[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 | * @internal @version \$Id$ |
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| 11 | * |
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| 12 | **/ |
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| 13 | /*****************************************************************************/ |
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| 14 | |
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[e4fe2b] | 15 | #include "config.h" |
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[6c44098] | 16 | |
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| 17 | #include "assert.h" |
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| 18 | #include "debug.h" |
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| 19 | #include "timing.h" |
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| 20 | |
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[d990001] | 21 | #include "cf_algorithm.h" |
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[6c44098] | 22 | #include "facFqBivar.h" |
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| 23 | #include "facBivar.h" |
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| 24 | |
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[615ca8] | 25 | #ifdef HAVE_NTL |
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[6c44098] | 26 | TIMING_DEFINE_PRINT(fac_uni_factorizer) |
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| 27 | TIMING_DEFINE_PRINT(fac_hensel_lift) |
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| 28 | TIMING_DEFINE_PRINT(fac_factor_recombination) |
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| 29 | |
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| 30 | CFList conv (const CFFList& L) |
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| 31 | { |
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| 32 | CFList result; |
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| 33 | for (CFFListIterator i= L; i.hasItem(); i++) |
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| 34 | result.append (i.getItem().factor()); |
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| 35 | return result; |
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| 36 | } |
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| 37 | |
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| 38 | bool testPoint (const CanonicalForm& F, CanonicalForm& G, int i) |
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| 39 | { |
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| 40 | G= F (i, 2); |
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| 41 | if (G.inCoeffDomain() || degree (F, 1) > degree (G, 1)) |
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| 42 | return false; |
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| 43 | |
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| 44 | if (degree (gcd (deriv (G, G.mvar()), G)) > 0) |
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| 45 | return false; |
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| 46 | return true; |
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| 47 | } |
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| 48 | |
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| 49 | CanonicalForm evalPoint (const CanonicalForm& F, int& i) |
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| 50 | { |
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| 51 | Variable x= Variable (1); |
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| 52 | Variable y= Variable (2); |
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| 53 | CanonicalForm result; |
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| 54 | |
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| 55 | int k; |
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| 56 | |
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| 57 | if (i == 0) |
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| 58 | { |
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| 59 | if (testPoint (F, result, i)) |
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| 60 | return result; |
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| 61 | } |
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| 62 | do |
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| 63 | { |
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| 64 | if (i > 0) |
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| 65 | k= 1; |
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| 66 | else |
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| 67 | k= 2; |
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| 68 | while (k < 3) |
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| 69 | { |
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| 70 | if (k == 1) |
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| 71 | { |
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| 72 | if (testPoint (F, result, i)) |
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| 73 | return result; |
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| 74 | } |
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| 75 | else |
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| 76 | { |
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| 77 | if (testPoint (F, result, -i)) |
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| 78 | return result; |
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| 79 | } |
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| 80 | k++; |
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| 81 | } |
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| 82 | i++; |
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| 83 | } while (1); |
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| 84 | } |
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| 85 | |
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| 86 | CFList biFactorize (const CanonicalForm& F, const Variable& v) |
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| 87 | { |
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| 88 | if (F.inCoeffDomain()) |
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| 89 | return CFList(F); |
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| 90 | |
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| 91 | bool extension= (v.level() != 1); |
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| 92 | CanonicalForm A; |
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| 93 | CanonicalForm multiplier= 1; |
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| 94 | if (isOn (SW_RATIONAL)) |
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| 95 | A= F*bCommonDen (F); |
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| 96 | else |
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| 97 | A= F; |
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| 98 | |
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| 99 | if (A.isUnivariate()) |
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| 100 | { |
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| 101 | CFFList buf; |
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| 102 | if (extension) |
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| 103 | buf= factorize (A, v); |
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| 104 | else |
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| 105 | buf= factorize (A, true); |
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| 106 | CFList result= conv (buf); |
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| 107 | if (result.getFirst().inCoeffDomain()) |
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| 108 | result.removeFirst(); |
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| 109 | return result; |
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| 110 | } |
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| 111 | |
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| 112 | CFMap N; |
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| 113 | A= compress (A, N); |
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| 114 | Variable y= A.mvar(); |
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| 115 | |
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| 116 | if (y.level() > 2) return CFList (F); |
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| 117 | Variable x= Variable (1); |
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| 118 | |
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| 119 | CanonicalForm contentAx= content (A, x); |
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| 120 | CanonicalForm contentAy= content (A); |
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| 121 | |
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| 122 | A= A/(contentAx*contentAy); |
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| 123 | CFFList contentAxFactors, contentAyFactors; |
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| 124 | |
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| 125 | if (extension) |
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| 126 | { |
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| 127 | if (!contentAx.inCoeffDomain()) |
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| 128 | { |
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| 129 | contentAxFactors= factorize (contentAx, v); |
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| 130 | if (contentAxFactors.getFirst().factor().inCoeffDomain()) |
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| 131 | contentAxFactors.removeFirst(); |
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| 132 | } |
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| 133 | if (!contentAy.inCoeffDomain()) |
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| 134 | { |
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| 135 | contentAyFactors= factorize (contentAy, v); |
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| 136 | if (contentAyFactors.getFirst().factor().inCoeffDomain()) |
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| 137 | contentAyFactors.removeFirst(); |
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| 138 | } |
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| 139 | } |
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| 140 | else |
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| 141 | { |
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| 142 | if (!contentAx.inCoeffDomain()) |
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| 143 | { |
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| 144 | contentAxFactors= factorize (contentAx, true); |
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| 145 | if (contentAxFactors.getFirst().factor().inCoeffDomain()) |
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| 146 | contentAxFactors.removeFirst(); |
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| 147 | } |
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| 148 | if (!contentAy.inCoeffDomain()) |
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| 149 | { |
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| 150 | contentAyFactors= factorize (contentAy, true); |
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| 151 | if (contentAyFactors.getFirst().factor().inCoeffDomain()) |
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| 152 | contentAyFactors.removeFirst(); |
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| 153 | } |
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| 154 | } |
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| 155 | |
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| 156 | //check trivial case |
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| 157 | if (degree (A) == 1 || degree (A, 1) == 1) |
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| 158 | { |
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| 159 | CFList factors; |
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| 160 | factors.append (A); |
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| 161 | |
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| 162 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 163 | conv (contentAyFactors), false, false, N); |
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| 164 | |
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| 165 | normalize (factors); |
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| 166 | return factors; |
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| 167 | } |
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| 168 | |
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| 169 | //trivial case |
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| 170 | CFList factors; |
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| 171 | if (A.inCoeffDomain()) |
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| 172 | { |
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| 173 | append (factors, conv (contentAxFactors)); |
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| 174 | append (factors, conv (contentAyFactors)); |
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| 175 | decompress (factors, N); |
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| 176 | return factors; |
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| 177 | } |
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| 178 | else if (A.isUnivariate()) |
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| 179 | { |
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| 180 | if (extension) |
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| 181 | factors= conv (factorize (A, v)); |
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| 182 | else |
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| 183 | factors= conv (factorize (A, true)); |
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| 184 | append (factors, conv (contentAxFactors)); |
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| 185 | append (factors, conv (contentAyFactors)); |
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| 186 | decompress (factors, N); |
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| 187 | return factors; |
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| 188 | } |
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| 189 | |
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| 190 | bool swap= false; |
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| 191 | if (degree (A) > degree (A, x)) |
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| 192 | { |
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| 193 | A= swapvar (A, y, x); |
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| 194 | swap= true; |
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| 195 | } |
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| 196 | |
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| 197 | CanonicalForm Aeval, bufAeval, buf; |
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| 198 | CFList uniFactors, list, bufUniFactors; |
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| 199 | DegreePattern degs; |
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| 200 | DegreePattern bufDegs; |
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| 201 | |
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| 202 | CanonicalForm Aeval2, bufAeval2; |
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| 203 | CFList bufUniFactors2, list2, uniFactors2; |
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| 204 | DegreePattern degs2; |
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| 205 | DegreePattern bufDegs2; |
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| 206 | bool swap2= false; |
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| 207 | |
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| 208 | // several univariate factorizations to obtain more information about the |
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| 209 | // degree pattern therefore usually less combinations have to be tried during |
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| 210 | // the recombination process |
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| 211 | int factorNums= 2; |
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| 212 | int subCheck1= substituteCheck (A, x); |
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| 213 | int subCheck2= substituteCheck (A, y); |
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| 214 | buf= swapvar (A,x,y); |
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| 215 | int evaluation, evaluation2, bufEvaluation= 0, bufEvaluation2= 0; |
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| 216 | for (int i= 0; i < factorNums; i++) |
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| 217 | { |
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| 218 | bufAeval= A; |
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| 219 | bufAeval= evalPoint (A, bufEvaluation); |
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| 220 | |
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| 221 | bufAeval2= buf; |
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| 222 | bufAeval2= evalPoint (buf, bufEvaluation2); |
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| 223 | |
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| 224 | |
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| 225 | // univariate factorization |
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| 226 | TIMING_START (fac_uni_factorizer); |
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| 227 | |
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| 228 | if (extension) |
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| 229 | bufUniFactors= conv (factorize (bufAeval, v)); |
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| 230 | else |
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| 231 | bufUniFactors= conv (factorize (bufAeval, true)); |
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| 232 | TIMING_END_AND_PRINT (fac_uni_factorizer, |
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| 233 | "time for univariate factorization: "); |
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| 234 | DEBOUTLN (cerr, "Lc (bufAeval)*prod (bufUniFactors)== bufAeval " << |
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| 235 | prod (bufUniFactors)*Lc (bufAeval) == bufAeval); |
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| 236 | |
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| 237 | TIMING_START (fac_uni_factorizer); |
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| 238 | if (extension) |
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| 239 | bufUniFactors2= conv (factorize (bufAeval2, v)); |
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| 240 | else |
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| 241 | bufUniFactors2= conv (factorize (bufAeval2, true)); |
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| 242 | TIMING_END_AND_PRINT (fac_uni_factorizer, |
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| 243 | "time for univariate factorization in y: "); |
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| 244 | DEBOUTLN (cerr, "Lc (Aeval2)*prod (uniFactors2)== Aeval2 " << |
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| 245 | prod (bufUniFactors2)*Lc (bufAeval2) == bufAeval2); |
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| 246 | |
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| 247 | if (bufUniFactors.getFirst().inCoeffDomain()) |
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| 248 | bufUniFactors.removeFirst(); |
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| 249 | if (bufUniFactors2.getFirst().inCoeffDomain()) |
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| 250 | bufUniFactors2.removeFirst(); |
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| 251 | if (bufUniFactors.length() == 1 || bufUniFactors2.length() == 1) |
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| 252 | { |
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| 253 | factors.append (A); |
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| 254 | |
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| 255 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 256 | conv (contentAyFactors), swap, swap2, N); |
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| 257 | |
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| 258 | if (isOn (SW_RATIONAL)) |
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| 259 | normalize (factors); |
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| 260 | return factors; |
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| 261 | } |
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| 262 | |
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| 263 | if (i == 0) |
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| 264 | { |
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| 265 | if (subCheck1 > 0) |
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| 266 | { |
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| 267 | int subCheck= substituteCheck (bufUniFactors); |
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| 268 | |
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| 269 | if (subCheck > 1 && (subCheck1%subCheck == 0)) |
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| 270 | { |
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| 271 | CanonicalForm bufA= A; |
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| 272 | subst (bufA, bufA, subCheck, x); |
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| 273 | factors= biFactorize (bufA, v); |
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| 274 | reverseSubst (factors, subCheck, x); |
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| 275 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 276 | conv (contentAyFactors), swap, swap2, N); |
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| 277 | if (isOn (SW_RATIONAL)) |
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| 278 | normalize (factors); |
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| 279 | return factors; |
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| 280 | } |
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| 281 | } |
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| 282 | |
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| 283 | if (subCheck2 > 0) |
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| 284 | { |
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| 285 | int subCheck= substituteCheck (bufUniFactors2); |
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| 286 | |
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| 287 | if (subCheck > 1 && (subCheck2%subCheck == 0)) |
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| 288 | { |
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| 289 | CanonicalForm bufA= A; |
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| 290 | subst (bufA, bufA, subCheck, y); |
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| 291 | factors= biFactorize (bufA, v); |
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| 292 | reverseSubst (factors, subCheck, y); |
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| 293 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 294 | conv (contentAyFactors), swap, swap2, N); |
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| 295 | if (isOn (SW_RATIONAL)) |
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| 296 | normalize (factors); |
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| 297 | return factors; |
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| 298 | } |
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| 299 | } |
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| 300 | } |
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| 301 | |
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| 302 | // degree analysis |
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| 303 | bufDegs = DegreePattern (bufUniFactors); |
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| 304 | bufDegs2= DegreePattern (bufUniFactors2); |
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| 305 | |
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| 306 | if (i == 0) |
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| 307 | { |
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| 308 | Aeval= bufAeval; |
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| 309 | evaluation= bufEvaluation; |
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| 310 | uniFactors= bufUniFactors; |
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| 311 | degs= bufDegs; |
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| 312 | Aeval2= bufAeval2; |
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| 313 | evaluation2= bufEvaluation2; |
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| 314 | uniFactors2= bufUniFactors2; |
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| 315 | degs2= bufDegs2; |
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| 316 | } |
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| 317 | else |
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| 318 | { |
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| 319 | degs.intersect (bufDegs); |
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| 320 | degs2.intersect (bufDegs2); |
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| 321 | if (bufUniFactors2.length() < uniFactors2.length()) |
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| 322 | { |
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| 323 | uniFactors2= bufUniFactors2; |
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| 324 | Aeval2= bufAeval2; |
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| 325 | evaluation2= bufEvaluation2; |
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| 326 | } |
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| 327 | if (bufUniFactors.length() < uniFactors.length()) |
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| 328 | { |
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| 329 | if (evaluation != 0) |
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| 330 | { |
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| 331 | uniFactors= bufUniFactors; |
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| 332 | Aeval= bufAeval; |
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| 333 | evaluation= bufEvaluation; |
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| 334 | } |
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| 335 | } |
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| 336 | } |
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| 337 | bufEvaluation++; |
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| 338 | bufEvaluation2++; |
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| 339 | } |
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| 340 | |
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| 341 | if (evaluation != 0 && (uniFactors.length() > uniFactors2.length() || |
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| 342 | (uniFactors.length() == uniFactors2.length() |
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| 343 | && degs.getLength() > degs2.getLength()))) |
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| 344 | { |
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| 345 | degs= degs2; |
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| 346 | uniFactors= uniFactors2; |
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| 347 | evaluation= evaluation2; |
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| 348 | Aeval= Aeval2; |
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| 349 | A= buf; |
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| 350 | swap2= true; |
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| 351 | } |
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| 352 | |
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| 353 | |
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| 354 | if (degs.getLength() == 1) // A is irreducible |
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| 355 | { |
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| 356 | factors.append (A); |
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| 357 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 358 | conv (contentAyFactors), swap, swap2, N); |
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| 359 | if (isOn (SW_RATIONAL)) |
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| 360 | normalize (factors); |
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| 361 | return factors; |
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| 362 | } |
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| 363 | |
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| 364 | A= A (y + evaluation, y); |
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| 365 | |
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[1a3011e] | 366 | int liftBound= degree (A, y) + 1; |
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[6c44098] | 367 | |
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| 368 | ExtensionInfo dummy= ExtensionInfo (false); |
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| 369 | bool earlySuccess= false; |
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| 370 | CFList earlyFactors; |
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| 371 | TIMING_START (fac_hensel_lift); |
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| 372 | uniFactors= henselLiftAndEarly |
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| 373 | (A, earlySuccess, earlyFactors, degs, liftBound, |
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| 374 | uniFactors, dummy, evaluation); |
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| 375 | TIMING_END_AND_PRINT (fac_hensel_lift, "time for hensel lifting: "); |
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| 376 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
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| 377 | |
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| 378 | CanonicalForm MODl= power (y, liftBound); |
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| 379 | |
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| 380 | factors= factorRecombination (uniFactors, A, MODl, degs, 1, |
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| 381 | uniFactors.length()/2); |
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| 382 | |
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| 383 | if (earlySuccess) |
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| 384 | factors= Union (earlyFactors, factors); |
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| 385 | else if (!earlySuccess && degs.getLength() == 1) |
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| 386 | factors= earlyFactors; |
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| 387 | |
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| 388 | for (CFListIterator i= factors; i.hasItem(); i++) |
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| 389 | i.getItem()= i.getItem() (y - evaluation, y); |
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| 390 | |
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| 391 | appendSwapDecompress (factors, conv (contentAxFactors), |
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| 392 | conv (contentAyFactors), swap, swap2, N); |
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| 393 | if (isOn (SW_RATIONAL)) |
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| 394 | normalize (factors); |
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| 395 | |
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| 396 | return factors; |
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| 397 | } |
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[615ca8] | 398 | |
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| 399 | #endif |
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