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 | * @internal @version \$Id$ |
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17 | * |
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18 | **/ |
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19 | /*****************************************************************************/ |
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20 | |
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21 | #include "config.h" |
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22 | |
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23 | #include "cf_assert.h" |
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24 | #include "debug.h" |
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25 | #include "timing.h" |
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26 | |
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27 | #include "canonicalform.h" |
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28 | #include "cf_defs.h" |
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29 | #include "cf_map_ext.h" |
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30 | #include "cf_random.h" |
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31 | #include "facHensel.h" |
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32 | #include "cf_map.h" |
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33 | #include "cf_gcd_smallp.h" |
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34 | #include "facFqBivarUtil.h" |
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35 | #include "facFqBivar.h" |
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36 | #include "cfNewtonPolygon.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 | TIMING_DEFINE_PRINT(fac_uni_factorizer) |
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42 | TIMING_DEFINE_PRINT(fac_hensel_lift) |
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43 | TIMING_DEFINE_PRINT(fac_factor_recombination) |
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44 | |
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45 | CanonicalForm prodMod0 (const CFList& L, const CanonicalForm& M) |
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46 | { |
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47 | if (L.isEmpty()) |
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48 | return 1; |
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49 | else if (L.length() == 1) |
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50 | return mod (L.getFirst()(0, 1) , M); |
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51 | else if (L.length() == 2) |
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52 | return mod (L.getFirst()(0, 1)*L.getLast()(0, 1), M); |
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53 | else |
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54 | { |
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55 | int l= L.length()/2; |
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56 | CFListIterator i= L; |
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57 | CFList tmp1, tmp2; |
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58 | CanonicalForm buf1, buf2; |
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59 | for (int j= 1; j <= l; j++, i++) |
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60 | tmp1.append (i.getItem()); |
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61 | tmp2= Difference (L, tmp1); |
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62 | buf1= prodMod0 (tmp1, M); |
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63 | buf2= prodMod0 (tmp2, M); |
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64 | return mod (buf1*buf2, M); |
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65 | } |
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66 | } |
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67 | |
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68 | CanonicalForm evalPoint (const CanonicalForm& F, CanonicalForm & eval, |
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69 | const Variable& alpha, CFList& list, const bool& GF, |
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70 | bool& fail) |
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71 | { |
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72 | fail= false; |
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73 | Variable x= Variable(2); |
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74 | Variable y= Variable(1); |
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75 | FFRandom genFF; |
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76 | GFRandom genGF; |
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77 | CanonicalForm random, mipo; |
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78 | double bound; |
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79 | int p= getCharacteristic (); |
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80 | if (alpha.level() != 1) |
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81 | { |
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82 | mipo= getMipo (alpha); |
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83 | int d= degree (mipo); |
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84 | bound= ipower (p, d); |
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85 | } |
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86 | else if (GF) |
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87 | { |
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88 | int d= getGFDegree(); |
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89 | bound= ipower (p, d); |
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90 | } |
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91 | else |
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92 | bound= p; |
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93 | |
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94 | random= 0; |
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95 | do |
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96 | { |
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97 | if (list.length() >= bound) |
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98 | { |
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99 | fail= true; |
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100 | break; |
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101 | } |
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102 | if (list.isEmpty()) |
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103 | random= 0; |
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104 | else if (GF) |
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105 | { |
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106 | if (list.length() == 1) |
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107 | random= getGFGenerator(); |
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108 | else |
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109 | random= genGF.generate(); |
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110 | } |
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111 | else if (list.length() < p || alpha.level() == 1) |
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112 | random= genFF.generate(); |
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113 | else if (alpha != x && list.length() >= p) |
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114 | { |
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115 | if (list.length() == p) |
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116 | random= alpha; |
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117 | else |
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118 | { |
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119 | AlgExtRandomF genAlgExt (alpha); |
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120 | random= genAlgExt.generate(); |
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121 | } |
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122 | } |
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123 | if (find (list, random)) continue; |
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124 | eval= F (random, x); |
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125 | if (degree (eval) != degree (F, y)) |
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126 | { //leading coeff vanishes |
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127 | if (!find (list, random)) |
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128 | list.append (random); |
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129 | continue; |
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130 | } |
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131 | if (degree (gcd (deriv (eval, eval.mvar()), eval), eval.mvar()) > 0) |
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132 | { //evaluated polynomial is not squarefree |
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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 | } while (find (list, random)); |
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138 | |
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139 | return random; |
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140 | } |
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141 | |
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142 | CFList |
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143 | uniFactorizer (const CanonicalForm& A, const Variable& alpha, const bool& GF) |
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144 | { |
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145 | Variable x= A.mvar(); |
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146 | ASSERT (A.isUnivariate(), "univariate polynomial expected"); |
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147 | CFFList factorsA; |
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148 | ZZ p= to_ZZ (getCharacteristic()); |
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149 | ZZ_p::init (p); |
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150 | if (GF) |
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151 | { |
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152 | Variable beta= rootOf (gf_mipo); |
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153 | int k= getGFDegree(); |
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154 | char cGFName= gf_name; |
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155 | setCharacteristic (getCharacteristic()); |
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156 | CanonicalForm buf= GF2FalphaRep (A, beta); |
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157 | if (getCharacteristic() > 2) |
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158 | { |
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159 | ZZ_pX NTLMipo= convertFacCF2NTLZZpX (gf_mipo); |
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160 | ZZ_pE::init (NTLMipo); |
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161 | ZZ_pEX NTLA= convertFacCF2NTLZZ_pEX (buf, NTLMipo); |
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162 | MakeMonic (NTLA); |
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163 | vec_pair_ZZ_pEX_long NTLFactorsA= CanZass (NTLA); |
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164 | ZZ_pE multi= to_ZZ_pE (1); |
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165 | factorsA= convertNTLvec_pair_ZZpEX_long2FacCFFList (NTLFactorsA, multi, |
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166 | x, beta); |
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167 | } |
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168 | else |
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169 | { |
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170 | GF2X NTLMipo= convertFacCF2NTLGF2X (gf_mipo); |
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171 | GF2E::init (NTLMipo); |
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172 | GF2EX NTLA= convertFacCF2NTLGF2EX (buf, NTLMipo); |
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173 | MakeMonic (NTLA); |
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174 | vec_pair_GF2EX_long NTLFactorsA= CanZass (NTLA); |
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175 | GF2E multi= to_GF2E (1); |
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176 | factorsA= convertNTLvec_pair_GF2EX_long2FacCFFList (NTLFactorsA, multi, |
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177 | x, beta); |
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178 | } |
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179 | setCharacteristic (getCharacteristic(), k, cGFName); |
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180 | for (CFFListIterator i= factorsA; i.hasItem(); i++) |
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181 | { |
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182 | buf= i.getItem().factor(); |
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183 | buf= Falpha2GFRep (buf); |
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184 | i.getItem()= CFFactor (buf, i.getItem().exp()); |
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185 | } |
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186 | } |
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187 | else if (alpha.level() != 1) |
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188 | { |
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189 | if (getCharacteristic() > 2) |
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190 | { |
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191 | ZZ_pX NTLMipo= convertFacCF2NTLZZpX (getMipo (alpha)); |
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192 | ZZ_pE::init (NTLMipo); |
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193 | ZZ_pEX NTLA= convertFacCF2NTLZZ_pEX (A, NTLMipo); |
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194 | MakeMonic (NTLA); |
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195 | vec_pair_ZZ_pEX_long NTLFactorsA= CanZass (NTLA); |
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196 | ZZ_pE multi= to_ZZ_pE (1); |
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197 | factorsA= convertNTLvec_pair_ZZpEX_long2FacCFFList (NTLFactorsA, multi, |
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198 | x, alpha); |
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199 | } |
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200 | else |
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201 | { |
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202 | GF2X NTLMipo= convertFacCF2NTLGF2X (getMipo (alpha)); |
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203 | GF2E::init (NTLMipo); |
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204 | GF2EX NTLA= convertFacCF2NTLGF2EX (A, NTLMipo); |
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205 | MakeMonic (NTLA); |
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206 | vec_pair_GF2EX_long NTLFactorsA= CanZass (NTLA); |
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207 | GF2E multi= to_GF2E (1); |
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208 | factorsA= convertNTLvec_pair_GF2EX_long2FacCFFList (NTLFactorsA, multi, |
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209 | x, alpha); |
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210 | } |
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211 | } |
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212 | else |
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213 | { |
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214 | if (getCharacteristic() > 2) |
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215 | { |
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216 | ZZ_pX NTLA= convertFacCF2NTLZZpX (A); |
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217 | MakeMonic (NTLA); |
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218 | vec_pair_ZZ_pX_long NTLFactorsA= CanZass (NTLA); |
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219 | ZZ_p multi= to_ZZ_p (1); |
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220 | factorsA= convertNTLvec_pair_ZZpX_long2FacCFFList (NTLFactorsA, multi, |
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221 | x); |
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222 | } |
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223 | else |
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224 | { |
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225 | GF2X NTLA= convertFacCF2NTLGF2X (A); |
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226 | vec_pair_GF2X_long NTLFactorsA= CanZass (NTLA); |
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227 | GF2 multi= to_GF2 (1); |
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228 | factorsA= convertNTLvec_pair_GF2X_long2FacCFFList (NTLFactorsA, multi, |
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229 | x); |
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230 | } |
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231 | } |
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232 | CFList uniFactors; |
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233 | for (CFFListIterator i= factorsA; i.hasItem(); i++) |
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234 | uniFactors.append (i.getItem().factor()); |
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235 | return uniFactors; |
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236 | } |
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237 | |
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238 | /// naive factor recombination as decribed in "Factoring |
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239 | /// multivariate polynomials over a finite field" by L Bernardin. |
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240 | CFList |
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241 | extFactorRecombination (CFList& factors, CanonicalForm& F, |
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242 | const CanonicalForm& M, const ExtensionInfo& info, |
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243 | DegreePattern& degs, const CanonicalForm& eval, int s, |
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244 | int thres) |
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245 | { |
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246 | if (factors.length() == 0) |
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247 | { |
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248 | F= 1; |
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249 | return CFList(); |
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250 | } |
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251 | |
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252 | Variable alpha= info.getAlpha(); |
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253 | Variable beta= info.getBeta(); |
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254 | CanonicalForm gamma= info.getGamma(); |
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255 | CanonicalForm delta= info.getDelta(); |
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256 | int k= info.getGFDegree(); |
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257 | |
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258 | Variable y= F.mvar(); |
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259 | Variable x= Variable (1); |
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260 | CFList source, dest; |
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261 | if (degs.getLength() <= 1 || factors.length() == 1) |
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262 | { |
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263 | CFList result= CFList(mapDown (F(y-eval, y), info, source, dest)); |
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264 | F= 1; |
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265 | return result; |
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266 | } |
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267 | |
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268 | DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, M) == F " << |
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269 | (LC (F, 1)*prodMod (factors, M) == F)); |
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270 | int degMipoBeta= 1; |
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271 | if (!k && beta.level() != 1) |
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272 | degMipoBeta= degree (getMipo (beta)); |
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273 | |
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274 | CFList T, S, Diff; |
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275 | T= factors; |
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276 | |
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277 | CFList result; |
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278 | CanonicalForm buf, buf2, quot; |
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279 | |
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280 | buf= F; |
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281 | |
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282 | CanonicalForm g, LCBuf= LC (buf, x); |
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283 | int * v= new int [T.length()]; |
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284 | for (int i= 0; i < T.length(); i++) |
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285 | v[i]= 0; |
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286 | |
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287 | CFArray TT; |
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288 | DegreePattern bufDegs1, bufDegs2; |
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289 | bufDegs1= degs; |
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290 | int subsetDeg; |
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291 | TT= copy (factors); |
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292 | bool nosubset= false; |
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293 | bool recombination= false; |
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294 | bool trueFactor= false; |
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295 | while (T.length() >= 2*s && s <= thres) |
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296 | { |
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297 | while (nosubset == false) |
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298 | { |
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299 | if (T.length() == s) |
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300 | { |
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301 | delete [] v; |
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302 | if (recombination) |
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303 | { |
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304 | T.insert (LCBuf); |
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305 | g= prodMod (T, M); |
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306 | T.removeFirst(); |
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307 | g /= content(g); |
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308 | g= g (y - eval, y); |
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309 | g /= Lc (g); |
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310 | appendTestMapDown (result, g, info, source, dest); |
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311 | F= 1; |
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312 | return result; |
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313 | } |
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314 | else |
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315 | { |
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316 | appendMapDown (result, F (y - eval, y), info, source, dest); |
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317 | F= 1; |
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318 | return result; |
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319 | } |
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320 | } |
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321 | S= subset (v, s, TT, nosubset); |
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322 | if (nosubset) break; |
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323 | subsetDeg= subsetDegree (S); |
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324 | // skip those combinations that are not possible |
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325 | if (!degs.find (subsetDeg)) |
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326 | continue; |
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327 | else |
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328 | { |
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329 | g= prodMod0 (S, M); |
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330 | g= mod (g*LCBuf, M); |
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331 | g /= content (g); |
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332 | if (fdivides (LC (g), LCBuf)) |
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333 | { |
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334 | S.insert (LCBuf); |
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335 | g= prodMod (S, M); |
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336 | S.removeFirst(); |
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337 | g /= content (g, x); |
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338 | if (fdivides (g, buf, quot)) |
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339 | { |
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340 | buf2= g (y - eval, y); |
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341 | buf2 /= Lc (buf2); |
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342 | |
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343 | if (!k && beta.level() == 1) |
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344 | { |
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345 | if (degree (buf2, alpha) < degMipoBeta) |
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346 | { |
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347 | buf= quot; |
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348 | LCBuf= LC (buf, x); |
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349 | recombination= true; |
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350 | appendTestMapDown (result, buf2, info, source, dest); |
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351 | trueFactor= true; |
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352 | } |
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353 | } |
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354 | else |
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355 | { |
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356 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
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357 | { |
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358 | buf= quot; |
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359 | LCBuf= LC (buf, x); |
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360 | recombination= true; |
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361 | appendTestMapDown (result, buf2, info, source, dest); |
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362 | trueFactor= true; |
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363 | } |
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364 | } |
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365 | if (trueFactor) |
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366 | { |
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367 | T= Difference (T, S); |
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368 | // compute new possible degree pattern |
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369 | bufDegs2= DegreePattern (T); |
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370 | bufDegs1.intersect (bufDegs2); |
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371 | bufDegs1.refine (); |
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372 | if (T.length() < 2*s || T.length() == s || |
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373 | bufDegs1.getLength() == 1) |
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374 | { |
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375 | delete [] v; |
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376 | if (recombination) |
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377 | { |
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378 | appendTestMapDown (result, buf (y - eval, y), info, source, |
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379 | dest); |
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380 | F= 1; |
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381 | return result; |
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382 | } |
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383 | else |
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384 | { |
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385 | appendMapDown (result, F (y - eval, y), info, source, dest); |
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386 | F= 1; |
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387 | return result; |
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388 | } |
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389 | } |
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390 | trueFactor= false; |
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391 | TT= copy (T); |
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392 | indexUpdate (v, s, T.length(), nosubset); |
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393 | if (nosubset) break; |
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394 | } |
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395 | } |
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396 | } |
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397 | } |
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398 | } |
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399 | s++; |
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400 | if (T.length() < 2*s || T.length() == s) |
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401 | { |
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402 | delete [] v; |
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403 | if (recombination) |
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404 | { |
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405 | appendTestMapDown (result, buf (y - eval, y), info, source, dest); |
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406 | F= 1; |
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407 | return result; |
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408 | } |
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409 | else |
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410 | { |
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411 | appendMapDown (result, F (y - eval, y), info, source, dest); |
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412 | F= 1; |
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413 | return result; |
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414 | } |
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415 | } |
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416 | for (int i= 0; i < T.length(); i++) |
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417 | v[i]= 0; |
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418 | nosubset= false; |
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419 | } |
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420 | if (T.length() < 2*s) |
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421 | { |
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422 | appendMapDown (result, F (y - eval, y), info, source, dest); |
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423 | F= 1; |
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424 | delete [] v; |
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425 | return result; |
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426 | } |
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427 | |
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428 | if (s > thres) |
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429 | { |
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430 | factors= T; |
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431 | F= buf; |
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432 | degs= bufDegs1; |
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433 | } |
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434 | |
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435 | delete [] v; |
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436 | return result; |
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437 | } |
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438 | |
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439 | /// naive factor recombination as decribed in "Factoring |
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440 | /// multivariate polynomials over a finite field" by L Bernardin. |
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441 | CFList |
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442 | factorRecombination (CFList& factors, CanonicalForm& F, |
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443 | const CanonicalForm& M, DegreePattern& degs, int s, |
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444 | int thres |
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445 | ) |
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446 | { |
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447 | if (factors.length() == 0) |
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448 | { |
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449 | F= 1; |
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450 | return CFList (); |
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451 | } |
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452 | if (degs.getLength() <= 1 || factors.length() == 1) |
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453 | { |
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454 | CFList result= CFList (F); |
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455 | F= 1; |
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456 | return result; |
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457 | } |
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458 | DEBOUTLN (cerr, "LC (F, 1)*prodMod (factors, M) == F " << |
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459 | (LC (F, 1)*prodMod (factors, M) == F)); |
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460 | CFList T, S; |
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461 | |
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462 | T= factors; |
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463 | CFList result; |
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464 | Variable y= Variable (2); |
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465 | Variable x= Variable (1); |
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466 | CanonicalForm LCBuf= LC (F, x); |
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467 | CanonicalForm g, quot, buf= F; |
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468 | int * v= new int [T.length()]; |
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469 | for (int i= 0; i < T.length(); i++) |
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470 | v[i]= 0; |
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471 | bool nosubset= false; |
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472 | CFArray TT; |
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473 | DegreePattern bufDegs1, bufDegs2; |
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474 | bufDegs1= degs; |
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475 | int subsetDeg; |
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476 | TT= copy (factors); |
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477 | bool recombination= false; |
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478 | while (T.length() >= 2*s && s <= thres) |
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479 | { |
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480 | while (nosubset == false) |
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481 | { |
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482 | if (T.length() == s) |
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483 | { |
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484 | delete [] v; |
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485 | if (recombination) |
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486 | { |
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487 | T.insert (LCBuf); |
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488 | g= prodMod (T, M); |
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489 | T.removeFirst(); |
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490 | result.append (g/content (g, x)); |
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491 | F= 1; |
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492 | return result; |
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493 | } |
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494 | else |
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495 | { |
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496 | 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 | } |
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501 | S= subset (v, s, TT, nosubset); |
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502 | if (nosubset) break; |
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503 | subsetDeg= subsetDegree (S); |
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504 | // skip those combinations that are not possible |
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505 | if (!degs.find (subsetDeg)) |
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506 | continue; |
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507 | else |
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508 | { |
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509 | g= prodMod0 (S, M); |
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510 | g= mod (g*LCBuf, M); |
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511 | g /= content (g); |
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512 | if (fdivides (LC(g), LCBuf)) |
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513 | { |
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514 | S.insert (LCBuf); |
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515 | g= prodMod (S, M); |
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516 | S.removeFirst(); |
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517 | g /= content (g, x); |
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518 | |
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519 | if (fdivides (g, buf, quot)) |
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520 | { |
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521 | recombination= true; |
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522 | result.append (g); |
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523 | buf= quot; |
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524 | LCBuf= LC (buf, x); |
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525 | T= Difference (T, S); |
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526 | |
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527 | // compute new possible degree pattern |
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528 | bufDegs2= DegreePattern (T); |
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529 | bufDegs1.intersect (bufDegs2); |
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530 | bufDegs1.refine (); |
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531 | if (T.length() < 2*s || T.length() == s || |
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532 | bufDegs1.getLength() == 1) |
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533 | { |
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534 | delete [] v; |
---|
535 | if (recombination) |
---|
536 | { |
---|
537 | result.append (buf); |
---|
538 | F= 1; |
---|
539 | return result; |
---|
540 | } |
---|
541 | else |
---|
542 | { |
---|
543 | result= CFList (F); |
---|
544 | F= 1; |
---|
545 | return result; |
---|
546 | } |
---|
547 | } |
---|
548 | TT= copy (T); |
---|
549 | indexUpdate (v, s, T.length(), nosubset); |
---|
550 | if (nosubset) break; |
---|
551 | } |
---|
552 | } |
---|
553 | } |
---|
554 | } |
---|
555 | s++; |
---|
556 | if (T.length() < 2*s || T.length() == s) |
---|
557 | { |
---|
558 | delete [] v; |
---|
559 | if (recombination) |
---|
560 | { |
---|
561 | result.append (buf); |
---|
562 | F= 1; |
---|
563 | return result; |
---|
564 | } |
---|
565 | else |
---|
566 | { |
---|
567 | result= CFList (F); |
---|
568 | F= 1; |
---|
569 | return result; |
---|
570 | } |
---|
571 | } |
---|
572 | for (int i= 0; i < T.length(); i++) |
---|
573 | v[i]= 0; |
---|
574 | nosubset= false; |
---|
575 | } |
---|
576 | delete [] v; |
---|
577 | if (T.length() < 2*s) |
---|
578 | { |
---|
579 | result.append (F); |
---|
580 | F= 1; |
---|
581 | return result; |
---|
582 | } |
---|
583 | |
---|
584 | if (s > thres) |
---|
585 | { |
---|
586 | factors= T; |
---|
587 | F= buf; |
---|
588 | degs= bufDegs1; |
---|
589 | } |
---|
590 | |
---|
591 | return result; |
---|
592 | } |
---|
593 | |
---|
594 | Variable chooseExtension (const Variable & alpha, const Variable& beta, int k) |
---|
595 | { |
---|
596 | zz_p::init (getCharacteristic()); |
---|
597 | zz_pX NTLIrredpoly; |
---|
598 | int i, m; |
---|
599 | // extension of F_p needed |
---|
600 | if (alpha.level() == 1 && beta.level() == 1 && k == 1) |
---|
601 | { |
---|
602 | i= 1; |
---|
603 | m= 2; |
---|
604 | } //extension of F_p(alpha) needed but want to factorize over F_p |
---|
605 | else if (alpha.level() != 1 && beta.level() == 1 && k == 1) |
---|
606 | { |
---|
607 | i= 1; |
---|
608 | m= degree (getMipo (alpha)) + 1; |
---|
609 | } //extension of F_p(alpha) needed for first time |
---|
610 | else if (alpha.level() != 1 && beta.level() == 1 && k != 1) |
---|
611 | { |
---|
612 | i= 2; |
---|
613 | m= degree (getMipo (alpha)); |
---|
614 | } |
---|
615 | else if (alpha.level() != 1 && beta.level() != 1 && k != 1) |
---|
616 | { |
---|
617 | m= degree (getMipo (beta)); |
---|
618 | i= degree (getMipo (alpha))/m + 1; |
---|
619 | } |
---|
620 | BuildIrred (NTLIrredpoly, i*m); |
---|
621 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
622 | return rootOf (newMipo); |
---|
623 | } |
---|
624 | |
---|
625 | CFList |
---|
626 | earlyFactorDetection (CanonicalForm& F, CFList& factors,int& adaptedLiftBound, |
---|
627 | DegreePattern& degs, bool& success, int deg) |
---|
628 | { |
---|
629 | DegreePattern bufDegs1= degs; |
---|
630 | DegreePattern bufDegs2; |
---|
631 | CFList result; |
---|
632 | CFList T= factors; |
---|
633 | CanonicalForm buf= F; |
---|
634 | Variable x= Variable (1); |
---|
635 | CanonicalForm LCBuf= LC (buf, x); |
---|
636 | CanonicalForm g, quot; |
---|
637 | CanonicalForm M= power (F.mvar(), deg); |
---|
638 | adaptedLiftBound= 0; |
---|
639 | int d= degree (F); |
---|
640 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
641 | { |
---|
642 | if (!bufDegs1.find (degree (i.getItem(), 1))) |
---|
643 | continue; |
---|
644 | else |
---|
645 | { |
---|
646 | g= i.getItem() (0, 1); |
---|
647 | g *= LCBuf; |
---|
648 | g= mod (g, M); |
---|
649 | if (fdivides (LC (g), LCBuf)) |
---|
650 | { |
---|
651 | g= mulMod2 (i.getItem(), LCBuf, M); |
---|
652 | g /= content (g, x); |
---|
653 | if (fdivides (g, buf, quot)) |
---|
654 | { |
---|
655 | result.append (g); |
---|
656 | buf= quot; |
---|
657 | d -= degree (g); |
---|
658 | LCBuf= LC (buf, x); |
---|
659 | T= Difference (T, CFList (i.getItem())); |
---|
660 | |
---|
661 | // compute new possible degree pattern |
---|
662 | bufDegs2= DegreePattern (T); |
---|
663 | bufDegs1.intersect (bufDegs2); |
---|
664 | bufDegs1.refine (); |
---|
665 | if (bufDegs1.getLength() <= 1) |
---|
666 | { |
---|
667 | result.append (buf); |
---|
668 | break; |
---|
669 | } |
---|
670 | } |
---|
671 | } |
---|
672 | } |
---|
673 | } |
---|
674 | adaptedLiftBound= d + 1; |
---|
675 | if (adaptedLiftBound < deg) |
---|
676 | { |
---|
677 | factors= T; |
---|
678 | degs= bufDegs1; |
---|
679 | F= buf; |
---|
680 | success= true; |
---|
681 | } |
---|
682 | if (bufDegs1.getLength() <= 1) |
---|
683 | degs= bufDegs1; |
---|
684 | return result; |
---|
685 | } |
---|
686 | |
---|
687 | CFList |
---|
688 | extEarlyFactorDetection (CanonicalForm& F, CFList& factors, |
---|
689 | int& adaptedLiftBound, DegreePattern& degs, |
---|
690 | bool& success, const ExtensionInfo& info, |
---|
691 | const CanonicalForm& eval, int deg) |
---|
692 | { |
---|
693 | Variable alpha= info.getAlpha(); |
---|
694 | Variable beta= info.getBeta(); |
---|
695 | CanonicalForm gamma= info.getGamma(); |
---|
696 | CanonicalForm delta= info.getDelta(); |
---|
697 | int k= info.getGFDegree(); |
---|
698 | DegreePattern bufDegs1= degs, bufDegs2; |
---|
699 | CFList result; |
---|
700 | CFList T= factors; |
---|
701 | Variable y= F.mvar(); |
---|
702 | Variable x= Variable (1); |
---|
703 | CanonicalForm buf= F, LCBuf= LC (buf, x), g, buf2; |
---|
704 | CanonicalForm M= power (y, deg); |
---|
705 | adaptedLiftBound= 0; |
---|
706 | bool trueFactor= false; |
---|
707 | int d= degree (F); |
---|
708 | CFList source, dest; |
---|
709 | int degMipoBeta= 1; |
---|
710 | if (!k && beta.level() != 1) |
---|
711 | degMipoBeta= degree (getMipo (beta)); |
---|
712 | CanonicalForm quot; |
---|
713 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
714 | { |
---|
715 | if (!bufDegs1.find (degree (i.getItem(), 1))) |
---|
716 | continue; |
---|
717 | else |
---|
718 | { |
---|
719 | g= i.getItem() (0, 1); |
---|
720 | g *= LCBuf; |
---|
721 | g= mod (g, M); |
---|
722 | if (fdivides (LC (g), LCBuf)) |
---|
723 | { |
---|
724 | g= mulMod2 (i.getItem(), LCBuf, M); |
---|
725 | g /= content (g, x); |
---|
726 | if (fdivides (g, buf, quot)) |
---|
727 | { |
---|
728 | buf2= g (y - eval, y); |
---|
729 | buf2 /= Lc (buf2); |
---|
730 | |
---|
731 | if (!k && beta == x) |
---|
732 | { |
---|
733 | if (degree (buf2, alpha) < degMipoBeta) |
---|
734 | { |
---|
735 | appendTestMapDown (result, buf2, info, source, dest); |
---|
736 | buf= quot; |
---|
737 | d -= degree (g); |
---|
738 | LCBuf= LC (buf, x); |
---|
739 | trueFactor= true; |
---|
740 | } |
---|
741 | } |
---|
742 | else |
---|
743 | { |
---|
744 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
745 | { |
---|
746 | appendTestMapDown (result, buf2, info, source, dest); |
---|
747 | buf= quot; |
---|
748 | d -= degree (g); |
---|
749 | LCBuf= LC (buf, x); |
---|
750 | trueFactor= true; |
---|
751 | } |
---|
752 | } |
---|
753 | if (trueFactor) |
---|
754 | { |
---|
755 | T= Difference (T, CFList (i.getItem())); |
---|
756 | |
---|
757 | // compute new possible degree pattern |
---|
758 | bufDegs2= DegreePattern (T); |
---|
759 | bufDegs1.intersect (bufDegs2); |
---|
760 | bufDegs1.refine (); |
---|
761 | trueFactor= false; |
---|
762 | if (bufDegs1.getLength() <= 1) |
---|
763 | { |
---|
764 | buf= buf (y - eval, y); |
---|
765 | buf /= Lc (buf); |
---|
766 | appendMapDown (result, buf, info, source, dest); |
---|
767 | break; |
---|
768 | } |
---|
769 | } |
---|
770 | } |
---|
771 | } |
---|
772 | } |
---|
773 | } |
---|
774 | adaptedLiftBound= d + 1; |
---|
775 | if (adaptedLiftBound < deg) |
---|
776 | { |
---|
777 | success= true; |
---|
778 | factors= T; |
---|
779 | degs= bufDegs1; |
---|
780 | F= buf; |
---|
781 | } |
---|
782 | if (bufDegs1.getLength() <= 1) |
---|
783 | degs= bufDegs1; |
---|
784 | |
---|
785 | return result; |
---|
786 | } |
---|
787 | |
---|
788 | int* |
---|
789 | getCombinations (int * rightSide, int sizeOfRightSide, int& sizeOfOutput, |
---|
790 | int degreeLC) |
---|
791 | { |
---|
792 | Variable x= Variable (1); |
---|
793 | int p= getCharacteristic(); |
---|
794 | int d= getGFDegree(); |
---|
795 | char cGFName= gf_name; |
---|
796 | setCharacteristic(0); |
---|
797 | CanonicalForm buf= 1; |
---|
798 | for (int i= 0; i < sizeOfRightSide; i++) |
---|
799 | buf *= (power (x, rightSide [i]) + 1); |
---|
800 | |
---|
801 | int j= 0; |
---|
802 | for (CFIterator i= buf; i.hasTerms(); i++, j++) |
---|
803 | { |
---|
804 | if (i.exp() < degreeLC) |
---|
805 | { |
---|
806 | j++; |
---|
807 | break; |
---|
808 | } |
---|
809 | } |
---|
810 | |
---|
811 | ASSERT ( j > 1, "j > 1 expected" ); |
---|
812 | |
---|
813 | int* result = new int [j - 1]; |
---|
814 | sizeOfOutput= j - 1; |
---|
815 | |
---|
816 | int i= 0; |
---|
817 | for (CFIterator m = buf; i < j - 1; i++, m++) |
---|
818 | result [i]= m.exp(); |
---|
819 | |
---|
820 | if (d > 1) |
---|
821 | setCharacteristic (p, d, cGFName); |
---|
822 | else |
---|
823 | setCharacteristic (p); |
---|
824 | return result; |
---|
825 | } |
---|
826 | |
---|
827 | int * |
---|
828 | getLiftPrecisions (const CanonicalForm& F, int& sizeOfOutput, int degreeLC) |
---|
829 | { |
---|
830 | int sizeOfNewtonPoly; |
---|
831 | int ** newtonPolyg= newtonPolygon (F, sizeOfNewtonPoly); |
---|
832 | int sizeOfRightSide; |
---|
833 | int * rightSide= getRightSide(newtonPolyg, sizeOfNewtonPoly, sizeOfRightSide); |
---|
834 | int * result= getCombinations(rightSide, sizeOfRightSide, sizeOfOutput, |
---|
835 | degreeLC); |
---|
836 | delete [] rightSide; |
---|
837 | for (int i= 0; i < sizeOfNewtonPoly; i++) |
---|
838 | delete [] newtonPolyg[i]; |
---|
839 | delete [] newtonPolyg; |
---|
840 | return result; |
---|
841 | } |
---|
842 | |
---|
843 | CFList |
---|
844 | henselLiftAndEarly (CanonicalForm& A, bool& earlySuccess, CFList& |
---|
845 | earlyFactors, DegreePattern& degs, int& liftBound, |
---|
846 | const CFList& uniFactors, const ExtensionInfo& info, |
---|
847 | const CanonicalForm& eval) |
---|
848 | { |
---|
849 | Variable alpha= info.getAlpha(); |
---|
850 | Variable beta= info.getBeta(); |
---|
851 | CanonicalForm gamma= info.getGamma(); |
---|
852 | CanonicalForm delta= info.getDelta(); |
---|
853 | bool extension= info.isInExtension(); |
---|
854 | |
---|
855 | int sizeOfLiftPre; |
---|
856 | int * liftPre= getLiftPrecisions (A, sizeOfLiftPre, degree (LC (A, 1), 2)); |
---|
857 | |
---|
858 | Variable x= Variable (1); |
---|
859 | Variable y= Variable (2); |
---|
860 | CFArray Pi; |
---|
861 | CFList diophant; |
---|
862 | CFList bufUniFactors= uniFactors; |
---|
863 | bufUniFactors.insert (LC (A, x)); |
---|
864 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length() - 1); |
---|
865 | earlySuccess= false; |
---|
866 | int newLiftBound= 0; |
---|
867 | |
---|
868 | int smallFactorDeg= tmin (11, liftPre [sizeOfLiftPre- 1] + 1);//this is a tunable parameter |
---|
869 | int dummy; |
---|
870 | if (smallFactorDeg >= liftBound || degree (A,y) <= 4) |
---|
871 | henselLift12 (A, bufUniFactors, liftBound, Pi, diophant, M); |
---|
872 | else if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
873 | { |
---|
874 | henselLift12 (A, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
---|
875 | if (!extension) |
---|
876 | earlyFactors= earlyFactorDetection (A, bufUniFactors, newLiftBound, |
---|
877 | degs, earlySuccess, smallFactorDeg); |
---|
878 | else |
---|
879 | earlyFactors= extEarlyFactorDetection (A, bufUniFactors, |
---|
880 | newLiftBound, degs, earlySuccess, info, eval, |
---|
881 | smallFactorDeg); |
---|
882 | if (degs.getLength() > 1 && !earlySuccess && |
---|
883 | smallFactorDeg != liftPre [sizeOfLiftPre-1] + 1) |
---|
884 | { |
---|
885 | if (newLiftBound >= liftPre[sizeOfLiftPre-1]+1) |
---|
886 | { |
---|
887 | bufUniFactors.insert (LC (A, x)); |
---|
888 | henselLiftResume12 (A, bufUniFactors, smallFactorDeg, |
---|
889 | liftPre[sizeOfLiftPre-1] + 1, Pi, diophant, M); |
---|
890 | if (!extension) |
---|
891 | earlyFactors= earlyFactorDetection (A, bufUniFactors, newLiftBound, |
---|
892 | degs, earlySuccess, liftPre[sizeOfLiftPre-1] + 1); |
---|
893 | else |
---|
894 | earlyFactors= extEarlyFactorDetection (A, bufUniFactors, |
---|
895 | newLiftBound, degs, earlySuccess, info, eval, |
---|
896 | liftPre[sizeOfLiftPre-1] + 1); |
---|
897 | } |
---|
898 | } |
---|
899 | else if (earlySuccess) |
---|
900 | liftBound= newLiftBound; |
---|
901 | |
---|
902 | int i= sizeOfLiftPre - 1; |
---|
903 | while (degs.getLength() > 1 && !earlySuccess && i - 1 >= 0) |
---|
904 | { |
---|
905 | if (newLiftBound >= liftPre[i] + 1) |
---|
906 | { |
---|
907 | bufUniFactors.insert (LC (A, x)); |
---|
908 | henselLiftResume12 (A, bufUniFactors, liftPre[i] + 1, |
---|
909 | liftPre[i-1] + 1, Pi, diophant, M); |
---|
910 | if (!extension) |
---|
911 | earlyFactors= earlyFactorDetection (A, bufUniFactors, newLiftBound, |
---|
912 | degs, earlySuccess, liftPre[i-1] + 1); |
---|
913 | else |
---|
914 | earlyFactors= extEarlyFactorDetection (A, bufUniFactors, |
---|
915 | newLiftBound, degs, earlySuccess, info, eval, |
---|
916 | liftPre[i-1] + 1); |
---|
917 | } |
---|
918 | else |
---|
919 | { |
---|
920 | liftBound= newLiftBound; |
---|
921 | break; |
---|
922 | } |
---|
923 | i--; |
---|
924 | } |
---|
925 | if (earlySuccess) |
---|
926 | liftBound= newLiftBound; |
---|
927 | //after here all factors are lifted to liftPre[sizeOfLiftPre-1] |
---|
928 | } |
---|
929 | else |
---|
930 | { |
---|
931 | henselLift12 (A, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
---|
932 | if (!extension) |
---|
933 | earlyFactors= earlyFactorDetection (A, bufUniFactors, newLiftBound, |
---|
934 | degs, earlySuccess, smallFactorDeg); |
---|
935 | else |
---|
936 | earlyFactors= extEarlyFactorDetection (A, bufUniFactors, |
---|
937 | newLiftBound, degs, earlySuccess, info, eval, |
---|
938 | smallFactorDeg); |
---|
939 | int i= 1; |
---|
940 | while ((degree (A,y)/4)*i + 4 <= smallFactorDeg) |
---|
941 | i++; |
---|
942 | dummy= tmin (degree (A,y)+1, (degree (A,y)/4)*i+4); |
---|
943 | if (degs.getLength() > 1 && !earlySuccess && dummy > smallFactorDeg) |
---|
944 | { |
---|
945 | bufUniFactors.insert (LC (A, x)); |
---|
946 | henselLiftResume12 (A, bufUniFactors, smallFactorDeg, |
---|
947 | dummy, Pi, diophant, M); |
---|
948 | if (!extension) |
---|
949 | earlyFactors= earlyFactorDetection (A, bufUniFactors, newLiftBound, |
---|
950 | degs, earlySuccess, dummy); |
---|
951 | else |
---|
952 | earlyFactors= extEarlyFactorDetection (A, bufUniFactors, |
---|
953 | newLiftBound, degs, earlySuccess, info, eval, |
---|
954 | dummy); |
---|
955 | } |
---|
956 | while (degs.getLength() > 1 && !earlySuccess && i < 4) |
---|
957 | { |
---|
958 | if (newLiftBound >= dummy) |
---|
959 | { |
---|
960 | bufUniFactors.insert (LC (A, x)); |
---|
961 | dummy= tmin (degree (A,y)+1, (degree (A,y)/4)*(i+1)+4); |
---|
962 | henselLiftResume12 (A, bufUniFactors, (degree (A,y)/4)*i + 4, |
---|
963 | dummy, Pi, diophant, M); |
---|
964 | if (!extension) |
---|
965 | earlyFactors= earlyFactorDetection (A, bufUniFactors, newLiftBound, |
---|
966 | degs, earlySuccess, dummy); |
---|
967 | else |
---|
968 | earlyFactors= extEarlyFactorDetection (A, bufUniFactors, |
---|
969 | newLiftBound, degs, earlySuccess, info, eval, |
---|
970 | dummy); |
---|
971 | } |
---|
972 | else |
---|
973 | { |
---|
974 | liftBound= newLiftBound; |
---|
975 | break; |
---|
976 | } |
---|
977 | i++; |
---|
978 | } |
---|
979 | if (earlySuccess) |
---|
980 | liftBound= newLiftBound; |
---|
981 | } |
---|
982 | |
---|
983 | if (!earlySuccess) |
---|
984 | liftBound= degree (A,y) + 1; |
---|
985 | |
---|
986 | delete [] liftPre; |
---|
987 | |
---|
988 | return bufUniFactors; |
---|
989 | } |
---|
990 | |
---|
991 | long isReduced (const mat_zz_p& M) |
---|
992 | { |
---|
993 | long i, j, nonZero; |
---|
994 | for (i = 1; i <= M.NumRows(); i++) |
---|
995 | { |
---|
996 | nonZero= 0; |
---|
997 | for (j = 1; j <= M.NumCols(); j++) |
---|
998 | { |
---|
999 | if (!IsZero (M (i,j))) |
---|
1000 | nonZero++; |
---|
1001 | } |
---|
1002 | if (nonZero != 1) |
---|
1003 | return 0; |
---|
1004 | } |
---|
1005 | return 1; |
---|
1006 | } |
---|
1007 | |
---|
1008 | long isReduced (const mat_zz_pE& M) |
---|
1009 | { |
---|
1010 | long i, j, nonZero; |
---|
1011 | for (i = 1; i <= M.NumRows(); i++) |
---|
1012 | { |
---|
1013 | nonZero= 0; |
---|
1014 | for (j = 1; j <= M.NumCols(); j++) |
---|
1015 | { |
---|
1016 | if (!IsZero (M (i,j))) |
---|
1017 | nonZero++; |
---|
1018 | } |
---|
1019 | if (nonZero != 1) |
---|
1020 | return 0; |
---|
1021 | } |
---|
1022 | return 1; |
---|
1023 | } |
---|
1024 | |
---|
1025 | int * extractZeroOneVecs (const mat_zz_p& M) |
---|
1026 | { |
---|
1027 | long i, j; |
---|
1028 | bool nonZeroOne= false; |
---|
1029 | int * result= new int [M.NumCols()]; |
---|
1030 | for (i = 1; i <= M.NumCols(); i++) |
---|
1031 | { |
---|
1032 | for (j = 1; j <= M.NumRows(); j++) |
---|
1033 | { |
---|
1034 | if (!(IsOne (M (j,i)) || IsZero (M (j,i)))) |
---|
1035 | { |
---|
1036 | nonZeroOne= true; |
---|
1037 | break; |
---|
1038 | } |
---|
1039 | } |
---|
1040 | if (!nonZeroOne) |
---|
1041 | result [i - 1]= 1; |
---|
1042 | else |
---|
1043 | result [i - 1]= 0; |
---|
1044 | nonZeroOne= false; |
---|
1045 | } |
---|
1046 | return result; |
---|
1047 | } |
---|
1048 | |
---|
1049 | int * extractZeroOneVecs (const mat_zz_pE& M) |
---|
1050 | { |
---|
1051 | long i, j; |
---|
1052 | bool nonZeroOne= false; |
---|
1053 | int * result= new int [M.NumCols()]; |
---|
1054 | for (i = 1; i <= M.NumCols(); i++) |
---|
1055 | { |
---|
1056 | for (j = 1; j <= M.NumRows(); j++) |
---|
1057 | { |
---|
1058 | if (!(IsOne (M (j,i)) || IsZero (M (j,i)))) |
---|
1059 | { |
---|
1060 | nonZeroOne= true; |
---|
1061 | break; |
---|
1062 | } |
---|
1063 | } |
---|
1064 | if (!nonZeroOne) |
---|
1065 | result [i - 1]= 1; |
---|
1066 | else |
---|
1067 | result [i - 1]= 0; |
---|
1068 | nonZeroOne= false; |
---|
1069 | } |
---|
1070 | return result; |
---|
1071 | } |
---|
1072 | |
---|
1073 | void |
---|
1074 | reconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const CFList& |
---|
1075 | factors, const int liftBound, int& factorsFound, int*& |
---|
1076 | factorsFoundIndex, mat_zz_pE& N, bool beenInThres |
---|
1077 | ) |
---|
1078 | { |
---|
1079 | Variable y= Variable (2); |
---|
1080 | Variable x= Variable (1); |
---|
1081 | CanonicalForm yToL= power (y, liftBound); |
---|
1082 | CanonicalForm quot, buf; |
---|
1083 | CFListIterator iter; |
---|
1084 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1085 | { |
---|
1086 | if (factorsFoundIndex [i - 1] == 1) |
---|
1087 | continue; |
---|
1088 | iter= factors; |
---|
1089 | if (beenInThres) |
---|
1090 | { |
---|
1091 | int count= 1; |
---|
1092 | while (count < i) |
---|
1093 | { |
---|
1094 | count++; |
---|
1095 | iter++; |
---|
1096 | } |
---|
1097 | buf= iter.getItem(); |
---|
1098 | } |
---|
1099 | else |
---|
1100 | { |
---|
1101 | buf= 1; |
---|
1102 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1103 | { |
---|
1104 | if (!IsZero (N (j,i))) |
---|
1105 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1106 | } |
---|
1107 | } |
---|
1108 | buf *= LC (F, x); |
---|
1109 | buf= mod (buf, yToL); |
---|
1110 | buf /= content (buf, x); |
---|
1111 | if (fdivides (buf, F, quot)) |
---|
1112 | { |
---|
1113 | factorsFoundIndex[i - 1]= 1; |
---|
1114 | factorsFound++; |
---|
1115 | F= quot; |
---|
1116 | F /= Lc (F); |
---|
1117 | reconstructedFactors.append (buf); |
---|
1118 | } |
---|
1119 | if (degree (F) <= 0) |
---|
1120 | return; |
---|
1121 | if (factorsFound + 1 == N.NumCols()) |
---|
1122 | { |
---|
1123 | reconstructedFactors.append (F); |
---|
1124 | return; |
---|
1125 | } |
---|
1126 | } |
---|
1127 | } |
---|
1128 | |
---|
1129 | void |
---|
1130 | reconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const CFList& |
---|
1131 | factors, const int liftBound, int& factorsFound, int*& |
---|
1132 | factorsFoundIndex, mat_zz_p& N, bool beenInThres |
---|
1133 | ) |
---|
1134 | { |
---|
1135 | Variable y= Variable (2); |
---|
1136 | Variable x= Variable (1); |
---|
1137 | CanonicalForm quot, buf; |
---|
1138 | CanonicalForm yToL= power (y, liftBound); |
---|
1139 | CFListIterator iter; |
---|
1140 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1141 | { |
---|
1142 | if (factorsFoundIndex [i - 1] == 1) |
---|
1143 | continue; |
---|
1144 | iter= factors; |
---|
1145 | if (beenInThres) |
---|
1146 | { |
---|
1147 | int count= 1; |
---|
1148 | while (count < i) |
---|
1149 | { |
---|
1150 | count++; |
---|
1151 | iter++; |
---|
1152 | } |
---|
1153 | buf= iter.getItem(); |
---|
1154 | } |
---|
1155 | else |
---|
1156 | { |
---|
1157 | buf= 1; |
---|
1158 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1159 | { |
---|
1160 | if (!IsZero (N (j,i))) |
---|
1161 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1162 | } |
---|
1163 | } |
---|
1164 | buf *= LC (F, x); |
---|
1165 | buf= mod (buf, yToL); |
---|
1166 | buf /= content (buf, x); |
---|
1167 | if (fdivides (buf, F, quot)) |
---|
1168 | { |
---|
1169 | factorsFoundIndex[i - 1]= 1; |
---|
1170 | factorsFound++; |
---|
1171 | F= quot; |
---|
1172 | F /= Lc (F); |
---|
1173 | reconstructedFactors.append (buf); |
---|
1174 | } |
---|
1175 | if (degree (F) <= 0) |
---|
1176 | return; |
---|
1177 | if (factorsFound + 1 == N.NumCols()) |
---|
1178 | { |
---|
1179 | reconstructedFactors.append (F); |
---|
1180 | return; |
---|
1181 | } |
---|
1182 | } |
---|
1183 | } |
---|
1184 | |
---|
1185 | CFList |
---|
1186 | reconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, int |
---|
1187 | precision, const mat_zz_pE& N |
---|
1188 | ) |
---|
1189 | { |
---|
1190 | Variable y= Variable (2); |
---|
1191 | Variable x= Variable (1); |
---|
1192 | CanonicalForm F= G; |
---|
1193 | CanonicalForm yToL= power (y, precision); |
---|
1194 | CanonicalForm quot, buf; |
---|
1195 | CFList result, factorsConsidered; |
---|
1196 | CFList bufFactors= factors; |
---|
1197 | CFListIterator iter; |
---|
1198 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1199 | { |
---|
1200 | if (zeroOneVecs [i - 1] == 0) |
---|
1201 | continue; |
---|
1202 | iter= factors; |
---|
1203 | buf= 1; |
---|
1204 | factorsConsidered= CFList(); |
---|
1205 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1206 | { |
---|
1207 | if (!IsZero (N (j,i))) |
---|
1208 | { |
---|
1209 | factorsConsidered.append (iter.getItem()); |
---|
1210 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1211 | } |
---|
1212 | } |
---|
1213 | buf *= LC (F, x); |
---|
1214 | buf= mod (buf, yToL); |
---|
1215 | buf /= content (buf, x); |
---|
1216 | if (fdivides (buf, F, quot)) |
---|
1217 | { |
---|
1218 | F= quot; |
---|
1219 | F /= Lc (F); |
---|
1220 | result.append (buf); |
---|
1221 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
1222 | } |
---|
1223 | if (degree (F) <= 0) |
---|
1224 | { |
---|
1225 | G= F; |
---|
1226 | factors= bufFactors; |
---|
1227 | return result; |
---|
1228 | } |
---|
1229 | } |
---|
1230 | G= F; |
---|
1231 | factors= bufFactors; |
---|
1232 | return result; |
---|
1233 | } |
---|
1234 | |
---|
1235 | CFList |
---|
1236 | monicReconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, |
---|
1237 | int precision, const mat_zz_pE& N |
---|
1238 | ) |
---|
1239 | { |
---|
1240 | Variable y= Variable (2); |
---|
1241 | Variable x= Variable (1); |
---|
1242 | CanonicalForm F= G; |
---|
1243 | CanonicalForm yToL= power (y, precision); |
---|
1244 | CanonicalForm quot, buf, buf2; |
---|
1245 | CFList result; |
---|
1246 | CFList bufFactors= factors; |
---|
1247 | CFList factorsConsidered; |
---|
1248 | CFListIterator iter; |
---|
1249 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1250 | { |
---|
1251 | if (zeroOneVecs [i - 1] == 0) |
---|
1252 | continue; |
---|
1253 | iter= factors; |
---|
1254 | buf= 1; |
---|
1255 | factorsConsidered= CFList(); |
---|
1256 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1257 | { |
---|
1258 | if (!IsZero (N (j,i))) |
---|
1259 | { |
---|
1260 | factorsConsidered.append (iter.getItem()); |
---|
1261 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1262 | } |
---|
1263 | } |
---|
1264 | buf2= buf; |
---|
1265 | buf *= LC (F, x); |
---|
1266 | buf= mod (buf, yToL); |
---|
1267 | buf /= content (buf, x); |
---|
1268 | if (fdivides (buf, F, quot)) |
---|
1269 | { |
---|
1270 | F= quot; |
---|
1271 | F /= Lc (F); |
---|
1272 | result.append (buf2); |
---|
1273 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
1274 | } |
---|
1275 | if (degree (F) <= 0) |
---|
1276 | { |
---|
1277 | G= F; |
---|
1278 | factors= bufFactors; |
---|
1279 | return result; |
---|
1280 | } |
---|
1281 | } |
---|
1282 | G= F; |
---|
1283 | factors= bufFactors; |
---|
1284 | return result; |
---|
1285 | } |
---|
1286 | |
---|
1287 | CFList |
---|
1288 | extReconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, int |
---|
1289 | precision, const mat_zz_p& N, const ExtensionInfo& info, |
---|
1290 | const CanonicalForm& evaluation |
---|
1291 | ) |
---|
1292 | { |
---|
1293 | Variable y= Variable (2); |
---|
1294 | Variable x= Variable (1); |
---|
1295 | Variable alpha= info.getAlpha(); |
---|
1296 | Variable beta= info.getBeta(); |
---|
1297 | int k= info.getGFDegree(); |
---|
1298 | CanonicalForm gamma= info.getGamma(); |
---|
1299 | CanonicalForm delta= info.getDelta(); |
---|
1300 | CanonicalForm F= G; |
---|
1301 | CanonicalForm yToL= power (y, precision); |
---|
1302 | CFList result; |
---|
1303 | CFList bufFactors= factors; |
---|
1304 | CFList factorsConsidered; |
---|
1305 | CanonicalForm buf2, quot, buf; |
---|
1306 | CFListIterator iter; |
---|
1307 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1308 | { |
---|
1309 | if (zeroOneVecs [i - 1] == 0) |
---|
1310 | continue; |
---|
1311 | iter= factors; |
---|
1312 | buf= 1; |
---|
1313 | factorsConsidered= CFList(); |
---|
1314 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1315 | { |
---|
1316 | if (!IsZero (N (j,i))) |
---|
1317 | { |
---|
1318 | factorsConsidered.append (iter.getItem()); |
---|
1319 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1320 | } |
---|
1321 | } |
---|
1322 | buf *= LC (F, x); |
---|
1323 | buf= mod (buf, yToL); |
---|
1324 | buf /= content (buf, x); |
---|
1325 | buf2= buf (y-evaluation, y); |
---|
1326 | if (!k && beta == x) |
---|
1327 | { |
---|
1328 | if (degree (buf2, alpha) < 1) |
---|
1329 | { |
---|
1330 | if (fdivides (buf, F, quot)) |
---|
1331 | { |
---|
1332 | F= quot; |
---|
1333 | F /= Lc (F); |
---|
1334 | result.append (buf2); |
---|
1335 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
1336 | } |
---|
1337 | } |
---|
1338 | } |
---|
1339 | else |
---|
1340 | { |
---|
1341 | CFList source, dest; |
---|
1342 | |
---|
1343 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
1344 | { |
---|
1345 | if (fdivides (buf, F, quot)) |
---|
1346 | { |
---|
1347 | F= quot; |
---|
1348 | F /= Lc (F); |
---|
1349 | result.append (buf2); |
---|
1350 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
1351 | } |
---|
1352 | } |
---|
1353 | } |
---|
1354 | if (degree (F) <= 0) |
---|
1355 | { |
---|
1356 | G= F; |
---|
1357 | factors= bufFactors; |
---|
1358 | return result; |
---|
1359 | } |
---|
1360 | } |
---|
1361 | G= F; |
---|
1362 | factors= bufFactors; |
---|
1363 | return result; |
---|
1364 | } |
---|
1365 | |
---|
1366 | CFList |
---|
1367 | reconstruction (CanonicalForm& G, CFList& factors, int* zeroOneVecs, |
---|
1368 | int precision, const mat_zz_p& N) |
---|
1369 | { |
---|
1370 | Variable y= Variable (2); |
---|
1371 | Variable x= Variable (1); |
---|
1372 | CanonicalForm F= G; |
---|
1373 | CanonicalForm yToL= power (y, precision); |
---|
1374 | CanonicalForm quot, buf; |
---|
1375 | CFList result; |
---|
1376 | CFList bufFactors= factors; |
---|
1377 | CFList factorsConsidered; |
---|
1378 | CFListIterator iter; |
---|
1379 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1380 | { |
---|
1381 | if (zeroOneVecs [i - 1] == 0) |
---|
1382 | continue; |
---|
1383 | iter= factors; |
---|
1384 | buf= 1; |
---|
1385 | factorsConsidered= CFList(); |
---|
1386 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1387 | { |
---|
1388 | if (!IsZero (N (j,i))) |
---|
1389 | { |
---|
1390 | factorsConsidered.append (iter.getItem()); |
---|
1391 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1392 | } |
---|
1393 | } |
---|
1394 | buf *= LC (F, x); |
---|
1395 | buf= mod (buf, yToL); |
---|
1396 | buf /= content (buf, x); |
---|
1397 | if (fdivides (buf, F, quot)) |
---|
1398 | { |
---|
1399 | F= quot; |
---|
1400 | F /= Lc (F); |
---|
1401 | result.append (buf); |
---|
1402 | bufFactors= Difference (bufFactors, factorsConsidered); |
---|
1403 | } |
---|
1404 | if (degree (F) <= 0) |
---|
1405 | { |
---|
1406 | G= F; |
---|
1407 | factors= bufFactors; |
---|
1408 | return result; |
---|
1409 | } |
---|
1410 | } |
---|
1411 | G= F; |
---|
1412 | factors= bufFactors; |
---|
1413 | return result; |
---|
1414 | } |
---|
1415 | |
---|
1416 | void |
---|
1417 | extReconstructionTry (CFList& reconstructedFactors, CanonicalForm& F, const |
---|
1418 | CFList& factors, const int liftBound, int& factorsFound, |
---|
1419 | int*& factorsFoundIndex, mat_zz_p& N, bool beenInThres, |
---|
1420 | const ExtensionInfo& info, const CanonicalForm& evaluation |
---|
1421 | ) |
---|
1422 | { |
---|
1423 | Variable y= Variable (2); |
---|
1424 | Variable x= Variable (1); |
---|
1425 | Variable alpha= info.getAlpha(); |
---|
1426 | Variable beta= info.getBeta(); |
---|
1427 | int k= info.getGFDegree(); |
---|
1428 | CanonicalForm gamma= info.getGamma(); |
---|
1429 | CanonicalForm delta= info.getDelta(); |
---|
1430 | CanonicalForm yToL= power (y, liftBound); |
---|
1431 | CanonicalForm quot, buf, buf2; |
---|
1432 | CFList source, dest; |
---|
1433 | CFListIterator iter; |
---|
1434 | for (long i= 1; i <= N.NumCols(); i++) |
---|
1435 | { |
---|
1436 | if (factorsFoundIndex [i - 1] == 1) |
---|
1437 | continue; |
---|
1438 | iter= factors; |
---|
1439 | if (beenInThres) |
---|
1440 | { |
---|
1441 | int count= 1; |
---|
1442 | while (count < i) |
---|
1443 | { |
---|
1444 | count++; |
---|
1445 | iter++; |
---|
1446 | } |
---|
1447 | buf= iter.getItem(); |
---|
1448 | } |
---|
1449 | else |
---|
1450 | { |
---|
1451 | buf= 1; |
---|
1452 | for (long j= 1; j <= N.NumRows(); j++, iter++) |
---|
1453 | { |
---|
1454 | if (!IsZero (N (j,i))) |
---|
1455 | buf= mulMod2 (buf, iter.getItem(), yToL); |
---|
1456 | } |
---|
1457 | } |
---|
1458 | buf *= LC (F, x); |
---|
1459 | buf= mod (buf, yToL); |
---|
1460 | buf /= content (buf, x); |
---|
1461 | buf2= buf (y - evaluation, y); |
---|
1462 | if (!k && beta == x) |
---|
1463 | { |
---|
1464 | if (degree (buf2, alpha) < 1) |
---|
1465 | { |
---|
1466 | if (fdivides (buf, F, quot)) |
---|
1467 | { |
---|
1468 | factorsFoundIndex[i - 1]= 1; |
---|
1469 | factorsFound++; |
---|
1470 | F= quot; |
---|
1471 | F /= Lc (F); |
---|
1472 | buf2= mapDown (buf2, info, source, dest); |
---|
1473 | reconstructedFactors.append (buf2); |
---|
1474 | } |
---|
1475 | } |
---|
1476 | } |
---|
1477 | else |
---|
1478 | { |
---|
1479 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
1480 | { |
---|
1481 | if (fdivides (buf, F, quot)) |
---|
1482 | { |
---|
1483 | factorsFoundIndex[i - 1]= 1; |
---|
1484 | factorsFound++; |
---|
1485 | F= quot; |
---|
1486 | F /= Lc (F); |
---|
1487 | buf2= mapDown (buf2, info, source, dest); |
---|
1488 | reconstructedFactors.append (buf2); |
---|
1489 | } |
---|
1490 | } |
---|
1491 | } |
---|
1492 | if (degree (F) <= 0) |
---|
1493 | return; |
---|
1494 | if (factorsFound + 1 == N.NumCols()) |
---|
1495 | { |
---|
1496 | CanonicalForm tmp= F (y - evaluation, y); |
---|
1497 | tmp= mapDown (tmp, info, source, dest); |
---|
1498 | reconstructedFactors.append (tmp); |
---|
1499 | return; |
---|
1500 | } |
---|
1501 | } |
---|
1502 | } |
---|
1503 | |
---|
1504 | //over Fp |
---|
1505 | int |
---|
1506 | liftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, int |
---|
1507 | start, int liftBound, int minBound, CFList& factors, |
---|
1508 | mat_zz_p& NTLN, CFList& diophant, CFMatrix& M, CFArray& |
---|
1509 | Pi, CFArray& bufQ, bool& irreducible |
---|
1510 | ) |
---|
1511 | { |
---|
1512 | CanonicalForm LCF= LC (F, 1); |
---|
1513 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
1514 | bool wasInBounds= false; |
---|
1515 | bool hitBound= false; |
---|
1516 | int l= (minBound+1)*2; |
---|
1517 | int stepSize= 2; |
---|
1518 | int oldL= l/2; |
---|
1519 | bool reduced= false; |
---|
1520 | mat_zz_p NTLK, *NTLC; |
---|
1521 | CFMatrix C; |
---|
1522 | CFArray buf; |
---|
1523 | CFListIterator j; |
---|
1524 | CanonicalForm truncF; |
---|
1525 | Variable y= F.mvar(); |
---|
1526 | while (l <= liftBound) |
---|
1527 | { |
---|
1528 | if (start) |
---|
1529 | { |
---|
1530 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
1531 | start= 0; |
---|
1532 | } |
---|
1533 | else |
---|
1534 | { |
---|
1535 | if (wasInBounds) |
---|
1536 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
1537 | else |
---|
1538 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
1539 | } |
---|
1540 | |
---|
1541 | factors.insert (LCF); |
---|
1542 | j= factors; |
---|
1543 | j++; |
---|
1544 | |
---|
1545 | truncF= mod (F, power (y, l)); |
---|
1546 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
1547 | { |
---|
1548 | if (!wasInBounds) |
---|
1549 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
1550 | else |
---|
1551 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
1552 | bufQ[i]); |
---|
1553 | } |
---|
1554 | |
---|
1555 | for (int i= 0; i < sizeBounds; i++) |
---|
1556 | { |
---|
1557 | if (bounds [i] + 1 <= l/2) |
---|
1558 | { |
---|
1559 | wasInBounds= true; |
---|
1560 | int k= tmin (bounds [i] + 1, l/2); |
---|
1561 | C= CFMatrix (l - k, factors.length() - 1); |
---|
1562 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
1563 | { |
---|
1564 | if (A[ii].size() - 1 >= i) |
---|
1565 | buf= getCoeffs (A[ii] [i], k); |
---|
1566 | writeInMatrix (C, buf, ii + 1, 0); |
---|
1567 | } |
---|
1568 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
1569 | NTLK= (*NTLC)*NTLN; |
---|
1570 | transpose (NTLK, NTLK); |
---|
1571 | kernel (NTLK, NTLK); |
---|
1572 | transpose (NTLK, NTLK); |
---|
1573 | NTLN *= NTLK; |
---|
1574 | |
---|
1575 | if (NTLN.NumCols() == 1) |
---|
1576 | { |
---|
1577 | irreducible= true; |
---|
1578 | break; |
---|
1579 | } |
---|
1580 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
1581 | { |
---|
1582 | reduced= true; |
---|
1583 | break; |
---|
1584 | } |
---|
1585 | } |
---|
1586 | } |
---|
1587 | |
---|
1588 | if (irreducible) |
---|
1589 | break; |
---|
1590 | if (reduced) |
---|
1591 | break; |
---|
1592 | oldL= l; |
---|
1593 | l += stepSize; |
---|
1594 | stepSize *= 2; |
---|
1595 | if (l > liftBound) |
---|
1596 | { |
---|
1597 | if (!hitBound) |
---|
1598 | { |
---|
1599 | l= liftBound; |
---|
1600 | hitBound= true; |
---|
1601 | } |
---|
1602 | else |
---|
1603 | break; |
---|
1604 | } |
---|
1605 | } |
---|
1606 | delete [] A; |
---|
1607 | return l; |
---|
1608 | } |
---|
1609 | |
---|
1610 | //over field extension |
---|
1611 | int |
---|
1612 | extLiftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
1613 | int liftBound, int minBound, int start, CFList& |
---|
1614 | factors, mat_zz_p& NTLN, CFList& diophant, |
---|
1615 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, bool& |
---|
1616 | irreducible, const CanonicalForm& evaluation, const |
---|
1617 | ExtensionInfo& info, CFList& source, CFList& dest |
---|
1618 | ) |
---|
1619 | { |
---|
1620 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
1621 | CanonicalForm LCF= LC (F, 1); |
---|
1622 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
1623 | bool wasInBounds= false; |
---|
1624 | bool hitBound= false; |
---|
1625 | int degMipo; |
---|
1626 | Variable alpha; |
---|
1627 | alpha= info.getAlpha(); |
---|
1628 | degMipo= degree (getMipo (alpha)); |
---|
1629 | |
---|
1630 | Variable gamma= info.getBeta(); |
---|
1631 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
1632 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
1633 | |
---|
1634 | int stepSize= 2; |
---|
1635 | int l= ((minBound+1)/degMipo+1)*2; |
---|
1636 | l= tmax (l, 2); |
---|
1637 | if (start > l) |
---|
1638 | l= start; |
---|
1639 | int startl= l; |
---|
1640 | int oldL= l/2; |
---|
1641 | bool reduced= false; |
---|
1642 | Variable y= F.mvar(); |
---|
1643 | Variable x= Variable (1); |
---|
1644 | CanonicalForm powX, imBasis, truncF; |
---|
1645 | CFMatrix Mat, C; |
---|
1646 | CFArray buf; |
---|
1647 | CFIterator iter; |
---|
1648 | mat_zz_p* NTLMat, *NTLC, NTLK; |
---|
1649 | CFListIterator j; |
---|
1650 | while (l <= liftBound) |
---|
1651 | { |
---|
1652 | if (start) |
---|
1653 | { |
---|
1654 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
1655 | start= 0; |
---|
1656 | } |
---|
1657 | else |
---|
1658 | { |
---|
1659 | if (wasInBounds) |
---|
1660 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
1661 | else |
---|
1662 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
1663 | } |
---|
1664 | |
---|
1665 | factors.insert (LCF); |
---|
1666 | |
---|
1667 | if (GF) |
---|
1668 | setCharacteristic (getCharacteristic()); |
---|
1669 | |
---|
1670 | powX= power (y-gamma, l); |
---|
1671 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
1672 | for (int i= 0; i < l*degMipo; i++) |
---|
1673 | { |
---|
1674 | imBasis= mod (power (y, i), powX); |
---|
1675 | imBasis= imBasis (power (y, degMipo), y); |
---|
1676 | imBasis= imBasis (y, gamma); |
---|
1677 | iter= imBasis; |
---|
1678 | for (; iter.hasTerms(); iter++) |
---|
1679 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
1680 | } |
---|
1681 | |
---|
1682 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
1683 | *NTLMat= inv (*NTLMat); |
---|
1684 | |
---|
1685 | if (GF) |
---|
1686 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
1687 | |
---|
1688 | j= factors; |
---|
1689 | j++; |
---|
1690 | |
---|
1691 | truncF= mod (F, power (y, l)); |
---|
1692 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
1693 | { |
---|
1694 | if (!wasInBounds) |
---|
1695 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
1696 | else |
---|
1697 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
1698 | bufQ[i]); |
---|
1699 | } |
---|
1700 | |
---|
1701 | for (int i= 0; i < sizeBounds; i++) |
---|
1702 | { |
---|
1703 | if (bounds [i] + 1 <= (l/2)*degMipo) |
---|
1704 | { |
---|
1705 | wasInBounds= true; |
---|
1706 | int k= tmin (bounds [i] + 1, (l/2)*degMipo); |
---|
1707 | C= CFMatrix (l*degMipo - k, factors.length() - 1); |
---|
1708 | |
---|
1709 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
1710 | { |
---|
1711 | if (A[ii].size() - 1 >= i) |
---|
1712 | { |
---|
1713 | if (GF) |
---|
1714 | { |
---|
1715 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
1716 | setCharacteristic (getCharacteristic()); |
---|
1717 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
1718 | if (alpha != gamma) |
---|
1719 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
1720 | gamma, source, dest |
---|
1721 | ); |
---|
1722 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
1723 | } |
---|
1724 | else |
---|
1725 | { |
---|
1726 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
1727 | if (alpha != gamma) |
---|
1728 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
1729 | gamma, source, dest |
---|
1730 | ); |
---|
1731 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
1732 | } |
---|
1733 | } |
---|
1734 | writeInMatrix (C, buf, ii + 1, 0); |
---|
1735 | if (GF) |
---|
1736 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
1737 | } |
---|
1738 | |
---|
1739 | if (GF) |
---|
1740 | setCharacteristic(getCharacteristic()); |
---|
1741 | |
---|
1742 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
1743 | NTLK= (*NTLC)*NTLN; |
---|
1744 | transpose (NTLK, NTLK); |
---|
1745 | kernel (NTLK, NTLK); |
---|
1746 | transpose (NTLK, NTLK); |
---|
1747 | NTLN *= NTLK; |
---|
1748 | |
---|
1749 | if (GF) |
---|
1750 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
1751 | |
---|
1752 | if (NTLN.NumCols() == 1) |
---|
1753 | { |
---|
1754 | irreducible= true; |
---|
1755 | break; |
---|
1756 | } |
---|
1757 | if (isReduced (NTLN) && l > startl) |
---|
1758 | { |
---|
1759 | reduced= true; |
---|
1760 | break; |
---|
1761 | } |
---|
1762 | } |
---|
1763 | } |
---|
1764 | |
---|
1765 | if (NTLN.NumCols() == 1) |
---|
1766 | { |
---|
1767 | irreducible= true; |
---|
1768 | break; |
---|
1769 | } |
---|
1770 | if (reduced) |
---|
1771 | break; |
---|
1772 | oldL= l; |
---|
1773 | l += stepSize; |
---|
1774 | stepSize *= 2; |
---|
1775 | if (l > liftBound) |
---|
1776 | { |
---|
1777 | if (!hitBound) |
---|
1778 | { |
---|
1779 | l= liftBound; |
---|
1780 | hitBound= true; |
---|
1781 | } |
---|
1782 | else |
---|
1783 | break; |
---|
1784 | } |
---|
1785 | } |
---|
1786 | delete [] A; |
---|
1787 | return l; |
---|
1788 | } |
---|
1789 | |
---|
1790 | // over Fq |
---|
1791 | int |
---|
1792 | liftAndComputeLattice (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
1793 | int start, int liftBound, int minBound, CFList& factors, |
---|
1794 | mat_zz_pE& NTLN, CFList& diophant, CFMatrix& M, CFArray& |
---|
1795 | Pi, CFArray& bufQ, bool& irreducible |
---|
1796 | ) |
---|
1797 | { |
---|
1798 | CanonicalForm LCF= LC (F, 1); |
---|
1799 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
1800 | bool wasInBounds= false; |
---|
1801 | bool hitBound= false; |
---|
1802 | int l= (minBound+1)*2; |
---|
1803 | int stepSize= 2; |
---|
1804 | int oldL= l/2; |
---|
1805 | bool reduced= false; |
---|
1806 | CFListIterator j; |
---|
1807 | mat_zz_pE* NTLC, NTLK; |
---|
1808 | CFArray buf; |
---|
1809 | CFMatrix C; |
---|
1810 | Variable y= F.mvar(); |
---|
1811 | CanonicalForm truncF; |
---|
1812 | while (l <= liftBound) |
---|
1813 | { |
---|
1814 | if (start) |
---|
1815 | { |
---|
1816 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
1817 | start= 0; |
---|
1818 | } |
---|
1819 | else |
---|
1820 | { |
---|
1821 | if (wasInBounds) |
---|
1822 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
1823 | else |
---|
1824 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
1825 | } |
---|
1826 | |
---|
1827 | factors.insert (LCF); |
---|
1828 | j= factors; |
---|
1829 | j++; |
---|
1830 | |
---|
1831 | truncF= mod (F, power (y,l)); |
---|
1832 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
1833 | { |
---|
1834 | if (l == (minBound+1)*2) |
---|
1835 | { |
---|
1836 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
1837 | } |
---|
1838 | else |
---|
1839 | { |
---|
1840 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
1841 | bufQ[i] |
---|
1842 | ); |
---|
1843 | } |
---|
1844 | } |
---|
1845 | |
---|
1846 | for (int i= 0; i < sizeBounds; i++) |
---|
1847 | { |
---|
1848 | if (bounds [i] + 1 <= l/2) |
---|
1849 | { |
---|
1850 | wasInBounds= true; |
---|
1851 | int k= tmin (bounds [i] + 1, l/2); |
---|
1852 | C= CFMatrix (l - k, factors.length() - 1); |
---|
1853 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
1854 | { |
---|
1855 | |
---|
1856 | if (A[ii].size() - 1 >= i) |
---|
1857 | buf= getCoeffs (A[ii] [i], k); |
---|
1858 | writeInMatrix (C, buf, ii + 1, 0); |
---|
1859 | } |
---|
1860 | |
---|
1861 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
1862 | NTLK= (*NTLC)*NTLN; |
---|
1863 | transpose (NTLK, NTLK); |
---|
1864 | kernel (NTLK, NTLK); |
---|
1865 | transpose (NTLK, NTLK); |
---|
1866 | NTLN *= NTLK; |
---|
1867 | |
---|
1868 | if (NTLN.NumCols() == 1) |
---|
1869 | { |
---|
1870 | irreducible= true; |
---|
1871 | break; |
---|
1872 | } |
---|
1873 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
1874 | { |
---|
1875 | reduced= true; |
---|
1876 | break; |
---|
1877 | } |
---|
1878 | } |
---|
1879 | } |
---|
1880 | |
---|
1881 | if (NTLN.NumCols() == 1) |
---|
1882 | { |
---|
1883 | irreducible= true; |
---|
1884 | break; |
---|
1885 | } |
---|
1886 | if (reduced) |
---|
1887 | break; |
---|
1888 | oldL= l; |
---|
1889 | l += stepSize; |
---|
1890 | stepSize *= 2; |
---|
1891 | if (l > liftBound) |
---|
1892 | { |
---|
1893 | if (!hitBound) |
---|
1894 | { |
---|
1895 | l= liftBound; |
---|
1896 | hitBound= true; |
---|
1897 | } |
---|
1898 | else |
---|
1899 | break; |
---|
1900 | } |
---|
1901 | } |
---|
1902 | delete [] A; |
---|
1903 | return l; |
---|
1904 | } |
---|
1905 | |
---|
1906 | int |
---|
1907 | liftAndComputeLatticeFq2Fp (const CanonicalForm& F, int* bounds, int sizeBounds, |
---|
1908 | int start, int liftBound, int minBound, CFList& |
---|
1909 | factors, mat_zz_p& NTLN, CFList& diophant, CFMatrix& |
---|
1910 | M, CFArray& Pi, CFArray& bufQ, bool& irreducible, |
---|
1911 | const Variable& alpha |
---|
1912 | ) |
---|
1913 | { |
---|
1914 | CanonicalForm LCF= LC (F, 1); |
---|
1915 | CFArray *A= new CFArray [factors.length() - 1]; |
---|
1916 | bool wasInBounds= false; |
---|
1917 | int l= (minBound+1)*2; |
---|
1918 | int oldL= l/2; |
---|
1919 | int stepSize= 2; |
---|
1920 | bool hitBound= false; |
---|
1921 | int extensionDeg= degree (getMipo (alpha)); |
---|
1922 | bool reduced= false; |
---|
1923 | CFListIterator j; |
---|
1924 | CFMatrix C; |
---|
1925 | CFArray buf; |
---|
1926 | mat_zz_p* NTLC, NTLK; |
---|
1927 | Variable y= F.mvar(); |
---|
1928 | CanonicalForm truncF; |
---|
1929 | while (l <= liftBound) |
---|
1930 | { |
---|
1931 | if (start) |
---|
1932 | { |
---|
1933 | henselLiftResume12 (F, factors, start, l, Pi, diophant, M); |
---|
1934 | start= 0; |
---|
1935 | } |
---|
1936 | else |
---|
1937 | { |
---|
1938 | if (wasInBounds) |
---|
1939 | henselLiftResume12 (F, factors, oldL, l, Pi, diophant, M); |
---|
1940 | else |
---|
1941 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
1942 | } |
---|
1943 | |
---|
1944 | factors.insert (LCF); |
---|
1945 | j= factors; |
---|
1946 | j++; |
---|
1947 | |
---|
1948 | truncF= mod (F, power (y,l)); |
---|
1949 | for (int i= 0; i < factors.length() - 1; i++, j++) |
---|
1950 | { |
---|
1951 | if (l == (minBound+1)*2) |
---|
1952 | { |
---|
1953 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ[i]); |
---|
1954 | } |
---|
1955 | else |
---|
1956 | { |
---|
1957 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
1958 | bufQ[i] |
---|
1959 | ); |
---|
1960 | } |
---|
1961 | } |
---|
1962 | |
---|
1963 | for (int i= 0; i < sizeBounds; i++) |
---|
1964 | { |
---|
1965 | if (bounds [i] + 1 <= l/2) |
---|
1966 | { |
---|
1967 | wasInBounds= true; |
---|
1968 | int k= tmin (bounds [i] + 1, l/2); |
---|
1969 | C= CFMatrix ((l - k)*extensionDeg, factors.length() - 1); |
---|
1970 | for (int ii= 0; ii < factors.length() - 1; ii++) |
---|
1971 | { |
---|
1972 | if (A[ii].size() - 1 >= i) |
---|
1973 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
1974 | writeInMatrix (C, buf, ii + 1, 0); |
---|
1975 | } |
---|
1976 | |
---|
1977 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
1978 | NTLK= (*NTLC)*NTLN; |
---|
1979 | transpose (NTLK, NTLK); |
---|
1980 | kernel (NTLK, NTLK); |
---|
1981 | transpose (NTLK, NTLK); |
---|
1982 | NTLN *= NTLK; |
---|
1983 | |
---|
1984 | if (NTLN.NumCols() == 1) |
---|
1985 | { |
---|
1986 | irreducible= true; |
---|
1987 | break; |
---|
1988 | } |
---|
1989 | if (isReduced (NTLN) && l > (minBound+1)*2) |
---|
1990 | { |
---|
1991 | reduced= true; |
---|
1992 | break; |
---|
1993 | } |
---|
1994 | } |
---|
1995 | } |
---|
1996 | |
---|
1997 | if (NTLN.NumCols() == 1) |
---|
1998 | { |
---|
1999 | irreducible= true; |
---|
2000 | break; |
---|
2001 | } |
---|
2002 | if (reduced) |
---|
2003 | break; |
---|
2004 | oldL= l; |
---|
2005 | l += stepSize; |
---|
2006 | stepSize *= 2; |
---|
2007 | if (l > liftBound) |
---|
2008 | { |
---|
2009 | if (!hitBound) |
---|
2010 | { |
---|
2011 | l= liftBound; |
---|
2012 | hitBound= true; |
---|
2013 | } |
---|
2014 | else |
---|
2015 | break; |
---|
2016 | } |
---|
2017 | } |
---|
2018 | delete [] A; |
---|
2019 | return l; |
---|
2020 | } |
---|
2021 | |
---|
2022 | CFList |
---|
2023 | increasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
2024 | int oldNumCols, int oldL, int precision |
---|
2025 | ) |
---|
2026 | { |
---|
2027 | bool irreducible= false; |
---|
2028 | int d; |
---|
2029 | int* bounds= computeBounds (F, d); |
---|
2030 | CFArray * A= new CFArray [factors.length()]; |
---|
2031 | CFArray bufQ= CFArray (factors.length()); |
---|
2032 | mat_zz_p NTLN; |
---|
2033 | ident (NTLN, factors.length()); |
---|
2034 | int minBound= bounds[0]; |
---|
2035 | for (int i= 1; i < d; i++) |
---|
2036 | { |
---|
2037 | if (bounds[i] != 0) |
---|
2038 | minBound= tmin (minBound, bounds[i]); |
---|
2039 | } |
---|
2040 | int l= tmax (2*(minBound + 1), oldL); |
---|
2041 | int oldL2= l/2; |
---|
2042 | int stepSize= 2; |
---|
2043 | bool useOldQs= false; |
---|
2044 | bool hitBound= false; |
---|
2045 | CFListIterator j; |
---|
2046 | CFMatrix C; |
---|
2047 | CFArray buf; |
---|
2048 | mat_zz_p* NTLC, NTLK; |
---|
2049 | Variable y= F.mvar(); |
---|
2050 | CanonicalForm truncF; |
---|
2051 | while (l <= precision) |
---|
2052 | { |
---|
2053 | j= factors; |
---|
2054 | truncF= mod (F, power (y,l)); |
---|
2055 | if (useOldQs) |
---|
2056 | { |
---|
2057 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2058 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
2059 | bufQ[i] |
---|
2060 | ); |
---|
2061 | } |
---|
2062 | else |
---|
2063 | { |
---|
2064 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2065 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
2066 | } |
---|
2067 | useOldQs= true; |
---|
2068 | for (int i= 0; i < d; i++) |
---|
2069 | { |
---|
2070 | if (bounds [i] + 1 <= l/2) |
---|
2071 | { |
---|
2072 | int k= tmin (bounds [i] + 1, l/2); |
---|
2073 | C= CFMatrix (l - k, factors.length()); |
---|
2074 | for (int ii= 0; ii < factors.length(); ii++) |
---|
2075 | { |
---|
2076 | if (A[ii].size() - 1 >= i) |
---|
2077 | buf= getCoeffs (A[ii] [i], k); |
---|
2078 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2079 | } |
---|
2080 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
2081 | NTLK= (*NTLC)*NTLN; |
---|
2082 | transpose (NTLK, NTLK); |
---|
2083 | kernel (NTLK, NTLK); |
---|
2084 | transpose (NTLK, NTLK); |
---|
2085 | NTLN *= NTLK; |
---|
2086 | if (NTLN.NumCols() == 1) |
---|
2087 | { |
---|
2088 | irreducible= true; |
---|
2089 | delete [] A; |
---|
2090 | delete [] bounds; |
---|
2091 | CanonicalForm G= F; |
---|
2092 | F= 1; |
---|
2093 | return CFList (G); |
---|
2094 | } |
---|
2095 | } |
---|
2096 | } |
---|
2097 | |
---|
2098 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
2099 | { |
---|
2100 | if (isReduced (NTLN)) |
---|
2101 | { |
---|
2102 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
2103 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
2104 | factorsFoundIndex[i]= 0; |
---|
2105 | int factorsFound2= 0; |
---|
2106 | CFList result; |
---|
2107 | CanonicalForm bufF= F; |
---|
2108 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
2109 | factorsFoundIndex, NTLN, false |
---|
2110 | ); |
---|
2111 | if (result.length() == NTLN.NumCols()) |
---|
2112 | { |
---|
2113 | delete [] factorsFoundIndex; |
---|
2114 | delete [] A; |
---|
2115 | delete [] bounds; |
---|
2116 | F= 1; |
---|
2117 | return result; |
---|
2118 | } |
---|
2119 | delete [] factorsFoundIndex; |
---|
2120 | } |
---|
2121 | else if (l == precision) |
---|
2122 | { |
---|
2123 | CanonicalForm bufF= F; |
---|
2124 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
2125 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN); |
---|
2126 | F= bufF; |
---|
2127 | delete [] zeroOne; |
---|
2128 | delete [] A; |
---|
2129 | delete [] bounds; |
---|
2130 | return result; |
---|
2131 | } |
---|
2132 | } |
---|
2133 | oldL2= l; |
---|
2134 | l += stepSize; |
---|
2135 | stepSize *= 2; |
---|
2136 | if (l > precision) |
---|
2137 | { |
---|
2138 | if (!hitBound) |
---|
2139 | { |
---|
2140 | l= precision; |
---|
2141 | hitBound= true; |
---|
2142 | } |
---|
2143 | else |
---|
2144 | break; |
---|
2145 | } |
---|
2146 | } |
---|
2147 | delete [] bounds; |
---|
2148 | delete [] A; |
---|
2149 | return CFList(); |
---|
2150 | } |
---|
2151 | |
---|
2152 | CFList |
---|
2153 | increasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
2154 | int oldNumCols, int oldL, const Variable&, |
---|
2155 | int precision |
---|
2156 | ) |
---|
2157 | { |
---|
2158 | bool irreducible= false; |
---|
2159 | int d; |
---|
2160 | int* bounds= computeBounds (F, d); |
---|
2161 | CFArray * A= new CFArray [factors.length()]; |
---|
2162 | CFArray bufQ= CFArray (factors.length()); |
---|
2163 | mat_zz_pE NTLN; |
---|
2164 | ident (NTLN, factors.length()); |
---|
2165 | int minBound= bounds[0]; |
---|
2166 | for (int i= 1; i < d; i++) |
---|
2167 | { |
---|
2168 | if (bounds[i] != 0) |
---|
2169 | minBound= tmin (minBound, bounds[i]); |
---|
2170 | } |
---|
2171 | int l= tmax (2*(minBound + 1), oldL); |
---|
2172 | int oldL2= l/2; |
---|
2173 | int stepSize= 2; |
---|
2174 | bool useOldQs= false; |
---|
2175 | bool hitBound= false; |
---|
2176 | CFListIterator j; |
---|
2177 | CFMatrix C; |
---|
2178 | mat_zz_pE* NTLC, NTLK; |
---|
2179 | CFArray buf; |
---|
2180 | Variable y= F.mvar(); |
---|
2181 | CanonicalForm truncF; |
---|
2182 | while (l <= precision) |
---|
2183 | { |
---|
2184 | j= factors; |
---|
2185 | truncF= mod (F, power (y,l)); |
---|
2186 | if (useOldQs) |
---|
2187 | { |
---|
2188 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2189 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
2190 | bufQ[i] |
---|
2191 | ); |
---|
2192 | } |
---|
2193 | else |
---|
2194 | { |
---|
2195 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2196 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
2197 | } |
---|
2198 | useOldQs= true; |
---|
2199 | for (int i= 0; i < d; i++) |
---|
2200 | { |
---|
2201 | if (bounds [i] + 1 <= l/2) |
---|
2202 | { |
---|
2203 | int k= tmin (bounds [i] + 1, l/2); |
---|
2204 | C= CFMatrix (l - k, factors.length()); |
---|
2205 | for (int ii= 0; ii < factors.length(); ii++) |
---|
2206 | { |
---|
2207 | if (A[ii].size() - 1 >= i) |
---|
2208 | buf= getCoeffs (A[ii] [i], k); |
---|
2209 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2210 | } |
---|
2211 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
2212 | NTLK= (*NTLC)*NTLN; |
---|
2213 | transpose (NTLK, NTLK); |
---|
2214 | kernel (NTLK, NTLK); |
---|
2215 | transpose (NTLK, NTLK); |
---|
2216 | NTLN *= NTLK; |
---|
2217 | if (NTLN.NumCols() == 1) |
---|
2218 | { |
---|
2219 | irreducible= true; |
---|
2220 | delete [] A; |
---|
2221 | delete [] bounds; |
---|
2222 | return CFList (F); |
---|
2223 | } |
---|
2224 | } |
---|
2225 | } |
---|
2226 | |
---|
2227 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
2228 | { |
---|
2229 | if (isReduced (NTLN)) |
---|
2230 | { |
---|
2231 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
2232 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
2233 | factorsFoundIndex[i]= 0; |
---|
2234 | int factorsFound2= 0; |
---|
2235 | CFList result; |
---|
2236 | CanonicalForm bufF= F; |
---|
2237 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
2238 | factorsFoundIndex, NTLN, false); |
---|
2239 | if (result.length() == NTLN.NumCols()) |
---|
2240 | { |
---|
2241 | delete [] factorsFoundIndex; |
---|
2242 | delete [] A; |
---|
2243 | delete [] bounds; |
---|
2244 | F= 1; |
---|
2245 | return result; |
---|
2246 | } |
---|
2247 | delete [] factorsFoundIndex; |
---|
2248 | } |
---|
2249 | else if (l == precision) |
---|
2250 | { |
---|
2251 | CanonicalForm bufF= F; |
---|
2252 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
2253 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN); |
---|
2254 | F= bufF; |
---|
2255 | delete [] zeroOne; |
---|
2256 | delete [] A; |
---|
2257 | delete [] bounds; |
---|
2258 | return result; |
---|
2259 | } |
---|
2260 | } |
---|
2261 | oldL2= l; |
---|
2262 | l += stepSize; |
---|
2263 | stepSize *= 2; |
---|
2264 | if (l > precision) |
---|
2265 | { |
---|
2266 | if (!hitBound) |
---|
2267 | { |
---|
2268 | l= precision; |
---|
2269 | hitBound= true; |
---|
2270 | } |
---|
2271 | else |
---|
2272 | break; |
---|
2273 | } |
---|
2274 | } |
---|
2275 | delete [] bounds; |
---|
2276 | delete [] A; |
---|
2277 | return CFList(); |
---|
2278 | } |
---|
2279 | |
---|
2280 | //over field extension |
---|
2281 | CFList |
---|
2282 | extIncreasePrecision (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
2283 | int oldNumCols, int oldL, const CanonicalForm& evaluation, |
---|
2284 | const ExtensionInfo& info, CFList& source, CFList& dest, |
---|
2285 | int precision |
---|
2286 | ) |
---|
2287 | { |
---|
2288 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
2289 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
2290 | Variable alpha= info.getAlpha(); |
---|
2291 | bool irreducible= false; |
---|
2292 | int d; |
---|
2293 | int* bounds= computeBounds (F, d); |
---|
2294 | |
---|
2295 | CFArray * A= new CFArray [factors.length()]; |
---|
2296 | CFArray bufQ= CFArray (factors.length()); |
---|
2297 | zz_p::init (getCharacteristic()); |
---|
2298 | mat_zz_p NTLN; |
---|
2299 | ident (NTLN, factors.length()); |
---|
2300 | int minBound= bounds[0]; |
---|
2301 | for (int i= 1; i < d; i++) |
---|
2302 | { |
---|
2303 | if (bounds[i] != 0) |
---|
2304 | minBound= tmin (minBound, bounds[i]); |
---|
2305 | } |
---|
2306 | int l= tmax (oldL, 2*((minBound+1)/degMipo+1)); |
---|
2307 | int oldL2= l/2; |
---|
2308 | int stepSize= 2; |
---|
2309 | bool useOldQs= false; |
---|
2310 | bool hitBound= false; |
---|
2311 | Variable gamma= info.getBeta(); |
---|
2312 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
2313 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
2314 | CFListIterator j; |
---|
2315 | Variable y= F.mvar(); |
---|
2316 | CanonicalForm powX, imBasis, truncF; |
---|
2317 | CFMatrix Mat, C; |
---|
2318 | CFIterator iter; |
---|
2319 | mat_zz_p* NTLMat,*NTLC, NTLK; |
---|
2320 | CFArray buf; |
---|
2321 | while (l <= precision) |
---|
2322 | { |
---|
2323 | j= factors; |
---|
2324 | if (GF) |
---|
2325 | setCharacteristic (getCharacteristic()); |
---|
2326 | powX= power (y-gamma, l); |
---|
2327 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
2328 | for (int i= 0; i < l*degMipo; i++) |
---|
2329 | { |
---|
2330 | imBasis= mod (power (y, i), powX); |
---|
2331 | imBasis= imBasis (power (y, degMipo), y); |
---|
2332 | imBasis= imBasis (y, gamma); |
---|
2333 | iter= imBasis; |
---|
2334 | for (; iter.hasTerms(); iter++) |
---|
2335 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
2336 | } |
---|
2337 | |
---|
2338 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
2339 | *NTLMat= inv (*NTLMat); |
---|
2340 | if (GF) |
---|
2341 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
2342 | |
---|
2343 | truncF= mod (F, power (y, l)); |
---|
2344 | if (useOldQs) |
---|
2345 | { |
---|
2346 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2347 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
2348 | bufQ[i] |
---|
2349 | ); |
---|
2350 | } |
---|
2351 | else |
---|
2352 | { |
---|
2353 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2354 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
2355 | } |
---|
2356 | useOldQs= true; |
---|
2357 | for (int i= 0; i < d; i++) |
---|
2358 | { |
---|
2359 | if (bounds [i] + 1 <= (l/2)*degMipo) |
---|
2360 | { |
---|
2361 | int k= tmin (bounds [i] + 1, (l/2)*degMipo); |
---|
2362 | C= CFMatrix (l*degMipo - k, factors.length()); |
---|
2363 | for (int ii= 0; ii < factors.length(); ii++) |
---|
2364 | { |
---|
2365 | if (A[ii].size() - 1 >= i) |
---|
2366 | { |
---|
2367 | if (GF) |
---|
2368 | { |
---|
2369 | A[ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
2370 | setCharacteristic (getCharacteristic()); |
---|
2371 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
2372 | if (alpha != gamma) |
---|
2373 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
2374 | gamma, source, dest |
---|
2375 | ); |
---|
2376 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
2377 | } |
---|
2378 | else |
---|
2379 | { |
---|
2380 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
2381 | if (alpha != gamma) |
---|
2382 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
2383 | gamma, source, dest |
---|
2384 | ); |
---|
2385 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
2386 | } |
---|
2387 | } |
---|
2388 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2389 | if (GF) |
---|
2390 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
2391 | } |
---|
2392 | |
---|
2393 | if (GF) |
---|
2394 | setCharacteristic(getCharacteristic()); |
---|
2395 | |
---|
2396 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
2397 | NTLK= (*NTLC)*NTLN; |
---|
2398 | transpose (NTLK, NTLK); |
---|
2399 | kernel (NTLK, NTLK); |
---|
2400 | transpose (NTLK, NTLK); |
---|
2401 | NTLN *= NTLK; |
---|
2402 | |
---|
2403 | if (GF) |
---|
2404 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
2405 | |
---|
2406 | if (NTLN.NumCols() == 1) |
---|
2407 | { |
---|
2408 | irreducible= true; |
---|
2409 | Variable y= Variable (2); |
---|
2410 | CanonicalForm tmp= F (y - evaluation, y); |
---|
2411 | CFList source, dest; |
---|
2412 | tmp= mapDown (tmp, info, source, dest); |
---|
2413 | delete [] A; |
---|
2414 | delete [] bounds; |
---|
2415 | return CFList (tmp); |
---|
2416 | } |
---|
2417 | } |
---|
2418 | } |
---|
2419 | |
---|
2420 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
2421 | { |
---|
2422 | if (isReduced (NTLN)) |
---|
2423 | { |
---|
2424 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
2425 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
2426 | factorsFoundIndex[i]= 0; |
---|
2427 | int factorsFound2= 0; |
---|
2428 | CFList result; |
---|
2429 | CanonicalForm bufF= F; |
---|
2430 | extReconstructionTry (result, bufF, factors,degree (F)+1, factorsFound2, |
---|
2431 | factorsFoundIndex, NTLN, false, info, evaluation |
---|
2432 | ); |
---|
2433 | if (result.length() == NTLN.NumCols()) |
---|
2434 | { |
---|
2435 | delete [] factorsFoundIndex; |
---|
2436 | delete [] A; |
---|
2437 | delete [] bounds; |
---|
2438 | F= 1; |
---|
2439 | return result; |
---|
2440 | } |
---|
2441 | delete [] factorsFoundIndex; |
---|
2442 | } |
---|
2443 | else if (l == precision) |
---|
2444 | { |
---|
2445 | CanonicalForm bufF= F; |
---|
2446 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
2447 | CFList result= extReconstruction (bufF, factors, zeroOne, precision, |
---|
2448 | NTLN, info, evaluation |
---|
2449 | ); |
---|
2450 | F= bufF; |
---|
2451 | delete [] zeroOne; |
---|
2452 | delete [] A; |
---|
2453 | delete [] bounds; |
---|
2454 | return result; |
---|
2455 | } |
---|
2456 | } |
---|
2457 | oldL2= l; |
---|
2458 | l += stepSize; |
---|
2459 | stepSize *= 2; |
---|
2460 | if (l > precision) |
---|
2461 | { |
---|
2462 | if (!hitBound) |
---|
2463 | { |
---|
2464 | hitBound= true; |
---|
2465 | l= precision; |
---|
2466 | } |
---|
2467 | else |
---|
2468 | break; |
---|
2469 | } |
---|
2470 | } |
---|
2471 | delete [] bounds; |
---|
2472 | delete [] A; |
---|
2473 | return CFList(); |
---|
2474 | } |
---|
2475 | |
---|
2476 | CFList |
---|
2477 | increasePrecision2 (const CanonicalForm& F, CFList& factors, |
---|
2478 | const Variable& alpha, int precision) |
---|
2479 | { |
---|
2480 | bool irreducible= false; |
---|
2481 | int d; |
---|
2482 | int* bounds= computeBounds (F, d); |
---|
2483 | CFArray * A= new CFArray [factors.length()]; |
---|
2484 | CFArray bufQ= CFArray (factors.length()); |
---|
2485 | zz_p::init (getCharacteristic()); |
---|
2486 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
2487 | zz_pE::init (NTLMipo); |
---|
2488 | mat_zz_pE NTLN; |
---|
2489 | ident (NTLN, factors.length()); |
---|
2490 | int minBound= bounds[0]; |
---|
2491 | for (int i= 1; i < d; i++) |
---|
2492 | { |
---|
2493 | if (bounds[i] != 0) |
---|
2494 | minBound= tmin (minBound, bounds[i]); |
---|
2495 | } |
---|
2496 | int l= tmin (2*(minBound + 1), precision); |
---|
2497 | int oldL= l/2; |
---|
2498 | int stepSize= 2; |
---|
2499 | bool useOldQs= false; |
---|
2500 | bool hitBound= false; |
---|
2501 | CFListIterator j; |
---|
2502 | CFMatrix C; |
---|
2503 | CFArray buf; |
---|
2504 | mat_zz_pE* NTLC, NTLK; |
---|
2505 | Variable y= F.mvar(); |
---|
2506 | CanonicalForm truncF; |
---|
2507 | while (l <= precision) |
---|
2508 | { |
---|
2509 | j= factors; |
---|
2510 | truncF= mod (F, power (y, l)); |
---|
2511 | if (useOldQs) |
---|
2512 | { |
---|
2513 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2514 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], bufQ[i]); |
---|
2515 | } |
---|
2516 | else |
---|
2517 | { |
---|
2518 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2519 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
2520 | } |
---|
2521 | useOldQs= true; |
---|
2522 | for (int i= 0; i < d; i++) |
---|
2523 | { |
---|
2524 | if (bounds [i] + 1 <= l/2) |
---|
2525 | { |
---|
2526 | int k= tmin (bounds [i] + 1, l/2); |
---|
2527 | C= CFMatrix (l - k, factors.length()); |
---|
2528 | for (int ii= 0; ii < factors.length(); ii++) |
---|
2529 | { |
---|
2530 | if (A[ii].size() - 1 >= i) |
---|
2531 | buf= getCoeffs (A[ii] [i], k); |
---|
2532 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2533 | } |
---|
2534 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
2535 | NTLK= (*NTLC)*NTLN; |
---|
2536 | transpose (NTLK, NTLK); |
---|
2537 | kernel (NTLK, NTLK); |
---|
2538 | transpose (NTLK, NTLK); |
---|
2539 | NTLN *= NTLK; |
---|
2540 | if (NTLN.NumCols() == 1) |
---|
2541 | { |
---|
2542 | irreducible= true; |
---|
2543 | delete [] A; |
---|
2544 | delete [] bounds; |
---|
2545 | return CFList (F); |
---|
2546 | } |
---|
2547 | } |
---|
2548 | } |
---|
2549 | |
---|
2550 | if (isReduced (NTLN) || l == precision) |
---|
2551 | { |
---|
2552 | CanonicalForm bufF= F; |
---|
2553 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
2554 | CFList bufFactors= factors; |
---|
2555 | CFList result= monicReconstruction (bufF, factors, zeroOne, precision, |
---|
2556 | NTLN |
---|
2557 | ); |
---|
2558 | if (result.length() != NTLN.NumCols() && l != precision) |
---|
2559 | factors= bufFactors; |
---|
2560 | if (result.length() == NTLN.NumCols()) |
---|
2561 | { |
---|
2562 | delete [] zeroOne; |
---|
2563 | delete [] A; |
---|
2564 | delete [] bounds; |
---|
2565 | return result; |
---|
2566 | } |
---|
2567 | if (l == precision) |
---|
2568 | { |
---|
2569 | delete [] zeroOne; |
---|
2570 | delete [] A; |
---|
2571 | delete [] bounds; |
---|
2572 | return Union (result, factors); |
---|
2573 | } |
---|
2574 | } |
---|
2575 | oldL= l; |
---|
2576 | l += stepSize; |
---|
2577 | stepSize *= 2; |
---|
2578 | if (l > precision) |
---|
2579 | { |
---|
2580 | if (!hitBound) |
---|
2581 | { |
---|
2582 | l= precision; |
---|
2583 | hitBound= true; |
---|
2584 | } |
---|
2585 | else |
---|
2586 | break; |
---|
2587 | } |
---|
2588 | } |
---|
2589 | delete [] bounds; |
---|
2590 | delete [] A; |
---|
2591 | return CFList(); |
---|
2592 | } |
---|
2593 | |
---|
2594 | CFList |
---|
2595 | increasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int factorsFound, |
---|
2596 | int oldNumCols, int oldL, const Variable& alpha, |
---|
2597 | int precision |
---|
2598 | ) |
---|
2599 | { |
---|
2600 | bool irreducible= false; |
---|
2601 | int d; |
---|
2602 | int* bounds= computeBounds (F, d); |
---|
2603 | int extensionDeg= degree (getMipo (alpha)); |
---|
2604 | CFArray * A= new CFArray [factors.length()]; |
---|
2605 | CFArray bufQ= CFArray (factors.length()); |
---|
2606 | mat_zz_p NTLN; |
---|
2607 | ident (NTLN, factors.length()); |
---|
2608 | int minBound= bounds[0]; |
---|
2609 | for (int i= 1; i < d; i++) |
---|
2610 | { |
---|
2611 | if (bounds[i] != 0) |
---|
2612 | minBound= tmin (minBound, bounds[i]); |
---|
2613 | } |
---|
2614 | int l= tmax (2*(minBound + 1), oldL); |
---|
2615 | int oldL2= l/2; |
---|
2616 | int stepSize= 2; |
---|
2617 | bool useOldQs= false; |
---|
2618 | bool hitBound= false; |
---|
2619 | CFListIterator j; |
---|
2620 | CFMatrix C; |
---|
2621 | mat_zz_p* NTLC, NTLK; |
---|
2622 | CFArray buf; |
---|
2623 | Variable y= F.mvar(); |
---|
2624 | CanonicalForm truncF; |
---|
2625 | while (l <= precision) |
---|
2626 | { |
---|
2627 | j= factors; |
---|
2628 | truncF= mod (F, power (y, l)); |
---|
2629 | if (useOldQs) |
---|
2630 | { |
---|
2631 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2632 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL2, bufQ[i], |
---|
2633 | bufQ[i] |
---|
2634 | ); |
---|
2635 | } |
---|
2636 | else |
---|
2637 | { |
---|
2638 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2639 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
2640 | } |
---|
2641 | useOldQs= true; |
---|
2642 | for (int i= 0; i < d; i++) |
---|
2643 | { |
---|
2644 | if (bounds [i] + 1 <= l/2) |
---|
2645 | { |
---|
2646 | int k= tmin (bounds [i] + 1, l/2); |
---|
2647 | C= CFMatrix ((l - k)*extensionDeg, factors.length()); |
---|
2648 | for (int ii= 0; ii < factors.length(); ii++) |
---|
2649 | { |
---|
2650 | if (A[ii].size() - 1 >= i) |
---|
2651 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
2652 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2653 | } |
---|
2654 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
2655 | NTLK= (*NTLC)*NTLN; |
---|
2656 | transpose (NTLK, NTLK); |
---|
2657 | kernel (NTLK, NTLK); |
---|
2658 | transpose (NTLK, NTLK); |
---|
2659 | NTLN *= NTLK; |
---|
2660 | if (NTLN.NumCols() == 1) |
---|
2661 | { |
---|
2662 | irreducible= true; |
---|
2663 | delete [] A; |
---|
2664 | delete [] bounds; |
---|
2665 | return CFList (F); |
---|
2666 | } |
---|
2667 | } |
---|
2668 | } |
---|
2669 | |
---|
2670 | if (NTLN.NumCols() < oldNumCols - factorsFound) |
---|
2671 | { |
---|
2672 | if (isReduced (NTLN)) |
---|
2673 | { |
---|
2674 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
2675 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
2676 | factorsFoundIndex[i]= 0; |
---|
2677 | int factorsFound2= 0; |
---|
2678 | CFList result; |
---|
2679 | CanonicalForm bufF= F; |
---|
2680 | reconstructionTry (result, bufF, factors, degree (F) + 1, factorsFound2, |
---|
2681 | factorsFoundIndex, NTLN, false |
---|
2682 | ); |
---|
2683 | if (result.length() == NTLN.NumCols()) |
---|
2684 | { |
---|
2685 | delete [] factorsFoundIndex; |
---|
2686 | delete [] A; |
---|
2687 | delete [] bounds; |
---|
2688 | F= 1; |
---|
2689 | return result; |
---|
2690 | } |
---|
2691 | delete [] factorsFoundIndex; |
---|
2692 | } |
---|
2693 | else if (l == precision) |
---|
2694 | { |
---|
2695 | CanonicalForm bufF= F; |
---|
2696 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
2697 | CFList result= reconstruction (bufF, factors, zeroOne, precision, NTLN); |
---|
2698 | F= bufF; |
---|
2699 | delete [] zeroOne; |
---|
2700 | delete [] A; |
---|
2701 | delete [] bounds; |
---|
2702 | return result; |
---|
2703 | } |
---|
2704 | } |
---|
2705 | oldL2= l; |
---|
2706 | l += stepSize; |
---|
2707 | stepSize *= 2; |
---|
2708 | if (l > precision) |
---|
2709 | { |
---|
2710 | if (!hitBound) |
---|
2711 | { |
---|
2712 | hitBound= true; |
---|
2713 | l= precision; |
---|
2714 | } |
---|
2715 | else |
---|
2716 | break; |
---|
2717 | } |
---|
2718 | } |
---|
2719 | delete [] bounds; |
---|
2720 | delete [] A; |
---|
2721 | return CFList(); |
---|
2722 | } |
---|
2723 | |
---|
2724 | CFList |
---|
2725 | increasePrecision (CanonicalForm& F, CFList& factors, int oldL, int |
---|
2726 | l, int d, int* bounds, CFArray& bufQ, mat_zz_p& NTLN |
---|
2727 | ) |
---|
2728 | { |
---|
2729 | CFList result= CFList(); |
---|
2730 | bool irreducible= false; |
---|
2731 | CFArray * A= new CFArray [factors.length()]; |
---|
2732 | int oldL2= oldL/2; |
---|
2733 | bool hitBound= false; |
---|
2734 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
2735 | { |
---|
2736 | ident (NTLN, factors.length()); |
---|
2737 | bufQ= CFArray (factors.length()); |
---|
2738 | } |
---|
2739 | bool useOldQs= false; |
---|
2740 | CFListIterator j; |
---|
2741 | CFMatrix C; |
---|
2742 | CFArray buf; |
---|
2743 | mat_zz_p* NTLC, NTLK; |
---|
2744 | CanonicalForm bufF, truncF; |
---|
2745 | CFList bufUniFactors; |
---|
2746 | Variable y= F.mvar(); |
---|
2747 | while (oldL <= l) |
---|
2748 | { |
---|
2749 | j= factors; |
---|
2750 | truncF= mod (F, power (y, oldL)); |
---|
2751 | if (useOldQs) |
---|
2752 | { |
---|
2753 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2754 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
2755 | bufQ[i] |
---|
2756 | ); |
---|
2757 | } |
---|
2758 | else |
---|
2759 | { |
---|
2760 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2761 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
2762 | } |
---|
2763 | useOldQs= true; |
---|
2764 | |
---|
2765 | for (int i= 0; i < d; i++) |
---|
2766 | { |
---|
2767 | if (bounds [i] + 1 <= oldL/2) |
---|
2768 | { |
---|
2769 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
2770 | C= CFMatrix (oldL - k, factors.length()); |
---|
2771 | for (int ii= 0; ii < factors.length(); ii++) |
---|
2772 | { |
---|
2773 | if (A[ii].size() - 1 >= i) |
---|
2774 | buf= getCoeffs (A[ii] [i], k); |
---|
2775 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2776 | } |
---|
2777 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
2778 | NTLK= (*NTLC)*NTLN; |
---|
2779 | transpose (NTLK, NTLK); |
---|
2780 | kernel (NTLK, NTLK); |
---|
2781 | transpose (NTLK, NTLK); |
---|
2782 | NTLN *= NTLK; |
---|
2783 | if (NTLN.NumCols() == 1) |
---|
2784 | { |
---|
2785 | irreducible= true; |
---|
2786 | delete [] A; |
---|
2787 | return CFList (F); |
---|
2788 | } |
---|
2789 | } |
---|
2790 | } |
---|
2791 | if (NTLN.NumCols() == 1) |
---|
2792 | { |
---|
2793 | irreducible= true; |
---|
2794 | delete [] A; |
---|
2795 | return CFList (F); |
---|
2796 | } |
---|
2797 | int * zeroOneVecs; |
---|
2798 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
2799 | bufF= F; |
---|
2800 | bufUniFactors= factors; |
---|
2801 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN); |
---|
2802 | delete [] zeroOneVecs; |
---|
2803 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < oldL && result.length() > 0) |
---|
2804 | { |
---|
2805 | F= bufF; |
---|
2806 | factors= bufUniFactors; |
---|
2807 | delete [] A; |
---|
2808 | return result; |
---|
2809 | } |
---|
2810 | |
---|
2811 | result= CFList(); |
---|
2812 | oldL2= oldL; |
---|
2813 | oldL *= 2; |
---|
2814 | if (oldL > l) |
---|
2815 | { |
---|
2816 | if (!hitBound) |
---|
2817 | { |
---|
2818 | oldL= l; |
---|
2819 | hitBound= true; |
---|
2820 | } |
---|
2821 | else |
---|
2822 | break; |
---|
2823 | } |
---|
2824 | } |
---|
2825 | delete [] A; |
---|
2826 | return result; |
---|
2827 | } |
---|
2828 | |
---|
2829 | CFList |
---|
2830 | increasePrecision (CanonicalForm& F, CFList& factors, int oldL, int |
---|
2831 | l, int d, int* bounds, CFArray& bufQ, mat_zz_pE& NTLN |
---|
2832 | ) |
---|
2833 | { |
---|
2834 | CFList result= CFList(); |
---|
2835 | bool irreducible= false; |
---|
2836 | CFArray * A= new CFArray [factors.length()]; |
---|
2837 | int oldL2= oldL/2; |
---|
2838 | bool hitBound= false; |
---|
2839 | bool useOldQs= false; |
---|
2840 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
2841 | ident (NTLN, factors.length()); |
---|
2842 | CFListIterator j; |
---|
2843 | CFMatrix C; |
---|
2844 | CFArray buf; |
---|
2845 | mat_zz_pE* NTLC, NTLK; |
---|
2846 | CanonicalForm bufF, truncF; |
---|
2847 | CFList bufUniFactors; |
---|
2848 | Variable y= F.mvar(); |
---|
2849 | while (oldL <= l) |
---|
2850 | { |
---|
2851 | j= factors; |
---|
2852 | truncF= mod (F, power (y, oldL)); |
---|
2853 | if (useOldQs) |
---|
2854 | { |
---|
2855 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2856 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
2857 | bufQ[i] |
---|
2858 | ); |
---|
2859 | } |
---|
2860 | else |
---|
2861 | { |
---|
2862 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2863 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
2864 | } |
---|
2865 | useOldQs= true; |
---|
2866 | |
---|
2867 | for (int i= 0; i < d; i++) |
---|
2868 | { |
---|
2869 | if (bounds [i] + 1 <= oldL/2) |
---|
2870 | { |
---|
2871 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
2872 | C= CFMatrix (oldL - k, factors.length()); |
---|
2873 | for (int ii= 0; ii < factors.length(); ii++) |
---|
2874 | { |
---|
2875 | if (A[ii].size() - 1 >= i) |
---|
2876 | buf= getCoeffs (A[ii] [i], k); |
---|
2877 | writeInMatrix (C, buf, ii + 1, 0); |
---|
2878 | } |
---|
2879 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
2880 | NTLK= (*NTLC)*NTLN; |
---|
2881 | transpose (NTLK, NTLK); |
---|
2882 | kernel (NTLK, NTLK); |
---|
2883 | transpose (NTLK, NTLK); |
---|
2884 | NTLN *= NTLK; |
---|
2885 | if (NTLN.NumCols() == 1) |
---|
2886 | { |
---|
2887 | irreducible= true; |
---|
2888 | delete [] A; |
---|
2889 | return CFList (F); |
---|
2890 | } |
---|
2891 | } |
---|
2892 | } |
---|
2893 | if (NTLN.NumCols() == 1) |
---|
2894 | { |
---|
2895 | irreducible= true; |
---|
2896 | delete [] A; |
---|
2897 | return CFList (F); |
---|
2898 | } |
---|
2899 | |
---|
2900 | int * zeroOneVecs; |
---|
2901 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
2902 | bufF= F; |
---|
2903 | bufUniFactors= factors; |
---|
2904 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN); |
---|
2905 | delete [] zeroOneVecs; |
---|
2906 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
2907 | { |
---|
2908 | F= bufF; |
---|
2909 | factors= bufUniFactors; |
---|
2910 | delete [] A; |
---|
2911 | return result; |
---|
2912 | } |
---|
2913 | |
---|
2914 | result= CFList(); |
---|
2915 | oldL2= oldL; |
---|
2916 | oldL *= 2; |
---|
2917 | if (oldL > l) |
---|
2918 | { |
---|
2919 | if (!hitBound) |
---|
2920 | { |
---|
2921 | oldL= l; |
---|
2922 | hitBound= true; |
---|
2923 | } |
---|
2924 | else |
---|
2925 | break; |
---|
2926 | } |
---|
2927 | } |
---|
2928 | delete [] A; |
---|
2929 | return result; |
---|
2930 | } |
---|
2931 | |
---|
2932 | //over field extension |
---|
2933 | CFList |
---|
2934 | extIncreasePrecision (CanonicalForm& F, CFList& factors, int oldL, int l, int d, |
---|
2935 | int* bounds, CFArray& bufQ, mat_zz_p& NTLN, const |
---|
2936 | CanonicalForm& evaluation, const ExtensionInfo& info, |
---|
2937 | CFList& source, CFList& dest |
---|
2938 | ) |
---|
2939 | { |
---|
2940 | CFList result= CFList(); |
---|
2941 | bool irreducible= false; |
---|
2942 | CFArray * A= new CFArray [factors.length()]; |
---|
2943 | int oldL2= oldL/2; //be careful |
---|
2944 | bool hitBound= false; |
---|
2945 | bool useOldQs= false; |
---|
2946 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
2947 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
2948 | Variable alpha= info.getAlpha(); |
---|
2949 | |
---|
2950 | Variable gamma= info.getBeta(); |
---|
2951 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
2952 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
2953 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
2954 | ident (NTLN, factors.length()); |
---|
2955 | Variable y= F.mvar(); |
---|
2956 | CFListIterator j; |
---|
2957 | CanonicalForm powX, imBasis, bufF, truncF; |
---|
2958 | CFMatrix Mat, C; |
---|
2959 | CFIterator iter; |
---|
2960 | mat_zz_p* NTLMat; |
---|
2961 | CFArray buf; |
---|
2962 | mat_zz_p* NTLC, NTLK; |
---|
2963 | CFList bufUniFactors; |
---|
2964 | while (oldL <= l) |
---|
2965 | { |
---|
2966 | j= factors; |
---|
2967 | if (GF) |
---|
2968 | setCharacteristic (getCharacteristic()); |
---|
2969 | |
---|
2970 | powX= power (y-gamma, oldL); |
---|
2971 | Mat= CFMatrix (oldL*degMipo, oldL*degMipo); |
---|
2972 | for (int i= 0; i < oldL*degMipo; i++) |
---|
2973 | { |
---|
2974 | imBasis= mod (power (y, i), powX); |
---|
2975 | imBasis= imBasis (power (y, degMipo), y); |
---|
2976 | imBasis= imBasis (y, gamma); |
---|
2977 | iter= imBasis; |
---|
2978 | for (; iter.hasTerms(); iter++) |
---|
2979 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
2980 | } |
---|
2981 | |
---|
2982 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
2983 | *NTLMat= inv (*NTLMat); |
---|
2984 | if (GF) |
---|
2985 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
2986 | |
---|
2987 | truncF= mod (F, power (y, oldL)); |
---|
2988 | if (useOldQs) |
---|
2989 | { |
---|
2990 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2991 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
2992 | bufQ[i]); |
---|
2993 | } |
---|
2994 | else |
---|
2995 | { |
---|
2996 | for (int i= 0; i < factors.length(); i++, j++) |
---|
2997 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
2998 | } |
---|
2999 | useOldQs= true; |
---|
3000 | |
---|
3001 | for (int i= 0; i < d; i++) |
---|
3002 | { |
---|
3003 | if (bounds [i] + 1 <= oldL/2) |
---|
3004 | { |
---|
3005 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
3006 | C= CFMatrix (oldL*degMipo - k, factors.length()); |
---|
3007 | for (int ii= 0; ii < factors.length(); ii++) |
---|
3008 | { |
---|
3009 | if (A[ii].size() - 1 >= i) |
---|
3010 | { |
---|
3011 | if (GF) |
---|
3012 | { |
---|
3013 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
3014 | setCharacteristic (getCharacteristic()); |
---|
3015 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
3016 | if (alpha != gamma) |
---|
3017 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
3018 | gamma, source, dest |
---|
3019 | ); |
---|
3020 | buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, *NTLMat); |
---|
3021 | } |
---|
3022 | else |
---|
3023 | { |
---|
3024 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
3025 | if (alpha != gamma) |
---|
3026 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
3027 | gamma, source, dest |
---|
3028 | ); |
---|
3029 | buf= getCoeffs (A[ii] [i], k, oldL, degMipo, gamma, 0, *NTLMat); |
---|
3030 | } |
---|
3031 | } |
---|
3032 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3033 | if (GF) |
---|
3034 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
3035 | } |
---|
3036 | |
---|
3037 | if (GF) |
---|
3038 | setCharacteristic(getCharacteristic()); |
---|
3039 | |
---|
3040 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
3041 | NTLK= (*NTLC)*NTLN; |
---|
3042 | transpose (NTLK, NTLK); |
---|
3043 | kernel (NTLK, NTLK); |
---|
3044 | transpose (NTLK, NTLK); |
---|
3045 | NTLN *= NTLK; |
---|
3046 | |
---|
3047 | if (GF) |
---|
3048 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
3049 | |
---|
3050 | if (NTLN.NumCols() == 1) |
---|
3051 | { |
---|
3052 | irreducible= true; |
---|
3053 | Variable y= Variable (2); |
---|
3054 | CanonicalForm tmp= F (y - evaluation, y); |
---|
3055 | CFList source, dest; |
---|
3056 | tmp= mapDown (tmp, info, source, dest); |
---|
3057 | delete [] A; |
---|
3058 | return CFList (tmp); |
---|
3059 | } |
---|
3060 | } |
---|
3061 | } |
---|
3062 | if (NTLN.NumCols() == 1) |
---|
3063 | { |
---|
3064 | irreducible= true; |
---|
3065 | Variable y= Variable (2); |
---|
3066 | CanonicalForm tmp= F (y - evaluation, y); |
---|
3067 | CFList source, dest; |
---|
3068 | tmp= mapDown (tmp, info, source, dest); |
---|
3069 | delete [] A; |
---|
3070 | return CFList (tmp); |
---|
3071 | } |
---|
3072 | |
---|
3073 | int * zeroOneVecs; |
---|
3074 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
3075 | bufF= F; |
---|
3076 | bufUniFactors= factors; |
---|
3077 | result= extReconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN, |
---|
3078 | info, evaluation |
---|
3079 | ); |
---|
3080 | delete [] zeroOneVecs; |
---|
3081 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
3082 | { |
---|
3083 | F= bufF; |
---|
3084 | factors= bufUniFactors; |
---|
3085 | return result; |
---|
3086 | } |
---|
3087 | |
---|
3088 | result= CFList(); |
---|
3089 | oldL2= oldL; |
---|
3090 | oldL *= 2; |
---|
3091 | if (oldL > l) |
---|
3092 | { |
---|
3093 | if (!hitBound) |
---|
3094 | { |
---|
3095 | oldL= l; |
---|
3096 | hitBound= true; |
---|
3097 | } |
---|
3098 | else |
---|
3099 | break; |
---|
3100 | } |
---|
3101 | } |
---|
3102 | delete [] A; |
---|
3103 | return result; |
---|
3104 | } |
---|
3105 | |
---|
3106 | CFList |
---|
3107 | increasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int oldL, int l, |
---|
3108 | int d, int* bounds, CFArray& bufQ, mat_zz_p& NTLN, |
---|
3109 | const Variable& alpha |
---|
3110 | ) |
---|
3111 | { |
---|
3112 | CFList result= CFList(); |
---|
3113 | bool irreducible= false; |
---|
3114 | CFArray * A= new CFArray [factors.length()]; |
---|
3115 | int extensionDeg= degree (getMipo (alpha)); |
---|
3116 | int oldL2= oldL/2; |
---|
3117 | bool hitBound= false; |
---|
3118 | bool useOldQs= false; |
---|
3119 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
3120 | ident (NTLN, factors.length()); |
---|
3121 | CFListIterator j; |
---|
3122 | CFMatrix C; |
---|
3123 | CFArray buf; |
---|
3124 | mat_zz_p* NTLC, NTLK; |
---|
3125 | CanonicalForm bufF, truncF; |
---|
3126 | CFList bufUniFactors; |
---|
3127 | Variable y= F.mvar(); |
---|
3128 | while (oldL <= l) |
---|
3129 | { |
---|
3130 | j= factors; |
---|
3131 | truncF= mod (F, power (y, oldL)); |
---|
3132 | if (useOldQs) |
---|
3133 | { |
---|
3134 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3135 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, oldL2, bufQ[i], |
---|
3136 | bufQ[i] |
---|
3137 | ); |
---|
3138 | } |
---|
3139 | else |
---|
3140 | { |
---|
3141 | for (int i= 0; i < factors.length(); i++, j++) |
---|
3142 | A[i]= logarithmicDerivative (truncF, j.getItem(), oldL, bufQ [i]); |
---|
3143 | } |
---|
3144 | useOldQs= true; |
---|
3145 | |
---|
3146 | for (int i= 0; i < d; i++) |
---|
3147 | { |
---|
3148 | if (bounds [i] + 1 <= oldL/2) |
---|
3149 | { |
---|
3150 | int k= tmin (bounds [i] + 1, oldL/2); |
---|
3151 | C= CFMatrix ((oldL - k)*extensionDeg, factors.length()); |
---|
3152 | for (int ii= 0; ii < factors.length(); ii++) |
---|
3153 | { |
---|
3154 | if (A[ii].size() - 1 >= i) |
---|
3155 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
3156 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3157 | } |
---|
3158 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
3159 | NTLK= (*NTLC)*NTLN; |
---|
3160 | transpose (NTLK, NTLK); |
---|
3161 | kernel (NTLK, NTLK); |
---|
3162 | transpose (NTLK, NTLK); |
---|
3163 | NTLN *= NTLK; |
---|
3164 | if (NTLN.NumCols() == 1) |
---|
3165 | { |
---|
3166 | irreducible= true; |
---|
3167 | delete [] A; |
---|
3168 | return CFList (F); |
---|
3169 | } |
---|
3170 | } |
---|
3171 | } |
---|
3172 | |
---|
3173 | int * zeroOneVecs; |
---|
3174 | zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
3175 | |
---|
3176 | bufF= F; |
---|
3177 | bufUniFactors= factors; |
---|
3178 | result= reconstruction (bufF, bufUniFactors, zeroOneVecs, oldL, NTLN); |
---|
3179 | delete [] zeroOneVecs; |
---|
3180 | if (degree (bufF) + 1 + degree (LC (bufF, 1)) < l && result.length() > 0) |
---|
3181 | { |
---|
3182 | F= bufF; |
---|
3183 | factors= bufUniFactors; |
---|
3184 | delete [] A; |
---|
3185 | return result; |
---|
3186 | } |
---|
3187 | |
---|
3188 | result= CFList(); |
---|
3189 | oldL2= oldL; |
---|
3190 | oldL *= 2; |
---|
3191 | if (oldL > l) |
---|
3192 | { |
---|
3193 | if (!hitBound) |
---|
3194 | { |
---|
3195 | oldL= l; |
---|
3196 | hitBound= true; |
---|
3197 | } |
---|
3198 | else |
---|
3199 | break; |
---|
3200 | } |
---|
3201 | } |
---|
3202 | delete [] A; |
---|
3203 | return result; |
---|
3204 | } |
---|
3205 | |
---|
3206 | CFList |
---|
3207 | furtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& |
---|
3208 | factors, int l, int liftBound, int d, int* |
---|
3209 | bounds, mat_zz_p& NTLN, CFList& diophant, |
---|
3210 | CFMatrix& M, CFArray& Pi, CFArray& bufQ |
---|
3211 | ) |
---|
3212 | { |
---|
3213 | CanonicalForm LCF= LC (F, 1); |
---|
3214 | CFList result; |
---|
3215 | bool irreducible= false; |
---|
3216 | CFList bufFactors= factors; |
---|
3217 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
3218 | bool useOldQs= false; |
---|
3219 | bool hitBound= false; |
---|
3220 | int oldL= l; |
---|
3221 | int stepSize= 8; //TODO choose better step size? |
---|
3222 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
3223 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
3224 | ident (NTLN, factors.length()); |
---|
3225 | CFListIterator j; |
---|
3226 | CFMatrix C; |
---|
3227 | CFArray buf; |
---|
3228 | mat_zz_p* NTLC, NTLK; |
---|
3229 | CanonicalForm bufF, truncF; |
---|
3230 | Variable y= F.mvar(); |
---|
3231 | while (l <= liftBound) |
---|
3232 | { |
---|
3233 | bufFactors.insert (LCF); |
---|
3234 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
3235 | bufFactors.insert (LCF); |
---|
3236 | bufFactors.removeFirst(); |
---|
3237 | j= bufFactors; |
---|
3238 | truncF= mod (F, power (y, l)); |
---|
3239 | if (useOldQs) |
---|
3240 | { |
---|
3241 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
3242 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
3243 | bufQ[i]); |
---|
3244 | } |
---|
3245 | else |
---|
3246 | { |
---|
3247 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
3248 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
3249 | } |
---|
3250 | for (int i= 0; i < d; i++) |
---|
3251 | { |
---|
3252 | if (bounds [i] + 1 <= l/2) |
---|
3253 | { |
---|
3254 | int k= tmin (bounds [i] + 1, l/2); |
---|
3255 | C= CFMatrix (l - k, bufFactors.length()); |
---|
3256 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
3257 | { |
---|
3258 | if (A[ii].size() - 1 >= i) |
---|
3259 | buf= getCoeffs (A[ii] [i], k); |
---|
3260 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3261 | } |
---|
3262 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
3263 | NTLK= (*NTLC)*NTLN; |
---|
3264 | transpose (NTLK, NTLK); |
---|
3265 | kernel (NTLK, NTLK); |
---|
3266 | transpose (NTLK, NTLK); |
---|
3267 | NTLN *= NTLK; |
---|
3268 | if (NTLN.NumCols() == 1) |
---|
3269 | { |
---|
3270 | irreducible= true; |
---|
3271 | break; |
---|
3272 | } |
---|
3273 | } |
---|
3274 | } |
---|
3275 | |
---|
3276 | if (NTLN.NumCols() == 1) |
---|
3277 | { |
---|
3278 | irreducible= true; |
---|
3279 | break; |
---|
3280 | } |
---|
3281 | |
---|
3282 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
3283 | bufF= F; |
---|
3284 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN); |
---|
3285 | delete [] zeroOneVecs; |
---|
3286 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
3287 | { |
---|
3288 | F= bufF; |
---|
3289 | factors= bufFactors; |
---|
3290 | delete [] A; |
---|
3291 | return result; |
---|
3292 | } |
---|
3293 | |
---|
3294 | if (isReduced (NTLN)) |
---|
3295 | { |
---|
3296 | int factorsFound= 0; |
---|
3297 | bufF= F; |
---|
3298 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
3299 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
3300 | factorsFoundIndex[i]= 0; |
---|
3301 | if (l < liftBound) |
---|
3302 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
3303 | factorsFoundIndex, NTLN, false |
---|
3304 | ); |
---|
3305 | else |
---|
3306 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
3307 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
3308 | NTLN, false |
---|
3309 | ); |
---|
3310 | |
---|
3311 | if (NTLN.NumCols() == result.length()) |
---|
3312 | { |
---|
3313 | delete [] A; |
---|
3314 | delete [] factorsFoundIndex; |
---|
3315 | return result; |
---|
3316 | } |
---|
3317 | delete [] factorsFoundIndex; |
---|
3318 | } |
---|
3319 | result= CFList(); |
---|
3320 | oldL= l; |
---|
3321 | stepSize *= 2; |
---|
3322 | l += stepSize; |
---|
3323 | if (l > liftBound) |
---|
3324 | { |
---|
3325 | if (!hitBound) |
---|
3326 | { |
---|
3327 | l= liftBound; |
---|
3328 | hitBound= true; |
---|
3329 | } |
---|
3330 | else |
---|
3331 | break; |
---|
3332 | } |
---|
3333 | } |
---|
3334 | if (irreducible) |
---|
3335 | { |
---|
3336 | delete [] A; |
---|
3337 | return CFList (F); |
---|
3338 | } |
---|
3339 | delete [] A; |
---|
3340 | factors= bufFactors; |
---|
3341 | return CFList(); |
---|
3342 | } |
---|
3343 | |
---|
3344 | //Fq |
---|
3345 | CFList |
---|
3346 | furtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& |
---|
3347 | factors, int l, int liftBound, int d, int* |
---|
3348 | bounds, mat_zz_pE& NTLN, CFList& diophant, |
---|
3349 | CFMatrix& M, CFArray& Pi, CFArray& bufQ |
---|
3350 | ) |
---|
3351 | { |
---|
3352 | CanonicalForm LCF= LC (F, 1); |
---|
3353 | CFList result; |
---|
3354 | bool irreducible= false; |
---|
3355 | CFList bufFactors= factors; |
---|
3356 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
3357 | bool useOldQs= false; |
---|
3358 | bool hitBound= false; |
---|
3359 | int oldL= l; |
---|
3360 | int stepSize= 8; //TODO choose better step size? |
---|
3361 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
3362 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
3363 | ident (NTLN, factors.length()); |
---|
3364 | CFListIterator j; |
---|
3365 | CFArray buf; |
---|
3366 | mat_zz_pE* NTLC, NTLK; |
---|
3367 | CanonicalForm bufF, truncF; |
---|
3368 | Variable y= F.mvar(); |
---|
3369 | while (l <= liftBound) |
---|
3370 | { |
---|
3371 | bufFactors.insert (LCF); |
---|
3372 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
3373 | j= bufFactors; |
---|
3374 | truncF= mod (F, power (y, l)); |
---|
3375 | if (useOldQs) |
---|
3376 | { |
---|
3377 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
3378 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
3379 | bufQ[i]); |
---|
3380 | } |
---|
3381 | else |
---|
3382 | { |
---|
3383 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
3384 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
3385 | } |
---|
3386 | for (int i= 0; i < d; i++) |
---|
3387 | { |
---|
3388 | if (bounds [i] + 1 <= l/2) |
---|
3389 | { |
---|
3390 | int k= tmin (bounds [i] + 1, l/2); |
---|
3391 | CFMatrix C= CFMatrix (l - k, bufFactors.length()); |
---|
3392 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
3393 | { |
---|
3394 | if (A[ii].size() - 1 >= i) |
---|
3395 | buf= getCoeffs (A[ii] [i], k); |
---|
3396 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3397 | } |
---|
3398 | NTLC= convertFacCFMatrix2NTLmat_zz_pE(C); |
---|
3399 | NTLK= (*NTLC)*NTLN; |
---|
3400 | transpose (NTLK, NTLK); |
---|
3401 | kernel (NTLK, NTLK); |
---|
3402 | transpose (NTLK, NTLK); |
---|
3403 | NTLN *= NTLK; |
---|
3404 | if (NTLN.NumCols() == 1) |
---|
3405 | { |
---|
3406 | irreducible= true; |
---|
3407 | break; |
---|
3408 | } |
---|
3409 | } |
---|
3410 | } |
---|
3411 | if (NTLN.NumCols() == 1) |
---|
3412 | { |
---|
3413 | irreducible= true; |
---|
3414 | break; |
---|
3415 | } |
---|
3416 | |
---|
3417 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
3418 | bufF= F; |
---|
3419 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN); |
---|
3420 | delete [] zeroOneVecs; |
---|
3421 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
3422 | { |
---|
3423 | F= bufF; |
---|
3424 | factors= bufFactors; |
---|
3425 | delete [] A; |
---|
3426 | return result; |
---|
3427 | } |
---|
3428 | |
---|
3429 | if (isReduced (NTLN)) |
---|
3430 | { |
---|
3431 | int factorsFound= 0; |
---|
3432 | bufF= F; |
---|
3433 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
3434 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
3435 | factorsFoundIndex[i]= 0; |
---|
3436 | if (l < liftBound) |
---|
3437 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
3438 | factorsFoundIndex, NTLN, false |
---|
3439 | ); |
---|
3440 | else |
---|
3441 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
3442 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
3443 | NTLN, false |
---|
3444 | ); |
---|
3445 | if (NTLN.NumCols() == result.length()) |
---|
3446 | { |
---|
3447 | delete [] A; |
---|
3448 | delete [] factorsFoundIndex; |
---|
3449 | return result; |
---|
3450 | } |
---|
3451 | delete [] factorsFoundIndex; |
---|
3452 | } |
---|
3453 | result= CFList(); |
---|
3454 | oldL= l; |
---|
3455 | stepSize *= 2; |
---|
3456 | l += stepSize; |
---|
3457 | if (l > liftBound) |
---|
3458 | { |
---|
3459 | if (!hitBound) |
---|
3460 | { |
---|
3461 | l= liftBound; |
---|
3462 | hitBound= true; |
---|
3463 | } |
---|
3464 | else |
---|
3465 | break; |
---|
3466 | } |
---|
3467 | } |
---|
3468 | if (irreducible) |
---|
3469 | { |
---|
3470 | delete [] A; |
---|
3471 | return CFList (F); |
---|
3472 | } |
---|
3473 | delete [] A; |
---|
3474 | factors= bufFactors; |
---|
3475 | return CFList(); |
---|
3476 | } |
---|
3477 | |
---|
3478 | //over field extension |
---|
3479 | CFList |
---|
3480 | extFurtherLiftingAndIncreasePrecision (CanonicalForm& F, CFList& factors, int l, |
---|
3481 | int liftBound, int d, int* bounds, |
---|
3482 | mat_zz_p& NTLN, CFList& diophant, |
---|
3483 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
3484 | const CanonicalForm& evaluation, const |
---|
3485 | ExtensionInfo& info, CFList& source, |
---|
3486 | CFList& dest |
---|
3487 | ) |
---|
3488 | { |
---|
3489 | CanonicalForm LCF= LC (F, 1); |
---|
3490 | CFList result; |
---|
3491 | bool irreducible= false; |
---|
3492 | CFList bufFactors= factors; |
---|
3493 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
3494 | bool useOldQs= false; |
---|
3495 | bool hitBound= false; |
---|
3496 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
3497 | int degMipo= degree (getMipo (info.getAlpha())); |
---|
3498 | Variable alpha= info.getAlpha(); |
---|
3499 | int oldL= l; //be careful |
---|
3500 | int stepSize= 8; |
---|
3501 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l),2); |
---|
3502 | Variable gamma= info.getBeta(); |
---|
3503 | CanonicalForm primElemAlpha= info.getGamma(); |
---|
3504 | CanonicalForm imPrimElemAlpha= info.getDelta(); |
---|
3505 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
3506 | ident (NTLN, factors.length()); |
---|
3507 | Variable y= F.mvar(); |
---|
3508 | CanonicalForm powX, imBasis, bufF, truncF; |
---|
3509 | CFMatrix Mat, C; |
---|
3510 | CFIterator iter; |
---|
3511 | mat_zz_p* NTLMat,*NTLC, NTLK; |
---|
3512 | CFListIterator j; |
---|
3513 | CFArray buf; |
---|
3514 | while (l <= liftBound) |
---|
3515 | { |
---|
3516 | bufFactors.insert (LCF); |
---|
3517 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
3518 | |
---|
3519 | if (GF) |
---|
3520 | setCharacteristic (getCharacteristic()); |
---|
3521 | |
---|
3522 | powX= power (y-gamma, l); |
---|
3523 | Mat= CFMatrix (l*degMipo, l*degMipo); |
---|
3524 | for (int i= 0; i < l*degMipo; i++) |
---|
3525 | { |
---|
3526 | |
---|
3527 | imBasis= mod (power (y, i), powX); |
---|
3528 | imBasis= imBasis (power (y, degMipo), y); |
---|
3529 | imBasis= imBasis (y, gamma); |
---|
3530 | iter= imBasis; |
---|
3531 | for (; iter.hasTerms(); iter++) |
---|
3532 | Mat (iter.exp()+ 1, i+1)= iter.coeff(); |
---|
3533 | } |
---|
3534 | |
---|
3535 | NTLMat= convertFacCFMatrix2NTLmat_zz_p (Mat); |
---|
3536 | *NTLMat= inv (*NTLMat); |
---|
3537 | |
---|
3538 | if (GF) |
---|
3539 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
3540 | |
---|
3541 | j= bufFactors; |
---|
3542 | truncF= mod (F, power (y, l)); |
---|
3543 | if (useOldQs) |
---|
3544 | { |
---|
3545 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
3546 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
3547 | bufQ[i]); |
---|
3548 | } |
---|
3549 | else |
---|
3550 | { |
---|
3551 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
3552 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
3553 | } |
---|
3554 | for (int i= 0; i < d; i++) |
---|
3555 | { |
---|
3556 | if (bounds [i] + 1 <= l/2) |
---|
3557 | { |
---|
3558 | int k= tmin (bounds [i] + 1, l/2); |
---|
3559 | C= CFMatrix (l*degMipo - k, bufFactors.length()); |
---|
3560 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
3561 | { |
---|
3562 | if (A[ii].size() - 1 >= i) |
---|
3563 | { |
---|
3564 | if (GF) |
---|
3565 | { |
---|
3566 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
3567 | setCharacteristic (getCharacteristic()); |
---|
3568 | A[ii] [i]= GF2FalphaRep (A[ii] [i], alpha); |
---|
3569 | if (alpha != gamma) |
---|
3570 | A [ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
3571 | gamma, source, dest |
---|
3572 | ); |
---|
3573 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
3574 | } |
---|
3575 | else |
---|
3576 | { |
---|
3577 | A [ii] [i]= A [ii] [i] (y-evaluation, y); |
---|
3578 | if (alpha != gamma) |
---|
3579 | A[ii] [i]= mapDown (A[ii] [i], imPrimElemAlpha, primElemAlpha, |
---|
3580 | gamma, source, dest |
---|
3581 | ); |
---|
3582 | buf= getCoeffs (A[ii] [i], k, l, degMipo, gamma, 0, *NTLMat); |
---|
3583 | } |
---|
3584 | } |
---|
3585 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3586 | if (GF) |
---|
3587 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
3588 | } |
---|
3589 | |
---|
3590 | if (GF) |
---|
3591 | setCharacteristic(getCharacteristic()); |
---|
3592 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
3593 | NTLK= (*NTLC)*NTLN; |
---|
3594 | transpose (NTLK, NTLK); |
---|
3595 | kernel (NTLK, NTLK); |
---|
3596 | transpose (NTLK, NTLK); |
---|
3597 | NTLN *= NTLK; |
---|
3598 | if (GF) |
---|
3599 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
3600 | |
---|
3601 | if (NTLN.NumCols() == 1) |
---|
3602 | { |
---|
3603 | irreducible= true; |
---|
3604 | break; |
---|
3605 | } |
---|
3606 | } |
---|
3607 | } |
---|
3608 | if (NTLN.NumCols() == 1) |
---|
3609 | { |
---|
3610 | irreducible= true; |
---|
3611 | break; |
---|
3612 | } |
---|
3613 | |
---|
3614 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
3615 | bufF= F; |
---|
3616 | result= extReconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN, info, |
---|
3617 | evaluation |
---|
3618 | ); |
---|
3619 | delete [] zeroOneVecs; |
---|
3620 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
3621 | { |
---|
3622 | F= bufF; |
---|
3623 | factors= bufFactors; |
---|
3624 | delete [] A; |
---|
3625 | return result; |
---|
3626 | } |
---|
3627 | |
---|
3628 | if (isReduced (NTLN)) |
---|
3629 | { |
---|
3630 | int factorsFound= 0; |
---|
3631 | bufF= F; |
---|
3632 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
3633 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
3634 | factorsFoundIndex[i]= 0; |
---|
3635 | if (l < degree (bufF) + 1 + degree (LCF)) |
---|
3636 | extReconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
3637 | factorsFoundIndex, NTLN, false, info, evaluation |
---|
3638 | ); |
---|
3639 | else |
---|
3640 | extReconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
3641 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
3642 | NTLN, false, info, evaluation |
---|
3643 | ); |
---|
3644 | if (NTLN.NumCols() == result.length()) |
---|
3645 | { |
---|
3646 | delete [] A; |
---|
3647 | delete [] factorsFoundIndex; |
---|
3648 | return result; |
---|
3649 | } |
---|
3650 | delete [] factorsFoundIndex; |
---|
3651 | } |
---|
3652 | result= CFList(); |
---|
3653 | oldL= l; |
---|
3654 | stepSize *= 2; |
---|
3655 | l += stepSize; |
---|
3656 | if (l > liftBound) |
---|
3657 | { |
---|
3658 | if (!hitBound) |
---|
3659 | { |
---|
3660 | l= liftBound; |
---|
3661 | hitBound= true; |
---|
3662 | } |
---|
3663 | else |
---|
3664 | break; |
---|
3665 | } |
---|
3666 | } |
---|
3667 | if (irreducible) |
---|
3668 | { |
---|
3669 | delete [] A; |
---|
3670 | Variable y= Variable (2); |
---|
3671 | CanonicalForm tmp= F (y - evaluation, y); |
---|
3672 | CFList source, dest; |
---|
3673 | tmp= mapDown (tmp, info, source, dest); |
---|
3674 | return CFList (tmp); |
---|
3675 | } |
---|
3676 | delete [] A; |
---|
3677 | factors= bufFactors; |
---|
3678 | return CFList(); |
---|
3679 | } |
---|
3680 | |
---|
3681 | CFList |
---|
3682 | furtherLiftingAndIncreasePrecisionFq2Fp (CanonicalForm& F, CFList& factors, int |
---|
3683 | l, int liftBound, int d, int* bounds, |
---|
3684 | mat_zz_p& NTLN, CFList& diophant, |
---|
3685 | CFMatrix& M, CFArray& Pi, CFArray& bufQ, |
---|
3686 | const Variable& alpha |
---|
3687 | ) |
---|
3688 | { |
---|
3689 | CanonicalForm LCF= LC (F, 1); |
---|
3690 | CFList result; |
---|
3691 | bool irreducible= false; |
---|
3692 | CFList bufFactors= factors; |
---|
3693 | CFArray *A = new CFArray [bufFactors.length()]; |
---|
3694 | bool useOldQs= false; |
---|
3695 | int extensionDeg= degree (getMipo (alpha)); |
---|
3696 | bool hitBound= false; |
---|
3697 | int oldL= l; |
---|
3698 | int stepSize= 8; //TODO choose better step size? |
---|
3699 | l += tmax (tmin (8, degree (F) + 1 + degree (LC (F, 1))-l), 2); |
---|
3700 | if (NTLN.NumRows() != factors.length()) //refined factors |
---|
3701 | ident (NTLN, factors.length()); |
---|
3702 | CFListIterator j; |
---|
3703 | CFMatrix C; |
---|
3704 | mat_zz_p* NTLC, NTLK; |
---|
3705 | CanonicalForm bufF, truncF; |
---|
3706 | Variable y= F.mvar(); |
---|
3707 | while (l <= liftBound) |
---|
3708 | { |
---|
3709 | bufFactors.insert (LCF); |
---|
3710 | henselLiftResume12 (F, bufFactors, oldL, l, Pi, diophant, M); |
---|
3711 | j= bufFactors; |
---|
3712 | truncF= mod (F, power (y, l)); |
---|
3713 | if (useOldQs) |
---|
3714 | { |
---|
3715 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
3716 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, oldL, bufQ[i], |
---|
3717 | bufQ[i]); |
---|
3718 | } |
---|
3719 | else |
---|
3720 | { |
---|
3721 | for (int i= 0; i < bufFactors.length(); i++, j++) |
---|
3722 | A[i]= logarithmicDerivative (truncF, j.getItem(), l, bufQ [i]); |
---|
3723 | } |
---|
3724 | for (int i= 0; i < d; i++) |
---|
3725 | { |
---|
3726 | if (bounds [i] + 1 <= l/2) |
---|
3727 | { |
---|
3728 | int k= tmin (bounds [i] + 1, l/2); |
---|
3729 | C= CFMatrix ((l - k)*extensionDeg, bufFactors.length()); |
---|
3730 | for (int ii= 0; ii < bufFactors.length(); ii++) |
---|
3731 | { |
---|
3732 | CFArray buf; |
---|
3733 | if (A[ii].size() - 1 >= i) |
---|
3734 | buf= getCoeffs (A[ii] [i], k, alpha); |
---|
3735 | writeInMatrix (C, buf, ii + 1, 0); |
---|
3736 | } |
---|
3737 | NTLC= convertFacCFMatrix2NTLmat_zz_p(C); |
---|
3738 | NTLK= (*NTLC)*NTLN; |
---|
3739 | transpose (NTLK, NTLK); |
---|
3740 | kernel (NTLK, NTLK); |
---|
3741 | transpose (NTLK, NTLK); |
---|
3742 | NTLN *= NTLK; |
---|
3743 | if (NTLN.NumCols() == 1) |
---|
3744 | { |
---|
3745 | irreducible= true; |
---|
3746 | break; |
---|
3747 | } |
---|
3748 | } |
---|
3749 | } |
---|
3750 | if (NTLN.NumCols() == 1) |
---|
3751 | { |
---|
3752 | irreducible= true; |
---|
3753 | break; |
---|
3754 | } |
---|
3755 | |
---|
3756 | int * zeroOneVecs= extractZeroOneVecs (NTLN); |
---|
3757 | CanonicalForm bufF= F; |
---|
3758 | result= reconstruction (bufF, bufFactors, zeroOneVecs, l, NTLN); |
---|
3759 | delete [] zeroOneVecs; |
---|
3760 | if (result.length() > 0 && degree (bufF) + 1 + degree (LC (bufF, 1)) <= l) |
---|
3761 | { |
---|
3762 | F= bufF; |
---|
3763 | factors= bufFactors; |
---|
3764 | delete [] A; |
---|
3765 | return result; |
---|
3766 | } |
---|
3767 | |
---|
3768 | if (isReduced (NTLN)) |
---|
3769 | { |
---|
3770 | int factorsFound= 0; |
---|
3771 | bufF= F; |
---|
3772 | int* factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
3773 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
3774 | factorsFoundIndex[i]= 0; |
---|
3775 | if (l < degree (bufF) + 1 + degree (LCF)) |
---|
3776 | reconstructionTry (result, bufF, bufFactors, l, factorsFound, |
---|
3777 | factorsFoundIndex, NTLN, false |
---|
3778 | ); |
---|
3779 | else |
---|
3780 | reconstructionTry (result, bufF, bufFactors, degree (bufF) + 1 + |
---|
3781 | degree (LCF), factorsFound, factorsFoundIndex, |
---|
3782 | NTLN, false |
---|
3783 | ); |
---|
3784 | if (NTLN.NumCols() == result.length()) |
---|
3785 | { |
---|
3786 | delete [] A; |
---|
3787 | delete [] factorsFoundIndex; |
---|
3788 | return result; |
---|
3789 | } |
---|
3790 | delete [] factorsFoundIndex; |
---|
3791 | } |
---|
3792 | result= CFList(); |
---|
3793 | oldL= l; |
---|
3794 | stepSize *= 2; |
---|
3795 | l += stepSize; |
---|
3796 | if (l > liftBound) |
---|
3797 | { |
---|
3798 | if (!hitBound) |
---|
3799 | { |
---|
3800 | l= liftBound; |
---|
3801 | hitBound= true; |
---|
3802 | } |
---|
3803 | else |
---|
3804 | break; |
---|
3805 | } |
---|
3806 | } |
---|
3807 | if (irreducible) |
---|
3808 | { |
---|
3809 | delete [] A; |
---|
3810 | return CFList (F); |
---|
3811 | } |
---|
3812 | delete [] A; |
---|
3813 | factors= bufFactors; |
---|
3814 | return CFList(); |
---|
3815 | } |
---|
3816 | |
---|
3817 | void |
---|
3818 | refineAndRestartLift (const CanonicalForm& F, const mat_zz_p& NTLN, int |
---|
3819 | liftBound, int l, CFList& factors, CFMatrix& M, CFArray& |
---|
3820 | Pi, CFList& diophant |
---|
3821 | ) |
---|
3822 | { |
---|
3823 | CFList bufFactors; |
---|
3824 | Variable y= Variable (2); |
---|
3825 | CanonicalForm LCF= LC (F, 1); |
---|
3826 | CFListIterator iter; |
---|
3827 | CanonicalForm buf; |
---|
3828 | for (long i= 1; i <= NTLN.NumCols(); i++) |
---|
3829 | { |
---|
3830 | iter= factors; |
---|
3831 | buf= 1; |
---|
3832 | for (long j= 1; j <= NTLN.NumRows(); j++, iter++) |
---|
3833 | { |
---|
3834 | if (!IsZero (NTLN (j,i))) |
---|
3835 | buf= mulNTL (buf, mod (iter.getItem(), y)); |
---|
3836 | } |
---|
3837 | bufFactors.append (buf); |
---|
3838 | } |
---|
3839 | factors= bufFactors; |
---|
3840 | M= CFMatrix (liftBound, factors.length()); |
---|
3841 | Pi= CFArray(); |
---|
3842 | diophant= CFList(); |
---|
3843 | factors.insert (LCF); |
---|
3844 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
3845 | } |
---|
3846 | |
---|
3847 | void |
---|
3848 | refineAndRestartLift (const CanonicalForm& F, const mat_zz_pE& NTLN, int |
---|
3849 | liftBound, int l, CFList& factors, CFMatrix& M, CFArray& |
---|
3850 | Pi, CFList& diophant |
---|
3851 | ) |
---|
3852 | { |
---|
3853 | CFList bufFactors; |
---|
3854 | Variable y= Variable (2); |
---|
3855 | CanonicalForm LCF= LC (F, 1); |
---|
3856 | CFListIterator iter; |
---|
3857 | CanonicalForm buf; |
---|
3858 | for (long i= 1; i <= NTLN.NumCols(); i++) |
---|
3859 | { |
---|
3860 | iter= factors; |
---|
3861 | buf= 1; |
---|
3862 | for (long j= 1; j <= NTLN.NumRows(); j++, iter++) |
---|
3863 | { |
---|
3864 | if (!IsZero (NTLN (j,i))) |
---|
3865 | buf= mulNTL (buf, mod (iter.getItem(), y)); |
---|
3866 | } |
---|
3867 | bufFactors.append (buf); |
---|
3868 | } |
---|
3869 | factors= bufFactors; |
---|
3870 | M= CFMatrix (liftBound, factors.length()); |
---|
3871 | Pi= CFArray(); |
---|
3872 | diophant= CFList(); |
---|
3873 | factors.insert (LCF); |
---|
3874 | henselLift12 (F, factors, l, Pi, diophant, M); |
---|
3875 | } |
---|
3876 | |
---|
3877 | CFList |
---|
3878 | earlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_p& N, |
---|
3879 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
3880 | int& factorsFound, bool beenInThres, CFMatrix& M, |
---|
3881 | CFArray& Pi, CFList& diophant |
---|
3882 | ) |
---|
3883 | { |
---|
3884 | int sizeOfLiftPre; |
---|
3885 | int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2)); |
---|
3886 | |
---|
3887 | Variable y= F.mvar(); |
---|
3888 | factorsFound= 0; |
---|
3889 | CanonicalForm LCF= LC (F, 1); |
---|
3890 | CFList result; |
---|
3891 | int smallFactorDeg= tmin (11, liftPre [sizeOfLiftPre- 1] + 1); |
---|
3892 | mat_zz_p NTLN= N; |
---|
3893 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
3894 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
3895 | factorsFoundIndex [i]= 0; |
---|
3896 | |
---|
3897 | if (degree (F) + 1 > smallFactorDeg) |
---|
3898 | { |
---|
3899 | if (l < smallFactorDeg) |
---|
3900 | { |
---|
3901 | factors.insert (LCF); |
---|
3902 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
3903 | l= smallFactorDeg; |
---|
3904 | } |
---|
3905 | reconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
3906 | factorsFoundIndex, NTLN, beenInThres |
---|
3907 | ); |
---|
3908 | if (result.length() == NTLN.NumCols()) |
---|
3909 | { |
---|
3910 | delete [] liftPre; |
---|
3911 | delete [] factorsFoundIndex; |
---|
3912 | return result; |
---|
3913 | } |
---|
3914 | } |
---|
3915 | |
---|
3916 | int i= sizeOfLiftPre - 1; |
---|
3917 | int dummy= 1; |
---|
3918 | if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
3919 | { |
---|
3920 | while (i > 0) |
---|
3921 | { |
---|
3922 | if (l < liftPre[i-1] + 1) |
---|
3923 | { |
---|
3924 | factors.insert (LCF); |
---|
3925 | henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M); |
---|
3926 | l= liftPre[i-1] + 1; |
---|
3927 | } |
---|
3928 | else |
---|
3929 | { |
---|
3930 | i--; |
---|
3931 | if (i != 0) |
---|
3932 | continue; |
---|
3933 | } |
---|
3934 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
3935 | factorsFoundIndex, NTLN, beenInThres |
---|
3936 | ); |
---|
3937 | if (result.length() == NTLN.NumCols()) |
---|
3938 | { |
---|
3939 | delete [] liftPre; |
---|
3940 | delete [] factorsFoundIndex; |
---|
3941 | return result; |
---|
3942 | } |
---|
3943 | i--; |
---|
3944 | } |
---|
3945 | } |
---|
3946 | else |
---|
3947 | { |
---|
3948 | i= 1; |
---|
3949 | while ((degree (F,y)/4)*i + 4 <= smallFactorDeg) |
---|
3950 | i++; |
---|
3951 | while (i < 4) |
---|
3952 | { |
---|
3953 | dummy= tmin (degree (F,y)+1, (degree (F,y)/4)*(i+1)+4); |
---|
3954 | if (l < dummy) |
---|
3955 | { |
---|
3956 | factors.insert (LCF); |
---|
3957 | henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M); |
---|
3958 | l= dummy; |
---|
3959 | } |
---|
3960 | else |
---|
3961 | { |
---|
3962 | i++; |
---|
3963 | if (i < 4) |
---|
3964 | continue; |
---|
3965 | } |
---|
3966 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
3967 | factorsFoundIndex, NTLN, beenInThres |
---|
3968 | ); |
---|
3969 | if (result.length() == NTLN.NumCols()) |
---|
3970 | { |
---|
3971 | delete [] liftPre; |
---|
3972 | delete [] factorsFoundIndex; |
---|
3973 | return result; |
---|
3974 | } |
---|
3975 | i++; |
---|
3976 | } |
---|
3977 | } |
---|
3978 | |
---|
3979 | delete [] liftPre; |
---|
3980 | delete [] factorsFoundIndex; |
---|
3981 | return result; |
---|
3982 | } |
---|
3983 | |
---|
3984 | CFList |
---|
3985 | earlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_pE& N, |
---|
3986 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
3987 | int& factorsFound, bool beenInThres, CFMatrix& M, |
---|
3988 | CFArray& Pi, CFList& diophant |
---|
3989 | ) |
---|
3990 | { |
---|
3991 | int sizeOfLiftPre; |
---|
3992 | int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2)); |
---|
3993 | Variable y= F.mvar(); |
---|
3994 | factorsFound= 0; |
---|
3995 | CanonicalForm LCF= LC (F, 1); |
---|
3996 | CFList result; |
---|
3997 | int smallFactorDeg= 11; |
---|
3998 | mat_zz_pE NTLN= N; |
---|
3999 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
4000 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
4001 | factorsFoundIndex [i]= 0; |
---|
4002 | |
---|
4003 | if (degree (F) + 1 > smallFactorDeg) |
---|
4004 | { |
---|
4005 | if (l < smallFactorDeg) |
---|
4006 | { |
---|
4007 | factors.insert (LCF); |
---|
4008 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
4009 | l= smallFactorDeg; |
---|
4010 | } |
---|
4011 | reconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
4012 | factorsFoundIndex, NTLN, beenInThres |
---|
4013 | ); |
---|
4014 | if (result.length() == NTLN.NumCols()) |
---|
4015 | { |
---|
4016 | delete [] liftPre; |
---|
4017 | delete [] factorsFoundIndex; |
---|
4018 | return result; |
---|
4019 | } |
---|
4020 | } |
---|
4021 | |
---|
4022 | int i= sizeOfLiftPre - 1; |
---|
4023 | int dummy= 1; |
---|
4024 | if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
4025 | { |
---|
4026 | while (i > 0) |
---|
4027 | { |
---|
4028 | if (l < liftPre[i-1] + 1) |
---|
4029 | { |
---|
4030 | factors.insert (LCF); |
---|
4031 | henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M); |
---|
4032 | l= liftPre[i-1] + 1; |
---|
4033 | } |
---|
4034 | else |
---|
4035 | { |
---|
4036 | i--; |
---|
4037 | if (i != 0) |
---|
4038 | continue; |
---|
4039 | } |
---|
4040 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
4041 | factorsFoundIndex, NTLN, beenInThres |
---|
4042 | ); |
---|
4043 | if (result.length() == NTLN.NumCols()) |
---|
4044 | { |
---|
4045 | delete [] liftPre; |
---|
4046 | delete [] factorsFoundIndex; |
---|
4047 | return result; |
---|
4048 | } |
---|
4049 | i--; |
---|
4050 | } |
---|
4051 | } |
---|
4052 | else |
---|
4053 | { |
---|
4054 | i= 1; |
---|
4055 | while ((degree (F,y)/4)*i + 4 <= smallFactorDeg) |
---|
4056 | i++; |
---|
4057 | while (i < 4) |
---|
4058 | { |
---|
4059 | dummy= tmin (degree (F,y)+1, (degree (F,y)/4)*(i+1)+4); |
---|
4060 | if (l < dummy) |
---|
4061 | { |
---|
4062 | factors.insert (LCF); |
---|
4063 | henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M); |
---|
4064 | l= dummy; |
---|
4065 | } |
---|
4066 | else |
---|
4067 | { |
---|
4068 | i++; |
---|
4069 | if (i < 4) |
---|
4070 | continue; |
---|
4071 | } |
---|
4072 | reconstructionTry (result, bufF, factors, l, factorsFound, |
---|
4073 | factorsFoundIndex, NTLN, beenInThres |
---|
4074 | ); |
---|
4075 | if (result.length() == NTLN.NumCols()) |
---|
4076 | { |
---|
4077 | delete [] liftPre; |
---|
4078 | delete [] factorsFoundIndex; |
---|
4079 | return result; |
---|
4080 | } |
---|
4081 | i++; |
---|
4082 | } |
---|
4083 | } |
---|
4084 | |
---|
4085 | delete [] liftPre; |
---|
4086 | delete [] factorsFoundIndex; |
---|
4087 | return result; |
---|
4088 | } |
---|
4089 | |
---|
4090 | //over field extension |
---|
4091 | CFList |
---|
4092 | extEarlyReconstructionAndLifting (const CanonicalForm& F, const mat_zz_p& N, |
---|
4093 | CanonicalForm& bufF, CFList& factors, int& l, |
---|
4094 | int& factorsFound, bool beenInThres, CFMatrix& |
---|
4095 | M, CFArray& Pi, CFList& diophant, const |
---|
4096 | ExtensionInfo& info, const CanonicalForm& |
---|
4097 | evaluation |
---|
4098 | ) |
---|
4099 | { |
---|
4100 | int sizeOfLiftPre; |
---|
4101 | int * liftPre= getLiftPrecisions (F, sizeOfLiftPre, degree (LC (F, 1), 2)); |
---|
4102 | Variable y= F.mvar(); |
---|
4103 | factorsFound= 0; |
---|
4104 | CanonicalForm LCF= LC (F, 1); |
---|
4105 | CFList result; |
---|
4106 | int smallFactorDeg= 11; |
---|
4107 | mat_zz_p NTLN= N; |
---|
4108 | int * factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
4109 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
4110 | factorsFoundIndex [i]= 0; |
---|
4111 | |
---|
4112 | if (degree (F) + 1 > smallFactorDeg) |
---|
4113 | { |
---|
4114 | if (l < smallFactorDeg) |
---|
4115 | { |
---|
4116 | factors.insert (LCF); |
---|
4117 | henselLiftResume12 (F, factors, l, smallFactorDeg, Pi, diophant, M); |
---|
4118 | l= smallFactorDeg; |
---|
4119 | } |
---|
4120 | extReconstructionTry (result, bufF, factors, smallFactorDeg, factorsFound, |
---|
4121 | factorsFoundIndex, NTLN, beenInThres, info, |
---|
4122 | evaluation |
---|
4123 | ); |
---|
4124 | if (result.length() == NTLN.NumCols()) |
---|
4125 | { |
---|
4126 | delete [] liftPre; |
---|
4127 | delete [] factorsFoundIndex; |
---|
4128 | return result; |
---|
4129 | } |
---|
4130 | } |
---|
4131 | |
---|
4132 | int i= sizeOfLiftPre - 1; |
---|
4133 | int dummy= 1; |
---|
4134 | if (sizeOfLiftPre > 1 && sizeOfLiftPre < 30) |
---|
4135 | { |
---|
4136 | while (i > 0) |
---|
4137 | { |
---|
4138 | if (l < liftPre[i-1] + 1) |
---|
4139 | { |
---|
4140 | factors.insert (LCF); |
---|
4141 | henselLiftResume12 (F, factors, l, liftPre[i-1] + 1, Pi, diophant, M); |
---|
4142 | l= liftPre[i-1] + 1; |
---|
4143 | } |
---|
4144 | else |
---|
4145 | { |
---|
4146 | i--; |
---|
4147 | if (i != 0) |
---|
4148 | continue; |
---|
4149 | } |
---|
4150 | extReconstructionTry (result, bufF, factors, l, factorsFound, |
---|
4151 | factorsFoundIndex, NTLN, beenInThres, info, |
---|
4152 | evaluation |
---|
4153 | ); |
---|
4154 | if (result.length() == NTLN.NumCols()) |
---|
4155 | { |
---|
4156 | delete [] liftPre; |
---|
4157 | delete [] factorsFoundIndex; |
---|
4158 | return result; |
---|
4159 | } |
---|
4160 | i--; |
---|
4161 | } |
---|
4162 | } |
---|
4163 | else |
---|
4164 | { |
---|
4165 | i= 1; |
---|
4166 | while ((degree (F,y)/4)*i + 4 <= smallFactorDeg) |
---|
4167 | i++; |
---|
4168 | while (i < 4) |
---|
4169 | { |
---|
4170 | dummy= tmin (degree (F,y)+1, (degree (F,y)/4)*(i+1)+4); |
---|
4171 | if (l < dummy) |
---|
4172 | { |
---|
4173 | factors.insert (LCF); |
---|
4174 | henselLiftResume12 (F, factors, l, dummy, Pi, diophant, M); |
---|
4175 | l= dummy; |
---|
4176 | } |
---|
4177 | else |
---|
4178 | { |
---|
4179 | i++; |
---|
4180 | if (i < 4) |
---|
4181 | continue; |
---|
4182 | } |
---|
4183 | extReconstructionTry (result, bufF, factors, l, factorsFound, |
---|
4184 | factorsFoundIndex, NTLN, beenInThres, info, |
---|
4185 | evaluation |
---|
4186 | ); |
---|
4187 | if (result.length() == NTLN.NumCols()) |
---|
4188 | { |
---|
4189 | delete [] liftPre; |
---|
4190 | delete [] factorsFoundIndex; |
---|
4191 | return result; |
---|
4192 | } |
---|
4193 | i++; |
---|
4194 | } |
---|
4195 | } |
---|
4196 | |
---|
4197 | delete [] liftPre; |
---|
4198 | delete [] factorsFoundIndex; |
---|
4199 | return result; |
---|
4200 | } |
---|
4201 | |
---|
4202 | CFList |
---|
4203 | sieveSmallFactors (const CanonicalForm& G, CFList& uniFactors, DegreePattern& |
---|
4204 | degPat, CanonicalForm& H, CFList& diophant, CFArray& Pi, |
---|
4205 | CFMatrix& M, bool& success, int d |
---|
4206 | ) |
---|
4207 | { |
---|
4208 | CanonicalForm F= G; |
---|
4209 | CFList bufUniFactors= uniFactors; |
---|
4210 | bufUniFactors.insert (LC (F, 1)); |
---|
4211 | int smallFactorDeg= d; |
---|
4212 | DegreePattern degs= degPat; |
---|
4213 | henselLift12 (F, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
---|
4214 | int adaptedLiftBound; |
---|
4215 | success= false; |
---|
4216 | CFList earlyFactors= earlyFactorDetection (F, bufUniFactors, adaptedLiftBound, |
---|
4217 | degs, success, smallFactorDeg |
---|
4218 | ); |
---|
4219 | if (degs.getLength() == 1) |
---|
4220 | { |
---|
4221 | degPat= degs; |
---|
4222 | return earlyFactors; |
---|
4223 | } |
---|
4224 | if (success) |
---|
4225 | { |
---|
4226 | H= F; |
---|
4227 | return earlyFactors; |
---|
4228 | } |
---|
4229 | int sizeOldF= size (F); |
---|
4230 | CFList result; |
---|
4231 | CanonicalForm bufF= F; |
---|
4232 | if (earlyFactors.length() > 0) |
---|
4233 | { |
---|
4234 | for (CFListIterator i= earlyFactors; i.hasItem(); i++) |
---|
4235 | bufF /= i.getItem(); |
---|
4236 | } |
---|
4237 | |
---|
4238 | if (size (bufF) < sizeOldF) |
---|
4239 | { |
---|
4240 | H= bufF; |
---|
4241 | success= true; |
---|
4242 | return earlyFactors; |
---|
4243 | } |
---|
4244 | else |
---|
4245 | { |
---|
4246 | uniFactors= bufUniFactors; |
---|
4247 | return CFList(); |
---|
4248 | } |
---|
4249 | } |
---|
4250 | |
---|
4251 | CFList |
---|
4252 | extSieveSmallFactors (const CanonicalForm& G, CFList& uniFactors, DegreePattern& |
---|
4253 | degPat, CanonicalForm& H, CFList& diophant, CFArray& Pi, |
---|
4254 | CFMatrix& M, bool& success, int d, const CanonicalForm& |
---|
4255 | evaluation, const ExtensionInfo& info |
---|
4256 | ) |
---|
4257 | { |
---|
4258 | CanonicalForm F= G; |
---|
4259 | CFList bufUniFactors= uniFactors; |
---|
4260 | bufUniFactors.insert (LC (F, 1)); |
---|
4261 | int smallFactorDeg= d; |
---|
4262 | DegreePattern degs= degPat; |
---|
4263 | henselLift12 (F, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
---|
4264 | int adaptedLiftBound; |
---|
4265 | success= false; |
---|
4266 | CFList earlyFactors= extEarlyFactorDetection (F, bufUniFactors, |
---|
4267 | adaptedLiftBound, degs, success, |
---|
4268 | info, evaluation, smallFactorDeg |
---|
4269 | ); |
---|
4270 | if (degs.getLength() == 1) |
---|
4271 | { |
---|
4272 | degPat= degs; |
---|
4273 | return earlyFactors; |
---|
4274 | } |
---|
4275 | if (success) |
---|
4276 | { |
---|
4277 | H= F; |
---|
4278 | return earlyFactors; |
---|
4279 | } |
---|
4280 | Variable y= F.mvar(); |
---|
4281 | CanonicalForm shiftedF= F (y - evaluation, y); |
---|
4282 | int sizeOldF= size (shiftedF); |
---|
4283 | CFList result; |
---|
4284 | CanonicalForm bufF= shiftedF; |
---|
4285 | if (earlyFactors.length() > 0) |
---|
4286 | { |
---|
4287 | for (CFListIterator i= earlyFactors; i.hasItem(); i++) |
---|
4288 | { |
---|
4289 | bufF /= i.getItem(); |
---|
4290 | result.append (i.getItem()); |
---|
4291 | } |
---|
4292 | } |
---|
4293 | |
---|
4294 | if (size (bufF) < sizeOldF) |
---|
4295 | { |
---|
4296 | H= bufF (y + evaluation, y); //shift back to zero |
---|
4297 | success= true; |
---|
4298 | return result; |
---|
4299 | } |
---|
4300 | else |
---|
4301 | { |
---|
4302 | uniFactors= bufUniFactors; |
---|
4303 | return CFList(); |
---|
4304 | } |
---|
4305 | } |
---|
4306 | |
---|
4307 | CFList |
---|
4308 | henselLiftAndLatticeRecombi (const CanonicalForm& G, const CFList& uniFactors, |
---|
4309 | const Variable& alpha, const DegreePattern& degPat |
---|
4310 | ) |
---|
4311 | { |
---|
4312 | DegreePattern degs= degPat; |
---|
4313 | CanonicalForm F= G; |
---|
4314 | CanonicalForm LCF= LC (F, 1); |
---|
4315 | Variable y= F.mvar(); |
---|
4316 | Variable x= Variable (1); |
---|
4317 | int d; |
---|
4318 | int* bounds= computeBounds (F, d); |
---|
4319 | |
---|
4320 | int minBound= bounds[0]; |
---|
4321 | for (int i= 1; i < d; i++) |
---|
4322 | { |
---|
4323 | if (bounds[i] != 0) |
---|
4324 | minBound= tmin (minBound, bounds[i]); |
---|
4325 | } |
---|
4326 | |
---|
4327 | CFList bufUniFactors= uniFactors; |
---|
4328 | CFArray Pi; |
---|
4329 | CFList diophant; |
---|
4330 | int liftBound= 2*totaldegree (F) - 1; |
---|
4331 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
4332 | |
---|
4333 | CFList smallFactors; |
---|
4334 | CanonicalForm H; |
---|
4335 | bool success; |
---|
4336 | smallFactors= sieveSmallFactors (F, bufUniFactors, degs, H, diophant, Pi, M, |
---|
4337 | success, 2*(minBound + 1) |
---|
4338 | ); |
---|
4339 | |
---|
4340 | if (smallFactors.length() > 0) |
---|
4341 | { |
---|
4342 | if (smallFactors.length() == 1) |
---|
4343 | { |
---|
4344 | if (smallFactors.getFirst() == F) |
---|
4345 | { |
---|
4346 | delete [] bounds; |
---|
4347 | return CFList (G); |
---|
4348 | } |
---|
4349 | } |
---|
4350 | if (degs.getLength() <= 1) |
---|
4351 | { |
---|
4352 | delete [] bounds; |
---|
4353 | return smallFactors; |
---|
4354 | } |
---|
4355 | } |
---|
4356 | |
---|
4357 | int index; |
---|
4358 | CanonicalForm tmp1, tmp2; |
---|
4359 | for (CFListIterator i= smallFactors; i.hasItem(); i++) |
---|
4360 | { |
---|
4361 | index= 1; |
---|
4362 | tmp1= mod (i.getItem(),y); |
---|
4363 | tmp1 /= Lc (tmp1); |
---|
4364 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
4365 | { |
---|
4366 | tmp2= mod (j.getItem(), y); |
---|
4367 | tmp2 /= Lc (tmp2); |
---|
4368 | if (tmp1 == tmp2) |
---|
4369 | { |
---|
4370 | index++; |
---|
4371 | j.remove(index); |
---|
4372 | break; |
---|
4373 | } |
---|
4374 | } |
---|
4375 | } |
---|
4376 | |
---|
4377 | if (bufUniFactors.isEmpty()) |
---|
4378 | { |
---|
4379 | delete [] bounds; |
---|
4380 | return smallFactors; |
---|
4381 | } |
---|
4382 | |
---|
4383 | if (success) |
---|
4384 | { |
---|
4385 | F= H; |
---|
4386 | delete [] bounds; |
---|
4387 | bounds= computeBounds (F, d); |
---|
4388 | LCF= LC (F, 1); |
---|
4389 | |
---|
4390 | minBound= bounds[0]; |
---|
4391 | for (int i= 1; i < d; i++) |
---|
4392 | { |
---|
4393 | if (bounds[i] != 0) |
---|
4394 | minBound= tmin (minBound, bounds[i]); |
---|
4395 | } |
---|
4396 | Pi= CFArray(); |
---|
4397 | diophant= CFList(); |
---|
4398 | liftBound= 2*totaldegree (F) - 1; |
---|
4399 | M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
4400 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
4401 | degs.intersect (bufDegs); |
---|
4402 | degs.refine(); |
---|
4403 | if (degs.getLength() <= 1) |
---|
4404 | { |
---|
4405 | smallFactors.append (F); |
---|
4406 | delete [] bounds; |
---|
4407 | return smallFactors; |
---|
4408 | } |
---|
4409 | } |
---|
4410 | |
---|
4411 | bool reduceFq2Fp= (degree (F) > getCharacteristic()); |
---|
4412 | bufUniFactors.insert (LCF); |
---|
4413 | int l= 1; |
---|
4414 | |
---|
4415 | zz_p::init (getCharacteristic()); |
---|
4416 | mat_zz_p NTLN; |
---|
4417 | if (alpha.level() != 1) |
---|
4418 | { |
---|
4419 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
4420 | zz_pE::init (NTLMipo); |
---|
4421 | } |
---|
4422 | mat_zz_pE NTLNe; |
---|
4423 | if (alpha.level() == 1) |
---|
4424 | ident (NTLN, bufUniFactors.length() - 1); |
---|
4425 | else |
---|
4426 | { |
---|
4427 | if (reduceFq2Fp) |
---|
4428 | ident (NTLN, bufUniFactors.length() - 1); |
---|
4429 | else |
---|
4430 | ident (NTLNe, bufUniFactors.length() - 1); |
---|
4431 | } |
---|
4432 | bool irreducible= false; |
---|
4433 | CFArray bufQ= CFArray (bufUniFactors.length() - 1); |
---|
4434 | |
---|
4435 | int oldL; |
---|
4436 | if (success) |
---|
4437 | { |
---|
4438 | int start= 0; |
---|
4439 | if (alpha.level() == 1) |
---|
4440 | oldL= liftAndComputeLattice (F, bounds, d, start, liftBound, minBound, |
---|
4441 | bufUniFactors, NTLN, diophant, M, Pi, bufQ, |
---|
4442 | irreducible |
---|
4443 | ); |
---|
4444 | else |
---|
4445 | { |
---|
4446 | if (reduceFq2Fp) |
---|
4447 | oldL= liftAndComputeLatticeFq2Fp (F, bounds, d, start, liftBound, |
---|
4448 | minBound, bufUniFactors, NTLN, |
---|
4449 | diophant, M, Pi, bufQ, irreducible, |
---|
4450 | alpha |
---|
4451 | ); |
---|
4452 | else |
---|
4453 | oldL= liftAndComputeLattice (F, bounds, d, start, liftBound, minBound, |
---|
4454 | bufUniFactors, NTLNe, diophant, M, Pi, bufQ, |
---|
4455 | irreducible |
---|
4456 | ); |
---|
4457 | } |
---|
4458 | } |
---|
4459 | else |
---|
4460 | { |
---|
4461 | if (alpha.level() == 1) |
---|
4462 | oldL= liftAndComputeLattice (F, bounds, d, 2*(minBound + 1), liftBound, |
---|
4463 | minBound, bufUniFactors, NTLN, diophant, M, |
---|
4464 | Pi, bufQ, irreducible |
---|
4465 | ); |
---|
4466 | else |
---|
4467 | { |
---|
4468 | if (reduceFq2Fp) |
---|
4469 | oldL= liftAndComputeLatticeFq2Fp (F, bounds, d, 2*(minBound + 1), |
---|
4470 | liftBound, minBound, bufUniFactors, |
---|
4471 | NTLN, diophant, M, Pi, bufQ, |
---|
4472 | irreducible, alpha |
---|
4473 | ); |
---|
4474 | else |
---|
4475 | oldL= liftAndComputeLattice (F, bounds, d, 2*(minBound + 1), liftBound, |
---|
4476 | minBound, bufUniFactors, NTLNe, diophant, |
---|
4477 | M, Pi, bufQ, irreducible |
---|
4478 | ); |
---|
4479 | } |
---|
4480 | } |
---|
4481 | |
---|
4482 | bufUniFactors.removeFirst(); |
---|
4483 | if (oldL > liftBound) |
---|
4484 | { |
---|
4485 | delete [] bounds; |
---|
4486 | return Union (smallFactors, |
---|
4487 | factorRecombination (bufUniFactors, F, |
---|
4488 | power (y, degree (F) + 1 + degree (LCF)), |
---|
4489 | degs, 1, bufUniFactors.length()/2 |
---|
4490 | ) |
---|
4491 | ); |
---|
4492 | } |
---|
4493 | |
---|
4494 | l= oldL; |
---|
4495 | if (irreducible) |
---|
4496 | { |
---|
4497 | delete [] bounds; |
---|
4498 | return Union (CFList (F), smallFactors); |
---|
4499 | } |
---|
4500 | |
---|
4501 | CanonicalForm yToL= power (y,l); |
---|
4502 | |
---|
4503 | CFList result; |
---|
4504 | if (l >= degree (F) + 1) |
---|
4505 | { |
---|
4506 | int * factorsFoundIndex; |
---|
4507 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
4508 | { |
---|
4509 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
4510 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
4511 | factorsFoundIndex[i]= 0; |
---|
4512 | } |
---|
4513 | else |
---|
4514 | { |
---|
4515 | factorsFoundIndex= new int [NTLNe.NumCols()]; |
---|
4516 | for (long i= 0; i < NTLNe.NumCols(); i++) |
---|
4517 | factorsFoundIndex[i]= 0; |
---|
4518 | } |
---|
4519 | int factorsFound= 0; |
---|
4520 | CanonicalForm bufF= F; |
---|
4521 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
4522 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
4523 | factorsFound, factorsFoundIndex, NTLN, false |
---|
4524 | ); |
---|
4525 | else |
---|
4526 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
4527 | factorsFound, factorsFoundIndex, NTLNe, false |
---|
4528 | ); |
---|
4529 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
4530 | { |
---|
4531 | if (result.length() == NTLN.NumCols()) |
---|
4532 | { |
---|
4533 | delete [] factorsFoundIndex; |
---|
4534 | delete [] bounds; |
---|
4535 | return Union (result, smallFactors); |
---|
4536 | } |
---|
4537 | } |
---|
4538 | else |
---|
4539 | { |
---|
4540 | if (result.length() == NTLNe.NumCols()) |
---|
4541 | { |
---|
4542 | delete [] factorsFoundIndex; |
---|
4543 | delete [] bounds; |
---|
4544 | return Union (result, smallFactors); |
---|
4545 | } |
---|
4546 | } |
---|
4547 | delete [] factorsFoundIndex; |
---|
4548 | } |
---|
4549 | if (l >= liftBound) |
---|
4550 | { |
---|
4551 | int * factorsFoundIndex; |
---|
4552 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
4553 | { |
---|
4554 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
4555 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
4556 | factorsFoundIndex[i]= 0; |
---|
4557 | } |
---|
4558 | else |
---|
4559 | { |
---|
4560 | factorsFoundIndex= new int [NTLNe.NumCols()]; |
---|
4561 | for (long i= 0; i < NTLNe.NumCols(); i++) |
---|
4562 | factorsFoundIndex[i]= 0; |
---|
4563 | } |
---|
4564 | CanonicalForm bufF= F; |
---|
4565 | int factorsFound= 0; |
---|
4566 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
4567 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1 + degree |
---|
4568 | (LCF), factorsFound, factorsFoundIndex, NTLN, false |
---|
4569 | ); |
---|
4570 | else |
---|
4571 | reconstructionTry (result, bufF, bufUniFactors, degree (F) + 1 + degree |
---|
4572 | (LCF), factorsFound, factorsFoundIndex, NTLNe, false |
---|
4573 | ); |
---|
4574 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
4575 | { |
---|
4576 | if (result.length() == NTLN.NumCols()) |
---|
4577 | { |
---|
4578 | delete [] factorsFoundIndex; |
---|
4579 | delete [] bounds; |
---|
4580 | return Union (result, smallFactors); |
---|
4581 | } |
---|
4582 | } |
---|
4583 | else |
---|
4584 | { |
---|
4585 | if (result.length() == NTLNe.NumCols()) |
---|
4586 | { |
---|
4587 | delete [] factorsFoundIndex; |
---|
4588 | delete [] bounds; |
---|
4589 | return Union (result, smallFactors); |
---|
4590 | } |
---|
4591 | } |
---|
4592 | delete [] factorsFoundIndex; |
---|
4593 | } |
---|
4594 | |
---|
4595 | result= CFList(); |
---|
4596 | bool beenInThres= false; |
---|
4597 | int thres= 100; |
---|
4598 | if (l <= thres) |
---|
4599 | { |
---|
4600 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
4601 | { |
---|
4602 | if (NTLN.NumCols() < bufUniFactors.length()) |
---|
4603 | { |
---|
4604 | refineAndRestartLift (F, NTLN, liftBound, l, bufUniFactors, M, Pi, |
---|
4605 | diophant |
---|
4606 | ); |
---|
4607 | beenInThres= true; |
---|
4608 | } |
---|
4609 | } |
---|
4610 | else |
---|
4611 | { |
---|
4612 | if (NTLNe.NumCols() < bufUniFactors.length()) |
---|
4613 | { |
---|
4614 | refineAndRestartLift (F, NTLNe, liftBound, l, bufUniFactors, M, Pi, |
---|
4615 | diophant |
---|
4616 | ); |
---|
4617 | beenInThres= true; |
---|
4618 | } |
---|
4619 | } |
---|
4620 | } |
---|
4621 | |
---|
4622 | CanonicalForm bufF= F; |
---|
4623 | int factorsFound= 0; |
---|
4624 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
4625 | { |
---|
4626 | result= earlyReconstructionAndLifting (F, NTLN, bufF, bufUniFactors, l, |
---|
4627 | factorsFound, beenInThres, M, Pi, |
---|
4628 | diophant |
---|
4629 | ); |
---|
4630 | |
---|
4631 | if (result.length() == NTLN.NumCols()) |
---|
4632 | { |
---|
4633 | delete [] bounds; |
---|
4634 | return Union (result, smallFactors); |
---|
4635 | } |
---|
4636 | } |
---|
4637 | else |
---|
4638 | { |
---|
4639 | result= earlyReconstructionAndLifting (F, NTLNe, bufF, bufUniFactors, l, |
---|
4640 | factorsFound, beenInThres, M, Pi, |
---|
4641 | diophant |
---|
4642 | ); |
---|
4643 | |
---|
4644 | if (result.length() == NTLNe.NumCols()) |
---|
4645 | { |
---|
4646 | delete [] bounds; |
---|
4647 | return Union (result, smallFactors); |
---|
4648 | } |
---|
4649 | } |
---|
4650 | |
---|
4651 | if (result.length() > 0) |
---|
4652 | { |
---|
4653 | if (beenInThres) |
---|
4654 | { |
---|
4655 | int index; |
---|
4656 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
4657 | { |
---|
4658 | index= 1; |
---|
4659 | tmp1= mod (i.getItem(), y); |
---|
4660 | tmp1 /= Lc (tmp1); |
---|
4661 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
4662 | { |
---|
4663 | tmp2= mod (j.getItem(), y); |
---|
4664 | tmp2 /= Lc (tmp2); |
---|
4665 | if (tmp1 == tmp2) |
---|
4666 | { |
---|
4667 | index++; |
---|
4668 | j.remove(index); |
---|
4669 | break; |
---|
4670 | } |
---|
4671 | } |
---|
4672 | } |
---|
4673 | } |
---|
4674 | else |
---|
4675 | { |
---|
4676 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
4677 | CFList bufBufUniFactors= bufUniFactors; |
---|
4678 | CFListIterator iter, iter2; |
---|
4679 | CanonicalForm buf; |
---|
4680 | CFList factorsConsidered; |
---|
4681 | CanonicalForm tmp; |
---|
4682 | for (int i= 0; i < NTLN.NumCols(); i++) |
---|
4683 | { |
---|
4684 | if (zeroOne [i] == 0) |
---|
4685 | continue; |
---|
4686 | iter= bufUniFactors; |
---|
4687 | buf= 1; |
---|
4688 | factorsConsidered= CFList(); |
---|
4689 | for (int j= 0; j < NTLN.NumRows(); j++, iter++) |
---|
4690 | { |
---|
4691 | if (!IsZero (NTLN (j + 1,i + 1))) |
---|
4692 | { |
---|
4693 | factorsConsidered.append (iter.getItem()); |
---|
4694 | buf *= mod (iter.getItem(), y); |
---|
4695 | } |
---|
4696 | } |
---|
4697 | buf /= Lc (buf); |
---|
4698 | for (iter2= result; iter2.hasItem(); iter2++) |
---|
4699 | { |
---|
4700 | tmp= mod (iter2.getItem(), y); |
---|
4701 | tmp /= Lc (tmp); |
---|
4702 | if (tmp == buf) |
---|
4703 | { |
---|
4704 | bufBufUniFactors= Difference (bufBufUniFactors, factorsConsidered); |
---|
4705 | break; |
---|
4706 | } |
---|
4707 | } |
---|
4708 | } |
---|
4709 | bufUniFactors= bufBufUniFactors; |
---|
4710 | delete [] zeroOne; |
---|
4711 | } |
---|
4712 | |
---|
4713 | int oldNumCols; |
---|
4714 | CFList resultBufF; |
---|
4715 | irreducible= false; |
---|
4716 | |
---|
4717 | if (alpha.level() == 1) |
---|
4718 | { |
---|
4719 | oldNumCols= NTLN.NumCols(); |
---|
4720 | resultBufF= increasePrecision (bufF, bufUniFactors, factorsFound, |
---|
4721 | oldNumCols, oldL, l |
---|
4722 | ); |
---|
4723 | } |
---|
4724 | else |
---|
4725 | { |
---|
4726 | if (reduceFq2Fp) |
---|
4727 | { |
---|
4728 | oldNumCols= NTLN.NumCols(); |
---|
4729 | |
---|
4730 | resultBufF= increasePrecisionFq2Fp (bufF, bufUniFactors, factorsFound, |
---|
4731 | oldNumCols, oldL, alpha, l |
---|
4732 | ); |
---|
4733 | } |
---|
4734 | else |
---|
4735 | { |
---|
4736 | oldNumCols= NTLNe.NumCols(); |
---|
4737 | |
---|
4738 | resultBufF= increasePrecision (bufF, bufUniFactors, factorsFound, |
---|
4739 | oldNumCols, oldL, alpha, l |
---|
4740 | ); |
---|
4741 | } |
---|
4742 | } |
---|
4743 | |
---|
4744 | if (bufUniFactors.isEmpty() || degree (bufF) <= 0) |
---|
4745 | { |
---|
4746 | delete [] bounds; |
---|
4747 | result= Union (resultBufF, result); |
---|
4748 | return Union (result, smallFactors); |
---|
4749 | } |
---|
4750 | |
---|
4751 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
4752 | i.getItem()= mod (i.getItem(), y); |
---|
4753 | |
---|
4754 | result= Union (result, resultBufF); |
---|
4755 | result= Union (result, smallFactors); |
---|
4756 | delete [] bounds; |
---|
4757 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
4758 | degs.intersect (bufDegs); |
---|
4759 | degs.refine(); |
---|
4760 | if (degs.getLength() == 1 || bufUniFactors.length() == 1) |
---|
4761 | { |
---|
4762 | result.append (bufF); |
---|
4763 | return result; |
---|
4764 | } |
---|
4765 | return Union (result, henselLiftAndLatticeRecombi (bufF, bufUniFactors, |
---|
4766 | alpha, degs |
---|
4767 | ) |
---|
4768 | ); |
---|
4769 | } |
---|
4770 | |
---|
4771 | if (l < liftBound) |
---|
4772 | { |
---|
4773 | if (alpha.level() == 1) |
---|
4774 | { |
---|
4775 | result=increasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
4776 | NTLN |
---|
4777 | ); |
---|
4778 | } |
---|
4779 | else |
---|
4780 | { |
---|
4781 | if (reduceFq2Fp) |
---|
4782 | { |
---|
4783 | result=increasePrecisionFq2Fp (F, bufUniFactors, oldL, l, d, bounds, |
---|
4784 | bufQ, NTLN, alpha |
---|
4785 | ); |
---|
4786 | } |
---|
4787 | else |
---|
4788 | { |
---|
4789 | result=increasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
4790 | NTLNe |
---|
4791 | ); |
---|
4792 | } |
---|
4793 | } |
---|
4794 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
4795 | { |
---|
4796 | if (result.length()== NTLN.NumCols()) |
---|
4797 | { |
---|
4798 | delete [] bounds; |
---|
4799 | result= Union (result, smallFactors); |
---|
4800 | return result; |
---|
4801 | } |
---|
4802 | } |
---|
4803 | else |
---|
4804 | { |
---|
4805 | if (result.length()== NTLNe.NumCols()) |
---|
4806 | { |
---|
4807 | delete [] bounds; |
---|
4808 | result= Union (result, smallFactors); |
---|
4809 | return result; |
---|
4810 | } |
---|
4811 | } |
---|
4812 | |
---|
4813 | if (result.isEmpty()) |
---|
4814 | { |
---|
4815 | if (alpha.level() == 1) |
---|
4816 | result= furtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
4817 | liftBound, d, bounds, NTLN, |
---|
4818 | diophant, M, Pi, bufQ |
---|
4819 | ); |
---|
4820 | else |
---|
4821 | { |
---|
4822 | if (reduceFq2Fp) |
---|
4823 | result= furtherLiftingAndIncreasePrecisionFq2Fp (F,bufUniFactors, l, |
---|
4824 | liftBound, d, bounds, |
---|
4825 | NTLN, diophant, M, |
---|
4826 | Pi, bufQ, alpha |
---|
4827 | ); |
---|
4828 | else |
---|
4829 | result= furtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
4830 | liftBound, d, bounds, |
---|
4831 | NTLNe, diophant, M, |
---|
4832 | Pi, bufQ |
---|
4833 | ); |
---|
4834 | } |
---|
4835 | |
---|
4836 | if (alpha.level() == 1 || (alpha.level() != 1 && reduceFq2Fp)) |
---|
4837 | { |
---|
4838 | if (result.length() == NTLN.NumCols()) |
---|
4839 | { |
---|
4840 | delete [] bounds; |
---|
4841 | result= Union (result, smallFactors); |
---|
4842 | return result; |
---|
4843 | } |
---|
4844 | } |
---|
4845 | else |
---|
4846 | { |
---|
4847 | if (result.length() == NTLNe.NumCols()) |
---|
4848 | { |
---|
4849 | delete [] bounds; |
---|
4850 | result= Union (result, smallFactors); |
---|
4851 | return result; |
---|
4852 | } |
---|
4853 | } |
---|
4854 | } |
---|
4855 | } |
---|
4856 | |
---|
4857 | DEBOUTLN (cerr, "lattice recombination failed"); |
---|
4858 | |
---|
4859 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
4860 | degs.intersect (bufDegs); |
---|
4861 | degs.refine(); |
---|
4862 | |
---|
4863 | delete [] bounds; |
---|
4864 | bounds= computeBounds (F, d); |
---|
4865 | minBound= bounds[0]; |
---|
4866 | for (int i= 1; i < d; i++) |
---|
4867 | { |
---|
4868 | if (bounds[i] != 0) |
---|
4869 | minBound= tmin (minBound, bounds[i]); |
---|
4870 | } |
---|
4871 | |
---|
4872 | if (minBound > 16 || result.length() == 0) |
---|
4873 | { |
---|
4874 | result= Union (result, smallFactors); |
---|
4875 | CanonicalForm MODl= power (y, degree (F) + 1 + degree (LC (F, 1))); |
---|
4876 | delete [] bounds; |
---|
4877 | return Union (result, factorRecombination (bufUniFactors, F, MODl, degs, 1, |
---|
4878 | bufUniFactors.length()/2 |
---|
4879 | ) |
---|
4880 | ); |
---|
4881 | } |
---|
4882 | else |
---|
4883 | { |
---|
4884 | result= Union (result, smallFactors); |
---|
4885 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
4886 | i.getItem()= mod (i.getItem(), y); |
---|
4887 | delete [] bounds; |
---|
4888 | return Union (result, henselLiftAndLatticeRecombi (F, bufUniFactors, alpha, |
---|
4889 | degs |
---|
4890 | ) |
---|
4891 | ); |
---|
4892 | } |
---|
4893 | } |
---|
4894 | |
---|
4895 | ExtensionInfo |
---|
4896 | init4ext (const ExtensionInfo& info, const CanonicalForm& evaluation, |
---|
4897 | int& degMipo |
---|
4898 | ) |
---|
4899 | { |
---|
4900 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
4901 | Variable alpha= info.getAlpha(); |
---|
4902 | if (GF) |
---|
4903 | { |
---|
4904 | degMipo= getGFDegree(); |
---|
4905 | CanonicalForm GFMipo= gf_mipo; |
---|
4906 | setCharacteristic (getCharacteristic()); |
---|
4907 | GFMipo.mapinto(); |
---|
4908 | alpha= rootOf (GFMipo); |
---|
4909 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
4910 | } |
---|
4911 | else |
---|
4912 | { |
---|
4913 | alpha= info.getAlpha(); |
---|
4914 | degMipo= degree (getMipo (alpha)); |
---|
4915 | } |
---|
4916 | |
---|
4917 | Variable gamma; |
---|
4918 | CanonicalForm primElemAlpha, imPrimElemAlpha; |
---|
4919 | if ((!GF && evaluation != alpha) || (GF && evaluation != getGFGenerator())) |
---|
4920 | { |
---|
4921 | CanonicalForm bufEvaluation; |
---|
4922 | if (GF) |
---|
4923 | { |
---|
4924 | setCharacteristic (getCharacteristic()); |
---|
4925 | bufEvaluation= GF2FalphaRep (evaluation, alpha); |
---|
4926 | } |
---|
4927 | else |
---|
4928 | bufEvaluation= evaluation; |
---|
4929 | CanonicalForm mipo= findMinPoly (bufEvaluation, alpha); |
---|
4930 | gamma= rootOf (mipo); |
---|
4931 | Variable V_buf; |
---|
4932 | bool fail= false; |
---|
4933 | primElemAlpha= primitiveElement (alpha, V_buf, fail); |
---|
4934 | imPrimElemAlpha= map (primElemAlpha, alpha, bufEvaluation, gamma); |
---|
4935 | |
---|
4936 | if (GF) |
---|
4937 | setCharacteristic (getCharacteristic(), degMipo, info.getGFName()); |
---|
4938 | } |
---|
4939 | else |
---|
4940 | gamma= alpha; |
---|
4941 | ExtensionInfo info2= ExtensionInfo (alpha, gamma, primElemAlpha, |
---|
4942 | imPrimElemAlpha, 1, info.getGFName(), true |
---|
4943 | ); |
---|
4944 | |
---|
4945 | return info2; |
---|
4946 | } |
---|
4947 | |
---|
4948 | CFList |
---|
4949 | extHenselLiftAndLatticeRecombi(const CanonicalForm& G, const CFList& uniFactors, |
---|
4950 | const ExtensionInfo& extInfo, const |
---|
4951 | DegreePattern& degPat, const CanonicalForm& eval |
---|
4952 | ) |
---|
4953 | { |
---|
4954 | CanonicalForm evaluation= eval; |
---|
4955 | ExtensionInfo info= extInfo; |
---|
4956 | Variable alpha; |
---|
4957 | DegreePattern degs= degPat; |
---|
4958 | CanonicalForm F= G; |
---|
4959 | Variable x= Variable (1); |
---|
4960 | Variable y= F.mvar(); |
---|
4961 | CFList bufUniFactors= uniFactors; |
---|
4962 | |
---|
4963 | |
---|
4964 | int degMipo; |
---|
4965 | ExtensionInfo info2= init4ext (info, evaluation, degMipo); |
---|
4966 | |
---|
4967 | CFList source, dest; |
---|
4968 | CanonicalForm LCF= LC (F, 1); |
---|
4969 | |
---|
4970 | int d; |
---|
4971 | int* bounds= computeBounds (F, d); |
---|
4972 | int minBound= bounds[0]; |
---|
4973 | for (int i= 1; i < d; i++) |
---|
4974 | { |
---|
4975 | if (bounds[i] != 0) |
---|
4976 | minBound= tmin (minBound, bounds[i]); |
---|
4977 | } |
---|
4978 | |
---|
4979 | |
---|
4980 | CFArray Pi; |
---|
4981 | CFList diophant; |
---|
4982 | int liftBound= tmax ((2*totaldegree (F) - 1)/degMipo + 1, degree (F) + 1 + |
---|
4983 | degree (LC (F, 1))); |
---|
4984 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
4985 | |
---|
4986 | CFList smallFactors; |
---|
4987 | CanonicalForm H; |
---|
4988 | bool success; |
---|
4989 | smallFactors= extSieveSmallFactors (F, bufUniFactors, degs, H, diophant, Pi, |
---|
4990 | M, success, minBound + 1, evaluation, info |
---|
4991 | ); |
---|
4992 | |
---|
4993 | if (smallFactors.length() > 0) |
---|
4994 | { |
---|
4995 | if (smallFactors.length() == 1) |
---|
4996 | { |
---|
4997 | if (smallFactors.getFirst() == F) |
---|
4998 | { |
---|
4999 | delete [] bounds; |
---|
5000 | CFList source, dest; |
---|
5001 | CanonicalForm tmp= G (y - evaluation, y); |
---|
5002 | tmp= mapDown (tmp, info, source, dest); |
---|
5003 | return CFList (tmp); |
---|
5004 | } |
---|
5005 | } |
---|
5006 | if (degs.getLength() <= 1) |
---|
5007 | { |
---|
5008 | delete [] bounds; |
---|
5009 | return smallFactors; |
---|
5010 | } |
---|
5011 | } |
---|
5012 | |
---|
5013 | int index; |
---|
5014 | CanonicalForm tmp1, tmp2; |
---|
5015 | for (CFListIterator i= smallFactors; i.hasItem(); i++) |
---|
5016 | { |
---|
5017 | index= 1; |
---|
5018 | tmp1= mod (i.getItem(), y - evaluation); |
---|
5019 | tmp1 /= Lc (tmp1); |
---|
5020 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
5021 | { |
---|
5022 | tmp2= mod (j.getItem(), y); |
---|
5023 | tmp2 /= Lc (tmp2); |
---|
5024 | if (tmp1 == tmp2) |
---|
5025 | { |
---|
5026 | index++; |
---|
5027 | j.remove(index); |
---|
5028 | break; |
---|
5029 | } |
---|
5030 | } |
---|
5031 | } |
---|
5032 | |
---|
5033 | if (bufUniFactors.isEmpty()) |
---|
5034 | { |
---|
5035 | delete [] bounds; |
---|
5036 | return smallFactors; |
---|
5037 | } |
---|
5038 | |
---|
5039 | if (success) |
---|
5040 | { |
---|
5041 | F= H; |
---|
5042 | delete [] bounds; |
---|
5043 | bounds= computeBounds (F, d); |
---|
5044 | LCF= LC (F, 1); |
---|
5045 | |
---|
5046 | minBound= bounds[0]; |
---|
5047 | for (int i= 1; i < d; i++) |
---|
5048 | { |
---|
5049 | if (bounds[i] != 0) |
---|
5050 | minBound= tmin (minBound, bounds[i]); |
---|
5051 | } |
---|
5052 | Pi= CFArray(); |
---|
5053 | diophant= CFList(); |
---|
5054 | liftBound=tmax ((2*totaldegree (F) - 1)/degMipo + 1, degree (F) + 1 + |
---|
5055 | degree (LC (F, 1))); |
---|
5056 | M= CFMatrix (liftBound, bufUniFactors.length()); |
---|
5057 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
5058 | degs.intersect (bufDegs); |
---|
5059 | degs.refine(); |
---|
5060 | if (degs.getLength() <= 1) |
---|
5061 | { |
---|
5062 | delete [] bounds; |
---|
5063 | CFList source, dest; |
---|
5064 | CanonicalForm tmp= F (y - evaluation, y); |
---|
5065 | tmp= mapDown (tmp, info, source, dest); |
---|
5066 | smallFactors.append (tmp); |
---|
5067 | return smallFactors; |
---|
5068 | } |
---|
5069 | } |
---|
5070 | |
---|
5071 | bufUniFactors.insert (LCF); |
---|
5072 | int l= 1; |
---|
5073 | |
---|
5074 | zz_p::init (getCharacteristic()); |
---|
5075 | zz_pX NTLMipo; |
---|
5076 | mat_zz_p NTLN; |
---|
5077 | |
---|
5078 | ident (NTLN, bufUniFactors.length() - 1); |
---|
5079 | bool irreducible= false; |
---|
5080 | CFArray bufQ= CFArray (bufUniFactors.length() - 1); |
---|
5081 | |
---|
5082 | int oldL; |
---|
5083 | if (success) |
---|
5084 | { |
---|
5085 | int start= 0; |
---|
5086 | oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound, start, |
---|
5087 | bufUniFactors, NTLN, diophant, M, Pi, bufQ, |
---|
5088 | irreducible, evaluation, info2, source, dest |
---|
5089 | ); |
---|
5090 | } |
---|
5091 | else |
---|
5092 | { |
---|
5093 | oldL= extLiftAndComputeLattice (F, bounds, d, liftBound, minBound, |
---|
5094 | minBound + 1, bufUniFactors, NTLN, diophant, |
---|
5095 | M, Pi, bufQ, irreducible, evaluation, info2, |
---|
5096 | source, dest |
---|
5097 | ); |
---|
5098 | } |
---|
5099 | |
---|
5100 | bufUniFactors.removeFirst(); |
---|
5101 | if (oldL > liftBound) |
---|
5102 | { |
---|
5103 | delete [] bounds; |
---|
5104 | return Union (smallFactors, extFactorRecombination |
---|
5105 | (bufUniFactors, F, |
---|
5106 | power (y, degree (F) + 1 + degree (LCF)),info, |
---|
5107 | degs, evaluation, 1, bufUniFactors.length()/2 |
---|
5108 | ) |
---|
5109 | ); |
---|
5110 | } |
---|
5111 | |
---|
5112 | l= oldL; |
---|
5113 | if (irreducible) |
---|
5114 | { |
---|
5115 | delete [] bounds; |
---|
5116 | CFList source, dest; |
---|
5117 | CanonicalForm tmp= F (y - evaluation, y); |
---|
5118 | tmp= mapDown (tmp, info, source, dest); |
---|
5119 | return Union (CFList (tmp), smallFactors); |
---|
5120 | } |
---|
5121 | |
---|
5122 | CanonicalForm yToL= power (y,l); |
---|
5123 | |
---|
5124 | CFList result; |
---|
5125 | if (l >= degree (F) + 1) |
---|
5126 | { |
---|
5127 | int * factorsFoundIndex; |
---|
5128 | |
---|
5129 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
5130 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
5131 | factorsFoundIndex[i]= 0; |
---|
5132 | |
---|
5133 | int factorsFound= 0; |
---|
5134 | CanonicalForm bufF= F; |
---|
5135 | |
---|
5136 | extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1, |
---|
5137 | factorsFound, factorsFoundIndex, NTLN, false, info, |
---|
5138 | evaluation |
---|
5139 | ); |
---|
5140 | |
---|
5141 | if (result.length() == NTLN.NumCols()) |
---|
5142 | { |
---|
5143 | delete [] factorsFoundIndex; |
---|
5144 | delete [] bounds; |
---|
5145 | return Union (result, smallFactors); |
---|
5146 | } |
---|
5147 | |
---|
5148 | delete [] factorsFoundIndex; |
---|
5149 | } |
---|
5150 | if (l >= liftBound) |
---|
5151 | { |
---|
5152 | int * factorsFoundIndex; |
---|
5153 | factorsFoundIndex= new int [NTLN.NumCols()]; |
---|
5154 | for (long i= 0; i < NTLN.NumCols(); i++) |
---|
5155 | factorsFoundIndex[i]= 0; |
---|
5156 | CanonicalForm bufF= F; |
---|
5157 | int factorsFound= 0; |
---|
5158 | |
---|
5159 | extReconstructionTry (result, bufF, bufUniFactors, degree (F) + 1 + degree |
---|
5160 | (LCF), factorsFound, factorsFoundIndex, NTLN, false, |
---|
5161 | info, evaluation |
---|
5162 | ); |
---|
5163 | |
---|
5164 | if (result.length() == NTLN.NumCols()) |
---|
5165 | { |
---|
5166 | delete [] factorsFoundIndex; |
---|
5167 | delete [] bounds; |
---|
5168 | return Union (result, smallFactors); |
---|
5169 | } |
---|
5170 | delete [] factorsFoundIndex; |
---|
5171 | } |
---|
5172 | |
---|
5173 | result= CFList(); |
---|
5174 | bool beenInThres= false; |
---|
5175 | int thres= 100; |
---|
5176 | if (l <= thres && bufUniFactors.length() > NTLN.NumCols()) |
---|
5177 | { |
---|
5178 | refineAndRestartLift (F, NTLN, 2*totaldegree (F)-1, l, bufUniFactors, M, Pi, |
---|
5179 | diophant |
---|
5180 | ); |
---|
5181 | beenInThres= true; |
---|
5182 | } |
---|
5183 | |
---|
5184 | |
---|
5185 | CanonicalForm bufF= F; |
---|
5186 | int factorsFound= 0; |
---|
5187 | |
---|
5188 | result= extEarlyReconstructionAndLifting (F, NTLN, bufF, bufUniFactors, l, |
---|
5189 | factorsFound, beenInThres, M, Pi, |
---|
5190 | diophant, info, evaluation |
---|
5191 | ); |
---|
5192 | |
---|
5193 | if (result.length() == NTLN.NumCols()) |
---|
5194 | { |
---|
5195 | delete [] bounds; |
---|
5196 | return Union (result, smallFactors); |
---|
5197 | } |
---|
5198 | |
---|
5199 | if (result.length() > 0) |
---|
5200 | { |
---|
5201 | if (beenInThres) |
---|
5202 | { |
---|
5203 | int index; |
---|
5204 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
5205 | { |
---|
5206 | index= 1; |
---|
5207 | tmp1= mod (i.getItem(), y-evaluation); |
---|
5208 | tmp1 /= Lc (tmp1); |
---|
5209 | for (CFListIterator j= bufUniFactors; j.hasItem(); j++, index++) |
---|
5210 | { |
---|
5211 | tmp2= mod (j.getItem(), y); |
---|
5212 | tmp2 /= Lc (tmp2); |
---|
5213 | if (tmp1 == tmp2) |
---|
5214 | { |
---|
5215 | index++; |
---|
5216 | j.remove(index); |
---|
5217 | break; |
---|
5218 | } |
---|
5219 | } |
---|
5220 | } |
---|
5221 | } |
---|
5222 | else |
---|
5223 | { |
---|
5224 | int * zeroOne= extractZeroOneVecs (NTLN); |
---|
5225 | CFList bufBufUniFactors= bufUniFactors; |
---|
5226 | CFListIterator iter, iter2; |
---|
5227 | CanonicalForm buf; |
---|
5228 | CFList factorsConsidered; |
---|
5229 | for (int i= 0; i < NTLN.NumCols(); i++) |
---|
5230 | { |
---|
5231 | if (zeroOne [i] == 0) |
---|
5232 | continue; |
---|
5233 | iter= bufUniFactors; |
---|
5234 | buf= 1; |
---|
5235 | factorsConsidered= CFList(); |
---|
5236 | for (int j= 0; j < NTLN.NumRows(); j++, iter++) |
---|
5237 | { |
---|
5238 | if (!IsZero (NTLN (j + 1,i + 1))) |
---|
5239 | { |
---|
5240 | factorsConsidered.append (iter.getItem()); |
---|
5241 | buf *= mod (iter.getItem(), y); |
---|
5242 | } |
---|
5243 | } |
---|
5244 | buf /= Lc (buf); |
---|
5245 | for (iter2= result; iter2.hasItem(); iter2++) |
---|
5246 | { |
---|
5247 | CanonicalForm tmp= mod (iter2.getItem(), y - evaluation); |
---|
5248 | tmp /= Lc (tmp); |
---|
5249 | if (tmp == buf) |
---|
5250 | { |
---|
5251 | bufBufUniFactors= Difference (bufBufUniFactors, factorsConsidered); |
---|
5252 | break; |
---|
5253 | } |
---|
5254 | } |
---|
5255 | } |
---|
5256 | bufUniFactors= bufBufUniFactors; |
---|
5257 | delete [] zeroOne; |
---|
5258 | } |
---|
5259 | |
---|
5260 | int oldNumCols; |
---|
5261 | CFList resultBufF; |
---|
5262 | irreducible= false; |
---|
5263 | |
---|
5264 | oldNumCols= NTLN.NumCols(); |
---|
5265 | resultBufF= extIncreasePrecision (bufF, bufUniFactors, factorsFound, |
---|
5266 | oldNumCols, oldL, evaluation, info2, |
---|
5267 | source, dest, l |
---|
5268 | ); |
---|
5269 | |
---|
5270 | if (bufUniFactors.isEmpty() || degree (bufF) <= 0) |
---|
5271 | { |
---|
5272 | delete [] bounds; |
---|
5273 | result= Union (resultBufF, result); |
---|
5274 | return Union (result, smallFactors); |
---|
5275 | } |
---|
5276 | |
---|
5277 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
5278 | i.getItem()= mod (i.getItem(), y); |
---|
5279 | |
---|
5280 | delete [] bounds; |
---|
5281 | CFList bufResult; |
---|
5282 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
5283 | degs.intersect (bufDegs); |
---|
5284 | degs.refine(); |
---|
5285 | result= Union (result, smallFactors); |
---|
5286 | if (degs.getLength() == 1 || bufUniFactors.length() == 1) |
---|
5287 | { |
---|
5288 | result.append (bufF); |
---|
5289 | return result; |
---|
5290 | } |
---|
5291 | return Union (result, extHenselLiftAndLatticeRecombi (bufF, bufUniFactors, |
---|
5292 | info, degs, evaluation |
---|
5293 | ) |
---|
5294 | ); |
---|
5295 | } |
---|
5296 | |
---|
5297 | if (l/degMipo < liftBound) |
---|
5298 | { |
---|
5299 | result=extIncreasePrecision (F, bufUniFactors, oldL, l, d, bounds, bufQ, |
---|
5300 | NTLN, evaluation, info2, source, dest |
---|
5301 | ); |
---|
5302 | |
---|
5303 | if (result.length()== NTLN.NumCols()) |
---|
5304 | { |
---|
5305 | delete [] bounds; |
---|
5306 | result= Union (result, smallFactors); |
---|
5307 | return result; |
---|
5308 | } |
---|
5309 | |
---|
5310 | if (result.isEmpty()) |
---|
5311 | { |
---|
5312 | result= extFurtherLiftingAndIncreasePrecision (F,bufUniFactors, l, |
---|
5313 | liftBound, d, bounds, NTLN, |
---|
5314 | diophant, M, Pi, bufQ, |
---|
5315 | evaluation, info2, source, |
---|
5316 | dest |
---|
5317 | ); |
---|
5318 | if (result.length()== NTLN.NumCols()) |
---|
5319 | { |
---|
5320 | delete [] bounds; |
---|
5321 | result= Union (result, smallFactors); |
---|
5322 | return result; |
---|
5323 | } |
---|
5324 | } |
---|
5325 | } |
---|
5326 | |
---|
5327 | DEBOUTLN (cerr, "lattice recombination failed"); |
---|
5328 | |
---|
5329 | DegreePattern bufDegs= DegreePattern (bufUniFactors); |
---|
5330 | degs.intersect (bufDegs); |
---|
5331 | degs.refine(); |
---|
5332 | |
---|
5333 | delete [] bounds; |
---|
5334 | bounds= computeBounds (F, d); |
---|
5335 | minBound= bounds[0]; |
---|
5336 | for (int i= 1; i < d; i++) |
---|
5337 | { |
---|
5338 | if (bounds[i] != 0) |
---|
5339 | minBound= tmin (minBound, bounds[i]); |
---|
5340 | } |
---|
5341 | |
---|
5342 | if (minBound > 16 || result.length() == 0) |
---|
5343 | { |
---|
5344 | result= Union (result, smallFactors); |
---|
5345 | CanonicalForm MODl= power (y, degree (F) + 1 + degree (LC (F, 1))); |
---|
5346 | delete [] bounds; |
---|
5347 | return Union (result, extFactorRecombination (bufUniFactors, F, MODl, info, |
---|
5348 | degs, evaluation, 1, |
---|
5349 | bufUniFactors.length()/2 |
---|
5350 | ) |
---|
5351 | ); |
---|
5352 | } |
---|
5353 | else |
---|
5354 | { |
---|
5355 | result= Union (result, smallFactors); |
---|
5356 | for (CFListIterator i= bufUniFactors; i.hasItem(); i++) |
---|
5357 | i.getItem()= mod (i.getItem(), y); |
---|
5358 | delete [] bounds; |
---|
5359 | return Union (result, extHenselLiftAndLatticeRecombi (F, bufUniFactors, |
---|
5360 | info, degs, evaluation |
---|
5361 | ) |
---|
5362 | ); |
---|
5363 | } |
---|
5364 | } |
---|
5365 | |
---|
5366 | CFList |
---|
5367 | extBiFactorize (const CanonicalForm& F, const ExtensionInfo& info); |
---|
5368 | |
---|
5369 | /// bivariate factorization over finite fields as decribed in "Factoring |
---|
5370 | /// multivariate polynomials over a finite field" by L Bernardin. |
---|
5371 | CFList |
---|
5372 | biFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
5373 | { |
---|
5374 | if (F.inCoeffDomain()) |
---|
5375 | return CFList(F); |
---|
5376 | |
---|
5377 | CanonicalForm A= F; |
---|
5378 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
5379 | |
---|
5380 | Variable alpha= info.getAlpha(); |
---|
5381 | Variable beta= info.getBeta(); |
---|
5382 | CanonicalForm gamma= info.getGamma(); |
---|
5383 | CanonicalForm delta= info.getDelta(); |
---|
5384 | int k= info.getGFDegree(); |
---|
5385 | bool extension= info.isInExtension(); |
---|
5386 | if (A.isUnivariate()) |
---|
5387 | { |
---|
5388 | if (extension == false) |
---|
5389 | return uniFactorizer (F, alpha, GF); |
---|
5390 | else |
---|
5391 | { |
---|
5392 | CFList source, dest; |
---|
5393 | A= mapDown (A, info, source, dest); |
---|
5394 | return uniFactorizer (A, beta, GF); |
---|
5395 | } |
---|
5396 | } |
---|
5397 | |
---|
5398 | CFMap N; |
---|
5399 | A= compress (A, N); |
---|
5400 | Variable y= A.mvar(); |
---|
5401 | |
---|
5402 | if (y.level() > 2) return CFList (F); |
---|
5403 | Variable x= Variable (1); |
---|
5404 | |
---|
5405 | //remove and factorize content |
---|
5406 | CanonicalForm contentAx= content (A, x); |
---|
5407 | CanonicalForm contentAy= content (A); |
---|
5408 | |
---|
5409 | A= A/(contentAx*contentAy); |
---|
5410 | CFList contentAxFactors, contentAyFactors; |
---|
5411 | |
---|
5412 | if (!extension) |
---|
5413 | { |
---|
5414 | contentAxFactors= uniFactorizer (contentAx, alpha, GF); |
---|
5415 | contentAyFactors= uniFactorizer (contentAy, alpha, GF); |
---|
5416 | } |
---|
5417 | |
---|
5418 | //trivial case |
---|
5419 | CFList factors; |
---|
5420 | if (A.inCoeffDomain()) |
---|
5421 | { |
---|
5422 | append (factors, contentAxFactors); |
---|
5423 | append (factors, contentAyFactors); |
---|
5424 | decompress (factors, N); |
---|
5425 | return factors; |
---|
5426 | } |
---|
5427 | else if (A.isUnivariate()) |
---|
5428 | { |
---|
5429 | factors= uniFactorizer (A, alpha, GF); |
---|
5430 | append (factors, contentAxFactors); |
---|
5431 | append (factors, contentAyFactors); |
---|
5432 | decompress (factors, N); |
---|
5433 | return factors; |
---|
5434 | } |
---|
5435 | |
---|
5436 | //check trivial case |
---|
5437 | if (degree (A) == 1 || degree (A, 1) == 1) |
---|
5438 | { |
---|
5439 | factors.append (A); |
---|
5440 | |
---|
5441 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
5442 | false, false, N); |
---|
5443 | |
---|
5444 | normalize (factors); |
---|
5445 | return factors; |
---|
5446 | } |
---|
5447 | |
---|
5448 | // check derivatives |
---|
5449 | bool derivXZero= false; |
---|
5450 | CanonicalForm derivX= deriv (A, x); |
---|
5451 | CanonicalForm gcdDerivX; |
---|
5452 | if (derivX.isZero()) |
---|
5453 | derivXZero= true; |
---|
5454 | else |
---|
5455 | { |
---|
5456 | gcdDerivX= gcd (A, derivX); |
---|
5457 | if (degree (gcdDerivX) > 0) |
---|
5458 | { |
---|
5459 | CanonicalForm g= A/gcdDerivX; |
---|
5460 | CFList factorsG= |
---|
5461 | Union (biFactorize (g, info), biFactorize (gcdDerivX, info)); |
---|
5462 | append (factorsG, contentAxFactors); |
---|
5463 | append (factorsG, contentAyFactors); |
---|
5464 | decompress (factorsG, N); |
---|
5465 | normalize (factors); |
---|
5466 | return factorsG; |
---|
5467 | } |
---|
5468 | } |
---|
5469 | bool derivYZero= false; |
---|
5470 | CanonicalForm derivY= deriv (A, y); |
---|
5471 | CanonicalForm gcdDerivY; |
---|
5472 | if (derivY.isZero()) |
---|
5473 | derivYZero= true; |
---|
5474 | else |
---|
5475 | { |
---|
5476 | gcdDerivY= gcd (A, derivY); |
---|
5477 | if (degree (gcdDerivY) > 0) |
---|
5478 | { |
---|
5479 | CanonicalForm g= A/gcdDerivY; |
---|
5480 | CFList factorsG= |
---|
5481 | Union (biFactorize (g, info), biFactorize (gcdDerivY, info)); |
---|
5482 | append (factorsG, contentAxFactors); |
---|
5483 | append (factorsG, contentAyFactors); |
---|
5484 | decompress (factorsG, N); |
---|
5485 | normalize (factors); |
---|
5486 | return factorsG; |
---|
5487 | } |
---|
5488 | } |
---|
5489 | //main variable is chosen s.t. the degree in x is minimal |
---|
5490 | bool swap= false; |
---|
5491 | if ((degree (A) > degree (A, x)) || derivXZero) |
---|
5492 | { |
---|
5493 | if (!derivYZero) |
---|
5494 | { |
---|
5495 | A= swapvar (A, y, x); |
---|
5496 | swap= derivXZero; |
---|
5497 | derivXZero= derivYZero; |
---|
5498 | derivYZero= swap; |
---|
5499 | swap= true; |
---|
5500 | } |
---|
5501 | } |
---|
5502 | |
---|
5503 | bool fail= false; |
---|
5504 | CanonicalForm Aeval, evaluation, bufAeval, bufEvaluation, buf; |
---|
5505 | CFList uniFactors, list, bufUniFactors; |
---|
5506 | DegreePattern degs; |
---|
5507 | DegreePattern bufDegs; |
---|
5508 | |
---|
5509 | bool fail2= false; |
---|
5510 | CanonicalForm Aeval2, evaluation2, bufAeval2, bufEvaluation2; |
---|
5511 | CFList bufUniFactors2, list2, uniFactors2; |
---|
5512 | DegreePattern degs2; |
---|
5513 | DegreePattern bufDegs2; |
---|
5514 | bool swap2= false; |
---|
5515 | |
---|
5516 | // several univariate factorizations to obtain more information about the |
---|
5517 | // degree pattern therefore usually less combinations have to be tried during |
---|
5518 | // the recombination process |
---|
5519 | int factorNums= 3; |
---|
5520 | int subCheck1= substituteCheck (A, x); |
---|
5521 | int subCheck2= substituteCheck (A, y); |
---|
5522 | for (int i= 0; i < factorNums; i++) |
---|
5523 | { |
---|
5524 | bufAeval= A; |
---|
5525 | bufEvaluation= evalPoint (A, bufAeval, alpha, list, GF, fail); |
---|
5526 | if (!derivXZero && !fail2) |
---|
5527 | { |
---|
5528 | buf= swapvar (A, x, y); |
---|
5529 | bufAeval2= buf; |
---|
5530 | bufEvaluation2= evalPoint (buf, bufAeval2, alpha, list2, GF, fail2); |
---|
5531 | } |
---|
5532 | // first try to change main variable if there is no valid evaluation point |
---|
5533 | if (fail && (i == 0)) |
---|
5534 | { |
---|
5535 | if (!derivXZero && !fail2) |
---|
5536 | { |
---|
5537 | bufEvaluation= bufEvaluation2; |
---|
5538 | int dummy= subCheck2; |
---|
5539 | subCheck2= subCheck1; |
---|
5540 | subCheck1= dummy; |
---|
5541 | A= buf; |
---|
5542 | bufAeval= bufAeval2; |
---|
5543 | swap2= true; |
---|
5544 | fail= false; |
---|
5545 | } |
---|
5546 | else |
---|
5547 | fail= true; |
---|
5548 | } |
---|
5549 | |
---|
5550 | // if there is no valid evaluation point pass to a field extension |
---|
5551 | if (fail && (i == 0)) |
---|
5552 | { |
---|
5553 | factors= extBiFactorize (A, info); |
---|
5554 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
5555 | swap, swap2, N); |
---|
5556 | normalize (factors); |
---|
5557 | return factors; |
---|
5558 | } |
---|
5559 | |
---|
5560 | // there is at least one valid evaluation point |
---|
5561 | // but we do not compute more univariate factorization over an extension |
---|
5562 | if (fail && (i != 0)) |
---|
5563 | break; |
---|
5564 | |
---|
5565 | // univariate factorization |
---|
5566 | TIMING_START (fac_uni_factorizer); |
---|
5567 | bufUniFactors= uniFactorizer (bufAeval, alpha, GF); |
---|
5568 | TIMING_END_AND_PRINT (fac_uni_factorizer, |
---|
5569 | "time for univariate factorization: "); |
---|
5570 | DEBOUTLN (cerr, "Lc (bufAeval)*prod (bufUniFactors)== bufAeval " << |
---|
5571 | prod (bufUniFactors)*Lc (bufAeval) == bufAeval); |
---|
5572 | |
---|
5573 | if (!derivXZero && !fail2) |
---|
5574 | { |
---|
5575 | TIMING_START (fac_uni_factorizer); |
---|
5576 | bufUniFactors2= uniFactorizer (bufAeval2, alpha, GF); |
---|
5577 | TIMING_END_AND_PRINT (fac_uni_factorizer, |
---|
5578 | "time for univariate factorization in y: "); |
---|
5579 | DEBOUTLN (cerr, "Lc (Aeval2)*prod (uniFactors2)== Aeval2 " << |
---|
5580 | prod (bufUniFactors2)*Lc (bufAeval2) == bufAeval2); |
---|
5581 | } |
---|
5582 | |
---|
5583 | if (bufUniFactors.length() == 1 || |
---|
5584 | (!fail2 && !derivXZero && (bufUniFactors2.length() == 1))) |
---|
5585 | { |
---|
5586 | if (extension) |
---|
5587 | { |
---|
5588 | CFList source, dest; |
---|
5589 | ExtensionInfo info2= ExtensionInfo (beta, alpha, delta, gamma, k, |
---|
5590 | info.getGFName(), info.isInExtension()); |
---|
5591 | appendMapDown (factors, A, info2, source, dest); |
---|
5592 | } |
---|
5593 | else |
---|
5594 | factors.append (A); |
---|
5595 | |
---|
5596 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
5597 | swap, swap2, N); |
---|
5598 | |
---|
5599 | normalize (factors); |
---|
5600 | return factors; |
---|
5601 | } |
---|
5602 | |
---|
5603 | if (i == 0) |
---|
5604 | { |
---|
5605 | if (subCheck1 > 0) |
---|
5606 | { |
---|
5607 | int subCheck= substituteCheck (bufUniFactors); |
---|
5608 | |
---|
5609 | if (subCheck > 1 && (subCheck1%subCheck == 0)) |
---|
5610 | { |
---|
5611 | CanonicalForm bufA= A; |
---|
5612 | subst (bufA, bufA, subCheck, x); |
---|
5613 | factors= biFactorize (bufA, info); |
---|
5614 | reverseSubst (factors, subCheck, x); |
---|
5615 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
5616 | swap, swap2, N); |
---|
5617 | normalize (factors); |
---|
5618 | return factors; |
---|
5619 | } |
---|
5620 | } |
---|
5621 | |
---|
5622 | if (!derivXZero && !fail2 && subCheck2 > 0) |
---|
5623 | { |
---|
5624 | int subCheck= substituteCheck (bufUniFactors2); |
---|
5625 | |
---|
5626 | if (subCheck > 1 && (subCheck2%subCheck == 0)) |
---|
5627 | { |
---|
5628 | CanonicalForm bufA= A; |
---|
5629 | subst (bufA, bufA, subCheck, y); |
---|
5630 | factors= biFactorize (bufA, info); |
---|
5631 | reverseSubst (factors, subCheck, y); |
---|
5632 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
5633 | swap, swap2, N); |
---|
5634 | normalize (factors); |
---|
5635 | return factors; |
---|
5636 | } |
---|
5637 | } |
---|
5638 | } |
---|
5639 | |
---|
5640 | // degree analysis |
---|
5641 | bufDegs = DegreePattern (bufUniFactors); |
---|
5642 | if (!derivXZero && !fail2) |
---|
5643 | bufDegs2= DegreePattern (bufUniFactors2); |
---|
5644 | |
---|
5645 | if (i == 0) |
---|
5646 | { |
---|
5647 | Aeval= bufAeval; |
---|
5648 | evaluation= bufEvaluation; |
---|
5649 | uniFactors= bufUniFactors; |
---|
5650 | degs= bufDegs; |
---|
5651 | if (!derivXZero && !fail2) |
---|
5652 | { |
---|
5653 | Aeval2= bufAeval2; |
---|
5654 | evaluation2= bufEvaluation2; |
---|
5655 | uniFactors2= bufUniFactors2; |
---|
5656 | degs2= bufDegs2; |
---|
5657 | } |
---|
5658 | } |
---|
5659 | else |
---|
5660 | { |
---|
5661 | degs.intersect (bufDegs); |
---|
5662 | if (!derivXZero && !fail2) |
---|
5663 | { |
---|
5664 | degs2.intersect (bufDegs2); |
---|
5665 | if (bufUniFactors2.length() < uniFactors2.length()) |
---|
5666 | { |
---|
5667 | uniFactors2= bufUniFactors2; |
---|
5668 | Aeval2= bufAeval2; |
---|
5669 | evaluation2= bufEvaluation2; |
---|
5670 | } |
---|
5671 | } |
---|
5672 | if (bufUniFactors.length() < uniFactors.length()) |
---|
5673 | { |
---|
5674 | uniFactors= bufUniFactors; |
---|
5675 | Aeval= bufAeval; |
---|
5676 | evaluation= bufEvaluation; |
---|
5677 | } |
---|
5678 | } |
---|
5679 | list.append (bufEvaluation); |
---|
5680 | if (!derivXZero && !fail2) |
---|
5681 | list2.append (bufEvaluation2); |
---|
5682 | } |
---|
5683 | |
---|
5684 | if (!derivXZero && !fail2) |
---|
5685 | { |
---|
5686 | if (uniFactors.length() > uniFactors2.length() || |
---|
5687 | (uniFactors.length() == uniFactors2.length() |
---|
5688 | && degs.getLength() > degs2.getLength())) |
---|
5689 | { |
---|
5690 | degs= degs2; |
---|
5691 | uniFactors= uniFactors2; |
---|
5692 | evaluation= evaluation2; |
---|
5693 | Aeval= Aeval2; |
---|
5694 | A= buf; |
---|
5695 | swap2= true; |
---|
5696 | } |
---|
5697 | } |
---|
5698 | |
---|
5699 | if (degs.getLength() == 1) // A is irreducible |
---|
5700 | { |
---|
5701 | if (extension) |
---|
5702 | { |
---|
5703 | CFList source, dest; |
---|
5704 | appendMapDown (factors, A, info, source, dest); |
---|
5705 | } |
---|
5706 | else |
---|
5707 | factors.append (A); |
---|
5708 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
5709 | swap, swap2, N); |
---|
5710 | normalize (factors); |
---|
5711 | return factors; |
---|
5712 | } |
---|
5713 | |
---|
5714 | A= A (y + evaluation, y); |
---|
5715 | |
---|
5716 | int liftBound= degree (A, y) + 1 + degree (LC(A, x)); |
---|
5717 | |
---|
5718 | int boundsLength; |
---|
5719 | int * bounds= computeBounds (A (y - evaluation, y), boundsLength); |
---|
5720 | int minBound= bounds[0]; |
---|
5721 | for (int i= 1; i < boundsLength; i++) |
---|
5722 | { |
---|
5723 | if (bounds[i] != 0) |
---|
5724 | minBound= tmin (minBound, bounds[i]); |
---|
5725 | } |
---|
5726 | |
---|
5727 | int degMipo= 1; |
---|
5728 | if (extension && alpha.level() != 1 && k==1) |
---|
5729 | degMipo= degree (getMipo (alpha)); |
---|
5730 | |
---|
5731 | DEBOUTLN (cerr, "uniFactors= " << uniFactors); |
---|
5732 | |
---|
5733 | if ((GF && !extension) || (GF && extension && k != 1)) |
---|
5734 | { |
---|
5735 | bool earlySuccess= false; |
---|
5736 | CFList earlyFactors; |
---|
5737 | TIMING_START (fac_hensel_lift); |
---|
5738 | uniFactors= henselLiftAndEarly |
---|
5739 | (A, earlySuccess, earlyFactors, degs, liftBound, |
---|
5740 | uniFactors, info, evaluation); |
---|
5741 | TIMING_END_AND_PRINT (fac_hensel_lift, "time for hensel lifting: "); |
---|
5742 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
5743 | |
---|
5744 | CanonicalForm MODl= power (y, liftBound); |
---|
5745 | |
---|
5746 | if (extension) |
---|
5747 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
5748 | evaluation, 1, uniFactors.length()/2); |
---|
5749 | else |
---|
5750 | factors= factorRecombination (uniFactors, A, MODl, degs, 1, |
---|
5751 | uniFactors.length()/2); |
---|
5752 | |
---|
5753 | if (earlySuccess) |
---|
5754 | factors= Union (earlyFactors, factors); |
---|
5755 | else if (!earlySuccess && degs.getLength() == 1) |
---|
5756 | factors= earlyFactors; |
---|
5757 | } |
---|
5758 | else if (degree (A) > 4 && beta.level() == 1 && (2*minBound)/degMipo < 32) |
---|
5759 | { |
---|
5760 | TIMING_START (fac_hensel_lift); |
---|
5761 | if (extension) |
---|
5762 | { |
---|
5763 | CFList lll= extHenselLiftAndLatticeRecombi (A, uniFactors, info, degs, |
---|
5764 | evaluation |
---|
5765 | ); |
---|
5766 | factors= Union (lll, factors); |
---|
5767 | } |
---|
5768 | else if (alpha.level() == 1 && !GF) |
---|
5769 | { |
---|
5770 | CFList lll= henselLiftAndLatticeRecombi (A, uniFactors, alpha, degs); |
---|
5771 | factors= Union (lll, factors); |
---|
5772 | } |
---|
5773 | else if (!extension && (alpha != x || GF)) |
---|
5774 | { |
---|
5775 | CFList lll= henselLiftAndLatticeRecombi (A, uniFactors, alpha, degs); |
---|
5776 | factors= Union (lll, factors); |
---|
5777 | } |
---|
5778 | TIMING_END_AND_PRINT (fac_hensel_lift, "time for hensel lifting: "); |
---|
5779 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
5780 | } |
---|
5781 | else |
---|
5782 | { |
---|
5783 | bool earlySuccess= false; |
---|
5784 | CFList earlyFactors; |
---|
5785 | TIMING_START (fac_hensel_lift); |
---|
5786 | uniFactors= henselLiftAndEarly |
---|
5787 | (A, earlySuccess, earlyFactors, degs, liftBound, |
---|
5788 | uniFactors, info, evaluation); |
---|
5789 | TIMING_END_AND_PRINT (fac_hensel_lift, "time for hensel lifting: "); |
---|
5790 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
5791 | |
---|
5792 | CanonicalForm MODl= power (y, liftBound); |
---|
5793 | if (!extension) |
---|
5794 | { |
---|
5795 | factors= factorRecombination (uniFactors, A, MODl, degs, 1, 3); |
---|
5796 | |
---|
5797 | int oldUniFactorsLength= uniFactors.length(); |
---|
5798 | if (degree (A) > 0) |
---|
5799 | { |
---|
5800 | CFList tmp; |
---|
5801 | if (alpha.level() == 1) |
---|
5802 | tmp= increasePrecision (A, uniFactors, 0, uniFactors.length(), 1, |
---|
5803 | liftBound |
---|
5804 | ); |
---|
5805 | else |
---|
5806 | { |
---|
5807 | if (degree (A) > getCharacteristic()) |
---|
5808 | tmp= increasePrecisionFq2Fp (A, uniFactors, 0, uniFactors.length(), |
---|
5809 | 1, alpha, liftBound |
---|
5810 | ); |
---|
5811 | else |
---|
5812 | tmp= increasePrecision (A, uniFactors, 0, uniFactors.length(), 1, |
---|
5813 | alpha, liftBound |
---|
5814 | ); |
---|
5815 | } |
---|
5816 | factors= Union (factors, tmp); |
---|
5817 | if (tmp.length() == 0 || (tmp.length() > 0 && uniFactors.length() != 0 |
---|
5818 | && uniFactors.length() != oldUniFactorsLength) |
---|
5819 | ) |
---|
5820 | { |
---|
5821 | DegreePattern bufDegs= DegreePattern (uniFactors); |
---|
5822 | degs.intersect (bufDegs); |
---|
5823 | degs.refine (); |
---|
5824 | factors= Union (factors, factorRecombination (uniFactors, A, MODl, |
---|
5825 | degs, 4, |
---|
5826 | uniFactors.length()/2 |
---|
5827 | ) |
---|
5828 | ); |
---|
5829 | } |
---|
5830 | } |
---|
5831 | } |
---|
5832 | else |
---|
5833 | { |
---|
5834 | if (beta.level() != 1 || k > 1) |
---|
5835 | { |
---|
5836 | if (k > 1) |
---|
5837 | { |
---|
5838 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
5839 | evaluation, 1, uniFactors.length()/2 |
---|
5840 | ); |
---|
5841 | } |
---|
5842 | else |
---|
5843 | { |
---|
5844 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
5845 | evaluation, 1, 3 |
---|
5846 | ); |
---|
5847 | if (degree (A) > 0) |
---|
5848 | { |
---|
5849 | CFList tmp= increasePrecision2 (A, uniFactors, alpha, liftBound); |
---|
5850 | DegreePattern bufDegs= DegreePattern (tmp); |
---|
5851 | degs.intersect (bufDegs); |
---|
5852 | degs.refine (); |
---|
5853 | factors= Union (factors, extFactorRecombination (tmp, A, MODl, info, |
---|
5854 | degs, evaluation, |
---|
5855 | 1, tmp.length()/2 |
---|
5856 | ) |
---|
5857 | ); |
---|
5858 | } |
---|
5859 | } |
---|
5860 | } |
---|
5861 | else |
---|
5862 | { |
---|
5863 | factors= extFactorRecombination (uniFactors, A, MODl, info, degs, |
---|
5864 | evaluation, 1, 3 |
---|
5865 | ); |
---|
5866 | int oldUniFactorsLength= uniFactors.length(); |
---|
5867 | if (degree (A) > 0) |
---|
5868 | { |
---|
5869 | int degMipo; |
---|
5870 | ExtensionInfo info2= init4ext (info, evaluation, degMipo); |
---|
5871 | |
---|
5872 | CFList source, dest; |
---|
5873 | CFList tmp= extIncreasePrecision (A, uniFactors, 0, |
---|
5874 | uniFactors.length(), 1, evaluation, |
---|
5875 | info2, source, dest, liftBound |
---|
5876 | ); |
---|
5877 | factors= Union (factors, tmp); |
---|
5878 | if (tmp.length() == 0 || (tmp.length() > 0 && uniFactors.length() != 0 |
---|
5879 | && uniFactors.length() != oldUniFactorsLength) |
---|
5880 | ) |
---|
5881 | { |
---|
5882 | DegreePattern bufDegs= DegreePattern (uniFactors); |
---|
5883 | degs.intersect (bufDegs); |
---|
5884 | degs.refine (); |
---|
5885 | factors= Union (factors,extFactorRecombination (uniFactors, A, MODl, |
---|
5886 | info, degs, evaluation, |
---|
5887 | 4, uniFactors.length()/2 |
---|
5888 | ) |
---|
5889 | ); |
---|
5890 | } |
---|
5891 | } |
---|
5892 | } |
---|
5893 | } |
---|
5894 | |
---|
5895 | if (earlySuccess) |
---|
5896 | factors= Union (earlyFactors, factors); |
---|
5897 | else if (!earlySuccess && degs.getLength() == 1) |
---|
5898 | factors= earlyFactors; |
---|
5899 | } |
---|
5900 | delete [] bounds; |
---|
5901 | if (!extension) |
---|
5902 | { |
---|
5903 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
5904 | i.getItem()= i.getItem() (y - evaluation, y); |
---|
5905 | } |
---|
5906 | |
---|
5907 | appendSwapDecompress (factors, contentAxFactors, contentAyFactors, |
---|
5908 | swap, swap2, N); |
---|
5909 | normalize (factors); |
---|
5910 | |
---|
5911 | return factors; |
---|
5912 | } |
---|
5913 | |
---|
5914 | CFList |
---|
5915 | extBiFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
5916 | { |
---|
5917 | |
---|
5918 | CanonicalForm A= F; |
---|
5919 | Variable alpha= info.getAlpha(); |
---|
5920 | Variable beta= info.getBeta(); |
---|
5921 | int k= info.getGFDegree(); |
---|
5922 | char cGFName= info.getGFName(); |
---|
5923 | CanonicalForm delta= info.getDelta(); |
---|
5924 | |
---|
5925 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
5926 | Variable x= Variable (1); |
---|
5927 | CFList factors; |
---|
5928 | if (!GF && alpha == x) // we are in F_p |
---|
5929 | { |
---|
5930 | bool extension= true; |
---|
5931 | int p= getCharacteristic(); |
---|
5932 | if (p*p < (1<<16)) // pass to GF if possible |
---|
5933 | { |
---|
5934 | setCharacteristic (getCharacteristic(), 2, 'Z'); |
---|
5935 | A= A.mapinto(); |
---|
5936 | ExtensionInfo info2= ExtensionInfo (extension); |
---|
5937 | factors= biFactorize (A, info2); |
---|
5938 | |
---|
5939 | Variable vBuf= rootOf (gf_mipo); |
---|
5940 | setCharacteristic (getCharacteristic()); |
---|
5941 | for (CFListIterator j= factors; j.hasItem(); j++) |
---|
5942 | j.getItem()= GF2FalphaRep (j.getItem(), vBuf); |
---|
5943 | } |
---|
5944 | else // not able to pass to GF, pass to F_p(\alpha) |
---|
5945 | { |
---|
5946 | CanonicalForm mipo= randomIrredpoly (2, x); |
---|
5947 | Variable v= rootOf (mipo); |
---|
5948 | ExtensionInfo info2= ExtensionInfo (v); |
---|
5949 | factors= biFactorize (A, info2); |
---|
5950 | } |
---|
5951 | return factors; |
---|
5952 | } |
---|
5953 | else if (!GF && (alpha != x)) // we are in F_p(\alpha) |
---|
5954 | { |
---|
5955 | if (k == 1) // need factorization over F_p |
---|
5956 | { |
---|
5957 | int extDeg= degree (getMipo (alpha)); |
---|
5958 | extDeg++; |
---|
5959 | CanonicalForm mipo= randomIrredpoly (extDeg + 1, x); |
---|
5960 | Variable v= rootOf (mipo); |
---|
5961 | ExtensionInfo info2= ExtensionInfo (v); |
---|
5962 | factors= biFactorize (A, info2); |
---|
5963 | } |
---|
5964 | else |
---|
5965 | { |
---|
5966 | if (beta == x) |
---|
5967 | { |
---|
5968 | Variable v= chooseExtension (alpha, beta, k); |
---|
5969 | CanonicalForm primElem, imPrimElem; |
---|
5970 | bool primFail= false; |
---|
5971 | Variable vBuf; |
---|
5972 | primElem= primitiveElement (alpha, vBuf, primFail); |
---|
5973 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
5974 | if (primFail) |
---|
5975 | ; //ERROR |
---|
5976 | else |
---|
5977 | imPrimElem= mapPrimElem (primElem, alpha, v); |
---|
5978 | |
---|
5979 | CFList source, dest; |
---|
5980 | CanonicalForm bufA= mapUp (A, alpha, v, primElem, imPrimElem, |
---|
5981 | source, dest); |
---|
5982 | ExtensionInfo info2= ExtensionInfo (v, alpha, imPrimElem, primElem); |
---|
5983 | factors= biFactorize (bufA, info2); |
---|
5984 | } |
---|
5985 | else |
---|
5986 | { |
---|
5987 | Variable v= chooseExtension (alpha, beta, k); |
---|
5988 | CanonicalForm primElem, imPrimElem; |
---|
5989 | bool primFail= false; |
---|
5990 | Variable vBuf; |
---|
5991 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
5992 | if (primFail) |
---|
5993 | ; //ERROR |
---|
5994 | else |
---|
5995 | imPrimElem= mapPrimElem (delta, beta, v); |
---|
5996 | |
---|
5997 | CFList source, dest; |
---|
5998 | CanonicalForm bufA= mapDown (A, info, source, dest); |
---|
5999 | source= CFList(); |
---|
6000 | dest= CFList(); |
---|
6001 | bufA= mapUp (bufA, beta, v, delta, imPrimElem, source, dest); |
---|
6002 | ExtensionInfo info2= ExtensionInfo (v, beta, imPrimElem, delta); |
---|
6003 | factors= biFactorize (bufA, info2); |
---|
6004 | } |
---|
6005 | } |
---|
6006 | return factors; |
---|
6007 | } |
---|
6008 | else // we are in GF (p^k) |
---|
6009 | { |
---|
6010 | int p= getCharacteristic(); |
---|
6011 | int extensionDeg= getGFDegree(); |
---|
6012 | bool extension= true; |
---|
6013 | if (k == 1) // need factorization over F_p |
---|
6014 | { |
---|
6015 | extensionDeg++; |
---|
6016 | if (ipower (p, extensionDeg) < (1<<16)) |
---|
6017 | // pass to GF(p^k+1) |
---|
6018 | { |
---|
6019 | setCharacteristic (p); |
---|
6020 | Variable vBuf= rootOf (gf_mipo); |
---|
6021 | A= GF2FalphaRep (A, vBuf); |
---|
6022 | setCharacteristic (p, extensionDeg, 'Z'); |
---|
6023 | ExtensionInfo info2= ExtensionInfo (extension); |
---|
6024 | factors= biFactorize (A.mapinto(), info2); |
---|
6025 | } |
---|
6026 | else // not able to pass to another GF, pass to F_p(\alpha) |
---|
6027 | { |
---|
6028 | setCharacteristic (p); |
---|
6029 | Variable vBuf= rootOf (gf_mipo); |
---|
6030 | A= GF2FalphaRep (A, vBuf); |
---|
6031 | Variable v= chooseExtension (vBuf, beta, k); |
---|
6032 | ExtensionInfo info2= ExtensionInfo (v, extension); |
---|
6033 | factors= biFactorize (A, info2); |
---|
6034 | } |
---|
6035 | } |
---|
6036 | else // need factorization over GF (p^k) |
---|
6037 | { |
---|
6038 | if (ipower (p, 2*extensionDeg) < (1<<16)) |
---|
6039 | // pass to GF (p^2k) |
---|
6040 | { |
---|
6041 | setCharacteristic (p, 2*extensionDeg, 'Z'); |
---|
6042 | ExtensionInfo info2= ExtensionInfo (k, cGFName, extension); |
---|
6043 | factors= biFactorize (GFMapUp (A, extensionDeg), info2); |
---|
6044 | setCharacteristic (p, extensionDeg, cGFName); |
---|
6045 | } |
---|
6046 | else // not able to pass to GF (p^2k), pass to F_p (\alpha) |
---|
6047 | { |
---|
6048 | setCharacteristic (p); |
---|
6049 | Variable v1= rootOf (gf_mipo); |
---|
6050 | A= GF2FalphaRep (A, v1); |
---|
6051 | Variable v2= chooseExtension (v1, v1, k); |
---|
6052 | CanonicalForm primElem, imPrimElem; |
---|
6053 | bool primFail= false; |
---|
6054 | Variable vBuf; |
---|
6055 | primElem= primitiveElement (v1, vBuf, primFail); |
---|
6056 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
6057 | if (primFail) |
---|
6058 | ; //ERROR |
---|
6059 | else |
---|
6060 | imPrimElem= mapPrimElem (primElem, v1, v2); |
---|
6061 | |
---|
6062 | CFList source, dest; |
---|
6063 | CanonicalForm bufA= mapUp (A, v1, v2, primElem, imPrimElem, |
---|
6064 | source, dest); |
---|
6065 | ExtensionInfo info2= ExtensionInfo (v2, v1, imPrimElem, primElem); |
---|
6066 | factors= biFactorize (bufA, info2); |
---|
6067 | setCharacteristic (p, k, cGFName); |
---|
6068 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
6069 | i.getItem()= Falpha2GFRep (i.getItem()); |
---|
6070 | } |
---|
6071 | } |
---|
6072 | return factors; |
---|
6073 | } |
---|
6074 | } |
---|
6075 | |
---|
6076 | #endif |
---|
6077 | /* HAVE_NTL */ |
---|
6078 | |
---|
6079 | |
---|