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. Precomputation of leading coefficients is |
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11 | * described in "Sparse Hensel lifting" by E. Kaltofen |
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12 | * |
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13 | * @author Martin Lee |
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14 | * |
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15 | **/ |
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16 | /*****************************************************************************/ |
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17 | |
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18 | #include "config.h" |
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19 | |
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20 | #include "cf_assert.h" |
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21 | #include "debug.h" |
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22 | #include "timing.h" |
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23 | |
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24 | #include "facFqFactorizeUtil.h" |
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25 | #include "facFqFactorize.h" |
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26 | #include "cf_random.h" |
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27 | #include "facHensel.h" |
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28 | #include "cf_gcd_smallp.h" |
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29 | #include "cf_map_ext.h" |
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30 | #include "algext.h" |
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31 | #include "facSparseHensel.h" |
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32 | #include "facMul.h" |
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33 | |
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34 | #ifdef HAVE_NTL |
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35 | #include "NTLconvert.h" |
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36 | |
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37 | TIMING_DEFINE_PRINT(fac_fq_bi_factorizer) |
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38 | TIMING_DEFINE_PRINT(fac_fq_hensel_lift) |
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39 | TIMING_DEFINE_PRINT(fac_fq_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 | Variable x= Variable (1); |
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50 | CanonicalForm G= swapvar (F, F.mvar(), x); |
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51 | CFList L; |
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52 | for (CFIterator i= G; i.hasTerms(); i++) |
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53 | L.append (i.coeff()); |
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54 | if (L.length() == 2) |
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55 | return swapvar (gcd (L.getFirst(), L.getLast()), F.mvar(), x); |
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56 | if (L.length() == 1) |
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57 | return LC (F, x); |
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58 | return swapvar (listGCD (L), F.mvar(), x); |
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59 | } |
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60 | |
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61 | static inline |
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62 | CanonicalForm |
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63 | listGCD (const CFList& L) |
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64 | { |
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65 | if (L.length() == 1) |
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66 | return L.getFirst(); |
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67 | if (L.length() == 2) |
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68 | return gcd (L.getFirst(), L.getLast()); |
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69 | else |
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70 | { |
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71 | CFList lHi, lLo; |
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72 | CanonicalForm resultHi, resultLo; |
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73 | int length= L.length()/2; |
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74 | int j= 0; |
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75 | for (CFListIterator i= L; j < length; i++, j++) |
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76 | lHi.append (i.getItem()); |
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77 | lLo= Difference (L, lHi); |
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78 | resultHi= listGCD (lHi); |
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79 | resultLo= listGCD (lLo); |
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80 | if (resultHi.isOne() || resultLo.isOne()) |
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81 | return 1; |
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82 | return gcd (resultHi, resultLo); |
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83 | } |
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84 | } |
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85 | |
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86 | static inline |
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87 | CanonicalForm |
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88 | myContent (const CanonicalForm& F, const Variable& x) |
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89 | { |
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90 | if (degree (F, x) <= 0) |
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91 | return 1; |
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92 | CanonicalForm G= F; |
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93 | bool swap= false; |
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94 | if (x != F.mvar()) |
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95 | { |
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96 | swap= true; |
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97 | G= swapvar (F, x, F.mvar()); |
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98 | } |
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99 | CFList L; |
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100 | Variable alpha; |
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101 | for (CFIterator i= G; i.hasTerms(); i++) |
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102 | L.append (i.coeff()); |
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103 | if (L.length() == 2) |
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104 | { |
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105 | if (swap) |
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106 | return swapvar (gcd (L.getFirst(), L.getLast()), F.mvar(), x); |
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107 | else |
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108 | return gcd (L.getFirst(), L.getLast()); |
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109 | } |
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110 | if (L.length() == 1) |
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111 | { |
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112 | return LC (F, x); |
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113 | } |
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114 | if (swap) |
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115 | return swapvar (listGCD (L), F.mvar(), x); |
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116 | else |
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117 | return listGCD (L); |
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118 | } |
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119 | |
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120 | CanonicalForm myCompress (const CanonicalForm& F, CFMap& N) |
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121 | { |
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122 | int n= F.level(); |
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123 | int * degsf= new int [n + 1]; |
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124 | int ** swap; |
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125 | swap= new int* [n + 1]; |
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126 | for (int i= 0; i <= n; i++) |
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127 | { |
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128 | degsf[i]= 0; |
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129 | swap [i]= new int [2]; |
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130 | swap [i] [0]= 0; |
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131 | swap [i] [1]= 0; |
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132 | } |
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133 | int i= 1; |
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134 | n= 1; |
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135 | degsf= degrees (F, degsf); |
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136 | |
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137 | CanonicalForm result= F; |
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138 | while ( i <= F.level() ) |
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139 | { |
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140 | while( degsf[i] == 0 ) i++; |
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141 | swap[n][0]= i; |
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142 | swap[n][1]= size (LC (F,i)); |
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143 | if (i != n) |
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144 | result= swapvar (result, Variable (n), Variable(i)); |
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145 | n++; i++; |
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146 | } |
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147 | |
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148 | int buf1, buf2; |
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149 | n--; |
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150 | |
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151 | for (i= 1; i < n; i++) |
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152 | { |
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153 | for (int j= 1; j < n - i + 1; j++) |
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154 | { |
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155 | if (swap[j][1] > swap[j + 1][1]) |
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156 | { |
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157 | buf1= swap [j + 1] [0]; |
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158 | buf2= swap [j + 1] [1]; |
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159 | swap[j + 1] [0]= swap[j] [0]; |
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160 | swap[j + 1] [1]= swap[j] [1]; |
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161 | swap[j][0]= buf1; |
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162 | swap[j][1]= buf2; |
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163 | result= swapvar (result, Variable (j + 1), Variable (j)); |
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164 | } |
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165 | } |
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166 | } |
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167 | |
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168 | for (i= n; i > 0; i--) |
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169 | { |
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170 | if (i != swap[i] [0]) |
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171 | N.newpair (Variable (i), Variable (swap[i] [0])); |
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172 | } |
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173 | |
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174 | for (i= 0; i <= n; i++) |
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175 | delete [] swap[i]; |
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176 | delete [] swap; |
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177 | |
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178 | delete [] degsf; |
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179 | |
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180 | return result; |
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181 | } |
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182 | |
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183 | CFList |
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184 | extFactorRecombination (const CFList& factors, const CanonicalForm& F, |
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185 | const CFList& M, const ExtensionInfo& info, |
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186 | const CFList& evaluation) |
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187 | { |
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188 | Variable alpha= info.getAlpha(); |
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189 | Variable beta= info.getBeta(); |
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190 | CanonicalForm gamma= info.getGamma(); |
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191 | CanonicalForm delta= info.getDelta(); |
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192 | int k= info.getGFDegree(); |
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193 | CFList source, dest; |
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194 | if (factors.length() == 1) |
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195 | { |
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196 | CanonicalForm buf= reverseShift (F, evaluation); |
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197 | return CFList (mapDown (buf, info, source, dest)); |
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198 | } |
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199 | if (factors.length() < 1) |
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200 | return CFList(); |
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201 | |
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202 | int degMipoBeta= 1; |
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203 | if (!k && beta.level() != 1) |
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204 | degMipoBeta= degree (getMipo (beta)); |
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205 | |
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206 | CFList T, S; |
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207 | T= factors; |
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208 | |
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209 | int s= 1; |
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210 | CFList result; |
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211 | CanonicalForm buf; |
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212 | |
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213 | buf= F; |
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214 | |
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215 | Variable x= Variable (1); |
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216 | CanonicalForm g, LCBuf= LC (buf, x); |
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217 | CanonicalForm buf2, quot; |
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218 | int * v= new int [T.length()]; |
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219 | for (int i= 0; i < T.length(); i++) |
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220 | v[i]= 0; |
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221 | bool noSubset= false; |
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222 | CFArray TT; |
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223 | TT= copy (factors); |
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224 | bool recombination= false; |
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225 | bool trueFactor= false; |
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226 | while (T.length() >= 2*s) |
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227 | { |
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228 | while (noSubset == false) |
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229 | { |
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230 | if (T.length() == s) |
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231 | { |
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232 | delete [] v; |
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233 | if (recombination) |
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234 | { |
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235 | T.insert (LCBuf); |
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236 | g= prodMod (T, M); |
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237 | T.removeFirst(); |
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238 | result.append (g/myContent (g)); |
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239 | g= reverseShift (g, evaluation); |
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240 | g /= Lc (g); |
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241 | appendTestMapDown (result, g, info, source, dest); |
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242 | return result; |
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243 | } |
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244 | else |
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245 | { |
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246 | buf= reverseShift (buf, evaluation); |
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247 | return CFList (buf); |
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248 | } |
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249 | } |
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250 | |
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251 | S= subset (v, s, TT, noSubset); |
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252 | if (noSubset) break; |
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253 | |
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254 | S.insert (LCBuf); |
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255 | g= prodMod (S, M); |
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256 | S.removeFirst(); |
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257 | g /= myContent (g); |
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258 | if (fdivides (g, buf, quot)) |
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259 | { |
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260 | buf2= reverseShift (g, evaluation); |
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261 | buf2 /= Lc (buf2); |
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262 | if (!k && beta == x) |
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263 | { |
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264 | if (degree (buf2, alpha) < degMipoBeta) |
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265 | { |
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266 | appendTestMapDown (result, buf2, info, source, dest); |
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267 | buf= quot; |
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268 | LCBuf= LC (buf, x); |
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269 | recombination= true; |
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270 | trueFactor= true; |
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271 | } |
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272 | } |
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273 | else |
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274 | { |
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275 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
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276 | { |
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277 | appendTestMapDown (result, buf2, info, source, dest); |
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278 | buf /= g; |
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279 | LCBuf= LC (buf, x); |
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280 | recombination= true; |
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281 | trueFactor= true; |
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282 | } |
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283 | } |
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284 | |
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285 | if (trueFactor) |
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286 | { |
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287 | T= Difference (T, S); |
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288 | |
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289 | if (T.length() < 2*s || T.length() == s) |
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290 | { |
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291 | buf= reverseShift (buf, evaluation); |
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292 | buf /= Lc (buf); |
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293 | appendTestMapDown (result, buf, info, source, dest); |
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294 | delete [] v; |
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295 | return result; |
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296 | } |
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297 | trueFactor= false; |
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298 | TT= copy (T); |
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299 | indexUpdate (v, s, T.length(), noSubset); |
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300 | if (noSubset) break; |
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301 | } |
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302 | } |
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303 | } |
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304 | s++; |
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305 | if (T.length() < 2*s || T.length() == s) |
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306 | { |
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307 | buf= reverseShift (buf, evaluation); |
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308 | appendTestMapDown (result, buf, info, source, dest); |
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309 | delete [] v; |
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310 | return result; |
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311 | } |
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312 | for (int i= 0; i < T.length(); i++) |
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313 | v[i]= 0; |
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314 | noSubset= false; |
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315 | } |
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316 | if (T.length() < 2*s) |
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317 | { |
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318 | buf= reverseShift (F, evaluation); |
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319 | appendMapDown (result, buf, info, source, dest); |
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320 | } |
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321 | |
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322 | delete [] v; |
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323 | return result; |
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324 | } |
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325 | |
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326 | CFList |
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327 | factorRecombination (const CanonicalForm& F, const CFList& factors, |
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328 | const CFList& M) |
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329 | { |
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330 | if (factors.length() == 1) |
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331 | return CFList(F); |
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332 | if (factors.length() < 1) |
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333 | return CFList(); |
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334 | |
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335 | CFList T, S; |
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336 | |
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337 | T= factors; |
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338 | |
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339 | int s= 1; |
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340 | CFList result; |
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341 | CanonicalForm LCBuf= LC (F, Variable (1)); |
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342 | CanonicalForm g, buf= F; |
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343 | int * v= new int [T.length()]; |
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344 | for (int i= 0; i < T.length(); i++) |
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345 | v[i]= 0; |
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346 | bool noSubset= false; |
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347 | CFArray TT; |
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348 | TT= copy (factors); |
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349 | Variable y= F.level() - 1; |
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350 | bool recombination= false; |
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351 | CanonicalForm h, quot; |
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352 | while (T.length() >= 2*s) |
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353 | { |
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354 | while (noSubset == false) |
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355 | { |
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356 | if (T.length() == s) |
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357 | { |
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358 | delete [] v; |
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359 | if (recombination) |
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360 | { |
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361 | T.insert (LC (buf)); |
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362 | g= prodMod (T, M); |
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363 | result.append (g/myContent (g)); |
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364 | return result; |
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365 | } |
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366 | else |
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367 | return CFList (F); |
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368 | } |
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369 | S= subset (v, s, TT, noSubset); |
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370 | if (noSubset) break; |
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371 | S.insert (LCBuf); |
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372 | g= prodMod (S, M); |
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373 | S.removeFirst(); |
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374 | g /= myContent (g); |
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375 | if (fdivides (g, buf, quot)) |
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376 | { |
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377 | recombination= true; |
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378 | result.append (g); |
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379 | buf= quot; |
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380 | LCBuf= LC (buf, Variable(1)); |
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381 | T= Difference (T, S); |
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382 | if (T.length() < 2*s || T.length() == s) |
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383 | { |
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384 | result.append (buf); |
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385 | delete [] v; |
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386 | return result; |
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387 | } |
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388 | TT= copy (T); |
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389 | indexUpdate (v, s, T.length(), noSubset); |
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390 | if (noSubset) break; |
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391 | } |
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392 | } |
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393 | s++; |
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394 | if (T.length() < 2*s || T.length() == s) |
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395 | { |
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396 | result.append (buf); |
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397 | delete [] v; |
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398 | return result; |
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399 | } |
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400 | for (int i= 0; i < T.length(); i++) |
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401 | v[i]= 0; |
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402 | noSubset= false; |
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403 | } |
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404 | if (T.length() < 2*s) |
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405 | result.append (F); |
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406 | |
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407 | delete [] v; |
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408 | return result; |
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409 | } |
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410 | |
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411 | int |
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412 | liftBoundAdaption (const CanonicalForm& F, const CFList& factors, bool& |
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413 | success, const int deg, const CFList& MOD, const int bound) |
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414 | { |
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415 | int adaptedLiftBound= 0; |
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416 | CanonicalForm buf= F; |
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417 | Variable y= F.mvar(); |
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418 | Variable x= Variable (1); |
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419 | CanonicalForm LCBuf= LC (buf, x); |
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420 | CanonicalForm g, quot; |
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421 | CFList M= MOD; |
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422 | M.append (power (y, deg)); |
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423 | int d= bound; |
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424 | int e= 0; |
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425 | int nBuf; |
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426 | for (CFListIterator i= factors; i.hasItem(); i++) |
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427 | { |
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428 | g= mulMod (i.getItem(), LCBuf, M); |
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429 | g /= myContent (g); |
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430 | if (fdivides (g, buf, quot)) |
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431 | { |
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432 | nBuf= degree (g, y) + degree (LC (g, 1), y); |
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433 | d -= nBuf; |
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434 | e= tmax (e, nBuf); |
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435 | buf= quot; |
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436 | LCBuf= LC (buf, x); |
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437 | } |
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438 | } |
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439 | adaptedLiftBound= d; |
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440 | |
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441 | if (adaptedLiftBound < deg) |
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442 | { |
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443 | if (adaptedLiftBound < degree (F) + 1) |
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444 | { |
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445 | if (d == 1) |
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446 | { |
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447 | if (e + 1 > deg) |
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448 | { |
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449 | adaptedLiftBound= deg; |
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450 | success= false; |
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451 | } |
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452 | else |
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453 | { |
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454 | success= true; |
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455 | if (e + 1 < degree (F) + 1) |
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456 | adaptedLiftBound= deg; |
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457 | else |
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458 | adaptedLiftBound= e + 1; |
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459 | } |
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460 | } |
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461 | else |
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462 | { |
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463 | success= true; |
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464 | adaptedLiftBound= deg; |
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465 | } |
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466 | } |
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467 | else |
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468 | { |
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469 | success= true; |
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470 | } |
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471 | } |
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472 | return adaptedLiftBound; |
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473 | } |
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474 | |
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475 | int |
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476 | extLiftBoundAdaption (const CanonicalForm& F, const CFList& factors, bool& |
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477 | success, const ExtensionInfo& info, const CFList& eval, |
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478 | const int deg, const CFList& MOD, const int bound) |
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479 | { |
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480 | Variable alpha= info.getAlpha(); |
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481 | Variable beta= info.getBeta(); |
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482 | CanonicalForm gamma= info.getGamma(); |
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483 | CanonicalForm delta= info.getDelta(); |
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484 | int k= info.getGFDegree(); |
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485 | int adaptedLiftBound= 0; |
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486 | CanonicalForm buf= F; |
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487 | Variable y= F.mvar(); |
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488 | Variable x= Variable (1); |
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489 | CanonicalForm LCBuf= LC (buf, x); |
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490 | CanonicalForm g, gg, quot; |
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491 | CFList M= MOD; |
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492 | M.append (power (y, deg)); |
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493 | adaptedLiftBound= 0; |
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494 | int d= bound; |
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495 | int e= 0; |
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496 | int nBuf; |
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497 | int degMipoBeta= 1; |
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498 | if (!k && beta.level() != 1) |
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499 | degMipoBeta= degree (getMipo (beta)); |
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500 | |
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501 | CFList source, dest; |
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502 | for (CFListIterator i= factors; i.hasItem(); i++) |
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503 | { |
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504 | g= mulMod (i.getItem(), LCBuf, M); |
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505 | g /= myContent (g); |
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506 | if (fdivides (g, buf, quot)) |
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507 | { |
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508 | gg= reverseShift (g, eval); |
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509 | gg /= Lc (gg); |
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510 | if (!k && beta == x) |
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511 | { |
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512 | if (degree (gg, alpha) < degMipoBeta) |
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513 | { |
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514 | buf= quot; |
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515 | nBuf= degree (g, y) + degree (LC (g, x), y); |
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516 | d -= nBuf; |
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517 | e= tmax (e, nBuf); |
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518 | LCBuf= LC (buf, x); |
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519 | } |
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520 | } |
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521 | else |
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522 | { |
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523 | if (!isInExtension (gg, gamma, k, delta, source, dest)) |
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524 | { |
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525 | buf= quot; |
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526 | nBuf= degree (g, y) + degree (LC (g, x), y); |
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527 | d -= nBuf; |
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528 | e= tmax (e, nBuf); |
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529 | LCBuf= LC (buf, x); |
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530 | } |
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531 | } |
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532 | } |
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533 | } |
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534 | adaptedLiftBound= d; |
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535 | |
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536 | if (adaptedLiftBound < deg) |
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537 | { |
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538 | if (adaptedLiftBound < degree (F) + 1) |
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539 | { |
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540 | if (d == 1) |
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541 | { |
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542 | if (e + 1 > deg) |
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543 | { |
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544 | adaptedLiftBound= deg; |
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545 | success= false; |
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546 | } |
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547 | else |
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548 | { |
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549 | success= true; |
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550 | if (e + 1 < degree (F) + 1) |
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551 | adaptedLiftBound= deg; |
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552 | else |
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553 | adaptedLiftBound= e + 1; |
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554 | } |
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555 | } |
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556 | else |
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557 | { |
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558 | success= true; |
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559 | adaptedLiftBound= deg; |
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560 | } |
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561 | } |
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562 | else |
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563 | { |
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564 | success= true; |
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565 | } |
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566 | } |
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567 | |
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568 | return adaptedLiftBound; |
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569 | } |
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570 | |
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571 | CFList |
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572 | earlyFactorDetect (CanonicalForm& F, CFList& factors, int& adaptedLiftBound, |
---|
573 | bool& success, const int deg, const CFList& MOD, |
---|
574 | const int bound) |
---|
575 | { |
---|
576 | CFList result; |
---|
577 | CFList T= factors; |
---|
578 | CanonicalForm buf= F; |
---|
579 | Variable y= F.mvar(); |
---|
580 | Variable x= Variable (1); |
---|
581 | CanonicalForm LCBuf= LC (buf, x); |
---|
582 | CanonicalForm g, quot; |
---|
583 | CFList M= MOD; |
---|
584 | M.append (power (y, deg)); |
---|
585 | adaptedLiftBound= 0; |
---|
586 | int d= bound; |
---|
587 | int e= 0; |
---|
588 | int nBuf; |
---|
589 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
590 | { |
---|
591 | g= mulMod (i.getItem(), LCBuf, M); |
---|
592 | g /= myContent (g); |
---|
593 | if (fdivides (g, buf, quot)) |
---|
594 | { |
---|
595 | result.append (g); |
---|
596 | nBuf= degree (g, y) + degree (LC (g, x), y); |
---|
597 | d -= nBuf; |
---|
598 | e= tmax (e, nBuf); |
---|
599 | buf= quot; |
---|
600 | LCBuf= LC (buf, x); |
---|
601 | T= Difference (T, CFList (i.getItem())); |
---|
602 | } |
---|
603 | } |
---|
604 | adaptedLiftBound= d; |
---|
605 | |
---|
606 | if (adaptedLiftBound < deg) |
---|
607 | { |
---|
608 | if (adaptedLiftBound < degree (F) + 1) |
---|
609 | { |
---|
610 | if (d == 1) |
---|
611 | adaptedLiftBound= tmin (e + 1, deg); |
---|
612 | else |
---|
613 | adaptedLiftBound= deg; |
---|
614 | } |
---|
615 | factors= T; |
---|
616 | F= buf; |
---|
617 | success= true; |
---|
618 | } |
---|
619 | return result; |
---|
620 | } |
---|
621 | |
---|
622 | CFList |
---|
623 | extEarlyFactorDetect (CanonicalForm& F, CFList& factors, int& adaptedLiftBound, |
---|
624 | bool& success, const ExtensionInfo& info, const CFList& |
---|
625 | eval, const int deg, const CFList& MOD, const int bound) |
---|
626 | { |
---|
627 | Variable alpha= info.getAlpha(); |
---|
628 | Variable beta= info.getBeta(); |
---|
629 | CanonicalForm gamma= info.getGamma(); |
---|
630 | CanonicalForm delta= info.getDelta(); |
---|
631 | int k= info.getGFDegree(); |
---|
632 | CFList result; |
---|
633 | CFList T= factors; |
---|
634 | CanonicalForm buf= F; |
---|
635 | Variable y= F.mvar(); |
---|
636 | Variable x= Variable (1); |
---|
637 | CanonicalForm LCBuf= LC (buf, x); |
---|
638 | CanonicalForm g, gg, quot; |
---|
639 | CFList M= MOD; |
---|
640 | M.append (power (y, deg)); |
---|
641 | adaptedLiftBound= 0; |
---|
642 | int d= bound; |
---|
643 | int e= 0; |
---|
644 | int nBuf; |
---|
645 | CFList source, dest; |
---|
646 | |
---|
647 | int degMipoBeta= 1; |
---|
648 | if (!k && beta.level() != 1) |
---|
649 | degMipoBeta= degree (getMipo (beta)); |
---|
650 | |
---|
651 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
652 | { |
---|
653 | g= mulMod (i.getItem(), LCBuf, M); |
---|
654 | g /= myContent (g); |
---|
655 | if (fdivides (g, buf, quot)) |
---|
656 | { |
---|
657 | gg= reverseShift (g, eval); |
---|
658 | gg /= Lc (gg); |
---|
659 | if (!k && beta == x) |
---|
660 | { |
---|
661 | if (degree (gg, alpha) < degMipoBeta) |
---|
662 | { |
---|
663 | appendTestMapDown (result, gg, info, source, dest); |
---|
664 | buf= quot; |
---|
665 | nBuf= degree (g, y) + degree (LC (g, x), y); |
---|
666 | d -= nBuf; |
---|
667 | e= tmax (e, nBuf); |
---|
668 | LCBuf= LC (buf, x); |
---|
669 | T= Difference (T, CFList (i.getItem())); |
---|
670 | } |
---|
671 | } |
---|
672 | else |
---|
673 | { |
---|
674 | if (!isInExtension (gg, gamma, k, delta, source, dest)) |
---|
675 | { |
---|
676 | appendTestMapDown (result, gg, info, source, dest); |
---|
677 | buf= quot; |
---|
678 | nBuf= degree (g, y) + degree (LC (g, x), y); |
---|
679 | d -= nBuf; |
---|
680 | e= tmax (e, nBuf); |
---|
681 | LCBuf= LC (buf, x); |
---|
682 | T= Difference (T, CFList (i.getItem())); |
---|
683 | } |
---|
684 | } |
---|
685 | } |
---|
686 | } |
---|
687 | adaptedLiftBound= d; |
---|
688 | |
---|
689 | if (adaptedLiftBound < deg) |
---|
690 | { |
---|
691 | if (adaptedLiftBound < degree (F) + 1) |
---|
692 | { |
---|
693 | if (d == 1) |
---|
694 | adaptedLiftBound= tmin (e + 1, deg); |
---|
695 | else |
---|
696 | adaptedLiftBound= deg; |
---|
697 | } |
---|
698 | success= true; |
---|
699 | factors= T; |
---|
700 | F= buf; |
---|
701 | } |
---|
702 | return result; |
---|
703 | } |
---|
704 | |
---|
705 | CFList |
---|
706 | evalPoints (const CanonicalForm& F, CFList & eval, const Variable& alpha, |
---|
707 | CFList& list, const bool& GF, bool& fail) |
---|
708 | { |
---|
709 | int k= F.level() - 1; |
---|
710 | Variable x= Variable (1); |
---|
711 | CFList result; |
---|
712 | FFRandom genFF; |
---|
713 | GFRandom genGF; |
---|
714 | int p= getCharacteristic (); |
---|
715 | double bound; |
---|
716 | if (alpha != x) |
---|
717 | { |
---|
718 | bound= pow ((double) p, (double) degree (getMipo(alpha))); |
---|
719 | bound= pow ((double) bound, (double) k); |
---|
720 | } |
---|
721 | else if (GF) |
---|
722 | { |
---|
723 | bound= pow ((double) p, (double) getGFDegree()); |
---|
724 | bound= pow ((double) bound, (double) k); |
---|
725 | } |
---|
726 | else |
---|
727 | bound= pow ((double) p, (double) k); |
---|
728 | |
---|
729 | CanonicalForm random; |
---|
730 | CanonicalForm deriv_x, gcd_deriv; |
---|
731 | do |
---|
732 | { |
---|
733 | random= 0; |
---|
734 | // possible overflow if list.length() does not fit into a int |
---|
735 | if (list.length() >= bound) |
---|
736 | { |
---|
737 | fail= true; |
---|
738 | break; |
---|
739 | } |
---|
740 | for (int i= 0; i < k; i++) |
---|
741 | { |
---|
742 | if (list.isEmpty()) |
---|
743 | result.append (0); |
---|
744 | else if (GF) |
---|
745 | { |
---|
746 | result.append (genGF.generate()); |
---|
747 | random += result.getLast()*power (x, i); |
---|
748 | } |
---|
749 | else if (alpha.level() != 1) |
---|
750 | { |
---|
751 | AlgExtRandomF genAlgExt (alpha); |
---|
752 | result.append (genAlgExt.generate()); |
---|
753 | random += result.getLast()*power (x, i); |
---|
754 | } |
---|
755 | else |
---|
756 | { |
---|
757 | result.append (genFF.generate()); |
---|
758 | random += result.getLast()*power (x, i); |
---|
759 | } |
---|
760 | } |
---|
761 | if (find (list, random)) |
---|
762 | { |
---|
763 | result= CFList(); |
---|
764 | continue; |
---|
765 | } |
---|
766 | int l= F.level(); |
---|
767 | eval.insert (F); |
---|
768 | bool bad= false; |
---|
769 | for (CFListIterator i= result; i.hasItem(); i++, l--) |
---|
770 | { |
---|
771 | eval.insert (eval.getFirst()(i.getItem(), l)); |
---|
772 | if (degree (eval.getFirst(), l - 1) != degree (F, l - 1)) |
---|
773 | { |
---|
774 | if (!find (list, random)) |
---|
775 | list.append (random); |
---|
776 | result= CFList(); |
---|
777 | eval= CFList(); |
---|
778 | bad= true; |
---|
779 | break; |
---|
780 | } |
---|
781 | } |
---|
782 | |
---|
783 | if (bad) |
---|
784 | continue; |
---|
785 | |
---|
786 | if (degree (eval.getFirst()) != degree (F, 1)) |
---|
787 | { |
---|
788 | if (!find (list, random)) |
---|
789 | list.append (random); |
---|
790 | result= CFList(); |
---|
791 | eval= CFList(); |
---|
792 | continue; |
---|
793 | } |
---|
794 | |
---|
795 | deriv_x= deriv (eval.getFirst(), x); |
---|
796 | gcd_deriv= gcd (eval.getFirst(), deriv_x); |
---|
797 | if (degree (gcd_deriv) > 0) |
---|
798 | { |
---|
799 | if (!find (list, random)) |
---|
800 | list.append (random); |
---|
801 | result= CFList(); |
---|
802 | eval= CFList(); |
---|
803 | continue; |
---|
804 | } |
---|
805 | CFListIterator i= eval; |
---|
806 | i++; |
---|
807 | CanonicalForm contentx= content (i.getItem(), x); |
---|
808 | if (degree (contentx) > 0) |
---|
809 | { |
---|
810 | if (!find (list, random)) |
---|
811 | list.append (random); |
---|
812 | result= CFList(); |
---|
813 | eval= CFList(); |
---|
814 | continue; |
---|
815 | } |
---|
816 | |
---|
817 | if (list.length() >= bound) |
---|
818 | { |
---|
819 | fail= true; |
---|
820 | break; |
---|
821 | } |
---|
822 | } while (find (list, random)); |
---|
823 | |
---|
824 | if (!eval.isEmpty()) |
---|
825 | eval.removeFirst(); |
---|
826 | |
---|
827 | return result; |
---|
828 | } |
---|
829 | |
---|
830 | static inline |
---|
831 | int newMainVariableSearch (CanonicalForm& A, CFList& Aeval, CFList& |
---|
832 | evaluation, const Variable& alpha, const int lev, |
---|
833 | CanonicalForm& g |
---|
834 | ) |
---|
835 | { |
---|
836 | Variable x= Variable (1); |
---|
837 | CanonicalForm derivI, buf; |
---|
838 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
839 | int swapLevel= 0; |
---|
840 | CFList list; |
---|
841 | bool fail= false; |
---|
842 | buf= A; |
---|
843 | Aeval= CFList(); |
---|
844 | evaluation= CFList(); |
---|
845 | for (int i= lev; i <= A.level(); i++) |
---|
846 | { |
---|
847 | derivI= deriv (buf, Variable (i)); |
---|
848 | if (!derivI.isZero()) |
---|
849 | { |
---|
850 | g= gcd (buf, derivI); |
---|
851 | if (degree (g) > 0) |
---|
852 | return -1; |
---|
853 | |
---|
854 | buf= swapvar (buf, x, Variable (i)); |
---|
855 | Aeval= CFList(); |
---|
856 | evaluation= CFList(); |
---|
857 | fail= false; |
---|
858 | evaluation= evalPoints (buf, Aeval, alpha, list, GF, fail); |
---|
859 | if (!fail) |
---|
860 | { |
---|
861 | A= buf; |
---|
862 | swapLevel= i; |
---|
863 | break; |
---|
864 | } |
---|
865 | else |
---|
866 | buf= A; |
---|
867 | } |
---|
868 | } |
---|
869 | return swapLevel; |
---|
870 | } |
---|
871 | |
---|
872 | CanonicalForm lcmContent (const CanonicalForm& A, CFList& contentAi) |
---|
873 | { |
---|
874 | int i= A.level(); |
---|
875 | contentAi.append (myContent (A, i)); |
---|
876 | contentAi.append (myContent (A, i - 1)); |
---|
877 | CanonicalForm result= lcm (contentAi.getFirst(), contentAi.getLast()); |
---|
878 | for (i= i - 2; i > 0; i--) |
---|
879 | { |
---|
880 | contentAi.append (content (A, i)); |
---|
881 | result= lcm (result, contentAi.getLast()); |
---|
882 | } |
---|
883 | return result; |
---|
884 | } |
---|
885 | |
---|
886 | CFList |
---|
887 | henselLiftAndEarly (CanonicalForm& A, CFList& MOD, int*& liftBounds, bool& |
---|
888 | earlySuccess, CFList& earlyFactors, const CFList& Aeval, |
---|
889 | const CFList& biFactors, const CFList& evaluation, |
---|
890 | const ExtensionInfo& info) |
---|
891 | { |
---|
892 | bool extension= info.isInExtension(); |
---|
893 | CFList bufFactors= biFactors; |
---|
894 | bufFactors.insert (LC (Aeval.getFirst(), 1)); |
---|
895 | |
---|
896 | sortList (bufFactors, Variable (1)); |
---|
897 | |
---|
898 | CFList diophant; |
---|
899 | CFArray Pi; |
---|
900 | int smallFactorDeg= 11; //tunable parameter |
---|
901 | CFList result; |
---|
902 | int adaptedLiftBound= 0; |
---|
903 | int liftBound= liftBounds[1]; |
---|
904 | |
---|
905 | earlySuccess= false; |
---|
906 | CFList earlyReconstFactors; |
---|
907 | CFListIterator j= Aeval; |
---|
908 | j++; |
---|
909 | CanonicalForm buf= j.getItem(); |
---|
910 | CFMatrix Mat= CFMatrix (liftBound, bufFactors.length() - 1); |
---|
911 | MOD= CFList (power (Variable (2), liftBounds[0])); |
---|
912 | if (smallFactorDeg >= liftBound) |
---|
913 | { |
---|
914 | result= henselLift23 (Aeval, bufFactors, liftBounds, diophant, Pi, Mat); |
---|
915 | } |
---|
916 | else if (smallFactorDeg >= degree (buf) + 1) |
---|
917 | { |
---|
918 | liftBounds[1]= degree (buf) + 1; |
---|
919 | result= henselLift23 (Aeval, bufFactors, liftBounds, diophant, Pi, Mat); |
---|
920 | if (Aeval.length() == 2) |
---|
921 | { |
---|
922 | if (!extension) |
---|
923 | earlyFactors= earlyFactorDetect |
---|
924 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
925 | degree (buf) + 1, MOD, liftBound); |
---|
926 | else |
---|
927 | earlyFactors= extEarlyFactorDetect |
---|
928 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
929 | info, evaluation, degree |
---|
930 | (buf) + 1, MOD, liftBound); |
---|
931 | } |
---|
932 | else |
---|
933 | { |
---|
934 | if (!extension) |
---|
935 | adaptedLiftBound= liftBoundAdaption (buf, result, earlySuccess, |
---|
936 | degree (buf) + 1, MOD, liftBound); |
---|
937 | else |
---|
938 | adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, info, |
---|
939 | evaluation, degree (buf) + 1, |
---|
940 | MOD, liftBound); |
---|
941 | } |
---|
942 | if (!earlySuccess) |
---|
943 | { |
---|
944 | result.insert (LC (buf, 1)); |
---|
945 | liftBounds[1]= adaptedLiftBound; |
---|
946 | liftBound= adaptedLiftBound; |
---|
947 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
948 | Pi, diophant, Mat, MOD); |
---|
949 | } |
---|
950 | else |
---|
951 | liftBounds[1]= adaptedLiftBound; |
---|
952 | } |
---|
953 | else if (smallFactorDeg < degree (buf) + 1) |
---|
954 | { |
---|
955 | liftBounds[1]= smallFactorDeg; |
---|
956 | result= henselLift23 (Aeval, bufFactors, liftBounds, diophant, Pi, Mat); |
---|
957 | if (Aeval.length() == 2) |
---|
958 | { |
---|
959 | if (!extension) |
---|
960 | earlyFactors= earlyFactorDetect (buf, result, adaptedLiftBound, |
---|
961 | earlySuccess, smallFactorDeg, MOD, |
---|
962 | liftBound); |
---|
963 | else |
---|
964 | earlyFactors= extEarlyFactorDetect (buf, result, adaptedLiftBound, |
---|
965 | earlySuccess, info, evaluation, |
---|
966 | smallFactorDeg, MOD, liftBound); |
---|
967 | } |
---|
968 | else |
---|
969 | { |
---|
970 | if (!extension) |
---|
971 | adaptedLiftBound= liftBoundAdaption (buf, result, earlySuccess, |
---|
972 | smallFactorDeg, MOD, liftBound); |
---|
973 | else |
---|
974 | adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, info, |
---|
975 | evaluation, smallFactorDeg, MOD, |
---|
976 | liftBound); |
---|
977 | } |
---|
978 | |
---|
979 | if (!earlySuccess) |
---|
980 | { |
---|
981 | result.insert (LC (buf, 1)); |
---|
982 | henselLiftResume (buf, result, smallFactorDeg, degree (buf) + 1, |
---|
983 | Pi, diophant, Mat, MOD); |
---|
984 | if (Aeval.length() == 2) |
---|
985 | { |
---|
986 | if (!extension) |
---|
987 | earlyFactors= earlyFactorDetect (buf, result, adaptedLiftBound, |
---|
988 | earlySuccess, degree (buf) + 1, |
---|
989 | MOD, liftBound); |
---|
990 | else |
---|
991 | earlyFactors= extEarlyFactorDetect (buf, result, adaptedLiftBound, |
---|
992 | earlySuccess, info, evaluation, |
---|
993 | degree (buf) + 1, MOD, |
---|
994 | liftBound); |
---|
995 | } |
---|
996 | else |
---|
997 | { |
---|
998 | if (!extension) |
---|
999 | adaptedLiftBound= liftBoundAdaption (buf, result, earlySuccess, |
---|
1000 | degree (buf) + 1, MOD,liftBound); |
---|
1001 | else |
---|
1002 | adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, |
---|
1003 | info, evaluation, |
---|
1004 | degree (buf) + 1, MOD, |
---|
1005 | liftBound); |
---|
1006 | } |
---|
1007 | if (!earlySuccess) |
---|
1008 | { |
---|
1009 | result.insert (LC (buf, 1)); |
---|
1010 | liftBounds[1]= adaptedLiftBound; |
---|
1011 | liftBound= adaptedLiftBound; |
---|
1012 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
1013 | Pi, diophant, Mat, MOD); |
---|
1014 | } |
---|
1015 | else |
---|
1016 | liftBounds[1]= adaptedLiftBound; |
---|
1017 | } |
---|
1018 | else |
---|
1019 | liftBounds[1]= adaptedLiftBound; |
---|
1020 | } |
---|
1021 | |
---|
1022 | MOD.append (power (Variable (3), liftBounds[1])); |
---|
1023 | |
---|
1024 | if (Aeval.length() > 2) |
---|
1025 | { |
---|
1026 | CFListIterator j= Aeval; |
---|
1027 | j++; |
---|
1028 | CFList bufEval; |
---|
1029 | bufEval.append (j.getItem()); |
---|
1030 | j++; |
---|
1031 | int liftBoundsLength= Aeval.getLast().level() - 1; |
---|
1032 | for (int i= 2; i <= liftBoundsLength && j.hasItem(); i++, j++) |
---|
1033 | { |
---|
1034 | earlySuccess= false; |
---|
1035 | result.insert (LC (bufEval.getFirst(), 1)); |
---|
1036 | bufEval.append (j.getItem()); |
---|
1037 | liftBound= liftBounds[i]; |
---|
1038 | Mat= CFMatrix (liftBounds[i], result.length() - 1); |
---|
1039 | |
---|
1040 | buf= j.getItem(); |
---|
1041 | if (smallFactorDeg >= liftBound) |
---|
1042 | result= henselLift (bufEval, result, MOD, diophant, Pi, Mat, |
---|
1043 | liftBounds[i - 1], liftBounds[i]); |
---|
1044 | else if (smallFactorDeg >= degree (buf) + 1) |
---|
1045 | { |
---|
1046 | result= henselLift (bufEval, result, MOD, diophant, Pi, Mat, |
---|
1047 | liftBounds[i - 1], degree (buf) + 1); |
---|
1048 | |
---|
1049 | if (Aeval.length() == i + 1) |
---|
1050 | { |
---|
1051 | if (!extension) |
---|
1052 | earlyFactors= earlyFactorDetect |
---|
1053 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1054 | degree (buf) + 1, MOD, liftBound); |
---|
1055 | else |
---|
1056 | earlyFactors= extEarlyFactorDetect |
---|
1057 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1058 | info, evaluation, degree (buf) + 1, MOD, liftBound); |
---|
1059 | } |
---|
1060 | else |
---|
1061 | { |
---|
1062 | if (!extension) |
---|
1063 | adaptedLiftBound= liftBoundAdaption |
---|
1064 | (buf, result, earlySuccess, degree (buf) |
---|
1065 | + 1, MOD, liftBound); |
---|
1066 | else |
---|
1067 | adaptedLiftBound= extLiftBoundAdaption |
---|
1068 | (buf, result, earlySuccess, info, evaluation, |
---|
1069 | degree (buf) + 1, MOD, liftBound); |
---|
1070 | } |
---|
1071 | |
---|
1072 | if (!earlySuccess) |
---|
1073 | { |
---|
1074 | result.insert (LC (buf, 1)); |
---|
1075 | liftBounds[i]= adaptedLiftBound; |
---|
1076 | liftBound= adaptedLiftBound; |
---|
1077 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
1078 | Pi, diophant, Mat, MOD); |
---|
1079 | } |
---|
1080 | else |
---|
1081 | { |
---|
1082 | liftBounds[i]= adaptedLiftBound; |
---|
1083 | } |
---|
1084 | } |
---|
1085 | else if (smallFactorDeg < degree (buf) + 1) |
---|
1086 | { |
---|
1087 | result= henselLift (bufEval, result, MOD, diophant, Pi, Mat, |
---|
1088 | liftBounds[i - 1], smallFactorDeg); |
---|
1089 | |
---|
1090 | if (Aeval.length() == i + 1) |
---|
1091 | { |
---|
1092 | if (!extension) |
---|
1093 | earlyFactors= earlyFactorDetect |
---|
1094 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1095 | smallFactorDeg, MOD, liftBound); |
---|
1096 | else |
---|
1097 | earlyFactors= extEarlyFactorDetect |
---|
1098 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1099 | info, evaluation, smallFactorDeg, MOD, liftBound); |
---|
1100 | } |
---|
1101 | else |
---|
1102 | { |
---|
1103 | if (!extension) |
---|
1104 | adaptedLiftBound= liftBoundAdaption |
---|
1105 | (buf, result, earlySuccess, |
---|
1106 | smallFactorDeg, MOD, liftBound); |
---|
1107 | else |
---|
1108 | adaptedLiftBound= extLiftBoundAdaption |
---|
1109 | (buf, result, earlySuccess, info, evaluation, |
---|
1110 | smallFactorDeg, MOD, liftBound); |
---|
1111 | } |
---|
1112 | |
---|
1113 | if (!earlySuccess) |
---|
1114 | { |
---|
1115 | result.insert (LC (buf, 1)); |
---|
1116 | henselLiftResume (buf, result, smallFactorDeg, |
---|
1117 | degree (buf) + 1, Pi, diophant, Mat, MOD); |
---|
1118 | if (Aeval.length() == i + 1) |
---|
1119 | { |
---|
1120 | if (!extension) |
---|
1121 | earlyFactors= earlyFactorDetect |
---|
1122 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1123 | degree (buf) + 1, MOD, liftBound); |
---|
1124 | else |
---|
1125 | earlyFactors= extEarlyFactorDetect |
---|
1126 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1127 | info, evaluation, degree (buf) + 1, MOD, |
---|
1128 | liftBound); |
---|
1129 | } |
---|
1130 | else |
---|
1131 | { |
---|
1132 | if (!extension) |
---|
1133 | adaptedLiftBound= liftBoundAdaption |
---|
1134 | (buf, result, earlySuccess, degree |
---|
1135 | (buf) + 1, MOD, liftBound); |
---|
1136 | else |
---|
1137 | adaptedLiftBound= extLiftBoundAdaption |
---|
1138 | (buf, result, earlySuccess, info, evaluation, |
---|
1139 | degree (buf) + 1, MOD, liftBound); |
---|
1140 | } |
---|
1141 | |
---|
1142 | if (!earlySuccess) |
---|
1143 | { |
---|
1144 | result.insert (LC (buf, 1)); |
---|
1145 | liftBounds[i]= adaptedLiftBound; |
---|
1146 | liftBound= adaptedLiftBound; |
---|
1147 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
1148 | Pi, diophant, Mat, MOD); |
---|
1149 | } |
---|
1150 | else |
---|
1151 | liftBounds[i]= adaptedLiftBound; |
---|
1152 | } |
---|
1153 | else |
---|
1154 | liftBounds[i]= adaptedLiftBound; |
---|
1155 | } |
---|
1156 | MOD.append (power (Variable (i + 2), liftBounds[i])); |
---|
1157 | bufEval.removeFirst(); |
---|
1158 | } |
---|
1159 | bufFactors= result; |
---|
1160 | } |
---|
1161 | else |
---|
1162 | bufFactors= result; |
---|
1163 | |
---|
1164 | if (earlySuccess) |
---|
1165 | A= buf; |
---|
1166 | return result; |
---|
1167 | } |
---|
1168 | |
---|
1169 | void |
---|
1170 | gcdFreeBasis (CFFList& factors1, CFFList& factors2) |
---|
1171 | { |
---|
1172 | CanonicalForm g; |
---|
1173 | int k= factors1.length(); |
---|
1174 | int l= factors2.length(); |
---|
1175 | int n= 1; |
---|
1176 | int m; |
---|
1177 | CFFListIterator j; |
---|
1178 | for (CFFListIterator i= factors1; (n < k && i.hasItem()); i++, n++) |
---|
1179 | { |
---|
1180 | m= 1; |
---|
1181 | for (j= factors2; (m < l && j.hasItem()); j++, m++) |
---|
1182 | { |
---|
1183 | g= gcd (i.getItem().factor(), j.getItem().factor()); |
---|
1184 | if (degree (g,1) > 0) |
---|
1185 | { |
---|
1186 | j.getItem()= CFFactor (j.getItem().factor()/g, j.getItem().exp()); |
---|
1187 | i.getItem()= CFFactor (i.getItem().factor()/g, i.getItem().exp()); |
---|
1188 | factors1.append (CFFactor (g, i.getItem().exp())); |
---|
1189 | factors2.append (CFFactor (g, j.getItem().exp())); |
---|
1190 | } |
---|
1191 | } |
---|
1192 | } |
---|
1193 | } |
---|
1194 | |
---|
1195 | CFList |
---|
1196 | distributeContent (const CFList& L, const CFList* differentSecondVarFactors, |
---|
1197 | int length |
---|
1198 | ) |
---|
1199 | { |
---|
1200 | CFList l= L; |
---|
1201 | CanonicalForm content= l.getFirst(); |
---|
1202 | |
---|
1203 | if (content.inCoeffDomain()) |
---|
1204 | return l; |
---|
1205 | |
---|
1206 | if (l.length() == 1) |
---|
1207 | { |
---|
1208 | CFList result; |
---|
1209 | for (int i= 0; i < length; i++) |
---|
1210 | { |
---|
1211 | if (differentSecondVarFactors[i].isEmpty()) |
---|
1212 | continue; |
---|
1213 | if (result.isEmpty()) |
---|
1214 | { |
---|
1215 | result= differentSecondVarFactors[i]; |
---|
1216 | for (CFListIterator iter= result; iter.hasItem(); iter++) |
---|
1217 | content /= iter.getItem(); |
---|
1218 | } |
---|
1219 | else |
---|
1220 | { |
---|
1221 | CFListIterator iter1= result; |
---|
1222 | for (CFListIterator iter2= differentSecondVarFactors[i];iter2.hasItem(); |
---|
1223 | iter2++, iter1++) |
---|
1224 | { |
---|
1225 | iter1.getItem() *= iter2.getItem(); |
---|
1226 | content /= iter2.getItem(); |
---|
1227 | } |
---|
1228 | } |
---|
1229 | } |
---|
1230 | result.insert (content); |
---|
1231 | return result; |
---|
1232 | } |
---|
1233 | |
---|
1234 | Variable v; |
---|
1235 | CFListIterator iter1, iter2; |
---|
1236 | CanonicalForm tmp, g; |
---|
1237 | CFList multiplier; |
---|
1238 | for (int i= 0; i < length; i++) |
---|
1239 | { |
---|
1240 | if (differentSecondVarFactors[i].isEmpty()) |
---|
1241 | continue; |
---|
1242 | iter1= l; |
---|
1243 | iter1++; |
---|
1244 | |
---|
1245 | v= Variable (i + 3); |
---|
1246 | tmp= 1; |
---|
1247 | for (iter2= differentSecondVarFactors[i]; iter2.hasItem(); |
---|
1248 | iter2++, iter1++) |
---|
1249 | { |
---|
1250 | if (degree (iter2.getItem(),v) == degree (iter1.getItem(),v)) |
---|
1251 | { |
---|
1252 | multiplier.append (1); |
---|
1253 | continue; |
---|
1254 | } |
---|
1255 | g= gcd (iter2.getItem(), content); |
---|
1256 | if (!g.inCoeffDomain()) |
---|
1257 | { |
---|
1258 | tmp *= g; |
---|
1259 | multiplier.append (g); |
---|
1260 | } |
---|
1261 | else |
---|
1262 | multiplier.append (1); |
---|
1263 | } |
---|
1264 | if (!tmp.isOne() && fdivides (tmp, content)) |
---|
1265 | { |
---|
1266 | iter1= l; |
---|
1267 | iter1++; |
---|
1268 | content /= tmp; |
---|
1269 | for (iter2= multiplier; iter2.hasItem(); iter1++, iter2++) |
---|
1270 | iter1.getItem() *= iter2.getItem(); |
---|
1271 | } |
---|
1272 | multiplier= CFList(); |
---|
1273 | } |
---|
1274 | |
---|
1275 | l.removeFirst(); |
---|
1276 | l.insert (content); |
---|
1277 | return l; |
---|
1278 | } |
---|
1279 | |
---|
1280 | CFList evaluateAtZero (const CanonicalForm& F) |
---|
1281 | { |
---|
1282 | CFList result; |
---|
1283 | CanonicalForm buf= F; |
---|
1284 | result.insert (buf); |
---|
1285 | for (int i= F.level(); i > 2; i--) |
---|
1286 | { |
---|
1287 | buf= buf (0, i); |
---|
1288 | result.insert (buf); |
---|
1289 | } |
---|
1290 | return result; |
---|
1291 | } |
---|
1292 | |
---|
1293 | CFList evaluateAtEval (const CanonicalForm& F, const CFArray& eval) |
---|
1294 | { |
---|
1295 | CFList result; |
---|
1296 | CanonicalForm buf= F; |
---|
1297 | result.insert (buf); |
---|
1298 | int k= eval.size(); |
---|
1299 | for (int i= 1; i < k; i++) |
---|
1300 | { |
---|
1301 | buf= buf (eval[i], i + 2); |
---|
1302 | result.insert (buf); |
---|
1303 | } |
---|
1304 | return result; |
---|
1305 | } |
---|
1306 | |
---|
1307 | CFList evaluateAtEval (const CanonicalForm& F, const CFList& evaluation, int l) |
---|
1308 | { |
---|
1309 | CFList result; |
---|
1310 | CanonicalForm buf= F; |
---|
1311 | result.insert (buf); |
---|
1312 | int k= evaluation.length() + l - 1; |
---|
1313 | CFListIterator j= evaluation; |
---|
1314 | for (int i= k; j.hasItem() && i > l; i--, j++) |
---|
1315 | { |
---|
1316 | if (F.level() < i) |
---|
1317 | continue; |
---|
1318 | buf= buf (j.getItem(), i); |
---|
1319 | result.insert (buf); |
---|
1320 | } |
---|
1321 | return result; |
---|
1322 | } |
---|
1323 | |
---|
1324 | int |
---|
1325 | testFactors (const CanonicalForm& G, const CFList& uniFactors, |
---|
1326 | const Variable& alpha, CanonicalForm& sqrfPartF, CFList& factors, |
---|
1327 | CFFList*& bufSqrfFactors, CFList& evalSqrfPartF, |
---|
1328 | const CFArray& evalPoint) |
---|
1329 | { |
---|
1330 | CanonicalForm tmp; |
---|
1331 | CFListIterator j; |
---|
1332 | for (CFListIterator i= uniFactors; i.hasItem(); i++) |
---|
1333 | { |
---|
1334 | tmp= i.getItem(); |
---|
1335 | if (i.hasItem()) |
---|
1336 | i++; |
---|
1337 | else |
---|
1338 | break; |
---|
1339 | for (j= i; j.hasItem(); j++) |
---|
1340 | { |
---|
1341 | if (tmp == j.getItem()) |
---|
1342 | return 0; |
---|
1343 | } |
---|
1344 | } |
---|
1345 | |
---|
1346 | CanonicalForm F= G; |
---|
1347 | CFFList sqrfFactorization= squarefreeFactorization (F, alpha); |
---|
1348 | |
---|
1349 | sqrfPartF= 1; |
---|
1350 | for (CFFListIterator i= sqrfFactorization; i.hasItem(); i++) |
---|
1351 | sqrfPartF *= i.getItem().factor(); |
---|
1352 | |
---|
1353 | evalSqrfPartF= evaluateAtEval (sqrfPartF, evalPoint); |
---|
1354 | |
---|
1355 | CanonicalForm test= evalSqrfPartF.getFirst() (evalPoint[0], 2); |
---|
1356 | |
---|
1357 | if (degree (test) != degree (sqrfPartF, 1)) |
---|
1358 | return 0; |
---|
1359 | |
---|
1360 | CFFList sqrfFactors; |
---|
1361 | CFList tmp2; |
---|
1362 | int k= 0; |
---|
1363 | factors= uniFactors; |
---|
1364 | CFFListIterator iter; |
---|
1365 | for (CFListIterator i= factors; i.hasItem(); i++, k++) |
---|
1366 | { |
---|
1367 | tmp= 1; |
---|
1368 | sqrfFactors= squarefreeFactorization (i.getItem(), alpha); |
---|
1369 | |
---|
1370 | for (iter= sqrfFactors; iter.hasItem(); iter++) |
---|
1371 | { |
---|
1372 | tmp2.append (iter.getItem().factor()); |
---|
1373 | tmp *= iter.getItem().factor(); |
---|
1374 | } |
---|
1375 | i.getItem()= tmp/Lc(tmp); |
---|
1376 | bufSqrfFactors [k]= sqrfFactors; |
---|
1377 | } |
---|
1378 | |
---|
1379 | for (int i= 0; i < factors.length() - 1; i++) |
---|
1380 | { |
---|
1381 | for (k= i + 1; k < factors.length(); k++) |
---|
1382 | { |
---|
1383 | gcdFreeBasis (bufSqrfFactors [i], bufSqrfFactors[k]); |
---|
1384 | } |
---|
1385 | } |
---|
1386 | |
---|
1387 | factors= CFList(); |
---|
1388 | for (int i= 0; i < uniFactors.length(); i++) |
---|
1389 | { |
---|
1390 | if (i == 0) |
---|
1391 | { |
---|
1392 | for (iter= bufSqrfFactors [i]; iter.hasItem(); iter++) |
---|
1393 | { |
---|
1394 | if (iter.getItem().factor().inCoeffDomain()) |
---|
1395 | continue; |
---|
1396 | iter.getItem()= CFFactor (iter.getItem().factor()/ |
---|
1397 | Lc (iter.getItem().factor()), |
---|
1398 | iter.getItem().exp()); |
---|
1399 | factors.append (iter.getItem().factor()); |
---|
1400 | } |
---|
1401 | } |
---|
1402 | else |
---|
1403 | { |
---|
1404 | for (iter= bufSqrfFactors [i]; iter.hasItem(); iter++) |
---|
1405 | { |
---|
1406 | if (iter.getItem().factor().inCoeffDomain()) |
---|
1407 | continue; |
---|
1408 | iter.getItem()= CFFactor (iter.getItem().factor()/ |
---|
1409 | Lc (iter.getItem().factor()), |
---|
1410 | iter.getItem().exp()); |
---|
1411 | if (!find (factors, iter.getItem().factor())) |
---|
1412 | factors.append (iter.getItem().factor()); |
---|
1413 | } |
---|
1414 | } |
---|
1415 | } |
---|
1416 | |
---|
1417 | test= prod (factors); |
---|
1418 | tmp= evalSqrfPartF.getFirst() (evalPoint[0],2); |
---|
1419 | if (test/Lc (test) != tmp/Lc (tmp)) |
---|
1420 | return 0; |
---|
1421 | else |
---|
1422 | return 1; |
---|
1423 | } |
---|
1424 | |
---|
1425 | CFList |
---|
1426 | precomputeLeadingCoeff (const CanonicalForm& LCF, const CFList& LCFFactors, |
---|
1427 | const Variable& alpha, const CFList& evaluation, |
---|
1428 | CFList* & differentSecondVarLCs, int lSecondVarLCs, |
---|
1429 | Variable& y |
---|
1430 | ) |
---|
1431 | { |
---|
1432 | y= Variable (1); |
---|
1433 | if (LCF.inCoeffDomain()) |
---|
1434 | { |
---|
1435 | CFList result; |
---|
1436 | for (int i= 1; i <= LCFFactors.length() + 1; i++) |
---|
1437 | result.append (1); |
---|
1438 | return result; |
---|
1439 | } |
---|
1440 | |
---|
1441 | CFMap N, M; |
---|
1442 | CFArray dummy= CFArray (2); |
---|
1443 | dummy [0]= LCF; |
---|
1444 | dummy [1]= Variable (2); |
---|
1445 | compress (dummy, M, N); |
---|
1446 | CanonicalForm F= M (LCF); |
---|
1447 | if (LCF.isUnivariate()) |
---|
1448 | { |
---|
1449 | CFList result; |
---|
1450 | int LCFLevel= LCF.level(); |
---|
1451 | bool found= false; |
---|
1452 | if (LCFLevel == 2) |
---|
1453 | { |
---|
1454 | //bivariate leading coefficients are already the true leading coefficients |
---|
1455 | result= LCFFactors; |
---|
1456 | found= true; |
---|
1457 | } |
---|
1458 | else |
---|
1459 | { |
---|
1460 | CFListIterator j; |
---|
1461 | for (int i= 0; i < lSecondVarLCs; i++) |
---|
1462 | { |
---|
1463 | for (j= differentSecondVarLCs[i]; j.hasItem(); j++) |
---|
1464 | { |
---|
1465 | if (j.getItem().level() == LCFLevel) |
---|
1466 | { |
---|
1467 | found= true; |
---|
1468 | break; |
---|
1469 | } |
---|
1470 | } |
---|
1471 | if (found) |
---|
1472 | { |
---|
1473 | result= differentSecondVarLCs [i]; |
---|
1474 | break; |
---|
1475 | } |
---|
1476 | } |
---|
1477 | if (!found) |
---|
1478 | result= LCFFactors; |
---|
1479 | } |
---|
1480 | if (found) |
---|
1481 | result.insert (Lc (LCF)); |
---|
1482 | else |
---|
1483 | result.append (LCF); |
---|
1484 | return result; |
---|
1485 | } |
---|
1486 | |
---|
1487 | CFList factors= LCFFactors; |
---|
1488 | |
---|
1489 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
1490 | i.getItem()= M (i.getItem()); |
---|
1491 | |
---|
1492 | CanonicalForm sqrfPartF; |
---|
1493 | CFFList * bufSqrfFactors= new CFFList [factors.length()]; |
---|
1494 | CFList evalSqrfPartF, bufFactors; |
---|
1495 | CFArray evalPoint= CFArray (evaluation.length() - 1); |
---|
1496 | CFArray buf= CFArray (evaluation.length()); |
---|
1497 | CFArray swap= CFArray (evaluation.length()); |
---|
1498 | CFListIterator iter= evaluation; |
---|
1499 | CanonicalForm vars=getVars (LCF); |
---|
1500 | for (int i= evaluation.length() +1; i > 1; i--, iter++) |
---|
1501 | { |
---|
1502 | buf[i-2]=iter.getItem(); |
---|
1503 | if (degree (vars, i) > 0) |
---|
1504 | swap[M(Variable (i)).level()-1]=buf[i-2]; |
---|
1505 | } |
---|
1506 | buf= swap; |
---|
1507 | for (int i= 0; i < evaluation.length() - 1; i++) |
---|
1508 | evalPoint[i]= buf[i+1]; |
---|
1509 | |
---|
1510 | int pass= testFactors (F, factors, alpha, sqrfPartF, |
---|
1511 | bufFactors, bufSqrfFactors, evalSqrfPartF, evalPoint); |
---|
1512 | |
---|
1513 | bool foundDifferent= false; |
---|
1514 | Variable z, x= y; |
---|
1515 | int j= 0; |
---|
1516 | if (!pass) |
---|
1517 | { |
---|
1518 | int lev= 0; |
---|
1519 | // LCF is non-constant here |
---|
1520 | CFList bufBufFactors; |
---|
1521 | CanonicalForm bufF; |
---|
1522 | for (int i= 0; i < lSecondVarLCs; i++) |
---|
1523 | { |
---|
1524 | if (!differentSecondVarLCs [i].isEmpty()) |
---|
1525 | { |
---|
1526 | bool allConstant= true; |
---|
1527 | for (iter= differentSecondVarLCs[i]; iter.hasItem(); iter++) |
---|
1528 | { |
---|
1529 | if (!iter.getItem().inCoeffDomain()) |
---|
1530 | { |
---|
1531 | allConstant= false; |
---|
1532 | y= Variable (iter.getItem().level()); |
---|
1533 | lev= M(y).level(); |
---|
1534 | } |
---|
1535 | } |
---|
1536 | if (allConstant) |
---|
1537 | continue; |
---|
1538 | |
---|
1539 | bufFactors= differentSecondVarLCs [i]; |
---|
1540 | for (iter= bufFactors; iter.hasItem(); iter++) |
---|
1541 | iter.getItem()= swapvar (iter.getItem(), x, y); |
---|
1542 | bufF= F; |
---|
1543 | z= Variable (lev); |
---|
1544 | bufF= swapvar (bufF, x, z); |
---|
1545 | bufBufFactors= bufFactors; |
---|
1546 | evalPoint= CFArray (evaluation.length() - 1); |
---|
1547 | for (int k= 0; k < evaluation.length()-1; k++) |
---|
1548 | { |
---|
1549 | if (k+1 != lev) |
---|
1550 | evalPoint[k]= buf[k+1]; |
---|
1551 | else |
---|
1552 | evalPoint[k]= buf[0]; |
---|
1553 | } |
---|
1554 | pass= testFactors (bufF, bufBufFactors, alpha, sqrfPartF, bufFactors, |
---|
1555 | bufSqrfFactors, evalSqrfPartF, evalPoint); |
---|
1556 | if (pass) |
---|
1557 | { |
---|
1558 | foundDifferent= true; |
---|
1559 | F= bufF; |
---|
1560 | CFList l= factors; |
---|
1561 | for (iter= l; iter.hasItem(); iter++) |
---|
1562 | iter.getItem()= swapvar (iter.getItem(), x, y); |
---|
1563 | differentSecondVarLCs [i]= l; |
---|
1564 | j= i; |
---|
1565 | break; |
---|
1566 | } |
---|
1567 | if (!pass && i == lSecondVarLCs - 1) |
---|
1568 | { |
---|
1569 | CFList result; |
---|
1570 | result.append (LCF); |
---|
1571 | for (int k= 1; k <= factors.length(); k++) |
---|
1572 | result.append (LCF); |
---|
1573 | y= Variable (1); |
---|
1574 | delete [] bufSqrfFactors; |
---|
1575 | return result; |
---|
1576 | } |
---|
1577 | } |
---|
1578 | } |
---|
1579 | } |
---|
1580 | if (!pass) |
---|
1581 | { |
---|
1582 | CFList result; |
---|
1583 | result.append (LCF); |
---|
1584 | for (int k= 1; k <= factors.length(); k++) |
---|
1585 | result.append (LCF); |
---|
1586 | y= Variable (1); |
---|
1587 | delete [] bufSqrfFactors; |
---|
1588 | return result; |
---|
1589 | } |
---|
1590 | else |
---|
1591 | factors= bufFactors; |
---|
1592 | |
---|
1593 | bufFactors= factors; |
---|
1594 | CFList evaluation2; |
---|
1595 | for (int i= 0; i < F.level()-1; i++) |
---|
1596 | evaluation2.insert (evalPoint[i]); |
---|
1597 | |
---|
1598 | CFList interMedResult; |
---|
1599 | CanonicalForm oldSqrfPartF= sqrfPartF; |
---|
1600 | sqrfPartF= shift2Zero (sqrfPartF, evalSqrfPartF, evaluation2); |
---|
1601 | if (factors.length() > 1) |
---|
1602 | { |
---|
1603 | CanonicalForm LC1= LC (oldSqrfPartF, 1); |
---|
1604 | CFList leadingCoeffs; |
---|
1605 | for (int i= 0; i < factors.length(); i++) |
---|
1606 | leadingCoeffs.append (LC1); |
---|
1607 | |
---|
1608 | CFList LC1eval= evaluateAtEval (LC1, evaluation2, 2); |
---|
1609 | CFList oldFactors= factors; |
---|
1610 | for (CFListIterator i= oldFactors; i.hasItem(); i++) |
---|
1611 | i.getItem() *= LC1eval.getFirst()/Lc (i.getItem()); |
---|
1612 | |
---|
1613 | bool success= false; |
---|
1614 | CanonicalForm oldSqrfPartFPowLC= oldSqrfPartF*power(LC1,factors.length()-1); |
---|
1615 | if (size (oldSqrfPartFPowLC)/getNumVars (oldSqrfPartFPowLC) < 500 && |
---|
1616 | LucksWangSparseHeuristic (oldSqrfPartFPowLC, |
---|
1617 | oldFactors, 2, leadingCoeffs, factors)) |
---|
1618 | { |
---|
1619 | interMedResult= recoverFactors (oldSqrfPartF, factors); |
---|
1620 | if (oldFactors.length() == interMedResult.length()) |
---|
1621 | success= true; |
---|
1622 | } |
---|
1623 | if (!success) |
---|
1624 | { |
---|
1625 | LC1= LC (evalSqrfPartF.getFirst(), 1); |
---|
1626 | |
---|
1627 | CFArray leadingCoeffs= CFArray (factors.length()); |
---|
1628 | for (int i= 0; i < factors.length(); i++) |
---|
1629 | leadingCoeffs[i]= LC1; |
---|
1630 | |
---|
1631 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
1632 | i.getItem() *= LC1 (0,2)/Lc (i.getItem()); |
---|
1633 | factors.insert (1); |
---|
1634 | |
---|
1635 | CanonicalForm |
---|
1636 | newSqrfPartF= evalSqrfPartF.getFirst()*power (LC1, factors.length() - 2); |
---|
1637 | |
---|
1638 | int liftBound= degree (newSqrfPartF,2) + 1; |
---|
1639 | |
---|
1640 | CFMatrix M= CFMatrix (liftBound, factors.length() - 1); |
---|
1641 | CFArray Pi; |
---|
1642 | CFList diophant; |
---|
1643 | nonMonicHenselLift12 (newSqrfPartF, factors, liftBound, Pi, diophant, M, |
---|
1644 | leadingCoeffs, false); |
---|
1645 | |
---|
1646 | if (sqrfPartF.level() > 2) |
---|
1647 | { |
---|
1648 | int* liftBounds= new int [sqrfPartF.level() - 1]; |
---|
1649 | liftBounds [0]= liftBound; |
---|
1650 | bool noOneToOne= false; |
---|
1651 | CFList *leadingCoeffs2= new CFList [sqrfPartF.level()-2]; |
---|
1652 | LC1= LC (evalSqrfPartF.getLast(), 1); |
---|
1653 | CFList LCs; |
---|
1654 | for (int i= 0; i < factors.length(); i++) |
---|
1655 | LCs.append (LC1); |
---|
1656 | leadingCoeffs2 [sqrfPartF.level() - 3]= LCs; |
---|
1657 | for (int i= sqrfPartF.level() - 1; i > 2; i--) |
---|
1658 | { |
---|
1659 | for (CFListIterator j= LCs; j.hasItem(); j++) |
---|
1660 | j.getItem()= j.getItem() (0, i + 1); |
---|
1661 | leadingCoeffs2 [i - 3]= LCs; |
---|
1662 | } |
---|
1663 | sqrfPartF *= power (LC1, factors.length()-1); |
---|
1664 | |
---|
1665 | int liftBoundsLength= sqrfPartF.level() - 1; |
---|
1666 | for (int i= 1; i < liftBoundsLength; i++) |
---|
1667 | liftBounds [i]= degree (sqrfPartF, i + 2) + 1; |
---|
1668 | evalSqrfPartF= evaluateAtZero (sqrfPartF); |
---|
1669 | evalSqrfPartF.removeFirst(); |
---|
1670 | factors= nonMonicHenselLift (evalSqrfPartF, factors, leadingCoeffs2, |
---|
1671 | diophant, Pi, liftBounds, sqrfPartF.level() - 1, noOneToOne); |
---|
1672 | delete [] leadingCoeffs2; |
---|
1673 | delete [] liftBounds; |
---|
1674 | } |
---|
1675 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
1676 | iter.getItem()= reverseShift (iter.getItem(), evaluation2); |
---|
1677 | |
---|
1678 | interMedResult= |
---|
1679 | recoverFactors (reverseShift(evalSqrfPartF.getLast(),evaluation2), |
---|
1680 | factors); |
---|
1681 | } |
---|
1682 | } |
---|
1683 | else |
---|
1684 | { |
---|
1685 | CanonicalForm contF=content (oldSqrfPartF,1); |
---|
1686 | factors= CFList (oldSqrfPartF/contF); |
---|
1687 | interMedResult= recoverFactors (oldSqrfPartF, factors); |
---|
1688 | } |
---|
1689 | |
---|
1690 | CFList result; |
---|
1691 | CFFListIterator k; |
---|
1692 | for (int i= 0; i < LCFFactors.length(); i++) |
---|
1693 | { |
---|
1694 | CanonicalForm tmp= 1; |
---|
1695 | for (k= bufSqrfFactors[i]; k.hasItem(); k++) |
---|
1696 | { |
---|
1697 | int pos= findItem (bufFactors, k.getItem().factor()); |
---|
1698 | if (pos) |
---|
1699 | tmp *= power (getItem (interMedResult, pos), k.getItem().exp()); |
---|
1700 | } |
---|
1701 | result.append (tmp); |
---|
1702 | } |
---|
1703 | |
---|
1704 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
1705 | { |
---|
1706 | F /= i.getItem(); |
---|
1707 | if (foundDifferent) |
---|
1708 | i.getItem()= swapvar (i.getItem(), x, z); |
---|
1709 | i.getItem()= N (i.getItem()); |
---|
1710 | } |
---|
1711 | |
---|
1712 | if (foundDifferent) |
---|
1713 | { |
---|
1714 | CFList l= differentSecondVarLCs [j]; |
---|
1715 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
1716 | i.getItem()= swapvar (i.getItem(), y, z); |
---|
1717 | differentSecondVarLCs [j]= l; |
---|
1718 | F= swapvar (F, x, z); |
---|
1719 | } |
---|
1720 | |
---|
1721 | result.insert (N (F)); |
---|
1722 | |
---|
1723 | result= distributeContent (result, differentSecondVarLCs, lSecondVarLCs); |
---|
1724 | |
---|
1725 | if (!result.getFirst().inCoeffDomain()) |
---|
1726 | { |
---|
1727 | CFListIterator i= result; |
---|
1728 | CanonicalForm tmp; |
---|
1729 | if (foundDifferent) |
---|
1730 | i.getItem()= swapvar (i.getItem(), Variable (2), y); |
---|
1731 | |
---|
1732 | tmp= i.getItem(); |
---|
1733 | |
---|
1734 | i++; |
---|
1735 | for (; i.hasItem(); i++) |
---|
1736 | { |
---|
1737 | if (foundDifferent) |
---|
1738 | i.getItem()= swapvar (i.getItem(), Variable (2), y)*tmp; |
---|
1739 | else |
---|
1740 | i.getItem() *= tmp; |
---|
1741 | } |
---|
1742 | } |
---|
1743 | else |
---|
1744 | y= Variable (1); |
---|
1745 | |
---|
1746 | delete [] bufSqrfFactors; |
---|
1747 | |
---|
1748 | return result; |
---|
1749 | } |
---|
1750 | |
---|
1751 | void |
---|
1752 | evaluationWRTDifferentSecondVars (CFList*& Aeval, const CFList& evaluation, |
---|
1753 | const CanonicalForm& A) |
---|
1754 | { |
---|
1755 | CanonicalForm tmp; |
---|
1756 | CFList tmp2; |
---|
1757 | CFListIterator iter; |
---|
1758 | for (int i= A.level(); i > 2; i--) |
---|
1759 | { |
---|
1760 | tmp= A; |
---|
1761 | tmp2= CFList(); |
---|
1762 | iter= evaluation; |
---|
1763 | bool preserveDegree= true; |
---|
1764 | for (int j= A.level(); j > 1; j--, iter++) |
---|
1765 | { |
---|
1766 | if (j == i) |
---|
1767 | continue; |
---|
1768 | else |
---|
1769 | { |
---|
1770 | tmp= tmp (iter.getItem(), j); |
---|
1771 | tmp2.insert (tmp); |
---|
1772 | if ((degree (tmp, i) != degree (A, i)) || |
---|
1773 | (degree (tmp, 1) != degree (A, 1))) |
---|
1774 | { |
---|
1775 | preserveDegree= false; |
---|
1776 | break; |
---|
1777 | } |
---|
1778 | if (!content(tmp).inCoeffDomain() || !content(tmp,1).inCoeffDomain()) |
---|
1779 | { |
---|
1780 | preserveDegree= false; |
---|
1781 | break; |
---|
1782 | } |
---|
1783 | } |
---|
1784 | } |
---|
1785 | if (preserveDegree) |
---|
1786 | Aeval [i - 3]= tmp2; |
---|
1787 | else |
---|
1788 | Aeval [i - 3]= CFList(); |
---|
1789 | } |
---|
1790 | } |
---|
1791 | |
---|
1792 | #endif |
---|
1793 | |
---|
1794 | static inline |
---|
1795 | CanonicalForm prodEval (const CFList& l, const CanonicalForm& evalPoint, |
---|
1796 | const Variable& v) |
---|
1797 | { |
---|
1798 | CanonicalForm result= 1; |
---|
1799 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
1800 | result *= i.getItem() (evalPoint, v); |
---|
1801 | return result; |
---|
1802 | } |
---|
1803 | |
---|
1804 | //recombine bivariate factors in case one bivariate factorization yields less |
---|
1805 | // factors than the other |
---|
1806 | CFList |
---|
1807 | recombination (const CFList& factors1, const CFList& factors2, int s, int thres, |
---|
1808 | const CanonicalForm& evalPoint, const Variable& x) |
---|
1809 | { |
---|
1810 | CFList T, S; |
---|
1811 | |
---|
1812 | T= factors1; |
---|
1813 | CFList result; |
---|
1814 | CanonicalForm buf; |
---|
1815 | int * v= new int [T.length()]; |
---|
1816 | for (int i= 0; i < T.length(); i++) |
---|
1817 | v[i]= 0; |
---|
1818 | bool nosubset= false; |
---|
1819 | CFArray TT; |
---|
1820 | TT= copy (factors1); |
---|
1821 | while (T.length() >= 2*s && s <= thres) |
---|
1822 | { |
---|
1823 | while (nosubset == false) |
---|
1824 | { |
---|
1825 | if (T.length() == s) |
---|
1826 | { |
---|
1827 | delete [] v; |
---|
1828 | result.append (prod (T)); |
---|
1829 | return result; |
---|
1830 | } |
---|
1831 | S= subset (v, s, TT, nosubset); |
---|
1832 | if (nosubset) break; |
---|
1833 | buf= prodEval (S, evalPoint, x); |
---|
1834 | buf /= Lc (buf); |
---|
1835 | if (find (factors2, buf)) |
---|
1836 | { |
---|
1837 | T= Difference (T, S); |
---|
1838 | result.append (prod (S)); |
---|
1839 | TT= copy (T); |
---|
1840 | indexUpdate (v, s, T.length(), nosubset); |
---|
1841 | if (nosubset) break; |
---|
1842 | } |
---|
1843 | } |
---|
1844 | s++; |
---|
1845 | if (T.length() < 2*s || T.length() == s) |
---|
1846 | { |
---|
1847 | delete [] v; |
---|
1848 | result.append (prod (T)); |
---|
1849 | return result; |
---|
1850 | } |
---|
1851 | for (int i= 0; i < T.length(); i++) |
---|
1852 | v[i]= 0; |
---|
1853 | nosubset= false; |
---|
1854 | } |
---|
1855 | |
---|
1856 | delete [] v; |
---|
1857 | if (T.length() < 2*s) |
---|
1858 | { |
---|
1859 | result.append (prod (T)); |
---|
1860 | return result; |
---|
1861 | } |
---|
1862 | |
---|
1863 | return result; |
---|
1864 | } |
---|
1865 | |
---|
1866 | #ifdef HAVE_NTL |
---|
1867 | void |
---|
1868 | factorizationWRTDifferentSecondVars (const CanonicalForm& A, CFList*& Aeval, |
---|
1869 | const ExtensionInfo& info, |
---|
1870 | int& minFactorsLength, bool& irred) |
---|
1871 | { |
---|
1872 | Variable x= Variable (1); |
---|
1873 | minFactorsLength= 0; |
---|
1874 | irred= false; |
---|
1875 | CFList factors; |
---|
1876 | Variable v; |
---|
1877 | for (int j= 0; j < A.level() - 2; j++) |
---|
1878 | { |
---|
1879 | if (!Aeval[j].isEmpty()) |
---|
1880 | { |
---|
1881 | v= Variable (Aeval[j].getFirst().level()); |
---|
1882 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
1883 | factors= GFBiSqrfFactorize (Aeval[j].getFirst()); |
---|
1884 | else if (info.getAlpha().level() == 1) |
---|
1885 | factors= FpBiSqrfFactorize (Aeval[j].getFirst()); |
---|
1886 | else |
---|
1887 | factors= FqBiSqrfFactorize (Aeval[j].getFirst(), info.getAlpha()); |
---|
1888 | |
---|
1889 | factors.removeFirst(); |
---|
1890 | if (minFactorsLength == 0) |
---|
1891 | minFactorsLength= factors.length(); |
---|
1892 | else |
---|
1893 | minFactorsLength= tmin (minFactorsLength, factors.length()); |
---|
1894 | |
---|
1895 | if (factors.length() == 1) |
---|
1896 | { |
---|
1897 | irred= true; |
---|
1898 | return; |
---|
1899 | } |
---|
1900 | sortList (factors, x); |
---|
1901 | Aeval [j]= factors; |
---|
1902 | } |
---|
1903 | } |
---|
1904 | } |
---|
1905 | |
---|
1906 | CFList conv (const CFArray & A) |
---|
1907 | { |
---|
1908 | CFList result; |
---|
1909 | for (int i= A.max(); i >= A.min(); i--) |
---|
1910 | result.insert (A[i]); |
---|
1911 | return result; |
---|
1912 | } |
---|
1913 | |
---|
1914 | void getLeadingCoeffs (const CanonicalForm& A, CFList*& Aeval, |
---|
1915 | const CFList& uniFactors, const CFList& evaluation |
---|
1916 | ) |
---|
1917 | { |
---|
1918 | CanonicalForm evalPoint; |
---|
1919 | int i; |
---|
1920 | CFListIterator iter, iter2; |
---|
1921 | Variable v; |
---|
1922 | CFList LCs, buf; |
---|
1923 | CFArray l; |
---|
1924 | int pos, index; |
---|
1925 | for (int j= 0; j < A.level() - 2; j++) |
---|
1926 | { |
---|
1927 | if (!Aeval[j].isEmpty()) |
---|
1928 | { |
---|
1929 | i= A.level(); |
---|
1930 | for (iter= evaluation; iter.hasItem(); iter++, i--) |
---|
1931 | { |
---|
1932 | if (i == Aeval[j].getFirst().level()) |
---|
1933 | { |
---|
1934 | evalPoint= iter.getItem(); |
---|
1935 | break; |
---|
1936 | } |
---|
1937 | } |
---|
1938 | |
---|
1939 | v= Variable (i); |
---|
1940 | if (Aeval[j].length() > uniFactors.length()) |
---|
1941 | Aeval[j]= recombination (Aeval[j], uniFactors, 1, |
---|
1942 | Aeval[j].length() - uniFactors.length() + 1, |
---|
1943 | evalPoint, v); |
---|
1944 | |
---|
1945 | buf= buildUniFactors (Aeval[j], evalPoint, v); |
---|
1946 | l= CFArray (uniFactors.length()); |
---|
1947 | index= 1; |
---|
1948 | for (iter= buf; iter.hasItem(); iter++, index++) |
---|
1949 | { |
---|
1950 | pos= findItem (uniFactors, iter.getItem()); |
---|
1951 | if (pos) |
---|
1952 | l[pos-1]= getItem (Aeval[j], index); |
---|
1953 | } |
---|
1954 | buf= conv (l); |
---|
1955 | Aeval [j]= buf; |
---|
1956 | |
---|
1957 | buf= buildUniFactors (Aeval[j], evalPoint, v); |
---|
1958 | LCs= CFList(); |
---|
1959 | for (iter= Aeval[j]; iter.hasItem(); iter++) |
---|
1960 | LCs.append (LC (iter.getItem(), 1)); |
---|
1961 | //normalize (LCs); |
---|
1962 | Aeval[j]= LCs; |
---|
1963 | } |
---|
1964 | } |
---|
1965 | } |
---|
1966 | |
---|
1967 | CFList |
---|
1968 | buildUniFactors (const CFList& biFactors, const CanonicalForm& evalPoint, |
---|
1969 | const Variable& y) |
---|
1970 | { |
---|
1971 | CFList result; |
---|
1972 | CanonicalForm tmp; |
---|
1973 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
1974 | { |
---|
1975 | tmp= mod (i.getItem(), y - evalPoint); |
---|
1976 | tmp /= Lc (tmp); |
---|
1977 | result.append (tmp); |
---|
1978 | } |
---|
1979 | return result; |
---|
1980 | } |
---|
1981 | |
---|
1982 | void refineBiFactors (const CanonicalForm& A, CFList& biFactors, |
---|
1983 | CFList* const& Aeval, const CFList& evaluation, |
---|
1984 | int minFactorsLength) |
---|
1985 | { |
---|
1986 | CFListIterator iter; |
---|
1987 | CanonicalForm evalPoint; |
---|
1988 | int i; |
---|
1989 | Variable v; |
---|
1990 | Variable y= Variable (2); |
---|
1991 | CFList list; |
---|
1992 | for (int j= 0; j < A.level() - 2; j++) |
---|
1993 | { |
---|
1994 | if (Aeval[j].length() == minFactorsLength) |
---|
1995 | { |
---|
1996 | i= A.level(); |
---|
1997 | |
---|
1998 | for (iter= evaluation; iter.hasItem(); iter++, i--) |
---|
1999 | { |
---|
2000 | if (i == Aeval[j].getFirst().level()) |
---|
2001 | { |
---|
2002 | evalPoint= iter.getItem(); |
---|
2003 | break; |
---|
2004 | } |
---|
2005 | } |
---|
2006 | |
---|
2007 | v= Variable (i); |
---|
2008 | list= buildUniFactors (Aeval[j], evalPoint, v); |
---|
2009 | |
---|
2010 | biFactors= recombination (biFactors, list, 1, |
---|
2011 | biFactors.length() - list.length() + 1, |
---|
2012 | evaluation.getLast(), y); |
---|
2013 | return; |
---|
2014 | } |
---|
2015 | } |
---|
2016 | } |
---|
2017 | |
---|
2018 | void prepareLeadingCoeffs (CFList*& LCs, int n, const CFList& leadingCoeffs, |
---|
2019 | const CFList& biFactors, const CFList& evaluation) |
---|
2020 | { |
---|
2021 | CFList l= leadingCoeffs; |
---|
2022 | LCs [n-3]= l; |
---|
2023 | CFListIterator j; |
---|
2024 | CFListIterator iter= evaluation; |
---|
2025 | for (int i= n - 1; i > 2; i--, iter++) |
---|
2026 | { |
---|
2027 | for (j= l; j.hasItem(); j++) |
---|
2028 | j.getItem()= j.getItem() (iter.getItem(), i + 1); |
---|
2029 | LCs [i - 3]= l; |
---|
2030 | } |
---|
2031 | l= LCs [0]; |
---|
2032 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
2033 | i.getItem()= i.getItem() (iter.getItem(), 3); |
---|
2034 | CFListIterator ii= biFactors; |
---|
2035 | CFList normalizeFactor; |
---|
2036 | for (CFListIterator i= l; i.hasItem(); i++, ii++) |
---|
2037 | normalizeFactor.append (Lc (LC (ii.getItem(), 1))/Lc (i.getItem())); |
---|
2038 | for (int i= 0; i < n-2; i++) |
---|
2039 | { |
---|
2040 | ii= normalizeFactor; |
---|
2041 | for (j= LCs [i]; j.hasItem(); j++, ii++) |
---|
2042 | j.getItem() *= ii.getItem(); |
---|
2043 | } |
---|
2044 | } |
---|
2045 | |
---|
2046 | CFList recoverFactors (const CanonicalForm& F, const CFList& factors) |
---|
2047 | { |
---|
2048 | CFList result; |
---|
2049 | CanonicalForm tmp, tmp2; |
---|
2050 | CanonicalForm G= F; |
---|
2051 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
2052 | { |
---|
2053 | tmp= i.getItem()/content (i.getItem(), 1); |
---|
2054 | if (fdivides (tmp, G, tmp2)) |
---|
2055 | { |
---|
2056 | G= tmp2; |
---|
2057 | result.append (tmp); |
---|
2058 | } |
---|
2059 | } |
---|
2060 | return result; |
---|
2061 | } |
---|
2062 | |
---|
2063 | CFList recoverFactors (const CanonicalForm& F, const CFList& factors, |
---|
2064 | const CFList& evaluation) |
---|
2065 | { |
---|
2066 | CFList result; |
---|
2067 | CanonicalForm tmp, tmp2; |
---|
2068 | CanonicalForm G= F; |
---|
2069 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
2070 | { |
---|
2071 | tmp= reverseShift (i.getItem(), evaluation); |
---|
2072 | tmp /= content (tmp, 1); |
---|
2073 | if (fdivides (tmp, G, tmp2)) |
---|
2074 | { |
---|
2075 | G= tmp2; |
---|
2076 | result.append (tmp); |
---|
2077 | } |
---|
2078 | } |
---|
2079 | return result; |
---|
2080 | } |
---|
2081 | |
---|
2082 | CFList |
---|
2083 | extNonMonicFactorRecombination (const CFList& factors, const CanonicalForm& F, |
---|
2084 | const ExtensionInfo& info) |
---|
2085 | { |
---|
2086 | Variable alpha= info.getAlpha(); |
---|
2087 | Variable beta= info.getBeta(); |
---|
2088 | CanonicalForm gamma= info.getGamma(); |
---|
2089 | CanonicalForm delta= info.getDelta(); |
---|
2090 | int k= info.getGFDegree(); |
---|
2091 | CFList source, dest; |
---|
2092 | |
---|
2093 | int degMipoBeta= 1; |
---|
2094 | if (!k && beta != Variable(1)) |
---|
2095 | degMipoBeta= degree (getMipo (beta)); |
---|
2096 | |
---|
2097 | CFList T, S; |
---|
2098 | T= factors; |
---|
2099 | int s= 1; |
---|
2100 | CFList result; |
---|
2101 | CanonicalForm quot, buf= F; |
---|
2102 | |
---|
2103 | CanonicalForm g; |
---|
2104 | CanonicalForm buf2; |
---|
2105 | int * v= new int [T.length()]; |
---|
2106 | for (int i= 0; i < T.length(); i++) |
---|
2107 | v[i]= 0; |
---|
2108 | bool noSubset= false; |
---|
2109 | CFArray TT; |
---|
2110 | TT= copy (factors); |
---|
2111 | bool recombination= false; |
---|
2112 | bool trueFactor= false; |
---|
2113 | while (T.length() >= 2*s) |
---|
2114 | { |
---|
2115 | while (noSubset == false) |
---|
2116 | { |
---|
2117 | if (T.length() == s) |
---|
2118 | { |
---|
2119 | delete [] v; |
---|
2120 | if (recombination) |
---|
2121 | { |
---|
2122 | g= prod (T); |
---|
2123 | T.removeFirst(); |
---|
2124 | result.append (g/myContent (g)); |
---|
2125 | g /= Lc (g); |
---|
2126 | appendTestMapDown (result, g, info, source, dest); |
---|
2127 | return result; |
---|
2128 | } |
---|
2129 | else |
---|
2130 | return CFList (buf/myContent(buf)); |
---|
2131 | } |
---|
2132 | |
---|
2133 | S= subset (v, s, TT, noSubset); |
---|
2134 | if (noSubset) break; |
---|
2135 | |
---|
2136 | g= prod (S); |
---|
2137 | g /= myContent (g); |
---|
2138 | if (fdivides (g, buf, quot)) |
---|
2139 | { |
---|
2140 | buf2= g; |
---|
2141 | buf2 /= Lc (buf2); |
---|
2142 | if (!k && beta.level() == 1) |
---|
2143 | { |
---|
2144 | if (degree (buf2, alpha) < degMipoBeta) |
---|
2145 | { |
---|
2146 | appendTestMapDown (result, buf2, info, source, dest); |
---|
2147 | buf= quot; |
---|
2148 | recombination= true; |
---|
2149 | trueFactor= true; |
---|
2150 | } |
---|
2151 | } |
---|
2152 | else |
---|
2153 | { |
---|
2154 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
2155 | { |
---|
2156 | appendTestMapDown (result, buf2, info, source, dest); |
---|
2157 | buf= quot; |
---|
2158 | recombination= true; |
---|
2159 | trueFactor= true; |
---|
2160 | } |
---|
2161 | } |
---|
2162 | if (trueFactor) |
---|
2163 | { |
---|
2164 | T= Difference (T, S); |
---|
2165 | |
---|
2166 | if (T.length() < 2*s || T.length() == s) |
---|
2167 | { |
---|
2168 | delete [] v; |
---|
2169 | buf /= myContent (buf); |
---|
2170 | buf /= Lc (buf); |
---|
2171 | appendTestMapDown (result, buf, info, source, dest); |
---|
2172 | return result; |
---|
2173 | } |
---|
2174 | trueFactor= false; |
---|
2175 | TT= copy (T); |
---|
2176 | indexUpdate (v, s, T.length(), noSubset); |
---|
2177 | if (noSubset) break; |
---|
2178 | } |
---|
2179 | } |
---|
2180 | } |
---|
2181 | s++; |
---|
2182 | if (T.length() < 2*s || T.length() == s) |
---|
2183 | { |
---|
2184 | delete [] v; |
---|
2185 | appendTestMapDown (result, buf/myContent(buf), info, source, dest); |
---|
2186 | return result; |
---|
2187 | } |
---|
2188 | for (int i= 0; i < T.length(); i++) |
---|
2189 | v[i]= 0; |
---|
2190 | noSubset= false; |
---|
2191 | } |
---|
2192 | if (T.length() < 2*s) |
---|
2193 | appendMapDown (result, F/myContent(F), info, source, dest); |
---|
2194 | |
---|
2195 | delete [] v; |
---|
2196 | return result; |
---|
2197 | } |
---|
2198 | |
---|
2199 | CFList |
---|
2200 | extFactorize (const CanonicalForm& F, const ExtensionInfo& info); |
---|
2201 | |
---|
2202 | CFList |
---|
2203 | multiFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
2204 | { |
---|
2205 | |
---|
2206 | if (F.inCoeffDomain()) |
---|
2207 | return CFList (F); |
---|
2208 | |
---|
2209 | // compress and find main Variable |
---|
2210 | CFMap N; |
---|
2211 | CanonicalForm A= myCompress (F, N); |
---|
2212 | |
---|
2213 | A /= Lc (A); // make monic |
---|
2214 | |
---|
2215 | Variable alpha= info.getAlpha(); |
---|
2216 | Variable beta= info.getBeta(); |
---|
2217 | CanonicalForm gamma= info.getGamma(); |
---|
2218 | CanonicalForm delta= info.getDelta(); |
---|
2219 | bool extension= info.isInExtension(); |
---|
2220 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
2221 | //univariate case |
---|
2222 | if (F.isUnivariate()) |
---|
2223 | { |
---|
2224 | if (extension == false) |
---|
2225 | return uniFactorizer (F, alpha, GF); |
---|
2226 | else |
---|
2227 | { |
---|
2228 | CFList source, dest; |
---|
2229 | A= mapDown (F, info, source, dest); |
---|
2230 | return uniFactorizer (A, beta, GF); |
---|
2231 | } |
---|
2232 | } |
---|
2233 | |
---|
2234 | //bivariate case |
---|
2235 | if (A.level() == 2) |
---|
2236 | { |
---|
2237 | CFList buf= biFactorize (F, info); |
---|
2238 | return buf; |
---|
2239 | } |
---|
2240 | |
---|
2241 | Variable x= Variable (1); |
---|
2242 | Variable y= Variable (2); |
---|
2243 | |
---|
2244 | // remove content |
---|
2245 | CFList contentAi; |
---|
2246 | CanonicalForm lcmCont= lcmContent (A, contentAi); |
---|
2247 | A /= lcmCont; |
---|
2248 | |
---|
2249 | // trivial after content removal |
---|
2250 | CFList contentAFactors; |
---|
2251 | if (A.inCoeffDomain()) |
---|
2252 | { |
---|
2253 | for (CFListIterator i= contentAi; i.hasItem(); i++) |
---|
2254 | { |
---|
2255 | if (i.getItem().inCoeffDomain()) |
---|
2256 | continue; |
---|
2257 | else |
---|
2258 | { |
---|
2259 | lcmCont /= i.getItem(); |
---|
2260 | contentAFactors= |
---|
2261 | Union (multiFactorize (lcmCont, info), |
---|
2262 | multiFactorize (i.getItem(), info)); |
---|
2263 | break; |
---|
2264 | } |
---|
2265 | } |
---|
2266 | decompress (contentAFactors, N); |
---|
2267 | normalize (contentAFactors); |
---|
2268 | return contentAFactors; |
---|
2269 | } |
---|
2270 | |
---|
2271 | // factorize content |
---|
2272 | contentAFactors= multiFactorize (lcmCont, info); |
---|
2273 | |
---|
2274 | // univariate after content removal |
---|
2275 | CFList factors; |
---|
2276 | if (A.isUnivariate ()) |
---|
2277 | { |
---|
2278 | factors= uniFactorizer (A, alpha, GF); |
---|
2279 | append (factors, contentAFactors); |
---|
2280 | decompress (factors, N); |
---|
2281 | return factors; |
---|
2282 | } |
---|
2283 | |
---|
2284 | // check main variable |
---|
2285 | int swapLevel= 0; |
---|
2286 | CanonicalForm derivZ; |
---|
2287 | CanonicalForm gcdDerivZ; |
---|
2288 | CanonicalForm bufA= A; |
---|
2289 | Variable z; |
---|
2290 | for (int i= 1; i <= A.level(); i++) |
---|
2291 | { |
---|
2292 | z= Variable (i); |
---|
2293 | derivZ= deriv (bufA, z); |
---|
2294 | if (derivZ.isZero()) |
---|
2295 | { |
---|
2296 | if (i == 1) |
---|
2297 | swapLevel= 1; |
---|
2298 | else |
---|
2299 | continue; |
---|
2300 | } |
---|
2301 | else |
---|
2302 | { |
---|
2303 | if (swapLevel == 1) |
---|
2304 | { |
---|
2305 | swapLevel= i; |
---|
2306 | bufA= swapvar (A, x, z); |
---|
2307 | } |
---|
2308 | gcdDerivZ= gcd (bufA, derivZ); |
---|
2309 | if (degree (gcdDerivZ) > 0 && !derivZ.isZero()) |
---|
2310 | { |
---|
2311 | CanonicalForm g= bufA/gcdDerivZ; |
---|
2312 | CFList factorsG= |
---|
2313 | Union (multiFactorize (g, info), |
---|
2314 | multiFactorize (gcdDerivZ, info)); |
---|
2315 | appendSwapDecompress (factorsG, contentAFactors, N, swapLevel, x); |
---|
2316 | normalize (factorsG); |
---|
2317 | return factorsG; |
---|
2318 | } |
---|
2319 | else |
---|
2320 | { |
---|
2321 | A= bufA; |
---|
2322 | break; |
---|
2323 | } |
---|
2324 | } |
---|
2325 | } |
---|
2326 | |
---|
2327 | |
---|
2328 | CFList Aeval, list, evaluation, bufEvaluation, bufAeval; |
---|
2329 | bool fail= false; |
---|
2330 | int swapLevel2= 0; |
---|
2331 | int level; |
---|
2332 | int factorNums= 3; |
---|
2333 | CanonicalForm bivarEval; |
---|
2334 | CFList biFactors, bufBiFactors; |
---|
2335 | CanonicalForm evalPoly; |
---|
2336 | int lift, bufLift; |
---|
2337 | double logarithm= (double) ilog2 (totaldegree (A)); |
---|
2338 | logarithm /= log2exp; |
---|
2339 | logarithm= ceil (logarithm); |
---|
2340 | if (factorNums < (int) logarithm) |
---|
2341 | factorNums= (int) logarithm; |
---|
2342 | CFList* bufAeval2= new CFList [A.level() - 2]; |
---|
2343 | CFList* Aeval2= new CFList [A.level() - 2]; |
---|
2344 | int counter; |
---|
2345 | int differentSecondVar= 0; |
---|
2346 | // several bivariate factorizations |
---|
2347 | for (int i= 0; i < factorNums; i++) |
---|
2348 | { |
---|
2349 | counter= 0; |
---|
2350 | bufA= A; |
---|
2351 | bufAeval= CFList(); |
---|
2352 | bufEvaluation= evalPoints (bufA, bufAeval, alpha, list, GF, fail); |
---|
2353 | evalPoly= 0; |
---|
2354 | |
---|
2355 | if (fail && (i == 0)) |
---|
2356 | { |
---|
2357 | if (!swapLevel) |
---|
2358 | level= 2; |
---|
2359 | else |
---|
2360 | level= swapLevel + 1; |
---|
2361 | |
---|
2362 | CanonicalForm g; |
---|
2363 | swapLevel2= newMainVariableSearch (A, Aeval, evaluation, alpha, level, g); |
---|
2364 | |
---|
2365 | if (!swapLevel2) // need to pass to an extension |
---|
2366 | { |
---|
2367 | factors= extFactorize (A, info); |
---|
2368 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, x); |
---|
2369 | normalize (factors); |
---|
2370 | delete [] bufAeval2; |
---|
2371 | delete [] Aeval2; |
---|
2372 | return factors; |
---|
2373 | } |
---|
2374 | else |
---|
2375 | { |
---|
2376 | if (swapLevel2 == -1) |
---|
2377 | { |
---|
2378 | CFList factorsG= |
---|
2379 | Union (multiFactorize (g, info), |
---|
2380 | multiFactorize (A/g, info)); |
---|
2381 | appendSwapDecompress (factorsG, contentAFactors, N, swapLevel, x); |
---|
2382 | normalize (factorsG); |
---|
2383 | delete [] bufAeval2; |
---|
2384 | delete [] Aeval2; |
---|
2385 | return factorsG; |
---|
2386 | } |
---|
2387 | fail= false; |
---|
2388 | bufAeval= Aeval; |
---|
2389 | bufA= A; |
---|
2390 | bufEvaluation= evaluation; |
---|
2391 | } |
---|
2392 | } |
---|
2393 | else if (fail && (i > 0)) |
---|
2394 | break; |
---|
2395 | |
---|
2396 | bivarEval= bufEvaluation.getLast(); |
---|
2397 | |
---|
2398 | evaluationWRTDifferentSecondVars (bufAeval2, bufEvaluation, A); |
---|
2399 | |
---|
2400 | for (int j= 0; j < A.level() - 2; j++) |
---|
2401 | { |
---|
2402 | if (!bufAeval2[j].isEmpty()) |
---|
2403 | counter++; |
---|
2404 | } |
---|
2405 | |
---|
2406 | bufLift= degree (A, y) + 1 + degree (LC(A, x), y); |
---|
2407 | |
---|
2408 | TIMING_START (fac_fq_bi_factorizer); |
---|
2409 | if (!GF && alpha.level() == 1) |
---|
2410 | bufBiFactors= FpBiSqrfFactorize (bufAeval.getFirst()); |
---|
2411 | else if (GF) |
---|
2412 | bufBiFactors= GFBiSqrfFactorize (bufAeval.getFirst()); |
---|
2413 | else |
---|
2414 | bufBiFactors= FqBiSqrfFactorize (bufAeval.getFirst(), alpha); |
---|
2415 | TIMING_END_AND_PRINT (fac_fq_bi_factorizer, |
---|
2416 | "time for bivariate factorization: "); |
---|
2417 | bufBiFactors.removeFirst(); |
---|
2418 | |
---|
2419 | if (bufBiFactors.length() == 1) |
---|
2420 | { |
---|
2421 | if (extension) |
---|
2422 | { |
---|
2423 | CFList source, dest; |
---|
2424 | A= mapDown (A, info, source, dest); |
---|
2425 | } |
---|
2426 | factors.append (A); |
---|
2427 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, |
---|
2428 | swapLevel2, x); |
---|
2429 | normalize (factors); |
---|
2430 | delete [] bufAeval2; |
---|
2431 | delete [] Aeval2; |
---|
2432 | return factors; |
---|
2433 | } |
---|
2434 | |
---|
2435 | if (i == 0) |
---|
2436 | { |
---|
2437 | Aeval= bufAeval; |
---|
2438 | evaluation= bufEvaluation; |
---|
2439 | biFactors= bufBiFactors; |
---|
2440 | lift= bufLift; |
---|
2441 | for (int j= 0; j < A.level() - 2; j++) |
---|
2442 | Aeval2 [j]= bufAeval2 [j]; |
---|
2443 | differentSecondVar= counter; |
---|
2444 | } |
---|
2445 | else |
---|
2446 | { |
---|
2447 | if (bufBiFactors.length() < biFactors.length() || |
---|
2448 | ((bufLift < lift) && (bufBiFactors.length() == biFactors.length())) || |
---|
2449 | counter > differentSecondVar) |
---|
2450 | { |
---|
2451 | Aeval= bufAeval; |
---|
2452 | evaluation= bufEvaluation; |
---|
2453 | biFactors= bufBiFactors; |
---|
2454 | lift= bufLift; |
---|
2455 | for (int j= 0; j < A.level() - 2; j++) |
---|
2456 | Aeval2 [j]= bufAeval2 [j]; |
---|
2457 | differentSecondVar= counter; |
---|
2458 | } |
---|
2459 | } |
---|
2460 | int k= 0; |
---|
2461 | for (CFListIterator j= bufEvaluation; j.hasItem(); j++, k++) |
---|
2462 | evalPoly += j.getItem()*power (x, k); |
---|
2463 | list.append (evalPoly); |
---|
2464 | } |
---|
2465 | |
---|
2466 | delete [] bufAeval2; |
---|
2467 | |
---|
2468 | sortList (biFactors, x); |
---|
2469 | |
---|
2470 | int minFactorsLength; |
---|
2471 | bool irred= false; |
---|
2472 | factorizationWRTDifferentSecondVars (A, Aeval2, info, minFactorsLength, irred); |
---|
2473 | |
---|
2474 | if (irred) |
---|
2475 | { |
---|
2476 | if (extension) |
---|
2477 | { |
---|
2478 | CFList source, dest; |
---|
2479 | A= mapDown (A, info, source, dest); |
---|
2480 | } |
---|
2481 | factors.append (A); |
---|
2482 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, |
---|
2483 | swapLevel2, x); |
---|
2484 | normalize (factors); |
---|
2485 | delete [] Aeval2; |
---|
2486 | return factors; |
---|
2487 | } |
---|
2488 | |
---|
2489 | if (minFactorsLength == 0) |
---|
2490 | minFactorsLength= biFactors.length(); |
---|
2491 | else if (biFactors.length() > minFactorsLength) |
---|
2492 | refineBiFactors (A, biFactors, Aeval2, evaluation, minFactorsLength); |
---|
2493 | minFactorsLength= tmin (minFactorsLength, biFactors.length()); |
---|
2494 | |
---|
2495 | if (differentSecondVar == A.level() - 2) |
---|
2496 | { |
---|
2497 | bool zeroOccured= false; |
---|
2498 | for (CFListIterator iter= evaluation; iter.hasItem(); iter++) |
---|
2499 | { |
---|
2500 | if (iter.getItem().isZero()) |
---|
2501 | { |
---|
2502 | zeroOccured= true; |
---|
2503 | break; |
---|
2504 | } |
---|
2505 | } |
---|
2506 | if (!zeroOccured) |
---|
2507 | { |
---|
2508 | factors= sparseHeuristic (A, biFactors, Aeval2, evaluation, minFactorsLength); |
---|
2509 | if (factors.length() == biFactors.length()) |
---|
2510 | { |
---|
2511 | if (extension) |
---|
2512 | factors= extNonMonicFactorRecombination (factors, A, info); |
---|
2513 | |
---|
2514 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, |
---|
2515 | swapLevel2, x); |
---|
2516 | normalize (factors); |
---|
2517 | delete [] Aeval2; |
---|
2518 | return factors; |
---|
2519 | } |
---|
2520 | else |
---|
2521 | factors= CFList(); |
---|
2522 | //TODO case where factors.length() > 0 |
---|
2523 | } |
---|
2524 | } |
---|
2525 | |
---|
2526 | CFList uniFactors= buildUniFactors (biFactors, evaluation.getLast(), y); |
---|
2527 | |
---|
2528 | CFList * oldAeval= new CFList [A.level() - 2]; //TODO use bufAeval2 for this |
---|
2529 | for (int i= 0; i < A.level() - 2; i++) |
---|
2530 | oldAeval[i]= Aeval2[i]; |
---|
2531 | |
---|
2532 | getLeadingCoeffs (A, Aeval2, uniFactors, evaluation); |
---|
2533 | |
---|
2534 | CFList biFactorsLCs; |
---|
2535 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
2536 | biFactorsLCs.append (LC (i.getItem(), 1)); |
---|
2537 | |
---|
2538 | Variable v; |
---|
2539 | CFList leadingCoeffs= precomputeLeadingCoeff (LC (A, 1), biFactorsLCs, alpha, |
---|
2540 | evaluation, Aeval2, A.level() - 2, v); |
---|
2541 | |
---|
2542 | if (v.level() != 1) |
---|
2543 | { |
---|
2544 | A= swapvar (A, y, v); |
---|
2545 | int i= A.level(); |
---|
2546 | CanonicalForm evalPoint; |
---|
2547 | for (CFListIterator iter= evaluation; iter.hasItem(); iter++, i--) |
---|
2548 | { |
---|
2549 | if (i == v.level()) |
---|
2550 | { |
---|
2551 | evalPoint= iter.getItem(); |
---|
2552 | iter.getItem()= evaluation.getLast(); |
---|
2553 | evaluation.removeLast(); |
---|
2554 | evaluation.append (evalPoint); |
---|
2555 | break; |
---|
2556 | } |
---|
2557 | } |
---|
2558 | for (i= 0; i < A.level() - 2; i++) |
---|
2559 | { |
---|
2560 | if (oldAeval[i].isEmpty()) |
---|
2561 | continue; |
---|
2562 | if (oldAeval[i].getFirst().level() == v.level()) |
---|
2563 | { |
---|
2564 | CFArray tmp= copy (oldAeval[i]); |
---|
2565 | for (int ii= 0; ii < tmp.size(); ii++) |
---|
2566 | tmp[ii]= swapvar (tmp[ii], v, y); |
---|
2567 | CFArray tmp2= CFArray (tmp.size()); |
---|
2568 | CanonicalForm buf; |
---|
2569 | for (int ii= 0; ii < tmp.size(); ii++) |
---|
2570 | { |
---|
2571 | buf= tmp[ii] (evaluation.getLast(),y); |
---|
2572 | buf /= Lc (buf); |
---|
2573 | tmp2[findItem (uniFactors, buf)-1]=tmp[ii]; |
---|
2574 | } |
---|
2575 | biFactors= CFList(); |
---|
2576 | for (int j= 0; j < tmp2.size(); j++) |
---|
2577 | biFactors.append (tmp2[j]); |
---|
2578 | } |
---|
2579 | } |
---|
2580 | } |
---|
2581 | |
---|
2582 | CFListIterator iter; |
---|
2583 | CanonicalForm oldA= A; |
---|
2584 | CFList oldBiFactors= biFactors; |
---|
2585 | if (!leadingCoeffs.getFirst().inCoeffDomain()) |
---|
2586 | { |
---|
2587 | CanonicalForm tmp= power (leadingCoeffs.getFirst(), biFactors.length() - 1); |
---|
2588 | A *= tmp; |
---|
2589 | tmp= leadingCoeffs.getFirst(); |
---|
2590 | iter= evaluation; |
---|
2591 | for (int i= A.level(); i > 2; i--, iter++) |
---|
2592 | tmp= tmp (iter.getItem(), i); |
---|
2593 | if (!tmp.inCoeffDomain()) |
---|
2594 | { |
---|
2595 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
2596 | { |
---|
2597 | i.getItem() *= tmp/LC (i.getItem(), 1); |
---|
2598 | i.getItem() /= Lc (i.getItem()); |
---|
2599 | } |
---|
2600 | } |
---|
2601 | } |
---|
2602 | |
---|
2603 | leadingCoeffs.removeFirst(); |
---|
2604 | |
---|
2605 | //prepare leading coefficients |
---|
2606 | CFList* leadingCoeffs2= new CFList [A.level() - 2]; |
---|
2607 | prepareLeadingCoeffs (leadingCoeffs2, A.level(), leadingCoeffs, biFactors, |
---|
2608 | evaluation); |
---|
2609 | |
---|
2610 | Aeval= evaluateAtEval (A, evaluation, 2); |
---|
2611 | CanonicalForm hh= Lc (Aeval.getFirst()); |
---|
2612 | for (iter= Aeval; iter.hasItem(); iter++) |
---|
2613 | iter.getItem() /= hh; |
---|
2614 | |
---|
2615 | A /= hh; |
---|
2616 | |
---|
2617 | if (size (A)/getNumVars (A) < 500 && |
---|
2618 | LucksWangSparseHeuristic (A, biFactors, 2, leadingCoeffs2 [A.level() - 3], |
---|
2619 | factors)) |
---|
2620 | { |
---|
2621 | int check= factors.length(); |
---|
2622 | factors= recoverFactors (A, factors); |
---|
2623 | |
---|
2624 | if (check == factors.length()) |
---|
2625 | { |
---|
2626 | if (extension) |
---|
2627 | factors= extNonMonicFactorRecombination (factors, A, info); |
---|
2628 | |
---|
2629 | if (v.level() != 1) |
---|
2630 | { |
---|
2631 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
2632 | iter.getItem()= swapvar (iter.getItem(), v, y); |
---|
2633 | } |
---|
2634 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, |
---|
2635 | swapLevel2, x); |
---|
2636 | normalize (factors); |
---|
2637 | delete [] Aeval2; |
---|
2638 | return factors; |
---|
2639 | } |
---|
2640 | else |
---|
2641 | factors= CFList(); |
---|
2642 | //TODO handle this case |
---|
2643 | } |
---|
2644 | |
---|
2645 | A= shift2Zero (A, Aeval, evaluation); |
---|
2646 | |
---|
2647 | for (iter= biFactors; iter.hasItem(); iter++) |
---|
2648 | iter.getItem()= iter.getItem () (y + evaluation.getLast(), y); |
---|
2649 | |
---|
2650 | for (int i= 0; i < A.level() - 2; i++) |
---|
2651 | { |
---|
2652 | if (i != A.level() - 3) |
---|
2653 | leadingCoeffs2[i]= CFList(); |
---|
2654 | } |
---|
2655 | for (iter= leadingCoeffs2[A.level() - 3]; iter.hasItem(); iter++) |
---|
2656 | { |
---|
2657 | iter.getItem()= shift2Zero (iter.getItem(), list, evaluation); |
---|
2658 | for (int i= A.level() - 4; i > -1; i--) |
---|
2659 | { |
---|
2660 | if (i + 1 == A.level() - 3) |
---|
2661 | leadingCoeffs2[i].append (iter.getItem() (0, i + 4)); |
---|
2662 | else |
---|
2663 | leadingCoeffs2[i].append (leadingCoeffs2[i+1].getLast() (0, i + 4)); |
---|
2664 | } |
---|
2665 | } |
---|
2666 | |
---|
2667 | CFArray Pi; |
---|
2668 | CFList diophant; |
---|
2669 | int* liftBounds= new int [A.level() - 1]; |
---|
2670 | int liftBoundsLength= A.level() - 1; |
---|
2671 | for (int i= 0; i < liftBoundsLength; i++) |
---|
2672 | liftBounds [i]= degree (A, i + 2) + 1; |
---|
2673 | |
---|
2674 | Aeval.removeFirst(); |
---|
2675 | bool noOneToOne= false; |
---|
2676 | factors= nonMonicHenselLift (Aeval, biFactors, leadingCoeffs2, diophant, |
---|
2677 | Pi, liftBounds, liftBoundsLength, noOneToOne); |
---|
2678 | |
---|
2679 | if (!noOneToOne) |
---|
2680 | { |
---|
2681 | int check= factors.length(); |
---|
2682 | A= oldA; |
---|
2683 | factors= recoverFactors (A, factors, evaluation); |
---|
2684 | if (check != factors.length()) |
---|
2685 | noOneToOne= true; |
---|
2686 | |
---|
2687 | if (extension && !noOneToOne) |
---|
2688 | factors= extNonMonicFactorRecombination (factors, A, info); |
---|
2689 | } |
---|
2690 | if (noOneToOne) |
---|
2691 | { |
---|
2692 | A= shift2Zero (oldA, Aeval, evaluation); |
---|
2693 | biFactors= oldBiFactors; |
---|
2694 | for (iter= biFactors; iter.hasItem(); iter++) |
---|
2695 | iter.getItem()= iter.getItem () (y + evaluation.getLast(), y); |
---|
2696 | CanonicalForm LCA= LC (Aeval.getFirst(), 1); |
---|
2697 | CanonicalForm yToLift= power (y, lift); |
---|
2698 | CFListIterator i= biFactors; |
---|
2699 | lift= degree (i.getItem(), 2) + degree (LC (i.getItem(), 1)) + 1; |
---|
2700 | i++; |
---|
2701 | |
---|
2702 | for (; i.hasItem(); i++) |
---|
2703 | lift= tmax (lift, degree (i.getItem(), 2) + degree (LC (i.getItem(), 1)) + 1); |
---|
2704 | |
---|
2705 | lift= tmax (degree (Aeval.getFirst() , 2) + 1, lift); |
---|
2706 | |
---|
2707 | i= biFactors; |
---|
2708 | yToLift= power (y, lift); |
---|
2709 | CanonicalForm dummy; |
---|
2710 | for (; i.hasItem(); i++) |
---|
2711 | { |
---|
2712 | LCA= LC (i.getItem(), 1); |
---|
2713 | extgcd (LCA, yToLift, LCA, dummy); |
---|
2714 | i.getItem()= mod (i.getItem()*LCA, yToLift); |
---|
2715 | } |
---|
2716 | |
---|
2717 | liftBoundsLength= F.level() - 1; |
---|
2718 | liftBounds= liftingBounds (A, lift); |
---|
2719 | |
---|
2720 | CFList MOD; |
---|
2721 | bool earlySuccess; |
---|
2722 | CFList earlyFactors, liftedFactors; |
---|
2723 | TIMING_START (fac_fq_hensel_lift); |
---|
2724 | liftedFactors= henselLiftAndEarly |
---|
2725 | (A, MOD, liftBounds, earlySuccess, earlyFactors, |
---|
2726 | Aeval, biFactors, evaluation, info); |
---|
2727 | TIMING_END_AND_PRINT (fac_fq_hensel_lift, "time for hensel lifting: "); |
---|
2728 | |
---|
2729 | if (!extension) |
---|
2730 | { |
---|
2731 | TIMING_START (fac_fq_factor_recombination); |
---|
2732 | factors= factorRecombination (A, liftedFactors, MOD); |
---|
2733 | TIMING_END_AND_PRINT (fac_fq_factor_recombination, |
---|
2734 | "time for factor recombination: "); |
---|
2735 | } |
---|
2736 | else |
---|
2737 | { |
---|
2738 | TIMING_START (fac_fq_factor_recombination); |
---|
2739 | factors= extFactorRecombination (liftedFactors, A, MOD, info, evaluation); |
---|
2740 | TIMING_END_AND_PRINT (fac_fq_factor_recombination, |
---|
2741 | "time for factor recombination: "); |
---|
2742 | } |
---|
2743 | |
---|
2744 | if (earlySuccess) |
---|
2745 | factors= Union (factors, earlyFactors); |
---|
2746 | if (!extension) |
---|
2747 | { |
---|
2748 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
2749 | { |
---|
2750 | int kk= Aeval.getLast().level(); |
---|
2751 | for (CFListIterator j= evaluation; j.hasItem(); j++, kk--) |
---|
2752 | { |
---|
2753 | if (i.getItem().level() < kk) |
---|
2754 | continue; |
---|
2755 | i.getItem()= i.getItem() (Variable (kk) - j.getItem(), kk); |
---|
2756 | } |
---|
2757 | } |
---|
2758 | } |
---|
2759 | } |
---|
2760 | |
---|
2761 | if (v.level() != 1) |
---|
2762 | { |
---|
2763 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
2764 | iter.getItem()= swapvar (iter.getItem(), v, y); |
---|
2765 | } |
---|
2766 | |
---|
2767 | swap (factors, swapLevel, swapLevel2, x); |
---|
2768 | append (factors, contentAFactors); |
---|
2769 | decompress (factors, N); |
---|
2770 | normalize (factors); |
---|
2771 | |
---|
2772 | delete[] liftBounds; |
---|
2773 | |
---|
2774 | return factors; |
---|
2775 | } |
---|
2776 | |
---|
2777 | /// multivariate factorization over an extension of the initial field |
---|
2778 | CFList |
---|
2779 | extFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
2780 | { |
---|
2781 | CanonicalForm A= F; |
---|
2782 | |
---|
2783 | Variable alpha= info.getAlpha(); |
---|
2784 | Variable beta= info.getBeta(); |
---|
2785 | int k= info.getGFDegree(); |
---|
2786 | char cGFName= info.getGFName(); |
---|
2787 | CanonicalForm delta= info.getDelta(); |
---|
2788 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
2789 | Variable w= Variable (1); |
---|
2790 | |
---|
2791 | CFList factors; |
---|
2792 | if (!GF && alpha == w) // we are in F_p |
---|
2793 | { |
---|
2794 | CFList factors; |
---|
2795 | bool extension= true; |
---|
2796 | int p= getCharacteristic(); |
---|
2797 | if (p*p < (1<<16)) // pass to GF if possible |
---|
2798 | { |
---|
2799 | setCharacteristic (getCharacteristic(), 2, 'Z'); |
---|
2800 | ExtensionInfo info= ExtensionInfo (extension); |
---|
2801 | A= A.mapinto(); |
---|
2802 | factors= multiFactorize (A, info); |
---|
2803 | |
---|
2804 | CanonicalForm mipo= gf_mipo; |
---|
2805 | setCharacteristic (getCharacteristic()); |
---|
2806 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
2807 | for (CFListIterator j= factors; j.hasItem(); j++) |
---|
2808 | j.getItem()= GF2FalphaRep (j.getItem(), vBuf); |
---|
2809 | } |
---|
2810 | else // not able to pass to GF, pass to F_p(\alpha) |
---|
2811 | { |
---|
2812 | CanonicalForm mipo= randomIrredpoly (2, w); |
---|
2813 | Variable v= rootOf (mipo); |
---|
2814 | ExtensionInfo info= ExtensionInfo (v); |
---|
2815 | factors= multiFactorize (A, info); |
---|
2816 | } |
---|
2817 | return factors; |
---|
2818 | } |
---|
2819 | else if (!GF && (alpha != w)) // we are in F_p(\alpha) |
---|
2820 | { |
---|
2821 | if (k == 1) // need factorization over F_p |
---|
2822 | { |
---|
2823 | int extDeg= degree (getMipo (alpha)); |
---|
2824 | extDeg++; |
---|
2825 | CanonicalForm mipo= randomIrredpoly (extDeg + 1, w); |
---|
2826 | Variable v= rootOf (mipo); |
---|
2827 | ExtensionInfo info= ExtensionInfo (v); |
---|
2828 | factors= multiFactorize (A, info); |
---|
2829 | } |
---|
2830 | else |
---|
2831 | { |
---|
2832 | if (beta == w) |
---|
2833 | { |
---|
2834 | Variable v= chooseExtension (alpha, beta, k); |
---|
2835 | CanonicalForm primElem, imPrimElem; |
---|
2836 | bool primFail= false; |
---|
2837 | Variable vBuf; |
---|
2838 | primElem= primitiveElement (alpha, vBuf, primFail); |
---|
2839 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
2840 | if (primFail) |
---|
2841 | ; //ERROR |
---|
2842 | else |
---|
2843 | imPrimElem= mapPrimElem (primElem, vBuf, v); |
---|
2844 | |
---|
2845 | CFList source, dest; |
---|
2846 | CanonicalForm bufA= mapUp (A, alpha, v, primElem, imPrimElem, |
---|
2847 | source, dest); |
---|
2848 | ExtensionInfo info= ExtensionInfo (v, alpha, imPrimElem, primElem); |
---|
2849 | factors= multiFactorize (bufA, info); |
---|
2850 | } |
---|
2851 | else |
---|
2852 | { |
---|
2853 | Variable v= chooseExtension (alpha, beta, k); |
---|
2854 | CanonicalForm primElem, imPrimElem; |
---|
2855 | bool primFail= false; |
---|
2856 | Variable vBuf; |
---|
2857 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
2858 | if (primFail) |
---|
2859 | ; //ERROR |
---|
2860 | else |
---|
2861 | imPrimElem= mapPrimElem (delta, beta, v); |
---|
2862 | |
---|
2863 | CFList source, dest; |
---|
2864 | CanonicalForm bufA= mapDown (A, info, source, dest); |
---|
2865 | source= CFList(); |
---|
2866 | dest= CFList(); |
---|
2867 | bufA= mapUp (bufA, beta, v, delta, imPrimElem, source, dest); |
---|
2868 | ExtensionInfo info= ExtensionInfo (v, beta, imPrimElem, delta); |
---|
2869 | factors= multiFactorize (bufA, info); |
---|
2870 | } |
---|
2871 | } |
---|
2872 | return factors; |
---|
2873 | } |
---|
2874 | else // we are in GF (p^k) |
---|
2875 | { |
---|
2876 | int p= getCharacteristic(); |
---|
2877 | int extensionDeg= getGFDegree(); |
---|
2878 | bool extension= true; |
---|
2879 | if (k == 1) // need factorization over F_p |
---|
2880 | { |
---|
2881 | extensionDeg++; |
---|
2882 | if (pow ((double) p, (double) extensionDeg) < (1<<16)) |
---|
2883 | // pass to GF(p^k+1) |
---|
2884 | { |
---|
2885 | CanonicalForm mipo= gf_mipo; |
---|
2886 | setCharacteristic (p); |
---|
2887 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
2888 | A= GF2FalphaRep (A, vBuf); |
---|
2889 | setCharacteristic (p, extensionDeg, 'Z'); |
---|
2890 | ExtensionInfo info= ExtensionInfo (extension); |
---|
2891 | factors= multiFactorize (A.mapinto(), info); |
---|
2892 | } |
---|
2893 | else // not able to pass to another GF, pass to F_p(\alpha) |
---|
2894 | { |
---|
2895 | CanonicalForm mipo= gf_mipo; |
---|
2896 | setCharacteristic (p); |
---|
2897 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
2898 | A= GF2FalphaRep (A, vBuf); |
---|
2899 | Variable v= chooseExtension (vBuf, beta, k); |
---|
2900 | ExtensionInfo info= ExtensionInfo (v, extension); |
---|
2901 | factors= multiFactorize (A, info); |
---|
2902 | } |
---|
2903 | } |
---|
2904 | else // need factorization over GF (p^k) |
---|
2905 | { |
---|
2906 | if (pow ((double) p, (double) 2*extensionDeg) < (1<<16)) |
---|
2907 | // pass to GF(p^2k) |
---|
2908 | { |
---|
2909 | setCharacteristic (p, 2*extensionDeg, 'Z'); |
---|
2910 | ExtensionInfo info= ExtensionInfo (k, cGFName, extension); |
---|
2911 | factors= multiFactorize (GFMapUp (A, extensionDeg), info); |
---|
2912 | setCharacteristic (p, extensionDeg, cGFName); |
---|
2913 | } |
---|
2914 | else // not able to pass to GF (p^2k), pass to F_p (\alpha) |
---|
2915 | { |
---|
2916 | CanonicalForm mipo= gf_mipo; |
---|
2917 | setCharacteristic (p); |
---|
2918 | Variable v1= rootOf (mipo.mapinto()); |
---|
2919 | A= GF2FalphaRep (A, v1); |
---|
2920 | Variable v2= chooseExtension (v1, v1, k); |
---|
2921 | CanonicalForm primElem, imPrimElem; |
---|
2922 | bool primFail= false; |
---|
2923 | Variable vBuf; |
---|
2924 | primElem= primitiveElement (v1, v1, primFail); |
---|
2925 | if (primFail) |
---|
2926 | ; //ERROR |
---|
2927 | else |
---|
2928 | imPrimElem= mapPrimElem (primElem, v1, v2); |
---|
2929 | CFList source, dest; |
---|
2930 | CanonicalForm bufA= mapUp (A, v1, v2, primElem, imPrimElem, |
---|
2931 | source, dest); |
---|
2932 | ExtensionInfo info= ExtensionInfo (v2, v1, imPrimElem, primElem); |
---|
2933 | factors= multiFactorize (bufA, info); |
---|
2934 | setCharacteristic (p, k, cGFName); |
---|
2935 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
2936 | i.getItem()= Falpha2GFRep (i.getItem()); |
---|
2937 | } |
---|
2938 | } |
---|
2939 | return factors; |
---|
2940 | } |
---|
2941 | } |
---|
2942 | |
---|
2943 | #endif |
---|
2944 | /* HAVE_NTL */ |
---|
2945 | |
---|