[493c477] | 1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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[ad8e1b] | 2 | /* $Id: cf_gcd.cc,v 1.65 2008-08-06 13:53:15 Singular Exp $ */ |
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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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[f63dbca] | 15 | #include "fac_util.h" |
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[71da5e] | 16 | #include "ftmpl_functions.h" |
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[49f1f45] | 17 | #include "ffreval.h" |
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[bb82f0] | 18 | #include "algext.h" |
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[598ff8b] | 19 | #include "fieldGCD.h" |
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[edb4893] | 20 | |
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[f11d7b] | 21 | #ifdef HAVE_NTL |
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[034eec] | 22 | #include <NTL/ZZX.h> |
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[f11d7b] | 23 | #include "NTLconvert.h" |
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[a7ec94] | 24 | bool isPurePoly(const CanonicalForm & ); |
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| 25 | static CanonicalForm gcd_univar_ntl0( const CanonicalForm &, const CanonicalForm & ); |
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| 26 | static CanonicalForm gcd_univar_ntlp( const CanonicalForm &, const CanonicalForm & ); |
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[f11d7b] | 27 | #endif |
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| 28 | |
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[a7ec94] | 29 | static CanonicalForm cf_content ( const CanonicalForm &, const CanonicalForm & ); |
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| 30 | static bool gcd_avoid_mtaildegree ( CanonicalForm &, CanonicalForm &, CanonicalForm & ); |
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| 31 | static void cf_prepgcd( const CanonicalForm &, const CanonicalForm &, int &, int &, int & ); |
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[edb4893] | 32 | |
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[6f62c3] | 33 | void out_cf(char *s1,const CanonicalForm &f,char *s2); |
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| 34 | |
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[110718] | 35 | CanonicalForm chinrem_gcd(const CanonicalForm & FF,const CanonicalForm & GG); |
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| 36 | CanonicalForm newGCD(CanonicalForm A, CanonicalForm B); |
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[f4b180] | 37 | |
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[f63dbca] | 38 | bool |
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| 39 | gcd_test_one ( const CanonicalForm & f, const CanonicalForm & g, bool swap ) |
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[9bab9f] | 40 | { |
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| 41 | int count = 0; |
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| 42 | // assume polys have same level; |
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| 43 | CFRandom * sample = CFRandomFactory::generate(); |
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[f63dbca] | 44 | REvaluation e( 2, tmax( f.level(), g.level() ), *sample ); |
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[9bab9f] | 45 | delete sample; |
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[f63dbca] | 46 | CanonicalForm lcf, lcg; |
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[6f62c3] | 47 | if ( swap ) |
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| 48 | { |
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[150dc8] | 49 | lcf = swapvar( LC( f ), Variable(1), f.mvar() ); |
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| 50 | lcg = swapvar( LC( g ), Variable(1), f.mvar() ); |
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[f63dbca] | 51 | } |
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[6f62c3] | 52 | else |
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| 53 | { |
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[150dc8] | 54 | lcf = LC( f, Variable(1) ); |
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| 55 | lcg = LC( g, Variable(1) ); |
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[f63dbca] | 56 | } |
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[df497a] | 57 | #define TEST_ONE_MAX 50 |
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| 58 | while ( ( e( lcf ).isZero() || e( lcg ).isZero() ) && count < TEST_ONE_MAX ) |
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| 59 | { |
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[150dc8] | 60 | e.nextpoint(); |
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| 61 | count++; |
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[9bab9f] | 62 | } |
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[df497a] | 63 | if ( count == TEST_ONE_MAX ) |
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[150dc8] | 64 | return false; |
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[f63dbca] | 65 | CanonicalForm F, G; |
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[6f62c3] | 66 | if ( swap ) |
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| 67 | { |
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[150dc8] | 68 | F=swapvar( f, Variable(1), f.mvar() ); |
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| 69 | G=swapvar( g, Variable(1), g.mvar() ); |
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[f63dbca] | 70 | } |
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[6f62c3] | 71 | else |
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| 72 | { |
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[150dc8] | 73 | F = f; |
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| 74 | G = g; |
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[f63dbca] | 75 | } |
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[9bab9f] | 76 | if ( e(F).taildegree() > 0 && e(G).taildegree() > 0 ) |
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[150dc8] | 77 | return false; |
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[9bab9f] | 78 | return gcd( e( F ), e( G ) ).degree() < 1; |
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| 79 | } |
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| 80 | |
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[dd3e561] | 81 | //{{{ static CanonicalForm icontent ( const CanonicalForm & f, const CanonicalForm & c ) |
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| 82 | //{{{ docu |
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| 83 | // |
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| 84 | // icontent() - return gcd of c and all coefficients of f which |
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| 85 | // are in a coefficient domain. |
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| 86 | // |
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| 87 | // Used by icontent(). |
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| 88 | // |
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| 89 | //}}} |
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[9bab9f] | 90 | static CanonicalForm |
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| 91 | icontent ( const CanonicalForm & f, const CanonicalForm & c ) |
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| 92 | { |
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[c30347] | 93 | if ( f.inBaseDomain() ) |
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| 94 | { |
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| 95 | if (c.isZero()) return abs(f); |
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| 96 | return bgcd( f, c ); |
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| 97 | } |
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[ef20c7] | 98 | //else if ( f.inCoeffDomain() ) |
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| 99 | // return gcd(f,c); |
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[c30347] | 100 | else |
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| 101 | { |
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[150dc8] | 102 | CanonicalForm g = c; |
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| 103 | for ( CFIterator i = f; i.hasTerms() && ! g.isOne(); i++ ) |
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| 104 | g = icontent( i.coeff(), g ); |
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| 105 | return g; |
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[9bab9f] | 106 | } |
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| 107 | } |
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[dd3e561] | 108 | //}}} |
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[9bab9f] | 109 | |
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[dd3e561] | 110 | //{{{ CanonicalForm icontent ( const CanonicalForm & f ) |
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| 111 | //{{{ docu |
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| 112 | // |
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| 113 | // icontent() - return gcd over all coefficients of f which are |
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| 114 | // in a coefficient domain. |
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| 115 | // |
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| 116 | //}}} |
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[9bab9f] | 117 | CanonicalForm |
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| 118 | icontent ( const CanonicalForm & f ) |
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| 119 | { |
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| 120 | return icontent( f, 0 ); |
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| 121 | } |
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[dd3e561] | 122 | //}}} |
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[9bab9f] | 123 | |
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[dd3e561] | 124 | //{{{ CanonicalForm extgcd ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & a, CanonicalForm & b ) |
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| 125 | //{{{ docu |
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| 126 | // |
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| 127 | // extgcd() - returns polynomial extended gcd of f and g. |
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| 128 | // |
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| 129 | // Returns gcd(f, g) and a and b sucht that f*a+g*b=gcd(f, g). |
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| 130 | // The gcd is calculated using an extended euclidean polynomial |
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| 131 | // remainder sequence, so f and g should be polynomials over an |
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| 132 | // euclidean domain. Normalizes result. |
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| 133 | // |
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| 134 | // Note: be sure that f and g have the same level! |
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| 135 | // |
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| 136 | //}}} |
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[9bab9f] | 137 | CanonicalForm |
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| 138 | extgcd ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & a, CanonicalForm & b ) |
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| 139 | { |
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[034eec] | 140 | #ifdef HAVE_NTL |
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[2667bc8] | 141 | if (isOn(SW_USE_NTL_GCD_P) && ( getCharacteristic() > 0 ) |
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[034eec] | 142 | && isPurePoly(f) && isPurePoly(g)) |
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| 143 | { |
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[c6eecb] | 144 | if (fac_NTL_char!=getCharacteristic()) |
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| 145 | { |
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| 146 | fac_NTL_char=getCharacteristic(); |
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| 147 | #ifdef NTL_ZZ |
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| 148 | ZZ r; |
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| 149 | r=getCharacteristic(); |
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| 150 | ZZ_pContext ccc(r); |
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| 151 | #else |
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| 152 | zz_pContext ccc(getCharacteristic()); |
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| 153 | #endif |
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| 154 | ccc.restore(); |
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| 155 | #ifdef NTL_ZZ |
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| 156 | ZZ_p::init(r); |
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| 157 | #else |
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| 158 | zz_p::init(getCharacteristic()); |
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| 159 | #endif |
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| 160 | } |
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| 161 | #ifdef NTL_ZZ |
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| 162 | ZZ_pX F1=convertFacCF2NTLZZpX(f); |
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| 163 | ZZ_pX G1=convertFacCF2NTLZZpX(g); |
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| 164 | ZZ_pX R; |
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| 165 | ZZ_pX A,B; |
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| 166 | XGCD(R,A,B,F1,G1); |
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| 167 | a=convertNTLZZpX2CF(A,f.mvar()); |
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| 168 | b=convertNTLZZpX2CF(B,f.mvar()); |
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| 169 | return convertNTLZZpX2CF(R,f.mvar()); |
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| 170 | #else |
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[034eec] | 171 | zz_pX F1=convertFacCF2NTLzzpX(f); |
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| 172 | zz_pX G1=convertFacCF2NTLzzpX(g); |
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| 173 | zz_pX R; |
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| 174 | zz_pX A,B; |
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| 175 | XGCD(R,A,B,F1,G1); |
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| 176 | a=convertNTLzzpX2CF(A,f.mvar()); |
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| 177 | b=convertNTLzzpX2CF(B,f.mvar()); |
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| 178 | return convertNTLzzpX2CF(R,f.mvar()); |
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[c6eecb] | 179 | #endif |
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[034eec] | 180 | } |
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| 181 | #endif |
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| 182 | CanonicalForm contf = content( f ); |
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| 183 | CanonicalForm contg = content( g ); |
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[9bab9f] | 184 | |
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[034eec] | 185 | CanonicalForm p0 = f / contf, p1 = g / contg; |
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| 186 | CanonicalForm f0 = 1, f1 = 0, g0 = 0, g1 = 1, q, r; |
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[9bab9f] | 187 | |
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[c6eecb] | 188 | while ( ! p1.isZero() ) |
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| 189 | { |
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[034eec] | 190 | divrem( p0, p1, q, r ); |
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| 191 | p0 = p1; p1 = r; |
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| 192 | r = g0 - g1 * q; |
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| 193 | g0 = g1; g1 = r; |
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| 194 | r = f0 - f1 * q; |
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| 195 | f0 = f1; f1 = r; |
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| 196 | } |
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| 197 | CanonicalForm contp0 = content( p0 ); |
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| 198 | a = f0 / ( contf * contp0 ); |
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| 199 | b = g0 / ( contg * contp0 ); |
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| 200 | p0 /= contp0; |
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[c6eecb] | 201 | if ( p0.sign() < 0 ) |
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| 202 | { |
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[034eec] | 203 | p0 = -p0; |
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| 204 | a = -a; |
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| 205 | b = -b; |
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| 206 | } |
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| 207 | return p0; |
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[9bab9f] | 208 | } |
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[dd3e561] | 209 | //}}} |
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[9bab9f] | 210 | |
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[a7ec94] | 211 | //{{{ static CanonicalForm balance ( const CanonicalForm & f, const CanonicalForm & q ) |
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| 212 | //{{{ docu |
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| 213 | // |
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| 214 | // balance() - map f from positive to symmetric representation |
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| 215 | // mod q. |
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| 216 | // |
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| 217 | // This makes sense for univariate polynomials over Z only. |
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| 218 | // q should be an integer. |
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| 219 | // |
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| 220 | // Used by gcd_poly_univar0(). |
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| 221 | // |
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| 222 | //}}} |
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[edb4893] | 223 | static CanonicalForm |
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[a7ec94] | 224 | balance ( const CanonicalForm & f, const CanonicalForm & q ) |
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[edb4893] | 225 | { |
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[a7ec94] | 226 | Variable x = f.mvar(); |
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| 227 | CanonicalForm result = 0, qh = q / 2; |
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| 228 | CanonicalForm c; |
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| 229 | CFIterator i; |
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| 230 | for ( i = f; i.hasTerms(); i++ ) { |
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| 231 | c = mod( i.coeff(), q ); |
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| 232 | if ( c > qh ) |
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| 233 | result += power( x, i.exp() ) * (c - q); |
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| 234 | else |
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| 235 | result += power( x, i.exp() ) * c; |
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[edb4893] | 236 | } |
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[a7ec94] | 237 | return result; |
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| 238 | } |
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| 239 | //}}} |
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| 240 | |
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| 241 | static CanonicalForm |
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| 242 | gcd_poly_univar0( const CanonicalForm & F, const CanonicalForm & G, bool primitive ) |
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| 243 | { |
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[f11d7b] | 244 | CanonicalForm f, g, c, cg, cl, BB, B, M, q, Dp, newD, D, newq; |
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| 245 | int p, i, n; |
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| 246 | |
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| 247 | if ( primitive ) |
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| 248 | { |
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| 249 | f = F; |
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| 250 | g = G; |
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| 251 | c = 1; |
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| 252 | } |
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| 253 | else |
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| 254 | { |
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| 255 | CanonicalForm cF = content( F ), cG = content( G ); |
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| 256 | f = F / cF; |
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| 257 | g = G / cG; |
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| 258 | c = bgcd( cF, cG ); |
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| 259 | } |
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| 260 | cg = gcd( f.lc(), g.lc() ); |
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| 261 | cl = ( f.lc() / cg ) * g.lc(); |
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[93b061] | 262 | // B = 2 * cg * tmin( |
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[150dc8] | 263 | // maxnorm(f)*power(CanonicalForm(2),f.degree())*isqrt(f.degree()+1), |
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| 264 | // maxnorm(g)*power(CanonicalForm(2),g.degree())*isqrt(g.degree()+1) |
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| 265 | // )+1; |
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[f11d7b] | 266 | M = tmin( maxNorm(f), maxNorm(g) ); |
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| 267 | BB = power(CanonicalForm(2),tmin(f.degree(),g.degree()))*M; |
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| 268 | q = 0; |
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| 269 | i = cf_getNumSmallPrimes() - 1; |
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| 270 | while ( true ) |
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| 271 | { |
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| 272 | B = BB; |
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| 273 | while ( i >= 0 && q < B ) |
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| 274 | { |
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| 275 | p = cf_getSmallPrime( i ); |
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| 276 | i--; |
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| 277 | while ( i >= 0 && mod( cl, p ) == 0 ) |
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| 278 | { |
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| 279 | p = cf_getSmallPrime( i ); |
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| 280 | i--; |
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| 281 | } |
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| 282 | setCharacteristic( p ); |
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| 283 | Dp = gcd( mapinto( f ), mapinto( g ) ); |
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| 284 | Dp = ( Dp / Dp.lc() ) * mapinto( cg ); |
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| 285 | setCharacteristic( 0 ); |
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| 286 | if ( Dp.degree() == 0 ) |
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| 287 | return c; |
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| 288 | if ( q.isZero() ) |
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| 289 | { |
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| 290 | D = mapinto( Dp ); |
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| 291 | q = p; |
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| 292 | B = power(CanonicalForm(2),D.degree())*M+1; |
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| 293 | } |
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| 294 | else |
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| 295 | { |
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| 296 | if ( Dp.degree() == D.degree() ) |
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| 297 | { |
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| 298 | chineseRemainder( D, q, mapinto( Dp ), p, newD, newq ); |
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| 299 | q = newq; |
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| 300 | D = newD; |
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[150dc8] | 301 | } |
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[f11d7b] | 302 | else if ( Dp.degree() < D.degree() ) |
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| 303 | { |
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| 304 | // all previous p's are bad primes |
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| 305 | q = p; |
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| 306 | D = mapinto( Dp ); |
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| 307 | B = power(CanonicalForm(2),D.degree())*M+1; |
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[150dc8] | 308 | } |
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[f11d7b] | 309 | // else p is a bad prime |
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| 310 | } |
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| 311 | } |
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| 312 | if ( i >= 0 ) |
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| 313 | { |
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| 314 | // now balance D mod q |
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| 315 | D = pp( balance( D, q ) ); |
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[ebc602] | 316 | if ( fdivides( D, f ) && fdivides( D, g ) ) |
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[f11d7b] | 317 | return D * c; |
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| 318 | else |
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| 319 | q = 0; |
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[edb4893] | 320 | } |
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[f11d7b] | 321 | else |
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[a7ec94] | 322 | return gcd_poly( F, G ); |
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[f11d7b] | 323 | DEBOUTLN( cerr, "another try ..." ); |
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| 324 | } |
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[edb4893] | 325 | } |
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| 326 | |
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[a7ec94] | 327 | static CanonicalForm |
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| 328 | gcd_poly_p( const CanonicalForm & f, const CanonicalForm & g ) |
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[9bab9f] | 329 | { |
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[df497a] | 330 | CanonicalForm pi, pi1; |
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[a7ec94] | 331 | CanonicalForm C, Ci, Ci1, Hi, bi, pi2; |
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[fda36e] | 332 | bool bpure; |
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[a7ec94] | 333 | int delta = degree( f ) - degree( g ); |
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[9bab9f] | 334 | |
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[a7ec94] | 335 | if ( delta >= 0 ) |
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[df497a] | 336 | { |
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[150dc8] | 337 | pi = f; pi1 = g; |
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[9bab9f] | 338 | } |
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[df497a] | 339 | else |
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| 340 | { |
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[a7ec94] | 341 | pi = g; pi1 = f; delta = -delta; |
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| 342 | } |
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| 343 | Ci = content( pi ); Ci1 = content( pi1 ); |
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| 344 | pi1 = pi1 / Ci1; pi = pi / Ci; |
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| 345 | C = gcd( Ci, Ci1 ); |
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| 346 | if ( !( pi.isUnivariate() && pi1.isUnivariate() ) ) |
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| 347 | { |
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[6f62c3] | 348 | //out_cf("F:",f,"\n"); |
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| 349 | //out_cf("G:",g,"\n"); |
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| 350 | //out_cf("newGCD:",newGCD(f,g),"\n"); |
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[110718] | 351 | if (isOn(SW_USE_GCD_P) && (getCharacteristic()>0)) |
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| 352 | { |
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| 353 | return newGCD(f,g); |
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| 354 | } |
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[fda36e] | 355 | if ( gcd_test_one( pi1, pi, true ) ) |
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[6f62c3] | 356 | { |
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| 357 | C=abs(C); |
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| 358 | //out_cf("GCD:",C,"\n"); |
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| 359 | return C; |
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| 360 | } |
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[fda36e] | 361 | bpure = false; |
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[a7ec94] | 362 | } |
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| 363 | else |
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| 364 | { |
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[fda36e] | 365 | bpure = isPurePoly(pi) && isPurePoly(pi1); |
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| 366 | #ifdef HAVE_NTL |
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| 367 | if ( isOn(SW_USE_NTL_GCD_P) && bpure ) |
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| 368 | return gcd_univar_ntlp(pi, pi1 ) * C; |
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[a7ec94] | 369 | #endif |
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[fda36e] | 370 | } |
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[a7ec94] | 371 | Variable v = f.mvar(); |
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| 372 | Hi = power( LC( pi1, v ), delta ); |
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| 373 | if ( (delta+1) % 2 ) |
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| 374 | bi = 1; |
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| 375 | else |
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| 376 | bi = -1; |
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| 377 | while ( degree( pi1, v ) > 0 ) { |
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| 378 | pi2 = psr( pi, pi1, v ); |
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| 379 | pi2 = pi2 / bi; |
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| 380 | pi = pi1; pi1 = pi2; |
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| 381 | if ( degree( pi1, v ) > 0 ) { |
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| 382 | delta = degree( pi, v ) - degree( pi1, v ); |
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| 383 | if ( (delta+1) % 2 ) |
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| 384 | bi = LC( pi, v ) * power( Hi, delta ); |
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| 385 | else |
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| 386 | bi = -LC( pi, v ) * power( Hi, delta ); |
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| 387 | Hi = power( LC( pi1, v ), delta ) / power( Hi, delta-1 ); |
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| 388 | } |
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[9bab9f] | 389 | } |
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[a7ec94] | 390 | if ( degree( pi1, v ) == 0 ) |
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[6f62c3] | 391 | { |
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| 392 | C=abs(C); |
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| 393 | //out_cf("GCD:",C,"\n"); |
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| 394 | return C; |
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| 395 | } |
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[fda36e] | 396 | pi /= content( pi ); |
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| 397 | if ( bpure ) |
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| 398 | pi /= pi.lc(); |
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[6f62c3] | 399 | C=abs(C*pi); |
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| 400 | //out_cf("GCD:",C,"\n"); |
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| 401 | return C; |
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[a7ec94] | 402 | } |
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| 403 | |
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| 404 | static CanonicalForm |
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| 405 | gcd_poly_0( const CanonicalForm & f, const CanonicalForm & g ) |
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| 406 | { |
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| 407 | CanonicalForm pi, pi1; |
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[df497a] | 408 | CanonicalForm C, Ci, Ci1, Hi, bi, pi2; |
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[a7ec94] | 409 | int delta = degree( f ) - degree( g ); |
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| 410 | |
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| 411 | if ( delta >= 0 ) |
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| 412 | { |
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| 413 | pi = f; pi1 = g; |
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| 414 | } |
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| 415 | else |
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| 416 | { |
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| 417 | pi = g; pi1 = f; delta = -delta; |
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| 418 | } |
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[9bab9f] | 419 | Ci = content( pi ); Ci1 = content( pi1 ); |
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| 420 | pi1 = pi1 / Ci1; pi = pi / Ci; |
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[df497a] | 421 | C = gcd( Ci, Ci1 ); |
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[034eec] | 422 | if ( pi.isUnivariate() && pi1.isUnivariate() ) |
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| 423 | { |
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| 424 | #ifdef HAVE_NTL |
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[a7ec94] | 425 | if ( isOn(SW_USE_NTL_GCD_0) && isPurePoly(pi) && isPurePoly(pi1) ) |
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| 426 | return gcd_univar_ntl0(pi, pi1 ) * C; |
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[df497a] | 427 | #endif |
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[a7ec94] | 428 | return gcd_poly_univar0( pi, pi1, true ) * C; |
---|
[edb4893] | 429 | } |
---|
[034eec] | 430 | else if ( gcd_test_one( pi1, pi, true ) ) |
---|
| 431 | return C; |
---|
[a7ec94] | 432 | Variable v = f.mvar(); |
---|
[9bab9f] | 433 | Hi = power( LC( pi1, v ), delta ); |
---|
| 434 | if ( (delta+1) % 2 ) |
---|
[150dc8] | 435 | bi = 1; |
---|
[9bab9f] | 436 | else |
---|
[150dc8] | 437 | bi = -1; |
---|
[6f62c3] | 438 | while ( degree( pi1, v ) > 0 ) |
---|
| 439 | { |
---|
[150dc8] | 440 | pi2 = psr( pi, pi1, v ); |
---|
| 441 | pi2 = pi2 / bi; |
---|
| 442 | pi = pi1; pi1 = pi2; |
---|
[6f62c3] | 443 | if ( degree( pi1, v ) > 0 ) |
---|
| 444 | { |
---|
[150dc8] | 445 | delta = degree( pi, v ) - degree( pi1, v ); |
---|
| 446 | if ( (delta+1) % 2 ) |
---|
| 447 | bi = LC( pi, v ) * power( Hi, delta ); |
---|
| 448 | else |
---|
| 449 | bi = -LC( pi, v ) * power( Hi, delta ); |
---|
| 450 | Hi = power( LC( pi1, v ), delta ) / power( Hi, delta-1 ); |
---|
| 451 | } |
---|
[9bab9f] | 452 | } |
---|
| 453 | if ( degree( pi1, v ) == 0 ) |
---|
[150dc8] | 454 | return C; |
---|
[df497a] | 455 | else |
---|
[150dc8] | 456 | return C * pp( pi ); |
---|
[9bab9f] | 457 | } |
---|
| 458 | |
---|
[b809a8] | 459 | //{{{ CanonicalForm gcd_poly ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
[dd3e561] | 460 | //{{{ docu |
---|
| 461 | // |
---|
| 462 | // gcd_poly() - calculate polynomial gcd. |
---|
| 463 | // |
---|
| 464 | // This is the dispatcher for polynomial gcd calculation. We call either |
---|
| 465 | // ezgcd(), sparsemod() or gcd_poly1() in dependecy on the current |
---|
| 466 | // characteristic and settings of SW_USE_EZGCD and SW_USE_SPARSEMOD, resp. |
---|
| 467 | // |
---|
| 468 | // Used by gcd() and gcd_poly_univar0(). |
---|
| 469 | // |
---|
| 470 | //}}} |
---|
[0b6919] | 471 | #if 0 |
---|
[bfc606] | 472 | int si_factor_reminder=1; |
---|
[0b6919] | 473 | #endif |
---|
[b809a8] | 474 | CanonicalForm gcd_poly ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
[f63dbca] | 475 | { |
---|
[110718] | 476 | CanonicalForm fc, gc, d1; |
---|
| 477 | int mp, cc, p1, pe; |
---|
| 478 | mp = f.level()+1; |
---|
[ed9927] | 479 | bool fc_isUnivariate=f.isUnivariate(); |
---|
| 480 | bool gc_isUnivariate=g.isUnivariate(); |
---|
| 481 | bool fc_and_gc_Univariate=fc_isUnivariate && gc_isUnivariate; |
---|
[1e6de6] | 482 | #if 1 |
---|
[c30347] | 483 | if (( getCharacteristic() == 0 ) |
---|
| 484 | && (f.level() >4) |
---|
| 485 | && (g.level() >4) |
---|
| 486 | && isOn( SW_USE_CHINREM_GCD) |
---|
[ed9927] | 487 | && (!fc_and_gc_Univariate) |
---|
[c30347] | 488 | && (isPurePoly_m(f)) |
---|
| 489 | && (isPurePoly_m(g)) |
---|
| 490 | ) |
---|
| 491 | { |
---|
| 492 | return chinrem_gcd( f, g ); |
---|
| 493 | } |
---|
| 494 | #endif |
---|
[ed9927] | 495 | cf_prepgcd( f, g, cc, p1, pe); |
---|
| 496 | if ( cc != 0 ) |
---|
[110718] | 497 | { |
---|
[ed9927] | 498 | if ( cc > 0 ) |
---|
[abfc3b] | 499 | { |
---|
[ed9927] | 500 | fc = replacevar( f, Variable(cc), Variable(mp) ); |
---|
| 501 | gc = g; |
---|
[e074407] | 502 | } |
---|
[ed9927] | 503 | else |
---|
[110718] | 504 | { |
---|
[ed9927] | 505 | fc = replacevar( g, Variable(-cc), Variable(mp) ); |
---|
| 506 | gc = f; |
---|
[110718] | 507 | } |
---|
[ed9927] | 508 | return cf_content( fc, gc ); |
---|
| 509 | } |
---|
| 510 | // now each appearing variable is in f and g |
---|
| 511 | fc = f; |
---|
| 512 | gc = g; |
---|
| 513 | if( gcd_avoid_mtaildegree ( fc, gc, d1 ) ) |
---|
| 514 | return d1; |
---|
| 515 | if ( getCharacteristic() != 0 ) |
---|
| 516 | { |
---|
[598ff8b] | 517 | if (isOn(SW_USE_fieldGCD) |
---|
| 518 | && (!fc_and_gc_Univariate) |
---|
| 519 | && (getCharacteristic() >100)) |
---|
| 520 | { |
---|
[ad8e1b] | 521 | return fieldGCD(f,g); |
---|
[598ff8b] | 522 | } |
---|
| 523 | else if (isOn( SW_USE_EZGCD_P ) && (!fc_and_gc_Univariate)) |
---|
[49f1f45] | 524 | { |
---|
[ed9927] | 525 | if ( pe == 1 ) |
---|
| 526 | fc = fin_ezgcd( fc, gc ); |
---|
| 527 | else if ( pe > 0 )// no variable at position 1 |
---|
[49f1f45] | 528 | { |
---|
[ed9927] | 529 | fc = replacevar( fc, Variable(pe), Variable(1) ); |
---|
| 530 | gc = replacevar( gc, Variable(pe), Variable(1) ); |
---|
| 531 | fc = replacevar( fin_ezgcd( fc, gc ), Variable(1), Variable(pe) ); |
---|
[49f1f45] | 532 | } |
---|
| 533 | else |
---|
| 534 | { |
---|
[ed9927] | 535 | pe = -pe; |
---|
| 536 | fc = swapvar( fc, Variable(pe), Variable(1) ); |
---|
| 537 | gc = swapvar( gc, Variable(pe), Variable(1) ); |
---|
| 538 | fc = swapvar( fin_ezgcd( fc, gc ), Variable(1), Variable(pe) ); |
---|
[49f1f45] | 539 | } |
---|
[c30347] | 540 | } |
---|
[ed9927] | 541 | else if (isOn(SW_USE_GCD_P)) |
---|
| 542 | { |
---|
| 543 | fc=newGCD(fc,gc); |
---|
| 544 | } |
---|
| 545 | else if ( p1 == fc.level() ) |
---|
| 546 | fc = gcd_poly_p( fc, gc ); |
---|
| 547 | else |
---|
| 548 | { |
---|
| 549 | fc = replacevar( fc, Variable(p1), Variable(mp) ); |
---|
| 550 | gc = replacevar( gc, Variable(p1), Variable(mp) ); |
---|
| 551 | fc = replacevar( gcd_poly_p( fc, gc ), Variable(mp), Variable(p1) ); |
---|
| 552 | } |
---|
[110718] | 553 | } |
---|
[c30347] | 554 | else if (!fc_and_gc_Univariate) |
---|
[110718] | 555 | { |
---|
[c30347] | 556 | if ( |
---|
| 557 | isOn(SW_USE_CHINREM_GCD) |
---|
[ed9927] | 558 | && (gc.level() >5) |
---|
| 559 | && (fc.level() >5) |
---|
| 560 | && (isPurePoly_m(fc)) && (isPurePoly_m(gc)) |
---|
[c30347] | 561 | ) |
---|
| 562 | { |
---|
[ed9927] | 563 | #if 0 |
---|
| 564 | if ( p1 == fc.level() ) |
---|
| 565 | fc = chinrem_gcd( fc, gc ); |
---|
| 566 | else |
---|
| 567 | { |
---|
| 568 | fc = replacevar( fc, Variable(p1), Variable(mp) ); |
---|
| 569 | gc = replacevar( gc, Variable(p1), Variable(mp) ); |
---|
| 570 | fc = replacevar( chinrem_gcd( fc, gc ), Variable(mp), Variable(p1) ); |
---|
| 571 | } |
---|
| 572 | #else |
---|
| 573 | fc = chinrem_gcd( fc, gc); |
---|
| 574 | #endif |
---|
[c30347] | 575 | } |
---|
[110718] | 576 | if ( isOn( SW_USE_EZGCD ) ) |
---|
| 577 | { |
---|
[ed9927] | 578 | if ( pe == 1 ) |
---|
| 579 | fc = ezgcd( fc, gc ); |
---|
| 580 | else if ( pe > 0 )// no variable at position 1 |
---|
| 581 | { |
---|
| 582 | fc = replacevar( fc, Variable(pe), Variable(1) ); |
---|
| 583 | gc = replacevar( gc, Variable(pe), Variable(1) ); |
---|
| 584 | fc = replacevar( ezgcd( fc, gc ), Variable(1), Variable(pe) ); |
---|
| 585 | } |
---|
| 586 | else |
---|
| 587 | { |
---|
| 588 | pe = -pe; |
---|
| 589 | fc = swapvar( fc, Variable(pe), Variable(1) ); |
---|
| 590 | gc = swapvar( gc, Variable(pe), Variable(1) ); |
---|
| 591 | fc = swapvar( ezgcd( fc, gc ), Variable(1), Variable(pe) ); |
---|
| 592 | } |
---|
[1b73cc0] | 593 | } |
---|
[110718] | 594 | else if ( |
---|
| 595 | isOn(SW_USE_CHINREM_GCD) |
---|
[ed9927] | 596 | && (isPurePoly_m(fc)) && (isPurePoly_m(gc)) |
---|
[110718] | 597 | ) |
---|
[de1a82] | 598 | { |
---|
[ed9927] | 599 | #if 0 |
---|
| 600 | if ( p1 == fc.level() ) |
---|
| 601 | fc = chinrem_gcd( fc, gc ); |
---|
| 602 | else |
---|
| 603 | { |
---|
| 604 | fc = replacevar( fc, Variable(p1), Variable(mp) ); |
---|
| 605 | gc = replacevar( gc, Variable(p1), Variable(mp) ); |
---|
| 606 | fc = replacevar( chinrem_gcd( fc, gc ), Variable(mp), Variable(p1) ); |
---|
| 607 | } |
---|
| 608 | #else |
---|
| 609 | fc = chinrem_gcd( fc, gc); |
---|
| 610 | #endif |
---|
[f63dbca] | 611 | } |
---|
[c30347] | 612 | else |
---|
| 613 | { |
---|
[ed9927] | 614 | fc = gcd_poly_0( fc, gc ); |
---|
[c30347] | 615 | } |
---|
[110718] | 616 | } |
---|
| 617 | else |
---|
| 618 | { |
---|
| 619 | fc = gcd_poly_0( fc, gc ); |
---|
| 620 | } |
---|
| 621 | if ( d1.degree() > 0 ) |
---|
| 622 | fc *= d1; |
---|
| 623 | return fc; |
---|
[f63dbca] | 624 | } |
---|
[dd3e561] | 625 | //}}} |
---|
[93b061] | 626 | |
---|
[dd3e561] | 627 | //{{{ static CanonicalForm cf_content ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 628 | //{{{ docu |
---|
| 629 | // |
---|
| 630 | // cf_content() - return gcd(g, content(f)). |
---|
| 631 | // |
---|
| 632 | // content(f) is calculated with respect to f's main variable. |
---|
| 633 | // |
---|
| 634 | // Used by gcd(), content(), content( CF, Variable ). |
---|
| 635 | // |
---|
| 636 | //}}} |
---|
[9bab9f] | 637 | static CanonicalForm |
---|
| 638 | cf_content ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 639 | { |
---|
[6f62c3] | 640 | if ( f.inPolyDomain() || ( f.inExtension() && ! getReduce( f.mvar() ) ) ) |
---|
| 641 | { |
---|
[150dc8] | 642 | CFIterator i = f; |
---|
| 643 | CanonicalForm result = g; |
---|
[6f62c3] | 644 | while ( i.hasTerms() && ! result.isOne() ) |
---|
| 645 | { |
---|
[a7ec94] | 646 | result = gcd( i.coeff(), result ); |
---|
[150dc8] | 647 | i++; |
---|
| 648 | } |
---|
| 649 | return result; |
---|
[9bab9f] | 650 | } |
---|
| 651 | else |
---|
[a7ec94] | 652 | return abs( f ); |
---|
[9bab9f] | 653 | } |
---|
[dd3e561] | 654 | //}}} |
---|
[9bab9f] | 655 | |
---|
[4ea0ab] | 656 | //{{{ CanonicalForm content ( const CanonicalForm & f ) |
---|
| 657 | //{{{ docu |
---|
| 658 | // |
---|
| 659 | // content() - return content(f) with respect to main variable. |
---|
| 660 | // |
---|
[dd3e561] | 661 | // Normalizes result. |
---|
| 662 | // |
---|
[4ea0ab] | 663 | //}}} |
---|
[9bab9f] | 664 | CanonicalForm |
---|
| 665 | content ( const CanonicalForm & f ) |
---|
| 666 | { |
---|
[6f62c3] | 667 | if ( f.inPolyDomain() || ( f.inExtension() && ! getReduce( f.mvar() ) ) ) |
---|
| 668 | { |
---|
[a7ec94] | 669 | CFIterator i = f; |
---|
| 670 | CanonicalForm result = abs( i.coeff() ); |
---|
| 671 | i++; |
---|
[6f62c3] | 672 | while ( i.hasTerms() && ! result.isOne() ) |
---|
| 673 | { |
---|
[a7ec94] | 674 | result = gcd( i.coeff(), result ); |
---|
| 675 | i++; |
---|
| 676 | } |
---|
| 677 | return result; |
---|
| 678 | } |
---|
| 679 | else |
---|
| 680 | return abs( f ); |
---|
[9bab9f] | 681 | } |
---|
[4ea0ab] | 682 | //}}} |
---|
[9bab9f] | 683 | |
---|
[dd3e561] | 684 | //{{{ CanonicalForm content ( const CanonicalForm & f, const Variable & x ) |
---|
| 685 | //{{{ docu |
---|
| 686 | // |
---|
| 687 | // content() - return content(f) with respect to x. |
---|
| 688 | // |
---|
| 689 | // x should be a polynomial variable. |
---|
| 690 | // |
---|
| 691 | //}}} |
---|
[9bab9f] | 692 | CanonicalForm |
---|
| 693 | content ( const CanonicalForm & f, const Variable & x ) |
---|
| 694 | { |
---|
[dd3e561] | 695 | ASSERT( x.level() > 0, "cannot calculate content with respect to algebraic variable" ); |
---|
| 696 | Variable y = f.mvar(); |
---|
| 697 | |
---|
| 698 | if ( y == x ) |
---|
[150dc8] | 699 | return cf_content( f, 0 ); |
---|
[dd3e561] | 700 | else if ( y < x ) |
---|
[150dc8] | 701 | return f; |
---|
[9bab9f] | 702 | else |
---|
[150dc8] | 703 | return swapvar( content( swapvar( f, y, x ), y ), y, x ); |
---|
[9bab9f] | 704 | } |
---|
[dd3e561] | 705 | //}}} |
---|
[9bab9f] | 706 | |
---|
[dd3e561] | 707 | //{{{ CanonicalForm vcontent ( const CanonicalForm & f, const Variable & x ) |
---|
| 708 | //{{{ docu |
---|
| 709 | // |
---|
| 710 | // vcontent() - return content of f with repect to variables >= x. |
---|
| 711 | // |
---|
| 712 | // The content is recursively calculated over all coefficients in |
---|
| 713 | // f having level less than x. x should be a polynomial |
---|
| 714 | // variable. |
---|
| 715 | // |
---|
| 716 | //}}} |
---|
[9bab9f] | 717 | CanonicalForm |
---|
| 718 | vcontent ( const CanonicalForm & f, const Variable & x ) |
---|
| 719 | { |
---|
[dd3e561] | 720 | ASSERT( x.level() > 0, "cannot calculate vcontent with respect to algebraic variable" ); |
---|
| 721 | |
---|
[9bab9f] | 722 | if ( f.mvar() <= x ) |
---|
[150dc8] | 723 | return content( f, x ); |
---|
[9bab9f] | 724 | else { |
---|
[150dc8] | 725 | CFIterator i; |
---|
| 726 | CanonicalForm d = 0; |
---|
| 727 | for ( i = f; i.hasTerms() && ! d.isOne(); i++ ) |
---|
| 728 | d = gcd( d, vcontent( i.coeff(), x ) ); |
---|
| 729 | return d; |
---|
[9bab9f] | 730 | } |
---|
| 731 | } |
---|
[dd3e561] | 732 | //}}} |
---|
[9bab9f] | 733 | |
---|
[4ea0ab] | 734 | //{{{ CanonicalForm pp ( const CanonicalForm & f ) |
---|
| 735 | //{{{ docu |
---|
| 736 | // |
---|
| 737 | // pp() - return primitive part of f. |
---|
| 738 | // |
---|
[dd3e561] | 739 | // Returns zero if f equals zero, otherwise f / content(f). |
---|
| 740 | // |
---|
[4ea0ab] | 741 | //}}} |
---|
[9bab9f] | 742 | CanonicalForm |
---|
| 743 | pp ( const CanonicalForm & f ) |
---|
| 744 | { |
---|
| 745 | if ( f.isZero() ) |
---|
[150dc8] | 746 | return f; |
---|
[9bab9f] | 747 | else |
---|
[150dc8] | 748 | return f / content( f ); |
---|
[9bab9f] | 749 | } |
---|
[4ea0ab] | 750 | //}}} |
---|
[9bab9f] | 751 | |
---|
[ff6222] | 752 | CanonicalForm |
---|
[9bab9f] | 753 | gcd ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 754 | { |
---|
[a7ec94] | 755 | bool b = f.isZero(); |
---|
| 756 | if ( b || g.isZero() ) |
---|
| 757 | { |
---|
| 758 | if ( b ) |
---|
| 759 | return abs( g ); |
---|
[abfc3b] | 760 | else |
---|
[a7ec94] | 761 | return abs( f ); |
---|
| 762 | } |
---|
| 763 | if ( f.inPolyDomain() || g.inPolyDomain() ) |
---|
| 764 | { |
---|
| 765 | if ( f.mvar() != g.mvar() ) |
---|
| 766 | { |
---|
| 767 | if ( f.mvar() > g.mvar() ) |
---|
| 768 | return cf_content( f, g ); |
---|
| 769 | else |
---|
| 770 | return cf_content( g, f ); |
---|
| 771 | } |
---|
[bb82f0] | 772 | if (isOn(SW_USE_QGCD)) |
---|
| 773 | { |
---|
| 774 | Variable m; |
---|
| 775 | if ((hasFirstAlgVar(f,m) || hasFirstAlgVar(g,m)) |
---|
| 776 | //&& f.isUnivariate() |
---|
| 777 | //&& g.isUnivariate() |
---|
| 778 | && (getCharacteristic() == 0) |
---|
| 779 | ) |
---|
[fc31bce] | 780 | { |
---|
[ad8e1b] | 781 | //if ((f.level()==g.level()) && f.isUnivariate() && g.isUnivariate()) |
---|
| 782 | // return univarQGCD(f,g); |
---|
| 783 | //else |
---|
[fc31bce] | 784 | return QGCD(f,g); |
---|
| 785 | } |
---|
[bb82f0] | 786 | } |
---|
| 787 | |
---|
[150dc8] | 788 | if ( f.inExtension() && getReduce( f.mvar() ) ) |
---|
[bb82f0] | 789 | return CanonicalForm(1); |
---|
[a7ec94] | 790 | else |
---|
| 791 | { |
---|
[ebc602] | 792 | if ( fdivides( f, g ) ) |
---|
[a7ec94] | 793 | return abs( f ); |
---|
[ebc602] | 794 | else if ( fdivides( g, f ) ) |
---|
[a7ec94] | 795 | return abs( g ); |
---|
| 796 | if ( !( getCharacteristic() == 0 && isOn( SW_RATIONAL ) ) ) |
---|
| 797 | { |
---|
| 798 | CanonicalForm d; |
---|
[5944b4] | 799 | #if 1 |
---|
[a7ec94] | 800 | do{ d = gcd_poly( f, g ); } |
---|
[ebc602] | 801 | while ((!fdivides(d,f)) || (!fdivides(d,g))); |
---|
[5944b4] | 802 | #else |
---|
| 803 | while(1) |
---|
[f4b180] | 804 | { |
---|
| 805 | d = gcd_poly( f, g ); |
---|
[5944b4] | 806 | if ((fdivides(d,f)) && (fdivides(d,g))) break; |
---|
| 807 | printf("g"); fflush(stdout); |
---|
| 808 | } |
---|
| 809 | #endif |
---|
[a7ec94] | 810 | return abs( d ); |
---|
| 811 | } |
---|
| 812 | else |
---|
| 813 | { |
---|
[150dc8] | 814 | CanonicalForm cdF = bCommonDen( f ); |
---|
| 815 | CanonicalForm cdG = bCommonDen( g ); |
---|
| 816 | Off( SW_RATIONAL ); |
---|
| 817 | CanonicalForm l = lcm( cdF, cdG ); |
---|
| 818 | On( SW_RATIONAL ); |
---|
| 819 | CanonicalForm F = f * l, G = g * l; |
---|
| 820 | Off( SW_RATIONAL ); |
---|
[a7ec94] | 821 | do { l = gcd_poly( F, G ); } |
---|
[ebc602] | 822 | while ((!fdivides(l,F)) || (!fdivides(l,G))); |
---|
[150dc8] | 823 | On( SW_RATIONAL ); |
---|
[a7ec94] | 824 | return abs( l ); |
---|
[150dc8] | 825 | } |
---|
| 826 | } |
---|
[a7ec94] | 827 | } |
---|
| 828 | if ( f.inBaseDomain() && g.inBaseDomain() ) |
---|
| 829 | return bgcd( f, g ); |
---|
[9bab9f] | 830 | else |
---|
[a7ec94] | 831 | return 1; |
---|
[9bab9f] | 832 | } |
---|
| 833 | |
---|
[dd3e561] | 834 | //{{{ CanonicalForm lcm ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 835 | //{{{ docu |
---|
| 836 | // |
---|
| 837 | // lcm() - return least common multiple of f and g. |
---|
| 838 | // |
---|
| 839 | // The lcm is calculated using the formula lcm(f, g) = f * g / gcd(f, g). |
---|
| 840 | // |
---|
| 841 | // Returns zero if one of f or g equals zero. |
---|
| 842 | // |
---|
| 843 | //}}} |
---|
[9bab9f] | 844 | CanonicalForm |
---|
| 845 | lcm ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 846 | { |
---|
[dd3e561] | 847 | if ( f.isZero() || g.isZero() ) |
---|
[a7ec94] | 848 | return 0; |
---|
[dd3e561] | 849 | else |
---|
[150dc8] | 850 | return ( f / gcd( f, g ) ) * g; |
---|
[9bab9f] | 851 | } |
---|
[dd3e561] | 852 | //}}} |
---|
[a7ec94] | 853 | |
---|
| 854 | #ifdef HAVE_NTL |
---|
| 855 | |
---|
| 856 | static CanonicalForm |
---|
| 857 | gcd_univar_ntl0( const CanonicalForm & F, const CanonicalForm & G ) |
---|
| 858 | { |
---|
| 859 | ZZX F1=convertFacCF2NTLZZX(F); |
---|
| 860 | ZZX G1=convertFacCF2NTLZZX(G); |
---|
| 861 | ZZX R=GCD(F1,G1); |
---|
| 862 | return convertNTLZZX2CF(R,F.mvar()); |
---|
| 863 | } |
---|
| 864 | |
---|
| 865 | static CanonicalForm |
---|
| 866 | gcd_univar_ntlp( const CanonicalForm & F, const CanonicalForm & G ) |
---|
| 867 | { |
---|
[c6eecb] | 868 | if (fac_NTL_char!=getCharacteristic()) |
---|
| 869 | { |
---|
| 870 | fac_NTL_char=getCharacteristic(); |
---|
| 871 | #ifdef NTL_ZZ |
---|
| 872 | ZZ r; |
---|
| 873 | r=getCharacteristic(); |
---|
| 874 | ZZ_pContext ccc(r); |
---|
| 875 | #else |
---|
[a7ec94] | 876 | zz_pContext ccc(getCharacteristic()); |
---|
[c6eecb] | 877 | #endif |
---|
[a7ec94] | 878 | ccc.restore(); |
---|
[c6eecb] | 879 | #ifdef NTL_ZZ |
---|
| 880 | ZZ_p::init(r); |
---|
| 881 | #else |
---|
[a7ec94] | 882 | zz_p::init(getCharacteristic()); |
---|
[c6eecb] | 883 | #endif |
---|
| 884 | } |
---|
| 885 | #ifdef NTL_ZZ |
---|
| 886 | ZZ_pX F1=convertFacCF2NTLZZpX(F); |
---|
| 887 | ZZ_pX G1=convertFacCF2NTLZZpX(G); |
---|
| 888 | ZZ_pX R=GCD(F1,G1); |
---|
| 889 | return convertNTLZZpX2CF(R,F.mvar()); |
---|
| 890 | #else |
---|
| 891 | zz_pX F1=convertFacCF2NTLzzpX(F); |
---|
| 892 | zz_pX G1=convertFacCF2NTLzzpX(G); |
---|
| 893 | zz_pX R=GCD(F1,G1); |
---|
| 894 | return convertNTLzzpX2CF(R,F.mvar()); |
---|
| 895 | #endif |
---|
[a7ec94] | 896 | } |
---|
| 897 | |
---|
| 898 | #endif |
---|
| 899 | |
---|
| 900 | static bool |
---|
| 901 | gcd_avoid_mtaildegree ( CanonicalForm & f1, CanonicalForm & g1, CanonicalForm & d1 ) |
---|
| 902 | { |
---|
| 903 | bool rdy = true; |
---|
| 904 | int df = f1.taildegree(); |
---|
| 905 | int dg = g1.taildegree(); |
---|
| 906 | |
---|
| 907 | d1 = d1.genOne(); |
---|
| 908 | if ( dg == 0 ) |
---|
| 909 | { |
---|
| 910 | if ( df == 0 ) |
---|
| 911 | return false; |
---|
| 912 | else |
---|
| 913 | { |
---|
| 914 | if ( f1.degree() == df ) |
---|
| 915 | d1 = cf_content( g1, LC( f1 ) ); |
---|
| 916 | else |
---|
| 917 | { |
---|
| 918 | f1 /= power( f1.mvar(), df ); |
---|
| 919 | rdy = false; |
---|
| 920 | } |
---|
| 921 | } |
---|
| 922 | } |
---|
| 923 | else |
---|
| 924 | { |
---|
| 925 | if ( df == 0) |
---|
| 926 | { |
---|
| 927 | if ( g1.degree() == dg ) |
---|
| 928 | d1 = cf_content( f1, LC( g1 ) ); |
---|
| 929 | else |
---|
| 930 | { |
---|
| 931 | g1 /= power( g1.mvar(), dg ); |
---|
| 932 | rdy = false; |
---|
| 933 | } |
---|
| 934 | } |
---|
| 935 | else |
---|
| 936 | { |
---|
| 937 | if ( df > dg ) |
---|
| 938 | d1 = power( f1.mvar(), dg ); |
---|
| 939 | else |
---|
| 940 | d1 = power( f1.mvar(), df ); |
---|
| 941 | if ( f1.degree() == df ) |
---|
| 942 | { |
---|
| 943 | if (g1.degree() == dg) |
---|
| 944 | d1 *= gcd( LC( f1 ), LC( g1 ) ); |
---|
| 945 | else |
---|
| 946 | { |
---|
| 947 | g1 /= power( g1.mvar(), dg); |
---|
| 948 | d1 *= cf_content( g1, LC( f1 ) ); |
---|
| 949 | } |
---|
| 950 | } |
---|
| 951 | else |
---|
| 952 | { |
---|
| 953 | f1 /= power( f1.mvar(), df ); |
---|
| 954 | if ( g1.degree() == dg ) |
---|
| 955 | d1 *= cf_content( f1, LC( g1 ) ); |
---|
| 956 | else |
---|
| 957 | { |
---|
| 958 | g1 /= power( g1.mvar(), dg ); |
---|
| 959 | rdy = false; |
---|
| 960 | } |
---|
| 961 | } |
---|
| 962 | } |
---|
| 963 | } |
---|
| 964 | return rdy; |
---|
| 965 | } |
---|
| 966 | |
---|
| 967 | /* |
---|
| 968 | * compute positions p1 and pe of optimal variables: |
---|
| 969 | * pe is used in "ezgcd" and |
---|
| 970 | * p1 in "gcd_poly1" |
---|
| 971 | */ |
---|
| 972 | static |
---|
| 973 | void optvalues ( const int * df, const int * dg, const int n, int & p1, int &pe ) |
---|
| 974 | { |
---|
| 975 | int i, o1, oe; |
---|
| 976 | if ( df[n] > dg[n] ) |
---|
| 977 | { |
---|
| 978 | o1 = df[n]; oe = dg[n]; |
---|
| 979 | } |
---|
| 980 | else |
---|
| 981 | { |
---|
| 982 | o1 = dg[n]; oe = df[n]; |
---|
| 983 | } |
---|
| 984 | i = n-1; |
---|
| 985 | while ( i > 0 ) |
---|
| 986 | { |
---|
| 987 | if ( df[i] != 0 ) |
---|
| 988 | { |
---|
| 989 | if ( df[i] > dg[i] ) |
---|
| 990 | { |
---|
| 991 | if ( o1 > df[i]) { o1 = df[i]; p1 = i; } |
---|
| 992 | if ( oe <= dg[i]) { oe = dg[i]; pe = i; } |
---|
| 993 | } |
---|
| 994 | else |
---|
| 995 | { |
---|
| 996 | if ( o1 > dg[i]) { o1 = dg[i]; p1 = i; } |
---|
| 997 | if ( oe <= df[i]) { oe = df[i]; pe = i; } |
---|
| 998 | } |
---|
| 999 | } |
---|
| 1000 | i--; |
---|
| 1001 | } |
---|
| 1002 | } |
---|
| 1003 | |
---|
| 1004 | /* |
---|
| 1005 | * make some changes of variables, see optvalues |
---|
| 1006 | */ |
---|
| 1007 | static void |
---|
| 1008 | cf_prepgcd( const CanonicalForm & f, const CanonicalForm & g, int & cc, int & p1, int &pe ) |
---|
| 1009 | { |
---|
| 1010 | int i, k, n; |
---|
| 1011 | n = f.level(); |
---|
| 1012 | cc = 0; |
---|
| 1013 | p1 = pe = n; |
---|
| 1014 | if ( n == 1 ) |
---|
| 1015 | return; |
---|
| 1016 | int * degsf = new int[n+1]; |
---|
| 1017 | int * degsg = new int[n+1]; |
---|
| 1018 | for ( i = n; i > 0; i-- ) |
---|
| 1019 | { |
---|
| 1020 | degsf[i] = degsg[i] = 0; |
---|
| 1021 | } |
---|
| 1022 | degsf = degrees( f, degsf ); |
---|
| 1023 | degsg = degrees( g, degsg ); |
---|
| 1024 | |
---|
| 1025 | k = 0; |
---|
| 1026 | for ( i = n-1; i > 0; i-- ) |
---|
| 1027 | { |
---|
[f4b180] | 1028 | if ( degsf[i] == 0 ) |
---|
[a7ec94] | 1029 | { |
---|
| 1030 | if ( degsg[i] != 0 ) |
---|
| 1031 | { |
---|
| 1032 | cc = -i; |
---|
| 1033 | break; |
---|
| 1034 | } |
---|
| 1035 | } |
---|
| 1036 | else |
---|
| 1037 | { |
---|
| 1038 | if ( degsg[i] == 0 ) |
---|
| 1039 | { |
---|
| 1040 | cc = i; |
---|
| 1041 | break; |
---|
| 1042 | } |
---|
| 1043 | else k++; |
---|
| 1044 | } |
---|
| 1045 | } |
---|
| 1046 | |
---|
| 1047 | if ( ( cc == 0 ) && ( k != 0 ) ) |
---|
| 1048 | optvalues( degsf, degsg, n, p1, pe ); |
---|
| 1049 | if ( ( pe != 1 ) && ( degsf[1] != 0 ) ) |
---|
| 1050 | pe = -pe; |
---|
[f4b180] | 1051 | |
---|
[a7ec94] | 1052 | delete [] degsf; |
---|
| 1053 | delete [] degsg; |
---|
| 1054 | } |
---|
[6f62c3] | 1055 | |
---|
| 1056 | |
---|
| 1057 | static CanonicalForm |
---|
| 1058 | balance_p ( const CanonicalForm & f, const CanonicalForm & q ) |
---|
| 1059 | { |
---|
| 1060 | Variable x = f.mvar(); |
---|
| 1061 | CanonicalForm result = 0, qh = q / 2; |
---|
| 1062 | CanonicalForm c; |
---|
| 1063 | CFIterator i; |
---|
| 1064 | for ( i = f; i.hasTerms(); i++ ) |
---|
| 1065 | { |
---|
| 1066 | c = i.coeff(); |
---|
| 1067 | if ( c.inCoeffDomain()) |
---|
| 1068 | { |
---|
| 1069 | if ( c > qh ) |
---|
| 1070 | result += power( x, i.exp() ) * (c - q); |
---|
| 1071 | else |
---|
| 1072 | result += power( x, i.exp() ) * c; |
---|
| 1073 | } |
---|
[f4b180] | 1074 | else |
---|
[6f62c3] | 1075 | result += power( x, i.exp() ) * balance_p(c,q); |
---|
| 1076 | } |
---|
| 1077 | return result; |
---|
| 1078 | } |
---|
| 1079 | |
---|
| 1080 | CanonicalForm chinrem_gcd ( const CanonicalForm & FF, const CanonicalForm & GG ) |
---|
| 1081 | { |
---|
| 1082 | CanonicalForm f, g, cg, cl, q, Dp, newD, D, newq; |
---|
[c992ec1] | 1083 | int p, i, dp_deg, d_deg;; |
---|
[6f62c3] | 1084 | |
---|
| 1085 | CanonicalForm cd = bCommonDen( FF ); |
---|
| 1086 | f=cd*FF; |
---|
| 1087 | f /=vcontent(f,Variable(1)); |
---|
[08a6ebb] | 1088 | //cd = bCommonDen( f ); f *=cd; |
---|
| 1089 | //f /=vcontent(f,Variable(1)); |
---|
[6f62c3] | 1090 | |
---|
| 1091 | cd = bCommonDen( GG ); |
---|
| 1092 | g=cd*GG; |
---|
| 1093 | g /=vcontent(g,Variable(1)); |
---|
[08a6ebb] | 1094 | //cd = bCommonDen( g ); g *=cd; |
---|
| 1095 | //g /=vcontent(g,Variable(1)); |
---|
[6f62c3] | 1096 | |
---|
| 1097 | q = 0; |
---|
| 1098 | i = cf_getNumBigPrimes() - 1; |
---|
| 1099 | cl = f.lc()* g.lc(); |
---|
| 1100 | |
---|
| 1101 | while ( true ) |
---|
| 1102 | { |
---|
| 1103 | p = cf_getBigPrime( i ); |
---|
| 1104 | i--; |
---|
| 1105 | while ( i >= 0 && mod( cl, p ) == 0 ) |
---|
| 1106 | { |
---|
| 1107 | p = cf_getBigPrime( i ); |
---|
| 1108 | i--; |
---|
| 1109 | } |
---|
[c30347] | 1110 | //printf("try p=%d\n",p); |
---|
[6f62c3] | 1111 | setCharacteristic( p ); |
---|
[c30347] | 1112 | Dp = gcd_poly( mapinto( f ), mapinto( g ) ); |
---|
[08a6ebb] | 1113 | Dp /=Dp.lc(); |
---|
[6f62c3] | 1114 | setCharacteristic( 0 ); |
---|
| 1115 | dp_deg=totaldegree(Dp); |
---|
| 1116 | if ( dp_deg == 0 ) |
---|
[c30347] | 1117 | { |
---|
| 1118 | //printf(" -> 1\n"); |
---|
[6f62c3] | 1119 | return CanonicalForm(1); |
---|
[c30347] | 1120 | } |
---|
[6f62c3] | 1121 | if ( q.isZero() ) |
---|
| 1122 | { |
---|
| 1123 | D = mapinto( Dp ); |
---|
| 1124 | d_deg=dp_deg; |
---|
| 1125 | q = p; |
---|
| 1126 | } |
---|
| 1127 | else |
---|
| 1128 | { |
---|
| 1129 | if ( dp_deg == d_deg ) |
---|
| 1130 | { |
---|
| 1131 | chineseRemainder( D, q, mapinto( Dp ), p, newD, newq ); |
---|
| 1132 | q = newq; |
---|
| 1133 | D = newD; |
---|
| 1134 | } |
---|
[f4b180] | 1135 | else if ( dp_deg < d_deg ) |
---|
[6f62c3] | 1136 | { |
---|
[c30347] | 1137 | //printf(" were all bad, try more\n"); |
---|
[6f62c3] | 1138 | // all previous p's are bad primes |
---|
| 1139 | q = p; |
---|
| 1140 | D = mapinto( Dp ); |
---|
| 1141 | d_deg=dp_deg; |
---|
| 1142 | } |
---|
[c30347] | 1143 | else |
---|
| 1144 | { |
---|
| 1145 | //printf(" was bad, try more\n"); |
---|
| 1146 | } |
---|
[f4b180] | 1147 | //else dp_deg > d_deg: bad prime |
---|
[6f62c3] | 1148 | } |
---|
[08a6ebb] | 1149 | if ( i >= 0 ) |
---|
[6f62c3] | 1150 | { |
---|
[c992ec1] | 1151 | CanonicalForm Dn= Farey(D,q); |
---|
| 1152 | int is_rat=isOn(SW_RATIONAL); |
---|
| 1153 | On(SW_RATIONAL); |
---|
| 1154 | CanonicalForm cd = bCommonDen( Dn ); // we need On(SW_RATIONAL) |
---|
| 1155 | if (!is_rat) Off(SW_RATIONAL); |
---|
| 1156 | Dn *=cd; |
---|
| 1157 | //Dn /=vcontent(Dn,Variable(1)); |
---|
| 1158 | if ( fdivides( Dn, f ) && fdivides( Dn, g ) ) |
---|
[6f62c3] | 1159 | { |
---|
[c30347] | 1160 | //printf(" -> success\n"); |
---|
[c992ec1] | 1161 | return Dn; |
---|
[6f62c3] | 1162 | } |
---|
[c992ec1] | 1163 | //else: try more primes |
---|
[6f62c3] | 1164 | } |
---|
| 1165 | else |
---|
[c992ec1] | 1166 | { // try other method |
---|
[c30347] | 1167 | //printf("try other gcd\n"); |
---|
[6f62c3] | 1168 | Off(SW_USE_CHINREM_GCD); |
---|
| 1169 | D=gcd_poly( f, g ); |
---|
| 1170 | On(SW_USE_CHINREM_GCD); |
---|
| 1171 | return D; |
---|
| 1172 | } |
---|
| 1173 | } |
---|
| 1174 | } |
---|
[bb82f0] | 1175 | #include "algext.cc" |
---|