[493c477] | 1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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[2dd068] | 2 | |
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[e4fe2b] | 3 | #include "config.h" |
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[b973c0] | 4 | |
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[650f2d8] | 5 | #include "cf_assert.h" |
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[b973c0] | 6 | |
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[2dd068] | 7 | #include "cf_defs.h" |
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| 8 | #include "cf_random.h" |
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| 9 | #include "cf_util.h" |
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| 10 | #include "fac_cantzass.h" |
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| 11 | #include "fac_sqrfree.h" |
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| 12 | #include "gmpext.h" |
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| 13 | |
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[ee668e] | 14 | #include <factory/cf_gmp.h> |
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[daa556] | 15 | |
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[2dd068] | 16 | static CanonicalForm randomPoly( int n, const Variable & x, const CFRandom & gen ); |
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| 17 | |
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| 18 | static CFFList CantorZassenhausFactorFFGF( const CanonicalForm & f, int d, int q, const CFRandom & ); |
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| 19 | |
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[a52291] | 20 | static CFFList CantorZassenhausFactorExt( const CanonicalForm & g, int s, mpz_t q, const CFRandom & gen ); |
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[2dd068] | 21 | |
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| 22 | static CFFList distinctDegreeFactorFFGF ( const CanonicalForm & f, int q ); |
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| 23 | |
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| 24 | static CFFList distinctDegreeFactorExt ( const CanonicalForm & f, int p, int n ); |
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| 25 | |
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| 26 | // calculates f^m % d |
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| 27 | |
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| 28 | static CanonicalForm powerMod( const CanonicalForm & f, int m, const CanonicalForm & d ); |
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| 29 | |
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| 30 | // calculates f^(p^s) % d |
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| 31 | |
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| 32 | static CanonicalForm powerMod( const CanonicalForm & f, int p, int s, const CanonicalForm & d ); |
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| 33 | |
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| 34 | // calculates f^((p^s-1)/2) % d |
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| 35 | |
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| 36 | static CanonicalForm powerMod2( const CanonicalForm & f, int p, int s, const CanonicalForm & d ); |
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| 37 | |
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[a52291] | 38 | static CanonicalForm powerMod2( const CanonicalForm & f, mpz_t q, int s, const CanonicalForm & d ); |
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[2dd068] | 39 | |
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[9c9e2a4] | 40 | CFFList FpFactorizeUnivariateCZ( const CanonicalForm& f, bool issqrfree, int numext, const Variable alpha, const Variable beta ) |
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[2dd068] | 41 | { |
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| 42 | CFFList F, G, H, HH; |
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| 43 | CanonicalForm fac; |
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| 44 | ListIterator<CFFactor> i, j, k; |
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| 45 | int d, q, n = 0; |
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| 46 | bool galoisfield = getGFDegree() > 1; |
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[a52291] | 47 | mpz_t qq; |
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[2dd068] | 48 | |
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| 49 | if ( galoisfield ) |
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[cd86ac] | 50 | q = ipower( getCharacteristic(), getGFDegree() ); |
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[2dd068] | 51 | else |
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[cd86ac] | 52 | q = getCharacteristic(); |
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[2dd068] | 53 | if ( numext > 0 ) { |
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[cd86ac] | 54 | if ( numext == 1 ) |
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| 55 | n = getMipo( alpha ).degree(); |
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| 56 | else |
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| 57 | n = getMipo( alpha ).degree() * getMipo( beta ).degree(); |
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[a52291] | 58 | mpz_init( qq ); |
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| 59 | mpz_ui_pow_ui ( qq, q, n ); |
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[2dd068] | 60 | } |
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| 61 | if ( LC( f ).isOne() ) |
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[cd86ac] | 62 | if ( issqrfree ) |
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| 63 | F.append( CFFactor( f, 1 ) ); |
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| 64 | else |
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| 65 | F = sqrFreeFp( f ); |
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[2dd068] | 66 | else { |
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[cd86ac] | 67 | if ( issqrfree ) |
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| 68 | F.append( CFFactor( f / LC( f ), 1 ) ); |
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| 69 | else |
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| 70 | F = sqrFreeFp( f / LC( f ) ); |
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| 71 | H.append( LC( f ) ); |
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[2dd068] | 72 | } |
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| 73 | for ( i = F; i.hasItem(); ++i ) { |
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[cd86ac] | 74 | d = i.getItem().exp(); |
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| 75 | if ( numext > 0 ) |
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| 76 | G = distinctDegreeFactorExt( i.getItem().factor(), q, n ); |
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| 77 | else |
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| 78 | G = distinctDegreeFactorFFGF( i.getItem().factor(), q ); |
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| 79 | for ( j = G; j.hasItem(); ++j ) { |
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| 80 | if ( numext > 0 ) { |
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[0509dde] | 81 | if ( numext == 1 ) { |
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| 82 | AlgExtRandomF tmpalpha( alpha ); |
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[a52291] | 83 | HH = CantorZassenhausFactorExt( j.getItem().factor(), j.getItem().exp(), qq, tmpalpha ); |
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[0509dde] | 84 | } |
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| 85 | else { |
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| 86 | AlgExtRandomF tmpalphabeta( alpha, beta ); |
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[a52291] | 87 | HH = CantorZassenhausFactorExt( j.getItem().factor(), j.getItem().exp(), qq, tmpalphabeta ); |
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[0509dde] | 88 | } |
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[cd86ac] | 89 | } |
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| 90 | else if ( galoisfield ) |
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| 91 | HH = CantorZassenhausFactorFFGF( j.getItem().factor(), j.getItem().exp(), q, GFRandom() ); |
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| 92 | else |
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| 93 | HH = CantorZassenhausFactorFFGF( j.getItem().factor(), j.getItem().exp(), q, FFRandom() ); |
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| 94 | for ( k = HH; k.hasItem(); ++k ) { |
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| 95 | fac = k.getItem().factor(); |
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| 96 | H.append( CFFactor( fac / LC( fac ), d ) ); |
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| 97 | } |
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| 98 | } |
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[2dd068] | 99 | } |
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| 100 | if ( numext > 0 ) |
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[a52291] | 101 | mpz_clear( qq ); |
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[2dd068] | 102 | return H; |
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| 103 | } |
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| 104 | |
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| 105 | CFFList distinctDegreeFactorFFGF ( const CanonicalForm & f, int q ) |
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| 106 | { |
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| 107 | int i; |
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| 108 | Variable x = f.mvar(); |
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| 109 | CanonicalForm g = f, h, r = x; |
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| 110 | CFFList F; |
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| 111 | i = 1; |
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| 112 | while ( g.degree(x) > 0 && i <= g.degree(x) ) { |
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[cd86ac] | 113 | r = powerMod( r, q, g ); |
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| 114 | h = gcd( g, r - x ); |
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| 115 | if ( h.degree(x) > 0 ) { |
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| 116 | F.append( CFFactor( h, i ) ); |
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| 117 | g /= h; |
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| 118 | } |
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| 119 | i++; |
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[2dd068] | 120 | } |
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| 121 | ASSERT( g.degree(x) == 0, "fatal fatal" ); |
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| 122 | return F; |
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| 123 | } |
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| 124 | |
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| 125 | CFFList distinctDegreeFactorExt ( const CanonicalForm & f, int p, int n ) |
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| 126 | { |
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| 127 | int i; |
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| 128 | Variable x = f.mvar(); |
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| 129 | CanonicalForm g = f, h, r = x; |
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| 130 | CFFList F; |
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| 131 | i = 1; |
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| 132 | while ( g.degree(x) > 0 && i <= g.degree(x) ) { |
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[cd86ac] | 133 | r = powerMod( r, p, n, g ); |
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| 134 | h = gcd( g, r - x ); |
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| 135 | if ( h.degree(x) > 0 ) { |
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| 136 | F.append( CFFactor( h, i ) ); |
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| 137 | g /= h; |
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| 138 | } |
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| 139 | i++; |
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[2dd068] | 140 | } |
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| 141 | ASSERT( g.degree(x) == 0, "fatal fatal" ); |
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| 142 | return F; |
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| 143 | } |
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| 144 | |
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| 145 | CFFList CantorZassenhausFactorFFGF( const CanonicalForm & g, int s, int q, const CFRandom & gen ) |
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| 146 | { |
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| 147 | CanonicalForm f = g; |
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| 148 | CanonicalForm b, f1; |
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| 149 | int d, d1; |
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| 150 | Variable x = f.mvar(); |
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[b973c0] | 151 | |
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[2dd068] | 152 | if ( (d=f.degree(x)) == s ) |
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[cd86ac] | 153 | return CFFactor( f, 1 ); |
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[2dd068] | 154 | else while ( 1 ) { |
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[cd86ac] | 155 | b = randomPoly( d, x, gen ); |
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| 156 | f1 = gcd( b, f ); |
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| 157 | if ( (d1 = f1.degree(x)) > 0 && d1 < d ) { |
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| 158 | CFFList firstFactor = CantorZassenhausFactorFFGF( f1, s, q, gen ); |
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| 159 | CFFList secondFactor = CantorZassenhausFactorFFGF( f/f1, s, q, gen ); |
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| 160 | return Union( firstFactor, secondFactor ); |
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| 161 | } else { |
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| 162 | f1 = gcd( f, powerMod2( b, q, s, f ) - 1 ); |
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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 | } |
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| 168 | } |
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[2dd068] | 169 | } |
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| 170 | } |
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| 171 | |
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[a52291] | 172 | CFFList CantorZassenhausFactorExt( const CanonicalForm & g, int s, mpz_t q, const CFRandom & gen ) |
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[2dd068] | 173 | { |
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| 174 | CanonicalForm f = g; |
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| 175 | CanonicalForm b, f1; |
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| 176 | int d, d1; |
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| 177 | Variable x = f.mvar(); |
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[b973c0] | 178 | |
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[2dd068] | 179 | if ( (d=f.degree(x)) == s ) |
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[cd86ac] | 180 | return CFFactor( f, 1 ); |
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[2dd068] | 181 | else while ( 1 ) { |
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[cd86ac] | 182 | b = randomPoly( d, x, gen ); |
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| 183 | f1 = gcd( b, f ); |
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| 184 | if ( (d1 = f1.degree(x)) > 0 && d1 < d ) { |
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| 185 | CFFList firstFactor = CantorZassenhausFactorExt( f1, s, q, gen ); |
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| 186 | CFFList secondFactor = CantorZassenhausFactorExt( f/f1, s, q, gen ); |
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| 187 | return Union( firstFactor, secondFactor ); |
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| 188 | } else { |
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| 189 | f1 = gcd( f, powerMod2( b, q, s, f ) - 1 ); |
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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 | } |
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| 195 | } |
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[2dd068] | 196 | } |
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| 197 | } |
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| 198 | |
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| 199 | CanonicalForm randomPoly( int d, const Variable & x, const CFRandom & g ) |
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| 200 | { |
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| 201 | CanonicalForm result = 0; |
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| 202 | for ( int i = 0; i < d; i++ ) |
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[cd86ac] | 203 | result += power( x, i ) * g.generate(); |
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[2dd068] | 204 | result += power( x, d ); |
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| 205 | return result; |
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| 206 | } |
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| 207 | |
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| 208 | CanonicalForm powerMod( const CanonicalForm & f, int m, const CanonicalForm & d ) |
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| 209 | { |
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| 210 | CanonicalForm prod = 1; |
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| 211 | CanonicalForm b = f % d; |
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| 212 | |
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| 213 | while ( m != 0 ) { |
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[cd86ac] | 214 | if ( m % 2 != 0 ) |
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| 215 | prod = (prod * b) % d; |
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| 216 | m /= 2; |
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| 217 | if ( m != 0 ) |
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| 218 | b = (b * b) % d; |
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[2dd068] | 219 | } |
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| 220 | return prod; |
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| 221 | } |
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| 222 | |
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| 223 | CanonicalForm powerMod( const CanonicalForm & f, int p, int s, const CanonicalForm & d ) |
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| 224 | { |
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| 225 | CanonicalForm prod = 1; |
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| 226 | CanonicalForm b = f % d; |
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| 227 | int odd; |
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| 228 | |
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[a52291] | 229 | mpz_t m; |
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[b973c0] | 230 | |
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[a52291] | 231 | mpz_init( m ); |
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| 232 | mpz_ui_pow_ui ( m, p, s ); |
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| 233 | while ( mpz_cmp_si( m, 0 ) != 0 ) |
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[cacfb6] | 234 | { |
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[a52291] | 235 | odd = mpz_fdiv_q_ui( m, m, 2 ); |
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[cd86ac] | 236 | if ( odd != 0 ) |
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| 237 | prod = (prod * b) % d; |
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[a52291] | 238 | if ( mpz_cmp_si( m, 0 ) != 0 ) |
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[cd86ac] | 239 | b = (b*b) % d; |
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[2dd068] | 240 | } |
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[a52291] | 241 | mpz_clear( m ); |
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[2dd068] | 242 | return prod; |
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| 243 | } |
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| 244 | |
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| 245 | CanonicalForm powerMod2( const CanonicalForm & f, int p, int s, const CanonicalForm & d ) |
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| 246 | { |
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| 247 | CanonicalForm prod = 1; |
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| 248 | CanonicalForm b = f % d; |
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| 249 | int odd; |
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| 250 | |
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[a52291] | 251 | mpz_t m; |
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[b973c0] | 252 | |
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[a52291] | 253 | mpz_init( m ); |
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| 254 | mpz_ui_pow_ui ( m, p, s ); |
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| 255 | mpz_sub_ui( m, m, 1 ); |
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| 256 | mpz_fdiv_q_ui( m, m, 2 ); |
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| 257 | while ( mpz_cmp_si( m, 0 ) != 0 ) |
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[cacfb6] | 258 | { |
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[a52291] | 259 | odd = mpz_fdiv_q_ui( m, m, 2 ); |
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[cd86ac] | 260 | if ( odd != 0 ) |
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| 261 | prod = (prod * b) % d; |
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[a52291] | 262 | if ( mpz_cmp_si( m, 0 ) != 0 ) |
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[cd86ac] | 263 | b = (b*b) % d; |
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[2dd068] | 264 | } |
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[a52291] | 265 | mpz_clear( m ); |
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[2dd068] | 266 | return prod; |
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| 267 | } |
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| 268 | |
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[a52291] | 269 | CanonicalForm powerMod2( const CanonicalForm & f, mpz_t q, int s, const CanonicalForm & d ) |
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[2dd068] | 270 | { |
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| 271 | CanonicalForm prod = 1; |
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| 272 | CanonicalForm b = f % d; |
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| 273 | int odd; |
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| 274 | |
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[a52291] | 275 | mpz_t m; |
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[b973c0] | 276 | |
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[a52291] | 277 | mpz_init( m ); |
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| 278 | mpz_pow_ui( m, q, s ); |
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| 279 | mpz_sub_ui( m, m, 1 ); |
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| 280 | mpz_fdiv_q_ui( m, m, 2 ); |
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| 281 | while ( mpz_cmp_si( m, 0 ) != 0 ) |
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[cacfb6] | 282 | { |
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[a52291] | 283 | odd = mpz_fdiv_q_ui( m, m, 2 ); |
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[cd86ac] | 284 | if ( odd != 0 ) |
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| 285 | prod = (prod * b) % d; |
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[a52291] | 286 | if ( mpz_cmp_si( m, 0 ) != 0 ) |
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[cd86ac] | 287 | b = (b*b) % d; |
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[2dd068] | 288 | } |
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[a52291] | 289 | mpz_clear( m ); |
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[2dd068] | 290 | return prod; |
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| 291 | } |
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