[493c477] | 1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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[9bab9f] | 2 | |
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[abddbe] | 3 | /** |
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| 4 | * @file cf_gcd.cc |
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| 5 | * |
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[1a82eb] | 6 | * gcd/content/lcm of polynomials |
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| 7 | * |
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| 8 | * To compute the GCD different variants are chosen automatically |
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[abddbe] | 9 | **/ |
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[9f7665] | 10 | |
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[e4fe2b] | 11 | #include "config.h" |
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[9f7665] | 12 | |
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[ab4548f] | 13 | |
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[2a95b2] | 14 | #include "timing.h" |
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[650f2d8] | 15 | #include "cf_assert.h" |
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[93b061] | 16 | #include "debug.h" |
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| 17 | |
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[9bab9f] | 18 | #include "cf_defs.h" |
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| 19 | #include "canonicalform.h" |
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| 20 | #include "cf_iter.h" |
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| 21 | #include "cf_reval.h" |
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[edb4893] | 22 | #include "cf_primes.h" |
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[fbefc9] | 23 | #include "cf_algorithm.h" |
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[1a82eb] | 24 | #include "cfEzgcd.h" |
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[da6b0c] | 25 | #include "cfGcdAlgExt.h" |
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[1a82eb] | 26 | #include "cfSubResGcd.h" |
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[2080e2] | 27 | #include "cfModGcd.h" |
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[6e62ce] | 28 | #include "FLINTconvert.h" |
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[85e90d] | 29 | #include "facAlgFuncUtil.h" |
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[845303c] | 30 | #include "templates/ftmpl_functions.h" |
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[edb4893] | 31 | |
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[f11d7b] | 32 | #ifdef HAVE_NTL |
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[034eec] | 33 | #include <NTL/ZZX.h> |
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[f11d7b] | 34 | #include "NTLconvert.h" |
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[a7ec94] | 35 | bool isPurePoly(const CanonicalForm & ); |
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[447349] | 36 | #endif |
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[f11d7b] | 37 | |
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[27bb97f] | 38 | void out_cf(const char *s1,const CanonicalForm &f,const char *s2); |
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[6f62c3] | 39 | |
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[b52d27] | 40 | /** static CanonicalForm icontent ( const CanonicalForm & f, const CanonicalForm & c ) |
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| 41 | * |
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| 42 | * icontent() - return gcd of c and all coefficients of f which |
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| 43 | * are in a coefficient domain. |
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| 44 | * |
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| 45 | * @sa icontent(). |
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| 46 | * |
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| 47 | **/ |
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[9bab9f] | 48 | static CanonicalForm |
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| 49 | icontent ( const CanonicalForm & f, const CanonicalForm & c ) |
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| 50 | { |
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[c30347] | 51 | if ( f.inBaseDomain() ) |
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| 52 | { |
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| 53 | if (c.isZero()) return abs(f); |
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| 54 | return bgcd( f, c ); |
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| 55 | } |
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[ef20c7] | 56 | //else if ( f.inCoeffDomain() ) |
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| 57 | // return gcd(f,c); |
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[c30347] | 58 | else |
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| 59 | { |
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[150dc8] | 60 | CanonicalForm g = c; |
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| 61 | for ( CFIterator i = f; i.hasTerms() && ! g.isOne(); i++ ) |
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| 62 | g = icontent( i.coeff(), g ); |
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| 63 | return g; |
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[9bab9f] | 64 | } |
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| 65 | } |
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[b52d27] | 66 | |
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| 67 | /** CanonicalForm icontent ( const CanonicalForm & f ) |
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| 68 | * |
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| 69 | * icontent() - return gcd over all coefficients of f which are |
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| 70 | * in a coefficient domain. |
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| 71 | * |
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| 72 | **/ |
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[9bab9f] | 73 | CanonicalForm |
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| 74 | icontent ( const CanonicalForm & f ) |
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| 75 | { |
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| 76 | return icontent( f, 0 ); |
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| 77 | } |
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[b52d27] | 78 | |
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[845303c] | 79 | #ifdef HAVE_FLINT |
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| 80 | static CanonicalForm |
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| 81 | gcd_univar_flintp (const CanonicalForm& F, const CanonicalForm& G) |
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| 82 | { |
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| 83 | nmod_poly_t F1, G1; |
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| 84 | convertFacCF2nmod_poly_t (F1, F); |
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| 85 | convertFacCF2nmod_poly_t (G1, G); |
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| 86 | nmod_poly_gcd (F1, F1, G1); |
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| 87 | CanonicalForm result= convertnmod_poly_t2FacCF (F1, F.mvar()); |
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| 88 | nmod_poly_clear (F1); |
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| 89 | nmod_poly_clear (G1); |
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| 90 | return result; |
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| 91 | } |
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| 92 | |
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| 93 | static CanonicalForm |
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| 94 | gcd_univar_flint0( const CanonicalForm & F, const CanonicalForm & G ) |
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| 95 | { |
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| 96 | fmpz_poly_t F1, G1; |
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| 97 | convertFacCF2Fmpz_poly_t(F1, F); |
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| 98 | convertFacCF2Fmpz_poly_t(G1, G); |
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| 99 | fmpz_poly_gcd (F1, F1, G1); |
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| 100 | CanonicalForm result= convertFmpz_poly_t2FacCF (F1, F.mvar()); |
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| 101 | fmpz_poly_clear (F1); |
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| 102 | fmpz_poly_clear (G1); |
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| 103 | return result; |
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| 104 | } |
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| 105 | #endif |
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| 106 | |
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| 107 | #ifdef HAVE_NTL |
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[0ad478] | 108 | #ifndef HAVE_FLINT |
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[845303c] | 109 | static CanonicalForm |
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| 110 | gcd_univar_ntl0( const CanonicalForm & F, const CanonicalForm & G ) |
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| 111 | { |
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| 112 | ZZX F1=convertFacCF2NTLZZX(F); |
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| 113 | ZZX G1=convertFacCF2NTLZZX(G); |
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| 114 | ZZX R=GCD(F1,G1); |
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| 115 | return convertNTLZZX2CF(R,F.mvar()); |
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| 116 | } |
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| 117 | |
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| 118 | static CanonicalForm |
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| 119 | gcd_univar_ntlp( const CanonicalForm & F, const CanonicalForm & G ) |
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| 120 | { |
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[0ad478] | 121 | int ch=getCharacteristic(); |
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| 122 | if (fac_NTL_char!=ch) |
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[845303c] | 123 | { |
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[0ad478] | 124 | fac_NTL_char=ch; |
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| 125 | zz_p::init(ch); |
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[845303c] | 126 | } |
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| 127 | zz_pX F1=convertFacCF2NTLzzpX(F); |
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| 128 | zz_pX G1=convertFacCF2NTLzzpX(G); |
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| 129 | zz_pX R=GCD(F1,G1); |
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| 130 | return convertNTLzzpX2CF(R,F.mvar()); |
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| 131 | } |
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| 132 | #endif |
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[0ad478] | 133 | #endif |
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[845303c] | 134 | |
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| 135 | //{{{ static CanonicalForm balance_p ( const CanonicalForm & f, const CanonicalForm & q ) |
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| 136 | //{{{ docu |
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| 137 | // |
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| 138 | // balance_p() - map f from positive to symmetric representation |
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| 139 | // mod q. |
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| 140 | // |
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| 141 | // This makes sense for univariate polynomials over Z only. |
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| 142 | // q should be an integer. |
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| 143 | // |
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| 144 | // Used by gcd_poly_univar0(). |
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| 145 | // |
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| 146 | //}}} |
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| 147 | |
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| 148 | static CanonicalForm |
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| 149 | balance_p ( const CanonicalForm & f, const CanonicalForm & q, const CanonicalForm & qh ) |
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| 150 | { |
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| 151 | Variable x = f.mvar(); |
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| 152 | CanonicalForm result = 0; |
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| 153 | CanonicalForm c; |
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| 154 | CFIterator i; |
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| 155 | for ( i = f; i.hasTerms(); i++ ) |
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| 156 | { |
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| 157 | c = i.coeff(); |
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| 158 | if ( c.inCoeffDomain()) |
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| 159 | { |
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| 160 | if ( c > qh ) |
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| 161 | result += power( x, i.exp() ) * (c - q); |
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| 162 | else |
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| 163 | result += power( x, i.exp() ) * c; |
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| 164 | } |
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| 165 | else |
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| 166 | result += power( x, i.exp() ) * balance_p(c,q,qh); |
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| 167 | } |
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| 168 | return result; |
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| 169 | } |
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| 170 | |
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| 171 | static CanonicalForm |
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| 172 | balance_p ( const CanonicalForm & f, const CanonicalForm & q ) |
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| 173 | { |
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| 174 | CanonicalForm qh = q / 2; |
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| 175 | return balance_p (f, q, qh); |
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| 176 | } |
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| 177 | |
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| 178 | static CanonicalForm gcd_poly_univar0( const CanonicalForm & F, const CanonicalForm & G, bool primitive ) |
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| 179 | { |
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| 180 | CanonicalForm f, g, c, cg, cl, BB, B, M, q, Dp, newD, D, newq; |
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| 181 | int p, i; |
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| 182 | |
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| 183 | if ( primitive ) |
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| 184 | { |
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| 185 | f = F; |
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| 186 | g = G; |
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| 187 | c = 1; |
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| 188 | } |
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| 189 | else |
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| 190 | { |
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| 191 | CanonicalForm cF = content( F ), cG = content( G ); |
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| 192 | f = F / cF; |
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| 193 | g = G / cG; |
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| 194 | c = bgcd( cF, cG ); |
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| 195 | } |
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| 196 | cg = gcd( f.lc(), g.lc() ); |
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| 197 | cl = ( f.lc() / cg ) * g.lc(); |
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| 198 | // B = 2 * cg * tmin( |
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| 199 | // maxnorm(f)*power(CanonicalForm(2),f.degree())*isqrt(f.degree()+1), |
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| 200 | // maxnorm(g)*power(CanonicalForm(2),g.degree())*isqrt(g.degree()+1) |
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| 201 | // )+1; |
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| 202 | M = tmin( maxNorm(f), maxNorm(g) ); |
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| 203 | BB = power(CanonicalForm(2),tmin(f.degree(),g.degree()))*M; |
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| 204 | q = 0; |
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| 205 | i = cf_getNumSmallPrimes() - 1; |
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| 206 | while ( true ) |
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| 207 | { |
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| 208 | B = BB; |
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| 209 | while ( i >= 0 && q < B ) |
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| 210 | { |
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| 211 | p = cf_getSmallPrime( i ); |
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| 212 | i--; |
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| 213 | while ( i >= 0 && mod( cl, p ) == 0 ) |
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| 214 | { |
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| 215 | p = cf_getSmallPrime( i ); |
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| 216 | i--; |
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| 217 | } |
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| 218 | setCharacteristic( p ); |
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| 219 | Dp = gcd( mapinto( f ), mapinto( g ) ); |
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| 220 | Dp = ( Dp / Dp.lc() ) * mapinto( cg ); |
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| 221 | setCharacteristic( 0 ); |
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| 222 | if ( Dp.degree() == 0 ) |
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| 223 | return c; |
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| 224 | if ( q.isZero() ) |
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| 225 | { |
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| 226 | D = mapinto( Dp ); |
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| 227 | q = p; |
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| 228 | B = power(CanonicalForm(2),D.degree())*M+1; |
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| 229 | } |
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| 230 | else |
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| 231 | { |
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| 232 | if ( Dp.degree() == D.degree() ) |
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| 233 | { |
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| 234 | chineseRemainder( D, q, mapinto( Dp ), p, newD, newq ); |
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| 235 | q = newq; |
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| 236 | D = newD; |
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| 237 | } |
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| 238 | else if ( Dp.degree() < D.degree() ) |
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| 239 | { |
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| 240 | // all previous p's are bad primes |
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| 241 | q = p; |
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| 242 | D = mapinto( Dp ); |
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| 243 | B = power(CanonicalForm(2),D.degree())*M+1; |
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| 244 | } |
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| 245 | // else p is a bad prime |
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| 246 | } |
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| 247 | } |
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| 248 | if ( i >= 0 ) |
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| 249 | { |
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| 250 | // now balance D mod q |
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| 251 | D = pp( balance_p( D, q ) ); |
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| 252 | if ( fdivides( D, f ) && fdivides( D, g ) ) |
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| 253 | return D * c; |
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| 254 | else |
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| 255 | q = 0; |
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| 256 | } |
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| 257 | else |
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| 258 | return gcd_poly( F, G ); |
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| 259 | DEBOUTLN( cerr, "another try ..." ); |
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| 260 | } |
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| 261 | } |
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| 262 | |
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| 263 | static CanonicalForm |
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| 264 | gcd_poly_p( const CanonicalForm & f, const CanonicalForm & g ) |
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| 265 | { |
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| 266 | if (f.inCoeffDomain() || g.inCoeffDomain()) //zero case should be caught by gcd |
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| 267 | return 1; |
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| 268 | CanonicalForm pi, pi1; |
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| 269 | CanonicalForm C, Ci, Ci1, Hi, bi, pi2; |
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| 270 | bool bpure, ezgcdon= isOn (SW_USE_EZGCD_P); |
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| 271 | int delta = degree( f ) - degree( g ); |
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| 272 | |
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| 273 | if ( delta >= 0 ) |
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| 274 | { |
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| 275 | pi = f; pi1 = g; |
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| 276 | } |
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| 277 | else |
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| 278 | { |
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| 279 | pi = g; pi1 = f; delta = -delta; |
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| 280 | } |
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| 281 | if (pi.isUnivariate()) |
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| 282 | Ci= 1; |
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| 283 | else |
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| 284 | { |
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| 285 | if (!ezgcdon) |
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| 286 | On (SW_USE_EZGCD_P); |
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| 287 | Ci = content( pi ); |
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| 288 | if (!ezgcdon) |
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| 289 | Off (SW_USE_EZGCD_P); |
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| 290 | pi = pi / Ci; |
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| 291 | } |
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| 292 | if (pi1.isUnivariate()) |
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| 293 | Ci1= 1; |
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| 294 | else |
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| 295 | { |
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| 296 | if (!ezgcdon) |
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| 297 | On (SW_USE_EZGCD_P); |
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| 298 | Ci1 = content( pi1 ); |
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| 299 | if (!ezgcdon) |
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| 300 | Off (SW_USE_EZGCD_P); |
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| 301 | pi1 = pi1 / Ci1; |
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| 302 | } |
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| 303 | C = gcd( Ci, Ci1 ); |
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| 304 | int d= 0; |
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| 305 | if ( !( pi.isUnivariate() && pi1.isUnivariate() ) ) |
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| 306 | { |
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| 307 | if ( gcd_test_one( pi1, pi, true, d ) ) |
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| 308 | { |
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| 309 | C=abs(C); |
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| 310 | //out_cf("GCD:",C,"\n"); |
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| 311 | return C; |
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| 312 | } |
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| 313 | bpure = false; |
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| 314 | } |
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| 315 | else |
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| 316 | { |
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| 317 | bpure = isPurePoly(pi) && isPurePoly(pi1); |
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| 318 | #ifdef HAVE_FLINT |
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| 319 | if (bpure && (CFFactory::gettype() != GaloisFieldDomain)) |
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| 320 | return gcd_univar_flintp(pi,pi1)*C; |
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| 321 | #else |
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| 322 | #ifdef HAVE_NTL |
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| 323 | if ( bpure && (CFFactory::gettype() != GaloisFieldDomain)) |
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| 324 | return gcd_univar_ntlp(pi, pi1 ) * C; |
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| 325 | #endif |
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| 326 | #endif |
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| 327 | } |
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| 328 | Variable v = f.mvar(); |
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| 329 | Hi = power( LC( pi1, v ), delta ); |
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| 330 | int maxNumVars= tmax (getNumVars (pi), getNumVars (pi1)); |
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| 331 | |
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| 332 | if (!(pi.isUnivariate() && pi1.isUnivariate())) |
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| 333 | { |
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| 334 | if (size (Hi)*size (pi)/(maxNumVars*3) > 500) //maybe this needs more tuning |
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| 335 | { |
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| 336 | On (SW_USE_FF_MOD_GCD); |
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| 337 | C *= gcd (pi, pi1); |
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| 338 | Off (SW_USE_FF_MOD_GCD); |
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| 339 | return C; |
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| 340 | } |
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| 341 | } |
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| 342 | |
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| 343 | if ( (delta+1) % 2 ) |
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| 344 | bi = 1; |
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| 345 | else |
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| 346 | bi = -1; |
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| 347 | CanonicalForm oldPi= pi, oldPi1= pi1, powHi; |
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| 348 | while ( degree( pi1, v ) > 0 ) |
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| 349 | { |
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| 350 | if (!(pi.isUnivariate() && pi1.isUnivariate())) |
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| 351 | { |
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| 352 | if (size (pi)/maxNumVars > 500 || size (pi1)/maxNumVars > 500) |
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| 353 | { |
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| 354 | On (SW_USE_FF_MOD_GCD); |
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| 355 | C *= gcd (oldPi, oldPi1); |
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| 356 | Off (SW_USE_FF_MOD_GCD); |
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| 357 | return C; |
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| 358 | } |
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| 359 | } |
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| 360 | pi2 = psr( pi, pi1, v ); |
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| 361 | pi2 = pi2 / bi; |
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| 362 | pi = pi1; pi1 = pi2; |
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| 363 | maxNumVars= tmax (getNumVars (pi), getNumVars (pi1)); |
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| 364 | if (!pi1.isUnivariate() && (size (pi1)/maxNumVars > 500)) |
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| 365 | { |
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| 366 | On (SW_USE_FF_MOD_GCD); |
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| 367 | C *= gcd (oldPi, oldPi1); |
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| 368 | Off (SW_USE_FF_MOD_GCD); |
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| 369 | return C; |
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| 370 | } |
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| 371 | if ( degree( pi1, v ) > 0 ) |
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| 372 | { |
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| 373 | delta = degree( pi, v ) - degree( pi1, v ); |
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| 374 | powHi= power (Hi, delta-1); |
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| 375 | if ( (delta+1) % 2 ) |
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| 376 | bi = LC( pi, v ) * powHi*Hi; |
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| 377 | else |
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| 378 | bi = -LC( pi, v ) * powHi*Hi; |
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| 379 | Hi = power( LC( pi1, v ), delta ) / powHi; |
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| 380 | if (!(pi.isUnivariate() && pi1.isUnivariate())) |
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| 381 | { |
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| 382 | if (size (Hi)*size (pi)/(maxNumVars*3) > 1500) //maybe this needs more tuning |
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| 383 | { |
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| 384 | On (SW_USE_FF_MOD_GCD); |
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| 385 | C *= gcd (oldPi, oldPi1); |
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| 386 | Off (SW_USE_FF_MOD_GCD); |
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| 387 | return C; |
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| 388 | } |
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| 389 | } |
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| 390 | } |
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| 391 | } |
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| 392 | if ( degree( pi1, v ) == 0 ) |
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| 393 | { |
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| 394 | C=abs(C); |
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| 395 | //out_cf("GCD:",C,"\n"); |
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| 396 | return C; |
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| 397 | } |
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| 398 | if (!pi.isUnivariate()) |
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| 399 | { |
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| 400 | if (!ezgcdon) |
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| 401 | On (SW_USE_EZGCD_P); |
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| 402 | Ci= gcd (LC (oldPi,v), LC (oldPi1,v)); |
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| 403 | pi /= LC (pi,v)/Ci; |
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| 404 | Ci= content (pi); |
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| 405 | pi /= Ci; |
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| 406 | if (!ezgcdon) |
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| 407 | Off (SW_USE_EZGCD_P); |
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| 408 | } |
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| 409 | if ( bpure ) |
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| 410 | pi /= pi.lc(); |
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| 411 | C=abs(C*pi); |
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| 412 | //out_cf("GCD:",C,"\n"); |
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| 413 | return C; |
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| 414 | } |
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| 415 | |
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| 416 | static CanonicalForm |
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| 417 | gcd_poly_0( const CanonicalForm & f, const CanonicalForm & g ) |
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| 418 | { |
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| 419 | CanonicalForm pi, pi1; |
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| 420 | CanonicalForm C, Ci, Ci1, Hi, bi, pi2; |
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| 421 | int delta = degree( f ) - degree( g ); |
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| 422 | |
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| 423 | if ( delta >= 0 ) |
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| 424 | { |
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| 425 | pi = f; pi1 = g; |
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| 426 | } |
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| 427 | else |
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| 428 | { |
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| 429 | pi = g; pi1 = f; delta = -delta; |
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| 430 | } |
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| 431 | Ci = content( pi ); Ci1 = content( pi1 ); |
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| 432 | pi1 = pi1 / Ci1; pi = pi / Ci; |
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| 433 | C = gcd( Ci, Ci1 ); |
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| 434 | int d= 0; |
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| 435 | if ( pi.isUnivariate() && pi1.isUnivariate() ) |
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| 436 | { |
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| 437 | #ifdef HAVE_FLINT |
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| 438 | if (isPurePoly(pi) && isPurePoly(pi1) ) |
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| 439 | return gcd_univar_flint0(pi, pi1 ) * C; |
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| 440 | #else |
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| 441 | #ifdef HAVE_NTL |
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| 442 | if ( isPurePoly(pi) && isPurePoly(pi1) ) |
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| 443 | return gcd_univar_ntl0(pi, pi1 ) * C; |
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| 444 | #endif |
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| 445 | #endif |
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| 446 | return gcd_poly_univar0( pi, pi1, true ) * C; |
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| 447 | } |
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| 448 | else if ( gcd_test_one( pi1, pi, true, d ) ) |
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| 449 | return C; |
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| 450 | Variable v = f.mvar(); |
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| 451 | Hi = power( LC( pi1, v ), delta ); |
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| 452 | if ( (delta+1) % 2 ) |
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| 453 | bi = 1; |
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| 454 | else |
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| 455 | bi = -1; |
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| 456 | while ( degree( pi1, v ) > 0 ) |
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| 457 | { |
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| 458 | pi2 = psr( pi, pi1, v ); |
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| 459 | pi2 = pi2 / bi; |
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| 460 | pi = pi1; pi1 = pi2; |
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| 461 | if ( degree( pi1, v ) > 0 ) |
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| 462 | { |
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| 463 | delta = degree( pi, v ) - degree( pi1, v ); |
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| 464 | if ( (delta+1) % 2 ) |
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| 465 | bi = LC( pi, v ) * power( Hi, delta ); |
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| 466 | else |
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| 467 | bi = -LC( pi, v ) * power( Hi, delta ); |
---|
| 468 | Hi = power( LC( pi1, v ), delta ) / power( Hi, delta-1 ); |
---|
| 469 | } |
---|
| 470 | } |
---|
| 471 | if ( degree( pi1, v ) == 0 ) |
---|
| 472 | return C; |
---|
| 473 | else |
---|
| 474 | return C * pp( pi ); |
---|
| 475 | } |
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| 476 | |
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[b52d27] | 477 | /** CanonicalForm gcd_poly ( const CanonicalForm & f, const CanonicalForm & g ) |
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| 478 | * |
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| 479 | * gcd_poly() - calculate polynomial gcd. |
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| 480 | * |
---|
| 481 | * This is the dispatcher for polynomial gcd calculation. |
---|
| 482 | * Different gcd variants get called depending the input, characteristic, and |
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| 483 | * on switches (cf_defs.h) |
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| 484 | * |
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[f37df2] | 485 | * With the current settings from Singular (i.e. SW_USE_EZGCD= on, |
---|
| 486 | * SW_USE_EZGCD_P= on, SW_USE_CHINREM_GCD= on, the EZ GCD variants are the |
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| 487 | * default algorithms for multivariate polynomial GCD computations) |
---|
| 488 | * |
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[b52d27] | 489 | * @sa gcd(), cf_defs.h |
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| 490 | * |
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| 491 | **/ |
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[b809a8] | 492 | CanonicalForm gcd_poly ( const CanonicalForm & f, const CanonicalForm & g ) |
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[f63dbca] | 493 | { |
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[34ecce] | 494 | CanonicalForm fc, gc; |
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[ed9927] | 495 | bool fc_isUnivariate=f.isUnivariate(); |
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| 496 | bool gc_isUnivariate=g.isUnivariate(); |
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| 497 | bool fc_and_gc_Univariate=fc_isUnivariate && gc_isUnivariate; |
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| 498 | fc = f; |
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| 499 | gc = g; |
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[0ad478] | 500 | int ch=getCharacteristic(); |
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| 501 | if ( ch != 0 ) |
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[ed9927] | 502 | { |
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[b2e2b0] | 503 | if (0) {} // dummy, to be able to build without NTL and FLINT |
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[6e62ce] | 504 | #if defined(HAVE_FLINT) && ( __FLINT_RELEASE >= 20503) |
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| 505 | if ( isOn( SW_USE_FL_GCD_P) |
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| 506 | && (CFFactory::gettype() != GaloisFieldDomain) |
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[a70b55] | 507 | #ifdef HAVE_NTL |
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| 508 | && (ch>10) // if we have NTL: it is better for char <11 |
---|
| 509 | #endif |
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[6e62ce] | 510 | &&(!hasAlgVar(fc)) && (!hasAlgVar(gc))) |
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| 511 | { |
---|
| 512 | return gcdFlintMP_Zp(fc,gc); |
---|
| 513 | } |
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| 514 | #endif |
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[2072126] | 515 | #ifdef HAVE_NTL |
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[e16f7d] | 516 | if ((!fc_and_gc_Univariate) && (isOn( SW_USE_EZGCD_P ))) |
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[49f1f45] | 517 | { |
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[08daea] | 518 | fc= EZGCD_P (fc, gc); |
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[c30347] | 519 | } |
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[bbec92] | 520 | #endif |
---|
[4b24c19] | 521 | #if defined(HAVE_NTL) || defined(HAVE_FLINT) |
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[10af64] | 522 | else if (isOn(SW_USE_FF_MOD_GCD) && !fc_and_gc_Univariate) |
---|
| 523 | { |
---|
| 524 | Variable a; |
---|
| 525 | if (hasFirstAlgVar (fc, a) || hasFirstAlgVar (gc, a)) |
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[52a933f] | 526 | fc=modGCDFq (fc, gc, a); |
---|
[b5c084] | 527 | else if (CFFactory::gettype() == GaloisFieldDomain) |
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[52a933f] | 528 | fc=modGCDGF (fc, gc); |
---|
[b5c084] | 529 | else |
---|
[52a933f] | 530 | fc=modGCDFp (fc, gc); |
---|
[10af64] | 531 | } |
---|
[2072126] | 532 | #endif |
---|
[b7cc2b] | 533 | else |
---|
[845303c] | 534 | fc = gcd_poly_p( fc, gc ); |
---|
[110718] | 535 | } |
---|
[6e62ce] | 536 | else if (!fc_and_gc_Univariate) /* && char==0*/ |
---|
[110718] | 537 | { |
---|
[6e62ce] | 538 | #if defined(HAVE_FLINT) && ( __FLINT_RELEASE >= 20503) |
---|
| 539 | if (( isOn( SW_USE_FL_GCD_0) ) |
---|
| 540 | &&(!hasAlgVar(fc)) && (!hasAlgVar(gc))) |
---|
| 541 | { |
---|
| 542 | return gcdFlintMP_QQ(fc,gc); |
---|
| 543 | } |
---|
| 544 | else |
---|
| 545 | #endif |
---|
[03c742] | 546 | #ifdef HAVE_NTL |
---|
[f7a4e9] | 547 | if ( isOn( SW_USE_EZGCD ) ) |
---|
| 548 | fc= ezgcd (fc, gc); |
---|
[0aeeee] | 549 | else |
---|
[845303c] | 550 | #endif |
---|
[9befb53] | 551 | #if defined(HAVE_NTL) || defined(HAVE_FLINT) |
---|
[0aeeee] | 552 | if (isOn(SW_USE_CHINREM_GCD)) |
---|
[52a933f] | 553 | fc = modGCDZ( fc, gc); |
---|
[c30347] | 554 | else |
---|
[9befb53] | 555 | #endif |
---|
[c30347] | 556 | { |
---|
[845303c] | 557 | fc = gcd_poly_0( fc, gc ); |
---|
[c30347] | 558 | } |
---|
[110718] | 559 | } |
---|
| 560 | else |
---|
| 561 | { |
---|
[845303c] | 562 | fc = gcd_poly_0( fc, gc ); |
---|
[110718] | 563 | } |
---|
[0ad478] | 564 | if ((ch>0)&&(!hasAlgVar(fc))) fc/=fc.lc(); |
---|
[110718] | 565 | return fc; |
---|
[f63dbca] | 566 | } |
---|
[b52d27] | 567 | |
---|
| 568 | /** static CanonicalForm cf_content ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 569 | * |
---|
| 570 | * cf_content() - return gcd(g, content(f)). |
---|
| 571 | * |
---|
| 572 | * content(f) is calculated with respect to f's main variable. |
---|
| 573 | * |
---|
| 574 | * @sa gcd(), content(), content( CF, Variable ). |
---|
| 575 | * |
---|
| 576 | **/ |
---|
[9bab9f] | 577 | static CanonicalForm |
---|
| 578 | cf_content ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 579 | { |
---|
[6f62c3] | 580 | if ( f.inPolyDomain() || ( f.inExtension() && ! getReduce( f.mvar() ) ) ) |
---|
| 581 | { |
---|
[150dc8] | 582 | CFIterator i = f; |
---|
| 583 | CanonicalForm result = g; |
---|
[6f62c3] | 584 | while ( i.hasTerms() && ! result.isOne() ) |
---|
| 585 | { |
---|
[a7ec94] | 586 | result = gcd( i.coeff(), result ); |
---|
[150dc8] | 587 | i++; |
---|
| 588 | } |
---|
| 589 | return result; |
---|
[9bab9f] | 590 | } |
---|
| 591 | else |
---|
[a7ec94] | 592 | return abs( f ); |
---|
[9bab9f] | 593 | } |
---|
[b52d27] | 594 | |
---|
| 595 | /** CanonicalForm content ( const CanonicalForm & f ) |
---|
| 596 | * |
---|
| 597 | * content() - return content(f) with respect to main variable. |
---|
| 598 | * |
---|
| 599 | * Normalizes result. |
---|
| 600 | * |
---|
| 601 | **/ |
---|
[9bab9f] | 602 | CanonicalForm |
---|
| 603 | content ( const CanonicalForm & f ) |
---|
| 604 | { |
---|
[6f62c3] | 605 | if ( f.inPolyDomain() || ( f.inExtension() && ! getReduce( f.mvar() ) ) ) |
---|
| 606 | { |
---|
[a7ec94] | 607 | CFIterator i = f; |
---|
| 608 | CanonicalForm result = abs( i.coeff() ); |
---|
| 609 | i++; |
---|
[6f62c3] | 610 | while ( i.hasTerms() && ! result.isOne() ) |
---|
| 611 | { |
---|
[a7ec94] | 612 | result = gcd( i.coeff(), result ); |
---|
| 613 | i++; |
---|
| 614 | } |
---|
| 615 | return result; |
---|
| 616 | } |
---|
| 617 | else |
---|
| 618 | return abs( f ); |
---|
[9bab9f] | 619 | } |
---|
[b52d27] | 620 | |
---|
| 621 | /** CanonicalForm content ( const CanonicalForm & f, const Variable & x ) |
---|
| 622 | * |
---|
| 623 | * content() - return content(f) with respect to x. |
---|
| 624 | * |
---|
| 625 | * x should be a polynomial variable. |
---|
| 626 | * |
---|
| 627 | **/ |
---|
[9bab9f] | 628 | CanonicalForm |
---|
| 629 | content ( const CanonicalForm & f, const Variable & x ) |
---|
| 630 | { |
---|
[92550d] | 631 | if (f.inBaseDomain()) return f; |
---|
[dd3e561] | 632 | ASSERT( x.level() > 0, "cannot calculate content with respect to algebraic variable" ); |
---|
| 633 | Variable y = f.mvar(); |
---|
| 634 | |
---|
| 635 | if ( y == x ) |
---|
[150dc8] | 636 | return cf_content( f, 0 ); |
---|
[dd3e561] | 637 | else if ( y < x ) |
---|
[150dc8] | 638 | return f; |
---|
[9bab9f] | 639 | else |
---|
[150dc8] | 640 | return swapvar( content( swapvar( f, y, x ), y ), y, x ); |
---|
[9bab9f] | 641 | } |
---|
[b52d27] | 642 | |
---|
| 643 | /** CanonicalForm vcontent ( const CanonicalForm & f, const Variable & x ) |
---|
| 644 | * |
---|
| 645 | * vcontent() - return content of f with repect to variables >= x. |
---|
| 646 | * |
---|
| 647 | * The content is recursively calculated over all coefficients in |
---|
| 648 | * f having level less than x. x should be a polynomial |
---|
| 649 | * variable. |
---|
| 650 | * |
---|
| 651 | **/ |
---|
[9bab9f] | 652 | CanonicalForm |
---|
| 653 | vcontent ( const CanonicalForm & f, const Variable & x ) |
---|
| 654 | { |
---|
[dd3e561] | 655 | ASSERT( x.level() > 0, "cannot calculate vcontent with respect to algebraic variable" ); |
---|
| 656 | |
---|
[9bab9f] | 657 | if ( f.mvar() <= x ) |
---|
[150dc8] | 658 | return content( f, x ); |
---|
[9bab9f] | 659 | else { |
---|
[150dc8] | 660 | CFIterator i; |
---|
| 661 | CanonicalForm d = 0; |
---|
| 662 | for ( i = f; i.hasTerms() && ! d.isOne(); i++ ) |
---|
| 663 | d = gcd( d, vcontent( i.coeff(), x ) ); |
---|
| 664 | return d; |
---|
[9bab9f] | 665 | } |
---|
| 666 | } |
---|
[b52d27] | 667 | |
---|
| 668 | /** CanonicalForm pp ( const CanonicalForm & f ) |
---|
| 669 | * |
---|
| 670 | * pp() - return primitive part of f. |
---|
| 671 | * |
---|
| 672 | * Returns zero if f equals zero, otherwise f / content(f). |
---|
| 673 | * |
---|
| 674 | **/ |
---|
[9bab9f] | 675 | CanonicalForm |
---|
| 676 | pp ( const CanonicalForm & f ) |
---|
| 677 | { |
---|
| 678 | if ( f.isZero() ) |
---|
[150dc8] | 679 | return f; |
---|
[9bab9f] | 680 | else |
---|
[150dc8] | 681 | return f / content( f ); |
---|
[9bab9f] | 682 | } |
---|
| 683 | |
---|
[ff6222] | 684 | CanonicalForm |
---|
[9bab9f] | 685 | gcd ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 686 | { |
---|
[a7ec94] | 687 | bool b = f.isZero(); |
---|
| 688 | if ( b || g.isZero() ) |
---|
| 689 | { |
---|
| 690 | if ( b ) |
---|
| 691 | return abs( g ); |
---|
[abfc3b] | 692 | else |
---|
[a7ec94] | 693 | return abs( f ); |
---|
| 694 | } |
---|
| 695 | if ( f.inPolyDomain() || g.inPolyDomain() ) |
---|
| 696 | { |
---|
| 697 | if ( f.mvar() != g.mvar() ) |
---|
| 698 | { |
---|
| 699 | if ( f.mvar() > g.mvar() ) |
---|
| 700 | return cf_content( f, g ); |
---|
| 701 | else |
---|
| 702 | return cf_content( g, f ); |
---|
| 703 | } |
---|
[bb82f0] | 704 | if (isOn(SW_USE_QGCD)) |
---|
| 705 | { |
---|
| 706 | Variable m; |
---|
[fc9f44] | 707 | if ( |
---|
| 708 | (getCharacteristic() == 0) && |
---|
[e6f7ee1] | 709 | (hasFirstAlgVar(f,m) || hasFirstAlgVar(g,m)) |
---|
[bb82f0] | 710 | ) |
---|
[fc31bce] | 711 | { |
---|
[713bdb] | 712 | bool on_rational = isOn(SW_RATIONAL); |
---|
| 713 | CanonicalForm r=QGCD(f,g); |
---|
[f06059] | 714 | On(SW_RATIONAL); |
---|
[713bdb] | 715 | CanonicalForm cdF = bCommonDen( r ); |
---|
| 716 | if (!on_rational) Off(SW_RATIONAL); |
---|
| 717 | return cdF*r; |
---|
[fc31bce] | 718 | } |
---|
[bb82f0] | 719 | } |
---|
[713bdb] | 720 | |
---|
[150dc8] | 721 | if ( f.inExtension() && getReduce( f.mvar() ) ) |
---|
[bb82f0] | 722 | return CanonicalForm(1); |
---|
[a7ec94] | 723 | else |
---|
| 724 | { |
---|
[ebc602] | 725 | if ( fdivides( f, g ) ) |
---|
[a7ec94] | 726 | return abs( f ); |
---|
[ebc602] | 727 | else if ( fdivides( g, f ) ) |
---|
[a7ec94] | 728 | return abs( g ); |
---|
| 729 | if ( !( getCharacteristic() == 0 && isOn( SW_RATIONAL ) ) ) |
---|
| 730 | { |
---|
| 731 | CanonicalForm d; |
---|
[64a501] | 732 | d = gcd_poly( f, g ); |
---|
[a7ec94] | 733 | return abs( d ); |
---|
| 734 | } |
---|
| 735 | else |
---|
| 736 | { |
---|
[150dc8] | 737 | CanonicalForm cdF = bCommonDen( f ); |
---|
| 738 | CanonicalForm cdG = bCommonDen( g ); |
---|
[5cf3215] | 739 | CanonicalForm F = f * cdF, G = g * cdG; |
---|
[150dc8] | 740 | Off( SW_RATIONAL ); |
---|
[5cf3215] | 741 | CanonicalForm l = gcd_poly( F, G ); |
---|
[150dc8] | 742 | On( SW_RATIONAL ); |
---|
[a7ec94] | 743 | return abs( l ); |
---|
[150dc8] | 744 | } |
---|
| 745 | } |
---|
[a7ec94] | 746 | } |
---|
| 747 | if ( f.inBaseDomain() && g.inBaseDomain() ) |
---|
| 748 | return bgcd( f, g ); |
---|
[9bab9f] | 749 | else |
---|
[a7ec94] | 750 | return 1; |
---|
[9bab9f] | 751 | } |
---|
| 752 | |
---|
[b52d27] | 753 | /** CanonicalForm lcm ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 754 | * |
---|
| 755 | * lcm() - return least common multiple of f and g. |
---|
| 756 | * |
---|
| 757 | * The lcm is calculated using the formula lcm(f, g) = f * g / gcd(f, g). |
---|
| 758 | * |
---|
| 759 | * Returns zero if one of f or g equals zero. |
---|
| 760 | * |
---|
| 761 | **/ |
---|
[9bab9f] | 762 | CanonicalForm |
---|
| 763 | lcm ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
| 764 | { |
---|
[dd3e561] | 765 | if ( f.isZero() || g.isZero() ) |
---|
[a7ec94] | 766 | return 0; |
---|
[dd3e561] | 767 | else |
---|
[150dc8] | 768 | return ( f / gcd( f, g ) ) * g; |
---|
[9bab9f] | 769 | } |
---|
[a7ec94] | 770 | |
---|