[7bf145] | 1 | /*****************************************************************************\ |
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[806c18] | 2 | * Computer Algebra System SINGULAR |
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[7bf145] | 3 | \*****************************************************************************/ |
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| 4 | /** @file facFqBivar.cc |
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[806c18] | 5 | * |
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[7bf145] | 6 | * This file provides functions for factorizing a bivariate polynomial over |
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[806c18] | 7 | * \f$ F_{p} \f$ , \f$ F_{p}(\alpha ) \f$ or GF, based on "Modern Computer |
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| 8 | * Algebra, Chapter 15" by J. von zur Gathen & J. Gerhard and "Factoring |
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| 9 | * multivariate polynomials over a finite field" by L. Bernardin. |
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[8c1a84] | 10 | * Factor Recombination is described in "Factoring polynomials over global |
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| 11 | * fields" by K. Belabas, M. van Hoeij, J. Klueners, A. Steel |
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[7bf145] | 12 | * |
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| 13 | * |
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| 14 | * @author Martin Lee |
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| 15 | * |
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| 16 | * @internal @version \$Id$ |
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| 17 | * |
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| 18 | **/ |
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| 19 | /*****************************************************************************/ |
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| 20 | |
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[e4fe2b] | 21 | #include "config.h" |
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[7bf145] | 22 | |
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[650f2d8] | 23 | #include "cf_assert.h" |
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[7bf145] | 24 | #include "debug.h" |
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| 25 | #include "timing.h" |
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| 26 | |
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| 27 | #include "canonicalform.h" |
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| 28 | #include "cf_defs.h" |
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| 29 | #include "cf_map_ext.h" |
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| 30 | #include "cf_random.h" |
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| 31 | #include "facHensel.h" |
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| 32 | #include "cf_map.h" |
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| 33 | #include "cf_gcd_smallp.h" |
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[11bf82] | 34 | #include "facFqBivarUtil.h" |
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[7bf145] | 35 | #include "facFqBivar.h" |
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[11bf82] | 36 | #include "cfNewtonPolygon.h" |
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[7bf145] | 37 | |
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| 38 | #ifdef HAVE_NTL |
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[da68804] | 39 | #include "NTLconvert.h" |
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[7bf145] | 40 | |
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[e76d7a6] | 41 | TIMING_DEFINE_PRINT(fac_uni_factorizer) |
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| 42 | TIMING_DEFINE_PRINT(fac_hensel_lift) |
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| 43 | TIMING_DEFINE_PRINT(fac_factor_recombination) |
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[7bf145] | 44 | |
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[806c18] | 45 | CanonicalForm prodMod0 (const CFList& L, const CanonicalForm& M) |
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[7bf145] | 46 | { |
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| 47 | if (L.isEmpty()) |
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| 48 | return 1; |
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| 49 | else if (L.length() == 1) |
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| 50 | return mod (L.getFirst()(0, 1) , M); |
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| 51 | else if (L.length() == 2) |
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| 52 | return mod (L.getFirst()(0, 1)*L.getLast()(0, 1), M); |
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| 53 | else |
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| 54 | { |
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| 55 | int l= L.length()/2; |
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| 56 | CFListIterator i= L; |
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| 57 | CFList tmp1, tmp2; |
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| 58 | CanonicalForm buf1, buf2; |
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[806c18] | 59 | for (int j= 1; j <= l; j++, i++) |
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[7bf145] | 60 | tmp1.append (i.getItem()); |
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| 61 | tmp2= Difference (L, tmp1); |
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| 62 | buf1= prodMod0 (tmp1, M); |
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| 63 | buf2= prodMod0 (tmp2, M); |
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| 64 | return mod (buf1*buf2, M); |
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| 65 | } |
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| 66 | } |
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| 67 | |
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[806c18] | 68 | CanonicalForm evalPoint (const CanonicalForm& F, CanonicalForm & eval, |
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[7bf145] | 69 | const Variable& alpha, CFList& list, const bool& GF, |
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[806c18] | 70 | bool& fail) |
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[7bf145] | 71 | { |
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| 72 | fail= false; |
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| 73 | Variable x= Variable(2); |
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| 74 | FFRandom genFF; |
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| 75 | GFRandom genGF; |
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| 76 | CanonicalForm random, mipo; |
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| 77 | double bound; |
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| 78 | int p= getCharacteristic (); |
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[1372ae] | 79 | if (alpha.level() != 1) |
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[7bf145] | 80 | { |
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| 81 | mipo= getMipo (alpha); |
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| 82 | int d= degree (mipo); |
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| 83 | bound= ipower (p, d); |
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| 84 | } |
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[806c18] | 85 | else if (GF) |
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[7bf145] | 86 | { |
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| 87 | int d= getGFDegree(); |
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| 88 | bound= ipower (p, d); |
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| 89 | } |
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| 90 | else |
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| 91 | bound= p; |
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| 92 | |
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[11bf82] | 93 | random= 0; |
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[806c18] | 94 | do |
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[7bf145] | 95 | { |
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| 96 | if (list.length() >= bound) |
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| 97 | { |
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| 98 | fail= true; |
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| 99 | break; |
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| 100 | } |
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[8db258] | 101 | if (list.isEmpty()) |
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| 102 | random= 0; |
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| 103 | else if (GF) |
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[11bf82] | 104 | { |
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| 105 | if (list.length() == 1) |
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| 106 | random= getGFGenerator(); |
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| 107 | else |
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| 108 | random= genGF.generate(); |
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| 109 | } |
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| 110 | else if (list.length() < p || alpha.level() == 1) |
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[7bf145] | 111 | random= genFF.generate(); |
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[806c18] | 112 | else if (alpha != x && list.length() >= p) |
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[7bf145] | 113 | { |
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[11bf82] | 114 | if (list.length() == p) |
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| 115 | random= alpha; |
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| 116 | else |
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| 117 | { |
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| 118 | AlgExtRandomF genAlgExt (alpha); |
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| 119 | random= genAlgExt.generate(); |
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| 120 | } |
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[7bf145] | 121 | } |
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| 122 | if (find (list, random)) continue; |
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| 123 | eval= F (random, x); |
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[806c18] | 124 | if (degree (eval) != degree (F, Variable (1))) |
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[7bf145] | 125 | { //leading coeff vanishes |
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| 126 | if (!find (list, random)) |
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| 127 | list.append (random); |
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| 128 | continue; |
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| 129 | } |
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[806c18] | 130 | if (degree (gcd (deriv (eval, eval.mvar()), eval), eval.mvar()) > 0) |
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[7bf145] | 131 | { //evaluated polynomial is not squarefree |
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| 132 | if (!find (list, random)) |
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| 133 | list.append (random); |
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| 134 | continue; |
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| 135 | } |
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| 136 | } while (find (list, random)); |
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| 137 | |
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| 138 | return random; |
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| 139 | } |
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| 140 | |
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[806c18] | 141 | CFList |
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| 142 | uniFactorizer (const CanonicalForm& A, const Variable& alpha, const bool& GF) |
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[7bf145] | 143 | { |
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| 144 | Variable x= A.mvar(); |
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| 145 | ASSERT (A.isUnivariate(), "univariate polynomial expected"); |
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| 146 | CFFList factorsA; |
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| 147 | ZZ p= to_ZZ (getCharacteristic()); |
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[806c18] | 148 | ZZ_p::init (p); |
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| 149 | if (GF) |
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[7bf145] | 150 | { |
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[806c18] | 151 | Variable beta= rootOf (gf_mipo); |
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[7bf145] | 152 | int k= getGFDegree(); |
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| 153 | char cGFName= gf_name; |
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[806c18] | 154 | setCharacteristic (getCharacteristic()); |
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| 155 | CanonicalForm buf= GF2FalphaRep (A, beta); |
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[7bf145] | 156 | if (getCharacteristic() > 2) |
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| 157 | { |
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| 158 | ZZ_pX NTLMipo= convertFacCF2NTLZZpX (gf_mipo); |
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| 159 | ZZ_pE::init (NTLMipo); |
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| 160 | ZZ_pEX NTLA= convertFacCF2NTLZZ_pEX (buf, NTLMipo); |
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| 161 | MakeMonic (NTLA); |
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| 162 | vec_pair_ZZ_pEX_long NTLFactorsA= CanZass (NTLA); |
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| 163 | ZZ_pE multi= to_ZZ_pE (1); |
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| 164 | factorsA= convertNTLvec_pair_ZZpEX_long2FacCFFList (NTLFactorsA, multi, |
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| 165 | x, beta); |
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| 166 | } |
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| 167 | else |
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| 168 | { |
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| 169 | GF2X NTLMipo= convertFacCF2NTLGF2X (gf_mipo); |
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| 170 | GF2E::init (NTLMipo); |
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| 171 | GF2EX NTLA= convertFacCF2NTLGF2EX (buf, NTLMipo); |
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| 172 | MakeMonic (NTLA); |
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| 173 | vec_pair_GF2EX_long NTLFactorsA= CanZass (NTLA); |
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| 174 | GF2E multi= to_GF2E (1); |
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| 175 | factorsA= convertNTLvec_pair_GF2EX_long2FacCFFList (NTLFactorsA, multi, |
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| 176 | x, beta); |
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| 177 | } |
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| 178 | setCharacteristic (getCharacteristic(), k, cGFName); |
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[806c18] | 179 | for (CFFListIterator i= factorsA; i.hasItem(); i++) |
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[7bf145] | 180 | { |
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| 181 | buf= i.getItem().factor(); |
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| 182 | buf= Falpha2GFRep (buf); |
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| 183 | i.getItem()= CFFactor (buf, i.getItem().exp()); |
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| 184 | } |
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[806c18] | 185 | } |
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[1372ae] | 186 | else if (alpha.level() != 1) |
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[7bf145] | 187 | { |
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| 188 | if (getCharacteristic() > 2) |
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| 189 | { |
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| 190 | ZZ_pX NTLMipo= convertFacCF2NTLZZpX (getMipo (alpha)); |
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[806c18] | 191 | ZZ_pE::init (NTLMipo); |
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[7bf145] | 192 | ZZ_pEX NTLA= convertFacCF2NTLZZ_pEX (A, NTLMipo); |
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| 193 | MakeMonic (NTLA); |
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| 194 | vec_pair_ZZ_pEX_long NTLFactorsA= CanZass (NTLA); |
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| 195 | ZZ_pE multi= to_ZZ_pE (1); |
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[806c18] | 196 | factorsA= convertNTLvec_pair_ZZpEX_long2FacCFFList (NTLFactorsA, multi, |
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[7bf145] | 197 | x, alpha); |
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| 198 | } |
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| 199 | else |
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| 200 | { |
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| 201 | GF2X NTLMipo= convertFacCF2NTLGF2X (getMipo (alpha)); |
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[806c18] | 202 | GF2E::init (NTLMipo); |
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[7bf145] | 203 | GF2EX NTLA= convertFacCF2NTLGF2EX (A, NTLMipo); |
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| 204 | MakeMonic (NTLA); |
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| 205 | vec_pair_GF2EX_long NTLFactorsA= CanZass (NTLA); |
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| 206 | GF2E multi= to_GF2E (1); |
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[806c18] | 207 | factorsA= convertNTLvec_pair_GF2EX_long2FacCFFList (NTLFactorsA, multi, |
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[7bf145] | 208 | x, alpha); |
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[806c18] | 209 | } |
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[7bf145] | 210 | } |
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[806c18] | 211 | else |
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[7bf145] | 212 | { |
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| 213 | if (getCharacteristic() > 2) |
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| 214 | { |
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| 215 | ZZ_pX NTLA= convertFacCF2NTLZZpX (A); |
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| 216 | MakeMonic (NTLA); |
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| 217 | vec_pair_ZZ_pX_long NTLFactorsA= CanZass (NTLA); |
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| 218 | ZZ_p multi= to_ZZ_p (1); |
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[806c18] | 219 | factorsA= convertNTLvec_pair_ZZpX_long2FacCFFList (NTLFactorsA, multi, |
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[7bf145] | 220 | x); |
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| 221 | } |
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| 222 | else |
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| 223 | { |
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| 224 | GF2X NTLA= convertFacCF2NTLGF2X (A); |
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| 225 | vec_pair_GF2X_long NTLFactorsA= CanZass (NTLA); |
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| 226 | GF2 multi= to_GF2 (1); |
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[806c18] | 227 | factorsA= convertNTLvec_pair_GF2X_long2FacCFFList (NTLFactorsA, multi, |
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[7bf145] | 228 | x); |
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| 229 | } |
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| 230 | } |
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| 231 | CFList uniFactors; |
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[806c18] | 232 | for (CFFListIterator i= factorsA; i.hasItem(); i++) |
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[7bf145] | 233 | uniFactors.append (i.getItem().factor()); |
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| 234 | return uniFactors; |
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[806c18] | 235 | } |
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| 236 | |
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| 237 | /// naive factor recombination as decribed in "Factoring |
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| 238 | /// multivariate polynomials over a finite field" by L Bernardin. |
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| 239 | CFList |
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[11bf82] | 240 | extFactorRecombination (CFList& factors, CanonicalForm& F, |
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[806c18] | 241 | const CanonicalForm& M, const ExtensionInfo& info, |
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[11bf82] | 242 | DegreePattern& degs, const CanonicalForm& eval, int s, |
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| 243 | int thres) |
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[806c18] | 244 | { |
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[7bf145] | 245 | if (factors.length() == 0) |
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[11bf82] | 246 | { |
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| 247 | F= 1; |
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[7bf145] | 248 | return CFList(); |
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[11bf82] | 249 | } |
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[7bf145] | 250 | |
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| 251 | Variable alpha= info.getAlpha(); |
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| 252 | Variable beta= info.getBeta(); |
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| 253 | CanonicalForm gamma= info.getGamma(); |
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| 254 | CanonicalForm delta= info.getDelta(); |
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| 255 | int k= info.getGFDegree(); |
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| 256 | |
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| 257 | Variable y= F.mvar(); |
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| 258 | CFList source, dest; |
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[806c18] | 259 | if (degs.getLength() <= 1 || factors.length() == 1) |
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[11bf82] | 260 | { |
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| 261 | CFList result= CFList(mapDown (F(y-eval, y), info, source, dest)); |
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| 262 | F= 1; |
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| 263 | return result; |
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| 264 | } |
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[806c18] | 265 | |
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| 266 | DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, M) == F " << |
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[7bf145] | 267 | (LC (F, 1)*prodMod (factors, M) == F)); |
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[ac8e1a] | 268 | int degMipoBeta= 1; |
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| 269 | if (!k && beta.level() != 1) |
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[7bf145] | 270 | degMipoBeta= degree (getMipo (beta)); |
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| 271 | |
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| 272 | CFList T, S, Diff; |
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| 273 | T= factors; |
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| 274 | |
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| 275 | CFList result; |
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[21b8f4c] | 276 | CanonicalForm buf, buf2, quot; |
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[11bf82] | 277 | |
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| 278 | buf= F; |
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[7bf145] | 279 | |
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| 280 | CanonicalForm g, LCBuf= LC (buf, Variable (1)); |
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[1673386] | 281 | int * v= new int [T.length()]; |
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[7bf145] | 282 | for (int i= 0; i < T.length(); i++) |
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| 283 | v[i]= 0; |
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| 284 | |
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| 285 | CFArray TT; |
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[806c18] | 286 | DegreePattern bufDegs1, bufDegs2; |
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[7bf145] | 287 | bufDegs1= degs; |
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| 288 | int subsetDeg; |
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[806c18] | 289 | TT= copy (factors); |
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[7bf145] | 290 | bool nosubset= false; |
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| 291 | bool recombination= false; |
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[93134c] | 292 | bool trueFactor= false; |
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[11bf82] | 293 | while (T.length() >= 2*s && s <= thres) |
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[7bf145] | 294 | { |
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[806c18] | 295 | while (nosubset == false) |
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[7bf145] | 296 | { |
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[806c18] | 297 | if (T.length() == s) |
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[7bf145] | 298 | { |
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[1673386] | 299 | delete [] v; |
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[806c18] | 300 | if (recombination) |
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[7bf145] | 301 | { |
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| 302 | T.insert (LCBuf); |
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| 303 | g= prodMod (T, M); |
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| 304 | T.removeFirst(); |
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| 305 | g /= content(g); |
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| 306 | g= g (y - eval, y); |
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| 307 | g /= Lc (g); |
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| 308 | appendTestMapDown (result, g, info, source, dest); |
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[11bf82] | 309 | F= 1; |
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[7bf145] | 310 | return result; |
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| 311 | } |
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| 312 | else |
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| 313 | { |
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| 314 | appendMapDown (result, F (y - eval, y), info, source, dest); |
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[11bf82] | 315 | F= 1; |
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[7bf145] | 316 | return result; |
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| 317 | } |
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| 318 | } |
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| 319 | S= subset (v, s, TT, nosubset); |
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| 320 | if (nosubset) break; |
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| 321 | subsetDeg= subsetDegree (S); |
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| 322 | // skip those combinations that are not possible |
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[806c18] | 323 | if (!degs.find (subsetDeg)) |
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[7bf145] | 324 | continue; |
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[806c18] | 325 | else |
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| 326 | { |
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[7bf145] | 327 | g= prodMod0 (S, M); |
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| 328 | g= mod (g*LCBuf, M); |
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| 329 | g /= content (g); |
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| 330 | if (fdivides (LC (g), LCBuf)) |
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| 331 | { |
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| 332 | S.insert (LCBuf); |
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| 333 | g= prodMod (S, M); |
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| 334 | S.removeFirst(); |
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| 335 | g /= content (g, Variable (1)); |
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[21b8f4c] | 336 | if (fdivides (g, buf, quot)) |
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[7bf145] | 337 | { |
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| 338 | buf2= g (y - eval, y); |
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[93134c] | 339 | buf2 /= Lc (buf2); |
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| 340 | |
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[11bf82] | 341 | if (!k && beta.level() == 1) |
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[7bf145] | 342 | { |
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| 343 | if (degree (buf2, alpha) < degMipoBeta) |
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[806c18] | 344 | { |
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[21b8f4c] | 345 | buf= quot; |
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[7bf145] | 346 | LCBuf= LC (buf, Variable (1)); |
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| 347 | recombination= true; |
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[93134c] | 348 | appendTestMapDown (result, buf2, info, source, dest); |
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| 349 | trueFactor= true; |
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[7bf145] | 350 | } |
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| 351 | } |
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[806c18] | 352 | else |
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[7bf145] | 353 | { |
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[f876a66] | 354 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
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[7bf145] | 355 | { |
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[21b8f4c] | 356 | buf= quot; |
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[7bf145] | 357 | LCBuf= LC (buf, Variable (1)); |
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| 358 | recombination= true; |
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[93134c] | 359 | appendTestMapDown (result, buf2, info, source, dest); |
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| 360 | trueFactor= true; |
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[7bf145] | 361 | } |
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| 362 | } |
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[93134c] | 363 | if (trueFactor) |
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[7bf145] | 364 | { |
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[93134c] | 365 | T= Difference (T, S); |
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| 366 | // compute new possible degree pattern |
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| 367 | bufDegs2= DegreePattern (T); |
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| 368 | bufDegs1.intersect (bufDegs2); |
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| 369 | bufDegs1.refine (); |
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| 370 | if (T.length() < 2*s || T.length() == s || |
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| 371 | bufDegs1.getLength() == 1) |
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[7bf145] | 372 | { |
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[1673386] | 373 | delete [] v; |
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[93134c] | 374 | if (recombination) |
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| 375 | { |
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| 376 | appendTestMapDown (result, buf (y - eval, y), info, source, |
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| 377 | dest); |
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[11bf82] | 378 | F= 1; |
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[93134c] | 379 | return result; |
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| 380 | } |
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| 381 | else |
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| 382 | { |
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| 383 | appendMapDown (result, F (y - eval, y), info, source, dest); |
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[11bf82] | 384 | F= 1; |
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[93134c] | 385 | return result; |
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| 386 | } |
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[7bf145] | 387 | } |
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[93134c] | 388 | trueFactor= false; |
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| 389 | TT= copy (T); |
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| 390 | indexUpdate (v, s, T.length(), nosubset); |
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| 391 | if (nosubset) break; |
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[7bf145] | 392 | } |
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| 393 | } |
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| 394 | } |
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| 395 | } |
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| 396 | } |
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| 397 | s++; |
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[806c18] | 398 | if (T.length() < 2*s || T.length() == s) |
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[7bf145] | 399 | { |
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[1673386] | 400 | delete [] v; |
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[7bf145] | 401 | if (recombination) |
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| 402 | { |
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| 403 | appendTestMapDown (result, buf (y - eval, y), info, source, dest); |
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[11bf82] | 404 | F= 1; |
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[7bf145] | 405 | return result; |
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| 406 | } |
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| 407 | else |
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| 408 | { |
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| 409 | appendMapDown (result, F (y - eval, y), info, source, dest); |
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[11bf82] | 410 | F= 1; |
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[7bf145] | 411 | return result; |
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| 412 | } |
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| 413 | } |
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| 414 | for (int i= 0; i < T.length(); i++) |
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| 415 | v[i]= 0; |
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| 416 | nosubset= false; |
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| 417 | } |
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[806c18] | 418 | if (T.length() < 2*s) |
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[11bf82] | 419 | { |
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[7bf145] | 420 | appendMapDown (result, F (y - eval, y), info, source, dest); |
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[11bf82] | 421 | F= 1; |
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| 422 | delete [] v; |
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| 423 | return result; |
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| 424 | } |
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| 425 | |
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| 426 | if (s > thres) |
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| 427 | { |
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| 428 | factors= T; |
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| 429 | F= buf; |
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| 430 | degs= bufDegs1; |
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| 431 | } |
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[7bf145] | 432 | |
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[1673386] | 433 | delete [] v; |
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[806c18] | 434 | return result; |
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| 435 | } |
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[7bf145] | 436 | |
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[806c18] | 437 | /// naive factor recombination as decribed in "Factoring |
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| 438 | /// multivariate polynomials over a finite field" by L Bernardin. |
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| 439 | CFList |
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[11bf82] | 440 | factorRecombination (CFList& factors, CanonicalForm& F, |
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| 441 | const CanonicalForm& M, DegreePattern& degs, int s, |
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| 442 | int thres |
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| 443 | ) |
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[7bf145] | 444 | { |
---|
| 445 | if (factors.length() == 0) |
---|
[11bf82] | 446 | { |
---|
| 447 | F= 1; |
---|
[7bf145] | 448 | return CFList (); |
---|
[11bf82] | 449 | } |
---|
[806c18] | 450 | if (degs.getLength() <= 1 || factors.length() == 1) |
---|
[11bf82] | 451 | { |
---|
| 452 | CFList result= CFList (F); |
---|
| 453 | F= 1; |
---|
| 454 | return result; |
---|
| 455 | } |
---|
[806c18] | 456 | DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, M) == F " << |
---|
[7bf145] | 457 | (LC (F, 1)*prodMod (factors, M) == F)); |
---|
| 458 | CFList T, S; |
---|
| 459 | |
---|
| 460 | T= factors; |
---|
| 461 | CFList result; |
---|
| 462 | CanonicalForm LCBuf= LC (F, Variable (1)); |
---|
[21b8f4c] | 463 | CanonicalForm g, quot, buf= F; |
---|
[1673386] | 464 | int * v= new int [T.length()]; |
---|
[7bf145] | 465 | for (int i= 0; i < T.length(); i++) |
---|
| 466 | v[i]= 0; |
---|
| 467 | bool nosubset= false; |
---|
| 468 | CFArray TT; |
---|
| 469 | DegreePattern bufDegs1, bufDegs2; |
---|
| 470 | bufDegs1= degs; |
---|
| 471 | int subsetDeg; |
---|
| 472 | TT= copy (factors); |
---|
| 473 | bool recombination= false; |
---|
[11bf82] | 474 | while (T.length() >= 2*s && s <= thres) |
---|
[7bf145] | 475 | { |
---|
[806c18] | 476 | while (nosubset == false) |
---|
[7bf145] | 477 | { |
---|
[806c18] | 478 | if (T.length() == s) |
---|
[7bf145] | 479 | { |
---|
[1673386] | 480 | delete [] v; |
---|
[7bf145] | 481 | if (recombination) |
---|
| 482 | { |
---|
| 483 | T.insert (LCBuf); |
---|
| 484 | g= prodMod (T, M); |
---|
| 485 | T.removeFirst(); |
---|
| 486 | result.append (g/content (g, Variable (1))); |
---|
[11bf82] | 487 | F= 1; |
---|
[7bf145] | 488 | return result; |
---|
| 489 | } |
---|
| 490 | else |
---|
[11bf82] | 491 | { |
---|
| 492 | result= CFList (F); |
---|
| 493 | F= 1; |
---|
| 494 | return result; |
---|
| 495 | } |
---|
[7bf145] | 496 | } |
---|
| 497 | S= subset (v, s, TT, nosubset); |
---|
| 498 | if (nosubset) break; |
---|
| 499 | subsetDeg= subsetDegree (S); |
---|
| 500 | // skip those combinations that are not possible |
---|
[806c18] | 501 | if (!degs.find (subsetDeg)) |
---|
[7bf145] | 502 | continue; |
---|
[806c18] | 503 | else |
---|
| 504 | { |
---|
[7bf145] | 505 | g= prodMod0 (S, M); |
---|
| 506 | g= mod (g*LCBuf, M); |
---|
| 507 | g /= content (g); |
---|
[806c18] | 508 | if (fdivides (LC(g), LCBuf)) |
---|
[7bf145] | 509 | { |
---|
| 510 | S.insert (LCBuf); |
---|
| 511 | g= prodMod (S, M); |
---|
| 512 | S.removeFirst(); |
---|
| 513 | g /= content (g, Variable (1)); |
---|
[21b8f4c] | 514 | |
---|
| 515 | if (fdivides (g, buf, quot)) |
---|
[7bf145] | 516 | { |
---|
| 517 | recombination= true; |
---|
| 518 | result.append (g); |
---|
[21b8f4c] | 519 | buf= quot; |
---|
[7bf145] | 520 | LCBuf= LC (buf, Variable(1)); |
---|
| 521 | T= Difference (T, S); |
---|
| 522 | |
---|
| 523 | // compute new possible degree pattern |
---|
| 524 | bufDegs2= DegreePattern (T); |
---|
| 525 | bufDegs1.intersect (bufDegs2); |
---|
| 526 | bufDegs1.refine (); |
---|
[806c18] | 527 | if (T.length() < 2*s || T.length() == s || |
---|
| 528 | bufDegs1.getLength() == 1) |
---|
[7bf145] | 529 | { |
---|
[1673386] | 530 | delete [] v; |
---|
[7bf145] | 531 | if (recombination) |
---|
| 532 | { |
---|
| 533 | result.append (buf); |
---|
[11bf82] | 534 | F= 1; |
---|
[7bf145] | 535 | return result; |
---|
| 536 | } |
---|
| 537 | else |
---|
[11bf82] | 538 | { |
---|
| 539 | result= CFList (F); |
---|
| 540 | F= 1; |
---|
| 541 | return result; |
---|
| 542 | } |
---|
[7bf145] | 543 | } |
---|
| 544 | TT= copy (T); |
---|
| 545 | indexUpdate (v, s, T.length(), nosubset); |
---|
[806c18] | 546 | if (nosubset) break; |
---|
| 547 | } |
---|
[7bf145] | 548 | } |
---|
| 549 | } |
---|
| 550 | } |
---|
| 551 | s++; |
---|
[806c18] | 552 | if (T.length() < 2*s || T.length() == s) |
---|
[7bf145] | 553 | { |
---|
[1673386] | 554 | delete [] v; |
---|
[7bf145] | 555 | if (recombination) |
---|
| 556 | { |
---|
| 557 | result.append (buf); |
---|
[11bf82] | 558 | F= 1; |
---|
[7bf145] | 559 | return result; |
---|
| 560 | } |
---|
| 561 | else |
---|
[11bf82] | 562 | { |
---|
| 563 | result= CFList (F); |
---|
| 564 | F= 1; |
---|
| 565 | return result; |
---|
| 566 | } |
---|
[7bf145] | 567 | } |
---|
| 568 | for (int i= 0; i < T.length(); i++) |
---|
| 569 | v[i]= 0; |
---|
| 570 | nosubset= false; |
---|
| 571 | } |
---|
[11bf82] | 572 | delete [] v; |
---|
[806c18] | 573 | if (T.length() < 2*s) |
---|
[11bf82] | 574 | { |
---|
[7bf145] | 575 | result.append (F); |
---|
[11bf82] | 576 | F= 1; |
---|
| 577 | return result; |
---|
| 578 | } |
---|
| 579 | |
---|
| 580 | if (s > thres) |
---|
| 581 | { |
---|
| 582 | factors= T; |
---|
| 583 | F= buf; |
---|
| 584 | degs= bufDegs1; |
---|
| 585 | } |
---|
[7bf145] | 586 | |
---|
[806c18] | 587 | return result; |
---|
| 588 | } |
---|
[7bf145] | 589 | |
---|
[11bf82] | 590 | Variable chooseExtension (const Variable & alpha, const Variable& beta, int k) |
---|
[7bf145] | 591 | { |
---|
[11bf82] | 592 | zz_p::init (getCharacteristic()); |
---|
| 593 | zz_pX NTLIrredpoly; |
---|
| 594 | int i, m; |
---|
| 595 | // extension of F_p needed |
---|
| 596 | if (alpha.level() == 1 && beta.level() == 1 && k == 1) |
---|
| 597 | { |
---|
| 598 | i= 1; |
---|
| 599 | m= 2; |
---|
| 600 | } //extension of F_p(alpha) needed but want to factorize over F_p |
---|
| 601 | else if (alpha.level() != 1 && beta.level() == 1 && k == 1) |
---|
| 602 | { |
---|
| 603 | i= 1; |
---|
| 604 | m= degree (getMipo (alpha)) + 1; |
---|
| 605 | } //extension of F_p(alpha) needed for first time |
---|
| 606 | else if (alpha.level() != 1 && beta.level() == 1 && k != 1) |
---|
| 607 | { |
---|
[7bf145] | 608 | i= 2; |
---|
[11bf82] | 609 | m= degree (getMipo (alpha)); |
---|
| 610 | } |
---|
| 611 | else if (alpha.level() != 1 && beta.level() != 1 && k != 1) |
---|
| 612 | { |
---|
| 613 | m= degree (getMipo (beta)); |
---|
| 614 | i= degree (getMipo (alpha))/m + 1; |
---|
| 615 | } |
---|
| 616 | BuildIrred (NTLIrredpoly, i*m); |
---|
| 617 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
[7bf145] | 618 | return rootOf (newMipo); |
---|
| 619 | } |
---|
| 620 | |
---|
[806c18] | 621 | CFList |
---|
| 622 | earlyFactorDetection (CanonicalForm& F, CFList& factors,int& adaptedLiftBound, |
---|
[7bf145] | 623 | DegreePattern& degs, bool& success, int deg) |
---|
| 624 | { |
---|
| 625 | DegreePattern bufDegs1= degs; |
---|
| 626 | DegreePattern bufDegs2; |
---|
| 627 | CFList result; |
---|
| 628 | CFList T= factors; |
---|
| 629 | CanonicalForm buf= F; |
---|
| 630 | CanonicalForm LCBuf= LC (buf, Variable (1)); |
---|
[21b8f4c] | 631 | CanonicalForm g, quot; |
---|
[7bf145] | 632 | CanonicalForm M= power (F.mvar(), deg); |
---|
| 633 | adaptedLiftBound= 0; |
---|
[11bf82] | 634 | int d= degree (F) + degree (LCBuf); |
---|
[806c18] | 635 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
[7bf145] | 636 | { |
---|
| 637 | if (!bufDegs1.find (degree (i.getItem(), 1))) |
---|
| 638 | continue; |
---|
| 639 | else |
---|
| 640 | { |
---|
| 641 | g= i.getItem() (0, 1); |
---|
| 642 | g *= LCBuf; |
---|
| 643 | g= mod (g, M); |
---|
| 644 | if (fdivides (LC (g), LCBuf)) |
---|
| 645 | { |
---|
| 646 | g= mulMod2 (i.getItem(), LCBuf, M); |
---|
| 647 | g /= content (g, Variable (1)); |
---|
[21b8f4c] | 648 | if (fdivides (g, buf, quot)) |
---|
[7bf145] | 649 | { |
---|
| 650 | result.append (g); |
---|
[21b8f4c] | 651 | buf= quot; |
---|
[7bf145] | 652 | d -= degree (g) + degree (LC (g, Variable (1))); |
---|
[806c18] | 653 | LCBuf= LC (buf, Variable (1)); |
---|
[7bf145] | 654 | T= Difference (T, CFList (i.getItem())); |
---|
| 655 | |
---|
| 656 | // compute new possible degree pattern |
---|
| 657 | bufDegs2= DegreePattern (T); |
---|
| 658 | bufDegs1.intersect (bufDegs2); |
---|
[806c18] | 659 | bufDegs1.refine (); |
---|
[7bf145] | 660 | if (bufDegs1.getLength() <= 1) |
---|
| 661 | { |
---|
| 662 | result.append (buf); |
---|
| 663 | break; |
---|
| 664 | } |
---|
| 665 | } |
---|
| 666 | } |
---|
| 667 | } |
---|
| 668 | } |
---|
| 669 | adaptedLiftBound= d + 1; |
---|
| 670 | if (d < deg) |
---|
| 671 | { |
---|
| 672 | factors= T; |
---|
| 673 | degs= bufDegs1; |
---|
| 674 | F= buf; |
---|
| 675 | success= true; |
---|
| 676 | } |
---|
| 677 | if (bufDegs1.getLength() <= 1) |
---|
| 678 | degs= bufDegs1; |
---|
| 679 | return result; |
---|
| 680 | } |
---|
| 681 | |
---|
[806c18] | 682 | CFList |
---|
| 683 | extEarlyFactorDetection (CanonicalForm& F, CFList& factors, |
---|
| 684 | int& adaptedLiftBound, DegreePattern& degs, |
---|
[7bf145] | 685 | bool& success, const ExtensionInfo& info, |
---|
| 686 | const CanonicalForm& eval, int deg) |
---|
| 687 | { |
---|
| 688 | Variable alpha= info.getAlpha(); |
---|
| 689 | Variable beta= info.getBeta(); |
---|
| 690 | CanonicalForm gamma= info.getGamma(); |
---|
| 691 | CanonicalForm delta= info.getDelta(); |
---|
| 692 | int k= info.getGFDegree(); |
---|
| 693 | DegreePattern bufDegs1= degs, bufDegs2; |
---|
[806c18] | 694 | CFList result; |
---|
[7bf145] | 695 | CFList T= factors; |
---|
| 696 | Variable y= F.mvar(); |
---|
| 697 | CanonicalForm buf= F, LCBuf= LC (buf, Variable (1)), g, buf2; |
---|
| 698 | CanonicalForm M= power (y, deg); |
---|
| 699 | adaptedLiftBound= 0; |
---|
[93134c] | 700 | bool trueFactor= false; |
---|
[11bf82] | 701 | int d= degree (F) + degree (LCBuf); |
---|
[7bf145] | 702 | CFList source, dest; |
---|
[ac8e1a] | 703 | int degMipoBeta= 1; |
---|
| 704 | if (!k && beta.level() != 1) |
---|
[7bf145] | 705 | degMipoBeta= degree (getMipo (beta)); |
---|
[21b8f4c] | 706 | CanonicalForm quot; |
---|
[806c18] | 707 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
[7bf145] | 708 | { |
---|
| 709 | if (!bufDegs1.find (degree (i.getItem(), 1))) |
---|
| 710 | continue; |
---|
| 711 | else |
---|
| 712 | { |
---|
| 713 | g= i.getItem() (0, 1); |
---|
| 714 | g *= LCBuf; |
---|
| 715 | g= mod (g, M); |
---|
| 716 | if (fdivides (LC (g), LCBuf)) |
---|
| 717 | { |
---|
| 718 | g= mulMod2 (i.getItem(), LCBuf, M); |
---|
| 719 | g /= content (g, Variable (1)); |
---|
[21b8f4c] | 720 | if (fdivides (g, buf, quot)) |
---|
[7bf145] | 721 | { |
---|
| 722 | buf2= g (y - eval, y); |
---|
| 723 | buf2 /= Lc (buf2); |
---|
[806c18] | 724 | |
---|
| 725 | if (!k && beta == Variable (1)) |
---|
[7bf145] | 726 | { |
---|
| 727 | if (degree (buf2, alpha) < degMipoBeta) |
---|
| 728 | { |
---|
| 729 | appendTestMapDown (result, buf2, info, source, dest); |
---|
[21b8f4c] | 730 | buf= quot; |
---|
[7bf145] | 731 | d -= degree (g) + degree (LC (g, Variable (1))); |
---|
[806c18] | 732 | LCBuf= LC (buf, Variable (1)); |
---|
[93134c] | 733 | trueFactor= true; |
---|
[7bf145] | 734 | } |
---|
| 735 | } |
---|
[806c18] | 736 | else |
---|
[7bf145] | 737 | { |
---|
[f876a66] | 738 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
[7bf145] | 739 | { |
---|
| 740 | appendTestMapDown (result, buf2, info, source, dest); |
---|
[21b8f4c] | 741 | buf= quot; |
---|
[7bf145] | 742 | d -= degree (g) + degree (LC (g, Variable (1))); |
---|
| 743 | LCBuf= LC (buf, Variable (1)); |
---|
[93134c] | 744 | trueFactor= true; |
---|
[7bf145] | 745 | } |
---|
[806c18] | 746 | } |
---|
[93134c] | 747 | if (trueFactor) |
---|
[7bf145] | 748 | { |
---|
[93134c] | 749 | T= Difference (T, CFList (i.getItem())); |
---|
| 750 | |
---|
| 751 | // compute new possible degree pattern |
---|
| 752 | bufDegs2= DegreePattern (T); |
---|
| 753 | bufDegs1.intersect (bufDegs2); |
---|
| 754 | bufDegs1.refine (); |
---|
| 755 | trueFactor= false; |
---|
| 756 | if (bufDegs1.getLength() <= 1) |
---|
| 757 | { |
---|
| 758 | buf= buf (y - eval, y); |
---|
| 759 | buf /= Lc (buf); |
---|
| 760 | appendMapDown (result, buf, info, source, dest); |
---|
| 761 | break; |
---|
| 762 | } |
---|
[7bf145] | 763 | } |
---|
| 764 | } |
---|
| 765 | } |
---|
| 766 | } |
---|
| 767 | } |
---|
| 768 | adaptedLiftBound= d + 1; |
---|
| 769 | if (adaptedLiftBound < deg) |
---|
| 770 | { |
---|
| 771 | success= true; |
---|
| 772 | factors= T; |
---|
| 773 | degs= bufDegs1; |
---|
| 774 | F= buf; |
---|
| 775 | } |
---|
| 776 | if (bufDegs1.getLength() <= 1) |
---|
| 777 | degs= bufDegs1; |
---|
| 778 | |
---|
| 779 | return result; |
---|
| 780 | } |
---|
| 781 | |
---|
| 782 | CFList |
---|
[806c18] | 783 | henselLiftAndEarly (CanonicalForm& A, bool& earlySuccess, CFList& |
---|
[7bf145] | 784 | earlyFactors, DegreePattern& degs, int& liftBound, |
---|
[806c18] | 785 | const CFList& uniFactors, const ExtensionInfo& info, |
---|
[7bf145] | 786 | const CanonicalForm& eval) |
---|
| 787 | { |
---|
| 788 | Variable alpha= info.getAlpha(); |
---|
| 789 | Variable beta= info.getBeta(); |
---|
| 790 | CanonicalForm gamma= info.getGamma(); |
---|
| 791 | CanonicalForm delta= info.getDelta(); |
---|
| 792 | bool extension= info.isInExtension(); |
---|
| 793 | |
---|
| 794 | Variable x= Variable (1); |
---|
| 795 | Variable y= Variable (2); |
---|
| 796 | CFArray Pi; |
---|
| 797 | CFList diophant; |
---|
| 798 | CFList bufUniFactors= uniFactors; |
---|
| 799 | bufUniFactors.insert (LC (A, x)); |
---|
| 800 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length() - 1); |
---|
| 801 | earlySuccess= false; |
---|
| 802 | int newLiftBound= 0; |
---|
| 803 | int smallFactorDeg= 11; //this is a tunable parameter |
---|
| 804 | if (smallFactorDeg >= liftBound) |
---|
| 805 | henselLift12 (A, bufUniFactors, liftBound, Pi, diophant, M); |
---|
| 806 | else if (smallFactorDeg >= degree (A, y) + 1) |
---|
| 807 | { |
---|
| 808 | henselLift12 (A, bufUniFactors, degree (A, y) + 1, Pi, diophant, M); |
---|
| 809 | if (!extension) |
---|
| 810 | earlyFactors= earlyFactorDetection (A, bufUniFactors, newLiftBound, |
---|
| 811 | degs, earlySuccess, degree (A, y) + 1); |
---|
| 812 | else |
---|
| 813 | earlyFactors= extEarlyFactorDetection (A, bufUniFactors, |
---|
[806c18] | 814 | newLiftBound, degs, earlySuccess, info, eval, |
---|
[7bf145] | 815 | degree (A, y) + 1); |
---|
| 816 | if (degs.getLength() > 1 && !earlySuccess) |
---|
| 817 | { |
---|
| 818 | if (newLiftBound > degree (A, y) + 1) |
---|
| 819 | { |
---|
| 820 | liftBound= newLiftBound; |
---|
| 821 | bufUniFactors.insert (LC(A, x)); |
---|
[806c18] | 822 | henselLiftResume12 (A, bufUniFactors, degree (A, y) + 1, liftBound, |
---|
[7bf145] | 823 | Pi, diophant, M); |
---|
| 824 | } |
---|
| 825 | } |
---|
| 826 | else if (earlySuccess) |
---|
| 827 | liftBound= newLiftBound; |
---|
| 828 | } |
---|
| 829 | else if (smallFactorDeg < degree (A, y) + 1) |
---|
[806c18] | 830 | { |
---|
[7bf145] | 831 | henselLift12 (A, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
---|
| 832 | if (!extension) |
---|
| 833 | earlyFactors= earlyFactorDetection (A, bufUniFactors, newLiftBound, |
---|
| 834 | degs, earlySuccess, |
---|
| 835 | smallFactorDeg); |
---|
| 836 | else |
---|
| 837 | earlyFactors= extEarlyFactorDetection (A, bufUniFactors, |
---|
| 838 | newLiftBound, degs, earlySuccess, |
---|
| 839 | info, eval, smallFactorDeg); |
---|
| 840 | if (degs.getLength() > 1 && !earlySuccess) |
---|
| 841 | { |
---|
| 842 | bufUniFactors.insert (LC (A, x)); |
---|
[806c18] | 843 | henselLiftResume12 (A, bufUniFactors, smallFactorDeg, degree (A, y) |
---|
[7bf145] | 844 | + 1, Pi, diophant, M); |
---|
| 845 | if (!extension) |
---|
[806c18] | 846 | earlyFactors= earlyFactorDetection (A, bufUniFactors, newLiftBound, |
---|
[7bf145] | 847 | degs, earlySuccess, degree (A, y) + 1); |
---|
| 848 | else |
---|
[806c18] | 849 | earlyFactors= extEarlyFactorDetection (A, bufUniFactors, |
---|
[7bf145] | 850 | newLiftBound, degs, earlySuccess, |
---|
| 851 | info, eval, degree(A,y) + 1); |
---|
| 852 | if (degs.getLength() > 1 && !earlySuccess) |
---|
| 853 | { |
---|
[806c18] | 854 | if (newLiftBound > degree (A, y) + 1) |
---|
| 855 | { |
---|
| 856 | bufUniFactors.insert (LC(A, x)); |
---|
| 857 | henselLiftResume12 (A, bufUniFactors, degree (A, y) + 1, liftBound, |
---|
[7bf145] | 858 | Pi, diophant, M); |
---|
[806c18] | 859 | } |
---|
[7bf145] | 860 | } |
---|
| 861 | else if (earlySuccess) |
---|
| 862 | liftBound= newLiftBound; |
---|
| 863 | } |
---|
| 864 | else if (earlySuccess) |
---|
| 865 | liftBound= newLiftBound; |
---|
| 866 | } |
---|
| 867 | if (newLiftBound > 0) |
---|
| 868 | liftBound= newLiftBound; |
---|
| 869 | return bufUniFactors; |
---|
| 870 | } |
---|
| 871 | |
---|
[11bf82] | 872 | long isReduced (const mat_zz_p& M) |
---|
[7bf145] | 873 | { |
---|
[11bf82] | 874 | long i, j, nonZero; |
---|
| 875 | for (i = 1; i <= M.NumRows(); i++) |
---|
[7bf145] | 876 | { |
---|
[11bf82] | 877 | nonZero= 0; |
---|
| 878 | for (j = 1; j <= M.NumCols(); j++) |
---|
[7bf145] | 879 | { |
---|
[11bf82] | 880 | if (!IsZero (M (i,j))) |
---|
| 881 | nonZero++; |
---|
[7bf145] | 882 | } |
---|
[11bf82] | 883 | if (nonZero != 1) |
---|
| 884 | return 0; |
---|
[7bf145] | 885 | } |
---|
[11bf82] | 886 | return 1; |
---|
| 887 | } |
---|
[7bf145] | 888 | |
---|
[11bf82] | 889 | long isReduced (const mat_zz_pE& M) |
---|
| 890 | { |
---|
| 891 | long i, j, nonZero; |
---|
| 892 | for (i = 1; i <= M.NumRows(); i++) |
---|
[806c18] | 893 | { |
---|
[11bf82] | 894 | nonZero= 0; |
---|
| 895 | for (j = 1; j <= M.NumCols(); j++) |
---|
| 896 | { |
---|
| 897 | if (!IsZero (M (i,j))) |
---|
[c1b9927] | 898 | nonZero++; |
---|
[11bf82] | 899 | } |
---|
| 900 | if (nonZero != 1) |
---|
| 901 | return 0; |
---|
[7bf145] | 902 | } |
---|
[11bf82] | 903 | return 1; |
---|
| 904 | } |
---|
[7bf145] | 905 | |
---|
[11bf82] | 906 | int * extractZeroOneVecs (const mat_zz_p& M) |
---|
| 907 | { |
---|
| 908 | long i, j; |
---|
| 909 | bool nonZeroOne= false; |
---|
| 910 | int * result= new int [M.NumCols()]; |
---|
| 911 | for (i = 1; i <= M.NumCols(); i++) |
---|
[7bf145] | 912 | { |
---|
[11bf82] | 913 | for (j = 1; j <= M.NumRows(); j++) |
---|
| 914 | { |
---|
| 915 | if (!(IsOne (M (j,i)) || IsZero (M (j,i)))) |
---|
| 916 | { |
---|
| 917 | nonZeroOne= true; |
---|
| 918 | break; |
---|
| 919 | } |
---|
| 920 | } |
---|
| 921 | if (!nonZeroOne) |
---|
| 922 | result [i - 1]= 1; |
---|
| 923 | else |
---|
| 924 | result [i - 1]= 0; |
---|
| 925 | nonZeroOne= false; |
---|
[7bf145] | 926 | } |
---|
[11bf82] | 927 | return result; |
---|
| 928 | } |
---|
[7bf145] | 929 | |
---|
[11bf82] | 930 | int * extractZeroOneVecs (const mat_zz_pE& M) |
---|
| 931 | { |
---|
| 932 | long i, j; |
---|
| 933 | bool nonZeroOne= false; |
---|
| 934 | int * result= new int [M.NumCols()]; |
---|
| 935 | for (i = 1; i <= M.NumCols(); i++) |
---|
[7bf145] | 936 | { |
---|
[11bf82] | 937 | for (j = 1; j <= M.NumRows(); j++) |
---|
[7bf145] | 938 | { |
---|
[11bf82] | 939 | if (!(IsOne (M (j,i)) || IsZero (M (j,i)))) |
---|
| 940 | { |
---|
| 941 | nonZeroOne= true; |
---|
| 942 | break; |
---|
| 943 | } |
---|
[7bf145] | 944 | } |
---|
[11bf82] | 945 | if (!nonZeroOne) |
---|
| 946 | result [i - 1]= 1; |
---|
| 947 | else |
---|
| 948 | result [i - 1]= 0; |
---|
| 949 | nonZeroOne= false; |
---|
[7bf145] | 950 | } |
---|
[11bf82] | 951 | return result; |
---|
| 952 | } |
---|
| 953 | |
---|
| 954 | void |
---|
| 955 | reconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const CFList& |
---|
| 956 | factors, const int liftBound, int& factorsFound, int*& |
---|
| 957 | factorsFoundIndex, mat_zz_pE& N, bool beenInThres |
---|
| 958 | ) |
---|
| 959 | { |
---|
| 960 | Variable y= Variable (2); |
---|
| 961 | Variable x= Variable (1); |
---|
| 962 | CanonicalForm yToL= power (y, liftBound); |
---|
[38ffb7] | 963 | CanonicalForm quot, buf; |
---|
| 964 | CFListIterator iter; |
---|
[11bf82] | 965 | for (long i= 1; i <= N.NumCols(); i++) |
---|
[7bf145] | 966 | { |
---|
[11bf82] | 967 | if (factorsFoundIndex [i - 1] == 1) |
---|
| 968 | continue; |
---|
[38ffb7] | 969 | iter= factors; |
---|
[11bf82] | 970 | if (beenInThres) |
---|
[7bf145] | 971 | { |
---|
[11bf82] | 972 | int count= 1; |
---|
| 973 | while (count < i) |
---|
| 974 | { |
---|
| 975 | count++; |
---|
| 976 | iter++; |
---|
| 977 | } |
---|
| 978 | buf= iter.getItem(); |
---|
[7bf145] | 979 | } |
---|
[11bf82] | 980 | else |
---|
[806c18] | 981 | { |
---|
[11bf82] | 982 | buf= 1; |
---|
| 983 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 984 | { |
---|
| 985 | if (!IsZero (N (j,i))) |
---|
| 986 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 987 | } |
---|
| 988 | } |
---|
| 989 | buf *= LC (F, x); |
---|
| 990 | buf= mod (buf, yToL); |
---|
| 991 | buf /= content (buf, x); |
---|
[21b8f4c] | 992 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 993 | { |
---|
| 994 | factorsFoundIndex[i - 1]= 1; |
---|
| 995 | factorsFound++; |
---|
[21b8f4c] | 996 | F= quot; |
---|
[11bf82] | 997 | F /= Lc (F); |
---|
| 998 | reconstructedFactors.append (buf); |
---|
| 999 | } |
---|
| 1000 | if (degree (F) <= 0) |
---|
| 1001 | return; |
---|
| 1002 | if (factorsFound + 1 == N.NumCols()) |
---|
| 1003 | { |
---|
| 1004 | reconstructedFactors.append (F); |
---|
| 1005 | return; |
---|
[7bf145] | 1006 | } |
---|
| 1007 | } |
---|
[11bf82] | 1008 | } |
---|
[7bf145] | 1009 | |
---|
[11bf82] | 1010 | void |
---|
| 1011 | reconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const CFList& |
---|
| 1012 | factors, const int liftBound, int& factorsFound, int*& |
---|
| 1013 | factorsFoundIndex, mat_zz_p& N, bool beenInThres |
---|
| 1014 | ) |
---|
| 1015 | { |
---|
| 1016 | Variable y= Variable (2); |
---|
[c1b9927] | 1017 | Variable x= Variable (1); |
---|
[38ffb7] | 1018 | CanonicalForm quot, buf; |
---|
[11bf82] | 1019 | CanonicalForm yToL= power (y, liftBound); |
---|
[38ffb7] | 1020 | CFListIterator iter; |
---|
[11bf82] | 1021 | for (long i= 1; i <= N.NumCols(); i++) |
---|
[7bf145] | 1022 | { |
---|
[11bf82] | 1023 | if (factorsFoundIndex [i - 1] == 1) |
---|
| 1024 | continue; |
---|
[38ffb7] | 1025 | iter= factors; |
---|
[11bf82] | 1026 | if (beenInThres) |
---|
[7bf145] | 1027 | { |
---|
[11bf82] | 1028 | int count= 1; |
---|
| 1029 | while (count < i) |
---|
| 1030 | { |
---|
| 1031 | count++; |
---|
| 1032 | iter++; |
---|
| 1033 | } |
---|
| 1034 | buf= iter.getItem(); |
---|
[7bf145] | 1035 | } |
---|
[11bf82] | 1036 | else |
---|
[7bf145] | 1037 | { |
---|
[11bf82] | 1038 | buf= 1; |
---|
| 1039 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
[806c18] | 1040 | { |
---|
[11bf82] | 1041 | if (!IsZero (N (j,i))) |
---|
| 1042 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
[7bf145] | 1043 | } |
---|
| 1044 | } |
---|
[11bf82] | 1045 | buf *= LC (F, x); |
---|
| 1046 | buf= mod (buf, yToL); |
---|
| 1047 | buf /= content (buf, x); |
---|
[21b8f4c] | 1048 | if (fdivides (buf, F, quot)) |
---|
[7bf145] | 1049 | { |
---|
[11bf82] | 1050 | factorsFoundIndex[i - 1]= 1; |
---|
| 1051 | factorsFound++; |
---|
[21b8f4c] | 1052 | F= quot; |
---|
[11bf82] | 1053 | F /= Lc (F); |
---|
| 1054 | reconstructedFactors.append (buf); |
---|
[7bf145] | 1055 | } |
---|
[11bf82] | 1056 | if (degree (F) <= 0) |
---|
| 1057 | return; |
---|
| 1058 | if (factorsFound + 1 == N.NumCols()) |
---|
| 1059 | { |
---|
| 1060 | reconstructedFactors.append (F); |
---|
| 1061 | return; |
---|
| 1062 | } |
---|
| 1063 | } |
---|
| 1064 | } |
---|
[7bf145] | 1065 | |
---|
[11bf82] | 1066 | CFList |
---|
| 1067 | reconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, int |
---|
| 1068 | precision, const mat_zz_pE& N |
---|
| 1069 | ) |
---|
| 1070 | { |
---|
| 1071 | Variable y= Variable (2); |
---|
| 1072 | Variable x= Variable (1); |
---|
| 1073 | CanonicalForm F= G; |
---|
| 1074 | CanonicalForm yToL= power (y, precision); |
---|
[38ffb7] | 1075 | CanonicalForm quot, buf; |
---|
| 1076 | CFList result, factorsConsidered; |
---|
[11bf82] | 1077 | CFList bufFactors= factors; |
---|
[38ffb7] | 1078 | CFListIterator iter; |
---|
[11bf82] | 1079 | for (long i= 1; i <= N.NumCols(); i++) |
---|
| 1080 | { |
---|
| 1081 | if (zeroOneVecs [i - 1] == 0) |
---|
| 1082 | continue; |
---|
[38ffb7] | 1083 | iter= factors; |
---|
| 1084 | buf= 1; |
---|
[11bf82] | 1085 | factorsConsidered= CFList(); |
---|
| 1086 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 1087 | { |
---|
| 1088 | if (!IsZero (N (j,i))) |
---|
| 1089 | { |
---|
| 1090 | factorsConsidered.append (iter.getItem()); |
---|
| 1091 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 1092 | } |
---|
| 1093 | } |
---|
| 1094 | buf *= LC (F, x); |
---|
| 1095 | buf= mod (buf, yToL); |
---|
| 1096 | buf /= content (buf, x); |
---|
[21b8f4c] | 1097 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 1098 | { |
---|
[21b8f4c] | 1099 | F= quot; |
---|
[11bf82] | 1100 | F /= Lc (F); |
---|
| 1101 | result.append (buf); |
---|
| 1102 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 1103 | } |
---|
| 1104 | if (degree (F) <= 0) |
---|
| 1105 | { |
---|
| 1106 | G= F; |
---|
| 1107 | factors= bufFactors; |
---|
| 1108 | return result; |
---|
| 1109 | } |
---|
| 1110 | } |
---|
| 1111 | G= F; |
---|
| 1112 | factors= bufFactors; |
---|
| 1113 | return result; |
---|
| 1114 | } |
---|
| 1115 | |
---|
| 1116 | CFList |
---|
| 1117 | monicReconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, |
---|
| 1118 | int precision, const mat_zz_pE& N |
---|
| 1119 | ) |
---|
| 1120 | { |
---|
| 1121 | Variable y= Variable (2); |
---|
| 1122 | Variable x= Variable (1); |
---|
| 1123 | CanonicalForm F= G; |
---|
| 1124 | CanonicalForm yToL= power (y, precision); |
---|
[38ffb7] | 1125 | CanonicalForm quot, buf, buf2; |
---|
[11bf82] | 1126 | CFList result; |
---|
| 1127 | CFList bufFactors= factors; |
---|
| 1128 | CFList factorsConsidered; |
---|
[38ffb7] | 1129 | CFListIterator iter; |
---|
[11bf82] | 1130 | for (long i= 1; i <= N.NumCols(); i++) |
---|
| 1131 | { |
---|
| 1132 | if (zeroOneVecs [i - 1] == 0) |
---|
| 1133 | continue; |
---|
[38ffb7] | 1134 | iter= factors; |
---|
| 1135 | buf= 1; |
---|
[11bf82] | 1136 | factorsConsidered= CFList(); |
---|
| 1137 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 1138 | { |
---|
| 1139 | if (!IsZero (N (j,i))) |
---|
| 1140 | { |
---|
| 1141 | factorsConsidered.append (iter.getItem()); |
---|
| 1142 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 1143 | } |
---|
| 1144 | } |
---|
[38ffb7] | 1145 | buf2= buf; |
---|
[11bf82] | 1146 | buf *= LC (F, x); |
---|
| 1147 | buf= mod (buf, yToL); |
---|
| 1148 | buf /= content (buf, x); |
---|
[21b8f4c] | 1149 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 1150 | { |
---|
[21b8f4c] | 1151 | F= quot; |
---|
[11bf82] | 1152 | F /= Lc (F); |
---|
| 1153 | result.append (buf2); |
---|
| 1154 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 1155 | } |
---|
| 1156 | if (degree (F) <= 0) |
---|
| 1157 | { |
---|
| 1158 | G= F; |
---|
| 1159 | factors= bufFactors; |
---|
| 1160 | return result; |
---|
| 1161 | } |
---|
| 1162 | } |
---|
| 1163 | G= F; |
---|
| 1164 | factors= bufFactors; |
---|
| 1165 | return result; |
---|
| 1166 | } |
---|
| 1167 | |
---|
| 1168 | CFList |
---|
| 1169 | extReconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, int |
---|
| 1170 | precision, const mat_zz_p& N, const ExtensionInfo& info, |
---|
| 1171 | const CanonicalForm& evaluation |
---|
| 1172 | ) |
---|
| 1173 | { |
---|
| 1174 | Variable y= Variable (2); |
---|
| 1175 | Variable x= Variable (1); |
---|
| 1176 | Variable alpha= info.getAlpha(); |
---|
| 1177 | Variable beta= info.getBeta(); |
---|
| 1178 | int k= info.getGFDegree(); |
---|
| 1179 | CanonicalForm gamma= info.getGamma(); |
---|
| 1180 | CanonicalForm delta= info.getDelta(); |
---|
| 1181 | CanonicalForm F= G; |
---|
| 1182 | CanonicalForm yToL= power (y, precision); |
---|
| 1183 | CFList result; |
---|
| 1184 | CFList bufFactors= factors; |
---|
| 1185 | CFList factorsConsidered; |
---|
[38ffb7] | 1186 | CanonicalForm buf2, quot, buf; |
---|
| 1187 | CFListIterator iter; |
---|
[11bf82] | 1188 | for (long i= 1; i <= N.NumCols(); i++) |
---|
| 1189 | { |
---|
| 1190 | if (zeroOneVecs [i - 1] == 0) |
---|
| 1191 | continue; |
---|
[38ffb7] | 1192 | iter= factors; |
---|
| 1193 | buf= 1; |
---|
[11bf82] | 1194 | factorsConsidered= CFList(); |
---|
| 1195 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 1196 | { |
---|
| 1197 | if (!IsZero (N (j,i))) |
---|
| 1198 | { |
---|
| 1199 | factorsConsidered.append (iter.getItem()); |
---|
| 1200 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 1201 | } |
---|
| 1202 | } |
---|
| 1203 | buf *= LC (F, x); |
---|
| 1204 | buf= mod (buf, yToL); |
---|
| 1205 | buf /= content (buf, x); |
---|
| 1206 | buf2= buf (y-evaluation, y); |
---|
| 1207 | if (!k && beta == Variable (1)) |
---|
| 1208 | { |
---|
| 1209 | if (degree (buf2, alpha) < 1) |
---|
| 1210 | { |
---|
[21b8f4c] | 1211 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 1212 | { |
---|
[21b8f4c] | 1213 | F= quot; |
---|
[11bf82] | 1214 | F /= Lc (F); |
---|
| 1215 | result.append (buf2); |
---|
| 1216 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 1217 | } |
---|
| 1218 | } |
---|
| 1219 | } |
---|
| 1220 | else |
---|
| 1221 | { |
---|
| 1222 | CFList source, dest; |
---|
[c1b9927] | 1223 | |
---|
[11bf82] | 1224 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
| 1225 | { |
---|
[21b8f4c] | 1226 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 1227 | { |
---|
[21b8f4c] | 1228 | F= quot; |
---|
[11bf82] | 1229 | F /= Lc (F); |
---|
| 1230 | result.append (buf2); |
---|
| 1231 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 1232 | } |
---|
| 1233 | } |
---|
| 1234 | } |
---|
| 1235 | if (degree (F) <= 0) |
---|
| 1236 | { |
---|
| 1237 | G= F; |
---|
| 1238 | factors= bufFactors; |
---|
| 1239 | return result; |
---|
| 1240 | } |
---|
| 1241 | } |
---|
| 1242 | G= F; |
---|
| 1243 | factors= bufFactors; |
---|
| 1244 | return result; |
---|
| 1245 | } |
---|
| 1246 | |
---|
| 1247 | CFList |
---|
| 1248 | reconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, |
---|
| 1249 | int precision, const mat_zz_p& N) |
---|
| 1250 | { |
---|
| 1251 | Variable y= Variable (2); |
---|
| 1252 | Variable x= Variable (1); |
---|
| 1253 | CanonicalForm F= G; |
---|
| 1254 | CanonicalForm yToL= power (y, precision); |
---|
[38ffb7] | 1255 | CanonicalForm quot, buf; |
---|
[11bf82] | 1256 | CFList result; |
---|
| 1257 | CFList bufFactors= factors; |
---|
| 1258 | CFList factorsConsidered; |
---|
[38ffb7] | 1259 | CFListIterator iter; |
---|
[11bf82] | 1260 | for (long i= 1; i <= N.NumCols(); i++) |
---|
| 1261 | { |
---|
| 1262 | if (zeroOneVecs [i - 1] == 0) |
---|
| 1263 | continue; |
---|
[38ffb7] | 1264 | iter= factors; |
---|
| 1265 | buf= 1; |
---|
[11bf82] | 1266 | factorsConsidered= CFList(); |
---|
| 1267 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 1268 | { |
---|
| 1269 | if (!IsZero (N (j,i))) |
---|
| 1270 | { |
---|
| 1271 | factorsConsidered.append (iter.getItem()); |
---|
| 1272 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 1273 | } |
---|
| 1274 | } |
---|
| 1275 | buf *= LC (F, x); |
---|
| 1276 | buf= mod (buf, yToL); |
---|
| 1277 | buf /= content (buf, x); |
---|
[21b8f4c] | 1278 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 1279 | { |
---|
[21b8f4c] | 1280 | F= quot; |
---|
[11bf82] | 1281 | F /= Lc (F); |
---|
| 1282 | result.append (buf); |
---|
| 1283 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 1284 | } |
---|
| 1285 | if (degree (F) <= 0) |
---|
| 1286 | { |
---|
| 1287 | G= F; |
---|
| 1288 | factors= bufFactors; |
---|
| 1289 | return result; |
---|
| 1290 | } |
---|
| 1291 | } |
---|
| 1292 | G= F; |
---|
| 1293 | factors= bufFactors; |
---|
| 1294 | return result; |
---|
| 1295 | } |
---|
| 1296 | |
---|
| 1297 | void |
---|
[c1b9927] | 1298 | extReconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const |
---|
[11bf82] | 1299 | CFList& factors, const int liftBound, int& factorsFound, |
---|
| 1300 | int*& factorsFoundIndex, mat_zz_p& N, bool beenInThres, |
---|
| 1301 | const ExtensionInfo& info, const CanonicalForm& evaluation |
---|
| 1302 | ) |
---|
| 1303 | { |
---|
| 1304 | Variable y= Variable (2); |
---|
| 1305 | Variable x= Variable (1); |
---|
| 1306 | Variable alpha= info.getAlpha(); |
---|
| 1307 | Variable beta= info.getBeta(); |
---|
| 1308 | int k= info.getGFDegree(); |
---|
| 1309 | CanonicalForm gamma= info.getGamma(); |
---|
| 1310 | CanonicalForm delta= info.getDelta(); |
---|
| 1311 | CanonicalForm yToL= power (y, liftBound); |
---|
[38ffb7] | 1312 | CanonicalForm quot, buf, buf2; |
---|
[11bf82] | 1313 | CFList source, dest; |
---|
[38ffb7] | 1314 | CFListIterator iter; |
---|
[11bf82] | 1315 | for (long i= 1; i <= N.NumCols(); i++) |
---|
| 1316 | { |
---|
| 1317 | if (factorsFoundIndex [i - 1] == 1) |
---|
| 1318 | continue; |
---|
[38ffb7] | 1319 | iter= factors; |
---|
[11bf82] | 1320 | if (beenInThres) |
---|
| 1321 | { |
---|
| 1322 | int count= 1; |
---|
| 1323 | while (count < i) |
---|
| 1324 | { |
---|
| 1325 | count++; |
---|
| 1326 | iter++; |
---|
| 1327 | } |
---|
| 1328 | buf= iter.getItem(); |
---|
| 1329 | } |
---|
| 1330 | else |
---|
| 1331 | { |
---|
| 1332 | buf= 1; |
---|
| 1333 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 1334 | { |
---|
| 1335 | if (!IsZero (N (j,i))) |
---|
| 1336 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 1337 | } |
---|
| 1338 | } |
---|
| 1339 | buf *= LC (F, x); |
---|
| 1340 | buf= mod (buf, yToL); |
---|
| 1341 | buf /= content (buf, x); |
---|
| 1342 | buf2= buf (y - evaluation, y); |
---|
| 1343 | if (!k && beta == Variable (1)) |
---|
| 1344 | { |
---|
| 1345 | if (degree (buf2, alpha) < 1) |
---|
| 1346 | { |
---|
[21b8f4c] | 1347 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 1348 | { |
---|
| 1349 | factorsFoundIndex[i - 1]= 1; |
---|
| 1350 | factorsFound++; |
---|
[21b8f4c] | 1351 | F= quot; |
---|
[11bf82] | 1352 | F /= Lc (F); |
---|
| 1353 | buf2= mapDown (buf2, info, source, dest); |
---|
| 1354 | reconstructedFactors.append (buf2); |
---|
| 1355 | } |
---|
| 1356 | } |
---|
| 1357 | } |
---|
| 1358 | else |
---|
| 1359 | { |
---|
| 1360 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
| 1361 | { |
---|
[21b8f4c] | 1362 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 1363 | { |
---|
| 1364 | factorsFoundIndex[i - 1]= 1; |
---|
| 1365 | factorsFound++; |
---|
[21b8f4c] | 1366 | F= quot; |
---|
[11bf82] | 1367 | F /= Lc (F); |
---|
| 1368 | buf2= mapDown (buf2, info, source, dest); |
---|
| 1369 | reconstructedFactors.append (buf2); |
---|
| 1370 | } |
---|
| 1371 | } |
---|
| 1372 | } |
---|
| 1373 | if (degree (F) <= 0) |
---|
| 1374 | return; |
---|
| 1375 | if (factorsFound + 1 == N.NumCols()) |
---|
| 1376 | { |
---|
| 1377 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 1378 | tmp= mapDown (tmp, info, source, dest); |
---|
| 1379 | reconstructedFactors.append (tmp); |
---|
| 1380 | return; |
---|
| 1381 | } |
---|
| 1382 | } |
---|
| 1383 | } |
---|
| 1384 | |
---|
| 1385 | //over Fp |
---|
| 1386 | int |
---|
| 1387 | liftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, int |
---|
| 1388 | start, int liftBound, int minBound, CFList& factors, |
---|
| 1389 | mat_zz_p& NTLN, CFList& diophant, CFMatrix& M, CFArray& |
---|
| 1390 | Pi, CFArray& bufQ, bool& irreducible |
---|
| 1391 | ) |
---|
| 1392 | { |
---|
| 1393 | CanonicalForm LCF= LC (F, 1); |
---|
| 1394 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
| 1395 | bool wasInBounds= false; |
---|
| 1396 | bool hitBound= false; |
---|
| 1397 | int l= (minBound+1)*2; |
---|
| 1398 | int stepSize= 2; |
---|
| 1399 | int oldL= l/2; |
---|
| 1400 | bool reduced= false; |
---|
[38ffb7] | 1401 | mat_zz_p NTLK, *NTLC; |
---|
| 1402 | CFMatrix C; |
---|
| 1403 | CFArray buf; |
---|
| 1404 | CFListIterator j; |
---|
[11bf82] | 1405 | while (l <= liftBound) |
---|
| 1406 | { |
---|
| 1407 | if (start) |
---|
| 1408 | { |
---|
| 1409 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
| 1410 | start= 0; |
---|
| 1411 | } |
---|
| 1412 | else |
---|
| 1413 | { |
---|
| 1414 | if (wasInBounds) |
---|
| 1415 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
| 1416 | else |
---|
| 1417 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 1418 | } |
---|
| 1419 | |
---|
| 1420 | factors.insert (LCF); |
---|
[38ffb7] | 1421 | j= factors; |
---|
[11bf82] | 1422 | j++; |
---|
| 1423 | |
---|
| 1424 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
| 1425 | { |
---|
| 1426 | if (!wasInBounds) |
---|
| 1427 | A[i]= logarithmicDerivative (F, j.getItem(), l, bufQ[i]); |
---|
| 1428 | else |
---|
| 1429 | A[i]= logarithmicDerivative (F, j.getItem(), l, oldL, bufQ[i], bufQ[i]); |
---|
| 1430 | } |
---|
| 1431 | |
---|
| 1432 | for (int i= 0; i < sizeBounds; i++) |
---|
| 1433 | { |
---|
| 1434 | if (bounds [i] + 1 <= l/2) |
---|
| 1435 | { |
---|
| 1436 | wasInBounds= true; |
---|
| 1437 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 1438 | C= CFMatrix (l - k, factors.length() - 1); |
---|
[11bf82] | 1439 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
| 1440 | { |
---|
| 1441 | if (A[ii].size() - 1 >= i) |
---|
| 1442 | buf= getCoeffs (A[ii] [i], k); |
---|
| 1443 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 1444 | } |
---|
[38ffb7] | 1445 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 1446 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 1447 | transpose (NTLK, NTLK); |
---|
| 1448 | kernel (NTLK, NTLK); |
---|
| 1449 | transpose (NTLK, NTLK); |
---|
| 1450 | NTLN *= NTLK; |
---|
| 1451 | |
---|
| 1452 | if (NTLN.NumCols() == 1) |
---|
| 1453 | { |
---|
| 1454 | irreducible= true; |
---|
| 1455 | break; |
---|
| 1456 | } |
---|
[3426de2] | 1457 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
[11bf82] | 1458 | { |
---|
| 1459 | reduced= true; |
---|
| 1460 | break; |
---|
| 1461 | } |
---|
| 1462 | } |
---|
| 1463 | } |
---|
| 1464 | |
---|
| 1465 | if (irreducible) |
---|
| 1466 | break; |
---|
| 1467 | if (reduced) |
---|
| 1468 | break; |
---|
| 1469 | oldL= l; |
---|
| 1470 | l += stepSize; |
---|
| 1471 | stepSize *= 2; |
---|
| 1472 | if (l > liftBound) |
---|
| 1473 | { |
---|
| 1474 | if (!hitBound) |
---|
| 1475 | { |
---|
| 1476 | l= liftBound; |
---|
| 1477 | hitBound= true; |
---|
| 1478 | } |
---|
| 1479 | else |
---|
| 1480 | break; |
---|
| 1481 | } |
---|
| 1482 | } |
---|
| 1483 | delete [] A; |
---|
| 1484 | return l; |
---|
| 1485 | } |
---|
| 1486 | |
---|
| 1487 | //over field extension |
---|
| 1488 | int |
---|
| 1489 | extLiftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
| 1490 | int liftBound, int minBound, int start, CFList& |
---|
| 1491 | factors, mat_zz_p& NTLN, CFList& diophant, |
---|
| 1492 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, bool& |
---|
| 1493 | irreducible, const CanonicalForm& evaluation, const |
---|
| 1494 | ExtensionInfo& info, CFList& source, CFList& dest |
---|
| 1495 | ) |
---|
| 1496 | { |
---|
| 1497 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
| 1498 | CanonicalForm LCF= LC (F, 1); |
---|
| 1499 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
| 1500 | bool wasInBounds= false; |
---|
| 1501 | bool hitBound= false; |
---|
| 1502 | int degMipo; |
---|
| 1503 | Variable alpha; |
---|
| 1504 | alpha= info.getAlpha(); |
---|
| 1505 | degMipo= degree (getMipo (alpha)); |
---|
| 1506 | |
---|
| 1507 | Variable gamma= info.getBeta(); |
---|
| 1508 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
| 1509 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
| 1510 | |
---|
| 1511 | int stepSize= 2; |
---|
| 1512 | int l= ((minBound+1)/degMipo+1)*2; |
---|
| 1513 | l= tmax (l, 2); |
---|
| 1514 | if (start > l) |
---|
| 1515 | l= start; |
---|
[3426de2] | 1516 | int startl= l; |
---|
[11bf82] | 1517 | int oldL= l/2; |
---|
| 1518 | bool reduced= false; |
---|
[38ffb7] | 1519 | Variable y= F.mvar(); |
---|
| 1520 | Variable x= Variable (1); |
---|
| 1521 | CanonicalForm powX, imBasis; |
---|
| 1522 | CFMatrix Mat, C; |
---|
| 1523 | CFArray buf; |
---|
| 1524 | CFIterator iter; |
---|
| 1525 | mat_zz_p* NTLMat, *NTLC, NTLK; |
---|
| 1526 | CFListIterator j; |
---|
[11bf82] | 1527 | while (l <= liftBound) |
---|
| 1528 | { |
---|
| 1529 | if (start) |
---|
| 1530 | { |
---|
| 1531 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
| 1532 | start= 0; |
---|
| 1533 | } |
---|
| 1534 | else |
---|
| 1535 | { |
---|
| 1536 | if (wasInBounds) |
---|
| 1537 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
| 1538 | else |
---|
| 1539 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 1540 | } |
---|
| 1541 | |
---|
| 1542 | factors.insert (LCF); |
---|
| 1543 | |
---|
| 1544 | if (GF) |
---|
| 1545 | setCharacteristic (getCharacteristic()); |
---|
| 1546 | |
---|
[38ffb7] | 1547 | powX= power (y-gamma, l); |
---|
| 1548 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
[11bf82] | 1549 | for (int i= 0; i < l*degMipo; i++) |
---|
| 1550 | { |
---|
[38ffb7] | 1551 | imBasis= mod (power (y, i), powX); |
---|
[11bf82] | 1552 | imBasis= imBasis (power (y, degMipo), y); |
---|
| 1553 | imBasis= imBasis (y, gamma); |
---|
[38ffb7] | 1554 | iter= imBasis; |
---|
[11bf82] | 1555 | for (; iter.hasTerms(); iter++) |
---|
| 1556 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
| 1557 | } |
---|
| 1558 | |
---|
[38ffb7] | 1559 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
[11bf82] | 1560 | *NTLMat= inv (*NTLMat); |
---|
| 1561 | |
---|
| 1562 | if (GF) |
---|
| 1563 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 1564 | |
---|
[38ffb7] | 1565 | j= factors; |
---|
[11bf82] | 1566 | j++; |
---|
| 1567 | |
---|
| 1568 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
| 1569 | { |
---|
| 1570 | if (!wasInBounds) |
---|
| 1571 | A[i]= logarithmicDerivative (F, j.getItem(), l, bufQ[i]); |
---|
| 1572 | else |
---|
| 1573 | A[i]= logarithmicDerivative (F, j.getItem(), l, oldL, bufQ[i], bufQ[i]); |
---|
| 1574 | } |
---|
| 1575 | |
---|
| 1576 | for (int i= 0; i < sizeBounds; i++) |
---|
| 1577 | { |
---|
| 1578 | if (bounds [i] + 1 <= (l/2)*degMipo) |
---|
| 1579 | { |
---|
| 1580 | wasInBounds= true; |
---|
| 1581 | int k= tmin (bounds [i] + 1, (l/2)*degMipo); |
---|
[38ffb7] | 1582 | C= CFMatrix (l*degMipo - k, factors.length() - 1); |
---|
[11bf82] | 1583 | |
---|
| 1584 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
| 1585 | { |
---|
| 1586 | if (A[ii].size() - 1 >= i) |
---|
| 1587 | { |
---|
| 1588 | if (GF) |
---|
| 1589 | { |
---|
| 1590 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 1591 | setCharacteristic (getCharacteristic()); |
---|
| 1592 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
| 1593 | if (alpha != gamma) |
---|
| 1594 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 1595 | gamma, source, dest |
---|
| 1596 | ); |
---|
| 1597 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
| 1598 | } |
---|
| 1599 | else |
---|
| 1600 | { |
---|
| 1601 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 1602 | if (alpha != gamma) |
---|
| 1603 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 1604 | gamma, source, dest |
---|
| 1605 | ); |
---|
| 1606 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
| 1607 | } |
---|
| 1608 | } |
---|
| 1609 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 1610 | if (GF) |
---|
| 1611 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 1612 | } |
---|
| 1613 | |
---|
| 1614 | if (GF) |
---|
| 1615 | setCharacteristic(getCharacteristic()); |
---|
| 1616 | |
---|
[38ffb7] | 1617 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 1618 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 1619 | transpose (NTLK, NTLK); |
---|
| 1620 | kernel (NTLK, NTLK); |
---|
| 1621 | transpose (NTLK, NTLK); |
---|
| 1622 | NTLN *= NTLK; |
---|
| 1623 | |
---|
| 1624 | if (GF) |
---|
| 1625 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 1626 | |
---|
| 1627 | if (NTLN.NumCols() == 1) |
---|
| 1628 | { |
---|
| 1629 | irreducible= true; |
---|
| 1630 | break; |
---|
| 1631 | } |
---|
[3426de2] | 1632 | if (isReduced (NTLN) && l > startl) |
---|
[11bf82] | 1633 | { |
---|
| 1634 | reduced= true; |
---|
| 1635 | break; |
---|
| 1636 | } |
---|
| 1637 | } |
---|
| 1638 | } |
---|
| 1639 | |
---|
| 1640 | if (NTLN.NumCols() == 1) |
---|
| 1641 | { |
---|
| 1642 | irreducible= true; |
---|
| 1643 | break; |
---|
| 1644 | } |
---|
| 1645 | if (reduced) |
---|
| 1646 | break; |
---|
| 1647 | oldL= l; |
---|
| 1648 | l += stepSize; |
---|
| 1649 | stepSize *= 2; |
---|
| 1650 | if (l > liftBound) |
---|
| 1651 | { |
---|
| 1652 | if (!hitBound) |
---|
| 1653 | { |
---|
| 1654 | l= liftBound; |
---|
| 1655 | hitBound= true; |
---|
| 1656 | } |
---|
| 1657 | else |
---|
| 1658 | break; |
---|
| 1659 | } |
---|
| 1660 | } |
---|
| 1661 | delete [] A; |
---|
| 1662 | return l; |
---|
| 1663 | } |
---|
| 1664 | |
---|
| 1665 | // over Fq |
---|
| 1666 | int |
---|
| 1667 | liftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
| 1668 | int start, int liftBound, int minBound, CFList& factors, |
---|
| 1669 | mat_zz_pE& NTLN, CFList& diophant, CFMatrix& M, CFArray& |
---|
| 1670 | Pi, CFArray& bufQ, bool& irreducible |
---|
| 1671 | ) |
---|
| 1672 | { |
---|
| 1673 | CanonicalForm LCF= LC (F, 1); |
---|
| 1674 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
| 1675 | bool wasInBounds= false; |
---|
| 1676 | bool hitBound= false; |
---|
| 1677 | int l= (minBound+1)*2; |
---|
| 1678 | int stepSize= 2; |
---|
| 1679 | int oldL= l/2; |
---|
| 1680 | bool reduced= false; |
---|
[38ffb7] | 1681 | CFListIterator j; |
---|
| 1682 | mat_zz_pE* NTLC, NTLK; |
---|
| 1683 | CFArray buf; |
---|
| 1684 | CFMatrix C; |
---|
[11bf82] | 1685 | while (l <= liftBound) |
---|
| 1686 | { |
---|
| 1687 | if (start) |
---|
| 1688 | { |
---|
| 1689 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
| 1690 | start= 0; |
---|
| 1691 | } |
---|
| 1692 | else |
---|
| 1693 | { |
---|
| 1694 | if (wasInBounds) |
---|
| 1695 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
| 1696 | else |
---|
| 1697 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 1698 | } |
---|
| 1699 | |
---|
| 1700 | factors.insert (LCF); |
---|
[38ffb7] | 1701 | j= factors; |
---|
[11bf82] | 1702 | j++; |
---|
| 1703 | |
---|
| 1704 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
| 1705 | { |
---|
| 1706 | if (l == (minBound+1)*2) |
---|
| 1707 | { |
---|
| 1708 | A[i]= logarithmicDerivative (F, j.getItem(), l, bufQ[i]); |
---|
| 1709 | } |
---|
| 1710 | else |
---|
| 1711 | { |
---|
| 1712 | A[i]= logarithmicDerivative (F, j.getItem(), l, oldL, bufQ[i], |
---|
| 1713 | bufQ[i] |
---|
| 1714 | ); |
---|
| 1715 | } |
---|
| 1716 | } |
---|
| 1717 | |
---|
| 1718 | for (int i= 0; i < sizeBounds; i++) |
---|
| 1719 | { |
---|
| 1720 | if (bounds [i] + 1 <= l/2) |
---|
| 1721 | { |
---|
| 1722 | wasInBounds= true; |
---|
| 1723 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 1724 | C= CFMatrix (l - k, factors.length() - 1); |
---|
[11bf82] | 1725 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
| 1726 | { |
---|
[38ffb7] | 1727 | |
---|
[11bf82] | 1728 | if (A[ii].size() - 1 >= i) |
---|
| 1729 | buf= getCoeffs (A[ii] [i], k); |
---|
| 1730 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 1731 | } |
---|
| 1732 | |
---|
[38ffb7] | 1733 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
| 1734 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 1735 | transpose (NTLK, NTLK); |
---|
| 1736 | kernel (NTLK, NTLK); |
---|
| 1737 | transpose (NTLK, NTLK); |
---|
| 1738 | NTLN *= NTLK; |
---|
| 1739 | |
---|
| 1740 | if (NTLN.NumCols() == 1) |
---|
| 1741 | { |
---|
| 1742 | irreducible= true; |
---|
| 1743 | break; |
---|
| 1744 | } |
---|
[3426de2] | 1745 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
[11bf82] | 1746 | { |
---|
| 1747 | reduced= true; |
---|
| 1748 | break; |
---|
| 1749 | } |
---|
| 1750 | } |
---|
| 1751 | } |
---|
| 1752 | |
---|
| 1753 | if (NTLN.NumCols() == 1) |
---|
| 1754 | { |
---|
| 1755 | irreducible= true; |
---|
| 1756 | break; |
---|
| 1757 | } |
---|
| 1758 | if (reduced) |
---|
| 1759 | break; |
---|
| 1760 | oldL= l; |
---|
| 1761 | l += stepSize; |
---|
| 1762 | stepSize *= 2; |
---|
| 1763 | if (l > liftBound) |
---|
| 1764 | { |
---|
| 1765 | if (!hitBound) |
---|
| 1766 | { |
---|
| 1767 | l= liftBound; |
---|
| 1768 | hitBound= true; |
---|
| 1769 | } |
---|
| 1770 | else |
---|
| 1771 | break; |
---|
| 1772 | } |
---|
| 1773 | } |
---|
| 1774 | delete [] A; |
---|
| 1775 | return l; |
---|
| 1776 | } |
---|
| 1777 | |
---|
| 1778 | int |
---|
| 1779 | liftAndComputeLatticeFq2Fp (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
| 1780 | int start, int liftBound, int minBound, CFList& |
---|
| 1781 | factors, mat_zz_p& NTLN, CFList& diophant, CFMatrix& |
---|
| 1782 | M, CFArray& Pi, CFArray& bufQ, bool& irreducible, |
---|
| 1783 | const Variable& alpha |
---|
| 1784 | ) |
---|
| 1785 | { |
---|
| 1786 | CanonicalForm LCF= LC (F, 1); |
---|
| 1787 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
| 1788 | bool wasInBounds= false; |
---|
| 1789 | int l= (minBound+1)*2; |
---|
| 1790 | int oldL= l/2; |
---|
| 1791 | int stepSize= 2; |
---|
| 1792 | bool hitBound= false; |
---|
| 1793 | int extensionDeg= degree (getMipo (alpha)); |
---|
| 1794 | bool reduced= false; |
---|
[38ffb7] | 1795 | CFListIterator j; |
---|
| 1796 | CFMatrix C; |
---|
| 1797 | CFArray buf; |
---|
| 1798 | mat_zz_p* NTLC, NTLK; |
---|
[11bf82] | 1799 | while (l <= liftBound) |
---|
| 1800 | { |
---|
| 1801 | if (start) |
---|
| 1802 | { |
---|
| 1803 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
| 1804 | start= 0; |
---|
| 1805 | } |
---|
| 1806 | else |
---|
| 1807 | { |
---|
| 1808 | if (wasInBounds) |
---|
| 1809 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
| 1810 | else |
---|
| 1811 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 1812 | } |
---|
| 1813 | |
---|
| 1814 | factors.insert (LCF); |
---|
[38ffb7] | 1815 | j= factors; |
---|
[11bf82] | 1816 | j++; |
---|
| 1817 | |
---|
| 1818 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
| 1819 | { |
---|
| 1820 | if (l == (minBound+1)*2) |
---|
| 1821 | { |
---|
| 1822 | A[i]= logarithmicDerivative (F, j.getItem(), l, bufQ[i]); |
---|
| 1823 | } |
---|
| 1824 | else |
---|
| 1825 | { |
---|
| 1826 | A[i]= logarithmicDerivative (F, j.getItem(), l, oldL, bufQ[i], |
---|
| 1827 | bufQ[i] |
---|
| 1828 | ); |
---|
| 1829 | } |
---|
| 1830 | } |
---|
| 1831 | |
---|
| 1832 | for (int i= 0; i < sizeBounds; i++) |
---|
| 1833 | { |
---|
| 1834 | if (bounds [i] + 1 <= l/2) |
---|
| 1835 | { |
---|
| 1836 | wasInBounds= true; |
---|
| 1837 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 1838 | C= CFMatrix ((l - k)*extensionDeg, factors.length() - 1); |
---|
[11bf82] | 1839 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
| 1840 | { |
---|
| 1841 | if (A[ii].size() - 1 >= i) |
---|
| 1842 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
| 1843 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 1844 | } |
---|
| 1845 | |
---|
[38ffb7] | 1846 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 1847 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 1848 | transpose (NTLK, NTLK); |
---|
| 1849 | kernel (NTLK, NTLK); |
---|
| 1850 | transpose (NTLK, NTLK); |
---|
| 1851 | NTLN *= NTLK; |
---|
| 1852 | |
---|
| 1853 | if (NTLN.NumCols() == 1) |
---|
| 1854 | { |
---|
| 1855 | irreducible= true; |
---|
| 1856 | break; |
---|
| 1857 | } |
---|
[3426de2] | 1858 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
[11bf82] | 1859 | { |
---|
| 1860 | reduced= true; |
---|
| 1861 | break; |
---|
| 1862 | } |
---|
| 1863 | } |
---|
| 1864 | } |
---|
| 1865 | |
---|
| 1866 | if (NTLN.NumCols() == 1) |
---|
| 1867 | { |
---|
| 1868 | irreducible= true; |
---|
| 1869 | break; |
---|
| 1870 | } |
---|
| 1871 | if (reduced) |
---|
| 1872 | break; |
---|
| 1873 | oldL= l; |
---|
| 1874 | l += stepSize; |
---|
| 1875 | stepSize *= 2; |
---|
| 1876 | if (l > liftBound) |
---|
| 1877 | { |
---|
| 1878 | if (!hitBound) |
---|
| 1879 | { |
---|
| 1880 | l= liftBound; |
---|
| 1881 | hitBound= true; |
---|
| 1882 | } |
---|
| 1883 | else |
---|
| 1884 | break; |
---|
| 1885 | } |
---|
| 1886 | } |
---|
| 1887 | delete [] A; |
---|
| 1888 | return l; |
---|
| 1889 | } |
---|
| 1890 | |
---|
| 1891 | CFList |
---|
| 1892 | increasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
| 1893 | int oldNumCols, int oldL, int precision |
---|
| 1894 | ) |
---|
| 1895 | { |
---|
| 1896 | bool irreducible= false; |
---|
| 1897 | int d; |
---|
| 1898 | int* bounds= computeBounds (F, d); |
---|
| 1899 | CFArray * A= new CFArray [factors.length()]; |
---|
| 1900 | CFArray bufQ= CFArray (factors.length()); |
---|
| 1901 | mat_zz_p NTLN; |
---|
| 1902 | ident (NTLN, factors.length()); |
---|
| 1903 | int minBound= bounds[0]; |
---|
| 1904 | for (int i= 1; i < d; i++) |
---|
| 1905 | { |
---|
| 1906 | if (bounds[i] != 0) |
---|
| 1907 | minBound= tmin (minBound, bounds[i]); |
---|
| 1908 | } |
---|
| 1909 | int l= tmax (2*(minBound + 1), oldL); |
---|
| 1910 | int oldL2= l/2; |
---|
| 1911 | int stepSize= 2; |
---|
| 1912 | bool useOldQs= false; |
---|
| 1913 | bool hitBound= false; |
---|
[38ffb7] | 1914 | CFListIterator j; |
---|
| 1915 | CFMatrix C; |
---|
| 1916 | CFArray buf; |
---|
| 1917 | mat_zz_p* NTLC, NTLK; |
---|
[11bf82] | 1918 | while (l <= precision) |
---|
| 1919 | { |
---|
[38ffb7] | 1920 | j= factors; |
---|
[11bf82] | 1921 | if (useOldQs) |
---|
| 1922 | { |
---|
| 1923 | for (int i= 0; i < factors.length(); i++, j++) |
---|
| 1924 | A[i]= logarithmicDerivative (F, j.getItem(), l, oldL2, bufQ[i], |
---|
| 1925 | bufQ[i] |
---|
| 1926 | ); |
---|
| 1927 | } |
---|
| 1928 | else |
---|
| 1929 | { |
---|
| 1930 | for (int i= 0; i < factors.length(); i++, j++) |
---|
| 1931 | A[i]= logarithmicDerivative (F, j.getItem(), l, bufQ [i]); |
---|
| 1932 | } |
---|
| 1933 | useOldQs= true; |
---|
| 1934 | for (int i= 0; i < d; i++) |
---|
| 1935 | { |
---|
| 1936 | if (bounds [i] + 1 <= l/2) |
---|
| 1937 | { |
---|
| 1938 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 1939 | C= CFMatrix (l - k, factors.length()); |
---|
[11bf82] | 1940 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 1941 | { |
---|
| 1942 | if (A[ii].size() - 1 >= i) |
---|
| 1943 | buf= getCoeffs (A[ii] [i], k); |
---|
| 1944 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 1945 | } |
---|
[38ffb7] | 1946 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 1947 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 1948 | transpose (NTLK, NTLK); |
---|
| 1949 | kernel (NTLK, NTLK); |
---|
| 1950 | transpose (NTLK, NTLK); |
---|
| 1951 | NTLN *= NTLK; |
---|
| 1952 | if (NTLN.NumCols() == 1) |
---|
| 1953 | { |
---|
| 1954 | irreducible= true; |
---|
| 1955 | delete [] A; |
---|
| 1956 | delete [] bounds; |
---|
| 1957 | CanonicalForm G= F; |
---|
| 1958 | F= 1; |
---|
| 1959 | return CFList (G); |
---|
| 1960 | } |
---|
| 1961 | } |
---|
| 1962 | } |
---|
| 1963 | |
---|
| 1964 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
| 1965 | { |
---|
| 1966 | if (isReduced (NTLN)) |
---|
| 1967 | { |
---|
| 1968 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 1969 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 1970 | factorsFoundIndex[i]= 0; |
---|
| 1971 | int factorsFound2= 0; |
---|
| 1972 | CFList result; |
---|
| 1973 | CanonicalForm bufF= F; |
---|
| 1974 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
| 1975 | factorsFoundIndex, NTLN, false |
---|
| 1976 | ); |
---|
[38ffb7] | 1977 | if (result.length() == NTLN.NumCols()) |
---|
[11bf82] | 1978 | { |
---|
| 1979 | delete [] factorsFoundIndex; |
---|
| 1980 | delete [] A; |
---|
| 1981 | delete [] bounds; |
---|
| 1982 | return result; |
---|
| 1983 | } |
---|
| 1984 | delete [] factorsFoundIndex; |
---|
| 1985 | } |
---|
| 1986 | else if (l == precision) |
---|
| 1987 | { |
---|
| 1988 | CanonicalForm bufF= F; |
---|
| 1989 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
| 1990 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN); |
---|
| 1991 | F= bufF; |
---|
| 1992 | delete [] zeroOne; |
---|
| 1993 | delete [] A; |
---|
| 1994 | delete [] bounds; |
---|
| 1995 | return result; |
---|
| 1996 | } |
---|
| 1997 | } |
---|
| 1998 | oldL2= l; |
---|
| 1999 | l += stepSize; |
---|
| 2000 | stepSize *= 2; |
---|
| 2001 | if (l > precision) |
---|
| 2002 | { |
---|
| 2003 | if (!hitBound) |
---|
| 2004 | { |
---|
| 2005 | l= precision; |
---|
| 2006 | hitBound= true; |
---|
| 2007 | } |
---|
| 2008 | else |
---|
| 2009 | break; |
---|
| 2010 | } |
---|
| 2011 | } |
---|
| 2012 | delete [] bounds; |
---|
| 2013 | delete [] A; |
---|
| 2014 | return CFList(); |
---|
| 2015 | } |
---|
| 2016 | |
---|
| 2017 | CFList |
---|
| 2018 | increasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
[0349c20] | 2019 | int oldNumCols, int oldL, const Variable&, |
---|
[11bf82] | 2020 | int precision |
---|
| 2021 | ) |
---|
| 2022 | { |
---|
| 2023 | bool irreducible= false; |
---|
| 2024 | int d; |
---|
| 2025 | int* bounds= computeBounds (F, d); |
---|
| 2026 | CFArray * A= new CFArray [factors.length()]; |
---|
| 2027 | CFArray bufQ= CFArray (factors.length()); |
---|
| 2028 | mat_zz_pE NTLN; |
---|
| 2029 | ident (NTLN, factors.length()); |
---|
| 2030 | int minBound= bounds[0]; |
---|
| 2031 | for (int i= 1; i < d; i++) |
---|
| 2032 | { |
---|
| 2033 | if (bounds[i] != 0) |
---|
| 2034 | minBound= tmin (minBound, bounds[i]); |
---|
| 2035 | } |
---|
| 2036 | int l= tmax (2*(minBound + 1), oldL); |
---|
| 2037 | int oldL2= l/2; |
---|
| 2038 | int stepSize= 2; |
---|
| 2039 | bool useOldQs= false; |
---|
| 2040 | bool hitBound= false; |
---|
[38ffb7] | 2041 | CFListIterator j; |
---|
| 2042 | CFMatrix C; |
---|
| 2043 | mat_zz_pE* NTLC, NTLK; |
---|
| 2044 | CFArray buf; |
---|
[11bf82] | 2045 | while (l <= precision) |
---|
| 2046 | { |
---|
[38ffb7] | 2047 | j= factors; |
---|
[11bf82] | 2048 | if (useOldQs) |
---|
| 2049 | { |
---|
| 2050 | for (int i= 0; i < factors.length(); i++, j++) |
---|
| 2051 | A[i]= logarithmicDerivative (F, j.getItem(), l, oldL2, bufQ[i], |
---|
| 2052 | bufQ[i] |
---|
| 2053 | ); |
---|
| 2054 | } |
---|
| 2055 | else |
---|
| 2056 | { |
---|
| 2057 | for (int i= 0; i < factors.length(); i++, j++) |
---|
| 2058 | A[i]= logarithmicDerivative (F, j.getItem(), l, bufQ [i]); |
---|
| 2059 | } |
---|
| 2060 | useOldQs= true; |
---|
| 2061 | for (int i= 0; i < d; i++) |
---|
| 2062 | { |
---|
| 2063 | if (bounds [i] + 1 <= l/2) |
---|
| 2064 | { |
---|
| 2065 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 2066 | C= CFMatrix (l - k, factors.length()); |
---|
[11bf82] | 2067 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 2068 | { |
---|
| 2069 | if (A[ii].size() - 1 >= i) |
---|
| 2070 | buf= getCoeffs (A[ii] [i], k); |
---|
| 2071 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 2072 | } |
---|
[38ffb7] | 2073 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
| 2074 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 2075 | transpose (NTLK, NTLK); |
---|
| 2076 | kernel (NTLK, NTLK); |
---|
| 2077 | transpose (NTLK, NTLK); |
---|
| 2078 | NTLN *= NTLK; |
---|
| 2079 | if (NTLN.NumCols() == 1) |
---|
| 2080 | { |
---|
| 2081 | irreducible= true; |
---|
| 2082 | delete [] A; |
---|
| 2083 | delete [] bounds; |
---|
| 2084 | return CFList (F); |
---|
| 2085 | } |
---|
| 2086 | } |
---|
| 2087 | } |
---|
| 2088 | |
---|
| 2089 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
| 2090 | { |
---|
| 2091 | if (isReduced (NTLN)) |
---|
| 2092 | { |
---|
| 2093 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 2094 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 2095 | factorsFoundIndex[i]= 0; |
---|
| 2096 | int factorsFound2= 0; |
---|
| 2097 | CFList result; |
---|
| 2098 | CanonicalForm bufF= F; |
---|
| 2099 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
| 2100 | factorsFoundIndex, NTLN, false); |
---|
| 2101 | if (result.length() == NTLN.NumCols()) |
---|
| 2102 | { |
---|
| 2103 | delete [] factorsFoundIndex; |
---|
| 2104 | delete [] A; |
---|
| 2105 | delete [] bounds; |
---|
| 2106 | return result; |
---|
| 2107 | } |
---|
| 2108 | delete [] factorsFoundIndex; |
---|
| 2109 | } |
---|
| 2110 | else if (l == precision) |
---|
| 2111 | { |
---|
| 2112 | CanonicalForm bufF= F; |
---|
| 2113 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
| 2114 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN); |
---|
| 2115 | F= bufF; |
---|
| 2116 | delete [] zeroOne; |
---|
| 2117 | delete [] A; |
---|
| 2118 | delete [] bounds; |
---|
| 2119 | return result; |
---|
| 2120 | } |
---|
| 2121 | } |
---|
| 2122 | oldL2= l; |
---|
| 2123 | l += stepSize; |
---|
| 2124 | stepSize *= 2; |
---|
| 2125 | if (l > precision) |
---|
| 2126 | { |
---|
| 2127 | if (!hitBound) |
---|
| 2128 | { |
---|
| 2129 | l= precision; |
---|
| 2130 | hitBound= true; |
---|
| 2131 | } |
---|
| 2132 | else |
---|
| 2133 | break; |
---|
| 2134 | } |
---|
| 2135 | } |
---|
| 2136 | delete [] bounds; |
---|
| 2137 | delete [] A; |
---|
| 2138 | return CFList(); |
---|
| 2139 | } |
---|
| 2140 | |
---|
| 2141 | //over field extension |
---|
| 2142 | CFList |
---|
| 2143 | extIncreasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
| 2144 | int oldNumCols, int oldL, const CanonicalForm& evaluation, |
---|
| 2145 | const ExtensionInfo& info, CFList& source, CFList& dest, |
---|
| 2146 | int precision |
---|
| 2147 | ) |
---|
| 2148 | { |
---|
| 2149 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
| 2150 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
| 2151 | Variable alpha= info.getAlpha(); |
---|
| 2152 | bool irreducible= false; |
---|
| 2153 | int d; |
---|
| 2154 | int* bounds= computeBounds (F, d); |
---|
| 2155 | |
---|
| 2156 | CFArray * A= new CFArray [factors.length()]; |
---|
| 2157 | CFArray bufQ= CFArray (factors.length()); |
---|
| 2158 | zz_p::init (getCharacteristic()); |
---|
| 2159 | mat_zz_p NTLN; |
---|
| 2160 | ident (NTLN, factors.length()); |
---|
| 2161 | int minBound= bounds[0]; |
---|
| 2162 | for (int i= 1; i < d; i++) |
---|
| 2163 | { |
---|
| 2164 | if (bounds[i] != 0) |
---|
| 2165 | minBound= tmin (minBound, bounds[i]); |
---|
| 2166 | } |
---|
| 2167 | int l= tmax (oldL, 2*((minBound+1)/degMipo+1)); |
---|
| 2168 | int oldL2= l/2; |
---|
| 2169 | int stepSize= 2; |
---|
| 2170 | bool useOldQs= false; |
---|
| 2171 | bool hitBound= false; |
---|
| 2172 | Variable gamma= info.getBeta(); |
---|
| 2173 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
| 2174 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
[38ffb7] | 2175 | CFListIterator j; |
---|
| 2176 | Variable y= F.mvar(); |
---|
| 2177 | CanonicalForm powX, imBasis; |
---|
| 2178 | CFMatrix Mat, C; |
---|
| 2179 | CFIterator iter; |
---|
| 2180 | mat_zz_p* NTLMat,*NTLC, NTLK; |
---|
| 2181 | CFArray buf; |
---|
[11bf82] | 2182 | while (l <= precision) |
---|
| 2183 | { |
---|
[38ffb7] | 2184 | j= factors; |
---|
[11bf82] | 2185 | if (GF) |
---|
| 2186 | setCharacteristic (getCharacteristic()); |
---|
[38ffb7] | 2187 | powX= power (y-gamma, l); |
---|
| 2188 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
[11bf82] | 2189 | for (int i= 0; i < l*degMipo; i++) |
---|
| 2190 | { |
---|
[38ffb7] | 2191 | imBasis= mod (power (y, i), powX); |
---|
[11bf82] | 2192 | imBasis= imBasis (power (y, degMipo), y); |
---|
| 2193 | imBasis= imBasis (y, gamma); |
---|
[38ffb7] | 2194 | iter= imBasis; |
---|
[11bf82] | 2195 | for (; iter.hasTerms(); iter++) |
---|
| 2196 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
| 2197 | } |
---|
| 2198 | |
---|
[38ffb7] | 2199 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
[11bf82] | 2200 | *NTLMat= inv (*NTLMat); |
---|
| 2201 | if (GF) |
---|
| 2202 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 2203 | |
---|
| 2204 | if (useOldQs) |
---|
| 2205 | { |
---|
| 2206 | for (int i= 0; i < factors.length(); i++, j++) |
---|
| 2207 | A[i]= logarithmicDerivative (F, j.getItem(), l, oldL2, bufQ[i], |
---|
| 2208 | bufQ[i] |
---|
| 2209 | ); |
---|
| 2210 | } |
---|
| 2211 | else |
---|
| 2212 | { |
---|
| 2213 | for (int i= 0; i < factors.length(); i++, j++) |
---|
| 2214 | A[i]= logarithmicDerivative (F, j.getItem(), l, bufQ [i]); |
---|
| 2215 | } |
---|
| 2216 | useOldQs= true; |
---|
| 2217 | for (int i= 0; i < d; i++) |
---|
| 2218 | { |
---|
| 2219 | if (bounds [i] + 1 <= (l/2)*degMipo) |
---|
| 2220 | { |
---|
| 2221 | int k= tmin (bounds [i] + 1, (l/2)*degMipo); |
---|
[38ffb7] | 2222 | C= CFMatrix (l*degMipo - k, factors.length()); |
---|
[11bf82] | 2223 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 2224 | { |
---|
| 2225 | if (A[ii].size() - 1 >= i) |
---|
| 2226 | { |
---|
| 2227 | if (GF) |
---|
| 2228 | { |
---|
| 2229 | A[ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 2230 | setCharacteristic (getCharacteristic()); |
---|
| 2231 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
| 2232 | if (alpha != gamma) |
---|
| 2233 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 2234 | gamma, source, dest |
---|
| 2235 | ); |
---|
| 2236 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
| 2237 | } |
---|
| 2238 | else |
---|
| 2239 | { |
---|
| 2240 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 2241 | if (alpha != gamma) |
---|
| 2242 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 2243 | gamma, source, dest |
---|
| 2244 | ); |
---|
| 2245 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
| 2246 | } |
---|
| 2247 | } |
---|
| 2248 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 2249 | if (GF) |
---|
| 2250 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 2251 | } |
---|
| 2252 | |
---|
| 2253 | if (GF) |
---|
| 2254 | setCharacteristic(getCharacteristic()); |
---|
| 2255 | |
---|
[38ffb7] | 2256 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 2257 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 2258 | transpose (NTLK, NTLK); |
---|
| 2259 | kernel (NTLK, NTLK); |
---|
| 2260 | transpose (NTLK, NTLK); |
---|
| 2261 | NTLN *= NTLK; |
---|
| 2262 | |
---|
| 2263 | if (GF) |
---|
| 2264 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 2265 | |
---|
| 2266 | if (NTLN.NumCols() == 1) |
---|
| 2267 | { |
---|
| 2268 | irreducible= true; |
---|
| 2269 | Variable y= Variable (2); |
---|
| 2270 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 2271 | CFList source, dest; |
---|
| 2272 | tmp= mapDown (tmp, info, source, dest); |
---|
| 2273 | delete [] A; |
---|
| 2274 | delete [] bounds; |
---|
| 2275 | return CFList (tmp); |
---|
| 2276 | } |
---|
| 2277 | } |
---|
| 2278 | } |
---|
| 2279 | |
---|
| 2280 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
| 2281 | { |
---|
| 2282 | if (isReduced (NTLN)) |
---|
| 2283 | { |
---|
[38ffb7] | 2284 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 2285 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 2286 | factorsFoundIndex[i]= 0; |
---|
| 2287 | int factorsFound2= 0; |
---|
| 2288 | CFList result; |
---|
| 2289 | CanonicalForm bufF= F; |
---|
| 2290 | extReconstructionTry (result, bufF, factors,degree (F)+1, factorsFound2, |
---|
| 2291 | factorsFoundIndex, NTLN, false, info, evaluation |
---|
| 2292 | ); |
---|
| 2293 | if (result.length() == NTLN.NumCols()) |
---|
| 2294 | { |
---|
| 2295 | delete [] factorsFoundIndex; |
---|
| 2296 | delete [] A; |
---|
| 2297 | delete [] bounds; |
---|
| 2298 | return result; |
---|
| 2299 | } |
---|
[11bf82] | 2300 | delete [] factorsFoundIndex; |
---|
| 2301 | } |
---|
| 2302 | else if (l == precision) |
---|
| 2303 | { |
---|
| 2304 | CanonicalForm bufF= F; |
---|
| 2305 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
| 2306 | CFList result= extReconstruction (bufF, factors, zeroOne, precision, |
---|
| 2307 | NTLN, info, evaluation |
---|
| 2308 | ); |
---|
| 2309 | F= bufF; |
---|
| 2310 | delete [] zeroOne; |
---|
| 2311 | delete [] A; |
---|
| 2312 | delete [] bounds; |
---|
| 2313 | return result; |
---|
| 2314 | } |
---|
| 2315 | } |
---|
| 2316 | oldL2= l; |
---|
| 2317 | l += stepSize; |
---|
| 2318 | stepSize *= 2; |
---|
| 2319 | if (l > precision) |
---|
| 2320 | { |
---|
| 2321 | if (!hitBound) |
---|
| 2322 | { |
---|
| 2323 | hitBound= true; |
---|
| 2324 | l= precision; |
---|
| 2325 | } |
---|
| 2326 | else |
---|
| 2327 | break; |
---|
| 2328 | } |
---|
| 2329 | } |
---|
| 2330 | delete [] bounds; |
---|
| 2331 | delete [] A; |
---|
| 2332 | return CFList(); |
---|
| 2333 | } |
---|
| 2334 | |
---|
| 2335 | CFList |
---|
| 2336 | increasePrecision2 (const CanonicalForm& F, CFList& factors, |
---|
| 2337 | const Variable& alpha, int precision) |
---|
| 2338 | { |
---|
| 2339 | bool irreducible= false; |
---|
| 2340 | int d; |
---|
| 2341 | int* bounds= computeBounds (F, d); |
---|
| 2342 | CFArray * A= new CFArray [factors.length()]; |
---|
| 2343 | CFArray bufQ= CFArray (factors.length()); |
---|
| 2344 | zz_p::init (getCharacteristic()); |
---|
| 2345 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 2346 | zz_pE::init (NTLMipo); |
---|
| 2347 | mat_zz_pE NTLN; |
---|
| 2348 | ident (NTLN, factors.length()); |
---|
| 2349 | int minBound= bounds[0]; |
---|
| 2350 | for (int i= 1; i < d; i++) |
---|
| 2351 | { |
---|
| 2352 | if (bounds[i] != 0) |
---|
| 2353 | minBound= tmin (minBound, bounds[i]); |
---|
| 2354 | } |
---|
| 2355 | int l= tmin (2*(minBound + 1), precision); |
---|
| 2356 | int oldL= l/2; |
---|
| 2357 | int stepSize= 2; |
---|
| 2358 | bool useOldQs= false; |
---|
| 2359 | bool hitBound= false; |
---|
| 2360 | Variable y= Variable (2); |
---|
[38ffb7] | 2361 | CFListIterator j; |
---|
| 2362 | CFMatrix C; |
---|
| 2363 | CFArray buf; |
---|
| 2364 | mat_zz_pE* NTLC, NTLK; |
---|
[11bf82] | 2365 | while (l <= precision) |
---|
| 2366 | { |
---|
[38ffb7] | 2367 | j= factors; |
---|
[11bf82] | 2368 | if (useOldQs) |
---|
| 2369 | { |
---|
| 2370 | for (int i= 0; i < factors.length(); i++, j++) |
---|
| 2371 | A[i]= logarithmicDerivative (F, j.getItem(), l, oldL, bufQ[i], bufQ[i]); |
---|
| 2372 | } |
---|
| 2373 | else |
---|
| 2374 | { |
---|
| 2375 | for (int i= 0; i < factors.length(); i++, j++) |
---|
| 2376 | A[i]= logarithmicDerivative (F, j.getItem(), l, bufQ [i]); |
---|
| 2377 | } |
---|
| 2378 | useOldQs= true; |
---|
| 2379 | for (int i= 0; i < d; i++) |
---|
| 2380 | { |
---|
| 2381 | if (bounds [i] + 1 <= l/2) |
---|
| 2382 | { |
---|
| 2383 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 2384 | C= CFMatrix (l - k, factors.length()); |
---|
[11bf82] | 2385 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 2386 | { |
---|
| 2387 | if (A[ii].size() - 1 >= i) |
---|
| 2388 | buf= getCoeffs (A[ii] [i], k); |
---|
| 2389 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 2390 | } |
---|
[38ffb7] | 2391 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
| 2392 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 2393 | transpose (NTLK, NTLK); |
---|
| 2394 | kernel (NTLK, NTLK); |
---|
| 2395 | transpose (NTLK, NTLK); |
---|
| 2396 | NTLN *= NTLK; |
---|
| 2397 | if (NTLN.NumCols() == 1) |
---|
| 2398 | { |
---|
| 2399 | irreducible= true; |
---|
| 2400 | delete [] A; |
---|
| 2401 | delete [] bounds; |
---|
| 2402 | return CFList (F); |
---|
| 2403 | } |
---|
| 2404 | } |
---|
| 2405 | } |
---|
| 2406 | |
---|
| 2407 | if (isReduced (NTLN) || l == precision) |
---|
| 2408 | { |
---|
| 2409 | CanonicalForm bufF= F; |
---|
| 2410 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
| 2411 | CFList bufFactors= factors; |
---|
| 2412 | CFList result= monicReconstruction (bufF, factors, zeroOne, precision, |
---|
| 2413 | NTLN |
---|
| 2414 | ); |
---|
| 2415 | if (result.length() != NTLN.NumCols() && l != precision) |
---|
| 2416 | factors= bufFactors; |
---|
| 2417 | if (result.length() == NTLN.NumCols()) |
---|
| 2418 | { |
---|
| 2419 | delete [] zeroOne; |
---|
| 2420 | delete [] A; |
---|
| 2421 | delete [] bounds; |
---|
| 2422 | return result; |
---|
| 2423 | } |
---|
| 2424 | if (l == precision) |
---|
| 2425 | { |
---|
| 2426 | delete [] zeroOne; |
---|
| 2427 | delete [] A; |
---|
| 2428 | delete [] bounds; |
---|
| 2429 | return Union (result, factors); |
---|
| 2430 | } |
---|
| 2431 | } |
---|
| 2432 | oldL= l; |
---|
| 2433 | l += stepSize; |
---|
| 2434 | stepSize *= 2; |
---|
| 2435 | if (l > precision) |
---|
| 2436 | { |
---|
| 2437 | if (!hitBound) |
---|
| 2438 | { |
---|
| 2439 | l= precision; |
---|
| 2440 | hitBound= true; |
---|
| 2441 | } |
---|
| 2442 | else |
---|
| 2443 | break; |
---|
| 2444 | } |
---|
| 2445 | } |
---|
| 2446 | delete [] bounds; |
---|
| 2447 | delete [] A; |
---|
| 2448 | return CFList(); |
---|
| 2449 | } |
---|
| 2450 | |
---|
| 2451 | CFList |
---|
| 2452 | increasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
| 2453 | int oldNumCols, int oldL, const Variable& alpha, |
---|
| 2454 | int precision |
---|
| 2455 | ) |
---|
| 2456 | { |
---|
| 2457 | bool irreducible= false; |
---|
| 2458 | int d; |
---|
| 2459 | int* bounds= computeBounds (F, d); |
---|
| 2460 | int extensionDeg= degree (getMipo (alpha)); |
---|
| 2461 | CFArray * A= new CFArray [factors.length()]; |
---|
| 2462 | CFArray bufQ= CFArray (factors.length()); |
---|
| 2463 | mat_zz_p NTLN; |
---|
| 2464 | ident (NTLN, factors.length()); |
---|
| 2465 | int minBound= bounds[0]; |
---|
| 2466 | for (int i= 1; i < d; i++) |
---|
| 2467 | { |
---|
| 2468 | if (bounds[i] != 0) |
---|
| 2469 | minBound= tmin (minBound, bounds[i]); |
---|
| 2470 | } |
---|
| 2471 | int l= tmax (2*(minBound + 1), oldL); |
---|
| 2472 | int oldL2= l/2; |
---|
| 2473 | int stepSize= 2; |
---|
| 2474 | bool useOldQs= false; |
---|
| 2475 | bool hitBound= false; |
---|
[38ffb7] | 2476 | CFListIterator j; |
---|
| 2477 | CFMatrix C; |
---|
| 2478 | mat_zz_p* NTLC, NTLK; |
---|
| 2479 | CFArray buf; |
---|
[11bf82] | 2480 | while (l <= precision) |
---|
| 2481 | { |
---|
[38ffb7] | 2482 | j= factors; |
---|
[11bf82] | 2483 | if (useOldQs) |
---|
| 2484 | { |
---|
| 2485 | for (int i= 0; i < factors.length(); i++, j++) |
---|
| 2486 | A[i]= logarithmicDerivative (F, j.getItem(), l, oldL2, bufQ[i], |
---|
| 2487 | bufQ[i] |
---|
| 2488 | ); |
---|
| 2489 | } |
---|
| 2490 | else |
---|
| 2491 | { |
---|
| 2492 | for (int i= 0; i < factors.length(); i++, j++) |
---|
| 2493 | A[i]= logarithmicDerivative (F, j.getItem(), l, bufQ [i]); |
---|
| 2494 | } |
---|
| 2495 | useOldQs= true; |
---|
| 2496 | for (int i= 0; i < d; i++) |
---|
| 2497 | { |
---|
| 2498 | if (bounds [i] + 1 <= l/2) |
---|
| 2499 | { |
---|
| 2500 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 2501 | C= CFMatrix ((l - k)*extensionDeg, factors.length()); |
---|
[11bf82] | 2502 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 2503 | { |
---|
| 2504 | if (A[ii].size() - 1 >= i) |
---|
| 2505 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
| 2506 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 2507 | } |
---|
[38ffb7] | 2508 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 2509 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 2510 | transpose (NTLK, NTLK); |
---|
| 2511 | kernel (NTLK, NTLK); |
---|
| 2512 | transpose (NTLK, NTLK); |
---|
| 2513 | NTLN *= NTLK; |
---|
| 2514 | if (NTLN.NumCols() == 1) |
---|
| 2515 | { |
---|
| 2516 | irreducible= true; |
---|
| 2517 | delete [] A; |
---|
| 2518 | delete [] bounds; |
---|
| 2519 | return CFList (F); |
---|
| 2520 | } |
---|
| 2521 | } |
---|
| 2522 | } |
---|
| 2523 | |
---|
| 2524 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
| 2525 | { |
---|
| 2526 | if (isReduced (NTLN)) |
---|
| 2527 | { |
---|
| 2528 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 2529 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 2530 | factorsFoundIndex[i]= 0; |
---|
| 2531 | int factorsFound2= 0; |
---|
| 2532 | CFList result; |
---|
| 2533 | CanonicalForm bufF= F; |
---|
| 2534 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
| 2535 | factorsFoundIndex, NTLN, false |
---|
| 2536 | ); |
---|
| 2537 | if (result.length() == NTLN.NumCols()) |
---|
| 2538 | { |
---|
| 2539 | delete [] factorsFoundIndex; |
---|
| 2540 | delete [] A; |
---|
| 2541 | delete [] bounds; |
---|
| 2542 | return result; |
---|
| 2543 | } |
---|
| 2544 | delete [] factorsFoundIndex; |
---|
| 2545 | } |
---|
| 2546 | else if (l == precision) |
---|
| 2547 | { |
---|
| 2548 | CanonicalForm bufF= F; |
---|
| 2549 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
| 2550 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN); |
---|
| 2551 | F= bufF; |
---|
| 2552 | delete [] zeroOne; |
---|
| 2553 | delete [] A; |
---|
| 2554 | delete [] bounds; |
---|
| 2555 | return result; |
---|
| 2556 | } |
---|
| 2557 | } |
---|
| 2558 | oldL2= l; |
---|
| 2559 | l += stepSize; |
---|
| 2560 | stepSize *= 2; |
---|
| 2561 | if (l > precision) |
---|
| 2562 | { |
---|
| 2563 | if (!hitBound) |
---|
| 2564 | { |
---|
| 2565 | hitBound= true; |
---|
| 2566 | l= precision; |
---|
| 2567 | } |
---|
| 2568 | else |
---|
| 2569 | break; |
---|
| 2570 | } |
---|
| 2571 | } |
---|
| 2572 | delete [] bounds; |
---|
| 2573 | delete [] A; |
---|
| 2574 | return CFList(); |
---|
| 2575 | } |
---|
| 2576 | |
---|
| 2577 | CFList |
---|
| 2578 | increasePrecision (CanonicalForm& F, CFList& factors, int oldL, int |
---|
| 2579 | l, int d, int* bounds, CFArray& bufQ, mat_zz_p& NTLN |
---|
| 2580 | ) |
---|
| 2581 | { |
---|
| 2582 | CFList result= CFList(); |
---|
| 2583 | bool irreducible= false; |
---|
| 2584 | CFArray * A= new CFArray [factors.length()]; |
---|
| 2585 | int oldL2= oldL/2; |
---|
| 2586 | bool hitBound= false; |
---|
| 2587 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 2588 | { |
---|
| 2589 | ident (NTLN, factors.length()); |
---|
| 2590 | bufQ= CFArray (factors.length()); |
---|
| 2591 | } |
---|
| 2592 | bool useOldQs= false; |
---|
[38ffb7] | 2593 | CFListIterator j; |
---|
| 2594 | CFMatrix C; |
---|
| 2595 | CFArray buf; |
---|
| 2596 | mat_zz_p* NTLC, NTLK; |
---|
| 2597 | CanonicalForm bufF; |
---|
| 2598 | CFList bufUniFactors; |
---|
[11bf82] | 2599 | while (oldL <= l) |
---|
| 2600 | { |
---|
[38ffb7] | 2601 | j= factors; |
---|
[11bf82] | 2602 | if (useOldQs) |
---|
| 2603 | { |
---|
| 2604 | for (int i= 0; i < factors.length(); i++, j++) |
---|
| 2605 | A[i]= logarithmicDerivative (F, j.getItem(), oldL, oldL2, bufQ[i], |
---|
| 2606 | bufQ[i] |
---|
| 2607 | ); |
---|
| 2608 | } |
---|
| 2609 | else |
---|
| 2610 | { |
---|
| 2611 | for (int i= 0; i < factors.length(); i++, j++) |
---|
| 2612 | A[i]= logarithmicDerivative (F, j.getItem(), oldL, bufQ [i]); |
---|
| 2613 | } |
---|
| 2614 | useOldQs= true; |
---|
| 2615 | |
---|
| 2616 | for (int i= 0; i < d; i++) |
---|
| 2617 | { |
---|
| 2618 | if (bounds [i] + 1 <= oldL/2) |
---|
| 2619 | { |
---|
| 2620 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
[38ffb7] | 2621 | C= CFMatrix (oldL - k, factors.length()); |
---|
[11bf82] | 2622 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 2623 | { |
---|
| 2624 | if (A[ii].size() - 1 >= i) |
---|
| 2625 | buf= getCoeffs (A[ii] [i], k); |
---|
| 2626 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 2627 | } |
---|
[38ffb7] | 2628 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 2629 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 2630 | transpose (NTLK, NTLK); |
---|
| 2631 | kernel (NTLK, NTLK); |
---|
| 2632 | transpose (NTLK, NTLK); |
---|
| 2633 | NTLN *= NTLK; |
---|
| 2634 | if (NTLN.NumCols() == 1) |
---|
| 2635 | { |
---|
| 2636 | irreducible= true; |
---|
| 2637 | delete [] A; |
---|
| 2638 | return CFList (F); |
---|
| 2639 | } |
---|
| 2640 | } |
---|
| 2641 | } |
---|
| 2642 | if (NTLN.NumCols() == 1) |
---|
| 2643 | { |
---|
| 2644 | irreducible= true; |
---|
| 2645 | delete [] A; |
---|
| 2646 | return CFList (F); |
---|
| 2647 | } |
---|
| 2648 | int * zeroOneVecs; |
---|
| 2649 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
[38ffb7] | 2650 | bufF= F; |
---|
| 2651 | bufUniFactors= factors; |
---|
[11bf82] | 2652 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN); |
---|
| 2653 | delete [] zeroOneVecs; |
---|
| 2654 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < oldL && result.length() > 0) |
---|
| 2655 | { |
---|
[c1b9927] | 2656 | F= bufF; |
---|
[11bf82] | 2657 | factors= bufUniFactors; |
---|
| 2658 | delete [] A; |
---|
| 2659 | return result; |
---|
| 2660 | } |
---|
| 2661 | |
---|
| 2662 | result= CFList(); |
---|
| 2663 | oldL2= oldL; |
---|
| 2664 | oldL *= 2; |
---|
| 2665 | if (oldL > l) |
---|
| 2666 | { |
---|
| 2667 | if (!hitBound) |
---|
| 2668 | { |
---|
| 2669 | oldL= l; |
---|
| 2670 | hitBound= true; |
---|
| 2671 | } |
---|
| 2672 | else |
---|
| 2673 | break; |
---|
| 2674 | } |
---|
| 2675 | } |
---|
| 2676 | delete [] A; |
---|
| 2677 | return result; |
---|
| 2678 | } |
---|
| 2679 | |
---|
| 2680 | CFList |
---|
| 2681 | increasePrecision (CanonicalForm& F, CFList& factors, int oldL, int |
---|
| 2682 | l, int d, int* bounds, CFArray& bufQ, mat_zz_pE& NTLN |
---|
| 2683 | ) |
---|
| 2684 | { |
---|
| 2685 | CFList result= CFList(); |
---|
| 2686 | bool irreducible= false; |
---|
| 2687 | CFArray * A= new CFArray [factors.length()]; |
---|
| 2688 | int oldL2= oldL/2; |
---|
| 2689 | bool hitBound= false; |
---|
| 2690 | bool useOldQs= false; |
---|
| 2691 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 2692 | ident (NTLN, factors.length()); |
---|
[38ffb7] | 2693 | CFListIterator j; |
---|
| 2694 | CFMatrix C; |
---|
| 2695 | CFArray buf; |
---|
| 2696 | mat_zz_pE* NTLC, NTLK; |
---|
| 2697 | CanonicalForm bufF; |
---|
| 2698 | CFList bufUniFactors; |
---|
[11bf82] | 2699 | while (oldL <= l) |
---|
| 2700 | { |
---|
[38ffb7] | 2701 | j= factors; |
---|
[11bf82] | 2702 | if (useOldQs) |
---|
| 2703 | { |
---|
| 2704 | for (int i= 0; i < factors.length(); i++, j++) |
---|
| 2705 | A[i]= logarithmicDerivative (F, j.getItem(), oldL, oldL2, bufQ[i], |
---|
| 2706 | bufQ[i] |
---|
| 2707 | ); |
---|
| 2708 | } |
---|
| 2709 | else |
---|
| 2710 | { |
---|
| 2711 | for (int i= 0; i < factors.length(); i++, j++) |
---|
| 2712 | A[i]= logarithmicDerivative (F, j.getItem(), oldL, bufQ [i]); |
---|
| 2713 | } |
---|
| 2714 | useOldQs= true; |
---|
| 2715 | |
---|
| 2716 | for (int i= 0; i < d; i++) |
---|
| 2717 | { |
---|
| 2718 | if (bounds [i] + 1 <= oldL/2) |
---|
| 2719 | { |
---|
| 2720 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
[38ffb7] | 2721 | C= CFMatrix (oldL - k, factors.length()); |
---|
[11bf82] | 2722 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 2723 | { |
---|
| 2724 | if (A[ii].size() - 1 >= i) |
---|
| 2725 | buf= getCoeffs (A[ii] [i], k); |
---|
| 2726 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 2727 | } |
---|
[38ffb7] | 2728 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
| 2729 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 2730 | transpose (NTLK, NTLK); |
---|
| 2731 | kernel (NTLK, NTLK); |
---|
| 2732 | transpose (NTLK, NTLK); |
---|
| 2733 | NTLN *= NTLK; |
---|
| 2734 | if (NTLN.NumCols() == 1) |
---|
| 2735 | { |
---|
| 2736 | irreducible= true; |
---|
| 2737 | delete [] A; |
---|
| 2738 | return CFList (F); |
---|
| 2739 | } |
---|
| 2740 | } |
---|
| 2741 | } |
---|
| 2742 | if (NTLN.NumCols() == 1) |
---|
| 2743 | { |
---|
| 2744 | irreducible= true; |
---|
| 2745 | delete [] A; |
---|
| 2746 | return CFList (F); |
---|
| 2747 | } |
---|
| 2748 | |
---|
| 2749 | int * zeroOneVecs; |
---|
| 2750 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
[38ffb7] | 2751 | bufF= F; |
---|
| 2752 | bufUniFactors= factors; |
---|
[11bf82] | 2753 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN); |
---|
| 2754 | delete [] zeroOneVecs; |
---|
| 2755 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
| 2756 | { |
---|
[c1b9927] | 2757 | F= bufF; |
---|
[11bf82] | 2758 | factors= bufUniFactors; |
---|
| 2759 | delete [] A; |
---|
| 2760 | return result; |
---|
| 2761 | } |
---|
| 2762 | |
---|
| 2763 | result= CFList(); |
---|
| 2764 | oldL2= oldL; |
---|
| 2765 | oldL *= 2; |
---|
| 2766 | if (oldL > l) |
---|
| 2767 | { |
---|
| 2768 | if (!hitBound) |
---|
| 2769 | { |
---|
| 2770 | oldL= l; |
---|
| 2771 | hitBound= true; |
---|
| 2772 | } |
---|
| 2773 | else |
---|
| 2774 | break; |
---|
| 2775 | } |
---|
| 2776 | } |
---|
| 2777 | delete [] A; |
---|
| 2778 | return result; |
---|
| 2779 | } |
---|
| 2780 | |
---|
| 2781 | //over field extension |
---|
| 2782 | CFList |
---|
| 2783 | extIncreasePrecision (CanonicalForm& F, CFList& factors, int oldL, int l, int d, |
---|
| 2784 | int* bounds, CFArray& bufQ, mat_zz_p& NTLN, const |
---|
| 2785 | CanonicalForm& evaluation, const ExtensionInfo& info, |
---|
| 2786 | CFList& source, CFList& dest |
---|
| 2787 | ) |
---|
| 2788 | { |
---|
| 2789 | CFList result= CFList(); |
---|
| 2790 | bool irreducible= false; |
---|
| 2791 | CFArray * A= new CFArray [factors.length()]; |
---|
| 2792 | int oldL2= oldL/2; //be careful |
---|
| 2793 | bool hitBound= false; |
---|
| 2794 | bool useOldQs= false; |
---|
| 2795 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
| 2796 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
| 2797 | Variable alpha= info.getAlpha(); |
---|
| 2798 | |
---|
| 2799 | Variable gamma= info.getBeta(); |
---|
| 2800 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
| 2801 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
| 2802 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 2803 | ident (NTLN, factors.length()); |
---|
[38ffb7] | 2804 | Variable y= F.mvar(); |
---|
| 2805 | CFListIterator j; |
---|
| 2806 | CanonicalForm powX, imBasis, bufF; |
---|
| 2807 | CFMatrix Mat, C; |
---|
| 2808 | CFIterator iter; |
---|
| 2809 | mat_zz_p* NTLMat; |
---|
| 2810 | CFArray buf; |
---|
| 2811 | mat_zz_p* NTLC, NTLK; |
---|
| 2812 | CFList bufUniFactors; |
---|
[11bf82] | 2813 | while (oldL <= l) |
---|
| 2814 | { |
---|
[38ffb7] | 2815 | j= factors; |
---|
[11bf82] | 2816 | if (GF) |
---|
| 2817 | setCharacteristic (getCharacteristic()); |
---|
[38ffb7] | 2818 | |
---|
| 2819 | powX= power (y-gamma, oldL); |
---|
| 2820 | Mat= CFMatrix (oldL*degMipo, oldL*degMipo); |
---|
[11bf82] | 2821 | for (int i= 0; i < oldL*degMipo; i++) |
---|
| 2822 | { |
---|
[38ffb7] | 2823 | imBasis= mod (power (y, i), powX); |
---|
[11bf82] | 2824 | imBasis= imBasis (power (y, degMipo), y); |
---|
| 2825 | imBasis= imBasis (y, gamma); |
---|
[38ffb7] | 2826 | iter= imBasis; |
---|
[11bf82] | 2827 | for (; iter.hasTerms(); iter++) |
---|
| 2828 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
| 2829 | } |
---|
| 2830 | |
---|
[38ffb7] | 2831 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
[11bf82] | 2832 | *NTLMat= inv (*NTLMat); |
---|
| 2833 | if (GF) |
---|
| 2834 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 2835 | |
---|
| 2836 | if (useOldQs) |
---|
| 2837 | { |
---|
| 2838 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[c1b9927] | 2839 | A[i]= logarithmicDerivative (F, j.getItem(), oldL, oldL2, bufQ[i], |
---|
[11bf82] | 2840 | bufQ[i]); |
---|
| 2841 | } |
---|
| 2842 | else |
---|
| 2843 | { |
---|
| 2844 | for (int i= 0; i < factors.length(); i++, j++) |
---|
| 2845 | A[i]= logarithmicDerivative (F, j.getItem(), oldL, bufQ [i]); |
---|
| 2846 | } |
---|
| 2847 | useOldQs= true; |
---|
| 2848 | |
---|
| 2849 | for (int i= 0; i < d; i++) |
---|
| 2850 | { |
---|
| 2851 | if (bounds [i] + 1 <= oldL/2) |
---|
| 2852 | { |
---|
| 2853 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
[38ffb7] | 2854 | C= CFMatrix (oldL*degMipo - k, factors.length()); |
---|
[11bf82] | 2855 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 2856 | { |
---|
| 2857 | if (A[ii].size() - 1 >= i) |
---|
| 2858 | { |
---|
| 2859 | if (GF) |
---|
| 2860 | { |
---|
| 2861 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 2862 | setCharacteristic (getCharacteristic()); |
---|
| 2863 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
| 2864 | if (alpha != gamma) |
---|
| 2865 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 2866 | gamma, source, dest |
---|
| 2867 | ); |
---|
| 2868 | buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, *NTLMat); |
---|
| 2869 | } |
---|
| 2870 | else |
---|
| 2871 | { |
---|
| 2872 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 2873 | if (alpha != gamma) |
---|
| 2874 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 2875 | gamma, source, dest |
---|
| 2876 | ); |
---|
| 2877 | buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, *NTLMat); |
---|
| 2878 | } |
---|
| 2879 | } |
---|
| 2880 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 2881 | if (GF) |
---|
| 2882 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 2883 | } |
---|
| 2884 | |
---|
| 2885 | if (GF) |
---|
| 2886 | setCharacteristic(getCharacteristic()); |
---|
| 2887 | |
---|
[38ffb7] | 2888 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 2889 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 2890 | transpose (NTLK, NTLK); |
---|
| 2891 | kernel (NTLK, NTLK); |
---|
| 2892 | transpose (NTLK, NTLK); |
---|
| 2893 | NTLN *= NTLK; |
---|
| 2894 | |
---|
| 2895 | if (GF) |
---|
| 2896 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 2897 | |
---|
| 2898 | if (NTLN.NumCols() == 1) |
---|
| 2899 | { |
---|
| 2900 | irreducible= true; |
---|
| 2901 | Variable y= Variable (2); |
---|
| 2902 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 2903 | CFList source, dest; |
---|
| 2904 | tmp= mapDown (tmp, info, source, dest); |
---|
| 2905 | delete [] A; |
---|
| 2906 | return CFList (tmp); |
---|
| 2907 | } |
---|
| 2908 | } |
---|
| 2909 | } |
---|
| 2910 | if (NTLN.NumCols() == 1) |
---|
| 2911 | { |
---|
| 2912 | irreducible= true; |
---|
| 2913 | Variable y= Variable (2); |
---|
| 2914 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 2915 | CFList source, dest; |
---|
| 2916 | tmp= mapDown (tmp, info, source, dest); |
---|
| 2917 | delete [] A; |
---|
| 2918 | return CFList (tmp); |
---|
| 2919 | } |
---|
| 2920 | |
---|
| 2921 | int * zeroOneVecs; |
---|
| 2922 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
[38ffb7] | 2923 | bufF= F; |
---|
| 2924 | bufUniFactors= factors; |
---|
[11bf82] | 2925 | result= extReconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN, |
---|
| 2926 | info, evaluation |
---|
| 2927 | ); |
---|
| 2928 | delete [] zeroOneVecs; |
---|
| 2929 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
| 2930 | { |
---|
[c1b9927] | 2931 | F= bufF; |
---|
[11bf82] | 2932 | factors= bufUniFactors; |
---|
| 2933 | return result; |
---|
| 2934 | } |
---|
| 2935 | |
---|
| 2936 | result= CFList(); |
---|
| 2937 | oldL2= oldL; |
---|
| 2938 | oldL *= 2; |
---|
| 2939 | if (oldL > l) |
---|
| 2940 | { |
---|
| 2941 | if (!hitBound) |
---|
| 2942 | { |
---|
| 2943 | oldL= l; |
---|
| 2944 | hitBound= true; |
---|
| 2945 | } |
---|
| 2946 | else |
---|
| 2947 | break; |
---|
| 2948 | } |
---|
| 2949 | } |
---|
| 2950 | delete [] A; |
---|
| 2951 | return result; |
---|
| 2952 | } |
---|
| 2953 | |
---|
| 2954 | CFList |
---|
| 2955 | increasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int oldL, int l, |
---|
| 2956 | int d, int* bounds, CFArray& bufQ, mat_zz_p& NTLN, |
---|
| 2957 | const Variable& alpha |
---|
| 2958 | ) |
---|
| 2959 | { |
---|
| 2960 | CFList result= CFList(); |
---|
| 2961 | bool irreducible= false; |
---|
| 2962 | CFArray * A= new CFArray [factors.length()]; |
---|
| 2963 | int extensionDeg= degree (getMipo (alpha)); |
---|
| 2964 | int oldL2= oldL/2; |
---|
| 2965 | bool hitBound= false; |
---|
| 2966 | bool useOldQs= false; |
---|
| 2967 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 2968 | ident (NTLN, factors.length()); |
---|
[38ffb7] | 2969 | CFListIterator j; |
---|
| 2970 | CFMatrix C; |
---|
| 2971 | CFArray buf; |
---|
| 2972 | mat_zz_p* NTLC, NTLK; |
---|
| 2973 | CanonicalForm bufF; |
---|
| 2974 | CFList bufUniFactors; |
---|
[11bf82] | 2975 | while (oldL <= l) |
---|
| 2976 | { |
---|
[38ffb7] | 2977 | j= factors; |
---|
[11bf82] | 2978 | if (useOldQs) |
---|
| 2979 | { |
---|
| 2980 | for (int i= 0; i < factors.length(); i++, j++) |
---|
| 2981 | A[i]= logarithmicDerivative (F, j.getItem(), oldL, oldL2, bufQ[i], |
---|
| 2982 | bufQ[i] |
---|
| 2983 | ); |
---|
| 2984 | } |
---|
| 2985 | else |
---|
| 2986 | { |
---|
| 2987 | for (int i= 0; i < factors.length(); i++, j++) |
---|
| 2988 | A[i]= logarithmicDerivative (F, j.getItem(), oldL, bufQ [i]); |
---|
| 2989 | } |
---|
| 2990 | useOldQs= true; |
---|
| 2991 | |
---|
| 2992 | for (int i= 0; i < d; i++) |
---|
| 2993 | { |
---|
| 2994 | if (bounds [i] + 1 <= oldL/2) |
---|
| 2995 | { |
---|
| 2996 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
[38ffb7] | 2997 | C= CFMatrix ((oldL - k)*extensionDeg, factors.length()); |
---|
[11bf82] | 2998 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 2999 | { |
---|
| 3000 | if (A[ii].size() - 1 >= i) |
---|
| 3001 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
| 3002 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 3003 | } |
---|
[38ffb7] | 3004 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 3005 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 3006 | transpose (NTLK, NTLK); |
---|
| 3007 | kernel (NTLK, NTLK); |
---|
| 3008 | transpose (NTLK, NTLK); |
---|
| 3009 | NTLN *= NTLK; |
---|
| 3010 | if (NTLN.NumCols() == 1) |
---|
| 3011 | { |
---|
| 3012 | irreducible= true; |
---|
| 3013 | delete [] A; |
---|
| 3014 | return CFList (F); |
---|
| 3015 | } |
---|
| 3016 | } |
---|
| 3017 | } |
---|
| 3018 | |
---|
| 3019 | int * zeroOneVecs; |
---|
| 3020 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
| 3021 | |
---|
[38ffb7] | 3022 | bufF= F; |
---|
| 3023 | bufUniFactors= factors; |
---|
[11bf82] | 3024 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN); |
---|
| 3025 | delete [] zeroOneVecs; |
---|
| 3026 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
| 3027 | { |
---|
[c1b9927] | 3028 | F= bufF; |
---|
[11bf82] | 3029 | factors= bufUniFactors; |
---|
| 3030 | delete [] A; |
---|
| 3031 | return result; |
---|
| 3032 | } |
---|
| 3033 | |
---|
| 3034 | result= CFList(); |
---|
| 3035 | oldL2= oldL; |
---|
| 3036 | oldL *= 2; |
---|
| 3037 | if (oldL > l) |
---|
| 3038 | { |
---|
| 3039 | if (!hitBound) |
---|
| 3040 | { |
---|
| 3041 | oldL= l; |
---|
| 3042 | hitBound= true; |
---|
| 3043 | } |
---|
| 3044 | else |
---|
| 3045 | break; |
---|
| 3046 | } |
---|
| 3047 | } |
---|
| 3048 | delete [] A; |
---|
| 3049 | return result; |
---|
| 3050 | } |
---|
| 3051 | |
---|
| 3052 | CFList |
---|
| 3053 | furtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& |
---|
| 3054 | factors, int l, int liftBound, int d, int* |
---|
| 3055 | bounds, mat_zz_p& NTLN, CFList& diophant, |
---|
| 3056 | CFMatrix& M, CFArray& Pi, CFArray& bufQ |
---|
| 3057 | ) |
---|
| 3058 | { |
---|
| 3059 | CanonicalForm LCF= LC (F, 1); |
---|
| 3060 | CFList result; |
---|
| 3061 | bool irreducible= false; |
---|
| 3062 | CFList bufFactors= factors; |
---|
| 3063 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
| 3064 | bool useOldQs= false; |
---|
| 3065 | bool hitBound= false; |
---|
| 3066 | int oldL= l; |
---|
| 3067 | int stepSize= 8; //TODO choose better step size? |
---|
| 3068 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
| 3069 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 3070 | ident (NTLN, factors.length()); |
---|
[38ffb7] | 3071 | CFListIterator j; |
---|
| 3072 | CFMatrix C; |
---|
| 3073 | CFArray buf; |
---|
| 3074 | mat_zz_p* NTLC, NTLK; |
---|
| 3075 | CanonicalForm bufF; |
---|
[11bf82] | 3076 | while (l <= liftBound) |
---|
| 3077 | { |
---|
| 3078 | bufFactors.insert (LCF); |
---|
| 3079 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
| 3080 | bufFactors.insert (LCF); |
---|
| 3081 | bufFactors.removeFirst(); |
---|
[38ffb7] | 3082 | j= bufFactors; |
---|
[11bf82] | 3083 | if (useOldQs) |
---|
| 3084 | { |
---|
| 3085 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
| 3086 | A[i]= logarithmicDerivative (F, j.getItem(), l, oldL, bufQ[i],bufQ[i]); |
---|
| 3087 | } |
---|
| 3088 | else |
---|
| 3089 | { |
---|
| 3090 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
| 3091 | A[i]= logarithmicDerivative (F, j.getItem(), l, bufQ [i]); |
---|
| 3092 | } |
---|
| 3093 | for (int i= 0; i < d; i++) |
---|
| 3094 | { |
---|
| 3095 | if (bounds [i] + 1 <= l/2) |
---|
| 3096 | { |
---|
| 3097 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 3098 | C= CFMatrix (l - k, bufFactors.length()); |
---|
[11bf82] | 3099 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
| 3100 | { |
---|
| 3101 | if (A[ii].size() - 1 >= i) |
---|
| 3102 | buf= getCoeffs (A[ii] [i], k); |
---|
| 3103 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 3104 | } |
---|
[38ffb7] | 3105 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 3106 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 3107 | transpose (NTLK, NTLK); |
---|
| 3108 | kernel (NTLK, NTLK); |
---|
| 3109 | transpose (NTLK, NTLK); |
---|
| 3110 | NTLN *= NTLK; |
---|
| 3111 | if (NTLN.NumCols() == 1) |
---|
| 3112 | { |
---|
| 3113 | irreducible= true; |
---|
| 3114 | break; |
---|
| 3115 | } |
---|
| 3116 | } |
---|
| 3117 | } |
---|
| 3118 | |
---|
| 3119 | if (NTLN.NumCols() == 1) |
---|
| 3120 | { |
---|
| 3121 | irreducible= true; |
---|
| 3122 | break; |
---|
| 3123 | } |
---|
| 3124 | |
---|
| 3125 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
[38ffb7] | 3126 | bufF= F; |
---|
[11bf82] | 3127 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN); |
---|
| 3128 | delete [] zeroOneVecs; |
---|
| 3129 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
| 3130 | { |
---|
| 3131 | F= bufF; |
---|
| 3132 | factors= bufFactors; |
---|
| 3133 | delete [] A; |
---|
| 3134 | return result; |
---|
| 3135 | } |
---|
| 3136 | |
---|
| 3137 | if (isReduced (NTLN)) |
---|
| 3138 | { |
---|
| 3139 | int factorsFound= 0; |
---|
[38ffb7] | 3140 | bufF= F; |
---|
[11bf82] | 3141 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 3142 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 3143 | factorsFoundIndex[i]= 0; |
---|
| 3144 | if (l < liftBound) |
---|
| 3145 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
| 3146 | factorsFoundIndex, NTLN, false |
---|
| 3147 | ); |
---|
| 3148 | else |
---|
| 3149 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
| 3150 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
| 3151 | NTLN, false |
---|
| 3152 | ); |
---|
| 3153 | |
---|
| 3154 | if (NTLN.NumCols() == result.length()) |
---|
| 3155 | { |
---|
| 3156 | delete [] A; |
---|
| 3157 | delete [] factorsFoundIndex; |
---|
| 3158 | return result; |
---|
| 3159 | } |
---|
| 3160 | delete [] factorsFoundIndex; |
---|
| 3161 | } |
---|
| 3162 | result= CFList(); |
---|
| 3163 | oldL= l; |
---|
| 3164 | stepSize *= 2; |
---|
| 3165 | l += stepSize; |
---|
| 3166 | if (l > liftBound) |
---|
| 3167 | { |
---|
| 3168 | if (!hitBound) |
---|
| 3169 | { |
---|
| 3170 | l= liftBound; |
---|
| 3171 | hitBound= true; |
---|
| 3172 | } |
---|
| 3173 | else |
---|
| 3174 | break; |
---|
| 3175 | } |
---|
| 3176 | } |
---|
| 3177 | if (irreducible) |
---|
| 3178 | { |
---|
| 3179 | delete [] A; |
---|
| 3180 | return CFList (F); |
---|
| 3181 | } |
---|
| 3182 | delete [] A; |
---|
| 3183 | factors= bufFactors; |
---|
| 3184 | return CFList(); |
---|
| 3185 | } |
---|
| 3186 | |
---|
| 3187 | //Fq |
---|
| 3188 | CFList |
---|
| 3189 | furtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& |
---|
| 3190 | factors, int l, int liftBound, int d, int* |
---|
| 3191 | bounds, mat_zz_pE& NTLN, CFList& diophant, |
---|
| 3192 | CFMatrix& M, CFArray& Pi, CFArray& bufQ |
---|
| 3193 | ) |
---|
| 3194 | { |
---|
| 3195 | CanonicalForm LCF= LC (F, 1); |
---|
| 3196 | CFList result; |
---|
| 3197 | bool irreducible= false; |
---|
| 3198 | CFList bufFactors= factors; |
---|
| 3199 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
| 3200 | bool useOldQs= false; |
---|
| 3201 | bool hitBound= false; |
---|
| 3202 | int oldL= l; |
---|
| 3203 | int stepSize= 8; //TODO choose better step size? |
---|
| 3204 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
| 3205 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 3206 | ident (NTLN, factors.length()); |
---|
[38ffb7] | 3207 | CFListIterator j; |
---|
| 3208 | CFArray buf; |
---|
| 3209 | mat_zz_pE* NTLC, NTLK; |
---|
| 3210 | CanonicalForm bufF; |
---|
[11bf82] | 3211 | while (l <= liftBound) |
---|
| 3212 | { |
---|
| 3213 | bufFactors.insert (LCF); |
---|
| 3214 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
[38ffb7] | 3215 | j= bufFactors; |
---|
[11bf82] | 3216 | if (useOldQs) |
---|
| 3217 | { |
---|
| 3218 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
| 3219 | A[i]= logarithmicDerivative (F, j.getItem(), l, oldL, bufQ[i],bufQ[i]); |
---|
| 3220 | } |
---|
| 3221 | else |
---|
| 3222 | { |
---|
| 3223 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
| 3224 | A[i]= logarithmicDerivative (F, j.getItem(), l, bufQ [i]); |
---|
| 3225 | } |
---|
| 3226 | for (int i= 0; i < d; i++) |
---|
| 3227 | { |
---|
| 3228 | if (bounds [i] + 1 <= l/2) |
---|
| 3229 | { |
---|
| 3230 | int k= tmin (bounds [i] + 1, l/2); |
---|
| 3231 | CFMatrix C= CFMatrix (l - k, bufFactors.length()); |
---|
| 3232 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
| 3233 | { |
---|
| 3234 | if (A[ii].size() - 1 >= i) |
---|
| 3235 | buf= getCoeffs (A[ii] [i], k); |
---|
| 3236 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 3237 | } |
---|
[38ffb7] | 3238 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
| 3239 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 3240 | transpose (NTLK, NTLK); |
---|
| 3241 | kernel (NTLK, NTLK); |
---|
| 3242 | transpose (NTLK, NTLK); |
---|
| 3243 | NTLN *= NTLK; |
---|
| 3244 | if (NTLN.NumCols() == 1) |
---|
| 3245 | { |
---|
| 3246 | irreducible= true; |
---|
| 3247 | break; |
---|
| 3248 | } |
---|
| 3249 | } |
---|
| 3250 | } |
---|
| 3251 | if (NTLN.NumCols() == 1) |
---|
| 3252 | { |
---|
| 3253 | irreducible= true; |
---|
| 3254 | break; |
---|
| 3255 | } |
---|
| 3256 | |
---|
[38ffb7] | 3257 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
| 3258 | bufF= F; |
---|
| 3259 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN); |
---|
| 3260 | delete [] zeroOneVecs; |
---|
| 3261 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
| 3262 | { |
---|
| 3263 | F= bufF; |
---|
| 3264 | factors= bufFactors; |
---|
| 3265 | delete [] A; |
---|
| 3266 | return result; |
---|
| 3267 | } |
---|
[11bf82] | 3268 | |
---|
| 3269 | if (isReduced (NTLN)) |
---|
| 3270 | { |
---|
| 3271 | int factorsFound= 0; |
---|
[38ffb7] | 3272 | bufF= F; |
---|
[11bf82] | 3273 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 3274 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 3275 | factorsFoundIndex[i]= 0; |
---|
| 3276 | if (l < liftBound) |
---|
| 3277 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
| 3278 | factorsFoundIndex, NTLN, false |
---|
| 3279 | ); |
---|
| 3280 | else |
---|
| 3281 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
| 3282 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
| 3283 | NTLN, false |
---|
| 3284 | ); |
---|
| 3285 | if (NTLN.NumCols() == result.length()) |
---|
| 3286 | { |
---|
| 3287 | delete [] A; |
---|
| 3288 | delete [] factorsFoundIndex; |
---|
| 3289 | return result; |
---|
| 3290 | } |
---|
| 3291 | delete [] factorsFoundIndex; |
---|
| 3292 | } |
---|
| 3293 | result= CFList(); |
---|
| 3294 | oldL= l; |
---|
| 3295 | stepSize *= 2; |
---|
| 3296 | l += stepSize; |
---|
| 3297 | if (l > liftBound) |
---|
| 3298 | { |
---|
| 3299 | if (!hitBound) |
---|
| 3300 | { |
---|
| 3301 | l= liftBound; |
---|
| 3302 | hitBound= true; |
---|
| 3303 | } |
---|
| 3304 | else |
---|
| 3305 | break; |
---|
| 3306 | } |
---|
| 3307 | } |
---|
| 3308 | if (irreducible) |
---|
| 3309 | { |
---|
| 3310 | delete [] A; |
---|
| 3311 | return CFList (F); |
---|
| 3312 | } |
---|
| 3313 | delete [] A; |
---|
| 3314 | factors= bufFactors; |
---|
| 3315 | return CFList(); |
---|
| 3316 | } |
---|
| 3317 | |
---|
| 3318 | //over field extension |
---|
| 3319 | CFList |
---|
| 3320 | extFurtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& factors, int l, |
---|
| 3321 | int liftBound, int d, int* bounds, |
---|
| 3322 | mat_zz_p& NTLN, CFList& diophant, |
---|
| 3323 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
| 3324 | const CanonicalForm& evaluation, const |
---|
| 3325 | ExtensionInfo& info, CFList& source, |
---|
| 3326 | CFList& dest |
---|
| 3327 | ) |
---|
| 3328 | { |
---|
| 3329 | CanonicalForm LCF= LC (F, 1); |
---|
| 3330 | CFList result; |
---|
| 3331 | bool irreducible= false; |
---|
| 3332 | CFList bufFactors= factors; |
---|
| 3333 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
| 3334 | bool useOldQs= false; |
---|
| 3335 | bool hitBound= false; |
---|
| 3336 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
| 3337 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
| 3338 | Variable alpha= info.getAlpha(); |
---|
| 3339 | int oldL= l; //be careful |
---|
| 3340 | int stepSize= 8; |
---|
| 3341 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l),2); |
---|
| 3342 | Variable gamma= info.getBeta(); |
---|
| 3343 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
| 3344 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
| 3345 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 3346 | ident (NTLN, factors.length()); |
---|
[38ffb7] | 3347 | Variable y= F.mvar(); |
---|
| 3348 | CanonicalForm powX, imBasis, bufF; |
---|
| 3349 | CFMatrix Mat, C; |
---|
| 3350 | CFIterator iter; |
---|
| 3351 | mat_zz_p* NTLMat,*NTLC, NTLK; |
---|
| 3352 | CFListIterator j; |
---|
| 3353 | CFArray buf; |
---|
[11bf82] | 3354 | while (l <= liftBound) |
---|
| 3355 | { |
---|
| 3356 | bufFactors.insert (LCF); |
---|
| 3357 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
| 3358 | |
---|
| 3359 | if (GF) |
---|
| 3360 | setCharacteristic (getCharacteristic()); |
---|
| 3361 | |
---|
[38ffb7] | 3362 | powX= power (y-gamma, l); |
---|
| 3363 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
[11bf82] | 3364 | for (int i= 0; i < l*degMipo; i++) |
---|
| 3365 | { |
---|
| 3366 | |
---|
[38ffb7] | 3367 | imBasis= mod (power (y, i), powX); |
---|
[11bf82] | 3368 | imBasis= imBasis (power (y, degMipo), y); |
---|
| 3369 | imBasis= imBasis (y, gamma); |
---|
[38ffb7] | 3370 | iter= imBasis; |
---|
[11bf82] | 3371 | for (; iter.hasTerms(); iter++) |
---|
| 3372 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
| 3373 | } |
---|
| 3374 | |
---|
[38ffb7] | 3375 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
[11bf82] | 3376 | *NTLMat= inv (*NTLMat); |
---|
| 3377 | |
---|
| 3378 | if (GF) |
---|
| 3379 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 3380 | |
---|
[38ffb7] | 3381 | j= bufFactors; |
---|
[11bf82] | 3382 | if (useOldQs) |
---|
| 3383 | { |
---|
| 3384 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
| 3385 | A[i]= logarithmicDerivative (F, j.getItem(), l, oldL, bufQ[i],bufQ[i]); |
---|
| 3386 | } |
---|
| 3387 | else |
---|
| 3388 | { |
---|
| 3389 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
| 3390 | A[i]= logarithmicDerivative (F, j.getItem(), l, bufQ [i]); |
---|
| 3391 | } |
---|
| 3392 | for (int i= 0; i < d; i++) |
---|
| 3393 | { |
---|
| 3394 | if (bounds [i] + 1 <= l/2) |
---|
| 3395 | { |
---|
| 3396 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 3397 | C= CFMatrix (l*degMipo - k, bufFactors.length()); |
---|
[11bf82] | 3398 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
| 3399 | { |
---|
| 3400 | if (A[ii].size() - 1 >= i) |
---|
| 3401 | { |
---|
| 3402 | if (GF) |
---|
| 3403 | { |
---|
| 3404 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 3405 | setCharacteristic (getCharacteristic()); |
---|
| 3406 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
| 3407 | if (alpha != gamma) |
---|
| 3408 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 3409 | gamma, source, dest |
---|
| 3410 | ); |
---|
| 3411 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
| 3412 | } |
---|
| 3413 | else |
---|
| 3414 | { |
---|
| 3415 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 3416 | if (alpha != gamma) |
---|
| 3417 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 3418 | gamma, source, dest |
---|
| 3419 | ); |
---|
| 3420 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
| 3421 | } |
---|
| 3422 | } |
---|
| 3423 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 3424 | if (GF) |
---|
| 3425 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 3426 | } |
---|
| 3427 | |
---|
| 3428 | if (GF) |
---|
| 3429 | setCharacteristic(getCharacteristic()); |
---|
[38ffb7] | 3430 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 3431 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 3432 | transpose (NTLK, NTLK); |
---|
| 3433 | kernel (NTLK, NTLK); |
---|
| 3434 | transpose (NTLK, NTLK); |
---|
| 3435 | NTLN *= NTLK; |
---|
| 3436 | if (GF) |
---|
| 3437 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 3438 | |
---|
| 3439 | if (NTLN.NumCols() == 1) |
---|
| 3440 | { |
---|
| 3441 | irreducible= true; |
---|
| 3442 | break; |
---|
| 3443 | } |
---|
| 3444 | } |
---|
| 3445 | } |
---|
| 3446 | if (NTLN.NumCols() == 1) |
---|
| 3447 | { |
---|
| 3448 | irreducible= true; |
---|
| 3449 | break; |
---|
| 3450 | } |
---|
| 3451 | |
---|
[38ffb7] | 3452 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
| 3453 | bufF= F; |
---|
| 3454 | result= extReconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN, info, |
---|
| 3455 | evaluation |
---|
| 3456 | ); |
---|
| 3457 | delete [] zeroOneVecs; |
---|
| 3458 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
| 3459 | { |
---|
| 3460 | F= bufF; |
---|
| 3461 | factors= bufFactors; |
---|
| 3462 | delete [] A; |
---|
| 3463 | return result; |
---|
| 3464 | } |
---|
[11bf82] | 3465 | |
---|
| 3466 | if (isReduced (NTLN)) |
---|
| 3467 | { |
---|
| 3468 | int factorsFound= 0; |
---|
[38ffb7] | 3469 | bufF= F; |
---|
[11bf82] | 3470 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 3471 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 3472 | factorsFoundIndex[i]= 0; |
---|
| 3473 | if (l < degree (bufF) + 1 + degree (LCF)) |
---|
| 3474 | extReconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
| 3475 | factorsFoundIndex, NTLN, false, info, evaluation |
---|
| 3476 | ); |
---|
| 3477 | else |
---|
| 3478 | extReconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
| 3479 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
| 3480 | NTLN, false, info, evaluation |
---|
| 3481 | ); |
---|
| 3482 | if (NTLN.NumCols() == result.length()) |
---|
| 3483 | { |
---|
| 3484 | delete [] A; |
---|
| 3485 | delete [] factorsFoundIndex; |
---|
| 3486 | return result; |
---|
| 3487 | } |
---|
| 3488 | delete [] factorsFoundIndex; |
---|
| 3489 | } |
---|
| 3490 | result= CFList(); |
---|
| 3491 | oldL= l; |
---|
| 3492 | stepSize *= 2; |
---|
| 3493 | l += stepSize; |
---|
| 3494 | if (l > liftBound) |
---|
| 3495 | { |
---|
| 3496 | if (!hitBound) |
---|
| 3497 | { |
---|
| 3498 | l= liftBound; |
---|
| 3499 | hitBound= true; |
---|
| 3500 | } |
---|
| 3501 | else |
---|
| 3502 | break; |
---|
| 3503 | } |
---|
| 3504 | } |
---|
| 3505 | if (irreducible) |
---|
| 3506 | { |
---|
| 3507 | delete [] A; |
---|
| 3508 | Variable y= Variable (2); |
---|
| 3509 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 3510 | CFList source, dest; |
---|
| 3511 | tmp= mapDown (tmp, info, source, dest); |
---|
| 3512 | return CFList (tmp); |
---|
| 3513 | } |
---|
| 3514 | delete [] A; |
---|
| 3515 | factors= bufFactors; |
---|
| 3516 | return CFList(); |
---|
| 3517 | } |
---|
| 3518 | |
---|
| 3519 | CFList |
---|
| 3520 | furtherLiftingAndIncreasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int |
---|
| 3521 | l, int liftBound, int d, int* bounds, |
---|
| 3522 | mat_zz_p& NTLN, CFList& diophant, |
---|
| 3523 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
| 3524 | const Variable& alpha |
---|
| 3525 | ) |
---|
| 3526 | { |
---|
| 3527 | CanonicalForm LCF= LC (F, 1); |
---|
| 3528 | CFList result; |
---|
| 3529 | bool irreducible= false; |
---|
| 3530 | CFList bufFactors= factors; |
---|
| 3531 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
| 3532 | bool useOldQs= false; |
---|
| 3533 | int extensionDeg= degree (getMipo (alpha)); |
---|
| 3534 | bool hitBound= false; |
---|
| 3535 | int oldL= l; |
---|
| 3536 | int stepSize= 8; //TODO choose better step size? |
---|
| 3537 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
| 3538 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 3539 | ident (NTLN, factors.length()); |
---|
[38ffb7] | 3540 | CFListIterator j; |
---|
| 3541 | CFMatrix C; |
---|
| 3542 | mat_zz_p* NTLC, NTLK; |
---|
| 3543 | CanonicalForm bufF; |
---|
[11bf82] | 3544 | while (l <= liftBound) |
---|
| 3545 | { |
---|
| 3546 | bufFactors.insert (LCF); |
---|
| 3547 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
[38ffb7] | 3548 | j= bufFactors; |
---|
[11bf82] | 3549 | if (useOldQs) |
---|
| 3550 | { |
---|
| 3551 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
| 3552 | A[i]= logarithmicDerivative (F, j.getItem(), l, oldL, bufQ[i],bufQ[i]); |
---|
| 3553 | } |
---|
| 3554 | else |
---|
| 3555 | { |
---|
| 3556 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
| 3557 | A[i]= logarithmicDerivative (F, j.getItem(), l, bufQ [i]); |
---|
| 3558 | } |
---|
| 3559 | for (int i= 0; i < d; i++) |
---|
| 3560 | { |
---|
| 3561 | if (bounds [i] + 1 <= l/2) |
---|
| 3562 | { |
---|
| 3563 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 3564 | C= CFMatrix ((l - k)*extensionDeg, bufFactors.length()); |
---|
[11bf82] | 3565 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
| 3566 | { |
---|
| 3567 | CFArray buf; |
---|
| 3568 | if (A[ii].size() - 1 >= i) |
---|
| 3569 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
| 3570 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 3571 | } |
---|
[38ffb7] | 3572 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 3573 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 3574 | transpose (NTLK, NTLK); |
---|
| 3575 | kernel (NTLK, NTLK); |
---|
| 3576 | transpose (NTLK, NTLK); |
---|
| 3577 | NTLN *= NTLK; |
---|
| 3578 | if (NTLN.NumCols() == 1) |
---|
| 3579 | { |
---|
| 3580 | irreducible= true; |
---|
| 3581 | break; |
---|
| 3582 | } |
---|
| 3583 | } |
---|
| 3584 | } |
---|
| 3585 | if (NTLN.NumCols() == 1) |
---|
| 3586 | { |
---|
| 3587 | irreducible= true; |
---|
| 3588 | break; |
---|
| 3589 | } |
---|
| 3590 | |
---|
[38ffb7] | 3591 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
| 3592 | CanonicalForm bufF= F; |
---|
| 3593 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN); |
---|
| 3594 | delete [] zeroOneVecs; |
---|
| 3595 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
| 3596 | { |
---|
| 3597 | F= bufF; |
---|
| 3598 | factors= bufFactors; |
---|
| 3599 | delete [] A; |
---|
| 3600 | return result; |
---|
| 3601 | } |
---|
[11bf82] | 3602 | |
---|
| 3603 | if (isReduced (NTLN)) |
---|
| 3604 | { |
---|
| 3605 | int factorsFound= 0; |
---|
[38ffb7] | 3606 | bufF= F; |
---|
[11bf82] | 3607 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 3608 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 3609 | factorsFoundIndex[i]= 0; |
---|
| 3610 | if (l < degree (bufF) + 1 + degree (LCF)) |
---|
| 3611 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
| 3612 | factorsFoundIndex, NTLN, false |
---|
| 3613 | ); |
---|
| 3614 | else |
---|
| 3615 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
| 3616 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
| 3617 | NTLN, false |
---|
| 3618 | ); |
---|
| 3619 | if (NTLN.NumCols() == result.length()) |
---|
| 3620 | { |
---|
| 3621 | delete [] A; |
---|
| 3622 | delete [] factorsFoundIndex; |
---|
| 3623 | return result; |
---|
| 3624 | } |
---|
| 3625 | delete [] factorsFoundIndex; |
---|
| 3626 | } |
---|
| 3627 | result= CFList(); |
---|
| 3628 | oldL= l; |
---|
| 3629 | stepSize *= 2; |
---|
| 3630 | l += stepSize; |
---|
| 3631 | if (l > liftBound) |
---|
| 3632 | { |
---|
| 3633 | if (!hitBound) |
---|
| 3634 | { |
---|
| 3635 | l= liftBound; |
---|
| 3636 | hitBound= true; |
---|
| 3637 | } |
---|
| 3638 | else |
---|
| 3639 | break; |
---|
| 3640 | } |
---|
| 3641 | } |
---|
| 3642 | if (irreducible) |
---|
| 3643 | { |
---|
| 3644 | delete [] A; |
---|
| 3645 | return CFList (F); |
---|
| 3646 | } |
---|
| 3647 | delete [] A; |
---|
| 3648 | factors= bufFactors; |
---|
| 3649 | return CFList(); |
---|
| 3650 | } |
---|
| 3651 | |
---|
| 3652 | void |
---|
| 3653 | refineAndRestartLift (const CanonicalForm& F, const mat_zz_p& NTLN, int |
---|
| 3654 | liftBound, int l, CFList& factors, CFMatrix& M, CFArray& |
---|
| 3655 | Pi, CFList& diophant |
---|
| 3656 | ) |
---|
| 3657 | { |
---|
| 3658 | CFList bufFactors; |
---|
| 3659 | Variable y= Variable (2); |
---|
| 3660 | CanonicalForm LCF= LC (F, 1); |
---|
[38ffb7] | 3661 | CFListIterator iter; |
---|
| 3662 | CanonicalForm buf; |
---|
[11bf82] | 3663 | for (long i= 1; i <= NTLN.NumCols(); i++) |
---|
| 3664 | { |
---|
[38ffb7] | 3665 | iter= factors; |
---|
| 3666 | buf= 1; |
---|
[11bf82] | 3667 | for (long j= 1; j <= NTLN.NumRows(); j++, iter++) |
---|
| 3668 | { |
---|
| 3669 | if (!IsZero (NTLN (j,i))) |
---|
| 3670 | buf= mulNTL (buf, mod (iter.getItem(), y)); |
---|
| 3671 | } |
---|
| 3672 | bufFactors.append (buf); |
---|
| 3673 | } |
---|
| 3674 | factors= bufFactors; |
---|
| 3675 | M= CFMatrix (liftBound, factors.length()); |
---|
| 3676 | Pi= CFArray(); |
---|
| 3677 | diophant= CFList(); |
---|
| 3678 | factors.insert (LCF); |
---|
| 3679 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 3680 | } |
---|
| 3681 | |
---|
| 3682 | void |
---|
| 3683 | refineAndRestartLift (const CanonicalForm& F, const mat_zz_pE& NTLN, int |
---|
| 3684 | liftBound, int l, CFList& factors, CFMatrix& M, CFArray& |
---|
| 3685 | Pi, CFList& diophant |
---|
| 3686 | ) |
---|
| 3687 | { |
---|
| 3688 | CFList bufFactors; |
---|
| 3689 | Variable y= Variable (2); |
---|
| 3690 | CanonicalForm LCF= LC (F, 1); |
---|
[38ffb7] | 3691 | CFListIterator iter; |
---|
| 3692 | CanonicalForm buf; |
---|
[c1b9927] | 3693 | for (long i= 1; i <= NTLN.NumCols(); i++) |
---|
[11bf82] | 3694 | { |
---|
[38ffb7] | 3695 | iter= factors; |
---|
| 3696 | buf= 1; |
---|
[11bf82] | 3697 | for (long j= 1; j <= NTLN.NumRows(); j++, iter++) |
---|
| 3698 | { |
---|
| 3699 | if (!IsZero (NTLN (j,i))) |
---|
| 3700 | buf= mulNTL (buf, mod (iter.getItem(), y)); |
---|
| 3701 | } |
---|
| 3702 | bufFactors.append (buf); |
---|
| 3703 | } |
---|
| 3704 | factors= bufFactors; |
---|
| 3705 | M= CFMatrix (liftBound, factors.length()); |
---|
| 3706 | Pi= CFArray(); |
---|
| 3707 | diophant= CFList(); |
---|
| 3708 | factors.insert (LCF); |
---|
| 3709 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 3710 | } |
---|
| 3711 | |
---|
| 3712 | CFList |
---|
| 3713 | earlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_p& N, |
---|
| 3714 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
| 3715 | int& factorsFound, bool beenInThres, CFMatrix& M, |
---|
| 3716 | CFArray& Pi, CFList& diophant |
---|
| 3717 | ) |
---|
| 3718 | { |
---|
| 3719 | bufF= F; |
---|
| 3720 | factorsFound= 0; |
---|
| 3721 | CanonicalForm LCF= LC (F, 1); |
---|
| 3722 | CFList result; |
---|
| 3723 | int smallFactorDeg= 11; |
---|
| 3724 | mat_zz_p NTLN= N; |
---|
| 3725 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 3726 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 3727 | factorsFoundIndex [i]= 0; |
---|
| 3728 | |
---|
| 3729 | if (degree (F) + 1 > smallFactorDeg) |
---|
| 3730 | { |
---|
| 3731 | if (l < smallFactorDeg) |
---|
| 3732 | { |
---|
| 3733 | factors.insert (LCF); |
---|
| 3734 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
| 3735 | l= smallFactorDeg; |
---|
| 3736 | } |
---|
| 3737 | reconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
| 3738 | factorsFoundIndex, NTLN, beenInThres |
---|
| 3739 | ); |
---|
| 3740 | if (result.length() == NTLN.NumCols()) |
---|
| 3741 | { |
---|
| 3742 | delete [] factorsFoundIndex; |
---|
| 3743 | return result; |
---|
| 3744 | } |
---|
| 3745 | } |
---|
| 3746 | |
---|
| 3747 | if (l < degree (bufF)/2+2) |
---|
| 3748 | { |
---|
| 3749 | factors.insert (LCF); |
---|
| 3750 | henselLiftResume12 (F, factors, l, degree (bufF)/2 + 2, Pi, diophant, M); |
---|
| 3751 | l= degree (bufF)/2 + 2; |
---|
| 3752 | } |
---|
| 3753 | reconstructionTry (result, bufF, factors, degree (bufF)/2 + 2, |
---|
| 3754 | factorsFound, factorsFoundIndex, NTLN, beenInThres |
---|
| 3755 | ); |
---|
| 3756 | if (result.length() == NTLN.NumCols()) |
---|
| 3757 | { |
---|
| 3758 | delete [] factorsFoundIndex; |
---|
| 3759 | return result; |
---|
| 3760 | } |
---|
| 3761 | |
---|
| 3762 | if (l < degree (F) + 1) |
---|
| 3763 | { |
---|
| 3764 | factors.insert (LCF); |
---|
| 3765 | henselLiftResume12 (F, factors, l, degree (bufF) + 1, Pi, diophant, M); |
---|
| 3766 | l= degree (bufF) + 1; |
---|
| 3767 | } |
---|
| 3768 | reconstructionTry (result, bufF, factors, degree (bufF) + 1, factorsFound, |
---|
| 3769 | factorsFoundIndex, NTLN, beenInThres |
---|
| 3770 | ); |
---|
| 3771 | if (result.length() == NTLN.NumCols()) |
---|
| 3772 | { |
---|
| 3773 | delete [] factorsFoundIndex; |
---|
| 3774 | return result; |
---|
| 3775 | } |
---|
| 3776 | delete [] factorsFoundIndex; |
---|
| 3777 | return result; |
---|
| 3778 | } |
---|
| 3779 | |
---|
| 3780 | CFList |
---|
| 3781 | earlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_pE& N, |
---|
| 3782 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
| 3783 | int& factorsFound, bool beenInThres, CFMatrix& M, |
---|
| 3784 | CFArray& Pi, CFList& diophant |
---|
| 3785 | ) |
---|
| 3786 | { |
---|
| 3787 | bufF= F; |
---|
| 3788 | factorsFound= 0; |
---|
| 3789 | CanonicalForm LCF= LC (F, 1); |
---|
| 3790 | CFList result; |
---|
| 3791 | int smallFactorDeg= 11; |
---|
| 3792 | mat_zz_pE NTLN= N; |
---|
| 3793 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 3794 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 3795 | factorsFoundIndex [i]= 0; |
---|
| 3796 | if (degree (F) + 1 > smallFactorDeg) |
---|
| 3797 | { |
---|
| 3798 | if (l < smallFactorDeg) |
---|
| 3799 | { |
---|
| 3800 | factors.insert (LCF); |
---|
| 3801 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
| 3802 | l= smallFactorDeg; |
---|
| 3803 | } |
---|
| 3804 | reconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
| 3805 | factorsFoundIndex, NTLN, beenInThres |
---|
| 3806 | ); |
---|
| 3807 | if (result.length() == NTLN.NumCols()) |
---|
| 3808 | { |
---|
| 3809 | delete [] factorsFoundIndex; |
---|
| 3810 | return result; |
---|
| 3811 | } |
---|
| 3812 | } |
---|
| 3813 | |
---|
| 3814 | if (l < degree (bufF)/2+2) |
---|
| 3815 | { |
---|
| 3816 | factors.insert (LCF); |
---|
| 3817 | henselLiftResume12 (F, factors, l, degree (bufF)/2 + 2, Pi, diophant, M); |
---|
| 3818 | l= degree (bufF)/2 + 2; |
---|
| 3819 | } |
---|
| 3820 | reconstructionTry (result, bufF, factors, degree (bufF)/2 + 2, |
---|
| 3821 | factorsFound, factorsFoundIndex, NTLN, beenInThres |
---|
| 3822 | ); |
---|
| 3823 | if (result.length() == NTLN.NumCols()) |
---|
| 3824 | { |
---|
| 3825 | delete [] factorsFoundIndex; |
---|
| 3826 | return result; |
---|
| 3827 | } |
---|
| 3828 | |
---|
| 3829 | if (l < degree (F) + 1) |
---|
| 3830 | { |
---|
| 3831 | factors.insert (LCF); |
---|
| 3832 | henselLiftResume12 (F, factors, l, degree (bufF) + 1, Pi, diophant, M); |
---|
| 3833 | l= degree (bufF) + 1; |
---|
| 3834 | } |
---|
| 3835 | reconstructionTry (result, bufF, factors, degree (bufF) + 1, factorsFound, |
---|
| 3836 | factorsFoundIndex, NTLN, beenInThres |
---|
| 3837 | ); |
---|
| 3838 | if (result.length() == NTLN.NumCols()) |
---|
| 3839 | { |
---|
| 3840 | delete [] factorsFoundIndex; |
---|
| 3841 | return result; |
---|
| 3842 | } |
---|
| 3843 | delete [] factorsFoundIndex; |
---|
| 3844 | return result; |
---|
| 3845 | } |
---|
| 3846 | |
---|
| 3847 | //over field extension |
---|
| 3848 | CFList |
---|
| 3849 | extEarlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_p& N, |
---|
| 3850 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
| 3851 | int& factorsFound, bool beenInThres, CFMatrix& |
---|
| 3852 | M, CFArray& Pi, CFList& diophant, const |
---|
| 3853 | ExtensionInfo& info, const CanonicalForm& |
---|
| 3854 | evaluation |
---|
| 3855 | ) |
---|
| 3856 | { |
---|
| 3857 | bufF= F; |
---|
| 3858 | factorsFound= 0; |
---|
| 3859 | CanonicalForm LCF= LC (F, 1); |
---|
| 3860 | CFList result; |
---|
| 3861 | int smallFactorDeg= 11; |
---|
| 3862 | mat_zz_p NTLN= N; |
---|
| 3863 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 3864 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 3865 | factorsFoundIndex [i]= 0; |
---|
| 3866 | |
---|
| 3867 | if (degree (F) + 1 > smallFactorDeg) |
---|
| 3868 | { |
---|
| 3869 | if (l < smallFactorDeg) |
---|
| 3870 | { |
---|
| 3871 | factors.insert (LCF); |
---|
| 3872 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
| 3873 | l= smallFactorDeg; |
---|
| 3874 | } |
---|
| 3875 | extReconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
| 3876 | factorsFoundIndex, NTLN, beenInThres, info, |
---|
| 3877 | evaluation |
---|
| 3878 | ); |
---|
| 3879 | if (result.length() == NTLN.NumCols()) |
---|
| 3880 | { |
---|
| 3881 | delete [] factorsFoundIndex; |
---|
| 3882 | return result; |
---|
| 3883 | } |
---|
| 3884 | } |
---|
| 3885 | |
---|
| 3886 | if (l < degree (bufF)/2+2) |
---|
| 3887 | { |
---|
| 3888 | factors.insert (LCF); |
---|
| 3889 | henselLiftResume12 (F, factors, l, degree (bufF)/2 + 2, Pi, diophant, M); |
---|
| 3890 | l= degree (bufF)/2 + 2; |
---|
| 3891 | } |
---|
| 3892 | extReconstructionTry (result, bufF, factors, degree (bufF)/2 + 2, |
---|
| 3893 | factorsFound, factorsFoundIndex, NTLN, beenInThres, info, |
---|
| 3894 | evaluation |
---|
| 3895 | ); |
---|
| 3896 | if (result.length() == NTLN.NumCols()) |
---|
| 3897 | { |
---|
| 3898 | delete [] factorsFoundIndex; |
---|
| 3899 | return result; |
---|
| 3900 | } |
---|
| 3901 | |
---|
| 3902 | if (l < degree (bufF) + 1) |
---|
| 3903 | { |
---|
| 3904 | factors.insert (LCF); |
---|
| 3905 | henselLiftResume12 (F, factors, l, degree (bufF) + 1, Pi, diophant, M); |
---|
| 3906 | l= degree (bufF) + 1; |
---|
| 3907 | } |
---|
| 3908 | |
---|
| 3909 | extReconstructionTry (result, bufF, factors, degree (bufF) + 1, factorsFound, |
---|
| 3910 | factorsFoundIndex, NTLN, beenInThres, info, evaluation |
---|
| 3911 | ); |
---|
| 3912 | if (result.length() == NTLN.NumCols()) |
---|
| 3913 | { |
---|
| 3914 | delete [] factorsFoundIndex; |
---|
| 3915 | return result; |
---|
| 3916 | } |
---|
| 3917 | delete [] factorsFoundIndex; |
---|
| 3918 | return result; |
---|
| 3919 | } |
---|
| 3920 | |
---|
| 3921 | CFList |
---|
[c1b9927] | 3922 | sieveSmallFactors (const CanonicalForm& G, CFList& uniFactors, DegreePattern& |
---|
[11bf82] | 3923 | degPat, CanonicalForm& H, CFList& diophant, CFArray& Pi, |
---|
| 3924 | CFMatrix& M, bool& success, int d |
---|
| 3925 | ) |
---|
| 3926 | { |
---|
| 3927 | CanonicalForm F= G; |
---|
| 3928 | CFList bufUniFactors= uniFactors; |
---|
| 3929 | bufUniFactors.insert (LC (F, 1)); |
---|
| 3930 | int smallFactorDeg= d; |
---|
| 3931 | DegreePattern degs= degPat; |
---|
| 3932 | henselLift12 (F, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
---|
| 3933 | int adaptedLiftBound; |
---|
| 3934 | success= false; |
---|
| 3935 | CFList earlyFactors= earlyFactorDetection (F, bufUniFactors, adaptedLiftBound, |
---|
| 3936 | degs, success, smallFactorDeg |
---|
| 3937 | ); |
---|
| 3938 | if (degs.getLength() == 1) |
---|
| 3939 | { |
---|
| 3940 | degPat= degs; |
---|
| 3941 | return earlyFactors; |
---|
| 3942 | } |
---|
| 3943 | if (success) |
---|
| 3944 | { |
---|
| 3945 | H= F; |
---|
| 3946 | return earlyFactors; |
---|
| 3947 | } |
---|
| 3948 | int sizeOldF= size (F); |
---|
| 3949 | CFList result; |
---|
| 3950 | CanonicalForm bufF= F; |
---|
| 3951 | if (earlyFactors.length() > 0) |
---|
| 3952 | { |
---|
| 3953 | for (CFListIterator i= earlyFactors; i.hasItem(); i++) |
---|
| 3954 | bufF /= i.getItem(); |
---|
| 3955 | } |
---|
| 3956 | |
---|
| 3957 | if (size (bufF) < sizeOldF) |
---|
| 3958 | { |
---|
| 3959 | H= bufF; |
---|
| 3960 | success= true; |
---|
| 3961 | return earlyFactors; |
---|
| 3962 | } |
---|
| 3963 | else |
---|
| 3964 | { |
---|
| 3965 | uniFactors= bufUniFactors; |
---|
| 3966 | return CFList(); |
---|
| 3967 | } |
---|
| 3968 | } |
---|
| 3969 | |
---|
| 3970 | CFList |
---|
| 3971 | extSieveSmallFactors (const CanonicalForm& G, CFList& uniFactors, DegreePattern& |
---|
| 3972 | degPat, CanonicalForm& H, CFList& diophant, CFArray& Pi, |
---|
| 3973 | CFMatrix& M, bool& success, int d, const CanonicalForm& |
---|
| 3974 | evaluation, const ExtensionInfo& info |
---|
| 3975 | ) |
---|
| 3976 | { |
---|
| 3977 | CanonicalForm F= G; |
---|
| 3978 | CFList bufUniFactors= uniFactors; |
---|
| 3979 | bufUniFactors.insert (LC (F, 1)); |
---|
| 3980 | int smallFactorDeg= d; |
---|
| 3981 | DegreePattern degs= degPat; |
---|
| 3982 | henselLift12 (F, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
---|
| 3983 | int adaptedLiftBound; |
---|
| 3984 | success= false; |
---|
| 3985 | CFList earlyFactors= extEarlyFactorDetection (F, bufUniFactors, |
---|
| 3986 | adaptedLiftBound, degs, success, |
---|
| 3987 | info, evaluation, smallFactorDeg |
---|
| 3988 | ); |
---|
| 3989 | if (degs.getLength() == 1) |
---|
| 3990 | { |
---|
| 3991 | degPat= degs; |
---|
| 3992 | return earlyFactors; |
---|
| 3993 | } |
---|
| 3994 | if (success) |
---|
| 3995 | { |
---|
| 3996 | H= F; |
---|
| 3997 | return earlyFactors; |
---|
| 3998 | } |
---|
| 3999 | Variable y= F.mvar(); |
---|
| 4000 | CanonicalForm shiftedF= F (y - evaluation, y); |
---|
| 4001 | int sizeOldF= size (shiftedF); |
---|
| 4002 | CFList result; |
---|
| 4003 | CanonicalForm bufF= shiftedF; |
---|
| 4004 | if (earlyFactors.length() > 0) |
---|
| 4005 | { |
---|
| 4006 | for (CFListIterator i= earlyFactors; i.hasItem(); i++) |
---|
| 4007 | { |
---|
| 4008 | bufF /= i.getItem(); |
---|
| 4009 | result.append (i.getItem()); |
---|
| 4010 | } |
---|
| 4011 | } |
---|
| 4012 | |
---|
| 4013 | if (size (bufF) < sizeOldF) |
---|
| 4014 | { |
---|
| 4015 | H= bufF (y + evaluation, y); //shift back to zero |
---|
| 4016 | success= true; |
---|
| 4017 | return result; |
---|
| 4018 | } |
---|
| 4019 | else |
---|
| 4020 | { |
---|
| 4021 | uniFactors= bufUniFactors; |
---|
| 4022 | return CFList(); |
---|
| 4023 | } |
---|
| 4024 | } |
---|
| 4025 | |
---|
| 4026 | CFList |
---|
| 4027 | henselLiftAndLatticeRecombi (const CanonicalForm& G, const CFList& uniFactors, |
---|
| 4028 | const Variable& alpha, const DegreePattern& degPat |
---|
| 4029 | ) |
---|
| 4030 | { |
---|
| 4031 | DegreePattern degs= degPat; |
---|
| 4032 | CanonicalForm F= G; |
---|
| 4033 | CanonicalForm LCF= LC (F, 1); |
---|
| 4034 | Variable y= F.mvar(); |
---|
| 4035 | Variable x= Variable (1); |
---|
| 4036 | int d; |
---|
| 4037 | int* bounds= computeBounds (F, d); |
---|
| 4038 | |
---|
| 4039 | int minBound= bounds[0]; |
---|
| 4040 | for (int i= 1; i < d; i++) |
---|
| 4041 | { |
---|
| 4042 | if (bounds[i] != 0) |
---|
| 4043 | minBound= tmin (minBound, bounds[i]); |
---|
| 4044 | } |
---|
| 4045 | |
---|
| 4046 | CFList bufUniFactors= uniFactors; |
---|
| 4047 | CFArray Pi; |
---|
| 4048 | CFList diophant; |
---|
| 4049 | int liftBound= 2*totaldegree (F) - 1; |
---|
| 4050 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
| 4051 | |
---|
| 4052 | CFList smallFactors; |
---|
| 4053 | CanonicalForm H; |
---|
| 4054 | bool success; |
---|
| 4055 | smallFactors= sieveSmallFactors (F, bufUniFactors, degs, H, diophant, Pi, M, |
---|
| 4056 | success, 2*(minBound + 1) |
---|
| 4057 | ); |
---|
| 4058 | |
---|
| 4059 | if (smallFactors.length() > 0) |
---|
| 4060 | { |
---|
| 4061 | if (smallFactors.length() == 1) |
---|
| 4062 | { |
---|
| 4063 | if (smallFactors.getFirst() == F) |
---|
| 4064 | { |
---|
| 4065 | delete [] bounds; |
---|
| 4066 | return CFList (G); |
---|
| 4067 | } |
---|
| 4068 | } |
---|
| 4069 | if (degs.getLength() <= 1) |
---|
| 4070 | { |
---|
| 4071 | delete [] bounds; |
---|
| 4072 | return smallFactors; |
---|
| 4073 | } |
---|
| 4074 | } |
---|
| 4075 | |
---|
| 4076 | int index; |
---|
[38ffb7] | 4077 | CanonicalForm tmp1, tmp2; |
---|
[11bf82] | 4078 | for (CFListIterator i= smallFactors; i.hasItem(); i++) |
---|
| 4079 | { |
---|
| 4080 | index= 1; |
---|
| 4081 | tmp1= mod (i.getItem(),y); |
---|
| 4082 | tmp1 /= Lc (tmp1); |
---|
| 4083 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
| 4084 | { |
---|
| 4085 | tmp2= mod (j.getItem(), y); |
---|
| 4086 | tmp2 /= Lc (tmp2); |
---|
| 4087 | if (tmp1 == tmp2) |
---|
| 4088 | { |
---|
| 4089 | index++; |
---|
| 4090 | j.remove(index); |
---|
| 4091 | break; |
---|
| 4092 | } |
---|
| 4093 | } |
---|
| 4094 | } |
---|
| 4095 | |
---|
| 4096 | if (bufUniFactors.isEmpty()) |
---|
| 4097 | { |
---|
| 4098 | delete [] bounds; |
---|
| 4099 | return smallFactors; |
---|
| 4100 | } |
---|
| 4101 | |
---|
| 4102 | if (success) |
---|
| 4103 | { |
---|
| 4104 | F= H; |
---|
| 4105 | delete [] bounds; |
---|
| 4106 | bounds= computeBounds (F, d); |
---|
| 4107 | LCF= LC (F, 1); |
---|
| 4108 | |
---|
| 4109 | minBound= bounds[0]; |
---|
| 4110 | for (int i= 1; i < d; i++) |
---|
| 4111 | { |
---|
| 4112 | if (bounds[i] != 0) |
---|
| 4113 | minBound= tmin (minBound, bounds[i]); |
---|
| 4114 | } |
---|
| 4115 | Pi= CFArray(); |
---|
| 4116 | diophant= CFList(); |
---|
| 4117 | liftBound= 2*totaldegree (F) - 1; |
---|
| 4118 | M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
| 4119 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 4120 | degs.intersect (bufDegs); |
---|
| 4121 | degs.refine(); |
---|
| 4122 | if (degs.getLength() <= 1) |
---|
| 4123 | { |
---|
| 4124 | smallFactors.append (F); |
---|
| 4125 | delete [] bounds; |
---|
| 4126 | return smallFactors; |
---|
| 4127 | } |
---|
| 4128 | } |
---|
| 4129 | |
---|
| 4130 | bool reduceFq2Fp= (degree (F) > getCharacteristic()); |
---|
| 4131 | bufUniFactors.insert (LCF); |
---|
| 4132 | int l= 1; |
---|
| 4133 | |
---|
| 4134 | zz_p::init (getCharacteristic()); |
---|
| 4135 | mat_zz_p NTLN; |
---|
| 4136 | if (alpha.level() != 1) |
---|
| 4137 | { |
---|
| 4138 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 4139 | zz_pE::init (NTLMipo); |
---|
| 4140 | } |
---|
| 4141 | mat_zz_pE NTLNe; |
---|
| 4142 | if (alpha.level() == 1) |
---|
| 4143 | ident (NTLN, bufUniFactors.length() - 1); |
---|
| 4144 | else |
---|
| 4145 | { |
---|
| 4146 | if (reduceFq2Fp) |
---|
| 4147 | ident (NTLN, bufUniFactors.length() - 1); |
---|
| 4148 | else |
---|
| 4149 | ident (NTLNe, bufUniFactors.length() - 1); |
---|
| 4150 | } |
---|
| 4151 | bool irreducible= false; |
---|
| 4152 | CFArray bufQ= CFArray (bufUniFactors.length() - 1); |
---|
| 4153 | |
---|
| 4154 | int oldL; |
---|
| 4155 | if (success) |
---|
| 4156 | { |
---|
| 4157 | int start= 0; |
---|
| 4158 | if (alpha.level() == 1) |
---|
| 4159 | oldL= liftAndComputeLattice (F, bounds, d, start, liftBound, minBound, |
---|
| 4160 | bufUniFactors, NTLN, diophant, M, Pi, bufQ, |
---|
| 4161 | irreducible |
---|
| 4162 | ); |
---|
| 4163 | else |
---|
| 4164 | { |
---|
| 4165 | if (reduceFq2Fp) |
---|
| 4166 | oldL= liftAndComputeLatticeFq2Fp (F, bounds, d, start, liftBound, |
---|
| 4167 | minBound, bufUniFactors, NTLN, |
---|
| 4168 | diophant, M, Pi, bufQ, irreducible, |
---|
| 4169 | alpha |
---|
| 4170 | ); |
---|
| 4171 | else |
---|
| 4172 | oldL= liftAndComputeLattice (F, bounds, d, start, liftBound, minBound, |
---|
| 4173 | bufUniFactors, NTLNe, diophant, M, Pi, bufQ, |
---|
| 4174 | irreducible |
---|
| 4175 | ); |
---|
| 4176 | } |
---|
| 4177 | } |
---|
| 4178 | else |
---|
| 4179 | { |
---|
| 4180 | if (alpha.level() == 1) |
---|
| 4181 | oldL= liftAndComputeLattice (F, bounds, d, 2*(minBound + 1), liftBound, |
---|
| 4182 | minBound, bufUniFactors, NTLN, diophant, M, |
---|
| 4183 | Pi, bufQ, irreducible |
---|
| 4184 | ); |
---|
| 4185 | else |
---|
| 4186 | { |
---|
| 4187 | if (reduceFq2Fp) |
---|
| 4188 | oldL= liftAndComputeLatticeFq2Fp (F, bounds, d, 2*(minBound + 1), |
---|
| 4189 | liftBound, minBound, bufUniFactors, |
---|
| 4190 | NTLN, diophant, M, Pi, bufQ, |
---|
| 4191 | irreducible, alpha |
---|
| 4192 | ); |
---|
| 4193 | else |
---|
| 4194 | oldL= liftAndComputeLattice (F, bounds, d, 2*(minBound + 1), liftBound, |
---|
| 4195 | minBound, bufUniFactors, NTLNe, diophant, |
---|
| 4196 | M, Pi, bufQ, irreducible |
---|
| 4197 | ); |
---|
| 4198 | } |
---|
| 4199 | } |
---|
| 4200 | |
---|
| 4201 | bufUniFactors.removeFirst(); |
---|
| 4202 | if (oldL > liftBound) |
---|
| 4203 | { |
---|
| 4204 | delete [] bounds; |
---|
| 4205 | return Union (smallFactors, |
---|
| 4206 | factorRecombination (bufUniFactors, F, |
---|
| 4207 | power (y, degree (F) + 1 + degree (LCF)), |
---|
| 4208 | degs, 1, bufUniFactors.length()/2 |
---|
| 4209 | ) |
---|
| 4210 | ); |
---|
| 4211 | } |
---|
| 4212 | |
---|
| 4213 | l= oldL; |
---|
| 4214 | if (irreducible) |
---|
| 4215 | { |
---|
| 4216 | delete [] bounds; |
---|
| 4217 | return Union (CFList (F), smallFactors); |
---|
| 4218 | } |
---|
| 4219 | |
---|
| 4220 | CanonicalForm yToL= power (y,l); |
---|
| 4221 | |
---|
| 4222 | CFList result; |
---|
| 4223 | if (l >= degree (F) + 1) |
---|
| 4224 | { |
---|
| 4225 | int * factorsFoundIndex; |
---|
| 4226 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4227 | { |
---|
| 4228 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 4229 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 4230 | factorsFoundIndex[i]= 0; |
---|
| 4231 | } |
---|
| 4232 | else |
---|
| 4233 | { |
---|
| 4234 | factorsFoundIndex= new int [NTLNe.NumCols()]; |
---|
| 4235 | for (long i= 0; i < NTLNe.NumCols(); i++) |
---|
| 4236 | factorsFoundIndex[i]= 0; |
---|
| 4237 | } |
---|
| 4238 | int factorsFound= 0; |
---|
| 4239 | CanonicalForm bufF= F; |
---|
| 4240 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4241 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
| 4242 | factorsFound, factorsFoundIndex, NTLN, false |
---|
| 4243 | ); |
---|
| 4244 | else |
---|
| 4245 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
| 4246 | factorsFound, factorsFoundIndex, NTLNe, false |
---|
| 4247 | ); |
---|
| 4248 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4249 | { |
---|
| 4250 | if (result.length() == NTLN.NumCols()) |
---|
| 4251 | { |
---|
| 4252 | delete [] factorsFoundIndex; |
---|
| 4253 | delete [] bounds; |
---|
| 4254 | return Union (result, smallFactors); |
---|
| 4255 | } |
---|
| 4256 | } |
---|
| 4257 | else |
---|
| 4258 | { |
---|
| 4259 | if (result.length() == NTLNe.NumCols()) |
---|
| 4260 | { |
---|
| 4261 | delete [] factorsFoundIndex; |
---|
| 4262 | delete [] bounds; |
---|
| 4263 | return Union (result, smallFactors); |
---|
| 4264 | } |
---|
| 4265 | } |
---|
| 4266 | delete [] factorsFoundIndex; |
---|
| 4267 | } |
---|
| 4268 | if (l >= liftBound) |
---|
| 4269 | { |
---|
| 4270 | int * factorsFoundIndex; |
---|
| 4271 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4272 | { |
---|
[c1b9927] | 4273 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
[11bf82] | 4274 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 4275 | factorsFoundIndex[i]= 0; |
---|
| 4276 | } |
---|
| 4277 | else |
---|
| 4278 | { |
---|
[c1b9927] | 4279 | factorsFoundIndex= new int [NTLNe.NumCols()]; |
---|
[11bf82] | 4280 | for (long i= 0; i < NTLNe.NumCols(); i++) |
---|
| 4281 | factorsFoundIndex[i]= 0; |
---|
| 4282 | } |
---|
| 4283 | CanonicalForm bufF= F; |
---|
| 4284 | int factorsFound= 0; |
---|
| 4285 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4286 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1 + degree |
---|
| 4287 | (LCF), factorsFound, factorsFoundIndex, NTLN, false |
---|
| 4288 | ); |
---|
| 4289 | else |
---|
| 4290 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1 + degree |
---|
| 4291 | (LCF), factorsFound, factorsFoundIndex, NTLNe, false |
---|
| 4292 | ); |
---|
| 4293 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4294 | { |
---|
| 4295 | if (result.length() == NTLN.NumCols()) |
---|
| 4296 | { |
---|
| 4297 | delete [] factorsFoundIndex; |
---|
| 4298 | delete [] bounds; |
---|
| 4299 | return Union (result, smallFactors); |
---|
| 4300 | } |
---|
| 4301 | } |
---|
| 4302 | else |
---|
| 4303 | { |
---|
| 4304 | if (result.length() == NTLNe.NumCols()) |
---|
| 4305 | { |
---|
| 4306 | delete [] factorsFoundIndex; |
---|
| 4307 | delete [] bounds; |
---|
| 4308 | return Union (result, smallFactors); |
---|
| 4309 | } |
---|
| 4310 | } |
---|
| 4311 | delete [] factorsFoundIndex; |
---|
| 4312 | } |
---|
| 4313 | |
---|
| 4314 | result= CFList(); |
---|
| 4315 | bool beenInThres= false; |
---|
| 4316 | int thres= 100; |
---|
| 4317 | if (l <= thres) |
---|
| 4318 | { |
---|
| 4319 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4320 | { |
---|
| 4321 | if (NTLN.NumCols() < bufUniFactors.length()) |
---|
| 4322 | { |
---|
[c1b9927] | 4323 | refineAndRestartLift (F, NTLN, liftBound, l, bufUniFactors, M, Pi, |
---|
[11bf82] | 4324 | diophant |
---|
| 4325 | ); |
---|
| 4326 | beenInThres= true; |
---|
| 4327 | } |
---|
| 4328 | } |
---|
| 4329 | else |
---|
| 4330 | { |
---|
| 4331 | if (NTLNe.NumCols() < bufUniFactors.length()) |
---|
| 4332 | { |
---|
| 4333 | refineAndRestartLift (F, NTLNe, liftBound, l, bufUniFactors, M, Pi, |
---|
| 4334 | diophant |
---|
| 4335 | ); |
---|
| 4336 | beenInThres= true; |
---|
| 4337 | } |
---|
| 4338 | } |
---|
| 4339 | } |
---|
| 4340 | |
---|
| 4341 | CanonicalForm bufF= F; |
---|
| 4342 | int factorsFound= 0; |
---|
| 4343 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4344 | { |
---|
| 4345 | result= earlyReconstructionAndLifting (F, NTLN, bufF, bufUniFactors, l, |
---|
| 4346 | factorsFound, beenInThres, M, Pi, |
---|
| 4347 | diophant |
---|
| 4348 | ); |
---|
| 4349 | |
---|
| 4350 | if (result.length() == NTLN.NumCols()) |
---|
| 4351 | { |
---|
| 4352 | delete [] bounds; |
---|
| 4353 | return Union (result, smallFactors); |
---|
| 4354 | } |
---|
| 4355 | } |
---|
| 4356 | else |
---|
| 4357 | { |
---|
| 4358 | result= earlyReconstructionAndLifting (F, NTLNe, bufF, bufUniFactors, l, |
---|
| 4359 | factorsFound, beenInThres, M, Pi, |
---|
| 4360 | diophant |
---|
| 4361 | ); |
---|
| 4362 | |
---|
| 4363 | if (result.length() == NTLNe.NumCols()) |
---|
| 4364 | { |
---|
| 4365 | delete [] bounds; |
---|
| 4366 | return Union (result, smallFactors); |
---|
| 4367 | } |
---|
| 4368 | } |
---|
| 4369 | |
---|
| 4370 | if (result.length() > 0) |
---|
| 4371 | { |
---|
| 4372 | if (beenInThres) |
---|
| 4373 | { |
---|
[38ffb7] | 4374 | int index; |
---|
| 4375 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
[11bf82] | 4376 | { |
---|
[38ffb7] | 4377 | index= 1; |
---|
| 4378 | tmp1= mod (i.getItem(), y); |
---|
| 4379 | tmp1 /= Lc (tmp1); |
---|
| 4380 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
[11bf82] | 4381 | { |
---|
[38ffb7] | 4382 | tmp2= mod (j.getItem(), y); |
---|
| 4383 | tmp2 /= Lc (tmp2); |
---|
| 4384 | if (tmp1 == tmp2) |
---|
| 4385 | { |
---|
| 4386 | index++; |
---|
| 4387 | j.remove(index); |
---|
| 4388 | break; |
---|
| 4389 | } |
---|
[11bf82] | 4390 | } |
---|
| 4391 | } |
---|
| 4392 | } |
---|
| 4393 | else |
---|
| 4394 | { |
---|
[38ffb7] | 4395 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
| 4396 | CFList bufBufUniFactors= bufUniFactors; |
---|
| 4397 | CFListIterator iter, iter2; |
---|
| 4398 | CanonicalForm buf; |
---|
[11bf82] | 4399 | CFList factorsConsidered; |
---|
[38ffb7] | 4400 | CanonicalForm tmp; |
---|
| 4401 | for (int i= 0; i < NTLN.NumCols(); i++) |
---|
[11bf82] | 4402 | { |
---|
[38ffb7] | 4403 | if (zeroOne [i] == 0) |
---|
| 4404 | continue; |
---|
| 4405 | iter= bufUniFactors; |
---|
| 4406 | buf= 1; |
---|
| 4407 | factorsConsidered= CFList(); |
---|
| 4408 | for (int j= 0; j < NTLN.NumRows(); j++, iter++) |
---|
[11bf82] | 4409 | { |
---|
[38ffb7] | 4410 | if (!IsZero (NTLN (j + 1,i + 1))) |
---|
| 4411 | { |
---|
| 4412 | factorsConsidered.append (iter.getItem()); |
---|
| 4413 | buf *= mod (iter.getItem(), y); |
---|
| 4414 | } |
---|
[11bf82] | 4415 | } |
---|
[38ffb7] | 4416 | buf /= Lc (buf); |
---|
| 4417 | for (iter2= result; iter2.hasItem(); iter2++) |
---|
[11bf82] | 4418 | { |
---|
[38ffb7] | 4419 | tmp= mod (iter2.getItem(), y); |
---|
| 4420 | tmp /= Lc (tmp); |
---|
| 4421 | if (tmp == buf) |
---|
| 4422 | { |
---|
| 4423 | bufBufUniFactors= Difference (bufBufUniFactors, factorsConsidered); |
---|
| 4424 | break; |
---|
| 4425 | } |
---|
[11bf82] | 4426 | } |
---|
| 4427 | } |
---|
[38ffb7] | 4428 | bufUniFactors= bufBufUniFactors; |
---|
| 4429 | delete [] zeroOne; |
---|
[11bf82] | 4430 | } |
---|
| 4431 | |
---|
| 4432 | int oldNumCols; |
---|
| 4433 | CFList resultBufF; |
---|
| 4434 | irreducible= false; |
---|
| 4435 | |
---|
| 4436 | if (alpha.level() == 1) |
---|
| 4437 | { |
---|
| 4438 | oldNumCols= NTLN.NumCols(); |
---|
| 4439 | resultBufF= increasePrecision (bufF, bufUniFactors, factorsFound, |
---|
| 4440 | oldNumCols, oldL, l |
---|
| 4441 | ); |
---|
| 4442 | } |
---|
| 4443 | else |
---|
| 4444 | { |
---|
| 4445 | if (reduceFq2Fp) |
---|
| 4446 | { |
---|
| 4447 | oldNumCols= NTLN.NumCols(); |
---|
| 4448 | |
---|
| 4449 | resultBufF= increasePrecisionFq2Fp (bufF, bufUniFactors, factorsFound, |
---|
| 4450 | oldNumCols, oldL, alpha, l |
---|
| 4451 | ); |
---|
| 4452 | } |
---|
| 4453 | else |
---|
| 4454 | { |
---|
| 4455 | oldNumCols= NTLNe.NumCols(); |
---|
| 4456 | |
---|
| 4457 | resultBufF= increasePrecision (bufF, bufUniFactors, factorsFound, |
---|
| 4458 | oldNumCols, oldL, alpha, l |
---|
| 4459 | ); |
---|
| 4460 | } |
---|
| 4461 | } |
---|
| 4462 | |
---|
| 4463 | if (bufUniFactors.isEmpty() || degree (bufF) <= 0) |
---|
| 4464 | { |
---|
| 4465 | delete [] bounds; |
---|
| 4466 | result= Union (resultBufF, result); |
---|
| 4467 | return Union (result, smallFactors); |
---|
| 4468 | } |
---|
| 4469 | |
---|
| 4470 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
| 4471 | i.getItem()= mod (i.getItem(), y); |
---|
| 4472 | |
---|
| 4473 | result= Union (result, resultBufF); |
---|
| 4474 | result= Union (result, smallFactors); |
---|
| 4475 | delete [] bounds; |
---|
| 4476 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 4477 | degs.intersect (bufDegs); |
---|
| 4478 | degs.refine(); |
---|
| 4479 | if (degs.getLength() == 1 || bufUniFactors.length() == 1) |
---|
| 4480 | { |
---|
| 4481 | result.append (bufF); |
---|
| 4482 | return result; |
---|
| 4483 | } |
---|
| 4484 | return Union (result, henselLiftAndLatticeRecombi (bufF, bufUniFactors, |
---|
| 4485 | alpha, degs |
---|
| 4486 | ) |
---|
| 4487 | ); |
---|
| 4488 | } |
---|
| 4489 | |
---|
| 4490 | if (l < liftBound) |
---|
| 4491 | { |
---|
| 4492 | if (alpha.level() == 1) |
---|
| 4493 | { |
---|
| 4494 | result=increasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
| 4495 | NTLN |
---|
| 4496 | ); |
---|
| 4497 | } |
---|
| 4498 | else |
---|
| 4499 | { |
---|
| 4500 | if (reduceFq2Fp) |
---|
| 4501 | { |
---|
| 4502 | result=increasePrecisionFq2Fp (F, bufUniFactors, oldL, l, d, bounds, |
---|
| 4503 | bufQ, NTLN, alpha |
---|
| 4504 | ); |
---|
| 4505 | } |
---|
| 4506 | else |
---|
| 4507 | { |
---|
| 4508 | result=increasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
| 4509 | NTLNe |
---|
| 4510 | ); |
---|
| 4511 | } |
---|
| 4512 | } |
---|
| 4513 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4514 | { |
---|
[c1b9927] | 4515 | if (result.length()== NTLN.NumCols()) |
---|
[11bf82] | 4516 | { |
---|
| 4517 | delete [] bounds; |
---|
| 4518 | result= Union (result, smallFactors); |
---|
| 4519 | return result; |
---|
| 4520 | } |
---|
| 4521 | } |
---|
| 4522 | else |
---|
| 4523 | { |
---|
[c1b9927] | 4524 | if (result.length()== NTLNe.NumCols()) |
---|
[11bf82] | 4525 | { |
---|
| 4526 | delete [] bounds; |
---|
| 4527 | result= Union (result, smallFactors); |
---|
| 4528 | return result; |
---|
| 4529 | } |
---|
| 4530 | } |
---|
| 4531 | |
---|
| 4532 | if (result.isEmpty()) |
---|
| 4533 | { |
---|
| 4534 | if (alpha.level() == 1) |
---|
| 4535 | result= furtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
| 4536 | liftBound, d, bounds, NTLN, |
---|
| 4537 | diophant, M, Pi, bufQ |
---|
| 4538 | ); |
---|
| 4539 | else |
---|
| 4540 | { |
---|
| 4541 | if (reduceFq2Fp) |
---|
| 4542 | result= furtherLiftingAndIncreasePrecisionFq2Fp (F,bufUniFactors, l, |
---|
| 4543 | liftBound, d, bounds, |
---|
| 4544 | NTLN, diophant, M, |
---|
| 4545 | Pi, bufQ, alpha |
---|
| 4546 | ); |
---|
| 4547 | else |
---|
| 4548 | result= furtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
| 4549 | liftBound, d, bounds, |
---|
| 4550 | NTLNe, diophant, M, |
---|
| 4551 | Pi, bufQ |
---|
| 4552 | ); |
---|
| 4553 | } |
---|
| 4554 | |
---|
| 4555 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4556 | { |
---|
[c1b9927] | 4557 | if (result.length() == NTLN.NumCols()) |
---|
[11bf82] | 4558 | { |
---|
| 4559 | delete [] bounds; |
---|
| 4560 | result= Union (result, smallFactors); |
---|
| 4561 | return result; |
---|
| 4562 | } |
---|
| 4563 | } |
---|
| 4564 | else |
---|
| 4565 | { |
---|
[c1b9927] | 4566 | if (result.length() == NTLNe.NumCols()) |
---|
[11bf82] | 4567 | { |
---|
| 4568 | delete [] bounds; |
---|
| 4569 | result= Union (result, smallFactors); |
---|
| 4570 | return result; |
---|
| 4571 | } |
---|
| 4572 | } |
---|
| 4573 | } |
---|
| 4574 | } |
---|
| 4575 | |
---|
| 4576 | DEBOUTLN (cerr, "lattice recombination failed"); |
---|
| 4577 | |
---|
| 4578 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 4579 | degs.intersect (bufDegs); |
---|
| 4580 | degs.refine(); |
---|
| 4581 | |
---|
| 4582 | delete [] bounds; |
---|
| 4583 | bounds= computeBounds (F, d); |
---|
| 4584 | minBound= bounds[0]; |
---|
| 4585 | for (int i= 1; i < d; i++) |
---|
| 4586 | { |
---|
| 4587 | if (bounds[i] != 0) |
---|
| 4588 | minBound= tmin (minBound, bounds[i]); |
---|
| 4589 | } |
---|
| 4590 | |
---|
| 4591 | if (minBound > 16 || result.length() == 0) |
---|
| 4592 | { |
---|
| 4593 | result= Union (result, smallFactors); |
---|
| 4594 | CanonicalForm MODl= power (y, degree (F) + 1 + degree (LC (F, 1))); |
---|
| 4595 | delete [] bounds; |
---|
| 4596 | return Union (result, factorRecombination (bufUniFactors, F, MODl, degs, 1, |
---|
| 4597 | bufUniFactors.length()/2 |
---|
| 4598 | ) |
---|
| 4599 | ); |
---|
| 4600 | } |
---|
| 4601 | else |
---|
| 4602 | { |
---|
| 4603 | result= Union (result, smallFactors); |
---|
| 4604 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
| 4605 | i.getItem()= mod (i.getItem(), y); |
---|
| 4606 | delete [] bounds; |
---|
| 4607 | return Union (result, henselLiftAndLatticeRecombi (F, bufUniFactors, alpha, |
---|
| 4608 | degs |
---|
| 4609 | ) |
---|
| 4610 | ); |
---|
| 4611 | } |
---|
| 4612 | } |
---|
| 4613 | |
---|
| 4614 | ExtensionInfo |
---|
| 4615 | init4ext (const ExtensionInfo& info, const CanonicalForm& evaluation, |
---|
| 4616 | int& degMipo |
---|
| 4617 | ) |
---|
| 4618 | { |
---|
| 4619 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
| 4620 | Variable alpha= info.getAlpha(); |
---|
| 4621 | if (GF) |
---|
| 4622 | { |
---|
| 4623 | degMipo= getGFDegree(); |
---|
| 4624 | CanonicalForm GFMipo= gf_mipo; |
---|
| 4625 | setCharacteristic (getCharacteristic()); |
---|
| 4626 | GFMipo.mapinto(); |
---|
| 4627 | alpha= rootOf (GFMipo); |
---|
| 4628 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 4629 | } |
---|
| 4630 | else |
---|
| 4631 | { |
---|
| 4632 | alpha= info.getAlpha(); |
---|
| 4633 | degMipo= degree (getMipo (alpha)); |
---|
| 4634 | } |
---|
| 4635 | |
---|
| 4636 | Variable gamma; |
---|
| 4637 | CanonicalForm primElemAlpha, imPrimElemAlpha; |
---|
| 4638 | if ((!GF && evaluation != alpha) || (GF && evaluation != getGFGenerator())) |
---|
| 4639 | { |
---|
| 4640 | CanonicalForm bufEvaluation; |
---|
| 4641 | if (GF) |
---|
| 4642 | { |
---|
| 4643 | setCharacteristic (getCharacteristic()); |
---|
| 4644 | bufEvaluation= GF2FalphaRep (evaluation, alpha); |
---|
| 4645 | } |
---|
| 4646 | else |
---|
| 4647 | bufEvaluation= evaluation; |
---|
| 4648 | CanonicalForm mipo= findMinPoly (bufEvaluation, alpha); |
---|
| 4649 | gamma= rootOf (mipo); |
---|
| 4650 | Variable V_buf; |
---|
[ac8e1a] | 4651 | bool fail= false; |
---|
[11bf82] | 4652 | primElemAlpha= primitiveElement (alpha, V_buf, fail); |
---|
| 4653 | imPrimElemAlpha= map (primElemAlpha, alpha, bufEvaluation, gamma); |
---|
| 4654 | |
---|
| 4655 | if (GF) |
---|
| 4656 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 4657 | } |
---|
| 4658 | else |
---|
| 4659 | gamma= alpha; |
---|
| 4660 | ExtensionInfo info2= ExtensionInfo (alpha, gamma, primElemAlpha, |
---|
| 4661 | imPrimElemAlpha, 1, info.getGFName(), true |
---|
| 4662 | ); |
---|
| 4663 | |
---|
| 4664 | return info2; |
---|
| 4665 | } |
---|
| 4666 | |
---|
| 4667 | CFList |
---|
| 4668 | extHenselLiftAndLatticeRecombi(const CanonicalForm& G, const CFList& uniFactors, |
---|
| 4669 | const ExtensionInfo& extInfo, const |
---|
| 4670 | DegreePattern& degPat, const CanonicalForm& eval |
---|
| 4671 | ) |
---|
| 4672 | { |
---|
| 4673 | CanonicalForm evaluation= eval; |
---|
| 4674 | ExtensionInfo info= extInfo; |
---|
| 4675 | Variable alpha; |
---|
| 4676 | DegreePattern degs= degPat; |
---|
| 4677 | CanonicalForm F= G; |
---|
| 4678 | Variable x= Variable (1); |
---|
| 4679 | Variable y= F.mvar(); |
---|
| 4680 | CFList bufUniFactors= uniFactors; |
---|
| 4681 | |
---|
| 4682 | |
---|
| 4683 | int degMipo; |
---|
| 4684 | ExtensionInfo info2= init4ext (info, evaluation, degMipo); |
---|
| 4685 | |
---|
| 4686 | CFList source, dest; |
---|
| 4687 | CanonicalForm LCF= LC (F, 1); |
---|
| 4688 | |
---|
| 4689 | int d; |
---|
| 4690 | int* bounds= computeBounds (F, d); |
---|
| 4691 | int minBound= bounds[0]; |
---|
| 4692 | for (int i= 1; i < d; i++) |
---|
| 4693 | { |
---|
| 4694 | if (bounds[i] != 0) |
---|
| 4695 | minBound= tmin (minBound, bounds[i]); |
---|
| 4696 | } |
---|
| 4697 | |
---|
| 4698 | |
---|
| 4699 | CFArray Pi; |
---|
| 4700 | CFList diophant; |
---|
| 4701 | int liftBound= tmax ((2*totaldegree (F) - 1)/degMipo + 1, degree (F) + 1 + |
---|
| 4702 | degree (LC (F, 1))); |
---|
| 4703 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
| 4704 | |
---|
| 4705 | CFList smallFactors; |
---|
| 4706 | CanonicalForm H; |
---|
| 4707 | bool success; |
---|
| 4708 | smallFactors= extSieveSmallFactors (F, bufUniFactors, degs, H, diophant, Pi, |
---|
| 4709 | M, success, minBound + 1, evaluation, info |
---|
| 4710 | ); |
---|
| 4711 | |
---|
| 4712 | if (smallFactors.length() > 0) |
---|
| 4713 | { |
---|
| 4714 | if (smallFactors.length() == 1) |
---|
| 4715 | { |
---|
| 4716 | if (smallFactors.getFirst() == F) |
---|
| 4717 | { |
---|
| 4718 | delete [] bounds; |
---|
| 4719 | CFList source, dest; |
---|
| 4720 | CanonicalForm tmp= G (y - evaluation, y); |
---|
| 4721 | tmp= mapDown (tmp, info, source, dest); |
---|
| 4722 | return CFList (tmp); |
---|
| 4723 | } |
---|
| 4724 | } |
---|
| 4725 | if (degs.getLength() <= 1) |
---|
| 4726 | { |
---|
| 4727 | delete [] bounds; |
---|
| 4728 | return smallFactors; |
---|
| 4729 | } |
---|
| 4730 | } |
---|
| 4731 | |
---|
| 4732 | int index; |
---|
[38ffb7] | 4733 | CanonicalForm tmp1, tmp2; |
---|
[11bf82] | 4734 | for (CFListIterator i= smallFactors; i.hasItem(); i++) |
---|
| 4735 | { |
---|
| 4736 | index= 1; |
---|
| 4737 | tmp1= mod (i.getItem(), y - evaluation); |
---|
| 4738 | tmp1 /= Lc (tmp1); |
---|
| 4739 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
| 4740 | { |
---|
| 4741 | tmp2= mod (j.getItem(), y); |
---|
| 4742 | tmp2 /= Lc (tmp2); |
---|
| 4743 | if (tmp1 == tmp2) |
---|
| 4744 | { |
---|
| 4745 | index++; |
---|
| 4746 | j.remove(index); |
---|
| 4747 | break; |
---|
| 4748 | } |
---|
| 4749 | } |
---|
| 4750 | } |
---|
| 4751 | |
---|
| 4752 | if (bufUniFactors.isEmpty()) |
---|
| 4753 | { |
---|
| 4754 | delete [] bounds; |
---|
| 4755 | return smallFactors; |
---|
| 4756 | } |
---|
| 4757 | |
---|
| 4758 | if (success) |
---|
| 4759 | { |
---|
| 4760 | F= H; |
---|
| 4761 | delete [] bounds; |
---|
| 4762 | bounds= computeBounds (F, d); |
---|
| 4763 | LCF= LC (F, 1); |
---|
| 4764 | |
---|
| 4765 | minBound= bounds[0]; |
---|
| 4766 | for (int i= 1; i < d; i++) |
---|
| 4767 | { |
---|
| 4768 | if (bounds[i] != 0) |
---|
| 4769 | minBound= tmin (minBound, bounds[i]); |
---|
| 4770 | } |
---|
| 4771 | Pi= CFArray(); |
---|
| 4772 | diophant= CFList(); |
---|
| 4773 | liftBound=tmax ((2*totaldegree (F) - 1)/degMipo + 1, degree (F) + 1 + |
---|
| 4774 | degree (LC (F, 1))); |
---|
| 4775 | M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
| 4776 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 4777 | degs.intersect (bufDegs); |
---|
| 4778 | degs.refine(); |
---|
| 4779 | if (degs.getLength() <= 1) |
---|
| 4780 | { |
---|
| 4781 | delete [] bounds; |
---|
| 4782 | CFList source, dest; |
---|
| 4783 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 4784 | tmp= mapDown (tmp, info, source, dest); |
---|
| 4785 | smallFactors.append (tmp); |
---|
| 4786 | return smallFactors; |
---|
| 4787 | } |
---|
| 4788 | } |
---|
| 4789 | |
---|
| 4790 | bufUniFactors.insert (LCF); |
---|
| 4791 | int l= 1; |
---|
| 4792 | |
---|
| 4793 | zz_p::init (getCharacteristic()); |
---|
| 4794 | zz_pX NTLMipo; |
---|
| 4795 | mat_zz_p NTLN; |
---|
| 4796 | |
---|
| 4797 | ident (NTLN, bufUniFactors.length() - 1); |
---|
| 4798 | bool irreducible= false; |
---|
| 4799 | CFArray bufQ= CFArray (bufUniFactors.length() - 1); |
---|
| 4800 | |
---|
| 4801 | int oldL; |
---|
| 4802 | if (success) |
---|
| 4803 | { |
---|
| 4804 | int start= 0; |
---|
| 4805 | oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound, start, |
---|
| 4806 | bufUniFactors, NTLN, diophant, M, Pi, bufQ, |
---|
| 4807 | irreducible, evaluation, info2, source, dest |
---|
| 4808 | ); |
---|
| 4809 | } |
---|
| 4810 | else |
---|
| 4811 | { |
---|
| 4812 | oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound, |
---|
| 4813 | minBound + 1, bufUniFactors, NTLN, diophant, |
---|
| 4814 | M, Pi, bufQ, irreducible, evaluation, info2, |
---|
| 4815 | source, dest |
---|
| 4816 | ); |
---|
| 4817 | } |
---|
| 4818 | |
---|
| 4819 | bufUniFactors.removeFirst(); |
---|
| 4820 | if (oldL > liftBound) |
---|
| 4821 | { |
---|
| 4822 | delete [] bounds; |
---|
| 4823 | return Union (smallFactors, extFactorRecombination |
---|
| 4824 | (bufUniFactors, F, |
---|
| 4825 | power (y, degree (F) + 1 + degree (LCF)),info, |
---|
| 4826 | degs, evaluation, 1, bufUniFactors.length()/2 |
---|
| 4827 | ) |
---|
| 4828 | ); |
---|
| 4829 | } |
---|
| 4830 | |
---|
| 4831 | l= oldL; |
---|
| 4832 | if (irreducible) |
---|
| 4833 | { |
---|
| 4834 | delete [] bounds; |
---|
| 4835 | CFList source, dest; |
---|
| 4836 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 4837 | tmp= mapDown (tmp, info, source, dest); |
---|
| 4838 | return Union (CFList (tmp), smallFactors); |
---|
| 4839 | } |
---|
| 4840 | |
---|
| 4841 | CanonicalForm yToL= power (y,l); |
---|
| 4842 | |
---|
| 4843 | CFList result; |
---|
| 4844 | if (l >= degree (F) + 1) |
---|
| 4845 | { |
---|
| 4846 | int * factorsFoundIndex; |
---|
| 4847 | |
---|
| 4848 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 4849 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 4850 | factorsFoundIndex[i]= 0; |
---|
| 4851 | |
---|
| 4852 | int factorsFound= 0; |
---|
| 4853 | CanonicalForm bufF= F; |
---|
| 4854 | |
---|
| 4855 | extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
| 4856 | factorsFound, factorsFoundIndex, NTLN, false, info, |
---|
| 4857 | evaluation |
---|
| 4858 | ); |
---|
| 4859 | |
---|
| 4860 | if (result.length() == NTLN.NumCols()) |
---|
| 4861 | { |
---|
| 4862 | delete [] factorsFoundIndex; |
---|
| 4863 | delete [] bounds; |
---|
| 4864 | return Union (result, smallFactors); |
---|
| 4865 | } |
---|
| 4866 | |
---|
| 4867 | delete [] factorsFoundIndex; |
---|
| 4868 | } |
---|
| 4869 | if (l >= liftBound) |
---|
| 4870 | { |
---|
| 4871 | int * factorsFoundIndex; |
---|
[38ffb7] | 4872 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 4873 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 4874 | factorsFoundIndex[i]= 0; |
---|
[11bf82] | 4875 | CanonicalForm bufF= F; |
---|
| 4876 | int factorsFound= 0; |
---|
| 4877 | |
---|
| 4878 | extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1 + degree |
---|
| 4879 | (LCF), factorsFound, factorsFoundIndex, NTLN, false, |
---|
| 4880 | info, evaluation |
---|
| 4881 | ); |
---|
| 4882 | |
---|
| 4883 | if (result.length() == NTLN.NumCols()) |
---|
| 4884 | { |
---|
| 4885 | delete [] factorsFoundIndex; |
---|
| 4886 | delete [] bounds; |
---|
| 4887 | return Union (result, smallFactors); |
---|
| 4888 | } |
---|
| 4889 | delete [] factorsFoundIndex; |
---|
| 4890 | } |
---|
| 4891 | |
---|
| 4892 | result= CFList(); |
---|
| 4893 | bool beenInThres= false; |
---|
| 4894 | int thres= 100; |
---|
| 4895 | if (l <= thres && bufUniFactors.length() > NTLN.NumCols()) |
---|
| 4896 | { |
---|
| 4897 | refineAndRestartLift (F, NTLN, 2*totaldegree (F)-1, l, bufUniFactors, M, Pi, |
---|
| 4898 | diophant |
---|
| 4899 | ); |
---|
| 4900 | beenInThres= true; |
---|
| 4901 | } |
---|
| 4902 | |
---|
| 4903 | |
---|
| 4904 | CanonicalForm bufF= F; |
---|
| 4905 | int factorsFound= 0; |
---|
| 4906 | |
---|
| 4907 | result= extEarlyReconstructionAndLifting (F, NTLN, bufF, bufUniFactors, l, |
---|
| 4908 | factorsFound, beenInThres, M, Pi, |
---|
| 4909 | diophant, info, evaluation |
---|
| 4910 | ); |
---|
| 4911 | |
---|
| 4912 | if (result.length() == NTLN.NumCols()) |
---|
| 4913 | { |
---|
| 4914 | delete [] bounds; |
---|
| 4915 | return Union (result, smallFactors); |
---|
| 4916 | } |
---|
| 4917 | |
---|
| 4918 | if (result.length() > 0) |
---|
| 4919 | { |
---|
| 4920 | if (beenInThres) |
---|
| 4921 | { |
---|
| 4922 | int index; |
---|
| 4923 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
| 4924 | { |
---|
| 4925 | index= 1; |
---|
| 4926 | tmp1= mod (i.getItem(), y-evaluation); |
---|
| 4927 | tmp1 /= Lc (tmp1); |
---|
| 4928 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
| 4929 | { |
---|
| 4930 | tmp2= mod (j.getItem(), y); |
---|
| 4931 | tmp2 /= Lc (tmp2); |
---|
| 4932 | if (tmp1 == tmp2) |
---|
| 4933 | { |
---|
| 4934 | index++; |
---|
| 4935 | j.remove(index); |
---|
| 4936 | break; |
---|
| 4937 | } |
---|
| 4938 | } |
---|
| 4939 | } |
---|
| 4940 | } |
---|
| 4941 | else |
---|
| 4942 | { |
---|
| 4943 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
| 4944 | CFList bufBufUniFactors= bufUniFactors; |
---|
[38ffb7] | 4945 | CFListIterator iter, iter2; |
---|
| 4946 | CanonicalForm buf; |
---|
| 4947 | CFList factorsConsidered; |
---|
[11bf82] | 4948 | for (int i= 0; i < NTLN.NumCols(); i++) |
---|
| 4949 | { |
---|
| 4950 | if (zeroOne [i] == 0) |
---|
| 4951 | continue; |
---|
[38ffb7] | 4952 | iter= bufUniFactors; |
---|
| 4953 | buf= 1; |
---|
| 4954 | factorsConsidered= CFList(); |
---|
[11bf82] | 4955 | for (int j= 0; j < NTLN.NumRows(); j++, iter++) |
---|
| 4956 | { |
---|
| 4957 | if (!IsZero (NTLN (j + 1,i + 1))) |
---|
| 4958 | { |
---|
| 4959 | factorsConsidered.append (iter.getItem()); |
---|
| 4960 | buf *= mod (iter.getItem(), y); |
---|
| 4961 | } |
---|
| 4962 | } |
---|
| 4963 | buf /= Lc (buf); |
---|
[38ffb7] | 4964 | for (iter2= result; iter2.hasItem(); iter2++) |
---|
[11bf82] | 4965 | { |
---|
| 4966 | CanonicalForm tmp= mod (iter2.getItem(), y - evaluation); |
---|
| 4967 | tmp /= Lc (tmp); |
---|
| 4968 | if (tmp == buf) |
---|
| 4969 | { |
---|
| 4970 | bufBufUniFactors= Difference (bufBufUniFactors, factorsConsidered); |
---|
| 4971 | break; |
---|
| 4972 | } |
---|
| 4973 | } |
---|
| 4974 | } |
---|
| 4975 | bufUniFactors= bufBufUniFactors; |
---|
| 4976 | delete [] zeroOne; |
---|
| 4977 | } |
---|
| 4978 | |
---|
| 4979 | int oldNumCols; |
---|
| 4980 | CFList resultBufF; |
---|
| 4981 | irreducible= false; |
---|
| 4982 | |
---|
| 4983 | oldNumCols= NTLN.NumCols(); |
---|
| 4984 | resultBufF= extIncreasePrecision (bufF, bufUniFactors, factorsFound, |
---|
| 4985 | oldNumCols, oldL, evaluation, info2, |
---|
| 4986 | source, dest, l |
---|
| 4987 | ); |
---|
| 4988 | |
---|
| 4989 | if (bufUniFactors.isEmpty() || degree (bufF) <= 0) |
---|
| 4990 | { |
---|
| 4991 | delete [] bounds; |
---|
| 4992 | result= Union (resultBufF, result); |
---|
| 4993 | return Union (result, smallFactors); |
---|
| 4994 | } |
---|
| 4995 | |
---|
| 4996 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
| 4997 | i.getItem()= mod (i.getItem(), y); |
---|
| 4998 | |
---|
| 4999 | delete [] bounds; |
---|
| 5000 | CFList bufResult; |
---|
| 5001 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 5002 | degs.intersect (bufDegs); |
---|
| 5003 | degs.refine(); |
---|
| 5004 | result= Union (result, smallFactors); |
---|
| 5005 | if (degs.getLength() == 1 || bufUniFactors.length() == 1) |
---|
| 5006 | { |
---|
| 5007 | result.append (bufF); |
---|
| 5008 | return result; |
---|
| 5009 | } |
---|
| 5010 | return Union (result, extHenselLiftAndLatticeRecombi (bufF, bufUniFactors, |
---|
| 5011 | info, degs, evaluation |
---|
| 5012 | ) |
---|
| 5013 | ); |
---|
| 5014 | } |
---|
| 5015 | |
---|
| 5016 | if (l/degMipo < liftBound) |
---|
| 5017 | { |
---|
| 5018 | result=extIncreasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
| 5019 | NTLN, evaluation, info2, source, dest |
---|
| 5020 | ); |
---|
| 5021 | |
---|
[c1b9927] | 5022 | if (result.length()== NTLN.NumCols()) |
---|
[11bf82] | 5023 | { |
---|
| 5024 | delete [] bounds; |
---|
| 5025 | result= Union (result, smallFactors); |
---|
| 5026 | return result; |
---|
| 5027 | } |
---|
| 5028 | |
---|
| 5029 | if (result.isEmpty()) |
---|
| 5030 | { |
---|
| 5031 | result= extFurtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
| 5032 | liftBound, d, bounds, NTLN, |
---|
| 5033 | diophant, M, Pi, bufQ, |
---|
| 5034 | evaluation, info2, source, |
---|
| 5035 | dest |
---|
| 5036 | ); |
---|
[c1b9927] | 5037 | if (result.length()== NTLN.NumCols()) |
---|
[11bf82] | 5038 | { |
---|
| 5039 | delete [] bounds; |
---|
| 5040 | result= Union (result, smallFactors); |
---|
| 5041 | return result; |
---|
| 5042 | } |
---|
| 5043 | } |
---|
| 5044 | } |
---|
| 5045 | |
---|
| 5046 | DEBOUTLN (cerr, "lattice recombination failed"); |
---|
| 5047 | |
---|
| 5048 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 5049 | degs.intersect (bufDegs); |
---|
| 5050 | degs.refine(); |
---|
| 5051 | |
---|
| 5052 | delete [] bounds; |
---|
| 5053 | bounds= computeBounds (F, d); |
---|
| 5054 | minBound= bounds[0]; |
---|
| 5055 | for (int i= 1; i < d; i++) |
---|
| 5056 | { |
---|
| 5057 | if (bounds[i] != 0) |
---|
| 5058 | minBound= tmin (minBound, bounds[i]); |
---|
| 5059 | } |
---|
| 5060 | |
---|
| 5061 | if (minBound > 16 || result.length() == 0) |
---|
| 5062 | { |
---|
| 5063 | result= Union (result, smallFactors); |
---|
| 5064 | CanonicalForm MODl= power (y, degree (F) + 1 + degree (LC (F, 1))); |
---|
| 5065 | delete [] bounds; |
---|
| 5066 | return Union (result, extFactorRecombination (bufUniFactors, F, MODl, info, |
---|
| 5067 | degs, evaluation, 1, |
---|
| 5068 | bufUniFactors.length()/2 |
---|
| 5069 | ) |
---|
| 5070 | ); |
---|
| 5071 | } |
---|
| 5072 | else |
---|
| 5073 | { |
---|
| 5074 | result= Union (result, smallFactors); |
---|
| 5075 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
| 5076 | i.getItem()= mod (i.getItem(), y); |
---|
| 5077 | delete [] bounds; |
---|
| 5078 | return Union (result, extHenselLiftAndLatticeRecombi (F, bufUniFactors, |
---|
| 5079 | info, degs, evaluation |
---|
| 5080 | ) |
---|
| 5081 | ); |
---|
| 5082 | } |
---|
| 5083 | } |
---|
| 5084 | |
---|
| 5085 | CFList |
---|
| 5086 | extBiFactorize (const CanonicalForm& F, const ExtensionInfo& info); |
---|
| 5087 | |
---|
| 5088 | /// bivariate factorization over finite fields as decribed in "Factoring |
---|
| 5089 | /// multivariate polynomials over a finite field" by L Bernardin. |
---|
| 5090 | CFList |
---|
| 5091 | biFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
| 5092 | { |
---|
| 5093 | if (F.inCoeffDomain()) |
---|
| 5094 | return CFList(F); |
---|
| 5095 | |
---|
| 5096 | CanonicalForm A= F; |
---|
| 5097 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
| 5098 | |
---|
| 5099 | Variable alpha= info.getAlpha(); |
---|
| 5100 | Variable beta= info.getBeta(); |
---|
| 5101 | CanonicalForm gamma= info.getGamma(); |
---|
| 5102 | CanonicalForm delta= info.getDelta(); |
---|
| 5103 | int k= info.getGFDegree(); |
---|
| 5104 | bool extension= info.isInExtension(); |
---|
| 5105 | if (A.isUnivariate()) |
---|
| 5106 | { |
---|
| 5107 | if (extension == false) |
---|
| 5108 | return uniFactorizer (F, alpha, GF); |
---|
| 5109 | else |
---|
| 5110 | { |
---|
| 5111 | CFList source, dest; |
---|
| 5112 | A= mapDown (A, info, source, dest); |
---|
| 5113 | return uniFactorizer (A, beta, GF); |
---|
| 5114 | } |
---|
| 5115 | } |
---|
| 5116 | |
---|
| 5117 | CFMap N; |
---|
| 5118 | A= compress (A, N); |
---|
| 5119 | Variable y= A.mvar(); |
---|
| 5120 | |
---|
| 5121 | if (y.level() > 2) return CFList (F); |
---|
| 5122 | Variable x= Variable (1); |
---|
| 5123 | |
---|
| 5124 | //remove and factorize content |
---|
| 5125 | CanonicalForm contentAx= content (A, x); |
---|
| 5126 | CanonicalForm contentAy= content (A); |
---|
| 5127 | |
---|
| 5128 | A= A/(contentAx*contentAy); |
---|
| 5129 | CFList contentAxFactors, contentAyFactors; |
---|
| 5130 | |
---|
| 5131 | if (!extension) |
---|
| 5132 | { |
---|
| 5133 | contentAxFactors= uniFactorizer (contentAx, alpha, GF); |
---|
| 5134 | contentAyFactors= uniFactorizer (contentAy, alpha, GF); |
---|
| 5135 | } |
---|
| 5136 | |
---|
| 5137 | //trivial case |
---|
| 5138 | CFList factors; |
---|
| 5139 | if (A.inCoeffDomain()) |
---|
| 5140 | { |
---|
| 5141 | append (factors, contentAxFactors); |
---|
| 5142 | append (factors, contentAyFactors); |
---|
| 5143 | decompress (factors, N); |
---|
| 5144 | return factors; |
---|
| 5145 | } |
---|
| 5146 | else if (A.isUnivariate()) |
---|
| 5147 | { |
---|
| 5148 | factors= uniFactorizer (A, alpha, GF); |
---|
| 5149 | append (factors, contentAxFactors); |
---|
| 5150 | append (factors, contentAyFactors); |
---|
| 5151 | decompress (factors, N); |
---|
| 5152 | return factors; |
---|
| 5153 | } |
---|
| 5154 | |
---|
[0777ea] | 5155 | //check trivial case |
---|
| 5156 | if (degree (A) == 1 || degree (A, 1) == 1) |
---|
| 5157 | { |
---|
| 5158 | factors.append (A); |
---|
| 5159 | |
---|
| 5160 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
| 5161 | false, false, N); |
---|
| 5162 | |
---|
| 5163 | normalize (factors); |
---|
| 5164 | return factors; |
---|
| 5165 | } |
---|
| 5166 | |
---|
[11bf82] | 5167 | // check derivatives |
---|
| 5168 | bool derivXZero= false; |
---|
| 5169 | CanonicalForm derivX= deriv (A, x); |
---|
| 5170 | CanonicalForm gcdDerivX; |
---|
| 5171 | if (derivX.isZero()) |
---|
| 5172 | derivXZero= true; |
---|
| 5173 | else |
---|
| 5174 | { |
---|
| 5175 | gcdDerivX= gcd (A, derivX); |
---|
| 5176 | if (degree (gcdDerivX) > 0) |
---|
| 5177 | { |
---|
| 5178 | CanonicalForm g= A/gcdDerivX; |
---|
| 5179 | CFList factorsG= |
---|
| 5180 | Union (biFactorize (g, info), biFactorize (gcdDerivX, info)); |
---|
| 5181 | append (factorsG, contentAxFactors); |
---|
| 5182 | append (factorsG, contentAyFactors); |
---|
| 5183 | decompress (factorsG, N); |
---|
| 5184 | normalize (factors); |
---|
| 5185 | return factorsG; |
---|
| 5186 | } |
---|
| 5187 | } |
---|
| 5188 | bool derivYZero= false; |
---|
| 5189 | CanonicalForm derivY= deriv (A, y); |
---|
| 5190 | CanonicalForm gcdDerivY; |
---|
| 5191 | if (derivY.isZero()) |
---|
| 5192 | derivYZero= true; |
---|
| 5193 | else |
---|
| 5194 | { |
---|
| 5195 | gcdDerivY= gcd (A, derivY); |
---|
| 5196 | if (degree (gcdDerivY) > 0) |
---|
| 5197 | { |
---|
| 5198 | CanonicalForm g= A/gcdDerivY; |
---|
| 5199 | CFList factorsG= |
---|
| 5200 | Union (biFactorize (g, info), biFactorize (gcdDerivY, info)); |
---|
| 5201 | append (factorsG, contentAxFactors); |
---|
| 5202 | append (factorsG, contentAyFactors); |
---|
| 5203 | decompress (factorsG, N); |
---|
| 5204 | normalize (factors); |
---|
| 5205 | return factorsG; |
---|
| 5206 | } |
---|
| 5207 | } |
---|
| 5208 | //main variable is chosen s.t. the degree in x is minimal |
---|
| 5209 | bool swap= false; |
---|
| 5210 | if ((degree (A) > degree (A, x)) || derivXZero) |
---|
| 5211 | { |
---|
| 5212 | if (!derivYZero) |
---|
| 5213 | { |
---|
| 5214 | A= swapvar (A, y, x); |
---|
| 5215 | swap= derivXZero; |
---|
| 5216 | derivXZero= derivYZero; |
---|
| 5217 | derivYZero= swap; |
---|
| 5218 | swap= true; |
---|
| 5219 | } |
---|
| 5220 | } |
---|
| 5221 | |
---|
| 5222 | bool fail= false; |
---|
| 5223 | CanonicalForm Aeval, evaluation, bufAeval, bufEvaluation, buf; |
---|
| 5224 | CFList uniFactors, list, bufUniFactors; |
---|
| 5225 | DegreePattern degs; |
---|
| 5226 | DegreePattern bufDegs; |
---|
| 5227 | |
---|
| 5228 | bool fail2= false; |
---|
| 5229 | CanonicalForm Aeval2, evaluation2, bufAeval2, bufEvaluation2; |
---|
| 5230 | CFList bufUniFactors2, list2, uniFactors2; |
---|
| 5231 | DegreePattern degs2; |
---|
| 5232 | DegreePattern bufDegs2; |
---|
| 5233 | bool swap2= false; |
---|
| 5234 | |
---|
| 5235 | // several univariate factorizations to obtain more information about the |
---|
| 5236 | // degree pattern therefore usually less combinations have to be tried during |
---|
| 5237 | // the recombination process |
---|
| 5238 | int factorNums= 3; |
---|
| 5239 | int subCheck1= substituteCheck (A, x); |
---|
| 5240 | int subCheck2= substituteCheck (A, y); |
---|
| 5241 | for (int i= 0; i < factorNums; i++) |
---|
| 5242 | { |
---|
| 5243 | bufAeval= A; |
---|
| 5244 | bufEvaluation= evalPoint (A, bufAeval, alpha, list, GF, fail); |
---|
| 5245 | if (!derivXZero && !fail2) |
---|
| 5246 | { |
---|
| 5247 | buf= swapvar (A, x, y); |
---|
| 5248 | bufAeval2= buf; |
---|
| 5249 | bufEvaluation2= evalPoint (buf, bufAeval2, alpha, list2, GF, fail2); |
---|
| 5250 | } |
---|
| 5251 | // first try to change main variable if there is no valid evaluation point |
---|
| 5252 | if (fail && (i == 0)) |
---|
| 5253 | { |
---|
| 5254 | if (!derivXZero && !fail2) |
---|
| 5255 | { |
---|
| 5256 | bufEvaluation= bufEvaluation2; |
---|
| 5257 | int dummy= subCheck2; |
---|
| 5258 | subCheck2= subCheck1; |
---|
| 5259 | subCheck1= dummy; |
---|
| 5260 | A= buf; |
---|
| 5261 | bufAeval= bufAeval2; |
---|
| 5262 | swap2= true; |
---|
| 5263 | fail= false; |
---|
| 5264 | } |
---|
| 5265 | else |
---|
| 5266 | fail= true; |
---|
| 5267 | } |
---|
| 5268 | |
---|
| 5269 | // if there is no valid evaluation point pass to a field extension |
---|
| 5270 | if (fail && (i == 0)) |
---|
| 5271 | { |
---|
| 5272 | factors= extBiFactorize (A, info); |
---|
| 5273 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
| 5274 | swap, swap2, N); |
---|
| 5275 | normalize (factors); |
---|
| 5276 | return factors; |
---|
| 5277 | } |
---|
| 5278 | |
---|
| 5279 | // there is at least one valid evaluation point |
---|
| 5280 | // but we do not compute more univariate factorization over an extension |
---|
| 5281 | if (fail && (i != 0)) |
---|
| 5282 | break; |
---|
| 5283 | |
---|
| 5284 | // univariate factorization |
---|
| 5285 | TIMING_START (fac_uni_factorizer); |
---|
| 5286 | bufUniFactors= uniFactorizer (bufAeval, alpha, GF); |
---|
| 5287 | TIMING_END_AND_PRINT (fac_uni_factorizer, |
---|
[7bf145] | 5288 | "time for univariate factorization: "); |
---|
[806c18] | 5289 | DEBOUTLN (cerr, "Lc (bufAeval)*prod (bufUniFactors)== bufAeval " << |
---|
[7bf145] | 5290 | prod (bufUniFactors)*Lc (bufAeval) == bufAeval); |
---|
| 5291 | |
---|
| 5292 | if (!derivXZero && !fail2) |
---|
| 5293 | { |
---|
| 5294 | TIMING_START (fac_uni_factorizer); |
---|
| 5295 | bufUniFactors2= uniFactorizer (bufAeval2, alpha, GF); |
---|
[806c18] | 5296 | TIMING_END_AND_PRINT (fac_uni_factorizer, |
---|
[7bf145] | 5297 | "time for univariate factorization in y: "); |
---|
[806c18] | 5298 | DEBOUTLN (cerr, "Lc (Aeval2)*prod (uniFactors2)== Aeval2 " << |
---|
[7bf145] | 5299 | prod (bufUniFactors2)*Lc (bufAeval2) == bufAeval2); |
---|
| 5300 | } |
---|
| 5301 | |
---|
[806c18] | 5302 | if (bufUniFactors.length() == 1 || |
---|
| 5303 | (!fail2 && !derivXZero && (bufUniFactors2.length() == 1))) |
---|
[7bf145] | 5304 | { |
---|
| 5305 | if (extension) |
---|
| 5306 | { |
---|
| 5307 | CFList source, dest; |
---|
[806c18] | 5308 | ExtensionInfo info2= ExtensionInfo (beta, alpha, delta, gamma, k, |
---|
[7bf145] | 5309 | info.getGFName(), info.isInExtension()); |
---|
| 5310 | appendMapDown (factors, A, info2, source, dest); |
---|
| 5311 | } |
---|
[806c18] | 5312 | else |
---|
[7bf145] | 5313 | factors.append (A); |
---|
| 5314 | |
---|
[806c18] | 5315 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
[7bf145] | 5316 | swap, swap2, N); |
---|
| 5317 | |
---|
| 5318 | normalize (factors); |
---|
| 5319 | return factors; |
---|
| 5320 | } |
---|
| 5321 | |
---|
[686ce3] | 5322 | if (i == 0) |
---|
| 5323 | { |
---|
[dd8047] | 5324 | if (subCheck1 > 0) |
---|
[686ce3] | 5325 | { |
---|
[dd8047] | 5326 | int subCheck= substituteCheck (bufUniFactors); |
---|
| 5327 | |
---|
| 5328 | if (subCheck > 1 && (subCheck1%subCheck == 0)) |
---|
| 5329 | { |
---|
| 5330 | CanonicalForm bufA= A; |
---|
| 5331 | subst (bufA, bufA, subCheck, x); |
---|
| 5332 | factors= biFactorize (bufA, info); |
---|
| 5333 | reverseSubst (factors, subCheck, x); |
---|
| 5334 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
| 5335 | swap, swap2, N); |
---|
| 5336 | normalize (factors); |
---|
| 5337 | return factors; |
---|
| 5338 | } |
---|
[686ce3] | 5339 | } |
---|
| 5340 | |
---|
[dd8047] | 5341 | if (!derivXZero && !fail2 && subCheck2 > 0) |
---|
[686ce3] | 5342 | { |
---|
[dd8047] | 5343 | int subCheck= substituteCheck (bufUniFactors2); |
---|
| 5344 | |
---|
| 5345 | if (subCheck > 1 && (subCheck2%subCheck == 0)) |
---|
[686ce3] | 5346 | { |
---|
| 5347 | CanonicalForm bufA= A; |
---|
| 5348 | subst (bufA, bufA, subCheck, y); |
---|
| 5349 | factors= biFactorize (bufA, info); |
---|
[2caede4] | 5350 | reverseSubst (factors, subCheck, y); |
---|
[686ce3] | 5351 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
| 5352 | swap, swap2, N); |
---|
| 5353 | normalize (factors); |
---|
| 5354 | return factors; |
---|
| 5355 | } |
---|
| 5356 | } |
---|
| 5357 | } |
---|
| 5358 | |
---|
[806c18] | 5359 | // degree analysis |
---|
| 5360 | bufDegs = DegreePattern (bufUniFactors); |
---|
[7bf145] | 5361 | if (!derivXZero && !fail2) |
---|
| 5362 | bufDegs2= DegreePattern (bufUniFactors2); |
---|
| 5363 | |
---|
[806c18] | 5364 | if (i == 0) |
---|
[7bf145] | 5365 | { |
---|
| 5366 | Aeval= bufAeval; |
---|
| 5367 | evaluation= bufEvaluation; |
---|
| 5368 | uniFactors= bufUniFactors; |
---|
| 5369 | degs= bufDegs; |
---|
| 5370 | if (!derivXZero && !fail2) |
---|
| 5371 | { |
---|
| 5372 | Aeval2= bufAeval2; |
---|
| 5373 | evaluation2= bufEvaluation2; |
---|
| 5374 | uniFactors2= bufUniFactors2; |
---|
| 5375 | degs2= bufDegs2; |
---|
| 5376 | } |
---|
| 5377 | } |
---|
[806c18] | 5378 | else |
---|
[7bf145] | 5379 | { |
---|
| 5380 | degs.intersect (bufDegs); |
---|
[806c18] | 5381 | if (!derivXZero && !fail2) |
---|
[7bf145] | 5382 | { |
---|
| 5383 | degs2.intersect (bufDegs2); |
---|
[806c18] | 5384 | if (bufUniFactors2.length() < uniFactors2.length()) |
---|
| 5385 | { |
---|
[7bf145] | 5386 | uniFactors2= bufUniFactors2; |
---|
| 5387 | Aeval2= bufAeval2; |
---|
| 5388 | evaluation2= bufEvaluation2; |
---|
| 5389 | } |
---|
[806c18] | 5390 | } |
---|
| 5391 | if (bufUniFactors.length() < uniFactors.length()) |
---|
| 5392 | { |
---|
[11bf82] | 5393 | if (!evaluation.isZero()) |
---|
| 5394 | { |
---|
| 5395 | uniFactors= bufUniFactors; |
---|
| 5396 | Aeval= bufAeval; |
---|
| 5397 | evaluation= bufEvaluation; |
---|
| 5398 | } |
---|
[7bf145] | 5399 | } |
---|
| 5400 | } |
---|
| 5401 | list.append (bufEvaluation); |
---|
| 5402 | if (!derivXZero && !fail2) |
---|
| 5403 | list2.append (bufEvaluation2); |
---|
| 5404 | } |
---|
[806c18] | 5405 | |
---|
[7bf145] | 5406 | if (!derivXZero && !fail2) |
---|
| 5407 | { |
---|
[11bf82] | 5408 | if (!evaluation.isZero() && (uniFactors.length() > uniFactors2.length() || |
---|
[806c18] | 5409 | (uniFactors.length() == uniFactors2.length() |
---|
[11bf82] | 5410 | && degs.getLength() > degs2.getLength()))) |
---|
[7bf145] | 5411 | { |
---|
| 5412 | degs= degs2; |
---|
| 5413 | uniFactors= uniFactors2; |
---|
| 5414 | evaluation= evaluation2; |
---|
| 5415 | Aeval= Aeval2; |
---|
| 5416 | A= buf; |
---|
| 5417 | swap2= true; |
---|
| 5418 | } |
---|
| 5419 | } |
---|
[806c18] | 5420 | |
---|
| 5421 | if (degs.getLength() == 1) // A is irreducible |
---|
[7bf145] | 5422 | { |
---|
[806c18] | 5423 | if (extension) |
---|
[7bf145] | 5424 | { |
---|
| 5425 | CFList source, dest; |
---|
[11bf82] | 5426 | appendMapDown (factors, A, info, source, dest); |
---|
[7bf145] | 5427 | } |
---|
[806c18] | 5428 | else |
---|
[7bf145] | 5429 | factors.append (A); |
---|
[806c18] | 5430 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
[7bf145] | 5431 | swap, swap2, N); |
---|
| 5432 | normalize (factors); |
---|
| 5433 | return factors; |
---|
| 5434 | } |
---|
| 5435 | |
---|
| 5436 | A= A (y + evaluation, y); |
---|
| 5437 | |
---|
[ac8e1a] | 5438 | int liftBound= degree (A, y) + 1 + degree (LC(A, x)); |
---|
[11bf82] | 5439 | |
---|
| 5440 | int boundsLength; |
---|
| 5441 | int * bounds= computeBounds (A (y - evaluation, y), boundsLength); |
---|
| 5442 | int minBound= bounds[0]; |
---|
| 5443 | for (int i= 1; i < boundsLength; i++) |
---|
| 5444 | { |
---|
| 5445 | if (bounds[i] != 0) |
---|
| 5446 | minBound= tmin (minBound, bounds[i]); |
---|
| 5447 | } |
---|
| 5448 | |
---|
| 5449 | int degMipo= 1; |
---|
| 5450 | if (extension && alpha.level() != 1 && k==1) |
---|
| 5451 | degMipo= degree (getMipo (alpha)); |
---|
[7bf145] | 5452 | |
---|
| 5453 | DEBOUTLN (cerr, "uniFactors= " << uniFactors); |
---|
[11bf82] | 5454 | |
---|
[ac8e1a] | 5455 | if ((GF && !extension) || (GF && extension && k != 1)) |
---|
[11bf82] | 5456 | { |
---|
| 5457 | bool earlySuccess= false; |
---|
| 5458 | CFList earlyFactors; |
---|
| 5459 | TIMING_START (fac_hensel_lift); |
---|
[c1b9927] | 5460 | uniFactors= henselLiftAndEarly |
---|
[7bf145] | 5461 | (A, earlySuccess, earlyFactors, degs, liftBound, |
---|
[806c18] | 5462 | uniFactors, info, evaluation); |
---|
[11bf82] | 5463 | TIMING_END_AND_PRINT (fac_hensel_lift, "time for hensel lifting: "); |
---|
| 5464 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
[7bf145] | 5465 | |
---|
[11bf82] | 5466 | CanonicalForm MODl= power (y, liftBound); |
---|
| 5467 | |
---|
| 5468 | if (extension) |
---|
| 5469 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
| 5470 | evaluation, 1, uniFactors.length()/2); |
---|
| 5471 | else |
---|
| 5472 | factors= factorRecombination (uniFactors, A, MODl, degs, 1, |
---|
| 5473 | uniFactors.length()/2); |
---|
| 5474 | |
---|
| 5475 | if (earlySuccess) |
---|
| 5476 | factors= Union (earlyFactors, factors); |
---|
| 5477 | else if (!earlySuccess && degs.getLength() == 1) |
---|
| 5478 | factors= earlyFactors; |
---|
| 5479 | } |
---|
| 5480 | else if (degree (A) > 4 && beta.level() == 1 && (2*minBound)/degMipo < 32) |
---|
| 5481 | { |
---|
| 5482 | TIMING_START (fac_hensel_lift); |
---|
| 5483 | if (extension) |
---|
| 5484 | { |
---|
| 5485 | CFList lll= extHenselLiftAndLatticeRecombi (A, uniFactors, info, degs, |
---|
| 5486 | evaluation |
---|
| 5487 | ); |
---|
| 5488 | factors= Union (lll, factors); |
---|
| 5489 | } |
---|
| 5490 | else if (alpha.level() == 1 && !GF) |
---|
| 5491 | { |
---|
| 5492 | CFList lll= henselLiftAndLatticeRecombi (A, uniFactors, alpha, degs); |
---|
| 5493 | factors= Union (lll, factors); |
---|
| 5494 | } |
---|
| 5495 | else if (!extension && (alpha != Variable (1) || GF)) |
---|
| 5496 | { |
---|
| 5497 | CFList lll= henselLiftAndLatticeRecombi (A, uniFactors, alpha, degs); |
---|
| 5498 | factors= Union (lll, factors); |
---|
| 5499 | } |
---|
| 5500 | TIMING_END_AND_PRINT (fac_hensel_lift, "time for hensel lifting: "); |
---|
| 5501 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
| 5502 | } |
---|
[806c18] | 5503 | else |
---|
[11bf82] | 5504 | { |
---|
| 5505 | bool earlySuccess= false; |
---|
| 5506 | CFList earlyFactors; |
---|
| 5507 | TIMING_START (fac_hensel_lift); |
---|
| 5508 | uniFactors= henselLiftAndEarly |
---|
| 5509 | (A, earlySuccess, earlyFactors, degs, liftBound, |
---|
| 5510 | uniFactors, info, evaluation); |
---|
| 5511 | TIMING_END_AND_PRINT (fac_hensel_lift, "time for hensel lifting: "); |
---|
| 5512 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
| 5513 | |
---|
| 5514 | CanonicalForm MODl= power (y, liftBound); |
---|
| 5515 | if (!extension) |
---|
| 5516 | { |
---|
| 5517 | factors= factorRecombination (uniFactors, A, MODl, degs, 1, 3); |
---|
| 5518 | |
---|
| 5519 | int oldUniFactorsLength= uniFactors.length(); |
---|
| 5520 | if (degree (A) > 0) |
---|
| 5521 | { |
---|
| 5522 | CFList tmp; |
---|
| 5523 | if (alpha.level() == 1) |
---|
| 5524 | tmp= increasePrecision (A, uniFactors, 0, uniFactors.length(), 1, |
---|
| 5525 | liftBound |
---|
| 5526 | ); |
---|
| 5527 | else |
---|
| 5528 | { |
---|
| 5529 | if (degree (A) > getCharacteristic()) |
---|
| 5530 | tmp= increasePrecisionFq2Fp (A, uniFactors, 0, uniFactors.length(), |
---|
| 5531 | 1, alpha, liftBound |
---|
| 5532 | ); |
---|
| 5533 | else |
---|
| 5534 | tmp= increasePrecision (A, uniFactors, 0, uniFactors.length(), 1, |
---|
| 5535 | alpha, liftBound |
---|
| 5536 | ); |
---|
| 5537 | } |
---|
| 5538 | factors= Union (factors, tmp); |
---|
| 5539 | if (tmp.length() == 0 || (tmp.length() > 0 && uniFactors.length() != 0 |
---|
| 5540 | && uniFactors.length() != oldUniFactorsLength) |
---|
| 5541 | ) |
---|
| 5542 | { |
---|
| 5543 | DegreePattern bufDegs= DegreePattern (uniFactors); |
---|
| 5544 | degs.intersect (bufDegs); |
---|
| 5545 | degs.refine (); |
---|
| 5546 | factors= Union (factors, factorRecombination (uniFactors, A, MODl, |
---|
| 5547 | degs, 4, |
---|
| 5548 | uniFactors.length()/2 |
---|
| 5549 | ) |
---|
| 5550 | ); |
---|
| 5551 | } |
---|
| 5552 | } |
---|
| 5553 | } |
---|
| 5554 | else |
---|
| 5555 | { |
---|
| 5556 | if (beta.level() != 1 || k > 1) |
---|
| 5557 | { |
---|
| 5558 | if (k > 1) |
---|
| 5559 | { |
---|
| 5560 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
| 5561 | evaluation, 1, uniFactors.length()/2 |
---|
| 5562 | ); |
---|
| 5563 | } |
---|
| 5564 | else |
---|
| 5565 | { |
---|
| 5566 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
| 5567 | evaluation, 1, 3 |
---|
| 5568 | ); |
---|
| 5569 | if (degree (A) > 0) |
---|
| 5570 | { |
---|
| 5571 | CFList tmp= increasePrecision2 (A, uniFactors, alpha, liftBound); |
---|
| 5572 | DegreePattern bufDegs= DegreePattern (tmp); |
---|
| 5573 | degs.intersect (bufDegs); |
---|
| 5574 | degs.refine (); |
---|
| 5575 | factors= Union (factors, extFactorRecombination (tmp, A, MODl, info, |
---|
| 5576 | degs, evaluation, |
---|
| 5577 | 1, tmp.length()/2 |
---|
| 5578 | ) |
---|
| 5579 | ); |
---|
| 5580 | } |
---|
| 5581 | } |
---|
| 5582 | } |
---|
| 5583 | else |
---|
| 5584 | { |
---|
| 5585 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
| 5586 | evaluation, 1, 3 |
---|
| 5587 | ); |
---|
| 5588 | int oldUniFactorsLength= uniFactors.length(); |
---|
| 5589 | if (degree (A) > 0) |
---|
| 5590 | { |
---|
| 5591 | int degMipo; |
---|
| 5592 | ExtensionInfo info2= init4ext (info, evaluation, degMipo); |
---|
| 5593 | |
---|
| 5594 | CFList source, dest; |
---|
| 5595 | CFList tmp= extIncreasePrecision (A, uniFactors, 0, |
---|
| 5596 | uniFactors.length(), 1, evaluation, |
---|
| 5597 | info2, source, dest, liftBound |
---|
| 5598 | ); |
---|
| 5599 | factors= Union (factors, tmp); |
---|
| 5600 | if (tmp.length() == 0 || (tmp.length() > 0 && uniFactors.length() != 0 |
---|
| 5601 | && uniFactors.length() != oldUniFactorsLength) |
---|
| 5602 | ) |
---|
| 5603 | { |
---|
| 5604 | DegreePattern bufDegs= DegreePattern (uniFactors); |
---|
| 5605 | degs.intersect (bufDegs); |
---|
| 5606 | degs.refine (); |
---|
| 5607 | factors= Union (factors,extFactorRecombination (uniFactors, A, MODl, |
---|
| 5608 | info, degs, evaluation, |
---|
| 5609 | 4, uniFactors.length()/2 |
---|
| 5610 | ) |
---|
| 5611 | ); |
---|
| 5612 | } |
---|
| 5613 | } |
---|
| 5614 | } |
---|
| 5615 | } |
---|
[806c18] | 5616 | |
---|
[11bf82] | 5617 | if (earlySuccess) |
---|
| 5618 | factors= Union (earlyFactors, factors); |
---|
| 5619 | else if (!earlySuccess && degs.getLength() == 1) |
---|
| 5620 | factors= earlyFactors; |
---|
| 5621 | } |
---|
| 5622 | delete [] bounds; |
---|
[7bf145] | 5623 | if (!extension) |
---|
| 5624 | { |
---|
| 5625 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
| 5626 | i.getItem()= i.getItem() (y - evaluation, y); |
---|
| 5627 | } |
---|
| 5628 | |
---|
[806c18] | 5629 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
[7bf145] | 5630 | swap, swap2, N); |
---|
[806c18] | 5631 | normalize (factors); |
---|
[7bf145] | 5632 | |
---|
| 5633 | return factors; |
---|
| 5634 | } |
---|
| 5635 | |
---|
[806c18] | 5636 | CFList |
---|
| 5637 | extBiFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
[7bf145] | 5638 | { |
---|
[806c18] | 5639 | |
---|
[7bf145] | 5640 | CanonicalForm A= F; |
---|
| 5641 | Variable alpha= info.getAlpha(); |
---|
| 5642 | Variable beta= info.getBeta(); |
---|
| 5643 | int k= info.getGFDegree(); |
---|
| 5644 | char cGFName= info.getGFName(); |
---|
| 5645 | CanonicalForm delta= info.getDelta(); |
---|
| 5646 | |
---|
| 5647 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
[806c18] | 5648 | Variable x= Variable (1); |
---|
[7bf145] | 5649 | CFList factors; |
---|
| 5650 | if (!GF && alpha == x) // we are in F_p |
---|
| 5651 | { |
---|
[806c18] | 5652 | bool extension= true; |
---|
[7bf145] | 5653 | int p= getCharacteristic(); |
---|
[806c18] | 5654 | if (p*p < (1<<16)) // pass to GF if possible |
---|
| 5655 | { |
---|
[7bf145] | 5656 | setCharacteristic (getCharacteristic(), 2, 'Z'); |
---|
| 5657 | A= A.mapinto(); |
---|
[11bf82] | 5658 | ExtensionInfo info2= ExtensionInfo (extension); |
---|
| 5659 | factors= biFactorize (A, info2); |
---|
[7bf145] | 5660 | |
---|
| 5661 | Variable vBuf= rootOf (gf_mipo); |
---|
| 5662 | setCharacteristic (getCharacteristic()); |
---|
[806c18] | 5663 | for (CFListIterator j= factors; j.hasItem(); j++) |
---|
| 5664 | j.getItem()= GF2FalphaRep (j.getItem(), vBuf); |
---|
[7bf145] | 5665 | } |
---|
[806c18] | 5666 | else // not able to pass to GF, pass to F_p(\alpha) |
---|
| 5667 | { |
---|
[11bf82] | 5668 | CanonicalForm mipo= randomIrredpoly (2, Variable (1)); |
---|
[7bf145] | 5669 | Variable v= rootOf (mipo); |
---|
[11bf82] | 5670 | ExtensionInfo info2= ExtensionInfo (v); |
---|
| 5671 | factors= biFactorize (A, info2); |
---|
[806c18] | 5672 | } |
---|
[7bf145] | 5673 | return factors; |
---|
| 5674 | } |
---|
| 5675 | else if (!GF && (alpha != x)) // we are in F_p(\alpha) |
---|
[806c18] | 5676 | { |
---|
[7bf145] | 5677 | if (k == 1) // need factorization over F_p |
---|
| 5678 | { |
---|
| 5679 | int extDeg= degree (getMipo (alpha)); |
---|
[806c18] | 5680 | extDeg++; |
---|
[7bf145] | 5681 | CanonicalForm mipo= randomIrredpoly (extDeg + 1, Variable (1)); |
---|
| 5682 | Variable v= rootOf (mipo); |
---|
[11bf82] | 5683 | ExtensionInfo info2= ExtensionInfo (v); |
---|
| 5684 | factors= biFactorize (A, info2); |
---|
[7bf145] | 5685 | } |
---|
[806c18] | 5686 | else |
---|
[7bf145] | 5687 | { |
---|
| 5688 | if (beta == Variable (1)) |
---|
| 5689 | { |
---|
[11bf82] | 5690 | Variable v= chooseExtension (alpha, beta, k); |
---|
[7bf145] | 5691 | CanonicalForm primElem, imPrimElem; |
---|
| 5692 | bool primFail= false; |
---|
| 5693 | Variable vBuf; |
---|
| 5694 | primElem= primitiveElement (alpha, vBuf, primFail); |
---|
| 5695 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
| 5696 | if (primFail) |
---|
| 5697 | ; //ERROR |
---|
| 5698 | else |
---|
[618da5] | 5699 | imPrimElem= mapPrimElem (primElem, alpha, v); |
---|
[7bf145] | 5700 | |
---|
| 5701 | CFList source, dest; |
---|
[806c18] | 5702 | CanonicalForm bufA= mapUp (A, alpha, v, primElem, imPrimElem, |
---|
[7bf145] | 5703 | source, dest); |
---|
[11bf82] | 5704 | ExtensionInfo info2= ExtensionInfo (v, alpha, imPrimElem, primElem); |
---|
| 5705 | factors= biFactorize (bufA, info2); |
---|
[7bf145] | 5706 | } |
---|
| 5707 | else |
---|
| 5708 | { |
---|
[11bf82] | 5709 | Variable v= chooseExtension (alpha, beta, k); |
---|
[7bf145] | 5710 | CanonicalForm primElem, imPrimElem; |
---|
| 5711 | bool primFail= false; |
---|
| 5712 | Variable vBuf; |
---|
| 5713 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
| 5714 | if (primFail) |
---|
| 5715 | ; //ERROR |
---|
| 5716 | else |
---|
[618da5] | 5717 | imPrimElem= mapPrimElem (delta, beta, v); |
---|
[7bf145] | 5718 | |
---|
| 5719 | CFList source, dest; |
---|
| 5720 | CanonicalForm bufA= mapDown (A, info, source, dest); |
---|
| 5721 | source= CFList(); |
---|
| 5722 | dest= CFList(); |
---|
| 5723 | bufA= mapUp (bufA, beta, v, delta, imPrimElem, source, dest); |
---|
[11bf82] | 5724 | ExtensionInfo info2= ExtensionInfo (v, beta, imPrimElem, delta); |
---|
| 5725 | factors= biFactorize (bufA, info2); |
---|
[7bf145] | 5726 | } |
---|
| 5727 | } |
---|
| 5728 | return factors; |
---|
| 5729 | } |
---|
| 5730 | else // we are in GF (p^k) |
---|
[806c18] | 5731 | { |
---|
[7bf145] | 5732 | int p= getCharacteristic(); |
---|
| 5733 | int extensionDeg= getGFDegree(); |
---|
| 5734 | bool extension= true; |
---|
| 5735 | if (k == 1) // need factorization over F_p |
---|
| 5736 | { |
---|
| 5737 | extensionDeg++; |
---|
[806c18] | 5738 | if (ipower (p, extensionDeg) < (1<<16)) |
---|
| 5739 | // pass to GF(p^k+1) |
---|
[7bf145] | 5740 | { |
---|
| 5741 | setCharacteristic (p); |
---|
[806c18] | 5742 | Variable vBuf= rootOf (gf_mipo); |
---|
| 5743 | A= GF2FalphaRep (A, vBuf); |
---|
| 5744 | setCharacteristic (p, extensionDeg, 'Z'); |
---|
[11bf82] | 5745 | ExtensionInfo info2= ExtensionInfo (extension); |
---|
| 5746 | factors= biFactorize (A.mapinto(), info2); |
---|
[7bf145] | 5747 | } |
---|
| 5748 | else // not able to pass to another GF, pass to F_p(\alpha) |
---|
[806c18] | 5749 | { |
---|
| 5750 | setCharacteristic (p); |
---|
| 5751 | Variable vBuf= rootOf (gf_mipo); |
---|
| 5752 | A= GF2FalphaRep (A, vBuf); |
---|
[11bf82] | 5753 | Variable v= chooseExtension (vBuf, beta, k); |
---|
| 5754 | ExtensionInfo info2= ExtensionInfo (v, extension); |
---|
| 5755 | factors= biFactorize (A, info2); |
---|
[7bf145] | 5756 | } |
---|
| 5757 | } |
---|
| 5758 | else // need factorization over GF (p^k) |
---|
| 5759 | { |
---|
[806c18] | 5760 | if (ipower (p, 2*extensionDeg) < (1<<16)) |
---|
[7bf145] | 5761 | // pass to GF (p^2k) |
---|
[806c18] | 5762 | { |
---|
| 5763 | setCharacteristic (p, 2*extensionDeg, 'Z'); |
---|
[11bf82] | 5764 | ExtensionInfo info2= ExtensionInfo (k, cGFName, extension); |
---|
| 5765 | factors= biFactorize (GFMapUp (A, extensionDeg), info2); |
---|
[806c18] | 5766 | setCharacteristic (p, extensionDeg, cGFName); |
---|
[7bf145] | 5767 | } |
---|
| 5768 | else // not able to pass to GF (p^2k), pass to F_p (\alpha) |
---|
[806c18] | 5769 | { |
---|
| 5770 | setCharacteristic (p); |
---|
| 5771 | Variable v1= rootOf (gf_mipo); |
---|
| 5772 | A= GF2FalphaRep (A, v1); |
---|
[11bf82] | 5773 | Variable v2= chooseExtension (v1, v1, k); |
---|
[7bf145] | 5774 | CanonicalForm primElem, imPrimElem; |
---|
| 5775 | bool primFail= false; |
---|
| 5776 | Variable vBuf; |
---|
| 5777 | primElem= primitiveElement (v1, vBuf, primFail); |
---|
| 5778 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
| 5779 | if (primFail) |
---|
| 5780 | ; //ERROR |
---|
| 5781 | else |
---|
[618da5] | 5782 | imPrimElem= mapPrimElem (primElem, v1, v2); |
---|
[7bf145] | 5783 | |
---|
| 5784 | CFList source, dest; |
---|
[806c18] | 5785 | CanonicalForm bufA= mapUp (A, v1, v2, primElem, imPrimElem, |
---|
[7bf145] | 5786 | source, dest); |
---|
[11bf82] | 5787 | ExtensionInfo info2= ExtensionInfo (v2, v1, imPrimElem, primElem); |
---|
| 5788 | factors= biFactorize (bufA, info2); |
---|
[806c18] | 5789 | setCharacteristic (p, k, cGFName); |
---|
| 5790 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
| 5791 | i.getItem()= Falpha2GFRep (i.getItem()); |
---|
[7bf145] | 5792 | } |
---|
| 5793 | } |
---|
| 5794 | return factors; |
---|
| 5795 | } |
---|
| 5796 | } |
---|
| 5797 | |
---|
| 5798 | #endif |
---|
| 5799 | /* HAVE_NTL */ |
---|
| 5800 | |
---|
| 5801 | |
---|