[493c477] | 1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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[341696] | 2 | /* $Id$ */ |
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[9bab9f] | 3 | |
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[ab4548f] | 4 | #include <config.h> |
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| 5 | |
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[9bab9f] | 6 | #include "assert.h" |
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[93b061] | 7 | #include "debug.h" |
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| 8 | |
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[9bab9f] | 9 | #include "cf_defs.h" |
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| 10 | #include "canonicalform.h" |
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| 11 | #include "cf_iter.h" |
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| 12 | #include "cf_reval.h" |
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[edb4893] | 13 | #include "cf_primes.h" |
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[fbefc9] | 14 | #include "cf_algorithm.h" |
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[2072126] | 15 | #include "cf_factory.h" |
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[f63dbca] | 16 | #include "fac_util.h" |
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[6db552] | 17 | #include "templates/ftmpl_functions.h" |
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[49f1f45] | 18 | #include "ffreval.h" |
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[bb82f0] | 19 | #include "algext.h" |
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[598ff8b] | 20 | #include "fieldGCD.h" |
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[10af64] | 21 | #include "cf_gcd_smallp.h" |
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[6e2ef0e] | 22 | #include "cf_map_ext.h" |
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| 23 | #include "cf_util.h" |
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[edb4893] | 24 | |
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[f11d7b] | 25 | #ifdef HAVE_NTL |
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[034eec] | 26 | #include <NTL/ZZX.h> |
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[f11d7b] | 27 | #include "NTLconvert.h" |
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[a7ec94] | 28 | bool isPurePoly(const CanonicalForm & ); |
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| 29 | static CanonicalForm gcd_univar_ntl0( const CanonicalForm &, const CanonicalForm & ); |
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[c4f4fd] | 30 | static CanonicalForm gcd_univar_ntlp( const CanonicalForm &, const CanonicalForm & ); |
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[f11d7b] | 31 | #endif |
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| 32 | |
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[a7ec94] | 33 | static CanonicalForm cf_content ( const CanonicalForm &, const CanonicalForm & ); |
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| 34 | static bool gcd_avoid_mtaildegree ( CanonicalForm &, CanonicalForm &, CanonicalForm & ); |
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| 35 | static void cf_prepgcd( const CanonicalForm &, const CanonicalForm &, int &, int &, int & ); |
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[edb4893] | 36 | |
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[27bb97f] | 37 | void out_cf(const char *s1,const CanonicalForm &f,const char *s2); |
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[6f62c3] | 38 | |
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[110718] | 39 | CanonicalForm chinrem_gcd(const CanonicalForm & FF,const CanonicalForm & GG); |
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| 40 | CanonicalForm newGCD(CanonicalForm A, CanonicalForm B); |
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[f4b180] | 41 | |
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[f63dbca] | 42 | bool |
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| 43 | gcd_test_one ( const CanonicalForm & f, const CanonicalForm & g, bool swap ) |
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[9bab9f] | 44 | { |
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| 45 | int count = 0; |
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| 46 | // assume polys have same level; |
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[6e2ef0e] | 47 | |
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| 48 | Variable v= Variable (1); |
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| 49 | bool algExtension= (hasFirstAlgVar (f, v) || hasFirstAlgVar (g, v)); |
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[f63dbca] | 50 | CanonicalForm lcf, lcg; |
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[6f62c3] | 51 | if ( swap ) |
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| 52 | { |
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[150dc8] | 53 | lcf = swapvar( LC( f ), Variable(1), f.mvar() ); |
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| 54 | lcg = swapvar( LC( g ), Variable(1), f.mvar() ); |
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[f63dbca] | 55 | } |
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[6f62c3] | 56 | else |
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| 57 | { |
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[150dc8] | 58 | lcf = LC( f, Variable(1) ); |
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| 59 | lcg = LC( g, Variable(1) ); |
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[f63dbca] | 60 | } |
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[6e2ef0e] | 61 | |
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[f63dbca] | 62 | CanonicalForm F, G; |
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[6f62c3] | 63 | if ( swap ) |
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| 64 | { |
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[150dc8] | 65 | F=swapvar( f, Variable(1), f.mvar() ); |
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| 66 | G=swapvar( g, Variable(1), g.mvar() ); |
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[f63dbca] | 67 | } |
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[6f62c3] | 68 | else |
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| 69 | { |
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[150dc8] | 70 | F = f; |
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| 71 | G = g; |
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[f63dbca] | 72 | } |
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[6e2ef0e] | 73 | |
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| 74 | #define TEST_ONE_MAX 50 |
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| 75 | int p= getCharacteristic(); |
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| 76 | bool passToGF= false; |
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| 77 | int k= 1; |
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| 78 | if (p > 0 && p < TEST_ONE_MAX && CFFactory::gettype() != GaloisFieldDomain && !algExtension) |
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| 79 | { |
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| 80 | if (p == 2) |
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| 81 | setCharacteristic (2, 6, 'Z'); |
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| 82 | else if (p == 3) |
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| 83 | setCharacteristic (3, 4, 'Z'); |
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| 84 | else if (p == 5 || p == 7) |
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| 85 | setCharacteristic (p, 3, 'Z'); |
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| 86 | else |
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| 87 | setCharacteristic (p, 2, 'Z'); |
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| 88 | passToGF= true; |
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| 89 | } |
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| 90 | else if (p > 0 && CFFactory::gettype() == GaloisFieldDomain && ipower (p , getGFDegree()) < TEST_ONE_MAX) |
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| 91 | { |
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| 92 | k= getGFDegree(); |
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| 93 | if (ipower (p, 2*k) > TEST_ONE_MAX) |
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| 94 | setCharacteristic (p, 2*k, gf_name); |
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| 95 | else |
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| 96 | setCharacteristic (p, 3*k, gf_name); |
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| 97 | F= GFMapUp (F, k); |
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| 98 | G= GFMapUp (G, k); |
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| 99 | lcf= GFMapUp (lcf, k); |
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| 100 | lcg= GFMapUp (lcg, k); |
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| 101 | } |
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| 102 | else if (p > 0 && p < TEST_ONE_MAX && algExtension) |
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| 103 | { |
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| 104 | bool extOfExt= false; |
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| 105 | int d= degree (getMipo (v)); |
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| 106 | CFList source, dest; |
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| 107 | Variable v2; |
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| 108 | CanonicalForm primElem, imPrimElem; |
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| 109 | if (p == 2 && d < 6) |
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| 110 | { |
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| 111 | zz_p::init (p); |
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| 112 | bool primFail= false; |
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| 113 | Variable vBuf; |
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| 114 | primElem= primitiveElement (v, vBuf, primFail); |
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| 115 | ASSERT (!primFail, "failure in integer factorizer"); |
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| 116 | if (d < 3) |
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| 117 | { |
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| 118 | zz_pX NTLIrredpoly; |
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| 119 | BuildIrred (NTLIrredpoly, d*3); |
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| 120 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
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| 121 | v2= rootOf (newMipo); |
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| 122 | } |
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| 123 | else |
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| 124 | { |
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| 125 | zz_pX NTLIrredpoly; |
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| 126 | BuildIrred (NTLIrredpoly, d*2); |
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| 127 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
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| 128 | v2= rootOf (newMipo); |
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| 129 | } |
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| 130 | imPrimElem= mapPrimElem (primElem, v, v2); |
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| 131 | extOfExt= true; |
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| 132 | } |
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| 133 | else if ((p == 3 && d < 4) || ((p == 5 || p == 7) && d < 3)) |
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| 134 | { |
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| 135 | zz_p::init (p); |
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| 136 | bool primFail= false; |
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| 137 | Variable vBuf; |
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| 138 | primElem= primitiveElement (v, vBuf, primFail); |
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| 139 | ASSERT (!primFail, "failure in integer factorizer"); |
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| 140 | zz_pX NTLIrredpoly; |
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| 141 | BuildIrred (NTLIrredpoly, d*2); |
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| 142 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
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| 143 | v2= rootOf (newMipo); |
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| 144 | imPrimElem= mapPrimElem (primElem, v, v2); |
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| 145 | extOfExt= true; |
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| 146 | } |
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| 147 | if (extOfExt) |
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| 148 | { |
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| 149 | F= mapUp (F, v, v2, primElem, imPrimElem, source, dest); |
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| 150 | G= mapUp (G, v, v2, primElem, imPrimElem, source, dest); |
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| 151 | lcf= mapUp (lcf, v, v2, primElem, imPrimElem, source, dest); |
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| 152 | lcg= mapUp (lcg, v, v2, primElem, imPrimElem, source, dest); |
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| 153 | v= v2; |
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| 154 | } |
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| 155 | } |
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| 156 | |
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| 157 | CFRandom * sample; |
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| 158 | if ((!algExtension && p > 0) || p == 0) |
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| 159 | sample = CFRandomFactory::generate(); |
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| 160 | else |
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| 161 | sample = AlgExtRandomF (v).clone(); |
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| 162 | |
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| 163 | REvaluation e( 2, tmax( f.level(), g.level() ), *sample ); |
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| 164 | delete sample; |
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| 165 | |
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| 166 | if (passToGF) |
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| 167 | { |
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| 168 | lcf= lcf.mapinto(); |
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| 169 | lcg= lcg.mapinto(); |
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| 170 | } |
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| 171 | |
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| 172 | CanonicalForm eval1, eval2; |
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| 173 | if (passToGF) |
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| 174 | { |
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| 175 | eval1= e (lcf); |
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| 176 | eval2= e (lcg); |
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| 177 | } |
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| 178 | else |
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| 179 | { |
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| 180 | eval1= e (lcf); |
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| 181 | eval2= e (lcg); |
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| 182 | } |
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| 183 | |
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| 184 | while ( ( eval1.isZero() || eval2.isZero() ) && count < TEST_ONE_MAX ) |
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| 185 | { |
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| 186 | e.nextpoint(); |
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| 187 | count++; |
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| 188 | eval1= e (lcf); |
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| 189 | eval2= e (lcg); |
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| 190 | } |
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| 191 | if ( count >= TEST_ONE_MAX ) |
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| 192 | { |
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| 193 | if (passToGF) |
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| 194 | setCharacteristic (p); |
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| 195 | if (k > 1) |
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| 196 | setCharacteristic (p, k, gf_name); |
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| 197 | return false; |
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| 198 | } |
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| 199 | |
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| 200 | |
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| 201 | if (passToGF) |
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| 202 | { |
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| 203 | F= F.mapinto(); |
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| 204 | G= G.mapinto(); |
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| 205 | eval1= e (F); |
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| 206 | eval2= e (G); |
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| 207 | } |
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| 208 | else |
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| 209 | { |
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| 210 | eval1= e (F); |
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| 211 | eval2= e (G); |
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| 212 | } |
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| 213 | |
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| 214 | if ( eval1.taildegree() > 0 && eval2.taildegree() > 0 ) |
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| 215 | { |
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| 216 | if (passToGF) |
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| 217 | setCharacteristic (p); |
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| 218 | if (k > 1) |
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| 219 | setCharacteristic (p, k, gf_name); |
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[150dc8] | 220 | return false; |
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[6e2ef0e] | 221 | } |
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| 222 | |
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| 223 | CanonicalForm c= gcd (eval1, eval2); |
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| 224 | bool result= c.degree() < 1; |
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| 225 | |
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| 226 | if (passToGF) |
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| 227 | setCharacteristic (p); |
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| 228 | if (k > 1) |
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| 229 | setCharacteristic (p, k, gf_name); |
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| 230 | return result; |
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[9bab9f] | 231 | } |
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| 232 | |
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[dd3e561] | 233 | //{{{ static CanonicalForm icontent ( const CanonicalForm & f, const CanonicalForm & c ) |
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| 234 | //{{{ docu |
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| 235 | // |
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| 236 | // icontent() - return gcd of c and all coefficients of f which |
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| 237 | // are in a coefficient domain. |
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| 238 | // |
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| 239 | // Used by icontent(). |
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| 240 | // |
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| 241 | //}}} |
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[9bab9f] | 242 | static CanonicalForm |
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| 243 | icontent ( const CanonicalForm & f, const CanonicalForm & c ) |
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| 244 | { |
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[c30347] | 245 | if ( f.inBaseDomain() ) |
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| 246 | { |
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| 247 | if (c.isZero()) return abs(f); |
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| 248 | return bgcd( f, c ); |
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| 249 | } |
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[ef20c7] | 250 | //else if ( f.inCoeffDomain() ) |
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| 251 | // return gcd(f,c); |
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[c30347] | 252 | else |
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| 253 | { |
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[150dc8] | 254 | CanonicalForm g = c; |
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| 255 | for ( CFIterator i = f; i.hasTerms() && ! g.isOne(); i++ ) |
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| 256 | g = icontent( i.coeff(), g ); |
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| 257 | return g; |
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[9bab9f] | 258 | } |
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| 259 | } |
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[dd3e561] | 260 | //}}} |
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[9bab9f] | 261 | |
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[dd3e561] | 262 | //{{{ CanonicalForm icontent ( const CanonicalForm & f ) |
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| 263 | //{{{ docu |
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| 264 | // |
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| 265 | // icontent() - return gcd over all coefficients of f which are |
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| 266 | // in a coefficient domain. |
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| 267 | // |
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| 268 | //}}} |
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[9bab9f] | 269 | CanonicalForm |
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| 270 | icontent ( const CanonicalForm & f ) |
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| 271 | { |
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| 272 | return icontent( f, 0 ); |
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| 273 | } |
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[dd3e561] | 274 | //}}} |
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[9bab9f] | 275 | |
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[dd3e561] | 276 | //{{{ CanonicalForm extgcd ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & a, CanonicalForm & b ) |
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| 277 | //{{{ docu |
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| 278 | // |
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| 279 | // extgcd() - returns polynomial extended gcd of f and g. |
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| 280 | // |
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| 281 | // Returns gcd(f, g) and a and b sucht that f*a+g*b=gcd(f, g). |
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| 282 | // The gcd is calculated using an extended euclidean polynomial |
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| 283 | // remainder sequence, so f and g should be polynomials over an |
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| 284 | // euclidean domain. Normalizes result. |
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| 285 | // |
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| 286 | // Note: be sure that f and g have the same level! |
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| 287 | // |
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| 288 | //}}} |
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[9bab9f] | 289 | CanonicalForm |
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| 290 | extgcd ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & a, CanonicalForm & b ) |
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| 291 | { |
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[034eec] | 292 | #ifdef HAVE_NTL |
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[963057] | 293 | if (isOn(SW_USE_NTL_GCD_P) && ( getCharacteristic() > 0 ) && (CFFactory::gettype() != GaloisFieldDomain) |
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[a86cda] | 294 | && (f.level()==g.level()) && isPurePoly(f) && isPurePoly(g)) |
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[034eec] | 295 | { |
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[c6eecb] | 296 | if (fac_NTL_char!=getCharacteristic()) |
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| 297 | { |
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| 298 | fac_NTL_char=getCharacteristic(); |
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| 299 | #ifdef NTL_ZZ |
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| 300 | ZZ r; |
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| 301 | r=getCharacteristic(); |
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| 302 | ZZ_pContext ccc(r); |
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| 303 | #else |
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| 304 | zz_pContext ccc(getCharacteristic()); |
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| 305 | #endif |
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| 306 | ccc.restore(); |
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| 307 | #ifdef NTL_ZZ |
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| 308 | ZZ_p::init(r); |
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| 309 | #else |
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| 310 | zz_p::init(getCharacteristic()); |
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| 311 | #endif |
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| 312 | } |
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| 313 | #ifdef NTL_ZZ |
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| 314 | ZZ_pX F1=convertFacCF2NTLZZpX(f); |
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| 315 | ZZ_pX G1=convertFacCF2NTLZZpX(g); |
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| 316 | ZZ_pX R; |
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| 317 | ZZ_pX A,B; |
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| 318 | XGCD(R,A,B,F1,G1); |
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| 319 | a=convertNTLZZpX2CF(A,f.mvar()); |
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| 320 | b=convertNTLZZpX2CF(B,f.mvar()); |
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| 321 | return convertNTLZZpX2CF(R,f.mvar()); |
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| 322 | #else |
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[034eec] | 323 | zz_pX F1=convertFacCF2NTLzzpX(f); |
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| 324 | zz_pX G1=convertFacCF2NTLzzpX(g); |
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| 325 | zz_pX R; |
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| 326 | zz_pX A,B; |
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| 327 | XGCD(R,A,B,F1,G1); |
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| 328 | a=convertNTLzzpX2CF(A,f.mvar()); |
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| 329 | b=convertNTLzzpX2CF(B,f.mvar()); |
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| 330 | return convertNTLzzpX2CF(R,f.mvar()); |
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[c6eecb] | 331 | #endif |
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[034eec] | 332 | } |
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[a86cda] | 333 | if (isOn(SW_USE_NTL_GCD_0) && ( getCharacteristic() ==0) |
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| 334 | && (f.level()==g.level()) && isPurePoly(f) && isPurePoly(g)) |
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| 335 | { |
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| 336 | CanonicalForm fc=bCommonDen(f); |
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| 337 | CanonicalForm gc=bCommonDen(g); |
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| 338 | ZZX F1=convertFacCF2NTLZZX(f*fc); |
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| 339 | ZZX G1=convertFacCF2NTLZZX(g*gc); |
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| 340 | ZZX R=GCD(F1,G1); |
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| 341 | CanonicalForm r=convertNTLZZX2CF(R,f.mvar()); |
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| 342 | ZZ RR; |
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| 343 | ZZX A,B; |
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| 344 | if (r.inCoeffDomain()) |
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| 345 | { |
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| 346 | XGCD(RR,A,B,F1,G1,1); |
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| 347 | CanonicalForm rr=convertZZ2CF(RR); |
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| 348 | ASSERT (!rr.isZero(), "NTL:XGCD failed"); |
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| 349 | a=convertNTLZZX2CF(A,f.mvar())*fc/rr; |
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| 350 | b=convertNTLZZX2CF(B,f.mvar())*gc/rr; |
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| 351 | return CanonicalForm(1); |
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| 352 | } |
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| 353 | else |
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| 354 | { |
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| 355 | fc=bCommonDen(f); |
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| 356 | gc=bCommonDen(g); |
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| 357 | F1=convertFacCF2NTLZZX(f*fc/r); |
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| 358 | G1=convertFacCF2NTLZZX(g*gc/r); |
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| 359 | XGCD(RR,A,B,F1,G1,1); |
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| 360 | a=convertNTLZZX2CF(A,f.mvar())*fc; |
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| 361 | b=convertNTLZZX2CF(B,f.mvar())*gc; |
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| 362 | CanonicalForm rr=convertZZ2CF(RR); |
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| 363 | ASSERT (!rr.isZero(), "NTL:XGCD failed"); |
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| 364 | r*=rr; |
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| 365 | if ( r.sign() < 0 ) { r= -r; a= -a; b= -b; } |
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| 366 | return r; |
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| 367 | } |
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| 368 | } |
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[034eec] | 369 | #endif |
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[a86cda] | 370 | // may contain bug in the co-factors, see track 107 |
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[034eec] | 371 | CanonicalForm contf = content( f ); |
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| 372 | CanonicalForm contg = content( g ); |
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[9bab9f] | 373 | |
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[034eec] | 374 | CanonicalForm p0 = f / contf, p1 = g / contg; |
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| 375 | CanonicalForm f0 = 1, f1 = 0, g0 = 0, g1 = 1, q, r; |
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[9bab9f] | 376 | |
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[c6eecb] | 377 | while ( ! p1.isZero() ) |
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| 378 | { |
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[034eec] | 379 | divrem( p0, p1, q, r ); |
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| 380 | p0 = p1; p1 = r; |
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| 381 | r = g0 - g1 * q; |
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| 382 | g0 = g1; g1 = r; |
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| 383 | r = f0 - f1 * q; |
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| 384 | f0 = f1; f1 = r; |
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| 385 | } |
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| 386 | CanonicalForm contp0 = content( p0 ); |
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| 387 | a = f0 / ( contf * contp0 ); |
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| 388 | b = g0 / ( contg * contp0 ); |
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| 389 | p0 /= contp0; |
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[c6eecb] | 390 | if ( p0.sign() < 0 ) |
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| 391 | { |
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[034eec] | 392 | p0 = -p0; |
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| 393 | a = -a; |
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| 394 | b = -b; |
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| 395 | } |
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| 396 | return p0; |
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[9bab9f] | 397 | } |
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[dd3e561] | 398 | //}}} |
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[9bab9f] | 399 | |
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[a7ec94] | 400 | //{{{ static CanonicalForm balance ( const CanonicalForm & f, const CanonicalForm & q ) |
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| 401 | //{{{ docu |
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| 402 | // |
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| 403 | // balance() - map f from positive to symmetric representation |
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| 404 | // mod q. |
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| 405 | // |
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| 406 | // This makes sense for univariate polynomials over Z only. |
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| 407 | // q should be an integer. |
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| 408 | // |
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| 409 | // Used by gcd_poly_univar0(). |
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| 410 | // |
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| 411 | //}}} |
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[edb4893] | 412 | static CanonicalForm |
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[a7ec94] | 413 | balance ( const CanonicalForm & f, const CanonicalForm & q ) |
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[edb4893] | 414 | { |
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[a7ec94] | 415 | Variable x = f.mvar(); |
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| 416 | CanonicalForm result = 0, qh = q / 2; |
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| 417 | CanonicalForm c; |
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| 418 | CFIterator i; |
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| 419 | for ( i = f; i.hasTerms(); i++ ) { |
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| 420 | c = mod( i.coeff(), q ); |
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| 421 | if ( c > qh ) |
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| 422 | result += power( x, i.exp() ) * (c - q); |
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| 423 | else |
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| 424 | result += power( x, i.exp() ) * c; |
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[edb4893] | 425 | } |
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[a7ec94] | 426 | return result; |
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| 427 | } |
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| 428 | //}}} |
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| 429 | |
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[01e8874] | 430 | static CanonicalForm gcd_poly_univar0( const CanonicalForm & F, const CanonicalForm & G, bool primitive ) |
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[a7ec94] | 431 | { |
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[f11d7b] | 432 | CanonicalForm f, g, c, cg, cl, BB, B, M, q, Dp, newD, D, newq; |
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[01e8874] | 433 | int p, i; |
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[f11d7b] | 434 | |
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| 435 | if ( primitive ) |
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| 436 | { |
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| 437 | f = F; |
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| 438 | g = G; |
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| 439 | c = 1; |
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| 440 | } |
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| 441 | else |
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| 442 | { |
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| 443 | CanonicalForm cF = content( F ), cG = content( G ); |
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| 444 | f = F / cF; |
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| 445 | g = G / cG; |
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| 446 | c = bgcd( cF, cG ); |
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| 447 | } |
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| 448 | cg = gcd( f.lc(), g.lc() ); |
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| 449 | cl = ( f.lc() / cg ) * g.lc(); |
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[93b061] | 450 | // B = 2 * cg * tmin( |
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[150dc8] | 451 | // maxnorm(f)*power(CanonicalForm(2),f.degree())*isqrt(f.degree()+1), |
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| 452 | // maxnorm(g)*power(CanonicalForm(2),g.degree())*isqrt(g.degree()+1) |
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| 453 | // )+1; |
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[f11d7b] | 454 | M = tmin( maxNorm(f), maxNorm(g) ); |
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| 455 | BB = power(CanonicalForm(2),tmin(f.degree(),g.degree()))*M; |
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| 456 | q = 0; |
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| 457 | i = cf_getNumSmallPrimes() - 1; |
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| 458 | while ( true ) |
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| 459 | { |
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| 460 | B = BB; |
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| 461 | while ( i >= 0 && q < B ) |
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| 462 | { |
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| 463 | p = cf_getSmallPrime( i ); |
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| 464 | i--; |
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| 465 | while ( i >= 0 && mod( cl, p ) == 0 ) |
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| 466 | { |
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| 467 | p = cf_getSmallPrime( i ); |
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| 468 | i--; |
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| 469 | } |
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| 470 | setCharacteristic( p ); |
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| 471 | Dp = gcd( mapinto( f ), mapinto( g ) ); |
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| 472 | Dp = ( Dp / Dp.lc() ) * mapinto( cg ); |
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| 473 | setCharacteristic( 0 ); |
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| 474 | if ( Dp.degree() == 0 ) |
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| 475 | return c; |
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| 476 | if ( q.isZero() ) |
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| 477 | { |
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| 478 | D = mapinto( Dp ); |
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| 479 | q = p; |
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| 480 | B = power(CanonicalForm(2),D.degree())*M+1; |
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| 481 | } |
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| 482 | else |
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| 483 | { |
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| 484 | if ( Dp.degree() == D.degree() ) |
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| 485 | { |
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| 486 | chineseRemainder( D, q, mapinto( Dp ), p, newD, newq ); |
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| 487 | q = newq; |
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| 488 | D = newD; |
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[150dc8] | 489 | } |
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[f11d7b] | 490 | else if ( Dp.degree() < D.degree() ) |
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| 491 | { |
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| 492 | // all previous p's are bad primes |
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| 493 | q = p; |
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| 494 | D = mapinto( Dp ); |
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| 495 | B = power(CanonicalForm(2),D.degree())*M+1; |
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[150dc8] | 496 | } |
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[f11d7b] | 497 | // else p is a bad prime |
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| 498 | } |
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| 499 | } |
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| 500 | if ( i >= 0 ) |
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| 501 | { |
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| 502 | // now balance D mod q |
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| 503 | D = pp( balance( D, q ) ); |
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[ebc602] | 504 | if ( fdivides( D, f ) && fdivides( D, g ) ) |
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[f11d7b] | 505 | return D * c; |
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| 506 | else |
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| 507 | q = 0; |
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[edb4893] | 508 | } |
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[f11d7b] | 509 | else |
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[a7ec94] | 510 | return gcd_poly( F, G ); |
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[f11d7b] | 511 | DEBOUTLN( cerr, "another try ..." ); |
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| 512 | } |
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[edb4893] | 513 | } |
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| 514 | |
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[c4f4fd] | 515 | static CanonicalForm |
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| 516 | gcd_poly_p( const CanonicalForm & f, const CanonicalForm & g ) |
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| 517 | { |
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| 518 | CanonicalForm pi, pi1; |
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| 519 | CanonicalForm C, Ci, Ci1, Hi, bi, pi2; |
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| 520 | bool bpure; |
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| 521 | int delta = degree( f ) - degree( g ); |
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| 522 | |
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| 523 | if ( delta >= 0 ) |
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| 524 | { |
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| 525 | pi = f; pi1 = g; |
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| 526 | } |
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| 527 | else |
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| 528 | { |
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| 529 | pi = g; pi1 = f; delta = -delta; |
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| 530 | } |
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| 531 | Ci = content( pi ); Ci1 = content( pi1 ); |
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| 532 | pi1 = pi1 / Ci1; pi = pi / Ci; |
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| 533 | C = gcd( Ci, Ci1 ); |
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| 534 | if ( !( pi.isUnivariate() && pi1.isUnivariate() ) ) |
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| 535 | { |
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| 536 | //out_cf("F:",f,"\n"); |
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| 537 | //out_cf("G:",g,"\n"); |
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| 538 | //out_cf("newGCD:",newGCD(f,g),"\n"); |
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| 539 | if (isOn(SW_USE_GCD_P) && (getCharacteristic()>0)) |
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| 540 | { |
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| 541 | return newGCD(f,g); |
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| 542 | } |
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| 543 | if ( gcd_test_one( pi1, pi, true ) ) |
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| 544 | { |
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| 545 | C=abs(C); |
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| 546 | //out_cf("GCD:",C,"\n"); |
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| 547 | return C; |
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| 548 | } |
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| 549 | bpure = false; |
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| 550 | } |
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| 551 | else |
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| 552 | { |
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| 553 | bpure = isPurePoly(pi) && isPurePoly(pi1); |
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| 554 | #ifdef HAVE_NTL |
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| 555 | if ( isOn(SW_USE_NTL_GCD_P) && bpure && (CFFactory::gettype() != GaloisFieldDomain)) |
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| 556 | return gcd_univar_ntlp(pi, pi1 ) * C; |
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| 557 | #endif |
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| 558 | } |
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| 559 | Variable v = f.mvar(); |
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| 560 | Hi = power( LC( pi1, v ), delta ); |
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| 561 | if ( (delta+1) % 2 ) |
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| 562 | bi = 1; |
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| 563 | else |
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| 564 | bi = -1; |
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[6e2ef0e] | 565 | int maxNumVars= tmax (getNumVars (pi), getNumVars (pi1)); |
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| 566 | CanonicalForm oldPi= pi, oldPi1= pi1; |
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[c4f4fd] | 567 | while ( degree( pi1, v ) > 0 ) |
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| 568 | { |
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[6e2ef0e] | 569 | if (!(pi.isUnivariate() && pi1.isUnivariate())) |
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| 570 | { |
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| 571 | if (size (pi)/maxNumVars > 500 || size (pi1)/maxNumVars > 500) |
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| 572 | { |
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| 573 | On (SW_USE_FF_MOD_GCD); |
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| 574 | C *= gcd (oldPi, oldPi1); |
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| 575 | Off (SW_USE_FF_MOD_GCD); |
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| 576 | return C; |
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| 577 | } |
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| 578 | } |
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[c4f4fd] | 579 | pi2 = psr( pi, pi1, v ); |
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| 580 | pi2 = pi2 / bi; |
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| 581 | pi = pi1; pi1 = pi2; |
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[6e2ef0e] | 582 | maxNumVars= tmax (getNumVars (pi), getNumVars (pi1)); |
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[c4f4fd] | 583 | if ( degree( pi1, v ) > 0 ) |
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| 584 | { |
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| 585 | delta = degree( pi, v ) - degree( pi1, v ); |
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| 586 | if ( (delta+1) % 2 ) |
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| 587 | bi = LC( pi, v ) * power( Hi, delta ); |
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| 588 | else |
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| 589 | bi = -LC( pi, v ) * power( Hi, delta ); |
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| 590 | Hi = power( LC( pi1, v ), delta ) / power( Hi, delta-1 ); |
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| 591 | } |
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| 592 | } |
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| 593 | if ( degree( pi1, v ) == 0 ) |
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| 594 | { |
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| 595 | C=abs(C); |
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| 596 | //out_cf("GCD:",C,"\n"); |
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| 597 | return C; |
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| 598 | } |
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| 599 | pi /= content( pi ); |
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| 600 | if ( bpure ) |
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| 601 | pi /= pi.lc(); |
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| 602 | C=abs(C*pi); |
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| 603 | //out_cf("GCD:",C,"\n"); |
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| 604 | return C; |
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| 605 | } |
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| 606 | |
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[a7ec94] | 607 | static CanonicalForm |
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| 608 | gcd_poly_0( const CanonicalForm & f, const CanonicalForm & g ) |
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| 609 | { |
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| 610 | CanonicalForm pi, pi1; |
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[df497a] | 611 | CanonicalForm C, Ci, Ci1, Hi, bi, pi2; |
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[a7ec94] | 612 | int delta = degree( f ) - degree( g ); |
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| 613 | |
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| 614 | if ( delta >= 0 ) |
---|
| 615 | { |
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| 616 | pi = f; pi1 = g; |
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| 617 | } |
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| 618 | else |
---|
| 619 | { |
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| 620 | pi = g; pi1 = f; delta = -delta; |
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| 621 | } |
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[9bab9f] | 622 | Ci = content( pi ); Ci1 = content( pi1 ); |
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| 623 | pi1 = pi1 / Ci1; pi = pi / Ci; |
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[df497a] | 624 | C = gcd( Ci, Ci1 ); |
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[034eec] | 625 | if ( pi.isUnivariate() && pi1.isUnivariate() ) |
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| 626 | { |
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| 627 | #ifdef HAVE_NTL |
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[a7ec94] | 628 | if ( isOn(SW_USE_NTL_GCD_0) && isPurePoly(pi) && isPurePoly(pi1) ) |
---|
| 629 | return gcd_univar_ntl0(pi, pi1 ) * C; |
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[df497a] | 630 | #endif |
---|
[a7ec94] | 631 | return gcd_poly_univar0( pi, pi1, true ) * C; |
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[edb4893] | 632 | } |
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[034eec] | 633 | else if ( gcd_test_one( pi1, pi, true ) ) |
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| 634 | return C; |
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[a7ec94] | 635 | Variable v = f.mvar(); |
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[9bab9f] | 636 | Hi = power( LC( pi1, v ), delta ); |
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| 637 | if ( (delta+1) % 2 ) |
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[150dc8] | 638 | bi = 1; |
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[9bab9f] | 639 | else |
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[150dc8] | 640 | bi = -1; |
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[6f62c3] | 641 | while ( degree( pi1, v ) > 0 ) |
---|
| 642 | { |
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[150dc8] | 643 | pi2 = psr( pi, pi1, v ); |
---|
| 644 | pi2 = pi2 / bi; |
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| 645 | pi = pi1; pi1 = pi2; |
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[6f62c3] | 646 | if ( degree( pi1, v ) > 0 ) |
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| 647 | { |
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[150dc8] | 648 | delta = degree( pi, v ) - degree( pi1, v ); |
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| 649 | if ( (delta+1) % 2 ) |
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| 650 | bi = LC( pi, v ) * power( Hi, delta ); |
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| 651 | else |
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| 652 | bi = -LC( pi, v ) * power( Hi, delta ); |
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| 653 | Hi = power( LC( pi1, v ), delta ) / power( Hi, delta-1 ); |
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| 654 | } |
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[9bab9f] | 655 | } |
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| 656 | if ( degree( pi1, v ) == 0 ) |
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[150dc8] | 657 | return C; |
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[df497a] | 658 | else |
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[150dc8] | 659 | return C * pp( pi ); |
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[9bab9f] | 660 | } |
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| 661 | |
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[b809a8] | 662 | //{{{ CanonicalForm gcd_poly ( const CanonicalForm & f, const CanonicalForm & g ) |
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[dd3e561] | 663 | //{{{ docu |
---|
| 664 | // |
---|
| 665 | // gcd_poly() - calculate polynomial gcd. |
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| 666 | // |
---|
| 667 | // This is the dispatcher for polynomial gcd calculation. We call either |
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| 668 | // ezgcd(), sparsemod() or gcd_poly1() in dependecy on the current |
---|
| 669 | // characteristic and settings of SW_USE_EZGCD and SW_USE_SPARSEMOD, resp. |
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| 670 | // |
---|
| 671 | // Used by gcd() and gcd_poly_univar0(). |
---|
| 672 | // |
---|
| 673 | //}}} |
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[0b6919] | 674 | #if 0 |
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[bfc606] | 675 | int si_factor_reminder=1; |
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[0b6919] | 676 | #endif |
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[b809a8] | 677 | CanonicalForm gcd_poly ( const CanonicalForm & f, const CanonicalForm & g ) |
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[f63dbca] | 678 | { |
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[110718] | 679 | CanonicalForm fc, gc, d1; |
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| 680 | int mp, cc, p1, pe; |
---|
| 681 | mp = f.level()+1; |
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[ed9927] | 682 | bool fc_isUnivariate=f.isUnivariate(); |
---|
| 683 | bool gc_isUnivariate=g.isUnivariate(); |
---|
| 684 | bool fc_and_gc_Univariate=fc_isUnivariate && gc_isUnivariate; |
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[1e6de6] | 685 | #if 1 |
---|
[c30347] | 686 | if (( getCharacteristic() == 0 ) |
---|
| 687 | && (f.level() >4) |
---|
| 688 | && (g.level() >4) |
---|
| 689 | && isOn( SW_USE_CHINREM_GCD) |
---|
[ed9927] | 690 | && (!fc_and_gc_Univariate) |
---|
[c30347] | 691 | && (isPurePoly_m(f)) |
---|
| 692 | && (isPurePoly_m(g)) |
---|
| 693 | ) |
---|
| 694 | { |
---|
| 695 | return chinrem_gcd( f, g ); |
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| 696 | } |
---|
| 697 | #endif |
---|
[ed9927] | 698 | cf_prepgcd( f, g, cc, p1, pe); |
---|
| 699 | if ( cc != 0 ) |
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[110718] | 700 | { |
---|
[ed9927] | 701 | if ( cc > 0 ) |
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[abfc3b] | 702 | { |
---|
[ed9927] | 703 | fc = replacevar( f, Variable(cc), Variable(mp) ); |
---|
| 704 | gc = g; |
---|
[e074407] | 705 | } |
---|
[ed9927] | 706 | else |
---|
[110718] | 707 | { |
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[ed9927] | 708 | fc = replacevar( g, Variable(-cc), Variable(mp) ); |
---|
| 709 | gc = f; |
---|
[110718] | 710 | } |
---|
[ed9927] | 711 | return cf_content( fc, gc ); |
---|
| 712 | } |
---|
| 713 | // now each appearing variable is in f and g |
---|
| 714 | fc = f; |
---|
| 715 | gc = g; |
---|
| 716 | if( gcd_avoid_mtaildegree ( fc, gc, d1 ) ) |
---|
| 717 | return d1; |
---|
| 718 | if ( getCharacteristic() != 0 ) |
---|
| 719 | { |
---|
[e6f7ee1] | 720 | if ((!fc_and_gc_Univariate) |
---|
| 721 | && isOn(SW_USE_fieldGCD) |
---|
[598ff8b] | 722 | && (getCharacteristic() >100)) |
---|
| 723 | { |
---|
[ad8e1b] | 724 | return fieldGCD(f,g); |
---|
[598ff8b] | 725 | } |
---|
[2072126] | 726 | #ifdef HAVE_NTL |
---|
[8ee3839] | 727 | else if ((!fc_and_gc_Univariate) && (isOn( SW_USE_EZGCD_P ))) |
---|
[49f1f45] | 728 | { |
---|
[08daea] | 729 | /*if ( pe == 1 ) |
---|
[c4f4fd] | 730 | fc = fin_ezgcd( fc, gc ); |
---|
| 731 | else if ( pe > 0 )// no variable at position 1 |
---|
| 732 | { |
---|
| 733 | fc = replacevar( fc, Variable(pe), Variable(1) ); |
---|
| 734 | gc = replacevar( gc, Variable(pe), Variable(1) ); |
---|
| 735 | fc = replacevar( fin_ezgcd( fc, gc ), Variable(1), Variable(pe) ); |
---|
| 736 | } |
---|
| 737 | else |
---|
| 738 | { |
---|
| 739 | pe = -pe; |
---|
| 740 | fc = swapvar( fc, Variable(pe), Variable(1) ); |
---|
| 741 | gc = swapvar( gc, Variable(pe), Variable(1) ); |
---|
| 742 | fc = swapvar( fin_ezgcd( fc, gc ), Variable(1), Variable(pe) ); |
---|
[08daea] | 743 | }*/ |
---|
| 744 | fc= EZGCD_P (fc, gc); |
---|
[c30347] | 745 | } |
---|
[2072126] | 746 | #endif |
---|
[ed9927] | 747 | else if (isOn(SW_USE_GCD_P)) |
---|
| 748 | { |
---|
| 749 | fc=newGCD(fc,gc); |
---|
| 750 | } |
---|
[2072126] | 751 | #ifdef HAVE_NTL |
---|
[10af64] | 752 | else if (isOn(SW_USE_FF_MOD_GCD) && !fc_and_gc_Univariate) |
---|
| 753 | { |
---|
| 754 | Variable a; |
---|
| 755 | if (hasFirstAlgVar (fc, a) || hasFirstAlgVar (gc, a)) |
---|
| 756 | { |
---|
| 757 | fc=GCD_Fp_extension (fc, gc, a); |
---|
| 758 | } |
---|
| 759 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
| 760 | { |
---|
| 761 | fc=GCD_GF (fc, gc); |
---|
| 762 | } |
---|
| 763 | fc=GCD_small_p (fc, gc); |
---|
| 764 | } |
---|
[2072126] | 765 | #endif |
---|
[ed9927] | 766 | else if ( p1 == fc.level() ) |
---|
| 767 | fc = gcd_poly_p( fc, gc ); |
---|
| 768 | else |
---|
| 769 | { |
---|
| 770 | fc = replacevar( fc, Variable(p1), Variable(mp) ); |
---|
| 771 | gc = replacevar( gc, Variable(p1), Variable(mp) ); |
---|
| 772 | fc = replacevar( gcd_poly_p( fc, gc ), Variable(mp), Variable(p1) ); |
---|
| 773 | } |
---|
[110718] | 774 | } |
---|
[c30347] | 775 | else if (!fc_and_gc_Univariate) |
---|
[110718] | 776 | { |
---|
[c30347] | 777 | if ( |
---|
| 778 | isOn(SW_USE_CHINREM_GCD) |
---|
[ed9927] | 779 | && (gc.level() >5) |
---|
| 780 | && (fc.level() >5) |
---|
| 781 | && (isPurePoly_m(fc)) && (isPurePoly_m(gc)) |
---|
[c30347] | 782 | ) |
---|
| 783 | { |
---|
[ed9927] | 784 | #if 0 |
---|
| 785 | if ( p1 == fc.level() ) |
---|
| 786 | fc = chinrem_gcd( fc, gc ); |
---|
| 787 | else |
---|
| 788 | { |
---|
| 789 | fc = replacevar( fc, Variable(p1), Variable(mp) ); |
---|
| 790 | gc = replacevar( gc, Variable(p1), Variable(mp) ); |
---|
| 791 | fc = replacevar( chinrem_gcd( fc, gc ), Variable(mp), Variable(p1) ); |
---|
| 792 | } |
---|
| 793 | #else |
---|
| 794 | fc = chinrem_gcd( fc, gc); |
---|
| 795 | #endif |
---|
[c30347] | 796 | } |
---|
[e6f7ee1] | 797 | else if ( isOn( SW_USE_EZGCD ) ) |
---|
[110718] | 798 | { |
---|
[ed9927] | 799 | if ( pe == 1 ) |
---|
| 800 | fc = ezgcd( fc, gc ); |
---|
| 801 | else if ( pe > 0 )// no variable at position 1 |
---|
| 802 | { |
---|
| 803 | fc = replacevar( fc, Variable(pe), Variable(1) ); |
---|
| 804 | gc = replacevar( gc, Variable(pe), Variable(1) ); |
---|
| 805 | fc = replacevar( ezgcd( fc, gc ), Variable(1), Variable(pe) ); |
---|
| 806 | } |
---|
| 807 | else |
---|
| 808 | { |
---|
| 809 | pe = -pe; |
---|
| 810 | fc = swapvar( fc, Variable(pe), Variable(1) ); |
---|
| 811 | gc = swapvar( gc, Variable(pe), Variable(1) ); |
---|
| 812 | fc = swapvar( ezgcd( fc, gc ), Variable(1), Variable(pe) ); |
---|
| 813 | } |
---|
[1b73cc0] | 814 | } |
---|
[110718] | 815 | else if ( |
---|
| 816 | isOn(SW_USE_CHINREM_GCD) |
---|
[ed9927] | 817 | && (isPurePoly_m(fc)) && (isPurePoly_m(gc)) |
---|
[110718] | 818 | ) |
---|
[de1a82] | 819 | { |
---|
[ed9927] | 820 | #if 0 |
---|
| 821 | if ( p1 == fc.level() ) |
---|
| 822 | fc = chinrem_gcd( fc, gc ); |
---|
| 823 | else |
---|
| 824 | { |
---|
| 825 | fc = replacevar( fc, Variable(p1), Variable(mp) ); |
---|
| 826 | gc = replacevar( gc, Variable(p1), Variable(mp) ); |
---|
| 827 | fc = replacevar( chinrem_gcd( fc, gc ), Variable(mp), Variable(p1) ); |
---|
| 828 | } |
---|
| 829 | #else |
---|
| 830 | fc = chinrem_gcd( fc, gc); |
---|
| 831 | #endif |
---|
[f63dbca] | 832 | } |
---|
[c30347] | 833 | else |
---|
| 834 | { |
---|
[ed9927] | 835 | fc = gcd_poly_0( fc, gc ); |
---|
[c30347] | 836 | } |
---|
[110718] | 837 | } |
---|
| 838 | else |
---|
| 839 | { |
---|
| 840 | fc = gcd_poly_0( fc, gc ); |
---|
| 841 | } |
---|
| 842 | if ( d1.degree() > 0 ) |
---|
| 843 | fc *= d1; |
---|
| 844 | return fc; |
---|
[f63dbca] | 845 | } |
---|
[dd3e561] | 846 | //}}} |
---|
[93b061] | 847 | |
---|
[dd3e561] | 848 | //{{{ static CanonicalForm cf_content ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 849 | //{{{ docu |
---|
| 850 | // |
---|
| 851 | // cf_content() - return gcd(g, content(f)). |
---|
| 852 | // |
---|
| 853 | // content(f) is calculated with respect to f's main variable. |
---|
| 854 | // |
---|
| 855 | // Used by gcd(), content(), content( CF, Variable ). |
---|
| 856 | // |
---|
| 857 | //}}} |
---|
[9bab9f] | 858 | static CanonicalForm |
---|
| 859 | cf_content ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 860 | { |
---|
[6f62c3] | 861 | if ( f.inPolyDomain() || ( f.inExtension() && ! getReduce( f.mvar() ) ) ) |
---|
| 862 | { |
---|
[150dc8] | 863 | CFIterator i = f; |
---|
| 864 | CanonicalForm result = g; |
---|
[6f62c3] | 865 | while ( i.hasTerms() && ! result.isOne() ) |
---|
| 866 | { |
---|
[a7ec94] | 867 | result = gcd( i.coeff(), result ); |
---|
[150dc8] | 868 | i++; |
---|
| 869 | } |
---|
| 870 | return result; |
---|
[9bab9f] | 871 | } |
---|
| 872 | else |
---|
[a7ec94] | 873 | return abs( f ); |
---|
[9bab9f] | 874 | } |
---|
[dd3e561] | 875 | //}}} |
---|
[9bab9f] | 876 | |
---|
[4ea0ab] | 877 | //{{{ CanonicalForm content ( const CanonicalForm & f ) |
---|
| 878 | //{{{ docu |
---|
| 879 | // |
---|
| 880 | // content() - return content(f) with respect to main variable. |
---|
| 881 | // |
---|
[dd3e561] | 882 | // Normalizes result. |
---|
| 883 | // |
---|
[4ea0ab] | 884 | //}}} |
---|
[9bab9f] | 885 | CanonicalForm |
---|
| 886 | content ( const CanonicalForm & f ) |
---|
| 887 | { |
---|
[6f62c3] | 888 | if ( f.inPolyDomain() || ( f.inExtension() && ! getReduce( f.mvar() ) ) ) |
---|
| 889 | { |
---|
[a7ec94] | 890 | CFIterator i = f; |
---|
| 891 | CanonicalForm result = abs( i.coeff() ); |
---|
| 892 | i++; |
---|
[6f62c3] | 893 | while ( i.hasTerms() && ! result.isOne() ) |
---|
| 894 | { |
---|
[a7ec94] | 895 | result = gcd( i.coeff(), result ); |
---|
| 896 | i++; |
---|
| 897 | } |
---|
| 898 | return result; |
---|
| 899 | } |
---|
| 900 | else |
---|
| 901 | return abs( f ); |
---|
[9bab9f] | 902 | } |
---|
[4ea0ab] | 903 | //}}} |
---|
[9bab9f] | 904 | |
---|
[dd3e561] | 905 | //{{{ CanonicalForm content ( const CanonicalForm & f, const Variable & x ) |
---|
| 906 | //{{{ docu |
---|
| 907 | // |
---|
| 908 | // content() - return content(f) with respect to x. |
---|
| 909 | // |
---|
| 910 | // x should be a polynomial variable. |
---|
| 911 | // |
---|
| 912 | //}}} |
---|
[9bab9f] | 913 | CanonicalForm |
---|
| 914 | content ( const CanonicalForm & f, const Variable & x ) |
---|
| 915 | { |
---|
[dd3e561] | 916 | ASSERT( x.level() > 0, "cannot calculate content with respect to algebraic variable" ); |
---|
| 917 | Variable y = f.mvar(); |
---|
| 918 | |
---|
| 919 | if ( y == x ) |
---|
[150dc8] | 920 | return cf_content( f, 0 ); |
---|
[dd3e561] | 921 | else if ( y < x ) |
---|
[150dc8] | 922 | return f; |
---|
[9bab9f] | 923 | else |
---|
[150dc8] | 924 | return swapvar( content( swapvar( f, y, x ), y ), y, x ); |
---|
[9bab9f] | 925 | } |
---|
[dd3e561] | 926 | //}}} |
---|
[9bab9f] | 927 | |
---|
[dd3e561] | 928 | //{{{ CanonicalForm vcontent ( const CanonicalForm & f, const Variable & x ) |
---|
| 929 | //{{{ docu |
---|
| 930 | // |
---|
| 931 | // vcontent() - return content of f with repect to variables >= x. |
---|
| 932 | // |
---|
| 933 | // The content is recursively calculated over all coefficients in |
---|
| 934 | // f having level less than x. x should be a polynomial |
---|
| 935 | // variable. |
---|
| 936 | // |
---|
| 937 | //}}} |
---|
[9bab9f] | 938 | CanonicalForm |
---|
| 939 | vcontent ( const CanonicalForm & f, const Variable & x ) |
---|
| 940 | { |
---|
[dd3e561] | 941 | ASSERT( x.level() > 0, "cannot calculate vcontent with respect to algebraic variable" ); |
---|
| 942 | |
---|
[9bab9f] | 943 | if ( f.mvar() <= x ) |
---|
[150dc8] | 944 | return content( f, x ); |
---|
[9bab9f] | 945 | else { |
---|
[150dc8] | 946 | CFIterator i; |
---|
| 947 | CanonicalForm d = 0; |
---|
| 948 | for ( i = f; i.hasTerms() && ! d.isOne(); i++ ) |
---|
| 949 | d = gcd( d, vcontent( i.coeff(), x ) ); |
---|
| 950 | return d; |
---|
[9bab9f] | 951 | } |
---|
| 952 | } |
---|
[dd3e561] | 953 | //}}} |
---|
[9bab9f] | 954 | |
---|
[4ea0ab] | 955 | //{{{ CanonicalForm pp ( const CanonicalForm & f ) |
---|
| 956 | //{{{ docu |
---|
| 957 | // |
---|
| 958 | // pp() - return primitive part of f. |
---|
| 959 | // |
---|
[dd3e561] | 960 | // Returns zero if f equals zero, otherwise f / content(f). |
---|
| 961 | // |
---|
[4ea0ab] | 962 | //}}} |
---|
[9bab9f] | 963 | CanonicalForm |
---|
| 964 | pp ( const CanonicalForm & f ) |
---|
| 965 | { |
---|
| 966 | if ( f.isZero() ) |
---|
[150dc8] | 967 | return f; |
---|
[9bab9f] | 968 | else |
---|
[150dc8] | 969 | return f / content( f ); |
---|
[9bab9f] | 970 | } |
---|
[4ea0ab] | 971 | //}}} |
---|
[9bab9f] | 972 | |
---|
[ff6222] | 973 | CanonicalForm |
---|
[9bab9f] | 974 | gcd ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 975 | { |
---|
[a7ec94] | 976 | bool b = f.isZero(); |
---|
| 977 | if ( b || g.isZero() ) |
---|
| 978 | { |
---|
| 979 | if ( b ) |
---|
| 980 | return abs( g ); |
---|
[abfc3b] | 981 | else |
---|
[a7ec94] | 982 | return abs( f ); |
---|
| 983 | } |
---|
| 984 | if ( f.inPolyDomain() || g.inPolyDomain() ) |
---|
| 985 | { |
---|
| 986 | if ( f.mvar() != g.mvar() ) |
---|
| 987 | { |
---|
| 988 | if ( f.mvar() > g.mvar() ) |
---|
| 989 | return cf_content( f, g ); |
---|
| 990 | else |
---|
| 991 | return cf_content( g, f ); |
---|
| 992 | } |
---|
[bb82f0] | 993 | if (isOn(SW_USE_QGCD)) |
---|
| 994 | { |
---|
| 995 | Variable m; |
---|
[fc9f44] | 996 | if ( |
---|
| 997 | (getCharacteristic() == 0) && |
---|
[e6f7ee1] | 998 | (hasFirstAlgVar(f,m) || hasFirstAlgVar(g,m)) |
---|
[bb82f0] | 999 | ) |
---|
[fc31bce] | 1000 | { |
---|
[713bdb] | 1001 | bool on_rational = isOn(SW_RATIONAL); |
---|
| 1002 | CanonicalForm r=QGCD(f,g); |
---|
[f06059] | 1003 | On(SW_RATIONAL); |
---|
[713bdb] | 1004 | CanonicalForm cdF = bCommonDen( r ); |
---|
| 1005 | if (!on_rational) Off(SW_RATIONAL); |
---|
| 1006 | return cdF*r; |
---|
[fc31bce] | 1007 | } |
---|
[bb82f0] | 1008 | } |
---|
[713bdb] | 1009 | |
---|
[150dc8] | 1010 | if ( f.inExtension() && getReduce( f.mvar() ) ) |
---|
[bb82f0] | 1011 | return CanonicalForm(1); |
---|
[a7ec94] | 1012 | else |
---|
| 1013 | { |
---|
[ebc602] | 1014 | if ( fdivides( f, g ) ) |
---|
[a7ec94] | 1015 | return abs( f ); |
---|
[ebc602] | 1016 | else if ( fdivides( g, f ) ) |
---|
[a7ec94] | 1017 | return abs( g ); |
---|
| 1018 | if ( !( getCharacteristic() == 0 && isOn( SW_RATIONAL ) ) ) |
---|
| 1019 | { |
---|
| 1020 | CanonicalForm d; |
---|
[64a501] | 1021 | d = gcd_poly( f, g ); |
---|
[a7ec94] | 1022 | return abs( d ); |
---|
| 1023 | } |
---|
| 1024 | else |
---|
| 1025 | { |
---|
[150dc8] | 1026 | CanonicalForm cdF = bCommonDen( f ); |
---|
| 1027 | CanonicalForm cdG = bCommonDen( g ); |
---|
| 1028 | Off( SW_RATIONAL ); |
---|
| 1029 | CanonicalForm l = lcm( cdF, cdG ); |
---|
| 1030 | On( SW_RATIONAL ); |
---|
| 1031 | CanonicalForm F = f * l, G = g * l; |
---|
| 1032 | Off( SW_RATIONAL ); |
---|
[64a501] | 1033 | l = gcd_poly( F, G ); |
---|
[150dc8] | 1034 | On( SW_RATIONAL ); |
---|
[a7ec94] | 1035 | return abs( l ); |
---|
[150dc8] | 1036 | } |
---|
| 1037 | } |
---|
[a7ec94] | 1038 | } |
---|
| 1039 | if ( f.inBaseDomain() && g.inBaseDomain() ) |
---|
| 1040 | return bgcd( f, g ); |
---|
[9bab9f] | 1041 | else |
---|
[a7ec94] | 1042 | return 1; |
---|
[9bab9f] | 1043 | } |
---|
| 1044 | |
---|
[dd3e561] | 1045 | //{{{ CanonicalForm lcm ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 1046 | //{{{ docu |
---|
| 1047 | // |
---|
| 1048 | // lcm() - return least common multiple of f and g. |
---|
| 1049 | // |
---|
| 1050 | // The lcm is calculated using the formula lcm(f, g) = f * g / gcd(f, g). |
---|
| 1051 | // |
---|
| 1052 | // Returns zero if one of f or g equals zero. |
---|
| 1053 | // |
---|
| 1054 | //}}} |
---|
[9bab9f] | 1055 | CanonicalForm |
---|
| 1056 | lcm ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 1057 | { |
---|
[dd3e561] | 1058 | if ( f.isZero() || g.isZero() ) |
---|
[a7ec94] | 1059 | return 0; |
---|
[dd3e561] | 1060 | else |
---|
[150dc8] | 1061 | return ( f / gcd( f, g ) ) * g; |
---|
[9bab9f] | 1062 | } |
---|
[dd3e561] | 1063 | //}}} |
---|
[a7ec94] | 1064 | |
---|
| 1065 | #ifdef HAVE_NTL |
---|
| 1066 | |
---|
| 1067 | static CanonicalForm |
---|
| 1068 | gcd_univar_ntl0( const CanonicalForm & F, const CanonicalForm & G ) |
---|
| 1069 | { |
---|
| 1070 | ZZX F1=convertFacCF2NTLZZX(F); |
---|
| 1071 | ZZX G1=convertFacCF2NTLZZX(G); |
---|
| 1072 | ZZX R=GCD(F1,G1); |
---|
| 1073 | return convertNTLZZX2CF(R,F.mvar()); |
---|
| 1074 | } |
---|
| 1075 | |
---|
[c4f4fd] | 1076 | static CanonicalForm |
---|
| 1077 | gcd_univar_ntlp( const CanonicalForm & F, const CanonicalForm & G ) |
---|
| 1078 | { |
---|
| 1079 | if (fac_NTL_char!=getCharacteristic()) |
---|
| 1080 | { |
---|
| 1081 | fac_NTL_char=getCharacteristic(); |
---|
| 1082 | #ifdef NTL_ZZ |
---|
| 1083 | ZZ r; |
---|
| 1084 | r=getCharacteristic(); |
---|
| 1085 | ZZ_pContext ccc(r); |
---|
| 1086 | #else |
---|
| 1087 | zz_pContext ccc(getCharacteristic()); |
---|
| 1088 | #endif |
---|
| 1089 | ccc.restore(); |
---|
| 1090 | #ifdef NTL_ZZ |
---|
| 1091 | ZZ_p::init(r); |
---|
| 1092 | #else |
---|
| 1093 | zz_p::init(getCharacteristic()); |
---|
| 1094 | #endif |
---|
| 1095 | } |
---|
| 1096 | #ifdef NTL_ZZ |
---|
| 1097 | ZZ_pX F1=convertFacCF2NTLZZpX(F); |
---|
| 1098 | ZZ_pX G1=convertFacCF2NTLZZpX(G); |
---|
| 1099 | ZZ_pX R=GCD(F1,G1); |
---|
| 1100 | return convertNTLZZpX2CF(R,F.mvar()); |
---|
| 1101 | #else |
---|
| 1102 | zz_pX F1=convertFacCF2NTLzzpX(F); |
---|
| 1103 | zz_pX G1=convertFacCF2NTLzzpX(G); |
---|
| 1104 | zz_pX R=GCD(F1,G1); |
---|
| 1105 | return convertNTLzzpX2CF(R,F.mvar()); |
---|
| 1106 | #endif |
---|
| 1107 | } |
---|
| 1108 | |
---|
[a7ec94] | 1109 | #endif |
---|
| 1110 | |
---|
| 1111 | static bool |
---|
| 1112 | gcd_avoid_mtaildegree ( CanonicalForm & f1, CanonicalForm & g1, CanonicalForm & d1 ) |
---|
| 1113 | { |
---|
| 1114 | bool rdy = true; |
---|
| 1115 | int df = f1.taildegree(); |
---|
| 1116 | int dg = g1.taildegree(); |
---|
| 1117 | |
---|
| 1118 | d1 = d1.genOne(); |
---|
| 1119 | if ( dg == 0 ) |
---|
| 1120 | { |
---|
| 1121 | if ( df == 0 ) |
---|
| 1122 | return false; |
---|
| 1123 | else |
---|
| 1124 | { |
---|
| 1125 | if ( f1.degree() == df ) |
---|
| 1126 | d1 = cf_content( g1, LC( f1 ) ); |
---|
| 1127 | else |
---|
| 1128 | { |
---|
| 1129 | f1 /= power( f1.mvar(), df ); |
---|
| 1130 | rdy = false; |
---|
| 1131 | } |
---|
| 1132 | } |
---|
| 1133 | } |
---|
| 1134 | else |
---|
| 1135 | { |
---|
| 1136 | if ( df == 0) |
---|
| 1137 | { |
---|
| 1138 | if ( g1.degree() == dg ) |
---|
| 1139 | d1 = cf_content( f1, LC( g1 ) ); |
---|
| 1140 | else |
---|
| 1141 | { |
---|
| 1142 | g1 /= power( g1.mvar(), dg ); |
---|
| 1143 | rdy = false; |
---|
| 1144 | } |
---|
| 1145 | } |
---|
| 1146 | else |
---|
| 1147 | { |
---|
| 1148 | if ( df > dg ) |
---|
| 1149 | d1 = power( f1.mvar(), dg ); |
---|
| 1150 | else |
---|
| 1151 | d1 = power( f1.mvar(), df ); |
---|
| 1152 | if ( f1.degree() == df ) |
---|
| 1153 | { |
---|
| 1154 | if (g1.degree() == dg) |
---|
| 1155 | d1 *= gcd( LC( f1 ), LC( g1 ) ); |
---|
| 1156 | else |
---|
| 1157 | { |
---|
| 1158 | g1 /= power( g1.mvar(), dg); |
---|
| 1159 | d1 *= cf_content( g1, LC( f1 ) ); |
---|
| 1160 | } |
---|
| 1161 | } |
---|
| 1162 | else |
---|
| 1163 | { |
---|
| 1164 | f1 /= power( f1.mvar(), df ); |
---|
| 1165 | if ( g1.degree() == dg ) |
---|
| 1166 | d1 *= cf_content( f1, LC( g1 ) ); |
---|
| 1167 | else |
---|
| 1168 | { |
---|
| 1169 | g1 /= power( g1.mvar(), dg ); |
---|
| 1170 | rdy = false; |
---|
| 1171 | } |
---|
| 1172 | } |
---|
| 1173 | } |
---|
| 1174 | } |
---|
| 1175 | return rdy; |
---|
| 1176 | } |
---|
| 1177 | |
---|
| 1178 | /* |
---|
| 1179 | * compute positions p1 and pe of optimal variables: |
---|
| 1180 | * pe is used in "ezgcd" and |
---|
| 1181 | * p1 in "gcd_poly1" |
---|
| 1182 | */ |
---|
| 1183 | static |
---|
| 1184 | void optvalues ( const int * df, const int * dg, const int n, int & p1, int &pe ) |
---|
| 1185 | { |
---|
| 1186 | int i, o1, oe; |
---|
| 1187 | if ( df[n] > dg[n] ) |
---|
| 1188 | { |
---|
| 1189 | o1 = df[n]; oe = dg[n]; |
---|
| 1190 | } |
---|
| 1191 | else |
---|
| 1192 | { |
---|
| 1193 | o1 = dg[n]; oe = df[n]; |
---|
| 1194 | } |
---|
| 1195 | i = n-1; |
---|
| 1196 | while ( i > 0 ) |
---|
| 1197 | { |
---|
| 1198 | if ( df[i] != 0 ) |
---|
| 1199 | { |
---|
| 1200 | if ( df[i] > dg[i] ) |
---|
| 1201 | { |
---|
| 1202 | if ( o1 > df[i]) { o1 = df[i]; p1 = i; } |
---|
| 1203 | if ( oe <= dg[i]) { oe = dg[i]; pe = i; } |
---|
| 1204 | } |
---|
| 1205 | else |
---|
| 1206 | { |
---|
| 1207 | if ( o1 > dg[i]) { o1 = dg[i]; p1 = i; } |
---|
| 1208 | if ( oe <= df[i]) { oe = df[i]; pe = i; } |
---|
| 1209 | } |
---|
| 1210 | } |
---|
| 1211 | i--; |
---|
| 1212 | } |
---|
| 1213 | } |
---|
| 1214 | |
---|
| 1215 | /* |
---|
| 1216 | * make some changes of variables, see optvalues |
---|
| 1217 | */ |
---|
| 1218 | static void |
---|
| 1219 | cf_prepgcd( const CanonicalForm & f, const CanonicalForm & g, int & cc, int & p1, int &pe ) |
---|
| 1220 | { |
---|
| 1221 | int i, k, n; |
---|
| 1222 | n = f.level(); |
---|
| 1223 | cc = 0; |
---|
| 1224 | p1 = pe = n; |
---|
| 1225 | if ( n == 1 ) |
---|
| 1226 | return; |
---|
| 1227 | int * degsf = new int[n+1]; |
---|
| 1228 | int * degsg = new int[n+1]; |
---|
| 1229 | for ( i = n; i > 0; i-- ) |
---|
| 1230 | { |
---|
| 1231 | degsf[i] = degsg[i] = 0; |
---|
| 1232 | } |
---|
| 1233 | degsf = degrees( f, degsf ); |
---|
| 1234 | degsg = degrees( g, degsg ); |
---|
| 1235 | |
---|
| 1236 | k = 0; |
---|
| 1237 | for ( i = n-1; i > 0; i-- ) |
---|
| 1238 | { |
---|
[f4b180] | 1239 | if ( degsf[i] == 0 ) |
---|
[a7ec94] | 1240 | { |
---|
| 1241 | if ( degsg[i] != 0 ) |
---|
| 1242 | { |
---|
| 1243 | cc = -i; |
---|
| 1244 | break; |
---|
| 1245 | } |
---|
| 1246 | } |
---|
| 1247 | else |
---|
| 1248 | { |
---|
| 1249 | if ( degsg[i] == 0 ) |
---|
| 1250 | { |
---|
| 1251 | cc = i; |
---|
| 1252 | break; |
---|
| 1253 | } |
---|
| 1254 | else k++; |
---|
| 1255 | } |
---|
| 1256 | } |
---|
| 1257 | |
---|
| 1258 | if ( ( cc == 0 ) && ( k != 0 ) ) |
---|
| 1259 | optvalues( degsf, degsg, n, p1, pe ); |
---|
| 1260 | if ( ( pe != 1 ) && ( degsf[1] != 0 ) ) |
---|
| 1261 | pe = -pe; |
---|
[f4b180] | 1262 | |
---|
[a7ec94] | 1263 | delete [] degsf; |
---|
| 1264 | delete [] degsg; |
---|
| 1265 | } |
---|
[6f62c3] | 1266 | |
---|
| 1267 | |
---|
| 1268 | static CanonicalForm |
---|
| 1269 | balance_p ( const CanonicalForm & f, const CanonicalForm & q ) |
---|
| 1270 | { |
---|
| 1271 | Variable x = f.mvar(); |
---|
| 1272 | CanonicalForm result = 0, qh = q / 2; |
---|
| 1273 | CanonicalForm c; |
---|
| 1274 | CFIterator i; |
---|
| 1275 | for ( i = f; i.hasTerms(); i++ ) |
---|
| 1276 | { |
---|
| 1277 | c = i.coeff(); |
---|
| 1278 | if ( c.inCoeffDomain()) |
---|
| 1279 | { |
---|
| 1280 | if ( c > qh ) |
---|
| 1281 | result += power( x, i.exp() ) * (c - q); |
---|
| 1282 | else |
---|
| 1283 | result += power( x, i.exp() ) * c; |
---|
| 1284 | } |
---|
[f4b180] | 1285 | else |
---|
[6f62c3] | 1286 | result += power( x, i.exp() ) * balance_p(c,q); |
---|
| 1287 | } |
---|
| 1288 | return result; |
---|
| 1289 | } |
---|
| 1290 | |
---|
| 1291 | CanonicalForm chinrem_gcd ( const CanonicalForm & FF, const CanonicalForm & GG ) |
---|
| 1292 | { |
---|
[01e8874] | 1293 | CanonicalForm f, g, cg, cl, q(0), Dp, newD, D, newq; |
---|
[c1b9927] | 1294 | int p, i, dp_deg, d_deg=-1; |
---|
[6f62c3] | 1295 | |
---|
[01e8874] | 1296 | CanonicalForm cd ( bCommonDen( FF )); |
---|
[6f62c3] | 1297 | f=cd*FF; |
---|
| 1298 | f /=vcontent(f,Variable(1)); |
---|
[08a6ebb] | 1299 | //cd = bCommonDen( f ); f *=cd; |
---|
| 1300 | //f /=vcontent(f,Variable(1)); |
---|
[6f62c3] | 1301 | |
---|
| 1302 | cd = bCommonDen( GG ); |
---|
| 1303 | g=cd*GG; |
---|
| 1304 | g /=vcontent(g,Variable(1)); |
---|
[08a6ebb] | 1305 | //cd = bCommonDen( g ); g *=cd; |
---|
| 1306 | //g /=vcontent(g,Variable(1)); |
---|
[6f62c3] | 1307 | |
---|
| 1308 | i = cf_getNumBigPrimes() - 1; |
---|
| 1309 | cl = f.lc()* g.lc(); |
---|
| 1310 | |
---|
| 1311 | while ( true ) |
---|
| 1312 | { |
---|
| 1313 | p = cf_getBigPrime( i ); |
---|
| 1314 | i--; |
---|
| 1315 | while ( i >= 0 && mod( cl, p ) == 0 ) |
---|
| 1316 | { |
---|
| 1317 | p = cf_getBigPrime( i ); |
---|
| 1318 | i--; |
---|
| 1319 | } |
---|
[c30347] | 1320 | //printf("try p=%d\n",p); |
---|
[6f62c3] | 1321 | setCharacteristic( p ); |
---|
[c30347] | 1322 | Dp = gcd_poly( mapinto( f ), mapinto( g ) ); |
---|
[08a6ebb] | 1323 | Dp /=Dp.lc(); |
---|
[6f62c3] | 1324 | setCharacteristic( 0 ); |
---|
| 1325 | dp_deg=totaldegree(Dp); |
---|
| 1326 | if ( dp_deg == 0 ) |
---|
[c30347] | 1327 | { |
---|
| 1328 | //printf(" -> 1\n"); |
---|
[6f62c3] | 1329 | return CanonicalForm(1); |
---|
[c30347] | 1330 | } |
---|
[6f62c3] | 1331 | if ( q.isZero() ) |
---|
| 1332 | { |
---|
| 1333 | D = mapinto( Dp ); |
---|
| 1334 | d_deg=dp_deg; |
---|
| 1335 | q = p; |
---|
| 1336 | } |
---|
| 1337 | else |
---|
| 1338 | { |
---|
| 1339 | if ( dp_deg == d_deg ) |
---|
| 1340 | { |
---|
| 1341 | chineseRemainder( D, q, mapinto( Dp ), p, newD, newq ); |
---|
| 1342 | q = newq; |
---|
| 1343 | D = newD; |
---|
| 1344 | } |
---|
[f4b180] | 1345 | else if ( dp_deg < d_deg ) |
---|
[6f62c3] | 1346 | { |
---|
[c30347] | 1347 | //printf(" were all bad, try more\n"); |
---|
[6f62c3] | 1348 | // all previous p's are bad primes |
---|
| 1349 | q = p; |
---|
| 1350 | D = mapinto( Dp ); |
---|
| 1351 | d_deg=dp_deg; |
---|
| 1352 | } |
---|
[c30347] | 1353 | else |
---|
| 1354 | { |
---|
| 1355 | //printf(" was bad, try more\n"); |
---|
| 1356 | } |
---|
[f4b180] | 1357 | //else dp_deg > d_deg: bad prime |
---|
[6f62c3] | 1358 | } |
---|
[08a6ebb] | 1359 | if ( i >= 0 ) |
---|
[6f62c3] | 1360 | { |
---|
[c992ec1] | 1361 | CanonicalForm Dn= Farey(D,q); |
---|
| 1362 | int is_rat=isOn(SW_RATIONAL); |
---|
| 1363 | On(SW_RATIONAL); |
---|
| 1364 | CanonicalForm cd = bCommonDen( Dn ); // we need On(SW_RATIONAL) |
---|
| 1365 | if (!is_rat) Off(SW_RATIONAL); |
---|
| 1366 | Dn *=cd; |
---|
| 1367 | //Dn /=vcontent(Dn,Variable(1)); |
---|
| 1368 | if ( fdivides( Dn, f ) && fdivides( Dn, g ) ) |
---|
[6f62c3] | 1369 | { |
---|
[c30347] | 1370 | //printf(" -> success\n"); |
---|
[c992ec1] | 1371 | return Dn; |
---|
[6f62c3] | 1372 | } |
---|
[c992ec1] | 1373 | //else: try more primes |
---|
[6f62c3] | 1374 | } |
---|
| 1375 | else |
---|
[c992ec1] | 1376 | { // try other method |
---|
[c30347] | 1377 | //printf("try other gcd\n"); |
---|
[6f62c3] | 1378 | Off(SW_USE_CHINREM_GCD); |
---|
| 1379 | D=gcd_poly( f, g ); |
---|
| 1380 | On(SW_USE_CHINREM_GCD); |
---|
| 1381 | return D; |
---|
| 1382 | } |
---|
| 1383 | } |
---|
| 1384 | } |
---|
[c5d0aed] | 1385 | |
---|