[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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[0e2e23] | 32 | #include "facMul.h" |
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[7bf145] | 33 | #include "cf_map.h" |
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| 34 | #include "cf_gcd_smallp.h" |
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[11bf82] | 35 | #include "facFqBivarUtil.h" |
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[7bf145] | 36 | #include "facFqBivar.h" |
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[11bf82] | 37 | #include "cfNewtonPolygon.h" |
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[f9da5e] | 38 | #include "algext.h" |
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[7bf145] | 39 | |
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| 40 | #ifdef HAVE_NTL |
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[da68804] | 41 | #include "NTLconvert.h" |
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[7bf145] | 42 | |
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[e76d7a6] | 43 | TIMING_DEFINE_PRINT(fac_uni_factorizer) |
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[0b618a7] | 44 | TIMING_DEFINE_PRINT(fac_hensel_lift12) |
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[7bf145] | 45 | |
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[ad0177] | 46 | CanonicalForm prodMod0 (const CFList& L, const CanonicalForm& M, const modpk& b) |
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[7bf145] | 47 | { |
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| 48 | if (L.isEmpty()) |
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| 49 | return 1; |
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| 50 | else if (L.length() == 1) |
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| 51 | return mod (L.getFirst()(0, 1) , M); |
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| 52 | else if (L.length() == 2) |
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[ad0177] | 53 | return mod (mulNTL (L.getFirst()(0, 1),L.getLast()(0, 1), b), M); |
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[7bf145] | 54 | else |
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| 55 | { |
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| 56 | int l= L.length()/2; |
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| 57 | CFListIterator i= L; |
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| 58 | CFList tmp1, tmp2; |
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| 59 | CanonicalForm buf1, buf2; |
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[806c18] | 60 | for (int j= 1; j <= l; j++, i++) |
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[7bf145] | 61 | tmp1.append (i.getItem()); |
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| 62 | tmp2= Difference (L, tmp1); |
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[ad0177] | 63 | buf1= prodMod0 (tmp1, M, b); |
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| 64 | buf2= prodMod0 (tmp2, M, b); |
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| 65 | return mod (mulNTL (buf1,buf2, b), M); |
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[7bf145] | 66 | } |
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| 67 | } |
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| 68 | |
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[806c18] | 69 | CanonicalForm evalPoint (const CanonicalForm& F, CanonicalForm & eval, |
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[7bf145] | 70 | const Variable& alpha, CFList& list, const bool& GF, |
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[806c18] | 71 | bool& fail) |
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[7bf145] | 72 | { |
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| 73 | fail= false; |
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| 74 | Variable x= Variable(2); |
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[a54114] | 75 | Variable y= Variable(1); |
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[7bf145] | 76 | FFRandom genFF; |
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| 77 | GFRandom genGF; |
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| 78 | CanonicalForm random, mipo; |
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| 79 | double bound; |
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| 80 | int p= getCharacteristic (); |
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[1372ae] | 81 | if (alpha.level() != 1) |
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[7bf145] | 82 | { |
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| 83 | mipo= getMipo (alpha); |
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| 84 | int d= degree (mipo); |
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| 85 | bound= ipower (p, d); |
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| 86 | } |
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[806c18] | 87 | else if (GF) |
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[7bf145] | 88 | { |
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| 89 | int d= getGFDegree(); |
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| 90 | bound= ipower (p, d); |
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| 91 | } |
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| 92 | else |
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| 93 | bound= p; |
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| 94 | |
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[11bf82] | 95 | random= 0; |
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[806c18] | 96 | do |
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[7bf145] | 97 | { |
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| 98 | if (list.length() >= bound) |
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| 99 | { |
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| 100 | fail= true; |
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| 101 | break; |
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| 102 | } |
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[8db258] | 103 | if (list.isEmpty()) |
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| 104 | random= 0; |
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| 105 | else if (GF) |
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[11bf82] | 106 | { |
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| 107 | if (list.length() == 1) |
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| 108 | random= getGFGenerator(); |
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| 109 | else |
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| 110 | random= genGF.generate(); |
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| 111 | } |
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| 112 | else if (list.length() < p || alpha.level() == 1) |
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[7bf145] | 113 | random= genFF.generate(); |
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[806c18] | 114 | else if (alpha != x && list.length() >= p) |
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[7bf145] | 115 | { |
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[11bf82] | 116 | if (list.length() == p) |
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| 117 | random= alpha; |
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| 118 | else |
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| 119 | { |
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| 120 | AlgExtRandomF genAlgExt (alpha); |
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| 121 | random= genAlgExt.generate(); |
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| 122 | } |
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[7bf145] | 123 | } |
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| 124 | if (find (list, random)) continue; |
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| 125 | eval= F (random, x); |
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[a54114] | 126 | if (degree (eval) != degree (F, y)) |
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[7bf145] | 127 | { //leading coeff vanishes |
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| 128 | if (!find (list, random)) |
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| 129 | list.append (random); |
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| 130 | continue; |
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| 131 | } |
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[806c18] | 132 | if (degree (gcd (deriv (eval, eval.mvar()), eval), eval.mvar()) > 0) |
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[7bf145] | 133 | { //evaluated polynomial is not squarefree |
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| 134 | if (!find (list, random)) |
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| 135 | list.append (random); |
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| 136 | continue; |
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| 137 | } |
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| 138 | } while (find (list, random)); |
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| 139 | |
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| 140 | return random; |
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| 141 | } |
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| 142 | |
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[806c18] | 143 | CFList |
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| 144 | uniFactorizer (const CanonicalForm& A, const Variable& alpha, const bool& GF) |
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[7bf145] | 145 | { |
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| 146 | Variable x= A.mvar(); |
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| 147 | ASSERT (A.isUnivariate(), "univariate polynomial expected"); |
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| 148 | CFFList factorsA; |
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| 149 | ZZ p= to_ZZ (getCharacteristic()); |
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[806c18] | 150 | ZZ_p::init (p); |
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| 151 | if (GF) |
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[7bf145] | 152 | { |
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[806c18] | 153 | Variable beta= rootOf (gf_mipo); |
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[7bf145] | 154 | int k= getGFDegree(); |
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| 155 | char cGFName= gf_name; |
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[806c18] | 156 | setCharacteristic (getCharacteristic()); |
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| 157 | CanonicalForm buf= GF2FalphaRep (A, beta); |
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[7bf145] | 158 | if (getCharacteristic() > 2) |
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| 159 | { |
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| 160 | ZZ_pX NTLMipo= convertFacCF2NTLZZpX (gf_mipo); |
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| 161 | ZZ_pE::init (NTLMipo); |
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| 162 | ZZ_pEX NTLA= convertFacCF2NTLZZ_pEX (buf, NTLMipo); |
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| 163 | MakeMonic (NTLA); |
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| 164 | vec_pair_ZZ_pEX_long NTLFactorsA= CanZass (NTLA); |
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| 165 | ZZ_pE multi= to_ZZ_pE (1); |
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| 166 | factorsA= convertNTLvec_pair_ZZpEX_long2FacCFFList (NTLFactorsA, multi, |
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| 167 | x, beta); |
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| 168 | } |
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| 169 | else |
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| 170 | { |
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| 171 | GF2X NTLMipo= convertFacCF2NTLGF2X (gf_mipo); |
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| 172 | GF2E::init (NTLMipo); |
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| 173 | GF2EX NTLA= convertFacCF2NTLGF2EX (buf, NTLMipo); |
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| 174 | MakeMonic (NTLA); |
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| 175 | vec_pair_GF2EX_long NTLFactorsA= CanZass (NTLA); |
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| 176 | GF2E multi= to_GF2E (1); |
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| 177 | factorsA= convertNTLvec_pair_GF2EX_long2FacCFFList (NTLFactorsA, multi, |
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| 178 | x, beta); |
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| 179 | } |
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| 180 | setCharacteristic (getCharacteristic(), k, cGFName); |
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[806c18] | 181 | for (CFFListIterator i= factorsA; i.hasItem(); i++) |
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[7bf145] | 182 | { |
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| 183 | buf= i.getItem().factor(); |
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| 184 | buf= Falpha2GFRep (buf); |
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| 185 | i.getItem()= CFFactor (buf, i.getItem().exp()); |
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| 186 | } |
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[806c18] | 187 | } |
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[1372ae] | 188 | else if (alpha.level() != 1) |
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[7bf145] | 189 | { |
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| 190 | if (getCharacteristic() > 2) |
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| 191 | { |
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| 192 | ZZ_pX NTLMipo= convertFacCF2NTLZZpX (getMipo (alpha)); |
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[806c18] | 193 | ZZ_pE::init (NTLMipo); |
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[7bf145] | 194 | ZZ_pEX NTLA= convertFacCF2NTLZZ_pEX (A, NTLMipo); |
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| 195 | MakeMonic (NTLA); |
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| 196 | vec_pair_ZZ_pEX_long NTLFactorsA= CanZass (NTLA); |
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| 197 | ZZ_pE multi= to_ZZ_pE (1); |
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[806c18] | 198 | factorsA= convertNTLvec_pair_ZZpEX_long2FacCFFList (NTLFactorsA, multi, |
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[7bf145] | 199 | x, alpha); |
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| 200 | } |
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| 201 | else |
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| 202 | { |
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| 203 | GF2X NTLMipo= convertFacCF2NTLGF2X (getMipo (alpha)); |
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[806c18] | 204 | GF2E::init (NTLMipo); |
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[7bf145] | 205 | GF2EX NTLA= convertFacCF2NTLGF2EX (A, NTLMipo); |
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| 206 | MakeMonic (NTLA); |
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| 207 | vec_pair_GF2EX_long NTLFactorsA= CanZass (NTLA); |
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| 208 | GF2E multi= to_GF2E (1); |
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[806c18] | 209 | factorsA= convertNTLvec_pair_GF2EX_long2FacCFFList (NTLFactorsA, multi, |
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[7bf145] | 210 | x, alpha); |
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[806c18] | 211 | } |
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[7bf145] | 212 | } |
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[806c18] | 213 | else |
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[7bf145] | 214 | { |
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| 215 | if (getCharacteristic() > 2) |
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| 216 | { |
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| 217 | ZZ_pX NTLA= convertFacCF2NTLZZpX (A); |
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| 218 | MakeMonic (NTLA); |
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| 219 | vec_pair_ZZ_pX_long NTLFactorsA= CanZass (NTLA); |
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| 220 | ZZ_p multi= to_ZZ_p (1); |
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[806c18] | 221 | factorsA= convertNTLvec_pair_ZZpX_long2FacCFFList (NTLFactorsA, multi, |
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[7bf145] | 222 | x); |
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| 223 | } |
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| 224 | else |
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| 225 | { |
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| 226 | GF2X NTLA= convertFacCF2NTLGF2X (A); |
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| 227 | vec_pair_GF2X_long NTLFactorsA= CanZass (NTLA); |
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| 228 | GF2 multi= to_GF2 (1); |
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[806c18] | 229 | factorsA= convertNTLvec_pair_GF2X_long2FacCFFList (NTLFactorsA, multi, |
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[7bf145] | 230 | x); |
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| 231 | } |
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| 232 | } |
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| 233 | CFList uniFactors; |
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[806c18] | 234 | for (CFFListIterator i= factorsA; i.hasItem(); i++) |
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[7bf145] | 235 | uniFactors.append (i.getItem().factor()); |
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| 236 | return uniFactors; |
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[806c18] | 237 | } |
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| 238 | |
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| 239 | /// naive factor recombination as decribed in "Factoring |
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| 240 | /// multivariate polynomials over a finite field" by L Bernardin. |
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| 241 | CFList |
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[11bf82] | 242 | extFactorRecombination (CFList& factors, CanonicalForm& F, |
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[09609a] | 243 | const CanonicalForm& N, const ExtensionInfo& info, |
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[11bf82] | 244 | DegreePattern& degs, const CanonicalForm& eval, int s, |
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| 245 | int thres) |
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[806c18] | 246 | { |
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[7bf145] | 247 | if (factors.length() == 0) |
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[11bf82] | 248 | { |
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| 249 | F= 1; |
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[7bf145] | 250 | return CFList(); |
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[11bf82] | 251 | } |
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[7bf145] | 252 | |
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| 253 | Variable alpha= info.getAlpha(); |
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| 254 | Variable beta= info.getBeta(); |
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| 255 | CanonicalForm gamma= info.getGamma(); |
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| 256 | CanonicalForm delta= info.getDelta(); |
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| 257 | int k= info.getGFDegree(); |
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| 258 | |
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[09609a] | 259 | CanonicalForm M= N; |
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| 260 | int l= degree (N); |
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[7bf145] | 261 | Variable y= F.mvar(); |
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[a54114] | 262 | Variable x= Variable (1); |
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[7bf145] | 263 | CFList source, dest; |
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[806c18] | 264 | if (degs.getLength() <= 1 || factors.length() == 1) |
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[11bf82] | 265 | { |
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| 266 | CFList result= CFList(mapDown (F(y-eval, y), info, source, dest)); |
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| 267 | F= 1; |
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| 268 | return result; |
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| 269 | } |
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[806c18] | 270 | |
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| 271 | DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, M) == F " << |
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[7bf145] | 272 | (LC (F, 1)*prodMod (factors, M) == F)); |
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[ac8e1a] | 273 | int degMipoBeta= 1; |
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| 274 | if (!k && beta.level() != 1) |
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[7bf145] | 275 | degMipoBeta= degree (getMipo (beta)); |
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| 276 | |
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| 277 | CFList T, S, Diff; |
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| 278 | T= factors; |
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| 279 | |
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| 280 | CFList result; |
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[21b8f4c] | 281 | CanonicalForm buf, buf2, quot; |
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[11bf82] | 282 | |
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| 283 | buf= F; |
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[7bf145] | 284 | |
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[a54114] | 285 | CanonicalForm g, LCBuf= LC (buf, x); |
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[1673386] | 286 | int * v= new int [T.length()]; |
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[7bf145] | 287 | for (int i= 0; i < T.length(); i++) |
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| 288 | v[i]= 0; |
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| 289 | |
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| 290 | CFArray TT; |
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[806c18] | 291 | DegreePattern bufDegs1, bufDegs2; |
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[7bf145] | 292 | bufDegs1= degs; |
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| 293 | int subsetDeg; |
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[806c18] | 294 | TT= copy (factors); |
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[7bf145] | 295 | bool nosubset= false; |
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| 296 | bool recombination= false; |
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[93134c] | 297 | bool trueFactor= false; |
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[bbb3fbf] | 298 | CanonicalForm test; |
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| 299 | CanonicalForm buf0= buf (0, x)*LCBuf; |
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[11bf82] | 300 | while (T.length() >= 2*s && s <= thres) |
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[7bf145] | 301 | { |
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[806c18] | 302 | while (nosubset == false) |
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[7bf145] | 303 | { |
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[806c18] | 304 | if (T.length() == s) |
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[7bf145] | 305 | { |
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[1673386] | 306 | delete [] v; |
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[806c18] | 307 | if (recombination) |
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[7bf145] | 308 | { |
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| 309 | T.insert (LCBuf); |
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| 310 | g= prodMod (T, M); |
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| 311 | T.removeFirst(); |
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| 312 | g /= content(g); |
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| 313 | g= g (y - eval, y); |
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| 314 | g /= Lc (g); |
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| 315 | appendTestMapDown (result, g, info, source, dest); |
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[11bf82] | 316 | F= 1; |
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[7bf145] | 317 | return result; |
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| 318 | } |
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| 319 | else |
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| 320 | { |
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| 321 | appendMapDown (result, F (y - eval, y), info, source, dest); |
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[11bf82] | 322 | F= 1; |
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[7bf145] | 323 | return result; |
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| 324 | } |
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| 325 | } |
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| 326 | S= subset (v, s, TT, nosubset); |
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| 327 | if (nosubset) break; |
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| 328 | subsetDeg= subsetDegree (S); |
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| 329 | // skip those combinations that are not possible |
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[806c18] | 330 | if (!degs.find (subsetDeg)) |
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[7bf145] | 331 | continue; |
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[806c18] | 332 | else |
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| 333 | { |
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[bbb3fbf] | 334 | test= prodMod0 (S, M); |
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| 335 | test *= LCBuf; |
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| 336 | test = mod (test, M); |
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| 337 | if (fdivides (test, buf0)) |
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[7bf145] | 338 | { |
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[bbb3fbf] | 339 | S.insert (LCBuf); |
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| 340 | g= prodMod (S, M); |
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| 341 | S.removeFirst(); |
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| 342 | g /= content (g, x); |
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| 343 | if (fdivides (g, buf, quot)) |
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[f047b56] | 344 | { |
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[bbb3fbf] | 345 | buf2= g (y - eval, y); |
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| 346 | buf2 /= Lc (buf2); |
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| 347 | |
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| 348 | if (!k && beta.level() == 1) |
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[7bf145] | 349 | { |
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[bbb3fbf] | 350 | if (degree (buf2, alpha) < degMipoBeta) |
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| 351 | { |
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| 352 | buf= quot; |
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| 353 | LCBuf= LC (buf, x); |
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| 354 | recombination= true; |
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| 355 | appendTestMapDown (result, buf2, info, source, dest); |
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| 356 | trueFactor= true; |
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| 357 | } |
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[7bf145] | 358 | } |
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[bbb3fbf] | 359 | else |
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[7bf145] | 360 | { |
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[bbb3fbf] | 361 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
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[7bf145] | 362 | { |
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[bbb3fbf] | 363 | buf= quot; |
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| 364 | LCBuf= LC (buf, x); |
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| 365 | recombination= true; |
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| 366 | appendTestMapDown (result, buf2, info, source, dest); |
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| 367 | trueFactor= true; |
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[f047b56] | 368 | } |
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[bbb3fbf] | 369 | } |
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| 370 | if (trueFactor) |
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| 371 | { |
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| 372 | T= Difference (T, S); |
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| 373 | l -= degree (g); |
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| 374 | M= power (y, l); |
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| 375 | buf0= buf (0, x)*LCBuf; |
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| 376 | |
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| 377 | // compute new possible degree pattern |
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| 378 | bufDegs2= DegreePattern (T); |
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| 379 | bufDegs1.intersect (bufDegs2); |
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| 380 | bufDegs1.refine (); |
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| 381 | if (T.length() < 2*s || T.length() == s || |
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| 382 | bufDegs1.getLength() == 1) |
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[f047b56] | 383 | { |
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[bbb3fbf] | 384 | delete [] v; |
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| 385 | if (recombination) |
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| 386 | { |
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| 387 | appendTestMapDown (result, buf (y - eval, y), info, source, |
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| 388 | dest); |
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| 389 | F= 1; |
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| 390 | return result; |
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| 391 | } |
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| 392 | else |
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| 393 | { |
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| 394 | appendMapDown (result, F (y - eval, y), info, source, dest); |
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| 395 | F= 1; |
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| 396 | return result; |
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| 397 | } |
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[7bf145] | 398 | } |
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[bbb3fbf] | 399 | trueFactor= false; |
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| 400 | TT= copy (T); |
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| 401 | indexUpdate (v, s, T.length(), nosubset); |
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| 402 | if (nosubset) break; |
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[7bf145] | 403 | } |
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| 404 | } |
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| 405 | } |
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| 406 | } |
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| 407 | } |
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| 408 | s++; |
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[806c18] | 409 | if (T.length() < 2*s || T.length() == s) |
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[7bf145] | 410 | { |
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[1673386] | 411 | delete [] v; |
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[7bf145] | 412 | if (recombination) |
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| 413 | { |
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| 414 | appendTestMapDown (result, buf (y - eval, y), info, source, dest); |
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[11bf82] | 415 | F= 1; |
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[7bf145] | 416 | return result; |
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| 417 | } |
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| 418 | else |
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| 419 | { |
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| 420 | appendMapDown (result, F (y - eval, y), info, source, dest); |
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[11bf82] | 421 | F= 1; |
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[7bf145] | 422 | return result; |
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| 423 | } |
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| 424 | } |
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| 425 | for (int i= 0; i < T.length(); i++) |
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| 426 | v[i]= 0; |
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| 427 | nosubset= false; |
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| 428 | } |
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[806c18] | 429 | if (T.length() < 2*s) |
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[11bf82] | 430 | { |
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[7bf145] | 431 | appendMapDown (result, F (y - eval, y), info, source, dest); |
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[11bf82] | 432 | F= 1; |
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| 433 | delete [] v; |
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| 434 | return result; |
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| 435 | } |
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| 436 | |
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| 437 | if (s > thres) |
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| 438 | { |
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| 439 | factors= T; |
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| 440 | F= buf; |
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| 441 | degs= bufDegs1; |
---|
| 442 | } |
---|
[7bf145] | 443 | |
---|
[1673386] | 444 | delete [] v; |
---|
[806c18] | 445 | return result; |
---|
| 446 | } |
---|
[7bf145] | 447 | |
---|
[806c18] | 448 | /// naive factor recombination as decribed in "Factoring |
---|
| 449 | /// multivariate polynomials over a finite field" by L Bernardin. |
---|
| 450 | CFList |
---|
[11bf82] | 451 | factorRecombination (CFList& factors, CanonicalForm& F, |
---|
[09609a] | 452 | const CanonicalForm& N, DegreePattern& degs, int s, |
---|
[d9357b] | 453 | int thres, const modpk& b |
---|
[11bf82] | 454 | ) |
---|
[7bf145] | 455 | { |
---|
| 456 | if (factors.length() == 0) |
---|
[11bf82] | 457 | { |
---|
| 458 | F= 1; |
---|
[7bf145] | 459 | return CFList (); |
---|
[11bf82] | 460 | } |
---|
[806c18] | 461 | if (degs.getLength() <= 1 || factors.length() == 1) |
---|
[11bf82] | 462 | { |
---|
| 463 | CFList result= CFList (F); |
---|
| 464 | F= 1; |
---|
| 465 | return result; |
---|
| 466 | } |
---|
[f3a82f4] | 467 | DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, N) == F " << |
---|
| 468 | (LC (F, 1)*prodMod (factors, N) == F)); |
---|
[7bf145] | 469 | CFList T, S; |
---|
| 470 | |
---|
[09609a] | 471 | CanonicalForm M= N; |
---|
| 472 | int l= degree (N); |
---|
[7bf145] | 473 | T= factors; |
---|
| 474 | CFList result; |
---|
[a54114] | 475 | Variable y= Variable (2); |
---|
| 476 | Variable x= Variable (1); |
---|
| 477 | CanonicalForm LCBuf= LC (F, x); |
---|
[21b8f4c] | 478 | CanonicalForm g, quot, buf= F; |
---|
[1673386] | 479 | int * v= new int [T.length()]; |
---|
[7bf145] | 480 | for (int i= 0; i < T.length(); i++) |
---|
| 481 | v[i]= 0; |
---|
| 482 | bool nosubset= false; |
---|
| 483 | CFArray TT; |
---|
| 484 | DegreePattern bufDegs1, bufDegs2; |
---|
| 485 | bufDegs1= degs; |
---|
| 486 | int subsetDeg; |
---|
| 487 | TT= copy (factors); |
---|
| 488 | bool recombination= false; |
---|
[bbb3fbf] | 489 | CanonicalForm test; |
---|
[41fea7] | 490 | CanonicalForm buf0= mulNTL (buf (0, x), LCBuf); |
---|
[ad0177] | 491 | bool isRat= (isOn (SW_RATIONAL) && getCharacteristic() == 0) || getCharacteristic() > 0; |
---|
[11bf82] | 492 | while (T.length() >= 2*s && s <= thres) |
---|
[7bf145] | 493 | { |
---|
[806c18] | 494 | while (nosubset == false) |
---|
[7bf145] | 495 | { |
---|
[806c18] | 496 | if (T.length() == s) |
---|
[7bf145] | 497 | { |
---|
[1673386] | 498 | delete [] v; |
---|
[7bf145] | 499 | if (recombination) |
---|
| 500 | { |
---|
| 501 | T.insert (LCBuf); |
---|
| 502 | g= prodMod (T, M); |
---|
[eb481b] | 503 | if (b.getp() != 0) |
---|
| 504 | g= b(g); |
---|
[7bf145] | 505 | T.removeFirst(); |
---|
[a54114] | 506 | result.append (g/content (g, x)); |
---|
[11bf82] | 507 | F= 1; |
---|
[7bf145] | 508 | return result; |
---|
| 509 | } |
---|
| 510 | else |
---|
[11bf82] | 511 | { |
---|
| 512 | result= CFList (F); |
---|
| 513 | F= 1; |
---|
| 514 | return result; |
---|
| 515 | } |
---|
[7bf145] | 516 | } |
---|
| 517 | S= subset (v, s, TT, nosubset); |
---|
| 518 | if (nosubset) break; |
---|
| 519 | subsetDeg= subsetDegree (S); |
---|
| 520 | // skip those combinations that are not possible |
---|
[806c18] | 521 | if (!degs.find (subsetDeg)) |
---|
[7bf145] | 522 | continue; |
---|
[806c18] | 523 | else |
---|
| 524 | { |
---|
[f9da5e] | 525 | if (!isRat) |
---|
| 526 | On (SW_RATIONAL); |
---|
| 527 | test= prodMod0 (S, M); |
---|
| 528 | if (!isRat) |
---|
| 529 | { |
---|
| 530 | test *= bCommonDen (test); |
---|
| 531 | Off (SW_RATIONAL); |
---|
| 532 | } |
---|
[ad0177] | 533 | test= mulNTL (test, LCBuf, b); |
---|
| 534 | test= mod (test, M); |
---|
| 535 | if (uniFdivides (test, buf0)) |
---|
[7bf145] | 536 | { |
---|
[f9da5e] | 537 | if (!isRat) |
---|
| 538 | On (SW_RATIONAL); |
---|
[bbb3fbf] | 539 | S.insert (LCBuf); |
---|
| 540 | g= prodMod (S, M); |
---|
| 541 | S.removeFirst(); |
---|
[f9da5e] | 542 | if (!isRat) |
---|
| 543 | { |
---|
| 544 | g *= bCommonDen(g); |
---|
| 545 | Off (SW_RATIONAL); |
---|
| 546 | } |
---|
[eb481b] | 547 | if (b.getp() != 0) |
---|
| 548 | g= b(g); |
---|
[ad0177] | 549 | if (!isRat) |
---|
| 550 | On (SW_RATIONAL); |
---|
[f9da5e] | 551 | g /= content (g, x); |
---|
[bbb3fbf] | 552 | if (fdivides (g, buf, quot)) |
---|
[7bf145] | 553 | { |
---|
[bbb3fbf] | 554 | recombination= true; |
---|
| 555 | result.append (g); |
---|
| 556 | buf= quot; |
---|
| 557 | LCBuf= LC (buf, x); |
---|
| 558 | T= Difference (T, S); |
---|
| 559 | l -= degree (g); |
---|
| 560 | M= power (y, l); |
---|
[ad0177] | 561 | if (!isRat) |
---|
| 562 | Off (SW_RATIONAL); |
---|
[41fea7] | 563 | buf0= mulNTL (buf (0, x), LCBuf); |
---|
[bbb3fbf] | 564 | // compute new possible degree pattern |
---|
| 565 | bufDegs2= DegreePattern (T); |
---|
| 566 | bufDegs1.intersect (bufDegs2); |
---|
| 567 | bufDegs1.refine (); |
---|
| 568 | if (T.length() < 2*s || T.length() == s || |
---|
| 569 | bufDegs1.getLength() == 1) |
---|
[f047b56] | 570 | { |
---|
[bbb3fbf] | 571 | delete [] v; |
---|
| 572 | if (recombination) |
---|
| 573 | { |
---|
| 574 | result.append (buf); |
---|
| 575 | F= 1; |
---|
| 576 | return result; |
---|
| 577 | } |
---|
| 578 | else |
---|
| 579 | { |
---|
| 580 | result= CFList (F); |
---|
| 581 | F= 1; |
---|
| 582 | return result; |
---|
| 583 | } |
---|
[7bf145] | 584 | } |
---|
[bbb3fbf] | 585 | TT= copy (T); |
---|
| 586 | indexUpdate (v, s, T.length(), nosubset); |
---|
| 587 | if (nosubset) break; |
---|
[806c18] | 588 | } |
---|
[ad0177] | 589 | if (!isRat) |
---|
| 590 | Off (SW_RATIONAL); |
---|
[7bf145] | 591 | } |
---|
| 592 | } |
---|
| 593 | } |
---|
| 594 | s++; |
---|
[806c18] | 595 | if (T.length() < 2*s || T.length() == s) |
---|
[7bf145] | 596 | { |
---|
[1673386] | 597 | delete [] v; |
---|
[7bf145] | 598 | if (recombination) |
---|
| 599 | { |
---|
| 600 | result.append (buf); |
---|
[11bf82] | 601 | F= 1; |
---|
[7bf145] | 602 | return result; |
---|
| 603 | } |
---|
| 604 | else |
---|
[11bf82] | 605 | { |
---|
| 606 | result= CFList (F); |
---|
| 607 | F= 1; |
---|
| 608 | return result; |
---|
| 609 | } |
---|
[7bf145] | 610 | } |
---|
| 611 | for (int i= 0; i < T.length(); i++) |
---|
| 612 | v[i]= 0; |
---|
| 613 | nosubset= false; |
---|
| 614 | } |
---|
[11bf82] | 615 | delete [] v; |
---|
[806c18] | 616 | if (T.length() < 2*s) |
---|
[11bf82] | 617 | { |
---|
[7bf145] | 618 | result.append (F); |
---|
[11bf82] | 619 | F= 1; |
---|
| 620 | return result; |
---|
| 621 | } |
---|
| 622 | |
---|
| 623 | if (s > thres) |
---|
| 624 | { |
---|
| 625 | factors= T; |
---|
| 626 | F= buf; |
---|
| 627 | degs= bufDegs1; |
---|
| 628 | } |
---|
[7bf145] | 629 | |
---|
[806c18] | 630 | return result; |
---|
| 631 | } |
---|
[7bf145] | 632 | |
---|
[11bf82] | 633 | Variable chooseExtension (const Variable & alpha, const Variable& beta, int k) |
---|
[7bf145] | 634 | { |
---|
[11bf82] | 635 | zz_p::init (getCharacteristic()); |
---|
| 636 | zz_pX NTLIrredpoly; |
---|
| 637 | int i, m; |
---|
| 638 | // extension of F_p needed |
---|
| 639 | if (alpha.level() == 1 && beta.level() == 1 && k == 1) |
---|
| 640 | { |
---|
| 641 | i= 1; |
---|
| 642 | m= 2; |
---|
| 643 | } //extension of F_p(alpha) needed but want to factorize over F_p |
---|
| 644 | else if (alpha.level() != 1 && beta.level() == 1 && k == 1) |
---|
| 645 | { |
---|
| 646 | i= 1; |
---|
| 647 | m= degree (getMipo (alpha)) + 1; |
---|
| 648 | } //extension of F_p(alpha) needed for first time |
---|
| 649 | else if (alpha.level() != 1 && beta.level() == 1 && k != 1) |
---|
| 650 | { |
---|
[7bf145] | 651 | i= 2; |
---|
[11bf82] | 652 | m= degree (getMipo (alpha)); |
---|
| 653 | } |
---|
| 654 | else if (alpha.level() != 1 && beta.level() != 1 && k != 1) |
---|
| 655 | { |
---|
| 656 | m= degree (getMipo (beta)); |
---|
| 657 | i= degree (getMipo (alpha))/m + 1; |
---|
| 658 | } |
---|
| 659 | BuildIrred (NTLIrredpoly, i*m); |
---|
| 660 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
[7bf145] | 661 | return rootOf (newMipo); |
---|
| 662 | } |
---|
| 663 | |
---|
[1a3011e] | 664 | void |
---|
| 665 | earlyFactorDetection (CFList& reconstructedFactors, CanonicalForm& F, CFList& |
---|
| 666 | factors, int& adaptedLiftBound, int*& factorsFoundIndex, |
---|
[d9357b] | 667 | DegreePattern& degs, bool& success, int deg, |
---|
| 668 | const modpk& b) |
---|
[7bf145] | 669 | { |
---|
| 670 | DegreePattern bufDegs1= degs; |
---|
| 671 | DegreePattern bufDegs2; |
---|
| 672 | CFList T= factors; |
---|
| 673 | CanonicalForm buf= F; |
---|
[a54114] | 674 | Variable x= Variable (1); |
---|
| 675 | CanonicalForm LCBuf= LC (buf, x); |
---|
[21b8f4c] | 676 | CanonicalForm g, quot; |
---|
[7bf145] | 677 | CanonicalForm M= power (F.mvar(), deg); |
---|
| 678 | adaptedLiftBound= 0; |
---|
[1a3011e] | 679 | int d= degree (F), l= 0; |
---|
[41fea7] | 680 | CanonicalForm buf0= mulNTL (buf (0,x), LCBuf); |
---|
| 681 | CanonicalForm buf1= mulNTL (buf (1,x), LCBuf); |
---|
[de222e] | 682 | CanonicalForm test0, test1; |
---|
[ad0177] | 683 | bool isRat= (isOn (SW_RATIONAL) && getCharacteristic() == 0) || getCharacteristic() > 0; |
---|
[1a3011e] | 684 | for (CFListIterator i= factors; i.hasItem(); i++, l++) |
---|
[7bf145] | 685 | { |
---|
[1a3011e] | 686 | if (!bufDegs1.find (degree (i.getItem(), 1)) || factorsFoundIndex[l] == 1) |
---|
[7bf145] | 687 | continue; |
---|
| 688 | else |
---|
| 689 | { |
---|
[de222e] | 690 | test1= mod (mulNTL (i.getItem() (1,x), LCBuf, b), M); |
---|
| 691 | if (uniFdivides (test1, buf1)) |
---|
[7bf145] | 692 | { |
---|
[de222e] | 693 | test0= mod (mulNTL (i.getItem() (0,x), LCBuf, b), M); |
---|
| 694 | if (uniFdivides (test0, buf0)) |
---|
[7bf145] | 695 | { |
---|
[f9da5e] | 696 | if (!isRat) |
---|
| 697 | On (SW_RATIONAL); |
---|
[de222e] | 698 | g= mulMod2 (i.getItem(), LCBuf, M); |
---|
[f9da5e] | 699 | if (!isRat) |
---|
| 700 | { |
---|
| 701 | g *= bCommonDen(g); |
---|
| 702 | Off (SW_RATIONAL); |
---|
| 703 | } |
---|
[de222e] | 704 | if (b.getp() != 0) |
---|
| 705 | g= b(g); |
---|
[ad0177] | 706 | if (!isRat) |
---|
| 707 | On (SW_RATIONAL); |
---|
[f9da5e] | 708 | g /= content (g, x); |
---|
[de222e] | 709 | if (fdivides (g, buf, quot)) |
---|
| 710 | { |
---|
| 711 | reconstructedFactors.append (g); |
---|
| 712 | factorsFoundIndex[l]= 1; |
---|
| 713 | buf= quot; |
---|
| 714 | d -= degree (g); |
---|
| 715 | LCBuf= LC (buf, x); |
---|
[ad0177] | 716 | if (!isRat) |
---|
| 717 | Off (SW_RATIONAL); |
---|
[41fea7] | 718 | buf0= mulNTL (buf (0,x), LCBuf); |
---|
| 719 | buf1= mulNTL (buf (1,x), LCBuf); |
---|
[de222e] | 720 | T= Difference (T, CFList (i.getItem())); |
---|
| 721 | F= buf; |
---|
| 722 | |
---|
| 723 | // compute new possible degree pattern |
---|
| 724 | bufDegs2= DegreePattern (T); |
---|
| 725 | bufDegs1.intersect (bufDegs2); |
---|
| 726 | bufDegs1.refine (); |
---|
| 727 | if (bufDegs1.getLength() <= 1) |
---|
| 728 | { |
---|
| 729 | reconstructedFactors.append (buf); |
---|
| 730 | break; |
---|
| 731 | } |
---|
| 732 | } |
---|
[ad0177] | 733 | if (!isRat) |
---|
| 734 | Off (SW_RATIONAL); |
---|
[7bf145] | 735 | } |
---|
| 736 | } |
---|
| 737 | } |
---|
| 738 | } |
---|
| 739 | adaptedLiftBound= d + 1; |
---|
[db65ada] | 740 | if (adaptedLiftBound < deg) |
---|
[7bf145] | 741 | { |
---|
| 742 | degs= bufDegs1; |
---|
[69c882] | 743 | success= true; |
---|
[7bf145] | 744 | } |
---|
| 745 | if (bufDegs1.getLength() <= 1) |
---|
| 746 | degs= bufDegs1; |
---|
| 747 | } |
---|
| 748 | |
---|
[1a3011e] | 749 | void |
---|
| 750 | extEarlyFactorDetection (CFList& reconstructedFactors, CanonicalForm& F, CFList& |
---|
| 751 | factors,int& adaptedLiftBound, int*& factorsFoundIndex, |
---|
| 752 | DegreePattern& degs, bool& success, const |
---|
| 753 | ExtensionInfo& info, const CanonicalForm& eval, int deg |
---|
| 754 | ) |
---|
[7bf145] | 755 | { |
---|
| 756 | Variable alpha= info.getAlpha(); |
---|
| 757 | Variable beta= info.getBeta(); |
---|
| 758 | CanonicalForm gamma= info.getGamma(); |
---|
| 759 | CanonicalForm delta= info.getDelta(); |
---|
| 760 | int k= info.getGFDegree(); |
---|
| 761 | DegreePattern bufDegs1= degs, bufDegs2; |
---|
[806c18] | 762 | CFList result; |
---|
[7bf145] | 763 | CFList T= factors; |
---|
| 764 | Variable y= F.mvar(); |
---|
[a54114] | 765 | Variable x= Variable (1); |
---|
| 766 | CanonicalForm buf= F, LCBuf= LC (buf, x), g, buf2; |
---|
[7bf145] | 767 | CanonicalForm M= power (y, deg); |
---|
| 768 | adaptedLiftBound= 0; |
---|
[93134c] | 769 | bool trueFactor= false; |
---|
[1a3011e] | 770 | int d= degree (F), l= 0; |
---|
[7bf145] | 771 | CFList source, dest; |
---|
[ac8e1a] | 772 | int degMipoBeta= 1; |
---|
| 773 | if (!k && beta.level() != 1) |
---|
[7bf145] | 774 | degMipoBeta= degree (getMipo (beta)); |
---|
[21b8f4c] | 775 | CanonicalForm quot; |
---|
[1a3011e] | 776 | for (CFListIterator i= factors; i.hasItem(); i++, l++) |
---|
[7bf145] | 777 | { |
---|
[1a3011e] | 778 | if (!bufDegs1.find (degree (i.getItem(), 1)) || factorsFoundIndex[l] == 1) |
---|
[7bf145] | 779 | continue; |
---|
| 780 | else |
---|
| 781 | { |
---|
[f047b56] | 782 | g= mulMod2 (i.getItem(), LCBuf, M); |
---|
| 783 | g /= content (g, x); |
---|
| 784 | if (fdivides (g, buf, quot)) |
---|
[7bf145] | 785 | { |
---|
[f047b56] | 786 | buf2= g (y - eval, y); |
---|
| 787 | buf2 /= Lc (buf2); |
---|
[806c18] | 788 | |
---|
[f047b56] | 789 | if (!k && beta == x) |
---|
| 790 | { |
---|
| 791 | if (degree (buf2, alpha) < degMipoBeta) |
---|
[7bf145] | 792 | { |
---|
[1a3011e] | 793 | appendTestMapDown (reconstructedFactors, buf2, info, source, dest); |
---|
| 794 | factorsFoundIndex[l]= 1; |
---|
[f047b56] | 795 | buf= quot; |
---|
| 796 | d -= degree (g); |
---|
| 797 | LCBuf= LC (buf, x); |
---|
| 798 | trueFactor= true; |
---|
[7bf145] | 799 | } |
---|
[f047b56] | 800 | } |
---|
| 801 | else |
---|
| 802 | { |
---|
| 803 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
[7bf145] | 804 | { |
---|
[1a3011e] | 805 | appendTestMapDown (reconstructedFactors, buf2, info, source, dest); |
---|
| 806 | factorsFoundIndex[l]= 1; |
---|
[f047b56] | 807 | buf= quot; |
---|
| 808 | d -= degree (g); |
---|
| 809 | LCBuf= LC (buf, x); |
---|
| 810 | trueFactor= true; |
---|
[806c18] | 811 | } |
---|
[f047b56] | 812 | } |
---|
| 813 | if (trueFactor) |
---|
| 814 | { |
---|
| 815 | T= Difference (T, CFList (i.getItem())); |
---|
[69c882] | 816 | F= buf; |
---|
[93134c] | 817 | |
---|
[f047b56] | 818 | // compute new possible degree pattern |
---|
| 819 | bufDegs2= DegreePattern (T); |
---|
| 820 | bufDegs1.intersect (bufDegs2); |
---|
| 821 | bufDegs1.refine (); |
---|
| 822 | trueFactor= false; |
---|
| 823 | if (bufDegs1.getLength() <= 1) |
---|
| 824 | { |
---|
| 825 | buf= buf (y - eval, y); |
---|
| 826 | buf /= Lc (buf); |
---|
[1a3011e] | 827 | appendMapDown (reconstructedFactors, buf, info, source, dest); |
---|
[f047b56] | 828 | break; |
---|
[7bf145] | 829 | } |
---|
| 830 | } |
---|
| 831 | } |
---|
| 832 | } |
---|
| 833 | } |
---|
| 834 | adaptedLiftBound= d + 1; |
---|
| 835 | if (adaptedLiftBound < deg) |
---|
| 836 | { |
---|
| 837 | degs= bufDegs1; |
---|
[69c882] | 838 | success= true; |
---|
[7bf145] | 839 | } |
---|
| 840 | if (bufDegs1.getLength() <= 1) |
---|
| 841 | degs= bufDegs1; |
---|
| 842 | } |
---|
| 843 | |
---|
[34e062] | 844 | int* |
---|
| 845 | getCombinations (int * rightSide, int sizeOfRightSide, int& sizeOfOutput, |
---|
| 846 | int degreeLC) |
---|
| 847 | { |
---|
| 848 | Variable x= Variable (1); |
---|
| 849 | int p= getCharacteristic(); |
---|
| 850 | int d= getGFDegree(); |
---|
| 851 | char cGFName= gf_name; |
---|
| 852 | setCharacteristic(0); |
---|
| 853 | CanonicalForm buf= 1; |
---|
| 854 | for (int i= 0; i < sizeOfRightSide; i++) |
---|
| 855 | buf *= (power (x, rightSide [i]) + 1); |
---|
| 856 | |
---|
| 857 | int j= 0; |
---|
| 858 | for (CFIterator i= buf; i.hasTerms(); i++, j++) |
---|
| 859 | { |
---|
| 860 | if (i.exp() < degreeLC) |
---|
| 861 | { |
---|
| 862 | j++; |
---|
| 863 | break; |
---|
| 864 | } |
---|
| 865 | } |
---|
| 866 | |
---|
| 867 | ASSERT ( j > 1, "j > 1 expected" ); |
---|
| 868 | |
---|
| 869 | int* result = new int [j - 1]; |
---|
| 870 | sizeOfOutput= j - 1; |
---|
| 871 | |
---|
| 872 | int i= 0; |
---|
| 873 | for (CFIterator m = buf; i < j - 1; i++, m++) |
---|
| 874 | result [i]= m.exp(); |
---|
| 875 | |
---|
| 876 | if (d > 1) |
---|
| 877 | setCharacteristic (p, d, cGFName); |
---|
| 878 | else |
---|
| 879 | setCharacteristic (p); |
---|
| 880 | return result; |
---|
| 881 | } |
---|
| 882 | |
---|
| 883 | int * |
---|
| 884 | getLiftPrecisions (const CanonicalForm& F, int& sizeOfOutput, int degreeLC) |
---|
| 885 | { |
---|
| 886 | int sizeOfNewtonPoly; |
---|
| 887 | int ** newtonPolyg= newtonPolygon (F, sizeOfNewtonPoly); |
---|
| 888 | int sizeOfRightSide; |
---|
| 889 | int * rightSide= getRightSide(newtonPolyg, sizeOfNewtonPoly, sizeOfRightSide); |
---|
| 890 | int * result= getCombinations(rightSide, sizeOfRightSide, sizeOfOutput, |
---|
| 891 | degreeLC); |
---|
| 892 | delete [] rightSide; |
---|
| 893 | for (int i= 0; i < sizeOfNewtonPoly; i++) |
---|
| 894 | delete [] newtonPolyg[i]; |
---|
| 895 | delete [] newtonPolyg; |
---|
| 896 | return result; |
---|
| 897 | } |
---|
| 898 | |
---|
[1a3011e] | 899 | void |
---|
[69c882] | 900 | deleteFactors (CFList& factors, int* factorsFoundIndex) |
---|
[1a3011e] | 901 | { |
---|
[69c882] | 902 | CFList result; |
---|
| 903 | int i= 0; |
---|
| 904 | for (CFListIterator iter= factors; iter.hasItem(); iter++, i++) |
---|
[1a3011e] | 905 | { |
---|
[69c882] | 906 | if (factorsFoundIndex[i] == 1) |
---|
| 907 | continue; |
---|
[1a3011e] | 908 | else |
---|
[69c882] | 909 | result.append (iter.getItem()); |
---|
[1a3011e] | 910 | } |
---|
[69c882] | 911 | factors= result; |
---|
[1a3011e] | 912 | } |
---|
| 913 | |
---|
[7bf145] | 914 | CFList |
---|
[806c18] | 915 | henselLiftAndEarly (CanonicalForm& A, bool& earlySuccess, CFList& |
---|
[7bf145] | 916 | earlyFactors, DegreePattern& degs, int& liftBound, |
---|
[806c18] | 917 | const CFList& uniFactors, const ExtensionInfo& info, |
---|
[69fdf90] | 918 | const CanonicalForm& eval, modpk& b) |
---|
[7bf145] | 919 | { |
---|
| 920 | Variable alpha= info.getAlpha(); |
---|
| 921 | Variable beta= info.getBeta(); |
---|
| 922 | CanonicalForm gamma= info.getGamma(); |
---|
| 923 | CanonicalForm delta= info.getDelta(); |
---|
| 924 | bool extension= info.isInExtension(); |
---|
| 925 | |
---|
[69076c] | 926 | int sizeOfLiftPre; |
---|
| 927 | int * liftPre= getLiftPrecisions (A, sizeOfLiftPre, degree (LC (A, 1), 2)); |
---|
| 928 | |
---|
[7bf145] | 929 | Variable x= Variable (1); |
---|
| 930 | Variable y= Variable (2); |
---|
| 931 | CFArray Pi; |
---|
| 932 | CFList diophant; |
---|
| 933 | CFList bufUniFactors= uniFactors; |
---|
[eb481b] | 934 | CanonicalForm bufA= A; |
---|
| 935 | CanonicalForm lcA0= 0; |
---|
[f9da5e] | 936 | bool mipoHasDen= false; |
---|
[eb481b] | 937 | if (getCharacteristic() == 0 && b.getp() != 0) |
---|
| 938 | { |
---|
[41fea7] | 939 | if (alpha.level() == 1) |
---|
| 940 | { |
---|
| 941 | lcA0= lc (A (0, 2)); |
---|
| 942 | A *= b.inverse (lcA0); |
---|
| 943 | A= b (A); |
---|
| 944 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
| 945 | i.getItem()= b (i.getItem()*b.inverse (lc (i.getItem()))); |
---|
| 946 | } |
---|
| 947 | else |
---|
| 948 | { |
---|
| 949 | lcA0= Lc (A (0,2)); |
---|
[f9da5e] | 950 | On (SW_RATIONAL); |
---|
| 951 | mipoHasDen= !bCommonDen(getMipo(alpha)).isOne(); |
---|
| 952 | Off (SW_RATIONAL); |
---|
| 953 | CanonicalForm lcA0inverse= b.inverse (lcA0); |
---|
[41fea7] | 954 | A *= lcA0inverse; |
---|
| 955 | A= b (A); |
---|
| 956 | // Lc of bufUniFactors is in Z |
---|
| 957 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
| 958 | i.getItem()= b (i.getItem()*b.inverse (lc (i.getItem()))); |
---|
| 959 | } |
---|
[eb481b] | 960 | } |
---|
[7bf145] | 961 | bufUniFactors.insert (LC (A, x)); |
---|
| 962 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length() - 1); |
---|
| 963 | earlySuccess= false; |
---|
| 964 | int newLiftBound= 0; |
---|
[69076c] | 965 | |
---|
| 966 | int smallFactorDeg= tmin (11, liftPre [sizeOfLiftPre- 1] + 1);//this is a tunable parameter |
---|
| 967 | int dummy; |
---|
[1a3011e] | 968 | int * factorsFoundIndex= new int [uniFactors.length()]; |
---|
| 969 | for (int i= 0; i < uniFactors.length(); i++) |
---|
| 970 | factorsFoundIndex [i]= 0; |
---|
| 971 | |
---|
[f9da5e] | 972 | CFList bufBufUniFactors; |
---|
| 973 | Variable v= alpha; |
---|
[69076c] | 974 | if (smallFactorDeg >= liftBound || degree (A,y) <= 4) |
---|
[69fdf90] | 975 | henselLift12 (A, bufUniFactors, liftBound, Pi, diophant, M, b, true); |
---|
[69076c] | 976 | else if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
[7bf145] | 977 | { |
---|
[69fdf90] | 978 | henselLift12 (A, bufUniFactors, smallFactorDeg, Pi, diophant, M, b, true); |
---|
[f9da5e] | 979 | if (mipoHasDen) |
---|
| 980 | { |
---|
| 981 | for (CFListIterator iter= bufUniFactors; iter.hasItem(); iter++) |
---|
| 982 | if (hasFirstAlgVar (iter.getItem(), v)) |
---|
| 983 | break; |
---|
| 984 | if (v != alpha) |
---|
| 985 | { |
---|
| 986 | bufBufUniFactors= bufUniFactors; |
---|
| 987 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
| 988 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
| 989 | A= replacevar (A, alpha, v); |
---|
| 990 | } |
---|
| 991 | } |
---|
| 992 | |
---|
[7bf145] | 993 | if (!extension) |
---|
[f9da5e] | 994 | { |
---|
| 995 | if (v==alpha) |
---|
| 996 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
| 997 | factorsFoundIndex, degs, earlySuccess, |
---|
| 998 | smallFactorDeg, b); |
---|
| 999 | else |
---|
| 1000 | earlyFactorDetection(earlyFactors, bufA, bufBufUniFactors, newLiftBound, |
---|
| 1001 | factorsFoundIndex, degs, earlySuccess, |
---|
| 1002 | smallFactorDeg, b); |
---|
| 1003 | } |
---|
[7bf145] | 1004 | else |
---|
[69c882] | 1005 | extEarlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
[1a3011e] | 1006 | factorsFoundIndex, degs, earlySuccess, info, |
---|
| 1007 | eval, smallFactorDeg); |
---|
[69076c] | 1008 | if (degs.getLength() > 1 && !earlySuccess && |
---|
| 1009 | smallFactorDeg != liftPre [sizeOfLiftPre-1] + 1) |
---|
[7bf145] | 1010 | { |
---|
[69076c] | 1011 | if (newLiftBound >= liftPre[sizeOfLiftPre-1]+1) |
---|
[7bf145] | 1012 | { |
---|
[69076c] | 1013 | bufUniFactors.insert (LC (A, x)); |
---|
| 1014 | henselLiftResume12 (A, bufUniFactors, smallFactorDeg, |
---|
[eb481b] | 1015 | liftPre[sizeOfLiftPre-1] + 1, Pi, diophant, M, b); |
---|
[f9da5e] | 1016 | if (v!=alpha) |
---|
| 1017 | { |
---|
| 1018 | bufBufUniFactors= bufUniFactors; |
---|
| 1019 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
| 1020 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
| 1021 | } |
---|
[69076c] | 1022 | if (!extension) |
---|
[f9da5e] | 1023 | { |
---|
| 1024 | if (v==alpha) |
---|
[69c882] | 1025 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
[1a3011e] | 1026 | factorsFoundIndex, degs, earlySuccess, |
---|
[eb481b] | 1027 | liftPre[sizeOfLiftPre-1] + 1, b); |
---|
[f9da5e] | 1028 | else |
---|
| 1029 | earlyFactorDetection (earlyFactors,bufA,bufBufUniFactors,newLiftBound, |
---|
| 1030 | factorsFoundIndex, degs, earlySuccess, |
---|
| 1031 | liftPre[sizeOfLiftPre-1] + 1, b); |
---|
| 1032 | } |
---|
[69076c] | 1033 | else |
---|
[f9da5e] | 1034 | extEarlyFactorDetection (earlyFactors,bufA,bufUniFactors,newLiftBound, |
---|
[1a3011e] | 1035 | factorsFoundIndex, degs, earlySuccess, info, |
---|
| 1036 | eval, liftPre[sizeOfLiftPre-1] + 1); |
---|
[7bf145] | 1037 | } |
---|
| 1038 | } |
---|
| 1039 | else if (earlySuccess) |
---|
| 1040 | liftBound= newLiftBound; |
---|
[69076c] | 1041 | |
---|
| 1042 | int i= sizeOfLiftPre - 1; |
---|
| 1043 | while (degs.getLength() > 1 && !earlySuccess && i - 1 >= 0) |
---|
| 1044 | { |
---|
| 1045 | if (newLiftBound >= liftPre[i] + 1) |
---|
| 1046 | { |
---|
| 1047 | bufUniFactors.insert (LC (A, x)); |
---|
| 1048 | henselLiftResume12 (A, bufUniFactors, liftPre[i] + 1, |
---|
[eb481b] | 1049 | liftPre[i-1] + 1, Pi, diophant, M, b); |
---|
[f9da5e] | 1050 | if (v!=alpha) |
---|
| 1051 | { |
---|
| 1052 | bufBufUniFactors= bufUniFactors; |
---|
| 1053 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
| 1054 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
| 1055 | } |
---|
[69076c] | 1056 | if (!extension) |
---|
[f9da5e] | 1057 | { |
---|
| 1058 | if (v==alpha) |
---|
[69c882] | 1059 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
[1a3011e] | 1060 | factorsFoundIndex, degs, earlySuccess, |
---|
[eb481b] | 1061 | liftPre[i-1] + 1, b); |
---|
[f9da5e] | 1062 | else |
---|
| 1063 | earlyFactorDetection (earlyFactors,bufA,bufBufUniFactors,newLiftBound, |
---|
| 1064 | factorsFoundIndex, degs, earlySuccess, |
---|
| 1065 | liftPre[i-1] + 1, b); |
---|
| 1066 | } |
---|
[69076c] | 1067 | else |
---|
[f9da5e] | 1068 | extEarlyFactorDetection (earlyFactors,bufA,bufUniFactors,newLiftBound, |
---|
[1a3011e] | 1069 | factorsFoundIndex, degs, earlySuccess, info, |
---|
| 1070 | eval, liftPre[i-1] + 1); |
---|
[69076c] | 1071 | } |
---|
| 1072 | else |
---|
| 1073 | { |
---|
| 1074 | liftBound= newLiftBound; |
---|
| 1075 | break; |
---|
| 1076 | } |
---|
| 1077 | i--; |
---|
| 1078 | } |
---|
| 1079 | if (earlySuccess) |
---|
| 1080 | liftBound= newLiftBound; |
---|
| 1081 | //after here all factors are lifted to liftPre[sizeOfLiftPre-1] |
---|
[7bf145] | 1082 | } |
---|
[69076c] | 1083 | else |
---|
[806c18] | 1084 | { |
---|
[69fdf90] | 1085 | henselLift12 (A, bufUniFactors, smallFactorDeg, Pi, diophant, M, b, true); |
---|
[f9da5e] | 1086 | if (mipoHasDen) |
---|
| 1087 | { |
---|
| 1088 | for (CFListIterator iter= bufUniFactors; iter.hasItem(); iter++) |
---|
| 1089 | if (hasFirstAlgVar (iter.getItem(), v)) |
---|
| 1090 | break; |
---|
| 1091 | if (v != alpha) |
---|
| 1092 | { |
---|
| 1093 | bufBufUniFactors= bufUniFactors; |
---|
| 1094 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
| 1095 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
| 1096 | A= replacevar (A, alpha, v); |
---|
| 1097 | } |
---|
| 1098 | } |
---|
[7bf145] | 1099 | if (!extension) |
---|
[f9da5e] | 1100 | { |
---|
| 1101 | if (v==alpha) |
---|
[69c882] | 1102 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
[1a3011e] | 1103 | factorsFoundIndex, degs, earlySuccess, |
---|
[eb481b] | 1104 | smallFactorDeg, b); |
---|
[f9da5e] | 1105 | else |
---|
| 1106 | earlyFactorDetection (earlyFactors, bufA, bufBufUniFactors, newLiftBound, |
---|
| 1107 | factorsFoundIndex, degs, earlySuccess, |
---|
| 1108 | smallFactorDeg, b); |
---|
| 1109 | } |
---|
[7bf145] | 1110 | else |
---|
[69c882] | 1111 | extEarlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
[1a3011e] | 1112 | factorsFoundIndex, degs, earlySuccess, info, |
---|
| 1113 | eval, smallFactorDeg); |
---|
[69076c] | 1114 | int i= 1; |
---|
| 1115 | while ((degree (A,y)/4)*i + 4 <= smallFactorDeg) |
---|
| 1116 | i++; |
---|
| 1117 | dummy= tmin (degree (A,y)+1, (degree (A,y)/4)*i+4); |
---|
| 1118 | if (degs.getLength() > 1 && !earlySuccess && dummy > smallFactorDeg) |
---|
[7bf145] | 1119 | { |
---|
| 1120 | bufUniFactors.insert (LC (A, x)); |
---|
[69076c] | 1121 | henselLiftResume12 (A, bufUniFactors, smallFactorDeg, |
---|
[eb481b] | 1122 | dummy, Pi, diophant, M, b); |
---|
[f9da5e] | 1123 | if (v!=alpha) |
---|
| 1124 | { |
---|
| 1125 | bufBufUniFactors= bufUniFactors; |
---|
| 1126 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
| 1127 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
| 1128 | } |
---|
[7bf145] | 1129 | if (!extension) |
---|
[f9da5e] | 1130 | { |
---|
| 1131 | if (v==alpha) |
---|
[69c882] | 1132 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
[eb481b] | 1133 | factorsFoundIndex, degs, earlySuccess, dummy, b); |
---|
[f9da5e] | 1134 | else |
---|
| 1135 | earlyFactorDetection (earlyFactors, bufA,bufBufUniFactors, newLiftBound, |
---|
| 1136 | factorsFoundIndex, degs, earlySuccess, dummy, b); |
---|
| 1137 | } |
---|
[7bf145] | 1138 | else |
---|
[f9da5e] | 1139 | extEarlyFactorDetection (earlyFactors, bufA,bufUniFactors, newLiftBound, |
---|
[1a3011e] | 1140 | factorsFoundIndex, degs, earlySuccess, info, |
---|
| 1141 | eval, dummy); |
---|
[69076c] | 1142 | } |
---|
| 1143 | while (degs.getLength() > 1 && !earlySuccess && i < 4) |
---|
| 1144 | { |
---|
| 1145 | if (newLiftBound >= dummy) |
---|
[7bf145] | 1146 | { |
---|
[69076c] | 1147 | bufUniFactors.insert (LC (A, x)); |
---|
| 1148 | dummy= tmin (degree (A,y)+1, (degree (A,y)/4)*(i+1)+4); |
---|
| 1149 | henselLiftResume12 (A, bufUniFactors, (degree (A,y)/4)*i + 4, |
---|
[eb481b] | 1150 | dummy, Pi, diophant, M, b); |
---|
[f9da5e] | 1151 | if (v!=alpha) |
---|
| 1152 | { |
---|
| 1153 | bufBufUniFactors= bufUniFactors; |
---|
| 1154 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
| 1155 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
| 1156 | } |
---|
[69076c] | 1157 | if (!extension) |
---|
[f9da5e] | 1158 | { |
---|
| 1159 | if (v==alpha) |
---|
[69c882] | 1160 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
[eb481b] | 1161 | factorsFoundIndex, degs, earlySuccess, dummy,b); |
---|
[f9da5e] | 1162 | else |
---|
| 1163 | earlyFactorDetection (earlyFactors,bufA,bufBufUniFactors,newLiftBound, |
---|
| 1164 | factorsFoundIndex, degs, earlySuccess, dummy,b); |
---|
| 1165 | } |
---|
[69076c] | 1166 | else |
---|
[f9da5e] | 1167 | extEarlyFactorDetection (earlyFactors,bufA,bufUniFactors,newLiftBound, |
---|
[1a3011e] | 1168 | factorsFoundIndex, degs, earlySuccess, info, |
---|
| 1169 | eval, dummy); |
---|
[7bf145] | 1170 | } |
---|
[69076c] | 1171 | else |
---|
| 1172 | { |
---|
[7bf145] | 1173 | liftBound= newLiftBound; |
---|
[69076c] | 1174 | break; |
---|
| 1175 | } |
---|
| 1176 | i++; |
---|
[7bf145] | 1177 | } |
---|
[69076c] | 1178 | if (earlySuccess) |
---|
[7bf145] | 1179 | liftBound= newLiftBound; |
---|
| 1180 | } |
---|
[69076c] | 1181 | |
---|
[69c882] | 1182 | A= bufA; |
---|
| 1183 | if (earlyFactors.length() > 0 && degs.getLength() > 1) |
---|
| 1184 | { |
---|
| 1185 | liftBound= degree (A,y) + 1; |
---|
| 1186 | earlySuccess= true; |
---|
| 1187 | deleteFactors (bufUniFactors, factorsFoundIndex); |
---|
| 1188 | } |
---|
| 1189 | |
---|
[1a3011e] | 1190 | delete [] factorsFoundIndex; |
---|
[69076c] | 1191 | delete [] liftPre; |
---|
| 1192 | |
---|
[7bf145] | 1193 | return bufUniFactors; |
---|
| 1194 | } |
---|
| 1195 | |
---|
[69fdf90] | 1196 | CFList |
---|
| 1197 | henselLiftAndEarly (CanonicalForm& A, bool& earlySuccess, CFList& |
---|
| 1198 | earlyFactors, DegreePattern& degs, int& liftBound, |
---|
| 1199 | const CFList& uniFactors, const ExtensionInfo& info, |
---|
| 1200 | const CanonicalForm& eval) |
---|
| 1201 | { |
---|
| 1202 | modpk dummy= modpk(); |
---|
| 1203 | return henselLiftAndEarly (A, earlySuccess, earlyFactors, degs, liftBound, |
---|
| 1204 | uniFactors, info, eval, dummy); |
---|
| 1205 | } |
---|
| 1206 | |
---|
[11bf82] | 1207 | long isReduced (const mat_zz_p& M) |
---|
[7bf145] | 1208 | { |
---|
[11bf82] | 1209 | long i, j, nonZero; |
---|
| 1210 | for (i = 1; i <= M.NumRows(); i++) |
---|
[7bf145] | 1211 | { |
---|
[11bf82] | 1212 | nonZero= 0; |
---|
| 1213 | for (j = 1; j <= M.NumCols(); j++) |
---|
[7bf145] | 1214 | { |
---|
[11bf82] | 1215 | if (!IsZero (M (i,j))) |
---|
| 1216 | nonZero++; |
---|
[7bf145] | 1217 | } |
---|
[11bf82] | 1218 | if (nonZero != 1) |
---|
| 1219 | return 0; |
---|
[7bf145] | 1220 | } |
---|
[11bf82] | 1221 | return 1; |
---|
| 1222 | } |
---|
[7bf145] | 1223 | |
---|
[11bf82] | 1224 | long isReduced (const mat_zz_pE& M) |
---|
| 1225 | { |
---|
| 1226 | long i, j, nonZero; |
---|
| 1227 | for (i = 1; i <= M.NumRows(); i++) |
---|
[806c18] | 1228 | { |
---|
[11bf82] | 1229 | nonZero= 0; |
---|
| 1230 | for (j = 1; j <= M.NumCols(); j++) |
---|
| 1231 | { |
---|
| 1232 | if (!IsZero (M (i,j))) |
---|
[c1b9927] | 1233 | nonZero++; |
---|
[11bf82] | 1234 | } |
---|
| 1235 | if (nonZero != 1) |
---|
| 1236 | return 0; |
---|
[7bf145] | 1237 | } |
---|
[11bf82] | 1238 | return 1; |
---|
| 1239 | } |
---|
[7bf145] | 1240 | |
---|
[11bf82] | 1241 | int * extractZeroOneVecs (const mat_zz_p& M) |
---|
| 1242 | { |
---|
| 1243 | long i, j; |
---|
| 1244 | bool nonZeroOne= false; |
---|
| 1245 | int * result= new int [M.NumCols()]; |
---|
| 1246 | for (i = 1; i <= M.NumCols(); i++) |
---|
[7bf145] | 1247 | { |
---|
[11bf82] | 1248 | for (j = 1; j <= M.NumRows(); j++) |
---|
| 1249 | { |
---|
| 1250 | if (!(IsOne (M (j,i)) || IsZero (M (j,i)))) |
---|
| 1251 | { |
---|
| 1252 | nonZeroOne= true; |
---|
| 1253 | break; |
---|
| 1254 | } |
---|
| 1255 | } |
---|
| 1256 | if (!nonZeroOne) |
---|
| 1257 | result [i - 1]= 1; |
---|
| 1258 | else |
---|
| 1259 | result [i - 1]= 0; |
---|
| 1260 | nonZeroOne= false; |
---|
[7bf145] | 1261 | } |
---|
[11bf82] | 1262 | return result; |
---|
| 1263 | } |
---|
[7bf145] | 1264 | |
---|
[11bf82] | 1265 | int * extractZeroOneVecs (const mat_zz_pE& M) |
---|
| 1266 | { |
---|
| 1267 | long i, j; |
---|
| 1268 | bool nonZeroOne= false; |
---|
| 1269 | int * result= new int [M.NumCols()]; |
---|
| 1270 | for (i = 1; i <= M.NumCols(); i++) |
---|
[7bf145] | 1271 | { |
---|
[11bf82] | 1272 | for (j = 1; j <= M.NumRows(); j++) |
---|
[7bf145] | 1273 | { |
---|
[11bf82] | 1274 | if (!(IsOne (M (j,i)) || IsZero (M (j,i)))) |
---|
| 1275 | { |
---|
| 1276 | nonZeroOne= true; |
---|
| 1277 | break; |
---|
| 1278 | } |
---|
[7bf145] | 1279 | } |
---|
[11bf82] | 1280 | if (!nonZeroOne) |
---|
| 1281 | result [i - 1]= 1; |
---|
| 1282 | else |
---|
| 1283 | result [i - 1]= 0; |
---|
| 1284 | nonZeroOne= false; |
---|
[7bf145] | 1285 | } |
---|
[11bf82] | 1286 | return result; |
---|
| 1287 | } |
---|
| 1288 | |
---|
| 1289 | void |
---|
| 1290 | reconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const CFList& |
---|
| 1291 | factors, const int liftBound, int& factorsFound, int*& |
---|
| 1292 | factorsFoundIndex, mat_zz_pE& N, bool beenInThres |
---|
| 1293 | ) |
---|
| 1294 | { |
---|
| 1295 | Variable y= Variable (2); |
---|
| 1296 | Variable x= Variable (1); |
---|
| 1297 | CanonicalForm yToL= power (y, liftBound); |
---|
[38ffb7] | 1298 | CanonicalForm quot, buf; |
---|
| 1299 | CFListIterator iter; |
---|
[11bf82] | 1300 | for (long i= 1; i <= N.NumCols(); i++) |
---|
[7bf145] | 1301 | { |
---|
[11bf82] | 1302 | if (factorsFoundIndex [i - 1] == 1) |
---|
| 1303 | continue; |
---|
[38ffb7] | 1304 | iter= factors; |
---|
[11bf82] | 1305 | if (beenInThres) |
---|
[7bf145] | 1306 | { |
---|
[11bf82] | 1307 | int count= 1; |
---|
| 1308 | while (count < i) |
---|
| 1309 | { |
---|
| 1310 | count++; |
---|
| 1311 | iter++; |
---|
| 1312 | } |
---|
| 1313 | buf= iter.getItem(); |
---|
[7bf145] | 1314 | } |
---|
[11bf82] | 1315 | else |
---|
[806c18] | 1316 | { |
---|
[11bf82] | 1317 | buf= 1; |
---|
| 1318 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 1319 | { |
---|
| 1320 | if (!IsZero (N (j,i))) |
---|
| 1321 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 1322 | } |
---|
| 1323 | } |
---|
| 1324 | buf *= LC (F, x); |
---|
| 1325 | buf= mod (buf, yToL); |
---|
| 1326 | buf /= content (buf, x); |
---|
[21b8f4c] | 1327 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 1328 | { |
---|
| 1329 | factorsFoundIndex[i - 1]= 1; |
---|
| 1330 | factorsFound++; |
---|
[21b8f4c] | 1331 | F= quot; |
---|
[11bf82] | 1332 | F /= Lc (F); |
---|
| 1333 | reconstructedFactors.append (buf); |
---|
| 1334 | } |
---|
| 1335 | if (degree (F) <= 0) |
---|
| 1336 | return; |
---|
| 1337 | if (factorsFound + 1 == N.NumCols()) |
---|
| 1338 | { |
---|
| 1339 | reconstructedFactors.append (F); |
---|
| 1340 | return; |
---|
[7bf145] | 1341 | } |
---|
| 1342 | } |
---|
[11bf82] | 1343 | } |
---|
[7bf145] | 1344 | |
---|
[11bf82] | 1345 | void |
---|
| 1346 | reconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const CFList& |
---|
| 1347 | factors, const int liftBound, int& factorsFound, int*& |
---|
| 1348 | factorsFoundIndex, mat_zz_p& N, bool beenInThres |
---|
| 1349 | ) |
---|
| 1350 | { |
---|
| 1351 | Variable y= Variable (2); |
---|
[c1b9927] | 1352 | Variable x= Variable (1); |
---|
[38ffb7] | 1353 | CanonicalForm quot, buf; |
---|
[11bf82] | 1354 | CanonicalForm yToL= power (y, liftBound); |
---|
[38ffb7] | 1355 | CFListIterator iter; |
---|
[11bf82] | 1356 | for (long i= 1; i <= N.NumCols(); i++) |
---|
[7bf145] | 1357 | { |
---|
[11bf82] | 1358 | if (factorsFoundIndex [i - 1] == 1) |
---|
| 1359 | continue; |
---|
[38ffb7] | 1360 | iter= factors; |
---|
[11bf82] | 1361 | if (beenInThres) |
---|
[7bf145] | 1362 | { |
---|
[11bf82] | 1363 | int count= 1; |
---|
| 1364 | while (count < i) |
---|
| 1365 | { |
---|
| 1366 | count++; |
---|
| 1367 | iter++; |
---|
| 1368 | } |
---|
| 1369 | buf= iter.getItem(); |
---|
[7bf145] | 1370 | } |
---|
[11bf82] | 1371 | else |
---|
[7bf145] | 1372 | { |
---|
[11bf82] | 1373 | buf= 1; |
---|
| 1374 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
[806c18] | 1375 | { |
---|
[11bf82] | 1376 | if (!IsZero (N (j,i))) |
---|
| 1377 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
[7bf145] | 1378 | } |
---|
| 1379 | } |
---|
[11bf82] | 1380 | buf *= LC (F, x); |
---|
| 1381 | buf= mod (buf, yToL); |
---|
| 1382 | buf /= content (buf, x); |
---|
[21b8f4c] | 1383 | if (fdivides (buf, F, quot)) |
---|
[7bf145] | 1384 | { |
---|
[11bf82] | 1385 | factorsFoundIndex[i - 1]= 1; |
---|
| 1386 | factorsFound++; |
---|
[21b8f4c] | 1387 | F= quot; |
---|
[11bf82] | 1388 | F /= Lc (F); |
---|
| 1389 | reconstructedFactors.append (buf); |
---|
[7bf145] | 1390 | } |
---|
[11bf82] | 1391 | if (degree (F) <= 0) |
---|
| 1392 | return; |
---|
| 1393 | if (factorsFound + 1 == N.NumCols()) |
---|
| 1394 | { |
---|
| 1395 | reconstructedFactors.append (F); |
---|
| 1396 | return; |
---|
| 1397 | } |
---|
| 1398 | } |
---|
| 1399 | } |
---|
[7bf145] | 1400 | |
---|
[11bf82] | 1401 | CFList |
---|
| 1402 | reconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, int |
---|
| 1403 | precision, const mat_zz_pE& N |
---|
| 1404 | ) |
---|
| 1405 | { |
---|
| 1406 | Variable y= Variable (2); |
---|
| 1407 | Variable x= Variable (1); |
---|
| 1408 | CanonicalForm F= G; |
---|
| 1409 | CanonicalForm yToL= power (y, precision); |
---|
[38ffb7] | 1410 | CanonicalForm quot, buf; |
---|
| 1411 | CFList result, factorsConsidered; |
---|
[11bf82] | 1412 | CFList bufFactors= factors; |
---|
[38ffb7] | 1413 | CFListIterator iter; |
---|
[11bf82] | 1414 | for (long i= 1; i <= N.NumCols(); i++) |
---|
| 1415 | { |
---|
| 1416 | if (zeroOneVecs [i - 1] == 0) |
---|
| 1417 | continue; |
---|
[38ffb7] | 1418 | iter= factors; |
---|
| 1419 | buf= 1; |
---|
[11bf82] | 1420 | factorsConsidered= CFList(); |
---|
| 1421 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 1422 | { |
---|
| 1423 | if (!IsZero (N (j,i))) |
---|
| 1424 | { |
---|
| 1425 | factorsConsidered.append (iter.getItem()); |
---|
| 1426 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 1427 | } |
---|
| 1428 | } |
---|
| 1429 | buf *= LC (F, x); |
---|
| 1430 | buf= mod (buf, yToL); |
---|
| 1431 | buf /= content (buf, x); |
---|
[21b8f4c] | 1432 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 1433 | { |
---|
[21b8f4c] | 1434 | F= quot; |
---|
[11bf82] | 1435 | F /= Lc (F); |
---|
| 1436 | result.append (buf); |
---|
| 1437 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 1438 | } |
---|
| 1439 | if (degree (F) <= 0) |
---|
| 1440 | { |
---|
| 1441 | G= F; |
---|
| 1442 | factors= bufFactors; |
---|
| 1443 | return result; |
---|
| 1444 | } |
---|
| 1445 | } |
---|
| 1446 | G= F; |
---|
| 1447 | factors= bufFactors; |
---|
| 1448 | return result; |
---|
| 1449 | } |
---|
| 1450 | |
---|
| 1451 | CFList |
---|
| 1452 | monicReconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, |
---|
| 1453 | int precision, const mat_zz_pE& N |
---|
| 1454 | ) |
---|
| 1455 | { |
---|
| 1456 | Variable y= Variable (2); |
---|
| 1457 | Variable x= Variable (1); |
---|
| 1458 | CanonicalForm F= G; |
---|
| 1459 | CanonicalForm yToL= power (y, precision); |
---|
[38ffb7] | 1460 | CanonicalForm quot, buf, buf2; |
---|
[11bf82] | 1461 | CFList result; |
---|
| 1462 | CFList bufFactors= factors; |
---|
| 1463 | CFList factorsConsidered; |
---|
[38ffb7] | 1464 | CFListIterator iter; |
---|
[11bf82] | 1465 | for (long i= 1; i <= N.NumCols(); i++) |
---|
| 1466 | { |
---|
| 1467 | if (zeroOneVecs [i - 1] == 0) |
---|
| 1468 | continue; |
---|
[38ffb7] | 1469 | iter= factors; |
---|
| 1470 | buf= 1; |
---|
[11bf82] | 1471 | factorsConsidered= CFList(); |
---|
| 1472 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 1473 | { |
---|
| 1474 | if (!IsZero (N (j,i))) |
---|
| 1475 | { |
---|
| 1476 | factorsConsidered.append (iter.getItem()); |
---|
| 1477 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 1478 | } |
---|
| 1479 | } |
---|
[38ffb7] | 1480 | buf2= buf; |
---|
[11bf82] | 1481 | buf *= LC (F, x); |
---|
| 1482 | buf= mod (buf, yToL); |
---|
| 1483 | buf /= content (buf, x); |
---|
[21b8f4c] | 1484 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 1485 | { |
---|
[21b8f4c] | 1486 | F= quot; |
---|
[11bf82] | 1487 | F /= Lc (F); |
---|
| 1488 | result.append (buf2); |
---|
| 1489 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 1490 | } |
---|
| 1491 | if (degree (F) <= 0) |
---|
| 1492 | { |
---|
| 1493 | G= F; |
---|
| 1494 | factors= bufFactors; |
---|
| 1495 | return result; |
---|
| 1496 | } |
---|
| 1497 | } |
---|
| 1498 | G= F; |
---|
| 1499 | factors= bufFactors; |
---|
| 1500 | return result; |
---|
| 1501 | } |
---|
| 1502 | |
---|
| 1503 | CFList |
---|
| 1504 | extReconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, int |
---|
| 1505 | precision, const mat_zz_p& N, const ExtensionInfo& info, |
---|
| 1506 | const CanonicalForm& evaluation |
---|
| 1507 | ) |
---|
| 1508 | { |
---|
| 1509 | Variable y= Variable (2); |
---|
| 1510 | Variable x= Variable (1); |
---|
| 1511 | Variable alpha= info.getAlpha(); |
---|
| 1512 | Variable beta= info.getBeta(); |
---|
| 1513 | int k= info.getGFDegree(); |
---|
| 1514 | CanonicalForm gamma= info.getGamma(); |
---|
| 1515 | CanonicalForm delta= info.getDelta(); |
---|
| 1516 | CanonicalForm F= G; |
---|
| 1517 | CanonicalForm yToL= power (y, precision); |
---|
| 1518 | CFList result; |
---|
| 1519 | CFList bufFactors= factors; |
---|
| 1520 | CFList factorsConsidered; |
---|
[38ffb7] | 1521 | CanonicalForm buf2, quot, buf; |
---|
| 1522 | CFListIterator iter; |
---|
[11bf82] | 1523 | for (long i= 1; i <= N.NumCols(); i++) |
---|
| 1524 | { |
---|
| 1525 | if (zeroOneVecs [i - 1] == 0) |
---|
| 1526 | continue; |
---|
[38ffb7] | 1527 | iter= factors; |
---|
| 1528 | buf= 1; |
---|
[11bf82] | 1529 | factorsConsidered= CFList(); |
---|
| 1530 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 1531 | { |
---|
| 1532 | if (!IsZero (N (j,i))) |
---|
| 1533 | { |
---|
| 1534 | factorsConsidered.append (iter.getItem()); |
---|
| 1535 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 1536 | } |
---|
| 1537 | } |
---|
| 1538 | buf *= LC (F, x); |
---|
| 1539 | buf= mod (buf, yToL); |
---|
| 1540 | buf /= content (buf, x); |
---|
| 1541 | buf2= buf (y-evaluation, y); |
---|
[a54114] | 1542 | if (!k && beta == x) |
---|
[11bf82] | 1543 | { |
---|
| 1544 | if (degree (buf2, alpha) < 1) |
---|
| 1545 | { |
---|
[21b8f4c] | 1546 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 1547 | { |
---|
[21b8f4c] | 1548 | F= quot; |
---|
[11bf82] | 1549 | F /= Lc (F); |
---|
| 1550 | result.append (buf2); |
---|
| 1551 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 1552 | } |
---|
| 1553 | } |
---|
| 1554 | } |
---|
| 1555 | else |
---|
| 1556 | { |
---|
| 1557 | CFList source, dest; |
---|
[c1b9927] | 1558 | |
---|
[11bf82] | 1559 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
| 1560 | { |
---|
[21b8f4c] | 1561 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 1562 | { |
---|
[21b8f4c] | 1563 | F= quot; |
---|
[11bf82] | 1564 | F /= Lc (F); |
---|
| 1565 | result.append (buf2); |
---|
| 1566 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 1567 | } |
---|
| 1568 | } |
---|
| 1569 | } |
---|
| 1570 | if (degree (F) <= 0) |
---|
| 1571 | { |
---|
| 1572 | G= F; |
---|
| 1573 | factors= bufFactors; |
---|
| 1574 | return result; |
---|
| 1575 | } |
---|
| 1576 | } |
---|
| 1577 | G= F; |
---|
| 1578 | factors= bufFactors; |
---|
| 1579 | return result; |
---|
| 1580 | } |
---|
| 1581 | |
---|
| 1582 | CFList |
---|
| 1583 | reconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, |
---|
| 1584 | int precision, const mat_zz_p& N) |
---|
| 1585 | { |
---|
| 1586 | Variable y= Variable (2); |
---|
| 1587 | Variable x= Variable (1); |
---|
| 1588 | CanonicalForm F= G; |
---|
| 1589 | CanonicalForm yToL= power (y, precision); |
---|
[38ffb7] | 1590 | CanonicalForm quot, buf; |
---|
[11bf82] | 1591 | CFList result; |
---|
| 1592 | CFList bufFactors= factors; |
---|
| 1593 | CFList factorsConsidered; |
---|
[38ffb7] | 1594 | CFListIterator iter; |
---|
[11bf82] | 1595 | for (long i= 1; i <= N.NumCols(); i++) |
---|
| 1596 | { |
---|
| 1597 | if (zeroOneVecs [i - 1] == 0) |
---|
| 1598 | continue; |
---|
[38ffb7] | 1599 | iter= factors; |
---|
| 1600 | buf= 1; |
---|
[11bf82] | 1601 | factorsConsidered= CFList(); |
---|
| 1602 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 1603 | { |
---|
| 1604 | if (!IsZero (N (j,i))) |
---|
| 1605 | { |
---|
| 1606 | factorsConsidered.append (iter.getItem()); |
---|
| 1607 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 1608 | } |
---|
| 1609 | } |
---|
| 1610 | buf *= LC (F, x); |
---|
| 1611 | buf= mod (buf, yToL); |
---|
| 1612 | buf /= content (buf, x); |
---|
[21b8f4c] | 1613 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 1614 | { |
---|
[21b8f4c] | 1615 | F= quot; |
---|
[11bf82] | 1616 | F /= Lc (F); |
---|
| 1617 | result.append (buf); |
---|
| 1618 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 1619 | } |
---|
| 1620 | if (degree (F) <= 0) |
---|
| 1621 | { |
---|
| 1622 | G= F; |
---|
| 1623 | factors= bufFactors; |
---|
| 1624 | return result; |
---|
| 1625 | } |
---|
| 1626 | } |
---|
| 1627 | G= F; |
---|
| 1628 | factors= bufFactors; |
---|
| 1629 | return result; |
---|
| 1630 | } |
---|
| 1631 | |
---|
| 1632 | void |
---|
[c1b9927] | 1633 | extReconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const |
---|
[11bf82] | 1634 | CFList& factors, const int liftBound, int& factorsFound, |
---|
| 1635 | int*& factorsFoundIndex, mat_zz_p& N, bool beenInThres, |
---|
| 1636 | const ExtensionInfo& info, const CanonicalForm& evaluation |
---|
| 1637 | ) |
---|
| 1638 | { |
---|
| 1639 | Variable y= Variable (2); |
---|
| 1640 | Variable x= Variable (1); |
---|
| 1641 | Variable alpha= info.getAlpha(); |
---|
| 1642 | Variable beta= info.getBeta(); |
---|
| 1643 | int k= info.getGFDegree(); |
---|
| 1644 | CanonicalForm gamma= info.getGamma(); |
---|
| 1645 | CanonicalForm delta= info.getDelta(); |
---|
| 1646 | CanonicalForm yToL= power (y, liftBound); |
---|
[38ffb7] | 1647 | CanonicalForm quot, buf, buf2; |
---|
[11bf82] | 1648 | CFList source, dest; |
---|
[38ffb7] | 1649 | CFListIterator iter; |
---|
[11bf82] | 1650 | for (long i= 1; i <= N.NumCols(); i++) |
---|
| 1651 | { |
---|
| 1652 | if (factorsFoundIndex [i - 1] == 1) |
---|
| 1653 | continue; |
---|
[38ffb7] | 1654 | iter= factors; |
---|
[11bf82] | 1655 | if (beenInThres) |
---|
| 1656 | { |
---|
| 1657 | int count= 1; |
---|
| 1658 | while (count < i) |
---|
| 1659 | { |
---|
| 1660 | count++; |
---|
| 1661 | iter++; |
---|
| 1662 | } |
---|
| 1663 | buf= iter.getItem(); |
---|
| 1664 | } |
---|
| 1665 | else |
---|
| 1666 | { |
---|
| 1667 | buf= 1; |
---|
| 1668 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 1669 | { |
---|
| 1670 | if (!IsZero (N (j,i))) |
---|
| 1671 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 1672 | } |
---|
| 1673 | } |
---|
| 1674 | buf *= LC (F, x); |
---|
| 1675 | buf= mod (buf, yToL); |
---|
| 1676 | buf /= content (buf, x); |
---|
| 1677 | buf2= buf (y - evaluation, y); |
---|
[a54114] | 1678 | if (!k && beta == x) |
---|
[11bf82] | 1679 | { |
---|
| 1680 | if (degree (buf2, alpha) < 1) |
---|
| 1681 | { |
---|
[21b8f4c] | 1682 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 1683 | { |
---|
| 1684 | factorsFoundIndex[i - 1]= 1; |
---|
| 1685 | factorsFound++; |
---|
[21b8f4c] | 1686 | F= quot; |
---|
[11bf82] | 1687 | F /= Lc (F); |
---|
| 1688 | buf2= mapDown (buf2, info, source, dest); |
---|
| 1689 | reconstructedFactors.append (buf2); |
---|
| 1690 | } |
---|
| 1691 | } |
---|
| 1692 | } |
---|
| 1693 | else |
---|
| 1694 | { |
---|
| 1695 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
| 1696 | { |
---|
[21b8f4c] | 1697 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 1698 | { |
---|
| 1699 | factorsFoundIndex[i - 1]= 1; |
---|
| 1700 | factorsFound++; |
---|
[21b8f4c] | 1701 | F= quot; |
---|
[11bf82] | 1702 | F /= Lc (F); |
---|
| 1703 | buf2= mapDown (buf2, info, source, dest); |
---|
| 1704 | reconstructedFactors.append (buf2); |
---|
| 1705 | } |
---|
| 1706 | } |
---|
| 1707 | } |
---|
| 1708 | if (degree (F) <= 0) |
---|
| 1709 | return; |
---|
| 1710 | if (factorsFound + 1 == N.NumCols()) |
---|
| 1711 | { |
---|
| 1712 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 1713 | tmp= mapDown (tmp, info, source, dest); |
---|
| 1714 | reconstructedFactors.append (tmp); |
---|
| 1715 | return; |
---|
| 1716 | } |
---|
| 1717 | } |
---|
| 1718 | } |
---|
| 1719 | |
---|
| 1720 | //over Fp |
---|
| 1721 | int |
---|
| 1722 | liftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, int |
---|
| 1723 | start, int liftBound, int minBound, CFList& factors, |
---|
| 1724 | mat_zz_p& NTLN, CFList& diophant, CFMatrix& M, CFArray& |
---|
| 1725 | Pi, CFArray& bufQ, bool& irreducible |
---|
| 1726 | ) |
---|
| 1727 | { |
---|
| 1728 | CanonicalForm LCF= LC (F, 1); |
---|
| 1729 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
| 1730 | bool wasInBounds= false; |
---|
| 1731 | bool hitBound= false; |
---|
| 1732 | int l= (minBound+1)*2; |
---|
| 1733 | int stepSize= 2; |
---|
| 1734 | int oldL= l/2; |
---|
| 1735 | bool reduced= false; |
---|
[38ffb7] | 1736 | mat_zz_p NTLK, *NTLC; |
---|
| 1737 | CFMatrix C; |
---|
| 1738 | CFArray buf; |
---|
| 1739 | CFListIterator j; |
---|
[5335ba] | 1740 | CanonicalForm truncF; |
---|
| 1741 | Variable y= F.mvar(); |
---|
[11bf82] | 1742 | while (l <= liftBound) |
---|
| 1743 | { |
---|
| 1744 | if (start) |
---|
| 1745 | { |
---|
| 1746 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
| 1747 | start= 0; |
---|
| 1748 | } |
---|
| 1749 | else |
---|
| 1750 | { |
---|
| 1751 | if (wasInBounds) |
---|
| 1752 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
| 1753 | else |
---|
| 1754 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 1755 | } |
---|
| 1756 | |
---|
| 1757 | factors.insert (LCF); |
---|
[38ffb7] | 1758 | j= factors; |
---|
[11bf82] | 1759 | j++; |
---|
| 1760 | |
---|
[5335ba] | 1761 | truncF= mod (F, power (y, l)); |
---|
[11bf82] | 1762 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
| 1763 | { |
---|
| 1764 | if (!wasInBounds) |
---|
[5335ba] | 1765 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
[11bf82] | 1766 | else |
---|
[5335ba] | 1767 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
| 1768 | bufQ[i]); |
---|
[11bf82] | 1769 | } |
---|
| 1770 | |
---|
| 1771 | for (int i= 0; i < sizeBounds; i++) |
---|
| 1772 | { |
---|
| 1773 | if (bounds [i] + 1 <= l/2) |
---|
| 1774 | { |
---|
| 1775 | wasInBounds= true; |
---|
| 1776 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 1777 | C= CFMatrix (l - k, factors.length() - 1); |
---|
[11bf82] | 1778 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
| 1779 | { |
---|
| 1780 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 1781 | { |
---|
[11bf82] | 1782 | buf= getCoeffs (A[ii] [i], k); |
---|
[9ebec2] | 1783 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 1784 | } |
---|
[11bf82] | 1785 | } |
---|
[38ffb7] | 1786 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 1787 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 1788 | transpose (NTLK, NTLK); |
---|
| 1789 | kernel (NTLK, NTLK); |
---|
| 1790 | transpose (NTLK, NTLK); |
---|
| 1791 | NTLN *= NTLK; |
---|
| 1792 | |
---|
| 1793 | if (NTLN.NumCols() == 1) |
---|
| 1794 | { |
---|
| 1795 | irreducible= true; |
---|
| 1796 | break; |
---|
| 1797 | } |
---|
[3426de2] | 1798 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
[11bf82] | 1799 | { |
---|
| 1800 | reduced= true; |
---|
| 1801 | break; |
---|
| 1802 | } |
---|
| 1803 | } |
---|
| 1804 | } |
---|
| 1805 | |
---|
| 1806 | if (irreducible) |
---|
| 1807 | break; |
---|
| 1808 | if (reduced) |
---|
| 1809 | break; |
---|
| 1810 | oldL= l; |
---|
| 1811 | l += stepSize; |
---|
| 1812 | stepSize *= 2; |
---|
| 1813 | if (l > liftBound) |
---|
| 1814 | { |
---|
| 1815 | if (!hitBound) |
---|
| 1816 | { |
---|
| 1817 | l= liftBound; |
---|
| 1818 | hitBound= true; |
---|
| 1819 | } |
---|
| 1820 | else |
---|
| 1821 | break; |
---|
| 1822 | } |
---|
| 1823 | } |
---|
| 1824 | delete [] A; |
---|
| 1825 | return l; |
---|
| 1826 | } |
---|
| 1827 | |
---|
| 1828 | //over field extension |
---|
| 1829 | int |
---|
| 1830 | extLiftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
| 1831 | int liftBound, int minBound, int start, CFList& |
---|
| 1832 | factors, mat_zz_p& NTLN, CFList& diophant, |
---|
| 1833 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, bool& |
---|
| 1834 | irreducible, const CanonicalForm& evaluation, const |
---|
| 1835 | ExtensionInfo& info, CFList& source, CFList& dest |
---|
| 1836 | ) |
---|
| 1837 | { |
---|
| 1838 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
| 1839 | CanonicalForm LCF= LC (F, 1); |
---|
| 1840 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
| 1841 | bool wasInBounds= false; |
---|
| 1842 | bool hitBound= false; |
---|
| 1843 | int degMipo; |
---|
| 1844 | Variable alpha; |
---|
| 1845 | alpha= info.getAlpha(); |
---|
| 1846 | degMipo= degree (getMipo (alpha)); |
---|
| 1847 | |
---|
| 1848 | Variable gamma= info.getBeta(); |
---|
| 1849 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
| 1850 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
| 1851 | |
---|
| 1852 | int stepSize= 2; |
---|
| 1853 | int l= ((minBound+1)/degMipo+1)*2; |
---|
| 1854 | l= tmax (l, 2); |
---|
| 1855 | if (start > l) |
---|
| 1856 | l= start; |
---|
[3426de2] | 1857 | int startl= l; |
---|
[11bf82] | 1858 | int oldL= l/2; |
---|
| 1859 | bool reduced= false; |
---|
[38ffb7] | 1860 | Variable y= F.mvar(); |
---|
| 1861 | Variable x= Variable (1); |
---|
[5335ba] | 1862 | CanonicalForm powX, imBasis, truncF; |
---|
[38ffb7] | 1863 | CFMatrix Mat, C; |
---|
| 1864 | CFArray buf; |
---|
| 1865 | CFIterator iter; |
---|
| 1866 | mat_zz_p* NTLMat, *NTLC, NTLK; |
---|
| 1867 | CFListIterator j; |
---|
[11bf82] | 1868 | while (l <= liftBound) |
---|
| 1869 | { |
---|
| 1870 | if (start) |
---|
| 1871 | { |
---|
| 1872 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
| 1873 | start= 0; |
---|
| 1874 | } |
---|
| 1875 | else |
---|
| 1876 | { |
---|
| 1877 | if (wasInBounds) |
---|
| 1878 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
| 1879 | else |
---|
| 1880 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 1881 | } |
---|
| 1882 | |
---|
| 1883 | factors.insert (LCF); |
---|
| 1884 | |
---|
| 1885 | if (GF) |
---|
| 1886 | setCharacteristic (getCharacteristic()); |
---|
| 1887 | |
---|
[38ffb7] | 1888 | powX= power (y-gamma, l); |
---|
| 1889 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
[11bf82] | 1890 | for (int i= 0; i < l*degMipo; i++) |
---|
| 1891 | { |
---|
[38ffb7] | 1892 | imBasis= mod (power (y, i), powX); |
---|
[11bf82] | 1893 | imBasis= imBasis (power (y, degMipo), y); |
---|
| 1894 | imBasis= imBasis (y, gamma); |
---|
[38ffb7] | 1895 | iter= imBasis; |
---|
[11bf82] | 1896 | for (; iter.hasTerms(); iter++) |
---|
| 1897 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
| 1898 | } |
---|
| 1899 | |
---|
[38ffb7] | 1900 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
[11bf82] | 1901 | *NTLMat= inv (*NTLMat); |
---|
| 1902 | |
---|
| 1903 | if (GF) |
---|
| 1904 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 1905 | |
---|
[38ffb7] | 1906 | j= factors; |
---|
[11bf82] | 1907 | j++; |
---|
| 1908 | |
---|
[5335ba] | 1909 | truncF= mod (F, power (y, l)); |
---|
[11bf82] | 1910 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
| 1911 | { |
---|
| 1912 | if (!wasInBounds) |
---|
[5335ba] | 1913 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
[11bf82] | 1914 | else |
---|
[5335ba] | 1915 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
| 1916 | bufQ[i]); |
---|
[11bf82] | 1917 | } |
---|
| 1918 | |
---|
| 1919 | for (int i= 0; i < sizeBounds; i++) |
---|
| 1920 | { |
---|
| 1921 | if (bounds [i] + 1 <= (l/2)*degMipo) |
---|
| 1922 | { |
---|
| 1923 | wasInBounds= true; |
---|
| 1924 | int k= tmin (bounds [i] + 1, (l/2)*degMipo); |
---|
[38ffb7] | 1925 | C= CFMatrix (l*degMipo - k, factors.length() - 1); |
---|
[11bf82] | 1926 | |
---|
| 1927 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
| 1928 | { |
---|
| 1929 | if (A[ii].size() - 1 >= i) |
---|
| 1930 | { |
---|
| 1931 | if (GF) |
---|
| 1932 | { |
---|
| 1933 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 1934 | setCharacteristic (getCharacteristic()); |
---|
| 1935 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
| 1936 | if (alpha != gamma) |
---|
| 1937 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 1938 | gamma, source, dest |
---|
| 1939 | ); |
---|
| 1940 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
| 1941 | } |
---|
| 1942 | else |
---|
| 1943 | { |
---|
| 1944 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 1945 | if (alpha != gamma) |
---|
| 1946 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 1947 | gamma, source, dest |
---|
| 1948 | ); |
---|
| 1949 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
| 1950 | } |
---|
[9ebec2] | 1951 | writeInMatrix (C, buf, ii + 1, 0); |
---|
[11bf82] | 1952 | } |
---|
| 1953 | if (GF) |
---|
| 1954 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 1955 | } |
---|
| 1956 | |
---|
| 1957 | if (GF) |
---|
| 1958 | setCharacteristic(getCharacteristic()); |
---|
| 1959 | |
---|
[38ffb7] | 1960 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 1961 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 1962 | transpose (NTLK, NTLK); |
---|
| 1963 | kernel (NTLK, NTLK); |
---|
| 1964 | transpose (NTLK, NTLK); |
---|
| 1965 | NTLN *= NTLK; |
---|
| 1966 | |
---|
| 1967 | if (GF) |
---|
| 1968 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 1969 | |
---|
| 1970 | if (NTLN.NumCols() == 1) |
---|
| 1971 | { |
---|
| 1972 | irreducible= true; |
---|
| 1973 | break; |
---|
| 1974 | } |
---|
[3426de2] | 1975 | if (isReduced (NTLN) && l > startl) |
---|
[11bf82] | 1976 | { |
---|
| 1977 | reduced= true; |
---|
| 1978 | break; |
---|
| 1979 | } |
---|
| 1980 | } |
---|
| 1981 | } |
---|
| 1982 | |
---|
| 1983 | if (NTLN.NumCols() == 1) |
---|
| 1984 | { |
---|
| 1985 | irreducible= true; |
---|
| 1986 | break; |
---|
| 1987 | } |
---|
| 1988 | if (reduced) |
---|
| 1989 | break; |
---|
| 1990 | oldL= l; |
---|
| 1991 | l += stepSize; |
---|
| 1992 | stepSize *= 2; |
---|
| 1993 | if (l > liftBound) |
---|
| 1994 | { |
---|
| 1995 | if (!hitBound) |
---|
| 1996 | { |
---|
| 1997 | l= liftBound; |
---|
| 1998 | hitBound= true; |
---|
| 1999 | } |
---|
| 2000 | else |
---|
| 2001 | break; |
---|
| 2002 | } |
---|
| 2003 | } |
---|
| 2004 | delete [] A; |
---|
| 2005 | return l; |
---|
| 2006 | } |
---|
| 2007 | |
---|
| 2008 | // over Fq |
---|
| 2009 | int |
---|
| 2010 | liftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
| 2011 | int start, int liftBound, int minBound, CFList& factors, |
---|
| 2012 | mat_zz_pE& NTLN, CFList& diophant, CFMatrix& M, CFArray& |
---|
| 2013 | Pi, CFArray& bufQ, bool& irreducible |
---|
| 2014 | ) |
---|
| 2015 | { |
---|
| 2016 | CanonicalForm LCF= LC (F, 1); |
---|
| 2017 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
| 2018 | bool wasInBounds= false; |
---|
| 2019 | bool hitBound= false; |
---|
| 2020 | int l= (minBound+1)*2; |
---|
| 2021 | int stepSize= 2; |
---|
| 2022 | int oldL= l/2; |
---|
| 2023 | bool reduced= false; |
---|
[38ffb7] | 2024 | CFListIterator j; |
---|
| 2025 | mat_zz_pE* NTLC, NTLK; |
---|
| 2026 | CFArray buf; |
---|
| 2027 | CFMatrix C; |
---|
[5335ba] | 2028 | Variable y= F.mvar(); |
---|
| 2029 | CanonicalForm truncF; |
---|
[11bf82] | 2030 | while (l <= liftBound) |
---|
| 2031 | { |
---|
| 2032 | if (start) |
---|
| 2033 | { |
---|
| 2034 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
| 2035 | start= 0; |
---|
| 2036 | } |
---|
| 2037 | else |
---|
| 2038 | { |
---|
| 2039 | if (wasInBounds) |
---|
| 2040 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
| 2041 | else |
---|
| 2042 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 2043 | } |
---|
| 2044 | |
---|
| 2045 | factors.insert (LCF); |
---|
[38ffb7] | 2046 | j= factors; |
---|
[11bf82] | 2047 | j++; |
---|
| 2048 | |
---|
[5335ba] | 2049 | truncF= mod (F, power (y,l)); |
---|
[11bf82] | 2050 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
| 2051 | { |
---|
| 2052 | if (l == (minBound+1)*2) |
---|
| 2053 | { |
---|
[5335ba] | 2054 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
[11bf82] | 2055 | } |
---|
| 2056 | else |
---|
| 2057 | { |
---|
[5335ba] | 2058 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
[11bf82] | 2059 | bufQ[i] |
---|
| 2060 | ); |
---|
| 2061 | } |
---|
| 2062 | } |
---|
| 2063 | |
---|
| 2064 | for (int i= 0; i < sizeBounds; i++) |
---|
| 2065 | { |
---|
| 2066 | if (bounds [i] + 1 <= l/2) |
---|
| 2067 | { |
---|
| 2068 | wasInBounds= true; |
---|
| 2069 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 2070 | C= CFMatrix (l - k, factors.length() - 1); |
---|
[11bf82] | 2071 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
| 2072 | { |
---|
[38ffb7] | 2073 | |
---|
[11bf82] | 2074 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 2075 | { |
---|
[11bf82] | 2076 | buf= getCoeffs (A[ii] [i], k); |
---|
[9ebec2] | 2077 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 2078 | } |
---|
[11bf82] | 2079 | } |
---|
| 2080 | |
---|
[38ffb7] | 2081 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
| 2082 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 2083 | transpose (NTLK, NTLK); |
---|
| 2084 | kernel (NTLK, NTLK); |
---|
| 2085 | transpose (NTLK, NTLK); |
---|
| 2086 | NTLN *= NTLK; |
---|
| 2087 | |
---|
| 2088 | if (NTLN.NumCols() == 1) |
---|
| 2089 | { |
---|
| 2090 | irreducible= true; |
---|
| 2091 | break; |
---|
| 2092 | } |
---|
[3426de2] | 2093 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
[11bf82] | 2094 | { |
---|
| 2095 | reduced= true; |
---|
| 2096 | break; |
---|
| 2097 | } |
---|
| 2098 | } |
---|
| 2099 | } |
---|
| 2100 | |
---|
| 2101 | if (NTLN.NumCols() == 1) |
---|
| 2102 | { |
---|
| 2103 | irreducible= true; |
---|
| 2104 | break; |
---|
| 2105 | } |
---|
| 2106 | if (reduced) |
---|
| 2107 | break; |
---|
| 2108 | oldL= l; |
---|
| 2109 | l += stepSize; |
---|
| 2110 | stepSize *= 2; |
---|
| 2111 | if (l > liftBound) |
---|
| 2112 | { |
---|
| 2113 | if (!hitBound) |
---|
| 2114 | { |
---|
| 2115 | l= liftBound; |
---|
| 2116 | hitBound= true; |
---|
| 2117 | } |
---|
| 2118 | else |
---|
| 2119 | break; |
---|
| 2120 | } |
---|
| 2121 | } |
---|
| 2122 | delete [] A; |
---|
| 2123 | return l; |
---|
| 2124 | } |
---|
| 2125 | |
---|
| 2126 | int |
---|
| 2127 | liftAndComputeLatticeFq2Fp (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
| 2128 | int start, int liftBound, int minBound, CFList& |
---|
| 2129 | factors, mat_zz_p& NTLN, CFList& diophant, CFMatrix& |
---|
| 2130 | M, CFArray& Pi, CFArray& bufQ, bool& irreducible, |
---|
| 2131 | const Variable& alpha |
---|
| 2132 | ) |
---|
| 2133 | { |
---|
| 2134 | CanonicalForm LCF= LC (F, 1); |
---|
| 2135 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
| 2136 | bool wasInBounds= false; |
---|
| 2137 | int l= (minBound+1)*2; |
---|
| 2138 | int oldL= l/2; |
---|
| 2139 | int stepSize= 2; |
---|
| 2140 | bool hitBound= false; |
---|
| 2141 | int extensionDeg= degree (getMipo (alpha)); |
---|
| 2142 | bool reduced= false; |
---|
[38ffb7] | 2143 | CFListIterator j; |
---|
| 2144 | CFMatrix C; |
---|
| 2145 | CFArray buf; |
---|
| 2146 | mat_zz_p* NTLC, NTLK; |
---|
[5335ba] | 2147 | Variable y= F.mvar(); |
---|
| 2148 | CanonicalForm truncF; |
---|
[11bf82] | 2149 | while (l <= liftBound) |
---|
| 2150 | { |
---|
| 2151 | if (start) |
---|
| 2152 | { |
---|
| 2153 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
| 2154 | start= 0; |
---|
| 2155 | } |
---|
| 2156 | else |
---|
| 2157 | { |
---|
| 2158 | if (wasInBounds) |
---|
| 2159 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
| 2160 | else |
---|
| 2161 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 2162 | } |
---|
| 2163 | |
---|
| 2164 | factors.insert (LCF); |
---|
[38ffb7] | 2165 | j= factors; |
---|
[11bf82] | 2166 | j++; |
---|
| 2167 | |
---|
[5335ba] | 2168 | truncF= mod (F, power (y,l)); |
---|
[11bf82] | 2169 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
| 2170 | { |
---|
| 2171 | if (l == (minBound+1)*2) |
---|
| 2172 | { |
---|
[5335ba] | 2173 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
[11bf82] | 2174 | } |
---|
| 2175 | else |
---|
| 2176 | { |
---|
[5335ba] | 2177 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
[11bf82] | 2178 | bufQ[i] |
---|
| 2179 | ); |
---|
| 2180 | } |
---|
| 2181 | } |
---|
| 2182 | |
---|
| 2183 | for (int i= 0; i < sizeBounds; i++) |
---|
| 2184 | { |
---|
| 2185 | if (bounds [i] + 1 <= l/2) |
---|
| 2186 | { |
---|
| 2187 | wasInBounds= true; |
---|
| 2188 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 2189 | C= CFMatrix ((l - k)*extensionDeg, factors.length() - 1); |
---|
[11bf82] | 2190 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
| 2191 | { |
---|
| 2192 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 2193 | { |
---|
[11bf82] | 2194 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
[9ebec2] | 2195 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 2196 | } |
---|
[11bf82] | 2197 | } |
---|
| 2198 | |
---|
[38ffb7] | 2199 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 2200 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 2201 | transpose (NTLK, NTLK); |
---|
| 2202 | kernel (NTLK, NTLK); |
---|
| 2203 | transpose (NTLK, NTLK); |
---|
| 2204 | NTLN *= NTLK; |
---|
| 2205 | |
---|
| 2206 | if (NTLN.NumCols() == 1) |
---|
| 2207 | { |
---|
| 2208 | irreducible= true; |
---|
| 2209 | break; |
---|
| 2210 | } |
---|
[3426de2] | 2211 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
[11bf82] | 2212 | { |
---|
| 2213 | reduced= true; |
---|
| 2214 | break; |
---|
| 2215 | } |
---|
| 2216 | } |
---|
| 2217 | } |
---|
| 2218 | |
---|
| 2219 | if (NTLN.NumCols() == 1) |
---|
| 2220 | { |
---|
| 2221 | irreducible= true; |
---|
| 2222 | break; |
---|
| 2223 | } |
---|
| 2224 | if (reduced) |
---|
| 2225 | break; |
---|
| 2226 | oldL= l; |
---|
| 2227 | l += stepSize; |
---|
| 2228 | stepSize *= 2; |
---|
| 2229 | if (l > liftBound) |
---|
| 2230 | { |
---|
| 2231 | if (!hitBound) |
---|
| 2232 | { |
---|
| 2233 | l= liftBound; |
---|
| 2234 | hitBound= true; |
---|
| 2235 | } |
---|
| 2236 | else |
---|
| 2237 | break; |
---|
| 2238 | } |
---|
| 2239 | } |
---|
| 2240 | delete [] A; |
---|
| 2241 | return l; |
---|
| 2242 | } |
---|
| 2243 | |
---|
| 2244 | CFList |
---|
| 2245 | increasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
| 2246 | int oldNumCols, int oldL, int precision |
---|
| 2247 | ) |
---|
| 2248 | { |
---|
| 2249 | bool irreducible= false; |
---|
| 2250 | int d; |
---|
| 2251 | int* bounds= computeBounds (F, d); |
---|
| 2252 | CFArray * A= new CFArray [factors.length()]; |
---|
| 2253 | CFArray bufQ= CFArray (factors.length()); |
---|
| 2254 | mat_zz_p NTLN; |
---|
| 2255 | ident (NTLN, factors.length()); |
---|
| 2256 | int minBound= bounds[0]; |
---|
| 2257 | for (int i= 1; i < d; i++) |
---|
| 2258 | { |
---|
| 2259 | if (bounds[i] != 0) |
---|
| 2260 | minBound= tmin (minBound, bounds[i]); |
---|
| 2261 | } |
---|
| 2262 | int l= tmax (2*(minBound + 1), oldL); |
---|
| 2263 | int oldL2= l/2; |
---|
| 2264 | int stepSize= 2; |
---|
| 2265 | bool useOldQs= false; |
---|
| 2266 | bool hitBound= false; |
---|
[38ffb7] | 2267 | CFListIterator j; |
---|
| 2268 | CFMatrix C; |
---|
| 2269 | CFArray buf; |
---|
| 2270 | mat_zz_p* NTLC, NTLK; |
---|
[5335ba] | 2271 | Variable y= F.mvar(); |
---|
| 2272 | CanonicalForm truncF; |
---|
[11bf82] | 2273 | while (l <= precision) |
---|
| 2274 | { |
---|
[38ffb7] | 2275 | j= factors; |
---|
[5335ba] | 2276 | truncF= mod (F, power (y,l)); |
---|
[11bf82] | 2277 | if (useOldQs) |
---|
| 2278 | { |
---|
| 2279 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 2280 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
[11bf82] | 2281 | bufQ[i] |
---|
| 2282 | ); |
---|
| 2283 | } |
---|
| 2284 | else |
---|
| 2285 | { |
---|
| 2286 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 2287 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 2288 | } |
---|
| 2289 | useOldQs= true; |
---|
| 2290 | for (int i= 0; i < d; i++) |
---|
| 2291 | { |
---|
| 2292 | if (bounds [i] + 1 <= l/2) |
---|
| 2293 | { |
---|
| 2294 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 2295 | C= CFMatrix (l - k, factors.length()); |
---|
[11bf82] | 2296 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 2297 | { |
---|
| 2298 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 2299 | { |
---|
[11bf82] | 2300 | buf= getCoeffs (A[ii] [i], k); |
---|
[9ebec2] | 2301 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 2302 | } |
---|
[11bf82] | 2303 | } |
---|
[38ffb7] | 2304 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 2305 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 2306 | transpose (NTLK, NTLK); |
---|
| 2307 | kernel (NTLK, NTLK); |
---|
| 2308 | transpose (NTLK, NTLK); |
---|
| 2309 | NTLN *= NTLK; |
---|
| 2310 | if (NTLN.NumCols() == 1) |
---|
| 2311 | { |
---|
| 2312 | irreducible= true; |
---|
| 2313 | delete [] A; |
---|
| 2314 | delete [] bounds; |
---|
| 2315 | CanonicalForm G= F; |
---|
| 2316 | F= 1; |
---|
| 2317 | return CFList (G); |
---|
| 2318 | } |
---|
| 2319 | } |
---|
| 2320 | } |
---|
| 2321 | |
---|
| 2322 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
| 2323 | { |
---|
| 2324 | if (isReduced (NTLN)) |
---|
| 2325 | { |
---|
| 2326 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 2327 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 2328 | factorsFoundIndex[i]= 0; |
---|
| 2329 | int factorsFound2= 0; |
---|
| 2330 | CFList result; |
---|
| 2331 | CanonicalForm bufF= F; |
---|
| 2332 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
| 2333 | factorsFoundIndex, NTLN, false |
---|
| 2334 | ); |
---|
[38ffb7] | 2335 | if (result.length() == NTLN.NumCols()) |
---|
[11bf82] | 2336 | { |
---|
| 2337 | delete [] factorsFoundIndex; |
---|
| 2338 | delete [] A; |
---|
| 2339 | delete [] bounds; |
---|
[3d0075] | 2340 | F= 1; |
---|
[11bf82] | 2341 | return result; |
---|
| 2342 | } |
---|
| 2343 | delete [] factorsFoundIndex; |
---|
| 2344 | } |
---|
| 2345 | else if (l == precision) |
---|
| 2346 | { |
---|
| 2347 | CanonicalForm bufF= F; |
---|
| 2348 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
| 2349 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN); |
---|
| 2350 | F= bufF; |
---|
| 2351 | delete [] zeroOne; |
---|
| 2352 | delete [] A; |
---|
| 2353 | delete [] bounds; |
---|
| 2354 | return result; |
---|
| 2355 | } |
---|
| 2356 | } |
---|
| 2357 | oldL2= l; |
---|
| 2358 | l += stepSize; |
---|
| 2359 | stepSize *= 2; |
---|
| 2360 | if (l > precision) |
---|
| 2361 | { |
---|
| 2362 | if (!hitBound) |
---|
| 2363 | { |
---|
| 2364 | l= precision; |
---|
| 2365 | hitBound= true; |
---|
| 2366 | } |
---|
| 2367 | else |
---|
| 2368 | break; |
---|
| 2369 | } |
---|
| 2370 | } |
---|
| 2371 | delete [] bounds; |
---|
| 2372 | delete [] A; |
---|
| 2373 | return CFList(); |
---|
| 2374 | } |
---|
| 2375 | |
---|
| 2376 | CFList |
---|
| 2377 | increasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
[0349c20] | 2378 | int oldNumCols, int oldL, const Variable&, |
---|
[11bf82] | 2379 | int precision |
---|
| 2380 | ) |
---|
| 2381 | { |
---|
| 2382 | bool irreducible= false; |
---|
| 2383 | int d; |
---|
| 2384 | int* bounds= computeBounds (F, d); |
---|
| 2385 | CFArray * A= new CFArray [factors.length()]; |
---|
| 2386 | CFArray bufQ= CFArray (factors.length()); |
---|
| 2387 | mat_zz_pE NTLN; |
---|
| 2388 | ident (NTLN, factors.length()); |
---|
| 2389 | int minBound= bounds[0]; |
---|
| 2390 | for (int i= 1; i < d; i++) |
---|
| 2391 | { |
---|
| 2392 | if (bounds[i] != 0) |
---|
| 2393 | minBound= tmin (minBound, bounds[i]); |
---|
| 2394 | } |
---|
| 2395 | int l= tmax (2*(minBound + 1), oldL); |
---|
| 2396 | int oldL2= l/2; |
---|
| 2397 | int stepSize= 2; |
---|
| 2398 | bool useOldQs= false; |
---|
| 2399 | bool hitBound= false; |
---|
[38ffb7] | 2400 | CFListIterator j; |
---|
| 2401 | CFMatrix C; |
---|
| 2402 | mat_zz_pE* NTLC, NTLK; |
---|
| 2403 | CFArray buf; |
---|
[5335ba] | 2404 | Variable y= F.mvar(); |
---|
| 2405 | CanonicalForm truncF; |
---|
[11bf82] | 2406 | while (l <= precision) |
---|
| 2407 | { |
---|
[38ffb7] | 2408 | j= factors; |
---|
[5335ba] | 2409 | truncF= mod (F, power (y,l)); |
---|
[11bf82] | 2410 | if (useOldQs) |
---|
| 2411 | { |
---|
| 2412 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 2413 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
[11bf82] | 2414 | bufQ[i] |
---|
| 2415 | ); |
---|
| 2416 | } |
---|
| 2417 | else |
---|
| 2418 | { |
---|
| 2419 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 2420 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 2421 | } |
---|
| 2422 | useOldQs= true; |
---|
| 2423 | for (int i= 0; i < d; i++) |
---|
| 2424 | { |
---|
| 2425 | if (bounds [i] + 1 <= l/2) |
---|
| 2426 | { |
---|
| 2427 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 2428 | C= CFMatrix (l - k, factors.length()); |
---|
[11bf82] | 2429 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 2430 | { |
---|
| 2431 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 2432 | { |
---|
[11bf82] | 2433 | buf= getCoeffs (A[ii] [i], k); |
---|
[9ebec2] | 2434 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 2435 | } |
---|
[11bf82] | 2436 | } |
---|
[38ffb7] | 2437 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
| 2438 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 2439 | transpose (NTLK, NTLK); |
---|
| 2440 | kernel (NTLK, NTLK); |
---|
| 2441 | transpose (NTLK, NTLK); |
---|
| 2442 | NTLN *= NTLK; |
---|
| 2443 | if (NTLN.NumCols() == 1) |
---|
| 2444 | { |
---|
| 2445 | irreducible= true; |
---|
| 2446 | delete [] A; |
---|
| 2447 | delete [] bounds; |
---|
| 2448 | return CFList (F); |
---|
| 2449 | } |
---|
| 2450 | } |
---|
| 2451 | } |
---|
| 2452 | |
---|
| 2453 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
| 2454 | { |
---|
| 2455 | if (isReduced (NTLN)) |
---|
| 2456 | { |
---|
| 2457 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 2458 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 2459 | factorsFoundIndex[i]= 0; |
---|
| 2460 | int factorsFound2= 0; |
---|
| 2461 | CFList result; |
---|
| 2462 | CanonicalForm bufF= F; |
---|
| 2463 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
| 2464 | factorsFoundIndex, NTLN, false); |
---|
| 2465 | if (result.length() == NTLN.NumCols()) |
---|
| 2466 | { |
---|
| 2467 | delete [] factorsFoundIndex; |
---|
| 2468 | delete [] A; |
---|
| 2469 | delete [] bounds; |
---|
[3d0075] | 2470 | F= 1; |
---|
[11bf82] | 2471 | return result; |
---|
| 2472 | } |
---|
| 2473 | delete [] factorsFoundIndex; |
---|
| 2474 | } |
---|
| 2475 | else if (l == precision) |
---|
| 2476 | { |
---|
| 2477 | CanonicalForm bufF= F; |
---|
| 2478 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
| 2479 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN); |
---|
| 2480 | F= bufF; |
---|
| 2481 | delete [] zeroOne; |
---|
| 2482 | delete [] A; |
---|
| 2483 | delete [] bounds; |
---|
| 2484 | return result; |
---|
| 2485 | } |
---|
| 2486 | } |
---|
| 2487 | oldL2= l; |
---|
| 2488 | l += stepSize; |
---|
| 2489 | stepSize *= 2; |
---|
| 2490 | if (l > precision) |
---|
| 2491 | { |
---|
| 2492 | if (!hitBound) |
---|
| 2493 | { |
---|
| 2494 | l= precision; |
---|
| 2495 | hitBound= true; |
---|
| 2496 | } |
---|
| 2497 | else |
---|
| 2498 | break; |
---|
| 2499 | } |
---|
| 2500 | } |
---|
| 2501 | delete [] bounds; |
---|
| 2502 | delete [] A; |
---|
| 2503 | return CFList(); |
---|
| 2504 | } |
---|
| 2505 | |
---|
| 2506 | //over field extension |
---|
| 2507 | CFList |
---|
| 2508 | extIncreasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
| 2509 | int oldNumCols, int oldL, const CanonicalForm& evaluation, |
---|
| 2510 | const ExtensionInfo& info, CFList& source, CFList& dest, |
---|
| 2511 | int precision |
---|
| 2512 | ) |
---|
| 2513 | { |
---|
| 2514 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
| 2515 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
| 2516 | Variable alpha= info.getAlpha(); |
---|
| 2517 | bool irreducible= false; |
---|
| 2518 | int d; |
---|
| 2519 | int* bounds= computeBounds (F, d); |
---|
| 2520 | |
---|
| 2521 | CFArray * A= new CFArray [factors.length()]; |
---|
| 2522 | CFArray bufQ= CFArray (factors.length()); |
---|
| 2523 | zz_p::init (getCharacteristic()); |
---|
| 2524 | mat_zz_p NTLN; |
---|
| 2525 | ident (NTLN, factors.length()); |
---|
| 2526 | int minBound= bounds[0]; |
---|
| 2527 | for (int i= 1; i < d; i++) |
---|
| 2528 | { |
---|
| 2529 | if (bounds[i] != 0) |
---|
| 2530 | minBound= tmin (minBound, bounds[i]); |
---|
| 2531 | } |
---|
| 2532 | int l= tmax (oldL, 2*((minBound+1)/degMipo+1)); |
---|
| 2533 | int oldL2= l/2; |
---|
| 2534 | int stepSize= 2; |
---|
| 2535 | bool useOldQs= false; |
---|
| 2536 | bool hitBound= false; |
---|
| 2537 | Variable gamma= info.getBeta(); |
---|
| 2538 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
| 2539 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
[38ffb7] | 2540 | CFListIterator j; |
---|
| 2541 | Variable y= F.mvar(); |
---|
[5335ba] | 2542 | CanonicalForm powX, imBasis, truncF; |
---|
[38ffb7] | 2543 | CFMatrix Mat, C; |
---|
| 2544 | CFIterator iter; |
---|
| 2545 | mat_zz_p* NTLMat,*NTLC, NTLK; |
---|
| 2546 | CFArray buf; |
---|
[11bf82] | 2547 | while (l <= precision) |
---|
| 2548 | { |
---|
[38ffb7] | 2549 | j= factors; |
---|
[11bf82] | 2550 | if (GF) |
---|
| 2551 | setCharacteristic (getCharacteristic()); |
---|
[38ffb7] | 2552 | powX= power (y-gamma, l); |
---|
| 2553 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
[11bf82] | 2554 | for (int i= 0; i < l*degMipo; i++) |
---|
| 2555 | { |
---|
[38ffb7] | 2556 | imBasis= mod (power (y, i), powX); |
---|
[11bf82] | 2557 | imBasis= imBasis (power (y, degMipo), y); |
---|
| 2558 | imBasis= imBasis (y, gamma); |
---|
[38ffb7] | 2559 | iter= imBasis; |
---|
[11bf82] | 2560 | for (; iter.hasTerms(); iter++) |
---|
| 2561 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
| 2562 | } |
---|
| 2563 | |
---|
[38ffb7] | 2564 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
[11bf82] | 2565 | *NTLMat= inv (*NTLMat); |
---|
| 2566 | if (GF) |
---|
| 2567 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 2568 | |
---|
[5335ba] | 2569 | truncF= mod (F, power (y, l)); |
---|
[11bf82] | 2570 | if (useOldQs) |
---|
| 2571 | { |
---|
| 2572 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 2573 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
[11bf82] | 2574 | bufQ[i] |
---|
| 2575 | ); |
---|
| 2576 | } |
---|
| 2577 | else |
---|
| 2578 | { |
---|
| 2579 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 2580 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 2581 | } |
---|
| 2582 | useOldQs= true; |
---|
| 2583 | for (int i= 0; i < d; i++) |
---|
| 2584 | { |
---|
| 2585 | if (bounds [i] + 1 <= (l/2)*degMipo) |
---|
| 2586 | { |
---|
| 2587 | int k= tmin (bounds [i] + 1, (l/2)*degMipo); |
---|
[38ffb7] | 2588 | C= CFMatrix (l*degMipo - k, factors.length()); |
---|
[11bf82] | 2589 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 2590 | { |
---|
| 2591 | if (A[ii].size() - 1 >= i) |
---|
| 2592 | { |
---|
| 2593 | if (GF) |
---|
| 2594 | { |
---|
| 2595 | A[ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 2596 | setCharacteristic (getCharacteristic()); |
---|
| 2597 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
| 2598 | if (alpha != gamma) |
---|
| 2599 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 2600 | gamma, source, dest |
---|
| 2601 | ); |
---|
| 2602 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
| 2603 | } |
---|
| 2604 | else |
---|
| 2605 | { |
---|
| 2606 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 2607 | if (alpha != gamma) |
---|
| 2608 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 2609 | gamma, source, dest |
---|
| 2610 | ); |
---|
| 2611 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
| 2612 | } |
---|
[9ebec2] | 2613 | writeInMatrix (C, buf, ii + 1, 0); |
---|
[11bf82] | 2614 | } |
---|
| 2615 | if (GF) |
---|
| 2616 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 2617 | } |
---|
| 2618 | |
---|
| 2619 | if (GF) |
---|
| 2620 | setCharacteristic(getCharacteristic()); |
---|
| 2621 | |
---|
[38ffb7] | 2622 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 2623 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 2624 | transpose (NTLK, NTLK); |
---|
| 2625 | kernel (NTLK, NTLK); |
---|
| 2626 | transpose (NTLK, NTLK); |
---|
| 2627 | NTLN *= NTLK; |
---|
| 2628 | |
---|
| 2629 | if (GF) |
---|
| 2630 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 2631 | |
---|
| 2632 | if (NTLN.NumCols() == 1) |
---|
| 2633 | { |
---|
| 2634 | irreducible= true; |
---|
| 2635 | Variable y= Variable (2); |
---|
| 2636 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 2637 | CFList source, dest; |
---|
| 2638 | tmp= mapDown (tmp, info, source, dest); |
---|
| 2639 | delete [] A; |
---|
| 2640 | delete [] bounds; |
---|
| 2641 | return CFList (tmp); |
---|
| 2642 | } |
---|
| 2643 | } |
---|
| 2644 | } |
---|
| 2645 | |
---|
| 2646 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
| 2647 | { |
---|
| 2648 | if (isReduced (NTLN)) |
---|
| 2649 | { |
---|
[38ffb7] | 2650 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 2651 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 2652 | factorsFoundIndex[i]= 0; |
---|
| 2653 | int factorsFound2= 0; |
---|
| 2654 | CFList result; |
---|
| 2655 | CanonicalForm bufF= F; |
---|
| 2656 | extReconstructionTry (result, bufF, factors,degree (F)+1, factorsFound2, |
---|
| 2657 | factorsFoundIndex, NTLN, false, info, evaluation |
---|
| 2658 | ); |
---|
| 2659 | if (result.length() == NTLN.NumCols()) |
---|
| 2660 | { |
---|
| 2661 | delete [] factorsFoundIndex; |
---|
| 2662 | delete [] A; |
---|
| 2663 | delete [] bounds; |
---|
[3d0075] | 2664 | F= 1; |
---|
[38ffb7] | 2665 | return result; |
---|
| 2666 | } |
---|
[11bf82] | 2667 | delete [] factorsFoundIndex; |
---|
| 2668 | } |
---|
| 2669 | else if (l == precision) |
---|
| 2670 | { |
---|
| 2671 | CanonicalForm bufF= F; |
---|
| 2672 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
| 2673 | CFList result= extReconstruction (bufF, factors, zeroOne, precision, |
---|
| 2674 | NTLN, info, evaluation |
---|
| 2675 | ); |
---|
| 2676 | F= bufF; |
---|
| 2677 | delete [] zeroOne; |
---|
| 2678 | delete [] A; |
---|
| 2679 | delete [] bounds; |
---|
| 2680 | return result; |
---|
| 2681 | } |
---|
| 2682 | } |
---|
| 2683 | oldL2= l; |
---|
| 2684 | l += stepSize; |
---|
| 2685 | stepSize *= 2; |
---|
| 2686 | if (l > precision) |
---|
| 2687 | { |
---|
| 2688 | if (!hitBound) |
---|
| 2689 | { |
---|
| 2690 | hitBound= true; |
---|
| 2691 | l= precision; |
---|
| 2692 | } |
---|
| 2693 | else |
---|
| 2694 | break; |
---|
| 2695 | } |
---|
| 2696 | } |
---|
| 2697 | delete [] bounds; |
---|
| 2698 | delete [] A; |
---|
| 2699 | return CFList(); |
---|
| 2700 | } |
---|
| 2701 | |
---|
| 2702 | CFList |
---|
| 2703 | increasePrecision2 (const CanonicalForm& F, CFList& factors, |
---|
| 2704 | const Variable& alpha, int precision) |
---|
| 2705 | { |
---|
| 2706 | bool irreducible= false; |
---|
| 2707 | int d; |
---|
| 2708 | int* bounds= computeBounds (F, d); |
---|
| 2709 | CFArray * A= new CFArray [factors.length()]; |
---|
| 2710 | CFArray bufQ= CFArray (factors.length()); |
---|
| 2711 | zz_p::init (getCharacteristic()); |
---|
| 2712 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 2713 | zz_pE::init (NTLMipo); |
---|
| 2714 | mat_zz_pE NTLN; |
---|
| 2715 | ident (NTLN, factors.length()); |
---|
| 2716 | int minBound= bounds[0]; |
---|
| 2717 | for (int i= 1; i < d; i++) |
---|
| 2718 | { |
---|
| 2719 | if (bounds[i] != 0) |
---|
| 2720 | minBound= tmin (minBound, bounds[i]); |
---|
| 2721 | } |
---|
| 2722 | int l= tmin (2*(minBound + 1), precision); |
---|
| 2723 | int oldL= l/2; |
---|
| 2724 | int stepSize= 2; |
---|
| 2725 | bool useOldQs= false; |
---|
| 2726 | bool hitBound= false; |
---|
[38ffb7] | 2727 | CFListIterator j; |
---|
| 2728 | CFMatrix C; |
---|
| 2729 | CFArray buf; |
---|
| 2730 | mat_zz_pE* NTLC, NTLK; |
---|
[5335ba] | 2731 | Variable y= F.mvar(); |
---|
| 2732 | CanonicalForm truncF; |
---|
[11bf82] | 2733 | while (l <= precision) |
---|
| 2734 | { |
---|
[38ffb7] | 2735 | j= factors; |
---|
[5335ba] | 2736 | truncF= mod (F, power (y, l)); |
---|
[11bf82] | 2737 | if (useOldQs) |
---|
| 2738 | { |
---|
| 2739 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 2740 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], bufQ[i]); |
---|
[11bf82] | 2741 | } |
---|
| 2742 | else |
---|
| 2743 | { |
---|
| 2744 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 2745 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 2746 | } |
---|
| 2747 | useOldQs= true; |
---|
| 2748 | for (int i= 0; i < d; i++) |
---|
| 2749 | { |
---|
| 2750 | if (bounds [i] + 1 <= l/2) |
---|
| 2751 | { |
---|
| 2752 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 2753 | C= CFMatrix (l - k, factors.length()); |
---|
[11bf82] | 2754 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 2755 | { |
---|
| 2756 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 2757 | { |
---|
[11bf82] | 2758 | buf= getCoeffs (A[ii] [i], k); |
---|
[9ebec2] | 2759 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 2760 | } |
---|
[11bf82] | 2761 | } |
---|
[38ffb7] | 2762 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
| 2763 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 2764 | transpose (NTLK, NTLK); |
---|
| 2765 | kernel (NTLK, NTLK); |
---|
| 2766 | transpose (NTLK, NTLK); |
---|
| 2767 | NTLN *= NTLK; |
---|
| 2768 | if (NTLN.NumCols() == 1) |
---|
| 2769 | { |
---|
| 2770 | irreducible= true; |
---|
| 2771 | delete [] A; |
---|
| 2772 | delete [] bounds; |
---|
| 2773 | return CFList (F); |
---|
| 2774 | } |
---|
| 2775 | } |
---|
| 2776 | } |
---|
| 2777 | |
---|
| 2778 | if (isReduced (NTLN) || l == precision) |
---|
| 2779 | { |
---|
| 2780 | CanonicalForm bufF= F; |
---|
| 2781 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
| 2782 | CFList bufFactors= factors; |
---|
| 2783 | CFList result= monicReconstruction (bufF, factors, zeroOne, precision, |
---|
| 2784 | NTLN |
---|
| 2785 | ); |
---|
| 2786 | if (result.length() != NTLN.NumCols() && l != precision) |
---|
| 2787 | factors= bufFactors; |
---|
| 2788 | if (result.length() == NTLN.NumCols()) |
---|
| 2789 | { |
---|
| 2790 | delete [] zeroOne; |
---|
| 2791 | delete [] A; |
---|
| 2792 | delete [] bounds; |
---|
| 2793 | return result; |
---|
| 2794 | } |
---|
| 2795 | if (l == precision) |
---|
| 2796 | { |
---|
| 2797 | delete [] zeroOne; |
---|
| 2798 | delete [] A; |
---|
| 2799 | delete [] bounds; |
---|
| 2800 | return Union (result, factors); |
---|
| 2801 | } |
---|
| 2802 | } |
---|
| 2803 | oldL= l; |
---|
| 2804 | l += stepSize; |
---|
| 2805 | stepSize *= 2; |
---|
| 2806 | if (l > precision) |
---|
| 2807 | { |
---|
| 2808 | if (!hitBound) |
---|
| 2809 | { |
---|
| 2810 | l= precision; |
---|
| 2811 | hitBound= true; |
---|
| 2812 | } |
---|
| 2813 | else |
---|
| 2814 | break; |
---|
| 2815 | } |
---|
| 2816 | } |
---|
| 2817 | delete [] bounds; |
---|
| 2818 | delete [] A; |
---|
| 2819 | return CFList(); |
---|
| 2820 | } |
---|
| 2821 | |
---|
| 2822 | CFList |
---|
| 2823 | increasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
| 2824 | int oldNumCols, int oldL, const Variable& alpha, |
---|
| 2825 | int precision |
---|
| 2826 | ) |
---|
| 2827 | { |
---|
| 2828 | bool irreducible= false; |
---|
| 2829 | int d; |
---|
| 2830 | int* bounds= computeBounds (F, d); |
---|
| 2831 | int extensionDeg= degree (getMipo (alpha)); |
---|
| 2832 | CFArray * A= new CFArray [factors.length()]; |
---|
| 2833 | CFArray bufQ= CFArray (factors.length()); |
---|
| 2834 | mat_zz_p NTLN; |
---|
| 2835 | ident (NTLN, factors.length()); |
---|
| 2836 | int minBound= bounds[0]; |
---|
| 2837 | for (int i= 1; i < d; i++) |
---|
| 2838 | { |
---|
| 2839 | if (bounds[i] != 0) |
---|
| 2840 | minBound= tmin (minBound, bounds[i]); |
---|
| 2841 | } |
---|
| 2842 | int l= tmax (2*(minBound + 1), oldL); |
---|
| 2843 | int oldL2= l/2; |
---|
| 2844 | int stepSize= 2; |
---|
| 2845 | bool useOldQs= false; |
---|
| 2846 | bool hitBound= false; |
---|
[38ffb7] | 2847 | CFListIterator j; |
---|
| 2848 | CFMatrix C; |
---|
| 2849 | mat_zz_p* NTLC, NTLK; |
---|
| 2850 | CFArray buf; |
---|
[5335ba] | 2851 | Variable y= F.mvar(); |
---|
| 2852 | CanonicalForm truncF; |
---|
[11bf82] | 2853 | while (l <= precision) |
---|
| 2854 | { |
---|
[38ffb7] | 2855 | j= factors; |
---|
[5335ba] | 2856 | truncF= mod (F, power (y, l)); |
---|
[11bf82] | 2857 | if (useOldQs) |
---|
| 2858 | { |
---|
| 2859 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 2860 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
[11bf82] | 2861 | bufQ[i] |
---|
| 2862 | ); |
---|
| 2863 | } |
---|
| 2864 | else |
---|
| 2865 | { |
---|
| 2866 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 2867 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 2868 | } |
---|
| 2869 | useOldQs= true; |
---|
| 2870 | for (int i= 0; i < d; i++) |
---|
| 2871 | { |
---|
| 2872 | if (bounds [i] + 1 <= l/2) |
---|
| 2873 | { |
---|
| 2874 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 2875 | C= CFMatrix ((l - k)*extensionDeg, factors.length()); |
---|
[11bf82] | 2876 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 2877 | { |
---|
| 2878 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 2879 | { |
---|
[11bf82] | 2880 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
[9ebec2] | 2881 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 2882 | } |
---|
[11bf82] | 2883 | } |
---|
[38ffb7] | 2884 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 2885 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 2886 | transpose (NTLK, NTLK); |
---|
| 2887 | kernel (NTLK, NTLK); |
---|
| 2888 | transpose (NTLK, NTLK); |
---|
| 2889 | NTLN *= NTLK; |
---|
| 2890 | if (NTLN.NumCols() == 1) |
---|
| 2891 | { |
---|
| 2892 | irreducible= true; |
---|
| 2893 | delete [] A; |
---|
| 2894 | delete [] bounds; |
---|
| 2895 | return CFList (F); |
---|
| 2896 | } |
---|
| 2897 | } |
---|
| 2898 | } |
---|
| 2899 | |
---|
| 2900 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
| 2901 | { |
---|
| 2902 | if (isReduced (NTLN)) |
---|
| 2903 | { |
---|
| 2904 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 2905 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 2906 | factorsFoundIndex[i]= 0; |
---|
| 2907 | int factorsFound2= 0; |
---|
| 2908 | CFList result; |
---|
| 2909 | CanonicalForm bufF= F; |
---|
| 2910 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
| 2911 | factorsFoundIndex, NTLN, false |
---|
| 2912 | ); |
---|
| 2913 | if (result.length() == NTLN.NumCols()) |
---|
| 2914 | { |
---|
| 2915 | delete [] factorsFoundIndex; |
---|
| 2916 | delete [] A; |
---|
| 2917 | delete [] bounds; |
---|
[3d0075] | 2918 | F= 1; |
---|
[11bf82] | 2919 | return result; |
---|
| 2920 | } |
---|
| 2921 | delete [] factorsFoundIndex; |
---|
| 2922 | } |
---|
| 2923 | else if (l == precision) |
---|
| 2924 | { |
---|
| 2925 | CanonicalForm bufF= F; |
---|
| 2926 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
| 2927 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN); |
---|
| 2928 | F= bufF; |
---|
| 2929 | delete [] zeroOne; |
---|
| 2930 | delete [] A; |
---|
| 2931 | delete [] bounds; |
---|
| 2932 | return result; |
---|
| 2933 | } |
---|
| 2934 | } |
---|
| 2935 | oldL2= l; |
---|
| 2936 | l += stepSize; |
---|
| 2937 | stepSize *= 2; |
---|
| 2938 | if (l > precision) |
---|
| 2939 | { |
---|
| 2940 | if (!hitBound) |
---|
| 2941 | { |
---|
| 2942 | hitBound= true; |
---|
| 2943 | l= precision; |
---|
| 2944 | } |
---|
| 2945 | else |
---|
| 2946 | break; |
---|
| 2947 | } |
---|
| 2948 | } |
---|
| 2949 | delete [] bounds; |
---|
| 2950 | delete [] A; |
---|
| 2951 | return CFList(); |
---|
| 2952 | } |
---|
| 2953 | |
---|
| 2954 | CFList |
---|
| 2955 | increasePrecision (CanonicalForm& F, CFList& factors, int oldL, int |
---|
| 2956 | l, int d, int* bounds, CFArray& bufQ, mat_zz_p& NTLN |
---|
| 2957 | ) |
---|
| 2958 | { |
---|
| 2959 | CFList result= CFList(); |
---|
| 2960 | bool irreducible= false; |
---|
| 2961 | CFArray * A= new CFArray [factors.length()]; |
---|
| 2962 | int oldL2= oldL/2; |
---|
| 2963 | bool hitBound= false; |
---|
| 2964 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 2965 | { |
---|
| 2966 | ident (NTLN, factors.length()); |
---|
| 2967 | bufQ= CFArray (factors.length()); |
---|
| 2968 | } |
---|
| 2969 | bool useOldQs= false; |
---|
[38ffb7] | 2970 | CFListIterator j; |
---|
| 2971 | CFMatrix C; |
---|
| 2972 | CFArray buf; |
---|
| 2973 | mat_zz_p* NTLC, NTLK; |
---|
[5335ba] | 2974 | CanonicalForm bufF, truncF; |
---|
[38ffb7] | 2975 | CFList bufUniFactors; |
---|
[5335ba] | 2976 | Variable y= F.mvar(); |
---|
[11bf82] | 2977 | while (oldL <= l) |
---|
| 2978 | { |
---|
[38ffb7] | 2979 | j= factors; |
---|
[5335ba] | 2980 | truncF= mod (F, power (y, oldL)); |
---|
[11bf82] | 2981 | if (useOldQs) |
---|
| 2982 | { |
---|
| 2983 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 2984 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
[11bf82] | 2985 | bufQ[i] |
---|
| 2986 | ); |
---|
| 2987 | } |
---|
| 2988 | else |
---|
| 2989 | { |
---|
| 2990 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 2991 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
[11bf82] | 2992 | } |
---|
| 2993 | useOldQs= true; |
---|
| 2994 | |
---|
| 2995 | for (int i= 0; i < d; i++) |
---|
| 2996 | { |
---|
| 2997 | if (bounds [i] + 1 <= oldL/2) |
---|
| 2998 | { |
---|
| 2999 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
[38ffb7] | 3000 | C= CFMatrix (oldL - k, factors.length()); |
---|
[11bf82] | 3001 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 3002 | { |
---|
| 3003 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 3004 | { |
---|
[11bf82] | 3005 | buf= getCoeffs (A[ii] [i], k); |
---|
[9ebec2] | 3006 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 3007 | } |
---|
[11bf82] | 3008 | } |
---|
[38ffb7] | 3009 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 3010 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 3011 | transpose (NTLK, NTLK); |
---|
| 3012 | kernel (NTLK, NTLK); |
---|
| 3013 | transpose (NTLK, NTLK); |
---|
| 3014 | NTLN *= NTLK; |
---|
| 3015 | if (NTLN.NumCols() == 1) |
---|
| 3016 | { |
---|
| 3017 | irreducible= true; |
---|
| 3018 | delete [] A; |
---|
| 3019 | return CFList (F); |
---|
| 3020 | } |
---|
| 3021 | } |
---|
| 3022 | } |
---|
| 3023 | if (NTLN.NumCols() == 1) |
---|
| 3024 | { |
---|
| 3025 | irreducible= true; |
---|
| 3026 | delete [] A; |
---|
| 3027 | return CFList (F); |
---|
| 3028 | } |
---|
| 3029 | int * zeroOneVecs; |
---|
| 3030 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
[38ffb7] | 3031 | bufF= F; |
---|
| 3032 | bufUniFactors= factors; |
---|
[11bf82] | 3033 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN); |
---|
| 3034 | delete [] zeroOneVecs; |
---|
| 3035 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < oldL && result.length() > 0) |
---|
| 3036 | { |
---|
[c1b9927] | 3037 | F= bufF; |
---|
[11bf82] | 3038 | factors= bufUniFactors; |
---|
| 3039 | delete [] A; |
---|
| 3040 | return result; |
---|
| 3041 | } |
---|
| 3042 | |
---|
| 3043 | result= CFList(); |
---|
| 3044 | oldL2= oldL; |
---|
| 3045 | oldL *= 2; |
---|
| 3046 | if (oldL > l) |
---|
| 3047 | { |
---|
| 3048 | if (!hitBound) |
---|
| 3049 | { |
---|
| 3050 | oldL= l; |
---|
| 3051 | hitBound= true; |
---|
| 3052 | } |
---|
| 3053 | else |
---|
| 3054 | break; |
---|
| 3055 | } |
---|
| 3056 | } |
---|
| 3057 | delete [] A; |
---|
| 3058 | return result; |
---|
| 3059 | } |
---|
| 3060 | |
---|
| 3061 | CFList |
---|
| 3062 | increasePrecision (CanonicalForm& F, CFList& factors, int oldL, int |
---|
| 3063 | l, int d, int* bounds, CFArray& bufQ, mat_zz_pE& NTLN |
---|
| 3064 | ) |
---|
| 3065 | { |
---|
| 3066 | CFList result= CFList(); |
---|
| 3067 | bool irreducible= false; |
---|
| 3068 | CFArray * A= new CFArray [factors.length()]; |
---|
| 3069 | int oldL2= oldL/2; |
---|
| 3070 | bool hitBound= false; |
---|
| 3071 | bool useOldQs= false; |
---|
| 3072 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 3073 | ident (NTLN, factors.length()); |
---|
[38ffb7] | 3074 | CFListIterator j; |
---|
| 3075 | CFMatrix C; |
---|
| 3076 | CFArray buf; |
---|
| 3077 | mat_zz_pE* NTLC, NTLK; |
---|
[5335ba] | 3078 | CanonicalForm bufF, truncF; |
---|
[38ffb7] | 3079 | CFList bufUniFactors; |
---|
[5335ba] | 3080 | Variable y= F.mvar(); |
---|
[11bf82] | 3081 | while (oldL <= l) |
---|
| 3082 | { |
---|
[38ffb7] | 3083 | j= factors; |
---|
[5335ba] | 3084 | truncF= mod (F, power (y, oldL)); |
---|
[11bf82] | 3085 | if (useOldQs) |
---|
| 3086 | { |
---|
| 3087 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 3088 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
[11bf82] | 3089 | bufQ[i] |
---|
| 3090 | ); |
---|
| 3091 | } |
---|
| 3092 | else |
---|
| 3093 | { |
---|
| 3094 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 3095 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
[11bf82] | 3096 | } |
---|
| 3097 | useOldQs= true; |
---|
| 3098 | |
---|
| 3099 | for (int i= 0; i < d; i++) |
---|
| 3100 | { |
---|
| 3101 | if (bounds [i] + 1 <= oldL/2) |
---|
| 3102 | { |
---|
| 3103 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
[38ffb7] | 3104 | C= CFMatrix (oldL - k, factors.length()); |
---|
[11bf82] | 3105 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 3106 | { |
---|
| 3107 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 3108 | { |
---|
[11bf82] | 3109 | buf= getCoeffs (A[ii] [i], k); |
---|
[9ebec2] | 3110 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 3111 | } |
---|
[11bf82] | 3112 | } |
---|
[38ffb7] | 3113 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
| 3114 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 3115 | transpose (NTLK, NTLK); |
---|
| 3116 | kernel (NTLK, NTLK); |
---|
| 3117 | transpose (NTLK, NTLK); |
---|
| 3118 | NTLN *= NTLK; |
---|
| 3119 | if (NTLN.NumCols() == 1) |
---|
| 3120 | { |
---|
| 3121 | irreducible= true; |
---|
| 3122 | delete [] A; |
---|
| 3123 | return CFList (F); |
---|
| 3124 | } |
---|
| 3125 | } |
---|
| 3126 | } |
---|
| 3127 | if (NTLN.NumCols() == 1) |
---|
| 3128 | { |
---|
| 3129 | irreducible= true; |
---|
| 3130 | delete [] A; |
---|
| 3131 | return CFList (F); |
---|
| 3132 | } |
---|
| 3133 | |
---|
| 3134 | int * zeroOneVecs; |
---|
| 3135 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
[38ffb7] | 3136 | bufF= F; |
---|
| 3137 | bufUniFactors= factors; |
---|
[11bf82] | 3138 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN); |
---|
| 3139 | delete [] zeroOneVecs; |
---|
| 3140 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
| 3141 | { |
---|
[c1b9927] | 3142 | F= bufF; |
---|
[11bf82] | 3143 | factors= bufUniFactors; |
---|
| 3144 | delete [] A; |
---|
| 3145 | return result; |
---|
| 3146 | } |
---|
| 3147 | |
---|
| 3148 | result= CFList(); |
---|
| 3149 | oldL2= oldL; |
---|
| 3150 | oldL *= 2; |
---|
| 3151 | if (oldL > l) |
---|
| 3152 | { |
---|
| 3153 | if (!hitBound) |
---|
| 3154 | { |
---|
| 3155 | oldL= l; |
---|
| 3156 | hitBound= true; |
---|
| 3157 | } |
---|
| 3158 | else |
---|
| 3159 | break; |
---|
| 3160 | } |
---|
| 3161 | } |
---|
| 3162 | delete [] A; |
---|
| 3163 | return result; |
---|
| 3164 | } |
---|
| 3165 | |
---|
| 3166 | //over field extension |
---|
| 3167 | CFList |
---|
| 3168 | extIncreasePrecision (CanonicalForm& F, CFList& factors, int oldL, int l, int d, |
---|
| 3169 | int* bounds, CFArray& bufQ, mat_zz_p& NTLN, const |
---|
| 3170 | CanonicalForm& evaluation, const ExtensionInfo& info, |
---|
| 3171 | CFList& source, CFList& dest |
---|
| 3172 | ) |
---|
| 3173 | { |
---|
| 3174 | CFList result= CFList(); |
---|
| 3175 | bool irreducible= false; |
---|
| 3176 | CFArray * A= new CFArray [factors.length()]; |
---|
| 3177 | int oldL2= oldL/2; //be careful |
---|
| 3178 | bool hitBound= false; |
---|
| 3179 | bool useOldQs= false; |
---|
| 3180 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
| 3181 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
| 3182 | Variable alpha= info.getAlpha(); |
---|
| 3183 | |
---|
| 3184 | Variable gamma= info.getBeta(); |
---|
| 3185 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
| 3186 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
| 3187 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 3188 | ident (NTLN, factors.length()); |
---|
[38ffb7] | 3189 | Variable y= F.mvar(); |
---|
| 3190 | CFListIterator j; |
---|
[5335ba] | 3191 | CanonicalForm powX, imBasis, bufF, truncF; |
---|
[38ffb7] | 3192 | CFMatrix Mat, C; |
---|
| 3193 | CFIterator iter; |
---|
| 3194 | mat_zz_p* NTLMat; |
---|
| 3195 | CFArray buf; |
---|
| 3196 | mat_zz_p* NTLC, NTLK; |
---|
| 3197 | CFList bufUniFactors; |
---|
[11bf82] | 3198 | while (oldL <= l) |
---|
| 3199 | { |
---|
[38ffb7] | 3200 | j= factors; |
---|
[11bf82] | 3201 | if (GF) |
---|
| 3202 | setCharacteristic (getCharacteristic()); |
---|
[38ffb7] | 3203 | |
---|
| 3204 | powX= power (y-gamma, oldL); |
---|
| 3205 | Mat= CFMatrix (oldL*degMipo, oldL*degMipo); |
---|
[11bf82] | 3206 | for (int i= 0; i < oldL*degMipo; i++) |
---|
| 3207 | { |
---|
[38ffb7] | 3208 | imBasis= mod (power (y, i), powX); |
---|
[11bf82] | 3209 | imBasis= imBasis (power (y, degMipo), y); |
---|
| 3210 | imBasis= imBasis (y, gamma); |
---|
[38ffb7] | 3211 | iter= imBasis; |
---|
[11bf82] | 3212 | for (; iter.hasTerms(); iter++) |
---|
| 3213 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
| 3214 | } |
---|
| 3215 | |
---|
[38ffb7] | 3216 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
[11bf82] | 3217 | *NTLMat= inv (*NTLMat); |
---|
| 3218 | if (GF) |
---|
| 3219 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 3220 | |
---|
[5335ba] | 3221 | truncF= mod (F, power (y, oldL)); |
---|
[11bf82] | 3222 | if (useOldQs) |
---|
| 3223 | { |
---|
| 3224 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 3225 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
[11bf82] | 3226 | bufQ[i]); |
---|
| 3227 | } |
---|
| 3228 | else |
---|
| 3229 | { |
---|
| 3230 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 3231 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
[11bf82] | 3232 | } |
---|
| 3233 | useOldQs= true; |
---|
| 3234 | |
---|
| 3235 | for (int i= 0; i < d; i++) |
---|
| 3236 | { |
---|
| 3237 | if (bounds [i] + 1 <= oldL/2) |
---|
| 3238 | { |
---|
| 3239 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
[38ffb7] | 3240 | C= CFMatrix (oldL*degMipo - k, factors.length()); |
---|
[11bf82] | 3241 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 3242 | { |
---|
| 3243 | if (A[ii].size() - 1 >= i) |
---|
| 3244 | { |
---|
| 3245 | if (GF) |
---|
| 3246 | { |
---|
| 3247 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 3248 | setCharacteristic (getCharacteristic()); |
---|
| 3249 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
| 3250 | if (alpha != gamma) |
---|
| 3251 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 3252 | gamma, source, dest |
---|
| 3253 | ); |
---|
| 3254 | buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, *NTLMat); |
---|
| 3255 | } |
---|
| 3256 | else |
---|
| 3257 | { |
---|
| 3258 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 3259 | if (alpha != gamma) |
---|
| 3260 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 3261 | gamma, source, dest |
---|
| 3262 | ); |
---|
| 3263 | buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, *NTLMat); |
---|
| 3264 | } |
---|
[9ebec2] | 3265 | writeInMatrix (C, buf, ii + 1, 0); |
---|
[11bf82] | 3266 | } |
---|
| 3267 | if (GF) |
---|
| 3268 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 3269 | } |
---|
| 3270 | |
---|
| 3271 | if (GF) |
---|
| 3272 | setCharacteristic(getCharacteristic()); |
---|
| 3273 | |
---|
[38ffb7] | 3274 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 3275 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 3276 | transpose (NTLK, NTLK); |
---|
| 3277 | kernel (NTLK, NTLK); |
---|
| 3278 | transpose (NTLK, NTLK); |
---|
| 3279 | NTLN *= NTLK; |
---|
| 3280 | |
---|
| 3281 | if (GF) |
---|
| 3282 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 3283 | |
---|
| 3284 | if (NTLN.NumCols() == 1) |
---|
| 3285 | { |
---|
| 3286 | irreducible= true; |
---|
| 3287 | Variable y= Variable (2); |
---|
| 3288 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 3289 | CFList source, dest; |
---|
| 3290 | tmp= mapDown (tmp, info, source, dest); |
---|
| 3291 | delete [] A; |
---|
| 3292 | return CFList (tmp); |
---|
| 3293 | } |
---|
| 3294 | } |
---|
| 3295 | } |
---|
| 3296 | if (NTLN.NumCols() == 1) |
---|
| 3297 | { |
---|
| 3298 | irreducible= true; |
---|
| 3299 | Variable y= Variable (2); |
---|
| 3300 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 3301 | CFList source, dest; |
---|
| 3302 | tmp= mapDown (tmp, info, source, dest); |
---|
| 3303 | delete [] A; |
---|
| 3304 | return CFList (tmp); |
---|
| 3305 | } |
---|
| 3306 | |
---|
| 3307 | int * zeroOneVecs; |
---|
| 3308 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
[38ffb7] | 3309 | bufF= F; |
---|
| 3310 | bufUniFactors= factors; |
---|
[11bf82] | 3311 | result= extReconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN, |
---|
| 3312 | info, evaluation |
---|
| 3313 | ); |
---|
| 3314 | delete [] zeroOneVecs; |
---|
| 3315 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
| 3316 | { |
---|
[c1b9927] | 3317 | F= bufF; |
---|
[11bf82] | 3318 | factors= bufUniFactors; |
---|
| 3319 | return result; |
---|
| 3320 | } |
---|
| 3321 | |
---|
| 3322 | result= CFList(); |
---|
| 3323 | oldL2= oldL; |
---|
| 3324 | oldL *= 2; |
---|
| 3325 | if (oldL > l) |
---|
| 3326 | { |
---|
| 3327 | if (!hitBound) |
---|
| 3328 | { |
---|
| 3329 | oldL= l; |
---|
| 3330 | hitBound= true; |
---|
| 3331 | } |
---|
| 3332 | else |
---|
| 3333 | break; |
---|
| 3334 | } |
---|
| 3335 | } |
---|
| 3336 | delete [] A; |
---|
| 3337 | return result; |
---|
| 3338 | } |
---|
| 3339 | |
---|
| 3340 | CFList |
---|
| 3341 | increasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int oldL, int l, |
---|
| 3342 | int d, int* bounds, CFArray& bufQ, mat_zz_p& NTLN, |
---|
| 3343 | const Variable& alpha |
---|
| 3344 | ) |
---|
| 3345 | { |
---|
| 3346 | CFList result= CFList(); |
---|
| 3347 | bool irreducible= false; |
---|
| 3348 | CFArray * A= new CFArray [factors.length()]; |
---|
| 3349 | int extensionDeg= degree (getMipo (alpha)); |
---|
| 3350 | int oldL2= oldL/2; |
---|
| 3351 | bool hitBound= false; |
---|
| 3352 | bool useOldQs= false; |
---|
| 3353 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 3354 | ident (NTLN, factors.length()); |
---|
[38ffb7] | 3355 | CFListIterator j; |
---|
| 3356 | CFMatrix C; |
---|
| 3357 | CFArray buf; |
---|
| 3358 | mat_zz_p* NTLC, NTLK; |
---|
[5335ba] | 3359 | CanonicalForm bufF, truncF; |
---|
[38ffb7] | 3360 | CFList bufUniFactors; |
---|
[5335ba] | 3361 | Variable y= F.mvar(); |
---|
[11bf82] | 3362 | while (oldL <= l) |
---|
| 3363 | { |
---|
[38ffb7] | 3364 | j= factors; |
---|
[5335ba] | 3365 | truncF= mod (F, power (y, oldL)); |
---|
[11bf82] | 3366 | if (useOldQs) |
---|
| 3367 | { |
---|
| 3368 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 3369 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
[11bf82] | 3370 | bufQ[i] |
---|
| 3371 | ); |
---|
| 3372 | } |
---|
| 3373 | else |
---|
| 3374 | { |
---|
| 3375 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 3376 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
[11bf82] | 3377 | } |
---|
| 3378 | useOldQs= true; |
---|
| 3379 | |
---|
| 3380 | for (int i= 0; i < d; i++) |
---|
| 3381 | { |
---|
| 3382 | if (bounds [i] + 1 <= oldL/2) |
---|
| 3383 | { |
---|
| 3384 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
[38ffb7] | 3385 | C= CFMatrix ((oldL - k)*extensionDeg, factors.length()); |
---|
[11bf82] | 3386 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 3387 | { |
---|
| 3388 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 3389 | { |
---|
[11bf82] | 3390 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
[9ebec2] | 3391 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 3392 | } |
---|
[11bf82] | 3393 | } |
---|
[38ffb7] | 3394 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 3395 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 3396 | transpose (NTLK, NTLK); |
---|
| 3397 | kernel (NTLK, NTLK); |
---|
| 3398 | transpose (NTLK, NTLK); |
---|
| 3399 | NTLN *= NTLK; |
---|
| 3400 | if (NTLN.NumCols() == 1) |
---|
| 3401 | { |
---|
| 3402 | irreducible= true; |
---|
| 3403 | delete [] A; |
---|
| 3404 | return CFList (F); |
---|
| 3405 | } |
---|
| 3406 | } |
---|
| 3407 | } |
---|
| 3408 | |
---|
| 3409 | int * zeroOneVecs; |
---|
| 3410 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
| 3411 | |
---|
[38ffb7] | 3412 | bufF= F; |
---|
| 3413 | bufUniFactors= factors; |
---|
[11bf82] | 3414 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN); |
---|
| 3415 | delete [] zeroOneVecs; |
---|
| 3416 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
| 3417 | { |
---|
[c1b9927] | 3418 | F= bufF; |
---|
[11bf82] | 3419 | factors= bufUniFactors; |
---|
| 3420 | delete [] A; |
---|
| 3421 | return result; |
---|
| 3422 | } |
---|
| 3423 | |
---|
| 3424 | result= CFList(); |
---|
| 3425 | oldL2= oldL; |
---|
| 3426 | oldL *= 2; |
---|
| 3427 | if (oldL > l) |
---|
| 3428 | { |
---|
| 3429 | if (!hitBound) |
---|
| 3430 | { |
---|
| 3431 | oldL= l; |
---|
| 3432 | hitBound= true; |
---|
| 3433 | } |
---|
| 3434 | else |
---|
| 3435 | break; |
---|
| 3436 | } |
---|
| 3437 | } |
---|
| 3438 | delete [] A; |
---|
| 3439 | return result; |
---|
| 3440 | } |
---|
| 3441 | |
---|
| 3442 | CFList |
---|
| 3443 | furtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& |
---|
| 3444 | factors, int l, int liftBound, int d, int* |
---|
| 3445 | bounds, mat_zz_p& NTLN, CFList& diophant, |
---|
| 3446 | CFMatrix& M, CFArray& Pi, CFArray& bufQ |
---|
| 3447 | ) |
---|
| 3448 | { |
---|
| 3449 | CanonicalForm LCF= LC (F, 1); |
---|
| 3450 | CFList result; |
---|
| 3451 | bool irreducible= false; |
---|
| 3452 | CFList bufFactors= factors; |
---|
| 3453 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
| 3454 | bool useOldQs= false; |
---|
| 3455 | bool hitBound= false; |
---|
| 3456 | int oldL= l; |
---|
| 3457 | int stepSize= 8; //TODO choose better step size? |
---|
| 3458 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
| 3459 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 3460 | ident (NTLN, factors.length()); |
---|
[38ffb7] | 3461 | CFListIterator j; |
---|
| 3462 | CFMatrix C; |
---|
| 3463 | CFArray buf; |
---|
| 3464 | mat_zz_p* NTLC, NTLK; |
---|
[5335ba] | 3465 | CanonicalForm bufF, truncF; |
---|
| 3466 | Variable y= F.mvar(); |
---|
[11bf82] | 3467 | while (l <= liftBound) |
---|
| 3468 | { |
---|
| 3469 | bufFactors.insert (LCF); |
---|
| 3470 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
| 3471 | bufFactors.insert (LCF); |
---|
| 3472 | bufFactors.removeFirst(); |
---|
[38ffb7] | 3473 | j= bufFactors; |
---|
[5335ba] | 3474 | truncF= mod (F, power (y, l)); |
---|
[11bf82] | 3475 | if (useOldQs) |
---|
| 3476 | { |
---|
| 3477 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
[5335ba] | 3478 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
| 3479 | bufQ[i]); |
---|
[11bf82] | 3480 | } |
---|
| 3481 | else |
---|
| 3482 | { |
---|
| 3483 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
[5335ba] | 3484 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 3485 | } |
---|
| 3486 | for (int i= 0; i < d; i++) |
---|
| 3487 | { |
---|
| 3488 | if (bounds [i] + 1 <= l/2) |
---|
| 3489 | { |
---|
| 3490 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 3491 | C= CFMatrix (l - k, bufFactors.length()); |
---|
[11bf82] | 3492 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
| 3493 | { |
---|
| 3494 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 3495 | { |
---|
[11bf82] | 3496 | buf= getCoeffs (A[ii] [i], k); |
---|
[9ebec2] | 3497 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 3498 | } |
---|
[11bf82] | 3499 | } |
---|
[38ffb7] | 3500 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 3501 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 3502 | transpose (NTLK, NTLK); |
---|
| 3503 | kernel (NTLK, NTLK); |
---|
| 3504 | transpose (NTLK, NTLK); |
---|
| 3505 | NTLN *= NTLK; |
---|
| 3506 | if (NTLN.NumCols() == 1) |
---|
| 3507 | { |
---|
| 3508 | irreducible= true; |
---|
| 3509 | break; |
---|
| 3510 | } |
---|
| 3511 | } |
---|
| 3512 | } |
---|
| 3513 | |
---|
| 3514 | if (NTLN.NumCols() == 1) |
---|
| 3515 | { |
---|
| 3516 | irreducible= true; |
---|
| 3517 | break; |
---|
| 3518 | } |
---|
| 3519 | |
---|
| 3520 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
[38ffb7] | 3521 | bufF= F; |
---|
[11bf82] | 3522 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN); |
---|
| 3523 | delete [] zeroOneVecs; |
---|
| 3524 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
| 3525 | { |
---|
| 3526 | F= bufF; |
---|
| 3527 | factors= bufFactors; |
---|
| 3528 | delete [] A; |
---|
| 3529 | return result; |
---|
| 3530 | } |
---|
| 3531 | |
---|
| 3532 | if (isReduced (NTLN)) |
---|
| 3533 | { |
---|
| 3534 | int factorsFound= 0; |
---|
[38ffb7] | 3535 | bufF= F; |
---|
[11bf82] | 3536 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 3537 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 3538 | factorsFoundIndex[i]= 0; |
---|
| 3539 | if (l < liftBound) |
---|
| 3540 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
| 3541 | factorsFoundIndex, NTLN, false |
---|
| 3542 | ); |
---|
| 3543 | else |
---|
| 3544 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
| 3545 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
| 3546 | NTLN, false |
---|
| 3547 | ); |
---|
| 3548 | |
---|
| 3549 | if (NTLN.NumCols() == result.length()) |
---|
| 3550 | { |
---|
| 3551 | delete [] A; |
---|
| 3552 | delete [] factorsFoundIndex; |
---|
| 3553 | return result; |
---|
| 3554 | } |
---|
| 3555 | delete [] factorsFoundIndex; |
---|
| 3556 | } |
---|
| 3557 | result= CFList(); |
---|
| 3558 | oldL= l; |
---|
| 3559 | stepSize *= 2; |
---|
| 3560 | l += stepSize; |
---|
| 3561 | if (l > liftBound) |
---|
| 3562 | { |
---|
| 3563 | if (!hitBound) |
---|
| 3564 | { |
---|
| 3565 | l= liftBound; |
---|
| 3566 | hitBound= true; |
---|
| 3567 | } |
---|
| 3568 | else |
---|
| 3569 | break; |
---|
| 3570 | } |
---|
| 3571 | } |
---|
| 3572 | if (irreducible) |
---|
| 3573 | { |
---|
| 3574 | delete [] A; |
---|
| 3575 | return CFList (F); |
---|
| 3576 | } |
---|
| 3577 | delete [] A; |
---|
| 3578 | factors= bufFactors; |
---|
| 3579 | return CFList(); |
---|
| 3580 | } |
---|
| 3581 | |
---|
| 3582 | //Fq |
---|
| 3583 | CFList |
---|
| 3584 | furtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& |
---|
| 3585 | factors, int l, int liftBound, int d, int* |
---|
| 3586 | bounds, mat_zz_pE& NTLN, CFList& diophant, |
---|
| 3587 | CFMatrix& M, CFArray& Pi, CFArray& bufQ |
---|
| 3588 | ) |
---|
| 3589 | { |
---|
| 3590 | CanonicalForm LCF= LC (F, 1); |
---|
| 3591 | CFList result; |
---|
| 3592 | bool irreducible= false; |
---|
| 3593 | CFList bufFactors= factors; |
---|
| 3594 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
| 3595 | bool useOldQs= false; |
---|
| 3596 | bool hitBound= false; |
---|
| 3597 | int oldL= l; |
---|
| 3598 | int stepSize= 8; //TODO choose better step size? |
---|
| 3599 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
| 3600 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 3601 | ident (NTLN, factors.length()); |
---|
[38ffb7] | 3602 | CFListIterator j; |
---|
| 3603 | CFArray buf; |
---|
| 3604 | mat_zz_pE* NTLC, NTLK; |
---|
[5335ba] | 3605 | CanonicalForm bufF, truncF; |
---|
| 3606 | Variable y= F.mvar(); |
---|
[11bf82] | 3607 | while (l <= liftBound) |
---|
| 3608 | { |
---|
| 3609 | bufFactors.insert (LCF); |
---|
| 3610 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
[38ffb7] | 3611 | j= bufFactors; |
---|
[5335ba] | 3612 | truncF= mod (F, power (y, l)); |
---|
[11bf82] | 3613 | if (useOldQs) |
---|
| 3614 | { |
---|
| 3615 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
[5335ba] | 3616 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
| 3617 | bufQ[i]); |
---|
[11bf82] | 3618 | } |
---|
| 3619 | else |
---|
| 3620 | { |
---|
| 3621 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
[5335ba] | 3622 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 3623 | } |
---|
| 3624 | for (int i= 0; i < d; i++) |
---|
| 3625 | { |
---|
| 3626 | if (bounds [i] + 1 <= l/2) |
---|
| 3627 | { |
---|
| 3628 | int k= tmin (bounds [i] + 1, l/2); |
---|
| 3629 | CFMatrix C= CFMatrix (l - k, bufFactors.length()); |
---|
| 3630 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
| 3631 | { |
---|
| 3632 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 3633 | { |
---|
[11bf82] | 3634 | buf= getCoeffs (A[ii] [i], k); |
---|
[9ebec2] | 3635 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 3636 | } |
---|
[11bf82] | 3637 | } |
---|
[38ffb7] | 3638 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
| 3639 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 3640 | transpose (NTLK, NTLK); |
---|
| 3641 | kernel (NTLK, NTLK); |
---|
| 3642 | transpose (NTLK, NTLK); |
---|
| 3643 | NTLN *= NTLK; |
---|
| 3644 | if (NTLN.NumCols() == 1) |
---|
| 3645 | { |
---|
| 3646 | irreducible= true; |
---|
| 3647 | break; |
---|
| 3648 | } |
---|
| 3649 | } |
---|
| 3650 | } |
---|
| 3651 | if (NTLN.NumCols() == 1) |
---|
| 3652 | { |
---|
| 3653 | irreducible= true; |
---|
| 3654 | break; |
---|
| 3655 | } |
---|
| 3656 | |
---|
[38ffb7] | 3657 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
| 3658 | bufF= F; |
---|
| 3659 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN); |
---|
| 3660 | delete [] zeroOneVecs; |
---|
| 3661 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
| 3662 | { |
---|
| 3663 | F= bufF; |
---|
| 3664 | factors= bufFactors; |
---|
| 3665 | delete [] A; |
---|
| 3666 | return result; |
---|
| 3667 | } |
---|
[11bf82] | 3668 | |
---|
| 3669 | if (isReduced (NTLN)) |
---|
| 3670 | { |
---|
| 3671 | int factorsFound= 0; |
---|
[38ffb7] | 3672 | bufF= F; |
---|
[11bf82] | 3673 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 3674 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 3675 | factorsFoundIndex[i]= 0; |
---|
| 3676 | if (l < liftBound) |
---|
| 3677 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
| 3678 | factorsFoundIndex, NTLN, false |
---|
| 3679 | ); |
---|
| 3680 | else |
---|
| 3681 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
| 3682 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
| 3683 | NTLN, false |
---|
| 3684 | ); |
---|
| 3685 | if (NTLN.NumCols() == result.length()) |
---|
| 3686 | { |
---|
| 3687 | delete [] A; |
---|
| 3688 | delete [] factorsFoundIndex; |
---|
| 3689 | return result; |
---|
| 3690 | } |
---|
| 3691 | delete [] factorsFoundIndex; |
---|
| 3692 | } |
---|
| 3693 | result= CFList(); |
---|
| 3694 | oldL= l; |
---|
| 3695 | stepSize *= 2; |
---|
| 3696 | l += stepSize; |
---|
| 3697 | if (l > liftBound) |
---|
| 3698 | { |
---|
| 3699 | if (!hitBound) |
---|
| 3700 | { |
---|
| 3701 | l= liftBound; |
---|
| 3702 | hitBound= true; |
---|
| 3703 | } |
---|
| 3704 | else |
---|
| 3705 | break; |
---|
| 3706 | } |
---|
| 3707 | } |
---|
| 3708 | if (irreducible) |
---|
| 3709 | { |
---|
| 3710 | delete [] A; |
---|
| 3711 | return CFList (F); |
---|
| 3712 | } |
---|
| 3713 | delete [] A; |
---|
| 3714 | factors= bufFactors; |
---|
| 3715 | return CFList(); |
---|
| 3716 | } |
---|
| 3717 | |
---|
| 3718 | //over field extension |
---|
| 3719 | CFList |
---|
| 3720 | extFurtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& factors, int l, |
---|
| 3721 | int liftBound, int d, int* bounds, |
---|
| 3722 | mat_zz_p& NTLN, CFList& diophant, |
---|
| 3723 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
| 3724 | const CanonicalForm& evaluation, const |
---|
| 3725 | ExtensionInfo& info, CFList& source, |
---|
| 3726 | CFList& dest |
---|
| 3727 | ) |
---|
| 3728 | { |
---|
| 3729 | CanonicalForm LCF= LC (F, 1); |
---|
| 3730 | CFList result; |
---|
| 3731 | bool irreducible= false; |
---|
| 3732 | CFList bufFactors= factors; |
---|
| 3733 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
| 3734 | bool useOldQs= false; |
---|
| 3735 | bool hitBound= false; |
---|
| 3736 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
| 3737 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
| 3738 | Variable alpha= info.getAlpha(); |
---|
| 3739 | int oldL= l; //be careful |
---|
| 3740 | int stepSize= 8; |
---|
| 3741 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l),2); |
---|
| 3742 | Variable gamma= info.getBeta(); |
---|
| 3743 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
| 3744 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
| 3745 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 3746 | ident (NTLN, factors.length()); |
---|
[38ffb7] | 3747 | Variable y= F.mvar(); |
---|
[5335ba] | 3748 | CanonicalForm powX, imBasis, bufF, truncF; |
---|
[38ffb7] | 3749 | CFMatrix Mat, C; |
---|
| 3750 | CFIterator iter; |
---|
| 3751 | mat_zz_p* NTLMat,*NTLC, NTLK; |
---|
| 3752 | CFListIterator j; |
---|
| 3753 | CFArray buf; |
---|
[11bf82] | 3754 | while (l <= liftBound) |
---|
| 3755 | { |
---|
| 3756 | bufFactors.insert (LCF); |
---|
| 3757 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
| 3758 | |
---|
| 3759 | if (GF) |
---|
| 3760 | setCharacteristic (getCharacteristic()); |
---|
| 3761 | |
---|
[38ffb7] | 3762 | powX= power (y-gamma, l); |
---|
| 3763 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
[11bf82] | 3764 | for (int i= 0; i < l*degMipo; i++) |
---|
| 3765 | { |
---|
| 3766 | |
---|
[38ffb7] | 3767 | imBasis= mod (power (y, i), powX); |
---|
[11bf82] | 3768 | imBasis= imBasis (power (y, degMipo), y); |
---|
| 3769 | imBasis= imBasis (y, gamma); |
---|
[38ffb7] | 3770 | iter= imBasis; |
---|
[11bf82] | 3771 | for (; iter.hasTerms(); iter++) |
---|
| 3772 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
| 3773 | } |
---|
| 3774 | |
---|
[38ffb7] | 3775 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
[11bf82] | 3776 | *NTLMat= inv (*NTLMat); |
---|
| 3777 | |
---|
| 3778 | if (GF) |
---|
| 3779 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 3780 | |
---|
[38ffb7] | 3781 | j= bufFactors; |
---|
[5335ba] | 3782 | truncF= mod (F, power (y, l)); |
---|
[11bf82] | 3783 | if (useOldQs) |
---|
| 3784 | { |
---|
| 3785 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
[5335ba] | 3786 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
| 3787 | bufQ[i]); |
---|
[11bf82] | 3788 | } |
---|
| 3789 | else |
---|
| 3790 | { |
---|
| 3791 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
[5335ba] | 3792 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 3793 | } |
---|
| 3794 | for (int i= 0; i < d; i++) |
---|
| 3795 | { |
---|
| 3796 | if (bounds [i] + 1 <= l/2) |
---|
| 3797 | { |
---|
| 3798 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 3799 | C= CFMatrix (l*degMipo - k, bufFactors.length()); |
---|
[11bf82] | 3800 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
| 3801 | { |
---|
| 3802 | if (A[ii].size() - 1 >= i) |
---|
| 3803 | { |
---|
| 3804 | if (GF) |
---|
| 3805 | { |
---|
| 3806 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 3807 | setCharacteristic (getCharacteristic()); |
---|
| 3808 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
| 3809 | if (alpha != gamma) |
---|
| 3810 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 3811 | gamma, source, dest |
---|
| 3812 | ); |
---|
| 3813 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
| 3814 | } |
---|
| 3815 | else |
---|
| 3816 | { |
---|
| 3817 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 3818 | if (alpha != gamma) |
---|
| 3819 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 3820 | gamma, source, dest |
---|
| 3821 | ); |
---|
| 3822 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
| 3823 | } |
---|
[9ebec2] | 3824 | writeInMatrix (C, buf, ii + 1, 0); |
---|
[11bf82] | 3825 | } |
---|
| 3826 | if (GF) |
---|
| 3827 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 3828 | } |
---|
| 3829 | |
---|
| 3830 | if (GF) |
---|
| 3831 | setCharacteristic(getCharacteristic()); |
---|
[38ffb7] | 3832 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 3833 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 3834 | transpose (NTLK, NTLK); |
---|
| 3835 | kernel (NTLK, NTLK); |
---|
| 3836 | transpose (NTLK, NTLK); |
---|
| 3837 | NTLN *= NTLK; |
---|
| 3838 | if (GF) |
---|
| 3839 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 3840 | |
---|
| 3841 | if (NTLN.NumCols() == 1) |
---|
| 3842 | { |
---|
| 3843 | irreducible= true; |
---|
| 3844 | break; |
---|
| 3845 | } |
---|
| 3846 | } |
---|
| 3847 | } |
---|
| 3848 | if (NTLN.NumCols() == 1) |
---|
| 3849 | { |
---|
| 3850 | irreducible= true; |
---|
| 3851 | break; |
---|
| 3852 | } |
---|
| 3853 | |
---|
[38ffb7] | 3854 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
| 3855 | bufF= F; |
---|
| 3856 | result= extReconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN, info, |
---|
| 3857 | evaluation |
---|
| 3858 | ); |
---|
| 3859 | delete [] zeroOneVecs; |
---|
| 3860 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
| 3861 | { |
---|
| 3862 | F= bufF; |
---|
| 3863 | factors= bufFactors; |
---|
| 3864 | delete [] A; |
---|
| 3865 | return result; |
---|
| 3866 | } |
---|
[11bf82] | 3867 | |
---|
| 3868 | if (isReduced (NTLN)) |
---|
| 3869 | { |
---|
| 3870 | int factorsFound= 0; |
---|
[38ffb7] | 3871 | bufF= F; |
---|
[11bf82] | 3872 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 3873 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 3874 | factorsFoundIndex[i]= 0; |
---|
| 3875 | if (l < degree (bufF) + 1 + degree (LCF)) |
---|
| 3876 | extReconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
| 3877 | factorsFoundIndex, NTLN, false, info, evaluation |
---|
| 3878 | ); |
---|
| 3879 | else |
---|
| 3880 | extReconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
| 3881 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
| 3882 | NTLN, false, info, evaluation |
---|
| 3883 | ); |
---|
| 3884 | if (NTLN.NumCols() == result.length()) |
---|
| 3885 | { |
---|
| 3886 | delete [] A; |
---|
| 3887 | delete [] factorsFoundIndex; |
---|
| 3888 | return result; |
---|
| 3889 | } |
---|
| 3890 | delete [] factorsFoundIndex; |
---|
| 3891 | } |
---|
| 3892 | result= CFList(); |
---|
| 3893 | oldL= l; |
---|
| 3894 | stepSize *= 2; |
---|
| 3895 | l += stepSize; |
---|
| 3896 | if (l > liftBound) |
---|
| 3897 | { |
---|
| 3898 | if (!hitBound) |
---|
| 3899 | { |
---|
| 3900 | l= liftBound; |
---|
| 3901 | hitBound= true; |
---|
| 3902 | } |
---|
| 3903 | else |
---|
| 3904 | break; |
---|
| 3905 | } |
---|
| 3906 | } |
---|
| 3907 | if (irreducible) |
---|
| 3908 | { |
---|
| 3909 | delete [] A; |
---|
| 3910 | Variable y= Variable (2); |
---|
| 3911 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 3912 | CFList source, dest; |
---|
| 3913 | tmp= mapDown (tmp, info, source, dest); |
---|
| 3914 | return CFList (tmp); |
---|
| 3915 | } |
---|
| 3916 | delete [] A; |
---|
| 3917 | factors= bufFactors; |
---|
| 3918 | return CFList(); |
---|
| 3919 | } |
---|
| 3920 | |
---|
| 3921 | CFList |
---|
| 3922 | furtherLiftingAndIncreasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int |
---|
| 3923 | l, int liftBound, int d, int* bounds, |
---|
| 3924 | mat_zz_p& NTLN, CFList& diophant, |
---|
| 3925 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
| 3926 | const Variable& alpha |
---|
| 3927 | ) |
---|
| 3928 | { |
---|
| 3929 | CanonicalForm LCF= LC (F, 1); |
---|
| 3930 | CFList result; |
---|
| 3931 | bool irreducible= false; |
---|
| 3932 | CFList bufFactors= factors; |
---|
| 3933 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
| 3934 | bool useOldQs= false; |
---|
| 3935 | int extensionDeg= degree (getMipo (alpha)); |
---|
| 3936 | bool hitBound= false; |
---|
| 3937 | int oldL= l; |
---|
| 3938 | int stepSize= 8; //TODO choose better step size? |
---|
| 3939 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
| 3940 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 3941 | ident (NTLN, factors.length()); |
---|
[38ffb7] | 3942 | CFListIterator j; |
---|
| 3943 | CFMatrix C; |
---|
| 3944 | mat_zz_p* NTLC, NTLK; |
---|
[5335ba] | 3945 | CanonicalForm bufF, truncF; |
---|
| 3946 | Variable y= F.mvar(); |
---|
[11bf82] | 3947 | while (l <= liftBound) |
---|
| 3948 | { |
---|
| 3949 | bufFactors.insert (LCF); |
---|
| 3950 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
[38ffb7] | 3951 | j= bufFactors; |
---|
[5335ba] | 3952 | truncF= mod (F, power (y, l)); |
---|
[11bf82] | 3953 | if (useOldQs) |
---|
| 3954 | { |
---|
| 3955 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
[5335ba] | 3956 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
| 3957 | bufQ[i]); |
---|
[11bf82] | 3958 | } |
---|
| 3959 | else |
---|
| 3960 | { |
---|
| 3961 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
[5335ba] | 3962 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 3963 | } |
---|
| 3964 | for (int i= 0; i < d; i++) |
---|
| 3965 | { |
---|
| 3966 | if (bounds [i] + 1 <= l/2) |
---|
| 3967 | { |
---|
| 3968 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 3969 | C= CFMatrix ((l - k)*extensionDeg, bufFactors.length()); |
---|
[11bf82] | 3970 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
| 3971 | { |
---|
| 3972 | CFArray buf; |
---|
| 3973 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 3974 | { |
---|
[11bf82] | 3975 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
[9ebec2] | 3976 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 3977 | } |
---|
[11bf82] | 3978 | } |
---|
[38ffb7] | 3979 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 3980 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 3981 | transpose (NTLK, NTLK); |
---|
| 3982 | kernel (NTLK, NTLK); |
---|
| 3983 | transpose (NTLK, NTLK); |
---|
| 3984 | NTLN *= NTLK; |
---|
| 3985 | if (NTLN.NumCols() == 1) |
---|
| 3986 | { |
---|
| 3987 | irreducible= true; |
---|
| 3988 | break; |
---|
| 3989 | } |
---|
| 3990 | } |
---|
| 3991 | } |
---|
| 3992 | if (NTLN.NumCols() == 1) |
---|
| 3993 | { |
---|
| 3994 | irreducible= true; |
---|
| 3995 | break; |
---|
| 3996 | } |
---|
| 3997 | |
---|
[38ffb7] | 3998 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
| 3999 | CanonicalForm bufF= F; |
---|
| 4000 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN); |
---|
| 4001 | delete [] zeroOneVecs; |
---|
| 4002 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
| 4003 | { |
---|
| 4004 | F= bufF; |
---|
| 4005 | factors= bufFactors; |
---|
| 4006 | delete [] A; |
---|
| 4007 | return result; |
---|
| 4008 | } |
---|
[11bf82] | 4009 | |
---|
| 4010 | if (isReduced (NTLN)) |
---|
| 4011 | { |
---|
| 4012 | int factorsFound= 0; |
---|
[38ffb7] | 4013 | bufF= F; |
---|
[11bf82] | 4014 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 4015 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 4016 | factorsFoundIndex[i]= 0; |
---|
| 4017 | if (l < degree (bufF) + 1 + degree (LCF)) |
---|
| 4018 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
| 4019 | factorsFoundIndex, NTLN, false |
---|
| 4020 | ); |
---|
| 4021 | else |
---|
| 4022 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
| 4023 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
| 4024 | NTLN, false |
---|
| 4025 | ); |
---|
| 4026 | if (NTLN.NumCols() == result.length()) |
---|
| 4027 | { |
---|
| 4028 | delete [] A; |
---|
| 4029 | delete [] factorsFoundIndex; |
---|
| 4030 | return result; |
---|
| 4031 | } |
---|
| 4032 | delete [] factorsFoundIndex; |
---|
| 4033 | } |
---|
| 4034 | result= CFList(); |
---|
| 4035 | oldL= l; |
---|
| 4036 | stepSize *= 2; |
---|
| 4037 | l += stepSize; |
---|
| 4038 | if (l > liftBound) |
---|
| 4039 | { |
---|
| 4040 | if (!hitBound) |
---|
| 4041 | { |
---|
| 4042 | l= liftBound; |
---|
| 4043 | hitBound= true; |
---|
| 4044 | } |
---|
| 4045 | else |
---|
| 4046 | break; |
---|
| 4047 | } |
---|
| 4048 | } |
---|
| 4049 | if (irreducible) |
---|
| 4050 | { |
---|
| 4051 | delete [] A; |
---|
| 4052 | return CFList (F); |
---|
| 4053 | } |
---|
| 4054 | delete [] A; |
---|
| 4055 | factors= bufFactors; |
---|
| 4056 | return CFList(); |
---|
| 4057 | } |
---|
| 4058 | |
---|
| 4059 | void |
---|
| 4060 | refineAndRestartLift (const CanonicalForm& F, const mat_zz_p& NTLN, int |
---|
| 4061 | liftBound, int l, CFList& factors, CFMatrix& M, CFArray& |
---|
| 4062 | Pi, CFList& diophant |
---|
| 4063 | ) |
---|
| 4064 | { |
---|
| 4065 | CFList bufFactors; |
---|
| 4066 | Variable y= Variable (2); |
---|
| 4067 | CanonicalForm LCF= LC (F, 1); |
---|
[38ffb7] | 4068 | CFListIterator iter; |
---|
| 4069 | CanonicalForm buf; |
---|
[11bf82] | 4070 | for (long i= 1; i <= NTLN.NumCols(); i++) |
---|
| 4071 | { |
---|
[38ffb7] | 4072 | iter= factors; |
---|
| 4073 | buf= 1; |
---|
[11bf82] | 4074 | for (long j= 1; j <= NTLN.NumRows(); j++, iter++) |
---|
| 4075 | { |
---|
| 4076 | if (!IsZero (NTLN (j,i))) |
---|
| 4077 | buf= mulNTL (buf, mod (iter.getItem(), y)); |
---|
| 4078 | } |
---|
| 4079 | bufFactors.append (buf); |
---|
| 4080 | } |
---|
| 4081 | factors= bufFactors; |
---|
| 4082 | M= CFMatrix (liftBound, factors.length()); |
---|
| 4083 | Pi= CFArray(); |
---|
| 4084 | diophant= CFList(); |
---|
| 4085 | factors.insert (LCF); |
---|
| 4086 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 4087 | } |
---|
| 4088 | |
---|
| 4089 | void |
---|
| 4090 | refineAndRestartLift (const CanonicalForm& F, const mat_zz_pE& NTLN, int |
---|
| 4091 | liftBound, int l, CFList& factors, CFMatrix& M, CFArray& |
---|
| 4092 | Pi, CFList& diophant |
---|
| 4093 | ) |
---|
| 4094 | { |
---|
| 4095 | CFList bufFactors; |
---|
| 4096 | Variable y= Variable (2); |
---|
| 4097 | CanonicalForm LCF= LC (F, 1); |
---|
[38ffb7] | 4098 | CFListIterator iter; |
---|
| 4099 | CanonicalForm buf; |
---|
[c1b9927] | 4100 | for (long i= 1; i <= NTLN.NumCols(); i++) |
---|
[11bf82] | 4101 | { |
---|
[38ffb7] | 4102 | iter= factors; |
---|
| 4103 | buf= 1; |
---|
[11bf82] | 4104 | for (long j= 1; j <= NTLN.NumRows(); j++, iter++) |
---|
| 4105 | { |
---|
| 4106 | if (!IsZero (NTLN (j,i))) |
---|
| 4107 | buf= mulNTL (buf, mod (iter.getItem(), y)); |
---|
| 4108 | } |
---|
| 4109 | bufFactors.append (buf); |
---|
| 4110 | } |
---|
| 4111 | factors= bufFactors; |
---|
| 4112 | M= CFMatrix (liftBound, factors.length()); |
---|
| 4113 | Pi= CFArray(); |
---|
| 4114 | diophant= CFList(); |
---|
| 4115 | factors.insert (LCF); |
---|
| 4116 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 4117 | } |
---|
| 4118 | |
---|
| 4119 | CFList |
---|
| 4120 | earlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_p& N, |
---|
| 4121 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
| 4122 | int& factorsFound, bool beenInThres, CFMatrix& M, |
---|
| 4123 | CFArray& Pi, CFList& diophant |
---|
| 4124 | ) |
---|
| 4125 | { |
---|
[a36fcb5] | 4126 | int sizeOfLiftPre; |
---|
| 4127 | int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2)); |
---|
| 4128 | |
---|
| 4129 | Variable y= F.mvar(); |
---|
[11bf82] | 4130 | factorsFound= 0; |
---|
| 4131 | CanonicalForm LCF= LC (F, 1); |
---|
| 4132 | CFList result; |
---|
[a36fcb5] | 4133 | int smallFactorDeg= tmin (11, liftPre [sizeOfLiftPre- 1] + 1); |
---|
[11bf82] | 4134 | mat_zz_p NTLN= N; |
---|
| 4135 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 4136 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 4137 | factorsFoundIndex [i]= 0; |
---|
| 4138 | |
---|
| 4139 | if (degree (F) + 1 > smallFactorDeg) |
---|
| 4140 | { |
---|
| 4141 | if (l < smallFactorDeg) |
---|
| 4142 | { |
---|
| 4143 | factors.insert (LCF); |
---|
| 4144 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
| 4145 | l= smallFactorDeg; |
---|
| 4146 | } |
---|
| 4147 | reconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
| 4148 | factorsFoundIndex, NTLN, beenInThres |
---|
| 4149 | ); |
---|
| 4150 | if (result.length() == NTLN.NumCols()) |
---|
| 4151 | { |
---|
[a36fcb5] | 4152 | delete [] liftPre; |
---|
[11bf82] | 4153 | delete [] factorsFoundIndex; |
---|
| 4154 | return result; |
---|
| 4155 | } |
---|
| 4156 | } |
---|
| 4157 | |
---|
[a36fcb5] | 4158 | int i= sizeOfLiftPre - 1; |
---|
| 4159 | int dummy= 1; |
---|
| 4160 | if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
[11bf82] | 4161 | { |
---|
[a36fcb5] | 4162 | while (i > 0) |
---|
| 4163 | { |
---|
| 4164 | if (l < liftPre[i-1] + 1) |
---|
| 4165 | { |
---|
| 4166 | factors.insert (LCF); |
---|
| 4167 | henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M); |
---|
| 4168 | l= liftPre[i-1] + 1; |
---|
| 4169 | } |
---|
| 4170 | else |
---|
| 4171 | { |
---|
| 4172 | i--; |
---|
| 4173 | if (i != 0) |
---|
| 4174 | continue; |
---|
| 4175 | } |
---|
| 4176 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
| 4177 | factorsFoundIndex, NTLN, beenInThres |
---|
| 4178 | ); |
---|
| 4179 | if (result.length() == NTLN.NumCols()) |
---|
| 4180 | { |
---|
| 4181 | delete [] liftPre; |
---|
| 4182 | delete [] factorsFoundIndex; |
---|
| 4183 | return result; |
---|
| 4184 | } |
---|
| 4185 | i--; |
---|
| 4186 | } |
---|
[11bf82] | 4187 | } |
---|
[a36fcb5] | 4188 | else |
---|
[11bf82] | 4189 | { |
---|
[a36fcb5] | 4190 | i= 1; |
---|
| 4191 | while ((degree (F,y)/4)*i + 4 <= smallFactorDeg) |
---|
| 4192 | i++; |
---|
| 4193 | while (i < 4) |
---|
| 4194 | { |
---|
| 4195 | dummy= tmin (degree (F,y)+1, (degree (F,y)/4)*(i+1)+4); |
---|
| 4196 | if (l < dummy) |
---|
| 4197 | { |
---|
| 4198 | factors.insert (LCF); |
---|
| 4199 | henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M); |
---|
| 4200 | l= dummy; |
---|
| 4201 | } |
---|
| 4202 | else |
---|
| 4203 | { |
---|
| 4204 | i++; |
---|
| 4205 | if (i < 4) |
---|
| 4206 | continue; |
---|
| 4207 | } |
---|
| 4208 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
| 4209 | factorsFoundIndex, NTLN, beenInThres |
---|
| 4210 | ); |
---|
| 4211 | if (result.length() == NTLN.NumCols()) |
---|
| 4212 | { |
---|
| 4213 | delete [] liftPre; |
---|
| 4214 | delete [] factorsFoundIndex; |
---|
| 4215 | return result; |
---|
| 4216 | } |
---|
| 4217 | i++; |
---|
| 4218 | } |
---|
[11bf82] | 4219 | } |
---|
| 4220 | |
---|
[a36fcb5] | 4221 | delete [] liftPre; |
---|
[11bf82] | 4222 | delete [] factorsFoundIndex; |
---|
| 4223 | return result; |
---|
| 4224 | } |
---|
| 4225 | |
---|
| 4226 | CFList |
---|
| 4227 | earlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_pE& N, |
---|
| 4228 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
| 4229 | int& factorsFound, bool beenInThres, CFMatrix& M, |
---|
| 4230 | CFArray& Pi, CFList& diophant |
---|
| 4231 | ) |
---|
| 4232 | { |
---|
[a36fcb5] | 4233 | int sizeOfLiftPre; |
---|
| 4234 | int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2)); |
---|
| 4235 | Variable y= F.mvar(); |
---|
[11bf82] | 4236 | factorsFound= 0; |
---|
| 4237 | CanonicalForm LCF= LC (F, 1); |
---|
| 4238 | CFList result; |
---|
| 4239 | int smallFactorDeg= 11; |
---|
| 4240 | mat_zz_pE NTLN= N; |
---|
| 4241 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 4242 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 4243 | factorsFoundIndex [i]= 0; |
---|
[a36fcb5] | 4244 | |
---|
[11bf82] | 4245 | if (degree (F) + 1 > smallFactorDeg) |
---|
| 4246 | { |
---|
| 4247 | if (l < smallFactorDeg) |
---|
| 4248 | { |
---|
| 4249 | factors.insert (LCF); |
---|
| 4250 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
| 4251 | l= smallFactorDeg; |
---|
| 4252 | } |
---|
| 4253 | reconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
| 4254 | factorsFoundIndex, NTLN, beenInThres |
---|
| 4255 | ); |
---|
| 4256 | if (result.length() == NTLN.NumCols()) |
---|
| 4257 | { |
---|
[a36fcb5] | 4258 | delete [] liftPre; |
---|
[11bf82] | 4259 | delete [] factorsFoundIndex; |
---|
| 4260 | return result; |
---|
| 4261 | } |
---|
| 4262 | } |
---|
| 4263 | |
---|
[a36fcb5] | 4264 | int i= sizeOfLiftPre - 1; |
---|
| 4265 | int dummy= 1; |
---|
| 4266 | if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
[11bf82] | 4267 | { |
---|
[a36fcb5] | 4268 | while (i > 0) |
---|
| 4269 | { |
---|
| 4270 | if (l < liftPre[i-1] + 1) |
---|
| 4271 | { |
---|
| 4272 | factors.insert (LCF); |
---|
| 4273 | henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M); |
---|
| 4274 | l= liftPre[i-1] + 1; |
---|
| 4275 | } |
---|
| 4276 | else |
---|
| 4277 | { |
---|
| 4278 | i--; |
---|
| 4279 | if (i != 0) |
---|
| 4280 | continue; |
---|
| 4281 | } |
---|
| 4282 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
| 4283 | factorsFoundIndex, NTLN, beenInThres |
---|
| 4284 | ); |
---|
| 4285 | if (result.length() == NTLN.NumCols()) |
---|
| 4286 | { |
---|
| 4287 | delete [] liftPre; |
---|
| 4288 | delete [] factorsFoundIndex; |
---|
| 4289 | return result; |
---|
| 4290 | } |
---|
| 4291 | i--; |
---|
| 4292 | } |
---|
[11bf82] | 4293 | } |
---|
[a36fcb5] | 4294 | else |
---|
[11bf82] | 4295 | { |
---|
[a36fcb5] | 4296 | i= 1; |
---|
| 4297 | while ((degree (F,y)/4)*i + 4 <= smallFactorDeg) |
---|
| 4298 | i++; |
---|
| 4299 | while (i < 4) |
---|
| 4300 | { |
---|
| 4301 | dummy= tmin (degree (F,y)+1, (degree (F,y)/4)*(i+1)+4); |
---|
| 4302 | if (l < dummy) |
---|
| 4303 | { |
---|
| 4304 | factors.insert (LCF); |
---|
| 4305 | henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M); |
---|
| 4306 | l= dummy; |
---|
| 4307 | } |
---|
| 4308 | else |
---|
| 4309 | { |
---|
| 4310 | i++; |
---|
| 4311 | if (i < 4) |
---|
| 4312 | continue; |
---|
| 4313 | } |
---|
| 4314 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
| 4315 | factorsFoundIndex, NTLN, beenInThres |
---|
| 4316 | ); |
---|
| 4317 | if (result.length() == NTLN.NumCols()) |
---|
| 4318 | { |
---|
| 4319 | delete [] liftPre; |
---|
| 4320 | delete [] factorsFoundIndex; |
---|
| 4321 | return result; |
---|
| 4322 | } |
---|
| 4323 | i++; |
---|
| 4324 | } |
---|
[11bf82] | 4325 | } |
---|
| 4326 | |
---|
[a36fcb5] | 4327 | delete [] liftPre; |
---|
[11bf82] | 4328 | delete [] factorsFoundIndex; |
---|
| 4329 | return result; |
---|
| 4330 | } |
---|
| 4331 | |
---|
| 4332 | //over field extension |
---|
| 4333 | CFList |
---|
| 4334 | extEarlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_p& N, |
---|
| 4335 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
| 4336 | int& factorsFound, bool beenInThres, CFMatrix& |
---|
| 4337 | M, CFArray& Pi, CFList& diophant, const |
---|
| 4338 | ExtensionInfo& info, const CanonicalForm& |
---|
| 4339 | evaluation |
---|
| 4340 | ) |
---|
| 4341 | { |
---|
[a36fcb5] | 4342 | int sizeOfLiftPre; |
---|
| 4343 | int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2)); |
---|
| 4344 | Variable y= F.mvar(); |
---|
[11bf82] | 4345 | factorsFound= 0; |
---|
| 4346 | CanonicalForm LCF= LC (F, 1); |
---|
| 4347 | CFList result; |
---|
| 4348 | int smallFactorDeg= 11; |
---|
| 4349 | mat_zz_p NTLN= N; |
---|
| 4350 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 4351 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 4352 | factorsFoundIndex [i]= 0; |
---|
| 4353 | |
---|
| 4354 | if (degree (F) + 1 > smallFactorDeg) |
---|
| 4355 | { |
---|
| 4356 | if (l < smallFactorDeg) |
---|
| 4357 | { |
---|
| 4358 | factors.insert (LCF); |
---|
| 4359 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
| 4360 | l= smallFactorDeg; |
---|
| 4361 | } |
---|
| 4362 | extReconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
| 4363 | factorsFoundIndex, NTLN, beenInThres, info, |
---|
| 4364 | evaluation |
---|
[a36fcb5] | 4365 | ); |
---|
[11bf82] | 4366 | if (result.length() == NTLN.NumCols()) |
---|
| 4367 | { |
---|
[a36fcb5] | 4368 | delete [] liftPre; |
---|
[11bf82] | 4369 | delete [] factorsFoundIndex; |
---|
| 4370 | return result; |
---|
| 4371 | } |
---|
| 4372 | } |
---|
| 4373 | |
---|
[a36fcb5] | 4374 | int i= sizeOfLiftPre - 1; |
---|
| 4375 | int dummy= 1; |
---|
| 4376 | if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
[11bf82] | 4377 | { |
---|
[a36fcb5] | 4378 | while (i > 0) |
---|
| 4379 | { |
---|
| 4380 | if (l < liftPre[i-1] + 1) |
---|
| 4381 | { |
---|
| 4382 | factors.insert (LCF); |
---|
| 4383 | henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M); |
---|
| 4384 | l= liftPre[i-1] + 1; |
---|
| 4385 | } |
---|
| 4386 | else |
---|
| 4387 | { |
---|
| 4388 | i--; |
---|
| 4389 | if (i != 0) |
---|
| 4390 | continue; |
---|
| 4391 | } |
---|
| 4392 | extReconstructionTry (result, bufF, factors, l, factorsFound, |
---|
| 4393 | factorsFoundIndex, NTLN, beenInThres, info, |
---|
| 4394 | evaluation |
---|
| 4395 | ); |
---|
| 4396 | if (result.length() == NTLN.NumCols()) |
---|
| 4397 | { |
---|
| 4398 | delete [] liftPre; |
---|
| 4399 | delete [] factorsFoundIndex; |
---|
| 4400 | return result; |
---|
| 4401 | } |
---|
| 4402 | i--; |
---|
| 4403 | } |
---|
[11bf82] | 4404 | } |
---|
[a36fcb5] | 4405 | else |
---|
[11bf82] | 4406 | { |
---|
[a36fcb5] | 4407 | i= 1; |
---|
| 4408 | while ((degree (F,y)/4)*i + 4 <= smallFactorDeg) |
---|
| 4409 | i++; |
---|
| 4410 | while (i < 4) |
---|
| 4411 | { |
---|
| 4412 | dummy= tmin (degree (F,y)+1, (degree (F,y)/4)*(i+1)+4); |
---|
| 4413 | if (l < dummy) |
---|
| 4414 | { |
---|
| 4415 | factors.insert (LCF); |
---|
| 4416 | henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M); |
---|
| 4417 | l= dummy; |
---|
| 4418 | } |
---|
| 4419 | else |
---|
| 4420 | { |
---|
| 4421 | i++; |
---|
| 4422 | if (i < 4) |
---|
| 4423 | continue; |
---|
| 4424 | } |
---|
| 4425 | extReconstructionTry (result, bufF, factors, l, factorsFound, |
---|
| 4426 | factorsFoundIndex, NTLN, beenInThres, info, |
---|
| 4427 | evaluation |
---|
| 4428 | ); |
---|
| 4429 | if (result.length() == NTLN.NumCols()) |
---|
| 4430 | { |
---|
| 4431 | delete [] liftPre; |
---|
| 4432 | delete [] factorsFoundIndex; |
---|
| 4433 | return result; |
---|
| 4434 | } |
---|
| 4435 | i++; |
---|
| 4436 | } |
---|
[11bf82] | 4437 | } |
---|
| 4438 | |
---|
[a36fcb5] | 4439 | delete [] liftPre; |
---|
[11bf82] | 4440 | delete [] factorsFoundIndex; |
---|
| 4441 | return result; |
---|
| 4442 | } |
---|
| 4443 | |
---|
| 4444 | CFList |
---|
[c1b9927] | 4445 | sieveSmallFactors (const CanonicalForm& G, CFList& uniFactors, DegreePattern& |
---|
[11bf82] | 4446 | degPat, CanonicalForm& H, CFList& diophant, CFArray& Pi, |
---|
| 4447 | CFMatrix& M, bool& success, int d |
---|
| 4448 | ) |
---|
| 4449 | { |
---|
| 4450 | CanonicalForm F= G; |
---|
| 4451 | CFList bufUniFactors= uniFactors; |
---|
| 4452 | bufUniFactors.insert (LC (F, 1)); |
---|
| 4453 | int smallFactorDeg= d; |
---|
| 4454 | DegreePattern degs= degPat; |
---|
| 4455 | henselLift12 (F, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
---|
| 4456 | int adaptedLiftBound; |
---|
| 4457 | success= false; |
---|
[1a3011e] | 4458 | int * factorsFoundIndex= new int [uniFactors.length()]; |
---|
| 4459 | for (int i= 0; i < uniFactors.length(); i++) |
---|
| 4460 | factorsFoundIndex [i]= 0; |
---|
| 4461 | CFList earlyFactors; |
---|
| 4462 | earlyFactorDetection (earlyFactors, F, bufUniFactors, adaptedLiftBound, |
---|
| 4463 | factorsFoundIndex, degs, success, smallFactorDeg); |
---|
| 4464 | delete [] factorsFoundIndex; |
---|
[11bf82] | 4465 | if (degs.getLength() == 1) |
---|
| 4466 | { |
---|
| 4467 | degPat= degs; |
---|
| 4468 | return earlyFactors; |
---|
| 4469 | } |
---|
| 4470 | if (success) |
---|
| 4471 | { |
---|
| 4472 | H= F; |
---|
| 4473 | return earlyFactors; |
---|
| 4474 | } |
---|
[69c882] | 4475 | int sizeOldF= size (G); |
---|
| 4476 | if (size (F) < sizeOldF) |
---|
[11bf82] | 4477 | { |
---|
[69c882] | 4478 | H= F; |
---|
[11bf82] | 4479 | success= true; |
---|
| 4480 | return earlyFactors; |
---|
| 4481 | } |
---|
| 4482 | else |
---|
| 4483 | { |
---|
| 4484 | uniFactors= bufUniFactors; |
---|
| 4485 | return CFList(); |
---|
| 4486 | } |
---|
| 4487 | } |
---|
| 4488 | |
---|
| 4489 | CFList |
---|
| 4490 | extSieveSmallFactors (const CanonicalForm& G, CFList& uniFactors, DegreePattern& |
---|
| 4491 | degPat, CanonicalForm& H, CFList& diophant, CFArray& Pi, |
---|
| 4492 | CFMatrix& M, bool& success, int d, const CanonicalForm& |
---|
| 4493 | evaluation, const ExtensionInfo& info |
---|
| 4494 | ) |
---|
| 4495 | { |
---|
| 4496 | CanonicalForm F= G; |
---|
| 4497 | CFList bufUniFactors= uniFactors; |
---|
| 4498 | bufUniFactors.insert (LC (F, 1)); |
---|
| 4499 | int smallFactorDeg= d; |
---|
| 4500 | DegreePattern degs= degPat; |
---|
| 4501 | henselLift12 (F, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
---|
| 4502 | int adaptedLiftBound; |
---|
| 4503 | success= false; |
---|
[1a3011e] | 4504 | int * factorsFoundIndex= new int [uniFactors.length()]; |
---|
| 4505 | for (int i= 0; i < uniFactors.length(); i++) |
---|
| 4506 | factorsFoundIndex [i]= 0; |
---|
| 4507 | CFList earlyFactors; |
---|
| 4508 | extEarlyFactorDetection (earlyFactors, F, bufUniFactors, adaptedLiftBound, |
---|
| 4509 | factorsFoundIndex, degs, success, info, evaluation, |
---|
| 4510 | smallFactorDeg); |
---|
| 4511 | delete [] factorsFoundIndex; |
---|
[11bf82] | 4512 | if (degs.getLength() == 1) |
---|
| 4513 | { |
---|
| 4514 | degPat= degs; |
---|
| 4515 | return earlyFactors; |
---|
| 4516 | } |
---|
| 4517 | if (success) |
---|
| 4518 | { |
---|
| 4519 | H= F; |
---|
| 4520 | return earlyFactors; |
---|
| 4521 | } |
---|
| 4522 | Variable y= F.mvar(); |
---|
[69c882] | 4523 | CanonicalForm shiftedF= G (y - evaluation, y); |
---|
[11bf82] | 4524 | int sizeOldF= size (shiftedF); |
---|
[69c882] | 4525 | if (size (F) < sizeOldF) |
---|
[11bf82] | 4526 | { |
---|
[69c882] | 4527 | H= F (y + evaluation, y); //shift back to zero |
---|
[11bf82] | 4528 | success= true; |
---|
[69c882] | 4529 | return earlyFactors; |
---|
[11bf82] | 4530 | } |
---|
| 4531 | else |
---|
| 4532 | { |
---|
| 4533 | uniFactors= bufUniFactors; |
---|
| 4534 | return CFList(); |
---|
| 4535 | } |
---|
| 4536 | } |
---|
| 4537 | |
---|
| 4538 | CFList |
---|
| 4539 | henselLiftAndLatticeRecombi (const CanonicalForm& G, const CFList& uniFactors, |
---|
| 4540 | const Variable& alpha, const DegreePattern& degPat |
---|
| 4541 | ) |
---|
| 4542 | { |
---|
| 4543 | DegreePattern degs= degPat; |
---|
| 4544 | CanonicalForm F= G; |
---|
| 4545 | CanonicalForm LCF= LC (F, 1); |
---|
| 4546 | Variable y= F.mvar(); |
---|
| 4547 | Variable x= Variable (1); |
---|
| 4548 | int d; |
---|
| 4549 | int* bounds= computeBounds (F, d); |
---|
| 4550 | |
---|
| 4551 | int minBound= bounds[0]; |
---|
| 4552 | for (int i= 1; i < d; i++) |
---|
| 4553 | { |
---|
| 4554 | if (bounds[i] != 0) |
---|
| 4555 | minBound= tmin (minBound, bounds[i]); |
---|
| 4556 | } |
---|
| 4557 | |
---|
| 4558 | CFList bufUniFactors= uniFactors; |
---|
| 4559 | CFArray Pi; |
---|
| 4560 | CFList diophant; |
---|
| 4561 | int liftBound= 2*totaldegree (F) - 1; |
---|
| 4562 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
| 4563 | |
---|
| 4564 | CFList smallFactors; |
---|
| 4565 | CanonicalForm H; |
---|
| 4566 | bool success; |
---|
| 4567 | smallFactors= sieveSmallFactors (F, bufUniFactors, degs, H, diophant, Pi, M, |
---|
| 4568 | success, 2*(minBound + 1) |
---|
| 4569 | ); |
---|
| 4570 | |
---|
| 4571 | if (smallFactors.length() > 0) |
---|
| 4572 | { |
---|
| 4573 | if (smallFactors.length() == 1) |
---|
| 4574 | { |
---|
| 4575 | if (smallFactors.getFirst() == F) |
---|
| 4576 | { |
---|
| 4577 | delete [] bounds; |
---|
| 4578 | return CFList (G); |
---|
| 4579 | } |
---|
| 4580 | } |
---|
| 4581 | if (degs.getLength() <= 1) |
---|
| 4582 | { |
---|
| 4583 | delete [] bounds; |
---|
| 4584 | return smallFactors; |
---|
| 4585 | } |
---|
| 4586 | } |
---|
| 4587 | |
---|
| 4588 | int index; |
---|
[38ffb7] | 4589 | CanonicalForm tmp1, tmp2; |
---|
[11bf82] | 4590 | for (CFListIterator i= smallFactors; i.hasItem(); i++) |
---|
| 4591 | { |
---|
| 4592 | index= 1; |
---|
| 4593 | tmp1= mod (i.getItem(),y); |
---|
| 4594 | tmp1 /= Lc (tmp1); |
---|
| 4595 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
| 4596 | { |
---|
| 4597 | tmp2= mod (j.getItem(), y); |
---|
| 4598 | tmp2 /= Lc (tmp2); |
---|
| 4599 | if (tmp1 == tmp2) |
---|
| 4600 | { |
---|
| 4601 | index++; |
---|
| 4602 | j.remove(index); |
---|
| 4603 | break; |
---|
| 4604 | } |
---|
| 4605 | } |
---|
| 4606 | } |
---|
| 4607 | |
---|
| 4608 | if (bufUniFactors.isEmpty()) |
---|
| 4609 | { |
---|
| 4610 | delete [] bounds; |
---|
| 4611 | return smallFactors; |
---|
| 4612 | } |
---|
| 4613 | |
---|
| 4614 | if (success) |
---|
| 4615 | { |
---|
| 4616 | F= H; |
---|
| 4617 | delete [] bounds; |
---|
| 4618 | bounds= computeBounds (F, d); |
---|
| 4619 | LCF= LC (F, 1); |
---|
| 4620 | |
---|
| 4621 | minBound= bounds[0]; |
---|
| 4622 | for (int i= 1; i < d; i++) |
---|
| 4623 | { |
---|
| 4624 | if (bounds[i] != 0) |
---|
| 4625 | minBound= tmin (minBound, bounds[i]); |
---|
| 4626 | } |
---|
| 4627 | Pi= CFArray(); |
---|
| 4628 | diophant= CFList(); |
---|
| 4629 | liftBound= 2*totaldegree (F) - 1; |
---|
| 4630 | M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
| 4631 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 4632 | degs.intersect (bufDegs); |
---|
| 4633 | degs.refine(); |
---|
| 4634 | if (degs.getLength() <= 1) |
---|
| 4635 | { |
---|
| 4636 | smallFactors.append (F); |
---|
| 4637 | delete [] bounds; |
---|
| 4638 | return smallFactors; |
---|
| 4639 | } |
---|
| 4640 | } |
---|
| 4641 | |
---|
| 4642 | bool reduceFq2Fp= (degree (F) > getCharacteristic()); |
---|
| 4643 | bufUniFactors.insert (LCF); |
---|
| 4644 | int l= 1; |
---|
| 4645 | |
---|
| 4646 | zz_p::init (getCharacteristic()); |
---|
| 4647 | mat_zz_p NTLN; |
---|
| 4648 | if (alpha.level() != 1) |
---|
| 4649 | { |
---|
| 4650 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 4651 | zz_pE::init (NTLMipo); |
---|
| 4652 | } |
---|
| 4653 | mat_zz_pE NTLNe; |
---|
| 4654 | if (alpha.level() == 1) |
---|
| 4655 | ident (NTLN, bufUniFactors.length() - 1); |
---|
| 4656 | else |
---|
| 4657 | { |
---|
| 4658 | if (reduceFq2Fp) |
---|
| 4659 | ident (NTLN, bufUniFactors.length() - 1); |
---|
| 4660 | else |
---|
| 4661 | ident (NTLNe, bufUniFactors.length() - 1); |
---|
| 4662 | } |
---|
| 4663 | bool irreducible= false; |
---|
| 4664 | CFArray bufQ= CFArray (bufUniFactors.length() - 1); |
---|
| 4665 | |
---|
| 4666 | int oldL; |
---|
| 4667 | if (success) |
---|
| 4668 | { |
---|
| 4669 | int start= 0; |
---|
| 4670 | if (alpha.level() == 1) |
---|
| 4671 | oldL= liftAndComputeLattice (F, bounds, d, start, liftBound, minBound, |
---|
| 4672 | bufUniFactors, NTLN, diophant, M, Pi, bufQ, |
---|
| 4673 | irreducible |
---|
| 4674 | ); |
---|
| 4675 | else |
---|
| 4676 | { |
---|
| 4677 | if (reduceFq2Fp) |
---|
| 4678 | oldL= liftAndComputeLatticeFq2Fp (F, bounds, d, start, liftBound, |
---|
| 4679 | minBound, bufUniFactors, NTLN, |
---|
| 4680 | diophant, M, Pi, bufQ, irreducible, |
---|
| 4681 | alpha |
---|
| 4682 | ); |
---|
| 4683 | else |
---|
| 4684 | oldL= liftAndComputeLattice (F, bounds, d, start, liftBound, minBound, |
---|
| 4685 | bufUniFactors, NTLNe, diophant, M, Pi, bufQ, |
---|
| 4686 | irreducible |
---|
| 4687 | ); |
---|
| 4688 | } |
---|
| 4689 | } |
---|
| 4690 | else |
---|
| 4691 | { |
---|
| 4692 | if (alpha.level() == 1) |
---|
| 4693 | oldL= liftAndComputeLattice (F, bounds, d, 2*(minBound + 1), liftBound, |
---|
| 4694 | minBound, bufUniFactors, NTLN, diophant, M, |
---|
| 4695 | Pi, bufQ, irreducible |
---|
| 4696 | ); |
---|
| 4697 | else |
---|
| 4698 | { |
---|
| 4699 | if (reduceFq2Fp) |
---|
| 4700 | oldL= liftAndComputeLatticeFq2Fp (F, bounds, d, 2*(minBound + 1), |
---|
| 4701 | liftBound, minBound, bufUniFactors, |
---|
| 4702 | NTLN, diophant, M, Pi, bufQ, |
---|
| 4703 | irreducible, alpha |
---|
| 4704 | ); |
---|
| 4705 | else |
---|
| 4706 | oldL= liftAndComputeLattice (F, bounds, d, 2*(minBound + 1), liftBound, |
---|
| 4707 | minBound, bufUniFactors, NTLNe, diophant, |
---|
| 4708 | M, Pi, bufQ, irreducible |
---|
| 4709 | ); |
---|
| 4710 | } |
---|
| 4711 | } |
---|
| 4712 | |
---|
| 4713 | bufUniFactors.removeFirst(); |
---|
| 4714 | if (oldL > liftBound) |
---|
| 4715 | { |
---|
| 4716 | delete [] bounds; |
---|
| 4717 | return Union (smallFactors, |
---|
| 4718 | factorRecombination (bufUniFactors, F, |
---|
| 4719 | power (y, degree (F) + 1 + degree (LCF)), |
---|
| 4720 | degs, 1, bufUniFactors.length()/2 |
---|
| 4721 | ) |
---|
| 4722 | ); |
---|
| 4723 | } |
---|
| 4724 | |
---|
| 4725 | l= oldL; |
---|
| 4726 | if (irreducible) |
---|
| 4727 | { |
---|
| 4728 | delete [] bounds; |
---|
| 4729 | return Union (CFList (F), smallFactors); |
---|
| 4730 | } |
---|
| 4731 | |
---|
| 4732 | CanonicalForm yToL= power (y,l); |
---|
| 4733 | |
---|
| 4734 | CFList result; |
---|
| 4735 | if (l >= degree (F) + 1) |
---|
| 4736 | { |
---|
| 4737 | int * factorsFoundIndex; |
---|
| 4738 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4739 | { |
---|
| 4740 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 4741 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 4742 | factorsFoundIndex[i]= 0; |
---|
| 4743 | } |
---|
| 4744 | else |
---|
| 4745 | { |
---|
| 4746 | factorsFoundIndex= new int [NTLNe.NumCols()]; |
---|
| 4747 | for (long i= 0; i < NTLNe.NumCols(); i++) |
---|
| 4748 | factorsFoundIndex[i]= 0; |
---|
| 4749 | } |
---|
| 4750 | int factorsFound= 0; |
---|
| 4751 | CanonicalForm bufF= F; |
---|
| 4752 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4753 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
| 4754 | factorsFound, factorsFoundIndex, NTLN, false |
---|
| 4755 | ); |
---|
| 4756 | else |
---|
| 4757 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
| 4758 | factorsFound, factorsFoundIndex, NTLNe, false |
---|
| 4759 | ); |
---|
| 4760 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4761 | { |
---|
| 4762 | if (result.length() == NTLN.NumCols()) |
---|
| 4763 | { |
---|
| 4764 | delete [] factorsFoundIndex; |
---|
| 4765 | delete [] bounds; |
---|
| 4766 | return Union (result, smallFactors); |
---|
| 4767 | } |
---|
| 4768 | } |
---|
| 4769 | else |
---|
| 4770 | { |
---|
| 4771 | if (result.length() == NTLNe.NumCols()) |
---|
| 4772 | { |
---|
| 4773 | delete [] factorsFoundIndex; |
---|
| 4774 | delete [] bounds; |
---|
| 4775 | return Union (result, smallFactors); |
---|
| 4776 | } |
---|
| 4777 | } |
---|
| 4778 | delete [] factorsFoundIndex; |
---|
| 4779 | } |
---|
| 4780 | if (l >= liftBound) |
---|
| 4781 | { |
---|
| 4782 | int * factorsFoundIndex; |
---|
| 4783 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4784 | { |
---|
[c1b9927] | 4785 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
[11bf82] | 4786 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 4787 | factorsFoundIndex[i]= 0; |
---|
| 4788 | } |
---|
| 4789 | else |
---|
| 4790 | { |
---|
[c1b9927] | 4791 | factorsFoundIndex= new int [NTLNe.NumCols()]; |
---|
[11bf82] | 4792 | for (long i= 0; i < NTLNe.NumCols(); i++) |
---|
| 4793 | factorsFoundIndex[i]= 0; |
---|
| 4794 | } |
---|
| 4795 | CanonicalForm bufF= F; |
---|
| 4796 | int factorsFound= 0; |
---|
| 4797 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4798 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1 + degree |
---|
| 4799 | (LCF), factorsFound, factorsFoundIndex, NTLN, false |
---|
| 4800 | ); |
---|
| 4801 | else |
---|
| 4802 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1 + degree |
---|
| 4803 | (LCF), factorsFound, factorsFoundIndex, NTLNe, false |
---|
| 4804 | ); |
---|
| 4805 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4806 | { |
---|
| 4807 | if (result.length() == NTLN.NumCols()) |
---|
| 4808 | { |
---|
| 4809 | delete [] factorsFoundIndex; |
---|
| 4810 | delete [] bounds; |
---|
| 4811 | return Union (result, smallFactors); |
---|
| 4812 | } |
---|
| 4813 | } |
---|
| 4814 | else |
---|
| 4815 | { |
---|
| 4816 | if (result.length() == NTLNe.NumCols()) |
---|
| 4817 | { |
---|
| 4818 | delete [] factorsFoundIndex; |
---|
| 4819 | delete [] bounds; |
---|
| 4820 | return Union (result, smallFactors); |
---|
| 4821 | } |
---|
| 4822 | } |
---|
| 4823 | delete [] factorsFoundIndex; |
---|
| 4824 | } |
---|
| 4825 | |
---|
| 4826 | result= CFList(); |
---|
| 4827 | bool beenInThres= false; |
---|
| 4828 | int thres= 100; |
---|
| 4829 | if (l <= thres) |
---|
| 4830 | { |
---|
| 4831 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4832 | { |
---|
| 4833 | if (NTLN.NumCols() < bufUniFactors.length()) |
---|
| 4834 | { |
---|
[c1b9927] | 4835 | refineAndRestartLift (F, NTLN, liftBound, l, bufUniFactors, M, Pi, |
---|
[11bf82] | 4836 | diophant |
---|
| 4837 | ); |
---|
| 4838 | beenInThres= true; |
---|
| 4839 | } |
---|
| 4840 | } |
---|
| 4841 | else |
---|
| 4842 | { |
---|
| 4843 | if (NTLNe.NumCols() < bufUniFactors.length()) |
---|
| 4844 | { |
---|
| 4845 | refineAndRestartLift (F, NTLNe, liftBound, l, bufUniFactors, M, Pi, |
---|
| 4846 | diophant |
---|
| 4847 | ); |
---|
| 4848 | beenInThres= true; |
---|
| 4849 | } |
---|
| 4850 | } |
---|
| 4851 | } |
---|
| 4852 | |
---|
| 4853 | CanonicalForm bufF= F; |
---|
| 4854 | int factorsFound= 0; |
---|
| 4855 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 4856 | { |
---|
| 4857 | result= earlyReconstructionAndLifting (F, NTLN, bufF, bufUniFactors, l, |
---|
| 4858 | factorsFound, beenInThres, M, Pi, |
---|
| 4859 | diophant |
---|
| 4860 | ); |
---|
| 4861 | |
---|
| 4862 | if (result.length() == NTLN.NumCols()) |
---|
| 4863 | { |
---|
| 4864 | delete [] bounds; |
---|
| 4865 | return Union (result, smallFactors); |
---|
| 4866 | } |
---|
| 4867 | } |
---|
| 4868 | else |
---|
| 4869 | { |
---|
| 4870 | result= earlyReconstructionAndLifting (F, NTLNe, bufF, bufUniFactors, l, |
---|
| 4871 | factorsFound, beenInThres, M, Pi, |
---|
| 4872 | diophant |
---|
| 4873 | ); |
---|
| 4874 | |
---|
| 4875 | if (result.length() == NTLNe.NumCols()) |
---|
| 4876 | { |
---|
| 4877 | delete [] bounds; |
---|
| 4878 | return Union (result, smallFactors); |
---|
| 4879 | } |
---|
| 4880 | } |
---|
| 4881 | |
---|
| 4882 | if (result.length() > 0) |
---|
| 4883 | { |
---|
| 4884 | if (beenInThres) |
---|
| 4885 | { |
---|
[38ffb7] | 4886 | int index; |
---|
| 4887 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
[11bf82] | 4888 | { |
---|
[38ffb7] | 4889 | index= 1; |
---|
| 4890 | tmp1= mod (i.getItem(), y); |
---|
| 4891 | tmp1 /= Lc (tmp1); |
---|
| 4892 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
[11bf82] | 4893 | { |
---|
[38ffb7] | 4894 | tmp2= mod (j.getItem(), y); |
---|
| 4895 | tmp2 /= Lc (tmp2); |
---|
| 4896 | if (tmp1 == tmp2) |
---|
| 4897 | { |
---|
| 4898 | index++; |
---|
| 4899 | j.remove(index); |
---|
| 4900 | break; |
---|
| 4901 | } |
---|
[11bf82] | 4902 | } |
---|
| 4903 | } |
---|
| 4904 | } |
---|
| 4905 | else |
---|
| 4906 | { |
---|
[38ffb7] | 4907 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
| 4908 | CFList bufBufUniFactors= bufUniFactors; |
---|
| 4909 | CFListIterator iter, iter2; |
---|
| 4910 | CanonicalForm buf; |
---|
[11bf82] | 4911 | CFList factorsConsidered; |
---|
[38ffb7] | 4912 | CanonicalForm tmp; |
---|
| 4913 | for (int i= 0; i < NTLN.NumCols(); i++) |
---|
[11bf82] | 4914 | { |
---|
[38ffb7] | 4915 | if (zeroOne [i] == 0) |
---|
| 4916 | continue; |
---|
| 4917 | iter= bufUniFactors; |
---|
| 4918 | buf= 1; |
---|
| 4919 | factorsConsidered= CFList(); |
---|
| 4920 | for (int j= 0; j < NTLN.NumRows(); j++, iter++) |
---|
[11bf82] | 4921 | { |
---|
[38ffb7] | 4922 | if (!IsZero (NTLN (j + 1,i + 1))) |
---|
| 4923 | { |
---|
| 4924 | factorsConsidered.append (iter.getItem()); |
---|
| 4925 | buf *= mod (iter.getItem(), y); |
---|
| 4926 | } |
---|
[11bf82] | 4927 | } |
---|
[38ffb7] | 4928 | buf /= Lc (buf); |
---|
| 4929 | for (iter2= result; iter2.hasItem(); iter2++) |
---|
[11bf82] | 4930 | { |
---|
[38ffb7] | 4931 | tmp= mod (iter2.getItem(), y); |
---|
| 4932 | tmp /= Lc (tmp); |
---|
| 4933 | if (tmp == buf) |
---|
| 4934 | { |
---|
| 4935 | bufBufUniFactors= Difference (bufBufUniFactors, factorsConsidered); |
---|
| 4936 | break; |
---|
| 4937 | } |
---|
[11bf82] | 4938 | } |
---|
| 4939 | } |
---|
[38ffb7] | 4940 | bufUniFactors= bufBufUniFactors; |
---|
| 4941 | delete [] zeroOne; |
---|
[11bf82] | 4942 | } |
---|
| 4943 | |
---|
| 4944 | int oldNumCols; |
---|
| 4945 | CFList resultBufF; |
---|
| 4946 | irreducible= false; |
---|
| 4947 | |
---|
| 4948 | if (alpha.level() == 1) |
---|
| 4949 | { |
---|
| 4950 | oldNumCols= NTLN.NumCols(); |
---|
| 4951 | resultBufF= increasePrecision (bufF, bufUniFactors, factorsFound, |
---|
| 4952 | oldNumCols, oldL, l |
---|
| 4953 | ); |
---|
| 4954 | } |
---|
| 4955 | else |
---|
| 4956 | { |
---|
| 4957 | if (reduceFq2Fp) |
---|
| 4958 | { |
---|
| 4959 | oldNumCols= NTLN.NumCols(); |
---|
| 4960 | |
---|
| 4961 | resultBufF= increasePrecisionFq2Fp (bufF, bufUniFactors, factorsFound, |
---|
| 4962 | oldNumCols, oldL, alpha, l |
---|
| 4963 | ); |
---|
| 4964 | } |
---|
| 4965 | else |
---|
| 4966 | { |
---|
| 4967 | oldNumCols= NTLNe.NumCols(); |
---|
| 4968 | |
---|
| 4969 | resultBufF= increasePrecision (bufF, bufUniFactors, factorsFound, |
---|
| 4970 | oldNumCols, oldL, alpha, l |
---|
| 4971 | ); |
---|
| 4972 | } |
---|
| 4973 | } |
---|
| 4974 | |
---|
| 4975 | if (bufUniFactors.isEmpty() || degree (bufF) <= 0) |
---|
| 4976 | { |
---|
| 4977 | delete [] bounds; |
---|
| 4978 | result= Union (resultBufF, result); |
---|
| 4979 | return Union (result, smallFactors); |
---|
| 4980 | } |
---|
| 4981 | |
---|
| 4982 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
| 4983 | i.getItem()= mod (i.getItem(), y); |
---|
| 4984 | |
---|
| 4985 | result= Union (result, resultBufF); |
---|
| 4986 | result= Union (result, smallFactors); |
---|
| 4987 | delete [] bounds; |
---|
| 4988 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 4989 | degs.intersect (bufDegs); |
---|
| 4990 | degs.refine(); |
---|
| 4991 | if (degs.getLength() == 1 || bufUniFactors.length() == 1) |
---|
| 4992 | { |
---|
| 4993 | result.append (bufF); |
---|
| 4994 | return result; |
---|
| 4995 | } |
---|
| 4996 | return Union (result, henselLiftAndLatticeRecombi (bufF, bufUniFactors, |
---|
| 4997 | alpha, degs |
---|
| 4998 | ) |
---|
| 4999 | ); |
---|
| 5000 | } |
---|
| 5001 | |
---|
| 5002 | if (l < liftBound) |
---|
| 5003 | { |
---|
| 5004 | if (alpha.level() == 1) |
---|
| 5005 | { |
---|
| 5006 | result=increasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
| 5007 | NTLN |
---|
| 5008 | ); |
---|
| 5009 | } |
---|
| 5010 | else |
---|
| 5011 | { |
---|
| 5012 | if (reduceFq2Fp) |
---|
| 5013 | { |
---|
| 5014 | result=increasePrecisionFq2Fp (F, bufUniFactors, oldL, l, d, bounds, |
---|
| 5015 | bufQ, NTLN, alpha |
---|
| 5016 | ); |
---|
| 5017 | } |
---|
| 5018 | else |
---|
| 5019 | { |
---|
| 5020 | result=increasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
| 5021 | NTLNe |
---|
| 5022 | ); |
---|
| 5023 | } |
---|
| 5024 | } |
---|
| 5025 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 5026 | { |
---|
[c1b9927] | 5027 | if (result.length()== NTLN.NumCols()) |
---|
[11bf82] | 5028 | { |
---|
| 5029 | delete [] bounds; |
---|
| 5030 | result= Union (result, smallFactors); |
---|
| 5031 | return result; |
---|
| 5032 | } |
---|
| 5033 | } |
---|
| 5034 | else |
---|
| 5035 | { |
---|
[c1b9927] | 5036 | if (result.length()== NTLNe.NumCols()) |
---|
[11bf82] | 5037 | { |
---|
| 5038 | delete [] bounds; |
---|
| 5039 | result= Union (result, smallFactors); |
---|
| 5040 | return result; |
---|
| 5041 | } |
---|
| 5042 | } |
---|
| 5043 | |
---|
| 5044 | if (result.isEmpty()) |
---|
| 5045 | { |
---|
| 5046 | if (alpha.level() == 1) |
---|
| 5047 | result= furtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
| 5048 | liftBound, d, bounds, NTLN, |
---|
| 5049 | diophant, M, Pi, bufQ |
---|
| 5050 | ); |
---|
| 5051 | else |
---|
| 5052 | { |
---|
| 5053 | if (reduceFq2Fp) |
---|
| 5054 | result= furtherLiftingAndIncreasePrecisionFq2Fp (F,bufUniFactors, l, |
---|
| 5055 | liftBound, d, bounds, |
---|
| 5056 | NTLN, diophant, M, |
---|
| 5057 | Pi, bufQ, alpha |
---|
| 5058 | ); |
---|
| 5059 | else |
---|
| 5060 | result= furtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
| 5061 | liftBound, d, bounds, |
---|
| 5062 | NTLNe, diophant, M, |
---|
| 5063 | Pi, bufQ |
---|
| 5064 | ); |
---|
| 5065 | } |
---|
| 5066 | |
---|
| 5067 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 5068 | { |
---|
[c1b9927] | 5069 | if (result.length() == NTLN.NumCols()) |
---|
[11bf82] | 5070 | { |
---|
| 5071 | delete [] bounds; |
---|
| 5072 | result= Union (result, smallFactors); |
---|
| 5073 | return result; |
---|
| 5074 | } |
---|
| 5075 | } |
---|
| 5076 | else |
---|
| 5077 | { |
---|
[c1b9927] | 5078 | if (result.length() == NTLNe.NumCols()) |
---|
[11bf82] | 5079 | { |
---|
| 5080 | delete [] bounds; |
---|
| 5081 | result= Union (result, smallFactors); |
---|
| 5082 | return result; |
---|
| 5083 | } |
---|
| 5084 | } |
---|
| 5085 | } |
---|
| 5086 | } |
---|
| 5087 | |
---|
| 5088 | DEBOUTLN (cerr, "lattice recombination failed"); |
---|
| 5089 | |
---|
| 5090 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 5091 | degs.intersect (bufDegs); |
---|
| 5092 | degs.refine(); |
---|
| 5093 | |
---|
| 5094 | delete [] bounds; |
---|
| 5095 | bounds= computeBounds (F, d); |
---|
| 5096 | minBound= bounds[0]; |
---|
| 5097 | for (int i= 1; i < d; i++) |
---|
| 5098 | { |
---|
| 5099 | if (bounds[i] != 0) |
---|
| 5100 | minBound= tmin (minBound, bounds[i]); |
---|
| 5101 | } |
---|
| 5102 | |
---|
| 5103 | if (minBound > 16 || result.length() == 0) |
---|
| 5104 | { |
---|
| 5105 | result= Union (result, smallFactors); |
---|
| 5106 | CanonicalForm MODl= power (y, degree (F) + 1 + degree (LC (F, 1))); |
---|
| 5107 | delete [] bounds; |
---|
| 5108 | return Union (result, factorRecombination (bufUniFactors, F, MODl, degs, 1, |
---|
| 5109 | bufUniFactors.length()/2 |
---|
| 5110 | ) |
---|
| 5111 | ); |
---|
| 5112 | } |
---|
| 5113 | else |
---|
| 5114 | { |
---|
| 5115 | result= Union (result, smallFactors); |
---|
| 5116 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
| 5117 | i.getItem()= mod (i.getItem(), y); |
---|
| 5118 | delete [] bounds; |
---|
| 5119 | return Union (result, henselLiftAndLatticeRecombi (F, bufUniFactors, alpha, |
---|
| 5120 | degs |
---|
| 5121 | ) |
---|
| 5122 | ); |
---|
| 5123 | } |
---|
| 5124 | } |
---|
| 5125 | |
---|
| 5126 | ExtensionInfo |
---|
| 5127 | init4ext (const ExtensionInfo& info, const CanonicalForm& evaluation, |
---|
| 5128 | int& degMipo |
---|
| 5129 | ) |
---|
| 5130 | { |
---|
| 5131 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
| 5132 | Variable alpha= info.getAlpha(); |
---|
| 5133 | if (GF) |
---|
| 5134 | { |
---|
| 5135 | degMipo= getGFDegree(); |
---|
| 5136 | CanonicalForm GFMipo= gf_mipo; |
---|
| 5137 | setCharacteristic (getCharacteristic()); |
---|
| 5138 | GFMipo.mapinto(); |
---|
| 5139 | alpha= rootOf (GFMipo); |
---|
| 5140 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 5141 | } |
---|
| 5142 | else |
---|
| 5143 | { |
---|
| 5144 | alpha= info.getAlpha(); |
---|
| 5145 | degMipo= degree (getMipo (alpha)); |
---|
| 5146 | } |
---|
| 5147 | |
---|
| 5148 | Variable gamma; |
---|
| 5149 | CanonicalForm primElemAlpha, imPrimElemAlpha; |
---|
| 5150 | if ((!GF && evaluation != alpha) || (GF && evaluation != getGFGenerator())) |
---|
| 5151 | { |
---|
| 5152 | CanonicalForm bufEvaluation; |
---|
| 5153 | if (GF) |
---|
| 5154 | { |
---|
| 5155 | setCharacteristic (getCharacteristic()); |
---|
| 5156 | bufEvaluation= GF2FalphaRep (evaluation, alpha); |
---|
| 5157 | } |
---|
| 5158 | else |
---|
| 5159 | bufEvaluation= evaluation; |
---|
| 5160 | CanonicalForm mipo= findMinPoly (bufEvaluation, alpha); |
---|
| 5161 | gamma= rootOf (mipo); |
---|
| 5162 | Variable V_buf; |
---|
[ac8e1a] | 5163 | bool fail= false; |
---|
[11bf82] | 5164 | primElemAlpha= primitiveElement (alpha, V_buf, fail); |
---|
| 5165 | imPrimElemAlpha= map (primElemAlpha, alpha, bufEvaluation, gamma); |
---|
| 5166 | |
---|
| 5167 | if (GF) |
---|
| 5168 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 5169 | } |
---|
| 5170 | else |
---|
| 5171 | gamma= alpha; |
---|
| 5172 | ExtensionInfo info2= ExtensionInfo (alpha, gamma, primElemAlpha, |
---|
| 5173 | imPrimElemAlpha, 1, info.getGFName(), true |
---|
| 5174 | ); |
---|
| 5175 | |
---|
| 5176 | return info2; |
---|
| 5177 | } |
---|
| 5178 | |
---|
| 5179 | CFList |
---|
| 5180 | extHenselLiftAndLatticeRecombi(const CanonicalForm& G, const CFList& uniFactors, |
---|
| 5181 | const ExtensionInfo& extInfo, const |
---|
| 5182 | DegreePattern& degPat, const CanonicalForm& eval |
---|
| 5183 | ) |
---|
| 5184 | { |
---|
| 5185 | CanonicalForm evaluation= eval; |
---|
| 5186 | ExtensionInfo info= extInfo; |
---|
| 5187 | Variable alpha; |
---|
| 5188 | DegreePattern degs= degPat; |
---|
| 5189 | CanonicalForm F= G; |
---|
| 5190 | Variable x= Variable (1); |
---|
| 5191 | Variable y= F.mvar(); |
---|
| 5192 | CFList bufUniFactors= uniFactors; |
---|
| 5193 | |
---|
| 5194 | |
---|
| 5195 | int degMipo; |
---|
| 5196 | ExtensionInfo info2= init4ext (info, evaluation, degMipo); |
---|
| 5197 | |
---|
| 5198 | CFList source, dest; |
---|
| 5199 | CanonicalForm LCF= LC (F, 1); |
---|
| 5200 | |
---|
| 5201 | int d; |
---|
| 5202 | int* bounds= computeBounds (F, d); |
---|
| 5203 | int minBound= bounds[0]; |
---|
| 5204 | for (int i= 1; i < d; i++) |
---|
| 5205 | { |
---|
| 5206 | if (bounds[i] != 0) |
---|
| 5207 | minBound= tmin (minBound, bounds[i]); |
---|
| 5208 | } |
---|
| 5209 | |
---|
| 5210 | |
---|
| 5211 | CFArray Pi; |
---|
| 5212 | CFList diophant; |
---|
| 5213 | int liftBound= tmax ((2*totaldegree (F) - 1)/degMipo + 1, degree (F) + 1 + |
---|
| 5214 | degree (LC (F, 1))); |
---|
| 5215 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
| 5216 | |
---|
| 5217 | CFList smallFactors; |
---|
| 5218 | CanonicalForm H; |
---|
| 5219 | bool success; |
---|
| 5220 | smallFactors= extSieveSmallFactors (F, bufUniFactors, degs, H, diophant, Pi, |
---|
| 5221 | M, success, minBound + 1, evaluation, info |
---|
| 5222 | ); |
---|
| 5223 | |
---|
| 5224 | if (smallFactors.length() > 0) |
---|
| 5225 | { |
---|
| 5226 | if (smallFactors.length() == 1) |
---|
| 5227 | { |
---|
| 5228 | if (smallFactors.getFirst() == F) |
---|
| 5229 | { |
---|
| 5230 | delete [] bounds; |
---|
| 5231 | CFList source, dest; |
---|
| 5232 | CanonicalForm tmp= G (y - evaluation, y); |
---|
| 5233 | tmp= mapDown (tmp, info, source, dest); |
---|
| 5234 | return CFList (tmp); |
---|
| 5235 | } |
---|
| 5236 | } |
---|
| 5237 | if (degs.getLength() <= 1) |
---|
| 5238 | { |
---|
| 5239 | delete [] bounds; |
---|
| 5240 | return smallFactors; |
---|
| 5241 | } |
---|
| 5242 | } |
---|
| 5243 | |
---|
| 5244 | int index; |
---|
[38ffb7] | 5245 | CanonicalForm tmp1, tmp2; |
---|
[11bf82] | 5246 | for (CFListIterator i= smallFactors; i.hasItem(); i++) |
---|
| 5247 | { |
---|
| 5248 | index= 1; |
---|
| 5249 | tmp1= mod (i.getItem(), y - evaluation); |
---|
| 5250 | tmp1 /= Lc (tmp1); |
---|
| 5251 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
| 5252 | { |
---|
| 5253 | tmp2= mod (j.getItem(), y); |
---|
| 5254 | tmp2 /= Lc (tmp2); |
---|
| 5255 | if (tmp1 == tmp2) |
---|
| 5256 | { |
---|
| 5257 | index++; |
---|
| 5258 | j.remove(index); |
---|
| 5259 | break; |
---|
| 5260 | } |
---|
| 5261 | } |
---|
| 5262 | } |
---|
| 5263 | |
---|
| 5264 | if (bufUniFactors.isEmpty()) |
---|
| 5265 | { |
---|
| 5266 | delete [] bounds; |
---|
| 5267 | return smallFactors; |
---|
| 5268 | } |
---|
| 5269 | |
---|
| 5270 | if (success) |
---|
| 5271 | { |
---|
| 5272 | F= H; |
---|
| 5273 | delete [] bounds; |
---|
| 5274 | bounds= computeBounds (F, d); |
---|
| 5275 | LCF= LC (F, 1); |
---|
| 5276 | |
---|
| 5277 | minBound= bounds[0]; |
---|
| 5278 | for (int i= 1; i < d; i++) |
---|
| 5279 | { |
---|
| 5280 | if (bounds[i] != 0) |
---|
| 5281 | minBound= tmin (minBound, bounds[i]); |
---|
| 5282 | } |
---|
| 5283 | Pi= CFArray(); |
---|
| 5284 | diophant= CFList(); |
---|
| 5285 | liftBound=tmax ((2*totaldegree (F) - 1)/degMipo + 1, degree (F) + 1 + |
---|
| 5286 | degree (LC (F, 1))); |
---|
| 5287 | M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
| 5288 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 5289 | degs.intersect (bufDegs); |
---|
| 5290 | degs.refine(); |
---|
| 5291 | if (degs.getLength() <= 1) |
---|
| 5292 | { |
---|
| 5293 | delete [] bounds; |
---|
| 5294 | CFList source, dest; |
---|
| 5295 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 5296 | tmp= mapDown (tmp, info, source, dest); |
---|
| 5297 | smallFactors.append (tmp); |
---|
| 5298 | return smallFactors; |
---|
| 5299 | } |
---|
| 5300 | } |
---|
| 5301 | |
---|
| 5302 | bufUniFactors.insert (LCF); |
---|
| 5303 | int l= 1; |
---|
| 5304 | |
---|
| 5305 | zz_p::init (getCharacteristic()); |
---|
| 5306 | zz_pX NTLMipo; |
---|
| 5307 | mat_zz_p NTLN; |
---|
| 5308 | |
---|
| 5309 | ident (NTLN, bufUniFactors.length() - 1); |
---|
| 5310 | bool irreducible= false; |
---|
| 5311 | CFArray bufQ= CFArray (bufUniFactors.length() - 1); |
---|
| 5312 | |
---|
| 5313 | int oldL; |
---|
| 5314 | if (success) |
---|
| 5315 | { |
---|
| 5316 | int start= 0; |
---|
| 5317 | oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound, start, |
---|
| 5318 | bufUniFactors, NTLN, diophant, M, Pi, bufQ, |
---|
| 5319 | irreducible, evaluation, info2, source, dest |
---|
| 5320 | ); |
---|
| 5321 | } |
---|
| 5322 | else |
---|
| 5323 | { |
---|
| 5324 | oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound, |
---|
| 5325 | minBound + 1, bufUniFactors, NTLN, diophant, |
---|
| 5326 | M, Pi, bufQ, irreducible, evaluation, info2, |
---|
| 5327 | source, dest |
---|
| 5328 | ); |
---|
| 5329 | } |
---|
| 5330 | |
---|
| 5331 | bufUniFactors.removeFirst(); |
---|
| 5332 | if (oldL > liftBound) |
---|
| 5333 | { |
---|
| 5334 | delete [] bounds; |
---|
| 5335 | return Union (smallFactors, extFactorRecombination |
---|
| 5336 | (bufUniFactors, F, |
---|
| 5337 | power (y, degree (F) + 1 + degree (LCF)),info, |
---|
| 5338 | degs, evaluation, 1, bufUniFactors.length()/2 |
---|
| 5339 | ) |
---|
| 5340 | ); |
---|
| 5341 | } |
---|
| 5342 | |
---|
| 5343 | l= oldL; |
---|
| 5344 | if (irreducible) |
---|
| 5345 | { |
---|
| 5346 | delete [] bounds; |
---|
| 5347 | CFList source, dest; |
---|
| 5348 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 5349 | tmp= mapDown (tmp, info, source, dest); |
---|
| 5350 | return Union (CFList (tmp), smallFactors); |
---|
| 5351 | } |
---|
| 5352 | |
---|
| 5353 | CanonicalForm yToL= power (y,l); |
---|
| 5354 | |
---|
| 5355 | CFList result; |
---|
| 5356 | if (l >= degree (F) + 1) |
---|
| 5357 | { |
---|
| 5358 | int * factorsFoundIndex; |
---|
| 5359 | |
---|
| 5360 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 5361 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 5362 | factorsFoundIndex[i]= 0; |
---|
| 5363 | |
---|
| 5364 | int factorsFound= 0; |
---|
| 5365 | CanonicalForm bufF= F; |
---|
| 5366 | |
---|
| 5367 | extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
| 5368 | factorsFound, factorsFoundIndex, NTLN, false, info, |
---|
| 5369 | evaluation |
---|
| 5370 | ); |
---|
| 5371 | |
---|
| 5372 | if (result.length() == NTLN.NumCols()) |
---|
| 5373 | { |
---|
| 5374 | delete [] factorsFoundIndex; |
---|
| 5375 | delete [] bounds; |
---|
| 5376 | return Union (result, smallFactors); |
---|
| 5377 | } |
---|
| 5378 | |
---|
| 5379 | delete [] factorsFoundIndex; |
---|
| 5380 | } |
---|
| 5381 | if (l >= liftBound) |
---|
| 5382 | { |
---|
| 5383 | int * factorsFoundIndex; |
---|
[38ffb7] | 5384 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 5385 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 5386 | factorsFoundIndex[i]= 0; |
---|
[11bf82] | 5387 | CanonicalForm bufF= F; |
---|
| 5388 | int factorsFound= 0; |
---|
| 5389 | |
---|
| 5390 | extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1 + degree |
---|
| 5391 | (LCF), factorsFound, factorsFoundIndex, NTLN, false, |
---|
| 5392 | info, evaluation |
---|
| 5393 | ); |
---|
| 5394 | |
---|
| 5395 | if (result.length() == NTLN.NumCols()) |
---|
| 5396 | { |
---|
| 5397 | delete [] factorsFoundIndex; |
---|
| 5398 | delete [] bounds; |
---|
| 5399 | return Union (result, smallFactors); |
---|
| 5400 | } |
---|
| 5401 | delete [] factorsFoundIndex; |
---|
| 5402 | } |
---|
| 5403 | |
---|
| 5404 | result= CFList(); |
---|
| 5405 | bool beenInThres= false; |
---|
| 5406 | int thres= 100; |
---|
| 5407 | if (l <= thres && bufUniFactors.length() > NTLN.NumCols()) |
---|
| 5408 | { |
---|
| 5409 | refineAndRestartLift (F, NTLN, 2*totaldegree (F)-1, l, bufUniFactors, M, Pi, |
---|
| 5410 | diophant |
---|
| 5411 | ); |
---|
| 5412 | beenInThres= true; |
---|
| 5413 | } |
---|
| 5414 | |
---|
| 5415 | |
---|
| 5416 | CanonicalForm bufF= F; |
---|
| 5417 | int factorsFound= 0; |
---|
| 5418 | |
---|
| 5419 | result= extEarlyReconstructionAndLifting (F, NTLN, bufF, bufUniFactors, l, |
---|
| 5420 | factorsFound, beenInThres, M, Pi, |
---|
| 5421 | diophant, info, evaluation |
---|
| 5422 | ); |
---|
| 5423 | |
---|
| 5424 | if (result.length() == NTLN.NumCols()) |
---|
| 5425 | { |
---|
| 5426 | delete [] bounds; |
---|
| 5427 | return Union (result, smallFactors); |
---|
| 5428 | } |
---|
| 5429 | |
---|
| 5430 | if (result.length() > 0) |
---|
| 5431 | { |
---|
| 5432 | if (beenInThres) |
---|
| 5433 | { |
---|
| 5434 | int index; |
---|
| 5435 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
| 5436 | { |
---|
| 5437 | index= 1; |
---|
| 5438 | tmp1= mod (i.getItem(), y-evaluation); |
---|
| 5439 | tmp1 /= Lc (tmp1); |
---|
| 5440 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
| 5441 | { |
---|
| 5442 | tmp2= mod (j.getItem(), y); |
---|
| 5443 | tmp2 /= Lc (tmp2); |
---|
| 5444 | if (tmp1 == tmp2) |
---|
| 5445 | { |
---|
| 5446 | index++; |
---|
| 5447 | j.remove(index); |
---|
| 5448 | break; |
---|
| 5449 | } |
---|
| 5450 | } |
---|
| 5451 | } |
---|
| 5452 | } |
---|
| 5453 | else |
---|
| 5454 | { |
---|
| 5455 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
| 5456 | CFList bufBufUniFactors= bufUniFactors; |
---|
[38ffb7] | 5457 | CFListIterator iter, iter2; |
---|
| 5458 | CanonicalForm buf; |
---|
| 5459 | CFList factorsConsidered; |
---|
[11bf82] | 5460 | for (int i= 0; i < NTLN.NumCols(); i++) |
---|
| 5461 | { |
---|
| 5462 | if (zeroOne [i] == 0) |
---|
| 5463 | continue; |
---|
[38ffb7] | 5464 | iter= bufUniFactors; |
---|
| 5465 | buf= 1; |
---|
| 5466 | factorsConsidered= CFList(); |
---|
[11bf82] | 5467 | for (int j= 0; j < NTLN.NumRows(); j++, iter++) |
---|
| 5468 | { |
---|
| 5469 | if (!IsZero (NTLN (j + 1,i + 1))) |
---|
| 5470 | { |
---|
| 5471 | factorsConsidered.append (iter.getItem()); |
---|
| 5472 | buf *= mod (iter.getItem(), y); |
---|
| 5473 | } |
---|
| 5474 | } |
---|
| 5475 | buf /= Lc (buf); |
---|
[38ffb7] | 5476 | for (iter2= result; iter2.hasItem(); iter2++) |
---|
[11bf82] | 5477 | { |
---|
| 5478 | CanonicalForm tmp= mod (iter2.getItem(), y - evaluation); |
---|
| 5479 | tmp /= Lc (tmp); |
---|
| 5480 | if (tmp == buf) |
---|
| 5481 | { |
---|
| 5482 | bufBufUniFactors= Difference (bufBufUniFactors, factorsConsidered); |
---|
| 5483 | break; |
---|
| 5484 | } |
---|
| 5485 | } |
---|
| 5486 | } |
---|
| 5487 | bufUniFactors= bufBufUniFactors; |
---|
| 5488 | delete [] zeroOne; |
---|
| 5489 | } |
---|
| 5490 | |
---|
| 5491 | int oldNumCols; |
---|
| 5492 | CFList resultBufF; |
---|
| 5493 | irreducible= false; |
---|
| 5494 | |
---|
| 5495 | oldNumCols= NTLN.NumCols(); |
---|
| 5496 | resultBufF= extIncreasePrecision (bufF, bufUniFactors, factorsFound, |
---|
| 5497 | oldNumCols, oldL, evaluation, info2, |
---|
| 5498 | source, dest, l |
---|
| 5499 | ); |
---|
| 5500 | |
---|
| 5501 | if (bufUniFactors.isEmpty() || degree (bufF) <= 0) |
---|
| 5502 | { |
---|
| 5503 | delete [] bounds; |
---|
| 5504 | result= Union (resultBufF, result); |
---|
| 5505 | return Union (result, smallFactors); |
---|
| 5506 | } |
---|
| 5507 | |
---|
| 5508 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
| 5509 | i.getItem()= mod (i.getItem(), y); |
---|
| 5510 | |
---|
| 5511 | delete [] bounds; |
---|
| 5512 | CFList bufResult; |
---|
| 5513 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 5514 | degs.intersect (bufDegs); |
---|
| 5515 | degs.refine(); |
---|
| 5516 | result= Union (result, smallFactors); |
---|
| 5517 | if (degs.getLength() == 1 || bufUniFactors.length() == 1) |
---|
| 5518 | { |
---|
| 5519 | result.append (bufF); |
---|
| 5520 | return result; |
---|
| 5521 | } |
---|
| 5522 | return Union (result, extHenselLiftAndLatticeRecombi (bufF, bufUniFactors, |
---|
| 5523 | info, degs, evaluation |
---|
| 5524 | ) |
---|
| 5525 | ); |
---|
| 5526 | } |
---|
| 5527 | |
---|
| 5528 | if (l/degMipo < liftBound) |
---|
| 5529 | { |
---|
| 5530 | result=extIncreasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
| 5531 | NTLN, evaluation, info2, source, dest |
---|
| 5532 | ); |
---|
| 5533 | |
---|
[c1b9927] | 5534 | if (result.length()== NTLN.NumCols()) |
---|
[11bf82] | 5535 | { |
---|
| 5536 | delete [] bounds; |
---|
| 5537 | result= Union (result, smallFactors); |
---|
| 5538 | return result; |
---|
| 5539 | } |
---|
| 5540 | |
---|
| 5541 | if (result.isEmpty()) |
---|
| 5542 | { |
---|
| 5543 | result= extFurtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
| 5544 | liftBound, d, bounds, NTLN, |
---|
| 5545 | diophant, M, Pi, bufQ, |
---|
| 5546 | evaluation, info2, source, |
---|
| 5547 | dest |
---|
| 5548 | ); |
---|
[c1b9927] | 5549 | if (result.length()== NTLN.NumCols()) |
---|
[11bf82] | 5550 | { |
---|
| 5551 | delete [] bounds; |
---|
| 5552 | result= Union (result, smallFactors); |
---|
| 5553 | return result; |
---|
| 5554 | } |
---|
| 5555 | } |
---|
| 5556 | } |
---|
| 5557 | |
---|
| 5558 | DEBOUTLN (cerr, "lattice recombination failed"); |
---|
| 5559 | |
---|
| 5560 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 5561 | degs.intersect (bufDegs); |
---|
| 5562 | degs.refine(); |
---|
| 5563 | |
---|
| 5564 | delete [] bounds; |
---|
| 5565 | bounds= computeBounds (F, d); |
---|
| 5566 | minBound= bounds[0]; |
---|
| 5567 | for (int i= 1; i < d; i++) |
---|
| 5568 | { |
---|
| 5569 | if (bounds[i] != 0) |
---|
| 5570 | minBound= tmin (minBound, bounds[i]); |
---|
| 5571 | } |
---|
| 5572 | |
---|
| 5573 | if (minBound > 16 || result.length() == 0) |
---|
| 5574 | { |
---|
| 5575 | result= Union (result, smallFactors); |
---|
| 5576 | CanonicalForm MODl= power (y, degree (F) + 1 + degree (LC (F, 1))); |
---|
| 5577 | delete [] bounds; |
---|
| 5578 | return Union (result, extFactorRecombination (bufUniFactors, F, MODl, info, |
---|
| 5579 | degs, evaluation, 1, |
---|
| 5580 | bufUniFactors.length()/2 |
---|
| 5581 | ) |
---|
| 5582 | ); |
---|
| 5583 | } |
---|
| 5584 | else |
---|
| 5585 | { |
---|
| 5586 | result= Union (result, smallFactors); |
---|
| 5587 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
| 5588 | i.getItem()= mod (i.getItem(), y); |
---|
| 5589 | delete [] bounds; |
---|
| 5590 | return Union (result, extHenselLiftAndLatticeRecombi (F, bufUniFactors, |
---|
| 5591 | info, degs, evaluation |
---|
| 5592 | ) |
---|
| 5593 | ); |
---|
| 5594 | } |
---|
| 5595 | } |
---|
| 5596 | |
---|
| 5597 | CFList |
---|
| 5598 | extBiFactorize (const CanonicalForm& F, const ExtensionInfo& info); |
---|
| 5599 | |
---|
| 5600 | /// bivariate factorization over finite fields as decribed in "Factoring |
---|
| 5601 | /// multivariate polynomials over a finite field" by L Bernardin. |
---|
| 5602 | CFList |
---|
| 5603 | biFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
| 5604 | { |
---|
| 5605 | if (F.inCoeffDomain()) |
---|
| 5606 | return CFList(F); |
---|
| 5607 | |
---|
| 5608 | CanonicalForm A= F; |
---|
| 5609 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
| 5610 | |
---|
| 5611 | Variable alpha= info.getAlpha(); |
---|
| 5612 | Variable beta= info.getBeta(); |
---|
| 5613 | CanonicalForm gamma= info.getGamma(); |
---|
| 5614 | CanonicalForm delta= info.getDelta(); |
---|
| 5615 | int k= info.getGFDegree(); |
---|
| 5616 | bool extension= info.isInExtension(); |
---|
| 5617 | if (A.isUnivariate()) |
---|
| 5618 | { |
---|
| 5619 | if (extension == false) |
---|
| 5620 | return uniFactorizer (F, alpha, GF); |
---|
| 5621 | else |
---|
| 5622 | { |
---|
| 5623 | CFList source, dest; |
---|
| 5624 | A= mapDown (A, info, source, dest); |
---|
| 5625 | return uniFactorizer (A, beta, GF); |
---|
| 5626 | } |
---|
| 5627 | } |
---|
| 5628 | |
---|
| 5629 | CFMap N; |
---|
| 5630 | A= compress (A, N); |
---|
| 5631 | Variable y= A.mvar(); |
---|
| 5632 | |
---|
| 5633 | if (y.level() > 2) return CFList (F); |
---|
| 5634 | Variable x= Variable (1); |
---|
| 5635 | |
---|
| 5636 | //remove and factorize content |
---|
| 5637 | CanonicalForm contentAx= content (A, x); |
---|
| 5638 | CanonicalForm contentAy= content (A); |
---|
| 5639 | |
---|
| 5640 | A= A/(contentAx*contentAy); |
---|
| 5641 | CFList contentAxFactors, contentAyFactors; |
---|
| 5642 | |
---|
| 5643 | if (!extension) |
---|
| 5644 | { |
---|
| 5645 | contentAxFactors= uniFactorizer (contentAx, alpha, GF); |
---|
| 5646 | contentAyFactors= uniFactorizer (contentAy, alpha, GF); |
---|
| 5647 | } |
---|
| 5648 | |
---|
| 5649 | //trivial case |
---|
| 5650 | CFList factors; |
---|
| 5651 | if (A.inCoeffDomain()) |
---|
| 5652 | { |
---|
| 5653 | append (factors, contentAxFactors); |
---|
| 5654 | append (factors, contentAyFactors); |
---|
| 5655 | decompress (factors, N); |
---|
| 5656 | return factors; |
---|
| 5657 | } |
---|
| 5658 | else if (A.isUnivariate()) |
---|
| 5659 | { |
---|
| 5660 | factors= uniFactorizer (A, alpha, GF); |
---|
| 5661 | append (factors, contentAxFactors); |
---|
| 5662 | append (factors, contentAyFactors); |
---|
| 5663 | decompress (factors, N); |
---|
| 5664 | return factors; |
---|
| 5665 | } |
---|
| 5666 | |
---|
[0777ea] | 5667 | //check trivial case |
---|
| 5668 | if (degree (A) == 1 || degree (A, 1) == 1) |
---|
| 5669 | { |
---|
| 5670 | factors.append (A); |
---|
| 5671 | |
---|
| 5672 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
| 5673 | false, false, N); |
---|
| 5674 | |
---|
| 5675 | normalize (factors); |
---|
| 5676 | return factors; |
---|
| 5677 | } |
---|
| 5678 | |
---|
[11bf82] | 5679 | // check derivatives |
---|
| 5680 | bool derivXZero= false; |
---|
| 5681 | CanonicalForm derivX= deriv (A, x); |
---|
| 5682 | CanonicalForm gcdDerivX; |
---|
| 5683 | if (derivX.isZero()) |
---|
| 5684 | derivXZero= true; |
---|
| 5685 | else |
---|
| 5686 | { |
---|
| 5687 | gcdDerivX= gcd (A, derivX); |
---|
| 5688 | if (degree (gcdDerivX) > 0) |
---|
| 5689 | { |
---|
| 5690 | CanonicalForm g= A/gcdDerivX; |
---|
| 5691 | CFList factorsG= |
---|
| 5692 | Union (biFactorize (g, info), biFactorize (gcdDerivX, info)); |
---|
| 5693 | append (factorsG, contentAxFactors); |
---|
| 5694 | append (factorsG, contentAyFactors); |
---|
| 5695 | decompress (factorsG, N); |
---|
| 5696 | normalize (factors); |
---|
| 5697 | return factorsG; |
---|
| 5698 | } |
---|
| 5699 | } |
---|
| 5700 | bool derivYZero= false; |
---|
| 5701 | CanonicalForm derivY= deriv (A, y); |
---|
| 5702 | CanonicalForm gcdDerivY; |
---|
| 5703 | if (derivY.isZero()) |
---|
| 5704 | derivYZero= true; |
---|
| 5705 | else |
---|
| 5706 | { |
---|
| 5707 | gcdDerivY= gcd (A, derivY); |
---|
| 5708 | if (degree (gcdDerivY) > 0) |
---|
| 5709 | { |
---|
| 5710 | CanonicalForm g= A/gcdDerivY; |
---|
| 5711 | CFList factorsG= |
---|
| 5712 | Union (biFactorize (g, info), biFactorize (gcdDerivY, info)); |
---|
| 5713 | append (factorsG, contentAxFactors); |
---|
| 5714 | append (factorsG, contentAyFactors); |
---|
| 5715 | decompress (factorsG, N); |
---|
| 5716 | normalize (factors); |
---|
| 5717 | return factorsG; |
---|
| 5718 | } |
---|
| 5719 | } |
---|
| 5720 | //main variable is chosen s.t. the degree in x is minimal |
---|
| 5721 | bool swap= false; |
---|
| 5722 | if ((degree (A) > degree (A, x)) || derivXZero) |
---|
| 5723 | { |
---|
| 5724 | if (!derivYZero) |
---|
| 5725 | { |
---|
| 5726 | A= swapvar (A, y, x); |
---|
| 5727 | swap= derivXZero; |
---|
| 5728 | derivXZero= derivYZero; |
---|
| 5729 | derivYZero= swap; |
---|
| 5730 | swap= true; |
---|
| 5731 | } |
---|
| 5732 | } |
---|
| 5733 | |
---|
| 5734 | bool fail= false; |
---|
| 5735 | CanonicalForm Aeval, evaluation, bufAeval, bufEvaluation, buf; |
---|
| 5736 | CFList uniFactors, list, bufUniFactors; |
---|
| 5737 | DegreePattern degs; |
---|
| 5738 | DegreePattern bufDegs; |
---|
| 5739 | |
---|
| 5740 | bool fail2= false; |
---|
| 5741 | CanonicalForm Aeval2, evaluation2, bufAeval2, bufEvaluation2; |
---|
| 5742 | CFList bufUniFactors2, list2, uniFactors2; |
---|
| 5743 | DegreePattern degs2; |
---|
| 5744 | DegreePattern bufDegs2; |
---|
| 5745 | bool swap2= false; |
---|
| 5746 | |
---|
| 5747 | // several univariate factorizations to obtain more information about the |
---|
| 5748 | // degree pattern therefore usually less combinations have to be tried during |
---|
| 5749 | // the recombination process |
---|
| 5750 | int factorNums= 3; |
---|
| 5751 | int subCheck1= substituteCheck (A, x); |
---|
| 5752 | int subCheck2= substituteCheck (A, y); |
---|
| 5753 | for (int i= 0; i < factorNums; i++) |
---|
| 5754 | { |
---|
| 5755 | bufAeval= A; |
---|
| 5756 | bufEvaluation= evalPoint (A, bufAeval, alpha, list, GF, fail); |
---|
| 5757 | if (!derivXZero && !fail2) |
---|
| 5758 | { |
---|
| 5759 | buf= swapvar (A, x, y); |
---|
| 5760 | bufAeval2= buf; |
---|
| 5761 | bufEvaluation2= evalPoint (buf, bufAeval2, alpha, list2, GF, fail2); |
---|
| 5762 | } |
---|
| 5763 | // first try to change main variable if there is no valid evaluation point |
---|
| 5764 | if (fail && (i == 0)) |
---|
| 5765 | { |
---|
| 5766 | if (!derivXZero && !fail2) |
---|
| 5767 | { |
---|
| 5768 | bufEvaluation= bufEvaluation2; |
---|
| 5769 | int dummy= subCheck2; |
---|
| 5770 | subCheck2= subCheck1; |
---|
| 5771 | subCheck1= dummy; |
---|
| 5772 | A= buf; |
---|
| 5773 | bufAeval= bufAeval2; |
---|
| 5774 | swap2= true; |
---|
| 5775 | fail= false; |
---|
| 5776 | } |
---|
| 5777 | else |
---|
| 5778 | fail= true; |
---|
| 5779 | } |
---|
| 5780 | |
---|
| 5781 | // if there is no valid evaluation point pass to a field extension |
---|
| 5782 | if (fail && (i == 0)) |
---|
| 5783 | { |
---|
| 5784 | factors= extBiFactorize (A, info); |
---|
| 5785 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
| 5786 | swap, swap2, N); |
---|
| 5787 | normalize (factors); |
---|
| 5788 | return factors; |
---|
| 5789 | } |
---|
| 5790 | |
---|
| 5791 | // there is at least one valid evaluation point |
---|
| 5792 | // but we do not compute more univariate factorization over an extension |
---|
| 5793 | if (fail && (i != 0)) |
---|
| 5794 | break; |
---|
| 5795 | |
---|
| 5796 | // univariate factorization |
---|
| 5797 | TIMING_START (fac_uni_factorizer); |
---|
| 5798 | bufUniFactors= uniFactorizer (bufAeval, alpha, GF); |
---|
| 5799 | TIMING_END_AND_PRINT (fac_uni_factorizer, |
---|
[7bf145] | 5800 | "time for univariate factorization: "); |
---|
[806c18] | 5801 | DEBOUTLN (cerr, "Lc (bufAeval)*prod (bufUniFactors)== bufAeval " << |
---|
[f3a82f4] | 5802 | (prod (bufUniFactors)*Lc (bufAeval) == bufAeval)); |
---|
[7bf145] | 5803 | |
---|
| 5804 | if (!derivXZero && !fail2) |
---|
| 5805 | { |
---|
| 5806 | TIMING_START (fac_uni_factorizer); |
---|
| 5807 | bufUniFactors2= uniFactorizer (bufAeval2, alpha, GF); |
---|
[806c18] | 5808 | TIMING_END_AND_PRINT (fac_uni_factorizer, |
---|
[7bf145] | 5809 | "time for univariate factorization in y: "); |
---|
[806c18] | 5810 | DEBOUTLN (cerr, "Lc (Aeval2)*prod (uniFactors2)== Aeval2 " << |
---|
[f3a82f4] | 5811 | (prod (bufUniFactors2)*Lc (bufAeval2) == bufAeval2)); |
---|
[7bf145] | 5812 | } |
---|
| 5813 | |
---|
[806c18] | 5814 | if (bufUniFactors.length() == 1 || |
---|
| 5815 | (!fail2 && !derivXZero && (bufUniFactors2.length() == 1))) |
---|
[7bf145] | 5816 | { |
---|
| 5817 | if (extension) |
---|
| 5818 | { |
---|
| 5819 | CFList source, dest; |
---|
[806c18] | 5820 | ExtensionInfo info2= ExtensionInfo (beta, alpha, delta, gamma, k, |
---|
[7bf145] | 5821 | info.getGFName(), info.isInExtension()); |
---|
| 5822 | appendMapDown (factors, A, info2, source, dest); |
---|
| 5823 | } |
---|
[806c18] | 5824 | else |
---|
[7bf145] | 5825 | factors.append (A); |
---|
| 5826 | |
---|
[806c18] | 5827 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
[7bf145] | 5828 | swap, swap2, N); |
---|
| 5829 | |
---|
| 5830 | normalize (factors); |
---|
| 5831 | return factors; |
---|
| 5832 | } |
---|
| 5833 | |
---|
[686ce3] | 5834 | if (i == 0) |
---|
| 5835 | { |
---|
[dd8047] | 5836 | if (subCheck1 > 0) |
---|
[686ce3] | 5837 | { |
---|
[dd8047] | 5838 | int subCheck= substituteCheck (bufUniFactors); |
---|
| 5839 | |
---|
| 5840 | if (subCheck > 1 && (subCheck1%subCheck == 0)) |
---|
| 5841 | { |
---|
| 5842 | CanonicalForm bufA= A; |
---|
| 5843 | subst (bufA, bufA, subCheck, x); |
---|
| 5844 | factors= biFactorize (bufA, info); |
---|
| 5845 | reverseSubst (factors, subCheck, x); |
---|
| 5846 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
| 5847 | swap, swap2, N); |
---|
| 5848 | normalize (factors); |
---|
| 5849 | return factors; |
---|
| 5850 | } |
---|
[686ce3] | 5851 | } |
---|
| 5852 | |
---|
[dd8047] | 5853 | if (!derivXZero && !fail2 && subCheck2 > 0) |
---|
[686ce3] | 5854 | { |
---|
[dd8047] | 5855 | int subCheck= substituteCheck (bufUniFactors2); |
---|
| 5856 | |
---|
| 5857 | if (subCheck > 1 && (subCheck2%subCheck == 0)) |
---|
[686ce3] | 5858 | { |
---|
| 5859 | CanonicalForm bufA= A; |
---|
| 5860 | subst (bufA, bufA, subCheck, y); |
---|
| 5861 | factors= biFactorize (bufA, info); |
---|
[2caede4] | 5862 | reverseSubst (factors, subCheck, y); |
---|
[686ce3] | 5863 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
| 5864 | swap, swap2, N); |
---|
| 5865 | normalize (factors); |
---|
| 5866 | return factors; |
---|
| 5867 | } |
---|
| 5868 | } |
---|
| 5869 | } |
---|
| 5870 | |
---|
[806c18] | 5871 | // degree analysis |
---|
| 5872 | bufDegs = DegreePattern (bufUniFactors); |
---|
[7bf145] | 5873 | if (!derivXZero && !fail2) |
---|
| 5874 | bufDegs2= DegreePattern (bufUniFactors2); |
---|
| 5875 | |
---|
[806c18] | 5876 | if (i == 0) |
---|
[7bf145] | 5877 | { |
---|
| 5878 | Aeval= bufAeval; |
---|
| 5879 | evaluation= bufEvaluation; |
---|
| 5880 | uniFactors= bufUniFactors; |
---|
| 5881 | degs= bufDegs; |
---|
| 5882 | if (!derivXZero && !fail2) |
---|
| 5883 | { |
---|
| 5884 | Aeval2= bufAeval2; |
---|
| 5885 | evaluation2= bufEvaluation2; |
---|
| 5886 | uniFactors2= bufUniFactors2; |
---|
| 5887 | degs2= bufDegs2; |
---|
| 5888 | } |
---|
| 5889 | } |
---|
[806c18] | 5890 | else |
---|
[7bf145] | 5891 | { |
---|
| 5892 | degs.intersect (bufDegs); |
---|
[806c18] | 5893 | if (!derivXZero && !fail2) |
---|
[7bf145] | 5894 | { |
---|
| 5895 | degs2.intersect (bufDegs2); |
---|
[806c18] | 5896 | if (bufUniFactors2.length() < uniFactors2.length()) |
---|
| 5897 | { |
---|
[7bf145] | 5898 | uniFactors2= bufUniFactors2; |
---|
| 5899 | Aeval2= bufAeval2; |
---|
| 5900 | evaluation2= bufEvaluation2; |
---|
| 5901 | } |
---|
[806c18] | 5902 | } |
---|
| 5903 | if (bufUniFactors.length() < uniFactors.length()) |
---|
| 5904 | { |
---|
[3af6b6] | 5905 | uniFactors= bufUniFactors; |
---|
| 5906 | Aeval= bufAeval; |
---|
| 5907 | evaluation= bufEvaluation; |
---|
[7bf145] | 5908 | } |
---|
| 5909 | } |
---|
| 5910 | list.append (bufEvaluation); |
---|
| 5911 | if (!derivXZero && !fail2) |
---|
| 5912 | list2.append (bufEvaluation2); |
---|
| 5913 | } |
---|
[806c18] | 5914 | |
---|
[7bf145] | 5915 | if (!derivXZero && !fail2) |
---|
| 5916 | { |
---|
[3af6b6] | 5917 | if (uniFactors.length() > uniFactors2.length() || |
---|
[806c18] | 5918 | (uniFactors.length() == uniFactors2.length() |
---|
[3af6b6] | 5919 | && degs.getLength() > degs2.getLength())) |
---|
[7bf145] | 5920 | { |
---|
| 5921 | degs= degs2; |
---|
| 5922 | uniFactors= uniFactors2; |
---|
| 5923 | evaluation= evaluation2; |
---|
| 5924 | Aeval= Aeval2; |
---|
| 5925 | A= buf; |
---|
| 5926 | swap2= true; |
---|
| 5927 | } |
---|
| 5928 | } |
---|
[806c18] | 5929 | |
---|
| 5930 | if (degs.getLength() == 1) // A is irreducible |
---|
[7bf145] | 5931 | { |
---|
[806c18] | 5932 | if (extension) |
---|
[7bf145] | 5933 | { |
---|
| 5934 | CFList source, dest; |
---|
[11bf82] | 5935 | appendMapDown (factors, A, info, source, dest); |
---|
[7bf145] | 5936 | } |
---|
[806c18] | 5937 | else |
---|
[7bf145] | 5938 | factors.append (A); |
---|
[806c18] | 5939 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
[7bf145] | 5940 | swap, swap2, N); |
---|
| 5941 | normalize (factors); |
---|
| 5942 | return factors; |
---|
| 5943 | } |
---|
| 5944 | |
---|
| 5945 | A= A (y + evaluation, y); |
---|
| 5946 | |
---|
[1a3011e] | 5947 | int liftBound= degree (A, y) + 1; |
---|
[11bf82] | 5948 | |
---|
| 5949 | int boundsLength; |
---|
| 5950 | int * bounds= computeBounds (A (y - evaluation, y), boundsLength); |
---|
| 5951 | int minBound= bounds[0]; |
---|
| 5952 | for (int i= 1; i < boundsLength; i++) |
---|
| 5953 | { |
---|
| 5954 | if (bounds[i] != 0) |
---|
| 5955 | minBound= tmin (minBound, bounds[i]); |
---|
| 5956 | } |
---|
| 5957 | |
---|
| 5958 | int degMipo= 1; |
---|
| 5959 | if (extension && alpha.level() != 1 && k==1) |
---|
| 5960 | degMipo= degree (getMipo (alpha)); |
---|
[7bf145] | 5961 | |
---|
| 5962 | DEBOUTLN (cerr, "uniFactors= " << uniFactors); |
---|
[11bf82] | 5963 | |
---|
[ac8e1a] | 5964 | if ((GF && !extension) || (GF && extension && k != 1)) |
---|
[11bf82] | 5965 | { |
---|
| 5966 | bool earlySuccess= false; |
---|
| 5967 | CFList earlyFactors; |
---|
[0b618a7] | 5968 | TIMING_START (fac_hensel_lift12); |
---|
[c1b9927] | 5969 | uniFactors= henselLiftAndEarly |
---|
[7bf145] | 5970 | (A, earlySuccess, earlyFactors, degs, liftBound, |
---|
[806c18] | 5971 | uniFactors, info, evaluation); |
---|
[0b618a7] | 5972 | TIMING_END_AND_PRINT (fac_hensel_lift12, "time for hensel lifting: "); |
---|
[11bf82] | 5973 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
[7bf145] | 5974 | |
---|
[11bf82] | 5975 | CanonicalForm MODl= power (y, liftBound); |
---|
| 5976 | |
---|
| 5977 | if (extension) |
---|
| 5978 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
| 5979 | evaluation, 1, uniFactors.length()/2); |
---|
| 5980 | else |
---|
| 5981 | factors= factorRecombination (uniFactors, A, MODl, degs, 1, |
---|
| 5982 | uniFactors.length()/2); |
---|
| 5983 | |
---|
| 5984 | if (earlySuccess) |
---|
| 5985 | factors= Union (earlyFactors, factors); |
---|
| 5986 | else if (!earlySuccess && degs.getLength() == 1) |
---|
| 5987 | factors= earlyFactors; |
---|
| 5988 | } |
---|
| 5989 | else if (degree (A) > 4 && beta.level() == 1 && (2*minBound)/degMipo < 32) |
---|
| 5990 | { |
---|
[0b618a7] | 5991 | TIMING_START (fac_hensel_lift12); |
---|
[11bf82] | 5992 | if (extension) |
---|
| 5993 | { |
---|
| 5994 | CFList lll= extHenselLiftAndLatticeRecombi (A, uniFactors, info, degs, |
---|
| 5995 | evaluation |
---|
| 5996 | ); |
---|
| 5997 | factors= Union (lll, factors); |
---|
| 5998 | } |
---|
| 5999 | else if (alpha.level() == 1 && !GF) |
---|
| 6000 | { |
---|
| 6001 | CFList lll= henselLiftAndLatticeRecombi (A, uniFactors, alpha, degs); |
---|
| 6002 | factors= Union (lll, factors); |
---|
| 6003 | } |
---|
[a54114] | 6004 | else if (!extension && (alpha != x || GF)) |
---|
[11bf82] | 6005 | { |
---|
| 6006 | CFList lll= henselLiftAndLatticeRecombi (A, uniFactors, alpha, degs); |
---|
| 6007 | factors= Union (lll, factors); |
---|
| 6008 | } |
---|
[0b618a7] | 6009 | TIMING_END_AND_PRINT (fac_hensel_lift12, "time for hensel lifting: "); |
---|
[11bf82] | 6010 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
| 6011 | } |
---|
[806c18] | 6012 | else |
---|
[11bf82] | 6013 | { |
---|
| 6014 | bool earlySuccess= false; |
---|
| 6015 | CFList earlyFactors; |
---|
[0b618a7] | 6016 | TIMING_START (fac_hensel_lift12); |
---|
[11bf82] | 6017 | uniFactors= henselLiftAndEarly |
---|
| 6018 | (A, earlySuccess, earlyFactors, degs, liftBound, |
---|
| 6019 | uniFactors, info, evaluation); |
---|
[0b618a7] | 6020 | TIMING_END_AND_PRINT (fac_hensel_lift12, "time for hensel lifting: "); |
---|
[11bf82] | 6021 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
| 6022 | |
---|
| 6023 | CanonicalForm MODl= power (y, liftBound); |
---|
| 6024 | if (!extension) |
---|
| 6025 | { |
---|
| 6026 | factors= factorRecombination (uniFactors, A, MODl, degs, 1, 3); |
---|
| 6027 | |
---|
| 6028 | int oldUniFactorsLength= uniFactors.length(); |
---|
| 6029 | if (degree (A) > 0) |
---|
| 6030 | { |
---|
| 6031 | CFList tmp; |
---|
| 6032 | if (alpha.level() == 1) |
---|
| 6033 | tmp= increasePrecision (A, uniFactors, 0, uniFactors.length(), 1, |
---|
| 6034 | liftBound |
---|
| 6035 | ); |
---|
| 6036 | else |
---|
| 6037 | { |
---|
| 6038 | if (degree (A) > getCharacteristic()) |
---|
| 6039 | tmp= increasePrecisionFq2Fp (A, uniFactors, 0, uniFactors.length(), |
---|
| 6040 | 1, alpha, liftBound |
---|
| 6041 | ); |
---|
| 6042 | else |
---|
| 6043 | tmp= increasePrecision (A, uniFactors, 0, uniFactors.length(), 1, |
---|
| 6044 | alpha, liftBound |
---|
| 6045 | ); |
---|
| 6046 | } |
---|
| 6047 | factors= Union (factors, tmp); |
---|
| 6048 | if (tmp.length() == 0 || (tmp.length() > 0 && uniFactors.length() != 0 |
---|
| 6049 | && uniFactors.length() != oldUniFactorsLength) |
---|
| 6050 | ) |
---|
| 6051 | { |
---|
| 6052 | DegreePattern bufDegs= DegreePattern (uniFactors); |
---|
| 6053 | degs.intersect (bufDegs); |
---|
| 6054 | degs.refine (); |
---|
| 6055 | factors= Union (factors, factorRecombination (uniFactors, A, MODl, |
---|
| 6056 | degs, 4, |
---|
| 6057 | uniFactors.length()/2 |
---|
| 6058 | ) |
---|
| 6059 | ); |
---|
| 6060 | } |
---|
| 6061 | } |
---|
| 6062 | } |
---|
| 6063 | else |
---|
| 6064 | { |
---|
| 6065 | if (beta.level() != 1 || k > 1) |
---|
| 6066 | { |
---|
| 6067 | if (k > 1) |
---|
| 6068 | { |
---|
| 6069 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
| 6070 | evaluation, 1, uniFactors.length()/2 |
---|
| 6071 | ); |
---|
| 6072 | } |
---|
| 6073 | else |
---|
| 6074 | { |
---|
| 6075 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
| 6076 | evaluation, 1, 3 |
---|
| 6077 | ); |
---|
| 6078 | if (degree (A) > 0) |
---|
| 6079 | { |
---|
| 6080 | CFList tmp= increasePrecision2 (A, uniFactors, alpha, liftBound); |
---|
| 6081 | DegreePattern bufDegs= DegreePattern (tmp); |
---|
| 6082 | degs.intersect (bufDegs); |
---|
| 6083 | degs.refine (); |
---|
| 6084 | factors= Union (factors, extFactorRecombination (tmp, A, MODl, info, |
---|
| 6085 | degs, evaluation, |
---|
| 6086 | 1, tmp.length()/2 |
---|
| 6087 | ) |
---|
| 6088 | ); |
---|
| 6089 | } |
---|
| 6090 | } |
---|
| 6091 | } |
---|
| 6092 | else |
---|
| 6093 | { |
---|
| 6094 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
| 6095 | evaluation, 1, 3 |
---|
| 6096 | ); |
---|
| 6097 | int oldUniFactorsLength= uniFactors.length(); |
---|
| 6098 | if (degree (A) > 0) |
---|
| 6099 | { |
---|
| 6100 | int degMipo; |
---|
| 6101 | ExtensionInfo info2= init4ext (info, evaluation, degMipo); |
---|
| 6102 | |
---|
| 6103 | CFList source, dest; |
---|
| 6104 | CFList tmp= extIncreasePrecision (A, uniFactors, 0, |
---|
| 6105 | uniFactors.length(), 1, evaluation, |
---|
| 6106 | info2, source, dest, liftBound |
---|
| 6107 | ); |
---|
| 6108 | factors= Union (factors, tmp); |
---|
| 6109 | if (tmp.length() == 0 || (tmp.length() > 0 && uniFactors.length() != 0 |
---|
| 6110 | && uniFactors.length() != oldUniFactorsLength) |
---|
| 6111 | ) |
---|
| 6112 | { |
---|
| 6113 | DegreePattern bufDegs= DegreePattern (uniFactors); |
---|
| 6114 | degs.intersect (bufDegs); |
---|
| 6115 | degs.refine (); |
---|
| 6116 | factors= Union (factors,extFactorRecombination (uniFactors, A, MODl, |
---|
| 6117 | info, degs, evaluation, |
---|
| 6118 | 4, uniFactors.length()/2 |
---|
| 6119 | ) |
---|
| 6120 | ); |
---|
| 6121 | } |
---|
| 6122 | } |
---|
| 6123 | } |
---|
| 6124 | } |
---|
[806c18] | 6125 | |
---|
[11bf82] | 6126 | if (earlySuccess) |
---|
| 6127 | factors= Union (earlyFactors, factors); |
---|
| 6128 | else if (!earlySuccess && degs.getLength() == 1) |
---|
| 6129 | factors= earlyFactors; |
---|
| 6130 | } |
---|
| 6131 | delete [] bounds; |
---|
[7bf145] | 6132 | if (!extension) |
---|
| 6133 | { |
---|
| 6134 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
| 6135 | i.getItem()= i.getItem() (y - evaluation, y); |
---|
| 6136 | } |
---|
| 6137 | |
---|
[806c18] | 6138 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
[7bf145] | 6139 | swap, swap2, N); |
---|
[806c18] | 6140 | normalize (factors); |
---|
[7bf145] | 6141 | |
---|
| 6142 | return factors; |
---|
| 6143 | } |
---|
| 6144 | |
---|
[806c18] | 6145 | CFList |
---|
| 6146 | extBiFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
[7bf145] | 6147 | { |
---|
[806c18] | 6148 | |
---|
[7bf145] | 6149 | CanonicalForm A= F; |
---|
| 6150 | Variable alpha= info.getAlpha(); |
---|
| 6151 | Variable beta= info.getBeta(); |
---|
| 6152 | int k= info.getGFDegree(); |
---|
| 6153 | char cGFName= info.getGFName(); |
---|
| 6154 | CanonicalForm delta= info.getDelta(); |
---|
| 6155 | |
---|
| 6156 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
[806c18] | 6157 | Variable x= Variable (1); |
---|
[7bf145] | 6158 | CFList factors; |
---|
| 6159 | if (!GF && alpha == x) // we are in F_p |
---|
| 6160 | { |
---|
[806c18] | 6161 | bool extension= true; |
---|
[7bf145] | 6162 | int p= getCharacteristic(); |
---|
[806c18] | 6163 | if (p*p < (1<<16)) // pass to GF if possible |
---|
| 6164 | { |
---|
[7bf145] | 6165 | setCharacteristic (getCharacteristic(), 2, 'Z'); |
---|
| 6166 | A= A.mapinto(); |
---|
[11bf82] | 6167 | ExtensionInfo info2= ExtensionInfo (extension); |
---|
| 6168 | factors= biFactorize (A, info2); |
---|
[7bf145] | 6169 | |
---|
| 6170 | Variable vBuf= rootOf (gf_mipo); |
---|
| 6171 | setCharacteristic (getCharacteristic()); |
---|
[806c18] | 6172 | for (CFListIterator j= factors; j.hasItem(); j++) |
---|
| 6173 | j.getItem()= GF2FalphaRep (j.getItem(), vBuf); |
---|
[7bf145] | 6174 | } |
---|
[806c18] | 6175 | else // not able to pass to GF, pass to F_p(\alpha) |
---|
| 6176 | { |
---|
[a54114] | 6177 | CanonicalForm mipo= randomIrredpoly (2, x); |
---|
[7bf145] | 6178 | Variable v= rootOf (mipo); |
---|
[11bf82] | 6179 | ExtensionInfo info2= ExtensionInfo (v); |
---|
| 6180 | factors= biFactorize (A, info2); |
---|
[806c18] | 6181 | } |
---|
[7bf145] | 6182 | return factors; |
---|
| 6183 | } |
---|
| 6184 | else if (!GF && (alpha != x)) // we are in F_p(\alpha) |
---|
[806c18] | 6185 | { |
---|
[7bf145] | 6186 | if (k == 1) // need factorization over F_p |
---|
| 6187 | { |
---|
| 6188 | int extDeg= degree (getMipo (alpha)); |
---|
[806c18] | 6189 | extDeg++; |
---|
[a54114] | 6190 | CanonicalForm mipo= randomIrredpoly (extDeg + 1, x); |
---|
[7bf145] | 6191 | Variable v= rootOf (mipo); |
---|
[11bf82] | 6192 | ExtensionInfo info2= ExtensionInfo (v); |
---|
| 6193 | factors= biFactorize (A, info2); |
---|
[7bf145] | 6194 | } |
---|
[806c18] | 6195 | else |
---|
[7bf145] | 6196 | { |
---|
[a54114] | 6197 | if (beta == x) |
---|
[7bf145] | 6198 | { |
---|
[11bf82] | 6199 | Variable v= chooseExtension (alpha, beta, k); |
---|
[7bf145] | 6200 | CanonicalForm primElem, imPrimElem; |
---|
| 6201 | bool primFail= false; |
---|
| 6202 | Variable vBuf; |
---|
| 6203 | primElem= primitiveElement (alpha, vBuf, primFail); |
---|
| 6204 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
| 6205 | if (primFail) |
---|
| 6206 | ; //ERROR |
---|
| 6207 | else |
---|
[618da5] | 6208 | imPrimElem= mapPrimElem (primElem, alpha, v); |
---|
[7bf145] | 6209 | |
---|
| 6210 | CFList source, dest; |
---|
[806c18] | 6211 | CanonicalForm bufA= mapUp (A, alpha, v, primElem, imPrimElem, |
---|
[7bf145] | 6212 | source, dest); |
---|
[11bf82] | 6213 | ExtensionInfo info2= ExtensionInfo (v, alpha, imPrimElem, primElem); |
---|
| 6214 | factors= biFactorize (bufA, info2); |
---|
[7bf145] | 6215 | } |
---|
| 6216 | else |
---|
| 6217 | { |
---|
[11bf82] | 6218 | Variable v= chooseExtension (alpha, beta, k); |
---|
[7bf145] | 6219 | CanonicalForm primElem, imPrimElem; |
---|
| 6220 | bool primFail= false; |
---|
| 6221 | Variable vBuf; |
---|
| 6222 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
| 6223 | if (primFail) |
---|
| 6224 | ; //ERROR |
---|
| 6225 | else |
---|
[618da5] | 6226 | imPrimElem= mapPrimElem (delta, beta, v); |
---|
[7bf145] | 6227 | |
---|
| 6228 | CFList source, dest; |
---|
| 6229 | CanonicalForm bufA= mapDown (A, info, source, dest); |
---|
| 6230 | source= CFList(); |
---|
| 6231 | dest= CFList(); |
---|
| 6232 | bufA= mapUp (bufA, beta, v, delta, imPrimElem, source, dest); |
---|
[11bf82] | 6233 | ExtensionInfo info2= ExtensionInfo (v, beta, imPrimElem, delta); |
---|
| 6234 | factors= biFactorize (bufA, info2); |
---|
[7bf145] | 6235 | } |
---|
| 6236 | } |
---|
| 6237 | return factors; |
---|
| 6238 | } |
---|
| 6239 | else // we are in GF (p^k) |
---|
[806c18] | 6240 | { |
---|
[7bf145] | 6241 | int p= getCharacteristic(); |
---|
| 6242 | int extensionDeg= getGFDegree(); |
---|
| 6243 | bool extension= true; |
---|
| 6244 | if (k == 1) // need factorization over F_p |
---|
| 6245 | { |
---|
| 6246 | extensionDeg++; |
---|
[806c18] | 6247 | if (ipower (p, extensionDeg) < (1<<16)) |
---|
| 6248 | // pass to GF(p^k+1) |
---|
[7bf145] | 6249 | { |
---|
| 6250 | setCharacteristic (p); |
---|
[806c18] | 6251 | Variable vBuf= rootOf (gf_mipo); |
---|
| 6252 | A= GF2FalphaRep (A, vBuf); |
---|
| 6253 | setCharacteristic (p, extensionDeg, 'Z'); |
---|
[11bf82] | 6254 | ExtensionInfo info2= ExtensionInfo (extension); |
---|
| 6255 | factors= biFactorize (A.mapinto(), info2); |
---|
[7bf145] | 6256 | } |
---|
| 6257 | else // not able to pass to another GF, pass to F_p(\alpha) |
---|
[806c18] | 6258 | { |
---|
| 6259 | setCharacteristic (p); |
---|
| 6260 | Variable vBuf= rootOf (gf_mipo); |
---|
| 6261 | A= GF2FalphaRep (A, vBuf); |
---|
[11bf82] | 6262 | Variable v= chooseExtension (vBuf, beta, k); |
---|
| 6263 | ExtensionInfo info2= ExtensionInfo (v, extension); |
---|
| 6264 | factors= biFactorize (A, info2); |
---|
[7bf145] | 6265 | } |
---|
| 6266 | } |
---|
| 6267 | else // need factorization over GF (p^k) |
---|
| 6268 | { |
---|
[806c18] | 6269 | if (ipower (p, 2*extensionDeg) < (1<<16)) |
---|
[7bf145] | 6270 | // pass to GF (p^2k) |
---|
[806c18] | 6271 | { |
---|
| 6272 | setCharacteristic (p, 2*extensionDeg, 'Z'); |
---|
[11bf82] | 6273 | ExtensionInfo info2= ExtensionInfo (k, cGFName, extension); |
---|
| 6274 | factors= biFactorize (GFMapUp (A, extensionDeg), info2); |
---|
[806c18] | 6275 | setCharacteristic (p, extensionDeg, cGFName); |
---|
[7bf145] | 6276 | } |
---|
| 6277 | else // not able to pass to GF (p^2k), pass to F_p (\alpha) |
---|
[806c18] | 6278 | { |
---|
| 6279 | setCharacteristic (p); |
---|
| 6280 | Variable v1= rootOf (gf_mipo); |
---|
| 6281 | A= GF2FalphaRep (A, v1); |
---|
[11bf82] | 6282 | Variable v2= chooseExtension (v1, v1, k); |
---|
[7bf145] | 6283 | CanonicalForm primElem, imPrimElem; |
---|
| 6284 | bool primFail= false; |
---|
| 6285 | Variable vBuf; |
---|
| 6286 | primElem= primitiveElement (v1, vBuf, primFail); |
---|
| 6287 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
| 6288 | if (primFail) |
---|
| 6289 | ; //ERROR |
---|
| 6290 | else |
---|
[618da5] | 6291 | imPrimElem= mapPrimElem (primElem, v1, v2); |
---|
[7bf145] | 6292 | |
---|
| 6293 | CFList source, dest; |
---|
[806c18] | 6294 | CanonicalForm bufA= mapUp (A, v1, v2, primElem, imPrimElem, |
---|
[7bf145] | 6295 | source, dest); |
---|
[11bf82] | 6296 | ExtensionInfo info2= ExtensionInfo (v2, v1, imPrimElem, primElem); |
---|
| 6297 | factors= biFactorize (bufA, info2); |
---|
[806c18] | 6298 | setCharacteristic (p, k, cGFName); |
---|
| 6299 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
| 6300 | i.getItem()= Falpha2GFRep (i.getItem()); |
---|
[7bf145] | 6301 | } |
---|
| 6302 | } |
---|
| 6303 | return factors; |
---|
| 6304 | } |
---|
| 6305 | } |
---|
| 6306 | |
---|
| 6307 | #endif |
---|
| 6308 | /* HAVE_NTL */ |
---|
| 6309 | |
---|
| 6310 | |
---|