[493c477] | 1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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[c992ec1] | 2 | /* $Id: cf_gcd.cc,v 1.53 2007-10-09 12:41:24 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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[edb4893] | 17 | |
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[f11d7b] | 18 | #ifdef HAVE_NTL |
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[034eec] | 19 | #include <NTL/ZZX.h> |
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[f11d7b] | 20 | #include "NTLconvert.h" |
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[a7ec94] | 21 | bool isPurePoly(const CanonicalForm & ); |
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| 22 | static CanonicalForm gcd_univar_ntl0( const CanonicalForm &, const CanonicalForm & ); |
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| 23 | static CanonicalForm gcd_univar_ntlp( const CanonicalForm &, const CanonicalForm & ); |
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[f11d7b] | 24 | #endif |
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| 25 | |
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[a7ec94] | 26 | static CanonicalForm gcd_poly( const CanonicalForm &, const CanonicalForm & ); |
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| 27 | static CanonicalForm cf_content ( const CanonicalForm &, const CanonicalForm & ); |
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| 28 | static bool gcd_avoid_mtaildegree ( CanonicalForm &, CanonicalForm &, CanonicalForm & ); |
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| 29 | static void cf_prepgcd( const CanonicalForm &, const CanonicalForm &, int &, int &, int & ); |
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[edb4893] | 30 | |
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[6f62c3] | 31 | void out_cf(char *s1,const CanonicalForm &f,char *s2); |
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| 32 | |
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| 33 | CanonicalForm |
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| 34 | chinrem_gcd ( const CanonicalForm & FF, const CanonicalForm & GG ); |
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[f4b180] | 35 | |
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[f63dbca] | 36 | bool |
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| 37 | gcd_test_one ( const CanonicalForm & f, const CanonicalForm & g, bool swap ) |
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[9bab9f] | 38 | { |
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| 39 | int count = 0; |
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| 40 | // assume polys have same level; |
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| 41 | CFRandom * sample = CFRandomFactory::generate(); |
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[f63dbca] | 42 | REvaluation e( 2, tmax( f.level(), g.level() ), *sample ); |
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[9bab9f] | 43 | delete sample; |
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[f63dbca] | 44 | CanonicalForm lcf, lcg; |
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[6f62c3] | 45 | if ( swap ) |
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| 46 | { |
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[150dc8] | 47 | lcf = swapvar( LC( f ), Variable(1), f.mvar() ); |
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| 48 | lcg = swapvar( LC( g ), Variable(1), f.mvar() ); |
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[f63dbca] | 49 | } |
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[6f62c3] | 50 | else |
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| 51 | { |
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[150dc8] | 52 | lcf = LC( f, Variable(1) ); |
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| 53 | lcg = LC( g, Variable(1) ); |
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[f63dbca] | 54 | } |
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[df497a] | 55 | #define TEST_ONE_MAX 50 |
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| 56 | while ( ( e( lcf ).isZero() || e( lcg ).isZero() ) && count < TEST_ONE_MAX ) |
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| 57 | { |
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[150dc8] | 58 | e.nextpoint(); |
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| 59 | count++; |
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[9bab9f] | 60 | } |
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[df497a] | 61 | if ( count == TEST_ONE_MAX ) |
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[150dc8] | 62 | return false; |
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[f63dbca] | 63 | CanonicalForm F, G; |
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[6f62c3] | 64 | if ( swap ) |
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| 65 | { |
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[150dc8] | 66 | F=swapvar( f, Variable(1), f.mvar() ); |
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| 67 | G=swapvar( g, Variable(1), g.mvar() ); |
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[f63dbca] | 68 | } |
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[6f62c3] | 69 | else |
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| 70 | { |
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[150dc8] | 71 | F = f; |
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| 72 | G = g; |
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[f63dbca] | 73 | } |
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[9bab9f] | 74 | if ( e(F).taildegree() > 0 && e(G).taildegree() > 0 ) |
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[150dc8] | 75 | return false; |
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[9bab9f] | 76 | return gcd( e( F ), e( G ) ).degree() < 1; |
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| 77 | } |
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| 78 | |
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[dd3e561] | 79 | //{{{ static CanonicalForm icontent ( const CanonicalForm & f, const CanonicalForm & c ) |
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| 80 | //{{{ docu |
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| 81 | // |
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| 82 | // icontent() - return gcd of c and all coefficients of f which |
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| 83 | // are in a coefficient domain. |
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| 84 | // |
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| 85 | // Used by icontent(). |
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| 86 | // |
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| 87 | //}}} |
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[9bab9f] | 88 | static CanonicalForm |
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| 89 | icontent ( const CanonicalForm & f, const CanonicalForm & c ) |
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| 90 | { |
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| 91 | if ( f.inCoeffDomain() ) |
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[150dc8] | 92 | return gcd( f, c ); |
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[9bab9f] | 93 | else { |
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[150dc8] | 94 | CanonicalForm g = c; |
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| 95 | for ( CFIterator i = f; i.hasTerms() && ! g.isOne(); i++ ) |
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| 96 | g = icontent( i.coeff(), g ); |
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| 97 | return g; |
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[9bab9f] | 98 | } |
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| 99 | } |
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[dd3e561] | 100 | //}}} |
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[9bab9f] | 101 | |
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[dd3e561] | 102 | //{{{ CanonicalForm icontent ( const CanonicalForm & f ) |
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| 103 | //{{{ docu |
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| 104 | // |
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| 105 | // icontent() - return gcd over all coefficients of f which are |
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| 106 | // in a coefficient domain. |
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| 107 | // |
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| 108 | //}}} |
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[9bab9f] | 109 | CanonicalForm |
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| 110 | icontent ( const CanonicalForm & f ) |
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| 111 | { |
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| 112 | return icontent( f, 0 ); |
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| 113 | } |
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[dd3e561] | 114 | //}}} |
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[9bab9f] | 115 | |
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[dd3e561] | 116 | //{{{ CanonicalForm extgcd ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & a, CanonicalForm & b ) |
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| 117 | //{{{ docu |
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| 118 | // |
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| 119 | // extgcd() - returns polynomial extended gcd of f and g. |
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| 120 | // |
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| 121 | // Returns gcd(f, g) and a and b sucht that f*a+g*b=gcd(f, g). |
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| 122 | // The gcd is calculated using an extended euclidean polynomial |
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| 123 | // remainder sequence, so f and g should be polynomials over an |
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| 124 | // euclidean domain. Normalizes result. |
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| 125 | // |
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| 126 | // Note: be sure that f and g have the same level! |
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| 127 | // |
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| 128 | //}}} |
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[9bab9f] | 129 | CanonicalForm |
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| 130 | extgcd ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & a, CanonicalForm & b ) |
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| 131 | { |
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[034eec] | 132 | #ifdef HAVE_NTL |
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[2667bc8] | 133 | if (isOn(SW_USE_NTL_GCD_P) && ( getCharacteristic() > 0 ) |
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[034eec] | 134 | && isPurePoly(f) && isPurePoly(g)) |
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| 135 | { |
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[c6eecb] | 136 | if (fac_NTL_char!=getCharacteristic()) |
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| 137 | { |
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| 138 | fac_NTL_char=getCharacteristic(); |
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| 139 | #ifdef NTL_ZZ |
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| 140 | ZZ r; |
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| 141 | r=getCharacteristic(); |
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| 142 | ZZ_pContext ccc(r); |
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| 143 | #else |
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| 144 | zz_pContext ccc(getCharacteristic()); |
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| 145 | #endif |
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| 146 | ccc.restore(); |
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| 147 | #ifdef NTL_ZZ |
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| 148 | ZZ_p::init(r); |
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| 149 | #else |
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| 150 | zz_p::init(getCharacteristic()); |
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| 151 | #endif |
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| 152 | } |
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| 153 | #ifdef NTL_ZZ |
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| 154 | ZZ_pX F1=convertFacCF2NTLZZpX(f); |
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| 155 | ZZ_pX G1=convertFacCF2NTLZZpX(g); |
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| 156 | ZZ_pX R; |
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| 157 | ZZ_pX A,B; |
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| 158 | XGCD(R,A,B,F1,G1); |
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| 159 | a=convertNTLZZpX2CF(A,f.mvar()); |
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| 160 | b=convertNTLZZpX2CF(B,f.mvar()); |
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| 161 | return convertNTLZZpX2CF(R,f.mvar()); |
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| 162 | #else |
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[034eec] | 163 | zz_pX F1=convertFacCF2NTLzzpX(f); |
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| 164 | zz_pX G1=convertFacCF2NTLzzpX(g); |
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| 165 | zz_pX R; |
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| 166 | zz_pX A,B; |
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| 167 | XGCD(R,A,B,F1,G1); |
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| 168 | a=convertNTLzzpX2CF(A,f.mvar()); |
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| 169 | b=convertNTLzzpX2CF(B,f.mvar()); |
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| 170 | return convertNTLzzpX2CF(R,f.mvar()); |
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[c6eecb] | 171 | #endif |
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[034eec] | 172 | } |
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| 173 | #endif |
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| 174 | CanonicalForm contf = content( f ); |
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| 175 | CanonicalForm contg = content( g ); |
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[9bab9f] | 176 | |
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[034eec] | 177 | CanonicalForm p0 = f / contf, p1 = g / contg; |
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| 178 | CanonicalForm f0 = 1, f1 = 0, g0 = 0, g1 = 1, q, r; |
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[9bab9f] | 179 | |
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[c6eecb] | 180 | while ( ! p1.isZero() ) |
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| 181 | { |
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[034eec] | 182 | divrem( p0, p1, q, r ); |
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| 183 | p0 = p1; p1 = r; |
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| 184 | r = g0 - g1 * q; |
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| 185 | g0 = g1; g1 = r; |
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| 186 | r = f0 - f1 * q; |
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| 187 | f0 = f1; f1 = r; |
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| 188 | } |
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| 189 | CanonicalForm contp0 = content( p0 ); |
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| 190 | a = f0 / ( contf * contp0 ); |
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| 191 | b = g0 / ( contg * contp0 ); |
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| 192 | p0 /= contp0; |
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[c6eecb] | 193 | if ( p0.sign() < 0 ) |
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| 194 | { |
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[034eec] | 195 | p0 = -p0; |
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| 196 | a = -a; |
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| 197 | b = -b; |
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| 198 | } |
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| 199 | return p0; |
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[9bab9f] | 200 | } |
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[dd3e561] | 201 | //}}} |
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[9bab9f] | 202 | |
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[a7ec94] | 203 | //{{{ static CanonicalForm balance ( const CanonicalForm & f, const CanonicalForm & q ) |
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| 204 | //{{{ docu |
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| 205 | // |
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| 206 | // balance() - map f from positive to symmetric representation |
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| 207 | // mod q. |
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| 208 | // |
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| 209 | // This makes sense for univariate polynomials over Z only. |
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| 210 | // q should be an integer. |
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| 211 | // |
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| 212 | // Used by gcd_poly_univar0(). |
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| 213 | // |
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| 214 | //}}} |
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[edb4893] | 215 | static CanonicalForm |
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[a7ec94] | 216 | balance ( const CanonicalForm & f, const CanonicalForm & q ) |
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[edb4893] | 217 | { |
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[a7ec94] | 218 | Variable x = f.mvar(); |
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| 219 | CanonicalForm result = 0, qh = q / 2; |
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| 220 | CanonicalForm c; |
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| 221 | CFIterator i; |
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| 222 | for ( i = f; i.hasTerms(); i++ ) { |
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| 223 | c = mod( i.coeff(), q ); |
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| 224 | if ( c > qh ) |
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| 225 | result += power( x, i.exp() ) * (c - q); |
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| 226 | else |
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| 227 | result += power( x, i.exp() ) * c; |
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[edb4893] | 228 | } |
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[a7ec94] | 229 | return result; |
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| 230 | } |
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| 231 | //}}} |
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| 232 | |
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| 233 | static CanonicalForm |
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| 234 | gcd_poly_univar0( const CanonicalForm & F, const CanonicalForm & G, bool primitive ) |
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| 235 | { |
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[f11d7b] | 236 | CanonicalForm f, g, c, cg, cl, BB, B, M, q, Dp, newD, D, newq; |
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| 237 | int p, i, n; |
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| 238 | |
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| 239 | if ( primitive ) |
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| 240 | { |
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| 241 | f = F; |
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| 242 | g = G; |
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| 243 | c = 1; |
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| 244 | } |
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| 245 | else |
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| 246 | { |
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| 247 | CanonicalForm cF = content( F ), cG = content( G ); |
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| 248 | f = F / cF; |
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| 249 | g = G / cG; |
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| 250 | c = bgcd( cF, cG ); |
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| 251 | } |
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| 252 | cg = gcd( f.lc(), g.lc() ); |
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| 253 | cl = ( f.lc() / cg ) * g.lc(); |
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[93b061] | 254 | // B = 2 * cg * tmin( |
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[150dc8] | 255 | // maxnorm(f)*power(CanonicalForm(2),f.degree())*isqrt(f.degree()+1), |
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| 256 | // maxnorm(g)*power(CanonicalForm(2),g.degree())*isqrt(g.degree()+1) |
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| 257 | // )+1; |
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[f11d7b] | 258 | M = tmin( maxNorm(f), maxNorm(g) ); |
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| 259 | BB = power(CanonicalForm(2),tmin(f.degree(),g.degree()))*M; |
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| 260 | q = 0; |
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| 261 | i = cf_getNumSmallPrimes() - 1; |
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| 262 | while ( true ) |
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| 263 | { |
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| 264 | B = BB; |
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| 265 | while ( i >= 0 && q < B ) |
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| 266 | { |
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| 267 | p = cf_getSmallPrime( i ); |
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| 268 | i--; |
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| 269 | while ( i >= 0 && mod( cl, p ) == 0 ) |
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| 270 | { |
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| 271 | p = cf_getSmallPrime( i ); |
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| 272 | i--; |
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| 273 | } |
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| 274 | setCharacteristic( p ); |
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| 275 | Dp = gcd( mapinto( f ), mapinto( g ) ); |
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| 276 | Dp = ( Dp / Dp.lc() ) * mapinto( cg ); |
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| 277 | setCharacteristic( 0 ); |
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| 278 | if ( Dp.degree() == 0 ) |
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| 279 | return c; |
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| 280 | if ( q.isZero() ) |
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| 281 | { |
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| 282 | D = mapinto( Dp ); |
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| 283 | q = p; |
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| 284 | B = power(CanonicalForm(2),D.degree())*M+1; |
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| 285 | } |
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| 286 | else |
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| 287 | { |
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| 288 | if ( Dp.degree() == D.degree() ) |
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| 289 | { |
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| 290 | chineseRemainder( D, q, mapinto( Dp ), p, newD, newq ); |
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| 291 | q = newq; |
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| 292 | D = newD; |
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[150dc8] | 293 | } |
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[f11d7b] | 294 | else if ( Dp.degree() < D.degree() ) |
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| 295 | { |
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| 296 | // all previous p's are bad primes |
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| 297 | q = p; |
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| 298 | D = mapinto( Dp ); |
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| 299 | B = power(CanonicalForm(2),D.degree())*M+1; |
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[150dc8] | 300 | } |
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[f11d7b] | 301 | // else p is a bad prime |
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| 302 | } |
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| 303 | } |
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| 304 | if ( i >= 0 ) |
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| 305 | { |
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| 306 | // now balance D mod q |
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| 307 | D = pp( balance( D, q ) ); |
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[ebc602] | 308 | if ( fdivides( D, f ) && fdivides( D, g ) ) |
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[f11d7b] | 309 | return D * c; |
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| 310 | else |
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| 311 | q = 0; |
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[edb4893] | 312 | } |
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[f11d7b] | 313 | else |
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[a7ec94] | 314 | return gcd_poly( F, G ); |
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[f11d7b] | 315 | DEBOUTLN( cerr, "another try ..." ); |
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| 316 | } |
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[edb4893] | 317 | } |
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| 318 | |
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[a7ec94] | 319 | static CanonicalForm |
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| 320 | gcd_poly_p( const CanonicalForm & f, const CanonicalForm & g ) |
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[9bab9f] | 321 | { |
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[df497a] | 322 | CanonicalForm pi, pi1; |
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[a7ec94] | 323 | CanonicalForm C, Ci, Ci1, Hi, bi, pi2; |
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[fda36e] | 324 | bool bpure; |
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[a7ec94] | 325 | int delta = degree( f ) - degree( g ); |
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[9bab9f] | 326 | |
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[a7ec94] | 327 | if ( delta >= 0 ) |
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[df497a] | 328 | { |
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[150dc8] | 329 | pi = f; pi1 = g; |
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[9bab9f] | 330 | } |
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[df497a] | 331 | else |
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| 332 | { |
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[a7ec94] | 333 | pi = g; pi1 = f; delta = -delta; |
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| 334 | } |
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| 335 | Ci = content( pi ); Ci1 = content( pi1 ); |
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| 336 | pi1 = pi1 / Ci1; pi = pi / Ci; |
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| 337 | C = gcd( Ci, Ci1 ); |
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| 338 | if ( !( pi.isUnivariate() && pi1.isUnivariate() ) ) |
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| 339 | { |
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[6f62c3] | 340 | #if 0 |
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| 341 | CanonicalForm newGCD(CanonicalForm A, CanonicalForm B); |
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| 342 | //out_cf("F:",f,"\n"); |
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| 343 | //out_cf("G:",g,"\n"); |
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| 344 | //out_cf("newGCD:",newGCD(f,g),"\n"); |
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| 345 | return newGCD(f,g); |
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| 346 | #endif |
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[fda36e] | 347 | if ( gcd_test_one( pi1, pi, true ) ) |
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[6f62c3] | 348 | { |
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| 349 | C=abs(C); |
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| 350 | //out_cf("GCD:",C,"\n"); |
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| 351 | return C; |
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| 352 | } |
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[fda36e] | 353 | bpure = false; |
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[a7ec94] | 354 | } |
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| 355 | else |
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| 356 | { |
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[fda36e] | 357 | bpure = isPurePoly(pi) && isPurePoly(pi1); |
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| 358 | #ifdef HAVE_NTL |
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| 359 | if ( isOn(SW_USE_NTL_GCD_P) && bpure ) |
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| 360 | return gcd_univar_ntlp(pi, pi1 ) * C; |
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[a7ec94] | 361 | #endif |
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[fda36e] | 362 | } |
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[a7ec94] | 363 | Variable v = f.mvar(); |
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| 364 | Hi = power( LC( pi1, v ), delta ); |
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| 365 | if ( (delta+1) % 2 ) |
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| 366 | bi = 1; |
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| 367 | else |
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| 368 | bi = -1; |
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| 369 | while ( degree( pi1, v ) > 0 ) { |
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| 370 | pi2 = psr( pi, pi1, v ); |
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| 371 | pi2 = pi2 / bi; |
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| 372 | pi = pi1; pi1 = pi2; |
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| 373 | if ( degree( pi1, v ) > 0 ) { |
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| 374 | delta = degree( pi, v ) - degree( pi1, v ); |
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| 375 | if ( (delta+1) % 2 ) |
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| 376 | bi = LC( pi, v ) * power( Hi, delta ); |
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| 377 | else |
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| 378 | bi = -LC( pi, v ) * power( Hi, delta ); |
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| 379 | Hi = power( LC( pi1, v ), delta ) / power( Hi, delta-1 ); |
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| 380 | } |
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[9bab9f] | 381 | } |
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[a7ec94] | 382 | if ( degree( pi1, v ) == 0 ) |
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[6f62c3] | 383 | { |
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| 384 | C=abs(C); |
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| 385 | //out_cf("GCD:",C,"\n"); |
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| 386 | return C; |
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| 387 | } |
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[fda36e] | 388 | pi /= content( pi ); |
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| 389 | if ( bpure ) |
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| 390 | pi /= pi.lc(); |
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[6f62c3] | 391 | C=abs(C*pi); |
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| 392 | //out_cf("GCD:",C,"\n"); |
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| 393 | return C; |
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[a7ec94] | 394 | } |
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| 395 | |
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| 396 | static CanonicalForm |
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| 397 | gcd_poly_0( const CanonicalForm & f, const CanonicalForm & g ) |
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| 398 | { |
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| 399 | CanonicalForm pi, pi1; |
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[df497a] | 400 | CanonicalForm C, Ci, Ci1, Hi, bi, pi2; |
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[a7ec94] | 401 | int delta = degree( f ) - degree( g ); |
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| 402 | |
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| 403 | if ( delta >= 0 ) |
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| 404 | { |
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| 405 | pi = f; pi1 = g; |
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| 406 | } |
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| 407 | else |
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| 408 | { |
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| 409 | pi = g; pi1 = f; delta = -delta; |
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| 410 | } |
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[9bab9f] | 411 | Ci = content( pi ); Ci1 = content( pi1 ); |
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| 412 | pi1 = pi1 / Ci1; pi = pi / Ci; |
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[df497a] | 413 | C = gcd( Ci, Ci1 ); |
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[034eec] | 414 | if ( pi.isUnivariate() && pi1.isUnivariate() ) |
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| 415 | { |
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| 416 | #ifdef HAVE_NTL |
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[a7ec94] | 417 | if ( isOn(SW_USE_NTL_GCD_0) && isPurePoly(pi) && isPurePoly(pi1) ) |
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| 418 | return gcd_univar_ntl0(pi, pi1 ) * C; |
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[df497a] | 419 | #endif |
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[a7ec94] | 420 | return gcd_poly_univar0( pi, pi1, true ) * C; |
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[edb4893] | 421 | } |
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[034eec] | 422 | else if ( gcd_test_one( pi1, pi, true ) ) |
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| 423 | return C; |
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[a7ec94] | 424 | Variable v = f.mvar(); |
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[9bab9f] | 425 | Hi = power( LC( pi1, v ), delta ); |
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| 426 | if ( (delta+1) % 2 ) |
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[150dc8] | 427 | bi = 1; |
---|
[9bab9f] | 428 | else |
---|
[150dc8] | 429 | bi = -1; |
---|
[6f62c3] | 430 | while ( degree( pi1, v ) > 0 ) |
---|
| 431 | { |
---|
[150dc8] | 432 | pi2 = psr( pi, pi1, v ); |
---|
| 433 | pi2 = pi2 / bi; |
---|
| 434 | pi = pi1; pi1 = pi2; |
---|
[6f62c3] | 435 | if ( degree( pi1, v ) > 0 ) |
---|
| 436 | { |
---|
[150dc8] | 437 | delta = degree( pi, v ) - degree( pi1, v ); |
---|
| 438 | if ( (delta+1) % 2 ) |
---|
| 439 | bi = LC( pi, v ) * power( Hi, delta ); |
---|
| 440 | else |
---|
| 441 | bi = -LC( pi, v ) * power( Hi, delta ); |
---|
| 442 | Hi = power( LC( pi1, v ), delta ) / power( Hi, delta-1 ); |
---|
| 443 | } |
---|
[9bab9f] | 444 | } |
---|
| 445 | if ( degree( pi1, v ) == 0 ) |
---|
[150dc8] | 446 | return C; |
---|
[df497a] | 447 | else |
---|
[150dc8] | 448 | return C * pp( pi ); |
---|
[9bab9f] | 449 | } |
---|
| 450 | |
---|
[a7ec94] | 451 | //{{{ static CanonicalForm gcd_poly ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
[dd3e561] | 452 | //{{{ docu |
---|
| 453 | // |
---|
| 454 | // gcd_poly() - calculate polynomial gcd. |
---|
| 455 | // |
---|
| 456 | // This is the dispatcher for polynomial gcd calculation. We call either |
---|
| 457 | // ezgcd(), sparsemod() or gcd_poly1() in dependecy on the current |
---|
| 458 | // characteristic and settings of SW_USE_EZGCD and SW_USE_SPARSEMOD, resp. |
---|
| 459 | // |
---|
| 460 | // Used by gcd() and gcd_poly_univar0(). |
---|
| 461 | // |
---|
| 462 | //}}} |
---|
[0b6919] | 463 | #if 0 |
---|
[bfc606] | 464 | int si_factor_reminder=1; |
---|
[0b6919] | 465 | #endif |
---|
[f63dbca] | 466 | static CanonicalForm |
---|
[a7ec94] | 467 | gcd_poly ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
[f63dbca] | 468 | { |
---|
[a7ec94] | 469 | CanonicalForm fc, gc, d1; |
---|
| 470 | int mp, cc, p1, pe; |
---|
| 471 | mp = f.level()+1; |
---|
| 472 | cf_prepgcd( f, g, cc, p1, pe); |
---|
| 473 | if ( cc != 0 ) |
---|
[abfc3b] | 474 | { |
---|
[a7ec94] | 475 | if ( cc > 0 ) |
---|
[0b6919] | 476 | { |
---|
[a7ec94] | 477 | fc = replacevar( f, Variable(cc), Variable(mp) ); |
---|
| 478 | gc = g; |
---|
[0b6919] | 479 | } |
---|
| 480 | else |
---|
[a7ec94] | 481 | { |
---|
| 482 | fc = replacevar( g, Variable(-cc), Variable(mp) ); |
---|
| 483 | gc = f; |
---|
| 484 | } |
---|
| 485 | return cf_content( fc, gc ); |
---|
[e074407] | 486 | } |
---|
[a7ec94] | 487 | // now each appearing variable is in f and g |
---|
| 488 | fc = f; |
---|
| 489 | gc = g; |
---|
| 490 | if( gcd_avoid_mtaildegree ( fc, gc, d1 ) ) |
---|
| 491 | return d1; |
---|
| 492 | if ( getCharacteristic() != 0 ) |
---|
[abfc3b] | 493 | { |
---|
[a7ec94] | 494 | if ( p1 == fc.level() ) |
---|
| 495 | fc = gcd_poly_p( fc, gc ); |
---|
| 496 | else |
---|
[bfc606] | 497 | { |
---|
[a7ec94] | 498 | fc = replacevar( fc, Variable(p1), Variable(mp) ); |
---|
| 499 | gc = replacevar( gc, Variable(p1), Variable(mp) ); |
---|
| 500 | fc = replacevar( gcd_poly_p( fc, gc ), Variable(mp), Variable(p1) ); |
---|
[bfc606] | 501 | } |
---|
[f63dbca] | 502 | } |
---|
[c992ec1] | 503 | else if (!fc.isUnivariate()) |
---|
[de1a82] | 504 | { |
---|
[c992ec1] | 505 | if ( isOn( SW_USE_EZGCD ) ) |
---|
[6f62c3] | 506 | { |
---|
[c992ec1] | 507 | if ( pe == 1 ) |
---|
| 508 | fc = ezgcd( fc, gc ); |
---|
| 509 | else if ( pe > 0 )// no variable at position 1 |
---|
| 510 | { |
---|
[6f62c3] | 511 | fc = replacevar( fc, Variable(pe), Variable(1) ); |
---|
| 512 | gc = replacevar( gc, Variable(pe), Variable(1) ); |
---|
| 513 | fc = replacevar( ezgcd( fc, gc ), Variable(1), Variable(pe) ); |
---|
[c992ec1] | 514 | } |
---|
| 515 | else |
---|
| 516 | { |
---|
[6f62c3] | 517 | pe = -pe; |
---|
| 518 | fc = swapvar( fc, Variable(pe), Variable(1) ); |
---|
| 519 | gc = swapvar( gc, Variable(pe), Variable(1) ); |
---|
| 520 | fc = swapvar( ezgcd( fc, gc ), Variable(1), Variable(pe) ); |
---|
[c992ec1] | 521 | } |
---|
| 522 | } |
---|
| 523 | else if ( |
---|
| 524 | isOn(SW_USE_CHINREM_GCD) |
---|
| 525 | && (!gc.isUnivariate()) |
---|
| 526 | && (isPurePoly_m(fc)) && (isPurePoly_m(gc)) |
---|
| 527 | ) |
---|
| 528 | { |
---|
| 529 | #if 0 |
---|
| 530 | if ( p1 == fc.level() ) |
---|
| 531 | fc = chinrem_gcd( fc, gc ); |
---|
| 532 | else |
---|
| 533 | { |
---|
| 534 | fc = replacevar( fc, Variable(p1), Variable(mp) ); |
---|
| 535 | gc = replacevar( gc, Variable(p1), Variable(mp) ); |
---|
| 536 | fc = replacevar( chinrem_gcd( fc, gc ), Variable(mp), Variable(p1) ); |
---|
| 537 | } |
---|
| 538 | #else |
---|
| 539 | fc = chinrem_gcd( fc, gc); |
---|
| 540 | #endif |
---|
[6f62c3] | 541 | } |
---|
[1b73cc0] | 542 | } |
---|
[de1a82] | 543 | else |
---|
| 544 | { |
---|
[c992ec1] | 545 | fc = gcd_poly_0( fc, gc ); |
---|
[f63dbca] | 546 | } |
---|
[a7ec94] | 547 | if ( d1.degree() > 0 ) |
---|
[c992ec1] | 548 | fc *= d1; |
---|
[a7ec94] | 549 | return fc; |
---|
[f63dbca] | 550 | } |
---|
[dd3e561] | 551 | //}}} |
---|
[93b061] | 552 | |
---|
[dd3e561] | 553 | //{{{ static CanonicalForm cf_content ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 554 | //{{{ docu |
---|
| 555 | // |
---|
| 556 | // cf_content() - return gcd(g, content(f)). |
---|
| 557 | // |
---|
| 558 | // content(f) is calculated with respect to f's main variable. |
---|
| 559 | // |
---|
| 560 | // Used by gcd(), content(), content( CF, Variable ). |
---|
| 561 | // |
---|
| 562 | //}}} |
---|
[9bab9f] | 563 | static CanonicalForm |
---|
| 564 | cf_content ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 565 | { |
---|
[6f62c3] | 566 | if ( f.inPolyDomain() || ( f.inExtension() && ! getReduce( f.mvar() ) ) ) |
---|
| 567 | { |
---|
[150dc8] | 568 | CFIterator i = f; |
---|
| 569 | CanonicalForm result = g; |
---|
[6f62c3] | 570 | while ( i.hasTerms() && ! result.isOne() ) |
---|
| 571 | { |
---|
[a7ec94] | 572 | result = gcd( i.coeff(), result ); |
---|
[150dc8] | 573 | i++; |
---|
| 574 | } |
---|
| 575 | return result; |
---|
[9bab9f] | 576 | } |
---|
| 577 | else |
---|
[a7ec94] | 578 | return abs( f ); |
---|
[9bab9f] | 579 | } |
---|
[dd3e561] | 580 | //}}} |
---|
[9bab9f] | 581 | |
---|
[4ea0ab] | 582 | //{{{ CanonicalForm content ( const CanonicalForm & f ) |
---|
| 583 | //{{{ docu |
---|
| 584 | // |
---|
| 585 | // content() - return content(f) with respect to main variable. |
---|
| 586 | // |
---|
[dd3e561] | 587 | // Normalizes result. |
---|
| 588 | // |
---|
[4ea0ab] | 589 | //}}} |
---|
[9bab9f] | 590 | CanonicalForm |
---|
| 591 | content ( const CanonicalForm & f ) |
---|
| 592 | { |
---|
[6f62c3] | 593 | if ( f.inPolyDomain() || ( f.inExtension() && ! getReduce( f.mvar() ) ) ) |
---|
| 594 | { |
---|
[a7ec94] | 595 | CFIterator i = f; |
---|
| 596 | CanonicalForm result = abs( i.coeff() ); |
---|
| 597 | i++; |
---|
[6f62c3] | 598 | while ( i.hasTerms() && ! result.isOne() ) |
---|
| 599 | { |
---|
[a7ec94] | 600 | result = gcd( i.coeff(), result ); |
---|
| 601 | i++; |
---|
| 602 | } |
---|
| 603 | return result; |
---|
| 604 | } |
---|
| 605 | else |
---|
| 606 | return abs( f ); |
---|
[9bab9f] | 607 | } |
---|
[4ea0ab] | 608 | //}}} |
---|
[9bab9f] | 609 | |
---|
[dd3e561] | 610 | //{{{ CanonicalForm content ( const CanonicalForm & f, const Variable & x ) |
---|
| 611 | //{{{ docu |
---|
| 612 | // |
---|
| 613 | // content() - return content(f) with respect to x. |
---|
| 614 | // |
---|
| 615 | // x should be a polynomial variable. |
---|
| 616 | // |
---|
| 617 | //}}} |
---|
[9bab9f] | 618 | CanonicalForm |
---|
| 619 | content ( const CanonicalForm & f, const Variable & x ) |
---|
| 620 | { |
---|
[dd3e561] | 621 | ASSERT( x.level() > 0, "cannot calculate content with respect to algebraic variable" ); |
---|
| 622 | Variable y = f.mvar(); |
---|
| 623 | |
---|
| 624 | if ( y == x ) |
---|
[150dc8] | 625 | return cf_content( f, 0 ); |
---|
[dd3e561] | 626 | else if ( y < x ) |
---|
[150dc8] | 627 | return f; |
---|
[9bab9f] | 628 | else |
---|
[150dc8] | 629 | return swapvar( content( swapvar( f, y, x ), y ), y, x ); |
---|
[9bab9f] | 630 | } |
---|
[dd3e561] | 631 | //}}} |
---|
[9bab9f] | 632 | |
---|
[dd3e561] | 633 | //{{{ CanonicalForm vcontent ( const CanonicalForm & f, const Variable & x ) |
---|
| 634 | //{{{ docu |
---|
| 635 | // |
---|
| 636 | // vcontent() - return content of f with repect to variables >= x. |
---|
| 637 | // |
---|
| 638 | // The content is recursively calculated over all coefficients in |
---|
| 639 | // f having level less than x. x should be a polynomial |
---|
| 640 | // variable. |
---|
| 641 | // |
---|
| 642 | //}}} |
---|
[9bab9f] | 643 | CanonicalForm |
---|
| 644 | vcontent ( const CanonicalForm & f, const Variable & x ) |
---|
| 645 | { |
---|
[dd3e561] | 646 | ASSERT( x.level() > 0, "cannot calculate vcontent with respect to algebraic variable" ); |
---|
| 647 | |
---|
[9bab9f] | 648 | if ( f.mvar() <= x ) |
---|
[150dc8] | 649 | return content( f, x ); |
---|
[9bab9f] | 650 | else { |
---|
[150dc8] | 651 | CFIterator i; |
---|
| 652 | CanonicalForm d = 0; |
---|
| 653 | for ( i = f; i.hasTerms() && ! d.isOne(); i++ ) |
---|
| 654 | d = gcd( d, vcontent( i.coeff(), x ) ); |
---|
| 655 | return d; |
---|
[9bab9f] | 656 | } |
---|
| 657 | } |
---|
[dd3e561] | 658 | //}}} |
---|
[9bab9f] | 659 | |
---|
[4ea0ab] | 660 | //{{{ CanonicalForm pp ( const CanonicalForm & f ) |
---|
| 661 | //{{{ docu |
---|
| 662 | // |
---|
| 663 | // pp() - return primitive part of f. |
---|
| 664 | // |
---|
[dd3e561] | 665 | // Returns zero if f equals zero, otherwise f / content(f). |
---|
| 666 | // |
---|
[4ea0ab] | 667 | //}}} |
---|
[9bab9f] | 668 | CanonicalForm |
---|
| 669 | pp ( const CanonicalForm & f ) |
---|
| 670 | { |
---|
| 671 | if ( f.isZero() ) |
---|
[150dc8] | 672 | return f; |
---|
[9bab9f] | 673 | else |
---|
[150dc8] | 674 | return f / content( f ); |
---|
[9bab9f] | 675 | } |
---|
[4ea0ab] | 676 | //}}} |
---|
[9bab9f] | 677 | |
---|
[ff6222] | 678 | CanonicalForm |
---|
[9bab9f] | 679 | gcd ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 680 | { |
---|
[a7ec94] | 681 | bool b = f.isZero(); |
---|
| 682 | if ( b || g.isZero() ) |
---|
| 683 | { |
---|
| 684 | if ( b ) |
---|
| 685 | return abs( g ); |
---|
[abfc3b] | 686 | else |
---|
[a7ec94] | 687 | return abs( f ); |
---|
| 688 | } |
---|
| 689 | if ( f.inPolyDomain() || g.inPolyDomain() ) |
---|
| 690 | { |
---|
| 691 | if ( f.mvar() != g.mvar() ) |
---|
| 692 | { |
---|
| 693 | if ( f.mvar() > g.mvar() ) |
---|
| 694 | return cf_content( f, g ); |
---|
| 695 | else |
---|
| 696 | return cf_content( g, f ); |
---|
| 697 | } |
---|
[150dc8] | 698 | if ( f.inExtension() && getReduce( f.mvar() ) ) |
---|
| 699 | return 1; |
---|
[a7ec94] | 700 | else |
---|
| 701 | { |
---|
[ebc602] | 702 | if ( fdivides( f, g ) ) |
---|
[a7ec94] | 703 | return abs( f ); |
---|
[ebc602] | 704 | else if ( fdivides( g, f ) ) |
---|
[a7ec94] | 705 | return abs( g ); |
---|
| 706 | if ( !( getCharacteristic() == 0 && isOn( SW_RATIONAL ) ) ) |
---|
| 707 | { |
---|
| 708 | CanonicalForm d; |
---|
[5944b4] | 709 | #if 1 |
---|
[a7ec94] | 710 | do{ d = gcd_poly( f, g ); } |
---|
[ebc602] | 711 | while ((!fdivides(d,f)) || (!fdivides(d,g))); |
---|
[5944b4] | 712 | #else |
---|
| 713 | while(1) |
---|
[f4b180] | 714 | { |
---|
| 715 | d = gcd_poly( f, g ); |
---|
[5944b4] | 716 | if ((fdivides(d,f)) && (fdivides(d,g))) break; |
---|
| 717 | printf("g"); fflush(stdout); |
---|
| 718 | } |
---|
| 719 | #endif |
---|
[a7ec94] | 720 | return abs( d ); |
---|
| 721 | } |
---|
| 722 | else |
---|
| 723 | { |
---|
[150dc8] | 724 | CanonicalForm cdF = bCommonDen( f ); |
---|
| 725 | CanonicalForm cdG = bCommonDen( g ); |
---|
| 726 | Off( SW_RATIONAL ); |
---|
| 727 | CanonicalForm l = lcm( cdF, cdG ); |
---|
| 728 | On( SW_RATIONAL ); |
---|
| 729 | CanonicalForm F = f * l, G = g * l; |
---|
| 730 | Off( SW_RATIONAL ); |
---|
[a7ec94] | 731 | do { l = gcd_poly( F, G ); } |
---|
[ebc602] | 732 | while ((!fdivides(l,F)) || (!fdivides(l,G))); |
---|
[150dc8] | 733 | On( SW_RATIONAL ); |
---|
[a7ec94] | 734 | return abs( l ); |
---|
[150dc8] | 735 | } |
---|
| 736 | } |
---|
[a7ec94] | 737 | } |
---|
| 738 | if ( f.inBaseDomain() && g.inBaseDomain() ) |
---|
| 739 | return bgcd( f, g ); |
---|
[9bab9f] | 740 | else |
---|
[a7ec94] | 741 | return 1; |
---|
[9bab9f] | 742 | } |
---|
| 743 | |
---|
[dd3e561] | 744 | //{{{ CanonicalForm lcm ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 745 | //{{{ docu |
---|
| 746 | // |
---|
| 747 | // lcm() - return least common multiple of f and g. |
---|
| 748 | // |
---|
| 749 | // The lcm is calculated using the formula lcm(f, g) = f * g / gcd(f, g). |
---|
| 750 | // |
---|
| 751 | // Returns zero if one of f or g equals zero. |
---|
| 752 | // |
---|
| 753 | //}}} |
---|
[9bab9f] | 754 | CanonicalForm |
---|
| 755 | lcm ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 756 | { |
---|
[dd3e561] | 757 | if ( f.isZero() || g.isZero() ) |
---|
[a7ec94] | 758 | return 0; |
---|
[dd3e561] | 759 | else |
---|
[150dc8] | 760 | return ( f / gcd( f, g ) ) * g; |
---|
[9bab9f] | 761 | } |
---|
[dd3e561] | 762 | //}}} |
---|
[a7ec94] | 763 | |
---|
| 764 | #ifdef HAVE_NTL |
---|
| 765 | |
---|
| 766 | static CanonicalForm |
---|
| 767 | gcd_univar_ntl0( const CanonicalForm & F, const CanonicalForm & G ) |
---|
| 768 | { |
---|
| 769 | ZZX F1=convertFacCF2NTLZZX(F); |
---|
| 770 | ZZX G1=convertFacCF2NTLZZX(G); |
---|
| 771 | ZZX R=GCD(F1,G1); |
---|
| 772 | return convertNTLZZX2CF(R,F.mvar()); |
---|
| 773 | } |
---|
| 774 | |
---|
| 775 | static CanonicalForm |
---|
| 776 | gcd_univar_ntlp( const CanonicalForm & F, const CanonicalForm & G ) |
---|
| 777 | { |
---|
[c6eecb] | 778 | if (fac_NTL_char!=getCharacteristic()) |
---|
| 779 | { |
---|
| 780 | fac_NTL_char=getCharacteristic(); |
---|
| 781 | #ifdef NTL_ZZ |
---|
| 782 | ZZ r; |
---|
| 783 | r=getCharacteristic(); |
---|
| 784 | ZZ_pContext ccc(r); |
---|
| 785 | #else |
---|
[a7ec94] | 786 | zz_pContext ccc(getCharacteristic()); |
---|
[c6eecb] | 787 | #endif |
---|
[a7ec94] | 788 | ccc.restore(); |
---|
[c6eecb] | 789 | #ifdef NTL_ZZ |
---|
| 790 | ZZ_p::init(r); |
---|
| 791 | #else |
---|
[a7ec94] | 792 | zz_p::init(getCharacteristic()); |
---|
[c6eecb] | 793 | #endif |
---|
| 794 | } |
---|
| 795 | #ifdef NTL_ZZ |
---|
| 796 | ZZ_pX F1=convertFacCF2NTLZZpX(F); |
---|
| 797 | ZZ_pX G1=convertFacCF2NTLZZpX(G); |
---|
| 798 | ZZ_pX R=GCD(F1,G1); |
---|
| 799 | return convertNTLZZpX2CF(R,F.mvar()); |
---|
| 800 | #else |
---|
| 801 | zz_pX F1=convertFacCF2NTLzzpX(F); |
---|
| 802 | zz_pX G1=convertFacCF2NTLzzpX(G); |
---|
| 803 | zz_pX R=GCD(F1,G1); |
---|
| 804 | return convertNTLzzpX2CF(R,F.mvar()); |
---|
| 805 | #endif |
---|
[a7ec94] | 806 | } |
---|
| 807 | |
---|
| 808 | #endif |
---|
| 809 | |
---|
| 810 | static bool |
---|
| 811 | gcd_avoid_mtaildegree ( CanonicalForm & f1, CanonicalForm & g1, CanonicalForm & d1 ) |
---|
| 812 | { |
---|
| 813 | bool rdy = true; |
---|
| 814 | int df = f1.taildegree(); |
---|
| 815 | int dg = g1.taildegree(); |
---|
| 816 | |
---|
| 817 | d1 = d1.genOne(); |
---|
| 818 | if ( dg == 0 ) |
---|
| 819 | { |
---|
| 820 | if ( df == 0 ) |
---|
| 821 | return false; |
---|
| 822 | else |
---|
| 823 | { |
---|
| 824 | if ( f1.degree() == df ) |
---|
| 825 | d1 = cf_content( g1, LC( f1 ) ); |
---|
| 826 | else |
---|
| 827 | { |
---|
| 828 | f1 /= power( f1.mvar(), df ); |
---|
| 829 | rdy = false; |
---|
| 830 | } |
---|
| 831 | } |
---|
| 832 | } |
---|
| 833 | else |
---|
| 834 | { |
---|
| 835 | if ( df == 0) |
---|
| 836 | { |
---|
| 837 | if ( g1.degree() == dg ) |
---|
| 838 | d1 = cf_content( f1, LC( g1 ) ); |
---|
| 839 | else |
---|
| 840 | { |
---|
| 841 | g1 /= power( g1.mvar(), dg ); |
---|
| 842 | rdy = false; |
---|
| 843 | } |
---|
| 844 | } |
---|
| 845 | else |
---|
| 846 | { |
---|
| 847 | if ( df > dg ) |
---|
| 848 | d1 = power( f1.mvar(), dg ); |
---|
| 849 | else |
---|
| 850 | d1 = power( f1.mvar(), df ); |
---|
| 851 | if ( f1.degree() == df ) |
---|
| 852 | { |
---|
| 853 | if (g1.degree() == dg) |
---|
| 854 | d1 *= gcd( LC( f1 ), LC( g1 ) ); |
---|
| 855 | else |
---|
| 856 | { |
---|
| 857 | g1 /= power( g1.mvar(), dg); |
---|
| 858 | d1 *= cf_content( g1, LC( f1 ) ); |
---|
| 859 | } |
---|
| 860 | } |
---|
| 861 | else |
---|
| 862 | { |
---|
| 863 | f1 /= power( f1.mvar(), df ); |
---|
| 864 | if ( g1.degree() == dg ) |
---|
| 865 | d1 *= cf_content( f1, LC( g1 ) ); |
---|
| 866 | else |
---|
| 867 | { |
---|
| 868 | g1 /= power( g1.mvar(), dg ); |
---|
| 869 | rdy = false; |
---|
| 870 | } |
---|
| 871 | } |
---|
| 872 | } |
---|
| 873 | } |
---|
| 874 | return rdy; |
---|
| 875 | } |
---|
| 876 | |
---|
| 877 | /* |
---|
| 878 | * compute positions p1 and pe of optimal variables: |
---|
| 879 | * pe is used in "ezgcd" and |
---|
| 880 | * p1 in "gcd_poly1" |
---|
| 881 | */ |
---|
| 882 | static |
---|
| 883 | void optvalues ( const int * df, const int * dg, const int n, int & p1, int &pe ) |
---|
| 884 | { |
---|
| 885 | int i, o1, oe; |
---|
| 886 | if ( df[n] > dg[n] ) |
---|
| 887 | { |
---|
| 888 | o1 = df[n]; oe = dg[n]; |
---|
| 889 | } |
---|
| 890 | else |
---|
| 891 | { |
---|
| 892 | o1 = dg[n]; oe = df[n]; |
---|
| 893 | } |
---|
| 894 | i = n-1; |
---|
| 895 | while ( i > 0 ) |
---|
| 896 | { |
---|
| 897 | if ( df[i] != 0 ) |
---|
| 898 | { |
---|
| 899 | if ( df[i] > dg[i] ) |
---|
| 900 | { |
---|
| 901 | if ( o1 > df[i]) { o1 = df[i]; p1 = i; } |
---|
| 902 | if ( oe <= dg[i]) { oe = dg[i]; pe = i; } |
---|
| 903 | } |
---|
| 904 | else |
---|
| 905 | { |
---|
| 906 | if ( o1 > dg[i]) { o1 = dg[i]; p1 = i; } |
---|
| 907 | if ( oe <= df[i]) { oe = df[i]; pe = i; } |
---|
| 908 | } |
---|
| 909 | } |
---|
| 910 | i--; |
---|
| 911 | } |
---|
| 912 | } |
---|
| 913 | |
---|
| 914 | /* |
---|
| 915 | * make some changes of variables, see optvalues |
---|
| 916 | */ |
---|
| 917 | static void |
---|
| 918 | cf_prepgcd( const CanonicalForm & f, const CanonicalForm & g, int & cc, int & p1, int &pe ) |
---|
| 919 | { |
---|
| 920 | int i, k, n; |
---|
| 921 | n = f.level(); |
---|
| 922 | cc = 0; |
---|
| 923 | p1 = pe = n; |
---|
| 924 | if ( n == 1 ) |
---|
| 925 | return; |
---|
| 926 | int * degsf = new int[n+1]; |
---|
| 927 | int * degsg = new int[n+1]; |
---|
| 928 | for ( i = n; i > 0; i-- ) |
---|
| 929 | { |
---|
| 930 | degsf[i] = degsg[i] = 0; |
---|
| 931 | } |
---|
| 932 | degsf = degrees( f, degsf ); |
---|
| 933 | degsg = degrees( g, degsg ); |
---|
| 934 | |
---|
| 935 | k = 0; |
---|
| 936 | for ( i = n-1; i > 0; i-- ) |
---|
| 937 | { |
---|
[f4b180] | 938 | if ( degsf[i] == 0 ) |
---|
[a7ec94] | 939 | { |
---|
| 940 | if ( degsg[i] != 0 ) |
---|
| 941 | { |
---|
| 942 | cc = -i; |
---|
| 943 | break; |
---|
| 944 | } |
---|
| 945 | } |
---|
| 946 | else |
---|
| 947 | { |
---|
| 948 | if ( degsg[i] == 0 ) |
---|
| 949 | { |
---|
| 950 | cc = i; |
---|
| 951 | break; |
---|
| 952 | } |
---|
| 953 | else k++; |
---|
| 954 | } |
---|
| 955 | } |
---|
| 956 | |
---|
| 957 | if ( ( cc == 0 ) && ( k != 0 ) ) |
---|
| 958 | optvalues( degsf, degsg, n, p1, pe ); |
---|
| 959 | if ( ( pe != 1 ) && ( degsf[1] != 0 ) ) |
---|
| 960 | pe = -pe; |
---|
[f4b180] | 961 | |
---|
[a7ec94] | 962 | delete [] degsf; |
---|
| 963 | delete [] degsg; |
---|
| 964 | } |
---|
[6f62c3] | 965 | |
---|
| 966 | |
---|
| 967 | static CanonicalForm |
---|
| 968 | balance_p ( const CanonicalForm & f, const CanonicalForm & q ) |
---|
| 969 | { |
---|
| 970 | Variable x = f.mvar(); |
---|
| 971 | CanonicalForm result = 0, qh = q / 2; |
---|
| 972 | CanonicalForm c; |
---|
| 973 | CFIterator i; |
---|
| 974 | for ( i = f; i.hasTerms(); i++ ) |
---|
| 975 | { |
---|
| 976 | c = i.coeff(); |
---|
| 977 | if ( c.inCoeffDomain()) |
---|
| 978 | { |
---|
| 979 | if ( c > qh ) |
---|
| 980 | result += power( x, i.exp() ) * (c - q); |
---|
| 981 | else |
---|
| 982 | result += power( x, i.exp() ) * c; |
---|
| 983 | } |
---|
[f4b180] | 984 | else |
---|
[6f62c3] | 985 | result += power( x, i.exp() ) * balance_p(c,q); |
---|
| 986 | } |
---|
| 987 | return result; |
---|
| 988 | } |
---|
| 989 | |
---|
| 990 | CanonicalForm chinrem_gcd ( const CanonicalForm & FF, const CanonicalForm & GG ) |
---|
| 991 | { |
---|
| 992 | CanonicalForm f, g, cg, cl, q, Dp, newD, D, newq; |
---|
[c992ec1] | 993 | int p, i, dp_deg, d_deg;; |
---|
[6f62c3] | 994 | |
---|
| 995 | CanonicalForm cd = bCommonDen( FF ); |
---|
| 996 | f=cd*FF; |
---|
| 997 | f /=vcontent(f,Variable(1)); |
---|
[08a6ebb] | 998 | //cd = bCommonDen( f ); f *=cd; |
---|
| 999 | //f /=vcontent(f,Variable(1)); |
---|
[6f62c3] | 1000 | |
---|
| 1001 | cd = bCommonDen( GG ); |
---|
| 1002 | g=cd*GG; |
---|
| 1003 | g /=vcontent(g,Variable(1)); |
---|
[08a6ebb] | 1004 | //cd = bCommonDen( g ); g *=cd; |
---|
| 1005 | //g /=vcontent(g,Variable(1)); |
---|
[6f62c3] | 1006 | |
---|
| 1007 | q = 0; |
---|
| 1008 | i = cf_getNumBigPrimes() - 1; |
---|
| 1009 | cl = f.lc()* g.lc(); |
---|
| 1010 | |
---|
| 1011 | while ( true ) |
---|
| 1012 | { |
---|
| 1013 | p = cf_getBigPrime( i ); |
---|
| 1014 | i--; |
---|
| 1015 | while ( i >= 0 && mod( cl, p ) == 0 ) |
---|
| 1016 | { |
---|
| 1017 | p = cf_getBigPrime( i ); |
---|
| 1018 | i--; |
---|
| 1019 | } |
---|
| 1020 | setCharacteristic( p ); |
---|
| 1021 | Dp = gcd( mapinto( f ), mapinto( g ) ); |
---|
[08a6ebb] | 1022 | Dp /=Dp.lc(); |
---|
[6f62c3] | 1023 | setCharacteristic( 0 ); |
---|
| 1024 | dp_deg=totaldegree(Dp); |
---|
| 1025 | if ( dp_deg == 0 ) |
---|
| 1026 | return CanonicalForm(1); |
---|
| 1027 | if ( q.isZero() ) |
---|
| 1028 | { |
---|
| 1029 | D = mapinto( Dp ); |
---|
| 1030 | d_deg=dp_deg; |
---|
| 1031 | q = p; |
---|
| 1032 | } |
---|
| 1033 | else |
---|
| 1034 | { |
---|
| 1035 | if ( dp_deg == d_deg ) |
---|
| 1036 | { |
---|
| 1037 | chineseRemainder( D, q, mapinto( Dp ), p, newD, newq ); |
---|
| 1038 | q = newq; |
---|
| 1039 | D = newD; |
---|
| 1040 | } |
---|
[f4b180] | 1041 | else if ( dp_deg < d_deg ) |
---|
[6f62c3] | 1042 | { |
---|
| 1043 | // all previous p's are bad primes |
---|
| 1044 | q = p; |
---|
| 1045 | D = mapinto( Dp ); |
---|
| 1046 | d_deg=dp_deg; |
---|
| 1047 | } |
---|
[f4b180] | 1048 | //else dp_deg > d_deg: bad prime |
---|
[6f62c3] | 1049 | } |
---|
[08a6ebb] | 1050 | if ( i >= 0 ) |
---|
[6f62c3] | 1051 | { |
---|
[c992ec1] | 1052 | CanonicalForm Dn= Farey(D,q); |
---|
| 1053 | int is_rat=isOn(SW_RATIONAL); |
---|
| 1054 | On(SW_RATIONAL); |
---|
| 1055 | CanonicalForm cd = bCommonDen( Dn ); // we need On(SW_RATIONAL) |
---|
| 1056 | if (!is_rat) Off(SW_RATIONAL); |
---|
| 1057 | Dn *=cd; |
---|
| 1058 | //Dn /=vcontent(Dn,Variable(1)); |
---|
| 1059 | if ( fdivides( Dn, f ) && fdivides( Dn, g ) ) |
---|
[6f62c3] | 1060 | { |
---|
[c992ec1] | 1061 | return Dn; |
---|
[6f62c3] | 1062 | } |
---|
[c992ec1] | 1063 | //else: try more primes |
---|
[6f62c3] | 1064 | } |
---|
| 1065 | else |
---|
[c992ec1] | 1066 | { // try other method |
---|
[6f62c3] | 1067 | Off(SW_USE_CHINREM_GCD); |
---|
| 1068 | D=gcd_poly( f, g ); |
---|
| 1069 | On(SW_USE_CHINREM_GCD); |
---|
| 1070 | return D; |
---|
| 1071 | } |
---|
| 1072 | } |
---|
| 1073 | } |
---|
| 1074 | |
---|