[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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| 15 | #include "assert.h" |
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| 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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[6c44098] | 30 | |
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[5f92d8] | 31 | // bound on coeffs of f (cf. Musser: Multivariate Polynomial Factorization, |
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| 32 | // Gelfond: Transcendental and Algebraic Numbers) |
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| 33 | modpk |
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[1ade96] | 34 | coeffBound ( const CanonicalForm & f, int p ) |
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| 35 | { |
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| 36 | int * degs = degrees( f ); |
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| 37 | int M = 0, i, k = f.level(); |
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[5f92d8] | 38 | CanonicalForm b= 1; |
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[1ade96] | 39 | for ( i = 1; i <= k; i++ ) |
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[5f92d8] | 40 | { |
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| 41 | M += degs[i]; |
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| 42 | b *= degs[i] + 1; |
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| 43 | } |
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| 44 | b /= power (CanonicalForm (2), k); |
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| 45 | b= b.sqrt() + 1; |
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| 46 | b *= 2 * maxNorm( f ) * power( CanonicalForm( 2 ), M ); |
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[1ade96] | 47 | CanonicalForm B = p; |
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| 48 | k = 1; |
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| 49 | while ( B < b ) { |
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| 50 | B *= p; |
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| 51 | k++; |
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| 52 | } |
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| 53 | return modpk( p, k ); |
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| 54 | } |
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| 55 | |
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[5f92d8] | 56 | void findGoodPrime(const CanonicalForm &f, int &start) |
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[1ade96] | 57 | { |
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| 58 | if (! f.inBaseDomain() ) |
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| 59 | { |
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| 60 | CFIterator i = f; |
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| 61 | for(;;) |
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| 62 | { |
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| 63 | if ( i.hasTerms() ) |
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| 64 | { |
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[5f92d8] | 65 | findGoodPrime(i.coeff(),start); |
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[4e6d2a] | 66 | if (0==cf_getBigPrime(start)) return; |
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| 67 | if((i.exp()!=0) && ((i.exp() % cf_getBigPrime(start))==0)) |
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[1ade96] | 68 | { |
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| 69 | start++; |
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| 70 | i=f; |
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| 71 | } |
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| 72 | else i++; |
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| 73 | } |
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| 74 | else break; |
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| 75 | } |
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| 76 | } |
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| 77 | else |
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| 78 | { |
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| 79 | if (f.inZ()) |
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| 80 | { |
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[4e6d2a] | 81 | if (0==cf_getBigPrime(start)) return; |
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| 82 | while((!f.isZero()) && (mod(f,cf_getBigPrime(start))==0)) |
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[1ade96] | 83 | { |
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| 84 | start++; |
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[4e6d2a] | 85 | if (0==cf_getBigPrime(start)) return; |
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[1ade96] | 86 | } |
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| 87 | } |
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| 88 | } |
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| 89 | } |
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| 90 | |
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[5f92d8] | 91 | modpk |
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| 92 | coeffBound ( const CanonicalForm & f, int p, const CanonicalForm& mipo ) |
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| 93 | { |
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| 94 | int * degs = degrees( f ); |
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| 95 | int M = 0, i, k = f.level(); |
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| 96 | CanonicalForm K= 1; |
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| 97 | for ( i = 1; i <= k; i++ ) |
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| 98 | { |
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| 99 | M += degs[i]; |
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| 100 | K *= degs[i] + 1; |
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| 101 | } |
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| 102 | K /= power (CanonicalForm (2), k); |
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| 103 | K= K.sqrt()+1; |
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| 104 | K *= power (CanonicalForm (2), M); |
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| 105 | int N= degree (mipo); |
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| 106 | CanonicalForm b; |
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[b4af1b] | 107 | b= 2*power (maxNorm (f), N)*power (maxNorm (mipo), 4*N)*K* |
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| 108 | power (CanonicalForm (2), N)*(CanonicalForm (M+1).sqrt()+1)* |
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| 109 | power (CanonicalForm (N+1).sqrt()+1, 7*N); |
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[5f92d8] | 110 | b /= power (abs (lc (mipo)), N); |
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| 111 | |
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| 112 | ZZX NTLmipo= convertFacCF2NTLZZX (mipo); |
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| 113 | ZZX NTLLcf= convertFacCF2NTLZZX (Lc (f)); |
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| 114 | ZZ NTLf= resultant (NTLmipo, NTLLcf); |
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| 115 | ZZ NTLD= discriminant (NTLmipo); |
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| 116 | b /= abs (convertZZ2CF (NTLf))*abs (convertZZ2CF (NTLD)); |
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| 117 | |
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| 118 | CanonicalForm B = p; |
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| 119 | k = 1; |
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| 120 | while ( B < b ) { |
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| 121 | B *= p; |
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| 122 | k++; |
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| 123 | } |
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| 124 | return modpk( p, k ); |
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| 125 | } |
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| 126 | |
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[6c44098] | 127 | CFList conv (const CFFList& L) |
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| 128 | { |
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| 129 | CFList result; |
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| 130 | for (CFFListIterator i= L; i.hasItem(); i++) |
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| 131 | result.append (i.getItem().factor()); |
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| 132 | return result; |
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| 133 | } |
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| 134 | |
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| 135 | bool testPoint (const CanonicalForm& F, CanonicalForm& G, int i) |
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| 136 | { |
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| 137 | G= F (i, 2); |
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| 138 | if (G.inCoeffDomain() || degree (F, 1) > degree (G, 1)) |
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| 139 | return false; |
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| 140 | |
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| 141 | if (degree (gcd (deriv (G, G.mvar()), G)) > 0) |
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| 142 | return false; |
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| 143 | return true; |
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| 144 | } |
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| 145 | |
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| 146 | CanonicalForm evalPoint (const CanonicalForm& F, int& i) |
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| 147 | { |
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| 148 | Variable x= Variable (1); |
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| 149 | Variable y= Variable (2); |
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| 150 | CanonicalForm result; |
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| 151 | |
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| 152 | int k; |
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| 153 | |
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| 154 | if (i == 0) |
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| 155 | { |
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| 156 | if (testPoint (F, result, i)) |
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| 157 | return result; |
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| 158 | } |
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| 159 | do |
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| 160 | { |
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| 161 | if (i > 0) |
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| 162 | k= 1; |
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| 163 | else |
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| 164 | k= 2; |
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| 165 | while (k < 3) |
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| 166 | { |
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| 167 | if (k == 1) |
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| 168 | { |
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| 169 | if (testPoint (F, result, i)) |
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| 170 | return result; |
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| 171 | } |
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| 172 | else |
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| 173 | { |
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| 174 | if (testPoint (F, result, -i)) |
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[fd4146] | 175 | { |
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| 176 | i= -i; |
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[6c44098] | 177 | return result; |
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[fd4146] | 178 | } |
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| 179 | else if (i < 0) |
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| 180 | i= -i; |
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[6c44098] | 181 | } |
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| 182 | k++; |
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| 183 | } |
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| 184 | i++; |
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| 185 | } while (1); |
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| 186 | } |
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| 187 | |
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[f8ac2df] | 188 | CFList |
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| 189 | earlyFactorDetection0 (CanonicalForm& F, CFList& factors,int& adaptedLiftBound, |
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| 190 | DegreePattern& degs, bool& success, int deg) |
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| 191 | { |
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| 192 | DegreePattern bufDegs1= degs; |
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| 193 | DegreePattern bufDegs2; |
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| 194 | CFList result; |
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| 195 | CFList T= factors; |
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| 196 | CanonicalForm buf= F; |
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| 197 | CanonicalForm LCBuf= LC (buf, Variable (1)); |
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| 198 | CanonicalForm g, quot; |
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| 199 | CanonicalForm M= power (F.mvar(), deg); |
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| 200 | adaptedLiftBound= 0; |
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| 201 | int d= degree (F) + degree (LCBuf, F.mvar()); |
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| 202 | for (CFListIterator i= factors; i.hasItem(); i++) |
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| 203 | { |
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| 204 | if (!bufDegs1.find (degree (i.getItem(), 1))) |
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| 205 | continue; |
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| 206 | else |
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| 207 | { |
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| 208 | g= i.getItem() (0, 1); |
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| 209 | g *= LCBuf; |
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| 210 | g= mod (g, M); |
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| 211 | if (fdivides (LC (g), LCBuf)) |
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| 212 | { |
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| 213 | g= mulMod2 (i.getItem(), LCBuf, M); |
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| 214 | g /= content (g, Variable (1)); |
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| 215 | if (fdivides (g, buf, quot)) |
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| 216 | { |
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| 217 | result.append (g); |
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| 218 | buf= quot; |
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| 219 | d -= degree (g) + degree (LC (g, Variable (1)), F.mvar()); |
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| 220 | LCBuf= LC (buf, Variable (1)); |
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| 221 | T= Difference (T, CFList (i.getItem())); |
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| 222 | |
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| 223 | // compute new possible degree pattern |
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| 224 | bufDegs2= DegreePattern (T); |
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| 225 | bufDegs1.intersect (bufDegs2); |
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| 226 | bufDegs1.refine (); |
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| 227 | if (bufDegs1.getLength() <= 1) |
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| 228 | { |
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| 229 | result.append (buf); |
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| 230 | break; |
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| 231 | } |
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| 232 | } |
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| 233 | } |
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| 234 | } |
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| 235 | } |
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| 236 | adaptedLiftBound= d + 1; |
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| 237 | if (d < deg) |
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| 238 | { |
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| 239 | factors= T; |
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| 240 | degs= bufDegs1; |
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| 241 | F= buf; |
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| 242 | success= true; |
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| 243 | } |
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| 244 | if (bufDegs1.getLength() <= 1) |
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| 245 | degs= bufDegs1; |
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| 246 | return result; |
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| 247 | } |
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| 248 | |
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| 249 | |
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| 250 | CFList |
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| 251 | henselLiftAndEarly0 (CanonicalForm& A, bool& earlySuccess, CFList& |
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| 252 | earlyFactors, DegreePattern& degs, int& liftBound, |
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| 253 | const CFList& uniFactors, const CanonicalForm& eval) |
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| 254 | { |
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| 255 | int sizeOfLiftPre; |
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| 256 | int * liftPre= getLiftPrecisions (A, sizeOfLiftPre, degree (LC (A, 1), 2)); |
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| 257 | |
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| 258 | Variable x= Variable (1); |
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| 259 | Variable y= Variable (2); |
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| 260 | CFArray Pi; |
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| 261 | CFList diophant; |
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| 262 | CFList bufUniFactors= uniFactors; |
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| 263 | bufUniFactors.insert (LC (A, x)); |
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| 264 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length() - 1); |
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| 265 | earlySuccess= false; |
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| 266 | int newLiftBound= 0; |
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| 267 | int smallFactorDeg= tmin (11, liftPre [sizeOfLiftPre- 1] + 1);//this is a tunable parameter |
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| 268 | if (smallFactorDeg >= liftBound || degree (A,y) <= 4) |
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| 269 | henselLift12 (A, bufUniFactors, liftBound, Pi, diophant, M); |
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| 270 | else if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
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| 271 | { |
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| 272 | henselLift12 (A, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
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| 273 | earlyFactors= earlyFactorDetection0 (A, bufUniFactors, newLiftBound, |
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| 274 | degs, earlySuccess, |
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| 275 | smallFactorDeg); |
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| 276 | if (degs.getLength() > 1 && !earlySuccess && |
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| 277 | smallFactorDeg != liftPre [sizeOfLiftPre-1] + 1) |
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| 278 | { |
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| 279 | if (newLiftBound > liftPre[sizeOfLiftPre-1]+1) |
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| 280 | { |
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| 281 | bufUniFactors.insert (LC (A, x)); |
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| 282 | henselLiftResume12 (A, bufUniFactors, smallFactorDeg, |
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| 283 | liftPre[sizeOfLiftPre-1] + 1, Pi, diophant, M); |
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| 284 | earlyFactors= earlyFactorDetection0 (A, bufUniFactors, newLiftBound, |
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| 285 | degs, earlySuccess, liftPre[sizeOfLiftPre-1] + 1); |
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| 286 | } |
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| 287 | } |
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| 288 | else if (earlySuccess) |
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| 289 | liftBound= newLiftBound; |
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| 290 | int i= sizeOfLiftPre - 1; |
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| 291 | while (degs.getLength() > 1 && !earlySuccess && i - 1 >= 0) |
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| 292 | { |
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| 293 | if (newLiftBound > liftPre[i] + 1) |
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| 294 | { |
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| 295 | bufUniFactors.insert (LC (A, x)); |
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| 296 | henselLiftResume12 (A, bufUniFactors, liftPre[i] + 1, |
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| 297 | liftPre[i-1] + 1, Pi, diophant, M); |
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| 298 | earlyFactors= earlyFactorDetection0 (A, bufUniFactors, newLiftBound, |
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| 299 | degs, earlySuccess, liftPre[i-1] + 1); |
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| 300 | } |
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| 301 | else |
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| 302 | { |
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| 303 | liftBound= newLiftBound; |
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| 304 | break; |
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| 305 | } |
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| 306 | i--; |
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| 307 | } |
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| 308 | if (earlySuccess) |
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| 309 | liftBound= newLiftBound; |
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| 310 | //after here all factors are lifted to liftPre[sizeOfLiftPre-1] |
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| 311 | } |
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| 312 | else |
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| 313 | { |
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| 314 | henselLift12 (A, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
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| 315 | earlyFactors= earlyFactorDetection0 (A, bufUniFactors, newLiftBound, |
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| 316 | degs, earlySuccess, |
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| 317 | smallFactorDeg); |
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| 318 | int i= 1; |
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| 319 | while ((degree (A,y)/4)*i + 4 <= smallFactorDeg) |
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| 320 | i++; |
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| 321 | if (degs.getLength() > 1 && !earlySuccess) |
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| 322 | { |
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| 323 | bufUniFactors.insert (LC (A, x)); |
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| 324 | henselLiftResume12 (A, bufUniFactors, smallFactorDeg, |
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| 325 | (degree (A, y)/4)*i + 4, Pi, diophant, M); |
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| 326 | earlyFactors= earlyFactorDetection0 (A, bufUniFactors, newLiftBound, |
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| 327 | degs, earlySuccess, (degree (A, y)/4)*i + 4); |
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| 328 | } |
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| 329 | while (degs.getLength() > 1 && !earlySuccess && i < 4) |
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| 330 | { |
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| 331 | if (newLiftBound > (degree (A, y)/4)*i + 4) |
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| 332 | { |
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| 333 | bufUniFactors.insert (LC (A, x)); |
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| 334 | henselLiftResume12 (A, bufUniFactors, (degree (A,y)/4)*i + 4, |
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| 335 | (degree (A, y)/4)*(i+1) + 4, Pi, diophant, M); |
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| 336 | earlyFactors= earlyFactorDetection0 (A, bufUniFactors, newLiftBound, |
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| 337 | degs, earlySuccess, (degree (A, y)/4)*(i+1) + 4); |
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| 338 | } |
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| 339 | else |
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| 340 | { |
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| 341 | liftBound= newLiftBound; |
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| 342 | break; |
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| 343 | } |
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| 344 | i++; |
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| 345 | } |
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| 346 | if (earlySuccess) |
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| 347 | liftBound= newLiftBound; |
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| 348 | } |
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| 349 | |
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| 350 | return bufUniFactors; |
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| 351 | } |
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| 352 | |
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[6c44098] | 353 | CFList biFactorize (const CanonicalForm& F, const Variable& v) |
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| 354 | { |
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| 355 | if (F.inCoeffDomain()) |
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| 356 | return CFList(F); |
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| 357 | |
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| 358 | bool extension= (v.level() != 1); |
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| 359 | CanonicalForm A; |
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| 360 | if (isOn (SW_RATIONAL)) |
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| 361 | A= F*bCommonDen (F); |
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| 362 | else |
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| 363 | A= F; |
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| 364 | |
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[b4af1b] | 365 | CanonicalForm mipo; |
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| 366 | if (extension) |
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| 367 | mipo= getMipo (v); |
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| 368 | |
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[6c44098] | 369 | if (A.isUnivariate()) |
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| 370 | { |
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| 371 | CFFList buf; |
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| 372 | if (extension) |
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| 373 | buf= factorize (A, v); |
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| 374 | else |
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| 375 | buf= factorize (A, true); |
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| 376 | CFList result= conv (buf); |
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| 377 | if (result.getFirst().inCoeffDomain()) |
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| 378 | result.removeFirst(); |
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| 379 | return result; |
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| 380 | } |
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| 381 | |
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| 382 | CFMap N; |
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| 383 | A= compress (A, N); |
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| 384 | Variable y= A.mvar(); |
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| 385 | |
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| 386 | if (y.level() > 2) return CFList (F); |
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| 387 | Variable x= Variable (1); |
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| 388 | |
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| 389 | CanonicalForm contentAx= content (A, x); |
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| 390 | CanonicalForm contentAy= content (A); |
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| 391 | |
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| 392 | A= A/(contentAx*contentAy); |
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| 393 | CFFList contentAxFactors, contentAyFactors; |
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| 394 | |
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| 395 | if (extension) |
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| 396 | { |
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| 397 | if (!contentAx.inCoeffDomain()) |
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| 398 | { |
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| 399 | contentAxFactors= factorize (contentAx, v); |
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| 400 | if (contentAxFactors.getFirst().factor().inCoeffDomain()) |
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| 401 | contentAxFactors.removeFirst(); |
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| 402 | } |
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| 403 | if (!contentAy.inCoeffDomain()) |
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| 404 | { |
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| 405 | contentAyFactors= factorize (contentAy, v); |
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| 406 | if (contentAyFactors.getFirst().factor().inCoeffDomain()) |
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| 407 | contentAyFactors.removeFirst(); |
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| 408 | } |
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| 409 | } |
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| 410 | else |
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| 411 | { |
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| 412 | if (!contentAx.inCoeffDomain()) |
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| 413 | { |
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| 414 | contentAxFactors= factorize (contentAx, true); |
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| 415 | if (contentAxFactors.getFirst().factor().inCoeffDomain()) |
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| 416 | contentAxFactors.removeFirst(); |
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| 417 | } |
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| 418 | if (!contentAy.inCoeffDomain()) |
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| 419 | { |
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| 420 | contentAyFactors= factorize (contentAy, true); |
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| 421 | if (contentAyFactors.getFirst().factor().inCoeffDomain()) |
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| 422 | contentAyFactors.removeFirst(); |
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| 423 | } |
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| 424 | } |
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| 425 | |
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| 426 | //check trivial case |
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[3c25c9] | 427 | if (degree (A) == 1 || degree (A, 1) == 1 || |
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| 428 | (size (A) == 2 && gcd (degree (A), degree (A,1)).isOne())) |
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[6c44098] | 429 | { |
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| 430 | CFList factors; |
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| 431 | factors.append (A); |
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| 432 | |
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| 433 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 434 | conv (contentAyFactors), false, false, N); |
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| 435 | |
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| 436 | normalize (factors); |
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| 437 | return factors; |
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| 438 | } |
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| 439 | |
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| 440 | //trivial case |
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| 441 | CFList factors; |
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| 442 | if (A.inCoeffDomain()) |
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| 443 | { |
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| 444 | append (factors, conv (contentAxFactors)); |
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| 445 | append (factors, conv (contentAyFactors)); |
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| 446 | decompress (factors, N); |
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| 447 | return factors; |
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| 448 | } |
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| 449 | else if (A.isUnivariate()) |
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| 450 | { |
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| 451 | if (extension) |
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| 452 | factors= conv (factorize (A, v)); |
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| 453 | else |
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| 454 | factors= conv (factorize (A, true)); |
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| 455 | append (factors, conv (contentAxFactors)); |
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| 456 | append (factors, conv (contentAyFactors)); |
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| 457 | decompress (factors, N); |
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| 458 | return factors; |
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| 459 | } |
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| 460 | |
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[9752db] | 461 | if (irreducibilityTest (A)) |
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| 462 | { |
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| 463 | CFList factors; |
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| 464 | factors.append (A); |
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| 465 | |
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| 466 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 467 | conv (contentAyFactors), false, false, N); |
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| 468 | |
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| 469 | normalize (factors); |
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| 470 | return factors; |
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| 471 | } |
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[6c44098] | 472 | bool swap= false; |
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| 473 | if (degree (A) > degree (A, x)) |
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| 474 | { |
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| 475 | A= swapvar (A, y, x); |
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| 476 | swap= true; |
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| 477 | } |
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| 478 | |
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| 479 | CanonicalForm Aeval, bufAeval, buf; |
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| 480 | CFList uniFactors, list, bufUniFactors; |
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| 481 | DegreePattern degs; |
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| 482 | DegreePattern bufDegs; |
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| 483 | |
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| 484 | CanonicalForm Aeval2, bufAeval2; |
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| 485 | CFList bufUniFactors2, list2, uniFactors2; |
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| 486 | DegreePattern degs2; |
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| 487 | DegreePattern bufDegs2; |
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| 488 | bool swap2= false; |
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| 489 | |
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| 490 | // several univariate factorizations to obtain more information about the |
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| 491 | // degree pattern therefore usually less combinations have to be tried during |
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| 492 | // the recombination process |
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| 493 | int factorNums= 2; |
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| 494 | int subCheck1= substituteCheck (A, x); |
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| 495 | int subCheck2= substituteCheck (A, y); |
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| 496 | buf= swapvar (A,x,y); |
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| 497 | int evaluation, evaluation2, bufEvaluation= 0, bufEvaluation2= 0; |
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| 498 | for (int i= 0; i < factorNums; i++) |
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| 499 | { |
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| 500 | bufAeval= A; |
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| 501 | bufAeval= evalPoint (A, bufEvaluation); |
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| 502 | |
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| 503 | bufAeval2= buf; |
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| 504 | bufAeval2= evalPoint (buf, bufEvaluation2); |
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| 505 | |
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| 506 | // univariate factorization |
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[0b618a7] | 507 | TIMING_START (uni_factorize); |
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[6c44098] | 508 | |
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| 509 | if (extension) |
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| 510 | bufUniFactors= conv (factorize (bufAeval, v)); |
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| 511 | else |
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| 512 | bufUniFactors= conv (factorize (bufAeval, true)); |
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[0b618a7] | 513 | TIMING_END_AND_PRINT (uni_factorize, |
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[6c44098] | 514 | "time for univariate factorization: "); |
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[27ab36] | 515 | DEBOUTLN (cerr, "prod (bufUniFactors)== bufAeval " << |
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| 516 | (prod (bufUniFactors) == bufAeval)); |
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[6c44098] | 517 | |
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[0b618a7] | 518 | TIMING_START (uni_factorize); |
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[6c44098] | 519 | if (extension) |
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| 520 | bufUniFactors2= conv (factorize (bufAeval2, v)); |
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| 521 | else |
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| 522 | bufUniFactors2= conv (factorize (bufAeval2, true)); |
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[0b618a7] | 523 | TIMING_END_AND_PRINT (uni_factorize, |
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[6c44098] | 524 | "time for univariate factorization in y: "); |
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[27ab36] | 525 | DEBOUTLN (cerr, "prod (bufuniFactors2)== bufAeval2 " << |
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| 526 | (prod (bufUniFactors2) == bufAeval2)); |
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[6c44098] | 527 | |
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| 528 | if (bufUniFactors.getFirst().inCoeffDomain()) |
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| 529 | bufUniFactors.removeFirst(); |
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| 530 | if (bufUniFactors2.getFirst().inCoeffDomain()) |
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| 531 | bufUniFactors2.removeFirst(); |
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| 532 | if (bufUniFactors.length() == 1 || bufUniFactors2.length() == 1) |
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| 533 | { |
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| 534 | factors.append (A); |
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| 535 | |
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| 536 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 537 | conv (contentAyFactors), swap, swap2, N); |
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| 538 | |
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| 539 | if (isOn (SW_RATIONAL)) |
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| 540 | normalize (factors); |
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| 541 | return factors; |
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| 542 | } |
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| 543 | |
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| 544 | if (i == 0) |
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| 545 | { |
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| 546 | if (subCheck1 > 0) |
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| 547 | { |
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| 548 | int subCheck= substituteCheck (bufUniFactors); |
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| 549 | |
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| 550 | if (subCheck > 1 && (subCheck1%subCheck == 0)) |
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| 551 | { |
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| 552 | CanonicalForm bufA= A; |
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| 553 | subst (bufA, bufA, subCheck, x); |
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| 554 | factors= biFactorize (bufA, v); |
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| 555 | reverseSubst (factors, subCheck, x); |
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| 556 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 557 | conv (contentAyFactors), swap, swap2, N); |
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| 558 | if (isOn (SW_RATIONAL)) |
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| 559 | normalize (factors); |
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| 560 | return factors; |
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| 561 | } |
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| 562 | } |
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| 563 | |
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| 564 | if (subCheck2 > 0) |
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| 565 | { |
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| 566 | int subCheck= substituteCheck (bufUniFactors2); |
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| 567 | |
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| 568 | if (subCheck > 1 && (subCheck2%subCheck == 0)) |
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| 569 | { |
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| 570 | CanonicalForm bufA= A; |
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| 571 | subst (bufA, bufA, subCheck, y); |
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| 572 | factors= biFactorize (bufA, v); |
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| 573 | reverseSubst (factors, subCheck, y); |
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| 574 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 575 | conv (contentAyFactors), swap, swap2, N); |
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| 576 | if (isOn (SW_RATIONAL)) |
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| 577 | normalize (factors); |
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| 578 | return factors; |
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| 579 | } |
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| 580 | } |
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| 581 | } |
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| 582 | |
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| 583 | // degree analysis |
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| 584 | bufDegs = DegreePattern (bufUniFactors); |
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| 585 | bufDegs2= DegreePattern (bufUniFactors2); |
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| 586 | |
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| 587 | if (i == 0) |
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| 588 | { |
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| 589 | Aeval= bufAeval; |
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| 590 | evaluation= bufEvaluation; |
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| 591 | uniFactors= bufUniFactors; |
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| 592 | degs= bufDegs; |
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| 593 | Aeval2= bufAeval2; |
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| 594 | evaluation2= bufEvaluation2; |
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| 595 | uniFactors2= bufUniFactors2; |
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| 596 | degs2= bufDegs2; |
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| 597 | } |
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| 598 | else |
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| 599 | { |
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| 600 | degs.intersect (bufDegs); |
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| 601 | degs2.intersect (bufDegs2); |
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| 602 | if (bufUniFactors2.length() < uniFactors2.length()) |
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| 603 | { |
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| 604 | uniFactors2= bufUniFactors2; |
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| 605 | Aeval2= bufAeval2; |
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| 606 | evaluation2= bufEvaluation2; |
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| 607 | } |
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| 608 | if (bufUniFactors.length() < uniFactors.length()) |
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| 609 | { |
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[fd4146] | 610 | uniFactors= bufUniFactors; |
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| 611 | Aeval= bufAeval; |
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| 612 | evaluation= bufEvaluation; |
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[6c44098] | 613 | } |
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| 614 | } |
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[fd4146] | 615 | if (bufEvaluation > 0) |
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| 616 | bufEvaluation++; |
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| 617 | else |
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| 618 | bufEvaluation= -bufEvaluation + 1; |
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| 619 | if (bufEvaluation > 0) |
---|
| 620 | bufEvaluation2++; |
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| 621 | else |
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| 622 | bufEvaluation2= -bufEvaluation2 + 1; |
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[6c44098] | 623 | } |
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| 624 | |
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[fd4146] | 625 | if (uniFactors.length() > uniFactors2.length() || |
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[6c44098] | 626 | (uniFactors.length() == uniFactors2.length() |
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[fd4146] | 627 | && degs.getLength() > degs2.getLength())) |
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[6c44098] | 628 | { |
---|
| 629 | degs= degs2; |
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| 630 | uniFactors= uniFactors2; |
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| 631 | evaluation= evaluation2; |
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| 632 | Aeval= Aeval2; |
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| 633 | A= buf; |
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| 634 | swap2= true; |
---|
| 635 | } |
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| 636 | |
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| 637 | if (degs.getLength() == 1) // A is irreducible |
---|
| 638 | { |
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| 639 | factors.append (A); |
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| 640 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 641 | conv (contentAyFactors), swap, swap2, N); |
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| 642 | if (isOn (SW_RATIONAL)) |
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| 643 | normalize (factors); |
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| 644 | return factors; |
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| 645 | } |
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| 646 | |
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| 647 | A= A (y + evaluation, y); |
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| 648 | |
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[1a3011e] | 649 | int liftBound= degree (A, y) + 1; |
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[6c44098] | 650 | |
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[1ade96] | 651 | modpk b= modpk(); |
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[f9da5e] | 652 | bool mipoHasDen= false; |
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| 653 | if (!extension) |
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[1ade96] | 654 | { |
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| 655 | Off (SW_RATIONAL); |
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| 656 | int i= 0; |
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[5f92d8] | 657 | findGoodPrime(F,i); |
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| 658 | findGoodPrime(Aeval,i); |
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| 659 | findGoodPrime(A,i); |
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[4e6d2a] | 660 | if (i >= cf_getNumBigPrimes()) |
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[3f8663] | 661 | printf ("out of primes\n"); //TODO exit |
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[1ade96] | 662 | |
---|
[4e6d2a] | 663 | int p=cf_getBigPrime(i); |
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[1ade96] | 664 | b = coeffBound( A, p ); |
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| 665 | modpk bb= coeffBound (Aeval, p); |
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| 666 | if (bb.getk() > b.getk() ) b=bb; |
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| 667 | bb= coeffBound (F, p); |
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| 668 | if (bb.getk() > b.getk() ) b=bb; |
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| 669 | } |
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[b4af1b] | 670 | else |
---|
| 671 | { |
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| 672 | A /= Lc (Aeval); |
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| 673 | // make factors elements of Z(a)[x] disable for modularDiophant |
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[d92248] | 674 | CanonicalForm multiplier= 1; |
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[b4af1b] | 675 | for (CFListIterator i= uniFactors; i.hasItem(); i++) |
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[d92248] | 676 | { |
---|
| 677 | multiplier *= bCommonDen (i.getItem()); |
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[b4af1b] | 678 | i.getItem()= i.getItem()*bCommonDen(i.getItem()); |
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[d92248] | 679 | } |
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| 680 | A *= multiplier; |
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| 681 | A *= bCommonDen (A); |
---|
| 682 | |
---|
[f9da5e] | 683 | mipoHasDen= !bCommonDen(mipo).isOne(); |
---|
| 684 | mipo *= bCommonDen (mipo); |
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[b4af1b] | 685 | Off (SW_RATIONAL); |
---|
| 686 | int i= 0; |
---|
| 687 | ZZX NTLmipo= convertFacCF2NTLZZX (mipo); |
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| 688 | CanonicalForm discMipo= convertZZ2CF (discriminant (NTLmipo)); |
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| 689 | findGoodPrime (F*discMipo,i); |
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| 690 | findGoodPrime (Aeval*discMipo,i); |
---|
| 691 | findGoodPrime (A*discMipo,i); |
---|
| 692 | |
---|
| 693 | int p=cf_getBigPrime(i); |
---|
| 694 | b = coeffBound( A, p, mipo ); |
---|
| 695 | modpk bb= coeffBound (Aeval, p, mipo); |
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| 696 | if (bb.getk() > b.getk() ) b=bb; |
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| 697 | bb= coeffBound (F, p, mipo); |
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| 698 | if (bb.getk() > b.getk() ) b=bb; |
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| 699 | } |
---|
[1ade96] | 700 | |
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[deb0f60] | 701 | ExtensionInfo dummy= ExtensionInfo (false); |
---|
[b4af1b] | 702 | if (extension) |
---|
| 703 | dummy= ExtensionInfo (v, false); |
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[6c44098] | 704 | bool earlySuccess= false; |
---|
| 705 | CFList earlyFactors; |
---|
[978ce3] | 706 | TIMING_START (fac_bi_hensel_lift); |
---|
[deb0f60] | 707 | uniFactors= henselLiftAndEarly |
---|
| 708 | (A, earlySuccess, earlyFactors, degs, liftBound, |
---|
[1ade96] | 709 | uniFactors, dummy, evaluation, b); |
---|
[978ce3] | 710 | TIMING_END_AND_PRINT (fac_bi_hensel_lift, "time for hensel lifting: "); |
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[6c44098] | 711 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
| 712 | |
---|
| 713 | CanonicalForm MODl= power (y, liftBound); |
---|
| 714 | |
---|
[f9da5e] | 715 | if (mipoHasDen) |
---|
| 716 | { |
---|
| 717 | Variable vv; |
---|
| 718 | for (CFListIterator iter= uniFactors; iter.hasItem(); iter++) |
---|
| 719 | if (hasFirstAlgVar (iter.getItem(), vv)) |
---|
| 720 | break; |
---|
| 721 | for (CFListIterator iter= uniFactors; iter.hasItem(); iter++) |
---|
| 722 | iter.getItem()= replacevar (iter.getItem(), vv, v); |
---|
| 723 | } |
---|
| 724 | |
---|
[6c44098] | 725 | factors= factorRecombination (uniFactors, A, MODl, degs, 1, |
---|
[1ade96] | 726 | uniFactors.length()/2, b); |
---|
| 727 | |
---|
[b4af1b] | 728 | On (SW_RATIONAL); |
---|
[6c44098] | 729 | |
---|
| 730 | if (earlySuccess) |
---|
| 731 | factors= Union (earlyFactors, factors); |
---|
| 732 | else if (!earlySuccess && degs.getLength() == 1) |
---|
| 733 | factors= earlyFactors; |
---|
| 734 | |
---|
| 735 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
| 736 | i.getItem()= i.getItem() (y - evaluation, y); |
---|
| 737 | |
---|
| 738 | appendSwapDecompress (factors, conv (contentAxFactors), |
---|
| 739 | conv (contentAyFactors), swap, swap2, N); |
---|
| 740 | if (isOn (SW_RATIONAL)) |
---|
| 741 | normalize (factors); |
---|
| 742 | |
---|
| 743 | return factors; |
---|
| 744 | } |
---|
[615ca8] | 745 | |
---|
| 746 | #endif |
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