[c1b52b] | 1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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| 2 | |
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| 3 | #include <config.h> |
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| 4 | |
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| 5 | #include "factory/cf_gmp.h" |
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| 6 | |
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| 7 | #include "assert.h" |
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| 8 | |
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| 9 | #include "cf_defs.h" |
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| 10 | #include "cf_random.h" |
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| 11 | #include "cf_util.h" |
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| 12 | #include "fac_cantzass.h" |
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| 13 | #include "fac_sqrfree.h" |
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| 14 | #include "gmpext.h" |
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| 15 | |
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[7fdedf] | 16 | #ifdef HAVE_FLINT |
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| 17 | #include"FLINTconvert.h" |
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| 18 | #endif |
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| 19 | |
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| 20 | #if !defined(HAVE_NTL) |
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[c1b52b] | 21 | static CanonicalForm randomPoly( int n, const Variable & x, const CFRandom & gen ); |
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| 22 | |
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| 23 | static CFFList CantorZassenhausFactorFFGF( const CanonicalForm & f, int d, int q, const CFRandom & ); |
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| 24 | |
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| 25 | static CFFList CantorZassenhausFactorExt( const CanonicalForm & g, int s, mpz_t q, const CFRandom & gen ); |
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| 26 | |
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| 27 | static CFFList distinctDegreeFactorFFGF ( const CanonicalForm & f, int q ); |
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| 28 | |
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| 29 | static CFFList distinctDegreeFactorExt ( const CanonicalForm & f, int p, int n ); |
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| 30 | |
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| 31 | // calculates f^m % d |
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| 32 | |
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| 33 | static CanonicalForm powerMod( const CanonicalForm & f, int m, const CanonicalForm & d ); |
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| 34 | |
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| 35 | // calculates f^(p^s) % d |
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| 36 | |
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| 37 | static CanonicalForm powerMod( const CanonicalForm & f, int p, int s, const CanonicalForm & d ); |
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| 38 | |
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| 39 | // calculates f^((p^s-1)/2) % d |
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| 40 | |
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| 41 | static CanonicalForm powerMod2( const CanonicalForm & f, int p, int s, const CanonicalForm & d ); |
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| 42 | |
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| 43 | static CanonicalForm powerMod2( const CanonicalForm & f, mpz_t q, int s, const CanonicalForm & d ); |
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| 44 | |
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| 45 | CFFList FpFactorizeUnivariateCZ( const CanonicalForm& f, bool issqrfree, int numext, const Variable alpha, const Variable beta ) |
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| 46 | { |
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| 47 | CFFList F, G, H, HH; |
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| 48 | CanonicalForm fac; |
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| 49 | ListIterator<CFFactor> i, j, k; |
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| 50 | int d, q, n = 0; |
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| 51 | bool galoisfield = getGFDegree() > 1; |
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| 52 | mpz_t qq; |
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| 53 | |
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| 54 | if ( galoisfield ) |
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| 55 | q = ipower( getCharacteristic(), getGFDegree() ); |
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| 56 | else |
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| 57 | q = getCharacteristic(); |
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| 58 | if ( numext > 0 ) { |
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| 59 | if ( numext == 1 ) |
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| 60 | n = getMipo( alpha ).degree(); |
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| 61 | else |
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| 62 | n = getMipo( alpha ).degree() * getMipo( beta ).degree(); |
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| 63 | mpz_init( qq ); |
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| 64 | mpz_ui_pow_ui ( qq, q, n ); |
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| 65 | } |
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| 66 | if ( LC( f ).isOne() ) |
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| 67 | if ( issqrfree ) |
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| 68 | F.append( CFFactor( f, 1 ) ); |
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| 69 | else |
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| 70 | F = sqrFreeFp( f ); |
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| 71 | else { |
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| 72 | if ( issqrfree ) |
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| 73 | F.append( CFFactor( f / LC( f ), 1 ) ); |
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| 74 | else |
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| 75 | F = sqrFreeFp( f / LC( f ) ); |
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| 76 | H.append( LC( f ) ); |
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| 77 | } |
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| 78 | for ( i = F; i.hasItem(); ++i ) { |
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| 79 | d = i.getItem().exp(); |
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| 80 | if ( numext > 0 ) |
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| 81 | G = distinctDegreeFactorExt( i.getItem().factor(), q, n ); |
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| 82 | else |
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| 83 | G = distinctDegreeFactorFFGF( i.getItem().factor(), q ); |
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| 84 | for ( j = G; j.hasItem(); ++j ) { |
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| 85 | if ( numext > 0 ) { |
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| 86 | if ( numext == 1 ) { |
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| 87 | AlgExtRandomF tmpalpha( alpha ); |
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| 88 | HH = CantorZassenhausFactorExt( j.getItem().factor(), j.getItem().exp(), qq, tmpalpha ); |
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| 89 | } |
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| 90 | else { |
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| 91 | AlgExtRandomF tmpalphabeta( alpha, beta ); |
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| 92 | HH = CantorZassenhausFactorExt( j.getItem().factor(), j.getItem().exp(), qq, tmpalphabeta ); |
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| 93 | } |
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| 94 | } |
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| 95 | else if ( galoisfield ) |
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| 96 | HH = CantorZassenhausFactorFFGF( j.getItem().factor(), j.getItem().exp(), q, GFRandom() ); |
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| 97 | else |
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| 98 | HH = CantorZassenhausFactorFFGF( j.getItem().factor(), j.getItem().exp(), q, FFRandom() ); |
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| 99 | for ( k = HH; k.hasItem(); ++k ) { |
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| 100 | fac = k.getItem().factor(); |
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| 101 | H.append( CFFactor( fac / LC( fac ), d ) ); |
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| 102 | } |
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| 103 | } |
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| 104 | } |
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| 105 | if ( numext > 0 ) |
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| 106 | mpz_clear( qq ); |
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| 107 | return H; |
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| 108 | } |
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| 109 | |
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| 110 | CFFList distinctDegreeFactorFFGF ( const CanonicalForm & f, int q ) |
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| 111 | { |
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| 112 | int i; |
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| 113 | Variable x = f.mvar(); |
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| 114 | CanonicalForm g = f, h, r = x; |
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| 115 | CFFList F; |
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| 116 | i = 1; |
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| 117 | while ( g.degree(x) > 0 && i <= g.degree(x) ) { |
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| 118 | r = powerMod( r, q, g ); |
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| 119 | h = gcd( g, r - x ); |
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| 120 | if ( h.degree(x) > 0 ) { |
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| 121 | F.append( CFFactor( h, i ) ); |
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| 122 | g /= h; |
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| 123 | } |
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| 124 | i++; |
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| 125 | } |
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| 126 | ASSERT( g.degree(x) == 0, "fatal fatal" ); |
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| 127 | return F; |
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| 128 | } |
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| 129 | |
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| 130 | CFFList distinctDegreeFactorExt ( const CanonicalForm & f, int p, int n ) |
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| 131 | { |
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| 132 | Variable x = f.mvar(); |
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[0009d2] | 133 | if (f.degree(x) <= 1) return CFFList(CFFactor(f,1)); |
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| 134 | int i; |
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[c1b52b] | 135 | CanonicalForm g = f, h, r = x; |
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| 136 | CFFList F; |
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| 137 | i = 1; |
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| 138 | while ( g.degree(x) > 0 && i <= g.degree(x) ) { |
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| 139 | r = powerMod( r, p, n, g ); |
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| 140 | h = gcd( g, r - x ); |
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| 141 | if ( h.degree(x) > 0 ) { |
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| 142 | F.append( CFFactor( h, i ) ); |
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| 143 | g /= h; |
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| 144 | } |
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| 145 | i++; |
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| 146 | } |
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| 147 | ASSERT( g.degree(x) == 0, "fatal fatal" ); |
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| 148 | return F; |
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| 149 | } |
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| 150 | |
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| 151 | CFFList CantorZassenhausFactorFFGF( const CanonicalForm & g, int s, int q, const CFRandom & gen ) |
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| 152 | { |
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| 153 | CanonicalForm f = g; |
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| 154 | CanonicalForm b, f1; |
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| 155 | int d, d1; |
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| 156 | Variable x = f.mvar(); |
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| 157 | |
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| 158 | if ( (d=f.degree(x)) == s ) |
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| 159 | return CFFactor( f, 1 ); |
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| 160 | else while ( 1 ) { |
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| 161 | b = randomPoly( d, x, gen ); |
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| 162 | f1 = gcd( b, f ); |
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| 163 | if ( (d1 = f1.degree(x)) > 0 && d1 < d ) { |
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| 164 | CFFList firstFactor = CantorZassenhausFactorFFGF( f1, s, q, gen ); |
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| 165 | CFFList secondFactor = CantorZassenhausFactorFFGF( f/f1, s, q, gen ); |
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| 166 | return Union( firstFactor, secondFactor ); |
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| 167 | } else { |
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| 168 | f1 = gcd( f, powerMod2( b, q, s, f ) - 1 ); |
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| 169 | if ( (d1 = f1.degree(x)) > 0 && d1 < d ) { |
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| 170 | CFFList firstFactor = CantorZassenhausFactorFFGF( f1, s, q, gen ); |
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| 171 | CFFList secondFactor = CantorZassenhausFactorFFGF( f/f1, s, q, gen ); |
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| 172 | return Union( firstFactor, secondFactor ); |
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| 173 | } |
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| 174 | } |
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| 175 | } |
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| 176 | } |
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| 177 | |
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| 178 | CFFList CantorZassenhausFactorExt( const CanonicalForm & g, int s, mpz_t q, const CFRandom & gen ) |
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| 179 | { |
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| 180 | CanonicalForm f = g; |
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| 181 | CanonicalForm b, f1; |
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| 182 | int d, d1; |
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| 183 | Variable x = f.mvar(); |
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| 184 | |
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| 185 | if ( (d=f.degree(x)) == s ) |
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| 186 | return CFFactor( f, 1 ); |
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| 187 | else while ( 1 ) { |
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| 188 | b = randomPoly( d, x, gen ); |
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| 189 | f1 = gcd( b, f ); |
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| 190 | if ( (d1 = f1.degree(x)) > 0 && d1 < d ) { |
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| 191 | CFFList firstFactor = CantorZassenhausFactorExt( f1, s, q, gen ); |
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| 192 | CFFList secondFactor = CantorZassenhausFactorExt( f/f1, s, q, gen ); |
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| 193 | return Union( firstFactor, secondFactor ); |
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| 194 | } else { |
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| 195 | f1 = gcd( f, powerMod2( b, q, s, f ) - 1 ); |
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| 196 | if ( (d1 = f1.degree(x)) > 0 && d1 < d ) { |
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| 197 | CFFList firstFactor = CantorZassenhausFactorExt( f1, s, q, gen ); |
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| 198 | CFFList secondFactor = CantorZassenhausFactorExt( f/f1, s, q, gen ); |
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| 199 | return Union( firstFactor, secondFactor ); |
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| 200 | } |
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| 201 | } |
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| 202 | } |
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| 203 | } |
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| 204 | |
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| 205 | CanonicalForm randomPoly( int d, const Variable & x, const CFRandom & g ) |
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| 206 | { |
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| 207 | CanonicalForm result = 0; |
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| 208 | for ( int i = 0; i < d; i++ ) |
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| 209 | result += power( x, i ) * g.generate(); |
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| 210 | result += power( x, d ); |
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| 211 | return result; |
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| 212 | } |
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| 213 | |
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| 214 | CanonicalForm powerMod( const CanonicalForm & f, int m, const CanonicalForm & d ) |
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| 215 | { |
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| 216 | CanonicalForm prod = 1; |
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| 217 | CanonicalForm b = f % d; |
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| 218 | |
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| 219 | while ( m != 0 ) { |
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| 220 | if ( m % 2 != 0 ) |
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| 221 | prod = (prod * b) % d; |
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| 222 | m /= 2; |
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| 223 | if ( m != 0 ) |
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| 224 | b = (b * b) % d; |
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| 225 | } |
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| 226 | return prod; |
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| 227 | } |
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| 228 | |
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| 229 | CanonicalForm powerMod( const CanonicalForm & f, int p, int s, const CanonicalForm & d ) |
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| 230 | { |
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| 231 | CanonicalForm prod = 1; |
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| 232 | CanonicalForm b = f % d; |
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| 233 | int odd; |
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| 234 | |
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| 235 | mpz_t m; |
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| 236 | |
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| 237 | mpz_init( m ); |
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| 238 | mpz_ui_pow_ui ( m, p, s ); |
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| 239 | while ( mpz_cmp_si( m, 0 ) != 0 ) |
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| 240 | { |
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| 241 | odd = mpz_fdiv_q_ui( m, m, 2 ); |
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| 242 | if ( odd != 0 ) |
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| 243 | prod = (prod * b) % d; |
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| 244 | if ( mpz_cmp_si( m, 0 ) != 0 ) |
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| 245 | b = (b*b) % d; |
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| 246 | } |
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| 247 | mpz_clear( m ); |
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| 248 | return prod; |
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| 249 | } |
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| 250 | |
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| 251 | CanonicalForm powerMod2( const CanonicalForm & f, int p, int s, const CanonicalForm & d ) |
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| 252 | { |
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| 253 | CanonicalForm prod = 1; |
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| 254 | CanonicalForm b = f % d; |
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| 255 | int odd; |
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| 256 | |
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| 257 | mpz_t m; |
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| 258 | |
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| 259 | mpz_init( m ); |
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| 260 | mpz_ui_pow_ui ( m, p, s ); |
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| 261 | mpz_sub_ui( m, m, 1 ); |
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| 262 | mpz_fdiv_q_ui( m, m, 2 ); |
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| 263 | while ( mpz_cmp_si( m, 0 ) != 0 ) |
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| 264 | { |
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| 265 | odd = mpz_fdiv_q_ui( m, m, 2 ); |
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| 266 | if ( odd != 0 ) |
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| 267 | prod = (prod * b) % d; |
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| 268 | if ( mpz_cmp_si( m, 0 ) != 0 ) |
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| 269 | b = (b*b) % d; |
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| 270 | } |
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| 271 | mpz_clear( m ); |
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| 272 | return prod; |
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| 273 | } |
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| 274 | |
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| 275 | CanonicalForm powerMod2( const CanonicalForm & f, mpz_t q, int s, const CanonicalForm & d ) |
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| 276 | { |
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| 277 | CanonicalForm prod = 1; |
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| 278 | CanonicalForm b = f % d; |
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| 279 | int odd; |
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| 280 | |
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| 281 | mpz_t m; |
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| 282 | |
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| 283 | mpz_init( m ); |
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| 284 | mpz_pow_ui( m, q, s ); |
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| 285 | mpz_sub_ui( m, m, 1 ); |
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| 286 | mpz_fdiv_q_ui( m, m, 2 ); |
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| 287 | while ( mpz_cmp_si( m, 0 ) != 0 ) |
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| 288 | { |
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| 289 | odd = mpz_fdiv_q_ui( m, m, 2 ); |
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| 290 | if ( odd != 0 ) |
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| 291 | prod = (prod * b) % d; |
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| 292 | if ( mpz_cmp_si( m, 0 ) != 0 ) |
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| 293 | b = (b*b) % d; |
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| 294 | } |
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| 295 | mpz_clear( m ); |
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| 296 | return prod; |
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| 297 | } |
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| 298 | #endif |
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