | CanonicalForm F, G, f, g, d, Fb, Gb, Db, Fbt, Gbt, Dbt, B0, B, D0, lcF, lcG, |
---|
| 4437 | lcD; |
---|
| 4438 | CFArray DD( 1, 2 ), lcDD( 1, 2 ); |
---|
| 4439 | int degF, degG, delta, count; |
---|
| 4440 | int maxeval; |
---|
| 4441 | maxeval= tmin((getCharacteristic()/ |
---|
| 4442 | (int)(ilog2(getCharacteristic())*log2exp))*2, maxNumEval); |
---|
| 4443 | count= 0; // number of eval. used |
---|
[9ff686] | 4444 | REvaluation b, bt; |
---|
| 4445 | int gcdfound = 0; |
---|
[08daea] | 4446 | Variable x = Variable(1); |
---|
| 4447 | |
---|
| 4448 | F= FF; |
---|
| 4449 | G= GG; |
---|
| 4450 | |
---|
| 4451 | CFMap M,N; |
---|
| 4452 | int smallestDegLev; |
---|
| 4453 | int best_level= compress4EZGCD (F, G, M, N, smallestDegLev); |
---|
| 4454 | |
---|
| 4455 | if (best_level == 0) return G.genOne(); |
---|
| 4456 | |
---|
| 4457 | F= M (F); |
---|
| 4458 | G= M (G); |
---|
| 4459 | |
---|
| 4460 | f = content( F, x ); g = content( G, x ); |
---|
| 4461 | d = gcd( f, g ); |
---|
| 4462 | F /= f; G /= g; |
---|
| 4463 | |
---|
| 4464 | if( F.isUnivariate() && G.isUnivariate() ) |
---|
| 4465 | { |
---|
| 4466 | if( F.mvar() == G.mvar() ) |
---|
| 4467 | d *= gcd( F, G ); |
---|
| 4468 | return N (d); |
---|
| 4469 | } |
---|
| 4470 | |
---|
| 4471 | int maxNumVars= tmax (getNumVars (F), getNumVars (G)); |
---|
[9ff686] | 4472 | Variable a, oldA; |
---|
[08daea] | 4473 | int sizeF= size (F); |
---|
| 4474 | int sizeG= size (G); |
---|
| 4475 | |
---|
| 4476 | if (sizeF/maxNumVars > sizePerVars1 && sizeG/maxNumVars > sizePerVars1) |
---|
| 4477 | { |
---|
| 4478 | if (hasFirstAlgVar (F, a) || hasFirstAlgVar (G, a)) |
---|
| 4479 | return N (d*GCD_Fp_extension (F, G, a)); |
---|
| 4480 | else if (CFFactory::gettype() == GaloisFieldDomain) |
---|
| 4481 | return N (d*GCD_GF (F, G)); |
---|
| 4482 | else |
---|
| 4483 | return N (d*GCD_small_p (F, G)); |
---|
| 4484 | } |
---|
| 4485 | |
---|
| 4486 | if( gcd_test_one( F, G, false ) ) |
---|
| 4487 | { |
---|
| 4488 | return N (d); |
---|
| 4489 | } |
---|
| 4490 | |
---|
[9ff686] | 4491 | bool passToGF= false; |
---|
| 4492 | bool extOfExt= false; |
---|
| 4493 | int p= getCharacteristic(); |
---|
| 4494 | bool algExtension= (hasFirstAlgVar(F,a) || hasFirstAlgVar(G,a)); |
---|
| 4495 | int k= 1; |
---|
| 4496 | CanonicalForm primElem, imPrimElem; |
---|
| 4497 | CFList source, dest; |
---|
| 4498 | if (p < 50 && CFFactory::gettype() != GaloisFieldDomain && !algExtension) |
---|
[08daea] | 4499 | { |
---|
[9ff686] | 4500 | if (p == 2) |
---|
| 4501 | setCharacteristic (2, 6, 'Z'); |
---|
| 4502 | else if (p == 3) |
---|
| 4503 | setCharacteristic (3, 4, 'Z'); |
---|
| 4504 | else if (p == 5 || p == 7) |
---|
| 4505 | setCharacteristic (p, 3, 'Z'); |
---|
| 4506 | else |
---|
| 4507 | setCharacteristic (p, 2, 'Z'); |
---|
| 4508 | passToGF= true; |
---|
| 4509 | F= F.mapinto(); |
---|
| 4510 | G= G.mapinto(); |
---|
| 4511 | maxeval= 2*ipower (p, getGFDegree()); |
---|
[08daea] | 4512 | } |
---|
[9ff686] | 4513 | else if (CFFactory::gettype() == GaloisFieldDomain && |
---|
| 4514 | ipower (p , getGFDegree()) < 50) |
---|
[08daea] | 4515 | { |
---|
[9ff686] | 4516 | k= getGFDegree(); |
---|
| 4517 | if (ipower (p, 2*k) > 50) |
---|
| 4518 | setCharacteristic (p, 2*k, gf_name); |
---|
[08daea] | 4519 | else |
---|
[9ff686] | 4520 | setCharacteristic (p, 3*k, gf_name); |
---|
| 4521 | F= GFMapUp (F, k); |
---|
| 4522 | G= GFMapUp (G, k); |
---|
| 4523 | maxeval= tmin (2*ipower (p, getGFDegree()), maxNumEval); |
---|
| 4524 | } |
---|
| 4525 | else if (p < 50 && algExtension && !CFFactory::gettype() == GaloisFieldDomain) |
---|
| 4526 | { |
---|
| 4527 | int d= degree (getMipo (a)); |
---|
| 4528 | oldA= a; |
---|
| 4529 | Variable v2; |
---|
| 4530 | if (p == 2 && d < 6) |
---|
| 4531 | { |
---|
| 4532 | zz_p::init (p); |
---|
| 4533 | bool primFail= false; |
---|
| 4534 | Variable vBuf; |
---|
| 4535 | primElem= primitiveElement (a, vBuf, primFail); |
---|
| 4536 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
| 4537 | if (d < 3) |
---|
| 4538 | { |
---|
| 4539 | zz_pX NTLIrredpoly; |
---|
| 4540 | BuildIrred (NTLIrredpoly, d*3); |
---|
| 4541 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
| 4542 | v2= rootOf (newMipo); |
---|
| 4543 | } |
---|
[08daea] | 4544 | else |
---|
[9ff686] | 4545 | { |
---|
| 4546 | zz_pX NTLIrredpoly; |
---|
| 4547 | BuildIrred (NTLIrredpoly, d*2); |
---|
| 4548 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
| 4549 | v2= rootOf (newMipo); |
---|
| 4550 | } |
---|
| 4551 | imPrimElem= mapPrimElem (primElem, a, v2); |
---|
| 4552 | extOfExt= true; |
---|
| 4553 | } |
---|
| 4554 | else if ((p == 3 && d < 4) || ((p == 5 || p == 7) && d < 3)) |
---|
| 4555 | { |
---|
| 4556 | zz_p::init (p); |
---|
| 4557 | bool primFail= false; |
---|
| 4558 | Variable vBuf; |
---|
| 4559 | primElem= primitiveElement (a, vBuf, primFail); |
---|
| 4560 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
| 4561 | zz_pX NTLIrredpoly; |
---|
| 4562 | BuildIrred (NTLIrredpoly, d*2); |
---|
| 4563 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
| 4564 | v2= rootOf (newMipo); |
---|
| 4565 | imPrimElem= mapPrimElem (primElem, a, v2); |
---|
| 4566 | extOfExt= true; |
---|
| 4567 | } |
---|
| 4568 | if (extOfExt) |
---|
| 4569 | { |
---|
| 4570 | maxeval= tmin (2*ipower (p, degree (getMipo (v2))), maxNumEval); |
---|
| 4571 | F= mapUp (F, a, v2, primElem, imPrimElem, source, dest); |
---|
| 4572 | G= mapUp (G, a, v2, primElem, imPrimElem, source, dest); |
---|
| 4573 | a= v2; |
---|
[08daea] | 4574 | } |
---|
| 4575 | } |
---|
[9ff686] | 4576 | |
---|
| 4577 | lcF = LC( F, x ); lcG = LC( G, x ); |
---|
| 4578 | lcD = gcd( lcF, lcG ); |
---|
| 4579 | |
---|
| 4580 | delta = 0; |
---|
| 4581 | degF = degree( F, x ); degG = degree( G, x ); |
---|
| 4582 | |
---|
| 4583 | if(hasFirstAlgVar(G,a)) |
---|
| 4584 | b = REvaluation( 2, tmax(F.level(), G.level()), AlgExtRandomF( a ) ); |
---|
| 4585 | else |
---|
| 4586 | { // both not in extension given by algebraic variable |
---|
| 4587 | if (CFFactory::gettype() != GaloisFieldDomain) |
---|
| 4588 | b = REvaluation( 2, tmax(F.level(), G.level()), FFRandom() ); |
---|
| 4589 | else |
---|
| 4590 | b = REvaluation( 2, tmax(F.level(), G.level()), GFRandom() ); |
---|
| 4591 | } |
---|
| 4592 | |
---|
[e26667] | 4593 | CanonicalForm cand, contcand; |
---|
[9ff686] | 4594 | CanonicalForm result; |
---|
| 4595 | int o, t; |
---|
| 4596 | o= 0; |
---|
| 4597 | t= 1; |
---|
| 4598 | int goodPointCount= 0; |
---|
[08daea] | 4599 | while( !gcdfound ) |
---|
| 4600 | { |
---|
[9ff686] | 4601 | if( !findeval_P( F, G, Fb, Gb, Db, b, delta, degF, degG, maxeval, count, o, |
---|
| 4602 | maxeval/maxNumVars, t )) |
---|
[08daea] | 4603 | { // too many eval. used --> try another method |
---|
[9ff686] | 4604 | Off (SW_USE_EZGCD_P); |
---|
| 4605 | result= gcd (F,G); |
---|
| 4606 | On (SW_USE_EZGCD_P); |
---|
| 4607 | if (passToGF) |
---|
[08daea] | 4608 | { |
---|
[0a7d0ca] | 4609 | CanonicalForm mipo= gf_mipo; |
---|
[9ff686] | 4610 | setCharacteristic (p); |
---|
[0a7d0ca] | 4611 | Variable alpha= rootOf (mipo.mapinto()); |
---|
[9ff686] | 4612 | result= GF2FalphaRep (result, alpha); |
---|
[08daea] | 4613 | } |
---|
[9ff686] | 4614 | if (k > 1) |
---|
| 4615 | { |
---|
| 4616 | result= GFMapDown (result, k); |
---|
| 4617 | setCharacteristic (p, k, gf_name); |
---|
| 4618 | } |
---|
| 4619 | if (extOfExt) |
---|
| 4620 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
| 4621 | return N (d*result); |
---|
[08daea] | 4622 | } |
---|
| 4623 | delta = degree( Db ); |
---|
| 4624 | if( delta == 0 ) |
---|
[9ff686] | 4625 | { |
---|
| 4626 | if (passToGF) |
---|
| 4627 | setCharacteristic (p); |
---|
| 4628 | if (k > 1) |
---|
| 4629 | setCharacteristic (p, k, gf_name); |
---|
[08daea] | 4630 | return N (d); |
---|
[9ff686] | 4631 | } |
---|
[08daea] | 4632 | while( true ) |
---|
| 4633 | { |
---|
| 4634 | bt = b; |
---|
[9ff686] | 4635 | if( !findeval_P(F,G,Fbt,Gbt,Dbt, bt, delta, degF, degG, maxeval, count, o, |
---|
| 4636 | maxeval/maxNumVars, t )) |
---|
[08daea] | 4637 | { // too many eval. used --> try another method |
---|
[9ff686] | 4638 | Off (SW_USE_EZGCD_P); |
---|
| 4639 | result= gcd (F,G); |
---|
| 4640 | On (SW_USE_EZGCD_P); |
---|
| 4641 | if (passToGF) |
---|
[08daea] | 4642 | { |
---|
[0a7d0ca] | 4643 | CanonicalForm mipo= gf_mipo; |
---|
[9ff686] | 4644 | setCharacteristic (p); |
---|
[0a7d0ca] | 4645 | Variable alpha= rootOf (mipo.mapinto()); |
---|
[9ff686] | 4646 | result= GF2FalphaRep (result, alpha); |
---|
[08daea] | 4647 | } |
---|
[9ff686] | 4648 | if (k > 1) |
---|
| 4649 | { |
---|
| 4650 | result= GFMapDown (result, k); |
---|
| 4651 | setCharacteristic (p, k, gf_name); |
---|
| 4652 | } |
---|
| 4653 | if (extOfExt) |
---|
| 4654 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
| 4655 | return N (d*result); |
---|
[08daea] | 4656 | } |
---|
| 4657 | int dd = degree( Dbt ); |
---|
| 4658 | if( dd == 0 ) |
---|
[9ff686] | 4659 | { |
---|
| 4660 | if (passToGF) |
---|
| 4661 | setCharacteristic (p); |
---|
| 4662 | if (k > 1) |
---|
| 4663 | setCharacteristic (p, k, gf_name); |
---|
[08daea] | 4664 | return N (d); |
---|
[9ff686] | 4665 | } |
---|
[08daea] | 4666 | if( dd == delta ) |
---|
[9ff686] | 4667 | { |
---|
| 4668 | goodPointCount++; |
---|
| 4669 | if (goodPointCount == 5) |
---|
| 4670 | break; |
---|
| 4671 | } |
---|
[08daea] | 4672 | if( dd < delta ) |
---|
| 4673 | { |
---|
[9ff686] | 4674 | goodPointCount= 0; |
---|
[08daea] | 4675 | delta = dd; |
---|
| 4676 | b = bt; |
---|
| 4677 | Db = Dbt; Fb = Fbt; Gb = Gbt; |
---|
| 4678 | } |
---|
[9ff686] | 4679 | if (delta == degF) |
---|
| 4680 | { |
---|
| 4681 | if (degF <= degG && fdivides (F, G)) |
---|
| 4682 | { |
---|
| 4683 | if (passToGF) |
---|
| 4684 | { |
---|
[0a7d0ca] | 4685 | CanonicalForm mipo= gf_mipo; |
---|
[9ff686] | 4686 | setCharacteristic (p); |
---|
[0a7d0ca] | 4687 | Variable alpha= rootOf (mipo.mapinto()); |
---|
[9ff686] | 4688 | F= GF2FalphaRep (F, alpha); |
---|
| 4689 | } |
---|
| 4690 | if (k > 1) |
---|
| 4691 | { |
---|
| 4692 | F= GFMapDown (F, k); |
---|
| 4693 | setCharacteristic (p, k, gf_name); |
---|
| 4694 | } |
---|
| 4695 | if (extOfExt) |
---|
| 4696 | F= mapDown (F, primElem, imPrimElem, oldA, dest, source); |
---|
| 4697 | return N (d*F); |
---|
| 4698 | } |
---|
| 4699 | else |
---|
| 4700 | delta--; |
---|
| 4701 | } |
---|
| 4702 | else if (delta == degG) |
---|
| 4703 | { |
---|
| 4704 | if (degG <= degF && fdivides (G, F)) |
---|
| 4705 | { |
---|
| 4706 | if (passToGF) |
---|
| 4707 | { |
---|
[0a7d0ca] | 4708 | CanonicalForm mipo= gf_mipo; |
---|
[9ff686] | 4709 | setCharacteristic (p); |
---|
[0a7d0ca] | 4710 | Variable alpha= rootOf (mipo.mapinto()); |
---|
[9ff686] | 4711 | G= GF2FalphaRep (G, alpha); |
---|
| 4712 | } |
---|
| 4713 | if (k > 1) |
---|
| 4714 | { |
---|
| 4715 | G= GFMapDown (G, k); |
---|
| 4716 | setCharacteristic (p, k, gf_name); |
---|
| 4717 | } |
---|
| 4718 | if (extOfExt) |
---|
| 4719 | G= mapDown (G, primElem, imPrimElem, oldA, dest, source); |
---|
| 4720 | return N (d*G); |
---|
| 4721 | } |
---|
| 4722 | else |
---|
| 4723 | delta--; |
---|
| 4724 | } |
---|
[08daea] | 4725 | } |
---|
| 4726 | if( delta != degF && delta != degG ) |
---|
| 4727 | { |
---|
| 4728 | bool B_is_F; |
---|
| 4729 | CanonicalForm xxx1, xxx2; |
---|
| 4730 | CanonicalForm buf; |
---|
| 4731 | DD[1] = Fb / Db; |
---|
| 4732 | buf= Gb/Db; |
---|
| 4733 | xxx1 = gcd( DD[1], Db ); |
---|
| 4734 | xxx2 = gcd( buf, Db ); |
---|
| 4735 | if (((xxx1.inCoeffDomain() && xxx2.inCoeffDomain()) && |
---|
[c1b9927] | 4736 | (size (F) <= size (G))) |
---|
[08daea] | 4737 | || (xxx1.inCoeffDomain() && !xxx2.inCoeffDomain())) |
---|
| 4738 | { |
---|
| 4739 | B = F; |
---|
| 4740 | DD[2] = Db; |
---|
| 4741 | lcDD[1] = lcF; |
---|
| 4742 | lcDD[2] = lcD; |
---|
| 4743 | B_is_F = true; |
---|
| 4744 | } |
---|
| 4745 | else if (((xxx1.inCoeffDomain() && xxx2.inCoeffDomain()) && |
---|
[c1b9927] | 4746 | (size (G) < size (F))) |
---|
[08daea] | 4747 | || (!xxx1.inCoeffDomain() && xxx2.inCoeffDomain())) |
---|
| 4748 | { |
---|
| 4749 | DD[1] = buf; |
---|
| 4750 | B = G; |
---|
| 4751 | DD[2] = Db; |
---|
| 4752 | lcDD[1] = lcG; |
---|
| 4753 | lcDD[2] = lcD; |
---|
| 4754 | B_is_F = false; |
---|
| 4755 | } |
---|
| 4756 | else // special case handling |
---|
| 4757 | { |
---|
[9ff686] | 4758 | Off (SW_USE_EZGCD_P); |
---|
| 4759 | result= gcd (F,G); |
---|
| 4760 | On (SW_USE_EZGCD_P); |
---|
| 4761 | if (passToGF) |
---|
| 4762 | { |
---|
[0a7d0ca] | 4763 | CanonicalForm mipo= gf_mipo; |
---|
[9ff686] | 4764 | setCharacteristic (p); |
---|
[0a7d0ca] | 4765 | Variable alpha= rootOf (mipo.mapinto()); |
---|
[9ff686] | 4766 | result= GF2FalphaRep (result, alpha); |
---|
| 4767 | } |
---|
| 4768 | if (k > 1) |
---|
[08daea] | 4769 | { |
---|
[9ff686] | 4770 | result= GFMapDown (result, k); |
---|
| 4771 | setCharacteristic (p, k, gf_name); |
---|
| 4772 | } |
---|
| 4773 | if (extOfExt) |
---|
| 4774 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
| 4775 | return N (d*result); |
---|
| 4776 | } |
---|
| 4777 | DD[2] = DD[2] * ( b( lcDD[2] ) / lc( DD[2] ) ); |
---|
| 4778 | DD[1] = DD[1] * ( b( lcDD[1] ) / lc( DD[1] ) ); |
---|
| 4779 | |
---|
| 4780 | if (size (B*lcDD[2])/maxNumVars > sizePerVars1) |
---|
| 4781 | { |
---|
| 4782 | if (algExtension) |
---|
| 4783 | { |
---|
| 4784 | result= GCD_Fp_extension (F, G, a); |
---|
| 4785 | if (extOfExt) |
---|
| 4786 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
| 4787 | return N (d*result); |
---|
| 4788 | } |
---|
| 4789 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
| 4790 | { |
---|
| 4791 | result= GCD_GF (F, G); |
---|
| 4792 | if (passToGF) |
---|
| 4793 | { |
---|
[0a7d0ca] | 4794 | CanonicalForm mipo= gf_mipo; |
---|
[9ff686] | 4795 | setCharacteristic (p); |
---|
[0a7d0ca] | 4796 | Variable alpha= rootOf (mipo.mapinto()); |
---|
[9ff686] | 4797 | result= GF2FalphaRep (result, alpha); |
---|
| 4798 | } |
---|
| 4799 | if (k > 1) |
---|
[08daea] | 4800 | { |
---|
[9ff686] | 4801 | result= GFMapDown (result, k); |
---|
| 4802 | setCharacteristic (p, k, gf_name); |
---|
[08daea] | 4803 | } |
---|
[9ff686] | 4804 | return N (d*result); |
---|
[08daea] | 4805 | } |
---|
| 4806 | else |
---|
[9ff686] | 4807 | return N (d*GCD_small_p (F,G)); |
---|
[08daea] | 4808 | } |
---|
| 4809 | |
---|
[0349c20] | 4810 | gcdfound= Hensel_P (B*lcD, DD, b, lcDD); |
---|
[08daea] | 4811 | |
---|
[9ff686] | 4812 | if (gcdfound == -1) |
---|
| 4813 | { |
---|
| 4814 | Off (SW_USE_EZGCD_P); |
---|
| 4815 | result= gcd (F,G); |
---|
| 4816 | On (SW_USE_EZGCD_P); |
---|
| 4817 | if (passToGF) |
---|
| 4818 | { |
---|
[0a7d0ca] | 4819 | CanonicalForm mipo= gf_mipo; |
---|
[9ff686] | 4820 | setCharacteristic (p); |
---|
[0a7d0ca] | 4821 | Variable alpha= rootOf (mipo.mapinto()); |
---|
[9ff686] | 4822 | result= GF2FalphaRep (result, alpha); |
---|
| 4823 | } |
---|
| 4824 | if (k > 1) |
---|
| 4825 | { |
---|
| 4826 | result= GFMapDown (result, k); |
---|
| 4827 | setCharacteristic (p, k, gf_name); |
---|
| 4828 | } |
---|
| 4829 | if (extOfExt) |
---|
| 4830 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
| 4831 | return N (d*result); |
---|
| 4832 | } |
---|
| 4833 | |
---|
| 4834 | if (gcdfound == 1) |
---|
[08daea] | 4835 | { |
---|
[e26667] | 4836 | contcand= content (DD[2], Variable (1)); |
---|
| 4837 | cand = DD[2] / contcand; |
---|
| 4838 | if (B_is_F) |
---|
| 4839 | gcdfound = fdivides( cand, G ) && cand*(DD[1]/(lcD/contcand)) == F; |
---|
| 4840 | else |
---|
| 4841 | gcdfound = fdivides( cand, F ) && cand*(DD[1]/(lcD/contcand)) == G; |
---|
[9ff686] | 4842 | |
---|
| 4843 | if (passToGF && gcdfound) |
---|
| 4844 | { |
---|
[0a7d0ca] | 4845 | CanonicalForm mipo= gf_mipo; |
---|
[9ff686] | 4846 | setCharacteristic (p); |
---|
[0a7d0ca] | 4847 | Variable alpha= rootOf (mipo.mapinto()); |
---|
[9ff686] | 4848 | cand= GF2FalphaRep (cand, alpha); |
---|
| 4849 | } |
---|
| 4850 | if (k > 1 && gcdfound) |
---|
| 4851 | { |
---|
| 4852 | cand= GFMapDown (cand, k); |
---|
| 4853 | setCharacteristic (p, k, gf_name); |
---|
| 4854 | } |
---|
| 4855 | if (extOfExt && gcdfound) |
---|
| 4856 | cand= mapDown (cand, primElem, imPrimElem, oldA, dest, source); |
---|
[08daea] | 4857 | } |
---|
| 4858 | } |
---|
[9ff686] | 4859 | delta--; |
---|
| 4860 | goodPointCount= 0; |
---|
[08daea] | 4861 | } |
---|
| 4862 | return N (d*cand); |
---|
| 4863 | } |
---|
| 4864 | |
---|
| 4865 | |
---|
[10af64] | 4866 | #endif |
---|