[6c44098] | 1 | /*****************************************************************************\ |
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| 2 | * Computer Algebra System SINGULAR |
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| 3 | \*****************************************************************************/ |
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| 4 | /** @file facBivar.cc |
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| 5 | * |
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| 6 | * bivariate factorization over Q(a) |
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| 7 | * |
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| 8 | * @author Martin Lee |
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| 9 | * |
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| 10 | **/ |
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| 11 | /*****************************************************************************/ |
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| 12 | |
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[e4fe2b] | 13 | #include "config.h" |
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[6c44098] | 14 | |
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[0851b0] | 15 | #include "cf_assert.h" |
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[6c44098] | 16 | #include "debug.h" |
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| 17 | #include "timing.h" |
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| 18 | |
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[d990001] | 19 | #include "cf_algorithm.h" |
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[6c44098] | 20 | #include "facFqBivar.h" |
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| 21 | #include "facBivar.h" |
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[f8ac2df] | 22 | #include "facHensel.h" |
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[0e2e23] | 23 | #include "facMul.h" |
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[1ade96] | 24 | #include "cf_primes.h" |
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[6c44098] | 25 | |
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[615ca8] | 26 | #ifdef HAVE_NTL |
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[978ce3] | 27 | TIMING_DEFINE_PRINT(fac_uni_factorizer) |
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| 28 | TIMING_DEFINE_PRINT(fac_bi_hensel_lift) |
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| 29 | TIMING_DEFINE_PRINT(fac_bi_factor_recombination) |
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[0851b0] | 30 | TIMING_DEFINE_PRINT(fac_bi_evaluation) |
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| 31 | TIMING_DEFINE_PRINT(fac_bi_shift_to_zero) |
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[6c44098] | 32 | |
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[5f92d8] | 33 | // bound on coeffs of f (cf. Musser: Multivariate Polynomial Factorization, |
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| 34 | // Gelfond: Transcendental and Algebraic Numbers) |
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| 35 | modpk |
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[1ade96] | 36 | coeffBound ( const CanonicalForm & f, int p ) |
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| 37 | { |
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| 38 | int * degs = degrees( f ); |
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| 39 | int M = 0, i, k = f.level(); |
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[5f92d8] | 40 | CanonicalForm b= 1; |
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[1ade96] | 41 | for ( i = 1; i <= k; i++ ) |
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[5f92d8] | 42 | { |
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| 43 | M += degs[i]; |
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| 44 | b *= degs[i] + 1; |
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| 45 | } |
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| 46 | b /= power (CanonicalForm (2), k); |
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| 47 | b= b.sqrt() + 1; |
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| 48 | b *= 2 * maxNorm( f ) * power( CanonicalForm( 2 ), M ); |
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[1ade96] | 49 | CanonicalForm B = p; |
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| 50 | k = 1; |
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| 51 | while ( B < b ) { |
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| 52 | B *= p; |
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| 53 | k++; |
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| 54 | } |
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| 55 | return modpk( p, k ); |
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| 56 | } |
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| 57 | |
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[5f92d8] | 58 | void findGoodPrime(const CanonicalForm &f, int &start) |
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[1ade96] | 59 | { |
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| 60 | if (! f.inBaseDomain() ) |
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| 61 | { |
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| 62 | CFIterator i = f; |
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| 63 | for(;;) |
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| 64 | { |
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| 65 | if ( i.hasTerms() ) |
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| 66 | { |
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[5f92d8] | 67 | findGoodPrime(i.coeff(),start); |
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[4e6d2a] | 68 | if (0==cf_getBigPrime(start)) return; |
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| 69 | if((i.exp()!=0) && ((i.exp() % cf_getBigPrime(start))==0)) |
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[1ade96] | 70 | { |
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| 71 | start++; |
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| 72 | i=f; |
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| 73 | } |
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| 74 | else i++; |
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| 75 | } |
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| 76 | else break; |
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| 77 | } |
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| 78 | } |
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| 79 | else |
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| 80 | { |
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| 81 | if (f.inZ()) |
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| 82 | { |
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[4e6d2a] | 83 | if (0==cf_getBigPrime(start)) return; |
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| 84 | while((!f.isZero()) && (mod(f,cf_getBigPrime(start))==0)) |
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[1ade96] | 85 | { |
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| 86 | start++; |
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[4e6d2a] | 87 | if (0==cf_getBigPrime(start)) return; |
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[1ade96] | 88 | } |
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| 89 | } |
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| 90 | } |
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| 91 | } |
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| 92 | |
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[5f92d8] | 93 | modpk |
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| 94 | coeffBound ( const CanonicalForm & f, int p, const CanonicalForm& mipo ) |
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| 95 | { |
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| 96 | int * degs = degrees( f ); |
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| 97 | int M = 0, i, k = f.level(); |
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| 98 | CanonicalForm K= 1; |
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| 99 | for ( i = 1; i <= k; i++ ) |
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| 100 | { |
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| 101 | M += degs[i]; |
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| 102 | K *= degs[i] + 1; |
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| 103 | } |
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[7e3d56] | 104 | K /= power (CanonicalForm (2), k/2); |
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[5f92d8] | 105 | K *= power (CanonicalForm (2), M); |
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| 106 | int N= degree (mipo); |
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| 107 | CanonicalForm b; |
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[b4af1b] | 108 | b= 2*power (maxNorm (f), N)*power (maxNorm (mipo), 4*N)*K* |
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[7e3d56] | 109 | power (CanonicalForm (2), N)* |
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| 110 | power (CanonicalForm (N+1), 4*N); |
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[5f92d8] | 111 | b /= power (abs (lc (mipo)), N); |
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| 112 | |
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| 113 | CanonicalForm B = p; |
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| 114 | k = 1; |
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| 115 | while ( B < b ) { |
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| 116 | B *= p; |
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| 117 | k++; |
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| 118 | } |
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| 119 | return modpk( p, k ); |
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| 120 | } |
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| 121 | |
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[6c44098] | 122 | CFList conv (const CFFList& L) |
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| 123 | { |
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| 124 | CFList result; |
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| 125 | for (CFFListIterator i= L; i.hasItem(); i++) |
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| 126 | result.append (i.getItem().factor()); |
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| 127 | return result; |
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| 128 | } |
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| 129 | |
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| 130 | bool testPoint (const CanonicalForm& F, CanonicalForm& G, int i) |
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| 131 | { |
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| 132 | G= F (i, 2); |
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| 133 | if (G.inCoeffDomain() || degree (F, 1) > degree (G, 1)) |
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| 134 | return false; |
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| 135 | |
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| 136 | if (degree (gcd (deriv (G, G.mvar()), G)) > 0) |
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| 137 | return false; |
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| 138 | return true; |
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| 139 | } |
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| 140 | |
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| 141 | CanonicalForm evalPoint (const CanonicalForm& F, int& i) |
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| 142 | { |
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| 143 | Variable x= Variable (1); |
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| 144 | Variable y= Variable (2); |
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| 145 | CanonicalForm result; |
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| 146 | |
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| 147 | int k; |
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| 148 | |
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| 149 | if (i == 0) |
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| 150 | { |
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| 151 | if (testPoint (F, result, i)) |
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| 152 | return result; |
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| 153 | } |
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| 154 | do |
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| 155 | { |
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| 156 | if (i > 0) |
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| 157 | k= 1; |
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| 158 | else |
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| 159 | k= 2; |
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| 160 | while (k < 3) |
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| 161 | { |
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| 162 | if (k == 1) |
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| 163 | { |
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| 164 | if (testPoint (F, result, i)) |
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| 165 | return result; |
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| 166 | } |
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| 167 | else |
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| 168 | { |
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| 169 | if (testPoint (F, result, -i)) |
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[fd4146] | 170 | { |
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| 171 | i= -i; |
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[6c44098] | 172 | return result; |
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[fd4146] | 173 | } |
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| 174 | else if (i < 0) |
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| 175 | i= -i; |
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[6c44098] | 176 | } |
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| 177 | k++; |
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| 178 | } |
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| 179 | i++; |
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| 180 | } while (1); |
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| 181 | } |
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| 182 | |
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| 183 | CFList biFactorize (const CanonicalForm& F, const Variable& v) |
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| 184 | { |
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| 185 | if (F.inCoeffDomain()) |
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| 186 | return CFList(F); |
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| 187 | |
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| 188 | bool extension= (v.level() != 1); |
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| 189 | CanonicalForm A; |
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| 190 | if (isOn (SW_RATIONAL)) |
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| 191 | A= F*bCommonDen (F); |
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| 192 | else |
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| 193 | A= F; |
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| 194 | |
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[b4af1b] | 195 | CanonicalForm mipo; |
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| 196 | if (extension) |
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| 197 | mipo= getMipo (v); |
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| 198 | |
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[6c44098] | 199 | if (A.isUnivariate()) |
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| 200 | { |
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| 201 | CFFList buf; |
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| 202 | if (extension) |
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| 203 | buf= factorize (A, v); |
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| 204 | else |
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| 205 | buf= factorize (A, true); |
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| 206 | CFList result= conv (buf); |
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| 207 | if (result.getFirst().inCoeffDomain()) |
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| 208 | result.removeFirst(); |
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| 209 | return result; |
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| 210 | } |
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| 211 | |
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| 212 | CFMap N; |
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| 213 | A= compress (A, N); |
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| 214 | Variable y= A.mvar(); |
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| 215 | |
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| 216 | if (y.level() > 2) return CFList (F); |
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| 217 | Variable x= Variable (1); |
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| 218 | |
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| 219 | CanonicalForm contentAx= content (A, x); |
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| 220 | CanonicalForm contentAy= content (A); |
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| 221 | |
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| 222 | A= A/(contentAx*contentAy); |
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| 223 | CFFList contentAxFactors, contentAyFactors; |
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| 224 | |
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| 225 | if (extension) |
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| 226 | { |
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| 227 | if (!contentAx.inCoeffDomain()) |
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| 228 | { |
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| 229 | contentAxFactors= factorize (contentAx, v); |
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| 230 | if (contentAxFactors.getFirst().factor().inCoeffDomain()) |
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| 231 | contentAxFactors.removeFirst(); |
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| 232 | } |
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| 233 | if (!contentAy.inCoeffDomain()) |
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| 234 | { |
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| 235 | contentAyFactors= factorize (contentAy, v); |
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| 236 | if (contentAyFactors.getFirst().factor().inCoeffDomain()) |
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| 237 | contentAyFactors.removeFirst(); |
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| 238 | } |
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| 239 | } |
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| 240 | else |
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| 241 | { |
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| 242 | if (!contentAx.inCoeffDomain()) |
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| 243 | { |
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| 244 | contentAxFactors= factorize (contentAx, true); |
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| 245 | if (contentAxFactors.getFirst().factor().inCoeffDomain()) |
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| 246 | contentAxFactors.removeFirst(); |
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| 247 | } |
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| 248 | if (!contentAy.inCoeffDomain()) |
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| 249 | { |
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| 250 | contentAyFactors= factorize (contentAy, true); |
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| 251 | if (contentAyFactors.getFirst().factor().inCoeffDomain()) |
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| 252 | contentAyFactors.removeFirst(); |
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| 253 | } |
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| 254 | } |
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| 255 | |
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| 256 | //check trivial case |
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[3c25c9] | 257 | if (degree (A) == 1 || degree (A, 1) == 1 || |
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| 258 | (size (A) == 2 && gcd (degree (A), degree (A,1)).isOne())) |
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[6c44098] | 259 | { |
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| 260 | CFList factors; |
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| 261 | factors.append (A); |
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| 262 | |
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| 263 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 264 | conv (contentAyFactors), false, false, N); |
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| 265 | |
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| 266 | normalize (factors); |
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| 267 | return factors; |
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| 268 | } |
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| 269 | |
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| 270 | //trivial case |
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| 271 | CFList factors; |
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| 272 | if (A.inCoeffDomain()) |
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| 273 | { |
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| 274 | append (factors, conv (contentAxFactors)); |
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| 275 | append (factors, conv (contentAyFactors)); |
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| 276 | decompress (factors, N); |
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| 277 | return factors; |
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| 278 | } |
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| 279 | else if (A.isUnivariate()) |
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| 280 | { |
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| 281 | if (extension) |
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| 282 | factors= conv (factorize (A, v)); |
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| 283 | else |
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| 284 | factors= conv (factorize (A, true)); |
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| 285 | append (factors, conv (contentAxFactors)); |
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| 286 | append (factors, conv (contentAyFactors)); |
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| 287 | decompress (factors, N); |
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| 288 | return factors; |
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| 289 | } |
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| 290 | |
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[9752db] | 291 | if (irreducibilityTest (A)) |
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| 292 | { |
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| 293 | CFList factors; |
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| 294 | factors.append (A); |
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| 295 | |
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| 296 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 297 | conv (contentAyFactors), false, false, N); |
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| 298 | |
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| 299 | normalize (factors); |
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| 300 | return factors; |
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| 301 | } |
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[6c44098] | 302 | bool swap= false; |
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| 303 | if (degree (A) > degree (A, x)) |
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| 304 | { |
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| 305 | A= swapvar (A, y, x); |
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| 306 | swap= true; |
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| 307 | } |
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| 308 | |
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| 309 | CanonicalForm Aeval, bufAeval, buf; |
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| 310 | CFList uniFactors, list, bufUniFactors; |
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| 311 | DegreePattern degs; |
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| 312 | DegreePattern bufDegs; |
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| 313 | |
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| 314 | CanonicalForm Aeval2, bufAeval2; |
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| 315 | CFList bufUniFactors2, list2, uniFactors2; |
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| 316 | DegreePattern degs2; |
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| 317 | DegreePattern bufDegs2; |
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| 318 | bool swap2= false; |
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| 319 | |
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| 320 | // several univariate factorizations to obtain more information about the |
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| 321 | // degree pattern therefore usually less combinations have to be tried during |
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| 322 | // the recombination process |
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| 323 | int factorNums= 2; |
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| 324 | int subCheck1= substituteCheck (A, x); |
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| 325 | int subCheck2= substituteCheck (A, y); |
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| 326 | buf= swapvar (A,x,y); |
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| 327 | int evaluation, evaluation2, bufEvaluation= 0, bufEvaluation2= 0; |
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| 328 | for (int i= 0; i < factorNums; i++) |
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| 329 | { |
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| 330 | bufAeval= A; |
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[0851b0] | 331 | TIMING_START (fac_bi_evaluation); |
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[6c44098] | 332 | bufAeval= evalPoint (A, bufEvaluation); |
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[0851b0] | 333 | TIMING_END_AND_PRINT (fac_bi_evaluation, "time for eval point over Q: "); |
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[6c44098] | 334 | |
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| 335 | bufAeval2= buf; |
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[0851b0] | 336 | TIMING_START (fac_bi_evaluation); |
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[6c44098] | 337 | bufAeval2= evalPoint (buf, bufEvaluation2); |
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[0851b0] | 338 | TIMING_END_AND_PRINT (fac_bi_evaluation, |
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| 339 | "time for eval point over Q in y: "); |
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[6c44098] | 340 | |
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| 341 | // univariate factorization |
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[0851b0] | 342 | TIMING_START (fac_uni_factorizer); |
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[6c44098] | 343 | if (extension) |
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| 344 | bufUniFactors= conv (factorize (bufAeval, v)); |
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| 345 | else |
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| 346 | bufUniFactors= conv (factorize (bufAeval, true)); |
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[0851b0] | 347 | TIMING_END_AND_PRINT (fac_uni_factorizer, |
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| 348 | "time for univariate factorization over Q: "); |
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[27ab36] | 349 | DEBOUTLN (cerr, "prod (bufUniFactors)== bufAeval " << |
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| 350 | (prod (bufUniFactors) == bufAeval)); |
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[6c44098] | 351 | |
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[b2c7a2] | 352 | if (bufUniFactors.getFirst().inCoeffDomain()) |
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| 353 | bufUniFactors.removeFirst(); |
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| 354 | |
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| 355 | if (bufUniFactors.length() == 1) |
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| 356 | { |
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| 357 | factors.append (A); |
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| 358 | |
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| 359 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 360 | conv (contentAyFactors), swap, swap2, N); |
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| 361 | |
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| 362 | if (isOn (SW_RATIONAL)) |
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| 363 | normalize (factors); |
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| 364 | return factors; |
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| 365 | } |
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| 366 | |
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[0851b0] | 367 | TIMING_START (fac_uni_factorizer); |
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[6c44098] | 368 | if (extension) |
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| 369 | bufUniFactors2= conv (factorize (bufAeval2, v)); |
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| 370 | else |
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| 371 | bufUniFactors2= conv (factorize (bufAeval2, true)); |
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[0851b0] | 372 | TIMING_END_AND_PRINT (fac_uni_factorizer, |
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| 373 | "time for univariate factorization in y over Q: "); |
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[27ab36] | 374 | DEBOUTLN (cerr, "prod (bufuniFactors2)== bufAeval2 " << |
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| 375 | (prod (bufUniFactors2) == bufAeval2)); |
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[6c44098] | 376 | |
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| 377 | if (bufUniFactors2.getFirst().inCoeffDomain()) |
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| 378 | bufUniFactors2.removeFirst(); |
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[b2c7a2] | 379 | if (bufUniFactors2.length() == 1) |
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[6c44098] | 380 | { |
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| 381 | factors.append (A); |
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| 382 | |
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| 383 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 384 | conv (contentAyFactors), swap, swap2, N); |
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| 385 | |
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| 386 | if (isOn (SW_RATIONAL)) |
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| 387 | normalize (factors); |
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| 388 | return factors; |
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| 389 | } |
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| 390 | |
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| 391 | if (i == 0) |
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| 392 | { |
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| 393 | if (subCheck1 > 0) |
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| 394 | { |
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| 395 | int subCheck= substituteCheck (bufUniFactors); |
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| 396 | |
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| 397 | if (subCheck > 1 && (subCheck1%subCheck == 0)) |
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| 398 | { |
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| 399 | CanonicalForm bufA= A; |
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| 400 | subst (bufA, bufA, subCheck, x); |
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| 401 | factors= biFactorize (bufA, v); |
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| 402 | reverseSubst (factors, subCheck, x); |
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| 403 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 404 | conv (contentAyFactors), swap, swap2, N); |
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| 405 | if (isOn (SW_RATIONAL)) |
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| 406 | normalize (factors); |
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| 407 | return factors; |
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| 408 | } |
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| 409 | } |
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| 410 | |
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| 411 | if (subCheck2 > 0) |
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| 412 | { |
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| 413 | int subCheck= substituteCheck (bufUniFactors2); |
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| 414 | |
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| 415 | if (subCheck > 1 && (subCheck2%subCheck == 0)) |
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| 416 | { |
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| 417 | CanonicalForm bufA= A; |
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| 418 | subst (bufA, bufA, subCheck, y); |
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| 419 | factors= biFactorize (bufA, v); |
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| 420 | reverseSubst (factors, subCheck, y); |
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| 421 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 422 | conv (contentAyFactors), swap, swap2, N); |
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| 423 | if (isOn (SW_RATIONAL)) |
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| 424 | normalize (factors); |
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| 425 | return factors; |
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| 426 | } |
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| 427 | } |
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| 428 | } |
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| 429 | |
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| 430 | // degree analysis |
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| 431 | bufDegs = DegreePattern (bufUniFactors); |
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| 432 | bufDegs2= DegreePattern (bufUniFactors2); |
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| 433 | |
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| 434 | if (i == 0) |
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| 435 | { |
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| 436 | Aeval= bufAeval; |
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| 437 | evaluation= bufEvaluation; |
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| 438 | uniFactors= bufUniFactors; |
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| 439 | degs= bufDegs; |
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| 440 | Aeval2= bufAeval2; |
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| 441 | evaluation2= bufEvaluation2; |
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| 442 | uniFactors2= bufUniFactors2; |
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| 443 | degs2= bufDegs2; |
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| 444 | } |
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| 445 | else |
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| 446 | { |
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| 447 | degs.intersect (bufDegs); |
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| 448 | degs2.intersect (bufDegs2); |
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| 449 | if (bufUniFactors2.length() < uniFactors2.length()) |
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| 450 | { |
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| 451 | uniFactors2= bufUniFactors2; |
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| 452 | Aeval2= bufAeval2; |
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| 453 | evaluation2= bufEvaluation2; |
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| 454 | } |
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| 455 | if (bufUniFactors.length() < uniFactors.length()) |
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| 456 | { |
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[fd4146] | 457 | uniFactors= bufUniFactors; |
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| 458 | Aeval= bufAeval; |
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| 459 | evaluation= bufEvaluation; |
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[6c44098] | 460 | } |
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| 461 | } |
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[fd4146] | 462 | if (bufEvaluation > 0) |
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| 463 | bufEvaluation++; |
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| 464 | else |
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| 465 | bufEvaluation= -bufEvaluation + 1; |
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| 466 | if (bufEvaluation > 0) |
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| 467 | bufEvaluation2++; |
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| 468 | else |
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| 469 | bufEvaluation2= -bufEvaluation2 + 1; |
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[6c44098] | 470 | } |
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| 471 | |
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[fd4146] | 472 | if (uniFactors.length() > uniFactors2.length() || |
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[6c44098] | 473 | (uniFactors.length() == uniFactors2.length() |
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[fd4146] | 474 | && degs.getLength() > degs2.getLength())) |
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[6c44098] | 475 | { |
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| 476 | degs= degs2; |
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| 477 | uniFactors= uniFactors2; |
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| 478 | evaluation= evaluation2; |
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| 479 | Aeval= Aeval2; |
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| 480 | A= buf; |
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| 481 | swap2= true; |
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| 482 | } |
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| 483 | |
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| 484 | if (degs.getLength() == 1) // A is irreducible |
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| 485 | { |
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| 486 | factors.append (A); |
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| 487 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 488 | conv (contentAyFactors), swap, swap2, N); |
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| 489 | if (isOn (SW_RATIONAL)) |
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| 490 | normalize (factors); |
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| 491 | return factors; |
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| 492 | } |
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| 493 | |
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[e0af3ef] | 494 | A *= bCommonDen (A); |
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[6c44098] | 495 | A= A (y + evaluation, y); |
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| 496 | |
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[1a3011e] | 497 | int liftBound= degree (A, y) + 1; |
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[6c44098] | 498 | |
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[1ade96] | 499 | modpk b= modpk(); |
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[f9da5e] | 500 | bool mipoHasDen= false; |
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[14e634] | 501 | CanonicalForm den= 1; |
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[f9da5e] | 502 | if (!extension) |
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[1ade96] | 503 | { |
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| 504 | Off (SW_RATIONAL); |
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| 505 | int i= 0; |
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[5f92d8] | 506 | findGoodPrime(F,i); |
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| 507 | findGoodPrime(Aeval,i); |
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| 508 | findGoodPrime(A,i); |
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[4e6d2a] | 509 | if (i >= cf_getNumBigPrimes()) |
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[3f8663] | 510 | printf ("out of primes\n"); //TODO exit |
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[1ade96] | 511 | |
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[4e6d2a] | 512 | int p=cf_getBigPrime(i); |
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[1ade96] | 513 | b = coeffBound( A, p ); |
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| 514 | modpk bb= coeffBound (Aeval, p); |
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| 515 | if (bb.getk() > b.getk() ) b=bb; |
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| 516 | bb= coeffBound (F, p); |
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| 517 | if (bb.getk() > b.getk() ) b=bb; |
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| 518 | } |
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[b4af1b] | 519 | else |
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| 520 | { |
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| 521 | A /= Lc (Aeval); |
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[14e634] | 522 | mipoHasDen= !bCommonDen(mipo).isOne(); |
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| 523 | mipo *= bCommonDen (mipo); |
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| 524 | ZZX NTLmipo= convertFacCF2NTLZZX (mipo); |
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| 525 | ZZX NTLLcf= convertFacCF2NTLZZX (Lc (A*bCommonDen (A))); |
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| 526 | ZZ NTLf= resultant (NTLmipo, NTLLcf); |
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| 527 | ZZ NTLD= discriminant (NTLmipo); |
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| 528 | den= abs (convertZZ2CF (NTLD*NTLf)); |
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| 529 | |
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[b4af1b] | 530 | // make factors elements of Z(a)[x] disable for modularDiophant |
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[d92248] | 531 | CanonicalForm multiplier= 1; |
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[b4af1b] | 532 | for (CFListIterator i= uniFactors; i.hasItem(); i++) |
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[d92248] | 533 | { |
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| 534 | multiplier *= bCommonDen (i.getItem()); |
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[b4af1b] | 535 | i.getItem()= i.getItem()*bCommonDen(i.getItem()); |
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[d92248] | 536 | } |
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| 537 | A *= multiplier; |
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| 538 | A *= bCommonDen (A); |
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| 539 | |
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[b4af1b] | 540 | Off (SW_RATIONAL); |
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| 541 | int i= 0; |
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[14e634] | 542 | CanonicalForm discMipo= convertZZ2CF (NTLD); |
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[b4af1b] | 543 | findGoodPrime (F*discMipo,i); |
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| 544 | findGoodPrime (Aeval*discMipo,i); |
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| 545 | findGoodPrime (A*discMipo,i); |
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| 546 | |
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| 547 | int p=cf_getBigPrime(i); |
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| 548 | b = coeffBound( A, p, mipo ); |
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| 549 | modpk bb= coeffBound (Aeval, p, mipo); |
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| 550 | if (bb.getk() > b.getk() ) b=bb; |
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| 551 | bb= coeffBound (F, p, mipo); |
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| 552 | if (bb.getk() > b.getk() ) b=bb; |
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| 553 | } |
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[1ade96] | 554 | |
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[deb0f60] | 555 | ExtensionInfo dummy= ExtensionInfo (false); |
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[b4af1b] | 556 | if (extension) |
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| 557 | dummy= ExtensionInfo (v, false); |
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[6c44098] | 558 | bool earlySuccess= false; |
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| 559 | CFList earlyFactors; |
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[978ce3] | 560 | TIMING_START (fac_bi_hensel_lift); |
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[deb0f60] | 561 | uniFactors= henselLiftAndEarly |
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| 562 | (A, earlySuccess, earlyFactors, degs, liftBound, |
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[14e634] | 563 | uniFactors, dummy, evaluation, b, den); |
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[0851b0] | 564 | TIMING_END_AND_PRINT (fac_bi_hensel_lift, |
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| 565 | "time for bivariate hensel lifting over Q: "); |
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[6c44098] | 566 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
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| 567 | |
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| 568 | CanonicalForm MODl= power (y, liftBound); |
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| 569 | |
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[f9da5e] | 570 | if (mipoHasDen) |
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| 571 | { |
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| 572 | Variable vv; |
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| 573 | for (CFListIterator iter= uniFactors; iter.hasItem(); iter++) |
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| 574 | if (hasFirstAlgVar (iter.getItem(), vv)) |
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| 575 | break; |
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| 576 | for (CFListIterator iter= uniFactors; iter.hasItem(); iter++) |
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| 577 | iter.getItem()= replacevar (iter.getItem(), vv, v); |
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| 578 | } |
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| 579 | |
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[e0af3ef] | 580 | On (SW_RATIONAL); |
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| 581 | A *= bCommonDen (A); |
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| 582 | Off (SW_RATIONAL); |
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| 583 | |
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[0851b0] | 584 | TIMING_START (fac_bi_factor_recombination); |
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[6c44098] | 585 | factors= factorRecombination (uniFactors, A, MODl, degs, 1, |
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[14e634] | 586 | uniFactors.length()/2, b, den); |
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[0851b0] | 587 | TIMING_END_AND_PRINT (fac_bi_factor_recombination, |
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| 588 | "time for bivariate factor recombination over Q: "); |
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[1ade96] | 589 | |
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[b4af1b] | 590 | On (SW_RATIONAL); |
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[6c44098] | 591 | |
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| 592 | if (earlySuccess) |
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| 593 | factors= Union (earlyFactors, factors); |
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| 594 | else if (!earlySuccess && degs.getLength() == 1) |
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| 595 | factors= earlyFactors; |
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| 596 | |
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| 597 | for (CFListIterator i= factors; i.hasItem(); i++) |
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| 598 | i.getItem()= i.getItem() (y - evaluation, y); |
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| 599 | |
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| 600 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 601 | conv (contentAyFactors), swap, swap2, N); |
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| 602 | if (isOn (SW_RATIONAL)) |
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| 603 | normalize (factors); |
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| 604 | |
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| 605 | return factors; |
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| 606 | } |
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[615ca8] | 607 | |
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| 608 | #endif |
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