1 | /*****************************************************************************\ |
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2 | * Computer Algebra System SINGULAR |
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3 | \*****************************************************************************/ |
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4 | /** @file facFqFactorize.cc |
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5 | * |
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6 | * This file implements functions for factoring a multivariate polynomial over |
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7 | * a finite field. |
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8 | * |
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9 | * ABSTRACT: "Efficient Multivariate Factorization over Finite Fields" by |
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10 | * L. Bernardin & M. Monagon. |
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11 | * |
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12 | * @author Martin Lee |
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13 | * |
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14 | * @internal @version \$Id$ |
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15 | * |
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16 | **/ |
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17 | /*****************************************************************************/ |
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18 | |
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19 | #include <config.h> |
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20 | |
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21 | #include "assert.h" |
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22 | #include "debug.h" |
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23 | #include "timing.h" |
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24 | |
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25 | #include "facFqFactorizeUtil.h" |
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26 | #include "facFqFactorize.h" |
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27 | #include "cf_random.h" |
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28 | #include "facHensel.h" |
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29 | #include "cf_gcd_smallp.h" |
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30 | #include "cf_map_ext.h" |
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31 | #include "algext.h" |
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32 | |
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33 | #ifdef HAVE_NTL |
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34 | #include <NTL/ZZ_pEX.h> |
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35 | #include "NTLconvert.h" |
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36 | |
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37 | TIMING_DEFINE_PRINT(fac_bi_factorizer); |
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38 | TIMING_DEFINE_PRINT(fac_hensel_lift); |
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39 | TIMING_DEFINE_PRINT(fac_factor_recombination); |
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40 | |
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41 | static inline |
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42 | CanonicalForm |
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43 | listGCD (const CFList& L); |
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44 | |
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45 | static inline |
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46 | CanonicalForm |
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47 | myContent (const CanonicalForm& F) |
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48 | { |
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49 | CanonicalForm G= swapvar (F, F.mvar(), Variable (1)); |
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50 | CFList L; |
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51 | Variable alpha; |
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52 | bool algExt= hasFirstAlgVar (G, alpha); |
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53 | for (CFIterator i= G; i.hasTerms(); i++) |
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54 | L.append (i.coeff()); |
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55 | if (L.length() == 2) |
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56 | { |
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57 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
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58 | if (GF) |
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59 | { |
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60 | return swapvar (GCD_GF (L.getFirst(), L.getLast()), F.mvar(), |
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61 | Variable (1)); |
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62 | } |
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63 | else if (!GF && algExt) |
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64 | { |
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65 | return swapvar (GCD_Fp_extension (L.getFirst(), L.getLast(), alpha), |
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66 | F.mvar(), Variable (1)); |
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67 | } |
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68 | else |
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69 | return swapvar (GCD_small_p (L.getFirst(), L.getLast()), F.mvar(), |
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70 | Variable (1)); |
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71 | } |
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72 | if (L.length() == 1) |
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73 | { |
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74 | return LC (F, Variable (1)); |
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75 | } |
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76 | return swapvar (listGCD (L), F.mvar(), Variable (1)); |
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77 | } |
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78 | |
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79 | static inline |
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80 | CanonicalForm |
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81 | listGCD (const CFList& L) |
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82 | { |
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83 | if (L.length() == 1) |
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84 | return L.getFirst(); |
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85 | Variable alpha; |
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86 | if (L.length() == 2) |
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87 | { |
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88 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
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89 | if (GF) |
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90 | { |
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91 | return GCD_GF (L.getFirst(), L.getLast()); |
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92 | } |
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93 | else if (!GF && (hasFirstAlgVar (L.getFirst(), alpha) || |
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94 | hasFirstAlgVar (L.getLast(), alpha))) |
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95 | { |
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96 | return GCD_Fp_extension (L.getFirst(), L.getLast(), alpha); |
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97 | } |
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98 | else |
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99 | return GCD_small_p (L.getFirst(), L.getLast()); |
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100 | } |
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101 | else |
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102 | { |
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103 | CFList lHi, lLo; |
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104 | CanonicalForm resultHi, resultLo; |
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105 | int length= L.length()/2; |
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106 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
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107 | int j= 0; |
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108 | for (CFListIterator i= L; j < length; i++, j++) |
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109 | lHi.append (i.getItem()); |
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110 | lLo= Difference (L, lHi); |
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111 | resultHi= listGCD (lHi); |
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112 | resultLo= listGCD (lLo); |
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113 | if (resultHi.isOne() || resultLo.isOne()) |
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114 | return 1; |
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115 | if (GF) |
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116 | { |
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117 | return GCD_GF (resultHi, resultLo); |
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118 | } |
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119 | else if (!GF && (hasFirstAlgVar (resultHi, alpha) || |
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120 | hasFirstAlgVar (resultLo, alpha))) |
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121 | { |
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122 | return GCD_Fp_extension (resultHi, resultLo, alpha); |
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123 | } |
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124 | else |
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125 | return GCD_small_p (resultHi, resultLo); |
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126 | } |
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127 | } |
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128 | |
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129 | static inline |
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130 | CanonicalForm |
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131 | myContent (const CanonicalForm& F, const Variable& x) |
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132 | { |
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133 | if (degree (F, x) <= 0) |
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134 | return 1; |
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135 | CanonicalForm G= F; |
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136 | bool swap= false; |
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137 | if (x != F.mvar()) |
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138 | { |
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139 | swap= true; |
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140 | G= swapvar (F, x, F.mvar()); |
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141 | } |
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142 | CFList L; |
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143 | Variable alpha; |
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144 | bool algExt= hasFirstAlgVar (G, alpha); |
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145 | for (CFIterator i= G; i.hasTerms(); i++) |
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146 | L.append (i.coeff()); |
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147 | if (L.length() == 2) |
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148 | { |
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149 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
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150 | if (GF) |
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151 | { |
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152 | if (swap) |
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153 | return swapvar(GCD_GF (L.getFirst(), L.getLast()), F.mvar(), x); |
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154 | else |
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155 | return GCD_GF (L.getFirst(), L.getLast()); |
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156 | } |
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157 | else if (!GF && algExt) |
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158 | { |
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159 | if (swap) |
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160 | return swapvar(GCD_Fp_extension (L.getFirst(), L.getLast(), alpha), |
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161 | F.mvar(), x); |
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162 | else |
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163 | return GCD_Fp_extension (L.getFirst(), L.getLast(), alpha); |
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164 | } |
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165 | else |
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166 | { |
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167 | if (swap) |
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168 | return swapvar (GCD_small_p (L.getFirst(), L.getLast()), F.mvar(), |
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169 | x); |
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170 | else |
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171 | return GCD_small_p (L.getFirst(), L.getLast()); |
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172 | } |
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173 | } |
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174 | if (L.length() == 1) |
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175 | { |
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176 | return LC (F, x); |
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177 | } |
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178 | if (swap) |
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179 | return swapvar (listGCD (L), F.mvar(), x); |
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180 | else |
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181 | return listGCD (L); |
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182 | } |
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183 | |
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184 | static inline |
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185 | CanonicalForm |
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186 | myLcm (const CanonicalForm& F, const CanonicalForm& G) |
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187 | { |
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188 | if ( F.isZero() || G.isZero() ) |
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189 | return 0; |
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190 | else |
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191 | { |
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192 | Variable alpha; |
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193 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
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194 | if (GF) |
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195 | return (F/GCD_GF (F, G))*G; |
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196 | else if (!GF && (hasFirstAlgVar (F, alpha) || |
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197 | hasFirstAlgVar (G, alpha))) |
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198 | return (F/GCD_Fp_extension (F, G, alpha))*G; |
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199 | else |
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200 | return (F/GCD_small_p (F, G))*G; |
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201 | } |
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202 | } |
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203 | |
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204 | |
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205 | static inline |
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206 | CanonicalForm myCompress (const CanonicalForm& F, CFMap& N) |
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207 | { |
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208 | int n= F.level(); |
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209 | int * degsf= new int [n + 1]; |
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210 | int ** swap; |
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211 | swap= new int* [n + 1]; |
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212 | for (int i= 0; i <= n; i++) |
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213 | { |
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214 | degsf[i]= 0; |
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215 | swap [i]= new int [2]; |
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216 | swap [i] [0]= 0; |
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217 | swap [i] [1]= 0; |
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218 | } |
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219 | int i= 1; |
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220 | n= 1; |
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221 | degsf= degrees (F, degsf); |
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222 | |
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223 | CanonicalForm result= F; |
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224 | while ( i <= F.level() ) |
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225 | { |
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226 | while( degsf[i] == 0 ) i++; |
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227 | swap[n][0]= i; |
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228 | swap[n][1]= degsf[i]; |
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229 | if (i != n) |
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230 | result= swapvar (result, Variable (n), Variable(i)); |
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231 | n++; i++; |
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232 | } |
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233 | |
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234 | int buf1, buf2; |
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235 | n--; |
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236 | |
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237 | for (i= 1; i < n; i++) |
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238 | { |
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239 | for (int j= 1; j < n - i + 1; j++) |
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240 | { |
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241 | if (swap[j][1] < swap[j + 1][1]) |
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242 | { |
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243 | buf1= swap [j + 1] [0]; |
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244 | buf2= swap [j + 1] [1]; |
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245 | swap[j + 1] [0]= swap[j] [0]; |
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246 | swap[j + 1] [1]= swap[j] [1]; |
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247 | swap[j][0]= buf1; |
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248 | swap[j][1]= buf2; |
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249 | result= swapvar (result, Variable (j + 1), Variable (j)); |
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250 | } |
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251 | } |
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252 | } |
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253 | |
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254 | for (i= n; i > 0; i--) |
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255 | { |
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256 | if (i != swap[i] [0]) |
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257 | N.newpair (Variable (i), Variable (swap[i] [0])); |
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258 | } |
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259 | |
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260 | for (i= 0; i <= n; i++) |
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261 | delete [] swap[i]; |
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262 | delete [] swap; |
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263 | |
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264 | delete [] degsf; |
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265 | |
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266 | return result; |
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267 | } |
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268 | |
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269 | CFList |
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270 | monicFactorRecombi (const CFList& factors,const CanonicalForm& F, const |
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271 | CanonicalForm& M, const DegreePattern& degs) |
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272 | { |
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273 | if (degs.getLength() == 1) |
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274 | return CFList(F); |
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275 | |
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276 | CFList T, S; |
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277 | |
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278 | T= factors; |
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279 | |
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280 | int s= 1; |
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281 | CFList result; |
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282 | CanonicalForm buf= F; |
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283 | CanonicalForm LCBuf= LC (buf, Variable (1)); |
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284 | CanonicalForm g, gg; |
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285 | int v [T.length()]; |
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286 | for (int i= 0; i < T.length(); i++) |
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287 | v[i]= 0; |
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288 | bool noSubset= false; |
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289 | CFArray TT; |
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290 | int subsetDeg; |
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291 | DegreePattern bufDegs1= degs, bufDegs2; |
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292 | TT= copy (factors); |
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293 | while (T.length() >= 2*s) |
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294 | { |
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295 | while (noSubset == false) |
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296 | { |
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297 | if (T.length() == s) |
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298 | { |
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299 | result.append (prodMod (T, M)); |
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300 | return result; |
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301 | } |
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302 | S= subset (v, s, TT, noSubset); |
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303 | if (noSubset) break; |
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304 | subsetDeg= subsetDegree (S); |
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305 | if (!degs.find (subsetDeg)) |
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306 | continue; |
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307 | else |
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308 | { |
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309 | g= prodMod0 (S, M); |
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310 | gg= mod (g*LCBuf, M); //univariate polys |
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311 | gg /= content (gg); |
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312 | if (fdivides (LC (gg), LCBuf)) |
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313 | { |
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314 | g= prodMod (S, M); |
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315 | gg= mulMod2 (LCBuf, g, M); |
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316 | gg /= content (gg, Variable (1)); |
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317 | if (fdivides (gg, buf)) |
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318 | { |
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319 | result.append (g); |
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320 | buf /= gg; |
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321 | LCBuf= LC (buf, Variable(1)); |
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322 | T= Difference (T, S); |
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323 | // compute new possible degree pattern |
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324 | bufDegs2= DegreePattern (T); |
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325 | bufDegs1.intersect (bufDegs2); |
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326 | bufDegs1.refine (); |
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327 | if (T.length() < 2*s || T.length() == s || |
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328 | bufDegs1.getLength() == 1) |
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329 | { |
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330 | result.append (prodMod (T, M)); |
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331 | return result; |
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332 | } |
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333 | TT= copy (T); |
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334 | indexUpdate (v, s, T.length(), noSubset); |
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335 | if (noSubset) break; |
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336 | } |
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337 | } |
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338 | } |
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339 | } |
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340 | s++; |
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341 | if (T.length() < 2*s || T.length() == s) |
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342 | { |
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343 | result.append (prodMod (T, M)); |
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344 | return result; |
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345 | } |
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346 | int v [T.length()]; |
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347 | for (int i= 0; i < T.length(); i++) |
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348 | v[i]= 0; |
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349 | noSubset= false; |
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350 | } |
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351 | if (T.length() < 2*s) |
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352 | result.append (prodMod (T, M)); |
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353 | |
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354 | return result; |
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355 | } |
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356 | |
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357 | CFList |
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358 | earlyMonicFactorDetect (CanonicalForm& F, CFList& factors, |
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359 | int& adaptedLiftBound, DegreePattern& degs, |
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360 | bool& success, int deg, const int bound) |
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361 | { |
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362 | DegreePattern bufDegs1= degs; |
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363 | DegreePattern bufDegs2; |
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364 | CFList result; |
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365 | CFList T= factors; |
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366 | CanonicalForm buf= F; |
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367 | CanonicalForm LCBuf= LC (buf, Variable (1)); |
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368 | CanonicalForm g, gg; |
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369 | CanonicalForm M= power (F.mvar(), deg); |
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370 | int d= bound; |
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371 | int e= 0; |
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372 | adaptedLiftBound= 0; |
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373 | for (CFListIterator i= factors; i.hasItem(); i++) |
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374 | { |
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375 | if (!bufDegs1.find (degree (i.getItem(), 1))) |
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376 | continue; |
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377 | else |
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378 | { |
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379 | gg= i.getItem() (0, 1); |
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380 | gg *= LCBuf; |
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381 | gg= mod (gg, M); |
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382 | if (fdivides (LC (gg), LCBuf)) |
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383 | { |
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384 | g= i.getItem(); |
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385 | gg= mulMod2 (g, LCBuf, M); |
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386 | gg /= content (gg, Variable (1)); |
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387 | if (fdivides (gg, buf)) |
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388 | { |
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389 | result.append (g); |
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390 | CanonicalForm bufbuf= buf; |
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391 | buf /= gg; |
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392 | d -= degree (gg) + degree (LC (gg, 1)); |
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393 | e= tmax (e, degree (gg) + degree (LC (gg, 1))); |
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394 | LCBuf= LC (buf, Variable (1)); |
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395 | T= Difference (T, CFList (i.getItem())); |
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396 | |
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397 | // compute new possible degree pattern |
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398 | bufDegs2= DegreePattern (T); |
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399 | bufDegs1.intersect (bufDegs2); |
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400 | bufDegs1.refine (); |
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401 | if (bufDegs1.getLength() <= 1) |
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402 | { |
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403 | result.append (prodMod (T, M)); |
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404 | break; |
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405 | } |
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406 | } |
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407 | } |
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408 | } |
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409 | } |
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410 | adaptedLiftBound= d; |
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411 | |
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412 | if (adaptedLiftBound < deg) |
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413 | { |
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414 | factors= T; |
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415 | degs= bufDegs1; |
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416 | if (adaptedLiftBound < degree (F) + 1) |
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417 | { |
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418 | if (d == 1) |
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419 | { |
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420 | if (e + 1 > deg) |
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421 | { |
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422 | success= false; |
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423 | adaptedLiftBound= deg; |
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424 | } |
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425 | else |
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426 | { |
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427 | F= buf; |
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428 | success= true; |
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429 | if (e + 1 < degree (F) + 1) |
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430 | adaptedLiftBound= deg; |
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431 | else |
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432 | adaptedLiftBound= e + 1; |
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433 | } |
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434 | } |
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435 | else |
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436 | { |
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437 | success= true; |
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438 | F= buf; |
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439 | adaptedLiftBound= deg; |
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440 | } |
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441 | } |
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442 | else |
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443 | { |
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444 | F= buf; |
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445 | success= true; |
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446 | } |
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447 | } |
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448 | if (bufDegs1.getLength() <= 1) |
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449 | { |
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450 | degs= bufDegs1; |
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451 | if (!success) |
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452 | adaptedLiftBound= deg; |
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453 | } |
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454 | |
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455 | return result; |
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456 | } |
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457 | |
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458 | CFList biFactorizer (const CanonicalForm& F, const Variable& alpha, |
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459 | CanonicalForm& bivarEval, int& liftBound) |
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460 | { |
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461 | CanonicalForm A= F; |
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462 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
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463 | |
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464 | if (A.isUnivariate()) |
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465 | return uniFactorizer (F, alpha, GF); |
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466 | |
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467 | |
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468 | CFMap N; |
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469 | A= compress (A, N); |
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470 | Variable y= A.mvar(); |
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471 | A /= Lc(A); |
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472 | |
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473 | if (y.level() > 2) return CFList (F); |
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474 | Variable x= Variable (1); |
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475 | |
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476 | //remove content and factorize content |
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477 | CanonicalForm contentAy= content (A, y); |
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478 | CanonicalForm contentAx= content (A, x); |
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479 | A= A/(contentAy*contentAx); |
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480 | CFList contentAyFactors= uniFactorizer (contentAy, alpha, GF); |
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481 | |
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482 | //trivial case |
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483 | CFList factors; |
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484 | if (A.inCoeffDomain()) |
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485 | { |
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486 | append (factors, contentAyFactors); |
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487 | decompress (factors, N); |
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488 | bivarEval= N (y - bivarEval); |
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489 | return factors; |
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490 | } |
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491 | else if (A.isUnivariate()) |
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492 | { |
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493 | if (A.mvar() == x) |
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494 | factors= uniFactorizer (A, alpha, GF); |
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495 | append (factors, contentAyFactors); |
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496 | decompress (factors, N); |
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497 | bivarEval= N (y - bivarEval); |
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498 | return factors; |
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499 | } |
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500 | bool fail; |
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501 | CanonicalForm Aeval, evaluation, bufAeval, bufEvaluation, buf; |
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502 | CFList uniFactors, list, bufUniFactors; |
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503 | DegreePattern degs; |
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504 | DegreePattern bufDegs; |
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505 | |
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506 | int factorNums= 5; |
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507 | double logarithm= (double) ilog2 (totaldegree (A)); |
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508 | logarithm /= log2exp; |
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509 | logarithm= ceil (logarithm); |
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510 | if (factorNums < (int) logarithm) |
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511 | factorNums= (int) logarithm; |
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512 | for (int i= 0; i < factorNums; i++) |
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513 | { |
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514 | if (i == 0) |
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515 | Aeval= A (bivarEval, y); |
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516 | else if (i > 0 && contentAx.inCoeffDomain()) |
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517 | { |
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518 | Aeval= A; |
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519 | evaluation= evalPoint (A, Aeval, alpha, list, GF, fail); |
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520 | } |
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521 | |
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522 | if (fail && (i != 0)) |
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523 | break; |
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524 | |
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525 | // univariate factorization |
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526 | uniFactors= uniFactorizer (Aeval, alpha, GF); |
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527 | |
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528 | if (uniFactors.length() == 1) |
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529 | { |
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530 | append (factors, contentAyFactors); |
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531 | if (contentAyFactors.isEmpty()) |
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532 | factors.append (F/lc(F)); |
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533 | else |
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534 | { |
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535 | A= A (y - bivarEval, y); |
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536 | A= A/lc (A); |
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537 | if (!LC(A, 1).isOne()) |
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538 | { |
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539 | CanonicalForm s,t; |
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540 | (void) extgcd (LC (A, 1), power (y, liftBound), s, t); |
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541 | A *= s; |
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542 | A= mod (A, power (y, liftBound)); |
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543 | } |
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544 | factors.append (A); |
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545 | } |
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546 | decompress (factors, N); |
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547 | bivarEval= N (bivarEval); |
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548 | return factors; |
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549 | } |
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550 | |
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551 | // degree analysis |
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552 | degs= DegreePattern (uniFactors); |
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553 | |
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554 | if (i == 0) |
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555 | { |
---|
556 | bufAeval= Aeval; |
---|
557 | bufEvaluation= bivarEval; |
---|
558 | bufUniFactors= uniFactors; |
---|
559 | bufDegs= degs; |
---|
560 | if (!contentAx.inCoeffDomain()) |
---|
561 | break; |
---|
562 | } |
---|
563 | else |
---|
564 | { |
---|
565 | bufDegs.intersect (degs); |
---|
566 | if (uniFactors.length() < bufUniFactors.length()) |
---|
567 | { |
---|
568 | bufUniFactors= uniFactors; |
---|
569 | bufAeval= Aeval; |
---|
570 | bufEvaluation= evaluation; |
---|
571 | } |
---|
572 | } |
---|
573 | |
---|
574 | if (bufDegs.getLength() == 1) |
---|
575 | { |
---|
576 | append (factors, contentAyFactors); |
---|
577 | if (contentAyFactors.isEmpty()) |
---|
578 | factors.append (F/lc(F)); |
---|
579 | else |
---|
580 | { |
---|
581 | A= A (y - bivarEval, y); |
---|
582 | A= A/lc (A); |
---|
583 | if (!LC(A, 1).isOne()) |
---|
584 | { |
---|
585 | CanonicalForm s,t; |
---|
586 | (void) extgcd (LC (A, 1), power (y, liftBound), s, t); |
---|
587 | A *= s; |
---|
588 | A= mod (A, power (y, liftBound)); |
---|
589 | } |
---|
590 | factors.append (A); |
---|
591 | } |
---|
592 | decompress (factors, N); |
---|
593 | bivarEval= N (bivarEval); |
---|
594 | return factors; |
---|
595 | } |
---|
596 | list.append (evaluation); |
---|
597 | } |
---|
598 | |
---|
599 | bivarEval= y - bufEvaluation; |
---|
600 | A= A (y + bufEvaluation, y); |
---|
601 | bufUniFactors.insert (LC (A, x)); |
---|
602 | |
---|
603 | // Hensel lifting |
---|
604 | CFList diophant; |
---|
605 | CFMatrix M= CFMatrix (liftBound, bufUniFactors.length() - 1); |
---|
606 | CFArray Pi; |
---|
607 | bool earlySuccess= false; |
---|
608 | int newLiftBound= 0; |
---|
609 | CFList earlyFactors; |
---|
610 | int smallFactorDeg= 11; //tunable parameter |
---|
611 | if (smallFactorDeg >= liftBound) |
---|
612 | henselLift12 (A, bufUniFactors, liftBound, Pi, diophant, M); |
---|
613 | else if (smallFactorDeg >= degree (A, y) + 1) |
---|
614 | { |
---|
615 | henselLift12 (A, bufUniFactors, degree (A, y) + 1, Pi, diophant, M); |
---|
616 | earlyFactors= earlyMonicFactorDetect (A, bufUniFactors, newLiftBound, |
---|
617 | bufDegs, earlySuccess, |
---|
618 | degree (A, y) + 1, liftBound); |
---|
619 | if (bufDegs.getLength() > 1 && !earlySuccess) |
---|
620 | { |
---|
621 | if (newLiftBound > degree (A, y) + 1) |
---|
622 | { |
---|
623 | liftBound= newLiftBound; |
---|
624 | bufUniFactors.insert (LC(A, x)); |
---|
625 | henselLiftResume12 (A, bufUniFactors, degree (A, y) + 1, liftBound, |
---|
626 | Pi, diophant, M); |
---|
627 | } |
---|
628 | } |
---|
629 | else if (earlySuccess) |
---|
630 | liftBound= newLiftBound; |
---|
631 | } |
---|
632 | else if (smallFactorDeg < degree (A, y) + 1) |
---|
633 | { |
---|
634 | henselLift12 (A, bufUniFactors, smallFactorDeg, Pi, diophant, M); |
---|
635 | earlyFactors= earlyMonicFactorDetect (A, bufUniFactors, newLiftBound, |
---|
636 | bufDegs, earlySuccess, |
---|
637 | smallFactorDeg, liftBound); |
---|
638 | if (bufDegs.getLength() > 1 && !earlySuccess) |
---|
639 | { |
---|
640 | bufUniFactors.insert (LC (A, x)); |
---|
641 | henselLiftResume12 (A, bufUniFactors, smallFactorDeg, degree (A, y) + |
---|
642 | 1, Pi, diophant, M); |
---|
643 | earlyFactors= earlyMonicFactorDetect (A, bufUniFactors, newLiftBound, |
---|
644 | bufDegs, earlySuccess, |
---|
645 | degree (A, y) + 1, liftBound); |
---|
646 | if (bufDegs.getLength() > 1 && !earlySuccess) |
---|
647 | { |
---|
648 | if (newLiftBound > degree (A, y) + 1) |
---|
649 | { |
---|
650 | if (newLiftBound < newLiftBound) |
---|
651 | liftBound= newLiftBound; |
---|
652 | bufUniFactors.insert (LC(A, x)); |
---|
653 | henselLiftResume12 (A, bufUniFactors, degree (A, y) + 1, liftBound, |
---|
654 | Pi, diophant, M); |
---|
655 | } |
---|
656 | } |
---|
657 | else if (earlySuccess) |
---|
658 | liftBound= newLiftBound; |
---|
659 | } |
---|
660 | else if (earlySuccess) |
---|
661 | liftBound= newLiftBound; |
---|
662 | } |
---|
663 | |
---|
664 | if (newLiftBound > 0) |
---|
665 | liftBound= newLiftBound; |
---|
666 | |
---|
667 | CanonicalForm MODl= power (y, liftBound); |
---|
668 | |
---|
669 | if (bufDegs.getLength() > 1) |
---|
670 | factors= monicFactorRecombi (bufUniFactors, A, MODl, bufDegs); |
---|
671 | |
---|
672 | if (earlySuccess) |
---|
673 | factors= Union (earlyFactors, factors); |
---|
674 | else if (!earlySuccess && bufDegs.getLength() == 1) |
---|
675 | factors= earlyFactors; |
---|
676 | |
---|
677 | decompressAppend (factors, contentAyFactors, N); |
---|
678 | |
---|
679 | bivarEval= N (bivarEval); |
---|
680 | |
---|
681 | return factors; |
---|
682 | } |
---|
683 | |
---|
684 | CFList |
---|
685 | extFactorRecombination (const CFList& factors, const CanonicalForm& F, |
---|
686 | const CFList& M, const ExtensionInfo& info, |
---|
687 | const CFList& evaluation) |
---|
688 | { |
---|
689 | Variable alpha= info.getAlpha(); |
---|
690 | Variable beta= info.getBeta(); |
---|
691 | CanonicalForm gamma= info.getGamma(); |
---|
692 | CanonicalForm delta= info.getDelta(); |
---|
693 | int k= info.getGFDegree(); |
---|
694 | CFList source, dest; |
---|
695 | if (factors.length() == 1) |
---|
696 | { |
---|
697 | CanonicalForm buf= reverseShift (F, evaluation); |
---|
698 | return CFList (mapDown (buf, info, source, dest)); |
---|
699 | } |
---|
700 | if (factors.length() < 1) |
---|
701 | return CFList(); |
---|
702 | |
---|
703 | int degMipoBeta; |
---|
704 | if (!k && beta.level() == 1) |
---|
705 | degMipoBeta= 1; |
---|
706 | else if (!k && beta.level() != 1) |
---|
707 | degMipoBeta= degree (getMipo (beta)); |
---|
708 | |
---|
709 | CFList T, S; |
---|
710 | T= factors; |
---|
711 | |
---|
712 | int s= 1; |
---|
713 | CFList result; |
---|
714 | CanonicalForm buf; |
---|
715 | if (beta != Variable (1)) |
---|
716 | buf= mapDown (F, gamma, delta, alpha, source, dest); |
---|
717 | else |
---|
718 | buf= F; |
---|
719 | |
---|
720 | CanonicalForm g, LCBuf= LC (buf, Variable (1)); |
---|
721 | CanonicalForm buf2; |
---|
722 | int v [T.length()]; |
---|
723 | for (int i= 0; i < T.length(); i++) |
---|
724 | v[i]= 0; |
---|
725 | bool noSubset= false; |
---|
726 | CFArray TT; |
---|
727 | int subsetDeg; |
---|
728 | TT= copy (factors); |
---|
729 | bool recombination= false; |
---|
730 | while (T.length() >= 2*s) |
---|
731 | { |
---|
732 | while (noSubset == false) |
---|
733 | { |
---|
734 | if (T.length() == s) |
---|
735 | { |
---|
736 | if (recombination) |
---|
737 | { |
---|
738 | T.insert (LCBuf); |
---|
739 | g= prodMod (T, M); |
---|
740 | T.removeFirst(); |
---|
741 | result.append (g/myContent (g)); |
---|
742 | g= reverseShift (g, evaluation); |
---|
743 | g /= Lc (g); |
---|
744 | appendTestMapDown (result, g, info, source, dest); |
---|
745 | return result; |
---|
746 | } |
---|
747 | else |
---|
748 | { |
---|
749 | buf= reverseShift (buf, evaluation); |
---|
750 | return CFList (buf); |
---|
751 | } |
---|
752 | return result; |
---|
753 | } |
---|
754 | |
---|
755 | S= subset (v, s, TT, noSubset); |
---|
756 | if (noSubset) break; |
---|
757 | |
---|
758 | S.insert (LCBuf); |
---|
759 | g= prodMod (S, M); |
---|
760 | S.removeFirst(); |
---|
761 | g /= myContent (g); |
---|
762 | if (fdivides (g, buf)) |
---|
763 | { |
---|
764 | buf2= reverseShift (g, evaluation); |
---|
765 | buf2 /= Lc (buf2); |
---|
766 | if (!k && beta == Variable (1)) |
---|
767 | { |
---|
768 | if (degree (buf2, alpha) < degMipoBeta) |
---|
769 | { |
---|
770 | appendTestMapDown (result, buf2, info, source, dest); |
---|
771 | buf /= g; |
---|
772 | LCBuf= LC (buf, Variable (1)); |
---|
773 | recombination= true; |
---|
774 | } |
---|
775 | } |
---|
776 | else |
---|
777 | { |
---|
778 | if (!isInExtension (buf2, delta, k)) |
---|
779 | { |
---|
780 | appendTestMapDown (result, buf2, info, source, dest); |
---|
781 | buf /= g; |
---|
782 | LCBuf= LC (buf, Variable (1)); |
---|
783 | recombination= true; |
---|
784 | } |
---|
785 | } |
---|
786 | T= Difference (T, S); |
---|
787 | |
---|
788 | if (T.length() < 2*s || T.length() == s) |
---|
789 | { |
---|
790 | buf= reverseShift (buf, evaluation); |
---|
791 | buf /= Lc (buf); |
---|
792 | appendTestMapDown (result, buf, info, source, dest); |
---|
793 | return result; |
---|
794 | } |
---|
795 | TT= copy (T); |
---|
796 | indexUpdate (v, s, T.length(), noSubset); |
---|
797 | if (noSubset) break; |
---|
798 | } |
---|
799 | } |
---|
800 | s++; |
---|
801 | if (T.length() < 2*s || T.length() == s) |
---|
802 | { |
---|
803 | buf= reverseShift (buf, evaluation); |
---|
804 | appendTestMapDown (result, buf, info, source, dest); |
---|
805 | return result; |
---|
806 | } |
---|
807 | int v [T.length()]; |
---|
808 | for (int i= 0; i < T.length(); i++) |
---|
809 | v[i]= 0; |
---|
810 | noSubset= false; |
---|
811 | } |
---|
812 | if (T.length() < 2*s) |
---|
813 | { |
---|
814 | buf= reverseShift (F, evaluation); |
---|
815 | appendMapDown (result, buf, info, source, dest); |
---|
816 | } |
---|
817 | |
---|
818 | return result; |
---|
819 | } |
---|
820 | |
---|
821 | CFList |
---|
822 | factorRecombination (const CanonicalForm& F, const CFList& factors, |
---|
823 | const CFList& M) |
---|
824 | { |
---|
825 | if (factors.length() == 1) |
---|
826 | return CFList(F); |
---|
827 | if (factors.length() < 1) |
---|
828 | return CFList(); |
---|
829 | |
---|
830 | CFList T, S; |
---|
831 | |
---|
832 | T= factors; |
---|
833 | |
---|
834 | int s= 1; |
---|
835 | CFList result; |
---|
836 | CanonicalForm LCBuf= LC (F, Variable (1)); |
---|
837 | CanonicalForm g, buf= F; |
---|
838 | int v [T.length()]; |
---|
839 | for (int i= 0; i < T.length(); i++) |
---|
840 | v[i]= 0; |
---|
841 | bool noSubset= false; |
---|
842 | CFArray TT; |
---|
843 | int subsetDeg; |
---|
844 | TT= copy (factors); |
---|
845 | Variable y= F.level() - 1; |
---|
846 | bool recombination= false; |
---|
847 | CanonicalForm h; |
---|
848 | while (T.length() >= 2*s) |
---|
849 | { |
---|
850 | while (noSubset == false) |
---|
851 | { |
---|
852 | if (T.length() == s) |
---|
853 | { |
---|
854 | if (recombination) |
---|
855 | { |
---|
856 | T.insert (LC (buf)); |
---|
857 | g= prodMod (T, M); |
---|
858 | result.append (g/myContent (g)); |
---|
859 | return result; |
---|
860 | } |
---|
861 | else |
---|
862 | return CFList (F); |
---|
863 | } |
---|
864 | S= subset (v, s, TT, noSubset); |
---|
865 | if (noSubset) break; |
---|
866 | S.insert (LCBuf); |
---|
867 | g= prodMod (S, M); |
---|
868 | S.removeFirst(); |
---|
869 | g /= myContent (g); |
---|
870 | if (fdivides (g, buf)) |
---|
871 | { |
---|
872 | recombination= true; |
---|
873 | result.append (g); |
---|
874 | buf /= g; |
---|
875 | LCBuf= LC (buf, Variable(1)); |
---|
876 | T= Difference (T, S); |
---|
877 | if (T.length() < 2*s || T.length() == s) |
---|
878 | { |
---|
879 | result.append (buf); |
---|
880 | return result; |
---|
881 | } |
---|
882 | TT= copy (T); |
---|
883 | indexUpdate (v, s, T.length(), noSubset); |
---|
884 | if (noSubset) break; |
---|
885 | } |
---|
886 | } |
---|
887 | s++; |
---|
888 | if (T.length() < 2*s || T.length() == s) |
---|
889 | { |
---|
890 | result.append (buf); |
---|
891 | return result; |
---|
892 | } |
---|
893 | int v [T.length()]; |
---|
894 | for (int i= 0; i < T.length(); i++) |
---|
895 | v[i]= 0; |
---|
896 | noSubset= false; |
---|
897 | } |
---|
898 | if (T.length() < 2*s) |
---|
899 | result.append (F); |
---|
900 | |
---|
901 | return result; |
---|
902 | } |
---|
903 | |
---|
904 | int |
---|
905 | liftBoundAdaption (const CanonicalForm& F, const CFList& factors, bool& |
---|
906 | success, const int deg, const CFList& MOD, const int bound) |
---|
907 | { |
---|
908 | int adaptedLiftBound= 0; |
---|
909 | CanonicalForm buf= F; |
---|
910 | Variable y= F.mvar(); |
---|
911 | CanonicalForm LCBuf= LC (buf, Variable (1)); |
---|
912 | CanonicalForm g; |
---|
913 | CFList M= MOD; |
---|
914 | M.append (power (y, deg)); |
---|
915 | int d= bound; |
---|
916 | int e= 0; |
---|
917 | int nBuf; |
---|
918 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
919 | { |
---|
920 | g= mulMod (i.getItem(), LCBuf, M); |
---|
921 | g /= myContent (g); |
---|
922 | if (fdivides (g, buf)) |
---|
923 | { |
---|
924 | nBuf= degree (g, y) + degree (LC (g, 1), y); |
---|
925 | d -= nBuf; |
---|
926 | e= tmax (e, nBuf); |
---|
927 | buf /= g; |
---|
928 | LCBuf= LC (buf, Variable (1)); |
---|
929 | } |
---|
930 | } |
---|
931 | adaptedLiftBound= d; |
---|
932 | |
---|
933 | if (adaptedLiftBound < deg) |
---|
934 | { |
---|
935 | if (adaptedLiftBound < degree (F) + 1) |
---|
936 | { |
---|
937 | if (d == 1) |
---|
938 | { |
---|
939 | if (e + 1 > deg) |
---|
940 | { |
---|
941 | adaptedLiftBound= deg; |
---|
942 | success= false; |
---|
943 | } |
---|
944 | else |
---|
945 | { |
---|
946 | success= true; |
---|
947 | if (e + 1 < degree (F) + 1) |
---|
948 | adaptedLiftBound= deg; |
---|
949 | else |
---|
950 | adaptedLiftBound= e + 1; |
---|
951 | } |
---|
952 | } |
---|
953 | else |
---|
954 | { |
---|
955 | success= true; |
---|
956 | adaptedLiftBound= deg; |
---|
957 | } |
---|
958 | } |
---|
959 | else |
---|
960 | { |
---|
961 | success= true; |
---|
962 | } |
---|
963 | } |
---|
964 | return adaptedLiftBound; |
---|
965 | } |
---|
966 | |
---|
967 | int |
---|
968 | extLiftBoundAdaption (const CanonicalForm& F, const CFList& factors, bool& |
---|
969 | success, const ExtensionInfo& info, const CFList& eval, |
---|
970 | const int deg, const CFList& MOD, const int bound) |
---|
971 | { |
---|
972 | Variable alpha= info.getAlpha(); |
---|
973 | Variable beta= info.getBeta(); |
---|
974 | CanonicalForm gamma= info.getGamma(); |
---|
975 | CanonicalForm delta= info.getDelta(); |
---|
976 | int k= info.getGFDegree(); |
---|
977 | int adaptedLiftBound= 0; |
---|
978 | CanonicalForm buf= F; |
---|
979 | Variable y= F.mvar(); |
---|
980 | CanonicalForm LCBuf= LC (buf, Variable (1)); |
---|
981 | CanonicalForm g, gg; |
---|
982 | CFList M= MOD; |
---|
983 | M.append (power (y, deg)); |
---|
984 | adaptedLiftBound= 0; |
---|
985 | int d= bound; |
---|
986 | int e= 0; |
---|
987 | int nBuf; |
---|
988 | int degMipoBeta; |
---|
989 | if (!k && beta.level() == 1) |
---|
990 | degMipoBeta= 1; |
---|
991 | else if (!k && beta.level() != 1) |
---|
992 | degMipoBeta= degree (getMipo (beta)); |
---|
993 | |
---|
994 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
995 | { |
---|
996 | g= mulMod (i.getItem(), LCBuf, M); |
---|
997 | g /= myContent (g); |
---|
998 | if (fdivides (g, buf)) |
---|
999 | { |
---|
1000 | gg= reverseShift (g, eval); |
---|
1001 | gg /= Lc (gg); |
---|
1002 | if (!k && beta == Variable (1)) |
---|
1003 | { |
---|
1004 | if (degree (gg, alpha) < degMipoBeta) |
---|
1005 | { |
---|
1006 | buf /= g; |
---|
1007 | nBuf= degree (g, y) + degree (LC (g, Variable (1)), y); |
---|
1008 | d -= nBuf; |
---|
1009 | e= tmax (e, nBuf); |
---|
1010 | LCBuf= LC (buf, Variable (1)); |
---|
1011 | } |
---|
1012 | } |
---|
1013 | else |
---|
1014 | { |
---|
1015 | if (!isInExtension (gg, delta, k)) |
---|
1016 | { |
---|
1017 | buf /= g; |
---|
1018 | nBuf= degree (g, y) + degree (LC (g, Variable (1)), y); |
---|
1019 | d -= nBuf; |
---|
1020 | e= tmax (e, nBuf); |
---|
1021 | LCBuf= LC (buf, Variable (1)); |
---|
1022 | } |
---|
1023 | } |
---|
1024 | } |
---|
1025 | } |
---|
1026 | adaptedLiftBound= d; |
---|
1027 | |
---|
1028 | if (adaptedLiftBound < deg) |
---|
1029 | { |
---|
1030 | if (adaptedLiftBound < degree (F) + 1) |
---|
1031 | { |
---|
1032 | if (d == 1) |
---|
1033 | { |
---|
1034 | if (e + 1 > deg) |
---|
1035 | { |
---|
1036 | adaptedLiftBound= deg; |
---|
1037 | success= false; |
---|
1038 | } |
---|
1039 | else |
---|
1040 | { |
---|
1041 | success= true; |
---|
1042 | if (e + 1 < degree (F) + 1) |
---|
1043 | adaptedLiftBound= deg; |
---|
1044 | else |
---|
1045 | adaptedLiftBound= e + 1; |
---|
1046 | } |
---|
1047 | } |
---|
1048 | else |
---|
1049 | { |
---|
1050 | success= true; |
---|
1051 | adaptedLiftBound= deg; |
---|
1052 | } |
---|
1053 | } |
---|
1054 | else |
---|
1055 | { |
---|
1056 | success= true; |
---|
1057 | } |
---|
1058 | } |
---|
1059 | |
---|
1060 | return adaptedLiftBound; |
---|
1061 | } |
---|
1062 | |
---|
1063 | CFList |
---|
1064 | earlyFactorDetect (CanonicalForm& F, CFList& factors, int& adaptedLiftBound, |
---|
1065 | bool& success, const int deg, const CFList& MOD, |
---|
1066 | const int bound) |
---|
1067 | { |
---|
1068 | CFList result; |
---|
1069 | CFList T= factors; |
---|
1070 | CanonicalForm buf= F; |
---|
1071 | Variable y= F.mvar(); |
---|
1072 | CanonicalForm LCBuf= LC (buf, Variable (1)); |
---|
1073 | CanonicalForm g; |
---|
1074 | CFList M= MOD; |
---|
1075 | M.append (power (y, deg)); |
---|
1076 | adaptedLiftBound= 0; |
---|
1077 | int d= bound; |
---|
1078 | int e= 0; |
---|
1079 | int nBuf; |
---|
1080 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
1081 | { |
---|
1082 | g= mulMod (i.getItem(), LCBuf, M); |
---|
1083 | g /= myContent (g); |
---|
1084 | if (fdivides (g, buf)) |
---|
1085 | { |
---|
1086 | result.append (g); |
---|
1087 | nBuf= degree (g, y) + degree (LC (g, Variable (1)), y); |
---|
1088 | d -= nBuf; |
---|
1089 | e= tmax (e, nBuf); |
---|
1090 | buf /= g; |
---|
1091 | LCBuf= LC (buf, Variable (1)); |
---|
1092 | T= Difference (T, CFList (i.getItem())); |
---|
1093 | } |
---|
1094 | } |
---|
1095 | adaptedLiftBound= d; |
---|
1096 | |
---|
1097 | if (adaptedLiftBound < deg) |
---|
1098 | { |
---|
1099 | if (adaptedLiftBound < degree (F) + 1) |
---|
1100 | { |
---|
1101 | if (d == 1) |
---|
1102 | adaptedLiftBound= tmin (e + 1, deg); |
---|
1103 | else |
---|
1104 | adaptedLiftBound= deg; |
---|
1105 | } |
---|
1106 | factors= T; |
---|
1107 | F= buf; |
---|
1108 | success= true; |
---|
1109 | } |
---|
1110 | return result; |
---|
1111 | } |
---|
1112 | |
---|
1113 | CFList |
---|
1114 | extEarlyFactorDetect (CanonicalForm& F, CFList& factors, int& adaptedLiftBound, |
---|
1115 | bool& success, const ExtensionInfo& info, const CFList& |
---|
1116 | eval, const int deg, const CFList& MOD, const int bound) |
---|
1117 | { |
---|
1118 | Variable alpha= info.getAlpha(); |
---|
1119 | Variable beta= info.getBeta(); |
---|
1120 | CanonicalForm gamma= info.getGamma(); |
---|
1121 | CanonicalForm delta= info.getDelta(); |
---|
1122 | int k= info.getGFDegree(); |
---|
1123 | CFList result; |
---|
1124 | CFList T= factors; |
---|
1125 | CanonicalForm buf= F; |
---|
1126 | Variable y= F.mvar(); |
---|
1127 | CanonicalForm LCBuf= LC (buf, Variable (1)); |
---|
1128 | CanonicalForm g, gg; |
---|
1129 | CFList M= MOD; |
---|
1130 | M.append (power (y, deg)); |
---|
1131 | adaptedLiftBound= 0; |
---|
1132 | int d= bound; |
---|
1133 | int e= 0; |
---|
1134 | int nBuf; |
---|
1135 | CFList source, dest; |
---|
1136 | |
---|
1137 | int degMipoBeta; |
---|
1138 | if (!k && beta.level() == 1) |
---|
1139 | degMipoBeta= 1; |
---|
1140 | else if (!k && beta.level() != 1) |
---|
1141 | degMipoBeta= degree (getMipo (beta)); |
---|
1142 | |
---|
1143 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
1144 | { |
---|
1145 | g= mulMod (i.getItem(), LCBuf, M); |
---|
1146 | g /= myContent (g); |
---|
1147 | if (fdivides (g, buf)) |
---|
1148 | { |
---|
1149 | gg= reverseShift (g, eval); |
---|
1150 | gg /= Lc (gg); |
---|
1151 | if (!k && beta == Variable (1)) |
---|
1152 | { |
---|
1153 | if (degree (gg, alpha) < degMipoBeta) |
---|
1154 | { |
---|
1155 | appendTestMapDown (result, gg, info, source, dest); |
---|
1156 | buf /= g; |
---|
1157 | nBuf= degree (g, y) + degree (LC (g, Variable (1)), y); |
---|
1158 | d -= nBuf; |
---|
1159 | e= tmax (e, nBuf); |
---|
1160 | LCBuf= LC (buf, Variable (1)); |
---|
1161 | } |
---|
1162 | } |
---|
1163 | else |
---|
1164 | { |
---|
1165 | if (!isInExtension (gg, delta, k)) |
---|
1166 | { |
---|
1167 | appendTestMapDown (result, gg, info, source, dest); |
---|
1168 | buf /= g; |
---|
1169 | nBuf= degree (g, y) + degree (LC (g, Variable (1)), y); |
---|
1170 | d -= nBuf; |
---|
1171 | e= tmax (e, nBuf); |
---|
1172 | LCBuf= LC (buf, Variable (1)); |
---|
1173 | } |
---|
1174 | } |
---|
1175 | T= Difference (T, CFList (i.getItem())); |
---|
1176 | } |
---|
1177 | } |
---|
1178 | adaptedLiftBound= d; |
---|
1179 | |
---|
1180 | if (adaptedLiftBound < deg) |
---|
1181 | { |
---|
1182 | if (adaptedLiftBound < degree (F) + 1) |
---|
1183 | { |
---|
1184 | if (d == 1) |
---|
1185 | adaptedLiftBound= tmin (e + 1, deg); |
---|
1186 | else |
---|
1187 | adaptedLiftBound= deg; |
---|
1188 | } |
---|
1189 | success= true; |
---|
1190 | factors= T; |
---|
1191 | F= buf; |
---|
1192 | } |
---|
1193 | return result; |
---|
1194 | } |
---|
1195 | |
---|
1196 | CFList |
---|
1197 | evalPoints (const CanonicalForm& F, CFList & eval, const Variable& alpha, |
---|
1198 | CFList& list, const bool& GF, bool& fail) |
---|
1199 | { |
---|
1200 | int k= F.level() - 1; |
---|
1201 | Variable x= Variable (1); |
---|
1202 | CFList result; |
---|
1203 | FFRandom genFF; |
---|
1204 | GFRandom genGF; |
---|
1205 | int p= getCharacteristic (); |
---|
1206 | double bound; |
---|
1207 | if (alpha != Variable (1)) |
---|
1208 | { |
---|
1209 | bound= pow ((double) p, (double) degree (getMipo(alpha))); |
---|
1210 | bound= pow ((double) bound, (double) k); |
---|
1211 | } |
---|
1212 | else if (GF) |
---|
1213 | { |
---|
1214 | bound= pow ((double) p, (double) getGFDegree()); |
---|
1215 | bound= pow ((double) bound, (double) k); |
---|
1216 | } |
---|
1217 | else |
---|
1218 | bound= pow ((double) p, (double) k); |
---|
1219 | |
---|
1220 | CanonicalForm random; |
---|
1221 | CanonicalForm deriv_x, gcd_deriv; |
---|
1222 | do |
---|
1223 | { |
---|
1224 | random= 0; |
---|
1225 | // possible overflow if list.length() does not fit into a int |
---|
1226 | if (list.length() >= bound) |
---|
1227 | { |
---|
1228 | fail= true; |
---|
1229 | break; |
---|
1230 | } |
---|
1231 | for (int i= 0; i < k; i++) |
---|
1232 | { |
---|
1233 | if (list.isEmpty()) |
---|
1234 | result.append (0); |
---|
1235 | else if (GF) |
---|
1236 | { |
---|
1237 | result.append (genGF.generate()); |
---|
1238 | random += result.getLast()*power (x, i); |
---|
1239 | } |
---|
1240 | else if (alpha.level() != 1) |
---|
1241 | { |
---|
1242 | AlgExtRandomF genAlgExt (alpha); |
---|
1243 | result.append (genAlgExt.generate()); |
---|
1244 | random += result.getLast()*power (x, i); |
---|
1245 | } |
---|
1246 | else |
---|
1247 | { |
---|
1248 | result.append (genFF.generate()); |
---|
1249 | random += result.getLast()*power (x, i); |
---|
1250 | } |
---|
1251 | } |
---|
1252 | if (find (list, random)) |
---|
1253 | { |
---|
1254 | result= CFList(); |
---|
1255 | continue; |
---|
1256 | } |
---|
1257 | int l= F.level(); |
---|
1258 | eval.insert (F); |
---|
1259 | for (CFListIterator i= result; i.hasItem(); i++, l--) |
---|
1260 | eval.insert (eval.getFirst()(i.getItem(), l)); |
---|
1261 | |
---|
1262 | if (degree (eval.getFirst()) != degree (F, 1)) |
---|
1263 | { |
---|
1264 | if (!find (list, random)) |
---|
1265 | list.append (random); |
---|
1266 | result= CFList(); |
---|
1267 | eval= CFList(); |
---|
1268 | continue; |
---|
1269 | } |
---|
1270 | |
---|
1271 | deriv_x= deriv (eval.getFirst(), x); |
---|
1272 | gcd_deriv= gcd (eval.getFirst(), deriv_x); |
---|
1273 | if (degree (gcd_deriv) > 0) |
---|
1274 | { |
---|
1275 | if (!find (list, random)) |
---|
1276 | list.append (random); |
---|
1277 | result= CFList(); |
---|
1278 | eval= CFList(); |
---|
1279 | continue; |
---|
1280 | } |
---|
1281 | CFListIterator i= eval; |
---|
1282 | i++; |
---|
1283 | CanonicalForm contentx= content (i.getItem(), x); |
---|
1284 | if (degree (contentx) > 0) |
---|
1285 | { |
---|
1286 | if (!find (list, random)) |
---|
1287 | list.append (random); |
---|
1288 | result= CFList(); |
---|
1289 | eval= CFList(); |
---|
1290 | continue; |
---|
1291 | } |
---|
1292 | |
---|
1293 | if (list.length() >= bound) |
---|
1294 | { |
---|
1295 | fail= true; |
---|
1296 | break; |
---|
1297 | } |
---|
1298 | } while (find (list, random)); |
---|
1299 | |
---|
1300 | if (!eval.isEmpty()) |
---|
1301 | eval.removeFirst(); |
---|
1302 | |
---|
1303 | return result; |
---|
1304 | } |
---|
1305 | |
---|
1306 | static inline |
---|
1307 | int newMainVariableSearch (CanonicalForm& A, CFList& Aeval, CFList& |
---|
1308 | evaluation, const Variable& alpha, const int lev) |
---|
1309 | { |
---|
1310 | Variable x= Variable (1); |
---|
1311 | CanonicalForm derivI, buf; |
---|
1312 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
1313 | int swapLevel= 0; |
---|
1314 | CFList list; |
---|
1315 | bool fail= false; |
---|
1316 | buf= A; |
---|
1317 | Aeval= CFList(); |
---|
1318 | evaluation= CFList(); |
---|
1319 | for (int i= lev; i <= A.level(); i++) |
---|
1320 | { |
---|
1321 | derivI= deriv (buf, Variable (i)); |
---|
1322 | if (!derivI.isZero()) |
---|
1323 | { |
---|
1324 | buf= swapvar (buf, x, Variable (i)); |
---|
1325 | Aeval= CFList(); |
---|
1326 | evaluation= CFList(); |
---|
1327 | fail= false; |
---|
1328 | evaluation= evalPoints (buf, Aeval, alpha, list, GF, fail); |
---|
1329 | if (!fail) |
---|
1330 | { |
---|
1331 | A= buf; |
---|
1332 | swapLevel= i; |
---|
1333 | break; |
---|
1334 | } |
---|
1335 | else |
---|
1336 | buf= A; |
---|
1337 | } |
---|
1338 | } |
---|
1339 | return swapLevel; |
---|
1340 | } |
---|
1341 | |
---|
1342 | static inline |
---|
1343 | CanonicalForm lcmContent (const CanonicalForm& A, CFList& contentAi) |
---|
1344 | { |
---|
1345 | int i= A.level(); |
---|
1346 | contentAi.append (myContent (A, i)); |
---|
1347 | contentAi.append (myContent (A, i - 1)); |
---|
1348 | CanonicalForm result= myLcm (contentAi.getFirst(), contentAi.getLast()); |
---|
1349 | for (i= i - 2; i > 0; i--) |
---|
1350 | { |
---|
1351 | contentAi.append (content (A, i)); |
---|
1352 | result= myLcm (result, contentAi.getLast()); |
---|
1353 | } |
---|
1354 | return result; |
---|
1355 | } |
---|
1356 | |
---|
1357 | CFList |
---|
1358 | henselLiftAndEarly (CanonicalForm& A, CFList& MOD, int*& liftBounds, bool& |
---|
1359 | earlySuccess, CFList& earlyFactors, const CFList& Aeval, |
---|
1360 | const CFList& biFactors, const CFList& evaluation, |
---|
1361 | const ExtensionInfo& info) |
---|
1362 | { |
---|
1363 | bool extension= info.isInExtension(); |
---|
1364 | CFList bufFactors= biFactors; |
---|
1365 | bufFactors.insert (LC (Aeval.getFirst(), 1)); |
---|
1366 | |
---|
1367 | sortList (bufFactors, Variable (1)); |
---|
1368 | |
---|
1369 | CFList diophant; |
---|
1370 | CFArray Pi; |
---|
1371 | int smallFactorDeg= 11; //tunable parameter |
---|
1372 | CFList result; |
---|
1373 | int newLiftBound= 0; |
---|
1374 | int adaptedLiftBound= 0; |
---|
1375 | int liftBound= liftBounds[1]; |
---|
1376 | |
---|
1377 | earlySuccess= false; |
---|
1378 | bool earlyReconst= false; |
---|
1379 | CFList earlyReconstFactors; |
---|
1380 | CFListIterator j= Aeval; |
---|
1381 | j++; |
---|
1382 | CanonicalForm buf= j.getItem(); |
---|
1383 | CFMatrix Mat= CFMatrix (liftBound, bufFactors.length() - 1); |
---|
1384 | MOD= CFList (power (Variable (2), liftBounds[0])); |
---|
1385 | if (smallFactorDeg >= liftBound) |
---|
1386 | { |
---|
1387 | result= henselLift23 (Aeval, bufFactors, liftBounds, diophant, Pi, Mat); |
---|
1388 | } |
---|
1389 | else if (smallFactorDeg >= degree (buf) + 1) |
---|
1390 | { |
---|
1391 | liftBounds[1]= degree (buf) + 1; |
---|
1392 | result= henselLift23 (Aeval, bufFactors, liftBounds, diophant, Pi, Mat); |
---|
1393 | if (Aeval.length() == 2) |
---|
1394 | { |
---|
1395 | if (!extension) |
---|
1396 | earlyFactors= earlyFactorDetect |
---|
1397 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1398 | degree (buf) + 1, MOD, liftBound); |
---|
1399 | else |
---|
1400 | earlyFactors= extEarlyFactorDetect |
---|
1401 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1402 | info, evaluation, degree |
---|
1403 | (buf) + 1, MOD, liftBound); |
---|
1404 | } |
---|
1405 | else |
---|
1406 | { |
---|
1407 | if (!extension) |
---|
1408 | adaptedLiftBound= liftBoundAdaption (buf, result, earlySuccess, |
---|
1409 | degree (buf) + 1, MOD, liftBound); |
---|
1410 | else |
---|
1411 | adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, info, |
---|
1412 | evaluation, degree (buf) + 1, |
---|
1413 | MOD, liftBound); |
---|
1414 | } |
---|
1415 | if (!earlySuccess) |
---|
1416 | { |
---|
1417 | result.insert (LC (buf, 1)); |
---|
1418 | liftBounds[1]= adaptedLiftBound; |
---|
1419 | liftBound= adaptedLiftBound; |
---|
1420 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
1421 | Pi, diophant, Mat, MOD); |
---|
1422 | } |
---|
1423 | else |
---|
1424 | liftBounds[1]= adaptedLiftBound; |
---|
1425 | } |
---|
1426 | else if (smallFactorDeg < degree (buf) + 1) |
---|
1427 | { |
---|
1428 | liftBounds[1]= smallFactorDeg; |
---|
1429 | result= henselLift23 (Aeval, bufFactors, liftBounds, diophant, Pi, Mat); |
---|
1430 | if (Aeval.length() == 2) |
---|
1431 | { |
---|
1432 | if (!extension) |
---|
1433 | earlyFactors= earlyFactorDetect (buf, result, adaptedLiftBound, |
---|
1434 | earlySuccess, smallFactorDeg, MOD, |
---|
1435 | liftBound); |
---|
1436 | else |
---|
1437 | earlyFactors= extEarlyFactorDetect (buf, result, adaptedLiftBound, |
---|
1438 | earlySuccess, info, evaluation, |
---|
1439 | smallFactorDeg, MOD, liftBound); |
---|
1440 | } |
---|
1441 | else |
---|
1442 | { |
---|
1443 | if (!extension) |
---|
1444 | adaptedLiftBound= liftBoundAdaption (buf, result, earlySuccess, |
---|
1445 | smallFactorDeg, MOD, liftBound); |
---|
1446 | else |
---|
1447 | adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, info, |
---|
1448 | evaluation, smallFactorDeg, MOD, |
---|
1449 | liftBound); |
---|
1450 | } |
---|
1451 | |
---|
1452 | if (!earlySuccess) |
---|
1453 | { |
---|
1454 | result.insert (LC (buf, 1)); |
---|
1455 | henselLiftResume (buf, result, smallFactorDeg, degree (buf) + 1, |
---|
1456 | Pi, diophant, Mat, MOD); |
---|
1457 | if (Aeval.length() == 2) |
---|
1458 | { |
---|
1459 | if (!extension) |
---|
1460 | earlyFactors= earlyFactorDetect (buf, result, adaptedLiftBound, |
---|
1461 | earlySuccess, degree (buf) + 1, |
---|
1462 | MOD, liftBound); |
---|
1463 | else |
---|
1464 | earlyFactors= extEarlyFactorDetect (buf, result, adaptedLiftBound, |
---|
1465 | earlySuccess, info, evaluation, |
---|
1466 | degree (buf) + 1, MOD, |
---|
1467 | liftBound); |
---|
1468 | } |
---|
1469 | else |
---|
1470 | { |
---|
1471 | if (!extension) |
---|
1472 | adaptedLiftBound= liftBoundAdaption (buf, result, earlySuccess, |
---|
1473 | degree (buf) + 1, MOD,liftBound); |
---|
1474 | else |
---|
1475 | adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, |
---|
1476 | info, evaluation, |
---|
1477 | degree (buf) + 1, MOD, |
---|
1478 | liftBound); |
---|
1479 | } |
---|
1480 | if (!earlySuccess) |
---|
1481 | { |
---|
1482 | result.insert (LC (buf, 1)); |
---|
1483 | liftBounds[1]= adaptedLiftBound; |
---|
1484 | liftBound= adaptedLiftBound; |
---|
1485 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
1486 | Pi, diophant, Mat, MOD); |
---|
1487 | } |
---|
1488 | else |
---|
1489 | liftBounds[1]= adaptedLiftBound; |
---|
1490 | } |
---|
1491 | else |
---|
1492 | liftBounds[1]= adaptedLiftBound; |
---|
1493 | } |
---|
1494 | |
---|
1495 | MOD.append (power (Variable (3), liftBounds[1])); |
---|
1496 | |
---|
1497 | if (Aeval.length() > 2) |
---|
1498 | { |
---|
1499 | CFListIterator j= Aeval; |
---|
1500 | j++; |
---|
1501 | CFList bufEval; |
---|
1502 | bufEval.append (j.getItem()); |
---|
1503 | j++; |
---|
1504 | int liftBoundsLength= Aeval.getLast().level() - 1; |
---|
1505 | for (int i= 2; i <= liftBoundsLength && j.hasItem(); i++, j++) |
---|
1506 | { |
---|
1507 | earlySuccess= false; |
---|
1508 | result.insert (LC (bufEval.getFirst(), 1)); |
---|
1509 | bufEval.append (j.getItem()); |
---|
1510 | liftBound= liftBounds[i]; |
---|
1511 | Mat= CFMatrix (liftBounds[i], result.length() - 1); |
---|
1512 | |
---|
1513 | buf= j.getItem(); |
---|
1514 | if (smallFactorDeg >= liftBound) |
---|
1515 | result= henselLift (bufEval, result, MOD, diophant, Pi, Mat, |
---|
1516 | liftBounds[i - 1], liftBounds[i]); |
---|
1517 | else if (smallFactorDeg >= degree (buf) + 1) |
---|
1518 | { |
---|
1519 | result= henselLift (bufEval, result, MOD, diophant, Pi, Mat, |
---|
1520 | liftBounds[i - 1], degree (buf) + 1); |
---|
1521 | |
---|
1522 | if (Aeval.length() == i + 1) |
---|
1523 | { |
---|
1524 | if (!extension) |
---|
1525 | earlyFactors= earlyFactorDetect |
---|
1526 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1527 | degree (buf) + 1, MOD, liftBound); |
---|
1528 | else |
---|
1529 | earlyFactors= extEarlyFactorDetect |
---|
1530 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1531 | info, evaluation, degree (buf) + 1, MOD, liftBound); |
---|
1532 | } |
---|
1533 | else |
---|
1534 | { |
---|
1535 | if (!extension) |
---|
1536 | adaptedLiftBound= liftBoundAdaption |
---|
1537 | (buf, result, earlySuccess, degree (buf) |
---|
1538 | + 1, MOD, liftBound); |
---|
1539 | else |
---|
1540 | adaptedLiftBound= extLiftBoundAdaption |
---|
1541 | (buf, result, earlySuccess, info, evaluation, |
---|
1542 | degree (buf) + 1, MOD, liftBound); |
---|
1543 | } |
---|
1544 | |
---|
1545 | if (!earlySuccess) |
---|
1546 | { |
---|
1547 | result.insert (LC (buf, 1)); |
---|
1548 | liftBounds[i]= adaptedLiftBound; |
---|
1549 | liftBound= adaptedLiftBound; |
---|
1550 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
1551 | Pi, diophant, Mat, MOD); |
---|
1552 | } |
---|
1553 | else |
---|
1554 | { |
---|
1555 | liftBounds[i]= adaptedLiftBound; |
---|
1556 | } |
---|
1557 | } |
---|
1558 | else if (smallFactorDeg < degree (buf) + 1) |
---|
1559 | { |
---|
1560 | result= henselLift (bufEval, result, MOD, diophant, Pi, Mat, |
---|
1561 | liftBounds[i - 1], smallFactorDeg); |
---|
1562 | |
---|
1563 | if (Aeval.length() == i + 1) |
---|
1564 | { |
---|
1565 | if (!extension) |
---|
1566 | earlyFactors= earlyFactorDetect |
---|
1567 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1568 | smallFactorDeg, MOD, liftBound); |
---|
1569 | else |
---|
1570 | earlyFactors= extEarlyFactorDetect |
---|
1571 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1572 | info, evaluation, smallFactorDeg, MOD, liftBound); |
---|
1573 | } |
---|
1574 | else |
---|
1575 | { |
---|
1576 | if (!extension) |
---|
1577 | adaptedLiftBound= liftBoundAdaption |
---|
1578 | (buf, result, earlySuccess, |
---|
1579 | smallFactorDeg, MOD, liftBound); |
---|
1580 | else |
---|
1581 | adaptedLiftBound= extLiftBoundAdaption |
---|
1582 | (buf, result, earlySuccess, info, evaluation, |
---|
1583 | smallFactorDeg, MOD, liftBound); |
---|
1584 | } |
---|
1585 | |
---|
1586 | if (!earlySuccess) |
---|
1587 | { |
---|
1588 | result.insert (LC (buf, 1)); |
---|
1589 | henselLiftResume (buf, result, smallFactorDeg, |
---|
1590 | degree (buf) + 1, Pi, diophant, Mat, MOD); |
---|
1591 | if (Aeval.length() == i + 1) |
---|
1592 | { |
---|
1593 | if (!extension) |
---|
1594 | earlyFactors= earlyFactorDetect |
---|
1595 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1596 | degree (buf) + 1, MOD, liftBound); |
---|
1597 | else |
---|
1598 | earlyFactors= extEarlyFactorDetect |
---|
1599 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1600 | info, evaluation, degree (buf) + 1, MOD, |
---|
1601 | liftBound); |
---|
1602 | } |
---|
1603 | else |
---|
1604 | { |
---|
1605 | if (!extension) |
---|
1606 | adaptedLiftBound= liftBoundAdaption |
---|
1607 | (buf, result, earlySuccess, degree |
---|
1608 | (buf) + 1, MOD, liftBound); |
---|
1609 | else |
---|
1610 | adaptedLiftBound= extLiftBoundAdaption |
---|
1611 | (buf, result, earlySuccess, info, evaluation, |
---|
1612 | degree (buf) + 1, MOD, liftBound); |
---|
1613 | } |
---|
1614 | |
---|
1615 | if (!earlySuccess) |
---|
1616 | { |
---|
1617 | result.insert (LC (buf, 1)); |
---|
1618 | liftBounds[i]= adaptedLiftBound; |
---|
1619 | liftBound= adaptedLiftBound; |
---|
1620 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
1621 | Pi, diophant, Mat, MOD); |
---|
1622 | } |
---|
1623 | else |
---|
1624 | liftBounds[i]= adaptedLiftBound; |
---|
1625 | } |
---|
1626 | else |
---|
1627 | liftBounds[i]= adaptedLiftBound; |
---|
1628 | } |
---|
1629 | MOD.append (power (Variable (i + 2), liftBounds[i])); |
---|
1630 | bufEval.removeFirst(); |
---|
1631 | } |
---|
1632 | bufFactors= result; |
---|
1633 | } |
---|
1634 | else |
---|
1635 | bufFactors= result; |
---|
1636 | |
---|
1637 | if (earlySuccess) |
---|
1638 | A= buf; |
---|
1639 | return result; |
---|
1640 | } |
---|
1641 | |
---|
1642 | CFList |
---|
1643 | extFactorize (const CanonicalForm& F, const ExtensionInfo& info); |
---|
1644 | |
---|
1645 | CFList |
---|
1646 | multiFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
1647 | { |
---|
1648 | |
---|
1649 | if (F.inCoeffDomain()) |
---|
1650 | return CFList (F); |
---|
1651 | |
---|
1652 | // compress and find main Variable |
---|
1653 | CFMap N; |
---|
1654 | CanonicalForm A= myCompress (F, N); |
---|
1655 | |
---|
1656 | A /= Lc (A); // make monic |
---|
1657 | |
---|
1658 | Variable alpha= info.getAlpha(); |
---|
1659 | Variable beta= info.getBeta(); |
---|
1660 | CanonicalForm gamma= info.getGamma(); |
---|
1661 | CanonicalForm delta= info.getDelta(); |
---|
1662 | int k= info.getGFDegree(); |
---|
1663 | bool extension= info.isInExtension(); |
---|
1664 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
1665 | //univariate case |
---|
1666 | if (F.isUnivariate()) |
---|
1667 | { |
---|
1668 | if (extension == false) |
---|
1669 | return uniFactorizer (F, alpha, GF); |
---|
1670 | else |
---|
1671 | { |
---|
1672 | CFList source, dest; |
---|
1673 | A= mapDown (F, info, source, dest); |
---|
1674 | return uniFactorizer (A, beta, GF); |
---|
1675 | } |
---|
1676 | } |
---|
1677 | |
---|
1678 | //bivariate case |
---|
1679 | if (A.level() == 2) |
---|
1680 | { |
---|
1681 | CFList buf= biFactorize (F, info); |
---|
1682 | return buf; |
---|
1683 | } |
---|
1684 | |
---|
1685 | Variable x= Variable (1); |
---|
1686 | Variable y= Variable (2); |
---|
1687 | |
---|
1688 | // remove content |
---|
1689 | CFList contentAi; |
---|
1690 | CanonicalForm lcmCont= lcmContent (A, contentAi); |
---|
1691 | A /= lcmCont; |
---|
1692 | |
---|
1693 | // trivial after content removal |
---|
1694 | CFList contentAFactors; |
---|
1695 | if (A.inCoeffDomain()) |
---|
1696 | { |
---|
1697 | for (CFListIterator i= contentAi; i.hasItem(); i++) |
---|
1698 | { |
---|
1699 | if (i.getItem().inCoeffDomain()) |
---|
1700 | continue; |
---|
1701 | else |
---|
1702 | { |
---|
1703 | lcmCont /= i.getItem(); |
---|
1704 | contentAFactors= |
---|
1705 | Union (multiFactorize (lcmCont, info), |
---|
1706 | multiFactorize (i.getItem(), info)); |
---|
1707 | break; |
---|
1708 | } |
---|
1709 | } |
---|
1710 | decompress (contentAFactors, N); |
---|
1711 | normalize (contentAFactors); |
---|
1712 | return contentAFactors; |
---|
1713 | } |
---|
1714 | |
---|
1715 | // factorize content |
---|
1716 | contentAFactors= multiFactorize (lcmCont, info); |
---|
1717 | |
---|
1718 | // univariate after content removal |
---|
1719 | CFList factors; |
---|
1720 | if (A.isUnivariate ()) |
---|
1721 | { |
---|
1722 | factors= uniFactorizer (A, alpha, GF); |
---|
1723 | append (factors, contentAFactors); |
---|
1724 | decompress (factors, N); |
---|
1725 | return factors; |
---|
1726 | } |
---|
1727 | |
---|
1728 | // check main variable |
---|
1729 | int swapLevel= 0; |
---|
1730 | CanonicalForm derivZ; |
---|
1731 | CanonicalForm gcdDerivZ; |
---|
1732 | CanonicalForm bufA= A; |
---|
1733 | Variable z; |
---|
1734 | for (int i= 1; i <= A.level(); i++) |
---|
1735 | { |
---|
1736 | z= Variable (i); |
---|
1737 | derivZ= deriv (bufA, z); |
---|
1738 | if (derivZ.isZero()) |
---|
1739 | { |
---|
1740 | if (i == 1) |
---|
1741 | swapLevel= 1; |
---|
1742 | else |
---|
1743 | continue; |
---|
1744 | } |
---|
1745 | else |
---|
1746 | { |
---|
1747 | if (swapLevel == 1) |
---|
1748 | { |
---|
1749 | swapLevel= i; |
---|
1750 | A= swapvar (A, x, z); |
---|
1751 | } |
---|
1752 | if (GF) |
---|
1753 | gcdDerivZ= GCD_GF (bufA, derivZ); |
---|
1754 | else if (alpha == Variable (1)) |
---|
1755 | gcdDerivZ= GCD_small_p (bufA, derivZ); |
---|
1756 | else |
---|
1757 | gcdDerivZ= GCD_Fp_extension (bufA, derivZ, alpha); |
---|
1758 | if (degree (gcdDerivZ) > 0 && !derivZ.isZero()) |
---|
1759 | { |
---|
1760 | CanonicalForm g= bufA/gcdDerivZ; |
---|
1761 | CFList factorsG= |
---|
1762 | Union (multiFactorize (g, info), |
---|
1763 | multiFactorize (gcdDerivZ, info)); |
---|
1764 | appendSwapDecompress (factorsG, contentAFactors, N, swapLevel, x); |
---|
1765 | normalize (factorsG); |
---|
1766 | return factorsG; |
---|
1767 | } |
---|
1768 | } |
---|
1769 | } |
---|
1770 | |
---|
1771 | |
---|
1772 | CFList Aeval, list, evaluation, bufEvaluation, bufAeval; |
---|
1773 | bool fail= false; |
---|
1774 | int swapLevel2= 0; |
---|
1775 | int level; |
---|
1776 | int factorNums= 3; |
---|
1777 | CanonicalForm bivarEval; |
---|
1778 | CFList biFactors, bufBiFactors; |
---|
1779 | CanonicalForm evalPoly; |
---|
1780 | int lift, bufLift; |
---|
1781 | double logarithm= (double) ilog2 (totaldegree (A)); |
---|
1782 | logarithm /= log2exp; |
---|
1783 | logarithm= ceil (logarithm); |
---|
1784 | if (factorNums < (int) logarithm) |
---|
1785 | factorNums= (int) logarithm; |
---|
1786 | // several bivariate factorizations |
---|
1787 | for (int i= 0; i < factorNums; i++) |
---|
1788 | { |
---|
1789 | bufA= A; |
---|
1790 | bufAeval= CFList(); |
---|
1791 | bufEvaluation= evalPoints (bufA, bufAeval, alpha, list, GF, fail); |
---|
1792 | evalPoly= 0; |
---|
1793 | |
---|
1794 | if (fail && (i == 0)) |
---|
1795 | { |
---|
1796 | if (!swapLevel) |
---|
1797 | level= 2; |
---|
1798 | else |
---|
1799 | level= swapLevel + 1; |
---|
1800 | |
---|
1801 | swapLevel2= newMainVariableSearch (A, Aeval, evaluation, alpha, level); |
---|
1802 | |
---|
1803 | if (!swapLevel2) // need to pass to an extension |
---|
1804 | { |
---|
1805 | factors= extFactorize (A, info); |
---|
1806 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, x); |
---|
1807 | normalize (factors); |
---|
1808 | return factors; |
---|
1809 | } |
---|
1810 | else |
---|
1811 | { |
---|
1812 | fail= false; |
---|
1813 | bufAeval= Aeval; |
---|
1814 | bufA= A; |
---|
1815 | bufEvaluation= evaluation; |
---|
1816 | } |
---|
1817 | } |
---|
1818 | else if (fail && (i > 0)) |
---|
1819 | break; |
---|
1820 | |
---|
1821 | bivarEval= bufEvaluation.getLast(); |
---|
1822 | bufEvaluation.removeLast(); |
---|
1823 | |
---|
1824 | bufLift= degree (A, y) + 1 + degree (LC(A, x), y); |
---|
1825 | |
---|
1826 | TIMING_START (fac_bi_factorizer); |
---|
1827 | bufBiFactors= biFactorizer (bufAeval.getFirst(), alpha, bivarEval, bufLift); |
---|
1828 | TIMING_END_AND_PRINT (fac_bi_factorizer, |
---|
1829 | "time for bivariate factorization: "); |
---|
1830 | |
---|
1831 | if (bufBiFactors.length() == 1) |
---|
1832 | { |
---|
1833 | if (extension) |
---|
1834 | { |
---|
1835 | CFList source, dest; |
---|
1836 | A= mapDown (A, info, source, dest); |
---|
1837 | } |
---|
1838 | factors.append (A); |
---|
1839 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, |
---|
1840 | swapLevel2, x); |
---|
1841 | normalize (factors); |
---|
1842 | return factors; |
---|
1843 | } |
---|
1844 | |
---|
1845 | bufEvaluation.append (-bivarEval[0]); |
---|
1846 | if (i == 0) |
---|
1847 | { |
---|
1848 | Aeval= bufAeval; |
---|
1849 | evaluation= bufEvaluation; |
---|
1850 | biFactors= bufBiFactors; |
---|
1851 | lift= bufLift; |
---|
1852 | } |
---|
1853 | else |
---|
1854 | { |
---|
1855 | if (bufBiFactors.length() < biFactors.length() || |
---|
1856 | ((bufLift < lift) && (bufBiFactors.length() == biFactors.length()))) |
---|
1857 | { |
---|
1858 | Aeval= bufAeval; |
---|
1859 | evaluation= bufEvaluation; |
---|
1860 | biFactors= bufBiFactors; |
---|
1861 | lift= bufLift; |
---|
1862 | } |
---|
1863 | } |
---|
1864 | int k= 0; |
---|
1865 | for (CFListIterator j= bufEvaluation; j.hasItem(); j++, k++) |
---|
1866 | evalPoly += j.getItem()*power (x, k); |
---|
1867 | list.append (evalPoly); |
---|
1868 | } |
---|
1869 | |
---|
1870 | //shifting to zero |
---|
1871 | A= shift2Zero (A, Aeval, evaluation); |
---|
1872 | |
---|
1873 | int* liftBounds; |
---|
1874 | int liftBoundsLength= F.level() - 1; |
---|
1875 | liftBounds= liftingBounds (A, lift); |
---|
1876 | |
---|
1877 | CFList MOD; |
---|
1878 | bool earlySuccess; |
---|
1879 | CFList earlyFactors; |
---|
1880 | TIMING_START (fac_hensel_lift); |
---|
1881 | CFList liftedFactors= henselLiftAndEarly |
---|
1882 | (A, MOD, liftBounds, earlySuccess, earlyFactors, |
---|
1883 | Aeval, biFactors, evaluation, info); |
---|
1884 | TIMING_END_AND_PRINT (fac_hensel_lift, "time for hensel lifting: "); |
---|
1885 | |
---|
1886 | if (!extension) |
---|
1887 | { |
---|
1888 | TIMING_START (fac_factor_recombination); |
---|
1889 | factors= factorRecombination (A, liftedFactors, MOD); |
---|
1890 | TIMING_END_AND_PRINT (fac_factor_recombination, |
---|
1891 | "time for factor recombination: "); |
---|
1892 | } |
---|
1893 | else |
---|
1894 | { |
---|
1895 | TIMING_START (fac_factor_recombination); |
---|
1896 | factors= extFactorRecombination (liftedFactors, A, MOD, info, evaluation); |
---|
1897 | TIMING_END_AND_PRINT (fac_factor_recombination, |
---|
1898 | "time for factor recombination: "); |
---|
1899 | } |
---|
1900 | |
---|
1901 | if (earlySuccess) |
---|
1902 | factors= Union (factors, earlyFactors); |
---|
1903 | |
---|
1904 | if (!extension) |
---|
1905 | { |
---|
1906 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
1907 | { |
---|
1908 | int kk= Aeval.getLast().level(); |
---|
1909 | for (CFListIterator j= evaluation; j.hasItem(); j++, kk--) |
---|
1910 | { |
---|
1911 | if (i.getItem().level() < kk) |
---|
1912 | continue; |
---|
1913 | i.getItem()= i.getItem() (Variable (kk) - j.getItem(), kk); |
---|
1914 | } |
---|
1915 | } |
---|
1916 | } |
---|
1917 | |
---|
1918 | swap (factors, swapLevel, swapLevel2, x); |
---|
1919 | append (factors, contentAFactors); |
---|
1920 | decompress (factors, N); |
---|
1921 | normalize (factors); |
---|
1922 | |
---|
1923 | delete[] liftBounds; |
---|
1924 | |
---|
1925 | return factors; |
---|
1926 | } |
---|
1927 | |
---|
1928 | /// multivariate factorization over an extension of the initial field |
---|
1929 | CFList |
---|
1930 | extFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
1931 | { |
---|
1932 | CanonicalForm A= F; |
---|
1933 | |
---|
1934 | Variable alpha= info.getAlpha(); |
---|
1935 | Variable beta= info.getBeta(); |
---|
1936 | int k= info.getGFDegree(); |
---|
1937 | char cGFName= info.getGFName(); |
---|
1938 | CanonicalForm delta= info.getDelta(); |
---|
1939 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
1940 | Variable w= Variable (1); |
---|
1941 | |
---|
1942 | CFList factors; |
---|
1943 | if (!GF && alpha == w) // we are in F_p |
---|
1944 | { |
---|
1945 | CFList factors; |
---|
1946 | bool extension= true; |
---|
1947 | int p= getCharacteristic(); |
---|
1948 | if (p*p < (1<<16)) // pass to GF if possible |
---|
1949 | { |
---|
1950 | setCharacteristic (getCharacteristic(), 2, 'Z'); |
---|
1951 | ExtensionInfo info= ExtensionInfo (extension); |
---|
1952 | A= A.mapinto(); |
---|
1953 | factors= multiFactorize (A, info); |
---|
1954 | |
---|
1955 | Variable vBuf= rootOf (gf_mipo); |
---|
1956 | setCharacteristic (getCharacteristic()); |
---|
1957 | for (CFListIterator j= factors; j.hasItem(); j++) |
---|
1958 | j.getItem()= GF2FalphaRep (j.getItem(), vBuf); |
---|
1959 | } |
---|
1960 | else // not able to pass to GF, pass to F_p(\alpha) |
---|
1961 | { |
---|
1962 | Variable v= chooseExtension (A, beta); |
---|
1963 | ExtensionInfo info= ExtensionInfo (v, extension); |
---|
1964 | factors= multiFactorize (A, info); |
---|
1965 | } |
---|
1966 | return factors; |
---|
1967 | } |
---|
1968 | else if (!GF && (alpha != w)) // we are in F_p(\alpha) |
---|
1969 | { |
---|
1970 | if (k == 1) // need factorization over F_p |
---|
1971 | { |
---|
1972 | int extDeg= degree (getMipo (alpha)); |
---|
1973 | extDeg++; |
---|
1974 | CanonicalForm mipo= randomIrredpoly (extDeg + 1, Variable (1)); |
---|
1975 | Variable v= rootOf (mipo); |
---|
1976 | ExtensionInfo info= ExtensionInfo (v); |
---|
1977 | factors= biFactorize (A, info); |
---|
1978 | } |
---|
1979 | else |
---|
1980 | { |
---|
1981 | if (beta == Variable (1)) |
---|
1982 | { |
---|
1983 | Variable v= chooseExtension (A, alpha); |
---|
1984 | CanonicalForm primElem, imPrimElem; |
---|
1985 | bool primFail= false; |
---|
1986 | Variable vBuf; |
---|
1987 | primElem= primitiveElement (alpha, vBuf, primFail); |
---|
1988 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
1989 | if (primFail) |
---|
1990 | ; //ERROR |
---|
1991 | else |
---|
1992 | imPrimElem= mapPrimElem (primElem, vBuf, v); |
---|
1993 | |
---|
1994 | CFList source, dest; |
---|
1995 | CanonicalForm bufA= mapUp (A, alpha, v, primElem, imPrimElem, |
---|
1996 | source, dest); |
---|
1997 | ExtensionInfo info= ExtensionInfo (v, alpha, imPrimElem, primElem); |
---|
1998 | factors= biFactorize (bufA, info); |
---|
1999 | } |
---|
2000 | else |
---|
2001 | { |
---|
2002 | Variable v= chooseExtension (A, alpha); |
---|
2003 | CanonicalForm primElem, imPrimElem; |
---|
2004 | bool primFail= false; |
---|
2005 | Variable vBuf; |
---|
2006 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
2007 | if (primFail) |
---|
2008 | ; //ERROR |
---|
2009 | else |
---|
2010 | imPrimElem= mapPrimElem (delta, beta, v); //oder mapPrimElem (primElem, vBuf, v); |
---|
2011 | |
---|
2012 | CFList source, dest; |
---|
2013 | CanonicalForm bufA= mapDown (A, info, source, dest); |
---|
2014 | source= CFList(); |
---|
2015 | dest= CFList(); |
---|
2016 | bufA= mapUp (bufA, beta, v, delta, imPrimElem, source, dest); |
---|
2017 | ExtensionInfo info= ExtensionInfo (v, beta, imPrimElem, delta); |
---|
2018 | factors= biFactorize (bufA, info); |
---|
2019 | } |
---|
2020 | } |
---|
2021 | return factors; |
---|
2022 | } |
---|
2023 | else // we are in GF (p^k) |
---|
2024 | { |
---|
2025 | int p= getCharacteristic(); |
---|
2026 | int extensionDeg= getGFDegree(); |
---|
2027 | bool extension= true; |
---|
2028 | if (k == 1) // need factorization over F_p |
---|
2029 | { |
---|
2030 | extensionDeg++; |
---|
2031 | if (pow ((double) p, (double) extensionDeg) < (1<<16)) |
---|
2032 | // pass to GF(p^k+1) |
---|
2033 | { |
---|
2034 | setCharacteristic (p); |
---|
2035 | Variable vBuf= rootOf (gf_mipo); |
---|
2036 | A= GF2FalphaRep (A, vBuf); |
---|
2037 | setCharacteristic (p, extensionDeg, 'Z'); |
---|
2038 | ExtensionInfo info= ExtensionInfo (extension); |
---|
2039 | factors= multiFactorize (A.mapinto(), info); |
---|
2040 | } |
---|
2041 | else // not able to pass to another GF, pass to F_p(\alpha) |
---|
2042 | { |
---|
2043 | setCharacteristic (p); |
---|
2044 | Variable vBuf= rootOf (gf_mipo); |
---|
2045 | A= GF2FalphaRep (A, vBuf); |
---|
2046 | Variable v= chooseExtension (A, beta); |
---|
2047 | ExtensionInfo info= ExtensionInfo (v, extension); |
---|
2048 | factors= multiFactorize (A, info); |
---|
2049 | } |
---|
2050 | } |
---|
2051 | else // need factorization over GF (p^k) |
---|
2052 | { |
---|
2053 | if (pow ((double) p, (double) 2*extensionDeg) < (1<<16)) |
---|
2054 | // pass to GF(p^2k) |
---|
2055 | { |
---|
2056 | setCharacteristic (p, 2*extensionDeg, 'Z'); |
---|
2057 | ExtensionInfo info= ExtensionInfo (k, cGFName, extension); |
---|
2058 | factors= multiFactorize (GFMapUp (A, extensionDeg), info); |
---|
2059 | setCharacteristic (p, extensionDeg, cGFName); |
---|
2060 | } |
---|
2061 | else // not able to pass to GF (p^2k), pass to F_p (\alpha) |
---|
2062 | { |
---|
2063 | setCharacteristic (p); |
---|
2064 | Variable v1= rootOf (gf_mipo); |
---|
2065 | A= GF2FalphaRep (A, v1); |
---|
2066 | Variable v2= chooseExtension (A, v1); |
---|
2067 | CanonicalForm primElem, imPrimElem; |
---|
2068 | bool primFail= false; |
---|
2069 | Variable vBuf; |
---|
2070 | primElem= primitiveElement (v1, vBuf, primFail); |
---|
2071 | if (primFail) |
---|
2072 | { |
---|
2073 | ; //ERROR |
---|
2074 | } |
---|
2075 | else |
---|
2076 | { |
---|
2077 | imPrimElem= mapPrimElem (primElem, vBuf, v2); |
---|
2078 | } |
---|
2079 | CFList source, dest; |
---|
2080 | CanonicalForm bufA= mapUp (A, alpha, beta, primElem, imPrimElem, |
---|
2081 | source, dest); |
---|
2082 | ExtensionInfo info= ExtensionInfo (v2, v1, imPrimElem, primElem); |
---|
2083 | factors= multiFactorize (bufA, info); |
---|
2084 | setCharacteristic (p, k, cGFName); |
---|
2085 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
2086 | i.getItem()= Falpha2GFRep (i.getItem()); |
---|
2087 | } |
---|
2088 | } |
---|
2089 | return factors; |
---|
2090 | } |
---|
2091 | } |
---|
2092 | |
---|
2093 | #endif |
---|
2094 | /* HAVE_NTL */ |
---|
2095 | |
---|