1 | /*****************************************************************************\ |
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2 | * Computer Algebra System SINGULAR |
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3 | \*****************************************************************************/ |
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4 | /** @file facFqBivar.cc |
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5 | * |
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6 | * This file provides functions for factorizing a bivariate polynomial over |
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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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10 | * Factor Recombination is described in "Factoring polynomials over global |
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11 | * fields" by K. Belabas, M. van Hoeij, J. Klueners, A. Steel |
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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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19 | #include "config.h" |
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20 | |
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21 | #include "cf_assert.h" |
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22 | #include "debug.h" |
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23 | #include "timing.h" |
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24 | |
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25 | #include "canonicalform.h" |
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26 | #include "cf_defs.h" |
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27 | #include "cf_map_ext.h" |
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28 | #include "cf_random.h" |
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29 | #include "facHensel.h" |
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30 | #include "facMul.h" |
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31 | #include "cf_map.h" |
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32 | #include "cf_gcd_smallp.h" |
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33 | #include "facFqBivarUtil.h" |
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34 | #include "facFqBivar.h" |
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35 | #include "cfNewtonPolygon.h" |
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36 | #include "algext.h" |
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37 | |
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38 | #ifdef HAVE_NTL |
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39 | #include "NTLconvert.h" |
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40 | |
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41 | #ifdef HAVE_FLINT |
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42 | #include "FLINTconvert.h" |
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43 | #endif |
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44 | |
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45 | TIMING_DEFINE_PRINT(fac_fq_uni_factorizer) |
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46 | TIMING_DEFINE_PRINT(fac_fq_bi_hensel_lift) |
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47 | TIMING_DEFINE_PRINT(fac_fq_bi_factor_recombination) |
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48 | TIMING_DEFINE_PRINT(fac_fq_bi_evaluation) |
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49 | TIMING_DEFINE_PRINT(fac_fq_bi_shift_to_zero) |
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50 | |
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51 | CanonicalForm prodMod0 (const CFList& L, const CanonicalForm& M, const modpk& b) |
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52 | { |
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53 | if (L.isEmpty()) |
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54 | return 1; |
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55 | else if (L.length() == 1) |
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56 | return mod (L.getFirst()(0, 1) , M); |
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57 | else if (L.length() == 2) |
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58 | return mod (mulNTL (L.getFirst()(0, 1),L.getLast()(0, 1), b), M); |
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59 | else |
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60 | { |
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61 | int l= L.length()/2; |
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62 | CFListIterator i= L; |
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63 | CFList tmp1, tmp2; |
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64 | CanonicalForm buf1, buf2; |
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65 | for (int j= 1; j <= l; j++, i++) |
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66 | tmp1.append (i.getItem()); |
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67 | tmp2= Difference (L, tmp1); |
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68 | buf1= prodMod0 (tmp1, M, b); |
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69 | buf2= prodMod0 (tmp2, M, b); |
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70 | return mod (mulNTL (buf1,buf2, b), M); |
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71 | } |
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72 | } |
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73 | |
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74 | CanonicalForm evalPoint (const CanonicalForm& F, CanonicalForm & eval, |
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75 | const Variable& alpha, CFList& list, const bool& GF, |
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76 | bool& fail) |
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77 | { |
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78 | fail= false; |
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79 | Variable x= Variable(2); |
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80 | Variable y= Variable(1); |
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81 | FFRandom genFF; |
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82 | GFRandom genGF; |
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83 | CanonicalForm random, mipo; |
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84 | double bound; |
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85 | int p= getCharacteristic (); |
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86 | if (alpha.level() != 1) |
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87 | { |
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88 | mipo= getMipo (alpha); |
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89 | int d= degree (mipo); |
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90 | bound= ipower (p, d); |
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91 | } |
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92 | else if (GF) |
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93 | { |
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94 | int d= getGFDegree(); |
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95 | bound= ipower (p, d); |
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96 | } |
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97 | else |
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98 | bound= p; |
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99 | |
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100 | random= 0; |
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101 | do |
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102 | { |
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103 | if (list.length() >= bound) |
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104 | { |
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105 | fail= true; |
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106 | break; |
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107 | } |
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108 | if (list.isEmpty()) |
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109 | random= 0; |
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110 | else if (GF) |
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111 | { |
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112 | if (list.length() == 1) |
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113 | random= getGFGenerator(); |
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114 | else |
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115 | random= genGF.generate(); |
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116 | } |
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117 | else if (list.length() < p || alpha.level() == 1) |
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118 | random= genFF.generate(); |
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119 | else if (alpha != x && list.length() >= p) |
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120 | { |
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121 | if (list.length() == p) |
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122 | random= alpha; |
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123 | else |
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124 | { |
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125 | AlgExtRandomF genAlgExt (alpha); |
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126 | random= genAlgExt.generate(); |
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127 | } |
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128 | } |
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129 | if (find (list, random)) continue; |
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130 | eval= F (random, x); |
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131 | if (degree (eval) != degree (F, y)) |
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132 | { //leading coeff vanishes |
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133 | if (!find (list, random)) |
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134 | list.append (random); |
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135 | continue; |
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136 | } |
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137 | if (degree (gcd (deriv (eval, eval.mvar()), eval), eval.mvar()) > 0) |
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138 | { //evaluated polynomial is not squarefree |
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139 | if (!find (list, random)) |
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140 | list.append (random); |
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141 | continue; |
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142 | } |
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143 | } while (find (list, random)); |
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144 | |
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145 | return random; |
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146 | } |
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147 | |
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148 | CFList |
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149 | uniFactorizer (const CanonicalForm& A, const Variable& alpha, const bool& GF) |
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150 | { |
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151 | Variable x= A.mvar(); |
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152 | if (A.inCoeffDomain()) |
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153 | return CFList(); |
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154 | ASSERT (A.isUnivariate(), |
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155 | "univariate polynomial expected or constant expected"); |
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156 | CFFList factorsA; |
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157 | if (fac_NTL_char != getCharacteristic()) |
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158 | { |
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159 | fac_NTL_char= getCharacteristic(); |
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160 | zz_p::init (getCharacteristic()); |
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161 | } |
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162 | if (GF) |
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163 | { |
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164 | int k= getGFDegree(); |
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165 | char cGFName= gf_name; |
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166 | CanonicalForm mipo= gf_mipo; |
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167 | setCharacteristic (getCharacteristic()); |
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168 | Variable beta= rootOf (mipo.mapinto()); |
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169 | CanonicalForm buf= GF2FalphaRep (A, beta); |
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170 | if (getCharacteristic() > 2) |
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171 | { |
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172 | zz_pX NTLMipo= convertFacCF2NTLzzpX (mipo.mapinto()); |
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173 | zz_pE::init (NTLMipo); |
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174 | zz_pEX NTLA= convertFacCF2NTLzz_pEX (buf, NTLMipo); |
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175 | MakeMonic (NTLA); |
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176 | vec_pair_zz_pEX_long NTLFactorsA= CanZass (NTLA); |
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177 | zz_pE multi= to_zz_pE (1); |
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178 | factorsA= convertNTLvec_pair_zzpEX_long2FacCFFList (NTLFactorsA, multi, |
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179 | x, beta); |
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180 | } |
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181 | else |
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182 | { |
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183 | GF2X NTLMipo= convertFacCF2NTLGF2X (mipo.mapinto()); |
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184 | GF2E::init (NTLMipo); |
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185 | GF2EX NTLA= convertFacCF2NTLGF2EX (buf, NTLMipo); |
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186 | MakeMonic (NTLA); |
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187 | vec_pair_GF2EX_long NTLFactorsA= CanZass (NTLA); |
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188 | GF2E multi= to_GF2E (1); |
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189 | factorsA= convertNTLvec_pair_GF2EX_long2FacCFFList (NTLFactorsA, multi, |
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190 | x, beta); |
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191 | } |
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192 | setCharacteristic (getCharacteristic(), k, cGFName); |
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193 | for (CFFListIterator i= factorsA; i.hasItem(); i++) |
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194 | { |
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195 | buf= i.getItem().factor(); |
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196 | buf= Falpha2GFRep (buf); |
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197 | i.getItem()= CFFactor (buf, i.getItem().exp()); |
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198 | } |
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199 | } |
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200 | else if (alpha.level() != 1) |
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201 | { |
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202 | if (getCharacteristic() > 2) |
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203 | { |
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204 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
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205 | zz_pE::init (NTLMipo); |
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206 | zz_pEX NTLA= convertFacCF2NTLzz_pEX (A, NTLMipo); |
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207 | MakeMonic (NTLA); |
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208 | vec_pair_zz_pEX_long NTLFactorsA= CanZass (NTLA); |
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209 | zz_pE multi= to_zz_pE (1); |
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210 | factorsA= convertNTLvec_pair_zzpEX_long2FacCFFList (NTLFactorsA, multi, |
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211 | x, alpha); |
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212 | } |
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213 | else |
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214 | { |
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215 | GF2X NTLMipo= convertFacCF2NTLGF2X (getMipo (alpha)); |
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216 | GF2E::init (NTLMipo); |
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217 | GF2EX NTLA= convertFacCF2NTLGF2EX (A, NTLMipo); |
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218 | MakeMonic (NTLA); |
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219 | vec_pair_GF2EX_long NTLFactorsA= CanZass (NTLA); |
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220 | GF2E multi= to_GF2E (1); |
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221 | factorsA= convertNTLvec_pair_GF2EX_long2FacCFFList (NTLFactorsA, multi, |
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222 | x, alpha); |
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223 | } |
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224 | } |
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225 | else |
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226 | { |
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227 | #ifdef HAVE_FLINT |
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228 | nmod_poly_t FLINTA; |
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229 | convertFacCF2nmod_poly_t (FLINTA, A); |
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230 | nmod_poly_factor_t result; |
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231 | nmod_poly_factor_init (result); |
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232 | mp_limb_t leadingCoeff= nmod_poly_factor (result, FLINTA); |
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233 | factorsA= convertFLINTnmod_poly_factor2FacCFFList (result, leadingCoeff, x); |
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234 | if (factorsA.getFirst().factor().inCoeffDomain()) |
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235 | factorsA.removeFirst(); |
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236 | nmod_poly_factor_clear (result); |
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237 | nmod_poly_clear (FLINTA); |
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238 | #else |
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239 | if (getCharacteristic() > 2) |
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240 | { |
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241 | zz_pX NTLA= convertFacCF2NTLzzpX (A); |
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242 | MakeMonic (NTLA); |
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243 | vec_pair_zz_pX_long NTLFactorsA= CanZass (NTLA); |
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244 | zz_p multi= to_zz_p (1); |
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245 | factorsA= convertNTLvec_pair_zzpX_long2FacCFFList (NTLFactorsA, multi, |
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246 | x); |
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247 | } |
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248 | else |
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249 | { |
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250 | GF2X NTLA= convertFacCF2NTLGF2X (A); |
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251 | vec_pair_GF2X_long NTLFactorsA= CanZass (NTLA); |
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252 | GF2 multi= to_GF2 (1); |
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253 | factorsA= convertNTLvec_pair_GF2X_long2FacCFFList (NTLFactorsA, multi, |
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254 | x); |
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255 | } |
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256 | #endif |
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257 | } |
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258 | CFList uniFactors; |
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259 | for (CFFListIterator i= factorsA; i.hasItem(); i++) |
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260 | uniFactors.append (i.getItem().factor()); |
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261 | return uniFactors; |
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262 | } |
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263 | |
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264 | /// naive factor recombination as decribed in "Factoring |
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265 | /// multivariate polynomials over a finite field" by L Bernardin. |
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266 | CFList |
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267 | extFactorRecombination (CFList& factors, CanonicalForm& F, |
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268 | const CanonicalForm& N, const ExtensionInfo& info, |
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269 | DegreePattern& degs, const CanonicalForm& eval, int s, |
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270 | int thres) |
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271 | { |
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272 | if (factors.length() == 0) |
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273 | { |
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274 | F= 1; |
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275 | return CFList(); |
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276 | } |
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277 | if (F.inCoeffDomain()) |
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278 | return CFList(); |
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279 | |
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280 | Variable alpha= info.getAlpha(); |
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281 | Variable beta= info.getBeta(); |
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282 | CanonicalForm gamma= info.getGamma(); |
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283 | CanonicalForm delta= info.getDelta(); |
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284 | int k= info.getGFDegree(); |
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285 | |
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286 | CanonicalForm M= N; |
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287 | int l= degree (N); |
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288 | Variable y= F.mvar(); |
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289 | Variable x= Variable (1); |
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290 | CFList source, dest; |
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291 | if (degs.getLength() <= 1 || factors.length() == 1) |
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292 | { |
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293 | CFList result= CFList(mapDown (F(y-eval, y), info, source, dest)); |
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294 | F= 1; |
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295 | return result; |
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296 | } |
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297 | |
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298 | DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, M) == F " << |
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299 | (mod (LC (F, 1)*prodMod (factors, M), M)/Lc (mod (LC (F, 1)*prodMod (factors, M), M)) == F/Lc (F))); |
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300 | int degMipoBeta= 1; |
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301 | if (!k && beta.level() != 1) |
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302 | degMipoBeta= degree (getMipo (beta)); |
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303 | |
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304 | CFList T, S, Diff; |
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305 | T= factors; |
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306 | |
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307 | CFList result; |
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308 | CanonicalForm buf, buf2, quot; |
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309 | |
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310 | buf= F; |
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311 | |
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312 | CanonicalForm g, LCBuf= LC (buf, x); |
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313 | int * v= new int [T.length()]; |
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314 | for (int i= 0; i < T.length(); i++) |
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315 | v[i]= 0; |
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316 | |
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317 | CFArray TT; |
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318 | DegreePattern bufDegs1, bufDegs2; |
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319 | bufDegs1= degs; |
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320 | int subsetDeg; |
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321 | TT= copy (factors); |
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322 | bool nosubset= false; |
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323 | bool recombination= false; |
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324 | bool trueFactor= false; |
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325 | CanonicalForm test; |
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326 | CanonicalForm buf0= buf (0, x)*LCBuf; |
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327 | while (T.length() >= 2*s && s <= thres) |
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328 | { |
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329 | while (nosubset == false) |
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330 | { |
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331 | if (T.length() == s) |
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332 | { |
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333 | delete [] v; |
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334 | if (recombination) |
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335 | { |
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336 | T.insert (LCBuf); |
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337 | g= prodMod (T, M); |
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338 | T.removeFirst(); |
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339 | g /= content(g); |
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340 | g= g (y - eval, y); |
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341 | g /= Lc (g); |
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342 | appendTestMapDown (result, g, info, source, dest); |
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343 | F= 1; |
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344 | return result; |
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345 | } |
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346 | else |
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347 | { |
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348 | appendMapDown (result, F (y - eval, y), info, source, dest); |
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349 | F= 1; |
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350 | return result; |
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351 | } |
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352 | } |
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353 | S= subset (v, s, TT, nosubset); |
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354 | if (nosubset) break; |
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355 | subsetDeg= subsetDegree (S); |
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356 | // skip those combinations that are not possible |
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357 | if (!degs.find (subsetDeg)) |
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358 | continue; |
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359 | else |
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360 | { |
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361 | test= prodMod0 (S, M); |
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362 | test *= LCBuf; |
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363 | test = mod (test, M); |
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364 | if (fdivides (test, buf0)) |
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365 | { |
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366 | S.insert (LCBuf); |
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367 | g= prodMod (S, M); |
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368 | S.removeFirst(); |
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369 | g /= content (g, x); |
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370 | if (fdivides (g, buf, quot)) |
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371 | { |
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372 | buf2= g (y - eval, y); |
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373 | buf2 /= Lc (buf2); |
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374 | |
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375 | if (!k && beta.level() == 1) |
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376 | { |
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377 | if (degree (buf2, alpha) < degMipoBeta) |
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378 | { |
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379 | buf= quot; |
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380 | LCBuf= LC (buf, x); |
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381 | recombination= true; |
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382 | appendTestMapDown (result, buf2, info, source, dest); |
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383 | trueFactor= true; |
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384 | } |
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385 | } |
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386 | else |
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387 | { |
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388 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
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389 | { |
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390 | buf= quot; |
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391 | LCBuf= LC (buf, x); |
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392 | recombination= true; |
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393 | appendTestMapDown (result, buf2, info, source, dest); |
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394 | trueFactor= true; |
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395 | } |
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396 | } |
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397 | if (trueFactor) |
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398 | { |
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399 | T= Difference (T, S); |
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400 | l -= degree (g); |
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401 | M= power (y, l); |
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402 | buf0= buf (0, x)*LCBuf; |
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403 | |
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404 | // compute new possible degree pattern |
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405 | bufDegs2= DegreePattern (T); |
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406 | bufDegs1.intersect (bufDegs2); |
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407 | bufDegs1.refine (); |
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408 | if (T.length() < 2*s || T.length() == s || |
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409 | bufDegs1.getLength() == 1) |
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410 | { |
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411 | delete [] v; |
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412 | if (recombination) |
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413 | { |
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414 | buf= buf (y-eval,y); |
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415 | buf /= Lc (buf); |
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416 | appendTestMapDown (result, buf, info, source, |
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417 | dest); |
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418 | F= 1; |
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419 | return result; |
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420 | } |
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421 | else |
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422 | { |
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423 | appendMapDown (result, F (y - eval, y), info, source, dest); |
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424 | F= 1; |
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425 | return result; |
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426 | } |
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427 | } |
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428 | trueFactor= false; |
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429 | TT= copy (T); |
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430 | indexUpdate (v, s, T.length(), nosubset); |
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431 | if (nosubset) break; |
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432 | } |
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433 | } |
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434 | } |
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435 | } |
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436 | } |
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437 | s++; |
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438 | if (T.length() < 2*s || T.length() == s) |
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439 | { |
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440 | delete [] v; |
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441 | if (recombination) |
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442 | { |
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443 | buf= buf (y-eval,y); |
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444 | buf /= Lc (buf); |
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445 | appendTestMapDown (result, buf, info, source, dest); |
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446 | F= 1; |
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447 | return result; |
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448 | } |
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449 | else |
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450 | { |
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451 | appendMapDown (result, F (y - eval, y), info, source, dest); |
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452 | F= 1; |
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453 | return result; |
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454 | } |
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455 | } |
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456 | for (int i= 0; i < T.length(); i++) |
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457 | v[i]= 0; |
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458 | nosubset= false; |
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459 | } |
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460 | if (T.length() < 2*s) |
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461 | { |
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462 | appendMapDown (result, F (y - eval, y), info, source, dest); |
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463 | F= 1; |
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464 | delete [] v; |
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465 | return result; |
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466 | } |
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467 | |
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468 | if (s > thres) |
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469 | { |
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470 | factors= T; |
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471 | F= buf; |
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472 | degs= bufDegs1; |
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473 | } |
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474 | |
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475 | delete [] v; |
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476 | return result; |
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477 | } |
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478 | |
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479 | /// naive factor recombination as decribed in "Factoring |
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480 | /// multivariate polynomials over a finite field" by L Bernardin. |
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481 | CFList |
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482 | factorRecombination (CFList& factors, CanonicalForm& F, |
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483 | const CanonicalForm& N, DegreePattern& degs, int s, |
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484 | int thres, const modpk& b, const CanonicalForm& den |
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485 | ) |
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486 | { |
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487 | if (factors.length() == 0) |
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488 | { |
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489 | F= 1; |
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490 | return CFList (); |
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491 | } |
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492 | if (F.inCoeffDomain()) |
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493 | return CFList(); |
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494 | if (degs.getLength() <= 1 || factors.length() == 1) |
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495 | { |
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496 | CFList result= CFList (F); |
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497 | F= 1; |
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498 | return result; |
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499 | } |
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500 | #ifdef DEBUGOUTPUT |
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501 | if (b.getp() == 0) |
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502 | DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, N) == F " << |
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503 | (mod (LC (F, 1)*prodMod (factors, N),N)/Lc (mod (LC (F, 1)*prodMod (factors, N),N)) == F/Lc(F))); |
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504 | else |
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505 | DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, N) == F " << |
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506 | (mod (b(LC (F, 1)*prodMod (factors, N)),N)/Lc (mod (b(LC (F, 1)*prodMod (factors, N)),N)) == F/Lc(F))); |
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507 | #endif |
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508 | |
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509 | CFList T, S; |
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510 | |
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511 | CanonicalForm M= N; |
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512 | int l= degree (N); |
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513 | T= factors; |
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514 | CFList result; |
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515 | Variable y= Variable (2); |
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516 | Variable x= Variable (1); |
---|
517 | CanonicalForm denom= den, denQuot; |
---|
518 | CanonicalForm LCBuf= LC (F, x)*denom; |
---|
519 | CanonicalForm g, quot, buf= F; |
---|
520 | int * v= new int [T.length()]; |
---|
521 | for (int i= 0; i < T.length(); i++) |
---|
522 | v[i]= 0; |
---|
523 | bool nosubset= false; |
---|
524 | CFArray TT; |
---|
525 | DegreePattern bufDegs1, bufDegs2; |
---|
526 | bufDegs1= degs; |
---|
527 | int subsetDeg; |
---|
528 | TT= copy (factors); |
---|
529 | bool recombination= false; |
---|
530 | CanonicalForm test; |
---|
531 | bool isRat= (isOn (SW_RATIONAL) && getCharacteristic() == 0) || |
---|
532 | getCharacteristic() > 0; |
---|
533 | if (!isRat) |
---|
534 | On (SW_RATIONAL); |
---|
535 | CanonicalForm buf0= mulNTL (buf (0, x), LCBuf); |
---|
536 | if (!isRat) |
---|
537 | Off (SW_RATIONAL); |
---|
538 | while (T.length() >= 2*s && s <= thres) |
---|
539 | { |
---|
540 | while (nosubset == false) |
---|
541 | { |
---|
542 | if (T.length() == s) |
---|
543 | { |
---|
544 | delete [] v; |
---|
545 | if (recombination) |
---|
546 | { |
---|
547 | T.insert (LCBuf); |
---|
548 | g= prodMod (T, M); |
---|
549 | if (b.getp() != 0) |
---|
550 | g= b(g); |
---|
551 | T.removeFirst(); |
---|
552 | result.append (g/content (g, x)); |
---|
553 | F= 1; |
---|
554 | return result; |
---|
555 | } |
---|
556 | else |
---|
557 | { |
---|
558 | result= CFList (F); |
---|
559 | F= 1; |
---|
560 | return result; |
---|
561 | } |
---|
562 | } |
---|
563 | S= subset (v, s, TT, nosubset); |
---|
564 | if (nosubset) break; |
---|
565 | subsetDeg= subsetDegree (S); |
---|
566 | // skip those combinations that are not possible |
---|
567 | if (!degs.find (subsetDeg)) |
---|
568 | continue; |
---|
569 | else |
---|
570 | { |
---|
571 | if (!isRat) |
---|
572 | On (SW_RATIONAL); |
---|
573 | test= prodMod0 (S, M); |
---|
574 | if (!isRat) |
---|
575 | { |
---|
576 | test *= bCommonDen (test); |
---|
577 | Off (SW_RATIONAL); |
---|
578 | } |
---|
579 | test= mulNTL (test, LCBuf, b); |
---|
580 | test= mod (test, M); |
---|
581 | if (uniFdivides (test, buf0)) |
---|
582 | { |
---|
583 | if (!isRat) |
---|
584 | On (SW_RATIONAL); |
---|
585 | S.insert (LCBuf); |
---|
586 | g= prodMod (S, M); |
---|
587 | S.removeFirst(); |
---|
588 | if (!isRat) |
---|
589 | { |
---|
590 | g *= bCommonDen(g); |
---|
591 | Off (SW_RATIONAL); |
---|
592 | } |
---|
593 | if (b.getp() != 0) |
---|
594 | g= b(g); |
---|
595 | if (!isRat) |
---|
596 | On (SW_RATIONAL); |
---|
597 | g /= content (g, x); |
---|
598 | if (!isRat) |
---|
599 | { |
---|
600 | On (SW_RATIONAL); |
---|
601 | if (!Lc (g).inBaseDomain()) |
---|
602 | g /= Lc (g); |
---|
603 | g *= bCommonDen (g); |
---|
604 | Off (SW_RATIONAL); |
---|
605 | g /= icontent (g); |
---|
606 | On (SW_RATIONAL); |
---|
607 | } |
---|
608 | if (fdivides (g, buf, quot)) |
---|
609 | { |
---|
610 | denom *= abs (lc (g)); |
---|
611 | recombination= true; |
---|
612 | result.append (g); |
---|
613 | if (b.getp() != 0) |
---|
614 | { |
---|
615 | denQuot= bCommonDen (quot); |
---|
616 | buf= quot*denQuot; |
---|
617 | Off (SW_RATIONAL); |
---|
618 | denom /= gcd (denom, denQuot); |
---|
619 | On (SW_RATIONAL); |
---|
620 | } |
---|
621 | else |
---|
622 | buf= quot; |
---|
623 | LCBuf= LC (buf, x)*denom; |
---|
624 | T= Difference (T, S); |
---|
625 | l -= degree (g); |
---|
626 | M= power (y, l); |
---|
627 | buf0= mulNTL (buf (0, x), LCBuf); |
---|
628 | if (!isRat) |
---|
629 | Off (SW_RATIONAL); |
---|
630 | // compute new possible degree pattern |
---|
631 | bufDegs2= DegreePattern (T); |
---|
632 | bufDegs1.intersect (bufDegs2); |
---|
633 | bufDegs1.refine (); |
---|
634 | if (T.length() < 2*s || T.length() == s || |
---|
635 | bufDegs1.getLength() == 1) |
---|
636 | { |
---|
637 | delete [] v; |
---|
638 | if (recombination) |
---|
639 | { |
---|
640 | result.append (buf); |
---|
641 | F= 1; |
---|
642 | return result; |
---|
643 | } |
---|
644 | else |
---|
645 | { |
---|
646 | result= CFList (F); |
---|
647 | F= 1; |
---|
648 | return result; |
---|
649 | } |
---|
650 | } |
---|
651 | TT= copy (T); |
---|
652 | indexUpdate (v, s, T.length(), nosubset); |
---|
653 | if (nosubset) break; |
---|
654 | } |
---|
655 | if (!isRat) |
---|
656 | Off (SW_RATIONAL); |
---|
657 | } |
---|
658 | } |
---|
659 | } |
---|
660 | s++; |
---|
661 | if (T.length() < 2*s || T.length() == s) |
---|
662 | { |
---|
663 | delete [] v; |
---|
664 | if (recombination) |
---|
665 | { |
---|
666 | result.append (buf); |
---|
667 | F= 1; |
---|
668 | return result; |
---|
669 | } |
---|
670 | else |
---|
671 | { |
---|
672 | result= CFList (F); |
---|
673 | F= 1; |
---|
674 | return result; |
---|
675 | } |
---|
676 | } |
---|
677 | for (int i= 0; i < T.length(); i++) |
---|
678 | v[i]= 0; |
---|
679 | nosubset= false; |
---|
680 | } |
---|
681 | delete [] v; |
---|
682 | if (T.length() < 2*s) |
---|
683 | { |
---|
684 | result.append (F); |
---|
685 | F= 1; |
---|
686 | return result; |
---|
687 | } |
---|
688 | |
---|
689 | if (s > thres) |
---|
690 | { |
---|
691 | factors= T; |
---|
692 | F= buf; |
---|
693 | degs= bufDegs1; |
---|
694 | } |
---|
695 | |
---|
696 | return result; |
---|
697 | } |
---|
698 | |
---|
699 | Variable chooseExtension (const Variable & alpha, const Variable& beta, int k) |
---|
700 | { |
---|
701 | if (fac_NTL_char != getCharacteristic()) |
---|
702 | { |
---|
703 | fac_NTL_char= getCharacteristic(); |
---|
704 | zz_p::init (getCharacteristic()); |
---|
705 | } |
---|
706 | zz_pX NTLIrredpoly; |
---|
707 | int i=1, m= 2; |
---|
708 | // extension of F_p needed |
---|
709 | if (alpha.level() == 1 && beta.level() == 1 && k == 1) |
---|
710 | { |
---|
711 | i= 1; |
---|
712 | m= 2; |
---|
713 | } //extension of F_p(alpha) needed but want to factorize over F_p |
---|
714 | else if (alpha.level() != 1 && beta.level() == 1 && k == 1) |
---|
715 | { |
---|
716 | i= 1; |
---|
717 | m= degree (getMipo (alpha)) + 1; |
---|
718 | } //extension of F_p(alpha) needed for first time |
---|
719 | else if (alpha.level() != 1 && beta.level() == 1 && k != 1) |
---|
720 | { |
---|
721 | i= 2; |
---|
722 | m= degree (getMipo (alpha)); |
---|
723 | } |
---|
724 | else if (alpha.level() != 1 && beta.level() != 1 && k != 1) |
---|
725 | { |
---|
726 | m= degree (getMipo (beta)); |
---|
727 | i= degree (getMipo (alpha))/m + 1; |
---|
728 | } |
---|
729 | BuildIrred (NTLIrredpoly, i*m); |
---|
730 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
731 | return rootOf (newMipo); |
---|
732 | } |
---|
733 | |
---|
734 | void |
---|
735 | earlyFactorDetection (CFList& reconstructedFactors, CanonicalForm& F, CFList& |
---|
736 | factors, int& adaptedLiftBound, int*& factorsFoundIndex, |
---|
737 | DegreePattern& degs, bool& success, int deg, |
---|
738 | const modpk& b, CanonicalForm& den) |
---|
739 | { |
---|
740 | DegreePattern bufDegs1= degs; |
---|
741 | DegreePattern bufDegs2; |
---|
742 | CFList T= factors; |
---|
743 | CanonicalForm buf= F; |
---|
744 | Variable x= Variable (1); |
---|
745 | CanonicalForm g, quot; |
---|
746 | CanonicalForm M= power (F.mvar(), deg); |
---|
747 | adaptedLiftBound= 0; |
---|
748 | int d= degree (F), l= 0; |
---|
749 | bool isRat= (isOn (SW_RATIONAL) && getCharacteristic() == 0) || getCharacteristic() > 0; |
---|
750 | if (!isRat) |
---|
751 | On (SW_RATIONAL); |
---|
752 | if (b.getp() != 0) |
---|
753 | buf *= bCommonDen (buf); |
---|
754 | CanonicalForm LCBuf= LC (buf, x)*den; |
---|
755 | CanonicalForm buf0= mulNTL (buf (0,x), LCBuf); |
---|
756 | CanonicalForm buf1= mulNTL (buf (1,x), LCBuf); |
---|
757 | if (!isRat) |
---|
758 | Off (SW_RATIONAL); |
---|
759 | CanonicalForm test0, test1; |
---|
760 | CanonicalForm denQuot; |
---|
761 | |
---|
762 | for (CFListIterator i= factors; i.hasItem(); i++, l++) |
---|
763 | { |
---|
764 | if (!bufDegs1.find (degree (i.getItem(), 1)) || factorsFoundIndex[l] == 1) |
---|
765 | continue; |
---|
766 | else |
---|
767 | { |
---|
768 | test1= mod (mulNTL (i.getItem() (1,x), LCBuf, b), M); |
---|
769 | if (uniFdivides (test1, buf1)) |
---|
770 | { |
---|
771 | test0= mod (mulNTL (i.getItem() (0,x), LCBuf, b), M); |
---|
772 | if (uniFdivides (test0, buf0)) |
---|
773 | { |
---|
774 | if (!isRat) |
---|
775 | On (SW_RATIONAL); |
---|
776 | g= mulMod2 (i.getItem(), LCBuf, M); |
---|
777 | if (!isRat) |
---|
778 | { |
---|
779 | g *= bCommonDen(g); |
---|
780 | Off (SW_RATIONAL); |
---|
781 | } |
---|
782 | if (b.getp() != 0) |
---|
783 | g= b(g); |
---|
784 | if (!isRat) |
---|
785 | On (SW_RATIONAL); |
---|
786 | g /= content (g, x); |
---|
787 | if (!isRat) |
---|
788 | { |
---|
789 | On (SW_RATIONAL); |
---|
790 | if (!Lc (g).inBaseDomain()) |
---|
791 | g /= Lc (g); |
---|
792 | g *= bCommonDen (g); |
---|
793 | Off (SW_RATIONAL); |
---|
794 | g /= icontent (g); |
---|
795 | On (SW_RATIONAL); |
---|
796 | } |
---|
797 | if (fdivides (g, buf, quot)) |
---|
798 | { |
---|
799 | den *= abs (lc (g)); |
---|
800 | reconstructedFactors.append (g); |
---|
801 | factorsFoundIndex[l]= 1; |
---|
802 | if (b.getp() != 0) |
---|
803 | { |
---|
804 | denQuot= bCommonDen (quot); |
---|
805 | buf= quot*denQuot; |
---|
806 | Off (SW_RATIONAL); |
---|
807 | den /= gcd (den, denQuot); |
---|
808 | On (SW_RATIONAL); |
---|
809 | } |
---|
810 | else |
---|
811 | buf= quot; |
---|
812 | d -= degree (g); |
---|
813 | LCBuf= LC (buf, x)*den; |
---|
814 | buf0= mulNTL (buf (0,x), LCBuf); |
---|
815 | buf1= mulNTL (buf (1,x), LCBuf); |
---|
816 | if (!isRat) |
---|
817 | Off (SW_RATIONAL); |
---|
818 | T= Difference (T, CFList (i.getItem())); |
---|
819 | F= buf; |
---|
820 | |
---|
821 | // compute new possible degree pattern |
---|
822 | bufDegs2= DegreePattern (T); |
---|
823 | bufDegs1.intersect (bufDegs2); |
---|
824 | bufDegs1.refine (); |
---|
825 | if (bufDegs1.getLength() <= 1) |
---|
826 | { |
---|
827 | if (!buf.inCoeffDomain()) |
---|
828 | { |
---|
829 | reconstructedFactors.append (buf); |
---|
830 | F= 1; |
---|
831 | } |
---|
832 | break; |
---|
833 | } |
---|
834 | } |
---|
835 | if (!isRat) |
---|
836 | Off (SW_RATIONAL); |
---|
837 | } |
---|
838 | } |
---|
839 | } |
---|
840 | } |
---|
841 | adaptedLiftBound= d + 1; |
---|
842 | if (adaptedLiftBound < deg) |
---|
843 | { |
---|
844 | degs= bufDegs1; |
---|
845 | success= true; |
---|
846 | } |
---|
847 | if (bufDegs1.getLength() <= 1) |
---|
848 | degs= bufDegs1; |
---|
849 | } |
---|
850 | |
---|
851 | void |
---|
852 | earlyFactorDetection (CFList& reconstructedFactors, CanonicalForm& F, CFList& |
---|
853 | factors, int& adaptedLiftBound, int*& factorsFoundIndex, |
---|
854 | DegreePattern& degs, bool& success, int deg, |
---|
855 | const modpk& b) |
---|
856 | { |
---|
857 | CanonicalForm den= 1; |
---|
858 | earlyFactorDetection (reconstructedFactors, F, factors, adaptedLiftBound, factorsFoundIndex, degs, success, deg,b, den); |
---|
859 | } |
---|
860 | |
---|
861 | void |
---|
862 | extEarlyFactorDetection (CFList& reconstructedFactors, CanonicalForm& F, CFList& |
---|
863 | factors,int& adaptedLiftBound, int*& factorsFoundIndex, |
---|
864 | DegreePattern& degs, bool& success, const |
---|
865 | ExtensionInfo& info, const CanonicalForm& eval, int deg |
---|
866 | ) |
---|
867 | { |
---|
868 | Variable alpha= info.getAlpha(); |
---|
869 | Variable beta= info.getBeta(); |
---|
870 | CanonicalForm gamma= info.getGamma(); |
---|
871 | CanonicalForm delta= info.getDelta(); |
---|
872 | int k= info.getGFDegree(); |
---|
873 | DegreePattern bufDegs1= degs, bufDegs2; |
---|
874 | CFList result; |
---|
875 | CFList T= factors; |
---|
876 | Variable y= F.mvar(); |
---|
877 | Variable x= Variable (1); |
---|
878 | CanonicalForm buf= F, LCBuf= LC (buf, x), g, buf2; |
---|
879 | CanonicalForm M= power (y, deg); |
---|
880 | adaptedLiftBound= 0; |
---|
881 | bool trueFactor= false; |
---|
882 | int d= degree (F), l= 0; |
---|
883 | CFList source, dest; |
---|
884 | int degMipoBeta= 1; |
---|
885 | if (!k && beta.level() != 1) |
---|
886 | degMipoBeta= degree (getMipo (beta)); |
---|
887 | CanonicalForm quot; |
---|
888 | for (CFListIterator i= factors; i.hasItem(); i++, l++) |
---|
889 | { |
---|
890 | if (!bufDegs1.find (degree (i.getItem(), 1)) || factorsFoundIndex[l] == 1) |
---|
891 | continue; |
---|
892 | else |
---|
893 | { |
---|
894 | g= mulMod2 (i.getItem(), LCBuf, M); |
---|
895 | g /= content (g, x); |
---|
896 | if (fdivides (g, buf, quot)) |
---|
897 | { |
---|
898 | buf2= g (y - eval, y); |
---|
899 | buf2 /= Lc (buf2); |
---|
900 | |
---|
901 | if (!k && beta == x) |
---|
902 | { |
---|
903 | if (degree (buf2, alpha) < degMipoBeta) |
---|
904 | { |
---|
905 | appendTestMapDown (reconstructedFactors, buf2, info, source, dest); |
---|
906 | factorsFoundIndex[l]= 1; |
---|
907 | buf= quot; |
---|
908 | d -= degree (g); |
---|
909 | LCBuf= LC (buf, x); |
---|
910 | trueFactor= true; |
---|
911 | } |
---|
912 | } |
---|
913 | else |
---|
914 | { |
---|
915 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
916 | { |
---|
917 | appendTestMapDown (reconstructedFactors, buf2, info, source, dest); |
---|
918 | factorsFoundIndex[l]= 1; |
---|
919 | buf= quot; |
---|
920 | d -= degree (g); |
---|
921 | LCBuf= LC (buf, x); |
---|
922 | trueFactor= true; |
---|
923 | } |
---|
924 | } |
---|
925 | if (trueFactor) |
---|
926 | { |
---|
927 | T= Difference (T, CFList (i.getItem())); |
---|
928 | F= buf; |
---|
929 | |
---|
930 | // compute new possible degree pattern |
---|
931 | bufDegs2= DegreePattern (T); |
---|
932 | bufDegs1.intersect (bufDegs2); |
---|
933 | bufDegs1.refine (); |
---|
934 | trueFactor= false; |
---|
935 | if (bufDegs1.getLength() <= 1) |
---|
936 | { |
---|
937 | if (!buf.inCoeffDomain()) |
---|
938 | { |
---|
939 | buf= buf (y - eval, y); |
---|
940 | buf /= Lc (buf); |
---|
941 | appendMapDown (reconstructedFactors, buf, info, source, dest); |
---|
942 | F= 1; |
---|
943 | } |
---|
944 | break; |
---|
945 | } |
---|
946 | } |
---|
947 | } |
---|
948 | } |
---|
949 | } |
---|
950 | adaptedLiftBound= d + 1; |
---|
951 | if (adaptedLiftBound < deg) |
---|
952 | { |
---|
953 | degs= bufDegs1; |
---|
954 | success= true; |
---|
955 | } |
---|
956 | if (bufDegs1.getLength() <= 1) |
---|
957 | degs= bufDegs1; |
---|
958 | } |
---|
959 | |
---|
960 | int* |
---|
961 | getCombinations (int * rightSide, int sizeOfRightSide, int& sizeOfOutput, |
---|
962 | int degreeLC) |
---|
963 | { |
---|
964 | Variable x= Variable (1); |
---|
965 | int p= getCharacteristic(); |
---|
966 | int d= getGFDegree(); |
---|
967 | char cGFName= gf_name; |
---|
968 | setCharacteristic(0); |
---|
969 | CanonicalForm buf= 1; |
---|
970 | for (int i= 0; i < sizeOfRightSide; i++) |
---|
971 | buf *= (power (x, rightSide [i]) + 1); |
---|
972 | |
---|
973 | int j= 0; |
---|
974 | for (CFIterator i= buf; i.hasTerms(); i++, j++) |
---|
975 | { |
---|
976 | if (i.exp() < degreeLC) |
---|
977 | { |
---|
978 | j++; |
---|
979 | break; |
---|
980 | } |
---|
981 | } |
---|
982 | |
---|
983 | ASSERT ( j > 1, "j > 1 expected" ); |
---|
984 | |
---|
985 | int* result = new int [j - 1]; |
---|
986 | sizeOfOutput= j - 1; |
---|
987 | |
---|
988 | int i= 0; |
---|
989 | for (CFIterator m = buf; i < j - 1; i++, m++) |
---|
990 | result [i]= m.exp(); |
---|
991 | |
---|
992 | if (d > 1) |
---|
993 | setCharacteristic (p, d, cGFName); |
---|
994 | else |
---|
995 | setCharacteristic (p); |
---|
996 | return result; |
---|
997 | } |
---|
998 | |
---|
999 | int * |
---|
1000 | getLiftPrecisions (const CanonicalForm& F, int& sizeOfOutput, int degreeLC) |
---|
1001 | { |
---|
1002 | int sizeOfNewtonPoly; |
---|
1003 | int ** newtonPolyg= newtonPolygon (F, sizeOfNewtonPoly); |
---|
1004 | int sizeOfRightSide; |
---|
1005 | int * rightSide= getRightSide(newtonPolyg, sizeOfNewtonPoly, sizeOfRightSide); |
---|
1006 | int * result= getCombinations(rightSide, sizeOfRightSide, sizeOfOutput, |
---|
1007 | degreeLC); |
---|
1008 | delete [] rightSide; |
---|
1009 | for (int i= 0; i < sizeOfNewtonPoly; i++) |
---|
1010 | delete [] newtonPolyg[i]; |
---|
1011 | delete [] newtonPolyg; |
---|
1012 | return result; |
---|
1013 | } |
---|
1014 | |
---|
1015 | void |
---|
1016 | deleteFactors (CFList& factors, int* factorsFoundIndex) |
---|
1017 | { |
---|
1018 | CFList result; |
---|
1019 | int i= 0; |
---|
1020 | for (CFListIterator iter= factors; iter.hasItem(); iter++, i++) |
---|
1021 | { |
---|
1022 | if (factorsFoundIndex[i] == 1) |
---|
1023 | continue; |
---|
1024 | else |
---|
1025 | result.append (iter.getItem()); |
---|
1026 | } |
---|
1027 | factors= result; |
---|
1028 | } |
---|
1029 | |
---|
1030 | CFList |
---|
1031 | henselLiftAndEarly (CanonicalForm& A, bool& earlySuccess, CFList& |
---|
1032 | earlyFactors, DegreePattern& degs, int& liftBound, |
---|
1033 | const CFList& uniFactors, const ExtensionInfo& info, |
---|
1034 | const CanonicalForm& eval,modpk& b, CanonicalForm& den) |
---|
1035 | { |
---|
1036 | Variable alpha= info.getAlpha(); |
---|
1037 | Variable beta= info.getBeta(); |
---|
1038 | CanonicalForm gamma= info.getGamma(); |
---|
1039 | CanonicalForm delta= info.getDelta(); |
---|
1040 | bool extension= info.isInExtension(); |
---|
1041 | |
---|
1042 | int sizeOfLiftPre; |
---|
1043 | int * liftPre= getLiftPrecisions (A, sizeOfLiftPre, degree (LC (A, 1), 2)); |
---|
1044 | |
---|
1045 | Variable x= Variable (1); |
---|
1046 | Variable y= Variable (2); |
---|
1047 | CFArray Pi; |
---|
1048 | CFList diophant; |
---|
1049 | CFList bufUniFactors= uniFactors; |
---|
1050 | On (SW_RATIONAL); |
---|
1051 | CanonicalForm bufA= A; |
---|
1052 | if (!Lc (A).inBaseDomain()) |
---|
1053 | { |
---|
1054 | bufA /= Lc (A); |
---|
1055 | CanonicalForm denBufA= bCommonDen (bufA); |
---|
1056 | bufA *= denBufA; |
---|
1057 | Off (SW_RATIONAL); |
---|
1058 | den /= gcd (den, denBufA); |
---|
1059 | } |
---|
1060 | else |
---|
1061 | { |
---|
1062 | bufA= A; |
---|
1063 | Off (SW_RATIONAL); |
---|
1064 | den /= gcd (den, Lc (A)); |
---|
1065 | } |
---|
1066 | CanonicalForm lcA0= 0; |
---|
1067 | bool mipoHasDen= false; |
---|
1068 | if (getCharacteristic() == 0 && b.getp() != 0) |
---|
1069 | { |
---|
1070 | if (alpha.level() == 1) |
---|
1071 | { |
---|
1072 | lcA0= lc (A (0, 2)); |
---|
1073 | A *= b.inverse (lcA0); |
---|
1074 | A= b (A); |
---|
1075 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
1076 | i.getItem()= b (i.getItem()*b.inverse (lc (i.getItem()))); |
---|
1077 | } |
---|
1078 | else |
---|
1079 | { |
---|
1080 | lcA0= Lc (A (0,2)); |
---|
1081 | On (SW_RATIONAL); |
---|
1082 | mipoHasDen= !bCommonDen(getMipo(alpha)).isOne(); |
---|
1083 | Off (SW_RATIONAL); |
---|
1084 | CanonicalForm lcA0inverse= b.inverse (lcA0); |
---|
1085 | A *= lcA0inverse; |
---|
1086 | A= b (A); |
---|
1087 | // Lc of bufUniFactors is in Z |
---|
1088 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
1089 | i.getItem()= b (i.getItem()*b.inverse (lc (i.getItem()))); |
---|
1090 | } |
---|
1091 | } |
---|
1092 | bufUniFactors.insert (LC (A, x)); |
---|
1093 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length() - 1); |
---|
1094 | earlySuccess= false; |
---|
1095 | int newLiftBound= 0; |
---|
1096 | |
---|
1097 | int smallFactorDeg= tmin (11, liftPre [sizeOfLiftPre- 1] + 1);//this is a tunable parameter |
---|
1098 | int dummy; |
---|
1099 | int * factorsFoundIndex= new int [uniFactors.length()]; |
---|
1100 | for (int i= 0; i < uniFactors.length(); i++) |
---|
1101 | factorsFoundIndex [i]= 0; |
---|
1102 | |
---|
1103 | CFList bufBufUniFactors; |
---|
1104 | Variable v= alpha; |
---|
1105 | if (smallFactorDeg >= liftBound || degree (A,y) <= 4) |
---|
1106 | henselLift12 (A, bufUniFactors, liftBound, Pi, diophant, M, b, true); |
---|
1107 | else if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
1108 | { |
---|
1109 | henselLift12 (A, bufUniFactors, smallFactorDeg, Pi, diophant, M, b, true); |
---|
1110 | if (mipoHasDen) |
---|
1111 | { |
---|
1112 | for (CFListIterator iter= bufUniFactors; iter.hasItem(); iter++) |
---|
1113 | if (hasFirstAlgVar (iter.getItem(), v)) |
---|
1114 | break; |
---|
1115 | if (v != alpha) |
---|
1116 | { |
---|
1117 | bufBufUniFactors= bufUniFactors; |
---|
1118 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
1119 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
1120 | A= replacevar (A, alpha, v); |
---|
1121 | } |
---|
1122 | } |
---|
1123 | |
---|
1124 | if (!extension) |
---|
1125 | { |
---|
1126 | if (v==alpha) |
---|
1127 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
1128 | factorsFoundIndex, degs, earlySuccess, |
---|
1129 | smallFactorDeg, b, den); |
---|
1130 | else |
---|
1131 | earlyFactorDetection(earlyFactors, bufA, bufBufUniFactors, newLiftBound, |
---|
1132 | factorsFoundIndex, degs, earlySuccess, |
---|
1133 | smallFactorDeg, b, den); |
---|
1134 | } |
---|
1135 | else |
---|
1136 | extEarlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
1137 | factorsFoundIndex, degs, earlySuccess, info, |
---|
1138 | eval, smallFactorDeg); |
---|
1139 | if (degs.getLength() > 1 && !earlySuccess && |
---|
1140 | smallFactorDeg != liftPre [sizeOfLiftPre-1] + 1) |
---|
1141 | { |
---|
1142 | if (newLiftBound >= liftPre[sizeOfLiftPre-1]+1) |
---|
1143 | { |
---|
1144 | bufUniFactors.insert (LC (A, x)); |
---|
1145 | henselLiftResume12 (A, bufUniFactors, smallFactorDeg, |
---|
1146 | liftPre[sizeOfLiftPre-1] + 1, Pi, diophant, M, b); |
---|
1147 | if (v!=alpha) |
---|
1148 | { |
---|
1149 | bufBufUniFactors= bufUniFactors; |
---|
1150 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
1151 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
1152 | } |
---|
1153 | if (!extension) |
---|
1154 | { |
---|
1155 | if (v==alpha) |
---|
1156 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
1157 | factorsFoundIndex, degs, earlySuccess, |
---|
1158 | liftPre[sizeOfLiftPre-1] + 1, b, den); |
---|
1159 | else |
---|
1160 | earlyFactorDetection (earlyFactors,bufA,bufBufUniFactors,newLiftBound, |
---|
1161 | factorsFoundIndex, degs, earlySuccess, |
---|
1162 | liftPre[sizeOfLiftPre-1] + 1, b, den); |
---|
1163 | } |
---|
1164 | else |
---|
1165 | extEarlyFactorDetection (earlyFactors,bufA,bufUniFactors,newLiftBound, |
---|
1166 | factorsFoundIndex, degs, earlySuccess, info, |
---|
1167 | eval, liftPre[sizeOfLiftPre-1] + 1); |
---|
1168 | } |
---|
1169 | } |
---|
1170 | else if (earlySuccess) |
---|
1171 | liftBound= newLiftBound; |
---|
1172 | |
---|
1173 | int i= sizeOfLiftPre - 1; |
---|
1174 | while (degs.getLength() > 1 && !earlySuccess && i - 1 >= 0) |
---|
1175 | { |
---|
1176 | if (newLiftBound >= liftPre[i] + 1) |
---|
1177 | { |
---|
1178 | bufUniFactors.insert (LC (A, x)); |
---|
1179 | henselLiftResume12 (A, bufUniFactors, liftPre[i] + 1, |
---|
1180 | liftPre[i-1] + 1, Pi, diophant, M, b); |
---|
1181 | if (v!=alpha) |
---|
1182 | { |
---|
1183 | bufBufUniFactors= bufUniFactors; |
---|
1184 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
1185 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
1186 | } |
---|
1187 | if (!extension) |
---|
1188 | { |
---|
1189 | if (v==alpha) |
---|
1190 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
1191 | factorsFoundIndex, degs, earlySuccess, |
---|
1192 | liftPre[i-1] + 1, b, den); |
---|
1193 | else |
---|
1194 | earlyFactorDetection (earlyFactors,bufA,bufBufUniFactors,newLiftBound, |
---|
1195 | factorsFoundIndex, degs, earlySuccess, |
---|
1196 | liftPre[i-1] + 1, b, den); |
---|
1197 | } |
---|
1198 | else |
---|
1199 | extEarlyFactorDetection (earlyFactors,bufA,bufUniFactors,newLiftBound, |
---|
1200 | factorsFoundIndex, degs, earlySuccess, info, |
---|
1201 | eval, liftPre[i-1] + 1); |
---|
1202 | } |
---|
1203 | else |
---|
1204 | { |
---|
1205 | liftBound= newLiftBound; |
---|
1206 | break; |
---|
1207 | } |
---|
1208 | i--; |
---|
1209 | } |
---|
1210 | if (earlySuccess) |
---|
1211 | liftBound= newLiftBound; |
---|
1212 | //after here all factors are lifted to liftPre[sizeOfLiftPre-1] |
---|
1213 | } |
---|
1214 | else |
---|
1215 | { |
---|
1216 | henselLift12 (A, bufUniFactors, smallFactorDeg, Pi, diophant, M, b, true); |
---|
1217 | if (mipoHasDen) |
---|
1218 | { |
---|
1219 | for (CFListIterator iter= bufUniFactors; iter.hasItem(); iter++) |
---|
1220 | if (hasFirstAlgVar (iter.getItem(), v)) |
---|
1221 | break; |
---|
1222 | if (v != alpha) |
---|
1223 | { |
---|
1224 | bufBufUniFactors= bufUniFactors; |
---|
1225 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
1226 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
1227 | A= replacevar (A, alpha, v); |
---|
1228 | } |
---|
1229 | } |
---|
1230 | if (!extension) |
---|
1231 | { |
---|
1232 | if (v==alpha) |
---|
1233 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
1234 | factorsFoundIndex, degs, earlySuccess, |
---|
1235 | smallFactorDeg, b, den); |
---|
1236 | else |
---|
1237 | earlyFactorDetection (earlyFactors, bufA, bufBufUniFactors, newLiftBound, |
---|
1238 | factorsFoundIndex, degs, earlySuccess, |
---|
1239 | smallFactorDeg, b, den); |
---|
1240 | } |
---|
1241 | else |
---|
1242 | extEarlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
1243 | factorsFoundIndex, degs, earlySuccess, info, |
---|
1244 | eval, smallFactorDeg); |
---|
1245 | int i= 1; |
---|
1246 | while ((degree (A,y)/4)*i + 4 <= smallFactorDeg) |
---|
1247 | i++; |
---|
1248 | dummy= tmin (degree (A,y)+1, (degree (A,y)/4)*i+4); |
---|
1249 | if (degs.getLength() > 1 && !earlySuccess && dummy > smallFactorDeg) |
---|
1250 | { |
---|
1251 | bufUniFactors.insert (LC (A, x)); |
---|
1252 | henselLiftResume12 (A, bufUniFactors, smallFactorDeg, |
---|
1253 | dummy, Pi, diophant, M, b); |
---|
1254 | if (v!=alpha) |
---|
1255 | { |
---|
1256 | bufBufUniFactors= bufUniFactors; |
---|
1257 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
1258 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
1259 | } |
---|
1260 | if (!extension) |
---|
1261 | { |
---|
1262 | if (v==alpha) |
---|
1263 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
1264 | factorsFoundIndex, degs, earlySuccess, dummy, b, |
---|
1265 | den); |
---|
1266 | else |
---|
1267 | earlyFactorDetection (earlyFactors, bufA,bufBufUniFactors, newLiftBound, |
---|
1268 | factorsFoundIndex, degs, earlySuccess, dummy, b, |
---|
1269 | den); |
---|
1270 | } |
---|
1271 | else |
---|
1272 | extEarlyFactorDetection (earlyFactors, bufA,bufUniFactors, newLiftBound, |
---|
1273 | factorsFoundIndex, degs, earlySuccess, info, |
---|
1274 | eval, dummy); |
---|
1275 | } |
---|
1276 | while (degs.getLength() > 1 && !earlySuccess && i < 4) |
---|
1277 | { |
---|
1278 | if (newLiftBound >= dummy) |
---|
1279 | { |
---|
1280 | bufUniFactors.insert (LC (A, x)); |
---|
1281 | dummy= tmin (degree (A,y)+1, (degree (A,y)/4)*(i+1)+4); |
---|
1282 | henselLiftResume12 (A, bufUniFactors, (degree (A,y)/4)*i + 4, |
---|
1283 | dummy, Pi, diophant, M, b); |
---|
1284 | if (v!=alpha) |
---|
1285 | { |
---|
1286 | bufBufUniFactors= bufUniFactors; |
---|
1287 | for (CFListIterator iter= bufBufUniFactors; iter.hasItem(); iter++) |
---|
1288 | iter.getItem()= replacevar (iter.getItem(), v, alpha); |
---|
1289 | } |
---|
1290 | if (!extension) |
---|
1291 | { |
---|
1292 | if (v==alpha) |
---|
1293 | earlyFactorDetection (earlyFactors, bufA, bufUniFactors, newLiftBound, |
---|
1294 | factorsFoundIndex, degs, earlySuccess, dummy,b, |
---|
1295 | den); |
---|
1296 | else |
---|
1297 | earlyFactorDetection (earlyFactors,bufA,bufBufUniFactors,newLiftBound, |
---|
1298 | factorsFoundIndex, degs, earlySuccess, dummy,b, |
---|
1299 | den); |
---|
1300 | } |
---|
1301 | else |
---|
1302 | extEarlyFactorDetection (earlyFactors,bufA,bufUniFactors,newLiftBound, |
---|
1303 | factorsFoundIndex, degs, earlySuccess, info, |
---|
1304 | eval, dummy); |
---|
1305 | } |
---|
1306 | else |
---|
1307 | { |
---|
1308 | liftBound= newLiftBound; |
---|
1309 | break; |
---|
1310 | } |
---|
1311 | i++; |
---|
1312 | } |
---|
1313 | if (earlySuccess) |
---|
1314 | liftBound= newLiftBound; |
---|
1315 | } |
---|
1316 | |
---|
1317 | A= bufA; |
---|
1318 | if (earlyFactors.length() > 0 && degs.getLength() > 1) |
---|
1319 | { |
---|
1320 | liftBound= degree (A,y) + 1; |
---|
1321 | earlySuccess= true; |
---|
1322 | deleteFactors (bufUniFactors, factorsFoundIndex); |
---|
1323 | } |
---|
1324 | |
---|
1325 | delete [] factorsFoundIndex; |
---|
1326 | delete [] liftPre; |
---|
1327 | |
---|
1328 | return bufUniFactors; |
---|
1329 | } |
---|
1330 | |
---|
1331 | CFList |
---|
1332 | henselLiftAndEarly (CanonicalForm& A, bool& earlySuccess, CFList& |
---|
1333 | earlyFactors, DegreePattern& degs, int& liftBound, |
---|
1334 | const CFList& uniFactors, const ExtensionInfo& info, |
---|
1335 | const CanonicalForm& eval) |
---|
1336 | { |
---|
1337 | modpk dummy= modpk(); |
---|
1338 | CanonicalForm den= 1; |
---|
1339 | return henselLiftAndEarly (A, earlySuccess, earlyFactors, degs, liftBound, |
---|
1340 | uniFactors, info, eval, dummy, den); |
---|
1341 | } |
---|
1342 | |
---|
1343 | long isReduced (const mat_zz_p& M) |
---|
1344 | { |
---|
1345 | long i, j, nonZero; |
---|
1346 | for (i = 1; i <= M.NumRows(); i++) |
---|
1347 | { |
---|
1348 | nonZero= 0; |
---|
1349 | for (j = 1; j <= M.NumCols(); j++) |
---|
1350 | { |
---|
1351 | if (!IsZero (M (i,j))) |
---|
1352 | nonZero++; |
---|
1353 | } |
---|
1354 | if (nonZero != 1) |
---|
1355 | return 0; |
---|
1356 | } |
---|
1357 | return 1; |
---|
1358 | } |
---|
1359 | |
---|
1360 | #ifdef HAVE_FLINT |
---|
1361 | long isReduced (const nmod_mat_t M) |
---|
1362 | { |
---|
1363 | long i, j, nonZero; |
---|
1364 | for (i = 1; i <= nmod_mat_nrows(M); i++) |
---|
1365 | { |
---|
1366 | nonZero= 0; |
---|
1367 | for (j = 1; j <= nmod_mat_ncols (M); j++) |
---|
1368 | { |
---|
1369 | if (!(nmod_mat_entry (M, i-1, j-1)==0)) |
---|
1370 | nonZero++; |
---|
1371 | } |
---|
1372 | if (nonZero != 1) |
---|
1373 | return 0; |
---|
1374 | } |
---|
1375 | return 1; |
---|
1376 | } |
---|
1377 | #endif |
---|
1378 | |
---|
1379 | long isReduced (const mat_zz_pE& M) |
---|
1380 | { |
---|
1381 | long i, j, nonZero; |
---|
1382 | for (i = 1; i <= M.NumRows(); i++) |
---|
1383 | { |
---|
1384 | nonZero= 0; |
---|
1385 | for (j = 1; j <= M.NumCols(); j++) |
---|
1386 | { |
---|
1387 | if (!IsZero (M (i,j))) |
---|
1388 | nonZero++; |
---|
1389 | } |
---|
1390 | if (nonZero != 1) |
---|
1391 | return 0; |
---|
1392 | } |
---|
1393 | return 1; |
---|
1394 | } |
---|
1395 | |
---|
1396 | int * extractZeroOneVecs (const mat_zz_p& M) |
---|
1397 | { |
---|
1398 | long i, j; |
---|
1399 | bool nonZeroOne= false; |
---|
1400 | int * result= new int [M.NumCols()]; |
---|
1401 | for (i = 1; i <= M.NumCols(); i++) |
---|
1402 | { |
---|
1403 | for (j = 1; j <= M.NumRows(); j++) |
---|
1404 | { |
---|
1405 | if (!(IsOne (M (j,i)) || IsZero (M (j,i)))) |
---|
1406 | { |
---|
1407 | nonZeroOne= true; |
---|
1408 | break; |
---|
1409 | } |
---|
1410 | } |
---|
1411 | if (!nonZeroOne) |
---|
1412 | result [i - 1]= 1; |
---|
1413 | else |
---|
1414 | result [i - 1]= 0; |
---|
1415 | nonZeroOne= false; |
---|
1416 | } |
---|
1417 | return result; |
---|
1418 | } |
---|
1419 | |
---|
1420 | #ifdef HAVE_FLINT |
---|
1421 | int * extractZeroOneVecs (const nmod_mat_t M) |
---|
1422 | { |
---|
1423 | long i, j; |
---|
1424 | bool nonZeroOne= false; |
---|
1425 | int * result= new int [nmod_mat_ncols (M)]; |
---|
1426 | for (i = 0; i < nmod_mat_ncols (M); i++) |
---|
1427 | { |
---|
1428 | for (j = 0; j < nmod_mat_nrows (M); j++) |
---|
1429 | { |
---|
1430 | if (!((nmod_mat_entry (M, j, i) == 1) || (nmod_mat_entry (M, j,i) == 0))) |
---|
1431 | { |
---|
1432 | nonZeroOne= true; |
---|
1433 | break; |
---|
1434 | } |
---|
1435 | } |
---|
1436 | if (!nonZeroOne) |
---|
1437 | result [i]= 1; |
---|
1438 | else |
---|
1439 | result [i]= 0; |
---|
1440 | nonZeroOne= false; |
---|
1441 | } |
---|
1442 | return result; |
---|
1443 | } |
---|
1444 | #endif |
---|
1445 | |
---|
1446 | int * extractZeroOneVecs (const mat_zz_pE& M) |
---|
1447 | { |
---|
1448 | long i, j; |
---|
1449 | bool nonZeroOne= false; |
---|
1450 | int * result= new int [M.NumCols()]; |
---|
1451 | for (i = 1; i <= M.NumCols(); i++) |
---|
1452 | { |
---|
1453 | for (j = 1; j <= M.NumRows(); j++) |
---|
1454 | { |
---|
1455 | if (!(IsOne (M (j,i)) || IsZero (M (j,i)))) |
---|
1456 | { |
---|
1457 | nonZeroOne= true; |
---|
1458 | break; |
---|
1459 | } |
---|
1460 | } |
---|
1461 | if (!nonZeroOne) |
---|
1462 | result [i - 1]= 1; |
---|
1463 | else |
---|
1464 | result [i - 1]= 0; |
---|
1465 | nonZeroOne= false; |
---|
1466 | } |
---|
1467 | return result; |
---|
1468 | } |
---|
1469 | |
---|
1470 | void |
---|
1471 | reconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const CFList& |
---|
1472 | factors, const int liftBound, int& factorsFound, int*& |
---|
1473 | factorsFoundIndex, mat_zz_pE& N, bool beenInThres |
---|
1474 | ) |
---|
1475 | { |
---|
1476 | Variable y= Variable (2); |
---|
1477 | Variable x= Variable (1); |
---|
1478 | CanonicalForm yToL= power (y, liftBound); |
---|
1479 | if (factors.length() == 2) |
---|
1480 | { |
---|
1481 | CanonicalForm tmp1, tmp2, tmp3; |
---|
1482 | tmp1= factors.getFirst(); |
---|
1483 | tmp2= factors.getLast(); |
---|
1484 | tmp1= mulMod2 (tmp1, LC (F,x), yToL); |
---|
1485 | tmp1 /= content (tmp1, x); |
---|
1486 | tmp2= mulMod2 (tmp2, LC (F,x), yToL); |
---|
1487 | tmp2 /= content (tmp2, x); |
---|
1488 | tmp3 = tmp1*tmp2; |
---|
1489 | if (tmp3/Lc (tmp3) == F/Lc (F)) |
---|
1490 | { |
---|
1491 | factorsFound++; |
---|
1492 | F= 1; |
---|
1493 | reconstructedFactors.append (tmp1); |
---|
1494 | reconstructedFactors.append (tmp2); |
---|
1495 | return; |
---|
1496 | } |
---|
1497 | } |
---|
1498 | CanonicalForm quot, buf; |
---|
1499 | CFListIterator iter; |
---|
1500 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1501 | { |
---|
1502 | if (factorsFoundIndex [i - 1] == 1) |
---|
1503 | continue; |
---|
1504 | iter= factors; |
---|
1505 | if (beenInThres) |
---|
1506 | { |
---|
1507 | int count= 1; |
---|
1508 | while (count < i) |
---|
1509 | { |
---|
1510 | count++; |
---|
1511 | iter++; |
---|
1512 | } |
---|
1513 | buf= iter.getItem(); |
---|
1514 | } |
---|
1515 | else |
---|
1516 | { |
---|
1517 | buf= 1; |
---|
1518 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1519 | { |
---|
1520 | if (!IsZero (N (j,i))) |
---|
1521 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1522 | } |
---|
1523 | } |
---|
1524 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
1525 | buf /= content (buf, x); |
---|
1526 | if (fdivides (buf, F, quot)) |
---|
1527 | { |
---|
1528 | factorsFoundIndex[i - 1]= 1; |
---|
1529 | factorsFound++; |
---|
1530 | F= quot; |
---|
1531 | F /= Lc (F); |
---|
1532 | reconstructedFactors.append (buf); |
---|
1533 | } |
---|
1534 | if (degree (F) <= 0) |
---|
1535 | return; |
---|
1536 | if (factorsFound + 1 == N.NumCols()) |
---|
1537 | { |
---|
1538 | reconstructedFactors.append (F); |
---|
1539 | return; |
---|
1540 | } |
---|
1541 | } |
---|
1542 | } |
---|
1543 | |
---|
1544 | void |
---|
1545 | reconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const CFList& |
---|
1546 | factors, const int liftBound, int& factorsFound, int*& |
---|
1547 | factorsFoundIndex, mat_zz_p& N, bool beenInThres |
---|
1548 | ) |
---|
1549 | { |
---|
1550 | Variable y= Variable (2); |
---|
1551 | Variable x= Variable (1); |
---|
1552 | CanonicalForm yToL= power (y, liftBound); |
---|
1553 | if (factors.length() == 2) |
---|
1554 | { |
---|
1555 | CanonicalForm tmp1, tmp2, tmp3; |
---|
1556 | tmp1= factors.getFirst(); |
---|
1557 | tmp2= factors.getLast(); |
---|
1558 | tmp1= mulMod2 (tmp1, LC (F,x), yToL); |
---|
1559 | tmp1 /= content (tmp1, x); |
---|
1560 | tmp2= mulMod2 (tmp2, LC (F,x), yToL); |
---|
1561 | tmp2 /= content (tmp2, x); |
---|
1562 | tmp3 = tmp1*tmp2; |
---|
1563 | if (tmp3/Lc (tmp3) == F/Lc (F)) |
---|
1564 | { |
---|
1565 | factorsFound++; |
---|
1566 | F= 1; |
---|
1567 | reconstructedFactors.append (tmp1); |
---|
1568 | reconstructedFactors.append (tmp2); |
---|
1569 | return; |
---|
1570 | } |
---|
1571 | } |
---|
1572 | CanonicalForm quot, buf; |
---|
1573 | CFListIterator iter; |
---|
1574 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1575 | { |
---|
1576 | if (factorsFoundIndex [i - 1] == 1) |
---|
1577 | continue; |
---|
1578 | iter= factors; |
---|
1579 | if (beenInThres) |
---|
1580 | { |
---|
1581 | int count= 1; |
---|
1582 | while (count < i) |
---|
1583 | { |
---|
1584 | count++; |
---|
1585 | iter++; |
---|
1586 | } |
---|
1587 | buf= iter.getItem(); |
---|
1588 | } |
---|
1589 | else |
---|
1590 | { |
---|
1591 | buf= 1; |
---|
1592 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1593 | { |
---|
1594 | if (!IsZero (N (j,i))) |
---|
1595 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1596 | } |
---|
1597 | } |
---|
1598 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
1599 | buf /= content (buf, x); |
---|
1600 | if (fdivides (buf, F, quot)) |
---|
1601 | { |
---|
1602 | factorsFoundIndex[i - 1]= 1; |
---|
1603 | factorsFound++; |
---|
1604 | F= quot; |
---|
1605 | F /= Lc (F); |
---|
1606 | reconstructedFactors.append (buf); |
---|
1607 | } |
---|
1608 | if (degree (F) <= 0) |
---|
1609 | return; |
---|
1610 | if (factorsFound + 1 == N.NumCols()) |
---|
1611 | { |
---|
1612 | reconstructedFactors.append (F); |
---|
1613 | return; |
---|
1614 | } |
---|
1615 | } |
---|
1616 | } |
---|
1617 | |
---|
1618 | #ifdef HAVE_FLINT |
---|
1619 | void |
---|
1620 | reconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const CFList& |
---|
1621 | factors, const int liftBound, int& factorsFound, int*& |
---|
1622 | factorsFoundIndex, nmod_mat_t N, bool beenInThres |
---|
1623 | ) |
---|
1624 | { |
---|
1625 | Variable y= Variable (2); |
---|
1626 | Variable x= Variable (1); |
---|
1627 | CanonicalForm yToL= power (y, liftBound); |
---|
1628 | if (factors.length() == 2) |
---|
1629 | { |
---|
1630 | CanonicalForm tmp1, tmp2, tmp3; |
---|
1631 | tmp1= factors.getFirst(); |
---|
1632 | tmp2= factors.getLast(); |
---|
1633 | tmp1= mulMod2 (tmp1, LC (F,x), yToL); |
---|
1634 | tmp1 /= content (tmp1, x); |
---|
1635 | tmp2= mulMod2 (tmp2, LC (F,x), yToL); |
---|
1636 | tmp2 /= content (tmp2, x); |
---|
1637 | tmp3 = tmp1*tmp2; |
---|
1638 | if (tmp3/Lc (tmp3) == F/Lc (F)) |
---|
1639 | { |
---|
1640 | factorsFound++; |
---|
1641 | F= 1; |
---|
1642 | reconstructedFactors.append (tmp1); |
---|
1643 | reconstructedFactors.append (tmp2); |
---|
1644 | return; |
---|
1645 | } |
---|
1646 | } |
---|
1647 | CanonicalForm quot, buf; |
---|
1648 | CFListIterator iter; |
---|
1649 | for (long i= 0; i < nmod_mat_ncols (N); i++) |
---|
1650 | { |
---|
1651 | if (factorsFoundIndex [i] == 1) |
---|
1652 | continue; |
---|
1653 | iter= factors; |
---|
1654 | if (beenInThres) |
---|
1655 | { |
---|
1656 | int count= 0; |
---|
1657 | while (count < i) |
---|
1658 | { |
---|
1659 | count++; |
---|
1660 | iter++; |
---|
1661 | } |
---|
1662 | buf= iter.getItem(); |
---|
1663 | } |
---|
1664 | else |
---|
1665 | { |
---|
1666 | buf= 1; |
---|
1667 | for (long j= 0; j < nmod_mat_nrows (N); j++, iter++) |
---|
1668 | { |
---|
1669 | if (!(nmod_mat_entry (N, j, i) == 0)) |
---|
1670 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1671 | } |
---|
1672 | } |
---|
1673 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
1674 | buf /= content (buf, x); |
---|
1675 | if (fdivides (buf, F, quot)) |
---|
1676 | { |
---|
1677 | factorsFoundIndex[i]= 1; |
---|
1678 | factorsFound++; |
---|
1679 | F= quot; |
---|
1680 | F /= Lc (F); |
---|
1681 | reconstructedFactors.append (buf); |
---|
1682 | } |
---|
1683 | if (degree (F) <= 0) |
---|
1684 | return; |
---|
1685 | if (factorsFound + 1 == nmod_mat_ncols (N)) |
---|
1686 | { |
---|
1687 | reconstructedFactors.append (F); |
---|
1688 | return; |
---|
1689 | } |
---|
1690 | } |
---|
1691 | } |
---|
1692 | #endif |
---|
1693 | |
---|
1694 | CFList |
---|
1695 | reconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, int |
---|
1696 | precision, const mat_zz_pE& N |
---|
1697 | ) |
---|
1698 | { |
---|
1699 | Variable y= Variable (2); |
---|
1700 | Variable x= Variable (1); |
---|
1701 | CanonicalForm F= G; |
---|
1702 | CanonicalForm yToL= power (y, precision); |
---|
1703 | CanonicalForm quot, buf; |
---|
1704 | CFList result, factorsConsidered; |
---|
1705 | CFList bufFactors= factors; |
---|
1706 | CFListIterator iter; |
---|
1707 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1708 | { |
---|
1709 | if (zeroOneVecs [i - 1] == 0) |
---|
1710 | continue; |
---|
1711 | iter= factors; |
---|
1712 | buf= 1; |
---|
1713 | factorsConsidered= CFList(); |
---|
1714 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1715 | { |
---|
1716 | if (!IsZero (N (j,i))) |
---|
1717 | { |
---|
1718 | factorsConsidered.append (iter.getItem()); |
---|
1719 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1720 | } |
---|
1721 | } |
---|
1722 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
1723 | buf /= content (buf, x); |
---|
1724 | if (fdivides (buf, F, quot)) |
---|
1725 | { |
---|
1726 | F= quot; |
---|
1727 | F /= Lc (F); |
---|
1728 | result.append (buf); |
---|
1729 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
1730 | } |
---|
1731 | if (degree (F) <= 0) |
---|
1732 | { |
---|
1733 | G= F; |
---|
1734 | factors= bufFactors; |
---|
1735 | return result; |
---|
1736 | } |
---|
1737 | } |
---|
1738 | G= F; |
---|
1739 | factors= bufFactors; |
---|
1740 | return result; |
---|
1741 | } |
---|
1742 | |
---|
1743 | CFList |
---|
1744 | monicReconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, |
---|
1745 | int precision, const mat_zz_pE& N |
---|
1746 | ) |
---|
1747 | { |
---|
1748 | Variable y= Variable (2); |
---|
1749 | Variable x= Variable (1); |
---|
1750 | CanonicalForm F= G; |
---|
1751 | CanonicalForm yToL= power (y, precision); |
---|
1752 | CanonicalForm quot, buf, buf2; |
---|
1753 | CFList result; |
---|
1754 | CFList bufFactors= factors; |
---|
1755 | CFList factorsConsidered; |
---|
1756 | CFListIterator iter; |
---|
1757 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1758 | { |
---|
1759 | if (zeroOneVecs [i - 1] == 0) |
---|
1760 | continue; |
---|
1761 | iter= factors; |
---|
1762 | buf= 1; |
---|
1763 | factorsConsidered= CFList(); |
---|
1764 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1765 | { |
---|
1766 | if (!IsZero (N (j,i))) |
---|
1767 | { |
---|
1768 | factorsConsidered.append (iter.getItem()); |
---|
1769 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1770 | } |
---|
1771 | } |
---|
1772 | buf2= buf; |
---|
1773 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
1774 | buf /= content (buf, x); |
---|
1775 | if (fdivides (buf, F, quot)) |
---|
1776 | { |
---|
1777 | F= quot; |
---|
1778 | F /= Lc (F); |
---|
1779 | result.append (buf2); |
---|
1780 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
1781 | } |
---|
1782 | if (degree (F) <= 0) |
---|
1783 | { |
---|
1784 | G= F; |
---|
1785 | factors= bufFactors; |
---|
1786 | return result; |
---|
1787 | } |
---|
1788 | } |
---|
1789 | G= F; |
---|
1790 | factors= bufFactors; |
---|
1791 | return result; |
---|
1792 | } |
---|
1793 | |
---|
1794 | CFList |
---|
1795 | extReconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, int |
---|
1796 | precision, const mat_zz_p& N, const ExtensionInfo& info, |
---|
1797 | const CanonicalForm& evaluation |
---|
1798 | ) |
---|
1799 | { |
---|
1800 | Variable y= Variable (2); |
---|
1801 | Variable x= Variable (1); |
---|
1802 | Variable alpha= info.getAlpha(); |
---|
1803 | Variable beta= info.getBeta(); |
---|
1804 | int k= info.getGFDegree(); |
---|
1805 | CanonicalForm gamma= info.getGamma(); |
---|
1806 | CanonicalForm delta= info.getDelta(); |
---|
1807 | CanonicalForm F= G; |
---|
1808 | CanonicalForm yToL= power (y, precision); |
---|
1809 | CFList result; |
---|
1810 | CFList bufFactors= factors; |
---|
1811 | CFList factorsConsidered; |
---|
1812 | CanonicalForm buf2, quot, buf; |
---|
1813 | CFListIterator iter; |
---|
1814 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1815 | { |
---|
1816 | if (zeroOneVecs [i - 1] == 0) |
---|
1817 | continue; |
---|
1818 | iter= factors; |
---|
1819 | buf= 1; |
---|
1820 | factorsConsidered= CFList(); |
---|
1821 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1822 | { |
---|
1823 | if (!IsZero (N (j,i))) |
---|
1824 | { |
---|
1825 | factorsConsidered.append (iter.getItem()); |
---|
1826 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1827 | } |
---|
1828 | } |
---|
1829 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
1830 | buf /= content (buf, x); |
---|
1831 | buf2= buf (y-evaluation, y); |
---|
1832 | buf2 /= Lc (buf2); |
---|
1833 | if (!k && beta == x) |
---|
1834 | { |
---|
1835 | if (degree (buf2, alpha) < 1) |
---|
1836 | { |
---|
1837 | if (fdivides (buf, F, quot)) |
---|
1838 | { |
---|
1839 | F= quot; |
---|
1840 | F /= Lc (F); |
---|
1841 | result.append (buf2); |
---|
1842 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
1843 | } |
---|
1844 | } |
---|
1845 | } |
---|
1846 | else |
---|
1847 | { |
---|
1848 | CFList source, dest; |
---|
1849 | |
---|
1850 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
1851 | { |
---|
1852 | if (fdivides (buf, F, quot)) |
---|
1853 | { |
---|
1854 | F= quot; |
---|
1855 | F /= Lc (F); |
---|
1856 | result.append (buf2); |
---|
1857 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
1858 | } |
---|
1859 | } |
---|
1860 | } |
---|
1861 | if (degree (F) <= 0) |
---|
1862 | { |
---|
1863 | G= F; |
---|
1864 | factors= bufFactors; |
---|
1865 | return result; |
---|
1866 | } |
---|
1867 | } |
---|
1868 | G= F; |
---|
1869 | factors= bufFactors; |
---|
1870 | return result; |
---|
1871 | } |
---|
1872 | |
---|
1873 | #ifdef HAVE_FLINT |
---|
1874 | CFList |
---|
1875 | extReconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, int |
---|
1876 | precision, const nmod_mat_t N, const ExtensionInfo& info, |
---|
1877 | const CanonicalForm& evaluation |
---|
1878 | ) |
---|
1879 | { |
---|
1880 | Variable y= Variable (2); |
---|
1881 | Variable x= Variable (1); |
---|
1882 | Variable alpha= info.getAlpha(); |
---|
1883 | Variable beta= info.getBeta(); |
---|
1884 | int k= info.getGFDegree(); |
---|
1885 | CanonicalForm gamma= info.getGamma(); |
---|
1886 | CanonicalForm delta= info.getDelta(); |
---|
1887 | CanonicalForm F= G; |
---|
1888 | CanonicalForm yToL= power (y, precision); |
---|
1889 | CFList result; |
---|
1890 | CFList bufFactors= factors; |
---|
1891 | CFList factorsConsidered; |
---|
1892 | CanonicalForm buf2, quot, buf; |
---|
1893 | CFListIterator iter; |
---|
1894 | for (long i= 0; i < nmod_mat_ncols(N); i++) |
---|
1895 | { |
---|
1896 | if (zeroOneVecs [i] == 0) |
---|
1897 | continue; |
---|
1898 | iter= factors; |
---|
1899 | buf= 1; |
---|
1900 | factorsConsidered= CFList(); |
---|
1901 | for (long j= 0; j < nmod_mat_ncols(N); j++, iter++) |
---|
1902 | { |
---|
1903 | if (!(nmod_mat_entry (N, j, i) == 0)) |
---|
1904 | { |
---|
1905 | factorsConsidered.append (iter.getItem()); |
---|
1906 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1907 | } |
---|
1908 | } |
---|
1909 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
1910 | buf /= content (buf, x); |
---|
1911 | buf2= buf (y-evaluation, y); |
---|
1912 | buf2 /= Lc (buf2); |
---|
1913 | if (!k && beta == x) |
---|
1914 | { |
---|
1915 | if (degree (buf2, alpha) < 1) |
---|
1916 | { |
---|
1917 | if (fdivides (buf, F, quot)) |
---|
1918 | { |
---|
1919 | F= quot; |
---|
1920 | F /= Lc (F); |
---|
1921 | result.append (buf2); |
---|
1922 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
1923 | } |
---|
1924 | } |
---|
1925 | } |
---|
1926 | else |
---|
1927 | { |
---|
1928 | CFList source, dest; |
---|
1929 | |
---|
1930 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
1931 | { |
---|
1932 | if (fdivides (buf, F, quot)) |
---|
1933 | { |
---|
1934 | F= quot; |
---|
1935 | F /= Lc (F); |
---|
1936 | result.append (buf2); |
---|
1937 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
1938 | } |
---|
1939 | } |
---|
1940 | } |
---|
1941 | if (degree (F) <= 0) |
---|
1942 | { |
---|
1943 | G= F; |
---|
1944 | factors= bufFactors; |
---|
1945 | return result; |
---|
1946 | } |
---|
1947 | } |
---|
1948 | G= F; |
---|
1949 | factors= bufFactors; |
---|
1950 | return result; |
---|
1951 | } |
---|
1952 | #endif |
---|
1953 | |
---|
1954 | CFList |
---|
1955 | reconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, |
---|
1956 | int precision, const mat_zz_p& N) |
---|
1957 | { |
---|
1958 | Variable y= Variable (2); |
---|
1959 | Variable x= Variable (1); |
---|
1960 | CanonicalForm F= G; |
---|
1961 | CanonicalForm yToL= power (y, precision); |
---|
1962 | CanonicalForm quot, buf; |
---|
1963 | CFList result; |
---|
1964 | CFList bufFactors= factors; |
---|
1965 | CFList factorsConsidered; |
---|
1966 | CFListIterator iter; |
---|
1967 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1968 | { |
---|
1969 | if (zeroOneVecs [i - 1] == 0) |
---|
1970 | continue; |
---|
1971 | iter= factors; |
---|
1972 | buf= 1; |
---|
1973 | factorsConsidered= CFList(); |
---|
1974 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1975 | { |
---|
1976 | if (!IsZero (N (j,i))) |
---|
1977 | { |
---|
1978 | factorsConsidered.append (iter.getItem()); |
---|
1979 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1980 | } |
---|
1981 | } |
---|
1982 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
1983 | buf /= content (buf, x); |
---|
1984 | if (fdivides (buf, F, quot)) |
---|
1985 | { |
---|
1986 | F= quot; |
---|
1987 | F /= Lc (F); |
---|
1988 | result.append (buf); |
---|
1989 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
1990 | } |
---|
1991 | if (degree (F) <= 0) |
---|
1992 | { |
---|
1993 | G= F; |
---|
1994 | factors= bufFactors; |
---|
1995 | return result; |
---|
1996 | } |
---|
1997 | } |
---|
1998 | G= F; |
---|
1999 | factors= bufFactors; |
---|
2000 | return result; |
---|
2001 | } |
---|
2002 | |
---|
2003 | #ifdef HAVE_FLINT |
---|
2004 | CFList |
---|
2005 | reconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, |
---|
2006 | int precision, const nmod_mat_t N) |
---|
2007 | { |
---|
2008 | Variable y= Variable (2); |
---|
2009 | Variable x= Variable (1); |
---|
2010 | CanonicalForm F= G; |
---|
2011 | CanonicalForm yToL= power (y, precision); |
---|
2012 | CanonicalForm quot, buf; |
---|
2013 | CFList result; |
---|
2014 | CFList bufFactors= factors; |
---|
2015 | CFList factorsConsidered; |
---|
2016 | CFListIterator iter; |
---|
2017 | for (long i= 0; i < nmod_mat_ncols (N); i++) |
---|
2018 | { |
---|
2019 | if (zeroOneVecs [i] == 0) |
---|
2020 | continue; |
---|
2021 | iter= factors; |
---|
2022 | buf= 1; |
---|
2023 | factorsConsidered= CFList(); |
---|
2024 | for (long j= 0; j < nmod_mat_nrows (N); j++, iter++) |
---|
2025 | { |
---|
2026 | if (!(nmod_mat_entry (N, j, i) == 0)) |
---|
2027 | { |
---|
2028 | factorsConsidered.append (iter.getItem()); |
---|
2029 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
2030 | } |
---|
2031 | } |
---|
2032 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
2033 | buf /= content (buf, x); |
---|
2034 | if (fdivides (buf, F, quot)) |
---|
2035 | { |
---|
2036 | F= quot; |
---|
2037 | F /= Lc (F); |
---|
2038 | result.append (buf); |
---|
2039 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
2040 | } |
---|
2041 | if (degree (F) <= 0) |
---|
2042 | { |
---|
2043 | G= F; |
---|
2044 | factors= bufFactors; |
---|
2045 | return result; |
---|
2046 | } |
---|
2047 | } |
---|
2048 | G= F; |
---|
2049 | factors= bufFactors; |
---|
2050 | return result; |
---|
2051 | } |
---|
2052 | #endif |
---|
2053 | |
---|
2054 | void |
---|
2055 | extReconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const |
---|
2056 | CFList& factors, const int liftBound, int& factorsFound, |
---|
2057 | int*& factorsFoundIndex, mat_zz_p& N, bool beenInThres, |
---|
2058 | const ExtensionInfo& info, const CanonicalForm& evaluation |
---|
2059 | ) |
---|
2060 | { |
---|
2061 | Variable y= Variable (2); |
---|
2062 | Variable x= Variable (1); |
---|
2063 | Variable alpha= info.getAlpha(); |
---|
2064 | Variable beta= info.getBeta(); |
---|
2065 | int k= info.getGFDegree(); |
---|
2066 | CanonicalForm gamma= info.getGamma(); |
---|
2067 | CanonicalForm delta= info.getDelta(); |
---|
2068 | CanonicalForm yToL= power (y, liftBound); |
---|
2069 | CFList source, dest; |
---|
2070 | if (factors.length() == 2) |
---|
2071 | { |
---|
2072 | CanonicalForm tmp1, tmp2, tmp3; |
---|
2073 | tmp1= factors.getFirst(); |
---|
2074 | tmp2= factors.getLast(); |
---|
2075 | tmp1= mulMod2 (tmp1, LC (F,x), yToL); |
---|
2076 | tmp1 /= content (tmp1, x); |
---|
2077 | tmp2= mulMod2 (tmp2, LC (F,x), yToL); |
---|
2078 | tmp2 /= content (tmp2, x); |
---|
2079 | tmp3 = tmp1*tmp2; |
---|
2080 | if (tmp3/Lc (tmp3) == F/Lc (F)) |
---|
2081 | { |
---|
2082 | tmp1= tmp1 (y - evaluation, y); |
---|
2083 | tmp2= tmp2 (y - evaluation, y); |
---|
2084 | tmp1 /= Lc (tmp1); |
---|
2085 | tmp2 /= Lc (tmp2); |
---|
2086 | if (!k && beta == x && degree (tmp2, alpha) < 1 && |
---|
2087 | degree (tmp1, alpha) < 1) |
---|
2088 | { |
---|
2089 | factorsFound++; |
---|
2090 | F= 1; |
---|
2091 | tmp1= mapDown (tmp1, info, source, dest); |
---|
2092 | tmp2= mapDown (tmp2, info, source, dest); |
---|
2093 | reconstructedFactors.append (tmp1); |
---|
2094 | reconstructedFactors.append (tmp2); |
---|
2095 | return; |
---|
2096 | } |
---|
2097 | else if (!isInExtension (tmp2, gamma, k, delta, source, dest) && |
---|
2098 | !isInExtension (tmp1, gamma, k, delta, source, dest)) |
---|
2099 | { |
---|
2100 | factorsFound++; |
---|
2101 | F= 1; |
---|
2102 | tmp1= mapDown (tmp1, info, source, dest); |
---|
2103 | tmp2= mapDown (tmp2, info, source, dest); |
---|
2104 | reconstructedFactors.append (tmp1); |
---|
2105 | reconstructedFactors.append (tmp2); |
---|
2106 | return; |
---|
2107 | } |
---|
2108 | } |
---|
2109 | } |
---|
2110 | CanonicalForm quot, buf, buf2; |
---|
2111 | CFListIterator iter; |
---|
2112 | for (long i= 1; i <= N.NumCols(); i++) |
---|
2113 | { |
---|
2114 | if (factorsFoundIndex [i - 1] == 1) |
---|
2115 | continue; |
---|
2116 | iter= factors; |
---|
2117 | if (beenInThres) |
---|
2118 | { |
---|
2119 | int count= 1; |
---|
2120 | while (count < i) |
---|
2121 | { |
---|
2122 | count++; |
---|
2123 | iter++; |
---|
2124 | } |
---|
2125 | buf= iter.getItem(); |
---|
2126 | } |
---|
2127 | else |
---|
2128 | { |
---|
2129 | buf= 1; |
---|
2130 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
2131 | { |
---|
2132 | if (!IsZero (N (j,i))) |
---|
2133 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
2134 | } |
---|
2135 | } |
---|
2136 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
2137 | buf /= content (buf, x); |
---|
2138 | buf2= buf (y - evaluation, y); |
---|
2139 | buf2 /= Lc (buf2); |
---|
2140 | if (!k && beta == x) |
---|
2141 | { |
---|
2142 | if (degree (buf2, alpha) < 1) |
---|
2143 | { |
---|
2144 | if (fdivides (buf, F, quot)) |
---|
2145 | { |
---|
2146 | factorsFoundIndex[i - 1]= 1; |
---|
2147 | factorsFound++; |
---|
2148 | F= quot; |
---|
2149 | F /= Lc (F); |
---|
2150 | buf2= mapDown (buf2, info, source, dest); |
---|
2151 | reconstructedFactors.append (buf2); |
---|
2152 | } |
---|
2153 | } |
---|
2154 | } |
---|
2155 | else |
---|
2156 | { |
---|
2157 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
2158 | { |
---|
2159 | if (fdivides (buf, F, quot)) |
---|
2160 | { |
---|
2161 | factorsFoundIndex[i - 1]= 1; |
---|
2162 | factorsFound++; |
---|
2163 | F= quot; |
---|
2164 | F /= Lc (F); |
---|
2165 | buf2= mapDown (buf2, info, source, dest); |
---|
2166 | reconstructedFactors.append (buf2); |
---|
2167 | } |
---|
2168 | } |
---|
2169 | } |
---|
2170 | if (degree (F) <= 0) |
---|
2171 | return; |
---|
2172 | if (factorsFound + 1 == N.NumCols()) |
---|
2173 | { |
---|
2174 | CanonicalForm tmp= F (y - evaluation, y); |
---|
2175 | tmp= mapDown (tmp, info, source, dest); |
---|
2176 | reconstructedFactors.append (tmp); |
---|
2177 | return; |
---|
2178 | } |
---|
2179 | } |
---|
2180 | } |
---|
2181 | |
---|
2182 | #ifdef HAVE_FLINT |
---|
2183 | void |
---|
2184 | extReconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const |
---|
2185 | CFList& factors, const int liftBound, int& factorsFound, |
---|
2186 | int*& factorsFoundIndex, nmod_mat_t N, bool beenInThres, |
---|
2187 | const ExtensionInfo& info, const CanonicalForm& evaluation |
---|
2188 | ) |
---|
2189 | { |
---|
2190 | Variable y= Variable (2); |
---|
2191 | Variable x= Variable (1); |
---|
2192 | Variable alpha= info.getAlpha(); |
---|
2193 | Variable beta= info.getBeta(); |
---|
2194 | int k= info.getGFDegree(); |
---|
2195 | CanonicalForm gamma= info.getGamma(); |
---|
2196 | CanonicalForm delta= info.getDelta(); |
---|
2197 | CanonicalForm yToL= power (y, liftBound); |
---|
2198 | CFList source, dest; |
---|
2199 | if (factors.length() == 2) |
---|
2200 | { |
---|
2201 | CanonicalForm tmp1, tmp2, tmp3; |
---|
2202 | tmp1= factors.getFirst(); |
---|
2203 | tmp2= factors.getLast(); |
---|
2204 | tmp1= mulMod2 (tmp1, LC (F,x), yToL); |
---|
2205 | tmp1 /= content (tmp1, x); |
---|
2206 | tmp2= mulMod2 (tmp2, LC (F,x), yToL); |
---|
2207 | tmp2 /= content (tmp2, x); |
---|
2208 | tmp3 = tmp1*tmp2; |
---|
2209 | if (tmp3/Lc (tmp3) == F/Lc (F)) |
---|
2210 | { |
---|
2211 | tmp1= tmp1 (y - evaluation, y); |
---|
2212 | tmp2= tmp2 (y - evaluation, y); |
---|
2213 | tmp1 /= Lc (tmp1); |
---|
2214 | tmp2 /= Lc (tmp2); |
---|
2215 | if (!k && beta == x && degree (tmp2, alpha) < 1 && |
---|
2216 | degree (tmp1, alpha) < 1) |
---|
2217 | { |
---|
2218 | factorsFound++; |
---|
2219 | F= 1; |
---|
2220 | tmp1= mapDown (tmp1, info, source, dest); |
---|
2221 | tmp2= mapDown (tmp2, info, source, dest); |
---|
2222 | reconstructedFactors.append (tmp1); |
---|
2223 | reconstructedFactors.append (tmp2); |
---|
2224 | return; |
---|
2225 | } |
---|
2226 | else if (!isInExtension (tmp2, gamma, k, delta, source, dest) && |
---|
2227 | !isInExtension (tmp1, gamma, k, delta, source, dest)) |
---|
2228 | { |
---|
2229 | factorsFound++; |
---|
2230 | F= 1; |
---|
2231 | tmp1= mapDown (tmp1, info, source, dest); |
---|
2232 | tmp2= mapDown (tmp2, info, source, dest); |
---|
2233 | reconstructedFactors.append (tmp1); |
---|
2234 | reconstructedFactors.append (tmp2); |
---|
2235 | return; |
---|
2236 | } |
---|
2237 | } |
---|
2238 | } |
---|
2239 | CanonicalForm quot, buf, buf2; |
---|
2240 | CFListIterator iter; |
---|
2241 | for (long i= 0; i < nmod_mat_ncols (N); i++) |
---|
2242 | { |
---|
2243 | if (factorsFoundIndex [i] == 1) |
---|
2244 | continue; |
---|
2245 | iter= factors; |
---|
2246 | if (beenInThres) |
---|
2247 | { |
---|
2248 | int count= 0; |
---|
2249 | while (count < i) |
---|
2250 | { |
---|
2251 | count++; |
---|
2252 | iter++; |
---|
2253 | } |
---|
2254 | buf= iter.getItem(); |
---|
2255 | } |
---|
2256 | else |
---|
2257 | { |
---|
2258 | buf= 1; |
---|
2259 | for (long j= 0; j < nmod_mat_nrows (N); j++, iter++) |
---|
2260 | { |
---|
2261 | if (!(nmod_mat_entry (N, j, i) == 0)) |
---|
2262 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
2263 | } |
---|
2264 | } |
---|
2265 | buf= mulMod2 (buf, LC (F,x), yToL); |
---|
2266 | buf /= content (buf, x); |
---|
2267 | buf2= buf (y - evaluation, y); |
---|
2268 | buf2 /= Lc (buf2); |
---|
2269 | if (!k && beta == x) |
---|
2270 | { |
---|
2271 | if (degree (buf2, alpha) < 1) |
---|
2272 | { |
---|
2273 | if (fdivides (buf, F, quot)) |
---|
2274 | { |
---|
2275 | factorsFoundIndex[i]= 1; |
---|
2276 | factorsFound++; |
---|
2277 | F= quot; |
---|
2278 | F /= Lc (F); |
---|
2279 | buf2= mapDown (buf2, info, source, dest); |
---|
2280 | reconstructedFactors.append (buf2); |
---|
2281 | } |
---|
2282 | } |
---|
2283 | } |
---|
2284 | else |
---|
2285 | { |
---|
2286 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
2287 | { |
---|
2288 | if (fdivides (buf, F, quot)) |
---|
2289 | { |
---|
2290 | factorsFoundIndex[i]= 1; |
---|
2291 | factorsFound++; |
---|
2292 | F= quot; |
---|
2293 | F /= Lc (F); |
---|
2294 | buf2= mapDown (buf2, info, source, dest); |
---|
2295 | reconstructedFactors.append (buf2); |
---|
2296 | } |
---|
2297 | } |
---|
2298 | } |
---|
2299 | if (degree (F) <= 0) |
---|
2300 | return; |
---|
2301 | if (factorsFound + 1 == nmod_mat_nrows (N)) |
---|
2302 | { |
---|
2303 | CanonicalForm tmp= F (y - evaluation, y); |
---|
2304 | tmp= mapDown (tmp, info, source, dest); |
---|
2305 | reconstructedFactors.append (tmp); |
---|
2306 | return; |
---|
2307 | } |
---|
2308 | } |
---|
2309 | } |
---|
2310 | #endif |
---|
2311 | |
---|
2312 | //over Fp |
---|
2313 | int |
---|
2314 | liftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, int |
---|
2315 | start, int liftBound, int minBound, CFList& factors, |
---|
2316 | mat_zz_p& NTLN, CFList& diophant, CFMatrix& M, CFArray& |
---|
2317 | Pi, CFArray& bufQ, bool& irreducible |
---|
2318 | ) |
---|
2319 | { |
---|
2320 | CanonicalForm LCF= LC (F, 1); |
---|
2321 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
2322 | bool wasInBounds= false; |
---|
2323 | bool hitBound= false; |
---|
2324 | int l= (minBound+1)*2; |
---|
2325 | int stepSize= 2; |
---|
2326 | int oldL= l/2; |
---|
2327 | bool reduced= false; |
---|
2328 | mat_zz_p NTLK, *NTLC; |
---|
2329 | CFMatrix C; |
---|
2330 | CFArray buf; |
---|
2331 | CFListIterator j; |
---|
2332 | CanonicalForm truncF; |
---|
2333 | Variable y= F.mvar(); |
---|
2334 | while (l <= liftBound) |
---|
2335 | { |
---|
2336 | if (start) |
---|
2337 | { |
---|
2338 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
2339 | start= 0; |
---|
2340 | } |
---|
2341 | else |
---|
2342 | { |
---|
2343 | if (wasInBounds) |
---|
2344 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
2345 | else |
---|
2346 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
2347 | } |
---|
2348 | |
---|
2349 | factors.insert (LCF); |
---|
2350 | j= factors; |
---|
2351 | j++; |
---|
2352 | |
---|
2353 | truncF= mod (F, power (y, l)); |
---|
2354 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
2355 | { |
---|
2356 | if (!wasInBounds) |
---|
2357 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
2358 | else |
---|
2359 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
2360 | bufQ[i]); |
---|
2361 | } |
---|
2362 | |
---|
2363 | for (int i= 0; i < sizeBounds; i++) |
---|
2364 | { |
---|
2365 | if (bounds [i] + 1 <= l/2) |
---|
2366 | { |
---|
2367 | wasInBounds= true; |
---|
2368 | int k= tmin (bounds [i] + 1, l/2); |
---|
2369 | C= CFMatrix (l - k, factors.length() - 1); |
---|
2370 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
2371 | { |
---|
2372 | if (A[ii].size() - 1 >= i) |
---|
2373 | { |
---|
2374 | buf= getCoeffs (A[ii] [i], k); |
---|
2375 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2376 | } |
---|
2377 | } |
---|
2378 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
2379 | NTLK= (*NTLC)*NTLN; |
---|
2380 | transpose (NTLK, NTLK); |
---|
2381 | kernel (NTLK, NTLK); |
---|
2382 | transpose (NTLK, NTLK); |
---|
2383 | NTLN *= NTLK; |
---|
2384 | |
---|
2385 | if (NTLN.NumCols() == 1) |
---|
2386 | { |
---|
2387 | irreducible= true; |
---|
2388 | break; |
---|
2389 | } |
---|
2390 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
2391 | { |
---|
2392 | reduced= true; |
---|
2393 | break; |
---|
2394 | } |
---|
2395 | } |
---|
2396 | } |
---|
2397 | |
---|
2398 | if (irreducible) |
---|
2399 | break; |
---|
2400 | if (reduced) |
---|
2401 | break; |
---|
2402 | oldL= l; |
---|
2403 | l += stepSize; |
---|
2404 | stepSize *= 2; |
---|
2405 | if (l > liftBound) |
---|
2406 | { |
---|
2407 | if (!hitBound) |
---|
2408 | { |
---|
2409 | l= liftBound; |
---|
2410 | hitBound= true; |
---|
2411 | } |
---|
2412 | else |
---|
2413 | break; |
---|
2414 | } |
---|
2415 | } |
---|
2416 | delete [] A; |
---|
2417 | if (!wasInBounds) |
---|
2418 | { |
---|
2419 | if (start) |
---|
2420 | henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M); |
---|
2421 | else |
---|
2422 | henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M); |
---|
2423 | factors.insert (LCF); |
---|
2424 | } |
---|
2425 | return l; |
---|
2426 | } |
---|
2427 | |
---|
2428 | #ifdef HAVE_FLINT |
---|
2429 | int |
---|
2430 | liftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, int |
---|
2431 | start, int liftBound, int minBound, CFList& factors, |
---|
2432 | nmod_mat_t FLINTN, CFList& diophant, CFMatrix& M,CFArray& |
---|
2433 | Pi, CFArray& bufQ, bool& irreducible |
---|
2434 | ) |
---|
2435 | { |
---|
2436 | CanonicalForm LCF= LC (F, 1); |
---|
2437 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
2438 | bool wasInBounds= false; |
---|
2439 | bool hitBound= false; |
---|
2440 | int l= (minBound+1)*2; |
---|
2441 | int stepSize= 2; |
---|
2442 | int oldL= l/2; |
---|
2443 | bool reduced= false; |
---|
2444 | long rank; |
---|
2445 | nmod_mat_t FLINTK, FLINTC, null; |
---|
2446 | CFMatrix C; |
---|
2447 | CFArray buf; |
---|
2448 | CFListIterator j; |
---|
2449 | CanonicalForm truncF; |
---|
2450 | Variable y= F.mvar(); |
---|
2451 | while (l <= liftBound) |
---|
2452 | { |
---|
2453 | if (start) |
---|
2454 | { |
---|
2455 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
2456 | start= 0; |
---|
2457 | } |
---|
2458 | else |
---|
2459 | { |
---|
2460 | if (wasInBounds) |
---|
2461 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
2462 | else |
---|
2463 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
2464 | } |
---|
2465 | |
---|
2466 | factors.insert (LCF); |
---|
2467 | j= factors; |
---|
2468 | j++; |
---|
2469 | |
---|
2470 | truncF= mod (F, power (y, l)); |
---|
2471 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
2472 | { |
---|
2473 | if (!wasInBounds) |
---|
2474 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
2475 | else |
---|
2476 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
2477 | bufQ[i]); |
---|
2478 | } |
---|
2479 | |
---|
2480 | for (int i= 0; i < sizeBounds; i++) |
---|
2481 | { |
---|
2482 | if (bounds [i] + 1 <= l/2) |
---|
2483 | { |
---|
2484 | wasInBounds= true; |
---|
2485 | int k= tmin (bounds [i] + 1, l/2); |
---|
2486 | C= CFMatrix (l - k, factors.length() - 1); |
---|
2487 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
2488 | { |
---|
2489 | if (A[ii].size() - 1 >= i) |
---|
2490 | { |
---|
2491 | buf= getCoeffs (A[ii] [i], k); |
---|
2492 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2493 | } |
---|
2494 | } |
---|
2495 | |
---|
2496 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
2497 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
2498 | getCharacteristic()); |
---|
2499 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
2500 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
2501 | getCharacteristic()); |
---|
2502 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
2503 | nmod_mat_clear (FLINTK); |
---|
2504 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
2505 | nmod_mat_clear (FLINTC); |
---|
2506 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
2507 | nmod_mat_clear (FLINTN); |
---|
2508 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
2509 | getCharacteristic()); |
---|
2510 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
2511 | |
---|
2512 | nmod_mat_clear (FLINTC); |
---|
2513 | nmod_mat_window_clear (FLINTK); |
---|
2514 | nmod_mat_clear (null); |
---|
2515 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
2516 | { |
---|
2517 | irreducible= true; |
---|
2518 | break; |
---|
2519 | } |
---|
2520 | if (isReduced (FLINTN) && l > (minBound+1)*2) |
---|
2521 | { |
---|
2522 | reduced= true; |
---|
2523 | break; |
---|
2524 | } |
---|
2525 | } |
---|
2526 | } |
---|
2527 | |
---|
2528 | if (irreducible) |
---|
2529 | break; |
---|
2530 | if (reduced) |
---|
2531 | break; |
---|
2532 | oldL= l; |
---|
2533 | l += stepSize; |
---|
2534 | stepSize *= 2; |
---|
2535 | if (l > liftBound) |
---|
2536 | { |
---|
2537 | if (!hitBound) |
---|
2538 | { |
---|
2539 | l= liftBound; |
---|
2540 | hitBound= true; |
---|
2541 | } |
---|
2542 | else |
---|
2543 | break; |
---|
2544 | } |
---|
2545 | } |
---|
2546 | delete [] A; |
---|
2547 | if (!wasInBounds) |
---|
2548 | { |
---|
2549 | if (start) |
---|
2550 | henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M); |
---|
2551 | else |
---|
2552 | henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M); |
---|
2553 | factors.insert (LCF); |
---|
2554 | } |
---|
2555 | return l; |
---|
2556 | } |
---|
2557 | #endif |
---|
2558 | |
---|
2559 | //over field extension |
---|
2560 | int |
---|
2561 | extLiftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
2562 | int liftBound, int minBound, int start, CFList& |
---|
2563 | factors, mat_zz_p& NTLN, CFList& diophant, |
---|
2564 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, bool& |
---|
2565 | irreducible, const CanonicalForm& evaluation, const |
---|
2566 | ExtensionInfo& info, CFList& source, CFList& dest |
---|
2567 | ) |
---|
2568 | { |
---|
2569 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
2570 | CanonicalForm LCF= LC (F, 1); |
---|
2571 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
2572 | bool wasInBounds= false; |
---|
2573 | bool hitBound= false; |
---|
2574 | int degMipo; |
---|
2575 | Variable alpha; |
---|
2576 | alpha= info.getAlpha(); |
---|
2577 | degMipo= degree (getMipo (alpha)); |
---|
2578 | |
---|
2579 | Variable gamma= info.getBeta(); |
---|
2580 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
2581 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
2582 | |
---|
2583 | int stepSize= 2; |
---|
2584 | int l= ((minBound+1)/degMipo+1)*2; |
---|
2585 | l= tmax (l, 2); |
---|
2586 | if (start > l) |
---|
2587 | l= start; |
---|
2588 | int oldL= l/2; |
---|
2589 | bool reduced= false; |
---|
2590 | Variable y= F.mvar(); |
---|
2591 | Variable x= Variable (1); |
---|
2592 | CanonicalForm powX, imBasis, truncF; |
---|
2593 | CFMatrix Mat, C; |
---|
2594 | CFArray buf; |
---|
2595 | CFIterator iter; |
---|
2596 | mat_zz_p* NTLMat, *NTLC, NTLK; |
---|
2597 | CFListIterator j; |
---|
2598 | while (l <= liftBound) |
---|
2599 | { |
---|
2600 | if (start) |
---|
2601 | { |
---|
2602 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
2603 | start= 0; |
---|
2604 | } |
---|
2605 | else |
---|
2606 | { |
---|
2607 | if (wasInBounds) |
---|
2608 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
2609 | else |
---|
2610 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
2611 | } |
---|
2612 | |
---|
2613 | factors.insert (LCF); |
---|
2614 | |
---|
2615 | if (GF) |
---|
2616 | setCharacteristic (getCharacteristic()); |
---|
2617 | |
---|
2618 | powX= power (y-gamma, l); |
---|
2619 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
2620 | for (int i= 0; i < l*degMipo; i++) |
---|
2621 | { |
---|
2622 | imBasis= mod (power (y, i), powX); |
---|
2623 | imBasis= imBasis (power (y, degMipo), y); |
---|
2624 | imBasis= imBasis (y, gamma); |
---|
2625 | iter= imBasis; |
---|
2626 | for (; iter.hasTerms(); iter++) |
---|
2627 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
2628 | } |
---|
2629 | |
---|
2630 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
2631 | *NTLMat= inv (*NTLMat); |
---|
2632 | |
---|
2633 | if (GF) |
---|
2634 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
2635 | |
---|
2636 | j= factors; |
---|
2637 | j++; |
---|
2638 | |
---|
2639 | truncF= mod (F, power (y, l)); |
---|
2640 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
2641 | { |
---|
2642 | if (!wasInBounds) |
---|
2643 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
2644 | else |
---|
2645 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
2646 | bufQ[i]); |
---|
2647 | } |
---|
2648 | |
---|
2649 | for (int i= 0; i < sizeBounds; i++) |
---|
2650 | { |
---|
2651 | if (bounds [i] + 1 <= (l/2)*degMipo) |
---|
2652 | { |
---|
2653 | wasInBounds= true; |
---|
2654 | int k= tmin (bounds [i] + 1, (l/2)*degMipo); |
---|
2655 | C= CFMatrix (l*degMipo - k, factors.length() - 1); |
---|
2656 | |
---|
2657 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
2658 | { |
---|
2659 | if (A[ii].size() - 1 >= i) |
---|
2660 | { |
---|
2661 | if (GF) |
---|
2662 | { |
---|
2663 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
2664 | setCharacteristic (getCharacteristic()); |
---|
2665 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
2666 | if (alpha != gamma) |
---|
2667 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
2668 | gamma, source, dest |
---|
2669 | ); |
---|
2670 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
2671 | } |
---|
2672 | else |
---|
2673 | { |
---|
2674 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
2675 | if (alpha != gamma) |
---|
2676 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
2677 | gamma, source, dest |
---|
2678 | ); |
---|
2679 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
2680 | } |
---|
2681 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2682 | } |
---|
2683 | if (GF) |
---|
2684 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
2685 | } |
---|
2686 | |
---|
2687 | if (GF) |
---|
2688 | setCharacteristic(getCharacteristic()); |
---|
2689 | |
---|
2690 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
2691 | NTLK= (*NTLC)*NTLN; |
---|
2692 | transpose (NTLK, NTLK); |
---|
2693 | kernel (NTLK, NTLK); |
---|
2694 | transpose (NTLK, NTLK); |
---|
2695 | NTLN *= NTLK; |
---|
2696 | |
---|
2697 | if (GF) |
---|
2698 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
2699 | |
---|
2700 | if (NTLN.NumCols() == 1) |
---|
2701 | { |
---|
2702 | irreducible= true; |
---|
2703 | break; |
---|
2704 | } |
---|
2705 | if (isReduced (NTLN)) |
---|
2706 | { |
---|
2707 | reduced= true; |
---|
2708 | break; |
---|
2709 | } |
---|
2710 | } |
---|
2711 | } |
---|
2712 | |
---|
2713 | if (NTLN.NumCols() == 1) |
---|
2714 | { |
---|
2715 | irreducible= true; |
---|
2716 | break; |
---|
2717 | } |
---|
2718 | if (reduced) |
---|
2719 | break; |
---|
2720 | oldL= l; |
---|
2721 | l += stepSize; |
---|
2722 | stepSize *= 2; |
---|
2723 | if (l > liftBound) |
---|
2724 | { |
---|
2725 | if (!hitBound) |
---|
2726 | { |
---|
2727 | l= liftBound; |
---|
2728 | hitBound= true; |
---|
2729 | } |
---|
2730 | else |
---|
2731 | break; |
---|
2732 | } |
---|
2733 | } |
---|
2734 | delete [] A; |
---|
2735 | if (!wasInBounds) |
---|
2736 | { |
---|
2737 | if (start) |
---|
2738 | henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M); |
---|
2739 | else |
---|
2740 | henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M); |
---|
2741 | factors.insert (LCF); |
---|
2742 | } |
---|
2743 | return l; |
---|
2744 | } |
---|
2745 | |
---|
2746 | /*#ifdef HAVE_FLINT |
---|
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, nmod_mat_t FLINTN, 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 | |
---|
2771 | int stepSize= 2; |
---|
2772 | int l= ((minBound+1)/degMipo+1)*2; |
---|
2773 | l= tmax (l, 2); |
---|
2774 | if (start > l) |
---|
2775 | l= start; |
---|
2776 | int oldL= l/2; |
---|
2777 | bool reduced= false; |
---|
2778 | Variable y= F.mvar(); |
---|
2779 | Variable x= Variable (1); |
---|
2780 | CanonicalForm powX, imBasis, truncF; |
---|
2781 | CFMatrix Mat, C; |
---|
2782 | CFArray buf; |
---|
2783 | CFIterator iter; |
---|
2784 | long rank; |
---|
2785 | nmod_mat_t FLINTMat, FLINTMatInv, FLINTC, FLINTK, null; |
---|
2786 | CFListIterator j; |
---|
2787 | while (l <= liftBound) |
---|
2788 | { |
---|
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 | } |
---|
2801 | |
---|
2802 | factors.insert (LCF); |
---|
2803 | |
---|
2804 | if (GF) |
---|
2805 | setCharacteristic (getCharacteristic()); |
---|
2806 | |
---|
2807 | powX= power (y-gamma, l); |
---|
2808 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
2809 | for (int i= 0; i < l*degMipo; i++) |
---|
2810 | { |
---|
2811 | imBasis= mod (power (y, i), powX); |
---|
2812 | imBasis= imBasis (power (y, degMipo), y); |
---|
2813 | imBasis= imBasis (y, gamma); |
---|
2814 | iter= imBasis; |
---|
2815 | for (; iter.hasTerms(); iter++) |
---|
2816 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
2817 | } |
---|
2818 | |
---|
2819 | convertFacCFMatrix2nmod_mat_t (FLINTMat, Mat); |
---|
2820 | nmod_mat_init (FLINTMatInv, nmod_mat_nrows (FLINTMat), |
---|
2821 | nmod_mat_nrows (FLINTMat), getCharacteristic()); |
---|
2822 | nmod_mat_inv (FLINTMatInv, FLINTMat); |
---|
2823 | |
---|
2824 | if (GF) |
---|
2825 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
2826 | |
---|
2827 | j= factors; |
---|
2828 | j++; |
---|
2829 | |
---|
2830 | truncF= mod (F, power (y, l)); |
---|
2831 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
2832 | { |
---|
2833 | if (!wasInBounds) |
---|
2834 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
2835 | else |
---|
2836 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
2837 | bufQ[i]); |
---|
2838 | } |
---|
2839 | |
---|
2840 | for (int i= 0; i < sizeBounds; i++) |
---|
2841 | { |
---|
2842 | if (bounds [i] + 1 <= (l/2)*degMipo) |
---|
2843 | { |
---|
2844 | wasInBounds= true; |
---|
2845 | int k= tmin (bounds [i] + 1, (l/2)*degMipo); |
---|
2846 | C= CFMatrix (l*degMipo - k, factors.length() - 1); |
---|
2847 | |
---|
2848 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
2849 | { |
---|
2850 | if (A[ii].size() - 1 >= i) |
---|
2851 | { |
---|
2852 | if (GF) |
---|
2853 | { |
---|
2854 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
2855 | setCharacteristic (getCharacteristic()); |
---|
2856 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
2857 | if (alpha != gamma) |
---|
2858 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
2859 | gamma, source, dest |
---|
2860 | ); |
---|
2861 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, FLINTMatInv); //TODO |
---|
2862 | } |
---|
2863 | else |
---|
2864 | { |
---|
2865 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
2866 | if (alpha != gamma) |
---|
2867 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
2868 | gamma, source, dest |
---|
2869 | ); |
---|
2870 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, FLINTMatInv); //TODO |
---|
2871 | } |
---|
2872 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2873 | } |
---|
2874 | if (GF) |
---|
2875 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
2876 | } |
---|
2877 | |
---|
2878 | if (GF) |
---|
2879 | setCharacteristic(getCharacteristic()); |
---|
2880 | |
---|
2881 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
2882 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
2883 | getCharacteristic()); |
---|
2884 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
2885 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
2886 | getCharacteristic()); |
---|
2887 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
2888 | nmod_mat_clear (FLINTK); |
---|
2889 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
2890 | nmod_mat_clear (FLINTC); |
---|
2891 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
2892 | nmod_mat_clear (FLINTN); |
---|
2893 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
2894 | getCharacteristic()); |
---|
2895 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
2896 | |
---|
2897 | nmod_mat_clear (FLINTC); |
---|
2898 | nmod_mat_window_clear (FLINTK); |
---|
2899 | nmod_mat_clear (null); |
---|
2900 | |
---|
2901 | if (GF) |
---|
2902 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
2903 | |
---|
2904 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
2905 | { |
---|
2906 | irreducible= true; |
---|
2907 | break; |
---|
2908 | } |
---|
2909 | if (isReduced (FLINTN)) |
---|
2910 | { |
---|
2911 | reduced= true; |
---|
2912 | break; |
---|
2913 | } |
---|
2914 | } |
---|
2915 | } |
---|
2916 | |
---|
2917 | nmod_mat_clear (FLINTMat); |
---|
2918 | nmod_mat_clear (FLINTMatInv); |
---|
2919 | |
---|
2920 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
2921 | { |
---|
2922 | irreducible= true; |
---|
2923 | break; |
---|
2924 | } |
---|
2925 | if (reduced) |
---|
2926 | break; |
---|
2927 | oldL= l; |
---|
2928 | l += stepSize; |
---|
2929 | stepSize *= 2; |
---|
2930 | if (l > liftBound) |
---|
2931 | { |
---|
2932 | if (!hitBound) |
---|
2933 | { |
---|
2934 | l= liftBound; |
---|
2935 | hitBound= true; |
---|
2936 | } |
---|
2937 | else |
---|
2938 | break; |
---|
2939 | } |
---|
2940 | } |
---|
2941 | delete [] A; |
---|
2942 | if (!wasInBounds) |
---|
2943 | { |
---|
2944 | if (start) |
---|
2945 | henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M); |
---|
2946 | else |
---|
2947 | henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M); |
---|
2948 | factors.insert (LCF); |
---|
2949 | } |
---|
2950 | return l; |
---|
2951 | } |
---|
2952 | #endif*/ |
---|
2953 | |
---|
2954 | // over Fq |
---|
2955 | int |
---|
2956 | liftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
2957 | int start, int liftBound, int minBound, CFList& factors, |
---|
2958 | mat_zz_pE& NTLN, CFList& diophant, CFMatrix& M, CFArray& |
---|
2959 | Pi, CFArray& bufQ, bool& irreducible |
---|
2960 | ) |
---|
2961 | { |
---|
2962 | CanonicalForm LCF= LC (F, 1); |
---|
2963 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
2964 | bool wasInBounds= false; |
---|
2965 | bool hitBound= false; |
---|
2966 | int l= (minBound+1)*2; |
---|
2967 | int stepSize= 2; |
---|
2968 | int oldL= l/2; |
---|
2969 | bool reduced= false; |
---|
2970 | CFListIterator j; |
---|
2971 | mat_zz_pE* NTLC, NTLK; |
---|
2972 | CFArray buf; |
---|
2973 | CFMatrix C; |
---|
2974 | Variable y= F.mvar(); |
---|
2975 | CanonicalForm truncF; |
---|
2976 | while (l <= liftBound) |
---|
2977 | { |
---|
2978 | if (start) |
---|
2979 | { |
---|
2980 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
2981 | start= 0; |
---|
2982 | } |
---|
2983 | else |
---|
2984 | { |
---|
2985 | if (wasInBounds) |
---|
2986 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
2987 | else |
---|
2988 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
2989 | } |
---|
2990 | |
---|
2991 | factors.insert (LCF); |
---|
2992 | j= factors; |
---|
2993 | j++; |
---|
2994 | |
---|
2995 | truncF= mod (F, power (y,l)); |
---|
2996 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
2997 | { |
---|
2998 | if (l == (minBound+1)*2) |
---|
2999 | { |
---|
3000 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
3001 | } |
---|
3002 | else |
---|
3003 | { |
---|
3004 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
3005 | bufQ[i] |
---|
3006 | ); |
---|
3007 | } |
---|
3008 | } |
---|
3009 | |
---|
3010 | for (int i= 0; i < sizeBounds; i++) |
---|
3011 | { |
---|
3012 | if (bounds [i] + 1 <= l/2) |
---|
3013 | { |
---|
3014 | wasInBounds= true; |
---|
3015 | int k= tmin (bounds [i] + 1, l/2); |
---|
3016 | C= CFMatrix (l - k, factors.length() - 1); |
---|
3017 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
3018 | { |
---|
3019 | |
---|
3020 | if (A[ii].size() - 1 >= i) |
---|
3021 | { |
---|
3022 | buf= getCoeffs (A[ii] [i], k); |
---|
3023 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3024 | } |
---|
3025 | } |
---|
3026 | |
---|
3027 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
3028 | NTLK= (*NTLC)*NTLN; |
---|
3029 | transpose (NTLK, NTLK); |
---|
3030 | kernel (NTLK, NTLK); |
---|
3031 | transpose (NTLK, NTLK); |
---|
3032 | NTLN *= NTLK; |
---|
3033 | |
---|
3034 | if (NTLN.NumCols() == 1) |
---|
3035 | { |
---|
3036 | irreducible= true; |
---|
3037 | break; |
---|
3038 | } |
---|
3039 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
3040 | { |
---|
3041 | reduced= true; |
---|
3042 | break; |
---|
3043 | } |
---|
3044 | } |
---|
3045 | } |
---|
3046 | |
---|
3047 | if (NTLN.NumCols() == 1) |
---|
3048 | { |
---|
3049 | irreducible= true; |
---|
3050 | break; |
---|
3051 | } |
---|
3052 | if (reduced) |
---|
3053 | break; |
---|
3054 | oldL= l; |
---|
3055 | l += stepSize; |
---|
3056 | stepSize *= 2; |
---|
3057 | if (l > liftBound) |
---|
3058 | { |
---|
3059 | if (!hitBound) |
---|
3060 | { |
---|
3061 | l= liftBound; |
---|
3062 | hitBound= true; |
---|
3063 | } |
---|
3064 | else |
---|
3065 | break; |
---|
3066 | } |
---|
3067 | } |
---|
3068 | delete [] A; |
---|
3069 | if (!wasInBounds) |
---|
3070 | { |
---|
3071 | if (start) |
---|
3072 | henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M); |
---|
3073 | else |
---|
3074 | henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M); |
---|
3075 | factors.insert (LCF); |
---|
3076 | } |
---|
3077 | return l; |
---|
3078 | } |
---|
3079 | |
---|
3080 | #ifdef HAVE_FLINT |
---|
3081 | int |
---|
3082 | liftAndComputeLatticeFq2Fp (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
3083 | int start, int liftBound, int minBound, CFList& |
---|
3084 | factors, nmod_mat_t FLINTN, CFList& diophant, |
---|
3085 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, bool& |
---|
3086 | irreducible, const Variable& alpha |
---|
3087 | ) |
---|
3088 | #else |
---|
3089 | int |
---|
3090 | liftAndComputeLatticeFq2Fp (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
3091 | int start, int liftBound, int minBound, CFList& |
---|
3092 | factors, mat_zz_p& NTLN, CFList& diophant, CFMatrix& |
---|
3093 | M, CFArray& Pi, CFArray& bufQ, bool& irreducible, |
---|
3094 | const Variable& alpha |
---|
3095 | ) |
---|
3096 | #endif |
---|
3097 | { |
---|
3098 | CanonicalForm LCF= LC (F, 1); |
---|
3099 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
3100 | bool wasInBounds= false; |
---|
3101 | int l= (minBound+1)*2; |
---|
3102 | int oldL= l/2; |
---|
3103 | int stepSize= 2; |
---|
3104 | bool hitBound= false; |
---|
3105 | int extensionDeg= degree (getMipo (alpha)); |
---|
3106 | bool reduced= false; |
---|
3107 | CFListIterator j; |
---|
3108 | CFMatrix C; |
---|
3109 | CFArray buf; |
---|
3110 | #ifdef HAVE_FLINT |
---|
3111 | long rank; |
---|
3112 | nmod_mat_t FLINTC, FLINTK, null; |
---|
3113 | #else |
---|
3114 | mat_zz_p* NTLC, NTLK; |
---|
3115 | #endif |
---|
3116 | Variable y= F.mvar(); |
---|
3117 | CanonicalForm truncF; |
---|
3118 | while (l <= liftBound) |
---|
3119 | { |
---|
3120 | if (start) |
---|
3121 | { |
---|
3122 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
3123 | start= 0; |
---|
3124 | } |
---|
3125 | else |
---|
3126 | { |
---|
3127 | if (wasInBounds) |
---|
3128 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
3129 | else |
---|
3130 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
3131 | } |
---|
3132 | |
---|
3133 | factors.insert (LCF); |
---|
3134 | j= factors; |
---|
3135 | j++; |
---|
3136 | |
---|
3137 | truncF= mod (F, power (y,l)); |
---|
3138 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
3139 | { |
---|
3140 | if (l == (minBound+1)*2) |
---|
3141 | { |
---|
3142 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
3143 | } |
---|
3144 | else |
---|
3145 | { |
---|
3146 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
3147 | bufQ[i] |
---|
3148 | ); |
---|
3149 | } |
---|
3150 | } |
---|
3151 | |
---|
3152 | for (int i= 0; i < sizeBounds; i++) |
---|
3153 | { |
---|
3154 | if (bounds [i] + 1 <= l/2) |
---|
3155 | { |
---|
3156 | wasInBounds= true; |
---|
3157 | int k= tmin (bounds [i] + 1, l/2); |
---|
3158 | C= CFMatrix ((l - k)*extensionDeg, factors.length() - 1); |
---|
3159 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
3160 | { |
---|
3161 | if (A[ii].size() - 1 >= i) |
---|
3162 | { |
---|
3163 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
3164 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3165 | } |
---|
3166 | } |
---|
3167 | |
---|
3168 | #ifdef HAVE_FLINT |
---|
3169 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
3170 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
3171 | getCharacteristic()); |
---|
3172 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
3173 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
3174 | getCharacteristic()); |
---|
3175 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
3176 | nmod_mat_clear (FLINTK); |
---|
3177 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
3178 | nmod_mat_clear (FLINTC); |
---|
3179 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
3180 | nmod_mat_clear (FLINTN); |
---|
3181 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
3182 | getCharacteristic()); |
---|
3183 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
3184 | |
---|
3185 | nmod_mat_clear (FLINTC); |
---|
3186 | nmod_mat_window_clear (FLINTK); |
---|
3187 | nmod_mat_clear (null); |
---|
3188 | #else |
---|
3189 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
3190 | NTLK= (*NTLC)*NTLN; |
---|
3191 | transpose (NTLK, NTLK); |
---|
3192 | kernel (NTLK, NTLK); |
---|
3193 | transpose (NTLK, NTLK); |
---|
3194 | NTLN *= NTLK; |
---|
3195 | #endif |
---|
3196 | |
---|
3197 | #ifdef HAVE_FLINT |
---|
3198 | if (nmod_mat_nrows (FLINTN) == 1) |
---|
3199 | #else |
---|
3200 | if (NTLN.NumCols() == 1) |
---|
3201 | #endif |
---|
3202 | { |
---|
3203 | irreducible= true; |
---|
3204 | break; |
---|
3205 | } |
---|
3206 | #ifdef HAVE_FLINT |
---|
3207 | if (isReduced (FLINTN) && l > (minBound+1)*2) |
---|
3208 | #else |
---|
3209 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
3210 | #endif |
---|
3211 | { |
---|
3212 | reduced= true; |
---|
3213 | break; |
---|
3214 | } |
---|
3215 | } |
---|
3216 | } |
---|
3217 | |
---|
3218 | #ifdef HAVE_FLINT |
---|
3219 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
3220 | #else |
---|
3221 | if (NTLN.NumCols() == 1) |
---|
3222 | #endif |
---|
3223 | { |
---|
3224 | irreducible= true; |
---|
3225 | break; |
---|
3226 | } |
---|
3227 | if (reduced) |
---|
3228 | break; |
---|
3229 | oldL= l; |
---|
3230 | l += stepSize; |
---|
3231 | stepSize *= 2; |
---|
3232 | if (l > liftBound) |
---|
3233 | { |
---|
3234 | if (!hitBound) |
---|
3235 | { |
---|
3236 | l= liftBound; |
---|
3237 | hitBound= true; |
---|
3238 | } |
---|
3239 | else |
---|
3240 | break; |
---|
3241 | } |
---|
3242 | } |
---|
3243 | delete [] A; |
---|
3244 | if (!wasInBounds) |
---|
3245 | { |
---|
3246 | if (start) |
---|
3247 | henselLiftResume12 (F, factors, start, degree (F) + 1, Pi, diophant, M); |
---|
3248 | else |
---|
3249 | henselLift12 (F, factors, degree (F) + 1, Pi, diophant, M); |
---|
3250 | factors.insert (LCF); |
---|
3251 | } |
---|
3252 | return l; |
---|
3253 | } |
---|
3254 | |
---|
3255 | CFList |
---|
3256 | increasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
3257 | int oldNumCols, int oldL, int precision |
---|
3258 | ) |
---|
3259 | { |
---|
3260 | int d; |
---|
3261 | bool isIrreducible= false; |
---|
3262 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
3263 | if (isIrreducible) |
---|
3264 | { |
---|
3265 | delete [] bounds; |
---|
3266 | CanonicalForm G= F; |
---|
3267 | F= 1; |
---|
3268 | return CFList (G); |
---|
3269 | } |
---|
3270 | CFArray * A= new CFArray [factors.length()]; |
---|
3271 | CFArray bufQ= CFArray (factors.length()); |
---|
3272 | #ifdef HAVE_FLINT |
---|
3273 | nmod_mat_t FLINTN; |
---|
3274 | nmod_mat_init (FLINTN,factors.length(),factors.length(), getCharacteristic()); |
---|
3275 | for (long i=factors.length()-1; i >= 0; i--) |
---|
3276 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
3277 | #else |
---|
3278 | mat_zz_p NTLN; |
---|
3279 | ident (NTLN, factors.length()); |
---|
3280 | #endif |
---|
3281 | int minBound= bounds[0]; |
---|
3282 | for (int i= 1; i < d; i++) |
---|
3283 | { |
---|
3284 | if (bounds[i] != 0) |
---|
3285 | minBound= tmin (minBound, bounds[i]); |
---|
3286 | } |
---|
3287 | int l= tmax (2*(minBound + 1), oldL); |
---|
3288 | int oldL2= l/2; |
---|
3289 | int stepSize= 2; |
---|
3290 | bool useOldQs= false; |
---|
3291 | bool hitBound= false; |
---|
3292 | CFListIterator j; |
---|
3293 | CFMatrix C; |
---|
3294 | CFArray buf; |
---|
3295 | #ifdef HAVE_FLINT |
---|
3296 | long rank; |
---|
3297 | nmod_mat_t FLINTC, FLINTK, null; |
---|
3298 | #else |
---|
3299 | mat_zz_p* NTLC, NTLK; |
---|
3300 | #endif |
---|
3301 | Variable y= F.mvar(); |
---|
3302 | CanonicalForm truncF; |
---|
3303 | while (l <= precision) |
---|
3304 | { |
---|
3305 | j= factors; |
---|
3306 | truncF= mod (F, power (y,l)); |
---|
3307 | if (useOldQs) |
---|
3308 | { |
---|
3309 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3310 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
3311 | bufQ[i] |
---|
3312 | ); |
---|
3313 | } |
---|
3314 | else |
---|
3315 | { |
---|
3316 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3317 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
3318 | } |
---|
3319 | useOldQs= true; |
---|
3320 | for (int i= 0; i < d; i++) |
---|
3321 | { |
---|
3322 | if (bounds [i] + 1 <= l/2) |
---|
3323 | { |
---|
3324 | int k= tmin (bounds [i] + 1, l/2); |
---|
3325 | C= CFMatrix (l - k, factors.length()); |
---|
3326 | for (int ii= 0; ii < factors.length(); ii++) |
---|
3327 | { |
---|
3328 | if (A[ii].size() - 1 >= i) |
---|
3329 | { |
---|
3330 | buf= getCoeffs (A[ii] [i], k); |
---|
3331 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3332 | } |
---|
3333 | } |
---|
3334 | #ifdef HAVE_FLINT |
---|
3335 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
3336 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
3337 | getCharacteristic()); |
---|
3338 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
3339 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
3340 | getCharacteristic()); |
---|
3341 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
3342 | nmod_mat_clear (FLINTK); |
---|
3343 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
3344 | nmod_mat_clear (FLINTC); |
---|
3345 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
3346 | nmod_mat_clear (FLINTN); |
---|
3347 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
3348 | getCharacteristic()); |
---|
3349 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
3350 | |
---|
3351 | nmod_mat_clear (FLINTC); |
---|
3352 | nmod_mat_window_clear (FLINTK); |
---|
3353 | nmod_mat_clear (null); |
---|
3354 | #else |
---|
3355 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
3356 | NTLK= (*NTLC)*NTLN; |
---|
3357 | transpose (NTLK, NTLK); |
---|
3358 | kernel (NTLK, NTLK); |
---|
3359 | transpose (NTLK, NTLK); |
---|
3360 | NTLN *= NTLK; |
---|
3361 | #endif |
---|
3362 | #ifdef HAVE_FLINT |
---|
3363 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
3364 | { |
---|
3365 | nmod_mat_clear (FLINTN); |
---|
3366 | #else |
---|
3367 | if (NTLN.NumCols() == 1) |
---|
3368 | { |
---|
3369 | #endif |
---|
3370 | delete [] A; |
---|
3371 | delete [] bounds; |
---|
3372 | CanonicalForm G= F; |
---|
3373 | F= 1; |
---|
3374 | return CFList (G); |
---|
3375 | } |
---|
3376 | } |
---|
3377 | } |
---|
3378 | |
---|
3379 | #ifdef HAVE_FLINT |
---|
3380 | if (nmod_mat_ncols (FLINTN) < oldNumCols - factorsFound) |
---|
3381 | { |
---|
3382 | if (isReduced (FLINTN)) |
---|
3383 | { |
---|
3384 | int * factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
3385 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
3386 | #else |
---|
3387 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
3388 | { |
---|
3389 | if (isReduced (NTLN)) |
---|
3390 | { |
---|
3391 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
3392 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
3393 | #endif |
---|
3394 | factorsFoundIndex[i]= 0; |
---|
3395 | int factorsFound2= 0; |
---|
3396 | CFList result; |
---|
3397 | CanonicalForm bufF= F; |
---|
3398 | #ifdef HAVE_FLINT |
---|
3399 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
3400 | factorsFoundIndex, FLINTN, false |
---|
3401 | ); |
---|
3402 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
3403 | { |
---|
3404 | nmod_mat_clear (FLINTN); |
---|
3405 | #else |
---|
3406 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
3407 | factorsFoundIndex, NTLN, false |
---|
3408 | ); |
---|
3409 | if (result.length() == NTLN.NumCols()) |
---|
3410 | { |
---|
3411 | #endif |
---|
3412 | delete [] factorsFoundIndex; |
---|
3413 | delete [] A; |
---|
3414 | delete [] bounds; |
---|
3415 | F= 1; |
---|
3416 | return result; |
---|
3417 | } |
---|
3418 | delete [] factorsFoundIndex; |
---|
3419 | } |
---|
3420 | else if (l == precision) |
---|
3421 | { |
---|
3422 | CanonicalForm bufF= F; |
---|
3423 | #ifdef HAVE_FLINT |
---|
3424 | int * zeroOne= extractZeroOneVecs (FLINTN); |
---|
3425 | CFList result= reconstruction (bufF,factors,zeroOne,precision,FLINTN); |
---|
3426 | nmod_mat_clear (FLINTN); |
---|
3427 | #else |
---|
3428 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
3429 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN); |
---|
3430 | #endif |
---|
3431 | F= bufF; |
---|
3432 | delete [] zeroOne; |
---|
3433 | delete [] A; |
---|
3434 | delete [] bounds; |
---|
3435 | return result; |
---|
3436 | } |
---|
3437 | } |
---|
3438 | oldL2= l; |
---|
3439 | l += stepSize; |
---|
3440 | stepSize *= 2; |
---|
3441 | if (l > precision) |
---|
3442 | { |
---|
3443 | if (!hitBound) |
---|
3444 | { |
---|
3445 | l= precision; |
---|
3446 | hitBound= true; |
---|
3447 | } |
---|
3448 | else |
---|
3449 | break; |
---|
3450 | } |
---|
3451 | } |
---|
3452 | #ifdef HAVE_FLINT |
---|
3453 | nmod_mat_clear (FLINTN); |
---|
3454 | #endif |
---|
3455 | delete [] bounds; |
---|
3456 | delete [] A; |
---|
3457 | return CFList(); |
---|
3458 | } |
---|
3459 | |
---|
3460 | CFList |
---|
3461 | increasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
3462 | int oldNumCols, int oldL, const Variable&, |
---|
3463 | int precision |
---|
3464 | ) |
---|
3465 | { |
---|
3466 | int d; |
---|
3467 | bool isIrreducible= false; |
---|
3468 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
3469 | if (isIrreducible) |
---|
3470 | { |
---|
3471 | delete [] bounds; |
---|
3472 | CanonicalForm G= F; |
---|
3473 | F= 1; |
---|
3474 | return CFList (G); |
---|
3475 | } |
---|
3476 | CFArray * A= new CFArray [factors.length()]; |
---|
3477 | CFArray bufQ= CFArray (factors.length()); |
---|
3478 | mat_zz_pE NTLN; |
---|
3479 | ident (NTLN, factors.length()); |
---|
3480 | int minBound= bounds[0]; |
---|
3481 | for (int i= 1; i < d; i++) |
---|
3482 | { |
---|
3483 | if (bounds[i] != 0) |
---|
3484 | minBound= tmin (minBound, bounds[i]); |
---|
3485 | } |
---|
3486 | int l= tmax (2*(minBound + 1), oldL); |
---|
3487 | int oldL2= l/2; |
---|
3488 | int stepSize= 2; |
---|
3489 | bool useOldQs= false; |
---|
3490 | bool hitBound= false; |
---|
3491 | CFListIterator j; |
---|
3492 | CFMatrix C; |
---|
3493 | mat_zz_pE* NTLC, NTLK; |
---|
3494 | CFArray buf; |
---|
3495 | Variable y= F.mvar(); |
---|
3496 | CanonicalForm truncF; |
---|
3497 | while (l <= precision) |
---|
3498 | { |
---|
3499 | j= factors; |
---|
3500 | truncF= mod (F, power (y,l)); |
---|
3501 | if (useOldQs) |
---|
3502 | { |
---|
3503 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3504 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
3505 | bufQ[i] |
---|
3506 | ); |
---|
3507 | } |
---|
3508 | else |
---|
3509 | { |
---|
3510 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3511 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
3512 | } |
---|
3513 | useOldQs= true; |
---|
3514 | for (int i= 0; i < d; i++) |
---|
3515 | { |
---|
3516 | if (bounds [i] + 1 <= l/2) |
---|
3517 | { |
---|
3518 | int k= tmin (bounds [i] + 1, l/2); |
---|
3519 | C= CFMatrix (l - k, factors.length()); |
---|
3520 | for (int ii= 0; ii < factors.length(); ii++) |
---|
3521 | { |
---|
3522 | if (A[ii].size() - 1 >= i) |
---|
3523 | { |
---|
3524 | buf= getCoeffs (A[ii] [i], k); |
---|
3525 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3526 | } |
---|
3527 | } |
---|
3528 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
3529 | NTLK= (*NTLC)*NTLN; |
---|
3530 | transpose (NTLK, NTLK); |
---|
3531 | kernel (NTLK, NTLK); |
---|
3532 | transpose (NTLK, NTLK); |
---|
3533 | NTLN *= NTLK; |
---|
3534 | if (NTLN.NumCols() == 1) |
---|
3535 | { |
---|
3536 | delete [] A; |
---|
3537 | delete [] bounds; |
---|
3538 | CanonicalForm G= F; |
---|
3539 | F= 1; |
---|
3540 | return CFList (G); |
---|
3541 | } |
---|
3542 | } |
---|
3543 | } |
---|
3544 | |
---|
3545 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
3546 | { |
---|
3547 | if (isReduced (NTLN)) |
---|
3548 | { |
---|
3549 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
3550 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
3551 | factorsFoundIndex[i]= 0; |
---|
3552 | int factorsFound2= 0; |
---|
3553 | CFList result; |
---|
3554 | CanonicalForm bufF= F; |
---|
3555 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
3556 | factorsFoundIndex, NTLN, false); |
---|
3557 | if (result.length() == NTLN.NumCols()) |
---|
3558 | { |
---|
3559 | delete [] factorsFoundIndex; |
---|
3560 | delete [] A; |
---|
3561 | delete [] bounds; |
---|
3562 | F= 1; |
---|
3563 | return result; |
---|
3564 | } |
---|
3565 | delete [] factorsFoundIndex; |
---|
3566 | } |
---|
3567 | else if (l == precision) |
---|
3568 | { |
---|
3569 | CanonicalForm bufF= F; |
---|
3570 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
3571 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN); |
---|
3572 | F= bufF; |
---|
3573 | delete [] zeroOne; |
---|
3574 | delete [] A; |
---|
3575 | delete [] bounds; |
---|
3576 | return result; |
---|
3577 | } |
---|
3578 | } |
---|
3579 | oldL2= l; |
---|
3580 | l += stepSize; |
---|
3581 | stepSize *= 2; |
---|
3582 | if (l > precision) |
---|
3583 | { |
---|
3584 | if (!hitBound) |
---|
3585 | { |
---|
3586 | l= precision; |
---|
3587 | hitBound= true; |
---|
3588 | } |
---|
3589 | else |
---|
3590 | break; |
---|
3591 | } |
---|
3592 | } |
---|
3593 | delete [] bounds; |
---|
3594 | delete [] A; |
---|
3595 | return CFList(); |
---|
3596 | } |
---|
3597 | |
---|
3598 | //over field extension |
---|
3599 | CFList |
---|
3600 | extIncreasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
3601 | int oldNumCols, int oldL, const CanonicalForm& evaluation, |
---|
3602 | const ExtensionInfo& info, CFList& source, CFList& dest, |
---|
3603 | int precision |
---|
3604 | ) |
---|
3605 | { |
---|
3606 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
3607 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
3608 | Variable alpha= info.getAlpha(); |
---|
3609 | int d; |
---|
3610 | bool isIrreducible= false; |
---|
3611 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
3612 | if (isIrreducible) |
---|
3613 | { |
---|
3614 | delete [] bounds; |
---|
3615 | Variable y= Variable (2); |
---|
3616 | CanonicalForm tmp= F (y - evaluation, y); |
---|
3617 | CFList source, dest; |
---|
3618 | tmp= mapDown (tmp, info, source, dest); |
---|
3619 | F= 1; |
---|
3620 | return CFList (tmp); |
---|
3621 | } |
---|
3622 | |
---|
3623 | CFArray * A= new CFArray [factors.length()]; |
---|
3624 | CFArray bufQ= CFArray (factors.length()); |
---|
3625 | if (fac_NTL_char != getCharacteristic()) |
---|
3626 | { |
---|
3627 | fac_NTL_char= getCharacteristic(); |
---|
3628 | zz_p::init (getCharacteristic()); |
---|
3629 | } |
---|
3630 | mat_zz_p NTLN; |
---|
3631 | ident (NTLN, factors.length()); |
---|
3632 | int minBound= bounds[0]; |
---|
3633 | for (int i= 1; i < d; i++) |
---|
3634 | { |
---|
3635 | if (bounds[i] != 0) |
---|
3636 | minBound= tmin (minBound, bounds[i]); |
---|
3637 | } |
---|
3638 | int l= tmax (oldL, 2*((minBound+1)/degMipo+1)); |
---|
3639 | int oldL2= l/2; |
---|
3640 | int stepSize= 2; |
---|
3641 | bool useOldQs= false; |
---|
3642 | bool hitBound= false; |
---|
3643 | Variable gamma= info.getBeta(); |
---|
3644 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
3645 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
3646 | CFListIterator j; |
---|
3647 | Variable y= F.mvar(); |
---|
3648 | CanonicalForm powX, imBasis, truncF; |
---|
3649 | CFMatrix Mat, C; |
---|
3650 | CFIterator iter; |
---|
3651 | mat_zz_p* NTLMat,*NTLC, NTLK; |
---|
3652 | CFArray buf; |
---|
3653 | while (l <= precision) |
---|
3654 | { |
---|
3655 | j= factors; |
---|
3656 | if (GF) |
---|
3657 | setCharacteristic (getCharacteristic()); |
---|
3658 | powX= power (y-gamma, l); |
---|
3659 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
3660 | for (int i= 0; i < l*degMipo; i++) |
---|
3661 | { |
---|
3662 | imBasis= mod (power (y, i), powX); |
---|
3663 | imBasis= imBasis (power (y, degMipo), y); |
---|
3664 | imBasis= imBasis (y, gamma); |
---|
3665 | iter= imBasis; |
---|
3666 | for (; iter.hasTerms(); iter++) |
---|
3667 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
3668 | } |
---|
3669 | |
---|
3670 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
3671 | *NTLMat= inv (*NTLMat); |
---|
3672 | if (GF) |
---|
3673 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
3674 | |
---|
3675 | truncF= mod (F, power (y, l)); |
---|
3676 | if (useOldQs) |
---|
3677 | { |
---|
3678 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3679 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
3680 | bufQ[i] |
---|
3681 | ); |
---|
3682 | } |
---|
3683 | else |
---|
3684 | { |
---|
3685 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3686 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
3687 | } |
---|
3688 | useOldQs= true; |
---|
3689 | for (int i= 0; i < d; i++) |
---|
3690 | { |
---|
3691 | if (bounds [i] + 1 <= (l/2)*degMipo) |
---|
3692 | { |
---|
3693 | int k= tmin (bounds [i] + 1, (l/2)*degMipo); |
---|
3694 | C= CFMatrix (l*degMipo - k, factors.length()); |
---|
3695 | for (int ii= 0; ii < factors.length(); ii++) |
---|
3696 | { |
---|
3697 | if (A[ii].size() - 1 >= i) |
---|
3698 | { |
---|
3699 | if (GF) |
---|
3700 | { |
---|
3701 | A[ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
3702 | setCharacteristic (getCharacteristic()); |
---|
3703 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
3704 | if (alpha != gamma) |
---|
3705 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
3706 | gamma, source, dest |
---|
3707 | ); |
---|
3708 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
3709 | } |
---|
3710 | else |
---|
3711 | { |
---|
3712 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
3713 | if (alpha != gamma) |
---|
3714 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
3715 | gamma, source, dest |
---|
3716 | ); |
---|
3717 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
3718 | } |
---|
3719 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3720 | } |
---|
3721 | if (GF) |
---|
3722 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
3723 | } |
---|
3724 | |
---|
3725 | if (GF) |
---|
3726 | setCharacteristic(getCharacteristic()); |
---|
3727 | |
---|
3728 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
3729 | NTLK= (*NTLC)*NTLN; |
---|
3730 | transpose (NTLK, NTLK); |
---|
3731 | kernel (NTLK, NTLK); |
---|
3732 | transpose (NTLK, NTLK); |
---|
3733 | NTLN *= NTLK; |
---|
3734 | |
---|
3735 | if (GF) |
---|
3736 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
3737 | |
---|
3738 | if (NTLN.NumCols() == 1) |
---|
3739 | { |
---|
3740 | Variable y= Variable (2); |
---|
3741 | CanonicalForm tmp= F (y - evaluation, y); |
---|
3742 | CFList source, dest; |
---|
3743 | tmp= mapDown (tmp, info, source, dest); |
---|
3744 | delete [] A; |
---|
3745 | delete [] bounds; |
---|
3746 | F= 1; |
---|
3747 | return CFList (tmp); |
---|
3748 | } |
---|
3749 | } |
---|
3750 | } |
---|
3751 | |
---|
3752 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
3753 | { |
---|
3754 | if (isReduced (NTLN)) |
---|
3755 | { |
---|
3756 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
3757 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
3758 | factorsFoundIndex[i]= 0; |
---|
3759 | int factorsFound2= 0; |
---|
3760 | CFList result; |
---|
3761 | CanonicalForm bufF= F; |
---|
3762 | extReconstructionTry (result, bufF, factors,degree (F)+1, factorsFound2, |
---|
3763 | factorsFoundIndex, NTLN, false, info, evaluation |
---|
3764 | ); |
---|
3765 | if (result.length() == NTLN.NumCols()) |
---|
3766 | { |
---|
3767 | delete [] factorsFoundIndex; |
---|
3768 | delete [] A; |
---|
3769 | delete [] bounds; |
---|
3770 | F= 1; |
---|
3771 | return result; |
---|
3772 | } |
---|
3773 | delete [] factorsFoundIndex; |
---|
3774 | } |
---|
3775 | else if (l == precision) |
---|
3776 | { |
---|
3777 | CanonicalForm bufF= F; |
---|
3778 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
3779 | CFList result= extReconstruction (bufF, factors, zeroOne, precision, |
---|
3780 | NTLN, info, evaluation |
---|
3781 | ); |
---|
3782 | F= bufF; |
---|
3783 | delete [] zeroOne; |
---|
3784 | delete [] A; |
---|
3785 | delete [] bounds; |
---|
3786 | return result; |
---|
3787 | } |
---|
3788 | } |
---|
3789 | oldL2= l; |
---|
3790 | l += stepSize; |
---|
3791 | stepSize *= 2; |
---|
3792 | if (l > precision) |
---|
3793 | { |
---|
3794 | if (!hitBound) |
---|
3795 | { |
---|
3796 | hitBound= true; |
---|
3797 | l= precision; |
---|
3798 | } |
---|
3799 | else |
---|
3800 | break; |
---|
3801 | } |
---|
3802 | } |
---|
3803 | delete [] bounds; |
---|
3804 | delete [] A; |
---|
3805 | return CFList(); |
---|
3806 | } |
---|
3807 | |
---|
3808 | CFList |
---|
3809 | increasePrecision2 (const CanonicalForm& F, CFList& factors, |
---|
3810 | const Variable& alpha, int precision) |
---|
3811 | { |
---|
3812 | int d; |
---|
3813 | bool isIrreducible= false; |
---|
3814 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
3815 | if (isIrreducible) |
---|
3816 | { |
---|
3817 | delete [] bounds; |
---|
3818 | return CFList (F); |
---|
3819 | } |
---|
3820 | CFArray * A= new CFArray [factors.length()]; |
---|
3821 | CFArray bufQ= CFArray (factors.length()); |
---|
3822 | if (fac_NTL_char != getCharacteristic()) |
---|
3823 | { |
---|
3824 | fac_NTL_char= getCharacteristic(); |
---|
3825 | zz_p::init (getCharacteristic()); |
---|
3826 | } |
---|
3827 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
3828 | zz_pE::init (NTLMipo); |
---|
3829 | mat_zz_pE NTLN; |
---|
3830 | ident (NTLN, factors.length()); |
---|
3831 | int minBound= bounds[0]; |
---|
3832 | for (int i= 1; i < d; i++) |
---|
3833 | { |
---|
3834 | if (bounds[i] != 0) |
---|
3835 | minBound= tmin (minBound, bounds[i]); |
---|
3836 | } |
---|
3837 | int l= tmin (2*(minBound + 1), precision); |
---|
3838 | int oldL= l/2; |
---|
3839 | int stepSize= 2; |
---|
3840 | bool useOldQs= false; |
---|
3841 | bool hitBound= false; |
---|
3842 | CFListIterator j; |
---|
3843 | CFMatrix C; |
---|
3844 | CFArray buf; |
---|
3845 | mat_zz_pE* NTLC, NTLK; |
---|
3846 | Variable y= F.mvar(); |
---|
3847 | CanonicalForm truncF; |
---|
3848 | while (l <= precision) |
---|
3849 | { |
---|
3850 | j= factors; |
---|
3851 | truncF= mod (F, power (y, l)); |
---|
3852 | if (useOldQs) |
---|
3853 | { |
---|
3854 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3855 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], bufQ[i]); |
---|
3856 | } |
---|
3857 | else |
---|
3858 | { |
---|
3859 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3860 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
3861 | } |
---|
3862 | useOldQs= true; |
---|
3863 | for (int i= 0; i < d; i++) |
---|
3864 | { |
---|
3865 | if (bounds [i] + 1 <= l/2) |
---|
3866 | { |
---|
3867 | int k= tmin (bounds [i] + 1, l/2); |
---|
3868 | C= CFMatrix (l - k, factors.length()); |
---|
3869 | for (int ii= 0; ii < factors.length(); ii++) |
---|
3870 | { |
---|
3871 | if (A[ii].size() - 1 >= i) |
---|
3872 | { |
---|
3873 | buf= getCoeffs (A[ii] [i], k); |
---|
3874 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3875 | } |
---|
3876 | } |
---|
3877 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
3878 | NTLK= (*NTLC)*NTLN; |
---|
3879 | transpose (NTLK, NTLK); |
---|
3880 | kernel (NTLK, NTLK); |
---|
3881 | transpose (NTLK, NTLK); |
---|
3882 | NTLN *= NTLK; |
---|
3883 | if (NTLN.NumCols() == 1) |
---|
3884 | { |
---|
3885 | delete [] A; |
---|
3886 | delete [] bounds; |
---|
3887 | return CFList (F); |
---|
3888 | } |
---|
3889 | } |
---|
3890 | } |
---|
3891 | |
---|
3892 | if (isReduced (NTLN) || l == precision) |
---|
3893 | { |
---|
3894 | CanonicalForm bufF= F; |
---|
3895 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
3896 | CFList bufFactors= factors; |
---|
3897 | CFList result= monicReconstruction (bufF, factors, zeroOne, precision, |
---|
3898 | NTLN |
---|
3899 | ); |
---|
3900 | if (result.length() != NTLN.NumCols() && l != precision) |
---|
3901 | factors= bufFactors; |
---|
3902 | if (result.length() == NTLN.NumCols()) |
---|
3903 | { |
---|
3904 | delete [] zeroOne; |
---|
3905 | delete [] A; |
---|
3906 | delete [] bounds; |
---|
3907 | return result; |
---|
3908 | } |
---|
3909 | if (l == precision) |
---|
3910 | { |
---|
3911 | delete [] zeroOne; |
---|
3912 | delete [] A; |
---|
3913 | delete [] bounds; |
---|
3914 | return Union (result, factors); |
---|
3915 | } |
---|
3916 | } |
---|
3917 | oldL= l; |
---|
3918 | l += stepSize; |
---|
3919 | stepSize *= 2; |
---|
3920 | if (l > precision) |
---|
3921 | { |
---|
3922 | if (!hitBound) |
---|
3923 | { |
---|
3924 | l= precision; |
---|
3925 | hitBound= true; |
---|
3926 | } |
---|
3927 | else |
---|
3928 | break; |
---|
3929 | } |
---|
3930 | } |
---|
3931 | delete [] bounds; |
---|
3932 | delete [] A; |
---|
3933 | return CFList(); |
---|
3934 | } |
---|
3935 | |
---|
3936 | CFList |
---|
3937 | increasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
3938 | int oldNumCols, int oldL, const Variable& alpha, |
---|
3939 | int precision |
---|
3940 | ) |
---|
3941 | { |
---|
3942 | int d; |
---|
3943 | bool isIrreducible= false; |
---|
3944 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
3945 | if (isIrreducible) |
---|
3946 | { |
---|
3947 | delete [] bounds; |
---|
3948 | CanonicalForm G= F; |
---|
3949 | F= 1; |
---|
3950 | return CFList (G); |
---|
3951 | } |
---|
3952 | int extensionDeg= degree (getMipo (alpha)); |
---|
3953 | CFArray * A= new CFArray [factors.length()]; |
---|
3954 | CFArray bufQ= CFArray (factors.length()); |
---|
3955 | #ifdef HAVE_FLINT |
---|
3956 | nmod_mat_t FLINTN; |
---|
3957 | nmod_mat_init (FLINTN,factors.length(),factors.length(), getCharacteristic()); |
---|
3958 | for (long i=factors.length()-1; i >= 0; i--) |
---|
3959 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
3960 | #else |
---|
3961 | mat_zz_p NTLN; |
---|
3962 | ident (NTLN, factors.length()); |
---|
3963 | #endif |
---|
3964 | int minBound= bounds[0]; |
---|
3965 | for (int i= 1; i < d; i++) |
---|
3966 | { |
---|
3967 | if (bounds[i] != 0) |
---|
3968 | minBound= tmin (minBound, bounds[i]); |
---|
3969 | } |
---|
3970 | int l= tmax (2*(minBound + 1), oldL); |
---|
3971 | int oldL2= l/2; |
---|
3972 | int stepSize= 2; |
---|
3973 | bool useOldQs= false; |
---|
3974 | bool hitBound= false; |
---|
3975 | CFListIterator j; |
---|
3976 | CFMatrix C; |
---|
3977 | #ifdef HAVE_FLINT |
---|
3978 | long rank; |
---|
3979 | nmod_mat_t FLINTC, FLINTK, null; |
---|
3980 | #else |
---|
3981 | mat_zz_p* NTLC, NTLK; |
---|
3982 | #endif |
---|
3983 | CFArray buf; |
---|
3984 | Variable y= F.mvar(); |
---|
3985 | CanonicalForm truncF; |
---|
3986 | while (l <= precision) |
---|
3987 | { |
---|
3988 | j= factors; |
---|
3989 | truncF= mod (F, power (y, l)); |
---|
3990 | if (useOldQs) |
---|
3991 | { |
---|
3992 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3993 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
3994 | bufQ[i] |
---|
3995 | ); |
---|
3996 | } |
---|
3997 | else |
---|
3998 | { |
---|
3999 | for (int i= 0; i < factors.length(); i++, j++) |
---|
4000 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
4001 | } |
---|
4002 | useOldQs= true; |
---|
4003 | for (int i= 0; i < d; i++) |
---|
4004 | { |
---|
4005 | if (bounds [i] + 1 <= l/2) |
---|
4006 | { |
---|
4007 | int k= tmin (bounds [i] + 1, l/2); |
---|
4008 | C= CFMatrix ((l - k)*extensionDeg, factors.length()); |
---|
4009 | for (int ii= 0; ii < factors.length(); ii++) |
---|
4010 | { |
---|
4011 | if (A[ii].size() - 1 >= i) |
---|
4012 | { |
---|
4013 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
4014 | writeInMatrix (C, buf, ii + 1, 0); |
---|
4015 | } |
---|
4016 | } |
---|
4017 | #ifdef HAVE_FLINT |
---|
4018 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
4019 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
4020 | getCharacteristic()); |
---|
4021 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
4022 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
4023 | getCharacteristic()); |
---|
4024 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
4025 | nmod_mat_clear (FLINTK); |
---|
4026 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
4027 | nmod_mat_clear (FLINTC); |
---|
4028 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
4029 | nmod_mat_clear (FLINTN); |
---|
4030 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
4031 | getCharacteristic()); |
---|
4032 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
4033 | |
---|
4034 | nmod_mat_clear (FLINTC); |
---|
4035 | nmod_mat_window_clear (FLINTK); |
---|
4036 | nmod_mat_clear (null); |
---|
4037 | #else |
---|
4038 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
4039 | NTLK= (*NTLC)*NTLN; |
---|
4040 | transpose (NTLK, NTLK); |
---|
4041 | kernel (NTLK, NTLK); |
---|
4042 | transpose (NTLK, NTLK); |
---|
4043 | NTLN *= NTLK; |
---|
4044 | #endif |
---|
4045 | #ifdef HAVE_FLINT |
---|
4046 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
4047 | { |
---|
4048 | nmod_mat_clear (FLINTN); |
---|
4049 | #else |
---|
4050 | if (NTLN.NumCols() == 1) |
---|
4051 | { |
---|
4052 | #endif |
---|
4053 | delete [] A; |
---|
4054 | delete [] bounds; |
---|
4055 | CanonicalForm G= F; |
---|
4056 | F= 1; |
---|
4057 | return CFList (G); |
---|
4058 | } |
---|
4059 | } |
---|
4060 | } |
---|
4061 | |
---|
4062 | #ifdef HAVE_FLINT |
---|
4063 | if (nmod_mat_ncols (FLINTN) < oldNumCols - factorsFound) |
---|
4064 | { |
---|
4065 | if (isReduced (FLINTN)) |
---|
4066 | { |
---|
4067 | int * factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
4068 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
4069 | #else |
---|
4070 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
4071 | { |
---|
4072 | if (isReduced (NTLN)) |
---|
4073 | { |
---|
4074 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
4075 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
4076 | #endif |
---|
4077 | factorsFoundIndex[i]= 0; |
---|
4078 | int factorsFound2= 0; |
---|
4079 | CFList result; |
---|
4080 | CanonicalForm bufF= F; |
---|
4081 | #ifdef HAVE_FLINT |
---|
4082 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
4083 | factorsFoundIndex, FLINTN, false |
---|
4084 | ); |
---|
4085 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
4086 | { |
---|
4087 | nmod_mat_clear (FLINTN); |
---|
4088 | #else |
---|
4089 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
4090 | factorsFoundIndex, NTLN, false |
---|
4091 | ); |
---|
4092 | if (result.length() == NTLN.NumCols()) |
---|
4093 | { |
---|
4094 | #endif |
---|
4095 | delete [] factorsFoundIndex; |
---|
4096 | delete [] A; |
---|
4097 | delete [] bounds; |
---|
4098 | F= 1; |
---|
4099 | return result; |
---|
4100 | } |
---|
4101 | delete [] factorsFoundIndex; |
---|
4102 | } |
---|
4103 | else if (l == precision) |
---|
4104 | { |
---|
4105 | CanonicalForm bufF= F; |
---|
4106 | #ifdef HAVE_FLINT |
---|
4107 | int * zeroOne= extractZeroOneVecs (FLINTN); |
---|
4108 | CFList result= reconstruction (bufF,factors,zeroOne,precision,FLINTN); |
---|
4109 | nmod_mat_clear (FLINTN); |
---|
4110 | #else |
---|
4111 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
4112 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN); |
---|
4113 | #endif |
---|
4114 | F= bufF; |
---|
4115 | delete [] zeroOne; |
---|
4116 | delete [] A; |
---|
4117 | delete [] bounds; |
---|
4118 | return result; |
---|
4119 | } |
---|
4120 | } |
---|
4121 | oldL2= l; |
---|
4122 | l += stepSize; |
---|
4123 | stepSize *= 2; |
---|
4124 | if (l > precision) |
---|
4125 | { |
---|
4126 | if (!hitBound) |
---|
4127 | { |
---|
4128 | hitBound= true; |
---|
4129 | l= precision; |
---|
4130 | } |
---|
4131 | else |
---|
4132 | break; |
---|
4133 | } |
---|
4134 | } |
---|
4135 | #ifdef HAVE_FLINT |
---|
4136 | nmod_mat_clear (FLINTN); |
---|
4137 | #endif |
---|
4138 | delete [] bounds; |
---|
4139 | delete [] A; |
---|
4140 | return CFList(); |
---|
4141 | } |
---|
4142 | |
---|
4143 | #ifdef HAVE_FLINT |
---|
4144 | CFList |
---|
4145 | increasePrecision (CanonicalForm& F, CFList& factors, int oldL, int |
---|
4146 | l, int d, int* bounds, CFArray& bufQ, nmod_mat_t FLINTN |
---|
4147 | ) |
---|
4148 | #else |
---|
4149 | CFList |
---|
4150 | increasePrecision (CanonicalForm& F, CFList& factors, int oldL, int |
---|
4151 | l, int d, int* bounds, CFArray& bufQ, mat_zz_p& NTLN |
---|
4152 | ) |
---|
4153 | #endif |
---|
4154 | { |
---|
4155 | CFList result= CFList(); |
---|
4156 | CFArray * A= new CFArray [factors.length()]; |
---|
4157 | int oldL2= oldL/2; |
---|
4158 | bool hitBound= false; |
---|
4159 | #ifdef HAVE_FLINT |
---|
4160 | if (nmod_mat_nrows (FLINTN) != factors.length()) //refined factors |
---|
4161 | { |
---|
4162 | nmod_mat_clear (FLINTN); |
---|
4163 | nmod_mat_init(FLINTN,factors.length(),factors.length(),getCharacteristic()); |
---|
4164 | for (long i=factors.length()-1; i >= 0; i--) |
---|
4165 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
4166 | bufQ= CFArray (factors.length()); |
---|
4167 | } |
---|
4168 | #else |
---|
4169 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
4170 | { |
---|
4171 | ident (NTLN, factors.length()); |
---|
4172 | bufQ= CFArray (factors.length()); |
---|
4173 | } |
---|
4174 | #endif |
---|
4175 | bool useOldQs= false; |
---|
4176 | CFListIterator j; |
---|
4177 | CFMatrix C; |
---|
4178 | CFArray buf; |
---|
4179 | #ifdef HAVE_FLINT |
---|
4180 | long rank; |
---|
4181 | nmod_mat_t FLINTC, FLINTK, null; |
---|
4182 | #else |
---|
4183 | mat_zz_p* NTLC, NTLK; |
---|
4184 | #endif |
---|
4185 | CanonicalForm bufF, truncF; |
---|
4186 | CFList bufUniFactors; |
---|
4187 | Variable y= F.mvar(); |
---|
4188 | while (oldL <= l) |
---|
4189 | { |
---|
4190 | j= factors; |
---|
4191 | truncF= mod (F, power (y, oldL)); |
---|
4192 | if (useOldQs) |
---|
4193 | { |
---|
4194 | for (int i= 0; i < factors.length(); i++, j++) |
---|
4195 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
4196 | bufQ[i] |
---|
4197 | ); |
---|
4198 | } |
---|
4199 | else |
---|
4200 | { |
---|
4201 | for (int i= 0; i < factors.length(); i++, j++) |
---|
4202 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
4203 | } |
---|
4204 | useOldQs= true; |
---|
4205 | |
---|
4206 | for (int i= 0; i < d; i++) |
---|
4207 | { |
---|
4208 | if (bounds [i] + 1 <= oldL/2) |
---|
4209 | { |
---|
4210 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
4211 | C= CFMatrix (oldL - k, factors.length()); |
---|
4212 | for (int ii= 0; ii < factors.length(); ii++) |
---|
4213 | { |
---|
4214 | if (A[ii].size() - 1 >= i) |
---|
4215 | { |
---|
4216 | buf= getCoeffs (A[ii] [i], k); |
---|
4217 | writeInMatrix (C, buf, ii + 1, 0); |
---|
4218 | } |
---|
4219 | } |
---|
4220 | #ifdef HAVE_FLINT |
---|
4221 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
4222 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
4223 | getCharacteristic()); |
---|
4224 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
4225 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
4226 | getCharacteristic()); |
---|
4227 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
4228 | nmod_mat_clear (FLINTK); |
---|
4229 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
4230 | nmod_mat_clear (FLINTC); |
---|
4231 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
4232 | nmod_mat_clear (FLINTN); |
---|
4233 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
4234 | getCharacteristic()); |
---|
4235 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
4236 | |
---|
4237 | nmod_mat_clear (FLINTC); |
---|
4238 | nmod_mat_window_clear (FLINTK); |
---|
4239 | nmod_mat_clear (null); |
---|
4240 | #else |
---|
4241 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
4242 | NTLK= (*NTLC)*NTLN; |
---|
4243 | transpose (NTLK, NTLK); |
---|
4244 | kernel (NTLK, NTLK); |
---|
4245 | transpose (NTLK, NTLK); |
---|
4246 | NTLN *= NTLK; |
---|
4247 | #endif |
---|
4248 | #ifdef HAVE_FLINT |
---|
4249 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
4250 | #else |
---|
4251 | if (NTLN.NumCols() == 1) |
---|
4252 | #endif |
---|
4253 | { |
---|
4254 | delete [] A; |
---|
4255 | return CFList (F); |
---|
4256 | } |
---|
4257 | } |
---|
4258 | } |
---|
4259 | #ifdef HAVE_FLINT |
---|
4260 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
4261 | #else |
---|
4262 | if (NTLN.NumCols() == 1) |
---|
4263 | #endif |
---|
4264 | { |
---|
4265 | delete [] A; |
---|
4266 | return CFList (F); |
---|
4267 | } |
---|
4268 | int * zeroOneVecs; |
---|
4269 | #ifdef HAVE_FLINT |
---|
4270 | zeroOneVecs= extractZeroOneVecs (FLINTN); |
---|
4271 | #else |
---|
4272 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
4273 | #endif |
---|
4274 | bufF= F; |
---|
4275 | bufUniFactors= factors; |
---|
4276 | #ifdef HAVE_FLINT |
---|
4277 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, FLINTN); |
---|
4278 | #else |
---|
4279 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN); |
---|
4280 | #endif |
---|
4281 | delete [] zeroOneVecs; |
---|
4282 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < oldL && result.length() > 0) |
---|
4283 | { |
---|
4284 | F= bufF; |
---|
4285 | factors= bufUniFactors; |
---|
4286 | delete [] A; |
---|
4287 | return result; |
---|
4288 | } |
---|
4289 | |
---|
4290 | result= CFList(); |
---|
4291 | oldL2= oldL; |
---|
4292 | oldL *= 2; |
---|
4293 | if (oldL > l) |
---|
4294 | { |
---|
4295 | if (!hitBound) |
---|
4296 | { |
---|
4297 | oldL= l; |
---|
4298 | hitBound= true; |
---|
4299 | } |
---|
4300 | else |
---|
4301 | break; |
---|
4302 | } |
---|
4303 | } |
---|
4304 | delete [] A; |
---|
4305 | return result; |
---|
4306 | } |
---|
4307 | |
---|
4308 | CFList |
---|
4309 | increasePrecision (CanonicalForm& F, CFList& factors, int oldL, int |
---|
4310 | l, int d, int* bounds, CFArray& bufQ, mat_zz_pE& NTLN |
---|
4311 | ) |
---|
4312 | { |
---|
4313 | CFList result= CFList(); |
---|
4314 | CFArray * A= new CFArray [factors.length()]; |
---|
4315 | int oldL2= oldL/2; |
---|
4316 | bool hitBound= false; |
---|
4317 | bool useOldQs= false; |
---|
4318 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
4319 | ident (NTLN, factors.length()); |
---|
4320 | CFListIterator j; |
---|
4321 | CFMatrix C; |
---|
4322 | CFArray buf; |
---|
4323 | mat_zz_pE* NTLC, NTLK; |
---|
4324 | CanonicalForm bufF, truncF; |
---|
4325 | CFList bufUniFactors; |
---|
4326 | Variable y= F.mvar(); |
---|
4327 | while (oldL <= l) |
---|
4328 | { |
---|
4329 | j= factors; |
---|
4330 | truncF= mod (F, power (y, oldL)); |
---|
4331 | if (useOldQs) |
---|
4332 | { |
---|
4333 | for (int i= 0; i < factors.length(); i++, j++) |
---|
4334 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
4335 | bufQ[i] |
---|
4336 | ); |
---|
4337 | } |
---|
4338 | else |
---|
4339 | { |
---|
4340 | for (int i= 0; i < factors.length(); i++, j++) |
---|
4341 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
4342 | } |
---|
4343 | useOldQs= true; |
---|
4344 | |
---|
4345 | for (int i= 0; i < d; i++) |
---|
4346 | { |
---|
4347 | if (bounds [i] + 1 <= oldL/2) |
---|
4348 | { |
---|
4349 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
4350 | C= CFMatrix (oldL - k, factors.length()); |
---|
4351 | for (int ii= 0; ii < factors.length(); ii++) |
---|
4352 | { |
---|
4353 | if (A[ii].size() - 1 >= i) |
---|
4354 | { |
---|
4355 | buf= getCoeffs (A[ii] [i], k); |
---|
4356 | writeInMatrix (C, buf, ii + 1, 0); |
---|
4357 | } |
---|
4358 | } |
---|
4359 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
4360 | NTLK= (*NTLC)*NTLN; |
---|
4361 | transpose (NTLK, NTLK); |
---|
4362 | kernel (NTLK, NTLK); |
---|
4363 | transpose (NTLK, NTLK); |
---|
4364 | NTLN *= NTLK; |
---|
4365 | if (NTLN.NumCols() == 1) |
---|
4366 | { |
---|
4367 | delete [] A; |
---|
4368 | return CFList (F); |
---|
4369 | } |
---|
4370 | } |
---|
4371 | } |
---|
4372 | if (NTLN.NumCols() == 1) |
---|
4373 | { |
---|
4374 | delete [] A; |
---|
4375 | return CFList (F); |
---|
4376 | } |
---|
4377 | |
---|
4378 | int * zeroOneVecs; |
---|
4379 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
4380 | bufF= F; |
---|
4381 | bufUniFactors= factors; |
---|
4382 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN); |
---|
4383 | delete [] zeroOneVecs; |
---|
4384 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
4385 | { |
---|
4386 | F= bufF; |
---|
4387 | factors= bufUniFactors; |
---|
4388 | delete [] A; |
---|
4389 | return result; |
---|
4390 | } |
---|
4391 | |
---|
4392 | result= CFList(); |
---|
4393 | oldL2= oldL; |
---|
4394 | oldL *= 2; |
---|
4395 | if (oldL > l) |
---|
4396 | { |
---|
4397 | if (!hitBound) |
---|
4398 | { |
---|
4399 | oldL= l; |
---|
4400 | hitBound= true; |
---|
4401 | } |
---|
4402 | else |
---|
4403 | break; |
---|
4404 | } |
---|
4405 | } |
---|
4406 | delete [] A; |
---|
4407 | return result; |
---|
4408 | } |
---|
4409 | |
---|
4410 | //over field extension |
---|
4411 | CFList |
---|
4412 | extIncreasePrecision (CanonicalForm& F, CFList& factors, int oldL, int l, int d, |
---|
4413 | int* bounds, CFArray& bufQ, mat_zz_p& NTLN, const |
---|
4414 | CanonicalForm& evaluation, const ExtensionInfo& info, |
---|
4415 | CFList& source, CFList& dest |
---|
4416 | ) |
---|
4417 | { |
---|
4418 | CFList result= CFList(); |
---|
4419 | CFArray * A= new CFArray [factors.length()]; |
---|
4420 | int oldL2= oldL/2; //be careful |
---|
4421 | bool hitBound= false; |
---|
4422 | bool useOldQs= false; |
---|
4423 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
4424 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
4425 | Variable alpha= info.getAlpha(); |
---|
4426 | |
---|
4427 | Variable gamma= info.getBeta(); |
---|
4428 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
4429 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
4430 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
4431 | ident (NTLN, factors.length()); |
---|
4432 | Variable y= F.mvar(); |
---|
4433 | CFListIterator j; |
---|
4434 | CanonicalForm powX, imBasis, bufF, truncF; |
---|
4435 | CFMatrix Mat, C; |
---|
4436 | CFIterator iter; |
---|
4437 | mat_zz_p* NTLMat; |
---|
4438 | CFArray buf; |
---|
4439 | mat_zz_p* NTLC, NTLK; |
---|
4440 | CFList bufUniFactors; |
---|
4441 | while (oldL <= l) |
---|
4442 | { |
---|
4443 | j= factors; |
---|
4444 | if (GF) |
---|
4445 | setCharacteristic (getCharacteristic()); |
---|
4446 | |
---|
4447 | powX= power (y-gamma, oldL); |
---|
4448 | Mat= CFMatrix (oldL*degMipo, oldL*degMipo); |
---|
4449 | for (int i= 0; i < oldL*degMipo; i++) |
---|
4450 | { |
---|
4451 | imBasis= mod (power (y, i), powX); |
---|
4452 | imBasis= imBasis (power (y, degMipo), y); |
---|
4453 | imBasis= imBasis (y, gamma); |
---|
4454 | iter= imBasis; |
---|
4455 | for (; iter.hasTerms(); iter++) |
---|
4456 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
4457 | } |
---|
4458 | |
---|
4459 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
4460 | *NTLMat= inv (*NTLMat); |
---|
4461 | if (GF) |
---|
4462 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
4463 | |
---|
4464 | truncF= mod (F, power (y, oldL)); |
---|
4465 | if (useOldQs) |
---|
4466 | { |
---|
4467 | for (int i= 0; i < factors.length(); i++, j++) |
---|
4468 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
4469 | bufQ[i]); |
---|
4470 | } |
---|
4471 | else |
---|
4472 | { |
---|
4473 | for (int i= 0; i < factors.length(); i++, j++) |
---|
4474 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
4475 | } |
---|
4476 | useOldQs= true; |
---|
4477 | |
---|
4478 | for (int i= 0; i < d; i++) |
---|
4479 | { |
---|
4480 | if (bounds [i] + 1 <= oldL/2) |
---|
4481 | { |
---|
4482 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
4483 | C= CFMatrix (oldL*degMipo - k, factors.length()); |
---|
4484 | for (int ii= 0; ii < factors.length(); ii++) |
---|
4485 | { |
---|
4486 | if (A[ii].size() - 1 >= i) |
---|
4487 | { |
---|
4488 | if (GF) |
---|
4489 | { |
---|
4490 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
4491 | setCharacteristic (getCharacteristic()); |
---|
4492 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
4493 | if (alpha != gamma) |
---|
4494 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
4495 | gamma, source, dest |
---|
4496 | ); |
---|
4497 | buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, *NTLMat); |
---|
4498 | } |
---|
4499 | else |
---|
4500 | { |
---|
4501 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
4502 | if (alpha != gamma) |
---|
4503 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
4504 | gamma, source, dest |
---|
4505 | ); |
---|
4506 | buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, *NTLMat); |
---|
4507 | } |
---|
4508 | writeInMatrix (C, buf, ii + 1, 0); |
---|
4509 | } |
---|
4510 | if (GF) |
---|
4511 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
4512 | } |
---|
4513 | |
---|
4514 | if (GF) |
---|
4515 | setCharacteristic(getCharacteristic()); |
---|
4516 | |
---|
4517 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
4518 | NTLK= (*NTLC)*NTLN; |
---|
4519 | transpose (NTLK, NTLK); |
---|
4520 | kernel (NTLK, NTLK); |
---|
4521 | transpose (NTLK, NTLK); |
---|
4522 | NTLN *= NTLK; |
---|
4523 | |
---|
4524 | if (GF) |
---|
4525 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
4526 | |
---|
4527 | if (NTLN.NumCols() == 1) |
---|
4528 | { |
---|
4529 | Variable y= Variable (2); |
---|
4530 | CanonicalForm tmp= F (y - evaluation, y); |
---|
4531 | CFList source, dest; |
---|
4532 | tmp= mapDown (tmp, info, source, dest); |
---|
4533 | delete [] A; |
---|
4534 | return CFList (tmp); |
---|
4535 | } |
---|
4536 | } |
---|
4537 | } |
---|
4538 | if (NTLN.NumCols() == 1) |
---|
4539 | { |
---|
4540 | Variable y= Variable (2); |
---|
4541 | CanonicalForm tmp= F (y - evaluation, y); |
---|
4542 | CFList source, dest; |
---|
4543 | tmp= mapDown (tmp, info, source, dest); |
---|
4544 | delete [] A; |
---|
4545 | return CFList (tmp); |
---|
4546 | } |
---|
4547 | |
---|
4548 | int * zeroOneVecs; |
---|
4549 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
4550 | bufF= F; |
---|
4551 | bufUniFactors= factors; |
---|
4552 | result= extReconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN, |
---|
4553 | info, evaluation |
---|
4554 | ); |
---|
4555 | delete [] zeroOneVecs; |
---|
4556 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
4557 | { |
---|
4558 | F= bufF; |
---|
4559 | factors= bufUniFactors; |
---|
4560 | return result; |
---|
4561 | } |
---|
4562 | |
---|
4563 | result= CFList(); |
---|
4564 | oldL2= oldL; |
---|
4565 | oldL *= 2; |
---|
4566 | if (oldL > l) |
---|
4567 | { |
---|
4568 | if (!hitBound) |
---|
4569 | { |
---|
4570 | oldL= l; |
---|
4571 | hitBound= true; |
---|
4572 | } |
---|
4573 | else |
---|
4574 | break; |
---|
4575 | } |
---|
4576 | } |
---|
4577 | delete [] A; |
---|
4578 | return result; |
---|
4579 | } |
---|
4580 | |
---|
4581 | #ifdef HAVE_FLINT |
---|
4582 | CFList |
---|
4583 | increasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int oldL, int l, |
---|
4584 | int d, int* bounds, CFArray& bufQ, nmod_mat_t FLINTN, |
---|
4585 | const Variable& alpha |
---|
4586 | ) |
---|
4587 | #else |
---|
4588 | CFList |
---|
4589 | increasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int oldL, int l, |
---|
4590 | int d, int* bounds, CFArray& bufQ, mat_zz_p& NTLN, |
---|
4591 | const Variable& alpha |
---|
4592 | ) |
---|
4593 | #endif |
---|
4594 | { |
---|
4595 | CFList result= CFList(); |
---|
4596 | CFArray * A= new CFArray [factors.length()]; |
---|
4597 | int extensionDeg= degree (getMipo (alpha)); |
---|
4598 | int oldL2= oldL/2; |
---|
4599 | bool hitBound= false; |
---|
4600 | bool useOldQs= false; |
---|
4601 | #ifdef HAVE_FLINT |
---|
4602 | if (nmod_mat_nrows (FLINTN) != factors.length()) //refined factors |
---|
4603 | { |
---|
4604 | nmod_mat_clear (FLINTN); |
---|
4605 | nmod_mat_init(FLINTN,factors.length(),factors.length(),getCharacteristic()); |
---|
4606 | for (long i=factors.length()-1; i >= 0; i--) |
---|
4607 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
4608 | } |
---|
4609 | #else |
---|
4610 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
4611 | ident (NTLN, factors.length()); |
---|
4612 | #endif |
---|
4613 | CFListIterator j; |
---|
4614 | CFMatrix C; |
---|
4615 | CFArray buf; |
---|
4616 | #ifdef HAVE_FLINT |
---|
4617 | long rank; |
---|
4618 | nmod_mat_t FLINTC, FLINTK, null; |
---|
4619 | #else |
---|
4620 | mat_zz_p* NTLC, NTLK; |
---|
4621 | #endif |
---|
4622 | CanonicalForm bufF, truncF; |
---|
4623 | CFList bufUniFactors; |
---|
4624 | Variable y= F.mvar(); |
---|
4625 | while (oldL <= l) |
---|
4626 | { |
---|
4627 | j= factors; |
---|
4628 | truncF= mod (F, power (y, oldL)); |
---|
4629 | if (useOldQs) |
---|
4630 | { |
---|
4631 | for (int i= 0; i < factors.length(); i++, j++) |
---|
4632 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
4633 | bufQ[i] |
---|
4634 | ); |
---|
4635 | } |
---|
4636 | else |
---|
4637 | { |
---|
4638 | for (int i= 0; i < factors.length(); i++, j++) |
---|
4639 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
4640 | } |
---|
4641 | useOldQs= true; |
---|
4642 | |
---|
4643 | for (int i= 0; i < d; i++) |
---|
4644 | { |
---|
4645 | if (bounds [i] + 1 <= oldL/2) |
---|
4646 | { |
---|
4647 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
4648 | C= CFMatrix ((oldL - k)*extensionDeg, factors.length()); |
---|
4649 | for (int ii= 0; ii < factors.length(); ii++) |
---|
4650 | { |
---|
4651 | if (A[ii].size() - 1 >= i) |
---|
4652 | { |
---|
4653 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
4654 | writeInMatrix (C, buf, ii + 1, 0); |
---|
4655 | } |
---|
4656 | } |
---|
4657 | #ifdef HAVE_FLINT |
---|
4658 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
4659 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
4660 | getCharacteristic()); |
---|
4661 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
4662 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
4663 | getCharacteristic()); |
---|
4664 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
4665 | nmod_mat_clear (FLINTK); |
---|
4666 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
4667 | nmod_mat_clear (FLINTC); |
---|
4668 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
4669 | nmod_mat_clear (FLINTN); |
---|
4670 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
4671 | getCharacteristic()); |
---|
4672 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
4673 | |
---|
4674 | nmod_mat_clear (FLINTC); |
---|
4675 | nmod_mat_window_clear (FLINTK); |
---|
4676 | nmod_mat_clear (null); |
---|
4677 | #else |
---|
4678 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
4679 | NTLK= (*NTLC)*NTLN; |
---|
4680 | transpose (NTLK, NTLK); |
---|
4681 | kernel (NTLK, NTLK); |
---|
4682 | transpose (NTLK, NTLK); |
---|
4683 | NTLN *= NTLK; |
---|
4684 | #endif |
---|
4685 | #ifdef HAVE_FLINT |
---|
4686 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
4687 | #else |
---|
4688 | if (NTLN.NumCols() == 1) |
---|
4689 | #endif |
---|
4690 | { |
---|
4691 | delete [] A; |
---|
4692 | return CFList (F); |
---|
4693 | } |
---|
4694 | } |
---|
4695 | } |
---|
4696 | |
---|
4697 | int * zeroOneVecs; |
---|
4698 | #ifdef HAVE_FLINT |
---|
4699 | zeroOneVecs= extractZeroOneVecs (FLINTN); |
---|
4700 | #else |
---|
4701 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
4702 | #endif |
---|
4703 | |
---|
4704 | bufF= F; |
---|
4705 | bufUniFactors= factors; |
---|
4706 | #ifdef HAVE_FLINT |
---|
4707 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, FLINTN); |
---|
4708 | #else |
---|
4709 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN); |
---|
4710 | #endif |
---|
4711 | delete [] zeroOneVecs; |
---|
4712 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
4713 | { |
---|
4714 | F= bufF; |
---|
4715 | factors= bufUniFactors; |
---|
4716 | delete [] A; |
---|
4717 | return result; |
---|
4718 | } |
---|
4719 | |
---|
4720 | result= CFList(); |
---|
4721 | oldL2= oldL; |
---|
4722 | oldL *= 2; |
---|
4723 | if (oldL > l) |
---|
4724 | { |
---|
4725 | if (!hitBound) |
---|
4726 | { |
---|
4727 | oldL= l; |
---|
4728 | hitBound= true; |
---|
4729 | } |
---|
4730 | else |
---|
4731 | break; |
---|
4732 | } |
---|
4733 | } |
---|
4734 | delete [] A; |
---|
4735 | return result; |
---|
4736 | } |
---|
4737 | |
---|
4738 | #ifdef HAVE_FLINT |
---|
4739 | CFList |
---|
4740 | furtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& |
---|
4741 | factors, int l, int liftBound, int d, int* |
---|
4742 | bounds, nmod_mat_t FLINTN, CFList& diophant, |
---|
4743 | CFMatrix& M, CFArray& Pi, CFArray& bufQ |
---|
4744 | ) |
---|
4745 | #else |
---|
4746 | CFList |
---|
4747 | furtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& |
---|
4748 | factors, int l, int liftBound, int d, int* |
---|
4749 | bounds, mat_zz_p& NTLN, CFList& diophant, |
---|
4750 | CFMatrix& M, CFArray& Pi, CFArray& bufQ |
---|
4751 | ) |
---|
4752 | #endif |
---|
4753 | { |
---|
4754 | CanonicalForm LCF= LC (F, 1); |
---|
4755 | CFList result; |
---|
4756 | bool irreducible= false; |
---|
4757 | CFList bufFactors= factors; |
---|
4758 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
4759 | bool useOldQs= false; |
---|
4760 | bool hitBound= false; |
---|
4761 | int oldL= l; |
---|
4762 | int stepSize= 8; //TODO choose better step size? |
---|
4763 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
4764 | #ifdef HAVE_FLINT |
---|
4765 | if (nmod_mat_nrows (FLINTN) != factors.length()) //refined factors |
---|
4766 | { |
---|
4767 | nmod_mat_clear (FLINTN); |
---|
4768 | nmod_mat_init(FLINTN,factors.length(),factors.length(),getCharacteristic()); |
---|
4769 | for (long i=factors.length()-1; i >= 0; i--) |
---|
4770 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
4771 | } |
---|
4772 | #else |
---|
4773 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
4774 | ident (NTLN, factors.length()); |
---|
4775 | #endif |
---|
4776 | CFListIterator j; |
---|
4777 | CFMatrix C; |
---|
4778 | CFArray buf; |
---|
4779 | #ifdef HAVE_FLINT |
---|
4780 | long rank; |
---|
4781 | nmod_mat_t FLINTC, FLINTK, null; |
---|
4782 | #else |
---|
4783 | mat_zz_p* NTLC, NTLK; |
---|
4784 | #endif |
---|
4785 | CanonicalForm bufF, truncF; |
---|
4786 | Variable y= F.mvar(); |
---|
4787 | while (l <= liftBound) |
---|
4788 | { |
---|
4789 | bufFactors.insert (LCF); |
---|
4790 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
4791 | bufFactors.insert (LCF); |
---|
4792 | bufFactors.removeFirst(); |
---|
4793 | j= bufFactors; |
---|
4794 | truncF= mod (F, power (y, l)); |
---|
4795 | if (useOldQs) |
---|
4796 | { |
---|
4797 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
4798 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
4799 | bufQ[i]); |
---|
4800 | } |
---|
4801 | else |
---|
4802 | { |
---|
4803 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
4804 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
4805 | } |
---|
4806 | for (int i= 0; i < d; i++) |
---|
4807 | { |
---|
4808 | if (bounds [i] + 1 <= l/2) |
---|
4809 | { |
---|
4810 | int k= tmin (bounds [i] + 1, l/2); |
---|
4811 | C= CFMatrix (l - k, bufFactors.length()); |
---|
4812 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
4813 | { |
---|
4814 | if (A[ii].size() - 1 >= i) |
---|
4815 | { |
---|
4816 | buf= getCoeffs (A[ii] [i], k); |
---|
4817 | writeInMatrix (C, buf, ii + 1, 0); |
---|
4818 | } |
---|
4819 | } |
---|
4820 | #ifdef HAVE_FLINT |
---|
4821 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
4822 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
4823 | getCharacteristic()); |
---|
4824 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
4825 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
4826 | getCharacteristic()); |
---|
4827 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
4828 | nmod_mat_clear (FLINTK); |
---|
4829 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
4830 | nmod_mat_clear (FLINTC); |
---|
4831 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
4832 | nmod_mat_clear (FLINTN); |
---|
4833 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
4834 | getCharacteristic()); |
---|
4835 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
4836 | |
---|
4837 | nmod_mat_clear (FLINTC); |
---|
4838 | nmod_mat_window_clear (FLINTK); |
---|
4839 | nmod_mat_clear (null); |
---|
4840 | #else |
---|
4841 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
4842 | NTLK= (*NTLC)*NTLN; |
---|
4843 | transpose (NTLK, NTLK); |
---|
4844 | kernel (NTLK, NTLK); |
---|
4845 | transpose (NTLK, NTLK); |
---|
4846 | NTLN *= NTLK; |
---|
4847 | #endif |
---|
4848 | #ifdef HAVE_FLINT |
---|
4849 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
4850 | #else |
---|
4851 | if (NTLN.NumCols() == 1) |
---|
4852 | #endif |
---|
4853 | { |
---|
4854 | irreducible= true; |
---|
4855 | break; |
---|
4856 | } |
---|
4857 | } |
---|
4858 | } |
---|
4859 | |
---|
4860 | #ifdef HAVE_FLINT |
---|
4861 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
4862 | #else |
---|
4863 | if (NTLN.NumCols() == 1) |
---|
4864 | #endif |
---|
4865 | { |
---|
4866 | irreducible= true; |
---|
4867 | break; |
---|
4868 | } |
---|
4869 | |
---|
4870 | #ifdef HAVE_FLINT |
---|
4871 | int * zeroOneVecs= extractZeroOneVecs (FLINTN); |
---|
4872 | #else |
---|
4873 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
4874 | #endif |
---|
4875 | bufF= F; |
---|
4876 | #ifdef HAVE_FLINT |
---|
4877 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, FLINTN); |
---|
4878 | #else |
---|
4879 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN); |
---|
4880 | #endif |
---|
4881 | delete [] zeroOneVecs; |
---|
4882 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
4883 | { |
---|
4884 | F= bufF; |
---|
4885 | factors= bufFactors; |
---|
4886 | delete [] A; |
---|
4887 | return result; |
---|
4888 | } |
---|
4889 | |
---|
4890 | #ifdef HAVE_FLINT |
---|
4891 | if (isReduced (FLINTN)) |
---|
4892 | #else |
---|
4893 | if (isReduced (NTLN)) |
---|
4894 | #endif |
---|
4895 | { |
---|
4896 | int factorsFound= 0; |
---|
4897 | bufF= F; |
---|
4898 | #ifdef HAVE_FLINT |
---|
4899 | int* factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
4900 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
4901 | #else |
---|
4902 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
4903 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
4904 | #endif |
---|
4905 | factorsFoundIndex[i]= 0; |
---|
4906 | #ifdef HAVE_FLINT |
---|
4907 | if (l < liftBound) |
---|
4908 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
4909 | factorsFoundIndex, FLINTN, false |
---|
4910 | ); |
---|
4911 | else |
---|
4912 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
4913 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
4914 | FLINTN, false |
---|
4915 | ); |
---|
4916 | |
---|
4917 | if (nmod_mat_ncols (FLINTN) == result.length()) |
---|
4918 | #else |
---|
4919 | if (l < liftBound) |
---|
4920 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
4921 | factorsFoundIndex, NTLN, false |
---|
4922 | ); |
---|
4923 | else |
---|
4924 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
4925 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
4926 | NTLN, false |
---|
4927 | ); |
---|
4928 | |
---|
4929 | if (NTLN.NumCols() == result.length()) |
---|
4930 | #endif |
---|
4931 | { |
---|
4932 | delete [] A; |
---|
4933 | delete [] factorsFoundIndex; |
---|
4934 | return result; |
---|
4935 | } |
---|
4936 | delete [] factorsFoundIndex; |
---|
4937 | } |
---|
4938 | result= CFList(); |
---|
4939 | oldL= l; |
---|
4940 | stepSize *= 2; |
---|
4941 | l += stepSize; |
---|
4942 | if (l > liftBound) |
---|
4943 | { |
---|
4944 | if (!hitBound) |
---|
4945 | { |
---|
4946 | l= liftBound; |
---|
4947 | hitBound= true; |
---|
4948 | } |
---|
4949 | else |
---|
4950 | break; |
---|
4951 | } |
---|
4952 | } |
---|
4953 | if (irreducible) |
---|
4954 | { |
---|
4955 | delete [] A; |
---|
4956 | return CFList (F); |
---|
4957 | } |
---|
4958 | delete [] A; |
---|
4959 | factors= bufFactors; |
---|
4960 | return CFList(); |
---|
4961 | } |
---|
4962 | |
---|
4963 | //Fq |
---|
4964 | CFList |
---|
4965 | furtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& |
---|
4966 | factors, int l, int liftBound, int d, int* |
---|
4967 | bounds, mat_zz_pE& NTLN, CFList& diophant, |
---|
4968 | CFMatrix& M, CFArray& Pi, CFArray& bufQ |
---|
4969 | ) |
---|
4970 | { |
---|
4971 | CanonicalForm LCF= LC (F, 1); |
---|
4972 | CFList result; |
---|
4973 | bool irreducible= false; |
---|
4974 | CFList bufFactors= factors; |
---|
4975 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
4976 | bool useOldQs= false; |
---|
4977 | bool hitBound= false; |
---|
4978 | int oldL= l; |
---|
4979 | int stepSize= 8; //TODO choose better step size? |
---|
4980 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
4981 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
4982 | ident (NTLN, factors.length()); |
---|
4983 | CFListIterator j; |
---|
4984 | CFArray buf; |
---|
4985 | mat_zz_pE* NTLC, NTLK; |
---|
4986 | CanonicalForm bufF, truncF; |
---|
4987 | Variable y= F.mvar(); |
---|
4988 | while (l <= liftBound) |
---|
4989 | { |
---|
4990 | bufFactors.insert (LCF); |
---|
4991 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
4992 | j= bufFactors; |
---|
4993 | truncF= mod (F, power (y, l)); |
---|
4994 | if (useOldQs) |
---|
4995 | { |
---|
4996 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
4997 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
4998 | bufQ[i]); |
---|
4999 | } |
---|
5000 | else |
---|
5001 | { |
---|
5002 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
5003 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
5004 | } |
---|
5005 | for (int i= 0; i < d; i++) |
---|
5006 | { |
---|
5007 | if (bounds [i] + 1 <= l/2) |
---|
5008 | { |
---|
5009 | int k= tmin (bounds [i] + 1, l/2); |
---|
5010 | CFMatrix C= CFMatrix (l - k, bufFactors.length()); |
---|
5011 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
5012 | { |
---|
5013 | if (A[ii].size() - 1 >= i) |
---|
5014 | { |
---|
5015 | buf= getCoeffs (A[ii] [i], k); |
---|
5016 | writeInMatrix (C, buf, ii + 1, 0); |
---|
5017 | } |
---|
5018 | } |
---|
5019 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
5020 | NTLK= (*NTLC)*NTLN; |
---|
5021 | transpose (NTLK, NTLK); |
---|
5022 | kernel (NTLK, NTLK); |
---|
5023 | transpose (NTLK, NTLK); |
---|
5024 | NTLN *= NTLK; |
---|
5025 | if (NTLN.NumCols() == 1) |
---|
5026 | { |
---|
5027 | irreducible= true; |
---|
5028 | break; |
---|
5029 | } |
---|
5030 | } |
---|
5031 | } |
---|
5032 | if (NTLN.NumCols() == 1) |
---|
5033 | { |
---|
5034 | irreducible= true; |
---|
5035 | break; |
---|
5036 | } |
---|
5037 | |
---|
5038 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
5039 | bufF= F; |
---|
5040 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN); |
---|
5041 | delete [] zeroOneVecs; |
---|
5042 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
5043 | { |
---|
5044 | F= bufF; |
---|
5045 | factors= bufFactors; |
---|
5046 | delete [] A; |
---|
5047 | return result; |
---|
5048 | } |
---|
5049 | |
---|
5050 | if (isReduced (NTLN)) |
---|
5051 | { |
---|
5052 | int factorsFound= 0; |
---|
5053 | bufF= F; |
---|
5054 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
5055 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
5056 | factorsFoundIndex[i]= 0; |
---|
5057 | if (l < liftBound) |
---|
5058 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
5059 | factorsFoundIndex, NTLN, false |
---|
5060 | ); |
---|
5061 | else |
---|
5062 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
5063 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
5064 | NTLN, false |
---|
5065 | ); |
---|
5066 | if (NTLN.NumCols() == result.length()) |
---|
5067 | { |
---|
5068 | delete [] A; |
---|
5069 | delete [] factorsFoundIndex; |
---|
5070 | return result; |
---|
5071 | } |
---|
5072 | delete [] factorsFoundIndex; |
---|
5073 | } |
---|
5074 | result= CFList(); |
---|
5075 | oldL= l; |
---|
5076 | stepSize *= 2; |
---|
5077 | l += stepSize; |
---|
5078 | if (l > liftBound) |
---|
5079 | { |
---|
5080 | if (!hitBound) |
---|
5081 | { |
---|
5082 | l= liftBound; |
---|
5083 | hitBound= true; |
---|
5084 | } |
---|
5085 | else |
---|
5086 | break; |
---|
5087 | } |
---|
5088 | } |
---|
5089 | if (irreducible) |
---|
5090 | { |
---|
5091 | delete [] A; |
---|
5092 | return CFList (F); |
---|
5093 | } |
---|
5094 | delete [] A; |
---|
5095 | factors= bufFactors; |
---|
5096 | return CFList(); |
---|
5097 | } |
---|
5098 | |
---|
5099 | //over field extension |
---|
5100 | CFList |
---|
5101 | extFurtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& factors, int l, |
---|
5102 | int liftBound, int d, int* bounds, |
---|
5103 | mat_zz_p& NTLN, CFList& diophant, |
---|
5104 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
5105 | const CanonicalForm& evaluation, const |
---|
5106 | ExtensionInfo& info, CFList& source, |
---|
5107 | CFList& dest |
---|
5108 | ) |
---|
5109 | { |
---|
5110 | CanonicalForm LCF= LC (F, 1); |
---|
5111 | CFList result; |
---|
5112 | bool irreducible= false; |
---|
5113 | CFList bufFactors= factors; |
---|
5114 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
5115 | bool useOldQs= false; |
---|
5116 | bool hitBound= false; |
---|
5117 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
5118 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
5119 | Variable alpha= info.getAlpha(); |
---|
5120 | int oldL= l; //be careful |
---|
5121 | int stepSize= 8; |
---|
5122 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l),2); |
---|
5123 | Variable gamma= info.getBeta(); |
---|
5124 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
5125 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
5126 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
5127 | ident (NTLN, factors.length()); |
---|
5128 | Variable y= F.mvar(); |
---|
5129 | CanonicalForm powX, imBasis, bufF, truncF; |
---|
5130 | CFMatrix Mat, C; |
---|
5131 | CFIterator iter; |
---|
5132 | mat_zz_p* NTLMat,*NTLC, NTLK; |
---|
5133 | CFListIterator j; |
---|
5134 | CFArray buf; |
---|
5135 | while (l <= liftBound) |
---|
5136 | { |
---|
5137 | bufFactors.insert (LCF); |
---|
5138 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
5139 | |
---|
5140 | if (GF) |
---|
5141 | setCharacteristic (getCharacteristic()); |
---|
5142 | |
---|
5143 | powX= power (y-gamma, l); |
---|
5144 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
5145 | for (int i= 0; i < l*degMipo; i++) |
---|
5146 | { |
---|
5147 | |
---|
5148 | imBasis= mod (power (y, i), powX); |
---|
5149 | imBasis= imBasis (power (y, degMipo), y); |
---|
5150 | imBasis= imBasis (y, gamma); |
---|
5151 | iter= imBasis; |
---|
5152 | for (; iter.hasTerms(); iter++) |
---|
5153 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
5154 | } |
---|
5155 | |
---|
5156 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
5157 | *NTLMat= inv (*NTLMat); |
---|
5158 | |
---|
5159 | if (GF) |
---|
5160 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
5161 | |
---|
5162 | j= bufFactors; |
---|
5163 | truncF= mod (F, power (y, l)); |
---|
5164 | if (useOldQs) |
---|
5165 | { |
---|
5166 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
5167 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
5168 | bufQ[i]); |
---|
5169 | } |
---|
5170 | else |
---|
5171 | { |
---|
5172 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
5173 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
5174 | } |
---|
5175 | for (int i= 0; i < d; i++) |
---|
5176 | { |
---|
5177 | if (bounds [i] + 1 <= l/2) |
---|
5178 | { |
---|
5179 | int k= tmin (bounds [i] + 1, l/2); |
---|
5180 | C= CFMatrix (l*degMipo - k, bufFactors.length()); |
---|
5181 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
5182 | { |
---|
5183 | if (A[ii].size() - 1 >= i) |
---|
5184 | { |
---|
5185 | if (GF) |
---|
5186 | { |
---|
5187 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
5188 | setCharacteristic (getCharacteristic()); |
---|
5189 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
5190 | if (alpha != gamma) |
---|
5191 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
5192 | gamma, source, dest |
---|
5193 | ); |
---|
5194 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
5195 | } |
---|
5196 | else |
---|
5197 | { |
---|
5198 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
5199 | if (alpha != gamma) |
---|
5200 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
5201 | gamma, source, dest |
---|
5202 | ); |
---|
5203 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
5204 | } |
---|
5205 | writeInMatrix (C, buf, ii + 1, 0); |
---|
5206 | } |
---|
5207 | if (GF) |
---|
5208 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
5209 | } |
---|
5210 | |
---|
5211 | if (GF) |
---|
5212 | setCharacteristic(getCharacteristic()); |
---|
5213 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
5214 | NTLK= (*NTLC)*NTLN; |
---|
5215 | transpose (NTLK, NTLK); |
---|
5216 | kernel (NTLK, NTLK); |
---|
5217 | transpose (NTLK, NTLK); |
---|
5218 | NTLN *= NTLK; |
---|
5219 | if (GF) |
---|
5220 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
5221 | |
---|
5222 | if (NTLN.NumCols() == 1) |
---|
5223 | { |
---|
5224 | irreducible= true; |
---|
5225 | break; |
---|
5226 | } |
---|
5227 | } |
---|
5228 | } |
---|
5229 | if (NTLN.NumCols() == 1) |
---|
5230 | { |
---|
5231 | irreducible= true; |
---|
5232 | break; |
---|
5233 | } |
---|
5234 | |
---|
5235 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
5236 | bufF= F; |
---|
5237 | result= extReconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN, info, |
---|
5238 | evaluation |
---|
5239 | ); |
---|
5240 | delete [] zeroOneVecs; |
---|
5241 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
5242 | { |
---|
5243 | F= bufF; |
---|
5244 | factors= bufFactors; |
---|
5245 | delete [] A; |
---|
5246 | return result; |
---|
5247 | } |
---|
5248 | |
---|
5249 | if (isReduced (NTLN)) |
---|
5250 | { |
---|
5251 | int factorsFound= 0; |
---|
5252 | bufF= F; |
---|
5253 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
5254 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
5255 | factorsFoundIndex[i]= 0; |
---|
5256 | if (l < degree (bufF) + 1 + degree (LCF)) |
---|
5257 | extReconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
5258 | factorsFoundIndex, NTLN, false, info, evaluation |
---|
5259 | ); |
---|
5260 | else |
---|
5261 | extReconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
5262 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
5263 | NTLN, false, info, evaluation |
---|
5264 | ); |
---|
5265 | if (NTLN.NumCols() == result.length()) |
---|
5266 | { |
---|
5267 | delete [] A; |
---|
5268 | delete [] factorsFoundIndex; |
---|
5269 | return result; |
---|
5270 | } |
---|
5271 | delete [] factorsFoundIndex; |
---|
5272 | } |
---|
5273 | result= CFList(); |
---|
5274 | oldL= l; |
---|
5275 | stepSize *= 2; |
---|
5276 | l += stepSize; |
---|
5277 | if (l > liftBound) |
---|
5278 | { |
---|
5279 | if (!hitBound) |
---|
5280 | { |
---|
5281 | l= liftBound; |
---|
5282 | hitBound= true; |
---|
5283 | } |
---|
5284 | else |
---|
5285 | break; |
---|
5286 | } |
---|
5287 | } |
---|
5288 | if (irreducible) |
---|
5289 | { |
---|
5290 | delete [] A; |
---|
5291 | Variable y= Variable (2); |
---|
5292 | CanonicalForm tmp= F (y - evaluation, y); |
---|
5293 | CFList source, dest; |
---|
5294 | tmp= mapDown (tmp, info, source, dest); |
---|
5295 | return CFList (tmp); |
---|
5296 | } |
---|
5297 | delete [] A; |
---|
5298 | factors= bufFactors; |
---|
5299 | return CFList(); |
---|
5300 | } |
---|
5301 | |
---|
5302 | #ifdef HAVE_FLINT |
---|
5303 | CFList |
---|
5304 | furtherLiftingAndIncreasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int |
---|
5305 | l, int liftBound, int d, int* bounds, |
---|
5306 | nmod_mat_t FLINTN, CFList& diophant, |
---|
5307 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
5308 | const Variable& alpha |
---|
5309 | ) |
---|
5310 | #else |
---|
5311 | CFList |
---|
5312 | furtherLiftingAndIncreasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int |
---|
5313 | l, int liftBound, int d, int* bounds, |
---|
5314 | mat_zz_p& NTLN, CFList& diophant, |
---|
5315 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
5316 | const Variable& alpha |
---|
5317 | ) |
---|
5318 | #endif |
---|
5319 | { |
---|
5320 | CanonicalForm LCF= LC (F, 1); |
---|
5321 | CFList result; |
---|
5322 | bool irreducible= false; |
---|
5323 | CFList bufFactors= factors; |
---|
5324 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
5325 | bool useOldQs= false; |
---|
5326 | int extensionDeg= degree (getMipo (alpha)); |
---|
5327 | bool hitBound= false; |
---|
5328 | int oldL= l; |
---|
5329 | int stepSize= 8; //TODO choose better step size? |
---|
5330 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
5331 | #ifdef HAVE_FLINT |
---|
5332 | if (nmod_mat_nrows (FLINTN) != factors.length()) //refined factors |
---|
5333 | { |
---|
5334 | nmod_mat_clear (FLINTN); |
---|
5335 | nmod_mat_init(FLINTN,factors.length(),factors.length(),getCharacteristic()); |
---|
5336 | for (long i=factors.length()-1; i >= 0; i--) |
---|
5337 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
5338 | } |
---|
5339 | #else |
---|
5340 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
5341 | ident (NTLN, factors.length()); |
---|
5342 | #endif |
---|
5343 | CFListIterator j; |
---|
5344 | CFMatrix C; |
---|
5345 | #ifdef HAVE_FLINT |
---|
5346 | long rank; |
---|
5347 | nmod_mat_t FLINTC, FLINTK, null; |
---|
5348 | #else |
---|
5349 | mat_zz_p* NTLC, NTLK; |
---|
5350 | #endif |
---|
5351 | CanonicalForm bufF, truncF; |
---|
5352 | Variable y= F.mvar(); |
---|
5353 | while (l <= liftBound) |
---|
5354 | { |
---|
5355 | bufFactors.insert (LCF); |
---|
5356 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
5357 | j= bufFactors; |
---|
5358 | truncF= mod (F, power (y, l)); |
---|
5359 | if (useOldQs) |
---|
5360 | { |
---|
5361 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
5362 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
5363 | bufQ[i]); |
---|
5364 | } |
---|
5365 | else |
---|
5366 | { |
---|
5367 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
5368 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
5369 | } |
---|
5370 | for (int i= 0; i < d; i++) |
---|
5371 | { |
---|
5372 | if (bounds [i] + 1 <= l/2) |
---|
5373 | { |
---|
5374 | int k= tmin (bounds [i] + 1, l/2); |
---|
5375 | C= CFMatrix ((l - k)*extensionDeg, bufFactors.length()); |
---|
5376 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
5377 | { |
---|
5378 | CFArray buf; |
---|
5379 | if (A[ii].size() - 1 >= i) |
---|
5380 | { |
---|
5381 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
5382 | writeInMatrix (C, buf, ii + 1, 0); |
---|
5383 | } |
---|
5384 | } |
---|
5385 | #ifdef HAVE_FLINT |
---|
5386 | convertFacCFMatrix2nmod_mat_t (FLINTC, C); |
---|
5387 | nmod_mat_init (FLINTK, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTN), |
---|
5388 | getCharacteristic()); |
---|
5389 | nmod_mat_mul (FLINTK, FLINTC, FLINTN); |
---|
5390 | nmod_mat_init (null, nmod_mat_ncols (FLINTK), nmod_mat_ncols (FLINTK), |
---|
5391 | getCharacteristic()); |
---|
5392 | rank= nmod_mat_nullspace (null, FLINTK); |
---|
5393 | nmod_mat_clear (FLINTK); |
---|
5394 | nmod_mat_window_init (FLINTK, null, 0, 0, nmod_mat_nrows(null), rank); |
---|
5395 | nmod_mat_clear (FLINTC); |
---|
5396 | nmod_mat_init_set (FLINTC, FLINTN); |
---|
5397 | nmod_mat_clear (FLINTN); |
---|
5398 | nmod_mat_init (FLINTN, nmod_mat_nrows (FLINTC), nmod_mat_ncols (FLINTK), |
---|
5399 | getCharacteristic()); |
---|
5400 | nmod_mat_mul (FLINTN, FLINTC, FLINTK); //no aliasing allowed!! |
---|
5401 | |
---|
5402 | nmod_mat_clear (FLINTC); |
---|
5403 | nmod_mat_window_clear (FLINTK); |
---|
5404 | nmod_mat_clear (null); |
---|
5405 | #else |
---|
5406 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
5407 | NTLK= (*NTLC)*NTLN; |
---|
5408 | transpose (NTLK, NTLK); |
---|
5409 | kernel (NTLK, NTLK); |
---|
5410 | transpose (NTLK, NTLK); |
---|
5411 | NTLN *= NTLK; |
---|
5412 | #endif |
---|
5413 | #ifdef HAVE_FLINT |
---|
5414 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
5415 | #else |
---|
5416 | if (NTLN.NumCols() == 1) |
---|
5417 | #endif |
---|
5418 | { |
---|
5419 | irreducible= true; |
---|
5420 | break; |
---|
5421 | } |
---|
5422 | } |
---|
5423 | } |
---|
5424 | #ifdef HAVE_FLINT |
---|
5425 | if (nmod_mat_ncols (FLINTN) == 1) |
---|
5426 | #else |
---|
5427 | if (NTLN.NumCols() == 1) |
---|
5428 | #endif |
---|
5429 | { |
---|
5430 | irreducible= true; |
---|
5431 | break; |
---|
5432 | } |
---|
5433 | |
---|
5434 | #ifdef HAVE_FLINT |
---|
5435 | int * zeroOneVecs= extractZeroOneVecs (FLINTN); |
---|
5436 | #else |
---|
5437 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
5438 | #endif |
---|
5439 | CanonicalForm bufF= F; |
---|
5440 | #ifdef HAVE_FLINT |
---|
5441 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, FLINTN); |
---|
5442 | #else |
---|
5443 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN); |
---|
5444 | #endif |
---|
5445 | delete [] zeroOneVecs; |
---|
5446 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
5447 | { |
---|
5448 | F= bufF; |
---|
5449 | factors= bufFactors; |
---|
5450 | delete [] A; |
---|
5451 | return result; |
---|
5452 | } |
---|
5453 | |
---|
5454 | #ifdef HAVE_FLINT |
---|
5455 | if (isReduced (FLINTN)) |
---|
5456 | #else |
---|
5457 | if (isReduced (NTLN)) |
---|
5458 | #endif |
---|
5459 | { |
---|
5460 | int factorsFound= 0; |
---|
5461 | bufF= F; |
---|
5462 | #ifdef HAVE_FLINT |
---|
5463 | int* factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
5464 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
5465 | #else |
---|
5466 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
5467 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
5468 | #endif |
---|
5469 | factorsFoundIndex[i]= 0; |
---|
5470 | #ifdef HAVE_FLINT |
---|
5471 | if (l < degree (bufF) + 1 + degree (LCF)) |
---|
5472 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
5473 | factorsFoundIndex, FLINTN, false |
---|
5474 | ); |
---|
5475 | else |
---|
5476 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
5477 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
5478 | FLINTN, false |
---|
5479 | ); |
---|
5480 | if (nmod_mat_ncols (FLINTN) == result.length()) |
---|
5481 | #else |
---|
5482 | if (l < degree (bufF) + 1 + degree (LCF)) |
---|
5483 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
5484 | factorsFoundIndex, NTLN, false |
---|
5485 | ); |
---|
5486 | else |
---|
5487 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
5488 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
5489 | NTLN, false |
---|
5490 | ); |
---|
5491 | if (NTLN.NumCols() == result.length()) |
---|
5492 | #endif |
---|
5493 | { |
---|
5494 | delete [] A; |
---|
5495 | delete [] factorsFoundIndex; |
---|
5496 | return result; |
---|
5497 | } |
---|
5498 | delete [] factorsFoundIndex; |
---|
5499 | } |
---|
5500 | result= CFList(); |
---|
5501 | oldL= l; |
---|
5502 | stepSize *= 2; |
---|
5503 | l += stepSize; |
---|
5504 | if (l > liftBound) |
---|
5505 | { |
---|
5506 | if (!hitBound) |
---|
5507 | { |
---|
5508 | l= liftBound; |
---|
5509 | hitBound= true; |
---|
5510 | } |
---|
5511 | else |
---|
5512 | break; |
---|
5513 | } |
---|
5514 | } |
---|
5515 | if (irreducible) |
---|
5516 | { |
---|
5517 | delete [] A; |
---|
5518 | return CFList (F); |
---|
5519 | } |
---|
5520 | delete [] A; |
---|
5521 | factors= bufFactors; |
---|
5522 | return CFList(); |
---|
5523 | } |
---|
5524 | |
---|
5525 | void |
---|
5526 | refineAndRestartLift (const CanonicalForm& F, const mat_zz_p& NTLN, int |
---|
5527 | liftBound, int l, CFList& factors, CFMatrix& M, CFArray& |
---|
5528 | Pi, CFList& diophant |
---|
5529 | ) |
---|
5530 | { |
---|
5531 | CFList bufFactors; |
---|
5532 | Variable y= Variable (2); |
---|
5533 | CanonicalForm LCF= LC (F, 1); |
---|
5534 | CFListIterator iter; |
---|
5535 | CanonicalForm buf; |
---|
5536 | for (long i= 1; i <= NTLN.NumCols(); i++) |
---|
5537 | { |
---|
5538 | iter= factors; |
---|
5539 | buf= 1; |
---|
5540 | for (long j= 1; j <= NTLN.NumRows(); j++, iter++) |
---|
5541 | { |
---|
5542 | if (!IsZero (NTLN (j,i))) |
---|
5543 | buf= mulNTL (buf, mod (iter.getItem(), y)); |
---|
5544 | } |
---|
5545 | bufFactors.append (buf); |
---|
5546 | } |
---|
5547 | factors= bufFactors; |
---|
5548 | M= CFMatrix (liftBound, factors.length()); |
---|
5549 | Pi= CFArray(); |
---|
5550 | diophant= CFList(); |
---|
5551 | factors.insert (LCF); |
---|
5552 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
5553 | } |
---|
5554 | |
---|
5555 | #ifdef HAVE_FLINT |
---|
5556 | void |
---|
5557 | refineAndRestartLift (const CanonicalForm& F, const nmod_mat_t FLINTN, int |
---|
5558 | liftBound, int l, CFList& factors, CFMatrix& M, CFArray& |
---|
5559 | Pi, CFList& diophant |
---|
5560 | ) |
---|
5561 | { |
---|
5562 | CFList bufFactors; |
---|
5563 | Variable y= Variable (2); |
---|
5564 | CanonicalForm LCF= LC (F, 1); |
---|
5565 | CFListIterator iter; |
---|
5566 | CanonicalForm buf; |
---|
5567 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
5568 | { |
---|
5569 | iter= factors; |
---|
5570 | buf= 1; |
---|
5571 | for (long j= 0; j < nmod_mat_nrows (FLINTN); j++, iter++) |
---|
5572 | { |
---|
5573 | if (!(nmod_mat_entry (FLINTN,j,i) == 0)) |
---|
5574 | buf= mulNTL (buf, mod (iter.getItem(), y)); |
---|
5575 | } |
---|
5576 | bufFactors.append (buf); |
---|
5577 | } |
---|
5578 | factors= bufFactors; |
---|
5579 | M= CFMatrix (liftBound, factors.length()); |
---|
5580 | Pi= CFArray(); |
---|
5581 | diophant= CFList(); |
---|
5582 | factors.insert (LCF); |
---|
5583 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
5584 | } |
---|
5585 | #endif |
---|
5586 | |
---|
5587 | void |
---|
5588 | refineAndRestartLift (const CanonicalForm& F, const mat_zz_pE& NTLN, int |
---|
5589 | liftBound, int l, CFList& factors, CFMatrix& M, CFArray& |
---|
5590 | Pi, CFList& diophant |
---|
5591 | ) |
---|
5592 | { |
---|
5593 | CFList bufFactors; |
---|
5594 | Variable y= Variable (2); |
---|
5595 | CanonicalForm LCF= LC (F, 1); |
---|
5596 | CFListIterator iter; |
---|
5597 | CanonicalForm buf; |
---|
5598 | for (long i= 1; i <= NTLN.NumCols(); i++) |
---|
5599 | { |
---|
5600 | iter= factors; |
---|
5601 | buf= 1; |
---|
5602 | for (long j= 1; j <= NTLN.NumRows(); j++, iter++) |
---|
5603 | { |
---|
5604 | if (!IsZero (NTLN (j,i))) |
---|
5605 | buf= mulNTL (buf, mod (iter.getItem(), y)); |
---|
5606 | } |
---|
5607 | bufFactors.append (buf); |
---|
5608 | } |
---|
5609 | factors= bufFactors; |
---|
5610 | M= CFMatrix (liftBound, factors.length()); |
---|
5611 | Pi= CFArray(); |
---|
5612 | diophant= CFList(); |
---|
5613 | factors.insert (LCF); |
---|
5614 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
5615 | } |
---|
5616 | |
---|
5617 | #ifdef HAVE_FLINT |
---|
5618 | CFList |
---|
5619 | earlyReconstructionAndLifting (const CanonicalForm& F, const nmod_mat_t N, |
---|
5620 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
5621 | int& factorsFound, bool beenInThres, CFMatrix& M, |
---|
5622 | CFArray& Pi, CFList& diophant, bool symmetric, |
---|
5623 | const CanonicalForm& evaluation |
---|
5624 | ) |
---|
5625 | #else |
---|
5626 | CFList |
---|
5627 | earlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_p& N, |
---|
5628 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
5629 | int& factorsFound, bool beenInThres, CFMatrix& M, |
---|
5630 | CFArray& Pi, CFList& diophant, bool symmetric, |
---|
5631 | const CanonicalForm& evaluation |
---|
5632 | ) |
---|
5633 | #endif |
---|
5634 | { |
---|
5635 | int sizeOfLiftPre; |
---|
5636 | int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2)); |
---|
5637 | |
---|
5638 | Variable y= F.mvar(); |
---|
5639 | factorsFound= 0; |
---|
5640 | CanonicalForm LCF= LC (F, 1); |
---|
5641 | CFList result; |
---|
5642 | int smallFactorDeg= tmin (11, liftPre [sizeOfLiftPre- 1] + 1); |
---|
5643 | #ifdef HAVE_FLINT |
---|
5644 | nmod_mat_t FLINTN; |
---|
5645 | nmod_mat_init_set (FLINTN, N); |
---|
5646 | int * factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
5647 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
5648 | #else |
---|
5649 | mat_zz_p NTLN= N; |
---|
5650 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
5651 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
5652 | #endif |
---|
5653 | factorsFoundIndex [i]= 0; |
---|
5654 | |
---|
5655 | if (degree (F) + 1 > smallFactorDeg) |
---|
5656 | { |
---|
5657 | if (l < smallFactorDeg) |
---|
5658 | { |
---|
5659 | factors.insert (LCF); |
---|
5660 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
5661 | l= smallFactorDeg; |
---|
5662 | } |
---|
5663 | #ifdef HAVE_FLINT |
---|
5664 | reconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
5665 | factorsFoundIndex, FLINTN, beenInThres |
---|
5666 | ); |
---|
5667 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
5668 | { |
---|
5669 | nmod_mat_clear (FLINTN); |
---|
5670 | #else |
---|
5671 | reconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
5672 | factorsFoundIndex, NTLN, beenInThres |
---|
5673 | ); |
---|
5674 | if (result.length() == NTLN.NumCols()) |
---|
5675 | { |
---|
5676 | #endif |
---|
5677 | delete [] liftPre; |
---|
5678 | delete [] factorsFoundIndex; |
---|
5679 | return result; |
---|
5680 | } |
---|
5681 | } |
---|
5682 | |
---|
5683 | int i= sizeOfLiftPre - 1; |
---|
5684 | int dummy= 1; |
---|
5685 | if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
5686 | { |
---|
5687 | while (i > 0) |
---|
5688 | { |
---|
5689 | if (l < liftPre[i-1] + 1) |
---|
5690 | { |
---|
5691 | factors.insert (LCF); |
---|
5692 | henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M); |
---|
5693 | l= liftPre[i-1] + 1; |
---|
5694 | } |
---|
5695 | else |
---|
5696 | { |
---|
5697 | i--; |
---|
5698 | if (i != 0) |
---|
5699 | continue; |
---|
5700 | } |
---|
5701 | #ifdef HAVE_FLINT |
---|
5702 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
5703 | factorsFoundIndex, FLINTN, beenInThres |
---|
5704 | ); |
---|
5705 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
5706 | { |
---|
5707 | nmod_mat_clear (FLINTN); |
---|
5708 | #else |
---|
5709 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
5710 | factorsFoundIndex, NTLN, beenInThres |
---|
5711 | ); |
---|
5712 | if (result.length() == NTLN.NumCols()) |
---|
5713 | { |
---|
5714 | #endif |
---|
5715 | delete [] liftPre; |
---|
5716 | delete [] factorsFoundIndex; |
---|
5717 | return result; |
---|
5718 | } |
---|
5719 | i--; |
---|
5720 | } |
---|
5721 | } |
---|
5722 | else |
---|
5723 | { |
---|
5724 | i= 1; |
---|
5725 | while (((degree (F,y)/4)*i+1) + 4 <= smallFactorDeg) |
---|
5726 | i++; |
---|
5727 | while (i < 5) |
---|
5728 | { |
---|
5729 | dummy= tmin (degree (F,y)+1, ((degree (F,y)/4)+1)*i+4); |
---|
5730 | if (l < dummy) |
---|
5731 | { |
---|
5732 | factors.insert (LCF); |
---|
5733 | henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M); |
---|
5734 | l= dummy; |
---|
5735 | if (i == 1 && degree (F)%4==0 && symmetric && factors.length() == 2 && |
---|
5736 | LC (F,1).inCoeffDomain() && |
---|
5737 | (degree (factors.getFirst(), 1) == degree (factors.getLast(),1))) |
---|
5738 | { |
---|
5739 | Variable x= Variable (1); |
---|
5740 | CanonicalForm g, h, gg, hh, multiplier1, multiplier2, check1, check2; |
---|
5741 | int m= degree (F)/4+1; |
---|
5742 | g= factors.getFirst(); |
---|
5743 | h= factors.getLast(); |
---|
5744 | g= mod (g, power (y,m)); |
---|
5745 | h= mod (h, power (y,m)); |
---|
5746 | g= g (y-evaluation, y); |
---|
5747 | h= h (y-evaluation, y); |
---|
5748 | gg= mod (swapvar (g,x,y),power (x,m)); |
---|
5749 | gg= gg (y + evaluation, y); |
---|
5750 | multiplier1= factors.getLast()[m-1][0]/gg[m-1][0]; |
---|
5751 | gg= div (gg, power (y,m)); |
---|
5752 | gg= gg*power (y,m); |
---|
5753 | hh= mod (swapvar (h,x,y),power (x,m)); |
---|
5754 | hh= hh (y + evaluation, y); |
---|
5755 | multiplier2= factors.getFirst()[m-1][0]/hh[m-1][0]; |
---|
5756 | hh= div (hh, power (y,m)); |
---|
5757 | hh= hh*power (y,m); |
---|
5758 | gg= multiplier1*gg+mod (factors.getLast(), power (y,m)); |
---|
5759 | hh= multiplier2*hh+mod (factors.getFirst(), power (y,m)); |
---|
5760 | check1= gg (y-evaluation,y); |
---|
5761 | check2= hh (y-evaluation,y); |
---|
5762 | check1= swapvar (check1, x, y); |
---|
5763 | if (check1/Lc (check1) == check2/Lc (check2)) |
---|
5764 | { |
---|
5765 | #ifdef HAVE_FLINT |
---|
5766 | nmod_mat_clear (FLINTN); |
---|
5767 | #endif |
---|
5768 | result.append (gg); |
---|
5769 | result.append (hh); |
---|
5770 | delete [] liftPre; |
---|
5771 | delete [] factorsFoundIndex; |
---|
5772 | return result; |
---|
5773 | } |
---|
5774 | } |
---|
5775 | } |
---|
5776 | else |
---|
5777 | { |
---|
5778 | i++; |
---|
5779 | if (i < 5) |
---|
5780 | continue; |
---|
5781 | } |
---|
5782 | #ifdef HAVE_FLINT |
---|
5783 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
5784 | factorsFoundIndex, FLINTN, beenInThres |
---|
5785 | ); |
---|
5786 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
5787 | { |
---|
5788 | nmod_mat_clear (FLINTN); |
---|
5789 | #else |
---|
5790 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
5791 | factorsFoundIndex, NTLN, beenInThres |
---|
5792 | ); |
---|
5793 | if (result.length() == NTLN.NumCols()) |
---|
5794 | { |
---|
5795 | #endif |
---|
5796 | delete [] liftPre; |
---|
5797 | delete [] factorsFoundIndex; |
---|
5798 | return result; |
---|
5799 | } |
---|
5800 | i++; |
---|
5801 | } |
---|
5802 | } |
---|
5803 | |
---|
5804 | #ifdef HAVE_FLINT |
---|
5805 | nmod_mat_clear (FLINTN); |
---|
5806 | #endif |
---|
5807 | delete [] liftPre; |
---|
5808 | delete [] factorsFoundIndex; |
---|
5809 | return result; |
---|
5810 | } |
---|
5811 | |
---|
5812 | CFList |
---|
5813 | earlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_pE& N, |
---|
5814 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
5815 | int& factorsFound, bool beenInThres, CFMatrix& M, |
---|
5816 | CFArray& Pi, CFList& diophant, bool symmetric, |
---|
5817 | const CanonicalForm& evaluation |
---|
5818 | ) |
---|
5819 | { |
---|
5820 | int sizeOfLiftPre; |
---|
5821 | int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2)); |
---|
5822 | Variable y= F.mvar(); |
---|
5823 | factorsFound= 0; |
---|
5824 | CanonicalForm LCF= LC (F, 1); |
---|
5825 | CFList result; |
---|
5826 | int smallFactorDeg= 11; |
---|
5827 | mat_zz_pE NTLN= N; |
---|
5828 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
5829 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
5830 | factorsFoundIndex [i]= 0; |
---|
5831 | |
---|
5832 | if (degree (F) + 1 > smallFactorDeg) |
---|
5833 | { |
---|
5834 | if (l < smallFactorDeg) |
---|
5835 | { |
---|
5836 | factors.insert (LCF); |
---|
5837 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
5838 | l= smallFactorDeg; |
---|
5839 | } |
---|
5840 | reconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
5841 | factorsFoundIndex, NTLN, beenInThres |
---|
5842 | ); |
---|
5843 | if (result.length() == NTLN.NumCols()) |
---|
5844 | { |
---|
5845 | delete [] liftPre; |
---|
5846 | delete [] factorsFoundIndex; |
---|
5847 | return result; |
---|
5848 | } |
---|
5849 | } |
---|
5850 | |
---|
5851 | int i= sizeOfLiftPre - 1; |
---|
5852 | int dummy= 1; |
---|
5853 | if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
5854 | { |
---|
5855 | while (i > 0) |
---|
5856 | { |
---|
5857 | if (l < liftPre[i-1] + 1) |
---|
5858 | { |
---|
5859 | factors.insert (LCF); |
---|
5860 | henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M); |
---|
5861 | l= liftPre[i-1] + 1; |
---|
5862 | } |
---|
5863 | else |
---|
5864 | { |
---|
5865 | i--; |
---|
5866 | if (i != 0) |
---|
5867 | continue; |
---|
5868 | } |
---|
5869 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
5870 | factorsFoundIndex, NTLN, beenInThres |
---|
5871 | ); |
---|
5872 | if (result.length() == NTLN.NumCols()) |
---|
5873 | { |
---|
5874 | delete [] liftPre; |
---|
5875 | delete [] factorsFoundIndex; |
---|
5876 | return result; |
---|
5877 | } |
---|
5878 | i--; |
---|
5879 | } |
---|
5880 | } |
---|
5881 | else |
---|
5882 | { |
---|
5883 | i= 1; |
---|
5884 | while ((degree (F,y)/4+1)*i + 4 <= smallFactorDeg) |
---|
5885 | i++; |
---|
5886 | while (i < 5) |
---|
5887 | { |
---|
5888 | dummy= tmin (degree (F,y)+1, (degree (F,y)/4+1)*i+4); |
---|
5889 | if (l < dummy) |
---|
5890 | { |
---|
5891 | factors.insert (LCF); |
---|
5892 | henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M); |
---|
5893 | l= dummy; |
---|
5894 | if (i == 1 && degree (F)%4==0 && symmetric && factors.length() == 2 && |
---|
5895 | LC (F,1).inCoeffDomain() && |
---|
5896 | (degree (factors.getFirst(), 1) == degree (factors.getLast(),1))) |
---|
5897 | { |
---|
5898 | Variable x= Variable (1); |
---|
5899 | CanonicalForm g, h, gg, hh, multiplier1, multiplier2, check1, check2; |
---|
5900 | int m= degree (F)/4+1; |
---|
5901 | g= factors.getFirst(); |
---|
5902 | h= factors.getLast(); |
---|
5903 | g= mod (g, power (y,m)); |
---|
5904 | h= mod (h, power (y,m)); |
---|
5905 | g= g (y-evaluation, y); |
---|
5906 | h= h (y-evaluation, y); |
---|
5907 | gg= mod (swapvar (g,x,y),power (x,m)); |
---|
5908 | gg= gg (y + evaluation, y); |
---|
5909 | multiplier1= factors.getLast()[m-1][0]/gg[m-1][0]; |
---|
5910 | gg= div (gg, power (y,m)); |
---|
5911 | gg= gg*power (y,m); |
---|
5912 | hh= mod (swapvar (h,x,y),power (x,m)); |
---|
5913 | hh= hh (y + evaluation, y); |
---|
5914 | multiplier2= factors.getFirst()[m-1][0]/hh[m-1][0]; |
---|
5915 | hh= div (hh, power (y,m)); |
---|
5916 | hh= hh*power (y,m); |
---|
5917 | gg= multiplier1*gg+mod (factors.getLast(), power (y,m)); |
---|
5918 | hh= multiplier2*hh+mod (factors.getFirst(), power (y,m)); |
---|
5919 | check1= gg (y-evaluation,y); |
---|
5920 | check2= hh (y-evaluation,y); |
---|
5921 | check1= swapvar (check1, x, y); |
---|
5922 | if (check1/Lc (check1) == check2/Lc (check2)) |
---|
5923 | { |
---|
5924 | result.append (gg); |
---|
5925 | result.append (hh); |
---|
5926 | delete [] liftPre; |
---|
5927 | delete [] factorsFoundIndex; |
---|
5928 | return result; |
---|
5929 | } |
---|
5930 | } |
---|
5931 | } |
---|
5932 | else |
---|
5933 | { |
---|
5934 | i++; |
---|
5935 | if (i < 5) |
---|
5936 | continue; |
---|
5937 | } |
---|
5938 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
5939 | factorsFoundIndex, NTLN, beenInThres |
---|
5940 | ); |
---|
5941 | if (result.length() == NTLN.NumCols()) |
---|
5942 | { |
---|
5943 | delete [] liftPre; |
---|
5944 | delete [] factorsFoundIndex; |
---|
5945 | return result; |
---|
5946 | } |
---|
5947 | i++; |
---|
5948 | } |
---|
5949 | } |
---|
5950 | |
---|
5951 | delete [] liftPre; |
---|
5952 | delete [] factorsFoundIndex; |
---|
5953 | return result; |
---|
5954 | } |
---|
5955 | |
---|
5956 | //over field extension |
---|
5957 | CFList |
---|
5958 | extEarlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_p& N, |
---|
5959 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
5960 | int& factorsFound, bool beenInThres, CFMatrix& |
---|
5961 | M, CFArray& Pi, CFList& diophant, const |
---|
5962 | ExtensionInfo& info, const CanonicalForm& |
---|
5963 | evaluation |
---|
5964 | ) |
---|
5965 | { |
---|
5966 | int sizeOfLiftPre; |
---|
5967 | int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2)); |
---|
5968 | Variable y= F.mvar(); |
---|
5969 | factorsFound= 0; |
---|
5970 | CanonicalForm LCF= LC (F, 1); |
---|
5971 | CFList result; |
---|
5972 | int smallFactorDeg= 11; |
---|
5973 | mat_zz_p NTLN= N; |
---|
5974 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
5975 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
5976 | factorsFoundIndex [i]= 0; |
---|
5977 | |
---|
5978 | if (degree (F) + 1 > smallFactorDeg) |
---|
5979 | { |
---|
5980 | if (l < smallFactorDeg) |
---|
5981 | { |
---|
5982 | factors.insert (LCF); |
---|
5983 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
5984 | l= smallFactorDeg; |
---|
5985 | } |
---|
5986 | extReconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
5987 | factorsFoundIndex, NTLN, beenInThres, info, |
---|
5988 | evaluation |
---|
5989 | ); |
---|
5990 | if (result.length() == NTLN.NumCols()) |
---|
5991 | { |
---|
5992 | delete [] liftPre; |
---|
5993 | delete [] factorsFoundIndex; |
---|
5994 | return result; |
---|
5995 | } |
---|
5996 | } |
---|
5997 | |
---|
5998 | int i= sizeOfLiftPre - 1; |
---|
5999 | int dummy= 1; |
---|
6000 | if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
6001 | { |
---|
6002 | while (i > 0) |
---|
6003 | { |
---|
6004 | if (l < liftPre[i-1] + 1) |
---|
6005 | { |
---|
6006 | factors.insert (LCF); |
---|
6007 | henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M); |
---|
6008 | l= liftPre[i-1] + 1; |
---|
6009 | } |
---|
6010 | else |
---|
6011 | { |
---|
6012 | i--; |
---|
6013 | if (i != 0) |
---|
6014 | continue; |
---|
6015 | } |
---|
6016 | extReconstructionTry (result, bufF, factors, l, factorsFound, |
---|
6017 | factorsFoundIndex, NTLN, beenInThres, info, |
---|
6018 | evaluation |
---|
6019 | ); |
---|
6020 | if (result.length() == NTLN.NumCols()) |
---|
6021 | { |
---|
6022 | delete [] liftPre; |
---|
6023 | delete [] factorsFoundIndex; |
---|
6024 | return result; |
---|
6025 | } |
---|
6026 | i--; |
---|
6027 | } |
---|
6028 | } |
---|
6029 | else |
---|
6030 | { |
---|
6031 | i= 1; |
---|
6032 | while ((degree (F,y)/4+1)*i + 4 <= smallFactorDeg) |
---|
6033 | i++; |
---|
6034 | while (i < 5) |
---|
6035 | { |
---|
6036 | dummy= tmin (degree (F,y)+1, (degree (F,y)/4+1)*i+4); |
---|
6037 | if (l < dummy) |
---|
6038 | { |
---|
6039 | factors.insert (LCF); |
---|
6040 | henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M); |
---|
6041 | l= dummy; |
---|
6042 | } |
---|
6043 | else |
---|
6044 | { |
---|
6045 | i++; |
---|
6046 | if (i < 5) |
---|
6047 | continue; |
---|
6048 | } |
---|
6049 | extReconstructionTry (result, bufF, factors, l, factorsFound, |
---|
6050 | factorsFoundIndex, NTLN, beenInThres, info, |
---|
6051 | evaluation |
---|
6052 | ); |
---|
6053 | if (result.length() == NTLN.NumCols()) |
---|
6054 | { |
---|
6055 | delete [] liftPre; |
---|
6056 | delete [] factorsFoundIndex; |
---|
6057 | return result; |
---|
6058 | } |
---|
6059 | i++; |
---|
6060 | } |
---|
6061 | } |
---|
6062 | |
---|
6063 | delete [] liftPre; |
---|
6064 | delete [] factorsFoundIndex; |
---|
6065 | return result; |
---|
6066 | } |
---|
6067 | |
---|
6068 | CFList |
---|
6069 | sieveSmallFactors (const CanonicalForm& G, CFList& uniFactors, DegreePattern& |
---|
6070 | degPat, CanonicalForm& H, CFList& diophant, CFArray& Pi, |
---|
6071 | CFMatrix& M, bool& success, int d |
---|
6072 | ) |
---|
6073 | { |
---|
6074 | CanonicalForm F= G; |
---|
6075 | CFList bufUniFactors= uniFactors; |
---|
6076 | bufUniFactors.insert (LC (F, 1)); |
---|
6077 | int smallFactorDeg= d; |
---|
6078 | DegreePattern degs= degPat; |
---|
6079 | henselLift12 (F, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
---|
6080 | int adaptedLiftBound; |
---|
6081 | success= false; |
---|
6082 | int * factorsFoundIndex= new int [uniFactors.length()]; |
---|
6083 | for (int i= 0; i < uniFactors.length(); i++) |
---|
6084 | factorsFoundIndex [i]= 0; |
---|
6085 | CFList earlyFactors; |
---|
6086 | earlyFactorDetection (earlyFactors, F, bufUniFactors, adaptedLiftBound, |
---|
6087 | factorsFoundIndex, degs, success, smallFactorDeg); |
---|
6088 | delete [] factorsFoundIndex; |
---|
6089 | if (degs.getLength() == 1) |
---|
6090 | { |
---|
6091 | degPat= degs; |
---|
6092 | return earlyFactors; |
---|
6093 | } |
---|
6094 | if (success) |
---|
6095 | { |
---|
6096 | H= F; |
---|
6097 | return earlyFactors; |
---|
6098 | } |
---|
6099 | int sizeOldF= size (G); |
---|
6100 | if (size (F) < sizeOldF) |
---|
6101 | { |
---|
6102 | H= F; |
---|
6103 | success= true; |
---|
6104 | return earlyFactors; |
---|
6105 | } |
---|
6106 | else |
---|
6107 | { |
---|
6108 | uniFactors= bufUniFactors; |
---|
6109 | return CFList(); |
---|
6110 | } |
---|
6111 | } |
---|
6112 | |
---|
6113 | CFList |
---|
6114 | extSieveSmallFactors (const CanonicalForm& G, CFList& uniFactors, DegreePattern& |
---|
6115 | degPat, CanonicalForm& H, CFList& diophant, CFArray& Pi, |
---|
6116 | CFMatrix& M, bool& success, int d, const CanonicalForm& |
---|
6117 | evaluation, const ExtensionInfo& info |
---|
6118 | ) |
---|
6119 | { |
---|
6120 | CanonicalForm F= G; |
---|
6121 | CFList bufUniFactors= uniFactors; |
---|
6122 | bufUniFactors.insert (LC (F, 1)); |
---|
6123 | int smallFactorDeg= d; |
---|
6124 | DegreePattern degs= degPat; |
---|
6125 | henselLift12 (F, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
---|
6126 | int adaptedLiftBound; |
---|
6127 | success= false; |
---|
6128 | int * factorsFoundIndex= new int [uniFactors.length()]; |
---|
6129 | for (int i= 0; i < uniFactors.length(); i++) |
---|
6130 | factorsFoundIndex [i]= 0; |
---|
6131 | CFList earlyFactors; |
---|
6132 | extEarlyFactorDetection (earlyFactors, F, bufUniFactors, adaptedLiftBound, |
---|
6133 | factorsFoundIndex, degs, success, info, evaluation, |
---|
6134 | smallFactorDeg); |
---|
6135 | delete [] factorsFoundIndex; |
---|
6136 | if (degs.getLength() == 1) |
---|
6137 | { |
---|
6138 | degPat= degs; |
---|
6139 | return earlyFactors; |
---|
6140 | } |
---|
6141 | if (success) |
---|
6142 | { |
---|
6143 | H= F; |
---|
6144 | return earlyFactors; |
---|
6145 | } |
---|
6146 | Variable y= F.mvar(); |
---|
6147 | int sizeOldF= size (G); |
---|
6148 | if (size (F) < sizeOldF) |
---|
6149 | { |
---|
6150 | H= F; |
---|
6151 | success= true; |
---|
6152 | return earlyFactors; |
---|
6153 | } |
---|
6154 | else |
---|
6155 | { |
---|
6156 | uniFactors= bufUniFactors; |
---|
6157 | return CFList(); |
---|
6158 | } |
---|
6159 | } |
---|
6160 | |
---|
6161 | CFList |
---|
6162 | henselLiftAndLatticeRecombi (const CanonicalForm& G, const CFList& uniFactors, |
---|
6163 | const Variable& alpha, const DegreePattern& degPat, |
---|
6164 | bool symmetric, const CanonicalForm& evaluation |
---|
6165 | ) |
---|
6166 | { |
---|
6167 | DegreePattern degs= degPat; |
---|
6168 | CanonicalForm F= G; |
---|
6169 | CanonicalForm LCF= LC (F, 1); |
---|
6170 | Variable y= F.mvar(); |
---|
6171 | Variable x= Variable (1); |
---|
6172 | int d; |
---|
6173 | bool isIrreducible= false; |
---|
6174 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
6175 | if (isIrreducible) |
---|
6176 | { |
---|
6177 | delete [] bounds; |
---|
6178 | return CFList (G); |
---|
6179 | } |
---|
6180 | int minBound= bounds[0]; |
---|
6181 | for (int i= 1; i < d; i++) |
---|
6182 | { |
---|
6183 | if (bounds[i] != 0) |
---|
6184 | minBound= tmin (minBound, bounds[i]); |
---|
6185 | } |
---|
6186 | |
---|
6187 | CFList bufUniFactors= uniFactors; |
---|
6188 | CFArray Pi; |
---|
6189 | CFList diophant; |
---|
6190 | int liftBound= 2*totaldegree (F) - 1; |
---|
6191 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
6192 | |
---|
6193 | CFList smallFactors; |
---|
6194 | CanonicalForm H; |
---|
6195 | bool success= false; |
---|
6196 | smallFactors= sieveSmallFactors (F, bufUniFactors, degs, H, diophant, Pi, M, |
---|
6197 | success, minBound + 1 |
---|
6198 | ); |
---|
6199 | |
---|
6200 | if (smallFactors.length() > 0) |
---|
6201 | { |
---|
6202 | if (smallFactors.length() == 1) |
---|
6203 | { |
---|
6204 | if (smallFactors.getFirst() == F) |
---|
6205 | { |
---|
6206 | delete [] bounds; |
---|
6207 | return CFList (G); |
---|
6208 | } |
---|
6209 | } |
---|
6210 | if (degs.getLength() <= 1) |
---|
6211 | { |
---|
6212 | delete [] bounds; |
---|
6213 | return smallFactors; |
---|
6214 | } |
---|
6215 | } |
---|
6216 | |
---|
6217 | int index; |
---|
6218 | CanonicalForm tmp1, tmp2; |
---|
6219 | for (CFListIterator i= smallFactors; i.hasItem(); i++) |
---|
6220 | { |
---|
6221 | index= 1; |
---|
6222 | tmp1= mod (i.getItem(),y); |
---|
6223 | tmp1 /= Lc (tmp1); |
---|
6224 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
6225 | { |
---|
6226 | tmp2= mod (j.getItem(), y); |
---|
6227 | tmp2 /= Lc (tmp2); |
---|
6228 | if (tmp1 == tmp2) |
---|
6229 | { |
---|
6230 | index++; |
---|
6231 | j.remove(index); |
---|
6232 | break; |
---|
6233 | } |
---|
6234 | } |
---|
6235 | } |
---|
6236 | |
---|
6237 | if (bufUniFactors.isEmpty()) |
---|
6238 | { |
---|
6239 | delete [] bounds; |
---|
6240 | return smallFactors; |
---|
6241 | } |
---|
6242 | |
---|
6243 | if (success) |
---|
6244 | { |
---|
6245 | F= H; |
---|
6246 | delete [] bounds; |
---|
6247 | bounds= computeBounds (F, d, isIrreducible); |
---|
6248 | if (isIrreducible) |
---|
6249 | { |
---|
6250 | smallFactors.append (F); |
---|
6251 | delete [] bounds; |
---|
6252 | return smallFactors; |
---|
6253 | } |
---|
6254 | LCF= LC (F, 1); |
---|
6255 | |
---|
6256 | minBound= bounds[0]; |
---|
6257 | for (int i= 1; i < d; i++) |
---|
6258 | { |
---|
6259 | if (bounds[i] != 0) |
---|
6260 | minBound= tmin (minBound, bounds[i]); |
---|
6261 | } |
---|
6262 | Pi= CFArray(); |
---|
6263 | diophant= CFList(); |
---|
6264 | liftBound= 2*totaldegree (F) - 1; |
---|
6265 | M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
6266 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
6267 | degs.intersect (bufDegs); |
---|
6268 | degs.refine(); |
---|
6269 | if (degs.getLength() <= 1) |
---|
6270 | { |
---|
6271 | smallFactors.append (F); |
---|
6272 | delete [] bounds; |
---|
6273 | return smallFactors; |
---|
6274 | } |
---|
6275 | } |
---|
6276 | |
---|
6277 | bool reduceFq2Fp= (degree (F) > getCharacteristic()); |
---|
6278 | bufUniFactors.insert (LCF); |
---|
6279 | int l= 1; |
---|
6280 | |
---|
6281 | #ifdef HAVE_FLINT |
---|
6282 | nmod_mat_t FLINTN; |
---|
6283 | #else |
---|
6284 | if (fac_NTL_char != getCharacteristic()) |
---|
6285 | { |
---|
6286 | fac_NTL_char= getCharacteristic(); |
---|
6287 | zz_p::init (getCharacteristic()); |
---|
6288 | } |
---|
6289 | mat_zz_p NTLN; |
---|
6290 | #endif |
---|
6291 | |
---|
6292 | if (alpha.level() != 1) |
---|
6293 | { |
---|
6294 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
6295 | zz_pE::init (NTLMipo); |
---|
6296 | } |
---|
6297 | mat_zz_pE NTLNe; |
---|
6298 | if (alpha.level() == 1) |
---|
6299 | { |
---|
6300 | #ifdef HAVE_FLINT |
---|
6301 | nmod_mat_init (FLINTN, bufUniFactors.length()-1, bufUniFactors.length()-1, getCharacteristic()); |
---|
6302 | for (long i= bufUniFactors.length()-2; i >= 0; i--) |
---|
6303 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
6304 | #else |
---|
6305 | ident (NTLN, bufUniFactors.length() - 1); |
---|
6306 | #endif |
---|
6307 | } |
---|
6308 | else |
---|
6309 | { |
---|
6310 | if (reduceFq2Fp) |
---|
6311 | #ifdef HAVE_FLINT |
---|
6312 | { |
---|
6313 | nmod_mat_init (FLINTN, bufUniFactors.length()-1, bufUniFactors.length()-1, getCharacteristic()); |
---|
6314 | for (long i= bufUniFactors.length()-2; i >= 0; i--) |
---|
6315 | nmod_mat_entry (FLINTN, i, i)= 1; |
---|
6316 | } |
---|
6317 | #else |
---|
6318 | ident (NTLN, bufUniFactors.length() - 1); |
---|
6319 | #endif |
---|
6320 | else |
---|
6321 | ident (NTLNe, bufUniFactors.length() - 1); |
---|
6322 | } |
---|
6323 | bool irreducible= false; |
---|
6324 | CFArray bufQ= CFArray (bufUniFactors.length() - 1); |
---|
6325 | |
---|
6326 | int oldL; |
---|
6327 | if (success) |
---|
6328 | { |
---|
6329 | int start= 0; |
---|
6330 | if (alpha.level() == 1) |
---|
6331 | oldL= liftAndComputeLattice (F, bounds, d, start, liftBound, minBound, |
---|
6332 | #ifdef HAVE_FLINT |
---|
6333 | bufUniFactors, FLINTN, diophant, M, Pi, bufQ, |
---|
6334 | #else |
---|
6335 | bufUniFactors, NTLN, diophant, M, Pi, bufQ, |
---|
6336 | #endif |
---|
6337 | irreducible |
---|
6338 | ); |
---|
6339 | else |
---|
6340 | { |
---|
6341 | if (reduceFq2Fp) |
---|
6342 | oldL= liftAndComputeLatticeFq2Fp (F, bounds, d, start, liftBound, |
---|
6343 | #ifdef HAVE_FLINT |
---|
6344 | minBound, bufUniFactors, FLINTN, |
---|
6345 | #else |
---|
6346 | minBound, bufUniFactors, NTLN, |
---|
6347 | #endif |
---|
6348 | diophant, M, Pi, bufQ, irreducible, |
---|
6349 | alpha |
---|
6350 | ); |
---|
6351 | else |
---|
6352 | oldL= liftAndComputeLattice (F, bounds, d, start, liftBound, minBound, |
---|
6353 | bufUniFactors, NTLNe, diophant, M, Pi, bufQ, |
---|
6354 | irreducible |
---|
6355 | ); |
---|
6356 | } |
---|
6357 | } |
---|
6358 | else |
---|
6359 | { |
---|
6360 | if (alpha.level() == 1) |
---|
6361 | { |
---|
6362 | oldL= liftAndComputeLattice (F, bounds, d, minBound + 1, liftBound, |
---|
6363 | #ifdef HAVE_FLINT |
---|
6364 | minBound, bufUniFactors, FLINTN, diophant, M, |
---|
6365 | #else |
---|
6366 | minBound, bufUniFactors, NTLN, diophant, M, |
---|
6367 | #endif |
---|
6368 | Pi, bufQ, irreducible |
---|
6369 | ); |
---|
6370 | } |
---|
6371 | else |
---|
6372 | { |
---|
6373 | if (reduceFq2Fp) |
---|
6374 | oldL= liftAndComputeLatticeFq2Fp (F, bounds, d, minBound + 1, |
---|
6375 | liftBound, minBound, bufUniFactors, |
---|
6376 | #ifdef HAVE_FLINT |
---|
6377 | FLINTN, diophant, M, Pi, bufQ, |
---|
6378 | #else |
---|
6379 | NTLN, diophant, M, Pi, bufQ, |
---|
6380 | #endif |
---|
6381 | irreducible, alpha |
---|
6382 | ); |
---|
6383 | else |
---|
6384 | oldL= liftAndComputeLattice (F, bounds, d, minBound + 1, liftBound, |
---|
6385 | minBound, bufUniFactors, NTLNe, diophant, |
---|
6386 | M, Pi, bufQ, irreducible |
---|
6387 | ); |
---|
6388 | } |
---|
6389 | } |
---|
6390 | |
---|
6391 | bufUniFactors.removeFirst(); |
---|
6392 | if (oldL > liftBound) |
---|
6393 | { |
---|
6394 | #ifdef HAVE_FLINT |
---|
6395 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6396 | nmod_mat_clear (FLINTN); |
---|
6397 | #endif |
---|
6398 | delete [] bounds; |
---|
6399 | return Union (smallFactors, |
---|
6400 | factorRecombination (bufUniFactors, F, |
---|
6401 | power (y, degree (F) + 1), |
---|
6402 | degs, 1, bufUniFactors.length()/2 |
---|
6403 | ) |
---|
6404 | ); |
---|
6405 | } |
---|
6406 | |
---|
6407 | l= oldL; |
---|
6408 | if (irreducible) |
---|
6409 | { |
---|
6410 | #ifdef HAVE_FLINT |
---|
6411 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6412 | nmod_mat_clear (FLINTN); |
---|
6413 | #endif |
---|
6414 | delete [] bounds; |
---|
6415 | return Union (CFList (F), smallFactors); |
---|
6416 | } |
---|
6417 | |
---|
6418 | CanonicalForm yToL= power (y,l); |
---|
6419 | |
---|
6420 | CFList result; |
---|
6421 | if (l >= degree (F) + 1) |
---|
6422 | { |
---|
6423 | int * factorsFoundIndex; |
---|
6424 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6425 | { |
---|
6426 | #ifdef HAVE_FLINT |
---|
6427 | factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
6428 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
6429 | #else |
---|
6430 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
6431 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
6432 | #endif |
---|
6433 | factorsFoundIndex[i]= 0; |
---|
6434 | } |
---|
6435 | else |
---|
6436 | { |
---|
6437 | factorsFoundIndex= new int [NTLNe.NumCols()]; |
---|
6438 | for (long i= 0; i < NTLNe.NumCols(); i++) |
---|
6439 | factorsFoundIndex[i]= 0; |
---|
6440 | } |
---|
6441 | int factorsFound= 0; |
---|
6442 | CanonicalForm bufF= F; |
---|
6443 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6444 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
6445 | #ifdef HAVE_FLINT |
---|
6446 | factorsFound, factorsFoundIndex, FLINTN, false |
---|
6447 | #else |
---|
6448 | factorsFound, factorsFoundIndex, NTLN, false |
---|
6449 | #endif |
---|
6450 | ); |
---|
6451 | else |
---|
6452 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
6453 | factorsFound, factorsFoundIndex, NTLNe, false |
---|
6454 | ); |
---|
6455 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6456 | { |
---|
6457 | #ifdef HAVE_FLINT |
---|
6458 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
6459 | { |
---|
6460 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6461 | nmod_mat_clear (FLINTN); |
---|
6462 | #else |
---|
6463 | if (result.length() == NTLN.NumCols()) |
---|
6464 | { |
---|
6465 | #endif |
---|
6466 | delete [] factorsFoundIndex; |
---|
6467 | delete [] bounds; |
---|
6468 | return Union (result, smallFactors); |
---|
6469 | } |
---|
6470 | } |
---|
6471 | else |
---|
6472 | { |
---|
6473 | if (result.length() == NTLNe.NumCols()) |
---|
6474 | { |
---|
6475 | delete [] factorsFoundIndex; |
---|
6476 | delete [] bounds; |
---|
6477 | return Union (result, smallFactors); |
---|
6478 | } |
---|
6479 | } |
---|
6480 | delete [] factorsFoundIndex; |
---|
6481 | } |
---|
6482 | if (l >= liftBound) |
---|
6483 | { |
---|
6484 | int * factorsFoundIndex; |
---|
6485 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6486 | { |
---|
6487 | #ifdef HAVE_FLINT |
---|
6488 | factorsFoundIndex= new int [nmod_mat_ncols (FLINTN)]; |
---|
6489 | for (long i= 0; i < nmod_mat_ncols (FLINTN); i++) |
---|
6490 | #else |
---|
6491 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
6492 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
6493 | #endif |
---|
6494 | factorsFoundIndex[i]= 0; |
---|
6495 | } |
---|
6496 | else |
---|
6497 | { |
---|
6498 | factorsFoundIndex= new int [NTLNe.NumCols()]; |
---|
6499 | for (long i= 0; i < NTLNe.NumCols(); i++) |
---|
6500 | factorsFoundIndex[i]= 0; |
---|
6501 | } |
---|
6502 | CanonicalForm bufF= F; |
---|
6503 | int factorsFound= 0; |
---|
6504 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6505 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
6506 | #ifdef HAVE_FLINT |
---|
6507 | factorsFound, factorsFoundIndex, FLINTN, false |
---|
6508 | #else |
---|
6509 | factorsFound, factorsFoundIndex, NTLN, false |
---|
6510 | #endif |
---|
6511 | ); |
---|
6512 | else |
---|
6513 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
6514 | factorsFound, factorsFoundIndex, NTLNe, false |
---|
6515 | ); |
---|
6516 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6517 | { |
---|
6518 | #ifdef HAVE_FLINT |
---|
6519 | if (result.length() == nmod_mat_ncols(FLINTN)) |
---|
6520 | { |
---|
6521 | nmod_mat_clear (FLINTN); |
---|
6522 | #else |
---|
6523 | if (result.length() == NTLN.NumCols()) |
---|
6524 | { |
---|
6525 | #endif |
---|
6526 | delete [] factorsFoundIndex; |
---|
6527 | delete [] bounds; |
---|
6528 | return Union (result, smallFactors); |
---|
6529 | } |
---|
6530 | } |
---|
6531 | else |
---|
6532 | { |
---|
6533 | if (result.length() == NTLNe.NumCols()) |
---|
6534 | { |
---|
6535 | delete [] factorsFoundIndex; |
---|
6536 | delete [] bounds; |
---|
6537 | return Union (result, smallFactors); |
---|
6538 | } |
---|
6539 | } |
---|
6540 | delete [] factorsFoundIndex; |
---|
6541 | } |
---|
6542 | |
---|
6543 | result= CFList(); |
---|
6544 | bool beenInThres= false; |
---|
6545 | int thres= 100; |
---|
6546 | if (l <= thres) |
---|
6547 | { |
---|
6548 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6549 | { |
---|
6550 | #ifdef HAVE_FLINT |
---|
6551 | if (nmod_mat_ncols (FLINTN) < bufUniFactors.length()) |
---|
6552 | { |
---|
6553 | refineAndRestartLift (F, FLINTN, liftBound, l, bufUniFactors, M, Pi, |
---|
6554 | #else |
---|
6555 | if (NTLN.NumCols() < bufUniFactors.length()) |
---|
6556 | { |
---|
6557 | refineAndRestartLift (F, NTLN, liftBound, l, bufUniFactors, M, Pi, |
---|
6558 | #endif |
---|
6559 | diophant |
---|
6560 | ); |
---|
6561 | beenInThres= true; |
---|
6562 | } |
---|
6563 | } |
---|
6564 | else |
---|
6565 | { |
---|
6566 | if (NTLNe.NumCols() < bufUniFactors.length()) |
---|
6567 | { |
---|
6568 | refineAndRestartLift (F, NTLNe, liftBound, l, bufUniFactors, M, Pi, |
---|
6569 | diophant |
---|
6570 | ); |
---|
6571 | beenInThres= true; |
---|
6572 | } |
---|
6573 | } |
---|
6574 | } |
---|
6575 | |
---|
6576 | CanonicalForm bufF= F; |
---|
6577 | int factorsFound= 0; |
---|
6578 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6579 | { |
---|
6580 | #ifdef HAVE_FLINT |
---|
6581 | result= earlyReconstructionAndLifting (F, FLINTN, bufF, bufUniFactors, l, |
---|
6582 | #else |
---|
6583 | result= earlyReconstructionAndLifting (F, NTLN, bufF, bufUniFactors, l, |
---|
6584 | #endif |
---|
6585 | factorsFound, beenInThres, M, Pi, |
---|
6586 | diophant, symmetric, evaluation |
---|
6587 | ); |
---|
6588 | |
---|
6589 | #ifdef HAVE_FLINT |
---|
6590 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
6591 | { |
---|
6592 | nmod_mat_clear (FLINTN); |
---|
6593 | #else |
---|
6594 | if (result.length() == NTLN.NumCols()) |
---|
6595 | { |
---|
6596 | #endif |
---|
6597 | delete [] bounds; |
---|
6598 | return Union (result, smallFactors); |
---|
6599 | } |
---|
6600 | } |
---|
6601 | else |
---|
6602 | { |
---|
6603 | result= earlyReconstructionAndLifting (F, NTLNe, bufF, bufUniFactors, l, |
---|
6604 | factorsFound, beenInThres, M, Pi, |
---|
6605 | diophant, symmetric, evaluation |
---|
6606 | ); |
---|
6607 | |
---|
6608 | if (result.length() == NTLNe.NumCols()) |
---|
6609 | { |
---|
6610 | delete [] bounds; |
---|
6611 | return Union (result, smallFactors); |
---|
6612 | } |
---|
6613 | } |
---|
6614 | |
---|
6615 | if (result.length() > 0) |
---|
6616 | { |
---|
6617 | if (beenInThres) |
---|
6618 | { |
---|
6619 | int index; |
---|
6620 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
6621 | { |
---|
6622 | index= 1; |
---|
6623 | tmp1= mod (i.getItem(), y); |
---|
6624 | tmp1 /= Lc (tmp1); |
---|
6625 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
6626 | { |
---|
6627 | tmp2= mod (j.getItem(), y); |
---|
6628 | tmp2 /= Lc (tmp2); |
---|
6629 | if (tmp1 == tmp2) |
---|
6630 | { |
---|
6631 | index++; |
---|
6632 | j.remove(index); |
---|
6633 | break; |
---|
6634 | } |
---|
6635 | } |
---|
6636 | } |
---|
6637 | } |
---|
6638 | else |
---|
6639 | { |
---|
6640 | int * zeroOne; |
---|
6641 | long numCols, numRows; |
---|
6642 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6643 | { |
---|
6644 | #ifdef HAVE_FLINT |
---|
6645 | numCols= nmod_mat_ncols (FLINTN); |
---|
6646 | numRows= nmod_mat_nrows (FLINTN); |
---|
6647 | zeroOne= extractZeroOneVecs (FLINTN); |
---|
6648 | #else |
---|
6649 | numCols= NTLN.NumCols(); |
---|
6650 | numRows= NTLN.NumRows(); |
---|
6651 | zeroOne= extractZeroOneVecs (NTLN); |
---|
6652 | #endif |
---|
6653 | } |
---|
6654 | else |
---|
6655 | { |
---|
6656 | numCols= NTLNe.NumCols(); |
---|
6657 | numRows= NTLNe.NumRows(); |
---|
6658 | zeroOne= extractZeroOneVecs (NTLNe); |
---|
6659 | } |
---|
6660 | CFList bufBufUniFactors= bufUniFactors; |
---|
6661 | CFListIterator iter, iter2; |
---|
6662 | CanonicalForm buf; |
---|
6663 | CFList factorsConsidered; |
---|
6664 | CanonicalForm tmp; |
---|
6665 | for (int i= 0; i < numCols; i++) |
---|
6666 | { |
---|
6667 | if (zeroOne [i] == 0) |
---|
6668 | continue; |
---|
6669 | iter= bufUniFactors; |
---|
6670 | buf= 1; |
---|
6671 | factorsConsidered= CFList(); |
---|
6672 | for (int j= 0; j < numRows; j++, iter++) |
---|
6673 | { |
---|
6674 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6675 | { |
---|
6676 | #ifdef HAVE_FLINT |
---|
6677 | if (!(nmod_mat_entry (FLINTN, j,i) == 0)) |
---|
6678 | #else |
---|
6679 | if (!IsZero (NTLN (j + 1,i + 1))) |
---|
6680 | #endif |
---|
6681 | { |
---|
6682 | factorsConsidered.append (iter.getItem()); |
---|
6683 | buf *= mod (iter.getItem(), y); |
---|
6684 | } |
---|
6685 | } |
---|
6686 | else |
---|
6687 | { |
---|
6688 | if (!IsZero (NTLNe (j + 1,i + 1))) |
---|
6689 | { |
---|
6690 | factorsConsidered.append (iter.getItem()); |
---|
6691 | buf *= mod (iter.getItem(), y); |
---|
6692 | } |
---|
6693 | } |
---|
6694 | } |
---|
6695 | buf /= Lc (buf); |
---|
6696 | for (iter2= result; iter2.hasItem(); iter2++) |
---|
6697 | { |
---|
6698 | tmp= mod (iter2.getItem(), y); |
---|
6699 | tmp /= Lc (tmp); |
---|
6700 | if (tmp == buf) |
---|
6701 | { |
---|
6702 | bufBufUniFactors= Difference (bufBufUniFactors, factorsConsidered); |
---|
6703 | break; |
---|
6704 | } |
---|
6705 | } |
---|
6706 | } |
---|
6707 | bufUniFactors= bufBufUniFactors; |
---|
6708 | delete [] zeroOne; |
---|
6709 | } |
---|
6710 | |
---|
6711 | int oldNumCols; |
---|
6712 | CFList resultBufF; |
---|
6713 | irreducible= false; |
---|
6714 | |
---|
6715 | if (alpha.level() == 1) |
---|
6716 | { |
---|
6717 | #ifdef HAVE_FLINT |
---|
6718 | oldNumCols= nmod_mat_ncols (FLINTN); |
---|
6719 | #else |
---|
6720 | oldNumCols= NTLN.NumCols(); |
---|
6721 | #endif |
---|
6722 | resultBufF= increasePrecision (bufF, bufUniFactors, factorsFound, |
---|
6723 | oldNumCols, oldL, l |
---|
6724 | ); |
---|
6725 | } |
---|
6726 | else |
---|
6727 | { |
---|
6728 | if (reduceFq2Fp) |
---|
6729 | { |
---|
6730 | #ifdef HAVE_FLINT |
---|
6731 | oldNumCols= nmod_mat_ncols (FLINTN); |
---|
6732 | #else |
---|
6733 | oldNumCols= NTLN.NumCols(); |
---|
6734 | #endif |
---|
6735 | |
---|
6736 | resultBufF= increasePrecisionFq2Fp (bufF, bufUniFactors, factorsFound, |
---|
6737 | oldNumCols, oldL, alpha, l |
---|
6738 | ); |
---|
6739 | } |
---|
6740 | else |
---|
6741 | { |
---|
6742 | oldNumCols= NTLNe.NumCols(); |
---|
6743 | |
---|
6744 | resultBufF= increasePrecision (bufF, bufUniFactors, factorsFound, |
---|
6745 | oldNumCols, oldL, alpha, l |
---|
6746 | ); |
---|
6747 | } |
---|
6748 | } |
---|
6749 | |
---|
6750 | if (bufUniFactors.isEmpty() || degree (bufF) <= 0) |
---|
6751 | { |
---|
6752 | #ifdef HAVE_FLINT |
---|
6753 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6754 | nmod_mat_clear (FLINTN); |
---|
6755 | #endif |
---|
6756 | delete [] bounds; |
---|
6757 | result= Union (resultBufF, result); |
---|
6758 | return Union (result, smallFactors); |
---|
6759 | } |
---|
6760 | |
---|
6761 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
6762 | i.getItem()= mod (i.getItem(), y); |
---|
6763 | |
---|
6764 | result= Union (result, resultBufF); |
---|
6765 | result= Union (result, smallFactors); |
---|
6766 | delete [] bounds; |
---|
6767 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
6768 | degs.intersect (bufDegs); |
---|
6769 | degs.refine(); |
---|
6770 | if (degs.getLength() == 1 || bufUniFactors.length() == 1) |
---|
6771 | { |
---|
6772 | #ifdef HAVE_FLINT |
---|
6773 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6774 | nmod_mat_clear (FLINTN); |
---|
6775 | #endif |
---|
6776 | result.append (bufF); |
---|
6777 | return result; |
---|
6778 | } |
---|
6779 | #ifdef HAVE_FLINT |
---|
6780 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6781 | nmod_mat_clear (FLINTN); |
---|
6782 | #endif |
---|
6783 | return Union (result, henselLiftAndLatticeRecombi (bufF, bufUniFactors, |
---|
6784 | alpha, degs, symmetric, |
---|
6785 | evaluation |
---|
6786 | ) |
---|
6787 | ); |
---|
6788 | } |
---|
6789 | |
---|
6790 | if (l < liftBound) |
---|
6791 | { |
---|
6792 | if (alpha.level() == 1) |
---|
6793 | { |
---|
6794 | result=increasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
6795 | #ifdef HAVE_FLINT |
---|
6796 | FLINTN |
---|
6797 | #else |
---|
6798 | NTLN |
---|
6799 | #endif |
---|
6800 | ); |
---|
6801 | } |
---|
6802 | else |
---|
6803 | { |
---|
6804 | if (reduceFq2Fp) |
---|
6805 | { |
---|
6806 | result=increasePrecisionFq2Fp (F, bufUniFactors, oldL, l, d, bounds, |
---|
6807 | #ifdef HAVE_FLINT |
---|
6808 | bufQ, FLINTN, alpha |
---|
6809 | #else |
---|
6810 | bufQ, NTLN, alpha |
---|
6811 | #endif |
---|
6812 | ); |
---|
6813 | } |
---|
6814 | else |
---|
6815 | { |
---|
6816 | result=increasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
6817 | NTLNe |
---|
6818 | ); |
---|
6819 | } |
---|
6820 | } |
---|
6821 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6822 | { |
---|
6823 | #ifdef HAVE_FLINT |
---|
6824 | if (result.length()== nmod_mat_ncols (FLINTN)) |
---|
6825 | { |
---|
6826 | nmod_mat_clear (FLINTN); |
---|
6827 | #else |
---|
6828 | if (result.length()== NTLN.NumCols()) |
---|
6829 | { |
---|
6830 | #endif |
---|
6831 | delete [] bounds; |
---|
6832 | result= Union (result, smallFactors); |
---|
6833 | return result; |
---|
6834 | } |
---|
6835 | } |
---|
6836 | else |
---|
6837 | { |
---|
6838 | if (result.length()== NTLNe.NumCols()) |
---|
6839 | { |
---|
6840 | delete [] bounds; |
---|
6841 | result= Union (result, smallFactors); |
---|
6842 | return result; |
---|
6843 | } |
---|
6844 | } |
---|
6845 | |
---|
6846 | if (result.isEmpty()) |
---|
6847 | { |
---|
6848 | if (alpha.level() == 1) |
---|
6849 | result= furtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
6850 | #ifdef HAVE_FLINT |
---|
6851 | liftBound,d,bounds,FLINTN, |
---|
6852 | #else |
---|
6853 | liftBound, d, bounds, NTLN, |
---|
6854 | #endif |
---|
6855 | diophant, M, Pi, bufQ |
---|
6856 | ); |
---|
6857 | else |
---|
6858 | { |
---|
6859 | if (reduceFq2Fp) |
---|
6860 | result= furtherLiftingAndIncreasePrecisionFq2Fp (F,bufUniFactors, l, |
---|
6861 | liftBound, d, bounds, |
---|
6862 | #ifdef HAVE_FLINT |
---|
6863 | FLINTN, diophant, M, |
---|
6864 | #else |
---|
6865 | NTLN, diophant, M, |
---|
6866 | #endif |
---|
6867 | Pi, bufQ, alpha |
---|
6868 | ); |
---|
6869 | else |
---|
6870 | result= furtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
6871 | liftBound, d, bounds, |
---|
6872 | NTLNe, diophant, M, |
---|
6873 | Pi, bufQ |
---|
6874 | ); |
---|
6875 | } |
---|
6876 | |
---|
6877 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6878 | { |
---|
6879 | #ifdef HAVE_FLINT |
---|
6880 | if (result.length() == nmod_mat_ncols (FLINTN)) |
---|
6881 | { |
---|
6882 | nmod_mat_clear (FLINTN); |
---|
6883 | #else |
---|
6884 | if (result.length() == NTLN.NumCols()) |
---|
6885 | { |
---|
6886 | #endif |
---|
6887 | delete [] bounds; |
---|
6888 | result= Union (result, smallFactors); |
---|
6889 | return result; |
---|
6890 | } |
---|
6891 | } |
---|
6892 | else |
---|
6893 | { |
---|
6894 | if (result.length() == NTLNe.NumCols()) |
---|
6895 | { |
---|
6896 | delete [] bounds; |
---|
6897 | result= Union (result, smallFactors); |
---|
6898 | return result; |
---|
6899 | } |
---|
6900 | } |
---|
6901 | } |
---|
6902 | } |
---|
6903 | |
---|
6904 | DEBOUTLN (cerr, "lattice recombination failed"); |
---|
6905 | |
---|
6906 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
6907 | degs.intersect (bufDegs); |
---|
6908 | degs.refine(); |
---|
6909 | |
---|
6910 | delete [] bounds; |
---|
6911 | bounds= computeBounds (F, d, isIrreducible); |
---|
6912 | #ifdef HAVE_FLINT |
---|
6913 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
6914 | nmod_mat_clear (FLINTN); |
---|
6915 | #endif |
---|
6916 | if (isIrreducible) |
---|
6917 | { |
---|
6918 | delete [] bounds; |
---|
6919 | result= Union (result, smallFactors); |
---|
6920 | result.append (F); |
---|
6921 | return result; |
---|
6922 | } |
---|
6923 | minBound= bounds[0]; |
---|
6924 | for (int i= 1; i < d; i++) |
---|
6925 | { |
---|
6926 | if (bounds[i] != 0) |
---|
6927 | minBound= tmin (minBound, bounds[i]); |
---|
6928 | } |
---|
6929 | |
---|
6930 | if (minBound > 16 || result.length() == 0) |
---|
6931 | { |
---|
6932 | result= Union (result, smallFactors); |
---|
6933 | CanonicalForm MODl= power (y, degree (F) + 1); |
---|
6934 | delete [] bounds; |
---|
6935 | return Union (result, factorRecombination (bufUniFactors, F, MODl, degs, 1, |
---|
6936 | bufUniFactors.length()/2 |
---|
6937 | ) |
---|
6938 | ); |
---|
6939 | } |
---|
6940 | else |
---|
6941 | { |
---|
6942 | result= Union (result, smallFactors); |
---|
6943 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
6944 | i.getItem()= mod (i.getItem(), y); |
---|
6945 | delete [] bounds; |
---|
6946 | return Union (result, henselLiftAndLatticeRecombi (F, bufUniFactors, alpha, |
---|
6947 | degs,symmetric, evaluation |
---|
6948 | ) |
---|
6949 | ); |
---|
6950 | } |
---|
6951 | } |
---|
6952 | |
---|
6953 | ExtensionInfo |
---|
6954 | init4ext (const ExtensionInfo& info, const CanonicalForm& evaluation, |
---|
6955 | int& degMipo |
---|
6956 | ) |
---|
6957 | { |
---|
6958 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
6959 | Variable alpha= info.getAlpha(); |
---|
6960 | if (GF) |
---|
6961 | { |
---|
6962 | degMipo= getGFDegree(); |
---|
6963 | CanonicalForm GFMipo= gf_mipo; |
---|
6964 | setCharacteristic (getCharacteristic()); |
---|
6965 | GFMipo.mapinto(); |
---|
6966 | alpha= rootOf (GFMipo); |
---|
6967 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
6968 | } |
---|
6969 | else |
---|
6970 | { |
---|
6971 | alpha= info.getAlpha(); |
---|
6972 | degMipo= degree (getMipo (alpha)); |
---|
6973 | } |
---|
6974 | |
---|
6975 | Variable gamma; |
---|
6976 | CanonicalForm primElemAlpha, imPrimElemAlpha; |
---|
6977 | if ((!GF && evaluation != alpha) || (GF && evaluation != getGFGenerator())) |
---|
6978 | { |
---|
6979 | CanonicalForm bufEvaluation; |
---|
6980 | if (GF) |
---|
6981 | { |
---|
6982 | setCharacteristic (getCharacteristic()); |
---|
6983 | bufEvaluation= GF2FalphaRep (evaluation, alpha); |
---|
6984 | } |
---|
6985 | else |
---|
6986 | bufEvaluation= evaluation; |
---|
6987 | CanonicalForm mipo= findMinPoly (bufEvaluation, alpha); |
---|
6988 | gamma= rootOf (mipo); |
---|
6989 | Variable V_buf; |
---|
6990 | bool fail= false; |
---|
6991 | primElemAlpha= primitiveElement (alpha, V_buf, fail); |
---|
6992 | imPrimElemAlpha= map (primElemAlpha, alpha, bufEvaluation, gamma); |
---|
6993 | |
---|
6994 | if (GF) |
---|
6995 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
6996 | } |
---|
6997 | else |
---|
6998 | gamma= alpha; |
---|
6999 | ExtensionInfo info2= ExtensionInfo (alpha, gamma, primElemAlpha, |
---|
7000 | imPrimElemAlpha, 1, info.getGFName(), true |
---|
7001 | ); |
---|
7002 | |
---|
7003 | return info2; |
---|
7004 | } |
---|
7005 | |
---|
7006 | CFList |
---|
7007 | extHenselLiftAndLatticeRecombi(const CanonicalForm& G, const CFList& uniFactors, |
---|
7008 | const ExtensionInfo& extInfo, const |
---|
7009 | DegreePattern& degPat, const CanonicalForm& eval |
---|
7010 | ) |
---|
7011 | { |
---|
7012 | CanonicalForm evaluation= eval; |
---|
7013 | ExtensionInfo info= extInfo; |
---|
7014 | Variable alpha; |
---|
7015 | DegreePattern degs= degPat; |
---|
7016 | CanonicalForm F= G; |
---|
7017 | Variable x= Variable (1); |
---|
7018 | Variable y= F.mvar(); |
---|
7019 | CFList bufUniFactors= uniFactors; |
---|
7020 | |
---|
7021 | |
---|
7022 | int degMipo; |
---|
7023 | ExtensionInfo info2= init4ext (info, evaluation, degMipo); |
---|
7024 | |
---|
7025 | CFList source, dest; |
---|
7026 | CanonicalForm LCF= LC (F, 1); |
---|
7027 | |
---|
7028 | int d; |
---|
7029 | bool isIrreducible= false; |
---|
7030 | int* bounds= computeBounds (F, d, isIrreducible); |
---|
7031 | if (isIrreducible) |
---|
7032 | { |
---|
7033 | delete [] bounds; |
---|
7034 | CFList source, dest; |
---|
7035 | CanonicalForm tmp= G (y - evaluation, y); |
---|
7036 | tmp= mapDown (tmp, info, source, dest); |
---|
7037 | return CFList (tmp); |
---|
7038 | } |
---|
7039 | int minBound= bounds[0]; |
---|
7040 | for (int i= 1; i < d; i++) |
---|
7041 | { |
---|
7042 | if (bounds[i] != 0) |
---|
7043 | minBound= tmin (minBound, bounds[i]); |
---|
7044 | } |
---|
7045 | |
---|
7046 | |
---|
7047 | CFArray Pi; |
---|
7048 | CFList diophant; |
---|
7049 | int liftBound= tmax ((2*totaldegree (F) - 1)/degMipo + 1, degree (F) + 1 + |
---|
7050 | degree (LC (F, 1))); |
---|
7051 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
7052 | |
---|
7053 | CFList smallFactors; |
---|
7054 | CanonicalForm H; |
---|
7055 | bool success= false; |
---|
7056 | smallFactors= extSieveSmallFactors (F, bufUniFactors, degs, H, diophant, Pi, |
---|
7057 | M, success, minBound + 1, evaluation, info |
---|
7058 | ); |
---|
7059 | |
---|
7060 | if (smallFactors.length() > 0) |
---|
7061 | { |
---|
7062 | if (smallFactors.length() == 1) |
---|
7063 | { |
---|
7064 | if (smallFactors.getFirst() == F) |
---|
7065 | { |
---|
7066 | delete [] bounds; |
---|
7067 | CFList source, dest; |
---|
7068 | CanonicalForm tmp= G (y - evaluation, y); |
---|
7069 | tmp= mapDown (tmp, info, source, dest); |
---|
7070 | return CFList (tmp); |
---|
7071 | } |
---|
7072 | } |
---|
7073 | if (degs.getLength() <= 1) |
---|
7074 | { |
---|
7075 | delete [] bounds; |
---|
7076 | return smallFactors; |
---|
7077 | } |
---|
7078 | } |
---|
7079 | |
---|
7080 | int index; |
---|
7081 | CanonicalForm tmp1, tmp2; |
---|
7082 | for (CFListIterator i= smallFactors; i.hasItem(); i++) |
---|
7083 | { |
---|
7084 | index= 1; |
---|
7085 | tmp1= mod (i.getItem(), y - evaluation); |
---|
7086 | tmp1 /= Lc (tmp1); |
---|
7087 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
7088 | { |
---|
7089 | tmp2= mod (j.getItem(), y); |
---|
7090 | tmp2 /= Lc (tmp2); |
---|
7091 | if (tmp1 == tmp2) |
---|
7092 | { |
---|
7093 | index++; |
---|
7094 | j.remove(index); |
---|
7095 | break; |
---|
7096 | } |
---|
7097 | } |
---|
7098 | } |
---|
7099 | |
---|
7100 | if (bufUniFactors.isEmpty()) |
---|
7101 | { |
---|
7102 | delete [] bounds; |
---|
7103 | return smallFactors; |
---|
7104 | } |
---|
7105 | |
---|
7106 | if (success) |
---|
7107 | { |
---|
7108 | F= H; |
---|
7109 | delete [] bounds; |
---|
7110 | bounds= computeBounds (F, d, isIrreducible); |
---|
7111 | if (isIrreducible) |
---|
7112 | { |
---|
7113 | delete [] bounds; |
---|
7114 | CFList source, dest; |
---|
7115 | CanonicalForm tmp= F (y - evaluation, y); |
---|
7116 | tmp= mapDown (tmp, info, source, dest); |
---|
7117 | smallFactors.append (tmp); |
---|
7118 | return smallFactors; |
---|
7119 | } |
---|
7120 | LCF= LC (F, 1); |
---|
7121 | |
---|
7122 | minBound= bounds[0]; |
---|
7123 | for (int i= 1; i < d; i++) |
---|
7124 | { |
---|
7125 | if (bounds[i] != 0) |
---|
7126 | minBound= tmin (minBound, bounds[i]); |
---|
7127 | } |
---|
7128 | Pi= CFArray(); |
---|
7129 | diophant= CFList(); |
---|
7130 | liftBound=tmax ((2*totaldegree (F) - 1)/degMipo + 1, degree (F) + 1 + |
---|
7131 | degree (LC (F, 1))); |
---|
7132 | M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
7133 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
7134 | degs.intersect (bufDegs); |
---|
7135 | degs.refine(); |
---|
7136 | if (degs.getLength() <= 1) |
---|
7137 | { |
---|
7138 | delete [] bounds; |
---|
7139 | CFList source, dest; |
---|
7140 | CanonicalForm tmp= F (y - evaluation, y); |
---|
7141 | tmp= mapDown (tmp, info, source, dest); |
---|
7142 | smallFactors.append (tmp); |
---|
7143 | return smallFactors; |
---|
7144 | } |
---|
7145 | } |
---|
7146 | |
---|
7147 | bufUniFactors.insert (LCF); |
---|
7148 | int l= 1; |
---|
7149 | |
---|
7150 | if (fac_NTL_char != getCharacteristic()) |
---|
7151 | { |
---|
7152 | fac_NTL_char= getCharacteristic(); |
---|
7153 | zz_p::init (getCharacteristic()); |
---|
7154 | } |
---|
7155 | zz_pX NTLMipo; |
---|
7156 | mat_zz_p NTLN; |
---|
7157 | |
---|
7158 | ident (NTLN, bufUniFactors.length() - 1); |
---|
7159 | bool irreducible= false; |
---|
7160 | CFArray bufQ= CFArray (bufUniFactors.length() - 1); |
---|
7161 | |
---|
7162 | int oldL; |
---|
7163 | if (success) |
---|
7164 | { |
---|
7165 | int start= 0; |
---|
7166 | oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound, start, |
---|
7167 | bufUniFactors, NTLN, diophant, M, Pi, bufQ, |
---|
7168 | irreducible, evaluation, info2, source, dest |
---|
7169 | ); |
---|
7170 | } |
---|
7171 | else |
---|
7172 | { |
---|
7173 | oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound, |
---|
7174 | minBound + 1, bufUniFactors, NTLN, diophant, |
---|
7175 | M, Pi, bufQ, irreducible, evaluation, info2, |
---|
7176 | source, dest |
---|
7177 | ); |
---|
7178 | } |
---|
7179 | |
---|
7180 | bufUniFactors.removeFirst(); |
---|
7181 | if (oldL > liftBound) |
---|
7182 | { |
---|
7183 | delete [] bounds; |
---|
7184 | return Union (smallFactors, extFactorRecombination |
---|
7185 | (bufUniFactors, F, |
---|
7186 | power (y, degree (F) + 1),info, |
---|
7187 | degs, evaluation, 1, bufUniFactors.length()/2 |
---|
7188 | ) |
---|
7189 | ); |
---|
7190 | } |
---|
7191 | |
---|
7192 | l= oldL; |
---|
7193 | if (irreducible) |
---|
7194 | { |
---|
7195 | delete [] bounds; |
---|
7196 | CFList source, dest; |
---|
7197 | CanonicalForm tmp= F (y - evaluation, y); |
---|
7198 | tmp= mapDown (tmp, info, source, dest); |
---|
7199 | return Union (CFList (tmp), smallFactors); |
---|
7200 | } |
---|
7201 | |
---|
7202 | CanonicalForm yToL= power (y,l); |
---|
7203 | |
---|
7204 | CFList result; |
---|
7205 | if (l >= degree (F) + 1) |
---|
7206 | { |
---|
7207 | int * factorsFoundIndex; |
---|
7208 | |
---|
7209 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
7210 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
7211 | factorsFoundIndex[i]= 0; |
---|
7212 | |
---|
7213 | int factorsFound= 0; |
---|
7214 | CanonicalForm bufF= F; |
---|
7215 | |
---|
7216 | extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
7217 | factorsFound, factorsFoundIndex, NTLN, false, info, |
---|
7218 | evaluation |
---|
7219 | ); |
---|
7220 | |
---|
7221 | if (result.length() == NTLN.NumCols()) |
---|
7222 | { |
---|
7223 | delete [] factorsFoundIndex; |
---|
7224 | delete [] bounds; |
---|
7225 | return Union (result, smallFactors); |
---|
7226 | } |
---|
7227 | |
---|
7228 | delete [] factorsFoundIndex; |
---|
7229 | } |
---|
7230 | if (l >= liftBound) |
---|
7231 | { |
---|
7232 | int * factorsFoundIndex; |
---|
7233 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
7234 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
7235 | factorsFoundIndex[i]= 0; |
---|
7236 | CanonicalForm bufF= F; |
---|
7237 | int factorsFound= 0; |
---|
7238 | |
---|
7239 | extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
7240 | factorsFound, factorsFoundIndex, NTLN, false, |
---|
7241 | info, evaluation |
---|
7242 | ); |
---|
7243 | |
---|
7244 | if (result.length() == NTLN.NumCols()) |
---|
7245 | { |
---|
7246 | delete [] factorsFoundIndex; |
---|
7247 | delete [] bounds; |
---|
7248 | return Union (result, smallFactors); |
---|
7249 | } |
---|
7250 | delete [] factorsFoundIndex; |
---|
7251 | } |
---|
7252 | |
---|
7253 | result= CFList(); |
---|
7254 | bool beenInThres= false; |
---|
7255 | int thres= 100; |
---|
7256 | if (l <= thres && bufUniFactors.length() > NTLN.NumCols()) |
---|
7257 | { |
---|
7258 | refineAndRestartLift (F, NTLN, 2*totaldegree (F)-1, l, bufUniFactors, M, Pi, |
---|
7259 | diophant |
---|
7260 | ); |
---|
7261 | beenInThres= true; |
---|
7262 | } |
---|
7263 | |
---|
7264 | |
---|
7265 | CanonicalForm bufF= F; |
---|
7266 | int factorsFound= 0; |
---|
7267 | |
---|
7268 | result= extEarlyReconstructionAndLifting (F, NTLN, bufF, bufUniFactors, l, |
---|
7269 | factorsFound, beenInThres, M, Pi, |
---|
7270 | diophant, info, evaluation |
---|
7271 | ); |
---|
7272 | |
---|
7273 | if (result.length() == NTLN.NumCols()) |
---|
7274 | { |
---|
7275 | delete [] bounds; |
---|
7276 | return Union (result, smallFactors); |
---|
7277 | } |
---|
7278 | |
---|
7279 | if (result.length() > 0) |
---|
7280 | { |
---|
7281 | if (beenInThres) |
---|
7282 | { |
---|
7283 | int index; |
---|
7284 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
7285 | { |
---|
7286 | index= 1; |
---|
7287 | tmp1= mod (i.getItem(), y-evaluation); |
---|
7288 | tmp1 /= Lc (tmp1); |
---|
7289 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
7290 | { |
---|
7291 | tmp2= mod (j.getItem(), y); |
---|
7292 | tmp2 /= Lc (tmp2); |
---|
7293 | if (tmp1 == tmp2) |
---|
7294 | { |
---|
7295 | index++; |
---|
7296 | j.remove(index); |
---|
7297 | break; |
---|
7298 | } |
---|
7299 | } |
---|
7300 | } |
---|
7301 | } |
---|
7302 | else |
---|
7303 | { |
---|
7304 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
7305 | CFList bufBufUniFactors= bufUniFactors; |
---|
7306 | CFListIterator iter, iter2; |
---|
7307 | CanonicalForm buf; |
---|
7308 | CFList factorsConsidered; |
---|
7309 | for (int i= 0; i < NTLN.NumCols(); i++) |
---|
7310 | { |
---|
7311 | if (zeroOne [i] == 0) |
---|
7312 | continue; |
---|
7313 | iter= bufUniFactors; |
---|
7314 | buf= 1; |
---|
7315 | factorsConsidered= CFList(); |
---|
7316 | for (int j= 0; j < NTLN.NumRows(); j++, iter++) |
---|
7317 | { |
---|
7318 | if (!IsZero (NTLN (j + 1,i + 1))) |
---|
7319 | { |
---|
7320 | factorsConsidered.append (iter.getItem()); |
---|
7321 | buf *= mod (iter.getItem(), y); |
---|
7322 | } |
---|
7323 | } |
---|
7324 | buf /= Lc (buf); |
---|
7325 | for (iter2= result; iter2.hasItem(); iter2++) |
---|
7326 | { |
---|
7327 | CanonicalForm tmp= mod (iter2.getItem(), y - evaluation); |
---|
7328 | tmp /= Lc (tmp); |
---|
7329 | if (tmp == buf) |
---|
7330 | { |
---|
7331 | bufBufUniFactors= Difference (bufBufUniFactors, factorsConsidered); |
---|
7332 | break; |
---|
7333 | } |
---|
7334 | } |
---|
7335 | } |
---|
7336 | bufUniFactors= bufBufUniFactors; |
---|
7337 | delete [] zeroOne; |
---|
7338 | } |
---|
7339 | |
---|
7340 | int oldNumCols; |
---|
7341 | CFList resultBufF; |
---|
7342 | irreducible= false; |
---|
7343 | |
---|
7344 | oldNumCols= NTLN.NumCols(); |
---|
7345 | resultBufF= extIncreasePrecision (bufF, bufUniFactors, factorsFound, |
---|
7346 | oldNumCols, oldL, evaluation, info2, |
---|
7347 | source, dest, l |
---|
7348 | ); |
---|
7349 | |
---|
7350 | if (bufUniFactors.isEmpty() || degree (bufF) <= 0) |
---|
7351 | { |
---|
7352 | delete [] bounds; |
---|
7353 | result= Union (resultBufF, result); |
---|
7354 | return Union (result, smallFactors); |
---|
7355 | } |
---|
7356 | |
---|
7357 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
7358 | i.getItem()= mod (i.getItem(), y); |
---|
7359 | |
---|
7360 | delete [] bounds; |
---|
7361 | CFList bufResult; |
---|
7362 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
7363 | degs.intersect (bufDegs); |
---|
7364 | degs.refine(); |
---|
7365 | result= Union (result, smallFactors); |
---|
7366 | if (degs.getLength() == 1 || bufUniFactors.length() == 1) |
---|
7367 | { |
---|
7368 | CFList source, dest; |
---|
7369 | CanonicalForm tmp= bufF (y - evaluation, y); |
---|
7370 | tmp= mapDown (tmp, info, source, dest); |
---|
7371 | result.append (tmp); |
---|
7372 | return result; |
---|
7373 | } |
---|
7374 | return Union (result, extHenselLiftAndLatticeRecombi (bufF, bufUniFactors, |
---|
7375 | info, degs, evaluation |
---|
7376 | ) |
---|
7377 | ); |
---|
7378 | } |
---|
7379 | |
---|
7380 | if (l/degMipo < liftBound) |
---|
7381 | { |
---|
7382 | result=extIncreasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
7383 | NTLN, evaluation, info2, source, dest |
---|
7384 | ); |
---|
7385 | |
---|
7386 | if (result.length()== NTLN.NumCols()) |
---|
7387 | { |
---|
7388 | delete [] bounds; |
---|
7389 | result= Union (result, smallFactors); |
---|
7390 | return result; |
---|
7391 | } |
---|
7392 | |
---|
7393 | if (result.isEmpty()) |
---|
7394 | { |
---|
7395 | result= extFurtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
7396 | liftBound, d, bounds, NTLN, |
---|
7397 | diophant, M, Pi, bufQ, |
---|
7398 | evaluation, info2, source, |
---|
7399 | dest |
---|
7400 | ); |
---|
7401 | if (result.length()== NTLN.NumCols()) |
---|
7402 | { |
---|
7403 | delete [] bounds; |
---|
7404 | result= Union (result, smallFactors); |
---|
7405 | return result; |
---|
7406 | } |
---|
7407 | } |
---|
7408 | } |
---|
7409 | |
---|
7410 | DEBOUTLN (cerr, "lattice recombination failed"); |
---|
7411 | |
---|
7412 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
7413 | degs.intersect (bufDegs); |
---|
7414 | degs.refine(); |
---|
7415 | |
---|
7416 | delete [] bounds; |
---|
7417 | bounds= computeBounds (F, d, isIrreducible); |
---|
7418 | if (isIrreducible) |
---|
7419 | { |
---|
7420 | delete [] bounds; |
---|
7421 | CFList source, dest; |
---|
7422 | CanonicalForm tmp= F (y - evaluation, y); |
---|
7423 | tmp= mapDown (tmp, info, source, dest); |
---|
7424 | smallFactors.append (tmp); |
---|
7425 | result= Union (result, smallFactors); |
---|
7426 | return result; |
---|
7427 | } |
---|
7428 | minBound= bounds[0]; |
---|
7429 | for (int i= 1; i < d; i++) |
---|
7430 | { |
---|
7431 | if (bounds[i] != 0) |
---|
7432 | minBound= tmin (minBound, bounds[i]); |
---|
7433 | } |
---|
7434 | |
---|
7435 | if (minBound > 16 || result.length() == 0) |
---|
7436 | { |
---|
7437 | result= Union (result, smallFactors); |
---|
7438 | CanonicalForm MODl= power (y, degree (F) + 1); |
---|
7439 | delete [] bounds; |
---|
7440 | return Union (result, extFactorRecombination (bufUniFactors, F, MODl, info, |
---|
7441 | degs, evaluation, 1, |
---|
7442 | bufUniFactors.length()/2 |
---|
7443 | ) |
---|
7444 | ); |
---|
7445 | } |
---|
7446 | else |
---|
7447 | { |
---|
7448 | result= Union (result, smallFactors); |
---|
7449 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
7450 | i.getItem()= mod (i.getItem(), y); |
---|
7451 | delete [] bounds; |
---|
7452 | return Union (result, extHenselLiftAndLatticeRecombi (F, bufUniFactors, |
---|
7453 | info, degs, evaluation |
---|
7454 | ) |
---|
7455 | ); |
---|
7456 | } |
---|
7457 | } |
---|
7458 | |
---|
7459 | CFList |
---|
7460 | extBiFactorize (const CanonicalForm& F, const ExtensionInfo& info); |
---|
7461 | |
---|
7462 | /// bivariate factorization over finite fields as decribed in "Factoring |
---|
7463 | /// multivariate polynomials over a finite field" by L Bernardin. |
---|
7464 | CFList |
---|
7465 | biFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
7466 | { |
---|
7467 | if (F.inCoeffDomain()) |
---|
7468 | return CFList(F); |
---|
7469 | |
---|
7470 | CanonicalForm A= F; |
---|
7471 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
7472 | |
---|
7473 | Variable alpha= info.getAlpha(); |
---|
7474 | Variable beta= info.getBeta(); |
---|
7475 | CanonicalForm gamma= info.getGamma(); |
---|
7476 | CanonicalForm delta= info.getDelta(); |
---|
7477 | int k= info.getGFDegree(); |
---|
7478 | bool extension= info.isInExtension(); |
---|
7479 | if (A.isUnivariate()) |
---|
7480 | { |
---|
7481 | if (extension == false) |
---|
7482 | return uniFactorizer (F, alpha, GF); |
---|
7483 | else |
---|
7484 | { |
---|
7485 | CFList source, dest; |
---|
7486 | A= mapDown (A, info, source, dest); |
---|
7487 | return uniFactorizer (A, beta, GF); |
---|
7488 | } |
---|
7489 | } |
---|
7490 | |
---|
7491 | CFMap N; |
---|
7492 | A= compress (A, N); |
---|
7493 | Variable y= A.mvar(); |
---|
7494 | |
---|
7495 | if (y.level() > 2) return CFList (F); |
---|
7496 | Variable x= Variable (1); |
---|
7497 | |
---|
7498 | //remove and factorize content |
---|
7499 | CanonicalForm contentAx= content (A, x); |
---|
7500 | CanonicalForm contentAy= content (A); |
---|
7501 | |
---|
7502 | A= A/(contentAx*contentAy); |
---|
7503 | CFList contentAxFactors, contentAyFactors; |
---|
7504 | |
---|
7505 | if (!extension) |
---|
7506 | { |
---|
7507 | contentAxFactors= uniFactorizer (contentAx, alpha, GF); |
---|
7508 | contentAyFactors= uniFactorizer (contentAy, alpha, GF); |
---|
7509 | } |
---|
7510 | |
---|
7511 | //trivial case |
---|
7512 | CFList factors; |
---|
7513 | if (A.inCoeffDomain()) |
---|
7514 | { |
---|
7515 | append (factors, contentAxFactors); |
---|
7516 | append (factors, contentAyFactors); |
---|
7517 | decompress (factors, N); |
---|
7518 | return factors; |
---|
7519 | } |
---|
7520 | else if (A.isUnivariate()) |
---|
7521 | { |
---|
7522 | factors= uniFactorizer (A, alpha, GF); |
---|
7523 | append (factors, contentAxFactors); |
---|
7524 | append (factors, contentAyFactors); |
---|
7525 | decompress (factors, N); |
---|
7526 | return factors; |
---|
7527 | } |
---|
7528 | |
---|
7529 | |
---|
7530 | //check trivial case |
---|
7531 | if (degree (A) == 1 || degree (A, 1) == 1 || |
---|
7532 | (size (A) == 2 && igcd (degree (A), degree (A,1))==1)) |
---|
7533 | { |
---|
7534 | factors.append (A); |
---|
7535 | |
---|
7536 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
7537 | false, false, N); |
---|
7538 | |
---|
7539 | if (!extension) |
---|
7540 | normalize (factors); |
---|
7541 | return factors; |
---|
7542 | } |
---|
7543 | |
---|
7544 | // check derivatives |
---|
7545 | bool derivXZero= false; |
---|
7546 | CanonicalForm derivX= deriv (A, x); |
---|
7547 | CanonicalForm gcdDerivX; |
---|
7548 | if (derivX.isZero()) |
---|
7549 | derivXZero= true; |
---|
7550 | else |
---|
7551 | { |
---|
7552 | gcdDerivX= gcd (A, derivX); |
---|
7553 | if (degree (gcdDerivX) > 0) |
---|
7554 | { |
---|
7555 | CanonicalForm g= A/gcdDerivX; |
---|
7556 | CFList factorsG= |
---|
7557 | Union (biFactorize (g, info), biFactorize (gcdDerivX, info)); |
---|
7558 | append (factorsG, contentAxFactors); |
---|
7559 | append (factorsG, contentAyFactors); |
---|
7560 | decompress (factorsG, N); |
---|
7561 | if (!extension) |
---|
7562 | normalize (factorsG); |
---|
7563 | return factorsG; |
---|
7564 | } |
---|
7565 | } |
---|
7566 | bool derivYZero= false; |
---|
7567 | CanonicalForm derivY= deriv (A, y); |
---|
7568 | CanonicalForm gcdDerivY; |
---|
7569 | if (derivY.isZero()) |
---|
7570 | derivYZero= true; |
---|
7571 | else |
---|
7572 | { |
---|
7573 | gcdDerivY= gcd (A, derivY); |
---|
7574 | if (degree (gcdDerivY) > 0) |
---|
7575 | { |
---|
7576 | CanonicalForm g= A/gcdDerivY; |
---|
7577 | CFList factorsG= |
---|
7578 | Union (biFactorize (g, info), biFactorize (gcdDerivY, info)); |
---|
7579 | append (factorsG, contentAxFactors); |
---|
7580 | append (factorsG, contentAyFactors); |
---|
7581 | decompress (factorsG, N); |
---|
7582 | if (!extension) |
---|
7583 | normalize (factorsG); |
---|
7584 | return factorsG; |
---|
7585 | } |
---|
7586 | } |
---|
7587 | //main variable is chosen s.t. the degree in x is minimal |
---|
7588 | bool swap= false; |
---|
7589 | if ((degree (A) > degree (A, x)) || derivXZero) |
---|
7590 | { |
---|
7591 | if (!derivYZero) |
---|
7592 | { |
---|
7593 | A= swapvar (A, y, x); |
---|
7594 | swap= derivXZero; |
---|
7595 | derivXZero= derivYZero; |
---|
7596 | derivYZero= swap; |
---|
7597 | swap= true; |
---|
7598 | } |
---|
7599 | } |
---|
7600 | |
---|
7601 | int boundsLength; |
---|
7602 | bool isIrreducible= false; |
---|
7603 | int * bounds= computeBounds (A, boundsLength, isIrreducible); |
---|
7604 | if (isIrreducible) |
---|
7605 | { |
---|
7606 | delete [] bounds; |
---|
7607 | factors.append (A); |
---|
7608 | |
---|
7609 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
7610 | swap, false, N); |
---|
7611 | |
---|
7612 | if (!extension) |
---|
7613 | normalize (factors); |
---|
7614 | return factors; |
---|
7615 | } |
---|
7616 | |
---|
7617 | bool fail= false; |
---|
7618 | CanonicalForm Aeval, evaluation, bufAeval, bufEvaluation, buf, tmp; |
---|
7619 | CFList uniFactors, list, bufUniFactors; |
---|
7620 | DegreePattern degs; |
---|
7621 | DegreePattern bufDegs; |
---|
7622 | |
---|
7623 | bool fail2= false; |
---|
7624 | CanonicalForm Aeval2, evaluation2, bufAeval2, bufEvaluation2; |
---|
7625 | CFList bufUniFactors2, list2, uniFactors2; |
---|
7626 | DegreePattern degs2; |
---|
7627 | DegreePattern bufDegs2; |
---|
7628 | bool swap2= false; |
---|
7629 | |
---|
7630 | // several univariate factorizations to obtain more information about the |
---|
7631 | // degree pattern therefore usually less combinations have to be tried during |
---|
7632 | // the recombination process |
---|
7633 | int factorNums= 3; |
---|
7634 | int subCheck1= substituteCheck (A, x); |
---|
7635 | int subCheck2= substituteCheck (A, y); |
---|
7636 | bool symmetric= false; |
---|
7637 | for (int i= 0; i < factorNums; i++) |
---|
7638 | { |
---|
7639 | bufAeval= A; |
---|
7640 | TIMING_START (fac_fq_bi_evaluation); |
---|
7641 | bufEvaluation= evalPoint (A, bufAeval, alpha, list, GF, fail); |
---|
7642 | TIMING_END_AND_PRINT (fac_fq_bi_evaluation, "time to find eval point: "); |
---|
7643 | if (!derivXZero && !fail2 && !symmetric) |
---|
7644 | { |
---|
7645 | if (i == 0) |
---|
7646 | { |
---|
7647 | buf= swapvar (A, x, y); |
---|
7648 | symmetric= (A/Lc (A) == buf/Lc (buf)); |
---|
7649 | } |
---|
7650 | bufAeval2= buf; |
---|
7651 | TIMING_START (fac_fq_bi_evaluation); |
---|
7652 | bufEvaluation2= evalPoint (buf, bufAeval2, alpha, list2, GF, fail2); |
---|
7653 | TIMING_END_AND_PRINT (fac_fq_bi_evaluation, |
---|
7654 | "time to find eval point wrt y: "); |
---|
7655 | } |
---|
7656 | // first try to change main variable if there is no valid evaluation point |
---|
7657 | if (fail && (i == 0)) |
---|
7658 | { |
---|
7659 | if (!derivXZero && !fail2 && !symmetric) |
---|
7660 | { |
---|
7661 | bufEvaluation= bufEvaluation2; |
---|
7662 | int dummy= subCheck2; |
---|
7663 | subCheck2= subCheck1; |
---|
7664 | subCheck1= dummy; |
---|
7665 | tmp= A; |
---|
7666 | A= buf; |
---|
7667 | buf= tmp; |
---|
7668 | bufAeval= bufAeval2; |
---|
7669 | swap2= true; |
---|
7670 | fail= false; |
---|
7671 | } |
---|
7672 | else |
---|
7673 | fail= true; |
---|
7674 | } |
---|
7675 | |
---|
7676 | // if there is no valid evaluation point pass to a field extension |
---|
7677 | if (fail && (i == 0)) |
---|
7678 | { |
---|
7679 | factors= extBiFactorize (A, info); |
---|
7680 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
7681 | swap, swap2, N); |
---|
7682 | normalize (factors); |
---|
7683 | return factors; |
---|
7684 | } |
---|
7685 | |
---|
7686 | // there is at least one valid evaluation point |
---|
7687 | // but we do not compute more univariate factorization over an extension |
---|
7688 | if (fail && (i != 0)) |
---|
7689 | break; |
---|
7690 | |
---|
7691 | // univariate factorization |
---|
7692 | TIMING_START (fac_fq_uni_factorizer); |
---|
7693 | bufUniFactors= uniFactorizer (bufAeval, alpha, GF); |
---|
7694 | TIMING_END_AND_PRINT (fac_fq_uni_factorizer, |
---|
7695 | "time for univariate factorization over Fq: "); |
---|
7696 | DEBOUTLN (cerr, "Lc (bufAeval)*prod (bufUniFactors)== bufAeval " << |
---|
7697 | (prod (bufUniFactors)*Lc (bufAeval) == bufAeval)); |
---|
7698 | |
---|
7699 | if (!derivXZero && !fail2 && !symmetric) |
---|
7700 | { |
---|
7701 | TIMING_START (fac_fq_uni_factorizer); |
---|
7702 | bufUniFactors2= uniFactorizer (bufAeval2, alpha, GF); |
---|
7703 | TIMING_END_AND_PRINT (fac_fq_uni_factorizer, |
---|
7704 | "time for univariate factorization in y over Fq: "); |
---|
7705 | DEBOUTLN (cerr, "Lc (bufAeval2)*prod (bufUniFactors2)== bufAeval2 " << |
---|
7706 | (prod (bufUniFactors2)*Lc (bufAeval2) == bufAeval2)); |
---|
7707 | } |
---|
7708 | |
---|
7709 | if (bufUniFactors.length() == 1 || |
---|
7710 | (!fail2 && !derivXZero && !symmetric && (bufUniFactors2.length() == 1))) |
---|
7711 | { |
---|
7712 | if (extension) |
---|
7713 | { |
---|
7714 | CFList source, dest; |
---|
7715 | appendMapDown (factors, A, info, source, dest); |
---|
7716 | } |
---|
7717 | else |
---|
7718 | factors.append (A); |
---|
7719 | |
---|
7720 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
7721 | swap, swap2, N); |
---|
7722 | |
---|
7723 | if (!extension) |
---|
7724 | normalize (factors); |
---|
7725 | return factors; |
---|
7726 | } |
---|
7727 | |
---|
7728 | if (i == 0 && !extension) |
---|
7729 | { |
---|
7730 | if (subCheck1 > 0) |
---|
7731 | { |
---|
7732 | int subCheck= substituteCheck (bufUniFactors); |
---|
7733 | |
---|
7734 | if (subCheck > 1 && (subCheck1%subCheck == 0)) |
---|
7735 | { |
---|
7736 | CanonicalForm bufA= A; |
---|
7737 | subst (bufA, bufA, subCheck, x); |
---|
7738 | factors= biFactorize (bufA, info); |
---|
7739 | reverseSubst (factors, subCheck, x); |
---|
7740 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
7741 | swap, swap2, N); |
---|
7742 | if (!extension) |
---|
7743 | normalize (factors); |
---|
7744 | return factors; |
---|
7745 | } |
---|
7746 | } |
---|
7747 | |
---|
7748 | if (!derivXZero && !fail2 && !symmetric && subCheck2 > 0) |
---|
7749 | { |
---|
7750 | int subCheck= substituteCheck (bufUniFactors2); |
---|
7751 | |
---|
7752 | if (subCheck > 1 && (subCheck2%subCheck == 0)) |
---|
7753 | { |
---|
7754 | CanonicalForm bufA= A; |
---|
7755 | subst (bufA, bufA, subCheck, y); |
---|
7756 | factors= biFactorize (bufA, info); |
---|
7757 | reverseSubst (factors, subCheck, y); |
---|
7758 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
7759 | swap, swap2, N); |
---|
7760 | if (!extension) |
---|
7761 | normalize (factors); |
---|
7762 | return factors; |
---|
7763 | } |
---|
7764 | } |
---|
7765 | } |
---|
7766 | |
---|
7767 | // degree analysis |
---|
7768 | bufDegs = DegreePattern (bufUniFactors); |
---|
7769 | if (!derivXZero && !fail2 && !symmetric) |
---|
7770 | bufDegs2= DegreePattern (bufUniFactors2); |
---|
7771 | |
---|
7772 | if (i == 0) |
---|
7773 | { |
---|
7774 | Aeval= bufAeval; |
---|
7775 | evaluation= bufEvaluation; |
---|
7776 | uniFactors= bufUniFactors; |
---|
7777 | degs= bufDegs; |
---|
7778 | if (!derivXZero && !fail2 && !symmetric) |
---|
7779 | { |
---|
7780 | Aeval2= bufAeval2; |
---|
7781 | evaluation2= bufEvaluation2; |
---|
7782 | uniFactors2= bufUniFactors2; |
---|
7783 | degs2= bufDegs2; |
---|
7784 | } |
---|
7785 | } |
---|
7786 | else |
---|
7787 | { |
---|
7788 | degs.intersect (bufDegs); |
---|
7789 | if (!derivXZero && !fail2 && !symmetric) |
---|
7790 | { |
---|
7791 | degs2.intersect (bufDegs2); |
---|
7792 | if (bufUniFactors2.length() < uniFactors2.length()) |
---|
7793 | { |
---|
7794 | uniFactors2= bufUniFactors2; |
---|
7795 | Aeval2= bufAeval2; |
---|
7796 | evaluation2= bufEvaluation2; |
---|
7797 | } |
---|
7798 | } |
---|
7799 | if (bufUniFactors.length() < uniFactors.length()) |
---|
7800 | { |
---|
7801 | uniFactors= bufUniFactors; |
---|
7802 | Aeval= bufAeval; |
---|
7803 | evaluation= bufEvaluation; |
---|
7804 | } |
---|
7805 | } |
---|
7806 | list.append (bufEvaluation); |
---|
7807 | if (!derivXZero && !fail2 && !symmetric) |
---|
7808 | list2.append (bufEvaluation2); |
---|
7809 | } |
---|
7810 | |
---|
7811 | if (!derivXZero && !fail2 && !symmetric) |
---|
7812 | { |
---|
7813 | if (uniFactors.length() > uniFactors2.length() || |
---|
7814 | (uniFactors.length() == uniFactors2.length() |
---|
7815 | && degs.getLength() > degs2.getLength())) |
---|
7816 | { |
---|
7817 | degs= degs2; |
---|
7818 | uniFactors= uniFactors2; |
---|
7819 | evaluation= evaluation2; |
---|
7820 | Aeval= Aeval2; |
---|
7821 | A= buf; |
---|
7822 | swap2= true; |
---|
7823 | } |
---|
7824 | } |
---|
7825 | |
---|
7826 | if (degs.getLength() == 1) // A is irreducible |
---|
7827 | { |
---|
7828 | if (extension) |
---|
7829 | { |
---|
7830 | CFList source, dest; |
---|
7831 | appendMapDown (factors, A, info, source, dest); |
---|
7832 | } |
---|
7833 | else |
---|
7834 | factors.append (A); |
---|
7835 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
7836 | swap, swap2, N); |
---|
7837 | if (!extension) |
---|
7838 | normalize (factors); |
---|
7839 | return factors; |
---|
7840 | } |
---|
7841 | |
---|
7842 | int liftBound= degree (A, y) + 1; |
---|
7843 | |
---|
7844 | if (swap2) |
---|
7845 | bounds= computeBounds (A, boundsLength, isIrreducible); |
---|
7846 | |
---|
7847 | int minBound= bounds[0]; |
---|
7848 | for (int i= 1; i < boundsLength; i++) |
---|
7849 | { |
---|
7850 | if (bounds[i] != 0) |
---|
7851 | minBound= tmin (minBound, bounds[i]); |
---|
7852 | } |
---|
7853 | |
---|
7854 | TIMING_START (fac_fq_bi_shift_to_zero); |
---|
7855 | A= A (y + evaluation, y); |
---|
7856 | TIMING_END_AND_PRINT (fac_fq_bi_shift_to_zero, |
---|
7857 | "time to shift eval to zero: "); |
---|
7858 | |
---|
7859 | int degMipo= 1; |
---|
7860 | if (extension && alpha.level() != 1 && k==1) |
---|
7861 | degMipo= degree (getMipo (alpha)); |
---|
7862 | |
---|
7863 | DEBOUTLN (cerr, "uniFactors= " << uniFactors); |
---|
7864 | |
---|
7865 | if ((GF && !extension) || (GF && extension && k != 1)) |
---|
7866 | { |
---|
7867 | bool earlySuccess= false; |
---|
7868 | CFList earlyFactors; |
---|
7869 | TIMING_START (fac_fq_bi_hensel_lift); |
---|
7870 | uniFactors= henselLiftAndEarly |
---|
7871 | (A, earlySuccess, earlyFactors, degs, liftBound, |
---|
7872 | uniFactors, info, evaluation); |
---|
7873 | TIMING_END_AND_PRINT (fac_fq_bi_hensel_lift, |
---|
7874 | "time for bivariate hensel lifting over Fq: "); |
---|
7875 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
7876 | |
---|
7877 | CanonicalForm MODl= power (y, liftBound); |
---|
7878 | |
---|
7879 | TIMING_START (fac_fq_bi_factor_recombination); |
---|
7880 | if (extension) |
---|
7881 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
7882 | evaluation, 1, uniFactors.length()/2); |
---|
7883 | else |
---|
7884 | factors= factorRecombination (uniFactors, A, MODl, degs, 1, |
---|
7885 | uniFactors.length()/2); |
---|
7886 | TIMING_END_AND_PRINT (fac_fq_bi_factor_recombination, |
---|
7887 | "time for naive bivariate factor recombi over Fq: "); |
---|
7888 | |
---|
7889 | if (earlySuccess) |
---|
7890 | factors= Union (earlyFactors, factors); |
---|
7891 | else if (!earlySuccess && degs.getLength() == 1) |
---|
7892 | factors= earlyFactors; |
---|
7893 | } |
---|
7894 | else if (degree (A) > 4 && beta.level() == 1 && (2*minBound)/degMipo < 32) |
---|
7895 | { |
---|
7896 | TIMING_START (fac_fq_bi_hensel_lift); |
---|
7897 | if (extension) |
---|
7898 | { |
---|
7899 | CFList lll= extHenselLiftAndLatticeRecombi (A, uniFactors, info, degs, |
---|
7900 | evaluation |
---|
7901 | ); |
---|
7902 | factors= Union (lll, factors); |
---|
7903 | } |
---|
7904 | else if (alpha.level() == 1 && !GF) |
---|
7905 | { |
---|
7906 | CFList lll= henselLiftAndLatticeRecombi (A, uniFactors, alpha, degs, |
---|
7907 | symmetric, evaluation); |
---|
7908 | factors= Union (lll, factors); |
---|
7909 | } |
---|
7910 | else if (!extension && (alpha != x || GF)) |
---|
7911 | { |
---|
7912 | CFList lll= henselLiftAndLatticeRecombi (A, uniFactors, alpha, degs, |
---|
7913 | symmetric, evaluation); |
---|
7914 | factors= Union (lll, factors); |
---|
7915 | } |
---|
7916 | TIMING_END_AND_PRINT (fac_fq_bi_hensel_lift, |
---|
7917 | "time to bivar lift and LLL recombi over Fq: "); |
---|
7918 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
7919 | } |
---|
7920 | else |
---|
7921 | { |
---|
7922 | bool earlySuccess= false; |
---|
7923 | CFList earlyFactors; |
---|
7924 | TIMING_START (fac_fq_bi_hensel_lift); |
---|
7925 | uniFactors= henselLiftAndEarly |
---|
7926 | (A, earlySuccess, earlyFactors, degs, liftBound, |
---|
7927 | uniFactors, info, evaluation); |
---|
7928 | TIMING_END_AND_PRINT (fac_fq_bi_hensel_lift, |
---|
7929 | "time for bivar hensel lifting over Fq: "); |
---|
7930 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
7931 | |
---|
7932 | CanonicalForm MODl= power (y, liftBound); |
---|
7933 | if (!extension) |
---|
7934 | { |
---|
7935 | TIMING_START (fac_fq_bi_factor_recombination); |
---|
7936 | factors= factorRecombination (uniFactors, A, MODl, degs, 1, 3); |
---|
7937 | TIMING_END_AND_PRINT (fac_fq_bi_factor_recombination, |
---|
7938 | "time for small subset naive recombi over Fq: "); |
---|
7939 | |
---|
7940 | int oldUniFactorsLength= uniFactors.length(); |
---|
7941 | if (degree (A) > 0) |
---|
7942 | { |
---|
7943 | CFList tmp; |
---|
7944 | TIMING_START (fac_fq_bi_hensel_lift); |
---|
7945 | if (alpha.level() == 1) |
---|
7946 | tmp= increasePrecision (A, uniFactors, 0, uniFactors.length(), 1, |
---|
7947 | liftBound |
---|
7948 | ); |
---|
7949 | else |
---|
7950 | { |
---|
7951 | if (degree (A) > getCharacteristic()) |
---|
7952 | tmp= increasePrecisionFq2Fp (A, uniFactors, 0, uniFactors.length(), |
---|
7953 | 1, alpha, liftBound |
---|
7954 | ); |
---|
7955 | else |
---|
7956 | tmp= increasePrecision (A, uniFactors, 0, uniFactors.length(), 1, |
---|
7957 | alpha, liftBound |
---|
7958 | ); |
---|
7959 | } |
---|
7960 | TIMING_END_AND_PRINT (fac_fq_bi_hensel_lift, |
---|
7961 | "time to increase precision: "); |
---|
7962 | factors= Union (factors, tmp); |
---|
7963 | if (tmp.length() == 0 || (tmp.length() > 0 && uniFactors.length() != 0 |
---|
7964 | && uniFactors.length() != oldUniFactorsLength) |
---|
7965 | ) |
---|
7966 | { |
---|
7967 | DegreePattern bufDegs= DegreePattern (uniFactors); |
---|
7968 | degs.intersect (bufDegs); |
---|
7969 | degs.refine (); |
---|
7970 | factors= Union (factors, factorRecombination (uniFactors, A, MODl, |
---|
7971 | degs, 4, |
---|
7972 | uniFactors.length()/2 |
---|
7973 | ) |
---|
7974 | ); |
---|
7975 | } |
---|
7976 | } |
---|
7977 | } |
---|
7978 | else |
---|
7979 | { |
---|
7980 | if (beta.level() != 1 || k > 1) |
---|
7981 | { |
---|
7982 | if (k > 1) |
---|
7983 | { |
---|
7984 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
7985 | evaluation, 1, uniFactors.length()/2 |
---|
7986 | ); |
---|
7987 | } |
---|
7988 | else |
---|
7989 | { |
---|
7990 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
7991 | evaluation, 1, 3 |
---|
7992 | ); |
---|
7993 | if (degree (A) > 0) |
---|
7994 | { |
---|
7995 | CFList tmp= increasePrecision2 (A, uniFactors, alpha, liftBound); |
---|
7996 | DegreePattern bufDegs= DegreePattern (tmp); |
---|
7997 | degs.intersect (bufDegs); |
---|
7998 | degs.refine (); |
---|
7999 | factors= Union (factors, extFactorRecombination (tmp, A, MODl, info, |
---|
8000 | degs, evaluation, |
---|
8001 | 1, tmp.length()/2 |
---|
8002 | ) |
---|
8003 | ); |
---|
8004 | } |
---|
8005 | } |
---|
8006 | } |
---|
8007 | else |
---|
8008 | { |
---|
8009 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
8010 | evaluation, 1, 3 |
---|
8011 | ); |
---|
8012 | int oldUniFactorsLength= uniFactors.length(); |
---|
8013 | if (degree (A) > 0) |
---|
8014 | { |
---|
8015 | int degMipo; |
---|
8016 | ExtensionInfo info2= init4ext (info, evaluation, degMipo); |
---|
8017 | |
---|
8018 | CFList source, dest; |
---|
8019 | CFList tmp= extIncreasePrecision (A, uniFactors, 0, |
---|
8020 | uniFactors.length(), 1, evaluation, |
---|
8021 | info2, source, dest, liftBound |
---|
8022 | ); |
---|
8023 | factors= Union (factors, tmp); |
---|
8024 | if (tmp.length() == 0 || (tmp.length() > 0 && uniFactors.length() != 0 |
---|
8025 | && uniFactors.length() != oldUniFactorsLength) |
---|
8026 | ) |
---|
8027 | { |
---|
8028 | DegreePattern bufDegs= DegreePattern (uniFactors); |
---|
8029 | degs.intersect (bufDegs); |
---|
8030 | degs.refine (); |
---|
8031 | factors= Union (factors,extFactorRecombination (uniFactors, A, MODl, |
---|
8032 | info, degs, evaluation, |
---|
8033 | 4, uniFactors.length()/2 |
---|
8034 | ) |
---|
8035 | ); |
---|
8036 | } |
---|
8037 | } |
---|
8038 | } |
---|
8039 | } |
---|
8040 | |
---|
8041 | if (earlySuccess) |
---|
8042 | factors= Union (earlyFactors, factors); |
---|
8043 | else if (!earlySuccess && degs.getLength() == 1) |
---|
8044 | factors= earlyFactors; |
---|
8045 | } |
---|
8046 | delete [] bounds; |
---|
8047 | if (!extension) |
---|
8048 | { |
---|
8049 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
8050 | i.getItem()= i.getItem() (y - evaluation, y); |
---|
8051 | } |
---|
8052 | |
---|
8053 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
8054 | swap, swap2, N); |
---|
8055 | if (!extension) |
---|
8056 | normalize (factors); |
---|
8057 | |
---|
8058 | return factors; |
---|
8059 | } |
---|
8060 | |
---|
8061 | CFList |
---|
8062 | extBiFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
8063 | { |
---|
8064 | |
---|
8065 | CanonicalForm A= F; |
---|
8066 | Variable alpha= info.getAlpha(); |
---|
8067 | Variable beta= info.getBeta(); |
---|
8068 | int k= info.getGFDegree(); |
---|
8069 | char cGFName= info.getGFName(); |
---|
8070 | CanonicalForm delta= info.getDelta(); |
---|
8071 | |
---|
8072 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
8073 | Variable x= Variable (1); |
---|
8074 | CFList factors; |
---|
8075 | if (!GF && alpha == x) // we are in F_p |
---|
8076 | { |
---|
8077 | bool extension= true; |
---|
8078 | int p= getCharacteristic(); |
---|
8079 | if (p*p < (1<<16)) // pass to GF if possible |
---|
8080 | { |
---|
8081 | setCharacteristic (getCharacteristic(), 2, 'Z'); |
---|
8082 | A= A.mapinto(); |
---|
8083 | ExtensionInfo info2= ExtensionInfo (extension); |
---|
8084 | factors= biFactorize (A, info2); |
---|
8085 | |
---|
8086 | CanonicalForm mipo= gf_mipo; |
---|
8087 | setCharacteristic (getCharacteristic()); |
---|
8088 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
8089 | for (CFListIterator j= factors; j.hasItem(); j++) |
---|
8090 | j.getItem()= GF2FalphaRep (j.getItem(), vBuf); |
---|
8091 | } |
---|
8092 | else // not able to pass to GF, pass to F_p(\alpha) |
---|
8093 | { |
---|
8094 | CanonicalForm mipo= randomIrredpoly (2, x); |
---|
8095 | Variable v= rootOf (mipo); |
---|
8096 | ExtensionInfo info2= ExtensionInfo (v); |
---|
8097 | factors= biFactorize (A, info2); |
---|
8098 | } |
---|
8099 | return factors; |
---|
8100 | } |
---|
8101 | else if (!GF && (alpha != x)) // we are in F_p(\alpha) |
---|
8102 | { |
---|
8103 | if (k == 1) // need factorization over F_p |
---|
8104 | { |
---|
8105 | int extDeg= degree (getMipo (alpha)); |
---|
8106 | extDeg++; |
---|
8107 | CanonicalForm mipo= randomIrredpoly (extDeg + 1, x); |
---|
8108 | Variable v= rootOf (mipo); |
---|
8109 | ExtensionInfo info2= ExtensionInfo (v); |
---|
8110 | factors= biFactorize (A, info2); |
---|
8111 | } |
---|
8112 | else |
---|
8113 | { |
---|
8114 | if (beta == x) |
---|
8115 | { |
---|
8116 | Variable v= chooseExtension (alpha, beta, k); |
---|
8117 | CanonicalForm primElem, imPrimElem; |
---|
8118 | bool primFail= false; |
---|
8119 | Variable vBuf; |
---|
8120 | primElem= primitiveElement (alpha, vBuf, primFail); |
---|
8121 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
8122 | if (primFail) |
---|
8123 | ; //ERROR |
---|
8124 | else |
---|
8125 | imPrimElem= mapPrimElem (primElem, alpha, v); |
---|
8126 | |
---|
8127 | CFList source, dest; |
---|
8128 | CanonicalForm bufA= mapUp (A, alpha, v, primElem, imPrimElem, |
---|
8129 | source, dest); |
---|
8130 | ExtensionInfo info2= ExtensionInfo (v, alpha, imPrimElem, primElem); |
---|
8131 | factors= biFactorize (bufA, info2); |
---|
8132 | } |
---|
8133 | else |
---|
8134 | { |
---|
8135 | Variable v= chooseExtension (alpha, beta, k); |
---|
8136 | CanonicalForm primElem, imPrimElem; |
---|
8137 | bool primFail= false; |
---|
8138 | Variable vBuf; |
---|
8139 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
8140 | if (primFail) |
---|
8141 | ; //ERROR |
---|
8142 | else |
---|
8143 | imPrimElem= mapPrimElem (delta, beta, v); |
---|
8144 | |
---|
8145 | CFList source, dest; |
---|
8146 | CanonicalForm bufA= mapDown (A, info, source, dest); |
---|
8147 | source= CFList(); |
---|
8148 | dest= CFList(); |
---|
8149 | bufA= mapUp (bufA, beta, v, delta, imPrimElem, source, dest); |
---|
8150 | ExtensionInfo info2= ExtensionInfo (v, beta, imPrimElem, delta); |
---|
8151 | factors= biFactorize (bufA, info2); |
---|
8152 | } |
---|
8153 | } |
---|
8154 | return factors; |
---|
8155 | } |
---|
8156 | else // we are in GF (p^k) |
---|
8157 | { |
---|
8158 | int p= getCharacteristic(); |
---|
8159 | int extensionDeg= getGFDegree(); |
---|
8160 | bool extension= true; |
---|
8161 | if (k == 1) // need factorization over F_p |
---|
8162 | { |
---|
8163 | extensionDeg++; |
---|
8164 | if (ipower (p, extensionDeg) < (1<<16)) |
---|
8165 | // pass to GF(p^k+1) |
---|
8166 | { |
---|
8167 | CanonicalForm mipo= gf_mipo; |
---|
8168 | setCharacteristic (p); |
---|
8169 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
8170 | A= GF2FalphaRep (A, vBuf); |
---|
8171 | setCharacteristic (p, extensionDeg, 'Z'); |
---|
8172 | ExtensionInfo info2= ExtensionInfo (extension); |
---|
8173 | factors= biFactorize (A.mapinto(), info2); |
---|
8174 | } |
---|
8175 | else // not able to pass to another GF, pass to F_p(\alpha) |
---|
8176 | { |
---|
8177 | CanonicalForm mipo= gf_mipo; |
---|
8178 | setCharacteristic (p); |
---|
8179 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
8180 | A= GF2FalphaRep (A, vBuf); |
---|
8181 | Variable v= chooseExtension (vBuf, beta, k); |
---|
8182 | ExtensionInfo info2= ExtensionInfo (v, extension); |
---|
8183 | factors= biFactorize (A, info2); |
---|
8184 | } |
---|
8185 | } |
---|
8186 | else // need factorization over GF (p^k) |
---|
8187 | { |
---|
8188 | if (ipower (p, 2*extensionDeg) < (1<<16)) |
---|
8189 | // pass to GF (p^2k) |
---|
8190 | { |
---|
8191 | setCharacteristic (p, 2*extensionDeg, 'Z'); |
---|
8192 | ExtensionInfo info2= ExtensionInfo (k, cGFName, extension); |
---|
8193 | factors= biFactorize (GFMapUp (A, extensionDeg), info2); |
---|
8194 | setCharacteristic (p, extensionDeg, cGFName); |
---|
8195 | } |
---|
8196 | else // not able to pass to GF (p^2k), pass to F_p (\alpha) |
---|
8197 | { |
---|
8198 | CanonicalForm mipo= gf_mipo; |
---|
8199 | setCharacteristic (p); |
---|
8200 | Variable v1= rootOf (mipo.mapinto()); |
---|
8201 | A= GF2FalphaRep (A, v1); |
---|
8202 | Variable v2= chooseExtension (v1, v1, k); |
---|
8203 | CanonicalForm primElem, imPrimElem; |
---|
8204 | bool primFail= false; |
---|
8205 | Variable vBuf; |
---|
8206 | primElem= primitiveElement (v1, vBuf, primFail); |
---|
8207 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
8208 | if (primFail) |
---|
8209 | ; //ERROR |
---|
8210 | else |
---|
8211 | imPrimElem= mapPrimElem (primElem, v1, v2); |
---|
8212 | |
---|
8213 | CFList source, dest; |
---|
8214 | CanonicalForm bufA= mapUp (A, v1, v2, primElem, imPrimElem, |
---|
8215 | source, dest); |
---|
8216 | ExtensionInfo info2= ExtensionInfo (v2, v1, imPrimElem, primElem); |
---|
8217 | factors= biFactorize (bufA, info2); |
---|
8218 | setCharacteristic (p, k, cGFName); |
---|
8219 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
8220 | i.getItem()= Falpha2GFRep (i.getItem()); |
---|
8221 | } |
---|
8222 | } |
---|
8223 | return factors; |
---|
8224 | } |
---|
8225 | } |
---|
8226 | |
---|
8227 | #endif |
---|
8228 | /* HAVE_NTL */ |
---|
8229 | |
---|
8230 | |
---|