[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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[fea494] | 10 | * Factor Recombination is described in "Factoring polynomials over global |
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[8c1a84] | 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 | **/ |
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| 17 | /*****************************************************************************/ |
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| 18 | |
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[9f7665] | 19 | |
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[e4fe2b] | 20 | #include "config.h" |
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[9f7665] | 21 | |
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[7bf145] | 22 | |
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[650f2d8] | 23 | #include "cf_assert.h" |
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[7fdedf] | 24 | #include "cf_util.h" |
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[7bf145] | 25 | #include "debug.h" |
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| 26 | #include "timing.h" |
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| 27 | |
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| 28 | #include "canonicalform.h" |
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| 29 | #include "cf_defs.h" |
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| 30 | #include "cf_map_ext.h" |
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| 31 | #include "cf_random.h" |
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| 32 | #include "facHensel.h" |
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[0e2e23] | 33 | #include "facMul.h" |
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[7bf145] | 34 | #include "cf_map.h" |
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[eed963] | 35 | #include "cf_irred.h" |
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[11bf82] | 36 | #include "facFqBivarUtil.h" |
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[7bf145] | 37 | #include "facFqBivar.h" |
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[11bf82] | 38 | #include "cfNewtonPolygon.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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[03c742] | 42 | #endif |
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[7bf145] | 43 | |
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[18a660] | 44 | #ifdef HAVE_FLINT |
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| 45 | #include "FLINTconvert.h" |
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| 46 | #endif |
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| 47 | |
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[978ce3] | 48 | TIMING_DEFINE_PRINT(fac_fq_uni_factorizer) |
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| 49 | TIMING_DEFINE_PRINT(fac_fq_bi_hensel_lift) |
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| 50 | TIMING_DEFINE_PRINT(fac_fq_bi_factor_recombination) |
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[0851b0] | 51 | TIMING_DEFINE_PRINT(fac_fq_bi_evaluation) |
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| 52 | TIMING_DEFINE_PRINT(fac_fq_bi_shift_to_zero) |
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[2d35fe] | 53 | TIMING_DEFINE_PRINT(fac_fq_logarithmic) |
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| 54 | TIMING_DEFINE_PRINT(fac_fq_compute_lattice_lift) |
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| 55 | TIMING_DEFINE_PRINT(fac_fq_till_reduced) |
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| 56 | TIMING_DEFINE_PRINT(fac_fq_reconstruction) |
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| 57 | TIMING_DEFINE_PRINT(fac_fq_lift) |
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| 58 | TIMING_DEFINE_PRINT(fac_fq_uni_total) |
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[7bf145] | 59 | |
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[ad0177] | 60 | CanonicalForm prodMod0 (const CFList& L, const CanonicalForm& M, const modpk& b) |
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[7bf145] | 61 | { |
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| 62 | if (L.isEmpty()) |
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| 63 | return 1; |
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| 64 | else if (L.length() == 1) |
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| 65 | return mod (L.getFirst()(0, 1) , M); |
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| 66 | else if (L.length() == 2) |
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[ad0177] | 67 | return mod (mulNTL (L.getFirst()(0, 1),L.getLast()(0, 1), b), M); |
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[7bf145] | 68 | else |
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| 69 | { |
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| 70 | int l= L.length()/2; |
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| 71 | CFListIterator i= L; |
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| 72 | CFList tmp1, tmp2; |
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| 73 | CanonicalForm buf1, buf2; |
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[806c18] | 74 | for (int j= 1; j <= l; j++, i++) |
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[7bf145] | 75 | tmp1.append (i.getItem()); |
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| 76 | tmp2= Difference (L, tmp1); |
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[ad0177] | 77 | buf1= prodMod0 (tmp1, M, b); |
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| 78 | buf2= prodMod0 (tmp2, M, b); |
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| 79 | return mod (mulNTL (buf1,buf2, b), M); |
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[7bf145] | 80 | } |
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| 81 | } |
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| 82 | |
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[03c742] | 83 | #if defined(HAVE_NTL) || defined(HAVE_FLINT) |
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[806c18] | 84 | CanonicalForm evalPoint (const CanonicalForm& F, CanonicalForm & eval, |
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[7bf145] | 85 | const Variable& alpha, CFList& list, const bool& GF, |
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[806c18] | 86 | bool& fail) |
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[7bf145] | 87 | { |
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| 88 | fail= false; |
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| 89 | Variable x= Variable(2); |
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[a54114] | 90 | Variable y= Variable(1); |
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[7bf145] | 91 | FFRandom genFF; |
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| 92 | GFRandom genGF; |
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| 93 | CanonicalForm random, mipo; |
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| 94 | double bound; |
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| 95 | int p= getCharacteristic (); |
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[1372ae] | 96 | if (alpha.level() != 1) |
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[7bf145] | 97 | { |
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| 98 | mipo= getMipo (alpha); |
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| 99 | int d= degree (mipo); |
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[67f82ef] | 100 | bound= pow ((double) p, (double) d); |
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[7bf145] | 101 | } |
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[806c18] | 102 | else if (GF) |
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[7bf145] | 103 | { |
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| 104 | int d= getGFDegree(); |
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| 105 | bound= ipower (p, d); |
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| 106 | } |
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| 107 | else |
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| 108 | bound= p; |
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| 109 | |
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[11bf82] | 110 | random= 0; |
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[806c18] | 111 | do |
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[7bf145] | 112 | { |
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| 113 | if (list.length() >= bound) |
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| 114 | { |
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| 115 | fail= true; |
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| 116 | break; |
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| 117 | } |
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[8db258] | 118 | if (list.isEmpty()) |
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| 119 | random= 0; |
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| 120 | else if (GF) |
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[11bf82] | 121 | { |
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| 122 | if (list.length() == 1) |
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| 123 | random= getGFGenerator(); |
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| 124 | else |
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| 125 | random= genGF.generate(); |
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| 126 | } |
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| 127 | else if (list.length() < p || alpha.level() == 1) |
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[7bf145] | 128 | random= genFF.generate(); |
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[806c18] | 129 | else if (alpha != x && list.length() >= p) |
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[7bf145] | 130 | { |
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[11bf82] | 131 | if (list.length() == p) |
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| 132 | random= alpha; |
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| 133 | else |
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| 134 | { |
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| 135 | AlgExtRandomF genAlgExt (alpha); |
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| 136 | random= genAlgExt.generate(); |
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| 137 | } |
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[7bf145] | 138 | } |
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| 139 | if (find (list, random)) continue; |
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| 140 | eval= F (random, x); |
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[a54114] | 141 | if (degree (eval) != degree (F, y)) |
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[7bf145] | 142 | { //leading coeff vanishes |
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| 143 | if (!find (list, random)) |
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| 144 | list.append (random); |
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| 145 | continue; |
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| 146 | } |
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[806c18] | 147 | if (degree (gcd (deriv (eval, eval.mvar()), eval), eval.mvar()) > 0) |
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[7bf145] | 148 | { //evaluated polynomial is not squarefree |
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| 149 | if (!find (list, random)) |
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| 150 | list.append (random); |
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| 151 | continue; |
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| 152 | } |
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| 153 | } while (find (list, random)); |
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| 154 | |
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| 155 | return random; |
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| 156 | } |
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| 157 | |
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[7032db] | 158 | #if defined(HAVE_NTL) || defined(HAVE_FLINT) |
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[806c18] | 159 | CFList |
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| 160 | uniFactorizer (const CanonicalForm& A, const Variable& alpha, const bool& GF) |
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[7bf145] | 161 | { |
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| 162 | Variable x= A.mvar(); |
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[18a660] | 163 | if (A.inCoeffDomain()) |
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| 164 | return CFList(); |
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| 165 | ASSERT (A.isUnivariate(), |
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[050d1b] | 166 | "univariate polynomial expected or constant expected"); |
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[7bf145] | 167 | CFFList factorsA; |
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[806c18] | 168 | if (GF) |
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[7bf145] | 169 | { |
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| 170 | int k= getGFDegree(); |
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| 171 | char cGFName= gf_name; |
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[0a7d0ca] | 172 | CanonicalForm mipo= gf_mipo; |
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[806c18] | 173 | setCharacteristic (getCharacteristic()); |
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[0a7d0ca] | 174 | Variable beta= rootOf (mipo.mapinto()); |
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[806c18] | 175 | CanonicalForm buf= GF2FalphaRep (A, beta); |
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[03c742] | 176 | #ifdef HAVE_NTL |
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[7bf145] | 177 | if (getCharacteristic() > 2) |
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[03c742] | 178 | #else |
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| 179 | if (getCharacteristic() > 0) |
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| 180 | #endif |
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[7bf145] | 181 | { |
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[9ee586] | 182 | #if (HAVE_FLINT && __FLINT_RELEASE >= 20400) |
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[45e474] | 183 | nmod_poly_t FLINTmipo, leadingCoeff; |
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| 184 | fq_nmod_ctx_t fq_con; |
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| 185 | fq_nmod_poly_t FLINTA; |
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| 186 | fq_nmod_poly_factor_t FLINTFactorsA; |
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| 187 | |
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| 188 | nmod_poly_init (FLINTmipo, getCharacteristic()); |
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| 189 | convertFacCF2nmod_poly_t (FLINTmipo, mipo.mapinto()); |
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| 190 | |
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| 191 | fq_nmod_ctx_init_modulus (fq_con, FLINTmipo, "Z"); |
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| 192 | |
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[7ed4f6c] | 193 | convertFacCF2Fq_nmod_poly_t (FLINTA, buf, fq_con); |
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[45e474] | 194 | fq_nmod_poly_make_monic (FLINTA, FLINTA, fq_con); |
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| 195 | |
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| 196 | fq_nmod_poly_factor_init (FLINTFactorsA, fq_con); |
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| 197 | nmod_poly_init (leadingCoeff, getCharacteristic()); |
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| 198 | |
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| 199 | fq_nmod_poly_factor (FLINTFactorsA, leadingCoeff, FLINTA, fq_con); |
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| 200 | |
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[7ed4f6c] | 201 | factorsA= convertFLINTFq_nmod_poly_factor2FacCFFList (FLINTFactorsA, x, |
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| 202 | beta, fq_con); |
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[45e474] | 203 | |
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| 204 | fq_nmod_poly_factor_clear (FLINTFactorsA, fq_con); |
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| 205 | fq_nmod_poly_clear (FLINTA, fq_con); |
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| 206 | nmod_poly_clear (FLINTmipo); |
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| 207 | nmod_poly_clear (leadingCoeff); |
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| 208 | fq_nmod_ctx_clear (fq_con); |
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| 209 | #else |
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[514ade] | 210 | if (fac_NTL_char != getCharacteristic()) |
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| 211 | { |
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| 212 | fac_NTL_char= getCharacteristic(); |
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| 213 | zz_p::init (getCharacteristic()); |
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| 214 | } |
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[9a12097] | 215 | zz_pX NTLMipo= convertFacCF2NTLzzpX (mipo.mapinto()); |
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| 216 | zz_pE::init (NTLMipo); |
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| 217 | zz_pEX NTLA= convertFacCF2NTLzz_pEX (buf, NTLMipo); |
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[7bf145] | 218 | MakeMonic (NTLA); |
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[9a12097] | 219 | vec_pair_zz_pEX_long NTLFactorsA= CanZass (NTLA); |
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| 220 | zz_pE multi= to_zz_pE (1); |
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| 221 | factorsA= convertNTLvec_pair_zzpEX_long2FacCFFList (NTLFactorsA, multi, |
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[7bf145] | 222 | x, beta); |
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[45e474] | 223 | #endif |
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[7bf145] | 224 | } |
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[03c742] | 225 | #ifdef HAVE_NTL |
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[7bf145] | 226 | else |
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| 227 | { |
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[0a7d0ca] | 228 | GF2X NTLMipo= convertFacCF2NTLGF2X (mipo.mapinto()); |
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[7bf145] | 229 | GF2E::init (NTLMipo); |
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| 230 | GF2EX NTLA= convertFacCF2NTLGF2EX (buf, NTLMipo); |
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| 231 | MakeMonic (NTLA); |
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| 232 | vec_pair_GF2EX_long NTLFactorsA= CanZass (NTLA); |
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| 233 | GF2E multi= to_GF2E (1); |
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| 234 | factorsA= convertNTLvec_pair_GF2EX_long2FacCFFList (NTLFactorsA, multi, |
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| 235 | x, beta); |
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| 236 | } |
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[03c742] | 237 | #endif |
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[7bf145] | 238 | setCharacteristic (getCharacteristic(), k, cGFName); |
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[806c18] | 239 | for (CFFListIterator i= factorsA; i.hasItem(); i++) |
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[7bf145] | 240 | { |
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| 241 | buf= i.getItem().factor(); |
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| 242 | buf= Falpha2GFRep (buf); |
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| 243 | i.getItem()= CFFactor (buf, i.getItem().exp()); |
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| 244 | } |
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[03f640] | 245 | prune (beta); |
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[806c18] | 246 | } |
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[1372ae] | 247 | else if (alpha.level() != 1) |
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[7bf145] | 248 | { |
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[03c742] | 249 | #ifdef HAVE_NTL |
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[7bf145] | 250 | if (getCharacteristic() > 2) |
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[03c742] | 251 | #else |
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| 252 | if (getCharacteristic() > 0) |
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| 253 | #endif |
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[7bf145] | 254 | { |
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[9ee586] | 255 | #if (HAVE_FLINT && __FLINT_RELEASE >= 20400) |
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[45e474] | 256 | nmod_poly_t FLINTmipo, leadingCoeff; |
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| 257 | fq_nmod_ctx_t fq_con; |
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| 258 | fq_nmod_poly_t FLINTA; |
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| 259 | fq_nmod_poly_factor_t FLINTFactorsA; |
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| 260 | |
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| 261 | nmod_poly_init (FLINTmipo, getCharacteristic()); |
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| 262 | convertFacCF2nmod_poly_t (FLINTmipo, getMipo (alpha)); |
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| 263 | |
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| 264 | fq_nmod_ctx_init_modulus (fq_con, FLINTmipo, "Z"); |
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| 265 | |
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| 266 | convertFacCF2Fq_nmod_poly_t (FLINTA, A, fq_con); |
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| 267 | fq_nmod_poly_make_monic (FLINTA, FLINTA, fq_con); |
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| 268 | |
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| 269 | fq_nmod_poly_factor_init (FLINTFactorsA, fq_con); |
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| 270 | nmod_poly_init (leadingCoeff, getCharacteristic()); |
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| 271 | |
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| 272 | fq_nmod_poly_factor (FLINTFactorsA, leadingCoeff, FLINTA, fq_con); |
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| 273 | |
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[7ed4f6c] | 274 | factorsA= convertFLINTFq_nmod_poly_factor2FacCFFList (FLINTFactorsA, x, |
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| 275 | alpha, fq_con); |
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[45e474] | 276 | |
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| 277 | fq_nmod_poly_factor_clear (FLINTFactorsA, fq_con); |
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| 278 | fq_nmod_poly_clear (FLINTA, fq_con); |
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| 279 | nmod_poly_clear (FLINTmipo); |
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| 280 | nmod_poly_clear (leadingCoeff); |
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| 281 | fq_nmod_ctx_clear (fq_con); |
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| 282 | #else |
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[514ade] | 283 | if (fac_NTL_char != getCharacteristic()) |
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| 284 | { |
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| 285 | fac_NTL_char= getCharacteristic(); |
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| 286 | zz_p::init (getCharacteristic()); |
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| 287 | } |
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[9a12097] | 288 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
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| 289 | zz_pE::init (NTLMipo); |
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| 290 | zz_pEX NTLA= convertFacCF2NTLzz_pEX (A, NTLMipo); |
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[7bf145] | 291 | MakeMonic (NTLA); |
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[9a12097] | 292 | vec_pair_zz_pEX_long NTLFactorsA= CanZass (NTLA); |
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| 293 | zz_pE multi= to_zz_pE (1); |
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| 294 | factorsA= convertNTLvec_pair_zzpEX_long2FacCFFList (NTLFactorsA, multi, |
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[7bf145] | 295 | x, alpha); |
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[45e474] | 296 | #endif |
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[7bf145] | 297 | } |
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[03c742] | 298 | #ifdef HAVE_NTL |
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[7bf145] | 299 | else |
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| 300 | { |
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| 301 | GF2X NTLMipo= convertFacCF2NTLGF2X (getMipo (alpha)); |
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[806c18] | 302 | GF2E::init (NTLMipo); |
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[7bf145] | 303 | GF2EX NTLA= convertFacCF2NTLGF2EX (A, NTLMipo); |
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| 304 | MakeMonic (NTLA); |
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| 305 | vec_pair_GF2EX_long NTLFactorsA= CanZass (NTLA); |
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| 306 | GF2E multi= to_GF2E (1); |
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[806c18] | 307 | factorsA= convertNTLvec_pair_GF2EX_long2FacCFFList (NTLFactorsA, multi, |
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[7bf145] | 308 | x, alpha); |
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[806c18] | 309 | } |
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[03c742] | 310 | #endif |
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[7bf145] | 311 | } |
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[806c18] | 312 | else |
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[7bf145] | 313 | { |
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[18a660] | 314 | #ifdef HAVE_FLINT |
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[03c742] | 315 | #ifdef HAVE_NTL |
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[0dff6bc] | 316 | if (degree (A) < 300) |
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[03c742] | 317 | #endif |
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[0dff6bc] | 318 | { |
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| 319 | nmod_poly_t FLINTA; |
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| 320 | convertFacCF2nmod_poly_t (FLINTA, A); |
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| 321 | nmod_poly_factor_t result; |
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| 322 | nmod_poly_factor_init (result); |
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| 323 | mp_limb_t leadingCoeff= nmod_poly_factor (result, FLINTA); |
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| 324 | factorsA= convertFLINTnmod_poly_factor2FacCFFList (result, leadingCoeff, x); |
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| 325 | if (factorsA.getFirst().factor().inCoeffDomain()) |
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| 326 | factorsA.removeFirst(); |
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| 327 | nmod_poly_factor_clear (result); |
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| 328 | nmod_poly_clear (FLINTA); |
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| 329 | } |
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[03c742] | 330 | #ifdef HAVE_NTL |
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[0dff6bc] | 331 | else |
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| 332 | #endif |
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[03c742] | 333 | #endif /* HAVE_FLINT */ |
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| 334 | #ifdef HAVE_NTL |
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[7bf145] | 335 | if (getCharacteristic() > 2) |
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| 336 | { |
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[514ade] | 337 | if (fac_NTL_char != getCharacteristic()) |
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| 338 | { |
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| 339 | fac_NTL_char= getCharacteristic(); |
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| 340 | zz_p::init (getCharacteristic()); |
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| 341 | } |
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[9a12097] | 342 | zz_pX NTLA= convertFacCF2NTLzzpX (A); |
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[7bf145] | 343 | MakeMonic (NTLA); |
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[9a12097] | 344 | vec_pair_zz_pX_long NTLFactorsA= CanZass (NTLA); |
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| 345 | zz_p multi= to_zz_p (1); |
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| 346 | factorsA= convertNTLvec_pair_zzpX_long2FacCFFList (NTLFactorsA, multi, |
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[7bf145] | 347 | x); |
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| 348 | } |
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| 349 | else |
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| 350 | { |
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| 351 | GF2X NTLA= convertFacCF2NTLGF2X (A); |
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| 352 | vec_pair_GF2X_long NTLFactorsA= CanZass (NTLA); |
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| 353 | GF2 multi= to_GF2 (1); |
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[806c18] | 354 | factorsA= convertNTLvec_pair_GF2X_long2FacCFFList (NTLFactorsA, multi, |
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[7bf145] | 355 | x); |
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| 356 | } |
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[03c742] | 357 | #endif |
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[7bf145] | 358 | } |
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| 359 | CFList uniFactors; |
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[806c18] | 360 | for (CFFListIterator i= factorsA; i.hasItem(); i++) |
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[7bf145] | 361 | uniFactors.append (i.getItem().factor()); |
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| 362 | return uniFactors; |
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[806c18] | 363 | } |
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[7032db] | 364 | #endif |
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[806c18] | 365 | |
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[b28747] | 366 | #if defined(HAVE_NTL) || defined(HAVE_FLINT) |
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[806c18] | 367 | /// naive factor recombination as decribed in "Factoring |
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| 368 | /// multivariate polynomials over a finite field" by L Bernardin. |
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| 369 | CFList |
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[11bf82] | 370 | extFactorRecombination (CFList& factors, CanonicalForm& F, |
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[09609a] | 371 | const CanonicalForm& N, const ExtensionInfo& info, |
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[11bf82] | 372 | DegreePattern& degs, const CanonicalForm& eval, int s, |
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| 373 | int thres) |
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[806c18] | 374 | { |
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[7bf145] | 375 | if (factors.length() == 0) |
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[11bf82] | 376 | { |
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| 377 | F= 1; |
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[7bf145] | 378 | return CFList(); |
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[11bf82] | 379 | } |
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[e0af3ef] | 380 | if (F.inCoeffDomain()) |
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| 381 | return CFList(); |
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[7bf145] | 382 | |
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| 383 | Variable alpha= info.getAlpha(); |
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| 384 | Variable beta= info.getBeta(); |
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| 385 | CanonicalForm gamma= info.getGamma(); |
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| 386 | CanonicalForm delta= info.getDelta(); |
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| 387 | int k= info.getGFDegree(); |
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| 388 | |
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[09609a] | 389 | CanonicalForm M= N; |
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| 390 | int l= degree (N); |
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[7bf145] | 391 | Variable y= F.mvar(); |
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[a54114] | 392 | Variable x= Variable (1); |
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[7bf145] | 393 | CFList source, dest; |
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[806c18] | 394 | if (degs.getLength() <= 1 || factors.length() == 1) |
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[11bf82] | 395 | { |
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| 396 | CFList result= CFList(mapDown (F(y-eval, y), info, source, dest)); |
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| 397 | F= 1; |
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| 398 | return result; |
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| 399 | } |
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[806c18] | 400 | |
---|
| 401 | DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, M) == F " << |
---|
[27ab36] | 402 | (mod (LC (F, 1)*prodMod (factors, M), M)/Lc (mod (LC (F, 1)*prodMod (factors, M), M)) == F/Lc (F))); |
---|
[ac8e1a] | 403 | int degMipoBeta= 1; |
---|
| 404 | if (!k && beta.level() != 1) |
---|
[7bf145] | 405 | degMipoBeta= degree (getMipo (beta)); |
---|
| 406 | |
---|
| 407 | CFList T, S, Diff; |
---|
| 408 | T= factors; |
---|
| 409 | |
---|
| 410 | CFList result; |
---|
[21b8f4c] | 411 | CanonicalForm buf, buf2, quot; |
---|
[11bf82] | 412 | |
---|
| 413 | buf= F; |
---|
[7bf145] | 414 | |
---|
[a54114] | 415 | CanonicalForm g, LCBuf= LC (buf, x); |
---|
[1673386] | 416 | int * v= new int [T.length()]; |
---|
[7bf145] | 417 | for (int i= 0; i < T.length(); i++) |
---|
| 418 | v[i]= 0; |
---|
| 419 | |
---|
| 420 | CFArray TT; |
---|
[806c18] | 421 | DegreePattern bufDegs1, bufDegs2; |
---|
[7bf145] | 422 | bufDegs1= degs; |
---|
| 423 | int subsetDeg; |
---|
[806c18] | 424 | TT= copy (factors); |
---|
[7bf145] | 425 | bool nosubset= false; |
---|
| 426 | bool recombination= false; |
---|
[93134c] | 427 | bool trueFactor= false; |
---|
[bbb3fbf] | 428 | CanonicalForm test; |
---|
| 429 | CanonicalForm buf0= buf (0, x)*LCBuf; |
---|
[11bf82] | 430 | while (T.length() >= 2*s && s <= thres) |
---|
[7bf145] | 431 | { |
---|
[806c18] | 432 | while (nosubset == false) |
---|
[7bf145] | 433 | { |
---|
[806c18] | 434 | if (T.length() == s) |
---|
[7bf145] | 435 | { |
---|
[1673386] | 436 | delete [] v; |
---|
[806c18] | 437 | if (recombination) |
---|
[7bf145] | 438 | { |
---|
| 439 | T.insert (LCBuf); |
---|
| 440 | g= prodMod (T, M); |
---|
| 441 | T.removeFirst(); |
---|
| 442 | g /= content(g); |
---|
| 443 | g= g (y - eval, y); |
---|
| 444 | g /= Lc (g); |
---|
| 445 | appendTestMapDown (result, g, info, source, dest); |
---|
[11bf82] | 446 | F= 1; |
---|
[7bf145] | 447 | return result; |
---|
| 448 | } |
---|
| 449 | else |
---|
| 450 | { |
---|
| 451 | appendMapDown (result, F (y - eval, y), info, source, dest); |
---|
[11bf82] | 452 | F= 1; |
---|
[7bf145] | 453 | return result; |
---|
| 454 | } |
---|
| 455 | } |
---|
| 456 | S= subset (v, s, TT, nosubset); |
---|
| 457 | if (nosubset) break; |
---|
| 458 | subsetDeg= subsetDegree (S); |
---|
| 459 | // skip those combinations that are not possible |
---|
[806c18] | 460 | if (!degs.find (subsetDeg)) |
---|
[7bf145] | 461 | continue; |
---|
[806c18] | 462 | else |
---|
| 463 | { |
---|
[bbb3fbf] | 464 | test= prodMod0 (S, M); |
---|
| 465 | test *= LCBuf; |
---|
| 466 | test = mod (test, M); |
---|
| 467 | if (fdivides (test, buf0)) |
---|
[7bf145] | 468 | { |
---|
[bbb3fbf] | 469 | S.insert (LCBuf); |
---|
| 470 | g= prodMod (S, M); |
---|
| 471 | S.removeFirst(); |
---|
| 472 | g /= content (g, x); |
---|
| 473 | if (fdivides (g, buf, quot)) |
---|
[f047b56] | 474 | { |
---|
[bbb3fbf] | 475 | buf2= g (y - eval, y); |
---|
| 476 | buf2 /= Lc (buf2); |
---|
| 477 | |
---|
| 478 | if (!k && beta.level() == 1) |
---|
[7bf145] | 479 | { |
---|
[bbb3fbf] | 480 | if (degree (buf2, alpha) < degMipoBeta) |
---|
| 481 | { |
---|
| 482 | buf= quot; |
---|
| 483 | LCBuf= LC (buf, x); |
---|
| 484 | recombination= true; |
---|
| 485 | appendTestMapDown (result, buf2, info, source, dest); |
---|
| 486 | trueFactor= true; |
---|
| 487 | } |
---|
[7bf145] | 488 | } |
---|
[bbb3fbf] | 489 | else |
---|
[7bf145] | 490 | { |
---|
[bbb3fbf] | 491 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
[7bf145] | 492 | { |
---|
[bbb3fbf] | 493 | buf= quot; |
---|
| 494 | LCBuf= LC (buf, x); |
---|
| 495 | recombination= true; |
---|
| 496 | appendTestMapDown (result, buf2, info, source, dest); |
---|
| 497 | trueFactor= true; |
---|
[f047b56] | 498 | } |
---|
[bbb3fbf] | 499 | } |
---|
| 500 | if (trueFactor) |
---|
| 501 | { |
---|
| 502 | T= Difference (T, S); |
---|
| 503 | l -= degree (g); |
---|
| 504 | M= power (y, l); |
---|
| 505 | buf0= buf (0, x)*LCBuf; |
---|
| 506 | |
---|
| 507 | // compute new possible degree pattern |
---|
| 508 | bufDegs2= DegreePattern (T); |
---|
| 509 | bufDegs1.intersect (bufDegs2); |
---|
| 510 | bufDegs1.refine (); |
---|
| 511 | if (T.length() < 2*s || T.length() == s || |
---|
| 512 | bufDegs1.getLength() == 1) |
---|
[f047b56] | 513 | { |
---|
[bbb3fbf] | 514 | delete [] v; |
---|
| 515 | if (recombination) |
---|
| 516 | { |
---|
[c49e6f] | 517 | buf= buf (y-eval,y); |
---|
| 518 | buf /= Lc (buf); |
---|
| 519 | appendTestMapDown (result, buf, info, source, |
---|
[bbb3fbf] | 520 | dest); |
---|
| 521 | F= 1; |
---|
| 522 | return result; |
---|
| 523 | } |
---|
| 524 | else |
---|
| 525 | { |
---|
| 526 | appendMapDown (result, F (y - eval, y), info, source, dest); |
---|
| 527 | F= 1; |
---|
| 528 | return result; |
---|
| 529 | } |
---|
[7bf145] | 530 | } |
---|
[bbb3fbf] | 531 | trueFactor= false; |
---|
| 532 | TT= copy (T); |
---|
| 533 | indexUpdate (v, s, T.length(), nosubset); |
---|
| 534 | if (nosubset) break; |
---|
[7bf145] | 535 | } |
---|
| 536 | } |
---|
| 537 | } |
---|
| 538 | } |
---|
| 539 | } |
---|
| 540 | s++; |
---|
[806c18] | 541 | if (T.length() < 2*s || T.length() == s) |
---|
[7bf145] | 542 | { |
---|
[1673386] | 543 | delete [] v; |
---|
[7bf145] | 544 | if (recombination) |
---|
| 545 | { |
---|
[c49e6f] | 546 | buf= buf (y-eval,y); |
---|
| 547 | buf /= Lc (buf); |
---|
| 548 | appendTestMapDown (result, buf, info, source, dest); |
---|
[11bf82] | 549 | F= 1; |
---|
[7bf145] | 550 | return result; |
---|
| 551 | } |
---|
| 552 | else |
---|
| 553 | { |
---|
| 554 | appendMapDown (result, F (y - eval, y), info, source, dest); |
---|
[11bf82] | 555 | F= 1; |
---|
[7bf145] | 556 | return result; |
---|
| 557 | } |
---|
| 558 | } |
---|
| 559 | for (int i= 0; i < T.length(); i++) |
---|
| 560 | v[i]= 0; |
---|
| 561 | nosubset= false; |
---|
| 562 | } |
---|
[806c18] | 563 | if (T.length() < 2*s) |
---|
[11bf82] | 564 | { |
---|
[7bf145] | 565 | appendMapDown (result, F (y - eval, y), info, source, dest); |
---|
[11bf82] | 566 | F= 1; |
---|
| 567 | delete [] v; |
---|
| 568 | return result; |
---|
| 569 | } |
---|
| 570 | |
---|
| 571 | if (s > thres) |
---|
| 572 | { |
---|
| 573 | factors= T; |
---|
| 574 | F= buf; |
---|
| 575 | degs= bufDegs1; |
---|
| 576 | } |
---|
[7bf145] | 577 | |
---|
[1673386] | 578 | delete [] v; |
---|
[806c18] | 579 | return result; |
---|
| 580 | } |
---|
[b28747] | 581 | #endif |
---|
[7bf145] | 582 | |
---|
[806c18] | 583 | /// naive factor recombination as decribed in "Factoring |
---|
| 584 | /// multivariate polynomials over a finite field" by L Bernardin. |
---|
| 585 | CFList |
---|
[11bf82] | 586 | factorRecombination (CFList& factors, CanonicalForm& F, |
---|
[2537fa0] | 587 | const CanonicalForm& N, DegreePattern& degs, const |
---|
| 588 | CanonicalForm& eval, int s, int thres, const modpk& b, |
---|
| 589 | const CanonicalForm& den |
---|
[11bf82] | 590 | ) |
---|
[7bf145] | 591 | { |
---|
| 592 | if (factors.length() == 0) |
---|
[11bf82] | 593 | { |
---|
| 594 | F= 1; |
---|
[7bf145] | 595 | return CFList (); |
---|
[11bf82] | 596 | } |
---|
[e0af3ef] | 597 | if (F.inCoeffDomain()) |
---|
| 598 | return CFList(); |
---|
[2537fa0] | 599 | Variable y= Variable (2); |
---|
[806c18] | 600 | if (degs.getLength() <= 1 || factors.length() == 1) |
---|
[11bf82] | 601 | { |
---|
[2537fa0] | 602 | CFList result= CFList (F(y-eval,y)); |
---|
[11bf82] | 603 | F= 1; |
---|
| 604 | return result; |
---|
| 605 | } |
---|
[27ab36] | 606 | #ifdef DEBUGOUTPUT |
---|
| 607 | if (b.getp() == 0) |
---|
| 608 | DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, N) == F " << |
---|
| 609 | (mod (LC (F, 1)*prodMod (factors, N),N)/Lc (mod (LC (F, 1)*prodMod (factors, N),N)) == F/Lc(F))); |
---|
| 610 | else |
---|
| 611 | DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, N) == F " << |
---|
| 612 | (mod (b(LC (F, 1)*prodMod (factors, N)),N)/Lc (mod (b(LC (F, 1)*prodMod (factors, N)),N)) == F/Lc(F))); |
---|
| 613 | #endif |
---|
[e0af3ef] | 614 | |
---|
[7bf145] | 615 | CFList T, S; |
---|
| 616 | |
---|
[09609a] | 617 | CanonicalForm M= N; |
---|
| 618 | int l= degree (N); |
---|
[7bf145] | 619 | T= factors; |
---|
| 620 | CFList result; |
---|
[a54114] | 621 | Variable x= Variable (1); |
---|
[14e634] | 622 | CanonicalForm denom= den, denQuot; |
---|
| 623 | CanonicalForm LCBuf= LC (F, x)*denom; |
---|
[21b8f4c] | 624 | CanonicalForm g, quot, buf= F; |
---|
[1673386] | 625 | int * v= new int [T.length()]; |
---|
[7bf145] | 626 | for (int i= 0; i < T.length(); i++) |
---|
| 627 | v[i]= 0; |
---|
| 628 | bool nosubset= false; |
---|
| 629 | CFArray TT; |
---|
| 630 | DegreePattern bufDegs1, bufDegs2; |
---|
| 631 | bufDegs1= degs; |
---|
| 632 | int subsetDeg; |
---|
| 633 | TT= copy (factors); |
---|
| 634 | bool recombination= false; |
---|
[bbb3fbf] | 635 | CanonicalForm test; |
---|
[e0af3ef] | 636 | bool isRat= (isOn (SW_RATIONAL) && getCharacteristic() == 0) || |
---|
| 637 | getCharacteristic() > 0; |
---|
[188d2fb] | 638 | if (!isRat) |
---|
| 639 | On (SW_RATIONAL); |
---|
| 640 | CanonicalForm buf0= mulNTL (buf (0, x), LCBuf); |
---|
| 641 | if (!isRat) |
---|
| 642 | Off (SW_RATIONAL); |
---|
[11bf82] | 643 | while (T.length() >= 2*s && s <= thres) |
---|
[7bf145] | 644 | { |
---|
[806c18] | 645 | while (nosubset == false) |
---|
[7bf145] | 646 | { |
---|
[806c18] | 647 | if (T.length() == s) |
---|
[7bf145] | 648 | { |
---|
[1673386] | 649 | delete [] v; |
---|
[7bf145] | 650 | if (recombination) |
---|
| 651 | { |
---|
| 652 | T.insert (LCBuf); |
---|
| 653 | g= prodMod (T, M); |
---|
[eb481b] | 654 | if (b.getp() != 0) |
---|
| 655 | g= b(g); |
---|
[7bf145] | 656 | T.removeFirst(); |
---|
[2537fa0] | 657 | g /= content (g,x); |
---|
| 658 | result.append (g(y-eval,y)); |
---|
[11bf82] | 659 | F= 1; |
---|
[7bf145] | 660 | return result; |
---|
| 661 | } |
---|
| 662 | else |
---|
[11bf82] | 663 | { |
---|
[2537fa0] | 664 | result= CFList (F(y-eval,y)); |
---|
[11bf82] | 665 | F= 1; |
---|
| 666 | return result; |
---|
| 667 | } |
---|
[7bf145] | 668 | } |
---|
| 669 | S= subset (v, s, TT, nosubset); |
---|
| 670 | if (nosubset) break; |
---|
| 671 | subsetDeg= subsetDegree (S); |
---|
| 672 | // skip those combinations that are not possible |
---|
[806c18] | 673 | if (!degs.find (subsetDeg)) |
---|
[7bf145] | 674 | continue; |
---|
[806c18] | 675 | else |
---|
| 676 | { |
---|
[f9da5e] | 677 | if (!isRat) |
---|
| 678 | On (SW_RATIONAL); |
---|
| 679 | test= prodMod0 (S, M); |
---|
| 680 | if (!isRat) |
---|
| 681 | { |
---|
| 682 | test *= bCommonDen (test); |
---|
| 683 | Off (SW_RATIONAL); |
---|
| 684 | } |
---|
[ad0177] | 685 | test= mulNTL (test, LCBuf, b); |
---|
| 686 | test= mod (test, M); |
---|
| 687 | if (uniFdivides (test, buf0)) |
---|
[7bf145] | 688 | { |
---|
[f9da5e] | 689 | if (!isRat) |
---|
| 690 | On (SW_RATIONAL); |
---|
[bbb3fbf] | 691 | S.insert (LCBuf); |
---|
| 692 | g= prodMod (S, M); |
---|
| 693 | S.removeFirst(); |
---|
[f9da5e] | 694 | if (!isRat) |
---|
| 695 | { |
---|
| 696 | g *= bCommonDen(g); |
---|
| 697 | Off (SW_RATIONAL); |
---|
| 698 | } |
---|
[eb481b] | 699 | if (b.getp() != 0) |
---|
| 700 | g= b(g); |
---|
[ad0177] | 701 | if (!isRat) |
---|
| 702 | On (SW_RATIONAL); |
---|
[f9da5e] | 703 | g /= content (g, x); |
---|
[96d5052] | 704 | if (!isRat) |
---|
| 705 | { |
---|
| 706 | On (SW_RATIONAL); |
---|
[14e634] | 707 | if (!Lc (g).inBaseDomain()) |
---|
| 708 | g /= Lc (g); |
---|
[96d5052] | 709 | g *= bCommonDen (g); |
---|
| 710 | Off (SW_RATIONAL); |
---|
| 711 | g /= icontent (g); |
---|
| 712 | On (SW_RATIONAL); |
---|
| 713 | } |
---|
[bbb3fbf] | 714 | if (fdivides (g, buf, quot)) |
---|
[7bf145] | 715 | { |
---|
[14e634] | 716 | denom *= abs (lc (g)); |
---|
[bbb3fbf] | 717 | recombination= true; |
---|
[2537fa0] | 718 | result.append (g (y-eval,y)); |
---|
[e0af3ef] | 719 | if (b.getp() != 0) |
---|
[14e634] | 720 | { |
---|
| 721 | denQuot= bCommonDen (quot); |
---|
| 722 | buf= quot*denQuot; |
---|
| 723 | Off (SW_RATIONAL); |
---|
| 724 | denom /= gcd (denom, denQuot); |
---|
| 725 | On (SW_RATIONAL); |
---|
| 726 | } |
---|
[e0af3ef] | 727 | else |
---|
| 728 | buf= quot; |
---|
[14e634] | 729 | LCBuf= LC (buf, x)*denom; |
---|
[bbb3fbf] | 730 | T= Difference (T, S); |
---|
| 731 | l -= degree (g); |
---|
| 732 | M= power (y, l); |
---|
[188d2fb] | 733 | buf0= mulNTL (buf (0, x), LCBuf); |
---|
[ad0177] | 734 | if (!isRat) |
---|
| 735 | Off (SW_RATIONAL); |
---|
[bbb3fbf] | 736 | // compute new possible degree pattern |
---|
| 737 | bufDegs2= DegreePattern (T); |
---|
| 738 | bufDegs1.intersect (bufDegs2); |
---|
| 739 | bufDegs1.refine (); |
---|
| 740 | if (T.length() < 2*s || T.length() == s || |
---|
| 741 | bufDegs1.getLength() == 1) |
---|
[f047b56] | 742 | { |
---|
[bbb3fbf] | 743 | delete [] v; |
---|
| 744 | if (recombination) |
---|
| 745 | { |
---|
[2537fa0] | 746 | result.append (buf (y-eval,y)); |
---|
[bbb3fbf] | 747 | F= 1; |
---|
| 748 | return result; |
---|
| 749 | } |
---|
| 750 | else |
---|
| 751 | { |
---|
[2537fa0] | 752 | result= CFList (F (y-eval,y)); |
---|
[bbb3fbf] | 753 | F= 1; |
---|
| 754 | return result; |
---|
| 755 | } |
---|
[7bf145] | 756 | } |
---|
[bbb3fbf] | 757 | TT= copy (T); |
---|
| 758 | indexUpdate (v, s, T.length(), nosubset); |
---|
| 759 | if (nosubset) break; |
---|
[806c18] | 760 | } |
---|
[ad0177] | 761 | if (!isRat) |
---|
| 762 | Off (SW_RATIONAL); |
---|
[7bf145] | 763 | } |
---|
| 764 | } |
---|
| 765 | } |
---|
| 766 | s++; |
---|
[806c18] | 767 | if (T.length() < 2*s || T.length() == s) |
---|
[7bf145] | 768 | { |
---|
[1673386] | 769 | delete [] v; |
---|
[7bf145] | 770 | if (recombination) |
---|
| 771 | { |
---|
[2537fa0] | 772 | result.append (buf(y-eval,y)); |
---|
[11bf82] | 773 | F= 1; |
---|
[7bf145] | 774 | return result; |
---|
| 775 | } |
---|
| 776 | else |
---|
[11bf82] | 777 | { |
---|
[2537fa0] | 778 | result= CFList (F(y-eval,y)); |
---|
[11bf82] | 779 | F= 1; |
---|
| 780 | return result; |
---|
| 781 | } |
---|
[7bf145] | 782 | } |
---|
| 783 | for (int i= 0; i < T.length(); i++) |
---|
| 784 | v[i]= 0; |
---|
| 785 | nosubset= false; |
---|
| 786 | } |
---|
[11bf82] | 787 | delete [] v; |
---|
[806c18] | 788 | if (T.length() < 2*s) |
---|
[11bf82] | 789 | { |
---|
[2537fa0] | 790 | result.append (F(y-eval,y)); |
---|
[11bf82] | 791 | F= 1; |
---|
| 792 | return result; |
---|
| 793 | } |
---|
| 794 | |
---|
| 795 | if (s > thres) |
---|
| 796 | { |
---|
| 797 | factors= T; |
---|
| 798 | F= buf; |
---|
| 799 | degs= bufDegs1; |
---|
| 800 | } |
---|
[7bf145] | 801 | |
---|
[806c18] | 802 | return result; |
---|
| 803 | } |
---|
[7bf145] | 804 | |
---|
[7032db] | 805 | #if defined(HAVE_NTL) || defined(HAVE_FLINT) |
---|
[11bf82] | 806 | Variable chooseExtension (const Variable & alpha, const Variable& beta, int k) |
---|
[7bf145] | 807 | { |
---|
[7a1151] | 808 | int i=1, m= 2; |
---|
[11bf82] | 809 | // extension of F_p needed |
---|
| 810 | if (alpha.level() == 1 && beta.level() == 1 && k == 1) |
---|
| 811 | { |
---|
| 812 | i= 1; |
---|
| 813 | m= 2; |
---|
| 814 | } //extension of F_p(alpha) needed but want to factorize over F_p |
---|
| 815 | else if (alpha.level() != 1 && beta.level() == 1 && k == 1) |
---|
| 816 | { |
---|
| 817 | i= 1; |
---|
| 818 | m= degree (getMipo (alpha)) + 1; |
---|
| 819 | } //extension of F_p(alpha) needed for first time |
---|
| 820 | else if (alpha.level() != 1 && beta.level() == 1 && k != 1) |
---|
| 821 | { |
---|
[7bf145] | 822 | i= 2; |
---|
[11bf82] | 823 | m= degree (getMipo (alpha)); |
---|
| 824 | } |
---|
| 825 | else if (alpha.level() != 1 && beta.level() != 1 && k != 1) |
---|
| 826 | { |
---|
| 827 | m= degree (getMipo (beta)); |
---|
| 828 | i= degree (getMipo (alpha))/m + 1; |
---|
| 829 | } |
---|
[f87a54f] | 830 | #if defined(HAVE_FLINT) |
---|
[9e20b9f] | 831 | nmod_poly_t Irredpoly; |
---|
| 832 | nmod_poly_init(Irredpoly,getCharacteristic()); |
---|
[03c742] | 833 | nmod_poly_randtest_monic_irreducible(Irredpoly,FLINTrandom,i*m+1); |
---|
| 834 | CanonicalForm newMipo= convertnmod_poly_t2FacCF(Irredpoly,Variable (1)); |
---|
[f87a54f] | 835 | #elif defined(HAVE_NTL) |
---|
[9e20b9f] | 836 | if (fac_NTL_char != getCharacteristic()) |
---|
| 837 | { |
---|
| 838 | fac_NTL_char= getCharacteristic(); |
---|
| 839 | zz_p::init (getCharacteristic()); |
---|
| 840 | } |
---|
| 841 | zz_pX NTLIrredpoly; |
---|
[f87a54f] | 842 | BuildIrred (NTLIrredpoly, i*m); |
---|
| 843 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
[7fdedf] | 844 | #else |
---|
| 845 | factoryError("NTL/FLINT missing: chooseExtension"); |
---|
[03c742] | 846 | #endif |
---|
[7bf145] | 847 | return rootOf (newMipo); |
---|
| 848 | } |
---|
[7032db] | 849 | #endif |
---|
[7bf145] | 850 | |
---|
[1a3011e] | 851 | void |
---|
| 852 | earlyFactorDetection (CFList& reconstructedFactors, CanonicalForm& F, CFList& |
---|
| 853 | factors, int& adaptedLiftBound, int*& factorsFoundIndex, |
---|
[fea494] | 854 | DegreePattern& degs, bool& success, int deg, const |
---|
[2537fa0] | 855 | CanonicalForm& eval, const modpk& b, CanonicalForm& den) |
---|
[7bf145] | 856 | { |
---|
| 857 | DegreePattern bufDegs1= degs; |
---|
| 858 | DegreePattern bufDegs2; |
---|
| 859 | CFList T= factors; |
---|
| 860 | CanonicalForm buf= F; |
---|
[a54114] | 861 | Variable x= Variable (1); |
---|
[2537fa0] | 862 | Variable y= Variable (2); |
---|
[21b8f4c] | 863 | CanonicalForm g, quot; |
---|
[7bf145] | 864 | CanonicalForm M= power (F.mvar(), deg); |
---|
| 865 | adaptedLiftBound= 0; |
---|
[1a3011e] | 866 | int d= degree (F), l= 0; |
---|
[7c4341] | 867 | bool isRat= (isOn (SW_RATIONAL) && getCharacteristic() == 0) || |
---|
| 868 | getCharacteristic() > 0; |
---|
[188d2fb] | 869 | if (!isRat) |
---|
| 870 | On (SW_RATIONAL); |
---|
[e0af3ef] | 871 | if (b.getp() != 0) |
---|
| 872 | buf *= bCommonDen (buf); |
---|
[14e634] | 873 | CanonicalForm LCBuf= LC (buf, x)*den; |
---|
[41fea7] | 874 | CanonicalForm buf0= mulNTL (buf (0,x), LCBuf); |
---|
| 875 | CanonicalForm buf1= mulNTL (buf (1,x), LCBuf); |
---|
[188d2fb] | 876 | if (!isRat) |
---|
| 877 | Off (SW_RATIONAL); |
---|
[de222e] | 878 | CanonicalForm test0, test1; |
---|
[14e634] | 879 | CanonicalForm denQuot; |
---|
[188d2fb] | 880 | |
---|
[1a3011e] | 881 | for (CFListIterator i= factors; i.hasItem(); i++, l++) |
---|
[7bf145] | 882 | { |
---|
[1a3011e] | 883 | if (!bufDegs1.find (degree (i.getItem(), 1)) || factorsFoundIndex[l] == 1) |
---|
[7bf145] | 884 | continue; |
---|
| 885 | else |
---|
| 886 | { |
---|
[de222e] | 887 | test1= mod (mulNTL (i.getItem() (1,x), LCBuf, b), M); |
---|
| 888 | if (uniFdivides (test1, buf1)) |
---|
[7bf145] | 889 | { |
---|
[de222e] | 890 | test0= mod (mulNTL (i.getItem() (0,x), LCBuf, b), M); |
---|
| 891 | if (uniFdivides (test0, buf0)) |
---|
[7bf145] | 892 | { |
---|
[f9da5e] | 893 | if (!isRat) |
---|
| 894 | On (SW_RATIONAL); |
---|
[de222e] | 895 | g= mulMod2 (i.getItem(), LCBuf, M); |
---|
[f9da5e] | 896 | if (!isRat) |
---|
| 897 | { |
---|
| 898 | g *= bCommonDen(g); |
---|
| 899 | Off (SW_RATIONAL); |
---|
| 900 | } |
---|
[de222e] | 901 | if (b.getp() != 0) |
---|
| 902 | g= b(g); |
---|
[ad0177] | 903 | if (!isRat) |
---|
| 904 | On (SW_RATIONAL); |
---|
[f9da5e] | 905 | g /= content (g, x); |
---|
[96d5052] | 906 | if (!isRat) |
---|
| 907 | { |
---|
| 908 | On (SW_RATIONAL); |
---|
[14e634] | 909 | if (!Lc (g).inBaseDomain()) |
---|
| 910 | g /= Lc (g); |
---|
[96d5052] | 911 | g *= bCommonDen (g); |
---|
| 912 | Off (SW_RATIONAL); |
---|
| 913 | g /= icontent (g); |
---|
| 914 | On (SW_RATIONAL); |
---|
| 915 | } |
---|
[de222e] | 916 | if (fdivides (g, buf, quot)) |
---|
| 917 | { |
---|
[14e634] | 918 | den *= abs (lc (g)); |
---|
[2537fa0] | 919 | reconstructedFactors.append (g (y-eval,y)); |
---|
[de222e] | 920 | factorsFoundIndex[l]= 1; |
---|
[e0af3ef] | 921 | if (b.getp() != 0) |
---|
[14e634] | 922 | { |
---|
| 923 | denQuot= bCommonDen (quot); |
---|
| 924 | buf= quot*denQuot; |
---|
| 925 | Off (SW_RATIONAL); |
---|
| 926 | den /= gcd (den, denQuot); |
---|
| 927 | On (SW_RATIONAL); |
---|
| 928 | } |
---|
[e0af3ef] | 929 | else |
---|
| 930 | buf= quot; |
---|
[de222e] | 931 | d -= degree (g); |
---|
[14e634] | 932 | LCBuf= LC (buf, x)*den; |
---|
[41fea7] | 933 | buf0= mulNTL (buf (0,x), LCBuf); |
---|
| 934 | buf1= mulNTL (buf (1,x), LCBuf); |
---|
[188d2fb] | 935 | if (!isRat) |
---|
| 936 | Off (SW_RATIONAL); |
---|
[de222e] | 937 | T= Difference (T, CFList (i.getItem())); |
---|
| 938 | F= buf; |
---|
| 939 | |
---|
| 940 | // compute new possible degree pattern |
---|
| 941 | bufDegs2= DegreePattern (T); |
---|
| 942 | bufDegs1.intersect (bufDegs2); |
---|
| 943 | bufDegs1.refine (); |
---|
| 944 | if (bufDegs1.getLength() <= 1) |
---|
| 945 | { |
---|
[e0af3ef] | 946 | if (!buf.inCoeffDomain()) |
---|
[0facdc] | 947 | { |
---|
[2537fa0] | 948 | reconstructedFactors.append (buf (y-eval,y)); |
---|
[0facdc] | 949 | F= 1; |
---|
| 950 | } |
---|
[de222e] | 951 | break; |
---|
| 952 | } |
---|
| 953 | } |
---|
[ad0177] | 954 | if (!isRat) |
---|
| 955 | Off (SW_RATIONAL); |
---|
[7bf145] | 956 | } |
---|
| 957 | } |
---|
| 958 | } |
---|
| 959 | } |
---|
| 960 | adaptedLiftBound= d + 1; |
---|
[db65ada] | 961 | if (adaptedLiftBound < deg) |
---|
[7bf145] | 962 | { |
---|
| 963 | degs= bufDegs1; |
---|
[69c882] | 964 | success= true; |
---|
[7bf145] | 965 | } |
---|
| 966 | if (bufDegs1.getLength() <= 1) |
---|
| 967 | degs= bufDegs1; |
---|
| 968 | } |
---|
| 969 | |
---|
[14e634] | 970 | void |
---|
| 971 | earlyFactorDetection (CFList& reconstructedFactors, CanonicalForm& F, CFList& |
---|
| 972 | factors, int& adaptedLiftBound, int*& factorsFoundIndex, |
---|
[2537fa0] | 973 | DegreePattern& degs, bool& success, int deg, const |
---|
| 974 | CanonicalForm& eval, const modpk& b) |
---|
[14e634] | 975 | { |
---|
| 976 | CanonicalForm den= 1; |
---|
[2537fa0] | 977 | earlyFactorDetection (reconstructedFactors, F, factors, adaptedLiftBound, |
---|
| 978 | factorsFoundIndex, degs, success, deg, eval, b, den); |
---|
[14e634] | 979 | } |
---|
| 980 | |
---|
[1a3011e] | 981 | void |
---|
| 982 | extEarlyFactorDetection (CFList& reconstructedFactors, CanonicalForm& F, CFList& |
---|
| 983 | factors,int& adaptedLiftBound, int*& factorsFoundIndex, |
---|
| 984 | DegreePattern& degs, bool& success, const |
---|
| 985 | ExtensionInfo& info, const CanonicalForm& eval, int deg |
---|
| 986 | ) |
---|
[7bf145] | 987 | { |
---|
| 988 | Variable alpha= info.getAlpha(); |
---|
| 989 | Variable beta= info.getBeta(); |
---|
| 990 | CanonicalForm gamma= info.getGamma(); |
---|
| 991 | CanonicalForm delta= info.getDelta(); |
---|
| 992 | int k= info.getGFDegree(); |
---|
| 993 | DegreePattern bufDegs1= degs, bufDegs2; |
---|
[806c18] | 994 | CFList result; |
---|
[7bf145] | 995 | CFList T= factors; |
---|
| 996 | Variable y= F.mvar(); |
---|
[a54114] | 997 | Variable x= Variable (1); |
---|
| 998 | CanonicalForm buf= F, LCBuf= LC (buf, x), g, buf2; |
---|
[7bf145] | 999 | CanonicalForm M= power (y, deg); |
---|
| 1000 | adaptedLiftBound= 0; |
---|
[93134c] | 1001 | bool trueFactor= false; |
---|
[1a3011e] | 1002 | int d= degree (F), l= 0; |
---|
[7bf145] | 1003 | CFList source, dest; |
---|
[ac8e1a] | 1004 | int degMipoBeta= 1; |
---|
| 1005 | if (!k && beta.level() != 1) |
---|
[7bf145] | 1006 | degMipoBeta= degree (getMipo (beta)); |
---|
[21b8f4c] | 1007 | CanonicalForm quot; |
---|
[1a3011e] | 1008 | for (CFListIterator i= factors; i.hasItem(); i++, l++) |
---|
[7bf145] | 1009 | { |
---|
[1a3011e] | 1010 | if (!bufDegs1.find (degree (i.getItem(), 1)) || factorsFoundIndex[l] == 1) |
---|
[7bf145] | 1011 | continue; |
---|
| 1012 | else |
---|
| 1013 | { |
---|
[f047b56] | 1014 | g= mulMod2 (i.getItem(), LCBuf, M); |
---|
| 1015 | g /= content (g, x); |
---|
| 1016 | if (fdivides (g, buf, quot)) |
---|
[7bf145] | 1017 | { |
---|
[f047b56] | 1018 | buf2= g (y - eval, y); |
---|
| 1019 | buf2 /= Lc (buf2); |
---|
[806c18] | 1020 | |
---|
[f047b56] | 1021 | if (!k && beta == x) |
---|
| 1022 | { |
---|
| 1023 | if (degree (buf2, alpha) < degMipoBeta) |
---|
[7bf145] | 1024 | { |
---|
[1a3011e] | 1025 | appendTestMapDown (reconstructedFactors, buf2, info, source, dest); |
---|
| 1026 | factorsFoundIndex[l]= 1; |
---|
[f047b56] | 1027 | buf= quot; |
---|
| 1028 | d -= degree (g); |
---|
| 1029 | LCBuf= LC (buf, x); |
---|
| 1030 | trueFactor= true; |
---|
[7bf145] | 1031 | } |
---|
[f047b56] | 1032 | } |
---|
| 1033 | else |
---|
| 1034 | { |
---|
| 1035 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
[7bf145] | 1036 | { |
---|
[1a3011e] | 1037 | appendTestMapDown (reconstructedFactors, buf2, info, source, dest); |
---|
| 1038 | factorsFoundIndex[l]= 1; |
---|
[f047b56] | 1039 | buf= quot; |
---|
| 1040 | d -= degree (g); |
---|
| 1041 | LCBuf= LC (buf, x); |
---|
| 1042 | trueFactor= true; |
---|
[806c18] | 1043 | } |
---|
[f047b56] | 1044 | } |
---|
| 1045 | if (trueFactor) |
---|
| 1046 | { |
---|
| 1047 | T= Difference (T, CFList (i.getItem())); |
---|
[69c882] | 1048 | F= buf; |
---|
[93134c] | 1049 | |
---|
[f047b56] | 1050 | // compute new possible degree pattern |
---|
| 1051 | bufDegs2= DegreePattern (T); |
---|
| 1052 | bufDegs1.intersect (bufDegs2); |
---|
| 1053 | bufDegs1.refine (); |
---|
| 1054 | trueFactor= false; |
---|
| 1055 | if (bufDegs1.getLength() <= 1) |
---|
| 1056 | { |
---|
[e0af3ef] | 1057 | if (!buf.inCoeffDomain()) |
---|
| 1058 | { |
---|
| 1059 | buf= buf (y - eval, y); |
---|
| 1060 | buf /= Lc (buf); |
---|
| 1061 | appendMapDown (reconstructedFactors, buf, info, source, dest); |
---|
[0facdc] | 1062 | F= 1; |
---|
[e0af3ef] | 1063 | } |
---|
[f047b56] | 1064 | break; |
---|
[7bf145] | 1065 | } |
---|
| 1066 | } |
---|
| 1067 | } |
---|
| 1068 | } |
---|
| 1069 | } |
---|
| 1070 | adaptedLiftBound= d + 1; |
---|
| 1071 | if (adaptedLiftBound < deg) |
---|
| 1072 | { |
---|
| 1073 | degs= bufDegs1; |
---|
[69c882] | 1074 | success= true; |
---|
[7bf145] | 1075 | } |
---|
| 1076 | if (bufDegs1.getLength() <= 1) |
---|
| 1077 | degs= bufDegs1; |
---|
| 1078 | } |
---|
| 1079 | |
---|
[34e062] | 1080 | int* |
---|
| 1081 | getCombinations (int * rightSide, int sizeOfRightSide, int& sizeOfOutput, |
---|
| 1082 | int degreeLC) |
---|
| 1083 | { |
---|
| 1084 | Variable x= Variable (1); |
---|
| 1085 | int p= getCharacteristic(); |
---|
| 1086 | int d= getGFDegree(); |
---|
| 1087 | char cGFName= gf_name; |
---|
| 1088 | setCharacteristic(0); |
---|
| 1089 | CanonicalForm buf= 1; |
---|
| 1090 | for (int i= 0; i < sizeOfRightSide; i++) |
---|
| 1091 | buf *= (power (x, rightSide [i]) + 1); |
---|
| 1092 | |
---|
| 1093 | int j= 0; |
---|
| 1094 | for (CFIterator i= buf; i.hasTerms(); i++, j++) |
---|
| 1095 | { |
---|
| 1096 | if (i.exp() < degreeLC) |
---|
| 1097 | { |
---|
| 1098 | j++; |
---|
| 1099 | break; |
---|
| 1100 | } |
---|
| 1101 | } |
---|
| 1102 | |
---|
| 1103 | ASSERT ( j > 1, "j > 1 expected" ); |
---|
| 1104 | |
---|
| 1105 | int* result = new int [j - 1]; |
---|
| 1106 | sizeOfOutput= j - 1; |
---|
| 1107 | |
---|
| 1108 | int i= 0; |
---|
| 1109 | for (CFIterator m = buf; i < j - 1; i++, m++) |
---|
| 1110 | result [i]= m.exp(); |
---|
| 1111 | |
---|
| 1112 | if (d > 1) |
---|
| 1113 | setCharacteristic (p, d, cGFName); |
---|
| 1114 | else |
---|
| 1115 | setCharacteristic (p); |
---|
| 1116 | return result; |
---|
| 1117 | } |
---|
| 1118 | |
---|
| 1119 | int * |
---|
| 1120 | getLiftPrecisions (const CanonicalForm& F, int& sizeOfOutput, int degreeLC) |
---|
| 1121 | { |
---|
| 1122 | int sizeOfNewtonPoly; |
---|
| 1123 | int ** newtonPolyg= newtonPolygon (F, sizeOfNewtonPoly); |
---|
| 1124 | int sizeOfRightSide; |
---|
| 1125 | int * rightSide= getRightSide(newtonPolyg, sizeOfNewtonPoly, sizeOfRightSide); |
---|
| 1126 | int * result= getCombinations(rightSide, sizeOfRightSide, sizeOfOutput, |
---|
| 1127 | degreeLC); |
---|
| 1128 | delete [] rightSide; |
---|
| 1129 | for (int i= 0; i < sizeOfNewtonPoly; i++) |
---|
| 1130 | delete [] newtonPolyg[i]; |
---|
| 1131 | delete [] newtonPolyg; |
---|
| 1132 | return result; |
---|
| 1133 | } |
---|
| 1134 | |
---|
[1a3011e] | 1135 | void |
---|
[69c882] | 1136 | deleteFactors (CFList& factors, int* factorsFoundIndex) |
---|
[1a3011e] | 1137 | { |
---|
[69c882] | 1138 | CFList result; |
---|
| 1139 | int i= 0; |
---|
| 1140 | for (CFListIterator iter= factors; iter.hasItem(); iter++, i++) |
---|
[1a3011e] | 1141 | { |
---|
[69c882] | 1142 | if (factorsFoundIndex[i] == 1) |
---|
| 1143 | continue; |
---|
[1a3011e] | 1144 | else |
---|
[69c882] | 1145 | result.append (iter.getItem()); |
---|
[1a3011e] | 1146 | } |
---|
[69c882] | 1147 | factors= result; |
---|
[1a3011e] | 1148 | } |
---|
| 1149 | |
---|
[03c742] | 1150 | #ifdef HAVE_NTL // henselLift12 |
---|
[7bf145] | 1151 | CFList |
---|
[806c18] | 1152 | henselLiftAndEarly (CanonicalForm& A, bool& earlySuccess, CFList& |
---|
[7bf145] | 1153 | earlyFactors, DegreePattern& degs, int& liftBound, |
---|
[806c18] | 1154 | const CFList& uniFactors, const ExtensionInfo& info, |
---|
[14e634] | 1155 | const CanonicalForm& eval,modpk& b, CanonicalForm& den) |
---|
[7bf145] | 1156 | { |
---|
| 1157 | Variable alpha= info.getAlpha(); |
---|
| 1158 | Variable beta= info.getBeta(); |
---|
| 1159 | CanonicalForm gamma= info.getGamma(); |
---|
| 1160 | CanonicalForm delta= info.getDelta(); |
---|
| 1161 | bool extension= info.isInExtension(); |
---|
| 1162 | |
---|
[69076c] | 1163 | int sizeOfLiftPre; |
---|
| 1164 | int * liftPre= getLiftPrecisions (A, sizeOfLiftPre, degree (LC (A, 1), 2)); |
---|
| 1165 | |
---|
[7bf145] | 1166 | Variable x= Variable (1); |
---|
| 1167 | Variable y= Variable (2); |
---|
| 1168 | CFArray Pi; |
---|
| 1169 | CFList diophant; |
---|
| 1170 | CFList bufUniFactors= uniFactors; |
---|
[14e634] | 1171 | On (SW_RATIONAL); |
---|
[eb481b] | 1172 | CanonicalForm bufA= A; |
---|
[14e634] | 1173 | if (!Lc (A).inBaseDomain()) |
---|
| 1174 | { |
---|
| 1175 | bufA /= Lc (A); |
---|
| 1176 | CanonicalForm denBufA= bCommonDen (bufA); |
---|
| 1177 | bufA *= denBufA; |
---|
| 1178 | Off (SW_RATIONAL); |
---|
| 1179 | den /= gcd (den, denBufA); |
---|
| 1180 | } |
---|
| 1181 | else |
---|
| 1182 | { |
---|
| 1183 | bufA= A; |
---|
| 1184 | Off (SW_RATIONAL); |
---|
| 1185 | den /= gcd (den, Lc (A)); |
---|
| 1186 | } |
---|
[eb481b] | 1187 | CanonicalForm lcA0= 0; |
---|
[f9da5e] | 1188 | bool mipoHasDen= false; |
---|
[eb481b] | 1189 | if (getCharacteristic() == 0 && b.getp() != 0) |
---|
| 1190 | { |
---|
[41fea7] | 1191 | if (alpha.level() == 1) |
---|
| 1192 | { |
---|
| 1193 | lcA0= lc (A (0, 2)); |
---|
| 1194 | A *= b.inverse (lcA0); |
---|
| 1195 | A= b (A); |
---|
| 1196 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
| 1197 | i.getItem()= b (i.getItem()*b.inverse (lc (i.getItem()))); |
---|
| 1198 | } |
---|
| 1199 | else |
---|
| 1200 | { |
---|
| 1201 | lcA0= Lc (A (0,2)); |
---|
[f9da5e] | 1202 | On (SW_RATIONAL); |
---|
| 1203 | mipoHasDen= !bCommonDen(getMipo(alpha)).isOne(); |
---|
| 1204 | Off (SW_RATIONAL); |
---|
| 1205 | CanonicalForm lcA0inverse= b.inverse (lcA0); |
---|
[41fea7] | 1206 | A *= lcA0inverse; |
---|
| 1207 | A= b (A); |
---|
| 1208 | // Lc of bufUniFactors is in Z |
---|
| 1209 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
| 1210 | i.getItem()= b (i.getItem()*b.inverse (lc (i.getItem()))); |
---|
| 1211 | } |
---|
[eb481b] | 1212 | } |
---|
[7bf145] | 1213 | bufUniFactors.insert (LC (A, x)); |
---|
| 1214 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length() - 1); |
---|
| 1215 | earlySuccess= false; |
---|
| 1216 | int newLiftBound= 0; |
---|
[69076c] | 1217 | |
---|
| 1218 | int smallFactorDeg= tmin (11, liftPre [sizeOfLiftPre- 1] + 1);//this is a tunable parameter |
---|
| 1219 | int dummy; |
---|
[1a3011e] | 1220 | int * factorsFoundIndex= new int [uniFactors.length()]; |
---|
| 1221 | for (int i= 0; i < uniFactors.length(); i++) |
---|
| 1222 | factorsFoundIndex [i]= 0; |
---|
| 1223 | |
---|
[f9da5e] | 1224 | CFList bufBufUniFactors; |
---|
| 1225 | Variable v= alpha; |
---|
[69076c] | 1226 | if (smallFactorDeg >= liftBound || degree (A,y) <= 4) |
---|
[69fdf90] | 1227 | henselLift12 (A, bufUniFactors, liftBound, Pi, diophant, M, b, true); |
---|
[69076c] | 1228 | else if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
[7bf145] | 1229 | { |
---|
[69fdf90] | 1230 | henselLift12 (A, bufUniFactors, smallFactorDeg, Pi, diophant, M, b, true); |
---|
[f9da5e] | 1231 | if (mipoHasDen) |
---|
| 1232 | { |
---|
| 1233 | for (CFListIterator iter= bufUniFactors; iter.hasItem(); iter++) |
---|
| 1234 | if (hasFirstAlgVar (iter.getItem(), v)) |
---|
| 1235 | break; |
---|
| 1236 | if (v != alpha) |
---|
| 1237 | { |
---|
| 1238 | bufBufUniFactors= bufUniFactors; |
---|
| 1239 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
| 1240 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
| 1241 | A= replacevar (A, alpha, v); |
---|
| 1242 | } |
---|
| 1243 | } |
---|
| 1244 | |
---|
[7bf145] | 1245 | if (!extension) |
---|
[f9da5e] | 1246 | { |
---|
| 1247 | if (v==alpha) |
---|
| 1248 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
| 1249 | factorsFoundIndex, degs, earlySuccess, |
---|
[2537fa0] | 1250 | smallFactorDeg, eval, b, den); |
---|
[f9da5e] | 1251 | else |
---|
| 1252 | earlyFactorDetection(earlyFactors, bufA, bufBufUniFactors, newLiftBound, |
---|
| 1253 | factorsFoundIndex, degs, earlySuccess, |
---|
[2537fa0] | 1254 | smallFactorDeg, eval, b, den); |
---|
[f9da5e] | 1255 | } |
---|
[7bf145] | 1256 | else |
---|
[69c882] | 1257 | extEarlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
[1a3011e] | 1258 | factorsFoundIndex, degs, earlySuccess, info, |
---|
| 1259 | eval, smallFactorDeg); |
---|
[69076c] | 1260 | if (degs.getLength() > 1 && !earlySuccess && |
---|
| 1261 | smallFactorDeg != liftPre [sizeOfLiftPre-1] + 1) |
---|
[7bf145] | 1262 | { |
---|
[69076c] | 1263 | if (newLiftBound >= liftPre[sizeOfLiftPre-1]+1) |
---|
[7bf145] | 1264 | { |
---|
[69076c] | 1265 | bufUniFactors.insert (LC (A, x)); |
---|
| 1266 | henselLiftResume12 (A, bufUniFactors, smallFactorDeg, |
---|
[eb481b] | 1267 | liftPre[sizeOfLiftPre-1] + 1, Pi, diophant, M, b); |
---|
[f9da5e] | 1268 | if (v!=alpha) |
---|
| 1269 | { |
---|
| 1270 | bufBufUniFactors= bufUniFactors; |
---|
| 1271 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
| 1272 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
| 1273 | } |
---|
[69076c] | 1274 | if (!extension) |
---|
[f9da5e] | 1275 | { |
---|
| 1276 | if (v==alpha) |
---|
[69c882] | 1277 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
[1a3011e] | 1278 | factorsFoundIndex, degs, earlySuccess, |
---|
[2537fa0] | 1279 | liftPre[sizeOfLiftPre-1] + 1, eval, b, den); |
---|
[f9da5e] | 1280 | else |
---|
| 1281 | earlyFactorDetection (earlyFactors,bufA,bufBufUniFactors,newLiftBound, |
---|
| 1282 | factorsFoundIndex, degs, earlySuccess, |
---|
[2537fa0] | 1283 | liftPre[sizeOfLiftPre-1] + 1, eval, b, den); |
---|
[f9da5e] | 1284 | } |
---|
[69076c] | 1285 | else |
---|
[f9da5e] | 1286 | extEarlyFactorDetection (earlyFactors,bufA,bufUniFactors,newLiftBound, |
---|
[1a3011e] | 1287 | factorsFoundIndex, degs, earlySuccess, info, |
---|
| 1288 | eval, liftPre[sizeOfLiftPre-1] + 1); |
---|
[7bf145] | 1289 | } |
---|
| 1290 | } |
---|
| 1291 | else if (earlySuccess) |
---|
| 1292 | liftBound= newLiftBound; |
---|
[69076c] | 1293 | |
---|
| 1294 | int i= sizeOfLiftPre - 1; |
---|
| 1295 | while (degs.getLength() > 1 && !earlySuccess && i - 1 >= 0) |
---|
| 1296 | { |
---|
| 1297 | if (newLiftBound >= liftPre[i] + 1) |
---|
| 1298 | { |
---|
| 1299 | bufUniFactors.insert (LC (A, x)); |
---|
| 1300 | henselLiftResume12 (A, bufUniFactors, liftPre[i] + 1, |
---|
[eb481b] | 1301 | liftPre[i-1] + 1, Pi, diophant, M, b); |
---|
[f9da5e] | 1302 | if (v!=alpha) |
---|
| 1303 | { |
---|
| 1304 | bufBufUniFactors= bufUniFactors; |
---|
| 1305 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
| 1306 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
| 1307 | } |
---|
[69076c] | 1308 | if (!extension) |
---|
[f9da5e] | 1309 | { |
---|
| 1310 | if (v==alpha) |
---|
[69c882] | 1311 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
[1a3011e] | 1312 | factorsFoundIndex, degs, earlySuccess, |
---|
[2537fa0] | 1313 | liftPre[i-1] + 1, eval, b, den); |
---|
[f9da5e] | 1314 | else |
---|
| 1315 | earlyFactorDetection (earlyFactors,bufA,bufBufUniFactors,newLiftBound, |
---|
| 1316 | factorsFoundIndex, degs, earlySuccess, |
---|
[2537fa0] | 1317 | liftPre[i-1] + 1, eval, b, den); |
---|
[f9da5e] | 1318 | } |
---|
[69076c] | 1319 | else |
---|
[f9da5e] | 1320 | extEarlyFactorDetection (earlyFactors,bufA,bufUniFactors,newLiftBound, |
---|
[1a3011e] | 1321 | factorsFoundIndex, degs, earlySuccess, info, |
---|
| 1322 | eval, liftPre[i-1] + 1); |
---|
[69076c] | 1323 | } |
---|
| 1324 | else |
---|
| 1325 | { |
---|
| 1326 | liftBound= newLiftBound; |
---|
| 1327 | break; |
---|
| 1328 | } |
---|
| 1329 | i--; |
---|
| 1330 | } |
---|
| 1331 | if (earlySuccess) |
---|
| 1332 | liftBound= newLiftBound; |
---|
| 1333 | //after here all factors are lifted to liftPre[sizeOfLiftPre-1] |
---|
[7bf145] | 1334 | } |
---|
[69076c] | 1335 | else |
---|
[806c18] | 1336 | { |
---|
[69fdf90] | 1337 | henselLift12 (A, bufUniFactors, smallFactorDeg, Pi, diophant, M, b, true); |
---|
[f9da5e] | 1338 | if (mipoHasDen) |
---|
| 1339 | { |
---|
| 1340 | for (CFListIterator iter= bufUniFactors; iter.hasItem(); iter++) |
---|
| 1341 | if (hasFirstAlgVar (iter.getItem(), v)) |
---|
| 1342 | break; |
---|
| 1343 | if (v != alpha) |
---|
| 1344 | { |
---|
| 1345 | bufBufUniFactors= bufUniFactors; |
---|
| 1346 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
| 1347 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
| 1348 | A= replacevar (A, alpha, v); |
---|
| 1349 | } |
---|
| 1350 | } |
---|
[7bf145] | 1351 | if (!extension) |
---|
[f9da5e] | 1352 | { |
---|
| 1353 | if (v==alpha) |
---|
[69c882] | 1354 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
[1a3011e] | 1355 | factorsFoundIndex, degs, earlySuccess, |
---|
[2537fa0] | 1356 | smallFactorDeg, eval, b, den); |
---|
[f9da5e] | 1357 | else |
---|
| 1358 | earlyFactorDetection (earlyFactors, bufA, bufBufUniFactors, newLiftBound, |
---|
| 1359 | factorsFoundIndex, degs, earlySuccess, |
---|
[2537fa0] | 1360 | smallFactorDeg, eval, b, den); |
---|
[f9da5e] | 1361 | } |
---|
[7bf145] | 1362 | else |
---|
[69c882] | 1363 | extEarlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
[1a3011e] | 1364 | factorsFoundIndex, degs, earlySuccess, info, |
---|
| 1365 | eval, smallFactorDeg); |
---|
[69076c] | 1366 | int i= 1; |
---|
| 1367 | while ((degree (A,y)/4)*i + 4 <= smallFactorDeg) |
---|
| 1368 | i++; |
---|
| 1369 | dummy= tmin (degree (A,y)+1, (degree (A,y)/4)*i+4); |
---|
| 1370 | if (degs.getLength() > 1 && !earlySuccess && dummy > smallFactorDeg) |
---|
[7bf145] | 1371 | { |
---|
| 1372 | bufUniFactors.insert (LC (A, x)); |
---|
[69076c] | 1373 | henselLiftResume12 (A, bufUniFactors, smallFactorDeg, |
---|
[eb481b] | 1374 | dummy, Pi, diophant, M, b); |
---|
[f9da5e] | 1375 | if (v!=alpha) |
---|
| 1376 | { |
---|
| 1377 | bufBufUniFactors= bufUniFactors; |
---|
| 1378 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
| 1379 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
| 1380 | } |
---|
[7bf145] | 1381 | if (!extension) |
---|
[f9da5e] | 1382 | { |
---|
| 1383 | if (v==alpha) |
---|
[69c882] | 1384 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
[2537fa0] | 1385 | factorsFoundIndex, degs, earlySuccess, dummy,eval, |
---|
| 1386 | b, den); |
---|
[f9da5e] | 1387 | else |
---|
| 1388 | earlyFactorDetection (earlyFactors, bufA,bufBufUniFactors, newLiftBound, |
---|
[2537fa0] | 1389 | factorsFoundIndex, degs, earlySuccess, dummy,eval, |
---|
| 1390 | b, den); |
---|
[f9da5e] | 1391 | } |
---|
[7bf145] | 1392 | else |
---|
[f9da5e] | 1393 | extEarlyFactorDetection (earlyFactors, bufA,bufUniFactors, newLiftBound, |
---|
[1a3011e] | 1394 | factorsFoundIndex, degs, earlySuccess, info, |
---|
| 1395 | eval, dummy); |
---|
[69076c] | 1396 | } |
---|
| 1397 | while (degs.getLength() > 1 && !earlySuccess && i < 4) |
---|
| 1398 | { |
---|
| 1399 | if (newLiftBound >= dummy) |
---|
[7bf145] | 1400 | { |
---|
[69076c] | 1401 | bufUniFactors.insert (LC (A, x)); |
---|
| 1402 | dummy= tmin (degree (A,y)+1, (degree (A,y)/4)*(i+1)+4); |
---|
| 1403 | henselLiftResume12 (A, bufUniFactors, (degree (A,y)/4)*i + 4, |
---|
[eb481b] | 1404 | dummy, Pi, diophant, M, b); |
---|
[f9da5e] | 1405 | if (v!=alpha) |
---|
| 1406 | { |
---|
| 1407 | bufBufUniFactors= bufUniFactors; |
---|
| 1408 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
| 1409 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
| 1410 | } |
---|
[69076c] | 1411 | if (!extension) |
---|
[f9da5e] | 1412 | { |
---|
| 1413 | if (v==alpha) |
---|
[69c882] | 1414 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
[2537fa0] | 1415 | factorsFoundIndex, degs, earlySuccess, dummy, |
---|
| 1416 | eval, b, den); |
---|
[f9da5e] | 1417 | else |
---|
| 1418 | earlyFactorDetection (earlyFactors,bufA,bufBufUniFactors,newLiftBound, |
---|
[2537fa0] | 1419 | factorsFoundIndex, degs, earlySuccess, dummy, |
---|
| 1420 | eval, b, den); |
---|
[f9da5e] | 1421 | } |
---|
[69076c] | 1422 | else |
---|
[f9da5e] | 1423 | extEarlyFactorDetection (earlyFactors,bufA,bufUniFactors,newLiftBound, |
---|
[1a3011e] | 1424 | factorsFoundIndex, degs, earlySuccess, info, |
---|
| 1425 | eval, dummy); |
---|
[7bf145] | 1426 | } |
---|
[69076c] | 1427 | else |
---|
| 1428 | { |
---|
[7bf145] | 1429 | liftBound= newLiftBound; |
---|
[69076c] | 1430 | break; |
---|
| 1431 | } |
---|
| 1432 | i++; |
---|
[7bf145] | 1433 | } |
---|
[69076c] | 1434 | if (earlySuccess) |
---|
[7bf145] | 1435 | liftBound= newLiftBound; |
---|
| 1436 | } |
---|
[69076c] | 1437 | |
---|
[69c882] | 1438 | A= bufA; |
---|
| 1439 | if (earlyFactors.length() > 0 && degs.getLength() > 1) |
---|
| 1440 | { |
---|
| 1441 | liftBound= degree (A,y) + 1; |
---|
| 1442 | earlySuccess= true; |
---|
| 1443 | deleteFactors (bufUniFactors, factorsFoundIndex); |
---|
| 1444 | } |
---|
| 1445 | |
---|
[1a3011e] | 1446 | delete [] factorsFoundIndex; |
---|
[69076c] | 1447 | delete [] liftPre; |
---|
| 1448 | |
---|
[7bf145] | 1449 | return bufUniFactors; |
---|
| 1450 | } |
---|
[03c742] | 1451 | #endif |
---|
[7bf145] | 1452 | |
---|
[03c742] | 1453 | #ifdef HAVE_NTL // henselLiftAndEarly |
---|
[69fdf90] | 1454 | CFList |
---|
| 1455 | henselLiftAndEarly (CanonicalForm& A, bool& earlySuccess, CFList& |
---|
| 1456 | earlyFactors, DegreePattern& degs, int& liftBound, |
---|
| 1457 | const CFList& uniFactors, const ExtensionInfo& info, |
---|
| 1458 | const CanonicalForm& eval) |
---|
| 1459 | { |
---|
| 1460 | modpk dummy= modpk(); |
---|
[14e634] | 1461 | CanonicalForm den= 1; |
---|
[69fdf90] | 1462 | return henselLiftAndEarly (A, earlySuccess, earlyFactors, degs, liftBound, |
---|
[14e634] | 1463 | uniFactors, info, eval, dummy, den); |
---|
[69fdf90] | 1464 | } |
---|
[03c742] | 1465 | #endif |
---|
[69fdf90] | 1466 | |
---|
[7032db] | 1467 | #ifdef HAVE_NTL |
---|
[11bf82] | 1468 | long isReduced (const mat_zz_p& M) |
---|
[7bf145] | 1469 | { |
---|
[11bf82] | 1470 | long i, j, nonZero; |
---|
| 1471 | for (i = 1; i <= M.NumRows(); i++) |
---|
[7bf145] | 1472 | { |
---|
[11bf82] | 1473 | nonZero= 0; |
---|
| 1474 | for (j = 1; j <= M.NumCols(); j++) |
---|
[7bf145] | 1475 | { |
---|
[11bf82] | 1476 | if (!IsZero (M (i,j))) |
---|
| 1477 | nonZero++; |
---|
[7bf145] | 1478 | } |
---|
[11bf82] | 1479 | if (nonZero != 1) |
---|
| 1480 | return 0; |
---|
[7bf145] | 1481 | } |
---|
[11bf82] | 1482 | return 1; |
---|
| 1483 | } |
---|
[87942fd] | 1484 | #endif |
---|
[7bf145] | 1485 | |
---|
[49660c] | 1486 | #ifdef HAVE_FLINT |
---|
| 1487 | long isReduced (const nmod_mat_t M) |
---|
| 1488 | { |
---|
| 1489 | long i, j, nonZero; |
---|
| 1490 | for (i = 1; i <= nmod_mat_nrows(M); i++) |
---|
| 1491 | { |
---|
| 1492 | nonZero= 0; |
---|
| 1493 | for (j = 1; j <= nmod_mat_ncols (M); j++) |
---|
| 1494 | { |
---|
| 1495 | if (!(nmod_mat_entry (M, i-1, j-1)==0)) |
---|
| 1496 | nonZero++; |
---|
| 1497 | } |
---|
| 1498 | if (nonZero != 1) |
---|
| 1499 | return 0; |
---|
| 1500 | } |
---|
| 1501 | return 1; |
---|
| 1502 | } |
---|
| 1503 | #endif |
---|
[03c742] | 1504 | |
---|
[7032db] | 1505 | #ifdef HAVE_NTL |
---|
[11bf82] | 1506 | long isReduced (const mat_zz_pE& M) |
---|
| 1507 | { |
---|
| 1508 | long i, j, nonZero; |
---|
| 1509 | for (i = 1; i <= M.NumRows(); i++) |
---|
[806c18] | 1510 | { |
---|
[11bf82] | 1511 | nonZero= 0; |
---|
| 1512 | for (j = 1; j <= M.NumCols(); j++) |
---|
| 1513 | { |
---|
| 1514 | if (!IsZero (M (i,j))) |
---|
[c1b9927] | 1515 | nonZero++; |
---|
[11bf82] | 1516 | } |
---|
| 1517 | if (nonZero != 1) |
---|
| 1518 | return 0; |
---|
[7bf145] | 1519 | } |
---|
[11bf82] | 1520 | return 1; |
---|
| 1521 | } |
---|
[03c742] | 1522 | #endif |
---|
[7bf145] | 1523 | |
---|
[7032db] | 1524 | #ifdef HAVE_NTL |
---|
[11bf82] | 1525 | int * extractZeroOneVecs (const mat_zz_p& M) |
---|
| 1526 | { |
---|
| 1527 | long i, j; |
---|
| 1528 | bool nonZeroOne= false; |
---|
| 1529 | int * result= new int [M.NumCols()]; |
---|
| 1530 | for (i = 1; i <= M.NumCols(); i++) |
---|
[7bf145] | 1531 | { |
---|
[11bf82] | 1532 | for (j = 1; j <= M.NumRows(); j++) |
---|
| 1533 | { |
---|
| 1534 | if (!(IsOne (M (j,i)) || IsZero (M (j,i)))) |
---|
| 1535 | { |
---|
| 1536 | nonZeroOne= true; |
---|
| 1537 | break; |
---|
| 1538 | } |
---|
| 1539 | } |
---|
| 1540 | if (!nonZeroOne) |
---|
| 1541 | result [i - 1]= 1; |
---|
| 1542 | else |
---|
| 1543 | result [i - 1]= 0; |
---|
| 1544 | nonZeroOne= false; |
---|
[7bf145] | 1545 | } |
---|
[11bf82] | 1546 | return result; |
---|
| 1547 | } |
---|
[87942fd] | 1548 | #endif |
---|
[7bf145] | 1549 | |
---|
[49660c] | 1550 | #ifdef HAVE_FLINT |
---|
| 1551 | int * extractZeroOneVecs (const nmod_mat_t M) |
---|
| 1552 | { |
---|
| 1553 | long i, j; |
---|
| 1554 | bool nonZeroOne= false; |
---|
| 1555 | int * result= new int [nmod_mat_ncols (M)]; |
---|
| 1556 | for (i = 0; i < nmod_mat_ncols (M); i++) |
---|
| 1557 | { |
---|
| 1558 | for (j = 0; j < nmod_mat_nrows (M); j++) |
---|
| 1559 | { |
---|
| 1560 | if (!((nmod_mat_entry (M, j, i) == 1) || (nmod_mat_entry (M, j,i) == 0))) |
---|
| 1561 | { |
---|
| 1562 | nonZeroOne= true; |
---|
| 1563 | break; |
---|
| 1564 | } |
---|
| 1565 | } |
---|
| 1566 | if (!nonZeroOne) |
---|
| 1567 | result [i]= 1; |
---|
| 1568 | else |
---|
| 1569 | result [i]= 0; |
---|
| 1570 | nonZeroOne= false; |
---|
| 1571 | } |
---|
| 1572 | return result; |
---|
| 1573 | } |
---|
| 1574 | #endif |
---|
| 1575 | |
---|
[7032db] | 1576 | #ifdef HAVE_NTL |
---|
[11bf82] | 1577 | int * extractZeroOneVecs (const mat_zz_pE& M) |
---|
| 1578 | { |
---|
| 1579 | long i, j; |
---|
| 1580 | bool nonZeroOne= false; |
---|
| 1581 | int * result= new int [M.NumCols()]; |
---|
| 1582 | for (i = 1; i <= M.NumCols(); i++) |
---|
[7bf145] | 1583 | { |
---|
[11bf82] | 1584 | for (j = 1; j <= M.NumRows(); j++) |
---|
[7bf145] | 1585 | { |
---|
[11bf82] | 1586 | if (!(IsOne (M (j,i)) || IsZero (M (j,i)))) |
---|
| 1587 | { |
---|
| 1588 | nonZeroOne= true; |
---|
| 1589 | break; |
---|
| 1590 | } |
---|
[7bf145] | 1591 | } |
---|
[11bf82] | 1592 | if (!nonZeroOne) |
---|
| 1593 | result [i - 1]= 1; |
---|
| 1594 | else |
---|
| 1595 | result [i - 1]= 0; |
---|
| 1596 | nonZeroOne= false; |
---|
[7bf145] | 1597 | } |
---|
[11bf82] | 1598 | return result; |
---|
| 1599 | } |
---|
[03c742] | 1600 | #endif |
---|
[11bf82] | 1601 | |
---|
[7032db] | 1602 | #ifdef HAVE_NTL |
---|
[11bf82] | 1603 | void |
---|
| 1604 | reconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const CFList& |
---|
| 1605 | factors, const int liftBound, int& factorsFound, int*& |
---|
[2537fa0] | 1606 | factorsFoundIndex, mat_zz_pE& N, const CanonicalForm& eval, |
---|
| 1607 | bool beenInThres |
---|
[11bf82] | 1608 | ) |
---|
| 1609 | { |
---|
| 1610 | Variable y= Variable (2); |
---|
| 1611 | Variable x= Variable (1); |
---|
| 1612 | CanonicalForm yToL= power (y, liftBound); |
---|
[2537fa0] | 1613 | CanonicalForm bufF= F (y-eval, y); |
---|
[3ed6758] | 1614 | if (factors.length() == 2) |
---|
| 1615 | { |
---|
[773d28] | 1616 | CanonicalForm tmp1, tmp2, tmp3; |
---|
[3ed6758] | 1617 | tmp1= factors.getFirst(); |
---|
| 1618 | tmp2= factors.getLast(); |
---|
[4dafdf] | 1619 | tmp1= mulMod2 (tmp1, LC (F,x), yToL); |
---|
[3ed6758] | 1620 | tmp1 /= content (tmp1, x); |
---|
[2537fa0] | 1621 | tmp1= tmp1 (y-eval, y); |
---|
[4dafdf] | 1622 | tmp2= mulMod2 (tmp2, LC (F,x), yToL); |
---|
[3ed6758] | 1623 | tmp2 /= content (tmp2, x); |
---|
[2537fa0] | 1624 | tmp2= tmp2 (y-eval, y); |
---|
[773d28] | 1625 | tmp3 = tmp1*tmp2; |
---|
[2537fa0] | 1626 | if (tmp3/Lc (tmp3) == bufF/Lc (bufF)) |
---|
[3ed6758] | 1627 | { |
---|
| 1628 | factorsFound++; |
---|
| 1629 | F= 1; |
---|
| 1630 | reconstructedFactors.append (tmp1); |
---|
| 1631 | reconstructedFactors.append (tmp2); |
---|
| 1632 | return; |
---|
| 1633 | } |
---|
| 1634 | } |
---|
[38ffb7] | 1635 | CanonicalForm quot, buf; |
---|
| 1636 | CFListIterator iter; |
---|
[11bf82] | 1637 | for (long i= 1; i <= N.NumCols(); i++) |
---|
[7bf145] | 1638 | { |
---|
[11bf82] | 1639 | if (factorsFoundIndex [i - 1] == 1) |
---|
| 1640 | continue; |
---|
[38ffb7] | 1641 | iter= factors; |
---|
[11bf82] | 1642 | if (beenInThres) |
---|
[7bf145] | 1643 | { |
---|
[11bf82] | 1644 | int count= 1; |
---|
| 1645 | while (count < i) |
---|
| 1646 | { |
---|
| 1647 | count++; |
---|
| 1648 | iter++; |
---|
| 1649 | } |
---|
| 1650 | buf= iter.getItem(); |
---|
[7bf145] | 1651 | } |
---|
[11bf82] | 1652 | else |
---|
[806c18] | 1653 | { |
---|
[11bf82] | 1654 | buf= 1; |
---|
| 1655 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 1656 | { |
---|
| 1657 | if (!IsZero (N (j,i))) |
---|
| 1658 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 1659 | } |
---|
| 1660 | } |
---|
[4dafdf] | 1661 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
[11bf82] | 1662 | buf /= content (buf, x); |
---|
[2537fa0] | 1663 | buf= buf (y-eval,y); |
---|
| 1664 | if (fdivides (buf, bufF, quot)) |
---|
[11bf82] | 1665 | { |
---|
| 1666 | factorsFoundIndex[i - 1]= 1; |
---|
| 1667 | factorsFound++; |
---|
[2537fa0] | 1668 | bufF= quot; |
---|
| 1669 | bufF /= Lc (bufF); |
---|
[11bf82] | 1670 | reconstructedFactors.append (buf); |
---|
| 1671 | } |
---|
[2537fa0] | 1672 | if (degree (bufF) <= 0) |
---|
[11bf82] | 1673 | return; |
---|
| 1674 | if (factorsFound + 1 == N.NumCols()) |
---|
| 1675 | { |
---|
[2537fa0] | 1676 | reconstructedFactors.append (bufF); |
---|
| 1677 | F= 1; |
---|
[11bf82] | 1678 | return; |
---|
[7bf145] | 1679 | } |
---|
| 1680 | } |
---|
[2537fa0] | 1681 | if (reconstructedFactors.length() != 0) |
---|
| 1682 | F= bufF (y+eval,y); |
---|
[11bf82] | 1683 | } |
---|
[03c742] | 1684 | #endif |
---|
[7bf145] | 1685 | |
---|
[7032db] | 1686 | #ifdef HAVE_NTL |
---|
[11bf82] | 1687 | void |
---|
| 1688 | reconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const CFList& |
---|
| 1689 | factors, const int liftBound, int& factorsFound, int*& |
---|
[2537fa0] | 1690 | factorsFoundIndex, mat_zz_p& N, const CanonicalForm& eval, |
---|
| 1691 | bool beenInThres |
---|
[11bf82] | 1692 | ) |
---|
| 1693 | { |
---|
| 1694 | Variable y= Variable (2); |
---|
[c1b9927] | 1695 | Variable x= Variable (1); |
---|
[11bf82] | 1696 | CanonicalForm yToL= power (y, liftBound); |
---|
[2537fa0] | 1697 | CanonicalForm bufF= F (y-eval, y); |
---|
[3ed6758] | 1698 | if (factors.length() == 2) |
---|
| 1699 | { |
---|
[773d28] | 1700 | CanonicalForm tmp1, tmp2, tmp3; |
---|
[3ed6758] | 1701 | tmp1= factors.getFirst(); |
---|
| 1702 | tmp2= factors.getLast(); |
---|
[4dafdf] | 1703 | tmp1= mulMod2 (tmp1, LC (F,x), yToL); |
---|
[3ed6758] | 1704 | tmp1 /= content (tmp1, x); |
---|
[2537fa0] | 1705 | tmp1= tmp1 (y-eval, y); |
---|
[4dafdf] | 1706 | tmp2= mulMod2 (tmp2, LC (F,x), yToL); |
---|
[3ed6758] | 1707 | tmp2 /= content (tmp2, x); |
---|
[2537fa0] | 1708 | tmp2= tmp2 (y-eval,y); |
---|
[773d28] | 1709 | tmp3 = tmp1*tmp2; |
---|
[2537fa0] | 1710 | if (tmp3/Lc (tmp3) == bufF/Lc (bufF)) |
---|
[3ed6758] | 1711 | { |
---|
| 1712 | factorsFound++; |
---|
| 1713 | F= 1; |
---|
| 1714 | reconstructedFactors.append (tmp1); |
---|
| 1715 | reconstructedFactors.append (tmp2); |
---|
| 1716 | return; |
---|
| 1717 | } |
---|
| 1718 | } |
---|
| 1719 | CanonicalForm quot, buf; |
---|
[38ffb7] | 1720 | CFListIterator iter; |
---|
[11bf82] | 1721 | for (long i= 1; i <= N.NumCols(); i++) |
---|
[7bf145] | 1722 | { |
---|
[11bf82] | 1723 | if (factorsFoundIndex [i - 1] == 1) |
---|
| 1724 | continue; |
---|
[38ffb7] | 1725 | iter= factors; |
---|
[11bf82] | 1726 | if (beenInThres) |
---|
[7bf145] | 1727 | { |
---|
[11bf82] | 1728 | int count= 1; |
---|
| 1729 | while (count < i) |
---|
| 1730 | { |
---|
| 1731 | count++; |
---|
| 1732 | iter++; |
---|
| 1733 | } |
---|
| 1734 | buf= iter.getItem(); |
---|
[7bf145] | 1735 | } |
---|
[11bf82] | 1736 | else |
---|
[7bf145] | 1737 | { |
---|
[11bf82] | 1738 | buf= 1; |
---|
| 1739 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
[806c18] | 1740 | { |
---|
[11bf82] | 1741 | if (!IsZero (N (j,i))) |
---|
| 1742 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
[7bf145] | 1743 | } |
---|
| 1744 | } |
---|
[4dafdf] | 1745 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
[11bf82] | 1746 | buf /= content (buf, x); |
---|
[2537fa0] | 1747 | buf= buf (y-eval,y); |
---|
| 1748 | if (fdivides (buf, bufF, quot)) |
---|
[7bf145] | 1749 | { |
---|
[11bf82] | 1750 | factorsFoundIndex[i - 1]= 1; |
---|
| 1751 | factorsFound++; |
---|
[2537fa0] | 1752 | bufF= quot; |
---|
| 1753 | bufF /= Lc (bufF); |
---|
[11bf82] | 1754 | reconstructedFactors.append (buf); |
---|
[7bf145] | 1755 | } |
---|
[2537fa0] | 1756 | if (degree (bufF) <= 0) |
---|
[11bf82] | 1757 | return; |
---|
| 1758 | if (factorsFound + 1 == N.NumCols()) |
---|
| 1759 | { |
---|
[2537fa0] | 1760 | reconstructedFactors.append (bufF); |
---|
| 1761 | F=1; |
---|
[11bf82] | 1762 | return; |
---|
| 1763 | } |
---|
| 1764 | } |
---|
[2537fa0] | 1765 | if (reconstructedFactors.length() != 0) |
---|
| 1766 | F= bufF (y+eval,y); |
---|
[11bf82] | 1767 | } |
---|
[87942fd] | 1768 | #endif |
---|
[7bf145] | 1769 | |
---|
[49660c] | 1770 | #ifdef HAVE_FLINT |
---|
| 1771 | void |
---|
| 1772 | reconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const CFList& |
---|
| 1773 | factors, const int liftBound, int& factorsFound, int*& |
---|
[2537fa0] | 1774 | factorsFoundIndex, nmod_mat_t N, const CanonicalForm& eval, |
---|
| 1775 | bool beenInThres |
---|
[49660c] | 1776 | ) |
---|
| 1777 | { |
---|
| 1778 | Variable y= Variable (2); |
---|
| 1779 | Variable x= Variable (1); |
---|
| 1780 | CanonicalForm yToL= power (y, liftBound); |
---|
[2537fa0] | 1781 | CanonicalForm bufF= F (y-eval, y); |
---|
[49660c] | 1782 | if (factors.length() == 2) |
---|
| 1783 | { |
---|
| 1784 | CanonicalForm tmp1, tmp2, tmp3; |
---|
| 1785 | tmp1= factors.getFirst(); |
---|
| 1786 | tmp2= factors.getLast(); |
---|
[4dafdf] | 1787 | tmp1= mulMod2 (tmp1, LC (F,x), yToL); |
---|
[49660c] | 1788 | tmp1 /= content (tmp1, x); |
---|
[2537fa0] | 1789 | tmp1= tmp1 (y-eval, y); |
---|
[4dafdf] | 1790 | tmp2= mulMod2 (tmp2, LC (F,x), yToL); |
---|
[49660c] | 1791 | tmp2 /= content (tmp2, x); |
---|
[2537fa0] | 1792 | tmp2= tmp2 (y-eval, y); |
---|
[49660c] | 1793 | tmp3 = tmp1*tmp2; |
---|
[2537fa0] | 1794 | if (tmp3/Lc (tmp3) == bufF/Lc (bufF)) |
---|
[49660c] | 1795 | { |
---|
| 1796 | factorsFound++; |
---|
| 1797 | F= 1; |
---|
| 1798 | reconstructedFactors.append (tmp1); |
---|
| 1799 | reconstructedFactors.append (tmp2); |
---|
| 1800 | return; |
---|
| 1801 | } |
---|
| 1802 | } |
---|
| 1803 | CanonicalForm quot, buf; |
---|
| 1804 | CFListIterator iter; |
---|
| 1805 | for (long i= 0; i < nmod_mat_ncols (N); i++) |
---|
| 1806 | { |
---|
| 1807 | if (factorsFoundIndex [i] == 1) |
---|
| 1808 | continue; |
---|
| 1809 | iter= factors; |
---|
| 1810 | if (beenInThres) |
---|
| 1811 | { |
---|
| 1812 | int count= 0; |
---|
| 1813 | while (count < i) |
---|
| 1814 | { |
---|
| 1815 | count++; |
---|
| 1816 | iter++; |
---|
| 1817 | } |
---|
| 1818 | buf= iter.getItem(); |
---|
| 1819 | } |
---|
| 1820 | else |
---|
| 1821 | { |
---|
| 1822 | buf= 1; |
---|
| 1823 | for (long j= 0; j < nmod_mat_nrows (N); j++, iter++) |
---|
| 1824 | { |
---|
| 1825 | if (!(nmod_mat_entry (N, j, i) == 0)) |
---|
| 1826 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 1827 | } |
---|
| 1828 | } |
---|
[4dafdf] | 1829 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
[49660c] | 1830 | buf /= content (buf, x); |
---|
[2537fa0] | 1831 | buf= buf (y-eval,y); |
---|
| 1832 | if (fdivides (buf, bufF, quot)) |
---|
[49660c] | 1833 | { |
---|
| 1834 | factorsFoundIndex[i]= 1; |
---|
| 1835 | factorsFound++; |
---|
[2537fa0] | 1836 | bufF= quot; |
---|
| 1837 | bufF /= Lc (bufF); |
---|
[49660c] | 1838 | reconstructedFactors.append (buf); |
---|
| 1839 | } |
---|
| 1840 | if (degree (F) <= 0) |
---|
| 1841 | return; |
---|
| 1842 | if (factorsFound + 1 == nmod_mat_ncols (N)) |
---|
| 1843 | { |
---|
[2537fa0] | 1844 | F= 1; |
---|
| 1845 | reconstructedFactors.append (bufF); |
---|
[49660c] | 1846 | return; |
---|
| 1847 | } |
---|
| 1848 | } |
---|
[2537fa0] | 1849 | if (reconstructedFactors.length() != 0) |
---|
| 1850 | F= bufF (y+eval,y); |
---|
[49660c] | 1851 | } |
---|
| 1852 | #endif |
---|
| 1853 | |
---|
[7032db] | 1854 | #ifdef HAVE_NTL |
---|
[11bf82] | 1855 | CFList |
---|
| 1856 | reconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, int |
---|
[2537fa0] | 1857 | precision, const mat_zz_pE& N, const CanonicalForm& eval |
---|
[11bf82] | 1858 | ) |
---|
| 1859 | { |
---|
| 1860 | Variable y= Variable (2); |
---|
| 1861 | Variable x= Variable (1); |
---|
| 1862 | CanonicalForm F= G; |
---|
| 1863 | CanonicalForm yToL= power (y, precision); |
---|
[38ffb7] | 1864 | CanonicalForm quot, buf; |
---|
| 1865 | CFList result, factorsConsidered; |
---|
[11bf82] | 1866 | CFList bufFactors= factors; |
---|
[38ffb7] | 1867 | CFListIterator iter; |
---|
[11bf82] | 1868 | for (long i= 1; i <= N.NumCols(); i++) |
---|
| 1869 | { |
---|
| 1870 | if (zeroOneVecs [i - 1] == 0) |
---|
| 1871 | continue; |
---|
[38ffb7] | 1872 | iter= factors; |
---|
| 1873 | buf= 1; |
---|
[11bf82] | 1874 | factorsConsidered= CFList(); |
---|
| 1875 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 1876 | { |
---|
| 1877 | if (!IsZero (N (j,i))) |
---|
| 1878 | { |
---|
| 1879 | factorsConsidered.append (iter.getItem()); |
---|
| 1880 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 1881 | } |
---|
| 1882 | } |
---|
[4dafdf] | 1883 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
[11bf82] | 1884 | buf /= content (buf, x); |
---|
[21b8f4c] | 1885 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 1886 | { |
---|
[21b8f4c] | 1887 | F= quot; |
---|
[11bf82] | 1888 | F /= Lc (F); |
---|
[2537fa0] | 1889 | result.append (buf (y-eval,y)); |
---|
[11bf82] | 1890 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 1891 | } |
---|
| 1892 | if (degree (F) <= 0) |
---|
| 1893 | { |
---|
| 1894 | G= F; |
---|
| 1895 | factors= bufFactors; |
---|
| 1896 | return result; |
---|
| 1897 | } |
---|
| 1898 | } |
---|
| 1899 | G= F; |
---|
| 1900 | factors= bufFactors; |
---|
| 1901 | return result; |
---|
| 1902 | } |
---|
[03c742] | 1903 | #endif |
---|
[11bf82] | 1904 | |
---|
[7032db] | 1905 | #ifdef HAVE_NTL |
---|
[11bf82] | 1906 | CFList |
---|
| 1907 | monicReconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, |
---|
| 1908 | int precision, const mat_zz_pE& N |
---|
| 1909 | ) |
---|
| 1910 | { |
---|
| 1911 | Variable y= Variable (2); |
---|
| 1912 | Variable x= Variable (1); |
---|
| 1913 | CanonicalForm F= G; |
---|
| 1914 | CanonicalForm yToL= power (y, precision); |
---|
[38ffb7] | 1915 | CanonicalForm quot, buf, buf2; |
---|
[11bf82] | 1916 | CFList result; |
---|
| 1917 | CFList bufFactors= factors; |
---|
| 1918 | CFList factorsConsidered; |
---|
[38ffb7] | 1919 | CFListIterator iter; |
---|
[11bf82] | 1920 | for (long i= 1; i <= N.NumCols(); i++) |
---|
| 1921 | { |
---|
| 1922 | if (zeroOneVecs [i - 1] == 0) |
---|
| 1923 | continue; |
---|
[38ffb7] | 1924 | iter= factors; |
---|
| 1925 | buf= 1; |
---|
[11bf82] | 1926 | factorsConsidered= CFList(); |
---|
| 1927 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 1928 | { |
---|
| 1929 | if (!IsZero (N (j,i))) |
---|
| 1930 | { |
---|
| 1931 | factorsConsidered.append (iter.getItem()); |
---|
| 1932 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 1933 | } |
---|
| 1934 | } |
---|
[38ffb7] | 1935 | buf2= buf; |
---|
[4dafdf] | 1936 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
[11bf82] | 1937 | buf /= content (buf, x); |
---|
[21b8f4c] | 1938 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 1939 | { |
---|
[21b8f4c] | 1940 | F= quot; |
---|
[11bf82] | 1941 | F /= Lc (F); |
---|
| 1942 | result.append (buf2); |
---|
| 1943 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 1944 | } |
---|
| 1945 | if (degree (F) <= 0) |
---|
| 1946 | { |
---|
| 1947 | G= F; |
---|
| 1948 | factors= bufFactors; |
---|
| 1949 | return result; |
---|
| 1950 | } |
---|
| 1951 | } |
---|
| 1952 | G= F; |
---|
| 1953 | factors= bufFactors; |
---|
| 1954 | return result; |
---|
| 1955 | } |
---|
[03c742] | 1956 | #endif |
---|
[11bf82] | 1957 | |
---|
[7032db] | 1958 | #ifdef HAVE_NTL |
---|
[11bf82] | 1959 | CFList |
---|
| 1960 | extReconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, int |
---|
| 1961 | precision, const mat_zz_p& N, const ExtensionInfo& info, |
---|
| 1962 | const CanonicalForm& evaluation |
---|
| 1963 | ) |
---|
| 1964 | { |
---|
| 1965 | Variable y= Variable (2); |
---|
| 1966 | Variable x= Variable (1); |
---|
| 1967 | Variable alpha= info.getAlpha(); |
---|
| 1968 | Variable beta= info.getBeta(); |
---|
| 1969 | int k= info.getGFDegree(); |
---|
| 1970 | CanonicalForm gamma= info.getGamma(); |
---|
| 1971 | CanonicalForm delta= info.getDelta(); |
---|
| 1972 | CanonicalForm F= G; |
---|
| 1973 | CanonicalForm yToL= power (y, precision); |
---|
| 1974 | CFList result; |
---|
| 1975 | CFList bufFactors= factors; |
---|
| 1976 | CFList factorsConsidered; |
---|
[38ffb7] | 1977 | CanonicalForm buf2, quot, buf; |
---|
| 1978 | CFListIterator iter; |
---|
[11bf82] | 1979 | for (long i= 1; i <= N.NumCols(); i++) |
---|
| 1980 | { |
---|
| 1981 | if (zeroOneVecs [i - 1] == 0) |
---|
| 1982 | continue; |
---|
[38ffb7] | 1983 | iter= factors; |
---|
| 1984 | buf= 1; |
---|
[11bf82] | 1985 | factorsConsidered= CFList(); |
---|
| 1986 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 1987 | { |
---|
| 1988 | if (!IsZero (N (j,i))) |
---|
| 1989 | { |
---|
| 1990 | factorsConsidered.append (iter.getItem()); |
---|
| 1991 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 1992 | } |
---|
| 1993 | } |
---|
[4dafdf] | 1994 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
[11bf82] | 1995 | buf /= content (buf, x); |
---|
| 1996 | buf2= buf (y-evaluation, y); |
---|
[c49e6f] | 1997 | buf2 /= Lc (buf2); |
---|
[a54114] | 1998 | if (!k && beta == x) |
---|
[11bf82] | 1999 | { |
---|
| 2000 | if (degree (buf2, alpha) < 1) |
---|
| 2001 | { |
---|
[21b8f4c] | 2002 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 2003 | { |
---|
[21b8f4c] | 2004 | F= quot; |
---|
[11bf82] | 2005 | F /= Lc (F); |
---|
| 2006 | result.append (buf2); |
---|
| 2007 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 2008 | } |
---|
| 2009 | } |
---|
| 2010 | } |
---|
| 2011 | else |
---|
| 2012 | { |
---|
| 2013 | CFList source, dest; |
---|
[c1b9927] | 2014 | |
---|
[11bf82] | 2015 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
| 2016 | { |
---|
[21b8f4c] | 2017 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 2018 | { |
---|
[21b8f4c] | 2019 | F= quot; |
---|
[11bf82] | 2020 | F /= Lc (F); |
---|
| 2021 | result.append (buf2); |
---|
| 2022 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 2023 | } |
---|
| 2024 | } |
---|
| 2025 | } |
---|
| 2026 | if (degree (F) <= 0) |
---|
| 2027 | { |
---|
| 2028 | G= F; |
---|
| 2029 | factors= bufFactors; |
---|
| 2030 | return result; |
---|
| 2031 | } |
---|
| 2032 | } |
---|
| 2033 | G= F; |
---|
| 2034 | factors= bufFactors; |
---|
| 2035 | return result; |
---|
| 2036 | } |
---|
[87942fd] | 2037 | #endif |
---|
[11bf82] | 2038 | |
---|
[49660c] | 2039 | #ifdef HAVE_FLINT |
---|
| 2040 | CFList |
---|
| 2041 | extReconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, int |
---|
| 2042 | precision, const nmod_mat_t N, const ExtensionInfo& info, |
---|
| 2043 | const CanonicalForm& evaluation |
---|
| 2044 | ) |
---|
| 2045 | { |
---|
| 2046 | Variable y= Variable (2); |
---|
| 2047 | Variable x= Variable (1); |
---|
| 2048 | Variable alpha= info.getAlpha(); |
---|
| 2049 | Variable beta= info.getBeta(); |
---|
| 2050 | int k= info.getGFDegree(); |
---|
| 2051 | CanonicalForm gamma= info.getGamma(); |
---|
| 2052 | CanonicalForm delta= info.getDelta(); |
---|
| 2053 | CanonicalForm F= G; |
---|
| 2054 | CanonicalForm yToL= power (y, precision); |
---|
| 2055 | CFList result; |
---|
| 2056 | CFList bufFactors= factors; |
---|
| 2057 | CFList factorsConsidered; |
---|
| 2058 | CanonicalForm buf2, quot, buf; |
---|
| 2059 | CFListIterator iter; |
---|
| 2060 | for (long i= 0; i < nmod_mat_ncols(N); i++) |
---|
| 2061 | { |
---|
| 2062 | if (zeroOneVecs [i] == 0) |
---|
| 2063 | continue; |
---|
| 2064 | iter= factors; |
---|
| 2065 | buf= 1; |
---|
| 2066 | factorsConsidered= CFList(); |
---|
[5b9b87] | 2067 | for (long j= 0; j < nmod_mat_nrows(N); j++, iter++) |
---|
[49660c] | 2068 | { |
---|
| 2069 | if (!(nmod_mat_entry (N, j, i) == 0)) |
---|
| 2070 | { |
---|
| 2071 | factorsConsidered.append (iter.getItem()); |
---|
| 2072 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 2073 | } |
---|
| 2074 | } |
---|
[4dafdf] | 2075 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
[49660c] | 2076 | buf /= content (buf, x); |
---|
| 2077 | buf2= buf (y-evaluation, y); |
---|
[c49e6f] | 2078 | buf2 /= Lc (buf2); |
---|
[49660c] | 2079 | if (!k && beta == x) |
---|
| 2080 | { |
---|
| 2081 | if (degree (buf2, alpha) < 1) |
---|
| 2082 | { |
---|
| 2083 | if (fdivides (buf, F, quot)) |
---|
| 2084 | { |
---|
| 2085 | F= quot; |
---|
| 2086 | F /= Lc (F); |
---|
| 2087 | result.append (buf2); |
---|
| 2088 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 2089 | } |
---|
| 2090 | } |
---|
| 2091 | } |
---|
| 2092 | else |
---|
| 2093 | { |
---|
| 2094 | CFList source, dest; |
---|
| 2095 | |
---|
| 2096 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
| 2097 | { |
---|
| 2098 | if (fdivides (buf, F, quot)) |
---|
| 2099 | { |
---|
| 2100 | F= quot; |
---|
| 2101 | F /= Lc (F); |
---|
| 2102 | result.append (buf2); |
---|
| 2103 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 2104 | } |
---|
| 2105 | } |
---|
| 2106 | } |
---|
| 2107 | if (degree (F) <= 0) |
---|
| 2108 | { |
---|
| 2109 | G= F; |
---|
| 2110 | factors= bufFactors; |
---|
| 2111 | return result; |
---|
| 2112 | } |
---|
| 2113 | } |
---|
| 2114 | G= F; |
---|
| 2115 | factors= bufFactors; |
---|
| 2116 | return result; |
---|
| 2117 | } |
---|
| 2118 | #endif |
---|
| 2119 | |
---|
[7032db] | 2120 | #ifdef HAVE_NTL |
---|
[11bf82] | 2121 | CFList |
---|
| 2122 | reconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, |
---|
[2537fa0] | 2123 | int precision, const mat_zz_p& N, const CanonicalForm& eval) |
---|
[11bf82] | 2124 | { |
---|
| 2125 | Variable y= Variable (2); |
---|
| 2126 | Variable x= Variable (1); |
---|
| 2127 | CanonicalForm F= G; |
---|
| 2128 | CanonicalForm yToL= power (y, precision); |
---|
[38ffb7] | 2129 | CanonicalForm quot, buf; |
---|
[11bf82] | 2130 | CFList result; |
---|
| 2131 | CFList bufFactors= factors; |
---|
| 2132 | CFList factorsConsidered; |
---|
[38ffb7] | 2133 | CFListIterator iter; |
---|
[11bf82] | 2134 | for (long i= 1; i <= N.NumCols(); i++) |
---|
| 2135 | { |
---|
| 2136 | if (zeroOneVecs [i - 1] == 0) |
---|
| 2137 | continue; |
---|
[38ffb7] | 2138 | iter= factors; |
---|
| 2139 | buf= 1; |
---|
[11bf82] | 2140 | factorsConsidered= CFList(); |
---|
| 2141 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 2142 | { |
---|
| 2143 | if (!IsZero (N (j,i))) |
---|
| 2144 | { |
---|
| 2145 | factorsConsidered.append (iter.getItem()); |
---|
| 2146 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 2147 | } |
---|
| 2148 | } |
---|
[4dafdf] | 2149 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
[11bf82] | 2150 | buf /= content (buf, x); |
---|
[21b8f4c] | 2151 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 2152 | { |
---|
[21b8f4c] | 2153 | F= quot; |
---|
[11bf82] | 2154 | F /= Lc (F); |
---|
[2537fa0] | 2155 | result.append (buf (y-eval,y)); |
---|
[11bf82] | 2156 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 2157 | } |
---|
| 2158 | if (degree (F) <= 0) |
---|
| 2159 | { |
---|
| 2160 | G= F; |
---|
| 2161 | factors= bufFactors; |
---|
| 2162 | return result; |
---|
| 2163 | } |
---|
| 2164 | } |
---|
| 2165 | G= F; |
---|
| 2166 | factors= bufFactors; |
---|
| 2167 | return result; |
---|
| 2168 | } |
---|
[87942fd] | 2169 | #endif |
---|
[11bf82] | 2170 | |
---|
[49660c] | 2171 | #ifdef HAVE_FLINT |
---|
| 2172 | CFList |
---|
| 2173 | reconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, |
---|
[2537fa0] | 2174 | int precision, const nmod_mat_t N, const CanonicalForm& eval) |
---|
[49660c] | 2175 | { |
---|
| 2176 | Variable y= Variable (2); |
---|
| 2177 | Variable x= Variable (1); |
---|
| 2178 | CanonicalForm F= G; |
---|
| 2179 | CanonicalForm yToL= power (y, precision); |
---|
| 2180 | CanonicalForm quot, buf; |
---|
| 2181 | CFList result; |
---|
| 2182 | CFList bufFactors= factors; |
---|
| 2183 | CFList factorsConsidered; |
---|
| 2184 | CFListIterator iter; |
---|
| 2185 | for (long i= 0; i < nmod_mat_ncols (N); i++) |
---|
| 2186 | { |
---|
| 2187 | if (zeroOneVecs [i] == 0) |
---|
| 2188 | continue; |
---|
| 2189 | iter= factors; |
---|
| 2190 | buf= 1; |
---|
| 2191 | factorsConsidered= CFList(); |
---|
| 2192 | for (long j= 0; j < nmod_mat_nrows (N); j++, iter++) |
---|
| 2193 | { |
---|
| 2194 | if (!(nmod_mat_entry (N, j, i) == 0)) |
---|
| 2195 | { |
---|
| 2196 | factorsConsidered.append (iter.getItem()); |
---|
| 2197 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 2198 | } |
---|
| 2199 | } |
---|
[4dafdf] | 2200 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
[49660c] | 2201 | buf /= content (buf, x); |
---|
| 2202 | if (fdivides (buf, F, quot)) |
---|
| 2203 | { |
---|
| 2204 | F= quot; |
---|
| 2205 | F /= Lc (F); |
---|
[2537fa0] | 2206 | result.append (buf (y-eval,y)); |
---|
[49660c] | 2207 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
| 2208 | } |
---|
| 2209 | if (degree (F) <= 0) |
---|
| 2210 | { |
---|
| 2211 | G= F; |
---|
| 2212 | factors= bufFactors; |
---|
| 2213 | return result; |
---|
| 2214 | } |
---|
| 2215 | } |
---|
| 2216 | G= F; |
---|
| 2217 | factors= bufFactors; |
---|
| 2218 | return result; |
---|
| 2219 | } |
---|
| 2220 | #endif |
---|
| 2221 | |
---|
[7032db] | 2222 | #ifdef HAVE_NTL |
---|
[11bf82] | 2223 | void |
---|
[c1b9927] | 2224 | extReconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const |
---|
[11bf82] | 2225 | CFList& factors, const int liftBound, int& factorsFound, |
---|
| 2226 | int*& factorsFoundIndex, mat_zz_p& N, bool beenInThres, |
---|
| 2227 | const ExtensionInfo& info, const CanonicalForm& evaluation |
---|
| 2228 | ) |
---|
| 2229 | { |
---|
| 2230 | Variable y= Variable (2); |
---|
| 2231 | Variable x= Variable (1); |
---|
| 2232 | Variable alpha= info.getAlpha(); |
---|
| 2233 | Variable beta= info.getBeta(); |
---|
| 2234 | int k= info.getGFDegree(); |
---|
| 2235 | CanonicalForm gamma= info.getGamma(); |
---|
| 2236 | CanonicalForm delta= info.getDelta(); |
---|
| 2237 | CanonicalForm yToL= power (y, liftBound); |
---|
| 2238 | CFList source, dest; |
---|
[3ed6758] | 2239 | if (factors.length() == 2) |
---|
| 2240 | { |
---|
[773d28] | 2241 | CanonicalForm tmp1, tmp2, tmp3; |
---|
[3ed6758] | 2242 | tmp1= factors.getFirst(); |
---|
| 2243 | tmp2= factors.getLast(); |
---|
[4dafdf] | 2244 | tmp1= mulMod2 (tmp1, LC (F,x), yToL); |
---|
[3ed6758] | 2245 | tmp1 /= content (tmp1, x); |
---|
[4dafdf] | 2246 | tmp2= mulMod2 (tmp2, LC (F,x), yToL); |
---|
[3ed6758] | 2247 | tmp2 /= content (tmp2, x); |
---|
[773d28] | 2248 | tmp3 = tmp1*tmp2; |
---|
| 2249 | if (tmp3/Lc (tmp3) == F/Lc (F)) |
---|
[3ed6758] | 2250 | { |
---|
| 2251 | tmp1= tmp1 (y - evaluation, y); |
---|
| 2252 | tmp2= tmp2 (y - evaluation, y); |
---|
[c49e6f] | 2253 | tmp1 /= Lc (tmp1); |
---|
| 2254 | tmp2 /= Lc (tmp2); |
---|
[773d28] | 2255 | if (!k && beta == x && degree (tmp2, alpha) < 1 && |
---|
| 2256 | degree (tmp1, alpha) < 1) |
---|
| 2257 | { |
---|
| 2258 | factorsFound++; |
---|
| 2259 | F= 1; |
---|
| 2260 | tmp1= mapDown (tmp1, info, source, dest); |
---|
| 2261 | tmp2= mapDown (tmp2, info, source, dest); |
---|
| 2262 | reconstructedFactors.append (tmp1); |
---|
| 2263 | reconstructedFactors.append (tmp2); |
---|
| 2264 | return; |
---|
| 2265 | } |
---|
| 2266 | else if (!isInExtension (tmp2, gamma, k, delta, source, dest) && |
---|
| 2267 | !isInExtension (tmp1, gamma, k, delta, source, dest)) |
---|
| 2268 | { |
---|
| 2269 | factorsFound++; |
---|
| 2270 | F= 1; |
---|
| 2271 | tmp1= mapDown (tmp1, info, source, dest); |
---|
| 2272 | tmp2= mapDown (tmp2, info, source, dest); |
---|
| 2273 | reconstructedFactors.append (tmp1); |
---|
| 2274 | reconstructedFactors.append (tmp2); |
---|
| 2275 | return; |
---|
| 2276 | } |
---|
[3ed6758] | 2277 | } |
---|
| 2278 | } |
---|
| 2279 | CanonicalForm quot, buf, buf2; |
---|
[38ffb7] | 2280 | CFListIterator iter; |
---|
[11bf82] | 2281 | for (long i= 1; i <= N.NumCols(); i++) |
---|
| 2282 | { |
---|
| 2283 | if (factorsFoundIndex [i - 1] == 1) |
---|
| 2284 | continue; |
---|
[38ffb7] | 2285 | iter= factors; |
---|
[11bf82] | 2286 | if (beenInThres) |
---|
| 2287 | { |
---|
| 2288 | int count= 1; |
---|
| 2289 | while (count < i) |
---|
| 2290 | { |
---|
| 2291 | count++; |
---|
| 2292 | iter++; |
---|
| 2293 | } |
---|
| 2294 | buf= iter.getItem(); |
---|
| 2295 | } |
---|
| 2296 | else |
---|
| 2297 | { |
---|
| 2298 | buf= 1; |
---|
| 2299 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
| 2300 | { |
---|
| 2301 | if (!IsZero (N (j,i))) |
---|
| 2302 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 2303 | } |
---|
| 2304 | } |
---|
[4dafdf] | 2305 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
[11bf82] | 2306 | buf /= content (buf, x); |
---|
| 2307 | buf2= buf (y - evaluation, y); |
---|
[c49e6f] | 2308 | buf2 /= Lc (buf2); |
---|
[a54114] | 2309 | if (!k && beta == x) |
---|
[11bf82] | 2310 | { |
---|
| 2311 | if (degree (buf2, alpha) < 1) |
---|
| 2312 | { |
---|
[21b8f4c] | 2313 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 2314 | { |
---|
| 2315 | factorsFoundIndex[i - 1]= 1; |
---|
| 2316 | factorsFound++; |
---|
[21b8f4c] | 2317 | F= quot; |
---|
[11bf82] | 2318 | F /= Lc (F); |
---|
| 2319 | buf2= mapDown (buf2, info, source, dest); |
---|
| 2320 | reconstructedFactors.append (buf2); |
---|
| 2321 | } |
---|
| 2322 | } |
---|
| 2323 | } |
---|
| 2324 | else |
---|
| 2325 | { |
---|
| 2326 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
| 2327 | { |
---|
[21b8f4c] | 2328 | if (fdivides (buf, F, quot)) |
---|
[11bf82] | 2329 | { |
---|
| 2330 | factorsFoundIndex[i - 1]= 1; |
---|
| 2331 | factorsFound++; |
---|
[21b8f4c] | 2332 | F= quot; |
---|
[11bf82] | 2333 | F /= Lc (F); |
---|
| 2334 | buf2= mapDown (buf2, info, source, dest); |
---|
| 2335 | reconstructedFactors.append (buf2); |
---|
| 2336 | } |
---|
| 2337 | } |
---|
| 2338 | } |
---|
| 2339 | if (degree (F) <= 0) |
---|
| 2340 | return; |
---|
| 2341 | if (factorsFound + 1 == N.NumCols()) |
---|
| 2342 | { |
---|
| 2343 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 2344 | tmp= mapDown (tmp, info, source, dest); |
---|
| 2345 | reconstructedFactors.append (tmp); |
---|
| 2346 | return; |
---|
| 2347 | } |
---|
| 2348 | } |
---|
| 2349 | } |
---|
[87942fd] | 2350 | #endif |
---|
[11bf82] | 2351 | |
---|
[49660c] | 2352 | #ifdef HAVE_FLINT |
---|
| 2353 | void |
---|
| 2354 | extReconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const |
---|
| 2355 | CFList& factors, const int liftBound, int& factorsFound, |
---|
| 2356 | int*& factorsFoundIndex, nmod_mat_t N, bool beenInThres, |
---|
| 2357 | const ExtensionInfo& info, const CanonicalForm& evaluation |
---|
| 2358 | ) |
---|
[11bf82] | 2359 | { |
---|
[49660c] | 2360 | Variable y= Variable (2); |
---|
| 2361 | Variable x= Variable (1); |
---|
| 2362 | Variable alpha= info.getAlpha(); |
---|
| 2363 | Variable beta= info.getBeta(); |
---|
| 2364 | int k= info.getGFDegree(); |
---|
| 2365 | CanonicalForm gamma= info.getGamma(); |
---|
| 2366 | CanonicalForm delta= info.getDelta(); |
---|
| 2367 | CanonicalForm yToL= power (y, liftBound); |
---|
| 2368 | CFList source, dest; |
---|
| 2369 | if (factors.length() == 2) |
---|
| 2370 | { |
---|
| 2371 | CanonicalForm tmp1, tmp2, tmp3; |
---|
| 2372 | tmp1= factors.getFirst(); |
---|
| 2373 | tmp2= factors.getLast(); |
---|
[4dafdf] | 2374 | tmp1= mulMod2 (tmp1, LC (F,x), yToL); |
---|
[49660c] | 2375 | tmp1 /= content (tmp1, x); |
---|
[4dafdf] | 2376 | tmp2= mulMod2 (tmp2, LC (F,x), yToL); |
---|
[49660c] | 2377 | tmp2 /= content (tmp2, x); |
---|
| 2378 | tmp3 = tmp1*tmp2; |
---|
| 2379 | if (tmp3/Lc (tmp3) == F/Lc (F)) |
---|
| 2380 | { |
---|
| 2381 | tmp1= tmp1 (y - evaluation, y); |
---|
| 2382 | tmp2= tmp2 (y - evaluation, y); |
---|
[c49e6f] | 2383 | tmp1 /= Lc (tmp1); |
---|
| 2384 | tmp2 /= Lc (tmp2); |
---|
[49660c] | 2385 | if (!k && beta == x && degree (tmp2, alpha) < 1 && |
---|
| 2386 | degree (tmp1, alpha) < 1) |
---|
| 2387 | { |
---|
| 2388 | factorsFound++; |
---|
| 2389 | F= 1; |
---|
| 2390 | tmp1= mapDown (tmp1, info, source, dest); |
---|
| 2391 | tmp2= mapDown (tmp2, info, source, dest); |
---|
| 2392 | reconstructedFactors.append (tmp1); |
---|
| 2393 | reconstructedFactors.append (tmp2); |
---|
| 2394 | return; |
---|
| 2395 | } |
---|
| 2396 | else if (!isInExtension (tmp2, gamma, k, delta, source, dest) && |
---|
| 2397 | !isInExtension (tmp1, gamma, k, delta, source, dest)) |
---|
| 2398 | { |
---|
| 2399 | factorsFound++; |
---|
| 2400 | F= 1; |
---|
| 2401 | tmp1= mapDown (tmp1, info, source, dest); |
---|
| 2402 | tmp2= mapDown (tmp2, info, source, dest); |
---|
| 2403 | reconstructedFactors.append (tmp1); |
---|
| 2404 | reconstructedFactors.append (tmp2); |
---|
| 2405 | return; |
---|
| 2406 | } |
---|
| 2407 | } |
---|
| 2408 | } |
---|
| 2409 | CanonicalForm quot, buf, buf2; |
---|
| 2410 | CFListIterator iter; |
---|
| 2411 | for (long i= 0; i < nmod_mat_ncols (N); i++) |
---|
| 2412 | { |
---|
| 2413 | if (factorsFoundIndex [i] == 1) |
---|
| 2414 | continue; |
---|
| 2415 | iter= factors; |
---|
| 2416 | if (beenInThres) |
---|
| 2417 | { |
---|
| 2418 | int count= 0; |
---|
| 2419 | while (count < i) |
---|
| 2420 | { |
---|
| 2421 | count++; |
---|
| 2422 | iter++; |
---|
| 2423 | } |
---|
| 2424 | buf= iter.getItem(); |
---|
| 2425 | } |
---|
| 2426 | else |
---|
| 2427 | { |
---|
| 2428 | buf= 1; |
---|
| 2429 | for (long j= 0; j < nmod_mat_nrows (N); j++, iter++) |
---|
| 2430 | { |
---|
| 2431 | if (!(nmod_mat_entry (N, j, i) == 0)) |
---|
| 2432 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
| 2433 | } |
---|
| 2434 | } |
---|
[4dafdf] | 2435 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
[49660c] | 2436 | buf /= content (buf, x); |
---|
| 2437 | buf2= buf (y - evaluation, y); |
---|
[c49e6f] | 2438 | buf2 /= Lc (buf2); |
---|
[49660c] | 2439 | if (!k && beta == x) |
---|
| 2440 | { |
---|
| 2441 | if (degree (buf2, alpha) < 1) |
---|
| 2442 | { |
---|
| 2443 | if (fdivides (buf, F, quot)) |
---|
| 2444 | { |
---|
| 2445 | factorsFoundIndex[i]= 1; |
---|
| 2446 | factorsFound++; |
---|
| 2447 | F= quot; |
---|
| 2448 | F /= Lc (F); |
---|
| 2449 | buf2= mapDown (buf2, info, source, dest); |
---|
| 2450 | reconstructedFactors.append (buf2); |
---|
| 2451 | } |
---|
| 2452 | } |
---|
| 2453 | } |
---|
| 2454 | else |
---|
| 2455 | { |
---|
| 2456 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
| 2457 | { |
---|
| 2458 | if (fdivides (buf, F, quot)) |
---|
| 2459 | { |
---|
| 2460 | factorsFoundIndex[i]= 1; |
---|
| 2461 | factorsFound++; |
---|
| 2462 | F= quot; |
---|
| 2463 | F /= Lc (F); |
---|
| 2464 | buf2= mapDown (buf2, info, source, dest); |
---|
| 2465 | reconstructedFactors.append (buf2); |
---|
| 2466 | } |
---|
| 2467 | } |
---|
| 2468 | } |
---|
| 2469 | if (degree (F) <= 0) |
---|
| 2470 | return; |
---|
| 2471 | if (factorsFound + 1 == nmod_mat_nrows (N)) |
---|
| 2472 | { |
---|
| 2473 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 2474 | tmp= mapDown (tmp, info, source, dest); |
---|
| 2475 | reconstructedFactors.append (tmp); |
---|
| 2476 | return; |
---|
| 2477 | } |
---|
| 2478 | } |
---|
| 2479 | } |
---|
| 2480 | #endif |
---|
| 2481 | |
---|
[7032db] | 2482 | #ifdef HAVE_NTL |
---|
[49660c] | 2483 | //over Fp |
---|
| 2484 | int |
---|
| 2485 | liftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, int |
---|
| 2486 | start, int liftBound, int minBound, CFList& factors, |
---|
| 2487 | mat_zz_p& NTLN, CFList& diophant, CFMatrix& M, CFArray& |
---|
| 2488 | Pi, CFArray& bufQ, bool& irreducible |
---|
| 2489 | ) |
---|
| 2490 | { |
---|
| 2491 | CanonicalForm LCF= LC (F, 1); |
---|
| 2492 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
| 2493 | bool wasInBounds= false; |
---|
| 2494 | bool hitBound= false; |
---|
| 2495 | int l= (minBound+1)*2; |
---|
| 2496 | int stepSize= 2; |
---|
| 2497 | int oldL= l/2; |
---|
| 2498 | bool reduced= false; |
---|
| 2499 | mat_zz_p NTLK, *NTLC; |
---|
| 2500 | CFMatrix C; |
---|
| 2501 | CFArray buf; |
---|
| 2502 | CFListIterator j; |
---|
| 2503 | CanonicalForm truncF; |
---|
| 2504 | Variable y= F.mvar(); |
---|
| 2505 | while (l <= liftBound) |
---|
| 2506 | { |
---|
[2d35fe] | 2507 | TIMING_START (fac_fq_compute_lattice_lift); |
---|
[49660c] | 2508 | if (start) |
---|
| 2509 | { |
---|
| 2510 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
| 2511 | start= 0; |
---|
| 2512 | } |
---|
| 2513 | else |
---|
| 2514 | { |
---|
| 2515 | if (wasInBounds) |
---|
| 2516 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
| 2517 | else |
---|
| 2518 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 2519 | } |
---|
[2d35fe] | 2520 | TIMING_END_AND_PRINT (fac_fq_compute_lattice_lift, |
---|
| 2521 | "time to lift in compute lattice: "); |
---|
[49660c] | 2522 | |
---|
| 2523 | factors.insert (LCF); |
---|
| 2524 | j= factors; |
---|
| 2525 | j++; |
---|
| 2526 | |
---|
| 2527 | truncF= mod (F, power (y, l)); |
---|
[2d35fe] | 2528 | TIMING_START (fac_fq_logarithmic); |
---|
[49660c] | 2529 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
| 2530 | { |
---|
| 2531 | if (!wasInBounds) |
---|
| 2532 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
| 2533 | else |
---|
| 2534 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
| 2535 | bufQ[i]); |
---|
| 2536 | } |
---|
[2d35fe] | 2537 | TIMING_END_AND_PRINT (fac_fq_logarithmic, |
---|
| 2538 | "time to compute logarithmic derivative: "); |
---|
[49660c] | 2539 | |
---|
| 2540 | for (int i= 0; i < sizeBounds; i++) |
---|
| 2541 | { |
---|
| 2542 | if (bounds [i] + 1 <= l/2) |
---|
| 2543 | { |
---|
| 2544 | wasInBounds= true; |
---|
| 2545 | int k= tmin (bounds [i] + 1, l/2); |
---|
| 2546 | C= CFMatrix (l - k, factors.length() - 1); |
---|
| 2547 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
| 2548 | { |
---|
| 2549 | if (A[ii].size() - 1 >= i) |
---|
| 2550 | { |
---|
| 2551 | buf= getCoeffs (A[ii] [i], k); |
---|
| 2552 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 2553 | } |
---|
| 2554 | } |
---|
| 2555 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 2556 | NTLK= (*NTLC)*NTLN; |
---|
| 2557 | transpose (NTLK, NTLK); |
---|
| 2558 | kernel (NTLK, NTLK); |
---|
| 2559 | transpose (NTLK, NTLK); |
---|
| 2560 | NTLN *= NTLK; |
---|
[ffd883] | 2561 | delete NTLC; |
---|
[49660c] | 2562 | |
---|
| 2563 | if (NTLN.NumCols() == 1) |
---|
| 2564 | { |
---|
| 2565 | irreducible= true; |
---|
| 2566 | break; |
---|
| 2567 | } |
---|
| 2568 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
| 2569 | { |
---|
| 2570 | reduced= true; |
---|
| 2571 | break; |
---|
| 2572 | } |
---|
| 2573 | } |
---|
| 2574 | } |
---|
| 2575 | |
---|
| 2576 | if (irreducible) |
---|
| 2577 | break; |
---|
| 2578 | if (reduced) |
---|
| 2579 | break; |
---|
| 2580 | oldL= l; |
---|
| 2581 | l += stepSize; |
---|
| 2582 | stepSize *= 2; |
---|
| 2583 | if (l > liftBound) |
---|
| 2584 | { |
---|
| 2585 | if (!hitBound) |
---|
| 2586 | { |
---|
| 2587 | l= liftBound; |
---|
| 2588 | hitBound= true; |
---|
| 2589 | } |
---|
| 2590 | else |
---|
| 2591 | break; |
---|
| 2592 | } |
---|
| 2593 | } |
---|
| 2594 | delete [] A; |
---|
[a209e1d] | 2595 | if (!wasInBounds) |
---|
| 2596 | { |
---|
| 2597 | if (start) |
---|
| 2598 | henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M); |
---|
| 2599 | else |
---|
| 2600 | henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M); |
---|
| 2601 | factors.insert (LCF); |
---|
| 2602 | } |
---|
[49660c] | 2603 | return l; |
---|
| 2604 | } |
---|
[87942fd] | 2605 | #endif |
---|
[49660c] | 2606 | |
---|
| 2607 | #ifdef HAVE_FLINT |
---|
[03c742] | 2608 | #ifdef HAVE_NTL // henselLift12 |
---|
[49660c] | 2609 | int |
---|
| 2610 | liftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, int |
---|
| 2611 | start, int liftBound, int minBound, CFList& factors, |
---|
| 2612 | nmod_mat_t FLINTN, CFList& diophant, CFMatrix& M,CFArray& |
---|
| 2613 | Pi, CFArray& bufQ, bool& irreducible |
---|
| 2614 | ) |
---|
| 2615 | { |
---|
| 2616 | CanonicalForm LCF= LC (F, 1); |
---|
| 2617 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
| 2618 | bool wasInBounds= false; |
---|
| 2619 | bool hitBound= false; |
---|
| 2620 | int l= (minBound+1)*2; |
---|
| 2621 | int stepSize= 2; |
---|
| 2622 | int oldL= l/2; |
---|
| 2623 | bool reduced= false; |
---|
| 2624 | long rank; |
---|
| 2625 | nmod_mat_t FLINTK, FLINTC, null; |
---|
| 2626 | CFMatrix C; |
---|
| 2627 | CFArray buf; |
---|
| 2628 | CFListIterator j; |
---|
| 2629 | CanonicalForm truncF; |
---|
| 2630 | Variable y= F.mvar(); |
---|
| 2631 | while (l <= liftBound) |
---|
| 2632 | { |
---|
[2d35fe] | 2633 | TIMING_START (fac_fq_compute_lattice_lift); |
---|
[49660c] | 2634 | if (start) |
---|
| 2635 | { |
---|
| 2636 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
| 2637 | start= 0; |
---|
| 2638 | } |
---|
| 2639 | else |
---|
| 2640 | { |
---|
| 2641 | if (wasInBounds) |
---|
| 2642 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
| 2643 | else |
---|
| 2644 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 2645 | } |
---|
[2d35fe] | 2646 | TIMING_END_AND_PRINT (fac_fq_compute_lattice_lift, |
---|
| 2647 | "time to lift in compute lattice: "); |
---|
[49660c] | 2648 | |
---|
| 2649 | factors.insert (LCF); |
---|
| 2650 | j= factors; |
---|
| 2651 | j++; |
---|
| 2652 | |
---|
| 2653 | truncF= mod (F, power (y, l)); |
---|
[2d35fe] | 2654 | TIMING_START (fac_fq_logarithmic); |
---|
[49660c] | 2655 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
| 2656 | { |
---|
| 2657 | if (!wasInBounds) |
---|
| 2658 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
| 2659 | else |
---|
| 2660 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
| 2661 | bufQ[i]); |
---|
| 2662 | } |
---|
[2d35fe] | 2663 | TIMING_END_AND_PRINT (fac_fq_logarithmic, |
---|
| 2664 | "time to compute logarithmic derivative: "); |
---|
[49660c] | 2665 | |
---|
| 2666 | for (int i= 0; i < sizeBounds; i++) |
---|
| 2667 | { |
---|
| 2668 | if (bounds [i] + 1 <= l/2) |
---|
| 2669 | { |
---|
| 2670 | wasInBounds= true; |
---|
| 2671 | int k= tmin (bounds [i] + 1, l/2); |
---|
| 2672 | C= CFMatrix (l - k, factors.length() - 1); |
---|
| 2673 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
| 2674 | { |
---|
| 2675 | if (A[ii].size() - 1 >= i) |
---|
| 2676 | { |
---|
| 2677 | buf= getCoeffs (A[ii] [i], k); |
---|
| 2678 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 2679 | } |
---|
| 2680 | } |
---|
| 2681 | |
---|
| 2682 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
| 2683 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
| 2684 | getCharacteristic()); |
---|
| 2685 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
| 2686 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
| 2687 | getCharacteristic()); |
---|
| 2688 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
| 2689 | nmod_mat_clear (FLINTK); |
---|
| 2690 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
| 2691 | nmod_mat_clear (FLINTC); |
---|
| 2692 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
| 2693 | nmod_mat_clear (FLINTN); |
---|
| 2694 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
| 2695 | getCharacteristic()); |
---|
| 2696 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
| 2697 | |
---|
| 2698 | nmod_mat_clear (FLINTC); |
---|
| 2699 | nmod_mat_window_clear (FLINTK); |
---|
| 2700 | nmod_mat_clear (null); |
---|
| 2701 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
| 2702 | { |
---|
| 2703 | irreducible= true; |
---|
| 2704 | break; |
---|
| 2705 | } |
---|
| 2706 | if (isReduced (FLINTN) && l > (minBound+1)*2) |
---|
| 2707 | { |
---|
| 2708 | reduced= true; |
---|
| 2709 | break; |
---|
| 2710 | } |
---|
| 2711 | } |
---|
| 2712 | } |
---|
| 2713 | |
---|
| 2714 | if (irreducible) |
---|
| 2715 | break; |
---|
| 2716 | if (reduced) |
---|
| 2717 | break; |
---|
| 2718 | oldL= l; |
---|
| 2719 | l += stepSize; |
---|
| 2720 | stepSize *= 2; |
---|
| 2721 | if (l > liftBound) |
---|
| 2722 | { |
---|
| 2723 | if (!hitBound) |
---|
| 2724 | { |
---|
| 2725 | l= liftBound; |
---|
| 2726 | hitBound= true; |
---|
| 2727 | } |
---|
| 2728 | else |
---|
| 2729 | break; |
---|
| 2730 | } |
---|
| 2731 | } |
---|
| 2732 | delete [] A; |
---|
[a209e1d] | 2733 | if (!wasInBounds) |
---|
| 2734 | { |
---|
| 2735 | if (start) |
---|
| 2736 | henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M); |
---|
| 2737 | else |
---|
| 2738 | henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M); |
---|
| 2739 | factors.insert (LCF); |
---|
| 2740 | } |
---|
[49660c] | 2741 | return l; |
---|
| 2742 | } |
---|
| 2743 | #endif |
---|
[03c742] | 2744 | #endif |
---|
[49660c] | 2745 | |
---|
[7032db] | 2746 | #ifdef HAVE_NTL |
---|
[49660c] | 2747 | //over field extension |
---|
| 2748 | int |
---|
| 2749 | extLiftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
| 2750 | int liftBound, int minBound, int start, CFList& |
---|
| 2751 | factors, mat_zz_p& NTLN, CFList& diophant, |
---|
| 2752 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, bool& |
---|
| 2753 | irreducible, const CanonicalForm& evaluation, const |
---|
| 2754 | ExtensionInfo& info, CFList& source, CFList& dest |
---|
| 2755 | ) |
---|
| 2756 | { |
---|
| 2757 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
| 2758 | CanonicalForm LCF= LC (F, 1); |
---|
| 2759 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
| 2760 | bool wasInBounds= false; |
---|
| 2761 | bool hitBound= false; |
---|
| 2762 | int degMipo; |
---|
| 2763 | Variable alpha; |
---|
| 2764 | alpha= info.getAlpha(); |
---|
| 2765 | degMipo= degree (getMipo (alpha)); |
---|
| 2766 | |
---|
| 2767 | Variable gamma= info.getBeta(); |
---|
| 2768 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
| 2769 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
| 2770 | |
---|
[11bf82] | 2771 | int stepSize= 2; |
---|
[49660c] | 2772 | int l= ((minBound+1)/degMipo+1)*2; |
---|
| 2773 | l= tmax (l, 2); |
---|
| 2774 | if (start > l) |
---|
| 2775 | l= start; |
---|
[11bf82] | 2776 | int oldL= l/2; |
---|
| 2777 | bool reduced= false; |
---|
[49660c] | 2778 | Variable y= F.mvar(); |
---|
| 2779 | Variable x= Variable (1); |
---|
| 2780 | CanonicalForm powX, imBasis, truncF; |
---|
| 2781 | CFMatrix Mat, C; |
---|
[38ffb7] | 2782 | CFArray buf; |
---|
[49660c] | 2783 | CFIterator iter; |
---|
| 2784 | mat_zz_p* NTLMat, *NTLC, NTLK; |
---|
[38ffb7] | 2785 | CFListIterator j; |
---|
[11bf82] | 2786 | while (l <= liftBound) |
---|
| 2787 | { |
---|
[2d35fe] | 2788 | TIMING_START (fac_fq_compute_lattice_lift); |
---|
[11bf82] | 2789 | if (start) |
---|
| 2790 | { |
---|
| 2791 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
| 2792 | start= 0; |
---|
| 2793 | } |
---|
| 2794 | else |
---|
| 2795 | { |
---|
| 2796 | if (wasInBounds) |
---|
| 2797 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
| 2798 | else |
---|
| 2799 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 2800 | } |
---|
[2d35fe] | 2801 | TIMING_END_AND_PRINT (fac_fq_compute_lattice_lift, |
---|
| 2802 | "time to lift in compute lattice: "); |
---|
[11bf82] | 2803 | |
---|
| 2804 | factors.insert (LCF); |
---|
[49660c] | 2805 | |
---|
| 2806 | if (GF) |
---|
| 2807 | setCharacteristic (getCharacteristic()); |
---|
| 2808 | |
---|
| 2809 | powX= power (y-gamma, l); |
---|
| 2810 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
| 2811 | for (int i= 0; i < l*degMipo; i++) |
---|
| 2812 | { |
---|
| 2813 | imBasis= mod (power (y, i), powX); |
---|
| 2814 | imBasis= imBasis (power (y, degMipo), y); |
---|
| 2815 | imBasis= imBasis (y, gamma); |
---|
| 2816 | iter= imBasis; |
---|
| 2817 | for (; iter.hasTerms(); iter++) |
---|
| 2818 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
| 2819 | } |
---|
| 2820 | |
---|
| 2821 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
| 2822 | *NTLMat= inv (*NTLMat); |
---|
| 2823 | |
---|
| 2824 | if (GF) |
---|
| 2825 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 2826 | |
---|
[38ffb7] | 2827 | j= factors; |
---|
[11bf82] | 2828 | j++; |
---|
| 2829 | |
---|
[5335ba] | 2830 | truncF= mod (F, power (y, l)); |
---|
[2d35fe] | 2831 | TIMING_START (fac_fq_logarithmic); |
---|
[11bf82] | 2832 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
| 2833 | { |
---|
| 2834 | if (!wasInBounds) |
---|
[5335ba] | 2835 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
[11bf82] | 2836 | else |
---|
[5335ba] | 2837 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
| 2838 | bufQ[i]); |
---|
[11bf82] | 2839 | } |
---|
[2d35fe] | 2840 | TIMING_END_AND_PRINT (fac_fq_logarithmic, |
---|
| 2841 | "time to compute logarithmic derivative: "); |
---|
[11bf82] | 2842 | |
---|
| 2843 | for (int i= 0; i < sizeBounds; i++) |
---|
| 2844 | { |
---|
[49660c] | 2845 | if (bounds [i] + 1 <= (l/2)*degMipo) |
---|
[11bf82] | 2846 | { |
---|
| 2847 | wasInBounds= true; |
---|
[49660c] | 2848 | int k= tmin (bounds [i] + 1, (l/2)*degMipo); |
---|
| 2849 | C= CFMatrix (l*degMipo - k, factors.length() - 1); |
---|
| 2850 | |
---|
[11bf82] | 2851 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
| 2852 | { |
---|
| 2853 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 2854 | { |
---|
[49660c] | 2855 | if (GF) |
---|
| 2856 | { |
---|
| 2857 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 2858 | setCharacteristic (getCharacteristic()); |
---|
| 2859 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
| 2860 | if (alpha != gamma) |
---|
| 2861 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 2862 | gamma, source, dest |
---|
| 2863 | ); |
---|
| 2864 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
| 2865 | } |
---|
| 2866 | else |
---|
| 2867 | { |
---|
| 2868 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 2869 | if (alpha != gamma) |
---|
| 2870 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 2871 | gamma, source, dest |
---|
| 2872 | ); |
---|
| 2873 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
| 2874 | } |
---|
[9ebec2] | 2875 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 2876 | } |
---|
[49660c] | 2877 | if (GF) |
---|
| 2878 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
[11bf82] | 2879 | } |
---|
[49660c] | 2880 | |
---|
| 2881 | if (GF) |
---|
| 2882 | setCharacteristic(getCharacteristic()); |
---|
| 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; |
---|
[ffd883] | 2890 | delete NTLC; |
---|
[11bf82] | 2891 | |
---|
[49660c] | 2892 | if (GF) |
---|
| 2893 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 2894 | |
---|
[11bf82] | 2895 | if (NTLN.NumCols() == 1) |
---|
| 2896 | { |
---|
| 2897 | irreducible= true; |
---|
| 2898 | break; |
---|
| 2899 | } |
---|
[49660c] | 2900 | if (isReduced (NTLN)) |
---|
[11bf82] | 2901 | { |
---|
| 2902 | reduced= true; |
---|
| 2903 | break; |
---|
| 2904 | } |
---|
| 2905 | } |
---|
| 2906 | } |
---|
| 2907 | |
---|
[ffd883] | 2908 | delete NTLMat; |
---|
| 2909 | |
---|
[49660c] | 2910 | if (NTLN.NumCols() == 1) |
---|
| 2911 | { |
---|
| 2912 | irreducible= true; |
---|
[11bf82] | 2913 | break; |
---|
[49660c] | 2914 | } |
---|
[11bf82] | 2915 | if (reduced) |
---|
| 2916 | break; |
---|
| 2917 | oldL= l; |
---|
| 2918 | l += stepSize; |
---|
| 2919 | stepSize *= 2; |
---|
| 2920 | if (l > liftBound) |
---|
| 2921 | { |
---|
| 2922 | if (!hitBound) |
---|
| 2923 | { |
---|
| 2924 | l= liftBound; |
---|
| 2925 | hitBound= true; |
---|
| 2926 | } |
---|
| 2927 | else |
---|
| 2928 | break; |
---|
| 2929 | } |
---|
| 2930 | } |
---|
| 2931 | delete [] A; |
---|
[a209e1d] | 2932 | if (!wasInBounds) |
---|
| 2933 | { |
---|
| 2934 | if (start) |
---|
| 2935 | henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M); |
---|
| 2936 | else |
---|
| 2937 | henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M); |
---|
| 2938 | factors.insert (LCF); |
---|
| 2939 | } |
---|
[11bf82] | 2940 | return l; |
---|
| 2941 | } |
---|
[87942fd] | 2942 | #endif |
---|
[11bf82] | 2943 | |
---|
[7c4341] | 2944 | #ifdef HAVE_FLINT |
---|
[03c742] | 2945 | #ifdef HAVE_NTL // henselLift12 |
---|
[11bf82] | 2946 | //over field extension |
---|
| 2947 | int |
---|
| 2948 | extLiftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
| 2949 | int liftBound, int minBound, int start, CFList& |
---|
[49660c] | 2950 | factors, nmod_mat_t FLINTN, CFList& diophant, |
---|
[11bf82] | 2951 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, bool& |
---|
| 2952 | irreducible, const CanonicalForm& evaluation, const |
---|
| 2953 | ExtensionInfo& info, CFList& source, CFList& dest |
---|
| 2954 | ) |
---|
| 2955 | { |
---|
| 2956 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
| 2957 | CanonicalForm LCF= LC (F, 1); |
---|
| 2958 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
| 2959 | bool wasInBounds= false; |
---|
| 2960 | bool hitBound= false; |
---|
| 2961 | int degMipo; |
---|
| 2962 | Variable alpha; |
---|
| 2963 | alpha= info.getAlpha(); |
---|
| 2964 | degMipo= degree (getMipo (alpha)); |
---|
| 2965 | |
---|
| 2966 | Variable gamma= info.getBeta(); |
---|
| 2967 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
| 2968 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
| 2969 | |
---|
| 2970 | int stepSize= 2; |
---|
| 2971 | int l= ((minBound+1)/degMipo+1)*2; |
---|
| 2972 | l= tmax (l, 2); |
---|
| 2973 | if (start > l) |
---|
| 2974 | l= start; |
---|
| 2975 | int oldL= l/2; |
---|
| 2976 | bool reduced= false; |
---|
[38ffb7] | 2977 | Variable y= F.mvar(); |
---|
| 2978 | Variable x= Variable (1); |
---|
[5335ba] | 2979 | CanonicalForm powX, imBasis, truncF; |
---|
[38ffb7] | 2980 | CFMatrix Mat, C; |
---|
| 2981 | CFArray buf; |
---|
| 2982 | CFIterator iter; |
---|
[49660c] | 2983 | long rank; |
---|
| 2984 | nmod_mat_t FLINTMat, FLINTMatInv, FLINTC, FLINTK, null; |
---|
[38ffb7] | 2985 | CFListIterator j; |
---|
[11bf82] | 2986 | while (l <= liftBound) |
---|
| 2987 | { |
---|
| 2988 | if (start) |
---|
| 2989 | { |
---|
| 2990 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
| 2991 | start= 0; |
---|
| 2992 | } |
---|
| 2993 | else |
---|
| 2994 | { |
---|
| 2995 | if (wasInBounds) |
---|
| 2996 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
| 2997 | else |
---|
| 2998 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 2999 | } |
---|
| 3000 | |
---|
| 3001 | factors.insert (LCF); |
---|
| 3002 | |
---|
| 3003 | if (GF) |
---|
| 3004 | setCharacteristic (getCharacteristic()); |
---|
| 3005 | |
---|
[38ffb7] | 3006 | powX= power (y-gamma, l); |
---|
| 3007 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
[11bf82] | 3008 | for (int i= 0; i < l*degMipo; i++) |
---|
| 3009 | { |
---|
[38ffb7] | 3010 | imBasis= mod (power (y, i), powX); |
---|
[11bf82] | 3011 | imBasis= imBasis (power (y, degMipo), y); |
---|
| 3012 | imBasis= imBasis (y, gamma); |
---|
[38ffb7] | 3013 | iter= imBasis; |
---|
[11bf82] | 3014 | for (; iter.hasTerms(); iter++) |
---|
| 3015 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
| 3016 | } |
---|
| 3017 | |
---|
[49660c] | 3018 | convertFacCFMatrix2nmod_mat_t (FLINTMat, Mat); |
---|
| 3019 | nmod_mat_init (FLINTMatInv, nmod_mat_nrows (FLINTMat), |
---|
| 3020 | nmod_mat_nrows (FLINTMat), getCharacteristic()); |
---|
| 3021 | nmod_mat_inv (FLINTMatInv, FLINTMat); |
---|
[11bf82] | 3022 | |
---|
| 3023 | if (GF) |
---|
| 3024 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 3025 | |
---|
[38ffb7] | 3026 | j= factors; |
---|
[11bf82] | 3027 | j++; |
---|
| 3028 | |
---|
[5335ba] | 3029 | truncF= mod (F, power (y, l)); |
---|
[11bf82] | 3030 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
| 3031 | { |
---|
| 3032 | if (!wasInBounds) |
---|
[5335ba] | 3033 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
[11bf82] | 3034 | else |
---|
[5335ba] | 3035 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
| 3036 | bufQ[i]); |
---|
[11bf82] | 3037 | } |
---|
| 3038 | |
---|
| 3039 | for (int i= 0; i < sizeBounds; i++) |
---|
| 3040 | { |
---|
| 3041 | if (bounds [i] + 1 <= (l/2)*degMipo) |
---|
| 3042 | { |
---|
| 3043 | wasInBounds= true; |
---|
| 3044 | int k= tmin (bounds [i] + 1, (l/2)*degMipo); |
---|
[38ffb7] | 3045 | C= CFMatrix (l*degMipo - k, factors.length() - 1); |
---|
[11bf82] | 3046 | |
---|
| 3047 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
| 3048 | { |
---|
| 3049 | if (A[ii].size() - 1 >= i) |
---|
| 3050 | { |
---|
| 3051 | if (GF) |
---|
| 3052 | { |
---|
| 3053 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 3054 | setCharacteristic (getCharacteristic()); |
---|
| 3055 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
| 3056 | if (alpha != gamma) |
---|
| 3057 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 3058 | gamma, source, dest |
---|
| 3059 | ); |
---|
[7c4341] | 3060 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, FLINTMatInv); |
---|
[11bf82] | 3061 | } |
---|
| 3062 | else |
---|
| 3063 | { |
---|
| 3064 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 3065 | if (alpha != gamma) |
---|
| 3066 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 3067 | gamma, source, dest |
---|
| 3068 | ); |
---|
[7c4341] | 3069 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, FLINTMatInv); |
---|
[11bf82] | 3070 | } |
---|
[9ebec2] | 3071 | writeInMatrix (C, buf, ii + 1, 0); |
---|
[11bf82] | 3072 | } |
---|
| 3073 | if (GF) |
---|
| 3074 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 3075 | } |
---|
| 3076 | |
---|
| 3077 | if (GF) |
---|
| 3078 | setCharacteristic(getCharacteristic()); |
---|
| 3079 | |
---|
[49660c] | 3080 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
| 3081 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
| 3082 | getCharacteristic()); |
---|
| 3083 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
| 3084 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
| 3085 | getCharacteristic()); |
---|
| 3086 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
| 3087 | nmod_mat_clear (FLINTK); |
---|
| 3088 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
| 3089 | nmod_mat_clear (FLINTC); |
---|
| 3090 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
| 3091 | nmod_mat_clear (FLINTN); |
---|
| 3092 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
| 3093 | getCharacteristic()); |
---|
| 3094 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
| 3095 | |
---|
| 3096 | nmod_mat_clear (FLINTC); |
---|
| 3097 | nmod_mat_window_clear (FLINTK); |
---|
| 3098 | nmod_mat_clear (null); |
---|
[11bf82] | 3099 | |
---|
| 3100 | if (GF) |
---|
| 3101 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 3102 | |
---|
[49660c] | 3103 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
[11bf82] | 3104 | { |
---|
| 3105 | irreducible= true; |
---|
| 3106 | break; |
---|
| 3107 | } |
---|
[49660c] | 3108 | if (isReduced (FLINTN)) |
---|
[11bf82] | 3109 | { |
---|
| 3110 | reduced= true; |
---|
| 3111 | break; |
---|
| 3112 | } |
---|
| 3113 | } |
---|
| 3114 | } |
---|
| 3115 | |
---|
[49660c] | 3116 | nmod_mat_clear (FLINTMat); |
---|
| 3117 | nmod_mat_clear (FLINTMatInv); |
---|
| 3118 | |
---|
| 3119 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
[11bf82] | 3120 | { |
---|
| 3121 | irreducible= true; |
---|
| 3122 | break; |
---|
| 3123 | } |
---|
| 3124 | if (reduced) |
---|
| 3125 | break; |
---|
| 3126 | oldL= l; |
---|
| 3127 | l += stepSize; |
---|
| 3128 | stepSize *= 2; |
---|
| 3129 | if (l > liftBound) |
---|
| 3130 | { |
---|
| 3131 | if (!hitBound) |
---|
| 3132 | { |
---|
| 3133 | l= liftBound; |
---|
| 3134 | hitBound= true; |
---|
| 3135 | } |
---|
| 3136 | else |
---|
| 3137 | break; |
---|
| 3138 | } |
---|
| 3139 | } |
---|
| 3140 | delete [] A; |
---|
[a209e1d] | 3141 | if (!wasInBounds) |
---|
| 3142 | { |
---|
| 3143 | if (start) |
---|
| 3144 | henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M); |
---|
| 3145 | else |
---|
| 3146 | henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M); |
---|
| 3147 | factors.insert (LCF); |
---|
| 3148 | } |
---|
[11bf82] | 3149 | return l; |
---|
| 3150 | } |
---|
[7c4341] | 3151 | #endif |
---|
[03c742] | 3152 | #endif |
---|
[11bf82] | 3153 | |
---|
| 3154 | // over Fq |
---|
[03c742] | 3155 | #ifdef HAVE_NTL |
---|
[11bf82] | 3156 | int |
---|
| 3157 | liftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
| 3158 | int start, int liftBound, int minBound, CFList& factors, |
---|
| 3159 | mat_zz_pE& NTLN, CFList& diophant, CFMatrix& M, CFArray& |
---|
| 3160 | Pi, CFArray& bufQ, bool& irreducible |
---|
| 3161 | ) |
---|
| 3162 | { |
---|
| 3163 | CanonicalForm LCF= LC (F, 1); |
---|
| 3164 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
| 3165 | bool wasInBounds= false; |
---|
| 3166 | bool hitBound= false; |
---|
| 3167 | int l= (minBound+1)*2; |
---|
| 3168 | int stepSize= 2; |
---|
| 3169 | int oldL= l/2; |
---|
| 3170 | bool reduced= false; |
---|
[38ffb7] | 3171 | CFListIterator j; |
---|
| 3172 | mat_zz_pE* NTLC, NTLK; |
---|
| 3173 | CFArray buf; |
---|
| 3174 | CFMatrix C; |
---|
[5335ba] | 3175 | Variable y= F.mvar(); |
---|
| 3176 | CanonicalForm truncF; |
---|
[11bf82] | 3177 | while (l <= liftBound) |
---|
| 3178 | { |
---|
[2d35fe] | 3179 | TIMING_START (fac_fq_compute_lattice_lift); |
---|
[11bf82] | 3180 | if (start) |
---|
| 3181 | { |
---|
| 3182 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
| 3183 | start= 0; |
---|
| 3184 | } |
---|
| 3185 | else |
---|
| 3186 | { |
---|
| 3187 | if (wasInBounds) |
---|
| 3188 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
| 3189 | else |
---|
| 3190 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 3191 | } |
---|
[2d35fe] | 3192 | TIMING_END_AND_PRINT (fac_fq_compute_lattice_lift, |
---|
| 3193 | "time to lift in compute lattice: "); |
---|
[11bf82] | 3194 | |
---|
| 3195 | factors.insert (LCF); |
---|
[38ffb7] | 3196 | j= factors; |
---|
[11bf82] | 3197 | j++; |
---|
| 3198 | |
---|
[5335ba] | 3199 | truncF= mod (F, power (y,l)); |
---|
[2d35fe] | 3200 | TIMING_START (fac_fq_logarithmic); |
---|
[11bf82] | 3201 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
| 3202 | { |
---|
| 3203 | if (l == (minBound+1)*2) |
---|
| 3204 | { |
---|
[5335ba] | 3205 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
[11bf82] | 3206 | } |
---|
| 3207 | else |
---|
| 3208 | { |
---|
[5335ba] | 3209 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
[11bf82] | 3210 | bufQ[i] |
---|
| 3211 | ); |
---|
| 3212 | } |
---|
| 3213 | } |
---|
[2d35fe] | 3214 | TIMING_END_AND_PRINT (fac_fq_logarithmic, |
---|
| 3215 | "time to compute logarithmic derivative: "); |
---|
[11bf82] | 3216 | |
---|
| 3217 | for (int i= 0; i < sizeBounds; i++) |
---|
| 3218 | { |
---|
| 3219 | if (bounds [i] + 1 <= l/2) |
---|
| 3220 | { |
---|
| 3221 | wasInBounds= true; |
---|
| 3222 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 3223 | C= CFMatrix (l - k, factors.length() - 1); |
---|
[11bf82] | 3224 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
| 3225 | { |
---|
[38ffb7] | 3226 | |
---|
[11bf82] | 3227 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 3228 | { |
---|
[11bf82] | 3229 | buf= getCoeffs (A[ii] [i], k); |
---|
[9ebec2] | 3230 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 3231 | } |
---|
[11bf82] | 3232 | } |
---|
| 3233 | |
---|
[38ffb7] | 3234 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
| 3235 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 3236 | transpose (NTLK, NTLK); |
---|
| 3237 | kernel (NTLK, NTLK); |
---|
| 3238 | transpose (NTLK, NTLK); |
---|
| 3239 | NTLN *= NTLK; |
---|
[ffd883] | 3240 | delete NTLC; |
---|
[11bf82] | 3241 | |
---|
| 3242 | if (NTLN.NumCols() == 1) |
---|
| 3243 | { |
---|
| 3244 | irreducible= true; |
---|
| 3245 | break; |
---|
| 3246 | } |
---|
[3426de2] | 3247 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
[11bf82] | 3248 | { |
---|
| 3249 | reduced= true; |
---|
| 3250 | break; |
---|
| 3251 | } |
---|
| 3252 | } |
---|
| 3253 | } |
---|
| 3254 | |
---|
| 3255 | if (NTLN.NumCols() == 1) |
---|
| 3256 | { |
---|
| 3257 | irreducible= true; |
---|
| 3258 | break; |
---|
| 3259 | } |
---|
| 3260 | if (reduced) |
---|
| 3261 | break; |
---|
| 3262 | oldL= l; |
---|
| 3263 | l += stepSize; |
---|
| 3264 | stepSize *= 2; |
---|
| 3265 | if (l > liftBound) |
---|
| 3266 | { |
---|
| 3267 | if (!hitBound) |
---|
| 3268 | { |
---|
| 3269 | l= liftBound; |
---|
| 3270 | hitBound= true; |
---|
| 3271 | } |
---|
| 3272 | else |
---|
| 3273 | break; |
---|
| 3274 | } |
---|
| 3275 | } |
---|
| 3276 | delete [] A; |
---|
[a209e1d] | 3277 | if (!wasInBounds) |
---|
| 3278 | { |
---|
| 3279 | if (start) |
---|
| 3280 | henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M); |
---|
| 3281 | else |
---|
| 3282 | henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M); |
---|
| 3283 | factors.insert (LCF); |
---|
| 3284 | } |
---|
[11bf82] | 3285 | return l; |
---|
| 3286 | } |
---|
[03c742] | 3287 | #endif |
---|
[11bf82] | 3288 | |
---|
[03c742] | 3289 | #ifdef HAVE_NTL // henselLift12 |
---|
[49660c] | 3290 | #ifdef HAVE_FLINT |
---|
| 3291 | int |
---|
| 3292 | liftAndComputeLatticeFq2Fp (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
| 3293 | int start, int liftBound, int minBound, CFList& |
---|
| 3294 | factors, nmod_mat_t FLINTN, CFList& diophant, |
---|
| 3295 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, bool& |
---|
| 3296 | irreducible, const Variable& alpha |
---|
| 3297 | ) |
---|
| 3298 | #else |
---|
[11bf82] | 3299 | int |
---|
| 3300 | liftAndComputeLatticeFq2Fp (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
| 3301 | int start, int liftBound, int minBound, CFList& |
---|
| 3302 | factors, mat_zz_p& NTLN, CFList& diophant, CFMatrix& |
---|
| 3303 | M, CFArray& Pi, CFArray& bufQ, bool& irreducible, |
---|
| 3304 | const Variable& alpha |
---|
| 3305 | ) |
---|
[49660c] | 3306 | #endif |
---|
[11bf82] | 3307 | { |
---|
| 3308 | CanonicalForm LCF= LC (F, 1); |
---|
| 3309 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
| 3310 | bool wasInBounds= false; |
---|
| 3311 | int l= (minBound+1)*2; |
---|
| 3312 | int oldL= l/2; |
---|
| 3313 | int stepSize= 2; |
---|
| 3314 | bool hitBound= false; |
---|
| 3315 | int extensionDeg= degree (getMipo (alpha)); |
---|
| 3316 | bool reduced= false; |
---|
[38ffb7] | 3317 | CFListIterator j; |
---|
| 3318 | CFMatrix C; |
---|
| 3319 | CFArray buf; |
---|
[49660c] | 3320 | #ifdef HAVE_FLINT |
---|
| 3321 | long rank; |
---|
| 3322 | nmod_mat_t FLINTC, FLINTK, null; |
---|
| 3323 | #else |
---|
[38ffb7] | 3324 | mat_zz_p* NTLC, NTLK; |
---|
[49660c] | 3325 | #endif |
---|
[5335ba] | 3326 | Variable y= F.mvar(); |
---|
| 3327 | CanonicalForm truncF; |
---|
[11bf82] | 3328 | while (l <= liftBound) |
---|
| 3329 | { |
---|
[2d35fe] | 3330 | TIMING_START (fac_fq_compute_lattice_lift); |
---|
[11bf82] | 3331 | if (start) |
---|
| 3332 | { |
---|
| 3333 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
| 3334 | start= 0; |
---|
| 3335 | } |
---|
| 3336 | else |
---|
| 3337 | { |
---|
| 3338 | if (wasInBounds) |
---|
| 3339 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
| 3340 | else |
---|
| 3341 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 3342 | } |
---|
[2d35fe] | 3343 | TIMING_END_AND_PRINT (fac_fq_compute_lattice_lift, |
---|
| 3344 | "time to lift in compute lattice: "); |
---|
[11bf82] | 3345 | |
---|
| 3346 | factors.insert (LCF); |
---|
[38ffb7] | 3347 | j= factors; |
---|
[11bf82] | 3348 | j++; |
---|
| 3349 | |
---|
[5335ba] | 3350 | truncF= mod (F, power (y,l)); |
---|
[2d35fe] | 3351 | TIMING_START (fac_fq_logarithmic); |
---|
[11bf82] | 3352 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
| 3353 | { |
---|
| 3354 | if (l == (minBound+1)*2) |
---|
| 3355 | { |
---|
[5335ba] | 3356 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
[11bf82] | 3357 | } |
---|
| 3358 | else |
---|
| 3359 | { |
---|
[5335ba] | 3360 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
[11bf82] | 3361 | bufQ[i] |
---|
| 3362 | ); |
---|
| 3363 | } |
---|
| 3364 | } |
---|
[2d35fe] | 3365 | TIMING_END_AND_PRINT (fac_fq_logarithmic, |
---|
| 3366 | "time to compute logarithmic derivative: "); |
---|
[11bf82] | 3367 | |
---|
| 3368 | for (int i= 0; i < sizeBounds; i++) |
---|
| 3369 | { |
---|
| 3370 | if (bounds [i] + 1 <= l/2) |
---|
| 3371 | { |
---|
| 3372 | wasInBounds= true; |
---|
| 3373 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 3374 | C= CFMatrix ((l - k)*extensionDeg, factors.length() - 1); |
---|
[11bf82] | 3375 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
| 3376 | { |
---|
| 3377 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 3378 | { |
---|
[11bf82] | 3379 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
[9ebec2] | 3380 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 3381 | } |
---|
[11bf82] | 3382 | } |
---|
| 3383 | |
---|
[49660c] | 3384 | #ifdef HAVE_FLINT |
---|
| 3385 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
| 3386 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
| 3387 | getCharacteristic()); |
---|
| 3388 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
| 3389 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
| 3390 | getCharacteristic()); |
---|
| 3391 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
| 3392 | nmod_mat_clear (FLINTK); |
---|
| 3393 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
| 3394 | nmod_mat_clear (FLINTC); |
---|
| 3395 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
| 3396 | nmod_mat_clear (FLINTN); |
---|
| 3397 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
| 3398 | getCharacteristic()); |
---|
| 3399 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
| 3400 | |
---|
| 3401 | nmod_mat_clear (FLINTC); |
---|
| 3402 | nmod_mat_window_clear (FLINTK); |
---|
| 3403 | nmod_mat_clear (null); |
---|
| 3404 | #else |
---|
[38ffb7] | 3405 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 3406 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 3407 | transpose (NTLK, NTLK); |
---|
| 3408 | kernel (NTLK, NTLK); |
---|
| 3409 | transpose (NTLK, NTLK); |
---|
| 3410 | NTLN *= NTLK; |
---|
[ffd883] | 3411 | delete NTLC; |
---|
[49660c] | 3412 | #endif |
---|
[11bf82] | 3413 | |
---|
[49660c] | 3414 | #ifdef HAVE_FLINT |
---|
| 3415 | if (nmod_mat_nrows (FLINTN) == 1) |
---|
| 3416 | #else |
---|
[11bf82] | 3417 | if (NTLN.NumCols() == 1) |
---|
[49660c] | 3418 | #endif |
---|
[11bf82] | 3419 | { |
---|
| 3420 | irreducible= true; |
---|
| 3421 | break; |
---|
| 3422 | } |
---|
[49660c] | 3423 | #ifdef HAVE_FLINT |
---|
| 3424 | if (isReduced (FLINTN) && l > (minBound+1)*2) |
---|
| 3425 | #else |
---|
[3426de2] | 3426 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
[49660c] | 3427 | #endif |
---|
[11bf82] | 3428 | { |
---|
| 3429 | reduced= true; |
---|
| 3430 | break; |
---|
| 3431 | } |
---|
| 3432 | } |
---|
| 3433 | } |
---|
| 3434 | |
---|
[49660c] | 3435 | #ifdef HAVE_FLINT |
---|
| 3436 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
| 3437 | #else |
---|
[11bf82] | 3438 | if (NTLN.NumCols() == 1) |
---|
[49660c] | 3439 | #endif |
---|
[11bf82] | 3440 | { |
---|
| 3441 | irreducible= true; |
---|
| 3442 | break; |
---|
| 3443 | } |
---|
| 3444 | if (reduced) |
---|
| 3445 | break; |
---|
| 3446 | oldL= l; |
---|
| 3447 | l += stepSize; |
---|
| 3448 | stepSize *= 2; |
---|
| 3449 | if (l > liftBound) |
---|
| 3450 | { |
---|
| 3451 | if (!hitBound) |
---|
| 3452 | { |
---|
| 3453 | l= liftBound; |
---|
| 3454 | hitBound= true; |
---|
| 3455 | } |
---|
| 3456 | else |
---|
| 3457 | break; |
---|
| 3458 | } |
---|
| 3459 | } |
---|
| 3460 | delete [] A; |
---|
[a209e1d] | 3461 | if (!wasInBounds) |
---|
| 3462 | { |
---|
| 3463 | if (start) |
---|
| 3464 | henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M); |
---|
| 3465 | else |
---|
| 3466 | henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M); |
---|
| 3467 | factors.insert (LCF); |
---|
| 3468 | } |
---|
[11bf82] | 3469 | return l; |
---|
| 3470 | } |
---|
[03c742] | 3471 | #endif |
---|
[11bf82] | 3472 | |
---|
[03c742] | 3473 | #ifdef HAVE_NTL // logarithmicDerivative |
---|
[11bf82] | 3474 | CFList |
---|
| 3475 | increasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
[2537fa0] | 3476 | int oldNumCols, int oldL, int precision, |
---|
| 3477 | const CanonicalForm& eval |
---|
[11bf82] | 3478 | ) |
---|
| 3479 | { |
---|
| 3480 | int d; |
---|
[542864] | 3481 | bool isIrreducible= false; |
---|
| 3482 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
[2537fa0] | 3483 | Variable y= F.mvar(); |
---|
[542864] | 3484 | if (isIrreducible) |
---|
| 3485 | { |
---|
| 3486 | delete [] bounds; |
---|
| 3487 | CanonicalForm G= F; |
---|
| 3488 | F= 1; |
---|
[2537fa0] | 3489 | return CFList (G (y-eval, y)); |
---|
[542864] | 3490 | } |
---|
[11bf82] | 3491 | CFArray * A= new CFArray [factors.length()]; |
---|
| 3492 | CFArray bufQ= CFArray (factors.length()); |
---|
[49660c] | 3493 | #ifdef HAVE_FLINT |
---|
| 3494 | nmod_mat_t FLINTN; |
---|
| 3495 | nmod_mat_init (FLINTN,factors.length(),factors.length(), getCharacteristic()); |
---|
| 3496 | for (long i=factors.length()-1; i >= 0; i--) |
---|
| 3497 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
| 3498 | #else |
---|
[11bf82] | 3499 | mat_zz_p NTLN; |
---|
| 3500 | ident (NTLN, factors.length()); |
---|
[49660c] | 3501 | #endif |
---|
[11bf82] | 3502 | int minBound= bounds[0]; |
---|
| 3503 | for (int i= 1; i < d; i++) |
---|
| 3504 | { |
---|
| 3505 | if (bounds[i] != 0) |
---|
| 3506 | minBound= tmin (minBound, bounds[i]); |
---|
| 3507 | } |
---|
| 3508 | int l= tmax (2*(minBound + 1), oldL); |
---|
| 3509 | int oldL2= l/2; |
---|
| 3510 | int stepSize= 2; |
---|
| 3511 | bool useOldQs= false; |
---|
| 3512 | bool hitBound= false; |
---|
[38ffb7] | 3513 | CFListIterator j; |
---|
| 3514 | CFMatrix C; |
---|
| 3515 | CFArray buf; |
---|
[49660c] | 3516 | #ifdef HAVE_FLINT |
---|
| 3517 | long rank; |
---|
| 3518 | nmod_mat_t FLINTC, FLINTK, null; |
---|
| 3519 | #else |
---|
[38ffb7] | 3520 | mat_zz_p* NTLC, NTLK; |
---|
[49660c] | 3521 | #endif |
---|
[5335ba] | 3522 | CanonicalForm truncF; |
---|
[11bf82] | 3523 | while (l <= precision) |
---|
| 3524 | { |
---|
[38ffb7] | 3525 | j= factors; |
---|
[5335ba] | 3526 | truncF= mod (F, power (y,l)); |
---|
[11bf82] | 3527 | if (useOldQs) |
---|
| 3528 | { |
---|
| 3529 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 3530 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
[11bf82] | 3531 | bufQ[i] |
---|
| 3532 | ); |
---|
| 3533 | } |
---|
| 3534 | else |
---|
| 3535 | { |
---|
| 3536 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 3537 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 3538 | } |
---|
| 3539 | useOldQs= true; |
---|
| 3540 | for (int i= 0; i < d; i++) |
---|
| 3541 | { |
---|
| 3542 | if (bounds [i] + 1 <= l/2) |
---|
| 3543 | { |
---|
| 3544 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 3545 | C= CFMatrix (l - k, factors.length()); |
---|
[11bf82] | 3546 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 3547 | { |
---|
| 3548 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 3549 | { |
---|
[11bf82] | 3550 | buf= getCoeffs (A[ii] [i], k); |
---|
[9ebec2] | 3551 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 3552 | } |
---|
[11bf82] | 3553 | } |
---|
[49660c] | 3554 | #ifdef HAVE_FLINT |
---|
| 3555 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
| 3556 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
| 3557 | getCharacteristic()); |
---|
| 3558 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
| 3559 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
| 3560 | getCharacteristic()); |
---|
| 3561 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
| 3562 | nmod_mat_clear (FLINTK); |
---|
| 3563 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
| 3564 | nmod_mat_clear (FLINTC); |
---|
| 3565 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
| 3566 | nmod_mat_clear (FLINTN); |
---|
| 3567 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
| 3568 | getCharacteristic()); |
---|
| 3569 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
| 3570 | |
---|
| 3571 | nmod_mat_clear (FLINTC); |
---|
| 3572 | nmod_mat_window_clear (FLINTK); |
---|
| 3573 | nmod_mat_clear (null); |
---|
| 3574 | #else |
---|
[38ffb7] | 3575 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 3576 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 3577 | transpose (NTLK, NTLK); |
---|
| 3578 | kernel (NTLK, NTLK); |
---|
| 3579 | transpose (NTLK, NTLK); |
---|
| 3580 | NTLN *= NTLK; |
---|
[ffd883] | 3581 | delete NTLC; |
---|
[49660c] | 3582 | #endif |
---|
| 3583 | #ifdef HAVE_FLINT |
---|
| 3584 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
| 3585 | { |
---|
| 3586 | nmod_mat_clear (FLINTN); |
---|
| 3587 | #else |
---|
[11bf82] | 3588 | if (NTLN.NumCols() == 1) |
---|
| 3589 | { |
---|
[49660c] | 3590 | #endif |
---|
[11bf82] | 3591 | delete [] A; |
---|
| 3592 | delete [] bounds; |
---|
| 3593 | CanonicalForm G= F; |
---|
| 3594 | F= 1; |
---|
[2537fa0] | 3595 | return CFList (G (y-eval,y)); |
---|
[11bf82] | 3596 | } |
---|
| 3597 | } |
---|
| 3598 | } |
---|
| 3599 | |
---|
[49660c] | 3600 | #ifdef HAVE_FLINT |
---|
| 3601 | if (nmod_mat_ncols (FLINTN) < oldNumCols - factorsFound) |
---|
| 3602 | { |
---|
| 3603 | if (isReduced (FLINTN)) |
---|
| 3604 | { |
---|
| 3605 | int * factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
| 3606 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
| 3607 | #else |
---|
[11bf82] | 3608 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
| 3609 | { |
---|
| 3610 | if (isReduced (NTLN)) |
---|
| 3611 | { |
---|
| 3612 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 3613 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
[49660c] | 3614 | #endif |
---|
[11bf82] | 3615 | factorsFoundIndex[i]= 0; |
---|
| 3616 | int factorsFound2= 0; |
---|
| 3617 | CFList result; |
---|
| 3618 | CanonicalForm bufF= F; |
---|
[49660c] | 3619 | #ifdef HAVE_FLINT |
---|
| 3620 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
[2537fa0] | 3621 | factorsFoundIndex, FLINTN, eval, false |
---|
[49660c] | 3622 | ); |
---|
| 3623 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
| 3624 | { |
---|
| 3625 | nmod_mat_clear (FLINTN); |
---|
| 3626 | #else |
---|
[11bf82] | 3627 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
[2537fa0] | 3628 | factorsFoundIndex, NTLN, eval, false |
---|
[11bf82] | 3629 | ); |
---|
[38ffb7] | 3630 | if (result.length() == NTLN.NumCols()) |
---|
[11bf82] | 3631 | { |
---|
[49660c] | 3632 | #endif |
---|
[11bf82] | 3633 | delete [] factorsFoundIndex; |
---|
| 3634 | delete [] A; |
---|
| 3635 | delete [] bounds; |
---|
[3d0075] | 3636 | F= 1; |
---|
[11bf82] | 3637 | return result; |
---|
| 3638 | } |
---|
| 3639 | delete [] factorsFoundIndex; |
---|
| 3640 | } |
---|
| 3641 | else if (l == precision) |
---|
| 3642 | { |
---|
| 3643 | CanonicalForm bufF= F; |
---|
[49660c] | 3644 | #ifdef HAVE_FLINT |
---|
| 3645 | int * zeroOne= extractZeroOneVecs (FLINTN); |
---|
[2537fa0] | 3646 | CFList result= reconstruction (bufF,factors,zeroOne,precision,FLINTN, eval); |
---|
[49660c] | 3647 | nmod_mat_clear (FLINTN); |
---|
| 3648 | #else |
---|
[11bf82] | 3649 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
[2537fa0] | 3650 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN, eval); |
---|
[49660c] | 3651 | #endif |
---|
[11bf82] | 3652 | F= bufF; |
---|
| 3653 | delete [] zeroOne; |
---|
| 3654 | delete [] A; |
---|
| 3655 | delete [] bounds; |
---|
| 3656 | return result; |
---|
| 3657 | } |
---|
| 3658 | } |
---|
| 3659 | oldL2= l; |
---|
| 3660 | l += stepSize; |
---|
| 3661 | stepSize *= 2; |
---|
| 3662 | if (l > precision) |
---|
| 3663 | { |
---|
| 3664 | if (!hitBound) |
---|
| 3665 | { |
---|
| 3666 | l= precision; |
---|
| 3667 | hitBound= true; |
---|
| 3668 | } |
---|
| 3669 | else |
---|
| 3670 | break; |
---|
| 3671 | } |
---|
| 3672 | } |
---|
[49660c] | 3673 | #ifdef HAVE_FLINT |
---|
| 3674 | nmod_mat_clear (FLINTN); |
---|
| 3675 | #endif |
---|
[11bf82] | 3676 | delete [] bounds; |
---|
| 3677 | delete [] A; |
---|
| 3678 | return CFList(); |
---|
| 3679 | } |
---|
[03c742] | 3680 | #endif |
---|
[11bf82] | 3681 | |
---|
[03c742] | 3682 | #ifdef HAVE_NTL // mat_zz_pE |
---|
[11bf82] | 3683 | CFList |
---|
| 3684 | increasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
[0349c20] | 3685 | int oldNumCols, int oldL, const Variable&, |
---|
[2537fa0] | 3686 | int precision, const CanonicalForm& eval |
---|
[11bf82] | 3687 | ) |
---|
| 3688 | { |
---|
| 3689 | int d; |
---|
[542864] | 3690 | bool isIrreducible= false; |
---|
[2537fa0] | 3691 | Variable y= F.mvar(); |
---|
[542864] | 3692 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
| 3693 | if (isIrreducible) |
---|
| 3694 | { |
---|
| 3695 | delete [] bounds; |
---|
| 3696 | CanonicalForm G= F; |
---|
| 3697 | F= 1; |
---|
[2537fa0] | 3698 | return CFList (G (y-eval,y)); |
---|
[542864] | 3699 | } |
---|
[11bf82] | 3700 | CFArray * A= new CFArray [factors.length()]; |
---|
| 3701 | CFArray bufQ= CFArray (factors.length()); |
---|
| 3702 | mat_zz_pE NTLN; |
---|
| 3703 | ident (NTLN, factors.length()); |
---|
| 3704 | int minBound= bounds[0]; |
---|
| 3705 | for (int i= 1; i < d; i++) |
---|
| 3706 | { |
---|
| 3707 | if (bounds[i] != 0) |
---|
| 3708 | minBound= tmin (minBound, bounds[i]); |
---|
| 3709 | } |
---|
| 3710 | int l= tmax (2*(minBound + 1), oldL); |
---|
| 3711 | int oldL2= l/2; |
---|
| 3712 | int stepSize= 2; |
---|
| 3713 | bool useOldQs= false; |
---|
| 3714 | bool hitBound= false; |
---|
[38ffb7] | 3715 | CFListIterator j; |
---|
| 3716 | CFMatrix C; |
---|
| 3717 | mat_zz_pE* NTLC, NTLK; |
---|
| 3718 | CFArray buf; |
---|
[5335ba] | 3719 | CanonicalForm truncF; |
---|
[11bf82] | 3720 | while (l <= precision) |
---|
| 3721 | { |
---|
[38ffb7] | 3722 | j= factors; |
---|
[5335ba] | 3723 | truncF= mod (F, power (y,l)); |
---|
[11bf82] | 3724 | if (useOldQs) |
---|
| 3725 | { |
---|
| 3726 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 3727 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
[11bf82] | 3728 | bufQ[i] |
---|
| 3729 | ); |
---|
| 3730 | } |
---|
| 3731 | else |
---|
| 3732 | { |
---|
| 3733 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 3734 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 3735 | } |
---|
| 3736 | useOldQs= true; |
---|
| 3737 | for (int i= 0; i < d; i++) |
---|
| 3738 | { |
---|
| 3739 | if (bounds [i] + 1 <= l/2) |
---|
| 3740 | { |
---|
| 3741 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 3742 | C= CFMatrix (l - k, factors.length()); |
---|
[11bf82] | 3743 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 3744 | { |
---|
| 3745 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 3746 | { |
---|
[11bf82] | 3747 | buf= getCoeffs (A[ii] [i], k); |
---|
[9ebec2] | 3748 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 3749 | } |
---|
[11bf82] | 3750 | } |
---|
[38ffb7] | 3751 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
| 3752 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 3753 | transpose (NTLK, NTLK); |
---|
| 3754 | kernel (NTLK, NTLK); |
---|
| 3755 | transpose (NTLK, NTLK); |
---|
| 3756 | NTLN *= NTLK; |
---|
[ffd883] | 3757 | delete NTLC; |
---|
[11bf82] | 3758 | if (NTLN.NumCols() == 1) |
---|
| 3759 | { |
---|
| 3760 | delete [] A; |
---|
| 3761 | delete [] bounds; |
---|
[542864] | 3762 | CanonicalForm G= F; |
---|
| 3763 | F= 1; |
---|
[2537fa0] | 3764 | return CFList (G (y-eval,y)); |
---|
[11bf82] | 3765 | } |
---|
| 3766 | } |
---|
| 3767 | } |
---|
| 3768 | |
---|
| 3769 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
| 3770 | { |
---|
| 3771 | if (isReduced (NTLN)) |
---|
| 3772 | { |
---|
| 3773 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 3774 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 3775 | factorsFoundIndex[i]= 0; |
---|
| 3776 | int factorsFound2= 0; |
---|
| 3777 | CFList result; |
---|
| 3778 | CanonicalForm bufF= F; |
---|
| 3779 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
[2537fa0] | 3780 | factorsFoundIndex, NTLN, eval, false); |
---|
[11bf82] | 3781 | if (result.length() == NTLN.NumCols()) |
---|
| 3782 | { |
---|
| 3783 | delete [] factorsFoundIndex; |
---|
| 3784 | delete [] A; |
---|
| 3785 | delete [] bounds; |
---|
[3d0075] | 3786 | F= 1; |
---|
[11bf82] | 3787 | return result; |
---|
| 3788 | } |
---|
| 3789 | delete [] factorsFoundIndex; |
---|
| 3790 | } |
---|
| 3791 | else if (l == precision) |
---|
| 3792 | { |
---|
| 3793 | CanonicalForm bufF= F; |
---|
| 3794 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
[2537fa0] | 3795 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN, eval); |
---|
[11bf82] | 3796 | F= bufF; |
---|
| 3797 | delete [] zeroOne; |
---|
| 3798 | delete [] A; |
---|
| 3799 | delete [] bounds; |
---|
| 3800 | return result; |
---|
| 3801 | } |
---|
| 3802 | } |
---|
| 3803 | oldL2= l; |
---|
| 3804 | l += stepSize; |
---|
| 3805 | stepSize *= 2; |
---|
| 3806 | if (l > precision) |
---|
| 3807 | { |
---|
| 3808 | if (!hitBound) |
---|
| 3809 | { |
---|
| 3810 | l= precision; |
---|
| 3811 | hitBound= true; |
---|
| 3812 | } |
---|
| 3813 | else |
---|
| 3814 | break; |
---|
| 3815 | } |
---|
| 3816 | } |
---|
| 3817 | delete [] bounds; |
---|
| 3818 | delete [] A; |
---|
| 3819 | return CFList(); |
---|
| 3820 | } |
---|
[03c742] | 3821 | #endif |
---|
[11bf82] | 3822 | |
---|
[03c742] | 3823 | #ifdef HAVE_NTL // logarithmicDerivative |
---|
[11bf82] | 3824 | //over field extension |
---|
| 3825 | CFList |
---|
| 3826 | extIncreasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
| 3827 | int oldNumCols, int oldL, const CanonicalForm& evaluation, |
---|
| 3828 | const ExtensionInfo& info, CFList& source, CFList& dest, |
---|
| 3829 | int precision |
---|
| 3830 | ) |
---|
| 3831 | { |
---|
| 3832 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
| 3833 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
| 3834 | Variable alpha= info.getAlpha(); |
---|
| 3835 | int d; |
---|
[542864] | 3836 | bool isIrreducible= false; |
---|
| 3837 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
| 3838 | if (isIrreducible) |
---|
| 3839 | { |
---|
| 3840 | delete [] bounds; |
---|
[c49e6f] | 3841 | Variable y= Variable (2); |
---|
| 3842 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 3843 | CFList source, dest; |
---|
| 3844 | tmp= mapDown (tmp, info, source, dest); |
---|
[542864] | 3845 | F= 1; |
---|
[c49e6f] | 3846 | return CFList (tmp); |
---|
[542864] | 3847 | } |
---|
[11bf82] | 3848 | |
---|
| 3849 | CFArray * A= new CFArray [factors.length()]; |
---|
| 3850 | CFArray bufQ= CFArray (factors.length()); |
---|
[7c4341] | 3851 | #ifdef HAVE_FLINT |
---|
| 3852 | nmod_mat_t FLINTN; |
---|
| 3853 | nmod_mat_init (FLINTN,factors.length(),factors.length(), getCharacteristic()); |
---|
| 3854 | for (long i=factors.length()-1; i >= 0; i--) |
---|
| 3855 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
| 3856 | #else |
---|
[bffe62d] | 3857 | if (fac_NTL_char != getCharacteristic()) |
---|
| 3858 | { |
---|
| 3859 | fac_NTL_char= getCharacteristic(); |
---|
| 3860 | zz_p::init (getCharacteristic()); |
---|
| 3861 | } |
---|
[11bf82] | 3862 | mat_zz_p NTLN; |
---|
| 3863 | ident (NTLN, factors.length()); |
---|
[7c4341] | 3864 | #endif |
---|
[11bf82] | 3865 | int minBound= bounds[0]; |
---|
| 3866 | for (int i= 1; i < d; i++) |
---|
| 3867 | { |
---|
| 3868 | if (bounds[i] != 0) |
---|
| 3869 | minBound= tmin (minBound, bounds[i]); |
---|
| 3870 | } |
---|
| 3871 | int l= tmax (oldL, 2*((minBound+1)/degMipo+1)); |
---|
| 3872 | int oldL2= l/2; |
---|
| 3873 | int stepSize= 2; |
---|
| 3874 | bool useOldQs= false; |
---|
| 3875 | bool hitBound= false; |
---|
| 3876 | Variable gamma= info.getBeta(); |
---|
| 3877 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
| 3878 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
[38ffb7] | 3879 | CFListIterator j; |
---|
| 3880 | Variable y= F.mvar(); |
---|
[5335ba] | 3881 | CanonicalForm powX, imBasis, truncF; |
---|
[38ffb7] | 3882 | CFMatrix Mat, C; |
---|
| 3883 | CFIterator iter; |
---|
[7c4341] | 3884 | #ifdef HAVE_FLINT |
---|
| 3885 | long rank; |
---|
| 3886 | nmod_mat_t FLINTMat, FLINTMatInv, FLINTC, FLINTK, null; |
---|
| 3887 | #else |
---|
[38ffb7] | 3888 | mat_zz_p* NTLMat,*NTLC, NTLK; |
---|
[7c4341] | 3889 | #endif |
---|
[38ffb7] | 3890 | CFArray buf; |
---|
[11bf82] | 3891 | while (l <= precision) |
---|
| 3892 | { |
---|
[38ffb7] | 3893 | j= factors; |
---|
[11bf82] | 3894 | if (GF) |
---|
| 3895 | setCharacteristic (getCharacteristic()); |
---|
[38ffb7] | 3896 | powX= power (y-gamma, l); |
---|
| 3897 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
[11bf82] | 3898 | for (int i= 0; i < l*degMipo; i++) |
---|
| 3899 | { |
---|
[38ffb7] | 3900 | imBasis= mod (power (y, i), powX); |
---|
[11bf82] | 3901 | imBasis= imBasis (power (y, degMipo), y); |
---|
| 3902 | imBasis= imBasis (y, gamma); |
---|
[38ffb7] | 3903 | iter= imBasis; |
---|
[11bf82] | 3904 | for (; iter.hasTerms(); iter++) |
---|
| 3905 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
| 3906 | } |
---|
| 3907 | |
---|
[7c4341] | 3908 | #ifdef HAVE_FLINT |
---|
| 3909 | convertFacCFMatrix2nmod_mat_t (FLINTMat, Mat); |
---|
| 3910 | nmod_mat_init (FLINTMatInv, nmod_mat_nrows (FLINTMat), |
---|
| 3911 | nmod_mat_nrows (FLINTMat), getCharacteristic()); |
---|
| 3912 | nmod_mat_inv (FLINTMatInv, FLINTMat); |
---|
| 3913 | #else |
---|
[38ffb7] | 3914 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
[11bf82] | 3915 | *NTLMat= inv (*NTLMat); |
---|
[7c4341] | 3916 | #endif |
---|
| 3917 | |
---|
[11bf82] | 3918 | if (GF) |
---|
| 3919 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 3920 | |
---|
[5335ba] | 3921 | truncF= mod (F, power (y, l)); |
---|
[11bf82] | 3922 | if (useOldQs) |
---|
| 3923 | { |
---|
| 3924 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 3925 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
[11bf82] | 3926 | bufQ[i] |
---|
| 3927 | ); |
---|
| 3928 | } |
---|
| 3929 | else |
---|
| 3930 | { |
---|
| 3931 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 3932 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 3933 | } |
---|
| 3934 | useOldQs= true; |
---|
| 3935 | for (int i= 0; i < d; i++) |
---|
| 3936 | { |
---|
| 3937 | if (bounds [i] + 1 <= (l/2)*degMipo) |
---|
| 3938 | { |
---|
| 3939 | int k= tmin (bounds [i] + 1, (l/2)*degMipo); |
---|
[38ffb7] | 3940 | C= CFMatrix (l*degMipo - k, factors.length()); |
---|
[11bf82] | 3941 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 3942 | { |
---|
| 3943 | if (A[ii].size() - 1 >= i) |
---|
| 3944 | { |
---|
| 3945 | if (GF) |
---|
| 3946 | { |
---|
| 3947 | A[ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 3948 | setCharacteristic (getCharacteristic()); |
---|
| 3949 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
| 3950 | if (alpha != gamma) |
---|
| 3951 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 3952 | gamma, source, dest |
---|
| 3953 | ); |
---|
[7c4341] | 3954 | #ifdef HAVE_FLINT |
---|
| 3955 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, FLINTMatInv); |
---|
| 3956 | #else |
---|
[11bf82] | 3957 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
[7c4341] | 3958 | #endif |
---|
[11bf82] | 3959 | } |
---|
| 3960 | else |
---|
| 3961 | { |
---|
| 3962 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 3963 | if (alpha != gamma) |
---|
| 3964 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 3965 | gamma, source, dest |
---|
| 3966 | ); |
---|
[7c4341] | 3967 | #ifdef HAVE_FLINT |
---|
| 3968 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, FLINTMatInv); |
---|
| 3969 | #else |
---|
[11bf82] | 3970 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
[7c4341] | 3971 | #endif |
---|
[11bf82] | 3972 | } |
---|
[9ebec2] | 3973 | writeInMatrix (C, buf, ii + 1, 0); |
---|
[11bf82] | 3974 | } |
---|
| 3975 | if (GF) |
---|
| 3976 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 3977 | } |
---|
| 3978 | |
---|
| 3979 | if (GF) |
---|
| 3980 | setCharacteristic(getCharacteristic()); |
---|
| 3981 | |
---|
[7c4341] | 3982 | #ifdef HAVE_FLINT |
---|
| 3983 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
| 3984 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
| 3985 | getCharacteristic()); |
---|
| 3986 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
| 3987 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
| 3988 | getCharacteristic()); |
---|
| 3989 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
| 3990 | nmod_mat_clear (FLINTK); |
---|
| 3991 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
| 3992 | nmod_mat_clear (FLINTC); |
---|
| 3993 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
| 3994 | nmod_mat_clear (FLINTN); |
---|
| 3995 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
| 3996 | getCharacteristic()); |
---|
| 3997 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
| 3998 | |
---|
| 3999 | nmod_mat_clear (FLINTC); |
---|
| 4000 | nmod_mat_window_clear (FLINTK); |
---|
| 4001 | nmod_mat_clear (null); |
---|
| 4002 | #else |
---|
[38ffb7] | 4003 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 4004 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 4005 | transpose (NTLK, NTLK); |
---|
| 4006 | kernel (NTLK, NTLK); |
---|
| 4007 | transpose (NTLK, NTLK); |
---|
| 4008 | NTLN *= NTLK; |
---|
[ffd883] | 4009 | delete NTLC; |
---|
[7c4341] | 4010 | #endif |
---|
[11bf82] | 4011 | |
---|
| 4012 | if (GF) |
---|
| 4013 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 4014 | |
---|
[7c4341] | 4015 | #ifdef HAVE_FLINT |
---|
| 4016 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
| 4017 | { |
---|
| 4018 | nmod_mat_clear (FLINTMat); |
---|
| 4019 | nmod_mat_clear (FLINTMatInv); |
---|
| 4020 | nmod_mat_clear (FLINTN); |
---|
| 4021 | #else |
---|
[11bf82] | 4022 | if (NTLN.NumCols() == 1) |
---|
| 4023 | { |
---|
[7c4341] | 4024 | delete NTLMat; |
---|
| 4025 | #endif |
---|
[11bf82] | 4026 | Variable y= Variable (2); |
---|
| 4027 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 4028 | CFList source, dest; |
---|
| 4029 | tmp= mapDown (tmp, info, source, dest); |
---|
| 4030 | delete [] A; |
---|
| 4031 | delete [] bounds; |
---|
[542864] | 4032 | F= 1; |
---|
[11bf82] | 4033 | return CFList (tmp); |
---|
| 4034 | } |
---|
| 4035 | } |
---|
| 4036 | } |
---|
| 4037 | |
---|
[7c4341] | 4038 | #ifdef HAVE_FLINT |
---|
| 4039 | nmod_mat_clear (FLINTMat); |
---|
| 4040 | nmod_mat_clear (FLINTMatInv); |
---|
| 4041 | #else |
---|
[ffd883] | 4042 | delete NTLMat; |
---|
[7c4341] | 4043 | #endif |
---|
[ffd883] | 4044 | |
---|
[7c4341] | 4045 | #ifdef HAVE_FLINT |
---|
| 4046 | if (nmod_mat_ncols (FLINTN) < oldNumCols - factorsFound) |
---|
| 4047 | { |
---|
| 4048 | if (isReduced (FLINTN)) |
---|
| 4049 | { |
---|
| 4050 | int * factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
| 4051 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
| 4052 | #else |
---|
[11bf82] | 4053 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
| 4054 | { |
---|
| 4055 | if (isReduced (NTLN)) |
---|
| 4056 | { |
---|
[38ffb7] | 4057 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 4058 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
[7c4341] | 4059 | #endif |
---|
[38ffb7] | 4060 | factorsFoundIndex[i]= 0; |
---|
| 4061 | int factorsFound2= 0; |
---|
| 4062 | CFList result; |
---|
| 4063 | CanonicalForm bufF= F; |
---|
[7c4341] | 4064 | #ifdef HAVE_FLINT |
---|
| 4065 | extReconstructionTry (result, bufF, factors,degree (F)+1, factorsFound2, |
---|
| 4066 | factorsFoundIndex, FLINTN, false, info, evaluation |
---|
| 4067 | ); |
---|
| 4068 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
| 4069 | { |
---|
| 4070 | nmod_mat_clear (FLINTN); |
---|
| 4071 | #else |
---|
[38ffb7] | 4072 | extReconstructionTry (result, bufF, factors,degree (F)+1, factorsFound2, |
---|
| 4073 | factorsFoundIndex, NTLN, false, info, evaluation |
---|
| 4074 | ); |
---|
| 4075 | if (result.length() == NTLN.NumCols()) |
---|
| 4076 | { |
---|
[7c4341] | 4077 | #endif |
---|
[38ffb7] | 4078 | delete [] factorsFoundIndex; |
---|
| 4079 | delete [] A; |
---|
| 4080 | delete [] bounds; |
---|
[3d0075] | 4081 | F= 1; |
---|
[38ffb7] | 4082 | return result; |
---|
| 4083 | } |
---|
[11bf82] | 4084 | delete [] factorsFoundIndex; |
---|
| 4085 | } |
---|
| 4086 | else if (l == precision) |
---|
| 4087 | { |
---|
| 4088 | CanonicalForm bufF= F; |
---|
[7c4341] | 4089 | #ifdef HAVE_FLINT |
---|
| 4090 | int * zeroOne= extractZeroOneVecs (FLINTN); |
---|
| 4091 | CFList result= extReconstruction (bufF, factors, zeroOne, precision, |
---|
| 4092 | FLINTN, info, evaluation |
---|
| 4093 | ); |
---|
| 4094 | nmod_mat_clear (FLINTN); |
---|
| 4095 | #else |
---|
[11bf82] | 4096 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
| 4097 | CFList result= extReconstruction (bufF, factors, zeroOne, precision, |
---|
| 4098 | NTLN, info, evaluation |
---|
| 4099 | ); |
---|
[7c4341] | 4100 | #endif |
---|
[11bf82] | 4101 | F= bufF; |
---|
| 4102 | delete [] zeroOne; |
---|
| 4103 | delete [] A; |
---|
| 4104 | delete [] bounds; |
---|
| 4105 | return result; |
---|
| 4106 | } |
---|
| 4107 | } |
---|
| 4108 | oldL2= l; |
---|
| 4109 | l += stepSize; |
---|
| 4110 | stepSize *= 2; |
---|
| 4111 | if (l > precision) |
---|
| 4112 | { |
---|
| 4113 | if (!hitBound) |
---|
| 4114 | { |
---|
| 4115 | hitBound= true; |
---|
| 4116 | l= precision; |
---|
| 4117 | } |
---|
| 4118 | else |
---|
| 4119 | break; |
---|
| 4120 | } |
---|
| 4121 | } |
---|
[7c4341] | 4122 | |
---|
| 4123 | #ifdef HAVE_FLINT |
---|
| 4124 | nmod_mat_clear (FLINTN); |
---|
| 4125 | #endif |
---|
[11bf82] | 4126 | delete [] bounds; |
---|
| 4127 | delete [] A; |
---|
| 4128 | return CFList(); |
---|
| 4129 | } |
---|
[03c742] | 4130 | #endif |
---|
[11bf82] | 4131 | |
---|
[03c742] | 4132 | #ifdef HAVE_NTL // mat_zz_pE |
---|
[11bf82] | 4133 | CFList |
---|
| 4134 | increasePrecision2 (const CanonicalForm& F, CFList& factors, |
---|
| 4135 | const Variable& alpha, int precision) |
---|
| 4136 | { |
---|
| 4137 | int d; |
---|
[542864] | 4138 | bool isIrreducible= false; |
---|
| 4139 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
| 4140 | if (isIrreducible) |
---|
| 4141 | { |
---|
| 4142 | delete [] bounds; |
---|
| 4143 | return CFList (F); |
---|
| 4144 | } |
---|
[11bf82] | 4145 | CFArray * A= new CFArray [factors.length()]; |
---|
| 4146 | CFArray bufQ= CFArray (factors.length()); |
---|
[bffe62d] | 4147 | if (fac_NTL_char != getCharacteristic()) |
---|
| 4148 | { |
---|
| 4149 | fac_NTL_char= getCharacteristic(); |
---|
| 4150 | zz_p::init (getCharacteristic()); |
---|
| 4151 | } |
---|
[11bf82] | 4152 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 4153 | zz_pE::init (NTLMipo); |
---|
| 4154 | mat_zz_pE NTLN; |
---|
| 4155 | ident (NTLN, factors.length()); |
---|
| 4156 | int minBound= bounds[0]; |
---|
| 4157 | for (int i= 1; i < d; i++) |
---|
| 4158 | { |
---|
| 4159 | if (bounds[i] != 0) |
---|
| 4160 | minBound= tmin (minBound, bounds[i]); |
---|
| 4161 | } |
---|
| 4162 | int l= tmin (2*(minBound + 1), precision); |
---|
| 4163 | int oldL= l/2; |
---|
| 4164 | int stepSize= 2; |
---|
| 4165 | bool useOldQs= false; |
---|
| 4166 | bool hitBound= false; |
---|
[38ffb7] | 4167 | CFListIterator j; |
---|
| 4168 | CFMatrix C; |
---|
| 4169 | CFArray buf; |
---|
| 4170 | mat_zz_pE* NTLC, NTLK; |
---|
[5335ba] | 4171 | Variable y= F.mvar(); |
---|
| 4172 | CanonicalForm truncF; |
---|
[11bf82] | 4173 | while (l <= precision) |
---|
| 4174 | { |
---|
[38ffb7] | 4175 | j= factors; |
---|
[5335ba] | 4176 | truncF= mod (F, power (y, l)); |
---|
[11bf82] | 4177 | if (useOldQs) |
---|
| 4178 | { |
---|
| 4179 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 4180 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], bufQ[i]); |
---|
[11bf82] | 4181 | } |
---|
| 4182 | else |
---|
| 4183 | { |
---|
| 4184 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 4185 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 4186 | } |
---|
| 4187 | useOldQs= true; |
---|
| 4188 | for (int i= 0; i < d; i++) |
---|
| 4189 | { |
---|
| 4190 | if (bounds [i] + 1 <= l/2) |
---|
| 4191 | { |
---|
| 4192 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 4193 | C= CFMatrix (l - k, factors.length()); |
---|
[11bf82] | 4194 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 4195 | { |
---|
| 4196 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 4197 | { |
---|
[11bf82] | 4198 | buf= getCoeffs (A[ii] [i], k); |
---|
[9ebec2] | 4199 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 4200 | } |
---|
[11bf82] | 4201 | } |
---|
[38ffb7] | 4202 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
| 4203 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 4204 | transpose (NTLK, NTLK); |
---|
| 4205 | kernel (NTLK, NTLK); |
---|
| 4206 | transpose (NTLK, NTLK); |
---|
| 4207 | NTLN *= NTLK; |
---|
[ffd883] | 4208 | delete NTLC; |
---|
| 4209 | |
---|
[11bf82] | 4210 | if (NTLN.NumCols() == 1) |
---|
| 4211 | { |
---|
| 4212 | delete [] A; |
---|
| 4213 | delete [] bounds; |
---|
| 4214 | return CFList (F); |
---|
| 4215 | } |
---|
| 4216 | } |
---|
| 4217 | } |
---|
| 4218 | |
---|
| 4219 | if (isReduced (NTLN) || l == precision) |
---|
| 4220 | { |
---|
| 4221 | CanonicalForm bufF= F; |
---|
| 4222 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
| 4223 | CFList bufFactors= factors; |
---|
| 4224 | CFList result= monicReconstruction (bufF, factors, zeroOne, precision, |
---|
| 4225 | NTLN |
---|
| 4226 | ); |
---|
| 4227 | if (result.length() != NTLN.NumCols() && l != precision) |
---|
| 4228 | factors= bufFactors; |
---|
| 4229 | if (result.length() == NTLN.NumCols()) |
---|
| 4230 | { |
---|
| 4231 | delete [] zeroOne; |
---|
| 4232 | delete [] A; |
---|
| 4233 | delete [] bounds; |
---|
| 4234 | return result; |
---|
| 4235 | } |
---|
| 4236 | if (l == precision) |
---|
| 4237 | { |
---|
| 4238 | delete [] zeroOne; |
---|
| 4239 | delete [] A; |
---|
| 4240 | delete [] bounds; |
---|
| 4241 | return Union (result, factors); |
---|
| 4242 | } |
---|
[72d624] | 4243 | delete [] zeroOne; |
---|
[11bf82] | 4244 | } |
---|
| 4245 | oldL= l; |
---|
| 4246 | l += stepSize; |
---|
| 4247 | stepSize *= 2; |
---|
| 4248 | if (l > precision) |
---|
| 4249 | { |
---|
| 4250 | if (!hitBound) |
---|
| 4251 | { |
---|
| 4252 | l= precision; |
---|
| 4253 | hitBound= true; |
---|
| 4254 | } |
---|
| 4255 | else |
---|
| 4256 | break; |
---|
| 4257 | } |
---|
| 4258 | } |
---|
| 4259 | delete [] bounds; |
---|
| 4260 | delete [] A; |
---|
| 4261 | return CFList(); |
---|
| 4262 | } |
---|
[03c742] | 4263 | #endif |
---|
[11bf82] | 4264 | |
---|
[03c742] | 4265 | #ifdef HAVE_NTL // logarithmicDerivative |
---|
[11bf82] | 4266 | CFList |
---|
| 4267 | increasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
| 4268 | int oldNumCols, int oldL, const Variable& alpha, |
---|
[2537fa0] | 4269 | int precision, const CanonicalForm& eval |
---|
[11bf82] | 4270 | ) |
---|
| 4271 | { |
---|
| 4272 | int d; |
---|
[542864] | 4273 | bool isIrreducible= false; |
---|
[2537fa0] | 4274 | Variable y= F.mvar(); |
---|
[542864] | 4275 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
| 4276 | if (isIrreducible) |
---|
| 4277 | { |
---|
| 4278 | delete [] bounds; |
---|
| 4279 | CanonicalForm G= F; |
---|
| 4280 | F= 1; |
---|
[2537fa0] | 4281 | return CFList (G (y-eval,y)); |
---|
[542864] | 4282 | } |
---|
[11bf82] | 4283 | int extensionDeg= degree (getMipo (alpha)); |
---|
| 4284 | CFArray * A= new CFArray [factors.length()]; |
---|
| 4285 | CFArray bufQ= CFArray (factors.length()); |
---|
[49660c] | 4286 | #ifdef HAVE_FLINT |
---|
| 4287 | nmod_mat_t FLINTN; |
---|
| 4288 | nmod_mat_init (FLINTN,factors.length(),factors.length(), getCharacteristic()); |
---|
| 4289 | for (long i=factors.length()-1; i >= 0; i--) |
---|
| 4290 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
| 4291 | #else |
---|
[11bf82] | 4292 | mat_zz_p NTLN; |
---|
| 4293 | ident (NTLN, factors.length()); |
---|
[49660c] | 4294 | #endif |
---|
[11bf82] | 4295 | int minBound= bounds[0]; |
---|
| 4296 | for (int i= 1; i < d; i++) |
---|
| 4297 | { |
---|
| 4298 | if (bounds[i] != 0) |
---|
| 4299 | minBound= tmin (minBound, bounds[i]); |
---|
| 4300 | } |
---|
| 4301 | int l= tmax (2*(minBound + 1), oldL); |
---|
| 4302 | int oldL2= l/2; |
---|
| 4303 | int stepSize= 2; |
---|
| 4304 | bool useOldQs= false; |
---|
| 4305 | bool hitBound= false; |
---|
[38ffb7] | 4306 | CFListIterator j; |
---|
| 4307 | CFMatrix C; |
---|
[49660c] | 4308 | #ifdef HAVE_FLINT |
---|
| 4309 | long rank; |
---|
| 4310 | nmod_mat_t FLINTC, FLINTK, null; |
---|
| 4311 | #else |
---|
[38ffb7] | 4312 | mat_zz_p* NTLC, NTLK; |
---|
[49660c] | 4313 | #endif |
---|
[38ffb7] | 4314 | CFArray buf; |
---|
[5335ba] | 4315 | CanonicalForm truncF; |
---|
[11bf82] | 4316 | while (l <= precision) |
---|
| 4317 | { |
---|
[38ffb7] | 4318 | j= factors; |
---|
[5335ba] | 4319 | truncF= mod (F, power (y, l)); |
---|
[11bf82] | 4320 | if (useOldQs) |
---|
| 4321 | { |
---|
| 4322 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 4323 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
[11bf82] | 4324 | bufQ[i] |
---|
| 4325 | ); |
---|
| 4326 | } |
---|
| 4327 | else |
---|
| 4328 | { |
---|
| 4329 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 4330 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 4331 | } |
---|
| 4332 | useOldQs= true; |
---|
| 4333 | for (int i= 0; i < d; i++) |
---|
| 4334 | { |
---|
| 4335 | if (bounds [i] + 1 <= l/2) |
---|
| 4336 | { |
---|
| 4337 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 4338 | C= CFMatrix ((l - k)*extensionDeg, factors.length()); |
---|
[11bf82] | 4339 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 4340 | { |
---|
| 4341 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 4342 | { |
---|
[11bf82] | 4343 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
[9ebec2] | 4344 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 4345 | } |
---|
[11bf82] | 4346 | } |
---|
[49660c] | 4347 | #ifdef HAVE_FLINT |
---|
| 4348 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
| 4349 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
| 4350 | getCharacteristic()); |
---|
| 4351 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
| 4352 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
| 4353 | getCharacteristic()); |
---|
| 4354 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
| 4355 | nmod_mat_clear (FLINTK); |
---|
| 4356 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
| 4357 | nmod_mat_clear (FLINTC); |
---|
| 4358 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
| 4359 | nmod_mat_clear (FLINTN); |
---|
| 4360 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
| 4361 | getCharacteristic()); |
---|
| 4362 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
| 4363 | |
---|
| 4364 | nmod_mat_clear (FLINTC); |
---|
| 4365 | nmod_mat_window_clear (FLINTK); |
---|
| 4366 | nmod_mat_clear (null); |
---|
| 4367 | #else |
---|
[38ffb7] | 4368 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 4369 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 4370 | transpose (NTLK, NTLK); |
---|
| 4371 | kernel (NTLK, NTLK); |
---|
| 4372 | transpose (NTLK, NTLK); |
---|
| 4373 | NTLN *= NTLK; |
---|
[ffd883] | 4374 | delete NTLC; |
---|
[49660c] | 4375 | #endif |
---|
| 4376 | #ifdef HAVE_FLINT |
---|
| 4377 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
| 4378 | { |
---|
| 4379 | nmod_mat_clear (FLINTN); |
---|
| 4380 | #else |
---|
[11bf82] | 4381 | if (NTLN.NumCols() == 1) |
---|
| 4382 | { |
---|
[49660c] | 4383 | #endif |
---|
[11bf82] | 4384 | delete [] A; |
---|
| 4385 | delete [] bounds; |
---|
[542864] | 4386 | CanonicalForm G= F; |
---|
| 4387 | F= 1; |
---|
[2537fa0] | 4388 | return CFList (G (y-eval,y)); |
---|
[11bf82] | 4389 | } |
---|
| 4390 | } |
---|
| 4391 | } |
---|
| 4392 | |
---|
[49660c] | 4393 | #ifdef HAVE_FLINT |
---|
| 4394 | if (nmod_mat_ncols (FLINTN) < oldNumCols - factorsFound) |
---|
| 4395 | { |
---|
| 4396 | if (isReduced (FLINTN)) |
---|
| 4397 | { |
---|
| 4398 | int * factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
| 4399 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
| 4400 | #else |
---|
[11bf82] | 4401 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
| 4402 | { |
---|
| 4403 | if (isReduced (NTLN)) |
---|
| 4404 | { |
---|
| 4405 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 4406 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
[49660c] | 4407 | #endif |
---|
[11bf82] | 4408 | factorsFoundIndex[i]= 0; |
---|
| 4409 | int factorsFound2= 0; |
---|
| 4410 | CFList result; |
---|
| 4411 | CanonicalForm bufF= F; |
---|
[49660c] | 4412 | #ifdef HAVE_FLINT |
---|
| 4413 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
[2537fa0] | 4414 | factorsFoundIndex, FLINTN, eval, false |
---|
[49660c] | 4415 | ); |
---|
| 4416 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
| 4417 | { |
---|
| 4418 | nmod_mat_clear (FLINTN); |
---|
| 4419 | #else |
---|
[11bf82] | 4420 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
[2537fa0] | 4421 | factorsFoundIndex, NTLN, eval, false |
---|
[11bf82] | 4422 | ); |
---|
| 4423 | if (result.length() == NTLN.NumCols()) |
---|
| 4424 | { |
---|
[49660c] | 4425 | #endif |
---|
[11bf82] | 4426 | delete [] factorsFoundIndex; |
---|
| 4427 | delete [] A; |
---|
| 4428 | delete [] bounds; |
---|
[3d0075] | 4429 | F= 1; |
---|
[11bf82] | 4430 | return result; |
---|
| 4431 | } |
---|
| 4432 | delete [] factorsFoundIndex; |
---|
| 4433 | } |
---|
| 4434 | else if (l == precision) |
---|
| 4435 | { |
---|
| 4436 | CanonicalForm bufF= F; |
---|
[49660c] | 4437 | #ifdef HAVE_FLINT |
---|
| 4438 | int * zeroOne= extractZeroOneVecs (FLINTN); |
---|
[2537fa0] | 4439 | CFList result= reconstruction (bufF,factors,zeroOne,precision,FLINTN, eval); |
---|
[49660c] | 4440 | nmod_mat_clear (FLINTN); |
---|
| 4441 | #else |
---|
[11bf82] | 4442 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
[2537fa0] | 4443 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN, eval); |
---|
[49660c] | 4444 | #endif |
---|
[11bf82] | 4445 | F= bufF; |
---|
| 4446 | delete [] zeroOne; |
---|
| 4447 | delete [] A; |
---|
| 4448 | delete [] bounds; |
---|
| 4449 | return result; |
---|
| 4450 | } |
---|
| 4451 | } |
---|
| 4452 | oldL2= l; |
---|
| 4453 | l += stepSize; |
---|
| 4454 | stepSize *= 2; |
---|
| 4455 | if (l > precision) |
---|
| 4456 | { |
---|
| 4457 | if (!hitBound) |
---|
| 4458 | { |
---|
| 4459 | hitBound= true; |
---|
| 4460 | l= precision; |
---|
| 4461 | } |
---|
| 4462 | else |
---|
| 4463 | break; |
---|
| 4464 | } |
---|
| 4465 | } |
---|
[49660c] | 4466 | #ifdef HAVE_FLINT |
---|
| 4467 | nmod_mat_clear (FLINTN); |
---|
| 4468 | #endif |
---|
[11bf82] | 4469 | delete [] bounds; |
---|
| 4470 | delete [] A; |
---|
| 4471 | return CFList(); |
---|
| 4472 | } |
---|
[03c742] | 4473 | #endif |
---|
[11bf82] | 4474 | |
---|
[03c742] | 4475 | #ifdef HAVE_NTL // logarithmicDerivative |
---|
[49660c] | 4476 | #ifdef HAVE_FLINT |
---|
| 4477 | CFList |
---|
| 4478 | increasePrecision (CanonicalForm& F, CFList& factors, int oldL, int |
---|
[2537fa0] | 4479 | l, int d, int* bounds, CFArray& bufQ, nmod_mat_t FLINTN, |
---|
| 4480 | const CanonicalForm& eval |
---|
[49660c] | 4481 | ) |
---|
| 4482 | #else |
---|
[11bf82] | 4483 | CFList |
---|
| 4484 | increasePrecision (CanonicalForm& F, CFList& factors, int oldL, int |
---|
[2537fa0] | 4485 | l, int d, int* bounds, CFArray& bufQ, mat_zz_p& NTLN, |
---|
| 4486 | const CanonicalForm& eval |
---|
[11bf82] | 4487 | ) |
---|
[49660c] | 4488 | #endif |
---|
[11bf82] | 4489 | { |
---|
| 4490 | CFList result= CFList(); |
---|
| 4491 | CFArray * A= new CFArray [factors.length()]; |
---|
| 4492 | int oldL2= oldL/2; |
---|
| 4493 | bool hitBound= false; |
---|
[49660c] | 4494 | #ifdef HAVE_FLINT |
---|
| 4495 | if (nmod_mat_nrows (FLINTN) != factors.length()) //refined factors |
---|
| 4496 | { |
---|
| 4497 | nmod_mat_clear (FLINTN); |
---|
| 4498 | nmod_mat_init(FLINTN,factors.length(),factors.length(),getCharacteristic()); |
---|
| 4499 | for (long i=factors.length()-1; i >= 0; i--) |
---|
| 4500 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
| 4501 | bufQ= CFArray (factors.length()); |
---|
| 4502 | } |
---|
| 4503 | #else |
---|
[11bf82] | 4504 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 4505 | { |
---|
| 4506 | ident (NTLN, factors.length()); |
---|
| 4507 | bufQ= CFArray (factors.length()); |
---|
| 4508 | } |
---|
[49660c] | 4509 | #endif |
---|
[11bf82] | 4510 | bool useOldQs= false; |
---|
[38ffb7] | 4511 | CFListIterator j; |
---|
| 4512 | CFMatrix C; |
---|
| 4513 | CFArray buf; |
---|
[49660c] | 4514 | #ifdef HAVE_FLINT |
---|
| 4515 | long rank; |
---|
| 4516 | nmod_mat_t FLINTC, FLINTK, null; |
---|
| 4517 | #else |
---|
[38ffb7] | 4518 | mat_zz_p* NTLC, NTLK; |
---|
[49660c] | 4519 | #endif |
---|
[5335ba] | 4520 | CanonicalForm bufF, truncF; |
---|
[38ffb7] | 4521 | CFList bufUniFactors; |
---|
[5335ba] | 4522 | Variable y= F.mvar(); |
---|
[11bf82] | 4523 | while (oldL <= l) |
---|
| 4524 | { |
---|
[38ffb7] | 4525 | j= factors; |
---|
[5335ba] | 4526 | truncF= mod (F, power (y, oldL)); |
---|
[11bf82] | 4527 | if (useOldQs) |
---|
| 4528 | { |
---|
| 4529 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 4530 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
[11bf82] | 4531 | bufQ[i] |
---|
| 4532 | ); |
---|
| 4533 | } |
---|
| 4534 | else |
---|
| 4535 | { |
---|
| 4536 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 4537 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
[11bf82] | 4538 | } |
---|
| 4539 | useOldQs= true; |
---|
| 4540 | |
---|
| 4541 | for (int i= 0; i < d; i++) |
---|
| 4542 | { |
---|
| 4543 | if (bounds [i] + 1 <= oldL/2) |
---|
| 4544 | { |
---|
| 4545 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
[38ffb7] | 4546 | C= CFMatrix (oldL - k, factors.length()); |
---|
[11bf82] | 4547 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 4548 | { |
---|
| 4549 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 4550 | { |
---|
[11bf82] | 4551 | buf= getCoeffs (A[ii] [i], k); |
---|
[9ebec2] | 4552 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 4553 | } |
---|
[11bf82] | 4554 | } |
---|
[49660c] | 4555 | #ifdef HAVE_FLINT |
---|
| 4556 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
| 4557 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
| 4558 | getCharacteristic()); |
---|
| 4559 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
| 4560 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
| 4561 | getCharacteristic()); |
---|
| 4562 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
| 4563 | nmod_mat_clear (FLINTK); |
---|
| 4564 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
| 4565 | nmod_mat_clear (FLINTC); |
---|
| 4566 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
| 4567 | nmod_mat_clear (FLINTN); |
---|
| 4568 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
| 4569 | getCharacteristic()); |
---|
| 4570 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
| 4571 | |
---|
| 4572 | nmod_mat_clear (FLINTC); |
---|
| 4573 | nmod_mat_window_clear (FLINTK); |
---|
| 4574 | nmod_mat_clear (null); |
---|
| 4575 | #else |
---|
[38ffb7] | 4576 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 4577 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 4578 | transpose (NTLK, NTLK); |
---|
| 4579 | kernel (NTLK, NTLK); |
---|
| 4580 | transpose (NTLK, NTLK); |
---|
| 4581 | NTLN *= NTLK; |
---|
[ffd883] | 4582 | delete NTLC; |
---|
[49660c] | 4583 | #endif |
---|
| 4584 | #ifdef HAVE_FLINT |
---|
| 4585 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
| 4586 | #else |
---|
[11bf82] | 4587 | if (NTLN.NumCols() == 1) |
---|
[49660c] | 4588 | #endif |
---|
[11bf82] | 4589 | { |
---|
| 4590 | delete [] A; |
---|
[2537fa0] | 4591 | return CFList (F (y-eval,y)); |
---|
[11bf82] | 4592 | } |
---|
| 4593 | } |
---|
| 4594 | } |
---|
[49660c] | 4595 | #ifdef HAVE_FLINT |
---|
| 4596 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
| 4597 | #else |
---|
[11bf82] | 4598 | if (NTLN.NumCols() == 1) |
---|
[49660c] | 4599 | #endif |
---|
[11bf82] | 4600 | { |
---|
| 4601 | delete [] A; |
---|
[2537fa0] | 4602 | return CFList (F (y-eval,y)); |
---|
[11bf82] | 4603 | } |
---|
| 4604 | int * zeroOneVecs; |
---|
[49660c] | 4605 | #ifdef HAVE_FLINT |
---|
| 4606 | zeroOneVecs= extractZeroOneVecs (FLINTN); |
---|
| 4607 | #else |
---|
[11bf82] | 4608 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
[49660c] | 4609 | #endif |
---|
[38ffb7] | 4610 | bufF= F; |
---|
| 4611 | bufUniFactors= factors; |
---|
[49660c] | 4612 | #ifdef HAVE_FLINT |
---|
[2537fa0] | 4613 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, FLINTN, eval); |
---|
[49660c] | 4614 | #else |
---|
[2537fa0] | 4615 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN, eval); |
---|
[49660c] | 4616 | #endif |
---|
[11bf82] | 4617 | delete [] zeroOneVecs; |
---|
| 4618 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < oldL && result.length() > 0) |
---|
| 4619 | { |
---|
[c1b9927] | 4620 | F= bufF; |
---|
[11bf82] | 4621 | factors= bufUniFactors; |
---|
| 4622 | delete [] A; |
---|
| 4623 | return result; |
---|
| 4624 | } |
---|
| 4625 | |
---|
| 4626 | result= CFList(); |
---|
| 4627 | oldL2= oldL; |
---|
| 4628 | oldL *= 2; |
---|
| 4629 | if (oldL > l) |
---|
| 4630 | { |
---|
| 4631 | if (!hitBound) |
---|
| 4632 | { |
---|
| 4633 | oldL= l; |
---|
| 4634 | hitBound= true; |
---|
| 4635 | } |
---|
| 4636 | else |
---|
| 4637 | break; |
---|
| 4638 | } |
---|
| 4639 | } |
---|
| 4640 | delete [] A; |
---|
| 4641 | return result; |
---|
| 4642 | } |
---|
[03c742] | 4643 | #endif |
---|
[11bf82] | 4644 | |
---|
[03c742] | 4645 | #ifdef HAVE_NTL // mat_zz_pE |
---|
[11bf82] | 4646 | CFList |
---|
| 4647 | increasePrecision (CanonicalForm& F, CFList& factors, int oldL, int |
---|
[2537fa0] | 4648 | l, int d, int* bounds, CFArray& bufQ, mat_zz_pE& NTLN, |
---|
| 4649 | const CanonicalForm& eval |
---|
[11bf82] | 4650 | ) |
---|
| 4651 | { |
---|
| 4652 | CFList result= CFList(); |
---|
| 4653 | CFArray * A= new CFArray [factors.length()]; |
---|
| 4654 | int oldL2= oldL/2; |
---|
| 4655 | bool hitBound= false; |
---|
| 4656 | bool useOldQs= false; |
---|
| 4657 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 4658 | ident (NTLN, factors.length()); |
---|
[38ffb7] | 4659 | CFListIterator j; |
---|
| 4660 | CFMatrix C; |
---|
| 4661 | CFArray buf; |
---|
| 4662 | mat_zz_pE* NTLC, NTLK; |
---|
[5335ba] | 4663 | CanonicalForm bufF, truncF; |
---|
[38ffb7] | 4664 | CFList bufUniFactors; |
---|
[5335ba] | 4665 | Variable y= F.mvar(); |
---|
[11bf82] | 4666 | while (oldL <= l) |
---|
| 4667 | { |
---|
[38ffb7] | 4668 | j= factors; |
---|
[5335ba] | 4669 | truncF= mod (F, power (y, oldL)); |
---|
[11bf82] | 4670 | if (useOldQs) |
---|
| 4671 | { |
---|
| 4672 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 4673 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
[11bf82] | 4674 | bufQ[i] |
---|
| 4675 | ); |
---|
| 4676 | } |
---|
| 4677 | else |
---|
| 4678 | { |
---|
| 4679 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 4680 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
[11bf82] | 4681 | } |
---|
| 4682 | useOldQs= true; |
---|
| 4683 | |
---|
| 4684 | for (int i= 0; i < d; i++) |
---|
| 4685 | { |
---|
| 4686 | if (bounds [i] + 1 <= oldL/2) |
---|
| 4687 | { |
---|
| 4688 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
[38ffb7] | 4689 | C= CFMatrix (oldL - k, factors.length()); |
---|
[11bf82] | 4690 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 4691 | { |
---|
| 4692 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 4693 | { |
---|
[11bf82] | 4694 | buf= getCoeffs (A[ii] [i], k); |
---|
[9ebec2] | 4695 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 4696 | } |
---|
[11bf82] | 4697 | } |
---|
[38ffb7] | 4698 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
| 4699 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 4700 | transpose (NTLK, NTLK); |
---|
| 4701 | kernel (NTLK, NTLK); |
---|
| 4702 | transpose (NTLK, NTLK); |
---|
| 4703 | NTLN *= NTLK; |
---|
[ffd883] | 4704 | delete NTLC; |
---|
| 4705 | |
---|
[11bf82] | 4706 | if (NTLN.NumCols() == 1) |
---|
| 4707 | { |
---|
| 4708 | delete [] A; |
---|
[2537fa0] | 4709 | return CFList (F (y-eval,y)); |
---|
[11bf82] | 4710 | } |
---|
| 4711 | } |
---|
| 4712 | } |
---|
| 4713 | if (NTLN.NumCols() == 1) |
---|
| 4714 | { |
---|
| 4715 | delete [] A; |
---|
[2537fa0] | 4716 | return CFList (F (y-eval,y)); |
---|
[11bf82] | 4717 | } |
---|
| 4718 | |
---|
| 4719 | int * zeroOneVecs; |
---|
| 4720 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
[38ffb7] | 4721 | bufF= F; |
---|
| 4722 | bufUniFactors= factors; |
---|
[2537fa0] | 4723 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN, eval); |
---|
[11bf82] | 4724 | delete [] zeroOneVecs; |
---|
| 4725 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
| 4726 | { |
---|
[c1b9927] | 4727 | F= bufF; |
---|
[11bf82] | 4728 | factors= bufUniFactors; |
---|
| 4729 | delete [] A; |
---|
| 4730 | return result; |
---|
| 4731 | } |
---|
| 4732 | |
---|
| 4733 | result= CFList(); |
---|
| 4734 | oldL2= oldL; |
---|
| 4735 | oldL *= 2; |
---|
| 4736 | if (oldL > l) |
---|
| 4737 | { |
---|
| 4738 | if (!hitBound) |
---|
| 4739 | { |
---|
| 4740 | oldL= l; |
---|
| 4741 | hitBound= true; |
---|
| 4742 | } |
---|
| 4743 | else |
---|
| 4744 | break; |
---|
| 4745 | } |
---|
| 4746 | } |
---|
| 4747 | delete [] A; |
---|
| 4748 | return result; |
---|
| 4749 | } |
---|
[03c742] | 4750 | #endif |
---|
[11bf82] | 4751 | |
---|
| 4752 | //over field extension |
---|
[03c742] | 4753 | #ifdef HAVE_NTL // logarithmicDerivative |
---|
[7c4341] | 4754 | #ifdef HAVE_FLINT |
---|
| 4755 | CFList |
---|
| 4756 | extIncreasePrecision (CanonicalForm& F, CFList& factors, int oldL, int l, int d, |
---|
| 4757 | int* bounds, CFArray& bufQ, nmod_mat_t FLINTN, const |
---|
| 4758 | CanonicalForm& evaluation, const ExtensionInfo& info, |
---|
| 4759 | CFList& source, CFList& dest |
---|
| 4760 | ) |
---|
| 4761 | #else |
---|
[11bf82] | 4762 | CFList |
---|
| 4763 | extIncreasePrecision (CanonicalForm& F, CFList& factors, int oldL, int l, int d, |
---|
| 4764 | int* bounds, CFArray& bufQ, mat_zz_p& NTLN, const |
---|
| 4765 | CanonicalForm& evaluation, const ExtensionInfo& info, |
---|
| 4766 | CFList& source, CFList& dest |
---|
| 4767 | ) |
---|
[7c4341] | 4768 | #endif |
---|
[11bf82] | 4769 | { |
---|
| 4770 | CFList result= CFList(); |
---|
| 4771 | CFArray * A= new CFArray [factors.length()]; |
---|
| 4772 | int oldL2= oldL/2; //be careful |
---|
| 4773 | bool hitBound= false; |
---|
| 4774 | bool useOldQs= false; |
---|
| 4775 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
| 4776 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
| 4777 | Variable alpha= info.getAlpha(); |
---|
| 4778 | |
---|
| 4779 | Variable gamma= info.getBeta(); |
---|
| 4780 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
| 4781 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
[7c4341] | 4782 | #ifdef HAVE_FLINT |
---|
| 4783 | nmod_mat_clear (FLINTN); |
---|
| 4784 | nmod_mat_init (FLINTN,factors.length(),factors.length(), getCharacteristic()); |
---|
| 4785 | for (long i=factors.length()-1; i >= 0; i--) |
---|
| 4786 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
| 4787 | #else |
---|
[11bf82] | 4788 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 4789 | ident (NTLN, factors.length()); |
---|
[7c4341] | 4790 | #endif |
---|
[38ffb7] | 4791 | Variable y= F.mvar(); |
---|
| 4792 | CFListIterator j; |
---|
[5335ba] | 4793 | CanonicalForm powX, imBasis, bufF, truncF; |
---|
[38ffb7] | 4794 | CFMatrix Mat, C; |
---|
| 4795 | CFIterator iter; |
---|
| 4796 | CFArray buf; |
---|
[7c4341] | 4797 | #ifdef HAVE_FLINT |
---|
| 4798 | long rank; |
---|
| 4799 | nmod_mat_t FLINTMat, FLINTMatInv, FLINTC, FLINTK, null; |
---|
| 4800 | #else |
---|
| 4801 | mat_zz_p* NTLC, NTLK, *NTLMat; |
---|
| 4802 | #endif |
---|
[38ffb7] | 4803 | CFList bufUniFactors; |
---|
[11bf82] | 4804 | while (oldL <= l) |
---|
| 4805 | { |
---|
[38ffb7] | 4806 | j= factors; |
---|
[11bf82] | 4807 | if (GF) |
---|
| 4808 | setCharacteristic (getCharacteristic()); |
---|
[38ffb7] | 4809 | |
---|
| 4810 | powX= power (y-gamma, oldL); |
---|
| 4811 | Mat= CFMatrix (oldL*degMipo, oldL*degMipo); |
---|
[11bf82] | 4812 | for (int i= 0; i < oldL*degMipo; i++) |
---|
| 4813 | { |
---|
[38ffb7] | 4814 | imBasis= mod (power (y, i), powX); |
---|
[11bf82] | 4815 | imBasis= imBasis (power (y, degMipo), y); |
---|
| 4816 | imBasis= imBasis (y, gamma); |
---|
[38ffb7] | 4817 | iter= imBasis; |
---|
[11bf82] | 4818 | for (; iter.hasTerms(); iter++) |
---|
| 4819 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
| 4820 | } |
---|
| 4821 | |
---|
[7c4341] | 4822 | #ifdef HAVE_FLINT |
---|
| 4823 | convertFacCFMatrix2nmod_mat_t (FLINTMat, Mat); |
---|
| 4824 | nmod_mat_init (FLINTMatInv, nmod_mat_nrows (FLINTMat), |
---|
| 4825 | nmod_mat_nrows (FLINTMat), getCharacteristic()); |
---|
| 4826 | nmod_mat_inv (FLINTMatInv, FLINTMat); |
---|
| 4827 | #else |
---|
[38ffb7] | 4828 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
[11bf82] | 4829 | *NTLMat= inv (*NTLMat); |
---|
[7c4341] | 4830 | #endif |
---|
| 4831 | |
---|
[11bf82] | 4832 | if (GF) |
---|
| 4833 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 4834 | |
---|
[5335ba] | 4835 | truncF= mod (F, power (y, oldL)); |
---|
[11bf82] | 4836 | if (useOldQs) |
---|
| 4837 | { |
---|
| 4838 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 4839 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
[11bf82] | 4840 | bufQ[i]); |
---|
| 4841 | } |
---|
| 4842 | else |
---|
| 4843 | { |
---|
| 4844 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 4845 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
[11bf82] | 4846 | } |
---|
| 4847 | useOldQs= true; |
---|
| 4848 | |
---|
| 4849 | for (int i= 0; i < d; i++) |
---|
| 4850 | { |
---|
| 4851 | if (bounds [i] + 1 <= oldL/2) |
---|
| 4852 | { |
---|
| 4853 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
[38ffb7] | 4854 | C= CFMatrix (oldL*degMipo - k, factors.length()); |
---|
[11bf82] | 4855 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 4856 | { |
---|
| 4857 | if (A[ii].size() - 1 >= i) |
---|
| 4858 | { |
---|
| 4859 | if (GF) |
---|
| 4860 | { |
---|
| 4861 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 4862 | setCharacteristic (getCharacteristic()); |
---|
| 4863 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
| 4864 | if (alpha != gamma) |
---|
| 4865 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 4866 | gamma, source, dest |
---|
| 4867 | ); |
---|
[7c4341] | 4868 | #ifdef HAVE_FLINT |
---|
| 4869 | buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, FLINTMatInv); |
---|
| 4870 | #else |
---|
[11bf82] | 4871 | buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, *NTLMat); |
---|
[7c4341] | 4872 | #endif |
---|
[11bf82] | 4873 | } |
---|
| 4874 | else |
---|
| 4875 | { |
---|
| 4876 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 4877 | if (alpha != gamma) |
---|
| 4878 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 4879 | gamma, source, dest |
---|
| 4880 | ); |
---|
[7c4341] | 4881 | #ifdef HAVE_FLINT |
---|
| 4882 | buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, FLINTMatInv); |
---|
| 4883 | #else |
---|
[11bf82] | 4884 | buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, *NTLMat); |
---|
[7c4341] | 4885 | #endif |
---|
[11bf82] | 4886 | } |
---|
[9ebec2] | 4887 | writeInMatrix (C, buf, ii + 1, 0); |
---|
[11bf82] | 4888 | } |
---|
| 4889 | if (GF) |
---|
| 4890 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 4891 | } |
---|
| 4892 | |
---|
| 4893 | if (GF) |
---|
| 4894 | setCharacteristic(getCharacteristic()); |
---|
| 4895 | |
---|
[7c4341] | 4896 | #ifdef HAVE_FLINT |
---|
| 4897 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
| 4898 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
| 4899 | getCharacteristic()); |
---|
| 4900 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
| 4901 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
| 4902 | getCharacteristic()); |
---|
| 4903 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
| 4904 | nmod_mat_clear (FLINTK); |
---|
| 4905 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
| 4906 | nmod_mat_clear (FLINTC); |
---|
| 4907 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
| 4908 | nmod_mat_clear (FLINTN); |
---|
| 4909 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
| 4910 | getCharacteristic()); |
---|
| 4911 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
| 4912 | |
---|
| 4913 | nmod_mat_clear (FLINTC); |
---|
| 4914 | nmod_mat_window_clear (FLINTK); |
---|
| 4915 | nmod_mat_clear (null); |
---|
| 4916 | #else |
---|
[38ffb7] | 4917 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 4918 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 4919 | transpose (NTLK, NTLK); |
---|
| 4920 | kernel (NTLK, NTLK); |
---|
| 4921 | transpose (NTLK, NTLK); |
---|
| 4922 | NTLN *= NTLK; |
---|
[ffd883] | 4923 | delete NTLC; |
---|
[7c4341] | 4924 | #endif |
---|
[11bf82] | 4925 | |
---|
| 4926 | if (GF) |
---|
| 4927 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 4928 | |
---|
[7c4341] | 4929 | #ifdef HAVE_FLINT |
---|
| 4930 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
| 4931 | { |
---|
| 4932 | nmod_mat_clear (FLINTMat); |
---|
| 4933 | nmod_mat_clear (FLINTMatInv); |
---|
| 4934 | #else |
---|
[11bf82] | 4935 | if (NTLN.NumCols() == 1) |
---|
| 4936 | { |
---|
[7c4341] | 4937 | delete NTLMat; |
---|
| 4938 | #endif |
---|
[11bf82] | 4939 | Variable y= Variable (2); |
---|
| 4940 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 4941 | CFList source, dest; |
---|
| 4942 | tmp= mapDown (tmp, info, source, dest); |
---|
| 4943 | delete [] A; |
---|
| 4944 | return CFList (tmp); |
---|
| 4945 | } |
---|
| 4946 | } |
---|
| 4947 | } |
---|
[ffd883] | 4948 | |
---|
[7c4341] | 4949 | #ifdef HAVE_FLINT |
---|
| 4950 | nmod_mat_clear (FLINTMat); |
---|
| 4951 | nmod_mat_clear (FLINTMatInv); |
---|
| 4952 | #else |
---|
[ffd883] | 4953 | delete NTLMat; |
---|
[7c4341] | 4954 | #endif |
---|
[ffd883] | 4955 | |
---|
[7c4341] | 4956 | #ifdef HAVE_FLINT |
---|
| 4957 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
| 4958 | #else |
---|
[11bf82] | 4959 | if (NTLN.NumCols() == 1) |
---|
[7c4341] | 4960 | #endif |
---|
[11bf82] | 4961 | { |
---|
| 4962 | Variable y= Variable (2); |
---|
| 4963 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 4964 | CFList source, dest; |
---|
| 4965 | tmp= mapDown (tmp, info, source, dest); |
---|
| 4966 | delete [] A; |
---|
| 4967 | return CFList (tmp); |
---|
| 4968 | } |
---|
| 4969 | |
---|
| 4970 | int * zeroOneVecs; |
---|
[38ffb7] | 4971 | bufF= F; |
---|
| 4972 | bufUniFactors= factors; |
---|
[7c4341] | 4973 | #ifdef HAVE_FLINT |
---|
| 4974 | zeroOneVecs= extractZeroOneVecs (FLINTN); |
---|
| 4975 | result= extReconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, FLINTN, |
---|
| 4976 | info, evaluation |
---|
| 4977 | ); |
---|
| 4978 | #else |
---|
| 4979 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
[11bf82] | 4980 | result= extReconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN, |
---|
| 4981 | info, evaluation |
---|
| 4982 | ); |
---|
[7c4341] | 4983 | #endif |
---|
[11bf82] | 4984 | delete [] zeroOneVecs; |
---|
| 4985 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
| 4986 | { |
---|
[c1b9927] | 4987 | F= bufF; |
---|
[11bf82] | 4988 | factors= bufUniFactors; |
---|
| 4989 | return result; |
---|
| 4990 | } |
---|
| 4991 | |
---|
| 4992 | result= CFList(); |
---|
| 4993 | oldL2= oldL; |
---|
| 4994 | oldL *= 2; |
---|
| 4995 | if (oldL > l) |
---|
| 4996 | { |
---|
| 4997 | if (!hitBound) |
---|
| 4998 | { |
---|
| 4999 | oldL= l; |
---|
| 5000 | hitBound= true; |
---|
| 5001 | } |
---|
| 5002 | else |
---|
| 5003 | break; |
---|
| 5004 | } |
---|
| 5005 | } |
---|
| 5006 | delete [] A; |
---|
| 5007 | return result; |
---|
| 5008 | } |
---|
[03c742] | 5009 | #endif |
---|
[11bf82] | 5010 | |
---|
[03c742] | 5011 | #ifdef HAVE_NTL // logarithmicDerivative |
---|
[49660c] | 5012 | #ifdef HAVE_FLINT |
---|
| 5013 | CFList |
---|
| 5014 | increasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int oldL, int l, |
---|
| 5015 | int d, int* bounds, CFArray& bufQ, nmod_mat_t FLINTN, |
---|
[2537fa0] | 5016 | const Variable& alpha, const CanonicalForm& eval |
---|
[49660c] | 5017 | ) |
---|
| 5018 | #else |
---|
[11bf82] | 5019 | CFList |
---|
| 5020 | increasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int oldL, int l, |
---|
| 5021 | int d, int* bounds, CFArray& bufQ, mat_zz_p& NTLN, |
---|
[2537fa0] | 5022 | const Variable& alpha, const CanonicalForm& eval |
---|
[11bf82] | 5023 | ) |
---|
[49660c] | 5024 | #endif |
---|
[11bf82] | 5025 | { |
---|
| 5026 | CFList result= CFList(); |
---|
| 5027 | CFArray * A= new CFArray [factors.length()]; |
---|
| 5028 | int extensionDeg= degree (getMipo (alpha)); |
---|
| 5029 | int oldL2= oldL/2; |
---|
| 5030 | bool hitBound= false; |
---|
| 5031 | bool useOldQs= false; |
---|
[49660c] | 5032 | #ifdef HAVE_FLINT |
---|
| 5033 | if (nmod_mat_nrows (FLINTN) != factors.length()) //refined factors |
---|
| 5034 | { |
---|
| 5035 | nmod_mat_clear (FLINTN); |
---|
| 5036 | nmod_mat_init(FLINTN,factors.length(),factors.length(),getCharacteristic()); |
---|
| 5037 | for (long i=factors.length()-1; i >= 0; i--) |
---|
| 5038 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
| 5039 | } |
---|
| 5040 | #else |
---|
[11bf82] | 5041 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 5042 | ident (NTLN, factors.length()); |
---|
[49660c] | 5043 | #endif |
---|
[38ffb7] | 5044 | CFListIterator j; |
---|
| 5045 | CFMatrix C; |
---|
| 5046 | CFArray buf; |
---|
[49660c] | 5047 | #ifdef HAVE_FLINT |
---|
| 5048 | long rank; |
---|
| 5049 | nmod_mat_t FLINTC, FLINTK, null; |
---|
| 5050 | #else |
---|
[38ffb7] | 5051 | mat_zz_p* NTLC, NTLK; |
---|
[49660c] | 5052 | #endif |
---|
[5335ba] | 5053 | CanonicalForm bufF, truncF; |
---|
[38ffb7] | 5054 | CFList bufUniFactors; |
---|
[5335ba] | 5055 | Variable y= F.mvar(); |
---|
[11bf82] | 5056 | while (oldL <= l) |
---|
| 5057 | { |
---|
[38ffb7] | 5058 | j= factors; |
---|
[5335ba] | 5059 | truncF= mod (F, power (y, oldL)); |
---|
[11bf82] | 5060 | if (useOldQs) |
---|
| 5061 | { |
---|
| 5062 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 5063 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
[11bf82] | 5064 | bufQ[i] |
---|
| 5065 | ); |
---|
| 5066 | } |
---|
| 5067 | else |
---|
| 5068 | { |
---|
| 5069 | for (int i= 0; i < factors.length(); i++, j++) |
---|
[5335ba] | 5070 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
[11bf82] | 5071 | } |
---|
| 5072 | useOldQs= true; |
---|
| 5073 | |
---|
| 5074 | for (int i= 0; i < d; i++) |
---|
| 5075 | { |
---|
| 5076 | if (bounds [i] + 1 <= oldL/2) |
---|
| 5077 | { |
---|
| 5078 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
[38ffb7] | 5079 | C= CFMatrix ((oldL - k)*extensionDeg, factors.length()); |
---|
[11bf82] | 5080 | for (int ii= 0; ii < factors.length(); ii++) |
---|
| 5081 | { |
---|
| 5082 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 5083 | { |
---|
[11bf82] | 5084 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
[9ebec2] | 5085 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 5086 | } |
---|
[11bf82] | 5087 | } |
---|
[49660c] | 5088 | #ifdef HAVE_FLINT |
---|
| 5089 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
| 5090 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
| 5091 | getCharacteristic()); |
---|
| 5092 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
| 5093 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
| 5094 | getCharacteristic()); |
---|
| 5095 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
| 5096 | nmod_mat_clear (FLINTK); |
---|
| 5097 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
| 5098 | nmod_mat_clear (FLINTC); |
---|
| 5099 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
| 5100 | nmod_mat_clear (FLINTN); |
---|
| 5101 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
| 5102 | getCharacteristic()); |
---|
| 5103 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
| 5104 | |
---|
| 5105 | nmod_mat_clear (FLINTC); |
---|
| 5106 | nmod_mat_window_clear (FLINTK); |
---|
| 5107 | nmod_mat_clear (null); |
---|
| 5108 | #else |
---|
[38ffb7] | 5109 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 5110 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 5111 | transpose (NTLK, NTLK); |
---|
| 5112 | kernel (NTLK, NTLK); |
---|
| 5113 | transpose (NTLK, NTLK); |
---|
| 5114 | NTLN *= NTLK; |
---|
[ffd883] | 5115 | delete NTLC; |
---|
[49660c] | 5116 | #endif |
---|
| 5117 | #ifdef HAVE_FLINT |
---|
| 5118 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
| 5119 | #else |
---|
[11bf82] | 5120 | if (NTLN.NumCols() == 1) |
---|
[49660c] | 5121 | #endif |
---|
[11bf82] | 5122 | { |
---|
| 5123 | delete [] A; |
---|
[2537fa0] | 5124 | return CFList (F(y-eval,y)); |
---|
[11bf82] | 5125 | } |
---|
| 5126 | } |
---|
| 5127 | } |
---|
| 5128 | |
---|
| 5129 | int * zeroOneVecs; |
---|
[49660c] | 5130 | #ifdef HAVE_FLINT |
---|
| 5131 | zeroOneVecs= extractZeroOneVecs (FLINTN); |
---|
| 5132 | #else |
---|
[11bf82] | 5133 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
[49660c] | 5134 | #endif |
---|
[11bf82] | 5135 | |
---|
[38ffb7] | 5136 | bufF= F; |
---|
| 5137 | bufUniFactors= factors; |
---|
[49660c] | 5138 | #ifdef HAVE_FLINT |
---|
[2537fa0] | 5139 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, FLINTN, eval); |
---|
[49660c] | 5140 | #else |
---|
[2537fa0] | 5141 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN, eval); |
---|
[49660c] | 5142 | #endif |
---|
[11bf82] | 5143 | delete [] zeroOneVecs; |
---|
| 5144 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
| 5145 | { |
---|
[c1b9927] | 5146 | F= bufF; |
---|
[11bf82] | 5147 | factors= bufUniFactors; |
---|
| 5148 | delete [] A; |
---|
| 5149 | return result; |
---|
| 5150 | } |
---|
| 5151 | |
---|
| 5152 | result= CFList(); |
---|
| 5153 | oldL2= oldL; |
---|
| 5154 | oldL *= 2; |
---|
| 5155 | if (oldL > l) |
---|
| 5156 | { |
---|
| 5157 | if (!hitBound) |
---|
| 5158 | { |
---|
| 5159 | oldL= l; |
---|
| 5160 | hitBound= true; |
---|
| 5161 | } |
---|
| 5162 | else |
---|
| 5163 | break; |
---|
| 5164 | } |
---|
| 5165 | } |
---|
| 5166 | delete [] A; |
---|
| 5167 | return result; |
---|
| 5168 | } |
---|
[03c742] | 5169 | #endif |
---|
[11bf82] | 5170 | |
---|
[03c742] | 5171 | #ifdef HAVE_NTL // logarithmicDerivative |
---|
[49660c] | 5172 | #ifdef HAVE_FLINT |
---|
| 5173 | CFList |
---|
| 5174 | furtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& |
---|
| 5175 | factors, int l, int liftBound, int d, int* |
---|
| 5176 | bounds, nmod_mat_t FLINTN, CFList& diophant, |
---|
[2537fa0] | 5177 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
| 5178 | const CanonicalForm& eval |
---|
[49660c] | 5179 | ) |
---|
| 5180 | #else |
---|
[11bf82] | 5181 | CFList |
---|
| 5182 | furtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& |
---|
| 5183 | factors, int l, int liftBound, int d, int* |
---|
| 5184 | bounds, mat_zz_p& NTLN, CFList& diophant, |
---|
[2537fa0] | 5185 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
| 5186 | const CanonicalForm& eval |
---|
[11bf82] | 5187 | ) |
---|
[49660c] | 5188 | #endif |
---|
[11bf82] | 5189 | { |
---|
| 5190 | CanonicalForm LCF= LC (F, 1); |
---|
| 5191 | CFList result; |
---|
| 5192 | bool irreducible= false; |
---|
| 5193 | CFList bufFactors= factors; |
---|
[949793] | 5194 | CFList bufBufFactors; |
---|
[11bf82] | 5195 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
| 5196 | bool useOldQs= false; |
---|
| 5197 | bool hitBound= false; |
---|
| 5198 | int oldL= l; |
---|
| 5199 | int stepSize= 8; //TODO choose better step size? |
---|
| 5200 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
[49660c] | 5201 | #ifdef HAVE_FLINT |
---|
| 5202 | if (nmod_mat_nrows (FLINTN) != factors.length()) //refined factors |
---|
| 5203 | { |
---|
| 5204 | nmod_mat_clear (FLINTN); |
---|
| 5205 | nmod_mat_init(FLINTN,factors.length(),factors.length(),getCharacteristic()); |
---|
| 5206 | for (long i=factors.length()-1; i >= 0; i--) |
---|
| 5207 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
| 5208 | } |
---|
| 5209 | #else |
---|
[11bf82] | 5210 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 5211 | ident (NTLN, factors.length()); |
---|
[49660c] | 5212 | #endif |
---|
[38ffb7] | 5213 | CFListIterator j; |
---|
| 5214 | CFMatrix C; |
---|
| 5215 | CFArray buf; |
---|
[49660c] | 5216 | #ifdef HAVE_FLINT |
---|
| 5217 | long rank; |
---|
| 5218 | nmod_mat_t FLINTC, FLINTK, null; |
---|
| 5219 | #else |
---|
[38ffb7] | 5220 | mat_zz_p* NTLC, NTLK; |
---|
[49660c] | 5221 | #endif |
---|
[5335ba] | 5222 | CanonicalForm bufF, truncF; |
---|
| 5223 | Variable y= F.mvar(); |
---|
[11bf82] | 5224 | while (l <= liftBound) |
---|
| 5225 | { |
---|
| 5226 | bufFactors.insert (LCF); |
---|
| 5227 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
[38ffb7] | 5228 | j= bufFactors; |
---|
[5335ba] | 5229 | truncF= mod (F, power (y, l)); |
---|
[11bf82] | 5230 | if (useOldQs) |
---|
| 5231 | { |
---|
| 5232 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
[5335ba] | 5233 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
| 5234 | bufQ[i]); |
---|
[11bf82] | 5235 | } |
---|
| 5236 | else |
---|
| 5237 | { |
---|
| 5238 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
[5335ba] | 5239 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 5240 | } |
---|
| 5241 | for (int i= 0; i < d; i++) |
---|
| 5242 | { |
---|
| 5243 | if (bounds [i] + 1 <= l/2) |
---|
| 5244 | { |
---|
| 5245 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 5246 | C= CFMatrix (l - k, bufFactors.length()); |
---|
[11bf82] | 5247 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
| 5248 | { |
---|
| 5249 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 5250 | { |
---|
[11bf82] | 5251 | buf= getCoeffs (A[ii] [i], k); |
---|
[9ebec2] | 5252 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 5253 | } |
---|
[11bf82] | 5254 | } |
---|
[49660c] | 5255 | #ifdef HAVE_FLINT |
---|
| 5256 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
| 5257 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
| 5258 | getCharacteristic()); |
---|
| 5259 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
| 5260 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
| 5261 | getCharacteristic()); |
---|
| 5262 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
| 5263 | nmod_mat_clear (FLINTK); |
---|
| 5264 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
| 5265 | nmod_mat_clear (FLINTC); |
---|
| 5266 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
| 5267 | nmod_mat_clear (FLINTN); |
---|
| 5268 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
| 5269 | getCharacteristic()); |
---|
| 5270 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
| 5271 | |
---|
| 5272 | nmod_mat_clear (FLINTC); |
---|
| 5273 | nmod_mat_window_clear (FLINTK); |
---|
| 5274 | nmod_mat_clear (null); |
---|
| 5275 | #else |
---|
[38ffb7] | 5276 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 5277 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 5278 | transpose (NTLK, NTLK); |
---|
| 5279 | kernel (NTLK, NTLK); |
---|
| 5280 | transpose (NTLK, NTLK); |
---|
| 5281 | NTLN *= NTLK; |
---|
[ffd883] | 5282 | delete NTLC; |
---|
[49660c] | 5283 | #endif |
---|
| 5284 | #ifdef HAVE_FLINT |
---|
| 5285 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
| 5286 | #else |
---|
[11bf82] | 5287 | if (NTLN.NumCols() == 1) |
---|
[49660c] | 5288 | #endif |
---|
[11bf82] | 5289 | { |
---|
| 5290 | irreducible= true; |
---|
| 5291 | break; |
---|
| 5292 | } |
---|
| 5293 | } |
---|
| 5294 | } |
---|
| 5295 | |
---|
[49660c] | 5296 | #ifdef HAVE_FLINT |
---|
| 5297 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
| 5298 | #else |
---|
[11bf82] | 5299 | if (NTLN.NumCols() == 1) |
---|
[49660c] | 5300 | #endif |
---|
[11bf82] | 5301 | { |
---|
| 5302 | irreducible= true; |
---|
| 5303 | break; |
---|
| 5304 | } |
---|
| 5305 | |
---|
[49660c] | 5306 | #ifdef HAVE_FLINT |
---|
| 5307 | int * zeroOneVecs= extractZeroOneVecs (FLINTN); |
---|
| 5308 | #else |
---|
[11bf82] | 5309 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
[49660c] | 5310 | #endif |
---|
[38ffb7] | 5311 | bufF= F; |
---|
[949793] | 5312 | bufBufFactors= bufFactors; |
---|
[49660c] | 5313 | #ifdef HAVE_FLINT |
---|
[2537fa0] | 5314 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, FLINTN, eval); |
---|
[49660c] | 5315 | #else |
---|
[2537fa0] | 5316 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN, eval); |
---|
[49660c] | 5317 | #endif |
---|
[11bf82] | 5318 | delete [] zeroOneVecs; |
---|
| 5319 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
| 5320 | { |
---|
| 5321 | F= bufF; |
---|
| 5322 | factors= bufFactors; |
---|
| 5323 | delete [] A; |
---|
| 5324 | return result; |
---|
| 5325 | } |
---|
[949793] | 5326 | else |
---|
| 5327 | { |
---|
| 5328 | bufF= F; |
---|
| 5329 | bufFactors= bufBufFactors; |
---|
| 5330 | } |
---|
[11bf82] | 5331 | |
---|
[49660c] | 5332 | #ifdef HAVE_FLINT |
---|
| 5333 | if (isReduced (FLINTN)) |
---|
| 5334 | #else |
---|
[11bf82] | 5335 | if (isReduced (NTLN)) |
---|
[49660c] | 5336 | #endif |
---|
[11bf82] | 5337 | { |
---|
| 5338 | int factorsFound= 0; |
---|
[38ffb7] | 5339 | bufF= F; |
---|
[49660c] | 5340 | #ifdef HAVE_FLINT |
---|
| 5341 | int* factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
| 5342 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
| 5343 | #else |
---|
[11bf82] | 5344 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 5345 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
[49660c] | 5346 | #endif |
---|
[11bf82] | 5347 | factorsFoundIndex[i]= 0; |
---|
[49660c] | 5348 | #ifdef HAVE_FLINT |
---|
| 5349 | if (l < liftBound) |
---|
| 5350 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
[2537fa0] | 5351 | factorsFoundIndex, FLINTN, eval, false |
---|
[49660c] | 5352 | ); |
---|
| 5353 | else |
---|
| 5354 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
| 5355 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
[2537fa0] | 5356 | FLINTN, eval, false |
---|
[49660c] | 5357 | ); |
---|
| 5358 | |
---|
| 5359 | if (nmod_mat_ncols (FLINTN) == result.length()) |
---|
| 5360 | #else |
---|
[11bf82] | 5361 | if (l < liftBound) |
---|
| 5362 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
[2537fa0] | 5363 | factorsFoundIndex, NTLN, eval, false |
---|
[11bf82] | 5364 | ); |
---|
| 5365 | else |
---|
| 5366 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
| 5367 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
[2537fa0] | 5368 | NTLN, eval, false |
---|
[11bf82] | 5369 | ); |
---|
| 5370 | |
---|
| 5371 | if (NTLN.NumCols() == result.length()) |
---|
[49660c] | 5372 | #endif |
---|
[11bf82] | 5373 | { |
---|
| 5374 | delete [] A; |
---|
| 5375 | delete [] factorsFoundIndex; |
---|
| 5376 | return result; |
---|
| 5377 | } |
---|
| 5378 | delete [] factorsFoundIndex; |
---|
| 5379 | } |
---|
| 5380 | result= CFList(); |
---|
| 5381 | oldL= l; |
---|
| 5382 | stepSize *= 2; |
---|
| 5383 | l += stepSize; |
---|
| 5384 | if (l > liftBound) |
---|
| 5385 | { |
---|
| 5386 | if (!hitBound) |
---|
| 5387 | { |
---|
| 5388 | l= liftBound; |
---|
| 5389 | hitBound= true; |
---|
| 5390 | } |
---|
| 5391 | else |
---|
| 5392 | break; |
---|
| 5393 | } |
---|
| 5394 | } |
---|
| 5395 | if (irreducible) |
---|
| 5396 | { |
---|
| 5397 | delete [] A; |
---|
[2537fa0] | 5398 | return CFList (F (y-eval,y)); |
---|
[11bf82] | 5399 | } |
---|
| 5400 | delete [] A; |
---|
| 5401 | factors= bufFactors; |
---|
| 5402 | return CFList(); |
---|
| 5403 | } |
---|
[03c742] | 5404 | #endif |
---|
[11bf82] | 5405 | |
---|
| 5406 | //Fq |
---|
[03c742] | 5407 | #ifdef HAVE_NTL |
---|
[11bf82] | 5408 | CFList |
---|
| 5409 | furtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& |
---|
| 5410 | factors, int l, int liftBound, int d, int* |
---|
| 5411 | bounds, mat_zz_pE& NTLN, CFList& diophant, |
---|
[2537fa0] | 5412 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
| 5413 | const CanonicalForm& eval |
---|
[11bf82] | 5414 | ) |
---|
| 5415 | { |
---|
| 5416 | CanonicalForm LCF= LC (F, 1); |
---|
| 5417 | CFList result; |
---|
| 5418 | bool irreducible= false; |
---|
| 5419 | CFList bufFactors= factors; |
---|
[949793] | 5420 | CFList bufBufFactors; |
---|
[11bf82] | 5421 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
| 5422 | bool useOldQs= false; |
---|
| 5423 | bool hitBound= false; |
---|
| 5424 | int oldL= l; |
---|
| 5425 | int stepSize= 8; //TODO choose better step size? |
---|
| 5426 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
| 5427 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 5428 | ident (NTLN, factors.length()); |
---|
[38ffb7] | 5429 | CFListIterator j; |
---|
| 5430 | CFArray buf; |
---|
| 5431 | mat_zz_pE* NTLC, NTLK; |
---|
[5335ba] | 5432 | CanonicalForm bufF, truncF; |
---|
| 5433 | Variable y= F.mvar(); |
---|
[11bf82] | 5434 | while (l <= liftBound) |
---|
| 5435 | { |
---|
| 5436 | bufFactors.insert (LCF); |
---|
| 5437 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
[38ffb7] | 5438 | j= bufFactors; |
---|
[5335ba] | 5439 | truncF= mod (F, power (y, l)); |
---|
[11bf82] | 5440 | if (useOldQs) |
---|
| 5441 | { |
---|
| 5442 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
[5335ba] | 5443 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
| 5444 | bufQ[i]); |
---|
[11bf82] | 5445 | } |
---|
| 5446 | else |
---|
| 5447 | { |
---|
| 5448 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
[5335ba] | 5449 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 5450 | } |
---|
| 5451 | for (int i= 0; i < d; i++) |
---|
| 5452 | { |
---|
| 5453 | if (bounds [i] + 1 <= l/2) |
---|
| 5454 | { |
---|
| 5455 | int k= tmin (bounds [i] + 1, l/2); |
---|
| 5456 | CFMatrix C= CFMatrix (l - k, bufFactors.length()); |
---|
| 5457 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
| 5458 | { |
---|
| 5459 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 5460 | { |
---|
[11bf82] | 5461 | buf= getCoeffs (A[ii] [i], k); |
---|
[9ebec2] | 5462 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 5463 | } |
---|
[11bf82] | 5464 | } |
---|
[38ffb7] | 5465 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
| 5466 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 5467 | transpose (NTLK, NTLK); |
---|
| 5468 | kernel (NTLK, NTLK); |
---|
| 5469 | transpose (NTLK, NTLK); |
---|
| 5470 | NTLN *= NTLK; |
---|
[ffd883] | 5471 | delete NTLC; |
---|
[11bf82] | 5472 | if (NTLN.NumCols() == 1) |
---|
| 5473 | { |
---|
| 5474 | irreducible= true; |
---|
| 5475 | break; |
---|
| 5476 | } |
---|
| 5477 | } |
---|
| 5478 | } |
---|
| 5479 | if (NTLN.NumCols() == 1) |
---|
| 5480 | { |
---|
| 5481 | irreducible= true; |
---|
| 5482 | break; |
---|
| 5483 | } |
---|
| 5484 | |
---|
[38ffb7] | 5485 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
| 5486 | bufF= F; |
---|
[949793] | 5487 | bufBufFactors= bufFactors; |
---|
[2537fa0] | 5488 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN, eval); |
---|
[38ffb7] | 5489 | delete [] zeroOneVecs; |
---|
| 5490 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
| 5491 | { |
---|
| 5492 | F= bufF; |
---|
| 5493 | factors= bufFactors; |
---|
| 5494 | delete [] A; |
---|
| 5495 | return result; |
---|
| 5496 | } |
---|
[949793] | 5497 | else |
---|
| 5498 | { |
---|
| 5499 | bufF= F; |
---|
| 5500 | bufFactors= bufBufFactors; |
---|
| 5501 | } |
---|
[11bf82] | 5502 | |
---|
| 5503 | if (isReduced (NTLN)) |
---|
| 5504 | { |
---|
| 5505 | int factorsFound= 0; |
---|
[38ffb7] | 5506 | bufF= F; |
---|
[11bf82] | 5507 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 5508 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 5509 | factorsFoundIndex[i]= 0; |
---|
| 5510 | if (l < liftBound) |
---|
| 5511 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
[2537fa0] | 5512 | factorsFoundIndex, NTLN, eval, false |
---|
[11bf82] | 5513 | ); |
---|
| 5514 | else |
---|
| 5515 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
| 5516 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
[2537fa0] | 5517 | NTLN, eval, false |
---|
[11bf82] | 5518 | ); |
---|
| 5519 | if (NTLN.NumCols() == result.length()) |
---|
| 5520 | { |
---|
| 5521 | delete [] A; |
---|
| 5522 | delete [] factorsFoundIndex; |
---|
| 5523 | return result; |
---|
| 5524 | } |
---|
| 5525 | delete [] factorsFoundIndex; |
---|
| 5526 | } |
---|
| 5527 | result= CFList(); |
---|
| 5528 | oldL= l; |
---|
| 5529 | stepSize *= 2; |
---|
| 5530 | l += stepSize; |
---|
| 5531 | if (l > liftBound) |
---|
| 5532 | { |
---|
| 5533 | if (!hitBound) |
---|
| 5534 | { |
---|
| 5535 | l= liftBound; |
---|
| 5536 | hitBound= true; |
---|
| 5537 | } |
---|
| 5538 | else |
---|
| 5539 | break; |
---|
| 5540 | } |
---|
| 5541 | } |
---|
| 5542 | if (irreducible) |
---|
| 5543 | { |
---|
| 5544 | delete [] A; |
---|
[2537fa0] | 5545 | return CFList (F (y-eval,y)); |
---|
[11bf82] | 5546 | } |
---|
| 5547 | delete [] A; |
---|
| 5548 | factors= bufFactors; |
---|
| 5549 | return CFList(); |
---|
| 5550 | } |
---|
[03c742] | 5551 | #endif |
---|
[11bf82] | 5552 | |
---|
| 5553 | //over field extension |
---|
[03c742] | 5554 | #ifdef HAVE_NTL // logarithmicDerivative |
---|
[7c4341] | 5555 | #ifdef HAVE_FLINT |
---|
| 5556 | CFList |
---|
| 5557 | extFurtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& factors, int l, |
---|
| 5558 | int liftBound, int d, int* bounds, |
---|
| 5559 | nmod_mat_t FLINTN, CFList& diophant, |
---|
| 5560 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
| 5561 | const CanonicalForm& evaluation, const |
---|
| 5562 | ExtensionInfo& info, CFList& source, |
---|
| 5563 | CFList& dest |
---|
| 5564 | ) |
---|
| 5565 | #else |
---|
[11bf82] | 5566 | CFList |
---|
| 5567 | extFurtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& factors, int l, |
---|
| 5568 | int liftBound, int d, int* bounds, |
---|
| 5569 | mat_zz_p& NTLN, CFList& diophant, |
---|
| 5570 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
| 5571 | const CanonicalForm& evaluation, const |
---|
| 5572 | ExtensionInfo& info, CFList& source, |
---|
| 5573 | CFList& dest |
---|
| 5574 | ) |
---|
[7c4341] | 5575 | #endif |
---|
[11bf82] | 5576 | { |
---|
| 5577 | CanonicalForm LCF= LC (F, 1); |
---|
| 5578 | CFList result; |
---|
| 5579 | bool irreducible= false; |
---|
| 5580 | CFList bufFactors= factors; |
---|
[949793] | 5581 | CFList bufBufFactors; |
---|
[11bf82] | 5582 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
| 5583 | bool useOldQs= false; |
---|
| 5584 | bool hitBound= false; |
---|
| 5585 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
| 5586 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
| 5587 | Variable alpha= info.getAlpha(); |
---|
| 5588 | int oldL= l; //be careful |
---|
| 5589 | int stepSize= 8; |
---|
| 5590 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l),2); |
---|
| 5591 | Variable gamma= info.getBeta(); |
---|
| 5592 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
| 5593 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
[7c4341] | 5594 | #ifdef HAVE_FLINT |
---|
| 5595 | nmod_mat_clear (FLINTN); |
---|
| 5596 | nmod_mat_init (FLINTN,factors.length(),factors.length(), getCharacteristic()); |
---|
| 5597 | for (long i=factors.length()-1; i >= 0; i--) |
---|
| 5598 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
| 5599 | #else |
---|
[11bf82] | 5600 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 5601 | ident (NTLN, factors.length()); |
---|
[7c4341] | 5602 | #endif |
---|
[38ffb7] | 5603 | Variable y= F.mvar(); |
---|
[5335ba] | 5604 | CanonicalForm powX, imBasis, bufF, truncF; |
---|
[38ffb7] | 5605 | CFMatrix Mat, C; |
---|
| 5606 | CFIterator iter; |
---|
[7c4341] | 5607 | #ifdef HAVE_FLINT |
---|
| 5608 | long rank; |
---|
| 5609 | nmod_mat_t FLINTMat, FLINTMatInv, FLINTC, FLINTK, null; |
---|
| 5610 | #else |
---|
[38ffb7] | 5611 | mat_zz_p* NTLMat,*NTLC, NTLK; |
---|
[7c4341] | 5612 | #endif |
---|
[38ffb7] | 5613 | CFListIterator j; |
---|
| 5614 | CFArray buf; |
---|
[11bf82] | 5615 | while (l <= liftBound) |
---|
| 5616 | { |
---|
| 5617 | bufFactors.insert (LCF); |
---|
| 5618 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
| 5619 | |
---|
| 5620 | if (GF) |
---|
| 5621 | setCharacteristic (getCharacteristic()); |
---|
| 5622 | |
---|
[38ffb7] | 5623 | powX= power (y-gamma, l); |
---|
| 5624 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
[11bf82] | 5625 | for (int i= 0; i < l*degMipo; i++) |
---|
| 5626 | { |
---|
| 5627 | |
---|
[38ffb7] | 5628 | imBasis= mod (power (y, i), powX); |
---|
[11bf82] | 5629 | imBasis= imBasis (power (y, degMipo), y); |
---|
| 5630 | imBasis= imBasis (y, gamma); |
---|
[38ffb7] | 5631 | iter= imBasis; |
---|
[11bf82] | 5632 | for (; iter.hasTerms(); iter++) |
---|
| 5633 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
| 5634 | } |
---|
| 5635 | |
---|
[7c4341] | 5636 | #ifdef HAVE_FLINT |
---|
| 5637 | convertFacCFMatrix2nmod_mat_t (FLINTMat, Mat); |
---|
| 5638 | nmod_mat_init (FLINTMatInv, nmod_mat_nrows (FLINTMat), |
---|
| 5639 | nmod_mat_nrows (FLINTMat), getCharacteristic()); |
---|
| 5640 | nmod_mat_inv (FLINTMatInv, FLINTMat); |
---|
| 5641 | #else |
---|
[38ffb7] | 5642 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
[11bf82] | 5643 | *NTLMat= inv (*NTLMat); |
---|
[7c4341] | 5644 | #endif |
---|
[11bf82] | 5645 | |
---|
| 5646 | if (GF) |
---|
| 5647 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 5648 | |
---|
[38ffb7] | 5649 | j= bufFactors; |
---|
[5335ba] | 5650 | truncF= mod (F, power (y, l)); |
---|
[11bf82] | 5651 | if (useOldQs) |
---|
| 5652 | { |
---|
| 5653 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
[5335ba] | 5654 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
| 5655 | bufQ[i]); |
---|
[11bf82] | 5656 | } |
---|
| 5657 | else |
---|
| 5658 | { |
---|
| 5659 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
[5335ba] | 5660 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 5661 | } |
---|
| 5662 | for (int i= 0; i < d; i++) |
---|
| 5663 | { |
---|
| 5664 | if (bounds [i] + 1 <= l/2) |
---|
| 5665 | { |
---|
| 5666 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 5667 | C= CFMatrix (l*degMipo - k, bufFactors.length()); |
---|
[11bf82] | 5668 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
| 5669 | { |
---|
| 5670 | if (A[ii].size() - 1 >= i) |
---|
| 5671 | { |
---|
| 5672 | if (GF) |
---|
| 5673 | { |
---|
| 5674 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 5675 | setCharacteristic (getCharacteristic()); |
---|
| 5676 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
| 5677 | if (alpha != gamma) |
---|
| 5678 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 5679 | gamma, source, dest |
---|
| 5680 | ); |
---|
[7c4341] | 5681 | #ifdef HAVE_FLINT |
---|
| 5682 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, FLINTMatInv); |
---|
| 5683 | #else |
---|
[11bf82] | 5684 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
[7c4341] | 5685 | #endif |
---|
[11bf82] | 5686 | } |
---|
| 5687 | else |
---|
| 5688 | { |
---|
| 5689 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
| 5690 | if (alpha != gamma) |
---|
| 5691 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
| 5692 | gamma, source, dest |
---|
| 5693 | ); |
---|
[7c4341] | 5694 | #ifdef HAVE_FLINT |
---|
| 5695 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, FLINTMatInv); |
---|
| 5696 | #else |
---|
[11bf82] | 5697 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
[7c4341] | 5698 | #endif |
---|
[11bf82] | 5699 | } |
---|
[9ebec2] | 5700 | writeInMatrix (C, buf, ii + 1, 0); |
---|
[11bf82] | 5701 | } |
---|
| 5702 | if (GF) |
---|
| 5703 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 5704 | } |
---|
| 5705 | |
---|
| 5706 | if (GF) |
---|
| 5707 | setCharacteristic(getCharacteristic()); |
---|
[7c4341] | 5708 | |
---|
| 5709 | #ifdef HAVE_FLINT |
---|
| 5710 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
| 5711 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
| 5712 | getCharacteristic()); |
---|
| 5713 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
| 5714 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
| 5715 | getCharacteristic()); |
---|
| 5716 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
| 5717 | nmod_mat_clear (FLINTK); |
---|
| 5718 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
| 5719 | nmod_mat_clear (FLINTC); |
---|
| 5720 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
| 5721 | nmod_mat_clear (FLINTN); |
---|
| 5722 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
| 5723 | getCharacteristic()); |
---|
| 5724 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
| 5725 | |
---|
| 5726 | nmod_mat_clear (FLINTC); |
---|
| 5727 | nmod_mat_window_clear (FLINTK); |
---|
| 5728 | nmod_mat_clear (null); |
---|
| 5729 | #else |
---|
[38ffb7] | 5730 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 5731 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 5732 | transpose (NTLK, NTLK); |
---|
| 5733 | kernel (NTLK, NTLK); |
---|
| 5734 | transpose (NTLK, NTLK); |
---|
| 5735 | NTLN *= NTLK; |
---|
[ffd883] | 5736 | delete NTLC; |
---|
[7c4341] | 5737 | #endif |
---|
| 5738 | |
---|
[11bf82] | 5739 | if (GF) |
---|
| 5740 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 5741 | |
---|
[7c4341] | 5742 | #ifdef HAVE_FLINT |
---|
| 5743 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
| 5744 | #else |
---|
[11bf82] | 5745 | if (NTLN.NumCols() == 1) |
---|
[7c4341] | 5746 | #endif |
---|
[11bf82] | 5747 | { |
---|
| 5748 | irreducible= true; |
---|
| 5749 | break; |
---|
| 5750 | } |
---|
| 5751 | } |
---|
| 5752 | } |
---|
[7c4341] | 5753 | |
---|
| 5754 | #ifdef HAVE_FLINT |
---|
| 5755 | nmod_mat_clear (FLINTMat); |
---|
| 5756 | nmod_mat_clear (FLINTMatInv); |
---|
| 5757 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
| 5758 | #else |
---|
[ffd883] | 5759 | delete NTLMat; |
---|
[11bf82] | 5760 | if (NTLN.NumCols() == 1) |
---|
[7c4341] | 5761 | #endif |
---|
[11bf82] | 5762 | { |
---|
| 5763 | irreducible= true; |
---|
| 5764 | break; |
---|
| 5765 | } |
---|
| 5766 | |
---|
[38ffb7] | 5767 | bufF= F; |
---|
[949793] | 5768 | bufBufFactors= bufFactors; |
---|
[7c4341] | 5769 | #ifdef HAVE_FLINT |
---|
| 5770 | int * zeroOneVecs= extractZeroOneVecs (FLINTN); |
---|
| 5771 | result= extReconstruction (bufF, bufFactors, zeroOneVecs, l, FLINTN, info, |
---|
| 5772 | evaluation |
---|
| 5773 | ); |
---|
| 5774 | #else |
---|
| 5775 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
[38ffb7] | 5776 | result= extReconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN, info, |
---|
| 5777 | evaluation |
---|
| 5778 | ); |
---|
[7c4341] | 5779 | #endif |
---|
[38ffb7] | 5780 | delete [] zeroOneVecs; |
---|
| 5781 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
| 5782 | { |
---|
| 5783 | F= bufF; |
---|
| 5784 | factors= bufFactors; |
---|
| 5785 | delete [] A; |
---|
| 5786 | return result; |
---|
| 5787 | } |
---|
[949793] | 5788 | else |
---|
| 5789 | { |
---|
| 5790 | bufF= F; |
---|
| 5791 | bufFactors= bufBufFactors; |
---|
| 5792 | } |
---|
[11bf82] | 5793 | |
---|
[7c4341] | 5794 | #ifdef HAVE_FLINT |
---|
| 5795 | if (isReduced (FLINTN)) |
---|
| 5796 | #else |
---|
[11bf82] | 5797 | if (isReduced (NTLN)) |
---|
[7c4341] | 5798 | #endif |
---|
[11bf82] | 5799 | { |
---|
| 5800 | int factorsFound= 0; |
---|
[38ffb7] | 5801 | bufF= F; |
---|
[7c4341] | 5802 | #ifdef HAVE_FLINT |
---|
| 5803 | int* factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
| 5804 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
| 5805 | #else |
---|
[11bf82] | 5806 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 5807 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
[7c4341] | 5808 | #endif |
---|
[11bf82] | 5809 | factorsFoundIndex[i]= 0; |
---|
[7c4341] | 5810 | #ifdef HAVE_FLINT |
---|
| 5811 | if (l < degree (bufF) + 1 + degree (LCF)) |
---|
| 5812 | extReconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
| 5813 | factorsFoundIndex, FLINTN, false, info, evaluation |
---|
| 5814 | ); |
---|
| 5815 | else |
---|
| 5816 | extReconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
| 5817 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
| 5818 | FLINTN, false, info, evaluation |
---|
| 5819 | ); |
---|
| 5820 | if (nmod_mat_ncols (FLINTN) == result.length()) |
---|
| 5821 | #else |
---|
[11bf82] | 5822 | if (l < degree (bufF) + 1 + degree (LCF)) |
---|
| 5823 | extReconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
| 5824 | factorsFoundIndex, NTLN, false, info, evaluation |
---|
| 5825 | ); |
---|
| 5826 | else |
---|
| 5827 | extReconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
| 5828 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
| 5829 | NTLN, false, info, evaluation |
---|
| 5830 | ); |
---|
| 5831 | if (NTLN.NumCols() == result.length()) |
---|
[7c4341] | 5832 | #endif |
---|
[11bf82] | 5833 | { |
---|
| 5834 | delete [] A; |
---|
| 5835 | delete [] factorsFoundIndex; |
---|
| 5836 | return result; |
---|
| 5837 | } |
---|
| 5838 | delete [] factorsFoundIndex; |
---|
| 5839 | } |
---|
| 5840 | result= CFList(); |
---|
| 5841 | oldL= l; |
---|
| 5842 | stepSize *= 2; |
---|
| 5843 | l += stepSize; |
---|
| 5844 | if (l > liftBound) |
---|
| 5845 | { |
---|
| 5846 | if (!hitBound) |
---|
| 5847 | { |
---|
| 5848 | l= liftBound; |
---|
| 5849 | hitBound= true; |
---|
| 5850 | } |
---|
| 5851 | else |
---|
| 5852 | break; |
---|
| 5853 | } |
---|
| 5854 | } |
---|
| 5855 | if (irreducible) |
---|
| 5856 | { |
---|
| 5857 | delete [] A; |
---|
| 5858 | Variable y= Variable (2); |
---|
| 5859 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 5860 | CFList source, dest; |
---|
| 5861 | tmp= mapDown (tmp, info, source, dest); |
---|
| 5862 | return CFList (tmp); |
---|
| 5863 | } |
---|
| 5864 | delete [] A; |
---|
| 5865 | factors= bufFactors; |
---|
| 5866 | return CFList(); |
---|
| 5867 | } |
---|
[03c742] | 5868 | #endif |
---|
[11bf82] | 5869 | |
---|
[03c742] | 5870 | #ifdef HAVE_NTL // logarithmicDerivative |
---|
[49660c] | 5871 | #ifdef HAVE_FLINT |
---|
| 5872 | CFList |
---|
| 5873 | furtherLiftingAndIncreasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int |
---|
| 5874 | l, int liftBound, int d, int* bounds, |
---|
| 5875 | nmod_mat_t FLINTN, CFList& diophant, |
---|
| 5876 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
[2537fa0] | 5877 | const Variable& alpha, |
---|
| 5878 | const CanonicalForm& eval |
---|
[49660c] | 5879 | ) |
---|
| 5880 | #else |
---|
[11bf82] | 5881 | CFList |
---|
| 5882 | furtherLiftingAndIncreasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int |
---|
| 5883 | l, int liftBound, int d, int* bounds, |
---|
| 5884 | mat_zz_p& NTLN, CFList& diophant, |
---|
| 5885 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
[2537fa0] | 5886 | const Variable& alpha, |
---|
| 5887 | const CanonicalForm& eval |
---|
[11bf82] | 5888 | ) |
---|
[49660c] | 5889 | #endif |
---|
[11bf82] | 5890 | { |
---|
| 5891 | CanonicalForm LCF= LC (F, 1); |
---|
| 5892 | CFList result; |
---|
| 5893 | bool irreducible= false; |
---|
| 5894 | CFList bufFactors= factors; |
---|
[949793] | 5895 | CFList bufBufFactors; |
---|
[11bf82] | 5896 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
| 5897 | bool useOldQs= false; |
---|
| 5898 | int extensionDeg= degree (getMipo (alpha)); |
---|
| 5899 | bool hitBound= false; |
---|
| 5900 | int oldL= l; |
---|
| 5901 | int stepSize= 8; //TODO choose better step size? |
---|
| 5902 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
[49660c] | 5903 | #ifdef HAVE_FLINT |
---|
| 5904 | if (nmod_mat_nrows (FLINTN) != factors.length()) //refined factors |
---|
| 5905 | { |
---|
| 5906 | nmod_mat_clear (FLINTN); |
---|
| 5907 | nmod_mat_init(FLINTN,factors.length(),factors.length(),getCharacteristic()); |
---|
| 5908 | for (long i=factors.length()-1; i >= 0; i--) |
---|
| 5909 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
| 5910 | } |
---|
| 5911 | #else |
---|
[11bf82] | 5912 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
| 5913 | ident (NTLN, factors.length()); |
---|
[49660c] | 5914 | #endif |
---|
[38ffb7] | 5915 | CFListIterator j; |
---|
| 5916 | CFMatrix C; |
---|
[49660c] | 5917 | #ifdef HAVE_FLINT |
---|
| 5918 | long rank; |
---|
| 5919 | nmod_mat_t FLINTC, FLINTK, null; |
---|
| 5920 | #else |
---|
[38ffb7] | 5921 | mat_zz_p* NTLC, NTLK; |
---|
[49660c] | 5922 | #endif |
---|
[5335ba] | 5923 | CanonicalForm bufF, truncF; |
---|
| 5924 | Variable y= F.mvar(); |
---|
[11bf82] | 5925 | while (l <= liftBound) |
---|
| 5926 | { |
---|
| 5927 | bufFactors.insert (LCF); |
---|
| 5928 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
[38ffb7] | 5929 | j= bufFactors; |
---|
[5335ba] | 5930 | truncF= mod (F, power (y, l)); |
---|
[11bf82] | 5931 | if (useOldQs) |
---|
| 5932 | { |
---|
| 5933 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
[5335ba] | 5934 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
| 5935 | bufQ[i]); |
---|
[11bf82] | 5936 | } |
---|
| 5937 | else |
---|
| 5938 | { |
---|
| 5939 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
[5335ba] | 5940 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
[11bf82] | 5941 | } |
---|
| 5942 | for (int i= 0; i < d; i++) |
---|
| 5943 | { |
---|
| 5944 | if (bounds [i] + 1 <= l/2) |
---|
| 5945 | { |
---|
| 5946 | int k= tmin (bounds [i] + 1, l/2); |
---|
[38ffb7] | 5947 | C= CFMatrix ((l - k)*extensionDeg, bufFactors.length()); |
---|
[11bf82] | 5948 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
| 5949 | { |
---|
| 5950 | CFArray buf; |
---|
| 5951 | if (A[ii].size() - 1 >= i) |
---|
[9ebec2] | 5952 | { |
---|
[11bf82] | 5953 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
[9ebec2] | 5954 | writeInMatrix (C, buf, ii + 1, 0); |
---|
| 5955 | } |
---|
[11bf82] | 5956 | } |
---|
[49660c] | 5957 | #ifdef HAVE_FLINT |
---|
| 5958 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
| 5959 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
| 5960 | getCharacteristic()); |
---|
| 5961 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
| 5962 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
| 5963 | getCharacteristic()); |
---|
| 5964 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
| 5965 | nmod_mat_clear (FLINTK); |
---|
| 5966 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
| 5967 | nmod_mat_clear (FLINTC); |
---|
| 5968 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
| 5969 | nmod_mat_clear (FLINTN); |
---|
| 5970 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
| 5971 | getCharacteristic()); |
---|
| 5972 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
| 5973 | |
---|
| 5974 | nmod_mat_clear (FLINTC); |
---|
| 5975 | nmod_mat_window_clear (FLINTK); |
---|
| 5976 | nmod_mat_clear (null); |
---|
| 5977 | #else |
---|
[38ffb7] | 5978 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
| 5979 | NTLK= (*NTLC)*NTLN; |
---|
[11bf82] | 5980 | transpose (NTLK, NTLK); |
---|
| 5981 | kernel (NTLK, NTLK); |
---|
| 5982 | transpose (NTLK, NTLK); |
---|
| 5983 | NTLN *= NTLK; |
---|
[ffd883] | 5984 | delete NTLC; |
---|
[49660c] | 5985 | #endif |
---|
| 5986 | #ifdef HAVE_FLINT |
---|
| 5987 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
| 5988 | #else |
---|
[11bf82] | 5989 | if (NTLN.NumCols() == 1) |
---|
[49660c] | 5990 | #endif |
---|
[11bf82] | 5991 | { |
---|
| 5992 | irreducible= true; |
---|
| 5993 | break; |
---|
| 5994 | } |
---|
| 5995 | } |
---|
| 5996 | } |
---|
[49660c] | 5997 | #ifdef HAVE_FLINT |
---|
| 5998 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
| 5999 | #else |
---|
[11bf82] | 6000 | if (NTLN.NumCols() == 1) |
---|
[49660c] | 6001 | #endif |
---|
[11bf82] | 6002 | { |
---|
| 6003 | irreducible= true; |
---|
| 6004 | break; |
---|
| 6005 | } |
---|
| 6006 | |
---|
[49660c] | 6007 | #ifdef HAVE_FLINT |
---|
| 6008 | int * zeroOneVecs= extractZeroOneVecs (FLINTN); |
---|
| 6009 | #else |
---|
[38ffb7] | 6010 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
[49660c] | 6011 | #endif |
---|
[38ffb7] | 6012 | CanonicalForm bufF= F; |
---|
[949793] | 6013 | bufBufFactors= bufFactors; |
---|
[49660c] | 6014 | #ifdef HAVE_FLINT |
---|
[2537fa0] | 6015 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, FLINTN, eval); |
---|
[49660c] | 6016 | #else |
---|
[2537fa0] | 6017 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN, eval); |
---|
[49660c] | 6018 | #endif |
---|
[38ffb7] | 6019 | delete [] zeroOneVecs; |
---|
| 6020 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
| 6021 | { |
---|
| 6022 | F= bufF; |
---|
| 6023 | factors= bufFactors; |
---|
| 6024 | delete [] A; |
---|
| 6025 | return result; |
---|
| 6026 | } |
---|
[949793] | 6027 | else |
---|
| 6028 | { |
---|
| 6029 | bufF= F; |
---|
| 6030 | bufFactors= bufBufFactors; |
---|
| 6031 | } |
---|
[11bf82] | 6032 | |
---|
[49660c] | 6033 | #ifdef HAVE_FLINT |
---|
| 6034 | if (isReduced (FLINTN)) |
---|
| 6035 | #else |
---|
[11bf82] | 6036 | if (isReduced (NTLN)) |
---|
[49660c] | 6037 | #endif |
---|
[11bf82] | 6038 | { |
---|
| 6039 | int factorsFound= 0; |
---|
[38ffb7] | 6040 | bufF= F; |
---|
[49660c] | 6041 | #ifdef HAVE_FLINT |
---|
| 6042 | int* factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
| 6043 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
| 6044 | #else |
---|
[11bf82] | 6045 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 6046 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
[49660c] | 6047 | #endif |
---|
[11bf82] | 6048 | factorsFoundIndex[i]= 0; |
---|
[49660c] | 6049 | #ifdef HAVE_FLINT |
---|
| 6050 | if (l < degree (bufF) + 1 + degree (LCF)) |
---|
| 6051 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
[2537fa0] | 6052 | factorsFoundIndex, FLINTN, eval, false |
---|
[49660c] | 6053 | ); |
---|
| 6054 | else |
---|
| 6055 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
| 6056 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
[2537fa0] | 6057 | FLINTN, eval, false |
---|
[49660c] | 6058 | ); |
---|
| 6059 | if (nmod_mat_ncols (FLINTN) == result.length()) |
---|
| 6060 | #else |
---|
[11bf82] | 6061 | if (l < degree (bufF) + 1 + degree (LCF)) |
---|
| 6062 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
[2537fa0] | 6063 | factorsFoundIndex, NTLN, eval, false |
---|
[11bf82] | 6064 | ); |
---|
| 6065 | else |
---|
| 6066 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
| 6067 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
[2537fa0] | 6068 | NTLN, eval, false |
---|
[11bf82] | 6069 | ); |
---|
| 6070 | if (NTLN.NumCols() == result.length()) |
---|
[49660c] | 6071 | #endif |
---|
[11bf82] | 6072 | { |
---|
| 6073 | delete [] A; |
---|
| 6074 | delete [] factorsFoundIndex; |
---|
| 6075 | return result; |
---|
| 6076 | } |
---|
| 6077 | delete [] factorsFoundIndex; |
---|
| 6078 | } |
---|
| 6079 | result= CFList(); |
---|
| 6080 | oldL= l; |
---|
| 6081 | stepSize *= 2; |
---|
| 6082 | l += stepSize; |
---|
| 6083 | if (l > liftBound) |
---|
| 6084 | { |
---|
| 6085 | if (!hitBound) |
---|
| 6086 | { |
---|
| 6087 | l= liftBound; |
---|
| 6088 | hitBound= true; |
---|
| 6089 | } |
---|
| 6090 | else |
---|
| 6091 | break; |
---|
| 6092 | } |
---|
| 6093 | } |
---|
| 6094 | if (irreducible) |
---|
| 6095 | { |
---|
| 6096 | delete [] A; |
---|
[2537fa0] | 6097 | return CFList (F (y-eval,y)); |
---|
[11bf82] | 6098 | } |
---|
| 6099 | delete [] A; |
---|
| 6100 | factors= bufFactors; |
---|
| 6101 | return CFList(); |
---|
| 6102 | } |
---|
[03c742] | 6103 | #endif |
---|
[11bf82] | 6104 | |
---|
[87942fd] | 6105 | #ifndef HAVE_FLINT |
---|
[11bf82] | 6106 | void |
---|
| 6107 | refineAndRestartLift (const CanonicalForm& F, const mat_zz_p& NTLN, int |
---|
| 6108 | liftBound, int l, CFList& factors, CFMatrix& M, CFArray& |
---|
| 6109 | Pi, CFList& diophant |
---|
| 6110 | ) |
---|
| 6111 | { |
---|
| 6112 | CFList bufFactors; |
---|
| 6113 | Variable y= Variable (2); |
---|
| 6114 | CanonicalForm LCF= LC (F, 1); |
---|
[38ffb7] | 6115 | CFListIterator iter; |
---|
| 6116 | CanonicalForm buf; |
---|
[11bf82] | 6117 | for (long i= 1; i <= NTLN.NumCols(); i++) |
---|
| 6118 | { |
---|
[38ffb7] | 6119 | iter= factors; |
---|
| 6120 | buf= 1; |
---|
[11bf82] | 6121 | for (long j= 1; j <= NTLN.NumRows(); j++, iter++) |
---|
| 6122 | { |
---|
| 6123 | if (!IsZero (NTLN (j,i))) |
---|
| 6124 | buf= mulNTL (buf, mod (iter.getItem(), y)); |
---|
| 6125 | } |
---|
| 6126 | bufFactors.append (buf); |
---|
| 6127 | } |
---|
| 6128 | factors= bufFactors; |
---|
| 6129 | M= CFMatrix (liftBound, factors.length()); |
---|
| 6130 | Pi= CFArray(); |
---|
| 6131 | diophant= CFList(); |
---|
| 6132 | factors.insert (LCF); |
---|
| 6133 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 6134 | } |
---|
[87942fd] | 6135 | #endif |
---|
[11bf82] | 6136 | |
---|
[49660c] | 6137 | #ifdef HAVE_FLINT |
---|
[03c742] | 6138 | #ifdef HAVE_NTL // henselLift12 |
---|
[49660c] | 6139 | void |
---|
| 6140 | refineAndRestartLift (const CanonicalForm& F, const nmod_mat_t FLINTN, int |
---|
| 6141 | liftBound, int l, CFList& factors, CFMatrix& M, CFArray& |
---|
| 6142 | Pi, CFList& diophant |
---|
| 6143 | ) |
---|
| 6144 | { |
---|
| 6145 | CFList bufFactors; |
---|
| 6146 | Variable y= Variable (2); |
---|
| 6147 | CanonicalForm LCF= LC (F, 1); |
---|
| 6148 | CFListIterator iter; |
---|
| 6149 | CanonicalForm buf; |
---|
| 6150 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
| 6151 | { |
---|
| 6152 | iter= factors; |
---|
| 6153 | buf= 1; |
---|
| 6154 | for (long j= 0; j < nmod_mat_nrows (FLINTN); j++, iter++) |
---|
| 6155 | { |
---|
| 6156 | if (!(nmod_mat_entry (FLINTN,j,i) == 0)) |
---|
| 6157 | buf= mulNTL (buf, mod (iter.getItem(), y)); |
---|
| 6158 | } |
---|
| 6159 | bufFactors.append (buf); |
---|
| 6160 | } |
---|
| 6161 | factors= bufFactors; |
---|
| 6162 | M= CFMatrix (liftBound, factors.length()); |
---|
| 6163 | Pi= CFArray(); |
---|
| 6164 | diophant= CFList(); |
---|
| 6165 | factors.insert (LCF); |
---|
| 6166 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 6167 | } |
---|
| 6168 | #endif |
---|
[03c742] | 6169 | #endif |
---|
[49660c] | 6170 | |
---|
[03c742] | 6171 | #ifdef HAVE_NTL // mat_zz_pE |
---|
[11bf82] | 6172 | void |
---|
| 6173 | refineAndRestartLift (const CanonicalForm& F, const mat_zz_pE& NTLN, int |
---|
| 6174 | liftBound, int l, CFList& factors, CFMatrix& M, CFArray& |
---|
| 6175 | Pi, CFList& diophant |
---|
| 6176 | ) |
---|
| 6177 | { |
---|
| 6178 | CFList bufFactors; |
---|
| 6179 | Variable y= Variable (2); |
---|
| 6180 | CanonicalForm LCF= LC (F, 1); |
---|
[38ffb7] | 6181 | CFListIterator iter; |
---|
| 6182 | CanonicalForm buf; |
---|
[c1b9927] | 6183 | for (long i= 1; i <= NTLN.NumCols(); i++) |
---|
[11bf82] | 6184 | { |
---|
[38ffb7] | 6185 | iter= factors; |
---|
| 6186 | buf= 1; |
---|
[11bf82] | 6187 | for (long j= 1; j <= NTLN.NumRows(); j++, iter++) |
---|
| 6188 | { |
---|
| 6189 | if (!IsZero (NTLN (j,i))) |
---|
| 6190 | buf= mulNTL (buf, mod (iter.getItem(), y)); |
---|
| 6191 | } |
---|
| 6192 | bufFactors.append (buf); |
---|
| 6193 | } |
---|
| 6194 | factors= bufFactors; |
---|
| 6195 | M= CFMatrix (liftBound, factors.length()); |
---|
| 6196 | Pi= CFArray(); |
---|
| 6197 | diophant= CFList(); |
---|
| 6198 | factors.insert (LCF); |
---|
| 6199 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
| 6200 | } |
---|
[03c742] | 6201 | #endif |
---|
[11bf82] | 6202 | |
---|
[49660c] | 6203 | #ifdef HAVE_FLINT |
---|
| 6204 | CFList |
---|
| 6205 | earlyReconstructionAndLifting (const CanonicalForm& F, const nmod_mat_t N, |
---|
| 6206 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
| 6207 | int& factorsFound, bool beenInThres, CFMatrix& M, |
---|
| 6208 | CFArray& Pi, CFList& diophant, bool symmetric, |
---|
| 6209 | const CanonicalForm& evaluation |
---|
| 6210 | ) |
---|
| 6211 | #else |
---|
[11bf82] | 6212 | CFList |
---|
| 6213 | earlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_p& N, |
---|
| 6214 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
| 6215 | int& factorsFound, bool beenInThres, CFMatrix& M, |
---|
[617dbc] | 6216 | CFArray& Pi, CFList& diophant, bool symmetric, |
---|
| 6217 | const CanonicalForm& evaluation |
---|
[11bf82] | 6218 | ) |
---|
[49660c] | 6219 | #endif |
---|
[11bf82] | 6220 | { |
---|
[a36fcb5] | 6221 | int sizeOfLiftPre; |
---|
| 6222 | int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2)); |
---|
| 6223 | |
---|
| 6224 | Variable y= F.mvar(); |
---|
[11bf82] | 6225 | factorsFound= 0; |
---|
| 6226 | CanonicalForm LCF= LC (F, 1); |
---|
| 6227 | CFList result; |
---|
[a36fcb5] | 6228 | int smallFactorDeg= tmin (11, liftPre [sizeOfLiftPre- 1] + 1); |
---|
[49660c] | 6229 | #ifdef HAVE_FLINT |
---|
| 6230 | nmod_mat_t FLINTN; |
---|
| 6231 | nmod_mat_init_set (FLINTN, N); |
---|
| 6232 | int * factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
| 6233 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
| 6234 | #else |
---|
[11bf82] | 6235 | mat_zz_p NTLN= N; |
---|
| 6236 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 6237 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
[49660c] | 6238 | #endif |
---|
[11bf82] | 6239 | factorsFoundIndex [i]= 0; |
---|
| 6240 | |
---|
| 6241 | if (degree (F) + 1 > smallFactorDeg) |
---|
| 6242 | { |
---|
| 6243 | if (l < smallFactorDeg) |
---|
| 6244 | { |
---|
[2d35fe] | 6245 | TIMING_START (fac_fq_lift); |
---|
[11bf82] | 6246 | factors.insert (LCF); |
---|
| 6247 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
[2d35fe] | 6248 | TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction0: "); |
---|
[11bf82] | 6249 | l= smallFactorDeg; |
---|
| 6250 | } |
---|
[49660c] | 6251 | #ifdef HAVE_FLINT |
---|
[2d35fe] | 6252 | TIMING_START (fac_fq_reconstruction); |
---|
[49660c] | 6253 | reconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
[2537fa0] | 6254 | factorsFoundIndex, FLINTN, evaluation, beenInThres |
---|
[49660c] | 6255 | ); |
---|
[2d35fe] | 6256 | TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct0: "); |
---|
[49660c] | 6257 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
| 6258 | { |
---|
| 6259 | nmod_mat_clear (FLINTN); |
---|
| 6260 | #else |
---|
[2d35fe] | 6261 | TIMING_START (fac_fq_reconstruction); |
---|
[11bf82] | 6262 | reconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
[2537fa0] | 6263 | factorsFoundIndex, NTLN, evaluation, beenInThres |
---|
[11bf82] | 6264 | ); |
---|
[2d35fe] | 6265 | TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct0: "); |
---|
[11bf82] | 6266 | if (result.length() == NTLN.NumCols()) |
---|
| 6267 | { |
---|
[49660c] | 6268 | #endif |
---|
[a36fcb5] | 6269 | delete [] liftPre; |
---|
[11bf82] | 6270 | delete [] factorsFoundIndex; |
---|
| 6271 | return result; |
---|
| 6272 | } |
---|
| 6273 | } |
---|
| 6274 | |
---|
[a36fcb5] | 6275 | int i= sizeOfLiftPre - 1; |
---|
| 6276 | int dummy= 1; |
---|
| 6277 | if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
[11bf82] | 6278 | { |
---|
[a36fcb5] | 6279 | while (i > 0) |
---|
| 6280 | { |
---|
| 6281 | if (l < liftPre[i-1] + 1) |
---|
| 6282 | { |
---|
| 6283 | factors.insert (LCF); |
---|
[2d35fe] | 6284 | TIMING_START (fac_fq_lift); |
---|
[a36fcb5] | 6285 | henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M); |
---|
[2d35fe] | 6286 | TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction1: "); |
---|
[a36fcb5] | 6287 | l= liftPre[i-1] + 1; |
---|
| 6288 | } |
---|
| 6289 | else |
---|
| 6290 | { |
---|
| 6291 | i--; |
---|
| 6292 | if (i != 0) |
---|
| 6293 | continue; |
---|
| 6294 | } |
---|
[49660c] | 6295 | #ifdef HAVE_FLINT |
---|
[2d35fe] | 6296 | TIMING_START (fac_fq_reconstruction); |
---|
[49660c] | 6297 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
[2537fa0] | 6298 | factorsFoundIndex, FLINTN, evaluation, beenInThres |
---|
[49660c] | 6299 | ); |
---|
[2d35fe] | 6300 | TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct1: "); |
---|
[49660c] | 6301 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
| 6302 | { |
---|
| 6303 | nmod_mat_clear (FLINTN); |
---|
| 6304 | #else |
---|
[2d35fe] | 6305 | TIMING_START (fac_fq_reconstruction); |
---|
[a36fcb5] | 6306 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
[2537fa0] | 6307 | factorsFoundIndex, NTLN, evaluation, beenInThres |
---|
[a36fcb5] | 6308 | ); |
---|
[2d35fe] | 6309 | TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct1: "); |
---|
[a36fcb5] | 6310 | if (result.length() == NTLN.NumCols()) |
---|
| 6311 | { |
---|
[49660c] | 6312 | #endif |
---|
[a36fcb5] | 6313 | delete [] liftPre; |
---|
| 6314 | delete [] factorsFoundIndex; |
---|
| 6315 | return result; |
---|
| 6316 | } |
---|
| 6317 | i--; |
---|
| 6318 | } |
---|
[11bf82] | 6319 | } |
---|
[a36fcb5] | 6320 | else |
---|
[11bf82] | 6321 | { |
---|
[a36fcb5] | 6322 | i= 1; |
---|
[c49e6f] | 6323 | while (((degree (F,y)/4)*i+1) + 4 <= smallFactorDeg) |
---|
[a36fcb5] | 6324 | i++; |
---|
[617dbc] | 6325 | while (i < 5) |
---|
[a36fcb5] | 6326 | { |
---|
[c49e6f] | 6327 | dummy= tmin (degree (F,y)+1, ((degree (F,y)/4)+1)*i+4); |
---|
[a36fcb5] | 6328 | if (l < dummy) |
---|
| 6329 | { |
---|
| 6330 | factors.insert (LCF); |
---|
[2d35fe] | 6331 | TIMING_START (fac_fq_lift); |
---|
[a36fcb5] | 6332 | henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M); |
---|
[2d35fe] | 6333 | TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction2: "); |
---|
[a36fcb5] | 6334 | l= dummy; |
---|
[617dbc] | 6335 | if (i == 1 && degree (F)%4==0 && symmetric && factors.length() == 2 && |
---|
| 6336 | LC (F,1).inCoeffDomain() && |
---|
| 6337 | (degree (factors.getFirst(), 1) == degree (factors.getLast(),1))) |
---|
| 6338 | { |
---|
| 6339 | Variable x= Variable (1); |
---|
| 6340 | CanonicalForm g, h, gg, hh, multiplier1, multiplier2, check1, check2; |
---|
| 6341 | int m= degree (F)/4+1; |
---|
| 6342 | g= factors.getFirst(); |
---|
| 6343 | h= factors.getLast(); |
---|
| 6344 | g= mod (g, power (y,m)); |
---|
| 6345 | h= mod (h, power (y,m)); |
---|
| 6346 | g= g (y-evaluation, y); |
---|
| 6347 | h= h (y-evaluation, y); |
---|
| 6348 | gg= mod (swapvar (g,x,y),power (x,m)); |
---|
| 6349 | gg= gg (y + evaluation, y); |
---|
| 6350 | multiplier1= factors.getLast()[m-1][0]/gg[m-1][0]; |
---|
| 6351 | gg= div (gg, power (y,m)); |
---|
| 6352 | gg= gg*power (y,m); |
---|
| 6353 | hh= mod (swapvar (h,x,y),power (x,m)); |
---|
| 6354 | hh= hh (y + evaluation, y); |
---|
| 6355 | multiplier2= factors.getFirst()[m-1][0]/hh[m-1][0]; |
---|
| 6356 | hh= div (hh, power (y,m)); |
---|
| 6357 | hh= hh*power (y,m); |
---|
| 6358 | gg= multiplier1*gg+mod (factors.getLast(), power (y,m)); |
---|
| 6359 | hh= multiplier2*hh+mod (factors.getFirst(), power (y,m)); |
---|
| 6360 | check1= gg (y-evaluation,y); |
---|
| 6361 | check2= hh (y-evaluation,y); |
---|
[2537fa0] | 6362 | CanonicalForm oldcheck1= check1; |
---|
[617dbc] | 6363 | check1= swapvar (check1, x, y); |
---|
| 6364 | if (check1/Lc (check1) == check2/Lc (check2)) |
---|
| 6365 | { |
---|
[49660c] | 6366 | #ifdef HAVE_FLINT |
---|
| 6367 | nmod_mat_clear (FLINTN); |
---|
| 6368 | #endif |
---|
[2537fa0] | 6369 | result.append (oldcheck1); |
---|
| 6370 | result.append (check2); |
---|
[617dbc] | 6371 | delete [] liftPre; |
---|
| 6372 | delete [] factorsFoundIndex; |
---|
| 6373 | return result; |
---|
| 6374 | } |
---|
| 6375 | } |
---|
[a36fcb5] | 6376 | } |
---|
| 6377 | else |
---|
| 6378 | { |
---|
| 6379 | i++; |
---|
[617dbc] | 6380 | if (i < 5) |
---|
[a36fcb5] | 6381 | continue; |
---|
| 6382 | } |
---|
[49660c] | 6383 | #ifdef HAVE_FLINT |
---|
[2d35fe] | 6384 | TIMING_START (fac_fq_reconstruction); |
---|
[49660c] | 6385 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
[2537fa0] | 6386 | factorsFoundIndex, FLINTN, evaluation, beenInThres |
---|
[49660c] | 6387 | ); |
---|
[2d35fe] | 6388 | TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct2: "); |
---|
[49660c] | 6389 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
| 6390 | { |
---|
| 6391 | nmod_mat_clear (FLINTN); |
---|
| 6392 | #else |
---|
[2d35fe] | 6393 | TIMING_START (fac_fq_reconstruction); |
---|
[a36fcb5] | 6394 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
[2537fa0] | 6395 | factorsFoundIndex, NTLN, evaluation, beenInThres |
---|
[a36fcb5] | 6396 | ); |
---|
[2d35fe] | 6397 | TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct2: "); |
---|
[a36fcb5] | 6398 | if (result.length() == NTLN.NumCols()) |
---|
| 6399 | { |
---|
[49660c] | 6400 | #endif |
---|
[a36fcb5] | 6401 | delete [] liftPre; |
---|
| 6402 | delete [] factorsFoundIndex; |
---|
| 6403 | return result; |
---|
| 6404 | } |
---|
| 6405 | i++; |
---|
| 6406 | } |
---|
[11bf82] | 6407 | } |
---|
| 6408 | |
---|
[49660c] | 6409 | #ifdef HAVE_FLINT |
---|
| 6410 | nmod_mat_clear (FLINTN); |
---|
| 6411 | #endif |
---|
[a36fcb5] | 6412 | delete [] liftPre; |
---|
[11bf82] | 6413 | delete [] factorsFoundIndex; |
---|
| 6414 | return result; |
---|
| 6415 | } |
---|
| 6416 | |
---|
[03c742] | 6417 | #ifdef HAVE_NTL // mat_zz_pE |
---|
[11bf82] | 6418 | CFList |
---|
| 6419 | earlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_pE& N, |
---|
| 6420 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
| 6421 | int& factorsFound, bool beenInThres, CFMatrix& M, |
---|
[eca69d] | 6422 | CFArray& Pi, CFList& diophant, bool symmetric, |
---|
| 6423 | const CanonicalForm& evaluation |
---|
[11bf82] | 6424 | ) |
---|
| 6425 | { |
---|
[a36fcb5] | 6426 | int sizeOfLiftPre; |
---|
| 6427 | int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2)); |
---|
| 6428 | Variable y= F.mvar(); |
---|
[11bf82] | 6429 | factorsFound= 0; |
---|
| 6430 | CanonicalForm LCF= LC (F, 1); |
---|
| 6431 | CFList result; |
---|
| 6432 | int smallFactorDeg= 11; |
---|
| 6433 | mat_zz_pE NTLN= N; |
---|
| 6434 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 6435 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
| 6436 | factorsFoundIndex [i]= 0; |
---|
[a36fcb5] | 6437 | |
---|
[11bf82] | 6438 | if (degree (F) + 1 > smallFactorDeg) |
---|
| 6439 | { |
---|
| 6440 | if (l < smallFactorDeg) |
---|
| 6441 | { |
---|
[2d35fe] | 6442 | TIMING_START (fac_fq_lift); |
---|
[11bf82] | 6443 | factors.insert (LCF); |
---|
| 6444 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
[2d35fe] | 6445 | TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction0: "); |
---|
[11bf82] | 6446 | l= smallFactorDeg; |
---|
| 6447 | } |
---|
[2d35fe] | 6448 | TIMING_START (fac_fq_reconstruction); |
---|
[11bf82] | 6449 | reconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
[2537fa0] | 6450 | factorsFoundIndex, NTLN, evaluation, beenInThres |
---|
[11bf82] | 6451 | ); |
---|
[2d35fe] | 6452 | TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct0: "); |
---|
[11bf82] | 6453 | if (result.length() == NTLN.NumCols()) |
---|
| 6454 | { |
---|
[a36fcb5] | 6455 | delete [] liftPre; |
---|
[11bf82] | 6456 | delete [] factorsFoundIndex; |
---|
| 6457 | return result; |
---|
| 6458 | } |
---|
| 6459 | } |
---|
| 6460 | |
---|
[a36fcb5] | 6461 | int i= sizeOfLiftPre - 1; |
---|
| 6462 | int dummy= 1; |
---|
| 6463 | if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
[11bf82] | 6464 | { |
---|
[a36fcb5] | 6465 | while (i > 0) |
---|
| 6466 | { |
---|
| 6467 | if (l < liftPre[i-1] + 1) |
---|
| 6468 | { |
---|
| 6469 | factors.insert (LCF); |
---|
[2d35fe] | 6470 | TIMING_START (fac_fq_lift); |
---|
[a36fcb5] | 6471 | henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M); |
---|
[2d35fe] | 6472 | TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction1: "); |
---|
[a36fcb5] | 6473 | l= liftPre[i-1] + 1; |
---|
| 6474 | } |
---|
| 6475 | else |
---|
| 6476 | { |
---|
| 6477 | i--; |
---|
| 6478 | if (i != 0) |
---|
| 6479 | continue; |
---|
| 6480 | } |
---|
[2d35fe] | 6481 | TIMING_START (fac_fq_reconstruction); |
---|
[a36fcb5] | 6482 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
[2537fa0] | 6483 | factorsFoundIndex, NTLN, evaluation, beenInThres |
---|
[a36fcb5] | 6484 | ); |
---|
[2d35fe] | 6485 | TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct1: "); |
---|
[a36fcb5] | 6486 | if (result.length() == NTLN.NumCols()) |
---|
| 6487 | { |
---|
| 6488 | delete [] liftPre; |
---|
| 6489 | delete [] factorsFoundIndex; |
---|
| 6490 | return result; |
---|
| 6491 | } |
---|
| 6492 | i--; |
---|
| 6493 | } |
---|
[11bf82] | 6494 | } |
---|
[a36fcb5] | 6495 | else |
---|
[11bf82] | 6496 | { |
---|
[a36fcb5] | 6497 | i= 1; |
---|
[c49e6f] | 6498 | while ((degree (F,y)/4+1)*i + 4 <= smallFactorDeg) |
---|
[a36fcb5] | 6499 | i++; |
---|
[617dbc] | 6500 | while (i < 5) |
---|
[a36fcb5] | 6501 | { |
---|
[c49e6f] | 6502 | dummy= tmin (degree (F,y)+1, (degree (F,y)/4+1)*i+4); |
---|
[a36fcb5] | 6503 | if (l < dummy) |
---|
| 6504 | { |
---|
| 6505 | factors.insert (LCF); |
---|
[2d35fe] | 6506 | TIMING_START (fac_fq_lift); |
---|
[a36fcb5] | 6507 | henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M); |
---|
[2d35fe] | 6508 | TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction2: "); |
---|
[a36fcb5] | 6509 | l= dummy; |
---|
[eca69d] | 6510 | if (i == 1 && degree (F)%4==0 && symmetric && factors.length() == 2 && |
---|
| 6511 | LC (F,1).inCoeffDomain() && |
---|
| 6512 | (degree (factors.getFirst(), 1) == degree (factors.getLast(),1))) |
---|
| 6513 | { |
---|
| 6514 | Variable x= Variable (1); |
---|
| 6515 | CanonicalForm g, h, gg, hh, multiplier1, multiplier2, check1, check2; |
---|
| 6516 | int m= degree (F)/4+1; |
---|
| 6517 | g= factors.getFirst(); |
---|
| 6518 | h= factors.getLast(); |
---|
| 6519 | g= mod (g, power (y,m)); |
---|
| 6520 | h= mod (h, power (y,m)); |
---|
| 6521 | g= g (y-evaluation, y); |
---|
| 6522 | h= h (y-evaluation, y); |
---|
| 6523 | gg= mod (swapvar (g,x,y),power (x,m)); |
---|
| 6524 | gg= gg (y + evaluation, y); |
---|
| 6525 | multiplier1= factors.getLast()[m-1][0]/gg[m-1][0]; |
---|
| 6526 | gg= div (gg, power (y,m)); |
---|
| 6527 | gg= gg*power (y,m); |
---|
| 6528 | hh= mod (swapvar (h,x,y),power (x,m)); |
---|
| 6529 | hh= hh (y + evaluation, y); |
---|
| 6530 | multiplier2= factors.getFirst()[m-1][0]/hh[m-1][0]; |
---|
| 6531 | hh= div (hh, power (y,m)); |
---|
| 6532 | hh= hh*power (y,m); |
---|
| 6533 | gg= multiplier1*gg+mod (factors.getLast(), power (y,m)); |
---|
| 6534 | hh= multiplier2*hh+mod (factors.getFirst(), power (y,m)); |
---|
| 6535 | check1= gg (y-evaluation,y); |
---|
| 6536 | check2= hh (y-evaluation,y); |
---|
[2d35fe] | 6537 | CanonicalForm oldcheck1= check1; |
---|
[eca69d] | 6538 | check1= swapvar (check1, x, y); |
---|
| 6539 | if (check1/Lc (check1) == check2/Lc (check2)) |
---|
| 6540 | { |
---|
[2d35fe] | 6541 | result.append (oldcheck1); |
---|
[2537fa0] | 6542 | result.append (check2); |
---|
[eca69d] | 6543 | delete [] liftPre; |
---|
| 6544 | delete [] factorsFoundIndex; |
---|
| 6545 | return result; |
---|
| 6546 | } |
---|
| 6547 | } |
---|
[a36fcb5] | 6548 | } |
---|
| 6549 | else |
---|
| 6550 | { |
---|
| 6551 | i++; |
---|
[617dbc] | 6552 | if (i < 5) |
---|
[a36fcb5] | 6553 | continue; |
---|
| 6554 | } |
---|
[2d35fe] | 6555 | TIMING_START (fac_fq_reconstruction); |
---|
[a36fcb5] | 6556 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
[2537fa0] | 6557 | factorsFoundIndex, NTLN, evaluation, beenInThres |
---|
[a36fcb5] | 6558 | ); |
---|
[2d35fe] | 6559 | TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct2: "); |
---|
[a36fcb5] | 6560 | if (result.length() == NTLN.NumCols()) |
---|
| 6561 | { |
---|
| 6562 | delete [] liftPre; |
---|
| 6563 | delete [] factorsFoundIndex; |
---|
| 6564 | return result; |
---|
| 6565 | } |
---|
| 6566 | i++; |
---|
| 6567 | } |
---|
[11bf82] | 6568 | } |
---|
| 6569 | |
---|
[a36fcb5] | 6570 | delete [] liftPre; |
---|
[11bf82] | 6571 | delete [] factorsFoundIndex; |
---|
| 6572 | return result; |
---|
| 6573 | } |
---|
[03c742] | 6574 | #endif |
---|
[11bf82] | 6575 | |
---|
| 6576 | //over field extension |
---|
[7c4341] | 6577 | #ifdef HAVE_FLINT |
---|
| 6578 | CFList |
---|
| 6579 | extEarlyReconstructionAndLifting (const CanonicalForm& F, const nmod_mat_t N, |
---|
| 6580 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
| 6581 | int& factorsFound, bool beenInThres, CFMatrix& |
---|
| 6582 | M, CFArray& Pi, CFList& diophant, const |
---|
| 6583 | ExtensionInfo& info, const CanonicalForm& |
---|
| 6584 | evaluation |
---|
| 6585 | ) |
---|
| 6586 | #else |
---|
[11bf82] | 6587 | CFList |
---|
| 6588 | extEarlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_p& N, |
---|
| 6589 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
| 6590 | int& factorsFound, bool beenInThres, CFMatrix& |
---|
| 6591 | M, CFArray& Pi, CFList& diophant, const |
---|
| 6592 | ExtensionInfo& info, const CanonicalForm& |
---|
| 6593 | evaluation |
---|
| 6594 | ) |
---|
[7c4341] | 6595 | #endif |
---|
[11bf82] | 6596 | { |
---|
[a36fcb5] | 6597 | int sizeOfLiftPre; |
---|
| 6598 | int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2)); |
---|
| 6599 | Variable y= F.mvar(); |
---|
[11bf82] | 6600 | factorsFound= 0; |
---|
| 6601 | CanonicalForm LCF= LC (F, 1); |
---|
| 6602 | CFList result; |
---|
| 6603 | int smallFactorDeg= 11; |
---|
[7c4341] | 6604 | #ifdef HAVE_FLINT |
---|
| 6605 | nmod_mat_t FLINTN; |
---|
| 6606 | nmod_mat_init_set (FLINTN, N); |
---|
| 6607 | int * factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
| 6608 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
| 6609 | #else |
---|
[11bf82] | 6610 | mat_zz_p NTLN= N; |
---|
| 6611 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 6612 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
[7c4341] | 6613 | #endif |
---|
[11bf82] | 6614 | factorsFoundIndex [i]= 0; |
---|
| 6615 | |
---|
| 6616 | if (degree (F) + 1 > smallFactorDeg) |
---|
| 6617 | { |
---|
| 6618 | if (l < smallFactorDeg) |
---|
| 6619 | { |
---|
[2d35fe] | 6620 | TIMING_START (fac_fq_lift); |
---|
[11bf82] | 6621 | factors.insert (LCF); |
---|
| 6622 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
[2d35fe] | 6623 | TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction0: "); |
---|
[11bf82] | 6624 | l= smallFactorDeg; |
---|
| 6625 | } |
---|
[2d35fe] | 6626 | TIMING_START (fac_fq_reconstruction); |
---|
[7c4341] | 6627 | #ifdef HAVE_FLINT |
---|
| 6628 | extReconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
| 6629 | factorsFoundIndex, FLINTN, beenInThres, info, |
---|
| 6630 | evaluation |
---|
| 6631 | ); |
---|
| 6632 | #else |
---|
[11bf82] | 6633 | extReconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
| 6634 | factorsFoundIndex, NTLN, beenInThres, info, |
---|
| 6635 | evaluation |
---|
[a36fcb5] | 6636 | ); |
---|
[7c4341] | 6637 | #endif |
---|
[2d35fe] | 6638 | TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct0: "); |
---|
[7c4341] | 6639 | #ifdef HAVE_FLINT |
---|
| 6640 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
| 6641 | { |
---|
| 6642 | nmod_mat_clear (FLINTN); |
---|
| 6643 | #else |
---|
[11bf82] | 6644 | if (result.length() == NTLN.NumCols()) |
---|
| 6645 | { |
---|
[7c4341] | 6646 | #endif |
---|
[a36fcb5] | 6647 | delete [] liftPre; |
---|
[11bf82] | 6648 | delete [] factorsFoundIndex; |
---|
| 6649 | return result; |
---|
| 6650 | } |
---|
| 6651 | } |
---|
| 6652 | |
---|
[a36fcb5] | 6653 | int i= sizeOfLiftPre - 1; |
---|
| 6654 | int dummy= 1; |
---|
| 6655 | if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
[11bf82] | 6656 | { |
---|
[a36fcb5] | 6657 | while (i > 0) |
---|
| 6658 | { |
---|
| 6659 | if (l < liftPre[i-1] + 1) |
---|
| 6660 | { |
---|
| 6661 | factors.insert (LCF); |
---|
[2d35fe] | 6662 | TIMING_START (fac_fq_lift); |
---|
[a36fcb5] | 6663 | henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M); |
---|
[2d35fe] | 6664 | TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction1: "); |
---|
[a36fcb5] | 6665 | l= liftPre[i-1] + 1; |
---|
| 6666 | } |
---|
| 6667 | else |
---|
| 6668 | { |
---|
| 6669 | i--; |
---|
| 6670 | if (i != 0) |
---|
| 6671 | continue; |
---|
| 6672 | } |
---|
[2d35fe] | 6673 | TIMING_START (fac_fq_reconstruction); |
---|
[7c4341] | 6674 | #ifdef HAVE_FLINT |
---|
| 6675 | extReconstructionTry (result, bufF, factors, l, factorsFound, |
---|
| 6676 | factorsFoundIndex, FLINTN, beenInThres, info, |
---|
| 6677 | evaluation |
---|
| 6678 | ); |
---|
| 6679 | #else |
---|
[a36fcb5] | 6680 | extReconstructionTry (result, bufF, factors, l, factorsFound, |
---|
| 6681 | factorsFoundIndex, NTLN, beenInThres, info, |
---|
| 6682 | evaluation |
---|
| 6683 | ); |
---|
[7c4341] | 6684 | #endif |
---|
[2d35fe] | 6685 | TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct1: "); |
---|
[7c4341] | 6686 | #ifdef HAVE_FLINT |
---|
| 6687 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
| 6688 | { |
---|
| 6689 | nmod_mat_clear (FLINTN); |
---|
| 6690 | #else |
---|
[a36fcb5] | 6691 | if (result.length() == NTLN.NumCols()) |
---|
| 6692 | { |
---|
[7c4341] | 6693 | #endif |
---|
[a36fcb5] | 6694 | delete [] liftPre; |
---|
| 6695 | delete [] factorsFoundIndex; |
---|
| 6696 | return result; |
---|
| 6697 | } |
---|
| 6698 | i--; |
---|
| 6699 | } |
---|
[11bf82] | 6700 | } |
---|
[a36fcb5] | 6701 | else |
---|
[11bf82] | 6702 | { |
---|
[a36fcb5] | 6703 | i= 1; |
---|
[c49e6f] | 6704 | while ((degree (F,y)/4+1)*i + 4 <= smallFactorDeg) |
---|
[a36fcb5] | 6705 | i++; |
---|
[617dbc] | 6706 | while (i < 5) |
---|
[a36fcb5] | 6707 | { |
---|
[c49e6f] | 6708 | dummy= tmin (degree (F,y)+1, (degree (F,y)/4+1)*i+4); |
---|
[a36fcb5] | 6709 | if (l < dummy) |
---|
| 6710 | { |
---|
| 6711 | factors.insert (LCF); |
---|
[2d35fe] | 6712 | TIMING_START (fac_fq_lift); |
---|
[a36fcb5] | 6713 | henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M); |
---|
[2d35fe] | 6714 | TIMING_END_AND_PRINT (fac_fq_lift, "time to lift in reconstruction2: "); |
---|
[a36fcb5] | 6715 | l= dummy; |
---|
| 6716 | } |
---|
| 6717 | else |
---|
| 6718 | { |
---|
| 6719 | i++; |
---|
[617dbc] | 6720 | if (i < 5) |
---|
[a36fcb5] | 6721 | continue; |
---|
| 6722 | } |
---|
[2d35fe] | 6723 | TIMING_START (fac_fq_reconstruction); |
---|
[7c4341] | 6724 | #ifdef HAVE_FLINT |
---|
| 6725 | extReconstructionTry (result, bufF, factors, l, factorsFound, |
---|
| 6726 | factorsFoundIndex, FLINTN, beenInThres, info, |
---|
| 6727 | evaluation |
---|
| 6728 | ); |
---|
| 6729 | #else |
---|
[a36fcb5] | 6730 | extReconstructionTry (result, bufF, factors, l, factorsFound, |
---|
| 6731 | factorsFoundIndex, NTLN, beenInThres, info, |
---|
| 6732 | evaluation |
---|
| 6733 | ); |
---|
[7c4341] | 6734 | #endif |
---|
[2d35fe] | 6735 | TIMING_END_AND_PRINT (fac_fq_reconstruction, "time to reconstruct2: "); |
---|
[7c4341] | 6736 | #ifdef HAVE_FLINT |
---|
| 6737 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
| 6738 | { |
---|
| 6739 | nmod_mat_clear (FLINTN); |
---|
| 6740 | #else |
---|
[a36fcb5] | 6741 | if (result.length() == NTLN.NumCols()) |
---|
| 6742 | { |
---|
[7c4341] | 6743 | #endif |
---|
[a36fcb5] | 6744 | delete [] liftPre; |
---|
| 6745 | delete [] factorsFoundIndex; |
---|
| 6746 | return result; |
---|
| 6747 | } |
---|
| 6748 | i++; |
---|
| 6749 | } |
---|
[11bf82] | 6750 | } |
---|
| 6751 | |
---|
[7c4341] | 6752 | #ifdef HAVE_FLINT |
---|
| 6753 | nmod_mat_clear (FLINTN); |
---|
| 6754 | #endif |
---|
[a36fcb5] | 6755 | delete [] liftPre; |
---|
[11bf82] | 6756 | delete [] factorsFoundIndex; |
---|
| 6757 | return result; |
---|
| 6758 | } |
---|
| 6759 | |
---|
[03c742] | 6760 | #ifdef HAVE_NTL // henselLift12 |
---|
[11bf82] | 6761 | CFList |
---|
[c1b9927] | 6762 | sieveSmallFactors (const CanonicalForm& G, CFList& uniFactors, DegreePattern& |
---|
[11bf82] | 6763 | degPat, CanonicalForm& H, CFList& diophant, CFArray& Pi, |
---|
[2537fa0] | 6764 | CFMatrix& M, bool& success, int d, const CanonicalForm& eval |
---|
[11bf82] | 6765 | ) |
---|
| 6766 | { |
---|
| 6767 | CanonicalForm F= G; |
---|
| 6768 | CFList bufUniFactors= uniFactors; |
---|
| 6769 | bufUniFactors.insert (LC (F, 1)); |
---|
| 6770 | int smallFactorDeg= d; |
---|
| 6771 | DegreePattern degs= degPat; |
---|
| 6772 | henselLift12 (F, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
---|
| 6773 | int adaptedLiftBound; |
---|
| 6774 | success= false; |
---|
[1a3011e] | 6775 | int * factorsFoundIndex= new int [uniFactors.length()]; |
---|
| 6776 | for (int i= 0; i < uniFactors.length(); i++) |
---|
| 6777 | factorsFoundIndex [i]= 0; |
---|
| 6778 | CFList earlyFactors; |
---|
| 6779 | earlyFactorDetection (earlyFactors, F, bufUniFactors, adaptedLiftBound, |
---|
[2537fa0] | 6780 | factorsFoundIndex, degs, success, smallFactorDeg, eval); |
---|
[1a3011e] | 6781 | delete [] factorsFoundIndex; |
---|
[11bf82] | 6782 | if (degs.getLength() == 1) |
---|
| 6783 | { |
---|
| 6784 | degPat= degs; |
---|
| 6785 | return earlyFactors; |
---|
| 6786 | } |
---|
| 6787 | if (success) |
---|
| 6788 | { |
---|
| 6789 | H= F; |
---|
| 6790 | return earlyFactors; |
---|
| 6791 | } |
---|
[69c882] | 6792 | int sizeOldF= size (G); |
---|
| 6793 | if (size (F) < sizeOldF) |
---|
[11bf82] | 6794 | { |
---|
[69c882] | 6795 | H= F; |
---|
[11bf82] | 6796 | success= true; |
---|
| 6797 | return earlyFactors; |
---|
| 6798 | } |
---|
| 6799 | else |
---|
| 6800 | { |
---|
| 6801 | uniFactors= bufUniFactors; |
---|
| 6802 | return CFList(); |
---|
| 6803 | } |
---|
| 6804 | } |
---|
[03c742] | 6805 | #endif |
---|
[11bf82] | 6806 | |
---|
[03c742] | 6807 | #ifdef HAVE_NTL // henselLift12 |
---|
[11bf82] | 6808 | CFList |
---|
| 6809 | extSieveSmallFactors (const CanonicalForm& G, CFList& uniFactors, DegreePattern& |
---|
| 6810 | degPat, CanonicalForm& H, CFList& diophant, CFArray& Pi, |
---|
| 6811 | CFMatrix& M, bool& success, int d, const CanonicalForm& |
---|
| 6812 | evaluation, const ExtensionInfo& info |
---|
| 6813 | ) |
---|
| 6814 | { |
---|
| 6815 | CanonicalForm F= G; |
---|
| 6816 | CFList bufUniFactors= uniFactors; |
---|
| 6817 | bufUniFactors.insert (LC (F, 1)); |
---|
| 6818 | int smallFactorDeg= d; |
---|
| 6819 | DegreePattern degs= degPat; |
---|
| 6820 | henselLift12 (F, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
---|
| 6821 | int adaptedLiftBound; |
---|
| 6822 | success= false; |
---|
[1a3011e] | 6823 | int * factorsFoundIndex= new int [uniFactors.length()]; |
---|
| 6824 | for (int i= 0; i < uniFactors.length(); i++) |
---|
| 6825 | factorsFoundIndex [i]= 0; |
---|
| 6826 | CFList earlyFactors; |
---|
| 6827 | extEarlyFactorDetection (earlyFactors, F, bufUniFactors, adaptedLiftBound, |
---|
| 6828 | factorsFoundIndex, degs, success, info, evaluation, |
---|
| 6829 | smallFactorDeg); |
---|
| 6830 | delete [] factorsFoundIndex; |
---|
[11bf82] | 6831 | if (degs.getLength() == 1) |
---|
| 6832 | { |
---|
| 6833 | degPat= degs; |
---|
| 6834 | return earlyFactors; |
---|
| 6835 | } |
---|
| 6836 | if (success) |
---|
| 6837 | { |
---|
| 6838 | H= F; |
---|
| 6839 | return earlyFactors; |
---|
| 6840 | } |
---|
| 6841 | Variable y= F.mvar(); |
---|
[773d28] | 6842 | int sizeOldF= size (G); |
---|
[69c882] | 6843 | if (size (F) < sizeOldF) |
---|
[11bf82] | 6844 | { |
---|
[773d28] | 6845 | H= F; |
---|
[11bf82] | 6846 | success= true; |
---|
[69c882] | 6847 | return earlyFactors; |
---|
[11bf82] | 6848 | } |
---|
| 6849 | else |
---|
| 6850 | { |
---|
| 6851 | uniFactors= bufUniFactors; |
---|
| 6852 | return CFList(); |
---|
| 6853 | } |
---|
| 6854 | } |
---|
[03c742] | 6855 | #endif |
---|
[11bf82] | 6856 | |
---|
[03c742] | 6857 | #ifdef HAVE_NTL // matrix Fq |
---|
[11bf82] | 6858 | CFList |
---|
| 6859 | henselLiftAndLatticeRecombi (const CanonicalForm& G, const CFList& uniFactors, |
---|
[617dbc] | 6860 | const Variable& alpha, const DegreePattern& degPat, |
---|
[2537fa0] | 6861 | bool symmetric, const CanonicalForm& eval |
---|
[11bf82] | 6862 | ) |
---|
| 6863 | { |
---|
| 6864 | DegreePattern degs= degPat; |
---|
| 6865 | CanonicalForm F= G; |
---|
| 6866 | CanonicalForm LCF= LC (F, 1); |
---|
| 6867 | Variable y= F.mvar(); |
---|
| 6868 | Variable x= Variable (1); |
---|
| 6869 | int d; |
---|
[542864] | 6870 | bool isIrreducible= false; |
---|
| 6871 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
| 6872 | if (isIrreducible) |
---|
| 6873 | { |
---|
| 6874 | delete [] bounds; |
---|
| 6875 | return CFList (G); |
---|
| 6876 | } |
---|
[11bf82] | 6877 | int minBound= bounds[0]; |
---|
| 6878 | for (int i= 1; i < d; i++) |
---|
| 6879 | { |
---|
| 6880 | if (bounds[i] != 0) |
---|
| 6881 | minBound= tmin (minBound, bounds[i]); |
---|
| 6882 | } |
---|
| 6883 | |
---|
| 6884 | CFList bufUniFactors= uniFactors; |
---|
| 6885 | CFArray Pi; |
---|
| 6886 | CFList diophant; |
---|
| 6887 | int liftBound= 2*totaldegree (F) - 1; |
---|
| 6888 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
| 6889 | |
---|
| 6890 | CFList smallFactors; |
---|
| 6891 | CanonicalForm H; |
---|
[773d28] | 6892 | bool success= false; |
---|
[11bf82] | 6893 | smallFactors= sieveSmallFactors (F, bufUniFactors, degs, H, diophant, Pi, M, |
---|
[2537fa0] | 6894 | success, minBound + 1, eval |
---|
[11bf82] | 6895 | ); |
---|
| 6896 | |
---|
| 6897 | if (smallFactors.length() > 0) |
---|
| 6898 | { |
---|
| 6899 | if (smallFactors.length() == 1) |
---|
| 6900 | { |
---|
| 6901 | if (smallFactors.getFirst() == F) |
---|
| 6902 | { |
---|
| 6903 | delete [] bounds; |
---|
[2537fa0] | 6904 | return CFList (G (y-eval,y)); |
---|
[11bf82] | 6905 | } |
---|
| 6906 | } |
---|
| 6907 | if (degs.getLength() <= 1) |
---|
| 6908 | { |
---|
| 6909 | delete [] bounds; |
---|
| 6910 | return smallFactors; |
---|
| 6911 | } |
---|
| 6912 | } |
---|
| 6913 | |
---|
| 6914 | int index; |
---|
[38ffb7] | 6915 | CanonicalForm tmp1, tmp2; |
---|
[11bf82] | 6916 | for (CFListIterator i= smallFactors; i.hasItem(); i++) |
---|
| 6917 | { |
---|
| 6918 | index= 1; |
---|
[2537fa0] | 6919 | tmp1= mod (i.getItem(),y-eval); |
---|
[11bf82] | 6920 | tmp1 /= Lc (tmp1); |
---|
| 6921 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
| 6922 | { |
---|
| 6923 | tmp2= mod (j.getItem(), y); |
---|
| 6924 | tmp2 /= Lc (tmp2); |
---|
| 6925 | if (tmp1 == tmp2) |
---|
| 6926 | { |
---|
| 6927 | index++; |
---|
| 6928 | j.remove(index); |
---|
| 6929 | break; |
---|
| 6930 | } |
---|
| 6931 | } |
---|
| 6932 | } |
---|
| 6933 | |
---|
| 6934 | if (bufUniFactors.isEmpty()) |
---|
| 6935 | { |
---|
| 6936 | delete [] bounds; |
---|
| 6937 | return smallFactors; |
---|
| 6938 | } |
---|
| 6939 | |
---|
| 6940 | if (success) |
---|
| 6941 | { |
---|
| 6942 | F= H; |
---|
| 6943 | delete [] bounds; |
---|
[542864] | 6944 | bounds= computeBounds (F, d, isIrreducible); |
---|
| 6945 | if (isIrreducible) |
---|
| 6946 | { |
---|
[2537fa0] | 6947 | smallFactors.append (F (y-eval,y)); |
---|
[542864] | 6948 | delete [] bounds; |
---|
| 6949 | return smallFactors; |
---|
| 6950 | } |
---|
[11bf82] | 6951 | LCF= LC (F, 1); |
---|
| 6952 | |
---|
| 6953 | minBound= bounds[0]; |
---|
| 6954 | for (int i= 1; i < d; i++) |
---|
| 6955 | { |
---|
| 6956 | if (bounds[i] != 0) |
---|
| 6957 | minBound= tmin (minBound, bounds[i]); |
---|
| 6958 | } |
---|
| 6959 | Pi= CFArray(); |
---|
| 6960 | diophant= CFList(); |
---|
| 6961 | liftBound= 2*totaldegree (F) - 1; |
---|
| 6962 | M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
| 6963 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 6964 | degs.intersect (bufDegs); |
---|
| 6965 | degs.refine(); |
---|
| 6966 | if (degs.getLength() <= 1) |
---|
| 6967 | { |
---|
[2537fa0] | 6968 | smallFactors.append (F (y-eval,y)); |
---|
[11bf82] | 6969 | delete [] bounds; |
---|
| 6970 | return smallFactors; |
---|
| 6971 | } |
---|
| 6972 | } |
---|
| 6973 | |
---|
| 6974 | bool reduceFq2Fp= (degree (F) > getCharacteristic()); |
---|
| 6975 | bufUniFactors.insert (LCF); |
---|
| 6976 | int l= 1; |
---|
| 6977 | |
---|
[49660c] | 6978 | #ifdef HAVE_FLINT |
---|
| 6979 | nmod_mat_t FLINTN; |
---|
[b2359c] | 6980 | #endif |
---|
| 6981 | |
---|
[bffe62d] | 6982 | if (fac_NTL_char != getCharacteristic()) |
---|
| 6983 | { |
---|
| 6984 | fac_NTL_char= getCharacteristic(); |
---|
| 6985 | zz_p::init (getCharacteristic()); |
---|
| 6986 | } |
---|
[11bf82] | 6987 | mat_zz_p NTLN; |
---|
[49660c] | 6988 | |
---|
[11bf82] | 6989 | if (alpha.level() != 1) |
---|
| 6990 | { |
---|
| 6991 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 6992 | zz_pE::init (NTLMipo); |
---|
| 6993 | } |
---|
| 6994 | mat_zz_pE NTLNe; |
---|
[b2359c] | 6995 | |
---|
[11bf82] | 6996 | if (alpha.level() == 1) |
---|
[49660c] | 6997 | { |
---|
| 6998 | #ifdef HAVE_FLINT |
---|
| 6999 | nmod_mat_init (FLINTN, bufUniFactors.length()-1, bufUniFactors.length()-1, getCharacteristic()); |
---|
| 7000 | for (long i= bufUniFactors.length()-2; i >= 0; i--) |
---|
| 7001 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
| 7002 | #else |
---|
[11bf82] | 7003 | ident (NTLN, bufUniFactors.length() - 1); |
---|
[49660c] | 7004 | #endif |
---|
| 7005 | } |
---|
[11bf82] | 7006 | else |
---|
| 7007 | { |
---|
| 7008 | if (reduceFq2Fp) |
---|
[49660c] | 7009 | #ifdef HAVE_FLINT |
---|
| 7010 | { |
---|
| 7011 | nmod_mat_init (FLINTN, bufUniFactors.length()-1, bufUniFactors.length()-1, getCharacteristic()); |
---|
| 7012 | for (long i= bufUniFactors.length()-2; i >= 0; i--) |
---|
| 7013 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
| 7014 | } |
---|
| 7015 | #else |
---|
[11bf82] | 7016 | ident (NTLN, bufUniFactors.length() - 1); |
---|
[49660c] | 7017 | #endif |
---|
[11bf82] | 7018 | else |
---|
| 7019 | ident (NTLNe, bufUniFactors.length() - 1); |
---|
| 7020 | } |
---|
| 7021 | bool irreducible= false; |
---|
| 7022 | CFArray bufQ= CFArray (bufUniFactors.length() - 1); |
---|
| 7023 | |
---|
| 7024 | int oldL; |
---|
[2d35fe] | 7025 | TIMING_START (fac_fq_till_reduced); |
---|
[11bf82] | 7026 | if (success) |
---|
| 7027 | { |
---|
| 7028 | int start= 0; |
---|
| 7029 | if (alpha.level() == 1) |
---|
| 7030 | oldL= liftAndComputeLattice (F, bounds, d, start, liftBound, minBound, |
---|
[49660c] | 7031 | #ifdef HAVE_FLINT |
---|
| 7032 | bufUniFactors, FLINTN, diophant, M, Pi, bufQ, |
---|
| 7033 | #else |
---|
[11bf82] | 7034 | bufUniFactors, NTLN, diophant, M, Pi, bufQ, |
---|
[49660c] | 7035 | #endif |
---|
[11bf82] | 7036 | irreducible |
---|
| 7037 | ); |
---|
| 7038 | else |
---|
| 7039 | { |
---|
| 7040 | if (reduceFq2Fp) |
---|
| 7041 | oldL= liftAndComputeLatticeFq2Fp (F, bounds, d, start, liftBound, |
---|
[49660c] | 7042 | #ifdef HAVE_FLINT |
---|
| 7043 | minBound, bufUniFactors, FLINTN, |
---|
| 7044 | #else |
---|
[11bf82] | 7045 | minBound, bufUniFactors, NTLN, |
---|
[49660c] | 7046 | #endif |
---|
[11bf82] | 7047 | diophant, M, Pi, bufQ, irreducible, |
---|
| 7048 | alpha |
---|
| 7049 | ); |
---|
| 7050 | else |
---|
| 7051 | oldL= liftAndComputeLattice (F, bounds, d, start, liftBound, minBound, |
---|
| 7052 | bufUniFactors, NTLNe, diophant, M, Pi, bufQ, |
---|
| 7053 | irreducible |
---|
| 7054 | ); |
---|
| 7055 | } |
---|
| 7056 | } |
---|
| 7057 | else |
---|
| 7058 | { |
---|
| 7059 | if (alpha.level() == 1) |
---|
[49660c] | 7060 | { |
---|
[a5450a8] | 7061 | oldL= liftAndComputeLattice (F, bounds, d, minBound + 1, liftBound, |
---|
[49660c] | 7062 | #ifdef HAVE_FLINT |
---|
| 7063 | minBound, bufUniFactors, FLINTN, diophant, M, |
---|
| 7064 | #else |
---|
[11bf82] | 7065 | minBound, bufUniFactors, NTLN, diophant, M, |
---|
[49660c] | 7066 | #endif |
---|
[11bf82] | 7067 | Pi, bufQ, irreducible |
---|
| 7068 | ); |
---|
[49660c] | 7069 | } |
---|
[11bf82] | 7070 | else |
---|
| 7071 | { |
---|
| 7072 | if (reduceFq2Fp) |
---|
[a5450a8] | 7073 | oldL= liftAndComputeLatticeFq2Fp (F, bounds, d, minBound + 1, |
---|
[11bf82] | 7074 | liftBound, minBound, bufUniFactors, |
---|
[49660c] | 7075 | #ifdef HAVE_FLINT |
---|
| 7076 | FLINTN, diophant, M, Pi, bufQ, |
---|
| 7077 | #else |
---|
[11bf82] | 7078 | NTLN, diophant, M, Pi, bufQ, |
---|
[49660c] | 7079 | #endif |
---|
[11bf82] | 7080 | irreducible, alpha |
---|
| 7081 | ); |
---|
| 7082 | else |
---|
[a5450a8] | 7083 | oldL= liftAndComputeLattice (F, bounds, d, minBound + 1, liftBound, |
---|
[11bf82] | 7084 | minBound, bufUniFactors, NTLNe, diophant, |
---|
| 7085 | M, Pi, bufQ, irreducible |
---|
| 7086 | ); |
---|
| 7087 | } |
---|
| 7088 | } |
---|
| 7089 | |
---|
[2d35fe] | 7090 | TIMING_END_AND_PRINT (fac_fq_till_reduced, |
---|
| 7091 | "time to compute a reduced lattice: "); |
---|
[11bf82] | 7092 | bufUniFactors.removeFirst(); |
---|
| 7093 | if (oldL > liftBound) |
---|
| 7094 | { |
---|
[49660c] | 7095 | #ifdef HAVE_FLINT |
---|
[f659855] | 7096 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 7097 | nmod_mat_clear (FLINTN); |
---|
[49660c] | 7098 | #endif |
---|
[11bf82] | 7099 | delete [] bounds; |
---|
| 7100 | return Union (smallFactors, |
---|
| 7101 | factorRecombination (bufUniFactors, F, |
---|
[a209e1d] | 7102 | power (y, degree (F) + 1), |
---|
[2537fa0] | 7103 | degs, eval, 1, bufUniFactors.length()/2 |
---|
[11bf82] | 7104 | ) |
---|
| 7105 | ); |
---|
| 7106 | } |
---|
| 7107 | |
---|
| 7108 | l= oldL; |
---|
| 7109 | if (irreducible) |
---|
| 7110 | { |
---|
[49660c] | 7111 | #ifdef HAVE_FLINT |
---|
[f659855] | 7112 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 7113 | nmod_mat_clear (FLINTN); |
---|
[49660c] | 7114 | #endif |
---|
[11bf82] | 7115 | delete [] bounds; |
---|
[2537fa0] | 7116 | return Union (CFList (F(y-eval,y)), smallFactors); |
---|
[11bf82] | 7117 | } |
---|
| 7118 | |
---|
| 7119 | CanonicalForm yToL= power (y,l); |
---|
| 7120 | |
---|
| 7121 | CFList result; |
---|
| 7122 | if (l >= degree (F) + 1) |
---|
| 7123 | { |
---|
| 7124 | int * factorsFoundIndex; |
---|
| 7125 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 7126 | { |
---|
[49660c] | 7127 | #ifdef HAVE_FLINT |
---|
| 7128 | factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
| 7129 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
| 7130 | #else |
---|
[11bf82] | 7131 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 7132 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
[49660c] | 7133 | #endif |
---|
[11bf82] | 7134 | factorsFoundIndex[i]= 0; |
---|
| 7135 | } |
---|
| 7136 | else |
---|
| 7137 | { |
---|
| 7138 | factorsFoundIndex= new int [NTLNe.NumCols()]; |
---|
| 7139 | for (long i= 0; i < NTLNe.NumCols(); i++) |
---|
| 7140 | factorsFoundIndex[i]= 0; |
---|
| 7141 | } |
---|
| 7142 | int factorsFound= 0; |
---|
| 7143 | CanonicalForm bufF= F; |
---|
| 7144 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 7145 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
[49660c] | 7146 | #ifdef HAVE_FLINT |
---|
[2537fa0] | 7147 | factorsFound, factorsFoundIndex, FLINTN, eval, false |
---|
[49660c] | 7148 | #else |
---|
[2537fa0] | 7149 | factorsFound, factorsFoundIndex, NTLN, eval, false |
---|
[49660c] | 7150 | #endif |
---|
[11bf82] | 7151 | ); |
---|
| 7152 | else |
---|
| 7153 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
[2537fa0] | 7154 | factorsFound, factorsFoundIndex, NTLNe, eval, false |
---|
[11bf82] | 7155 | ); |
---|
| 7156 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 7157 | { |
---|
[49660c] | 7158 | #ifdef HAVE_FLINT |
---|
| 7159 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
| 7160 | { |
---|
[f659855] | 7161 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 7162 | nmod_mat_clear (FLINTN); |
---|
[49660c] | 7163 | #else |
---|
[11bf82] | 7164 | if (result.length() == NTLN.NumCols()) |
---|
| 7165 | { |
---|
[49660c] | 7166 | #endif |
---|
[11bf82] | 7167 | delete [] factorsFoundIndex; |
---|
| 7168 | delete [] bounds; |
---|
| 7169 | return Union (result, smallFactors); |
---|
| 7170 | } |
---|
| 7171 | } |
---|
| 7172 | else |
---|
| 7173 | { |
---|
| 7174 | if (result.length() == NTLNe.NumCols()) |
---|
| 7175 | { |
---|
| 7176 | delete [] factorsFoundIndex; |
---|
| 7177 | delete [] bounds; |
---|
| 7178 | return Union (result, smallFactors); |
---|
| 7179 | } |
---|
| 7180 | } |
---|
| 7181 | delete [] factorsFoundIndex; |
---|
| 7182 | } |
---|
| 7183 | if (l >= liftBound) |
---|
| 7184 | { |
---|
| 7185 | int * factorsFoundIndex; |
---|
| 7186 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 7187 | { |
---|
[49660c] | 7188 | #ifdef HAVE_FLINT |
---|
| 7189 | factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
| 7190 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
| 7191 | #else |
---|
[c1b9927] | 7192 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
[11bf82] | 7193 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
[49660c] | 7194 | #endif |
---|
[11bf82] | 7195 | factorsFoundIndex[i]= 0; |
---|
| 7196 | } |
---|
| 7197 | else |
---|
| 7198 | { |
---|
[c1b9927] | 7199 | factorsFoundIndex= new int [NTLNe.NumCols()]; |
---|
[11bf82] | 7200 | for (long i= 0; i < NTLNe.NumCols(); i++) |
---|
| 7201 | factorsFoundIndex[i]= 0; |
---|
| 7202 | } |
---|
| 7203 | CanonicalForm bufF= F; |
---|
| 7204 | int factorsFound= 0; |
---|
| 7205 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
[894604] | 7206 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
[49660c] | 7207 | #ifdef HAVE_FLINT |
---|
[2537fa0] | 7208 | factorsFound, factorsFoundIndex, FLINTN, eval, false |
---|
[49660c] | 7209 | #else |
---|
[2537fa0] | 7210 | factorsFound, factorsFoundIndex, NTLN, eval, false |
---|
[49660c] | 7211 | #endif |
---|
[11bf82] | 7212 | ); |
---|
| 7213 | else |
---|
[894604] | 7214 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
[2537fa0] | 7215 | factorsFound, factorsFoundIndex, NTLNe, eval, false |
---|
[11bf82] | 7216 | ); |
---|
| 7217 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 7218 | { |
---|
[49660c] | 7219 | #ifdef HAVE_FLINT |
---|
| 7220 | if (result.length() == nmod_mat_ncols(FLINTN)) |
---|
| 7221 | { |
---|
| 7222 | nmod_mat_clear (FLINTN); |
---|
| 7223 | #else |
---|
[11bf82] | 7224 | if (result.length() == NTLN.NumCols()) |
---|
| 7225 | { |
---|
[49660c] | 7226 | #endif |
---|
[11bf82] | 7227 | delete [] factorsFoundIndex; |
---|
| 7228 | delete [] bounds; |
---|
| 7229 | return Union (result, smallFactors); |
---|
| 7230 | } |
---|
| 7231 | } |
---|
| 7232 | else |
---|
| 7233 | { |
---|
| 7234 | if (result.length() == NTLNe.NumCols()) |
---|
| 7235 | { |
---|
| 7236 | delete [] factorsFoundIndex; |
---|
| 7237 | delete [] bounds; |
---|
| 7238 | return Union (result, smallFactors); |
---|
| 7239 | } |
---|
| 7240 | } |
---|
| 7241 | delete [] factorsFoundIndex; |
---|
| 7242 | } |
---|
| 7243 | |
---|
| 7244 | result= CFList(); |
---|
| 7245 | bool beenInThres= false; |
---|
| 7246 | int thres= 100; |
---|
| 7247 | if (l <= thres) |
---|
| 7248 | { |
---|
| 7249 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 7250 | { |
---|
[49660c] | 7251 | #ifdef HAVE_FLINT |
---|
| 7252 | if (nmod_mat_ncols (FLINTN) < bufUniFactors.length()) |
---|
| 7253 | { |
---|
| 7254 | refineAndRestartLift (F, FLINTN, liftBound, l, bufUniFactors, M, Pi, |
---|
| 7255 | #else |
---|
[11bf82] | 7256 | if (NTLN.NumCols() < bufUniFactors.length()) |
---|
| 7257 | { |
---|
[c1b9927] | 7258 | refineAndRestartLift (F, NTLN, liftBound, l, bufUniFactors, M, Pi, |
---|
[49660c] | 7259 | #endif |
---|
[11bf82] | 7260 | diophant |
---|
| 7261 | ); |
---|
| 7262 | beenInThres= true; |
---|
| 7263 | } |
---|
| 7264 | } |
---|
| 7265 | else |
---|
| 7266 | { |
---|
| 7267 | if (NTLNe.NumCols() < bufUniFactors.length()) |
---|
| 7268 | { |
---|
| 7269 | refineAndRestartLift (F, NTLNe, liftBound, l, bufUniFactors, M, Pi, |
---|
| 7270 | diophant |
---|
| 7271 | ); |
---|
| 7272 | beenInThres= true; |
---|
| 7273 | } |
---|
| 7274 | } |
---|
| 7275 | } |
---|
| 7276 | |
---|
| 7277 | CanonicalForm bufF= F; |
---|
| 7278 | int factorsFound= 0; |
---|
| 7279 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 7280 | { |
---|
[49660c] | 7281 | #ifdef HAVE_FLINT |
---|
| 7282 | result= earlyReconstructionAndLifting (F, FLINTN, bufF, bufUniFactors, l, |
---|
| 7283 | #else |
---|
[11bf82] | 7284 | result= earlyReconstructionAndLifting (F, NTLN, bufF, bufUniFactors, l, |
---|
[49660c] | 7285 | #endif |
---|
[11bf82] | 7286 | factorsFound, beenInThres, M, Pi, |
---|
[2537fa0] | 7287 | diophant, symmetric, eval |
---|
[11bf82] | 7288 | ); |
---|
| 7289 | |
---|
[49660c] | 7290 | #ifdef HAVE_FLINT |
---|
| 7291 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
| 7292 | { |
---|
| 7293 | nmod_mat_clear (FLINTN); |
---|
| 7294 | #else |
---|
[11bf82] | 7295 | if (result.length() == NTLN.NumCols()) |
---|
| 7296 | { |
---|
[49660c] | 7297 | #endif |
---|
[11bf82] | 7298 | delete [] bounds; |
---|
| 7299 | return Union (result, smallFactors); |
---|
| 7300 | } |
---|
| 7301 | } |
---|
| 7302 | else |
---|
| 7303 | { |
---|
| 7304 | result= earlyReconstructionAndLifting (F, NTLNe, bufF, bufUniFactors, l, |
---|
| 7305 | factorsFound, beenInThres, M, Pi, |
---|
[2537fa0] | 7306 | diophant, symmetric, eval |
---|
[11bf82] | 7307 | ); |
---|
| 7308 | |
---|
| 7309 | if (result.length() == NTLNe.NumCols()) |
---|
| 7310 | { |
---|
| 7311 | delete [] bounds; |
---|
| 7312 | return Union (result, smallFactors); |
---|
| 7313 | } |
---|
| 7314 | } |
---|
| 7315 | |
---|
| 7316 | if (result.length() > 0) |
---|
| 7317 | { |
---|
| 7318 | if (beenInThres) |
---|
| 7319 | { |
---|
[38ffb7] | 7320 | int index; |
---|
| 7321 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
[11bf82] | 7322 | { |
---|
[38ffb7] | 7323 | index= 1; |
---|
[2537fa0] | 7324 | tmp1= mod (i.getItem(), y-eval); |
---|
[38ffb7] | 7325 | tmp1 /= Lc (tmp1); |
---|
| 7326 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
[11bf82] | 7327 | { |
---|
[38ffb7] | 7328 | tmp2= mod (j.getItem(), y); |
---|
| 7329 | tmp2 /= Lc (tmp2); |
---|
| 7330 | if (tmp1 == tmp2) |
---|
| 7331 | { |
---|
| 7332 | index++; |
---|
| 7333 | j.remove(index); |
---|
| 7334 | break; |
---|
| 7335 | } |
---|
[11bf82] | 7336 | } |
---|
| 7337 | } |
---|
| 7338 | } |
---|
| 7339 | else |
---|
| 7340 | { |
---|
[9d572a5] | 7341 | int * zeroOne; |
---|
| 7342 | long numCols, numRows; |
---|
| 7343 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 7344 | { |
---|
[49660c] | 7345 | #ifdef HAVE_FLINT |
---|
| 7346 | numCols= nmod_mat_ncols (FLINTN); |
---|
| 7347 | numRows= nmod_mat_nrows (FLINTN); |
---|
| 7348 | zeroOne= extractZeroOneVecs (FLINTN); |
---|
| 7349 | #else |
---|
[9d572a5] | 7350 | numCols= NTLN.NumCols(); |
---|
| 7351 | numRows= NTLN.NumRows(); |
---|
| 7352 | zeroOne= extractZeroOneVecs (NTLN); |
---|
[49660c] | 7353 | #endif |
---|
[9d572a5] | 7354 | } |
---|
| 7355 | else |
---|
| 7356 | { |
---|
| 7357 | numCols= NTLNe.NumCols(); |
---|
| 7358 | numRows= NTLNe.NumRows(); |
---|
| 7359 | zeroOne= extractZeroOneVecs (NTLNe); |
---|
| 7360 | } |
---|
[38ffb7] | 7361 | CFList bufBufUniFactors= bufUniFactors; |
---|
| 7362 | CFListIterator iter, iter2; |
---|
| 7363 | CanonicalForm buf; |
---|
[11bf82] | 7364 | CFList factorsConsidered; |
---|
[38ffb7] | 7365 | CanonicalForm tmp; |
---|
[9d572a5] | 7366 | for (int i= 0; i < numCols; i++) |
---|
[11bf82] | 7367 | { |
---|
[38ffb7] | 7368 | if (zeroOne [i] == 0) |
---|
| 7369 | continue; |
---|
| 7370 | iter= bufUniFactors; |
---|
| 7371 | buf= 1; |
---|
| 7372 | factorsConsidered= CFList(); |
---|
[9d572a5] | 7373 | for (int j= 0; j < numRows; j++, iter++) |
---|
[11bf82] | 7374 | { |
---|
[9d572a5] | 7375 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
[38ffb7] | 7376 | { |
---|
[49660c] | 7377 | #ifdef HAVE_FLINT |
---|
| 7378 | if (!(nmod_mat_entry (FLINTN, j,i) == 0)) |
---|
| 7379 | #else |
---|
[9d572a5] | 7380 | if (!IsZero (NTLN (j + 1,i + 1))) |
---|
[49660c] | 7381 | #endif |
---|
[9d572a5] | 7382 | { |
---|
| 7383 | factorsConsidered.append (iter.getItem()); |
---|
| 7384 | buf *= mod (iter.getItem(), y); |
---|
| 7385 | } |
---|
| 7386 | } |
---|
| 7387 | else |
---|
| 7388 | { |
---|
| 7389 | if (!IsZero (NTLNe (j + 1,i + 1))) |
---|
| 7390 | { |
---|
| 7391 | factorsConsidered.append (iter.getItem()); |
---|
| 7392 | buf *= mod (iter.getItem(), y); |
---|
| 7393 | } |
---|
[38ffb7] | 7394 | } |
---|
[11bf82] | 7395 | } |
---|
[38ffb7] | 7396 | buf /= Lc (buf); |
---|
| 7397 | for (iter2= result; iter2.hasItem(); iter2++) |
---|
[11bf82] | 7398 | { |
---|
[2537fa0] | 7399 | tmp= mod (iter2.getItem(), y-eval); |
---|
[38ffb7] | 7400 | tmp /= Lc (tmp); |
---|
| 7401 | if (tmp == buf) |
---|
| 7402 | { |
---|
| 7403 | bufBufUniFactors= Difference (bufBufUniFactors, factorsConsidered); |
---|
| 7404 | break; |
---|
| 7405 | } |
---|
[11bf82] | 7406 | } |
---|
| 7407 | } |
---|
[38ffb7] | 7408 | bufUniFactors= bufBufUniFactors; |
---|
| 7409 | delete [] zeroOne; |
---|
[11bf82] | 7410 | } |
---|
| 7411 | |
---|
| 7412 | int oldNumCols; |
---|
| 7413 | CFList resultBufF; |
---|
| 7414 | irreducible= false; |
---|
| 7415 | |
---|
| 7416 | if (alpha.level() == 1) |
---|
| 7417 | { |
---|
[49660c] | 7418 | #ifdef HAVE_FLINT |
---|
| 7419 | oldNumCols= nmod_mat_ncols (FLINTN); |
---|
| 7420 | #else |
---|
[11bf82] | 7421 | oldNumCols= NTLN.NumCols(); |
---|
[49660c] | 7422 | #endif |
---|
[11bf82] | 7423 | resultBufF= increasePrecision (bufF, bufUniFactors, factorsFound, |
---|
[2537fa0] | 7424 | oldNumCols, oldL, l, eval |
---|
[11bf82] | 7425 | ); |
---|
| 7426 | } |
---|
| 7427 | else |
---|
| 7428 | { |
---|
| 7429 | if (reduceFq2Fp) |
---|
| 7430 | { |
---|
[49660c] | 7431 | #ifdef HAVE_FLINT |
---|
| 7432 | oldNumCols= nmod_mat_ncols (FLINTN); |
---|
| 7433 | #else |
---|
[11bf82] | 7434 | oldNumCols= NTLN.NumCols(); |
---|
[49660c] | 7435 | #endif |
---|
[11bf82] | 7436 | |
---|
| 7437 | resultBufF= increasePrecisionFq2Fp (bufF, bufUniFactors, factorsFound, |
---|
[2537fa0] | 7438 | oldNumCols, oldL, alpha, l, eval |
---|
[11bf82] | 7439 | ); |
---|
| 7440 | } |
---|
| 7441 | else |
---|
| 7442 | { |
---|
| 7443 | oldNumCols= NTLNe.NumCols(); |
---|
| 7444 | |
---|
| 7445 | resultBufF= increasePrecision (bufF, bufUniFactors, factorsFound, |
---|
[2537fa0] | 7446 | oldNumCols, oldL, alpha, l, eval |
---|
[11bf82] | 7447 | ); |
---|
| 7448 | } |
---|
| 7449 | } |
---|
| 7450 | |
---|
| 7451 | if (bufUniFactors.isEmpty() || degree (bufF) <= 0) |
---|
| 7452 | { |
---|
[49660c] | 7453 | #ifdef HAVE_FLINT |
---|
[f659855] | 7454 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 7455 | nmod_mat_clear (FLINTN); |
---|
[49660c] | 7456 | #endif |
---|
[11bf82] | 7457 | delete [] bounds; |
---|
| 7458 | result= Union (resultBufF, result); |
---|
| 7459 | return Union (result, smallFactors); |
---|
| 7460 | } |
---|
| 7461 | |
---|
| 7462 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
| 7463 | i.getItem()= mod (i.getItem(), y); |
---|
| 7464 | |
---|
| 7465 | result= Union (result, resultBufF); |
---|
| 7466 | result= Union (result, smallFactors); |
---|
| 7467 | delete [] bounds; |
---|
| 7468 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 7469 | degs.intersect (bufDegs); |
---|
| 7470 | degs.refine(); |
---|
| 7471 | if (degs.getLength() == 1 || bufUniFactors.length() == 1) |
---|
| 7472 | { |
---|
[49660c] | 7473 | #ifdef HAVE_FLINT |
---|
[f659855] | 7474 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 7475 | nmod_mat_clear (FLINTN); |
---|
[49660c] | 7476 | #endif |
---|
[2537fa0] | 7477 | result.append (bufF (y-eval,y)); |
---|
[11bf82] | 7478 | return result; |
---|
| 7479 | } |
---|
[49660c] | 7480 | #ifdef HAVE_FLINT |
---|
[f659855] | 7481 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 7482 | nmod_mat_clear (FLINTN); |
---|
[49660c] | 7483 | #endif |
---|
[11bf82] | 7484 | return Union (result, henselLiftAndLatticeRecombi (bufF, bufUniFactors, |
---|
[617dbc] | 7485 | alpha, degs, symmetric, |
---|
[2537fa0] | 7486 | eval |
---|
[11bf82] | 7487 | ) |
---|
| 7488 | ); |
---|
| 7489 | } |
---|
| 7490 | |
---|
| 7491 | if (l < liftBound) |
---|
| 7492 | { |
---|
| 7493 | if (alpha.level() == 1) |
---|
| 7494 | { |
---|
| 7495 | result=increasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
[49660c] | 7496 | #ifdef HAVE_FLINT |
---|
[2537fa0] | 7497 | FLINTN, eval |
---|
[49660c] | 7498 | #else |
---|
[2537fa0] | 7499 | NTLN, eval |
---|
[49660c] | 7500 | #endif |
---|
[11bf82] | 7501 | ); |
---|
| 7502 | } |
---|
| 7503 | else |
---|
| 7504 | { |
---|
| 7505 | if (reduceFq2Fp) |
---|
| 7506 | { |
---|
| 7507 | result=increasePrecisionFq2Fp (F, bufUniFactors, oldL, l, d, bounds, |
---|
[49660c] | 7508 | #ifdef HAVE_FLINT |
---|
[2537fa0] | 7509 | bufQ, FLINTN, alpha, eval |
---|
[49660c] | 7510 | #else |
---|
[2537fa0] | 7511 | bufQ, NTLN, alpha, eval |
---|
[49660c] | 7512 | #endif |
---|
[11bf82] | 7513 | ); |
---|
| 7514 | } |
---|
| 7515 | else |
---|
| 7516 | { |
---|
| 7517 | result=increasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
[2537fa0] | 7518 | NTLNe, eval |
---|
[11bf82] | 7519 | ); |
---|
| 7520 | } |
---|
| 7521 | } |
---|
| 7522 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 7523 | { |
---|
[49660c] | 7524 | #ifdef HAVE_FLINT |
---|
| 7525 | if (result.length()== nmod_mat_ncols (FLINTN)) |
---|
| 7526 | { |
---|
| 7527 | nmod_mat_clear (FLINTN); |
---|
| 7528 | #else |
---|
[c1b9927] | 7529 | if (result.length()== NTLN.NumCols()) |
---|
[11bf82] | 7530 | { |
---|
[49660c] | 7531 | #endif |
---|
[11bf82] | 7532 | delete [] bounds; |
---|
| 7533 | result= Union (result, smallFactors); |
---|
| 7534 | return result; |
---|
| 7535 | } |
---|
| 7536 | } |
---|
| 7537 | else |
---|
| 7538 | { |
---|
[c1b9927] | 7539 | if (result.length()== NTLNe.NumCols()) |
---|
[11bf82] | 7540 | { |
---|
| 7541 | delete [] bounds; |
---|
| 7542 | result= Union (result, smallFactors); |
---|
| 7543 | return result; |
---|
| 7544 | } |
---|
| 7545 | } |
---|
| 7546 | |
---|
| 7547 | if (result.isEmpty()) |
---|
| 7548 | { |
---|
| 7549 | if (alpha.level() == 1) |
---|
| 7550 | result= furtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
[49660c] | 7551 | #ifdef HAVE_FLINT |
---|
| 7552 | liftBound,d,bounds,FLINTN, |
---|
| 7553 | #else |
---|
[11bf82] | 7554 | liftBound, d, bounds, NTLN, |
---|
[49660c] | 7555 | #endif |
---|
[2537fa0] | 7556 | diophant, M, Pi, bufQ, eval |
---|
[11bf82] | 7557 | ); |
---|
| 7558 | else |
---|
| 7559 | { |
---|
| 7560 | if (reduceFq2Fp) |
---|
| 7561 | result= furtherLiftingAndIncreasePrecisionFq2Fp (F,bufUniFactors, l, |
---|
| 7562 | liftBound, d, bounds, |
---|
[49660c] | 7563 | #ifdef HAVE_FLINT |
---|
| 7564 | FLINTN, diophant, M, |
---|
| 7565 | #else |
---|
[11bf82] | 7566 | NTLN, diophant, M, |
---|
[49660c] | 7567 | #endif |
---|
[2537fa0] | 7568 | Pi, bufQ, alpha, eval |
---|
[11bf82] | 7569 | ); |
---|
| 7570 | else |
---|
| 7571 | result= furtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
| 7572 | liftBound, d, bounds, |
---|
| 7573 | NTLNe, diophant, M, |
---|
[2537fa0] | 7574 | Pi, bufQ, eval |
---|
[11bf82] | 7575 | ); |
---|
| 7576 | } |
---|
| 7577 | |
---|
| 7578 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 7579 | { |
---|
[49660c] | 7580 | #ifdef HAVE_FLINT |
---|
| 7581 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
| 7582 | { |
---|
| 7583 | nmod_mat_clear (FLINTN); |
---|
| 7584 | #else |
---|
[c1b9927] | 7585 | if (result.length() == NTLN.NumCols()) |
---|
[11bf82] | 7586 | { |
---|
[49660c] | 7587 | #endif |
---|
[11bf82] | 7588 | delete [] bounds; |
---|
| 7589 | result= Union (result, smallFactors); |
---|
| 7590 | return result; |
---|
| 7591 | } |
---|
| 7592 | } |
---|
| 7593 | else |
---|
| 7594 | { |
---|
[c1b9927] | 7595 | if (result.length() == NTLNe.NumCols()) |
---|
[11bf82] | 7596 | { |
---|
| 7597 | delete [] bounds; |
---|
| 7598 | result= Union (result, smallFactors); |
---|
| 7599 | return result; |
---|
| 7600 | } |
---|
| 7601 | } |
---|
| 7602 | } |
---|
| 7603 | } |
---|
| 7604 | |
---|
| 7605 | DEBOUTLN (cerr, "lattice recombination failed"); |
---|
| 7606 | |
---|
| 7607 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 7608 | degs.intersect (bufDegs); |
---|
| 7609 | degs.refine(); |
---|
| 7610 | |
---|
| 7611 | delete [] bounds; |
---|
[542864] | 7612 | bounds= computeBounds (F, d, isIrreducible); |
---|
[49660c] | 7613 | #ifdef HAVE_FLINT |
---|
[f659855] | 7614 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
| 7615 | nmod_mat_clear (FLINTN); |
---|
[49660c] | 7616 | #endif |
---|
[542864] | 7617 | if (isIrreducible) |
---|
| 7618 | { |
---|
| 7619 | delete [] bounds; |
---|
| 7620 | result= Union (result, smallFactors); |
---|
[2537fa0] | 7621 | result.append (F (y-eval,y)); |
---|
[542864] | 7622 | return result; |
---|
| 7623 | } |
---|
[11bf82] | 7624 | minBound= bounds[0]; |
---|
| 7625 | for (int i= 1; i < d; i++) |
---|
| 7626 | { |
---|
| 7627 | if (bounds[i] != 0) |
---|
| 7628 | minBound= tmin (minBound, bounds[i]); |
---|
| 7629 | } |
---|
| 7630 | |
---|
| 7631 | if (minBound > 16 || result.length() == 0) |
---|
| 7632 | { |
---|
| 7633 | result= Union (result, smallFactors); |
---|
[894604] | 7634 | CanonicalForm MODl= power (y, degree (F) + 1); |
---|
[11bf82] | 7635 | delete [] bounds; |
---|
[2537fa0] | 7636 | return Union (result, factorRecombination (bufUniFactors, F, MODl, degs, |
---|
| 7637 | eval, 1, bufUniFactors.length()/2 |
---|
[11bf82] | 7638 | ) |
---|
| 7639 | ); |
---|
| 7640 | } |
---|
| 7641 | else |
---|
| 7642 | { |
---|
| 7643 | result= Union (result, smallFactors); |
---|
| 7644 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
| 7645 | i.getItem()= mod (i.getItem(), y); |
---|
| 7646 | delete [] bounds; |
---|
| 7647 | return Union (result, henselLiftAndLatticeRecombi (F, bufUniFactors, alpha, |
---|
[2537fa0] | 7648 | degs,symmetric, eval |
---|
[11bf82] | 7649 | ) |
---|
| 7650 | ); |
---|
| 7651 | } |
---|
| 7652 | } |
---|
[03c742] | 7653 | #endif |
---|
[11bf82] | 7654 | |
---|
[3023cd] | 7655 | #ifdef HAVE_NTL // findMinPoly |
---|
[11bf82] | 7656 | ExtensionInfo |
---|
| 7657 | init4ext (const ExtensionInfo& info, const CanonicalForm& evaluation, |
---|
| 7658 | int& degMipo |
---|
| 7659 | ) |
---|
| 7660 | { |
---|
| 7661 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
| 7662 | Variable alpha= info.getAlpha(); |
---|
| 7663 | if (GF) |
---|
| 7664 | { |
---|
| 7665 | degMipo= getGFDegree(); |
---|
| 7666 | CanonicalForm GFMipo= gf_mipo; |
---|
| 7667 | setCharacteristic (getCharacteristic()); |
---|
| 7668 | GFMipo.mapinto(); |
---|
| 7669 | alpha= rootOf (GFMipo); |
---|
| 7670 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 7671 | } |
---|
| 7672 | else |
---|
| 7673 | { |
---|
| 7674 | alpha= info.getAlpha(); |
---|
| 7675 | degMipo= degree (getMipo (alpha)); |
---|
| 7676 | } |
---|
| 7677 | |
---|
| 7678 | Variable gamma; |
---|
| 7679 | CanonicalForm primElemAlpha, imPrimElemAlpha; |
---|
| 7680 | if ((!GF && evaluation != alpha) || (GF && evaluation != getGFGenerator())) |
---|
| 7681 | { |
---|
| 7682 | CanonicalForm bufEvaluation; |
---|
| 7683 | if (GF) |
---|
| 7684 | { |
---|
| 7685 | setCharacteristic (getCharacteristic()); |
---|
| 7686 | bufEvaluation= GF2FalphaRep (evaluation, alpha); |
---|
| 7687 | } |
---|
| 7688 | else |
---|
| 7689 | bufEvaluation= evaluation; |
---|
| 7690 | CanonicalForm mipo= findMinPoly (bufEvaluation, alpha); |
---|
| 7691 | gamma= rootOf (mipo); |
---|
| 7692 | Variable V_buf; |
---|
[ac8e1a] | 7693 | bool fail= false; |
---|
[11bf82] | 7694 | primElemAlpha= primitiveElement (alpha, V_buf, fail); |
---|
| 7695 | imPrimElemAlpha= map (primElemAlpha, alpha, bufEvaluation, gamma); |
---|
| 7696 | |
---|
| 7697 | if (GF) |
---|
| 7698 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
| 7699 | } |
---|
| 7700 | else |
---|
| 7701 | gamma= alpha; |
---|
| 7702 | ExtensionInfo info2= ExtensionInfo (alpha, gamma, primElemAlpha, |
---|
| 7703 | imPrimElemAlpha, 1, info.getGFName(), true |
---|
| 7704 | ); |
---|
| 7705 | |
---|
| 7706 | return info2; |
---|
| 7707 | } |
---|
[3023cd] | 7708 | #endif |
---|
[11bf82] | 7709 | |
---|
[3ecc88f] | 7710 | #ifdef HAVE_NTL // extSieveSmallFactors,... |
---|
[11bf82] | 7711 | CFList |
---|
| 7712 | extHenselLiftAndLatticeRecombi(const CanonicalForm& G, const CFList& uniFactors, |
---|
| 7713 | const ExtensionInfo& extInfo, const |
---|
| 7714 | DegreePattern& degPat, const CanonicalForm& eval |
---|
| 7715 | ) |
---|
| 7716 | { |
---|
| 7717 | CanonicalForm evaluation= eval; |
---|
| 7718 | ExtensionInfo info= extInfo; |
---|
| 7719 | Variable alpha; |
---|
| 7720 | DegreePattern degs= degPat; |
---|
| 7721 | CanonicalForm F= G; |
---|
| 7722 | Variable x= Variable (1); |
---|
| 7723 | Variable y= F.mvar(); |
---|
| 7724 | CFList bufUniFactors= uniFactors; |
---|
| 7725 | |
---|
| 7726 | |
---|
| 7727 | int degMipo; |
---|
| 7728 | ExtensionInfo info2= init4ext (info, evaluation, degMipo); |
---|
| 7729 | |
---|
| 7730 | CFList source, dest; |
---|
| 7731 | CanonicalForm LCF= LC (F, 1); |
---|
| 7732 | |
---|
| 7733 | int d; |
---|
[542864] | 7734 | bool isIrreducible= false; |
---|
| 7735 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
| 7736 | if (isIrreducible) |
---|
| 7737 | { |
---|
| 7738 | delete [] bounds; |
---|
[773d28] | 7739 | CFList source, dest; |
---|
| 7740 | CanonicalForm tmp= G (y - evaluation, y); |
---|
| 7741 | tmp= mapDown (tmp, info, source, dest); |
---|
| 7742 | return CFList (tmp); |
---|
[542864] | 7743 | } |
---|
[11bf82] | 7744 | int minBound= bounds[0]; |
---|
| 7745 | for (int i= 1; i < d; i++) |
---|
| 7746 | { |
---|
| 7747 | if (bounds[i] != 0) |
---|
| 7748 | minBound= tmin (minBound, bounds[i]); |
---|
| 7749 | } |
---|
| 7750 | |
---|
| 7751 | |
---|
| 7752 | CFArray Pi; |
---|
| 7753 | CFList diophant; |
---|
| 7754 | int liftBound= tmax ((2*totaldegree (F) - 1)/degMipo + 1, degree (F) + 1 + |
---|
| 7755 | degree (LC (F, 1))); |
---|
| 7756 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
| 7757 | |
---|
| 7758 | CFList smallFactors; |
---|
| 7759 | CanonicalForm H; |
---|
[773d28] | 7760 | bool success= false; |
---|
[11bf82] | 7761 | smallFactors= extSieveSmallFactors (F, bufUniFactors, degs, H, diophant, Pi, |
---|
| 7762 | M, success, minBound + 1, evaluation, info |
---|
| 7763 | ); |
---|
| 7764 | |
---|
| 7765 | if (smallFactors.length() > 0) |
---|
| 7766 | { |
---|
| 7767 | if (smallFactors.length() == 1) |
---|
| 7768 | { |
---|
| 7769 | if (smallFactors.getFirst() == F) |
---|
| 7770 | { |
---|
| 7771 | delete [] bounds; |
---|
| 7772 | CFList source, dest; |
---|
| 7773 | CanonicalForm tmp= G (y - evaluation, y); |
---|
| 7774 | tmp= mapDown (tmp, info, source, dest); |
---|
| 7775 | return CFList (tmp); |
---|
| 7776 | } |
---|
| 7777 | } |
---|
| 7778 | if (degs.getLength() <= 1) |
---|
| 7779 | { |
---|
| 7780 | delete [] bounds; |
---|
| 7781 | return smallFactors; |
---|
| 7782 | } |
---|
| 7783 | } |
---|
| 7784 | |
---|
| 7785 | int index; |
---|
[38ffb7] | 7786 | CanonicalForm tmp1, tmp2; |
---|
[11bf82] | 7787 | for (CFListIterator i= smallFactors; i.hasItem(); i++) |
---|
| 7788 | { |
---|
| 7789 | index= 1; |
---|
| 7790 | tmp1= mod (i.getItem(), y - evaluation); |
---|
| 7791 | tmp1 /= Lc (tmp1); |
---|
| 7792 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
| 7793 | { |
---|
| 7794 | tmp2= mod (j.getItem(), y); |
---|
| 7795 | tmp2 /= Lc (tmp2); |
---|
| 7796 | if (tmp1 == tmp2) |
---|
| 7797 | { |
---|
| 7798 | index++; |
---|
| 7799 | j.remove(index); |
---|
| 7800 | break; |
---|
| 7801 | } |
---|
| 7802 | } |
---|
| 7803 | } |
---|
| 7804 | |
---|
| 7805 | if (bufUniFactors.isEmpty()) |
---|
| 7806 | { |
---|
| 7807 | delete [] bounds; |
---|
| 7808 | return smallFactors; |
---|
| 7809 | } |
---|
| 7810 | |
---|
| 7811 | if (success) |
---|
| 7812 | { |
---|
[24119a4] | 7813 | F= H/Lc(H); |
---|
[11bf82] | 7814 | delete [] bounds; |
---|
[542864] | 7815 | bounds= computeBounds (F, d, isIrreducible); |
---|
| 7816 | if (isIrreducible) |
---|
| 7817 | { |
---|
| 7818 | delete [] bounds; |
---|
| 7819 | CFList source, dest; |
---|
| 7820 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 7821 | tmp= mapDown (tmp, info, source, dest); |
---|
| 7822 | smallFactors.append (tmp); |
---|
| 7823 | return smallFactors; |
---|
| 7824 | } |
---|
[11bf82] | 7825 | LCF= LC (F, 1); |
---|
| 7826 | |
---|
| 7827 | minBound= bounds[0]; |
---|
| 7828 | for (int i= 1; i < d; i++) |
---|
| 7829 | { |
---|
| 7830 | if (bounds[i] != 0) |
---|
| 7831 | minBound= tmin (minBound, bounds[i]); |
---|
| 7832 | } |
---|
| 7833 | Pi= CFArray(); |
---|
| 7834 | diophant= CFList(); |
---|
| 7835 | liftBound=tmax ((2*totaldegree (F) - 1)/degMipo + 1, degree (F) + 1 + |
---|
| 7836 | degree (LC (F, 1))); |
---|
| 7837 | M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
| 7838 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 7839 | degs.intersect (bufDegs); |
---|
| 7840 | degs.refine(); |
---|
| 7841 | if (degs.getLength() <= 1) |
---|
| 7842 | { |
---|
| 7843 | delete [] bounds; |
---|
| 7844 | CFList source, dest; |
---|
| 7845 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 7846 | tmp= mapDown (tmp, info, source, dest); |
---|
| 7847 | smallFactors.append (tmp); |
---|
| 7848 | return smallFactors; |
---|
| 7849 | } |
---|
| 7850 | } |
---|
| 7851 | |
---|
| 7852 | bufUniFactors.insert (LCF); |
---|
| 7853 | int l= 1; |
---|
| 7854 | |
---|
[7c4341] | 7855 | #ifdef HAVE_FLINT |
---|
| 7856 | nmod_mat_t FLINTN; |
---|
| 7857 | nmod_mat_init (FLINTN, bufUniFactors.length()-1, bufUniFactors.length()-1, |
---|
| 7858 | getCharacteristic()); |
---|
| 7859 | for (long i= bufUniFactors.length()-2; i >= 0; i--) |
---|
| 7860 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
| 7861 | #else |
---|
[bffe62d] | 7862 | if (fac_NTL_char != getCharacteristic()) |
---|
| 7863 | { |
---|
| 7864 | fac_NTL_char= getCharacteristic(); |
---|
| 7865 | zz_p::init (getCharacteristic()); |
---|
| 7866 | } |
---|
[11bf82] | 7867 | zz_pX NTLMipo; |
---|
| 7868 | mat_zz_p NTLN; |
---|
| 7869 | |
---|
| 7870 | ident (NTLN, bufUniFactors.length() - 1); |
---|
[7c4341] | 7871 | #endif |
---|
[11bf82] | 7872 | bool irreducible= false; |
---|
| 7873 | CFArray bufQ= CFArray (bufUniFactors.length() - 1); |
---|
| 7874 | |
---|
| 7875 | int oldL; |
---|
[2d35fe] | 7876 | TIMING_START (fac_fq_till_reduced); |
---|
[11bf82] | 7877 | if (success) |
---|
| 7878 | { |
---|
| 7879 | int start= 0; |
---|
[7c4341] | 7880 | #ifdef HAVE_FLINT |
---|
| 7881 | oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound, start, |
---|
| 7882 | bufUniFactors, FLINTN, diophant,M, Pi, bufQ, |
---|
| 7883 | irreducible, evaluation, info2, source, dest |
---|
| 7884 | ); |
---|
| 7885 | #else |
---|
[11bf82] | 7886 | oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound, start, |
---|
| 7887 | bufUniFactors, NTLN, diophant, M, Pi, bufQ, |
---|
| 7888 | irreducible, evaluation, info2, source, dest |
---|
| 7889 | ); |
---|
[7c4341] | 7890 | #endif |
---|
[11bf82] | 7891 | } |
---|
| 7892 | else |
---|
| 7893 | { |
---|
[7c4341] | 7894 | #ifdef HAVE_FLINT |
---|
| 7895 | oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound, |
---|
| 7896 | minBound+1, bufUniFactors, FLINTN, diophant, |
---|
| 7897 | M, Pi, bufQ, irreducible, evaluation, info2, |
---|
| 7898 | source, dest |
---|
| 7899 | ); |
---|
| 7900 | #else |
---|
[11bf82] | 7901 | oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound, |
---|
| 7902 | minBound + 1, bufUniFactors, NTLN, diophant, |
---|
| 7903 | M, Pi, bufQ, irreducible, evaluation, info2, |
---|
| 7904 | source, dest |
---|
| 7905 | ); |
---|
[7c4341] | 7906 | #endif |
---|
[11bf82] | 7907 | } |
---|
[2d35fe] | 7908 | TIMING_END_AND_PRINT (fac_fq_till_reduced, |
---|
| 7909 | "time to compute a reduced lattice: "); |
---|
[11bf82] | 7910 | |
---|
| 7911 | bufUniFactors.removeFirst(); |
---|
| 7912 | if (oldL > liftBound) |
---|
| 7913 | { |
---|
[7c4341] | 7914 | #ifdef HAVE_FLINT |
---|
| 7915 | nmod_mat_clear (FLINTN); |
---|
| 7916 | #endif |
---|
[11bf82] | 7917 | delete [] bounds; |
---|
| 7918 | return Union (smallFactors, extFactorRecombination |
---|
| 7919 | (bufUniFactors, F, |
---|
[894604] | 7920 | power (y, degree (F) + 1),info, |
---|
[11bf82] | 7921 | degs, evaluation, 1, bufUniFactors.length()/2 |
---|
| 7922 | ) |
---|
| 7923 | ); |
---|
| 7924 | } |
---|
| 7925 | |
---|
| 7926 | l= oldL; |
---|
| 7927 | if (irreducible) |
---|
| 7928 | { |
---|
[7c4341] | 7929 | #ifdef HAVE_FLINT |
---|
| 7930 | nmod_mat_clear (FLINTN); |
---|
| 7931 | #endif |
---|
[11bf82] | 7932 | delete [] bounds; |
---|
| 7933 | CFList source, dest; |
---|
| 7934 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 7935 | tmp= mapDown (tmp, info, source, dest); |
---|
| 7936 | return Union (CFList (tmp), smallFactors); |
---|
| 7937 | } |
---|
| 7938 | |
---|
| 7939 | CanonicalForm yToL= power (y,l); |
---|
| 7940 | |
---|
| 7941 | CFList result; |
---|
| 7942 | if (l >= degree (F) + 1) |
---|
| 7943 | { |
---|
| 7944 | int * factorsFoundIndex; |
---|
| 7945 | |
---|
[7c4341] | 7946 | #ifdef HAVE_FLINT |
---|
| 7947 | factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
| 7948 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
| 7949 | #else |
---|
[11bf82] | 7950 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 7951 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
[7c4341] | 7952 | #endif |
---|
[11bf82] | 7953 | factorsFoundIndex[i]= 0; |
---|
| 7954 | |
---|
| 7955 | int factorsFound= 0; |
---|
| 7956 | CanonicalForm bufF= F; |
---|
| 7957 | |
---|
[7c4341] | 7958 | #ifdef HAVE_FLINT |
---|
| 7959 | extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
| 7960 | factorsFound, factorsFoundIndex, FLINTN, false, info, |
---|
| 7961 | evaluation |
---|
| 7962 | ); |
---|
| 7963 | |
---|
| 7964 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
| 7965 | { |
---|
| 7966 | nmod_mat_clear (FLINTN); |
---|
| 7967 | #else |
---|
[11bf82] | 7968 | extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
| 7969 | factorsFound, factorsFoundIndex, NTLN, false, info, |
---|
| 7970 | evaluation |
---|
| 7971 | ); |
---|
| 7972 | |
---|
| 7973 | if (result.length() == NTLN.NumCols()) |
---|
| 7974 | { |
---|
[7c4341] | 7975 | #endif |
---|
[11bf82] | 7976 | delete [] factorsFoundIndex; |
---|
| 7977 | delete [] bounds; |
---|
| 7978 | return Union (result, smallFactors); |
---|
| 7979 | } |
---|
| 7980 | |
---|
| 7981 | delete [] factorsFoundIndex; |
---|
| 7982 | } |
---|
| 7983 | if (l >= liftBound) |
---|
| 7984 | { |
---|
| 7985 | int * factorsFoundIndex; |
---|
[7c4341] | 7986 | #ifdef HAVE_FLINT |
---|
| 7987 | factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
| 7988 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
| 7989 | #else |
---|
[38ffb7] | 7990 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
| 7991 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
[7c4341] | 7992 | #endif |
---|
[38ffb7] | 7993 | factorsFoundIndex[i]= 0; |
---|
[11bf82] | 7994 | CanonicalForm bufF= F; |
---|
| 7995 | int factorsFound= 0; |
---|
| 7996 | |
---|
[7c4341] | 7997 | #ifdef HAVE_FLINT |
---|
| 7998 | extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
| 7999 | factorsFound, factorsFoundIndex, FLINTN, false, |
---|
| 8000 | info, evaluation |
---|
| 8001 | ); |
---|
| 8002 | |
---|
| 8003 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
| 8004 | { |
---|
| 8005 | nmod_mat_clear (FLINTN); |
---|
| 8006 | #else |
---|
[894604] | 8007 | extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
| 8008 | factorsFound, factorsFoundIndex, NTLN, false, |
---|
[11bf82] | 8009 | info, evaluation |
---|
| 8010 | ); |
---|
| 8011 | |
---|
| 8012 | if (result.length() == NTLN.NumCols()) |
---|
| 8013 | { |
---|
[7c4341] | 8014 | #endif |
---|
[11bf82] | 8015 | delete [] factorsFoundIndex; |
---|
| 8016 | delete [] bounds; |
---|
| 8017 | return Union (result, smallFactors); |
---|
| 8018 | } |
---|
| 8019 | delete [] factorsFoundIndex; |
---|
| 8020 | } |
---|
| 8021 | |
---|
| 8022 | result= CFList(); |
---|
| 8023 | bool beenInThres= false; |
---|
| 8024 | int thres= 100; |
---|
[7c4341] | 8025 | #ifdef HAVE_FLINT |
---|
| 8026 | if (l <= thres && bufUniFactors.length() > nmod_mat_ncols (FLINTN)) |
---|
| 8027 | { |
---|
| 8028 | refineAndRestartLift (F, FLINTN, 2*totaldegree (F)-1, l, bufUniFactors, M, Pi, |
---|
| 8029 | diophant |
---|
| 8030 | ); |
---|
| 8031 | #else |
---|
[11bf82] | 8032 | if (l <= thres && bufUniFactors.length() > NTLN.NumCols()) |
---|
| 8033 | { |
---|
| 8034 | refineAndRestartLift (F, NTLN, 2*totaldegree (F)-1, l, bufUniFactors, M, Pi, |
---|
| 8035 | diophant |
---|
| 8036 | ); |
---|
[7c4341] | 8037 | #endif |
---|
[11bf82] | 8038 | beenInThres= true; |
---|
| 8039 | } |
---|
| 8040 | |
---|
| 8041 | |
---|
| 8042 | CanonicalForm bufF= F; |
---|
| 8043 | int factorsFound= 0; |
---|
| 8044 | |
---|
[7c4341] | 8045 | #ifdef HAVE_FLINT |
---|
| 8046 | result= extEarlyReconstructionAndLifting (F, FLINTN, bufF, bufUniFactors, l, |
---|
| 8047 | factorsFound, beenInThres, M, Pi, |
---|
| 8048 | diophant, info, evaluation |
---|
| 8049 | ); |
---|
| 8050 | |
---|
| 8051 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
| 8052 | { |
---|
| 8053 | nmod_mat_clear (FLINTN); |
---|
| 8054 | #else |
---|
[11bf82] | 8055 | result= extEarlyReconstructionAndLifting (F, NTLN, bufF, bufUniFactors, l, |
---|
| 8056 | factorsFound, beenInThres, M, Pi, |
---|
| 8057 | diophant, info, evaluation |
---|
| 8058 | ); |
---|
| 8059 | |
---|
| 8060 | if (result.length() == NTLN.NumCols()) |
---|
| 8061 | { |
---|
[7c4341] | 8062 | #endif |
---|
[11bf82] | 8063 | delete [] bounds; |
---|
| 8064 | return Union (result, smallFactors); |
---|
| 8065 | } |
---|
| 8066 | |
---|
| 8067 | if (result.length() > 0) |
---|
| 8068 | { |
---|
| 8069 | if (beenInThres) |
---|
| 8070 | { |
---|
| 8071 | int index; |
---|
| 8072 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
| 8073 | { |
---|
| 8074 | index= 1; |
---|
| 8075 | tmp1= mod (i.getItem(), y-evaluation); |
---|
| 8076 | tmp1 /= Lc (tmp1); |
---|
| 8077 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
| 8078 | { |
---|
| 8079 | tmp2= mod (j.getItem(), y); |
---|
| 8080 | tmp2 /= Lc (tmp2); |
---|
| 8081 | if (tmp1 == tmp2) |
---|
| 8082 | { |
---|
| 8083 | index++; |
---|
| 8084 | j.remove(index); |
---|
| 8085 | break; |
---|
| 8086 | } |
---|
| 8087 | } |
---|
| 8088 | } |
---|
| 8089 | } |
---|
| 8090 | else |
---|
| 8091 | { |
---|
[7c4341] | 8092 | #ifdef HAVE_FLINT |
---|
| 8093 | int * zeroOne= extractZeroOneVecs (FLINTN); |
---|
| 8094 | #else |
---|
[11bf82] | 8095 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
[7c4341] | 8096 | #endif |
---|
[11bf82] | 8097 | CFList bufBufUniFactors= bufUniFactors; |
---|
[38ffb7] | 8098 | CFListIterator iter, iter2; |
---|
| 8099 | CanonicalForm buf; |
---|
| 8100 | CFList factorsConsidered; |
---|
[7c4341] | 8101 | #ifdef HAVE_FLINT |
---|
| 8102 | for (int i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
| 8103 | #else |
---|
[11bf82] | 8104 | for (int i= 0; i < NTLN.NumCols(); i++) |
---|
[7c4341] | 8105 | #endif |
---|
[11bf82] | 8106 | { |
---|
| 8107 | if (zeroOne [i] == 0) |
---|
| 8108 | continue; |
---|
[38ffb7] | 8109 | iter= bufUniFactors; |
---|
| 8110 | buf= 1; |
---|
| 8111 | factorsConsidered= CFList(); |
---|
[7c4341] | 8112 | #ifdef HAVE_FLINT |
---|
| 8113 | for (int j= 0; j < nmod_mat_nrows (FLINTN); j++, iter++) |
---|
| 8114 | { |
---|
| 8115 | if (!(nmod_mat_entry (FLINTN, j, i) == 0)) |
---|
| 8116 | #else |
---|
[11bf82] | 8117 | for (int j= 0; j < NTLN.NumRows(); j++, iter++) |
---|
| 8118 | { |
---|
| 8119 | if (!IsZero (NTLN (j + 1,i + 1))) |
---|
[7c4341] | 8120 | #endif |
---|
[11bf82] | 8121 | { |
---|
| 8122 | factorsConsidered.append (iter.getItem()); |
---|
| 8123 | buf *= mod (iter.getItem(), y); |
---|
| 8124 | } |
---|
| 8125 | } |
---|
| 8126 | buf /= Lc (buf); |
---|
[38ffb7] | 8127 | for (iter2= result; iter2.hasItem(); iter2++) |
---|
[11bf82] | 8128 | { |
---|
| 8129 | CanonicalForm tmp= mod (iter2.getItem(), y - evaluation); |
---|
| 8130 | tmp /= Lc (tmp); |
---|
| 8131 | if (tmp == buf) |
---|
| 8132 | { |
---|
| 8133 | bufBufUniFactors= Difference (bufBufUniFactors, factorsConsidered); |
---|
| 8134 | break; |
---|
| 8135 | } |
---|
| 8136 | } |
---|
| 8137 | } |
---|
| 8138 | bufUniFactors= bufBufUniFactors; |
---|
| 8139 | delete [] zeroOne; |
---|
| 8140 | } |
---|
| 8141 | |
---|
| 8142 | int oldNumCols; |
---|
| 8143 | CFList resultBufF; |
---|
| 8144 | irreducible= false; |
---|
| 8145 | |
---|
[7c4341] | 8146 | #ifdef HAVE_FLINT //TODO |
---|
| 8147 | oldNumCols= nmod_mat_ncols (FLINTN); |
---|
| 8148 | resultBufF= extIncreasePrecision (bufF, bufUniFactors, factorsFound, |
---|
| 8149 | oldNumCols, oldL, evaluation, info2, |
---|
| 8150 | source, dest, l |
---|
| 8151 | ); |
---|
| 8152 | nmod_mat_clear (FLINTN); |
---|
| 8153 | #else |
---|
[11bf82] | 8154 | oldNumCols= NTLN.NumCols(); |
---|
| 8155 | resultBufF= extIncreasePrecision (bufF, bufUniFactors, factorsFound, |
---|
| 8156 | oldNumCols, oldL, evaluation, info2, |
---|
| 8157 | source, dest, l |
---|
| 8158 | ); |
---|
[7c4341] | 8159 | #endif |
---|
[11bf82] | 8160 | if (bufUniFactors.isEmpty() || degree (bufF) <= 0) |
---|
| 8161 | { |
---|
| 8162 | delete [] bounds; |
---|
| 8163 | result= Union (resultBufF, result); |
---|
| 8164 | return Union (result, smallFactors); |
---|
| 8165 | } |
---|
| 8166 | |
---|
| 8167 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
| 8168 | i.getItem()= mod (i.getItem(), y); |
---|
| 8169 | |
---|
| 8170 | delete [] bounds; |
---|
| 8171 | CFList bufResult; |
---|
| 8172 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 8173 | degs.intersect (bufDegs); |
---|
| 8174 | degs.refine(); |
---|
| 8175 | result= Union (result, smallFactors); |
---|
| 8176 | if (degs.getLength() == 1 || bufUniFactors.length() == 1) |
---|
| 8177 | { |
---|
[c49e6f] | 8178 | CFList source, dest; |
---|
| 8179 | CanonicalForm tmp= bufF (y - evaluation, y); |
---|
| 8180 | tmp= mapDown (tmp, info, source, dest); |
---|
| 8181 | result.append (tmp); |
---|
[11bf82] | 8182 | return result; |
---|
| 8183 | } |
---|
| 8184 | return Union (result, extHenselLiftAndLatticeRecombi (bufF, bufUniFactors, |
---|
| 8185 | info, degs, evaluation |
---|
| 8186 | ) |
---|
| 8187 | ); |
---|
| 8188 | } |
---|
| 8189 | |
---|
| 8190 | if (l/degMipo < liftBound) |
---|
| 8191 | { |
---|
[7c4341] | 8192 | #ifdef HAVE_FLINT |
---|
| 8193 | result=extIncreasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
| 8194 | FLINTN, evaluation, info2, source, dest |
---|
| 8195 | ); |
---|
| 8196 | |
---|
| 8197 | if (result.length()== nmod_mat_ncols (FLINTN)) |
---|
| 8198 | { |
---|
| 8199 | nmod_mat_clear (FLINTN); |
---|
| 8200 | #else |
---|
[11bf82] | 8201 | result=extIncreasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
| 8202 | NTLN, evaluation, info2, source, dest |
---|
| 8203 | ); |
---|
| 8204 | |
---|
[c1b9927] | 8205 | if (result.length()== NTLN.NumCols()) |
---|
[11bf82] | 8206 | { |
---|
[7c4341] | 8207 | #endif |
---|
[11bf82] | 8208 | delete [] bounds; |
---|
| 8209 | result= Union (result, smallFactors); |
---|
| 8210 | return result; |
---|
| 8211 | } |
---|
| 8212 | |
---|
| 8213 | if (result.isEmpty()) |
---|
| 8214 | { |
---|
[7c4341] | 8215 | #ifdef HAVE_FLINT |
---|
| 8216 | result= extFurtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
| 8217 | liftBound, d,bounds,FLINTN, |
---|
| 8218 | diophant, M, Pi, bufQ, |
---|
| 8219 | evaluation, info2, source, |
---|
| 8220 | dest |
---|
| 8221 | ); |
---|
| 8222 | if (result.length()== nmod_mat_ncols (FLINTN)) |
---|
| 8223 | { |
---|
| 8224 | nmod_mat_clear (FLINTN); |
---|
| 8225 | #else |
---|
[11bf82] | 8226 | result= extFurtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
| 8227 | liftBound, d, bounds, NTLN, |
---|
| 8228 | diophant, M, Pi, bufQ, |
---|
| 8229 | evaluation, info2, source, |
---|
| 8230 | dest |
---|
| 8231 | ); |
---|
[c1b9927] | 8232 | if (result.length()== NTLN.NumCols()) |
---|
[11bf82] | 8233 | { |
---|
[7c4341] | 8234 | #endif |
---|
[11bf82] | 8235 | delete [] bounds; |
---|
| 8236 | result= Union (result, smallFactors); |
---|
| 8237 | return result; |
---|
| 8238 | } |
---|
| 8239 | } |
---|
| 8240 | } |
---|
| 8241 | |
---|
[7c4341] | 8242 | #ifdef HAVE_FLINT |
---|
| 8243 | nmod_mat_clear (FLINTN); |
---|
| 8244 | #endif |
---|
| 8245 | |
---|
[11bf82] | 8246 | DEBOUTLN (cerr, "lattice recombination failed"); |
---|
| 8247 | |
---|
| 8248 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
| 8249 | degs.intersect (bufDegs); |
---|
| 8250 | degs.refine(); |
---|
| 8251 | |
---|
| 8252 | delete [] bounds; |
---|
[542864] | 8253 | bounds= computeBounds (F, d, isIrreducible); |
---|
| 8254 | if (isIrreducible) |
---|
| 8255 | { |
---|
| 8256 | delete [] bounds; |
---|
| 8257 | CFList source, dest; |
---|
| 8258 | CanonicalForm tmp= F (y - evaluation, y); |
---|
| 8259 | tmp= mapDown (tmp, info, source, dest); |
---|
| 8260 | smallFactors.append (tmp); |
---|
| 8261 | result= Union (result, smallFactors); |
---|
| 8262 | return result; |
---|
| 8263 | } |
---|
[11bf82] | 8264 | minBound= bounds[0]; |
---|
| 8265 | for (int i= 1; i < d; i++) |
---|
| 8266 | { |
---|
| 8267 | if (bounds[i] != 0) |
---|
| 8268 | minBound= tmin (minBound, bounds[i]); |
---|
| 8269 | } |
---|
| 8270 | |
---|
| 8271 | if (minBound > 16 || result.length() == 0) |
---|
| 8272 | { |
---|
| 8273 | result= Union (result, smallFactors); |
---|
[894604] | 8274 | CanonicalForm MODl= power (y, degree (F) + 1); |
---|
[11bf82] | 8275 | delete [] bounds; |
---|
| 8276 | return Union (result, extFactorRecombination (bufUniFactors, F, MODl, info, |
---|
| 8277 | degs, evaluation, 1, |
---|
| 8278 | bufUniFactors.length()/2 |
---|
| 8279 | ) |
---|
| 8280 | ); |
---|
| 8281 | } |
---|
| 8282 | else |
---|
| 8283 | { |
---|
| 8284 | result= Union (result, smallFactors); |
---|
| 8285 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
| 8286 | i.getItem()= mod (i.getItem(), y); |
---|
| 8287 | delete [] bounds; |
---|
| 8288 | return Union (result, extHenselLiftAndLatticeRecombi (F, bufUniFactors, |
---|
| 8289 | info, degs, evaluation |
---|
| 8290 | ) |
---|
| 8291 | ); |
---|
| 8292 | } |
---|
| 8293 | } |
---|
[03c742] | 8294 | #endif |
---|
[11bf82] | 8295 | |
---|
[03c742] | 8296 | #ifdef HAVE_NTL // henselLiftAndLatticeRecombi |
---|
[11bf82] | 8297 | CFList |
---|
| 8298 | extBiFactorize (const CanonicalForm& F, const ExtensionInfo& info); |
---|
| 8299 | |
---|
| 8300 | /// bivariate factorization over finite fields as decribed in "Factoring |
---|
| 8301 | /// multivariate polynomials over a finite field" by L Bernardin. |
---|
| 8302 | CFList |
---|
| 8303 | biFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
| 8304 | { |
---|
| 8305 | if (F.inCoeffDomain()) |
---|
| 8306 | return CFList(F); |
---|
| 8307 | |
---|
| 8308 | CanonicalForm A= F; |
---|
| 8309 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
| 8310 | |
---|
| 8311 | Variable alpha= info.getAlpha(); |
---|
| 8312 | Variable beta= info.getBeta(); |
---|
| 8313 | CanonicalForm gamma= info.getGamma(); |
---|
| 8314 | CanonicalForm delta= info.getDelta(); |
---|
| 8315 | int k= info.getGFDegree(); |
---|
| 8316 | bool extension= info.isInExtension(); |
---|
| 8317 | if (A.isUnivariate()) |
---|
| 8318 | { |
---|
| 8319 | if (extension == false) |
---|
| 8320 | return uniFactorizer (F, alpha, GF); |
---|
| 8321 | else |
---|
| 8322 | { |
---|
| 8323 | CFList source, dest; |
---|
| 8324 | A= mapDown (A, info, source, dest); |
---|
| 8325 | return uniFactorizer (A, beta, GF); |
---|
| 8326 | } |
---|
| 8327 | } |
---|
| 8328 | |
---|
| 8329 | CFMap N; |
---|
| 8330 | A= compress (A, N); |
---|
| 8331 | Variable y= A.mvar(); |
---|
| 8332 | |
---|
| 8333 | if (y.level() > 2) return CFList (F); |
---|
| 8334 | Variable x= Variable (1); |
---|
| 8335 | |
---|
| 8336 | //remove and factorize content |
---|
| 8337 | CanonicalForm contentAx= content (A, x); |
---|
| 8338 | CanonicalForm contentAy= content (A); |
---|
| 8339 | |
---|
| 8340 | A= A/(contentAx*contentAy); |
---|
| 8341 | CFList contentAxFactors, contentAyFactors; |
---|
| 8342 | |
---|
| 8343 | if (!extension) |
---|
| 8344 | { |
---|
| 8345 | contentAxFactors= uniFactorizer (contentAx, alpha, GF); |
---|
| 8346 | contentAyFactors= uniFactorizer (contentAy, alpha, GF); |
---|
| 8347 | } |
---|
| 8348 | |
---|
| 8349 | //trivial case |
---|
| 8350 | CFList factors; |
---|
| 8351 | if (A.inCoeffDomain()) |
---|
| 8352 | { |
---|
| 8353 | append (factors, contentAxFactors); |
---|
| 8354 | append (factors, contentAyFactors); |
---|
| 8355 | decompress (factors, N); |
---|
| 8356 | return factors; |
---|
| 8357 | } |
---|
| 8358 | else if (A.isUnivariate()) |
---|
| 8359 | { |
---|
| 8360 | factors= uniFactorizer (A, alpha, GF); |
---|
| 8361 | append (factors, contentAxFactors); |
---|
| 8362 | append (factors, contentAyFactors); |
---|
| 8363 | decompress (factors, N); |
---|
| 8364 | return factors; |
---|
| 8365 | } |
---|
| 8366 | |
---|
[fea494] | 8367 | |
---|
[0777ea] | 8368 | //check trivial case |
---|
[fea494] | 8369 | if (degree (A) == 1 || degree (A, 1) == 1 || |
---|
[86aa4d5] | 8370 | (size (A) == 2 && igcd (degree (A), degree (A,1))==1)) |
---|
[0777ea] | 8371 | { |
---|
| 8372 | factors.append (A); |
---|
| 8373 | |
---|
| 8374 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
| 8375 | false, false, N); |
---|
| 8376 | |
---|
[0facdc] | 8377 | if (!extension) |
---|
| 8378 | normalize (factors); |
---|
[0777ea] | 8379 | return factors; |
---|
| 8380 | } |
---|
| 8381 | |
---|
[11bf82] | 8382 | // check derivatives |
---|
| 8383 | bool derivXZero= false; |
---|
| 8384 | CanonicalForm derivX= deriv (A, x); |
---|
| 8385 | CanonicalForm gcdDerivX; |
---|
| 8386 | if (derivX.isZero()) |
---|
| 8387 | derivXZero= true; |
---|
| 8388 | else |
---|
| 8389 | { |
---|
| 8390 | gcdDerivX= gcd (A, derivX); |
---|
| 8391 | if (degree (gcdDerivX) > 0) |
---|
| 8392 | { |
---|
| 8393 | CanonicalForm g= A/gcdDerivX; |
---|
| 8394 | CFList factorsG= |
---|
| 8395 | Union (biFactorize (g, info), biFactorize (gcdDerivX, info)); |
---|
| 8396 | append (factorsG, contentAxFactors); |
---|
| 8397 | append (factorsG, contentAyFactors); |
---|
| 8398 | decompress (factorsG, N); |
---|
[0facdc] | 8399 | if (!extension) |
---|
| 8400 | normalize (factorsG); |
---|
[11bf82] | 8401 | return factorsG; |
---|
| 8402 | } |
---|
| 8403 | } |
---|
| 8404 | bool derivYZero= false; |
---|
| 8405 | CanonicalForm derivY= deriv (A, y); |
---|
| 8406 | CanonicalForm gcdDerivY; |
---|
| 8407 | if (derivY.isZero()) |
---|
| 8408 | derivYZero= true; |
---|
| 8409 | else |
---|
| 8410 | { |
---|
| 8411 | gcdDerivY= gcd (A, derivY); |
---|
| 8412 | if (degree (gcdDerivY) > 0) |
---|
| 8413 | { |
---|
| 8414 | CanonicalForm g= A/gcdDerivY; |
---|
| 8415 | CFList factorsG= |
---|
| 8416 | Union (biFactorize (g, info), biFactorize (gcdDerivY, info)); |
---|
| 8417 | append (factorsG, contentAxFactors); |
---|
| 8418 | append (factorsG, contentAyFactors); |
---|
| 8419 | decompress (factorsG, N); |
---|
[0facdc] | 8420 | if (!extension) |
---|
| 8421 | normalize (factorsG); |
---|
[11bf82] | 8422 | return factorsG; |
---|
| 8423 | } |
---|
| 8424 | } |
---|
| 8425 | //main variable is chosen s.t. the degree in x is minimal |
---|
| 8426 | bool swap= false; |
---|
| 8427 | if ((degree (A) > degree (A, x)) || derivXZero) |
---|
| 8428 | { |
---|
| 8429 | if (!derivYZero) |
---|
| 8430 | { |
---|
| 8431 | A= swapvar (A, y, x); |
---|
| 8432 | swap= derivXZero; |
---|
| 8433 | derivXZero= derivYZero; |
---|
| 8434 | derivYZero= swap; |
---|
| 8435 | swap= true; |
---|
| 8436 | } |
---|
| 8437 | } |
---|
| 8438 | |
---|
[542864] | 8439 | int boundsLength; |
---|
| 8440 | bool isIrreducible= false; |
---|
| 8441 | int * bounds= computeBounds (A, boundsLength, isIrreducible); |
---|
| 8442 | if (isIrreducible) |
---|
| 8443 | { |
---|
| 8444 | delete [] bounds; |
---|
| 8445 | factors.append (A); |
---|
| 8446 | |
---|
| 8447 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
| 8448 | swap, false, N); |
---|
| 8449 | |
---|
[0facdc] | 8450 | if (!extension) |
---|
| 8451 | normalize (factors); |
---|
[542864] | 8452 | return factors; |
---|
| 8453 | } |
---|
| 8454 | |
---|
[93e7364] | 8455 | int minBound= bounds[0]; |
---|
| 8456 | for (int i= 1; i < boundsLength; i++) |
---|
| 8457 | { |
---|
| 8458 | if (bounds[i] != 0) |
---|
| 8459 | minBound= tmin (minBound, bounds[i]); |
---|
| 8460 | } |
---|
| 8461 | |
---|
| 8462 | int boundsLength2; |
---|
| 8463 | int * bounds2= computeBoundsWrtDiffMainvar (A, boundsLength2, isIrreducible); |
---|
| 8464 | int minBound2= bounds2[0]; |
---|
| 8465 | for (int i= 1; i < boundsLength2; i++) |
---|
| 8466 | { |
---|
| 8467 | if (bounds2[i] != 0) |
---|
| 8468 | minBound2= tmin (minBound2, bounds2[i]); |
---|
| 8469 | } |
---|
| 8470 | |
---|
| 8471 | |
---|
[11bf82] | 8472 | bool fail= false; |
---|
[617dbc] | 8473 | CanonicalForm Aeval, evaluation, bufAeval, bufEvaluation, buf, tmp; |
---|
[11bf82] | 8474 | CFList uniFactors, list, bufUniFactors; |
---|
| 8475 | DegreePattern degs; |
---|
| 8476 | DegreePattern bufDegs; |
---|
| 8477 | |
---|
| 8478 | bool fail2= false; |
---|
| 8479 | CanonicalForm Aeval2, evaluation2, bufAeval2, bufEvaluation2; |
---|
| 8480 | CFList bufUniFactors2, list2, uniFactors2; |
---|
| 8481 | DegreePattern degs2; |
---|
| 8482 | DegreePattern bufDegs2; |
---|
| 8483 | bool swap2= false; |
---|
| 8484 | |
---|
| 8485 | // several univariate factorizations to obtain more information about the |
---|
| 8486 | // degree pattern therefore usually less combinations have to be tried during |
---|
| 8487 | // the recombination process |
---|
| 8488 | int factorNums= 3; |
---|
| 8489 | int subCheck1= substituteCheck (A, x); |
---|
| 8490 | int subCheck2= substituteCheck (A, y); |
---|
[617dbc] | 8491 | bool symmetric= false; |
---|
[2d35fe] | 8492 | |
---|
| 8493 | TIMING_START (fac_fq_uni_total); |
---|
[11bf82] | 8494 | for (int i= 0; i < factorNums; i++) |
---|
| 8495 | { |
---|
| 8496 | bufAeval= A; |
---|
[0851b0] | 8497 | TIMING_START (fac_fq_bi_evaluation); |
---|
[11bf82] | 8498 | bufEvaluation= evalPoint (A, bufAeval, alpha, list, GF, fail); |
---|
[0851b0] | 8499 | TIMING_END_AND_PRINT (fac_fq_bi_evaluation, "time to find eval point: "); |
---|
[3ef0a0] | 8500 | if (!derivXZero && !fail2 && !symmetric) |
---|
[11bf82] | 8501 | { |
---|
[617dbc] | 8502 | if (i == 0) |
---|
| 8503 | { |
---|
| 8504 | buf= swapvar (A, x, y); |
---|
| 8505 | symmetric= (A/Lc (A) == buf/Lc (buf)); |
---|
| 8506 | } |
---|
[11bf82] | 8507 | bufAeval2= buf; |
---|
[0851b0] | 8508 | TIMING_START (fac_fq_bi_evaluation); |
---|
[11bf82] | 8509 | bufEvaluation2= evalPoint (buf, bufAeval2, alpha, list2, GF, fail2); |
---|
[0851b0] | 8510 | TIMING_END_AND_PRINT (fac_fq_bi_evaluation, |
---|
| 8511 | "time to find eval point wrt y: "); |
---|
[11bf82] | 8512 | } |
---|
| 8513 | // first try to change main variable if there is no valid evaluation point |
---|
| 8514 | if (fail && (i == 0)) |
---|
| 8515 | { |
---|
[3ef0a0] | 8516 | if (!derivXZero && !fail2 && !symmetric) |
---|
[11bf82] | 8517 | { |
---|
| 8518 | bufEvaluation= bufEvaluation2; |
---|
| 8519 | int dummy= subCheck2; |
---|
| 8520 | subCheck2= subCheck1; |
---|
| 8521 | subCheck1= dummy; |
---|
[617dbc] | 8522 | tmp= A; |
---|
[11bf82] | 8523 | A= buf; |
---|
[617dbc] | 8524 | buf= tmp; |
---|
[11bf82] | 8525 | bufAeval= bufAeval2; |
---|
| 8526 | swap2= true; |
---|
| 8527 | fail= false; |
---|
| 8528 | } |
---|
| 8529 | else |
---|
| 8530 | fail= true; |
---|
| 8531 | } |
---|
| 8532 | |
---|
| 8533 | // if there is no valid evaluation point pass to a field extension |
---|
| 8534 | if (fail && (i == 0)) |
---|
| 8535 | { |
---|
| 8536 | factors= extBiFactorize (A, info); |
---|
| 8537 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
| 8538 | swap, swap2, N); |
---|
| 8539 | normalize (factors); |
---|
[93e7364] | 8540 | delete [] bounds; |
---|
| 8541 | delete [] bounds2; |
---|
[11bf82] | 8542 | return factors; |
---|
| 8543 | } |
---|
| 8544 | |
---|
| 8545 | // there is at least one valid evaluation point |
---|
| 8546 | // but we do not compute more univariate factorization over an extension |
---|
| 8547 | if (fail && (i != 0)) |
---|
| 8548 | break; |
---|
| 8549 | |
---|
| 8550 | // univariate factorization |
---|
[978ce3] | 8551 | TIMING_START (fac_fq_uni_factorizer); |
---|
[11bf82] | 8552 | bufUniFactors= uniFactorizer (bufAeval, alpha, GF); |
---|
[978ce3] | 8553 | TIMING_END_AND_PRINT (fac_fq_uni_factorizer, |
---|
[0851b0] | 8554 | "time for univariate factorization over Fq: "); |
---|
[806c18] | 8555 | DEBOUTLN (cerr, "Lc (bufAeval)*prod (bufUniFactors)== bufAeval " << |
---|
[f3a82f4] | 8556 | (prod (bufUniFactors)*Lc (bufAeval) == bufAeval)); |
---|
[7bf145] | 8557 | |
---|
[3ef0a0] | 8558 | if (!derivXZero && !fail2 && !symmetric) |
---|
[7bf145] | 8559 | { |
---|
[978ce3] | 8560 | TIMING_START (fac_fq_uni_factorizer); |
---|
[7bf145] | 8561 | bufUniFactors2= uniFactorizer (bufAeval2, alpha, GF); |
---|
[978ce3] | 8562 | TIMING_END_AND_PRINT (fac_fq_uni_factorizer, |
---|
[0851b0] | 8563 | "time for univariate factorization in y over Fq: "); |
---|
[27ab36] | 8564 | DEBOUTLN (cerr, "Lc (bufAeval2)*prod (bufUniFactors2)== bufAeval2 " << |
---|
[f3a82f4] | 8565 | (prod (bufUniFactors2)*Lc (bufAeval2) == bufAeval2)); |
---|
[7bf145] | 8566 | } |
---|
| 8567 | |
---|
[806c18] | 8568 | if (bufUniFactors.length() == 1 || |
---|
[3ef0a0] | 8569 | (!fail2 && !derivXZero && !symmetric && (bufUniFactors2.length() == 1))) |
---|
[7bf145] | 8570 | { |
---|
| 8571 | if (extension) |
---|
| 8572 | { |
---|
| 8573 | CFList source, dest; |
---|
[da984c] | 8574 | appendMapDown (factors, A, info, source, dest); |
---|
[7bf145] | 8575 | } |
---|
[806c18] | 8576 | else |
---|
[7bf145] | 8577 | factors.append (A); |
---|
| 8578 | |
---|
[806c18] | 8579 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
[7bf145] | 8580 | swap, swap2, N); |
---|
| 8581 | |
---|
[0facdc] | 8582 | if (!extension) |
---|
| 8583 | normalize (factors); |
---|
[93e7364] | 8584 | delete [] bounds; |
---|
| 8585 | delete [] bounds2; |
---|
[7bf145] | 8586 | return factors; |
---|
| 8587 | } |
---|
| 8588 | |
---|
[c49e6f] | 8589 | if (i == 0 && !extension) |
---|
[686ce3] | 8590 | { |
---|
[dd8047] | 8591 | if (subCheck1 > 0) |
---|
[686ce3] | 8592 | { |
---|
[dd8047] | 8593 | int subCheck= substituteCheck (bufUniFactors); |
---|
| 8594 | |
---|
| 8595 | if (subCheck > 1 && (subCheck1%subCheck == 0)) |
---|
| 8596 | { |
---|
| 8597 | CanonicalForm bufA= A; |
---|
| 8598 | subst (bufA, bufA, subCheck, x); |
---|
| 8599 | factors= biFactorize (bufA, info); |
---|
| 8600 | reverseSubst (factors, subCheck, x); |
---|
| 8601 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
| 8602 | swap, swap2, N); |
---|
[0facdc] | 8603 | if (!extension) |
---|
| 8604 | normalize (factors); |
---|
[93e7364] | 8605 | delete [] bounds; |
---|
| 8606 | delete [] bounds2; |
---|
[dd8047] | 8607 | return factors; |
---|
| 8608 | } |
---|
[686ce3] | 8609 | } |
---|
| 8610 | |
---|
[3ef0a0] | 8611 | if (!derivXZero && !fail2 && !symmetric && subCheck2 > 0) |
---|
[686ce3] | 8612 | { |
---|
[dd8047] | 8613 | int subCheck= substituteCheck (bufUniFactors2); |
---|
| 8614 | |
---|
| 8615 | if (subCheck > 1 && (subCheck2%subCheck == 0)) |
---|
[686ce3] | 8616 | { |
---|
| 8617 | CanonicalForm bufA= A; |
---|
| 8618 | subst (bufA, bufA, subCheck, y); |
---|
| 8619 | factors= biFactorize (bufA, info); |
---|
[2caede4] | 8620 | reverseSubst (factors, subCheck, y); |
---|
[686ce3] | 8621 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
| 8622 | swap, swap2, N); |
---|
[0facdc] | 8623 | if (!extension) |
---|
| 8624 | normalize (factors); |
---|
[93e7364] | 8625 | delete [] bounds; |
---|
| 8626 | delete [] bounds2; |
---|
[686ce3] | 8627 | return factors; |
---|
| 8628 | } |
---|
| 8629 | } |
---|
| 8630 | } |
---|
| 8631 | |
---|
[806c18] | 8632 | // degree analysis |
---|
| 8633 | bufDegs = DegreePattern (bufUniFactors); |
---|
[3ef0a0] | 8634 | if (!derivXZero && !fail2 && !symmetric) |
---|
[7bf145] | 8635 | bufDegs2= DegreePattern (bufUniFactors2); |
---|
| 8636 | |
---|
[806c18] | 8637 | if (i == 0) |
---|
[7bf145] | 8638 | { |
---|
| 8639 | Aeval= bufAeval; |
---|
| 8640 | evaluation= bufEvaluation; |
---|
| 8641 | uniFactors= bufUniFactors; |
---|
| 8642 | degs= bufDegs; |
---|
[3ef0a0] | 8643 | if (!derivXZero && !fail2 && !symmetric) |
---|
[7bf145] | 8644 | { |
---|
| 8645 | Aeval2= bufAeval2; |
---|
| 8646 | evaluation2= bufEvaluation2; |
---|
| 8647 | uniFactors2= bufUniFactors2; |
---|
| 8648 | degs2= bufDegs2; |
---|
| 8649 | } |
---|
| 8650 | } |
---|
[806c18] | 8651 | else |
---|
[7bf145] | 8652 | { |
---|
| 8653 | degs.intersect (bufDegs); |
---|
[3ef0a0] | 8654 | if (!derivXZero && !fail2 && !symmetric) |
---|
[7bf145] | 8655 | { |
---|
| 8656 | degs2.intersect (bufDegs2); |
---|
[806c18] | 8657 | if (bufUniFactors2.length() < uniFactors2.length()) |
---|
| 8658 | { |
---|
[7bf145] | 8659 | uniFactors2= bufUniFactors2; |
---|
| 8660 | Aeval2= bufAeval2; |
---|
| 8661 | evaluation2= bufEvaluation2; |
---|
| 8662 | } |
---|
[806c18] | 8663 | } |
---|
| 8664 | if (bufUniFactors.length() < uniFactors.length()) |
---|
| 8665 | { |
---|
[3af6b6] | 8666 | uniFactors= bufUniFactors; |
---|
| 8667 | Aeval= bufAeval; |
---|
| 8668 | evaluation= bufEvaluation; |
---|
[7bf145] | 8669 | } |
---|
| 8670 | } |
---|
| 8671 | list.append (bufEvaluation); |
---|
[3ef0a0] | 8672 | if (!derivXZero && !fail2 && !symmetric) |
---|
[7bf145] | 8673 | list2.append (bufEvaluation2); |
---|
| 8674 | } |
---|
[2d35fe] | 8675 | TIMING_END_AND_PRINT (fac_fq_uni_total, |
---|
| 8676 | "total time for univariate factorizations: "); |
---|
[806c18] | 8677 | |
---|
[3ef0a0] | 8678 | if (!derivXZero && !fail2 && !symmetric) |
---|
[7bf145] | 8679 | { |
---|
[93e7364] | 8680 | if ((uniFactors.length() > uniFactors2.length() && minBound2 <= minBound)|| |
---|
[806c18] | 8681 | (uniFactors.length() == uniFactors2.length() |
---|
[93e7364] | 8682 | && degs.getLength() > degs2.getLength() && minBound2 <= minBound)) |
---|
[7bf145] | 8683 | { |
---|
| 8684 | degs= degs2; |
---|
| 8685 | uniFactors= uniFactors2; |
---|
| 8686 | evaluation= evaluation2; |
---|
| 8687 | Aeval= Aeval2; |
---|
| 8688 | A= buf; |
---|
| 8689 | swap2= true; |
---|
| 8690 | } |
---|
| 8691 | } |
---|
[806c18] | 8692 | |
---|
| 8693 | if (degs.getLength() == 1) // A is irreducible |
---|
[7bf145] | 8694 | { |
---|
[806c18] | 8695 | if (extension) |
---|
[7bf145] | 8696 | { |
---|
| 8697 | CFList source, dest; |
---|
[11bf82] | 8698 | appendMapDown (factors, A, info, source, dest); |
---|
[7bf145] | 8699 | } |
---|
[806c18] | 8700 | else |
---|
[7bf145] | 8701 | factors.append (A); |
---|
[806c18] | 8702 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
[7bf145] | 8703 | swap, swap2, N); |
---|
[0facdc] | 8704 | if (!extension) |
---|
| 8705 | normalize (factors); |
---|
[93e7364] | 8706 | delete [] bounds; |
---|
| 8707 | delete [] bounds2; |
---|
[7bf145] | 8708 | return factors; |
---|
| 8709 | } |
---|
| 8710 | |
---|
[1a3011e] | 8711 | int liftBound= degree (A, y) + 1; |
---|
[11bf82] | 8712 | |
---|
[542864] | 8713 | if (swap2) |
---|
[11bf82] | 8714 | { |
---|
[93e7364] | 8715 | delete [] bounds; |
---|
| 8716 | bounds= bounds2; |
---|
| 8717 | minBound= minBound2; |
---|
[11bf82] | 8718 | } |
---|
| 8719 | |
---|
[0851b0] | 8720 | TIMING_START (fac_fq_bi_shift_to_zero); |
---|
[3c25c9] | 8721 | A= A (y + evaluation, y); |
---|
[0851b0] | 8722 | TIMING_END_AND_PRINT (fac_fq_bi_shift_to_zero, |
---|
| 8723 | "time to shift eval to zero: "); |
---|
[3c25c9] | 8724 | |
---|
[11bf82] | 8725 | int degMipo= 1; |
---|
| 8726 | if (extension && alpha.level() != 1 && k==1) |
---|
| 8727 | degMipo= degree (getMipo (alpha)); |
---|
[7bf145] | 8728 | |
---|
| 8729 | DEBOUTLN (cerr, "uniFactors= " << uniFactors); |
---|
[11bf82] | 8730 | |
---|
[ac8e1a] | 8731 | if ((GF && !extension) || (GF && extension && k != 1)) |
---|
[11bf82] | 8732 | { |
---|
| 8733 | bool earlySuccess= false; |
---|
| 8734 | CFList earlyFactors; |
---|
[978ce3] | 8735 | TIMING_START (fac_fq_bi_hensel_lift); |
---|
[c1b9927] | 8736 | uniFactors= henselLiftAndEarly |
---|
[7bf145] | 8737 | (A, earlySuccess, earlyFactors, degs, liftBound, |
---|
[806c18] | 8738 | uniFactors, info, evaluation); |
---|
[0851b0] | 8739 | TIMING_END_AND_PRINT (fac_fq_bi_hensel_lift, |
---|
| 8740 | "time for bivariate hensel lifting over Fq: "); |
---|
[11bf82] | 8741 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
[7bf145] | 8742 | |
---|
[11bf82] | 8743 | CanonicalForm MODl= power (y, liftBound); |
---|
| 8744 | |
---|
[0851b0] | 8745 | TIMING_START (fac_fq_bi_factor_recombination); |
---|
[11bf82] | 8746 | if (extension) |
---|
| 8747 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
| 8748 | evaluation, 1, uniFactors.length()/2); |
---|
| 8749 | else |
---|
[2537fa0] | 8750 | factors= factorRecombination (uniFactors, A, MODl, degs, evaluation, 1, |
---|
[11bf82] | 8751 | uniFactors.length()/2); |
---|
[0851b0] | 8752 | TIMING_END_AND_PRINT (fac_fq_bi_factor_recombination, |
---|
| 8753 | "time for naive bivariate factor recombi over Fq: "); |
---|
[11bf82] | 8754 | |
---|
| 8755 | if (earlySuccess) |
---|
| 8756 | factors= Union (earlyFactors, factors); |
---|
| 8757 | else if (!earlySuccess && degs.getLength() == 1) |
---|
| 8758 | factors= earlyFactors; |
---|
| 8759 | } |
---|
| 8760 | else if (degree (A) > 4 && beta.level() == 1 && (2*minBound)/degMipo < 32) |
---|
| 8761 | { |
---|
[978ce3] | 8762 | TIMING_START (fac_fq_bi_hensel_lift); |
---|
[11bf82] | 8763 | if (extension) |
---|
| 8764 | { |
---|
| 8765 | CFList lll= extHenselLiftAndLatticeRecombi (A, uniFactors, info, degs, |
---|
| 8766 | evaluation |
---|
| 8767 | ); |
---|
| 8768 | factors= Union (lll, factors); |
---|
| 8769 | } |
---|
| 8770 | else if (alpha.level() == 1 && !GF) |
---|
| 8771 | { |
---|
[fea494] | 8772 | CFList lll= henselLiftAndLatticeRecombi (A, uniFactors, alpha, degs, |
---|
[617dbc] | 8773 | symmetric, evaluation); |
---|
[11bf82] | 8774 | factors= Union (lll, factors); |
---|
| 8775 | } |
---|
[a54114] | 8776 | else if (!extension && (alpha != x || GF)) |
---|
[11bf82] | 8777 | { |
---|
[617dbc] | 8778 | CFList lll= henselLiftAndLatticeRecombi (A, uniFactors, alpha, degs, |
---|
| 8779 | symmetric, evaluation); |
---|
[11bf82] | 8780 | factors= Union (lll, factors); |
---|
| 8781 | } |
---|
[0851b0] | 8782 | TIMING_END_AND_PRINT (fac_fq_bi_hensel_lift, |
---|
| 8783 | "time to bivar lift and LLL recombi over Fq: "); |
---|
[11bf82] | 8784 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
| 8785 | } |
---|
[806c18] | 8786 | else |
---|
[11bf82] | 8787 | { |
---|
| 8788 | bool earlySuccess= false; |
---|
| 8789 | CFList earlyFactors; |
---|
[978ce3] | 8790 | TIMING_START (fac_fq_bi_hensel_lift); |
---|
[11bf82] | 8791 | uniFactors= henselLiftAndEarly |
---|
| 8792 | (A, earlySuccess, earlyFactors, degs, liftBound, |
---|
| 8793 | uniFactors, info, evaluation); |
---|
[0851b0] | 8794 | TIMING_END_AND_PRINT (fac_fq_bi_hensel_lift, |
---|
| 8795 | "time for bivar hensel lifting over Fq: "); |
---|
[11bf82] | 8796 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
| 8797 | |
---|
| 8798 | CanonicalForm MODl= power (y, liftBound); |
---|
| 8799 | if (!extension) |
---|
| 8800 | { |
---|
[0851b0] | 8801 | TIMING_START (fac_fq_bi_factor_recombination); |
---|
[2537fa0] | 8802 | factors= factorRecombination (uniFactors, A, MODl, degs, evaluation, 1, 3); |
---|
[0851b0] | 8803 | TIMING_END_AND_PRINT (fac_fq_bi_factor_recombination, |
---|
| 8804 | "time for small subset naive recombi over Fq: "); |
---|
[11bf82] | 8805 | |
---|
| 8806 | int oldUniFactorsLength= uniFactors.length(); |
---|
| 8807 | if (degree (A) > 0) |
---|
| 8808 | { |
---|
| 8809 | CFList tmp; |
---|
[0851b0] | 8810 | TIMING_START (fac_fq_bi_hensel_lift); |
---|
[11bf82] | 8811 | if (alpha.level() == 1) |
---|
| 8812 | tmp= increasePrecision (A, uniFactors, 0, uniFactors.length(), 1, |
---|
[2537fa0] | 8813 | liftBound, evaluation |
---|
[11bf82] | 8814 | ); |
---|
| 8815 | else |
---|
| 8816 | { |
---|
| 8817 | if (degree (A) > getCharacteristic()) |
---|
| 8818 | tmp= increasePrecisionFq2Fp (A, uniFactors, 0, uniFactors.length(), |
---|
[2537fa0] | 8819 | 1, alpha, liftBound, evaluation |
---|
[11bf82] | 8820 | ); |
---|
| 8821 | else |
---|
| 8822 | tmp= increasePrecision (A, uniFactors, 0, uniFactors.length(), 1, |
---|
[2537fa0] | 8823 | alpha, liftBound, evaluation |
---|
[11bf82] | 8824 | ); |
---|
| 8825 | } |
---|
[0851b0] | 8826 | TIMING_END_AND_PRINT (fac_fq_bi_hensel_lift, |
---|
| 8827 | "time to increase precision: "); |
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[11bf82] | 8828 | factors= Union (factors, tmp); |
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| 8829 | if (tmp.length() == 0 || (tmp.length() > 0 && uniFactors.length() != 0 |
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| 8830 | && uniFactors.length() != oldUniFactorsLength) |
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| 8831 | ) |
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| 8832 | { |
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| 8833 | DegreePattern bufDegs= DegreePattern (uniFactors); |
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| 8834 | degs.intersect (bufDegs); |
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| 8835 | degs.refine (); |
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| 8836 | factors= Union (factors, factorRecombination (uniFactors, A, MODl, |
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[2537fa0] | 8837 | degs, evaluation, 4, |
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[11bf82] | 8838 | uniFactors.length()/2 |
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| 8839 | ) |
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| 8840 | ); |
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| 8841 | } |
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| 8842 | } |
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| 8843 | } |
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| 8844 | else |
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| 8845 | { |
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| 8846 | if (beta.level() != 1 || k > 1) |
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| 8847 | { |
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| 8848 | if (k > 1) |
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| 8849 | { |
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| 8850 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
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| 8851 | evaluation, 1, uniFactors.length()/2 |
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| 8852 | ); |
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| 8853 | } |
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| 8854 | else |
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| 8855 | { |
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| 8856 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
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| 8857 | evaluation, 1, 3 |
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| 8858 | ); |
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| 8859 | if (degree (A) > 0) |
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| 8860 | { |
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| 8861 | CFList tmp= increasePrecision2 (A, uniFactors, alpha, liftBound); |
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| 8862 | DegreePattern bufDegs= DegreePattern (tmp); |
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| 8863 | degs.intersect (bufDegs); |
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| 8864 | degs.refine (); |
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| 8865 | factors= Union (factors, extFactorRecombination (tmp, A, MODl, info, |
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| 8866 | degs, evaluation, |
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| 8867 | 1, tmp.length()/2 |
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| 8868 | ) |
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| 8869 | ); |
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| 8870 | } |
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| 8871 | } |
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| 8872 | } |
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| 8873 | else |
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| 8874 | { |
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| 8875 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
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| 8876 | evaluation, 1, 3 |
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| 8877 | ); |
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| 8878 | int oldUniFactorsLength= uniFactors.length(); |
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| 8879 | if (degree (A) > 0) |
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| 8880 | { |
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| 8881 | int degMipo; |
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| 8882 | ExtensionInfo info2= init4ext (info, evaluation, degMipo); |
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| 8883 | |
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| 8884 | CFList source, dest; |
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| 8885 | CFList tmp= extIncreasePrecision (A, uniFactors, 0, |
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| 8886 | uniFactors.length(), 1, evaluation, |
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| 8887 | info2, source, dest, liftBound |
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| 8888 | ); |
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| 8889 | factors= Union (factors, tmp); |
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| 8890 | if (tmp.length() == 0 || (tmp.length() > 0 && uniFactors.length() != 0 |
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| 8891 | && uniFactors.length() != oldUniFactorsLength) |
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| 8892 | ) |
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| 8893 | { |
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| 8894 | DegreePattern bufDegs= DegreePattern (uniFactors); |
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| 8895 | degs.intersect (bufDegs); |
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| 8896 | degs.refine (); |
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| 8897 | factors= Union (factors,extFactorRecombination (uniFactors, A, MODl, |
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| 8898 | info, degs, evaluation, |
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| 8899 | 4, uniFactors.length()/2 |
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| 8900 | ) |
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| 8901 | ); |
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| 8902 | } |
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| 8903 | } |
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| 8904 | } |
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| 8905 | } |
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[806c18] | 8906 | |
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[11bf82] | 8907 | if (earlySuccess) |
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| 8908 | factors= Union (earlyFactors, factors); |
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| 8909 | else if (!earlySuccess && degs.getLength() == 1) |
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| 8910 | factors= earlyFactors; |
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| 8911 | } |
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[93e7364] | 8912 | |
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| 8913 | if (!swap2) |
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| 8914 | delete [] bounds2; |
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[11bf82] | 8915 | delete [] bounds; |
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[7bf145] | 8916 | |
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[806c18] | 8917 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
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[7bf145] | 8918 | swap, swap2, N); |
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[0facdc] | 8919 | if (!extension) |
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| 8920 | normalize (factors); |
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[7bf145] | 8921 | |
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| 8922 | return factors; |
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| 8923 | } |
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[03c742] | 8924 | #endif |
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[7bf145] | 8925 | |
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[b28747] | 8926 | #ifdef HAVE_NTL // biFactorize |
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[806c18] | 8927 | CFList |
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| 8928 | extBiFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
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[7bf145] | 8929 | { |
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[806c18] | 8930 | |
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[7bf145] | 8931 | CanonicalForm A= F; |
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| 8932 | Variable alpha= info.getAlpha(); |
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| 8933 | Variable beta= info.getBeta(); |
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| 8934 | int k= info.getGFDegree(); |
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| 8935 | char cGFName= info.getGFName(); |
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| 8936 | CanonicalForm delta= info.getDelta(); |
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| 8937 | |
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| 8938 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
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[806c18] | 8939 | Variable x= Variable (1); |
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[7bf145] | 8940 | CFList factors; |
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| 8941 | if (!GF && alpha == x) // we are in F_p |
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| 8942 | { |
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[806c18] | 8943 | bool extension= true; |
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[7bf145] | 8944 | int p= getCharacteristic(); |
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[806c18] | 8945 | if (p*p < (1<<16)) // pass to GF if possible |
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| 8946 | { |
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[7bf145] | 8947 | setCharacteristic (getCharacteristic(), 2, 'Z'); |
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| 8948 | A= A.mapinto(); |
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[11bf82] | 8949 | ExtensionInfo info2= ExtensionInfo (extension); |
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| 8950 | factors= biFactorize (A, info2); |
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[7bf145] | 8951 | |
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[0a7d0ca] | 8952 | CanonicalForm mipo= gf_mipo; |
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[7bf145] | 8953 | setCharacteristic (getCharacteristic()); |
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[0a7d0ca] | 8954 | Variable vBuf= rootOf (mipo.mapinto()); |
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[806c18] | 8955 | for (CFListIterator j= factors; j.hasItem(); j++) |
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| 8956 | j.getItem()= GF2FalphaRep (j.getItem(), vBuf); |
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[03f640] | 8957 | prune (vBuf); |
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[7bf145] | 8958 | } |
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[806c18] | 8959 | else // not able to pass to GF, pass to F_p(\alpha) |
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| 8960 | { |
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[a54114] | 8961 | CanonicalForm mipo= randomIrredpoly (2, x); |
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[7bf145] | 8962 | Variable v= rootOf (mipo); |
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[11bf82] | 8963 | ExtensionInfo info2= ExtensionInfo (v); |
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| 8964 | factors= biFactorize (A, info2); |
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[03f640] | 8965 | prune (v); |
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[806c18] | 8966 | } |
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[7bf145] | 8967 | return factors; |
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| 8968 | } |
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| 8969 | else if (!GF && (alpha != x)) // we are in F_p(\alpha) |
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[806c18] | 8970 | { |
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[7bf145] | 8971 | if (k == 1) // need factorization over F_p |
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| 8972 | { |
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| 8973 | int extDeg= degree (getMipo (alpha)); |
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[806c18] | 8974 | extDeg++; |
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[eed963] | 8975 | CanonicalForm mipo= randomIrredpoly (extDeg, x); |
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[7bf145] | 8976 | Variable v= rootOf (mipo); |
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[11bf82] | 8977 | ExtensionInfo info2= ExtensionInfo (v); |
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| 8978 | factors= biFactorize (A, info2); |
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[03f640] | 8979 | prune (v); |
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[7bf145] | 8980 | } |
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[806c18] | 8981 | else |
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[7bf145] | 8982 | { |
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[a54114] | 8983 | if (beta == x) |
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[7bf145] | 8984 | { |
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[11bf82] | 8985 | Variable v= chooseExtension (alpha, beta, k); |
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[7bf145] | 8986 | CanonicalForm primElem, imPrimElem; |
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| 8987 | bool primFail= false; |
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| 8988 | Variable vBuf; |
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| 8989 | primElem= primitiveElement (alpha, vBuf, primFail); |
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| 8990 | ASSERT (!primFail, "failure in integer factorizer"); |
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| 8991 | if (primFail) |
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| 8992 | ; //ERROR |
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| 8993 | else |
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[618da5] | 8994 | imPrimElem= mapPrimElem (primElem, alpha, v); |
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[7bf145] | 8995 | |
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| 8996 | CFList source, dest; |
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[806c18] | 8997 | CanonicalForm bufA= mapUp (A, alpha, v, primElem, imPrimElem, |
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[7bf145] | 8998 | source, dest); |
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[11bf82] | 8999 | ExtensionInfo info2= ExtensionInfo (v, alpha, imPrimElem, primElem); |
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| 9000 | factors= biFactorize (bufA, info2); |
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[03f640] | 9001 | prune (v); |
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[7bf145] | 9002 | } |
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| 9003 | else |
---|
| 9004 | { |
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[11bf82] | 9005 | Variable v= chooseExtension (alpha, beta, k); |
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[7bf145] | 9006 | CanonicalForm primElem, imPrimElem; |
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| 9007 | bool primFail= false; |
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| 9008 | Variable vBuf; |
---|
| 9009 | ASSERT (!primFail, "failure in integer factorizer"); |
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| 9010 | if (primFail) |
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| 9011 | ; //ERROR |
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| 9012 | else |
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[618da5] | 9013 | imPrimElem= mapPrimElem (delta, beta, v); |
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[7bf145] | 9014 | |
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| 9015 | CFList source, dest; |
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| 9016 | CanonicalForm bufA= mapDown (A, info, source, dest); |
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| 9017 | source= CFList(); |
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| 9018 | dest= CFList(); |
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| 9019 | bufA= mapUp (bufA, beta, v, delta, imPrimElem, source, dest); |
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[11bf82] | 9020 | ExtensionInfo info2= ExtensionInfo (v, beta, imPrimElem, delta); |
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| 9021 | factors= biFactorize (bufA, info2); |
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[03f640] | 9022 | prune (v); |
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[7bf145] | 9023 | } |
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| 9024 | } |
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| 9025 | return factors; |
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| 9026 | } |
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| 9027 | else // we are in GF (p^k) |
---|
[806c18] | 9028 | { |
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[7bf145] | 9029 | int p= getCharacteristic(); |
---|
| 9030 | int extensionDeg= getGFDegree(); |
---|
| 9031 | bool extension= true; |
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| 9032 | if (k == 1) // need factorization over F_p |
---|
| 9033 | { |
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| 9034 | extensionDeg++; |
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[806c18] | 9035 | if (ipower (p, extensionDeg) < (1<<16)) |
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| 9036 | // pass to GF(p^k+1) |
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[7bf145] | 9037 | { |
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[0a7d0ca] | 9038 | CanonicalForm mipo= gf_mipo; |
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[7bf145] | 9039 | setCharacteristic (p); |
---|
[0a7d0ca] | 9040 | Variable vBuf= rootOf (mipo.mapinto()); |
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[806c18] | 9041 | A= GF2FalphaRep (A, vBuf); |
---|
| 9042 | setCharacteristic (p, extensionDeg, 'Z'); |
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[11bf82] | 9043 | ExtensionInfo info2= ExtensionInfo (extension); |
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| 9044 | factors= biFactorize (A.mapinto(), info2); |
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[03f640] | 9045 | prune (vBuf); |
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[7bf145] | 9046 | } |
---|
| 9047 | else // not able to pass to another GF, pass to F_p(\alpha) |
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[806c18] | 9048 | { |
---|
[0a7d0ca] | 9049 | CanonicalForm mipo= gf_mipo; |
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[806c18] | 9050 | setCharacteristic (p); |
---|
[0a7d0ca] | 9051 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
[806c18] | 9052 | A= GF2FalphaRep (A, vBuf); |
---|
[11bf82] | 9053 | Variable v= chooseExtension (vBuf, beta, k); |
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| 9054 | ExtensionInfo info2= ExtensionInfo (v, extension); |
---|
| 9055 | factors= biFactorize (A, info2); |
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[03f640] | 9056 | prune (vBuf); |
---|
[7bf145] | 9057 | } |
---|
| 9058 | } |
---|
| 9059 | else // need factorization over GF (p^k) |
---|
| 9060 | { |
---|
[806c18] | 9061 | if (ipower (p, 2*extensionDeg) < (1<<16)) |
---|
[7bf145] | 9062 | // pass to GF (p^2k) |
---|
[806c18] | 9063 | { |
---|
| 9064 | setCharacteristic (p, 2*extensionDeg, 'Z'); |
---|
[11bf82] | 9065 | ExtensionInfo info2= ExtensionInfo (k, cGFName, extension); |
---|
| 9066 | factors= biFactorize (GFMapUp (A, extensionDeg), info2); |
---|
[806c18] | 9067 | setCharacteristic (p, extensionDeg, cGFName); |
---|
[7bf145] | 9068 | } |
---|
| 9069 | else // not able to pass to GF (p^2k), pass to F_p (\alpha) |
---|
[806c18] | 9070 | { |
---|
[0a7d0ca] | 9071 | CanonicalForm mipo= gf_mipo; |
---|
[806c18] | 9072 | setCharacteristic (p); |
---|
[0a7d0ca] | 9073 | Variable v1= rootOf (mipo.mapinto()); |
---|
[806c18] | 9074 | A= GF2FalphaRep (A, v1); |
---|
[11bf82] | 9075 | Variable v2= chooseExtension (v1, v1, k); |
---|
[7bf145] | 9076 | CanonicalForm primElem, imPrimElem; |
---|
| 9077 | bool primFail= false; |
---|
| 9078 | Variable vBuf; |
---|
| 9079 | primElem= primitiveElement (v1, vBuf, primFail); |
---|
| 9080 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
| 9081 | if (primFail) |
---|
| 9082 | ; //ERROR |
---|
| 9083 | else |
---|
[618da5] | 9084 | imPrimElem= mapPrimElem (primElem, v1, v2); |
---|
[7bf145] | 9085 | |
---|
| 9086 | CFList source, dest; |
---|
[806c18] | 9087 | CanonicalForm bufA= mapUp (A, v1, v2, primElem, imPrimElem, |
---|
[7bf145] | 9088 | source, dest); |
---|
[11bf82] | 9089 | ExtensionInfo info2= ExtensionInfo (v2, v1, imPrimElem, primElem); |
---|
| 9090 | factors= biFactorize (bufA, info2); |
---|
[806c18] | 9091 | setCharacteristic (p, k, cGFName); |
---|
| 9092 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
| 9093 | i.getItem()= Falpha2GFRep (i.getItem()); |
---|
[03f640] | 9094 | prune (v1); |
---|
[7bf145] | 9095 | } |
---|
| 9096 | } |
---|
| 9097 | return factors; |
---|
| 9098 | } |
---|
| 9099 | } |
---|
| 9100 | #endif |
---|
[b28747] | 9101 | #endif |
---|