[dea3d2] | 1 | /*****************************************************************************\ |
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| 2 | * Computer Algebra System SINGULAR |
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| 3 | \*****************************************************************************/ |
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[058c1d] | 4 | /** @file facAbsFact.cc |
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[dea3d2] | 5 | * |
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| 6 | * @author Martin Lee |
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| 7 | * |
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| 8 | **/ |
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| 9 | /*****************************************************************************/ |
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| 10 | |
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[712a5a] | 11 | #include "config.h" |
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| 12 | |
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[17a710] | 13 | #include "timing.h" |
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| 14 | #include "debug.h" |
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| 15 | |
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[5275c0] | 16 | #include "facAbsFact.h" |
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[17a710] | 17 | #include "facBivar.h" |
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| 18 | #include "facFqBivar.h" |
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[dea3d2] | 19 | #include "cf_reval.h" |
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| 20 | #include "cf_primes.h" |
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| 21 | #include "cf_algorithm.h" |
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| 22 | #ifdef HAVE_FLINT |
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| 23 | #include "FLINTconvert.h" |
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| 24 | #include <flint/fmpz_poly_factor.h> |
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| 25 | #endif |
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| 26 | #ifdef HAVE_NTL |
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| 27 | #include "NTLconvert.h" |
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| 28 | #include <NTL/LLL.h> |
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| 29 | #endif |
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| 30 | |
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[160ec6] | 31 | #ifdef HAVE_NTL |
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[dea3d2] | 32 | |
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[17a710] | 33 | TIMING_DEFINE_PRINT(fac_Qa_factorize) |
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| 34 | TIMING_DEFINE_PRINT(fac_evalpoint) |
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| 35 | |
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[160ec6] | 36 | //TODO optimize choice of p -> choose p as large as possible (better than small p since factorization mod p does not require field extension, also less lifting) |
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[17a710] | 37 | int choosePoint (const CanonicalForm& F, int tdegF, CFArray& eval, bool rec) |
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[dea3d2] | 38 | { |
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| 39 | REvaluation E1 (1, 1, IntRandom (25)); |
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| 40 | REvaluation E2 (2, 2, IntRandom (25)); |
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[17a710] | 41 | if (rec) |
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| 42 | { |
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| 43 | E1.nextpoint(); |
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| 44 | E2.nextpoint(); |
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| 45 | } |
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| 46 | CanonicalForm f, f1, f2, Fp; |
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| 47 | int i, p; |
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[dea3d2] | 48 | eval=CFArray (2); |
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| 49 | while (1) |
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| 50 | { |
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[17a710] | 51 | f1= E1(F); |
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| 52 | if (!f1.isZero() && factorize (f1).length() == 2) |
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[dea3d2] | 53 | { |
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| 54 | Off (SW_RATIONAL); |
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[17a710] | 55 | f= E2(f1); |
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| 56 | f2= E2 (F); |
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[809d63] | 57 | if ((!f.isZero()) && (abs(f)>cf_getSmallPrime (cf_getNumSmallPrimes()-1))) |
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[dea3d2] | 58 | { |
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[17a710] | 59 | for (i= cf_getNumPrimes()-1; i >= 0; i--) |
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[dea3d2] | 60 | { |
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| 61 | if (f % CanonicalForm (cf_getPrime (i)) == 0) |
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| 62 | { |
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[17a710] | 63 | p= cf_getPrime(i); |
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| 64 | Fp= mod (F,p); |
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[809d63] | 65 | if (totaldegree (Fp) == tdegF && |
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| 66 | degree (mod (f2,p), 1) == degree (F,1) && |
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| 67 | degree (mod (f1, p),2) == degree (F,2)) |
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[dea3d2] | 68 | { |
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| 69 | eval[0]= E1[1]; |
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| 70 | eval[1]= E2[2]; |
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[17a710] | 71 | return p; |
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[dea3d2] | 72 | } |
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| 73 | } |
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| 74 | } |
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| 75 | } |
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| 76 | else if (!f.isZero()) |
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| 77 | { |
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[17a710] | 78 | for (i= cf_getNumSmallPrimes()-1; i >= 0; i--) |
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[dea3d2] | 79 | { |
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| 80 | if (f % CanonicalForm (cf_getSmallPrime (i)) == 0) |
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| 81 | { |
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[17a710] | 82 | p= cf_getSmallPrime (i); |
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| 83 | Fp= mod (F,p); |
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[809d63] | 84 | if (totaldegree (Fp) == tdegF && |
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| 85 | degree (mod (f2, p),1) == degree (F,1) && |
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| 86 | degree (mod (f1,p),2) == degree (F,2)) |
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[dea3d2] | 87 | { |
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| 88 | eval[0]= E1[1]; |
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| 89 | eval[1]= E2[2]; |
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[17a710] | 90 | return p; |
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[dea3d2] | 91 | } |
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| 92 | } |
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| 93 | } |
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| 94 | } |
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| 95 | E2.nextpoint(); |
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| 96 | On (SW_RATIONAL); |
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| 97 | } |
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| 98 | E1.nextpoint(); |
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| 99 | } |
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| 100 | return 0; |
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| 101 | } |
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| 102 | |
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[809d63] | 103 | //G is assumed to be bivariate, irreducible over Q, primitive wrt x and y, compressed |
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[efd410] | 104 | CFAFList absFactorizeMain (const CanonicalForm& G) |
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[dea3d2] | 105 | { |
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| 106 | CanonicalForm F= bCommonDen (G)*G; |
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| 107 | Off (SW_RATIONAL); |
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| 108 | F /= icontent (F); |
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| 109 | On (SW_RATIONAL); |
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| 110 | CFArray eval; |
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| 111 | int minTdeg, tdegF= totaldegree (F); |
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| 112 | CanonicalForm Fp, smallestFactor; |
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| 113 | int p; |
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[17a710] | 114 | CFFList factors; |
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| 115 | Variable alpha; |
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| 116 | bool rec= false; |
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| 117 | Variable x= Variable (1); |
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| 118 | Variable y= Variable (2); |
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[809d63] | 119 | CanonicalForm bufF= F; |
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| 120 | CFFListIterator iter; |
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[17a710] | 121 | differentevalpoint: |
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[dea3d2] | 122 | while (1) |
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| 123 | { |
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[17a710] | 124 | TIMING_START (fac_evalpoint); |
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| 125 | p= choosePoint (F, tdegF, eval, rec); |
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| 126 | TIMING_END_AND_PRINT (fac_evalpoint, "time to find eval point: "); |
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[dea3d2] | 127 | |
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| 128 | setCharacteristic (p); |
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| 129 | Fp=F.mapinto(); |
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[17a710] | 130 | factors= factorize (Fp); |
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| 131 | |
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| 132 | if (factors.getFirst().factor().inCoeffDomain()) |
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| 133 | factors.removeFirst(); |
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[809d63] | 134 | |
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[17a710] | 135 | if (factors.length() == 1 && factors.getFirst().exp() == 1) |
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| 136 | { |
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[809d63] | 137 | if (absIrredTest (Fp)) |
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[17a710] | 138 | { |
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| 139 | setCharacteristic(0); |
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[386b3d] | 140 | return CFAFList (CFAFactor (G, 1, 1)); |
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[17a710] | 141 | } |
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| 142 | else |
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| 143 | { |
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| 144 | setCharacteristic (0); |
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| 145 | if (modularIrredTestWithShift (F)) |
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| 146 | { |
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[386b3d] | 147 | return CFAFList (CFAFactor (G, 1, 1)); |
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[17a710] | 148 | } |
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| 149 | rec= true; |
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| 150 | continue; |
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| 151 | } |
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| 152 | } |
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[809d63] | 153 | iter= factors; |
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[dea3d2] | 154 | smallestFactor= iter.getItem().factor(); |
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[17a710] | 155 | while (smallestFactor.isUnivariate() && iter.hasItem()) |
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| 156 | { |
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| 157 | iter++; |
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| 158 | if (!iter.hasItem()) |
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| 159 | break; |
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| 160 | smallestFactor= iter.getItem().factor(); |
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| 161 | } |
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[809d63] | 162 | |
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[dea3d2] | 163 | minTdeg= totaldegree (smallestFactor); |
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[17a710] | 164 | if (iter.hasItem()) |
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| 165 | iter++; |
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[dea3d2] | 166 | for (; iter.hasItem(); iter++) |
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| 167 | { |
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[809d63] | 168 | if (!iter.getItem().factor().isUnivariate() && |
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| 169 | (totaldegree (iter.getItem().factor()) < minTdeg)) |
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[dea3d2] | 170 | { |
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| 171 | smallestFactor= iter.getItem().factor(); |
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| 172 | minTdeg= totaldegree (smallestFactor); |
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| 173 | } |
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| 174 | } |
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| 175 | if (tdegF % minTdeg == 0) |
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| 176 | break; |
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[17a710] | 177 | setCharacteristic(0); |
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| 178 | rec=true; |
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[dea3d2] | 179 | } |
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| 180 | CanonicalForm Gp= Fp/smallestFactor; |
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[17a710] | 181 | Gp= Gp /Lc (Gp); |
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| 182 | |
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| 183 | CanonicalForm Gpy= Gp (eval[0].mapinto(), 1); |
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| 184 | CanonicalForm smallestFactorEvaly= smallestFactor (eval[0].mapinto(),1); |
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| 185 | CanonicalForm Gpx= Gp (eval[1].mapinto(), 2); |
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| 186 | CanonicalForm smallestFactorEvalx= smallestFactor (eval[1].mapinto(),2); |
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| 187 | |
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[809d63] | 188 | bool xValid= !(Gpx.inCoeffDomain() || smallestFactorEvalx.inCoeffDomain() || |
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| 189 | !gcd (Gpx, smallestFactorEvalx).inCoeffDomain()); |
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| 190 | bool yValid= !(Gpy.inCoeffDomain() || smallestFactorEvaly.inCoeffDomain() || |
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| 191 | !gcd (Gpy, smallestFactorEvaly).inCoeffDomain()); |
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[17a710] | 192 | if (!xValid && !yValid) |
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| 193 | { |
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| 194 | rec= true; |
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| 195 | setCharacteristic (0); |
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| 196 | goto differentevalpoint; |
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| 197 | } |
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| 198 | |
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[dea3d2] | 199 | setCharacteristic (0); |
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| 200 | |
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[17a710] | 201 | CanonicalForm mipo; |
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| 202 | |
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| 203 | int loop, i; |
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| 204 | if (xValid && yValid) |
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| 205 | { |
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| 206 | loop= 3; |
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| 207 | i=1; |
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| 208 | } |
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| 209 | else if (xValid) |
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| 210 | { |
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| 211 | loop= 3; |
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| 212 | i=2; |
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| 213 | } |
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| 214 | else |
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| 215 | { |
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| 216 | loop= 2; |
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| 217 | i=1; |
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| 218 | } |
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| 219 | |
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| 220 | CFArray mipos= CFArray (loop-i); |
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| 221 | for (; i < loop; i++) |
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| 222 | { |
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| 223 | CanonicalForm Fi= F(eval[i-1],i); |
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| 224 | |
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| 225 | int s= tdegF/minTdeg + 1; |
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| 226 | CanonicalForm bound= power (maxNorm (Fi), 2*(s-1)); |
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| 227 | bound *= power (CanonicalForm (s),s-1); |
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| 228 | bound *= power (CanonicalForm (2), ((s-1)*(s-1))/2); //possible int overflow |
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| 229 | |
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| 230 | CanonicalForm B = p; |
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| 231 | long k = 1L; |
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| 232 | while ( B < bound ) { |
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| 233 | B *= p; |
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| 234 | k++; |
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| 235 | } |
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| 236 | |
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| 237 | //TODO take floor (log2(k)) |
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| 238 | k= k+1; |
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[e4e36c] | 239 | #ifdef HAVE_FLINT |
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[17a710] | 240 | fmpz_poly_t FLINTFi; |
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| 241 | convertFacCF2Fmpz_poly_t (FLINTFi, Fi); |
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| 242 | setCharacteristic (p); |
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| 243 | nmod_poly_t FLINTFpi, FLINTGpi; |
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| 244 | if (i == 2) |
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| 245 | { |
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[809d63] | 246 | convertFacCF2nmod_poly_t (FLINTFpi, |
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| 247 | smallestFactorEvalx/lc (smallestFactorEvalx)); |
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[17a710] | 248 | convertFacCF2nmod_poly_t (FLINTGpi, Gpx/lc (Gpx)); |
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| 249 | } |
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| 250 | else |
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| 251 | { |
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[809d63] | 252 | convertFacCF2nmod_poly_t (FLINTFpi, |
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| 253 | smallestFactorEvaly/lc (smallestFactorEvaly)); |
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[17a710] | 254 | convertFacCF2nmod_poly_t (FLINTGpi, Gpy/lc (Gpy)); |
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| 255 | } |
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| 256 | nmod_poly_factor_t nmodFactors; |
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| 257 | nmod_poly_factor_init (nmodFactors); |
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| 258 | nmod_poly_factor_insert (nmodFactors, FLINTFpi, 1L); |
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| 259 | nmod_poly_factor_insert (nmodFactors, FLINTGpi, 1L); |
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| 260 | |
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| 261 | long * link= new long [2]; |
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| 262 | fmpz_poly_t *v= new fmpz_poly_t[2]; |
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| 263 | fmpz_poly_t *w= new fmpz_poly_t[2]; |
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| 264 | fmpz_poly_init(v[0]); |
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| 265 | fmpz_poly_init(v[1]); |
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| 266 | fmpz_poly_init(w[0]); |
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| 267 | fmpz_poly_init(w[1]); |
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| 268 | |
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| 269 | fmpz_poly_factor_t liftedFactors; |
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| 270 | fmpz_poly_factor_init (liftedFactors); |
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[809d63] | 271 | _fmpz_poly_hensel_start_lift (liftedFactors, link, v, w, FLINTFi, |
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| 272 | nmodFactors, k); |
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[17a710] | 273 | |
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| 274 | nmod_poly_factor_clear (nmodFactors); |
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| 275 | nmod_poly_clear (FLINTFpi); |
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| 276 | nmod_poly_clear (FLINTGpi); |
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| 277 | |
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| 278 | setCharacteristic(0); |
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[809d63] | 279 | CanonicalForm liftedSmallestFactor= |
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| 280 | convertFmpz_poly_t2FacCF ((fmpz_poly_t &)liftedFactors->p[0],Variable (1)); |
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[17a710] | 281 | |
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[809d63] | 282 | CanonicalForm otherFactor= |
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| 283 | convertFmpz_poly_t2FacCF ((fmpz_poly_t &)liftedFactors->p[1],Variable (1)); |
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[e4e36c] | 284 | modpk pk= modpk (p, k); |
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| 285 | #else |
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| 286 | modpk pk= modpk (p, k); |
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| 287 | ZZX NTLFi=convertFacCF2NTLZZX (pk (Fi*pk.inverse (lc(Fi)))); |
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| 288 | setCharacteristic (p); |
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| 289 | |
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| 290 | if (fac_NTL_char != p) |
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| 291 | { |
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| 292 | fac_NTL_char= p; |
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| 293 | zz_p::init (p); |
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| 294 | } |
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| 295 | zz_pX NTLFpi, NTLGpi; |
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| 296 | if (i == 2) |
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| 297 | { |
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| 298 | NTLFpi= convertFacCF2NTLzzpX (smallestFactorEvalx/lc (smallestFactorEvalx)); |
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| 299 | NTLGpi= convertFacCF2NTLzzpX (Gpx/lc (Gpx)); |
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| 300 | } |
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| 301 | else |
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| 302 | { |
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| 303 | NTLFpi= convertFacCF2NTLzzpX (smallestFactorEvaly/lc (smallestFactorEvaly)); |
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| 304 | NTLGpi= convertFacCF2NTLzzpX (Gpy/lc (Gpy)); |
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| 305 | } |
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| 306 | vec_zz_pX modFactors; |
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| 307 | modFactors.SetLength(2); |
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| 308 | modFactors[0]= NTLFpi; |
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| 309 | modFactors[1]= NTLGpi; |
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| 310 | vec_ZZX liftedFactors; |
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| 311 | MultiLift (liftedFactors, modFactors, NTLFi, (long) k); |
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| 312 | setCharacteristic(0); |
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| 313 | CanonicalForm liftedSmallestFactor= |
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| 314 | convertNTLZZX2CF (liftedFactors[0],Variable (1)); |
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| 315 | |
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| 316 | CanonicalForm otherFactor= |
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| 317 | convertNTLZZX2CF (liftedFactors[1], Variable (1)); |
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| 318 | #endif |
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[17a710] | 319 | |
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| 320 | Off (SW_SYMMETRIC_FF); |
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| 321 | liftedSmallestFactor= pk (liftedSmallestFactor); |
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| 322 | if (i == 2) |
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| 323 | liftedSmallestFactor= liftedSmallestFactor (eval[0],1); |
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| 324 | else |
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| 325 | liftedSmallestFactor= liftedSmallestFactor (eval[1],1); |
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| 326 | |
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| 327 | On (SW_SYMMETRIC_FF); |
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| 328 | CFMatrix M= CFMatrix (s, s); |
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| 329 | M(s,s)= power (CanonicalForm (p), k); |
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| 330 | for (int j= 1; j < s; j++) |
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| 331 | { |
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| 332 | M (j,j)= 1; |
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| 333 | M (j+1,j)= -liftedSmallestFactor; |
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| 334 | } |
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| 335 | |
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| 336 | mat_ZZ NTLM= *convertFacCFMatrix2NTLmat_ZZ (M); |
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| 337 | |
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| 338 | ZZ det; |
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| 339 | |
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| 340 | transpose (NTLM, NTLM); |
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| 341 | (void) LLL (det, NTLM, 1L, 1L); //use floating point LLL ? |
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| 342 | transpose (NTLM, NTLM); |
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| 343 | M= *convertNTLmat_ZZ2FacCFMatrix (NTLM); |
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| 344 | |
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| 345 | mipo= 0; |
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| 346 | for (int j= 1; j <= s; j++) |
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| 347 | mipo += M (j,1)*power (x,s-j); |
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| 348 | |
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| 349 | CFFList mipoFactors= factorize (mipo); |
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| 350 | mipoFactors.removeFirst(); |
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| 351 | |
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[e4e36c] | 352 | #ifdef HAVE_FLINT |
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[17a710] | 353 | fmpz_poly_clear (v[0]); |
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| 354 | fmpz_poly_clear (v[1]); |
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| 355 | fmpz_poly_clear (w[0]); |
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| 356 | fmpz_poly_clear (w[1]); |
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| 357 | delete [] v; |
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| 358 | delete [] w; |
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| 359 | delete [] link; |
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| 360 | fmpz_poly_factor_clear (liftedFactors); |
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[e4e36c] | 361 | #endif |
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[17a710] | 362 | |
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| 363 | if (mipoFactors.length() > 1 || |
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| 364 | (mipoFactors.length() == 1 && mipoFactors.getFirst().exp() > 1)) |
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| 365 | { |
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| 366 | if (i+1 >= loop && ((loop-i == 1) || (loop-i==2 && mipos[0].isZero()))) |
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| 367 | { |
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| 368 | rec=true; |
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| 369 | goto differentevalpoint; |
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| 370 | } |
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| 371 | } |
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| 372 | else |
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| 373 | mipos[loop-i-1]= mipo; |
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| 374 | } |
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| 375 | |
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| 376 | On (SW_RATIONAL); |
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| 377 | if (xValid && yValid && !mipos[0].isZero() && !mipos[1].isZero()) |
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| 378 | { |
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| 379 | if (maxNorm (mipos[0]) < maxNorm (mipos[1])) |
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| 380 | alpha= rootOf (mipos[0]); |
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| 381 | else |
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| 382 | alpha= rootOf (mipos[1]); |
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| 383 | } |
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[809d63] | 384 | else if (xValid && yValid) |
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[17a710] | 385 | { |
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[809d63] | 386 | if (mipos[0].isZero()) |
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| 387 | alpha= rootOf (mipos[1]); |
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| 388 | else |
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| 389 | alpha= rootOf (mipos[0]); |
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[17a710] | 390 | } |
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[809d63] | 391 | else |
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| 392 | alpha= rootOf (mipo); |
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[17a710] | 393 | |
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| 394 | CanonicalForm F1; |
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| 395 | CFFList QaF1Factors; |
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| 396 | int wrongMipo= 0; |
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| 397 | if (xValid && yValid) |
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| 398 | { |
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| 399 | if (degree (F,1) > minTdeg) |
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| 400 | F1= F (eval[1], 2); |
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| 401 | else |
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| 402 | F1= F (eval[0], 1); |
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| 403 | } |
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| 404 | else if (xValid) |
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| 405 | F1= F (eval[1], 2); |
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| 406 | else |
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| 407 | F1= F (eval[0], 1); |
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| 408 | |
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[809d63] | 409 | bool swap= false; |
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| 410 | if (F1.level() == 2) |
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| 411 | { |
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| 412 | swap= true; |
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| 413 | F1=swapvar (F1, x, y); |
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| 414 | F= swapvar (F, x, y); |
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| 415 | } |
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| 416 | |
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[17a710] | 417 | QaF1Factors= factorize (F1, alpha); |
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| 418 | if (QaF1Factors.getFirst().factor().inCoeffDomain()) |
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| 419 | QaF1Factors.removeFirst(); |
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[809d63] | 420 | for (iter= QaF1Factors; iter.hasItem(); iter++) |
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[17a710] | 421 | { |
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| 422 | if (degree (iter.getItem().factor()) > minTdeg) |
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| 423 | wrongMipo++; |
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| 424 | } |
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| 425 | |
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| 426 | if (wrongMipo == QaF1Factors.length()) |
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| 427 | { |
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[809d63] | 428 | if (xValid && yValid && !mipos[0].isZero() && !mipos[1].isZero()) |
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[17a710] | 429 | { |
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[809d63] | 430 | if (maxNorm (mipos[0]) < maxNorm (mipos[1])) //try the other minpoly |
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[17a710] | 431 | alpha= rootOf (mipos[1]); |
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| 432 | else |
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| 433 | alpha= rootOf (mipos[0]); |
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| 434 | } |
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[809d63] | 435 | else |
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| 436 | { |
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| 437 | rec= true; |
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| 438 | F= bufF; |
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| 439 | goto differentevalpoint; |
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| 440 | } |
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[17a710] | 441 | |
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| 442 | wrongMipo= 0; |
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| 443 | QaF1Factors= factorize (F1, alpha); |
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| 444 | if (QaF1Factors.getFirst().factor().inCoeffDomain()) |
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| 445 | QaF1Factors.removeFirst(); |
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[809d63] | 446 | for (iter= QaF1Factors; iter.hasItem(); iter++) |
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[17a710] | 447 | { |
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| 448 | if (degree (iter.getItem().factor()) > minTdeg) |
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| 449 | wrongMipo++; |
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| 450 | } |
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| 451 | if (wrongMipo == QaF1Factors.length()) |
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| 452 | { |
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| 453 | rec= true; |
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[809d63] | 454 | F= bufF; |
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[17a710] | 455 | goto differentevalpoint; |
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| 456 | } |
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| 457 | } |
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| 458 | |
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[809d63] | 459 | CanonicalForm evaluation; |
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| 460 | if (swap) |
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| 461 | evaluation= eval[0]; |
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| 462 | else |
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| 463 | evaluation= eval[1]; |
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[17a710] | 464 | |
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[809d63] | 465 | F *= bCommonDen (F); |
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| 466 | F= F (y + evaluation, y); |
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[17a710] | 467 | |
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[809d63] | 468 | int liftBound= degree (F,y) + 1; |
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[17a710] | 469 | |
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| 470 | modpk b= modpk(); |
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| 471 | |
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| 472 | CanonicalForm den= 1; |
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| 473 | |
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| 474 | mipo= getMipo (alpha); |
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| 475 | |
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| 476 | CFList uniFactors; |
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[809d63] | 477 | for (iter=QaF1Factors; iter.hasItem(); iter++) |
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[17a710] | 478 | uniFactors.append (iter.getItem().factor()); |
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| 479 | |
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[809d63] | 480 | F /= Lc (F1); |
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| 481 | ZZX NTLmipo= convertFacCF2NTLZZX (mipo); |
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| 482 | ZZX NTLLcf= convertFacCF2NTLZZX (Lc (F*bCommonDen (F))); |
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| 483 | ZZ NTLf= resultant (NTLmipo, NTLLcf); |
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| 484 | ZZ NTLD= discriminant (NTLmipo); |
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| 485 | den= abs (convertZZ2CF (NTLD*NTLf)); |
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[17a710] | 486 | |
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[809d63] | 487 | // make factors elements of Z(a)[x] disable for modularDiophant |
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| 488 | CanonicalForm multiplier= 1; |
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| 489 | for (CFListIterator i= uniFactors; i.hasItem(); i++) |
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| 490 | { |
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| 491 | multiplier *= bCommonDen (i.getItem()); |
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| 492 | i.getItem()= i.getItem()*bCommonDen(i.getItem()); |
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| 493 | } |
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| 494 | F *= multiplier; |
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| 495 | F *= bCommonDen (F); |
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[17a710] | 496 | |
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[809d63] | 497 | Off (SW_RATIONAL); |
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| 498 | int ii= 0; |
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| 499 | CanonicalForm discMipo= convertZZ2CF (NTLD); |
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| 500 | findGoodPrime (bufF*discMipo,ii); |
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| 501 | findGoodPrime (F1*discMipo,ii); |
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| 502 | findGoodPrime (F*discMipo,ii); |
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| 503 | |
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| 504 | int pp=cf_getBigPrime(ii); |
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| 505 | b = coeffBound( F, pp, mipo ); |
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| 506 | modpk bb= coeffBound (F1, pp, mipo); |
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| 507 | if (bb.getk() > b.getk() ) b=bb; |
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| 508 | bb= coeffBound (F, pp, mipo); |
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| 509 | if (bb.getk() > b.getk() ) b=bb; |
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[17a710] | 510 | |
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| 511 | ExtensionInfo dummy= ExtensionInfo (alpha, false); |
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| 512 | DegreePattern degs= DegreePattern (uniFactors); |
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| 513 | |
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| 514 | bool earlySuccess= false; |
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| 515 | CFList earlyFactors; |
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| 516 | TIMING_START (fac_bi_hensel_lift); |
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| 517 | uniFactors= henselLiftAndEarly |
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[809d63] | 518 | (F, earlySuccess, earlyFactors, degs, liftBound, |
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| 519 | uniFactors, dummy, evaluation, b, den); |
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[17a710] | 520 | TIMING_END_AND_PRINT (fac_bi_hensel_lift, |
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| 521 | "time for bivariate hensel lifting over Q: "); |
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| 522 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
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| 523 | |
---|
[809d63] | 524 | CanonicalForm MODl= power (y, liftBound); |
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[17a710] | 525 | |
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[dea3d2] | 526 | On (SW_RATIONAL); |
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[809d63] | 527 | F *= bCommonDen (F); |
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[17a710] | 528 | Off (SW_RATIONAL); |
---|
| 529 | |
---|
| 530 | CFList biFactors; |
---|
| 531 | |
---|
| 532 | TIMING_START (fac_bi_factor_recombination); |
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[e1a221] | 533 | biFactors= factorRecombination (uniFactors, F, MODl, degs, evaluation, 1, |
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| 534 | uniFactors.length()/2, b, den); |
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[17a710] | 535 | TIMING_END_AND_PRINT (fac_bi_factor_recombination, |
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| 536 | "time for bivariate factor recombination over Q: "); |
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| 537 | |
---|
| 538 | On (SW_RATIONAL); |
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| 539 | |
---|
| 540 | if (earlySuccess) |
---|
| 541 | biFactors= Union (earlyFactors, biFactors); |
---|
| 542 | else if (!earlySuccess && degs.getLength() == 1) |
---|
| 543 | biFactors= earlyFactors; |
---|
| 544 | |
---|
| 545 | bool swap2= false; |
---|
| 546 | appendSwapDecompress (biFactors, CFList(), CFList(), swap, swap2, CFMap()); |
---|
| 547 | if (isOn (SW_RATIONAL)) |
---|
| 548 | normalize (biFactors); |
---|
| 549 | |
---|
| 550 | CFAFList result; |
---|
| 551 | bool found= false; |
---|
| 552 | |
---|
[809d63] | 553 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
[17a710] | 554 | { |
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[809d63] | 555 | if (totaldegree (i.getItem()) == minTdeg) |
---|
[17a710] | 556 | { |
---|
[809d63] | 557 | result= CFAFList (CFAFactor (i.getItem(), getMipo (alpha), 1)); |
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[17a710] | 558 | found= true; |
---|
| 559 | break; |
---|
| 560 | } |
---|
| 561 | } |
---|
| 562 | |
---|
[809d63] | 563 | if (!found) |
---|
[17a710] | 564 | { |
---|
| 565 | rec= true; |
---|
[809d63] | 566 | F= bufF; |
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[17a710] | 567 | goto differentevalpoint; |
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| 568 | } |
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| 569 | |
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| 570 | return result; |
---|
[dea3d2] | 571 | } |
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[809d63] | 572 | |
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[dea3d2] | 573 | #endif |
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| 574 | |
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| 575 | |
---|