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() == 0) |
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66 | return 0; |
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67 | if (L.length() == 1) |
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68 | return L.getFirst(); |
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69 | if (L.length() == 2) |
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70 | return gcd (L.getFirst(), L.getLast()); |
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71 | else |
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72 | { |
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73 | CFList lHi, lLo; |
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74 | CanonicalForm resultHi, resultLo; |
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75 | int length= L.length()/2; |
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76 | int j= 0; |
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77 | for (CFListIterator i= L; j < length; i++, j++) |
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78 | lHi.append (i.getItem()); |
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79 | lLo= Difference (L, lHi); |
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80 | resultHi= listGCD (lHi); |
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81 | resultLo= listGCD (lLo); |
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82 | if (resultHi.isOne() || resultLo.isOne()) |
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83 | return 1; |
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84 | return gcd (resultHi, resultLo); |
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85 | } |
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86 | } |
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87 | |
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88 | static inline |
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89 | CanonicalForm |
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90 | myContent (const CanonicalForm& F, const Variable& x) |
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91 | { |
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92 | if (degree (F, x) <= 0) |
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93 | return 1; |
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94 | CanonicalForm G= F; |
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95 | bool swap= false; |
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96 | if (x != F.mvar()) |
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97 | { |
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98 | swap= true; |
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99 | G= swapvar (F, x, F.mvar()); |
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100 | } |
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101 | CFList L; |
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102 | Variable alpha; |
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103 | for (CFIterator i= G; i.hasTerms(); i++) |
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104 | L.append (i.coeff()); |
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105 | if (L.length() == 2) |
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106 | { |
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107 | if (swap) |
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108 | return swapvar (gcd (L.getFirst(), L.getLast()), F.mvar(), x); |
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109 | else |
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110 | return gcd (L.getFirst(), L.getLast()); |
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111 | } |
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112 | if (L.length() == 1) |
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113 | { |
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114 | return LC (F, x); |
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115 | } |
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116 | if (swap) |
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117 | return swapvar (listGCD (L), F.mvar(), x); |
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118 | else |
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119 | return listGCD (L); |
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120 | } |
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121 | |
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122 | CanonicalForm myCompress (const CanonicalForm& F, CFMap& N) |
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123 | { |
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124 | int n= F.level(); |
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125 | int * degsf= new int [n + 1]; |
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126 | int ** swap; |
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127 | swap= new int* [n + 1]; |
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128 | for (int i= 0; i <= n; i++) |
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129 | { |
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130 | degsf[i]= 0; |
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131 | swap [i]= new int [2]; |
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132 | swap [i] [0]= 0; |
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133 | swap [i] [1]= 0; |
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134 | } |
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135 | int i= 1; |
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136 | n= 1; |
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137 | degsf= degrees (F, degsf); |
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138 | |
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139 | CanonicalForm result= F; |
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140 | while ( i <= F.level() ) |
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141 | { |
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142 | while( degsf[i] == 0 ) i++; |
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143 | swap[n][0]= i; |
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144 | swap[n][1]= size (LC (F,i)); |
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145 | if (i != n) |
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146 | result= swapvar (result, Variable (n), Variable(i)); |
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147 | n++; i++; |
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148 | } |
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149 | |
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150 | int buf1, buf2; |
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151 | n--; |
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152 | |
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153 | for (i= 1; i < n; i++) |
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154 | { |
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155 | for (int j= 1; j < n - i + 1; j++) |
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156 | { |
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157 | if (swap[j][1] > swap[j + 1][1]) |
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158 | { |
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159 | buf1= swap [j + 1] [0]; |
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160 | buf2= swap [j + 1] [1]; |
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161 | swap[j + 1] [0]= swap[j] [0]; |
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162 | swap[j + 1] [1]= swap[j] [1]; |
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163 | swap[j][0]= buf1; |
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164 | swap[j][1]= buf2; |
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165 | result= swapvar (result, Variable (j + 1), Variable (j)); |
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166 | } |
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167 | } |
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168 | } |
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169 | |
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170 | for (i= n; i > 0; i--) |
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171 | { |
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172 | if (i != swap[i] [0]) |
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173 | N.newpair (Variable (i), Variable (swap[i] [0])); |
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174 | } |
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175 | |
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176 | for (i= 0; i <= n; i++) |
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177 | delete [] swap[i]; |
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178 | delete [] swap; |
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179 | |
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180 | delete [] degsf; |
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181 | |
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182 | return result; |
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183 | } |
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184 | |
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185 | CFList |
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186 | extFactorRecombination (const CFList& factors, const CanonicalForm& F, |
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187 | const CFList& M, const ExtensionInfo& info, |
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188 | const CFList& evaluation) |
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189 | { |
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190 | Variable alpha= info.getAlpha(); |
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191 | Variable beta= info.getBeta(); |
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192 | CanonicalForm gamma= info.getGamma(); |
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193 | CanonicalForm delta= info.getDelta(); |
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194 | int k= info.getGFDegree(); |
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195 | CFList source, dest; |
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196 | if (factors.length() == 1) |
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197 | { |
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198 | CanonicalForm buf= reverseShift (F, evaluation); |
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199 | return CFList (mapDown (buf, info, source, dest)); |
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200 | } |
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201 | if (factors.length() < 1) |
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202 | return CFList(); |
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203 | |
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204 | int degMipoBeta= 1; |
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205 | if (!k && beta.level() != 1) |
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206 | degMipoBeta= degree (getMipo (beta)); |
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207 | |
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208 | CFList T, S; |
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209 | T= factors; |
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210 | |
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211 | int s= 1; |
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212 | CFList result; |
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213 | CanonicalForm buf; |
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214 | |
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215 | buf= F; |
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216 | |
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217 | Variable x= Variable (1); |
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218 | CanonicalForm g, LCBuf= LC (buf, x); |
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219 | CanonicalForm buf2, quot; |
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220 | int * v= new int [T.length()]; |
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221 | for (int i= 0; i < T.length(); i++) |
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222 | v[i]= 0; |
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223 | bool noSubset= false; |
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224 | CFArray TT; |
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225 | TT= copy (factors); |
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226 | bool recombination= false; |
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227 | bool trueFactor= false; |
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228 | while (T.length() >= 2*s) |
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229 | { |
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230 | while (noSubset == false) |
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231 | { |
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232 | if (T.length() == s) |
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233 | { |
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234 | delete [] v; |
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235 | if (recombination) |
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236 | { |
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237 | T.insert (LCBuf); |
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238 | g= prodMod (T, M); |
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239 | T.removeFirst(); |
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240 | result.append (g/myContent (g)); |
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241 | g= reverseShift (g, evaluation); |
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242 | g /= Lc (g); |
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243 | appendTestMapDown (result, g, info, source, dest); |
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244 | return result; |
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245 | } |
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246 | else |
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247 | { |
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248 | buf= reverseShift (buf, evaluation); |
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249 | return CFList (buf); |
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250 | } |
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251 | } |
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252 | |
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253 | S= subset (v, s, TT, noSubset); |
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254 | if (noSubset) break; |
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255 | |
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256 | S.insert (LCBuf); |
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257 | g= prodMod (S, M); |
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258 | S.removeFirst(); |
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259 | g /= myContent (g); |
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260 | if (fdivides (g, buf, quot)) |
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261 | { |
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262 | buf2= reverseShift (g, evaluation); |
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263 | buf2 /= Lc (buf2); |
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264 | if (!k && beta == x) |
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265 | { |
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266 | if (degree (buf2, alpha) < degMipoBeta) |
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267 | { |
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268 | appendTestMapDown (result, buf2, info, source, dest); |
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269 | buf= quot; |
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270 | LCBuf= LC (buf, x); |
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271 | recombination= true; |
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272 | trueFactor= true; |
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273 | } |
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274 | } |
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275 | else |
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276 | { |
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277 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
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278 | { |
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279 | appendTestMapDown (result, buf2, info, source, dest); |
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280 | buf /= g; |
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281 | LCBuf= LC (buf, x); |
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282 | recombination= true; |
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283 | trueFactor= true; |
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284 | } |
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285 | } |
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286 | |
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287 | if (trueFactor) |
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288 | { |
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289 | T= Difference (T, S); |
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290 | |
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291 | if (T.length() < 2*s || T.length() == s) |
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292 | { |
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293 | buf= reverseShift (buf, evaluation); |
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294 | buf /= Lc (buf); |
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295 | appendTestMapDown (result, buf, info, source, dest); |
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296 | delete [] v; |
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297 | return result; |
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298 | } |
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299 | trueFactor= false; |
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300 | TT= copy (T); |
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301 | indexUpdate (v, s, T.length(), noSubset); |
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302 | if (noSubset) break; |
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303 | } |
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304 | } |
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305 | } |
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306 | s++; |
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307 | if (T.length() < 2*s || T.length() == s) |
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308 | { |
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309 | buf= reverseShift (buf, evaluation); |
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310 | appendTestMapDown (result, buf, info, source, dest); |
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311 | delete [] v; |
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312 | return result; |
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313 | } |
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314 | for (int i= 0; i < T.length(); i++) |
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315 | v[i]= 0; |
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316 | noSubset= false; |
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317 | } |
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318 | if (T.length() < 2*s) |
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319 | { |
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320 | buf= reverseShift (F, evaluation); |
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321 | appendMapDown (result, buf, info, source, dest); |
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322 | } |
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323 | |
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324 | delete [] v; |
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325 | return result; |
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326 | } |
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327 | |
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328 | CFList |
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329 | factorRecombination (const CanonicalForm& F, const CFList& factors, |
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330 | const CFList& M) |
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331 | { |
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332 | if (factors.length() == 1) |
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333 | return CFList(F); |
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334 | if (factors.length() < 1) |
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335 | return CFList(); |
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336 | |
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337 | CFList T, S; |
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338 | |
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339 | T= factors; |
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340 | |
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341 | int s= 1; |
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342 | CFList result; |
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343 | CanonicalForm LCBuf= LC (F, Variable (1)); |
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344 | CanonicalForm g, buf= F; |
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345 | int * v= new int [T.length()]; |
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346 | for (int i= 0; i < T.length(); i++) |
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347 | v[i]= 0; |
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348 | bool noSubset= false; |
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349 | CFArray TT; |
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350 | TT= copy (factors); |
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351 | Variable y= F.level() - 1; |
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352 | bool recombination= false; |
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353 | CanonicalForm h, quot; |
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354 | while (T.length() >= 2*s) |
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355 | { |
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356 | while (noSubset == false) |
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357 | { |
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358 | if (T.length() == s) |
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359 | { |
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360 | delete [] v; |
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361 | if (recombination) |
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362 | { |
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363 | T.insert (LC (buf)); |
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364 | g= prodMod (T, M); |
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365 | result.append (g/myContent (g)); |
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366 | return result; |
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367 | } |
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368 | else |
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369 | return CFList (F); |
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370 | } |
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371 | S= subset (v, s, TT, noSubset); |
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372 | if (noSubset) break; |
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373 | S.insert (LCBuf); |
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374 | g= prodMod (S, M); |
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375 | S.removeFirst(); |
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376 | g /= myContent (g); |
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377 | if (fdivides (g, buf, quot)) |
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378 | { |
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379 | recombination= true; |
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380 | result.append (g); |
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381 | buf= quot; |
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382 | LCBuf= LC (buf, Variable(1)); |
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383 | T= Difference (T, S); |
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384 | if (T.length() < 2*s || T.length() == s) |
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385 | { |
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386 | result.append (buf); |
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387 | delete [] v; |
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388 | return result; |
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389 | } |
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390 | TT= copy (T); |
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391 | indexUpdate (v, s, T.length(), noSubset); |
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392 | if (noSubset) break; |
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393 | } |
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394 | } |
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395 | s++; |
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396 | if (T.length() < 2*s || T.length() == s) |
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397 | { |
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398 | result.append (buf); |
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399 | delete [] v; |
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400 | return result; |
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401 | } |
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402 | for (int i= 0; i < T.length(); i++) |
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403 | v[i]= 0; |
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404 | noSubset= false; |
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405 | } |
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406 | if (T.length() < 2*s) |
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407 | result.append (F); |
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408 | |
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409 | delete [] v; |
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410 | return result; |
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411 | } |
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412 | |
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413 | int |
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414 | liftBoundAdaption (const CanonicalForm& F, const CFList& factors, bool& |
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415 | success, const int deg, const CFList& MOD, const int bound) |
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416 | { |
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417 | int adaptedLiftBound= 0; |
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418 | CanonicalForm buf= F; |
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419 | Variable y= F.mvar(); |
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420 | Variable x= Variable (1); |
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421 | CanonicalForm LCBuf= LC (buf, x); |
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422 | CanonicalForm g, quot; |
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423 | CFList M= MOD; |
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424 | M.append (power (y, deg)); |
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425 | int d= bound; |
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426 | int e= 0; |
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427 | int nBuf; |
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428 | for (CFListIterator i= factors; i.hasItem(); i++) |
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429 | { |
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430 | g= mulMod (i.getItem(), LCBuf, M); |
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431 | g /= myContent (g); |
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432 | if (fdivides (g, buf, quot)) |
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433 | { |
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434 | nBuf= degree (g, y) + degree (LC (g, 1), y); |
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435 | d -= nBuf; |
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436 | e= tmax (e, nBuf); |
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437 | buf= quot; |
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438 | LCBuf= LC (buf, x); |
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439 | } |
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440 | } |
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441 | adaptedLiftBound= d; |
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442 | |
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443 | if (adaptedLiftBound < deg) |
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444 | { |
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445 | if (adaptedLiftBound < degree (F) + 1) |
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446 | { |
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447 | if (d == 1) |
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448 | { |
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449 | if (e + 1 > deg) |
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450 | { |
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451 | adaptedLiftBound= deg; |
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452 | success= false; |
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453 | } |
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454 | else |
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455 | { |
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456 | success= true; |
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457 | if (e + 1 < degree (F) + 1) |
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458 | adaptedLiftBound= deg; |
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459 | else |
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460 | adaptedLiftBound= e + 1; |
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461 | } |
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462 | } |
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463 | else |
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464 | { |
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465 | success= true; |
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466 | adaptedLiftBound= deg; |
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467 | } |
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468 | } |
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469 | else |
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470 | { |
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471 | success= true; |
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472 | } |
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473 | } |
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474 | return adaptedLiftBound; |
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475 | } |
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476 | |
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477 | int |
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478 | extLiftBoundAdaption (const CanonicalForm& F, const CFList& factors, bool& |
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479 | success, const ExtensionInfo& info, const CFList& eval, |
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480 | const int deg, const CFList& MOD, const int bound) |
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481 | { |
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482 | Variable alpha= info.getAlpha(); |
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483 | Variable beta= info.getBeta(); |
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484 | CanonicalForm gamma= info.getGamma(); |
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485 | CanonicalForm delta= info.getDelta(); |
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486 | int k= info.getGFDegree(); |
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487 | int adaptedLiftBound= 0; |
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488 | CanonicalForm buf= F; |
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489 | Variable y= F.mvar(); |
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490 | Variable x= Variable (1); |
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491 | CanonicalForm LCBuf= LC (buf, x); |
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492 | CanonicalForm g, gg, quot; |
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493 | CFList M= MOD; |
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494 | M.append (power (y, deg)); |
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495 | adaptedLiftBound= 0; |
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496 | int d= bound; |
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497 | int e= 0; |
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498 | int nBuf; |
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499 | int degMipoBeta= 1; |
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500 | if (!k && beta.level() != 1) |
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501 | degMipoBeta= degree (getMipo (beta)); |
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502 | |
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503 | CFList source, dest; |
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504 | for (CFListIterator i= factors; i.hasItem(); i++) |
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505 | { |
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506 | g= mulMod (i.getItem(), LCBuf, M); |
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507 | g /= myContent (g); |
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508 | if (fdivides (g, buf, quot)) |
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509 | { |
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510 | gg= reverseShift (g, eval); |
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511 | gg /= Lc (gg); |
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512 | if (!k && beta == x) |
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513 | { |
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514 | if (degree (gg, alpha) < degMipoBeta) |
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515 | { |
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516 | buf= quot; |
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517 | nBuf= degree (g, y) + degree (LC (g, x), y); |
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518 | d -= nBuf; |
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519 | e= tmax (e, nBuf); |
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520 | LCBuf= LC (buf, x); |
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521 | } |
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522 | } |
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523 | else |
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524 | { |
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525 | if (!isInExtension (gg, gamma, k, delta, source, dest)) |
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526 | { |
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527 | buf= quot; |
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528 | nBuf= degree (g, y) + degree (LC (g, x), y); |
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529 | d -= nBuf; |
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530 | e= tmax (e, nBuf); |
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531 | LCBuf= LC (buf, x); |
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532 | } |
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533 | } |
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534 | } |
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535 | } |
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536 | adaptedLiftBound= d; |
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537 | |
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538 | if (adaptedLiftBound < deg) |
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539 | { |
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540 | if (adaptedLiftBound < degree (F) + 1) |
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541 | { |
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542 | if (d == 1) |
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543 | { |
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544 | if (e + 1 > deg) |
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545 | { |
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546 | adaptedLiftBound= deg; |
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547 | success= false; |
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548 | } |
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549 | else |
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550 | { |
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551 | success= true; |
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552 | if (e + 1 < degree (F) + 1) |
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553 | adaptedLiftBound= deg; |
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554 | else |
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555 | adaptedLiftBound= e + 1; |
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556 | } |
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557 | } |
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558 | else |
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559 | { |
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560 | success= true; |
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561 | adaptedLiftBound= deg; |
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562 | } |
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563 | } |
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564 | else |
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565 | { |
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566 | success= true; |
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567 | } |
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568 | } |
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569 | |
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570 | return adaptedLiftBound; |
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571 | } |
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572 | |
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573 | CFList |
---|
574 | earlyFactorDetect (CanonicalForm& F, CFList& factors, int& adaptedLiftBound, |
---|
575 | bool& success, const int deg, const CFList& MOD, |
---|
576 | const int bound) |
---|
577 | { |
---|
578 | CFList result; |
---|
579 | CFList T= factors; |
---|
580 | CanonicalForm buf= F; |
---|
581 | Variable y= F.mvar(); |
---|
582 | Variable x= Variable (1); |
---|
583 | CanonicalForm LCBuf= LC (buf, x); |
---|
584 | CanonicalForm g, quot; |
---|
585 | CFList M= MOD; |
---|
586 | M.append (power (y, deg)); |
---|
587 | adaptedLiftBound= 0; |
---|
588 | int d= bound; |
---|
589 | int e= 0; |
---|
590 | int nBuf; |
---|
591 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
592 | { |
---|
593 | g= mulMod (i.getItem(), LCBuf, M); |
---|
594 | g /= myContent (g); |
---|
595 | if (fdivides (g, buf, quot)) |
---|
596 | { |
---|
597 | result.append (g); |
---|
598 | nBuf= degree (g, y) + degree (LC (g, x), y); |
---|
599 | d -= nBuf; |
---|
600 | e= tmax (e, nBuf); |
---|
601 | buf= quot; |
---|
602 | LCBuf= LC (buf, x); |
---|
603 | T= Difference (T, CFList (i.getItem())); |
---|
604 | } |
---|
605 | } |
---|
606 | adaptedLiftBound= d; |
---|
607 | |
---|
608 | if (adaptedLiftBound < deg) |
---|
609 | { |
---|
610 | if (adaptedLiftBound < degree (F) + 1) |
---|
611 | { |
---|
612 | if (d == 1) |
---|
613 | adaptedLiftBound= tmin (e + 1, deg); |
---|
614 | else |
---|
615 | adaptedLiftBound= deg; |
---|
616 | } |
---|
617 | factors= T; |
---|
618 | F= buf; |
---|
619 | success= true; |
---|
620 | } |
---|
621 | return result; |
---|
622 | } |
---|
623 | |
---|
624 | CFList |
---|
625 | extEarlyFactorDetect (CanonicalForm& F, CFList& factors, int& adaptedLiftBound, |
---|
626 | bool& success, const ExtensionInfo& info, const CFList& |
---|
627 | eval, const int deg, const CFList& MOD, const int bound) |
---|
628 | { |
---|
629 | Variable alpha= info.getAlpha(); |
---|
630 | Variable beta= info.getBeta(); |
---|
631 | CanonicalForm gamma= info.getGamma(); |
---|
632 | CanonicalForm delta= info.getDelta(); |
---|
633 | int k= info.getGFDegree(); |
---|
634 | CFList result; |
---|
635 | CFList T= factors; |
---|
636 | CanonicalForm buf= F; |
---|
637 | Variable y= F.mvar(); |
---|
638 | Variable x= Variable (1); |
---|
639 | CanonicalForm LCBuf= LC (buf, x); |
---|
640 | CanonicalForm g, gg, quot; |
---|
641 | CFList M= MOD; |
---|
642 | M.append (power (y, deg)); |
---|
643 | adaptedLiftBound= 0; |
---|
644 | int d= bound; |
---|
645 | int e= 0; |
---|
646 | int nBuf; |
---|
647 | CFList source, dest; |
---|
648 | |
---|
649 | int degMipoBeta= 1; |
---|
650 | if (!k && beta.level() != 1) |
---|
651 | degMipoBeta= degree (getMipo (beta)); |
---|
652 | |
---|
653 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
654 | { |
---|
655 | g= mulMod (i.getItem(), LCBuf, M); |
---|
656 | g /= myContent (g); |
---|
657 | if (fdivides (g, buf, quot)) |
---|
658 | { |
---|
659 | gg= reverseShift (g, eval); |
---|
660 | gg /= Lc (gg); |
---|
661 | if (!k && beta == x) |
---|
662 | { |
---|
663 | if (degree (gg, alpha) < degMipoBeta) |
---|
664 | { |
---|
665 | appendTestMapDown (result, gg, info, source, dest); |
---|
666 | buf= quot; |
---|
667 | nBuf= degree (g, y) + degree (LC (g, x), y); |
---|
668 | d -= nBuf; |
---|
669 | e= tmax (e, nBuf); |
---|
670 | LCBuf= LC (buf, x); |
---|
671 | T= Difference (T, CFList (i.getItem())); |
---|
672 | } |
---|
673 | } |
---|
674 | else |
---|
675 | { |
---|
676 | if (!isInExtension (gg, gamma, k, delta, source, dest)) |
---|
677 | { |
---|
678 | appendTestMapDown (result, gg, info, source, dest); |
---|
679 | buf= quot; |
---|
680 | nBuf= degree (g, y) + degree (LC (g, x), y); |
---|
681 | d -= nBuf; |
---|
682 | e= tmax (e, nBuf); |
---|
683 | LCBuf= LC (buf, x); |
---|
684 | T= Difference (T, CFList (i.getItem())); |
---|
685 | } |
---|
686 | } |
---|
687 | } |
---|
688 | } |
---|
689 | adaptedLiftBound= d; |
---|
690 | |
---|
691 | if (adaptedLiftBound < deg) |
---|
692 | { |
---|
693 | if (adaptedLiftBound < degree (F) + 1) |
---|
694 | { |
---|
695 | if (d == 1) |
---|
696 | adaptedLiftBound= tmin (e + 1, deg); |
---|
697 | else |
---|
698 | adaptedLiftBound= deg; |
---|
699 | } |
---|
700 | success= true; |
---|
701 | factors= T; |
---|
702 | F= buf; |
---|
703 | } |
---|
704 | return result; |
---|
705 | } |
---|
706 | |
---|
707 | #define CHAR_THRESHOLD 8 |
---|
708 | CFList |
---|
709 | evalPoints (const CanonicalForm& F, CFList & eval, const Variable& alpha, |
---|
710 | CFList& list, const bool& GF, bool& fail) |
---|
711 | { |
---|
712 | int k= F.level() - 1; |
---|
713 | Variable x= Variable (1); |
---|
714 | CFList result; |
---|
715 | FFRandom genFF; |
---|
716 | GFRandom genGF; |
---|
717 | int p= getCharacteristic (); |
---|
718 | if (p < CHAR_THRESHOLD) |
---|
719 | { |
---|
720 | if (!GF && alpha.level() == 1) |
---|
721 | { |
---|
722 | fail= true; |
---|
723 | return CFList(); |
---|
724 | } |
---|
725 | else if (!GF && alpha.level() != 1) |
---|
726 | { |
---|
727 | if ((p == 2 && degree (getMipo (alpha)) < 6) || |
---|
728 | (p == 3 && degree (getMipo (alpha)) < 4) || |
---|
729 | (p == 5 && degree (getMipo (alpha)) < 3)) |
---|
730 | { |
---|
731 | fail= true; |
---|
732 | return CFList(); |
---|
733 | } |
---|
734 | } |
---|
735 | } |
---|
736 | double bound; |
---|
737 | if (alpha != x) |
---|
738 | { |
---|
739 | bound= pow ((double) p, (double) degree (getMipo(alpha))); |
---|
740 | bound *= (double) k; |
---|
741 | } |
---|
742 | else if (GF) |
---|
743 | { |
---|
744 | bound= pow ((double) p, (double) getGFDegree()); |
---|
745 | bound *= (double) k; |
---|
746 | } |
---|
747 | else |
---|
748 | bound= pow ((double) p, (double) k); |
---|
749 | |
---|
750 | CanonicalForm random; |
---|
751 | CanonicalForm deriv_x, gcd_deriv; |
---|
752 | do |
---|
753 | { |
---|
754 | random= 0; |
---|
755 | // possible overflow if list.length() does not fit into a int |
---|
756 | if (list.length() >= bound) |
---|
757 | { |
---|
758 | fail= true; |
---|
759 | break; |
---|
760 | } |
---|
761 | for (int i= 0; i < k; i++) |
---|
762 | { |
---|
763 | if (list.isEmpty()) |
---|
764 | result.append (0); |
---|
765 | else if (GF) |
---|
766 | { |
---|
767 | result.append (genGF.generate()); |
---|
768 | random += result.getLast()*power (x, i); |
---|
769 | } |
---|
770 | else if (alpha.level() != 1) |
---|
771 | { |
---|
772 | AlgExtRandomF genAlgExt (alpha); |
---|
773 | result.append (genAlgExt.generate()); |
---|
774 | random += result.getLast()*power (x, i); |
---|
775 | } |
---|
776 | else |
---|
777 | { |
---|
778 | result.append (genFF.generate()); |
---|
779 | random += result.getLast()*power (x, i); |
---|
780 | } |
---|
781 | } |
---|
782 | if (find (list, random)) |
---|
783 | { |
---|
784 | result= CFList(); |
---|
785 | continue; |
---|
786 | } |
---|
787 | int l= F.level(); |
---|
788 | eval.insert (F); |
---|
789 | bool bad= false; |
---|
790 | for (CFListIterator i= result; i.hasItem(); i++, l--) |
---|
791 | { |
---|
792 | eval.insert (eval.getFirst()(i.getItem(), l)); |
---|
793 | if (degree (eval.getFirst(), l - 1) != degree (F, l - 1)) |
---|
794 | { |
---|
795 | if (!find (list, random)) |
---|
796 | list.append (random); |
---|
797 | result= CFList(); |
---|
798 | eval= CFList(); |
---|
799 | bad= true; |
---|
800 | break; |
---|
801 | } |
---|
802 | } |
---|
803 | |
---|
804 | if (bad) |
---|
805 | continue; |
---|
806 | |
---|
807 | if (degree (eval.getFirst()) != degree (F, 1)) |
---|
808 | { |
---|
809 | if (!find (list, random)) |
---|
810 | list.append (random); |
---|
811 | result= CFList(); |
---|
812 | eval= CFList(); |
---|
813 | continue; |
---|
814 | } |
---|
815 | |
---|
816 | deriv_x= deriv (eval.getFirst(), x); |
---|
817 | gcd_deriv= gcd (eval.getFirst(), deriv_x); |
---|
818 | if (degree (gcd_deriv) > 0) |
---|
819 | { |
---|
820 | if (!find (list, random)) |
---|
821 | list.append (random); |
---|
822 | result= CFList(); |
---|
823 | eval= CFList(); |
---|
824 | continue; |
---|
825 | } |
---|
826 | CFListIterator i= eval; |
---|
827 | i++; |
---|
828 | CanonicalForm contentx= content (i.getItem(), x); |
---|
829 | if (degree (contentx) > 0) |
---|
830 | { |
---|
831 | if (!find (list, random)) |
---|
832 | list.append (random); |
---|
833 | result= CFList(); |
---|
834 | eval= CFList(); |
---|
835 | continue; |
---|
836 | } |
---|
837 | |
---|
838 | if (list.length() >= bound) |
---|
839 | { |
---|
840 | fail= true; |
---|
841 | break; |
---|
842 | } |
---|
843 | } while (find (list, random)); |
---|
844 | |
---|
845 | if (!eval.isEmpty()) |
---|
846 | eval.removeFirst(); |
---|
847 | |
---|
848 | return result; |
---|
849 | } |
---|
850 | |
---|
851 | static inline |
---|
852 | int newMainVariableSearch (CanonicalForm& A, CFList& Aeval, CFList& |
---|
853 | evaluation, const Variable& alpha, const int lev, |
---|
854 | CanonicalForm& g |
---|
855 | ) |
---|
856 | { |
---|
857 | Variable x= Variable (1); |
---|
858 | CanonicalForm derivI, buf; |
---|
859 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
860 | int swapLevel= 0; |
---|
861 | CFList list; |
---|
862 | bool fail= false; |
---|
863 | buf= A; |
---|
864 | Aeval= CFList(); |
---|
865 | evaluation= CFList(); |
---|
866 | for (int i= lev; i <= A.level(); i++) |
---|
867 | { |
---|
868 | derivI= deriv (buf, Variable (i)); |
---|
869 | if (!derivI.isZero()) |
---|
870 | { |
---|
871 | g= gcd (buf, derivI); |
---|
872 | if (degree (g) > 0) |
---|
873 | return -1; |
---|
874 | |
---|
875 | buf= swapvar (buf, x, Variable (i)); |
---|
876 | Aeval= CFList(); |
---|
877 | evaluation= CFList(); |
---|
878 | fail= false; |
---|
879 | evaluation= evalPoints (buf, Aeval, alpha, list, GF, fail); |
---|
880 | if (!fail) |
---|
881 | { |
---|
882 | A= buf; |
---|
883 | swapLevel= i; |
---|
884 | break; |
---|
885 | } |
---|
886 | else |
---|
887 | buf= A; |
---|
888 | } |
---|
889 | } |
---|
890 | return swapLevel; |
---|
891 | } |
---|
892 | |
---|
893 | CanonicalForm lcmContent (const CanonicalForm& A, CFList& contentAi) |
---|
894 | { |
---|
895 | int i= A.level(); |
---|
896 | contentAi.append (myContent (A, i)); |
---|
897 | contentAi.append (myContent (A, i - 1)); |
---|
898 | CanonicalForm result= lcm (contentAi.getFirst(), contentAi.getLast()); |
---|
899 | for (i= i - 2; i > 0; i--) |
---|
900 | { |
---|
901 | contentAi.append (content (A, i)); |
---|
902 | result= lcm (result, contentAi.getLast()); |
---|
903 | } |
---|
904 | return result; |
---|
905 | } |
---|
906 | |
---|
907 | CFList |
---|
908 | henselLiftAndEarly (CanonicalForm& A, CFList& MOD, int*& liftBounds, bool& |
---|
909 | earlySuccess, CFList& earlyFactors, const CFList& Aeval, |
---|
910 | const CFList& biFactors, const CFList& evaluation, |
---|
911 | const ExtensionInfo& info) |
---|
912 | { |
---|
913 | bool extension= info.isInExtension(); |
---|
914 | CFList bufFactors= biFactors; |
---|
915 | bufFactors.insert (LC (Aeval.getFirst(), 1)); |
---|
916 | |
---|
917 | sortList (bufFactors, Variable (1)); |
---|
918 | |
---|
919 | CFList diophant; |
---|
920 | CFArray Pi; |
---|
921 | int smallFactorDeg= 11; //tunable parameter |
---|
922 | CFList result; |
---|
923 | int adaptedLiftBound= 0; |
---|
924 | int liftBound= liftBounds[1]; |
---|
925 | |
---|
926 | earlySuccess= false; |
---|
927 | CFList earlyReconstFactors; |
---|
928 | CFListIterator j= Aeval; |
---|
929 | j++; |
---|
930 | CanonicalForm buf= j.getItem(); |
---|
931 | CFMatrix Mat= CFMatrix (liftBound, bufFactors.length() - 1); |
---|
932 | MOD= CFList (power (Variable (2), liftBounds[0])); |
---|
933 | if (smallFactorDeg >= liftBound) |
---|
934 | { |
---|
935 | result= henselLift23 (Aeval, bufFactors, liftBounds, diophant, Pi, Mat); |
---|
936 | } |
---|
937 | else if (smallFactorDeg >= degree (buf) + 1) |
---|
938 | { |
---|
939 | liftBounds[1]= degree (buf) + 1; |
---|
940 | result= henselLift23 (Aeval, bufFactors, liftBounds, diophant, Pi, Mat); |
---|
941 | if (Aeval.length() == 2) |
---|
942 | { |
---|
943 | if (!extension) |
---|
944 | earlyFactors= earlyFactorDetect |
---|
945 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
946 | degree (buf) + 1, MOD, liftBound); |
---|
947 | else |
---|
948 | earlyFactors= extEarlyFactorDetect |
---|
949 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
950 | info, evaluation, degree |
---|
951 | (buf) + 1, MOD, liftBound); |
---|
952 | } |
---|
953 | else |
---|
954 | { |
---|
955 | if (!extension) |
---|
956 | adaptedLiftBound= liftBoundAdaption (buf, result, earlySuccess, |
---|
957 | degree (buf) + 1, MOD, liftBound); |
---|
958 | else |
---|
959 | adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, info, |
---|
960 | evaluation, degree (buf) + 1, |
---|
961 | MOD, liftBound); |
---|
962 | } |
---|
963 | if (!earlySuccess) |
---|
964 | { |
---|
965 | result.insert (LC (buf, 1)); |
---|
966 | liftBounds[1]= adaptedLiftBound; |
---|
967 | liftBound= adaptedLiftBound; |
---|
968 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
969 | Pi, diophant, Mat, MOD); |
---|
970 | } |
---|
971 | else |
---|
972 | liftBounds[1]= adaptedLiftBound; |
---|
973 | } |
---|
974 | else if (smallFactorDeg < degree (buf) + 1) |
---|
975 | { |
---|
976 | liftBounds[1]= smallFactorDeg; |
---|
977 | result= henselLift23 (Aeval, bufFactors, liftBounds, diophant, Pi, Mat); |
---|
978 | if (Aeval.length() == 2) |
---|
979 | { |
---|
980 | if (!extension) |
---|
981 | earlyFactors= earlyFactorDetect (buf, result, adaptedLiftBound, |
---|
982 | earlySuccess, smallFactorDeg, MOD, |
---|
983 | liftBound); |
---|
984 | else |
---|
985 | earlyFactors= extEarlyFactorDetect (buf, result, adaptedLiftBound, |
---|
986 | earlySuccess, info, evaluation, |
---|
987 | smallFactorDeg, MOD, liftBound); |
---|
988 | } |
---|
989 | else |
---|
990 | { |
---|
991 | if (!extension) |
---|
992 | adaptedLiftBound= liftBoundAdaption (buf, result, earlySuccess, |
---|
993 | smallFactorDeg, MOD, liftBound); |
---|
994 | else |
---|
995 | adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, info, |
---|
996 | evaluation, smallFactorDeg, MOD, |
---|
997 | liftBound); |
---|
998 | } |
---|
999 | |
---|
1000 | if (!earlySuccess) |
---|
1001 | { |
---|
1002 | result.insert (LC (buf, 1)); |
---|
1003 | henselLiftResume (buf, result, smallFactorDeg, degree (buf) + 1, |
---|
1004 | Pi, diophant, Mat, MOD); |
---|
1005 | if (Aeval.length() == 2) |
---|
1006 | { |
---|
1007 | if (!extension) |
---|
1008 | earlyFactors= earlyFactorDetect (buf, result, adaptedLiftBound, |
---|
1009 | earlySuccess, degree (buf) + 1, |
---|
1010 | MOD, liftBound); |
---|
1011 | else |
---|
1012 | earlyFactors= extEarlyFactorDetect (buf, result, adaptedLiftBound, |
---|
1013 | earlySuccess, info, evaluation, |
---|
1014 | degree (buf) + 1, MOD, |
---|
1015 | liftBound); |
---|
1016 | } |
---|
1017 | else |
---|
1018 | { |
---|
1019 | if (!extension) |
---|
1020 | adaptedLiftBound= liftBoundAdaption (buf, result, earlySuccess, |
---|
1021 | degree (buf) + 1, MOD,liftBound); |
---|
1022 | else |
---|
1023 | adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, |
---|
1024 | info, evaluation, |
---|
1025 | degree (buf) + 1, MOD, |
---|
1026 | liftBound); |
---|
1027 | } |
---|
1028 | if (!earlySuccess) |
---|
1029 | { |
---|
1030 | result.insert (LC (buf, 1)); |
---|
1031 | liftBounds[1]= adaptedLiftBound; |
---|
1032 | liftBound= adaptedLiftBound; |
---|
1033 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
1034 | Pi, diophant, Mat, MOD); |
---|
1035 | } |
---|
1036 | else |
---|
1037 | liftBounds[1]= adaptedLiftBound; |
---|
1038 | } |
---|
1039 | else |
---|
1040 | liftBounds[1]= adaptedLiftBound; |
---|
1041 | } |
---|
1042 | |
---|
1043 | MOD.append (power (Variable (3), liftBounds[1])); |
---|
1044 | |
---|
1045 | if (Aeval.length() > 2) |
---|
1046 | { |
---|
1047 | CFListIterator j= Aeval; |
---|
1048 | j++; |
---|
1049 | CFList bufEval; |
---|
1050 | bufEval.append (j.getItem()); |
---|
1051 | j++; |
---|
1052 | int liftBoundsLength= Aeval.getLast().level() - 1; |
---|
1053 | for (int i= 2; i <= liftBoundsLength && j.hasItem(); i++, j++) |
---|
1054 | { |
---|
1055 | earlySuccess= false; |
---|
1056 | result.insert (LC (bufEval.getFirst(), 1)); |
---|
1057 | bufEval.append (j.getItem()); |
---|
1058 | liftBound= liftBounds[i]; |
---|
1059 | Mat= CFMatrix (liftBounds[i], result.length() - 1); |
---|
1060 | |
---|
1061 | buf= j.getItem(); |
---|
1062 | if (smallFactorDeg >= liftBound) |
---|
1063 | result= henselLift (bufEval, result, MOD, diophant, Pi, Mat, |
---|
1064 | liftBounds[i - 1], liftBounds[i]); |
---|
1065 | else if (smallFactorDeg >= degree (buf) + 1) |
---|
1066 | { |
---|
1067 | result= henselLift (bufEval, result, MOD, diophant, Pi, Mat, |
---|
1068 | liftBounds[i - 1], degree (buf) + 1); |
---|
1069 | |
---|
1070 | if (Aeval.length() == i + 1) |
---|
1071 | { |
---|
1072 | if (!extension) |
---|
1073 | earlyFactors= earlyFactorDetect |
---|
1074 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1075 | degree (buf) + 1, MOD, liftBound); |
---|
1076 | else |
---|
1077 | earlyFactors= extEarlyFactorDetect |
---|
1078 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1079 | info, evaluation, degree (buf) + 1, MOD, liftBound); |
---|
1080 | } |
---|
1081 | else |
---|
1082 | { |
---|
1083 | if (!extension) |
---|
1084 | adaptedLiftBound= liftBoundAdaption |
---|
1085 | (buf, result, earlySuccess, degree (buf) |
---|
1086 | + 1, MOD, liftBound); |
---|
1087 | else |
---|
1088 | adaptedLiftBound= extLiftBoundAdaption |
---|
1089 | (buf, result, earlySuccess, info, evaluation, |
---|
1090 | degree (buf) + 1, MOD, liftBound); |
---|
1091 | } |
---|
1092 | |
---|
1093 | if (!earlySuccess) |
---|
1094 | { |
---|
1095 | result.insert (LC (buf, 1)); |
---|
1096 | liftBounds[i]= adaptedLiftBound; |
---|
1097 | liftBound= adaptedLiftBound; |
---|
1098 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
1099 | Pi, diophant, Mat, MOD); |
---|
1100 | } |
---|
1101 | else |
---|
1102 | { |
---|
1103 | liftBounds[i]= adaptedLiftBound; |
---|
1104 | } |
---|
1105 | } |
---|
1106 | else if (smallFactorDeg < degree (buf) + 1) |
---|
1107 | { |
---|
1108 | result= henselLift (bufEval, result, MOD, diophant, Pi, Mat, |
---|
1109 | liftBounds[i - 1], smallFactorDeg); |
---|
1110 | |
---|
1111 | if (Aeval.length() == i + 1) |
---|
1112 | { |
---|
1113 | if (!extension) |
---|
1114 | earlyFactors= earlyFactorDetect |
---|
1115 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1116 | smallFactorDeg, MOD, liftBound); |
---|
1117 | else |
---|
1118 | earlyFactors= extEarlyFactorDetect |
---|
1119 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1120 | info, evaluation, smallFactorDeg, MOD, liftBound); |
---|
1121 | } |
---|
1122 | else |
---|
1123 | { |
---|
1124 | if (!extension) |
---|
1125 | adaptedLiftBound= liftBoundAdaption |
---|
1126 | (buf, result, earlySuccess, |
---|
1127 | smallFactorDeg, MOD, liftBound); |
---|
1128 | else |
---|
1129 | adaptedLiftBound= extLiftBoundAdaption |
---|
1130 | (buf, result, earlySuccess, info, evaluation, |
---|
1131 | smallFactorDeg, MOD, liftBound); |
---|
1132 | } |
---|
1133 | |
---|
1134 | if (!earlySuccess) |
---|
1135 | { |
---|
1136 | result.insert (LC (buf, 1)); |
---|
1137 | henselLiftResume (buf, result, smallFactorDeg, |
---|
1138 | degree (buf) + 1, Pi, diophant, Mat, MOD); |
---|
1139 | if (Aeval.length() == i + 1) |
---|
1140 | { |
---|
1141 | if (!extension) |
---|
1142 | earlyFactors= earlyFactorDetect |
---|
1143 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1144 | degree (buf) + 1, MOD, liftBound); |
---|
1145 | else |
---|
1146 | earlyFactors= extEarlyFactorDetect |
---|
1147 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
1148 | info, evaluation, degree (buf) + 1, MOD, |
---|
1149 | liftBound); |
---|
1150 | } |
---|
1151 | else |
---|
1152 | { |
---|
1153 | if (!extension) |
---|
1154 | adaptedLiftBound= liftBoundAdaption |
---|
1155 | (buf, result, earlySuccess, degree |
---|
1156 | (buf) + 1, MOD, liftBound); |
---|
1157 | else |
---|
1158 | adaptedLiftBound= extLiftBoundAdaption |
---|
1159 | (buf, result, earlySuccess, info, evaluation, |
---|
1160 | degree (buf) + 1, MOD, liftBound); |
---|
1161 | } |
---|
1162 | |
---|
1163 | if (!earlySuccess) |
---|
1164 | { |
---|
1165 | result.insert (LC (buf, 1)); |
---|
1166 | liftBounds[i]= adaptedLiftBound; |
---|
1167 | liftBound= adaptedLiftBound; |
---|
1168 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
1169 | Pi, diophant, Mat, MOD); |
---|
1170 | } |
---|
1171 | else |
---|
1172 | liftBounds[i]= adaptedLiftBound; |
---|
1173 | } |
---|
1174 | else |
---|
1175 | liftBounds[i]= adaptedLiftBound; |
---|
1176 | } |
---|
1177 | MOD.append (power (Variable (i + 2), liftBounds[i])); |
---|
1178 | bufEval.removeFirst(); |
---|
1179 | } |
---|
1180 | bufFactors= result; |
---|
1181 | } |
---|
1182 | else |
---|
1183 | bufFactors= result; |
---|
1184 | |
---|
1185 | if (earlySuccess) |
---|
1186 | A= buf; |
---|
1187 | return result; |
---|
1188 | } |
---|
1189 | |
---|
1190 | void |
---|
1191 | gcdFreeBasis (CFFList& factors1, CFFList& factors2) |
---|
1192 | { |
---|
1193 | CanonicalForm g; |
---|
1194 | int k= factors1.length(); |
---|
1195 | int l= factors2.length(); |
---|
1196 | int n= 1; |
---|
1197 | int m; |
---|
1198 | CFFListIterator j; |
---|
1199 | for (CFFListIterator i= factors1; (n < k && i.hasItem()); i++, n++) |
---|
1200 | { |
---|
1201 | m= 1; |
---|
1202 | for (j= factors2; (m < l && j.hasItem()); j++, m++) |
---|
1203 | { |
---|
1204 | g= gcd (i.getItem().factor(), j.getItem().factor()); |
---|
1205 | if (degree (g,1) > 0) |
---|
1206 | { |
---|
1207 | j.getItem()= CFFactor (j.getItem().factor()/g, j.getItem().exp()); |
---|
1208 | i.getItem()= CFFactor (i.getItem().factor()/g, i.getItem().exp()); |
---|
1209 | factors1.append (CFFactor (g, i.getItem().exp())); |
---|
1210 | factors2.append (CFFactor (g, j.getItem().exp())); |
---|
1211 | } |
---|
1212 | } |
---|
1213 | } |
---|
1214 | } |
---|
1215 | |
---|
1216 | CFList |
---|
1217 | distributeContent (const CFList& L, const CFList* differentSecondVarFactors, |
---|
1218 | int length |
---|
1219 | ) |
---|
1220 | { |
---|
1221 | CFList l= L; |
---|
1222 | CanonicalForm content= l.getFirst(); |
---|
1223 | |
---|
1224 | if (content.inCoeffDomain()) |
---|
1225 | return l; |
---|
1226 | |
---|
1227 | if (l.length() == 1) |
---|
1228 | { |
---|
1229 | CFList result; |
---|
1230 | for (int i= 0; i < length; i++) |
---|
1231 | { |
---|
1232 | if (differentSecondVarFactors[i].isEmpty()) |
---|
1233 | continue; |
---|
1234 | if (result.isEmpty()) |
---|
1235 | { |
---|
1236 | result= differentSecondVarFactors[i]; |
---|
1237 | for (CFListIterator iter= result; iter.hasItem(); iter++) |
---|
1238 | content /= iter.getItem(); |
---|
1239 | } |
---|
1240 | else |
---|
1241 | { |
---|
1242 | CFListIterator iter1= result; |
---|
1243 | for (CFListIterator iter2= differentSecondVarFactors[i];iter2.hasItem(); |
---|
1244 | iter2++, iter1++) |
---|
1245 | { |
---|
1246 | iter1.getItem() *= iter2.getItem(); |
---|
1247 | content /= iter2.getItem(); |
---|
1248 | } |
---|
1249 | } |
---|
1250 | } |
---|
1251 | result.insert (content); |
---|
1252 | return result; |
---|
1253 | } |
---|
1254 | |
---|
1255 | Variable v; |
---|
1256 | CFListIterator iter1, iter2; |
---|
1257 | CanonicalForm tmp, g; |
---|
1258 | CFList multiplier; |
---|
1259 | for (int i= 0; i < length; i++) |
---|
1260 | { |
---|
1261 | if (differentSecondVarFactors[i].isEmpty()) |
---|
1262 | continue; |
---|
1263 | iter1= l; |
---|
1264 | iter1++; |
---|
1265 | |
---|
1266 | tmp= 1; |
---|
1267 | for (iter2= differentSecondVarFactors[i]; iter2.hasItem(); |
---|
1268 | iter2++, iter1++) |
---|
1269 | { |
---|
1270 | if (iter2.getItem().inCoeffDomain()) |
---|
1271 | { |
---|
1272 | multiplier.append (1); |
---|
1273 | continue; |
---|
1274 | } |
---|
1275 | v= iter2.getItem().mvar(); |
---|
1276 | if (degree (iter2.getItem()) == degree (iter1.getItem(),v)) |
---|
1277 | { |
---|
1278 | multiplier.append (1); |
---|
1279 | continue; |
---|
1280 | } |
---|
1281 | g= gcd (iter2.getItem(), content); |
---|
1282 | if (!g.inCoeffDomain()) |
---|
1283 | { |
---|
1284 | tmp *= g; |
---|
1285 | multiplier.append (g); |
---|
1286 | } |
---|
1287 | else |
---|
1288 | multiplier.append (1); |
---|
1289 | } |
---|
1290 | if (!tmp.isOne() && fdivides (tmp, content)) |
---|
1291 | { |
---|
1292 | iter1= l; |
---|
1293 | iter1++; |
---|
1294 | content /= tmp; |
---|
1295 | for (iter2= multiplier; iter2.hasItem(); iter1++, iter2++) |
---|
1296 | iter1.getItem() *= iter2.getItem(); |
---|
1297 | } |
---|
1298 | multiplier= CFList(); |
---|
1299 | } |
---|
1300 | |
---|
1301 | l.removeFirst(); |
---|
1302 | l.insert (content); |
---|
1303 | return l; |
---|
1304 | } |
---|
1305 | |
---|
1306 | int |
---|
1307 | testFactors (const CanonicalForm& G, const CFList& uniFactors, |
---|
1308 | const Variable& alpha, CanonicalForm& sqrfPartF, CFList& factors, |
---|
1309 | CFFList*& bufSqrfFactors, CFList& evalSqrfPartF, |
---|
1310 | const CFArray& evalPoint) |
---|
1311 | { |
---|
1312 | CanonicalForm tmp; |
---|
1313 | CFListIterator j; |
---|
1314 | for (CFListIterator i= uniFactors; i.hasItem(); i++) |
---|
1315 | { |
---|
1316 | tmp= i.getItem(); |
---|
1317 | if (i.hasItem()) |
---|
1318 | i++; |
---|
1319 | else |
---|
1320 | break; |
---|
1321 | for (j= i; j.hasItem(); j++) |
---|
1322 | { |
---|
1323 | if (tmp == j.getItem()) |
---|
1324 | return 0; |
---|
1325 | } |
---|
1326 | } |
---|
1327 | |
---|
1328 | CanonicalForm F= G; |
---|
1329 | CFFList sqrfFactorization; |
---|
1330 | if (getCharacteristic() > 0) |
---|
1331 | sqrfFactorization= squarefreeFactorization (F, alpha); |
---|
1332 | else |
---|
1333 | sqrfFactorization= sqrFree (F); |
---|
1334 | |
---|
1335 | sqrfPartF= 1; |
---|
1336 | for (CFFListIterator i= sqrfFactorization; i.hasItem(); i++) |
---|
1337 | sqrfPartF *= i.getItem().factor(); |
---|
1338 | |
---|
1339 | evalSqrfPartF= evaluateAtEval (sqrfPartF, evalPoint); |
---|
1340 | |
---|
1341 | CanonicalForm test= evalSqrfPartF.getFirst() (evalPoint[0], 2); |
---|
1342 | |
---|
1343 | if (degree (test) != degree (sqrfPartF, 1) || test.inCoeffDomain()) |
---|
1344 | return 0; |
---|
1345 | |
---|
1346 | CFFList sqrfFactors; |
---|
1347 | CFList tmp2; |
---|
1348 | int k= 0; |
---|
1349 | factors= uniFactors; |
---|
1350 | CFFListIterator iter; |
---|
1351 | for (CFListIterator i= factors; i.hasItem(); i++, k++) |
---|
1352 | { |
---|
1353 | tmp= 1; |
---|
1354 | if (getCharacteristic() > 0) |
---|
1355 | sqrfFactors= squarefreeFactorization (i.getItem(), alpha); |
---|
1356 | else |
---|
1357 | sqrfFactors= sqrFree (i.getItem()); |
---|
1358 | |
---|
1359 | for (iter= sqrfFactors; iter.hasItem(); iter++) |
---|
1360 | { |
---|
1361 | tmp2.append (iter.getItem().factor()); |
---|
1362 | tmp *= iter.getItem().factor(); |
---|
1363 | } |
---|
1364 | i.getItem()= tmp/Lc(tmp); |
---|
1365 | bufSqrfFactors [k]= sqrfFactors; |
---|
1366 | } |
---|
1367 | |
---|
1368 | for (int i= 0; i < factors.length() - 1; i++) |
---|
1369 | { |
---|
1370 | for (k= i + 1; k < factors.length(); k++) |
---|
1371 | { |
---|
1372 | gcdFreeBasis (bufSqrfFactors [i], bufSqrfFactors[k]); |
---|
1373 | } |
---|
1374 | } |
---|
1375 | |
---|
1376 | factors= CFList(); |
---|
1377 | for (int i= 0; i < uniFactors.length(); i++) |
---|
1378 | { |
---|
1379 | if (i == 0) |
---|
1380 | { |
---|
1381 | for (iter= bufSqrfFactors [i]; iter.hasItem(); iter++) |
---|
1382 | { |
---|
1383 | if (iter.getItem().factor().inCoeffDomain()) |
---|
1384 | continue; |
---|
1385 | iter.getItem()= CFFactor (iter.getItem().factor()/ |
---|
1386 | Lc (iter.getItem().factor()), |
---|
1387 | iter.getItem().exp()); |
---|
1388 | factors.append (iter.getItem().factor()); |
---|
1389 | } |
---|
1390 | } |
---|
1391 | else |
---|
1392 | { |
---|
1393 | for (iter= bufSqrfFactors [i]; iter.hasItem(); iter++) |
---|
1394 | { |
---|
1395 | if (iter.getItem().factor().inCoeffDomain()) |
---|
1396 | continue; |
---|
1397 | iter.getItem()= CFFactor (iter.getItem().factor()/ |
---|
1398 | Lc (iter.getItem().factor()), |
---|
1399 | iter.getItem().exp()); |
---|
1400 | if (!find (factors, iter.getItem().factor())) |
---|
1401 | factors.append (iter.getItem().factor()); |
---|
1402 | } |
---|
1403 | } |
---|
1404 | } |
---|
1405 | |
---|
1406 | test= prod (factors); |
---|
1407 | tmp= evalSqrfPartF.getFirst() (evalPoint[0],2); |
---|
1408 | if (test/Lc (test) != tmp/Lc (tmp)) |
---|
1409 | return 0; |
---|
1410 | else |
---|
1411 | return 1; |
---|
1412 | } |
---|
1413 | |
---|
1414 | CFList |
---|
1415 | precomputeLeadingCoeff (const CanonicalForm& LCF, const CFList& LCFFactors, |
---|
1416 | const Variable& alpha, const CFList& evaluation, |
---|
1417 | CFList* & differentSecondVarLCs, int lSecondVarLCs, |
---|
1418 | Variable& y |
---|
1419 | ) |
---|
1420 | { |
---|
1421 | y= Variable (1); |
---|
1422 | if (LCF.inCoeffDomain()) |
---|
1423 | { |
---|
1424 | CFList result; |
---|
1425 | for (int i= 1; i <= LCFFactors.length() + 1; i++) |
---|
1426 | result.append (1); |
---|
1427 | return result; |
---|
1428 | } |
---|
1429 | |
---|
1430 | CFMap N, M; |
---|
1431 | CFArray dummy= CFArray (2); |
---|
1432 | dummy [0]= LCF; |
---|
1433 | dummy [1]= Variable (2); |
---|
1434 | compress (dummy, M, N); |
---|
1435 | CanonicalForm F= M (LCF); |
---|
1436 | if (LCF.isUnivariate()) |
---|
1437 | { |
---|
1438 | CFList result; |
---|
1439 | int LCFLevel= LCF.level(); |
---|
1440 | bool found= false; |
---|
1441 | if (LCFLevel == 2) |
---|
1442 | { |
---|
1443 | //bivariate leading coefficients are already the true leading coefficients |
---|
1444 | result= LCFFactors; |
---|
1445 | found= true; |
---|
1446 | } |
---|
1447 | else |
---|
1448 | { |
---|
1449 | CFListIterator j; |
---|
1450 | for (int i= 0; i < lSecondVarLCs; i++) |
---|
1451 | { |
---|
1452 | for (j= differentSecondVarLCs[i]; j.hasItem(); j++) |
---|
1453 | { |
---|
1454 | if (j.getItem().level() == LCFLevel) |
---|
1455 | { |
---|
1456 | found= true; |
---|
1457 | break; |
---|
1458 | } |
---|
1459 | } |
---|
1460 | if (found) |
---|
1461 | { |
---|
1462 | result= differentSecondVarLCs [i]; |
---|
1463 | break; |
---|
1464 | } |
---|
1465 | } |
---|
1466 | if (!found) |
---|
1467 | result= LCFFactors; |
---|
1468 | } |
---|
1469 | if (found) |
---|
1470 | result.insert (Lc (LCF)); |
---|
1471 | else |
---|
1472 | { |
---|
1473 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
1474 | i.getItem() *= LCF; |
---|
1475 | result.insert (LCF); |
---|
1476 | } |
---|
1477 | return result; |
---|
1478 | } |
---|
1479 | |
---|
1480 | CFList factors= LCFFactors; |
---|
1481 | |
---|
1482 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
1483 | i.getItem()= M (i.getItem()); |
---|
1484 | |
---|
1485 | CanonicalForm sqrfPartF; |
---|
1486 | CFFList * bufSqrfFactors= new CFFList [factors.length()]; |
---|
1487 | CFList evalSqrfPartF, bufFactors; |
---|
1488 | CFArray evalPoint= CFArray (evaluation.length() - 1); |
---|
1489 | CFArray buf= CFArray (evaluation.length()); |
---|
1490 | CFArray swap= CFArray (evaluation.length()); |
---|
1491 | CFListIterator iter= evaluation; |
---|
1492 | CanonicalForm vars=getVars (LCF)*Variable (2); |
---|
1493 | for (int i= evaluation.length() +1; i > 1; i--, iter++) |
---|
1494 | { |
---|
1495 | buf[i-2]=iter.getItem(); |
---|
1496 | if (degree (vars, i) > 0) |
---|
1497 | swap[M(Variable (i)).level()-1]=buf[i-2]; |
---|
1498 | } |
---|
1499 | buf= swap; |
---|
1500 | for (int i= 0; i < evaluation.length() - 1; i++) |
---|
1501 | evalPoint[i]= buf[i+1]; |
---|
1502 | |
---|
1503 | int pass= testFactors (F, factors, alpha, sqrfPartF, |
---|
1504 | bufFactors, bufSqrfFactors, evalSqrfPartF, evalPoint); |
---|
1505 | |
---|
1506 | bool foundDifferent= false; |
---|
1507 | Variable z, x= y; |
---|
1508 | int j= 0; |
---|
1509 | if (!pass) |
---|
1510 | { |
---|
1511 | int lev= 0; |
---|
1512 | // LCF is non-constant here |
---|
1513 | CFList bufBufFactors; |
---|
1514 | CanonicalForm bufF; |
---|
1515 | for (int i= 0; i < lSecondVarLCs; i++) |
---|
1516 | { |
---|
1517 | if (!differentSecondVarLCs [i].isEmpty()) |
---|
1518 | { |
---|
1519 | bool allConstant= true; |
---|
1520 | for (iter= differentSecondVarLCs[i]; iter.hasItem(); iter++) |
---|
1521 | { |
---|
1522 | if (!iter.getItem().inCoeffDomain()) |
---|
1523 | { |
---|
1524 | allConstant= false; |
---|
1525 | y= Variable (iter.getItem().level()); |
---|
1526 | lev= M(y).level(); |
---|
1527 | } |
---|
1528 | } |
---|
1529 | if (allConstant) |
---|
1530 | continue; |
---|
1531 | |
---|
1532 | bufFactors= differentSecondVarLCs [i]; |
---|
1533 | for (iter= bufFactors; iter.hasItem(); iter++) |
---|
1534 | iter.getItem()= swapvar (iter.getItem(), x, y); |
---|
1535 | bufF= F; |
---|
1536 | z= Variable (lev); |
---|
1537 | bufF= swapvar (bufF, x, z); |
---|
1538 | bufBufFactors= bufFactors; |
---|
1539 | evalPoint= CFArray (evaluation.length() - 1); |
---|
1540 | for (int k= 0; k < evaluation.length()-1; k++) |
---|
1541 | { |
---|
1542 | if (N (Variable (k+1)).level() != y.level()) |
---|
1543 | evalPoint[k]= buf[k+1]; |
---|
1544 | else |
---|
1545 | evalPoint[k]= buf[0]; |
---|
1546 | } |
---|
1547 | pass= testFactors (bufF, bufBufFactors, alpha, sqrfPartF, bufFactors, |
---|
1548 | bufSqrfFactors, evalSqrfPartF, evalPoint); |
---|
1549 | if (pass) |
---|
1550 | { |
---|
1551 | foundDifferent= true; |
---|
1552 | F= bufF; |
---|
1553 | CFList l= factors; |
---|
1554 | for (iter= l; iter.hasItem(); iter++) |
---|
1555 | iter.getItem()= swapvar (iter.getItem(), x, y); |
---|
1556 | differentSecondVarLCs [i]= l; |
---|
1557 | j= i; |
---|
1558 | break; |
---|
1559 | } |
---|
1560 | if (!pass && i == lSecondVarLCs - 1) |
---|
1561 | { |
---|
1562 | CFList result; |
---|
1563 | result.append (LCF); |
---|
1564 | for (int k= 1; k <= factors.length(); k++) |
---|
1565 | result.append (LCF); |
---|
1566 | y= Variable (1); |
---|
1567 | delete [] bufSqrfFactors; |
---|
1568 | return result; |
---|
1569 | } |
---|
1570 | } |
---|
1571 | } |
---|
1572 | } |
---|
1573 | if (!pass) |
---|
1574 | { |
---|
1575 | CFList result; |
---|
1576 | result.append (LCF); |
---|
1577 | for (int k= 1; k <= factors.length(); k++) |
---|
1578 | result.append (LCF); |
---|
1579 | y= Variable (1); |
---|
1580 | delete [] bufSqrfFactors; |
---|
1581 | return result; |
---|
1582 | } |
---|
1583 | else |
---|
1584 | factors= bufFactors; |
---|
1585 | |
---|
1586 | bufFactors= factors; |
---|
1587 | |
---|
1588 | CFMap MM, NN; |
---|
1589 | dummy [0]= sqrfPartF; |
---|
1590 | dummy [1]= 1; |
---|
1591 | compress (dummy, MM, NN); |
---|
1592 | sqrfPartF= MM (sqrfPartF); |
---|
1593 | CanonicalForm varsSqrfPartF= getVars (sqrfPartF); |
---|
1594 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
1595 | iter.getItem()= MM (iter.getItem()); |
---|
1596 | |
---|
1597 | CFList evaluation2; |
---|
1598 | for (int i= 2; i <= varsSqrfPartF.level(); i++) |
---|
1599 | evaluation2.insert (evalPoint[NN (Variable (i)).level()-2]); |
---|
1600 | |
---|
1601 | CFList interMedResult; |
---|
1602 | CanonicalForm oldSqrfPartF= sqrfPartF; |
---|
1603 | sqrfPartF= shift2Zero (sqrfPartF, evalSqrfPartF, evaluation2); |
---|
1604 | if (factors.length() > 1) |
---|
1605 | { |
---|
1606 | CanonicalForm LC1= LC (oldSqrfPartF, 1); |
---|
1607 | CFList leadingCoeffs; |
---|
1608 | for (int i= 0; i < factors.length(); i++) |
---|
1609 | leadingCoeffs.append (LC1); |
---|
1610 | |
---|
1611 | CFList LC1eval= evaluateAtEval (LC1, evaluation2, 2); |
---|
1612 | CFList oldFactors= factors; |
---|
1613 | for (CFListIterator i= oldFactors; i.hasItem(); i++) |
---|
1614 | i.getItem() *= LC1eval.getFirst()/Lc (i.getItem()); |
---|
1615 | |
---|
1616 | bool success= false; |
---|
1617 | CanonicalForm oldSqrfPartFPowLC= oldSqrfPartF*power(LC1,factors.length()-1); |
---|
1618 | CFList heuResult; |
---|
1619 | if (size (oldSqrfPartFPowLC)/getNumVars (oldSqrfPartFPowLC) < 500 && |
---|
1620 | LucksWangSparseHeuristic (oldSqrfPartFPowLC, |
---|
1621 | oldFactors, 2, leadingCoeffs, heuResult)) |
---|
1622 | { |
---|
1623 | interMedResult= recoverFactors (oldSqrfPartF, heuResult); |
---|
1624 | if (oldFactors.length() == interMedResult.length()) |
---|
1625 | success= true; |
---|
1626 | } |
---|
1627 | if (!success) |
---|
1628 | { |
---|
1629 | LC1= LC (evalSqrfPartF.getFirst(), 1); |
---|
1630 | |
---|
1631 | CFArray leadingCoeffs= CFArray (factors.length()); |
---|
1632 | for (int i= 0; i < factors.length(); i++) |
---|
1633 | leadingCoeffs[i]= LC1; |
---|
1634 | |
---|
1635 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
1636 | i.getItem() *= LC1 (0,2)/Lc (i.getItem()); |
---|
1637 | factors.insert (1); |
---|
1638 | |
---|
1639 | CanonicalForm |
---|
1640 | newSqrfPartF= evalSqrfPartF.getFirst()*power (LC1, factors.length() - 2); |
---|
1641 | |
---|
1642 | int liftBound= degree (newSqrfPartF,2) + 1; |
---|
1643 | |
---|
1644 | CFMatrix M= CFMatrix (liftBound, factors.length() - 1); |
---|
1645 | CFArray Pi; |
---|
1646 | CFList diophant; |
---|
1647 | nonMonicHenselLift12 (newSqrfPartF, factors, liftBound, Pi, diophant, M, |
---|
1648 | leadingCoeffs, false); |
---|
1649 | |
---|
1650 | if (sqrfPartF.level() > 2) |
---|
1651 | { |
---|
1652 | int* liftBounds= new int [sqrfPartF.level() - 1]; |
---|
1653 | liftBounds [0]= liftBound; |
---|
1654 | bool noOneToOne= false; |
---|
1655 | CFList *leadingCoeffs2= new CFList [sqrfPartF.level()-2]; |
---|
1656 | LC1= LC (evalSqrfPartF.getLast(), 1); |
---|
1657 | CFList LCs; |
---|
1658 | for (int i= 0; i < factors.length(); i++) |
---|
1659 | LCs.append (LC1); |
---|
1660 | leadingCoeffs2 [sqrfPartF.level() - 3]= LCs; |
---|
1661 | for (int i= sqrfPartF.level() - 1; i > 2; i--) |
---|
1662 | { |
---|
1663 | for (CFListIterator j= LCs; j.hasItem(); j++) |
---|
1664 | j.getItem()= j.getItem() (0, i + 1); |
---|
1665 | leadingCoeffs2 [i - 3]= LCs; |
---|
1666 | } |
---|
1667 | sqrfPartF *= power (LC1, factors.length()-1); |
---|
1668 | |
---|
1669 | int liftBoundsLength= sqrfPartF.level() - 1; |
---|
1670 | for (int i= 1; i < liftBoundsLength; i++) |
---|
1671 | liftBounds [i]= degree (sqrfPartF, i + 2) + 1; |
---|
1672 | evalSqrfPartF= evaluateAtZero (sqrfPartF); |
---|
1673 | evalSqrfPartF.removeFirst(); |
---|
1674 | factors= nonMonicHenselLift (evalSqrfPartF, factors, leadingCoeffs2, |
---|
1675 | diophant, Pi, liftBounds, sqrfPartF.level() - 1, noOneToOne); |
---|
1676 | delete [] leadingCoeffs2; |
---|
1677 | delete [] liftBounds; |
---|
1678 | } |
---|
1679 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
1680 | iter.getItem()= reverseShift (iter.getItem(), evaluation2); |
---|
1681 | |
---|
1682 | interMedResult= |
---|
1683 | recoverFactors (reverseShift(evalSqrfPartF.getLast(),evaluation2), |
---|
1684 | factors); |
---|
1685 | } |
---|
1686 | } |
---|
1687 | else |
---|
1688 | { |
---|
1689 | CanonicalForm contF=content (oldSqrfPartF,1); |
---|
1690 | factors= CFList (oldSqrfPartF/contF); |
---|
1691 | interMedResult= recoverFactors (oldSqrfPartF, factors); |
---|
1692 | } |
---|
1693 | |
---|
1694 | for (CFListIterator iter= interMedResult; iter.hasItem(); iter++) |
---|
1695 | iter.getItem()= NN (iter.getItem()); |
---|
1696 | |
---|
1697 | CFList result; |
---|
1698 | CFFListIterator k; |
---|
1699 | for (int i= 0; i < LCFFactors.length(); i++) |
---|
1700 | { |
---|
1701 | CanonicalForm tmp= 1; |
---|
1702 | for (k= bufSqrfFactors[i]; k.hasItem(); k++) |
---|
1703 | { |
---|
1704 | int pos= findItem (bufFactors, k.getItem().factor()); |
---|
1705 | if (pos) |
---|
1706 | tmp *= power (getItem (interMedResult, pos), k.getItem().exp()); |
---|
1707 | } |
---|
1708 | result.append (tmp); |
---|
1709 | } |
---|
1710 | |
---|
1711 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
1712 | { |
---|
1713 | F /= i.getItem(); |
---|
1714 | if (foundDifferent) |
---|
1715 | i.getItem()= swapvar (i.getItem(), x, z); |
---|
1716 | i.getItem()= N (i.getItem()); |
---|
1717 | } |
---|
1718 | |
---|
1719 | if (foundDifferent) |
---|
1720 | { |
---|
1721 | CFList l= differentSecondVarLCs [j]; |
---|
1722 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
1723 | i.getItem()= swapvar (i.getItem(), y, z); |
---|
1724 | differentSecondVarLCs [j]= l; |
---|
1725 | F= swapvar (F, x, z); |
---|
1726 | } |
---|
1727 | |
---|
1728 | result.insert (N (F)); |
---|
1729 | |
---|
1730 | result= distributeContent (result, differentSecondVarLCs, lSecondVarLCs); |
---|
1731 | |
---|
1732 | if (!result.getFirst().inCoeffDomain()) |
---|
1733 | { |
---|
1734 | CFListIterator i= result; |
---|
1735 | CanonicalForm tmp; |
---|
1736 | if (foundDifferent) |
---|
1737 | i.getItem()= swapvar (i.getItem(), Variable (2), y); |
---|
1738 | |
---|
1739 | tmp= i.getItem(); |
---|
1740 | |
---|
1741 | i++; |
---|
1742 | for (; i.hasItem(); i++) |
---|
1743 | { |
---|
1744 | if (foundDifferent) |
---|
1745 | i.getItem()= swapvar (i.getItem(), Variable (2), y)*tmp; |
---|
1746 | else |
---|
1747 | i.getItem() *= tmp; |
---|
1748 | } |
---|
1749 | } |
---|
1750 | else |
---|
1751 | y= Variable (1); |
---|
1752 | |
---|
1753 | delete [] bufSqrfFactors; |
---|
1754 | |
---|
1755 | return result; |
---|
1756 | } |
---|
1757 | |
---|
1758 | void |
---|
1759 | evaluationWRTDifferentSecondVars (CFList*& Aeval, const CFList& evaluation, |
---|
1760 | const CanonicalForm& A) |
---|
1761 | { |
---|
1762 | CanonicalForm tmp; |
---|
1763 | CFList tmp2; |
---|
1764 | CFListIterator iter; |
---|
1765 | bool preserveDegree= true; |
---|
1766 | Variable x= Variable (1); |
---|
1767 | int j, degAi, degA1= degree (A,1); |
---|
1768 | for (int i= A.level(); i > 2; i--) |
---|
1769 | { |
---|
1770 | tmp= A; |
---|
1771 | tmp2= CFList(); |
---|
1772 | iter= evaluation; |
---|
1773 | preserveDegree= true; |
---|
1774 | degAi= degree (A,i); |
---|
1775 | for (j= A.level(); j > 1; j--, iter++) |
---|
1776 | { |
---|
1777 | if (j == i) |
---|
1778 | continue; |
---|
1779 | else |
---|
1780 | { |
---|
1781 | tmp= tmp (iter.getItem(), j); |
---|
1782 | tmp2.insert (tmp); |
---|
1783 | if ((degree (tmp, i) != degAi) || |
---|
1784 | (degree (tmp, 1) != degA1)) |
---|
1785 | { |
---|
1786 | preserveDegree= false; |
---|
1787 | break; |
---|
1788 | } |
---|
1789 | } |
---|
1790 | } |
---|
1791 | if (!content(tmp,1).inCoeffDomain()) |
---|
1792 | preserveDegree= false; |
---|
1793 | if (!(gcd (deriv (tmp,x), tmp)).inCoeffDomain()) |
---|
1794 | preserveDegree= false; |
---|
1795 | if (preserveDegree) |
---|
1796 | Aeval [i - 3]= tmp2; |
---|
1797 | else |
---|
1798 | Aeval [i - 3]= CFList(); |
---|
1799 | } |
---|
1800 | } |
---|
1801 | |
---|
1802 | #endif |
---|
1803 | |
---|
1804 | static inline |
---|
1805 | CanonicalForm prodEval (const CFList& l, const CanonicalForm& evalPoint, |
---|
1806 | const Variable& v) |
---|
1807 | { |
---|
1808 | CanonicalForm result= 1; |
---|
1809 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
1810 | result *= i.getItem() (evalPoint, v); |
---|
1811 | return result; |
---|
1812 | } |
---|
1813 | |
---|
1814 | //recombine bivariate factors in case one bivariate factorization yields less |
---|
1815 | // factors than the other |
---|
1816 | CFList |
---|
1817 | recombination (const CFList& factors1, const CFList& factors2, int s, int thres, |
---|
1818 | const CanonicalForm& evalPoint, const Variable& x) |
---|
1819 | { |
---|
1820 | CFList T, S; |
---|
1821 | |
---|
1822 | T= factors1; |
---|
1823 | CFList result; |
---|
1824 | CanonicalForm buf; |
---|
1825 | int * v= new int [T.length()]; |
---|
1826 | for (int i= 0; i < T.length(); i++) |
---|
1827 | v[i]= 0; |
---|
1828 | bool nosubset= false; |
---|
1829 | CFArray TT; |
---|
1830 | TT= copy (factors1); |
---|
1831 | while (T.length() >= 2*s && s <= thres) |
---|
1832 | { |
---|
1833 | while (nosubset == false) |
---|
1834 | { |
---|
1835 | if (T.length() == s) |
---|
1836 | { |
---|
1837 | delete [] v; |
---|
1838 | result.append (prod (T)); |
---|
1839 | return result; |
---|
1840 | } |
---|
1841 | S= subset (v, s, TT, nosubset); |
---|
1842 | if (nosubset) break; |
---|
1843 | buf= prodEval (S, evalPoint, x); |
---|
1844 | buf /= Lc (buf); |
---|
1845 | if (find (factors2, buf)) |
---|
1846 | { |
---|
1847 | T= Difference (T, S); |
---|
1848 | result.append (prod (S)); |
---|
1849 | TT= copy (T); |
---|
1850 | indexUpdate (v, s, T.length(), nosubset); |
---|
1851 | if (nosubset) break; |
---|
1852 | } |
---|
1853 | } |
---|
1854 | s++; |
---|
1855 | if (T.length() < 2*s || T.length() == s) |
---|
1856 | { |
---|
1857 | delete [] v; |
---|
1858 | result.append (prod (T)); |
---|
1859 | return result; |
---|
1860 | } |
---|
1861 | for (int i= 0; i < T.length(); i++) |
---|
1862 | v[i]= 0; |
---|
1863 | nosubset= false; |
---|
1864 | } |
---|
1865 | |
---|
1866 | delete [] v; |
---|
1867 | if (T.length() < 2*s) |
---|
1868 | { |
---|
1869 | result.append (prod (T)); |
---|
1870 | return result; |
---|
1871 | } |
---|
1872 | |
---|
1873 | return result; |
---|
1874 | } |
---|
1875 | |
---|
1876 | #ifdef HAVE_NTL |
---|
1877 | void |
---|
1878 | factorizationWRTDifferentSecondVars (const CanonicalForm& A, CFList*& Aeval, |
---|
1879 | const ExtensionInfo& info, |
---|
1880 | int& minFactorsLength, bool& irred) |
---|
1881 | { |
---|
1882 | Variable x= Variable (1); |
---|
1883 | minFactorsLength= 0; |
---|
1884 | irred= false; |
---|
1885 | CFList factors; |
---|
1886 | Variable v; |
---|
1887 | for (int j= 0; j < A.level() - 2; j++) |
---|
1888 | { |
---|
1889 | if (!Aeval[j].isEmpty()) |
---|
1890 | { |
---|
1891 | v= Variable (Aeval[j].getFirst().level()); |
---|
1892 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
1893 | factors= GFBiSqrfFactorize (Aeval[j].getFirst()); |
---|
1894 | else if (info.getAlpha().level() == 1) |
---|
1895 | factors= FpBiSqrfFactorize (Aeval[j].getFirst()); |
---|
1896 | else |
---|
1897 | factors= FqBiSqrfFactorize (Aeval[j].getFirst(), info.getAlpha()); |
---|
1898 | |
---|
1899 | factors.removeFirst(); |
---|
1900 | if (minFactorsLength == 0) |
---|
1901 | minFactorsLength= factors.length(); |
---|
1902 | else |
---|
1903 | minFactorsLength= tmin (minFactorsLength, factors.length()); |
---|
1904 | |
---|
1905 | if (factors.length() == 1) |
---|
1906 | { |
---|
1907 | irred= true; |
---|
1908 | return; |
---|
1909 | } |
---|
1910 | sortList (factors, x); |
---|
1911 | Aeval [j]= factors; |
---|
1912 | } |
---|
1913 | } |
---|
1914 | } |
---|
1915 | |
---|
1916 | CFList conv (const CFArray & A) |
---|
1917 | { |
---|
1918 | CFList result; |
---|
1919 | for (int i= A.max(); i >= A.min(); i--) |
---|
1920 | result.insert (A[i]); |
---|
1921 | return result; |
---|
1922 | } |
---|
1923 | |
---|
1924 | |
---|
1925 | void getLeadingCoeffs (const CanonicalForm& A, CFList*& Aeval, |
---|
1926 | const CFList& uniFactors, const CFList& evaluation |
---|
1927 | ) |
---|
1928 | { |
---|
1929 | CFListIterator iter; |
---|
1930 | CFList LCs; |
---|
1931 | for (int j= 0; j < A.level() - 2; j++) |
---|
1932 | { |
---|
1933 | if (!Aeval[j].isEmpty()) |
---|
1934 | { |
---|
1935 | LCs= CFList(); |
---|
1936 | for (iter= Aeval[j]; iter.hasItem(); iter++) |
---|
1937 | LCs.append (LC (iter.getItem(), 1)); |
---|
1938 | //normalize (LCs); |
---|
1939 | Aeval[j]= LCs; |
---|
1940 | } |
---|
1941 | } |
---|
1942 | } |
---|
1943 | |
---|
1944 | void sortByUniFactors (CFList*& Aeval, int AevalLength, |
---|
1945 | const CFList& uniFactors, const CFList& evaluation |
---|
1946 | ) |
---|
1947 | { |
---|
1948 | CanonicalForm evalPoint; |
---|
1949 | int i; |
---|
1950 | CFListIterator iter, iter2; |
---|
1951 | Variable v; |
---|
1952 | CFList LCs, buf; |
---|
1953 | CFArray l; |
---|
1954 | int pos, index; |
---|
1955 | for (int j= 0; j < AevalLength; j++) |
---|
1956 | { |
---|
1957 | if (!Aeval[j].isEmpty()) |
---|
1958 | { |
---|
1959 | i= evaluation.length() + 1; |
---|
1960 | for (iter= evaluation; iter.hasItem(); iter++, i--) |
---|
1961 | { |
---|
1962 | if (i == Aeval[j].getFirst().level()) |
---|
1963 | { |
---|
1964 | evalPoint= iter.getItem(); |
---|
1965 | break; |
---|
1966 | } |
---|
1967 | } |
---|
1968 | |
---|
1969 | v= Variable (i); |
---|
1970 | if (Aeval[j].length() > uniFactors.length()) |
---|
1971 | Aeval[j]= recombination (Aeval[j], uniFactors, 1, |
---|
1972 | Aeval[j].length() - uniFactors.length() + 1, |
---|
1973 | evalPoint, v); |
---|
1974 | |
---|
1975 | buf= buildUniFactors (Aeval[j], evalPoint, v); |
---|
1976 | l= CFArray (uniFactors.length()); |
---|
1977 | index= 1; |
---|
1978 | for (iter= buf; iter.hasItem(); iter++, index++) |
---|
1979 | { |
---|
1980 | pos= findItem (uniFactors, iter.getItem()); |
---|
1981 | if (pos) |
---|
1982 | l[pos-1]= getItem (Aeval[j], index); |
---|
1983 | } |
---|
1984 | buf= conv (l); |
---|
1985 | Aeval [j]= buf; |
---|
1986 | |
---|
1987 | buf= buildUniFactors (Aeval[j], evalPoint, v); |
---|
1988 | } |
---|
1989 | } |
---|
1990 | } |
---|
1991 | |
---|
1992 | CFList |
---|
1993 | buildUniFactors (const CFList& biFactors, const CanonicalForm& evalPoint, |
---|
1994 | const Variable& y) |
---|
1995 | { |
---|
1996 | CFList result; |
---|
1997 | CanonicalForm tmp; |
---|
1998 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
1999 | { |
---|
2000 | tmp= mod (i.getItem(), y - evalPoint); |
---|
2001 | tmp /= Lc (tmp); |
---|
2002 | result.append (tmp); |
---|
2003 | } |
---|
2004 | return result; |
---|
2005 | } |
---|
2006 | |
---|
2007 | void refineBiFactors (const CanonicalForm& A, CFList& biFactors, |
---|
2008 | CFList* const& Aeval, const CFList& evaluation, |
---|
2009 | int minFactorsLength) |
---|
2010 | { |
---|
2011 | CFListIterator iter; |
---|
2012 | CanonicalForm evalPoint; |
---|
2013 | int i; |
---|
2014 | Variable v; |
---|
2015 | Variable y= Variable (2); |
---|
2016 | CFList list; |
---|
2017 | for (int j= 0; j < A.level() - 2; j++) |
---|
2018 | { |
---|
2019 | if (Aeval[j].length() == minFactorsLength) |
---|
2020 | { |
---|
2021 | i= A.level(); |
---|
2022 | |
---|
2023 | for (iter= evaluation; iter.hasItem(); iter++, i--) |
---|
2024 | { |
---|
2025 | if (i == Aeval[j].getFirst().level()) |
---|
2026 | { |
---|
2027 | evalPoint= iter.getItem(); |
---|
2028 | break; |
---|
2029 | } |
---|
2030 | } |
---|
2031 | |
---|
2032 | v= Variable (i); |
---|
2033 | list= buildUniFactors (Aeval[j], evalPoint, v); |
---|
2034 | |
---|
2035 | biFactors= recombination (biFactors, list, 1, |
---|
2036 | biFactors.length() - list.length() + 1, |
---|
2037 | evaluation.getLast(), y); |
---|
2038 | return; |
---|
2039 | } |
---|
2040 | } |
---|
2041 | } |
---|
2042 | |
---|
2043 | void prepareLeadingCoeffs (CFList*& LCs, int n, const CFList& leadingCoeffs, |
---|
2044 | const CFList& biFactors, const CFList& evaluation) |
---|
2045 | { |
---|
2046 | CFList l= leadingCoeffs; |
---|
2047 | LCs [n-3]= l; |
---|
2048 | CFListIterator j; |
---|
2049 | CFListIterator iter= evaluation; |
---|
2050 | for (int i= n - 1; i > 2; i--, iter++) |
---|
2051 | { |
---|
2052 | for (j= l; j.hasItem(); j++) |
---|
2053 | j.getItem()= j.getItem() (iter.getItem(), i + 1); |
---|
2054 | LCs [i - 3]= l; |
---|
2055 | } |
---|
2056 | l= LCs [0]; |
---|
2057 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
2058 | i.getItem()= i.getItem() (iter.getItem(), 3); |
---|
2059 | CFListIterator ii= biFactors; |
---|
2060 | CFList normalizeFactor; |
---|
2061 | for (CFListIterator i= l; i.hasItem(); i++, ii++) |
---|
2062 | normalizeFactor.append (Lc (LC (ii.getItem(), 1))/Lc (i.getItem())); |
---|
2063 | for (int i= 0; i < n-2; i++) |
---|
2064 | { |
---|
2065 | ii= normalizeFactor; |
---|
2066 | for (j= LCs [i]; j.hasItem(); j++, ii++) |
---|
2067 | j.getItem() *= ii.getItem(); |
---|
2068 | } |
---|
2069 | } |
---|
2070 | |
---|
2071 | CFList |
---|
2072 | extNonMonicFactorRecombination (const CFList& factors, const CanonicalForm& F, |
---|
2073 | const ExtensionInfo& info) |
---|
2074 | { |
---|
2075 | Variable alpha= info.getAlpha(); |
---|
2076 | Variable beta= info.getBeta(); |
---|
2077 | CanonicalForm gamma= info.getGamma(); |
---|
2078 | CanonicalForm delta= info.getDelta(); |
---|
2079 | int k= info.getGFDegree(); |
---|
2080 | CFList source, dest; |
---|
2081 | |
---|
2082 | int degMipoBeta= 1; |
---|
2083 | if (!k && beta != Variable(1)) |
---|
2084 | degMipoBeta= degree (getMipo (beta)); |
---|
2085 | |
---|
2086 | CFList T, S; |
---|
2087 | T= factors; |
---|
2088 | int s= 1; |
---|
2089 | CFList result; |
---|
2090 | CanonicalForm quot, buf= F; |
---|
2091 | |
---|
2092 | CanonicalForm g; |
---|
2093 | CanonicalForm buf2; |
---|
2094 | int * v= new int [T.length()]; |
---|
2095 | for (int i= 0; i < T.length(); i++) |
---|
2096 | v[i]= 0; |
---|
2097 | bool noSubset= false; |
---|
2098 | CFArray TT; |
---|
2099 | TT= copy (factors); |
---|
2100 | bool recombination= false; |
---|
2101 | bool trueFactor= false; |
---|
2102 | while (T.length() >= 2*s) |
---|
2103 | { |
---|
2104 | while (noSubset == false) |
---|
2105 | { |
---|
2106 | if (T.length() == s) |
---|
2107 | { |
---|
2108 | delete [] v; |
---|
2109 | if (recombination) |
---|
2110 | { |
---|
2111 | g= prod (T); |
---|
2112 | T.removeFirst(); |
---|
2113 | result.append (g/myContent (g)); |
---|
2114 | g /= Lc (g); |
---|
2115 | appendTestMapDown (result, g, info, source, dest); |
---|
2116 | return result; |
---|
2117 | } |
---|
2118 | else |
---|
2119 | return CFList (buf/myContent(buf)); |
---|
2120 | } |
---|
2121 | |
---|
2122 | S= subset (v, s, TT, noSubset); |
---|
2123 | if (noSubset) break; |
---|
2124 | |
---|
2125 | g= prod (S); |
---|
2126 | g /= myContent (g); |
---|
2127 | if (fdivides (g, buf, quot)) |
---|
2128 | { |
---|
2129 | buf2= g; |
---|
2130 | buf2 /= Lc (buf2); |
---|
2131 | if (!k && beta.level() == 1) |
---|
2132 | { |
---|
2133 | if (degree (buf2, alpha) < degMipoBeta) |
---|
2134 | { |
---|
2135 | appendTestMapDown (result, buf2, info, source, dest); |
---|
2136 | buf= quot; |
---|
2137 | recombination= true; |
---|
2138 | trueFactor= true; |
---|
2139 | } |
---|
2140 | } |
---|
2141 | else |
---|
2142 | { |
---|
2143 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
2144 | { |
---|
2145 | appendTestMapDown (result, buf2, info, source, dest); |
---|
2146 | buf= quot; |
---|
2147 | recombination= true; |
---|
2148 | trueFactor= true; |
---|
2149 | } |
---|
2150 | } |
---|
2151 | if (trueFactor) |
---|
2152 | { |
---|
2153 | T= Difference (T, S); |
---|
2154 | |
---|
2155 | if (T.length() < 2*s || T.length() == s) |
---|
2156 | { |
---|
2157 | delete [] v; |
---|
2158 | buf /= myContent (buf); |
---|
2159 | buf /= Lc (buf); |
---|
2160 | appendTestMapDown (result, buf, info, source, dest); |
---|
2161 | return result; |
---|
2162 | } |
---|
2163 | trueFactor= false; |
---|
2164 | TT= copy (T); |
---|
2165 | indexUpdate (v, s, T.length(), noSubset); |
---|
2166 | if (noSubset) break; |
---|
2167 | } |
---|
2168 | } |
---|
2169 | } |
---|
2170 | s++; |
---|
2171 | if (T.length() < 2*s || T.length() == s) |
---|
2172 | { |
---|
2173 | delete [] v; |
---|
2174 | appendTestMapDown (result, buf/myContent(buf), info, source, dest); |
---|
2175 | return result; |
---|
2176 | } |
---|
2177 | for (int i= 0; i < T.length(); i++) |
---|
2178 | v[i]= 0; |
---|
2179 | noSubset= false; |
---|
2180 | } |
---|
2181 | if (T.length() < 2*s) |
---|
2182 | appendMapDown (result, F/myContent(F), info, source, dest); |
---|
2183 | |
---|
2184 | delete [] v; |
---|
2185 | return result; |
---|
2186 | } |
---|
2187 | |
---|
2188 | CFList |
---|
2189 | extFactorize (const CanonicalForm& F, const ExtensionInfo& info); |
---|
2190 | |
---|
2191 | CFList |
---|
2192 | multiFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
2193 | { |
---|
2194 | |
---|
2195 | if (F.inCoeffDomain()) |
---|
2196 | return CFList (F); |
---|
2197 | |
---|
2198 | // compress and find main Variable |
---|
2199 | CFMap N; |
---|
2200 | CanonicalForm A= myCompress (F, N); |
---|
2201 | |
---|
2202 | A /= Lc (A); // make monic |
---|
2203 | |
---|
2204 | Variable alpha= info.getAlpha(); |
---|
2205 | Variable beta= info.getBeta(); |
---|
2206 | CanonicalForm gamma= info.getGamma(); |
---|
2207 | CanonicalForm delta= info.getDelta(); |
---|
2208 | bool extension= info.isInExtension(); |
---|
2209 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
2210 | //univariate case |
---|
2211 | if (F.isUnivariate()) |
---|
2212 | { |
---|
2213 | if (extension == false) |
---|
2214 | return uniFactorizer (F, alpha, GF); |
---|
2215 | else |
---|
2216 | { |
---|
2217 | CFList source, dest; |
---|
2218 | A= mapDown (F, info, source, dest); |
---|
2219 | return uniFactorizer (A, beta, GF); |
---|
2220 | } |
---|
2221 | } |
---|
2222 | |
---|
2223 | //bivariate case |
---|
2224 | if (A.level() == 2) |
---|
2225 | { |
---|
2226 | CFList buf= biFactorize (F, info); |
---|
2227 | return buf; |
---|
2228 | } |
---|
2229 | |
---|
2230 | Variable x= Variable (1); |
---|
2231 | Variable y= Variable (2); |
---|
2232 | |
---|
2233 | // remove content |
---|
2234 | CFList contentAi; |
---|
2235 | CanonicalForm lcmCont= lcmContent (A, contentAi); |
---|
2236 | A /= lcmCont; |
---|
2237 | |
---|
2238 | // trivial after content removal |
---|
2239 | CFList contentAFactors; |
---|
2240 | if (A.inCoeffDomain()) |
---|
2241 | { |
---|
2242 | for (CFListIterator i= contentAi; i.hasItem(); i++) |
---|
2243 | { |
---|
2244 | if (i.getItem().inCoeffDomain()) |
---|
2245 | continue; |
---|
2246 | else |
---|
2247 | { |
---|
2248 | lcmCont /= i.getItem(); |
---|
2249 | contentAFactors= |
---|
2250 | Union (multiFactorize (lcmCont, info), |
---|
2251 | multiFactorize (i.getItem(), info)); |
---|
2252 | break; |
---|
2253 | } |
---|
2254 | } |
---|
2255 | decompress (contentAFactors, N); |
---|
2256 | if (!extension) |
---|
2257 | normalize (contentAFactors); |
---|
2258 | return contentAFactors; |
---|
2259 | } |
---|
2260 | |
---|
2261 | // factorize content |
---|
2262 | contentAFactors= multiFactorize (lcmCont, info); |
---|
2263 | |
---|
2264 | // univariate after content removal |
---|
2265 | CFList factors; |
---|
2266 | if (A.isUnivariate ()) |
---|
2267 | { |
---|
2268 | factors= uniFactorizer (A, alpha, GF); |
---|
2269 | append (factors, contentAFactors); |
---|
2270 | decompress (factors, N); |
---|
2271 | return factors; |
---|
2272 | } |
---|
2273 | |
---|
2274 | // check main variable |
---|
2275 | int swapLevel= 0; |
---|
2276 | CanonicalForm derivZ; |
---|
2277 | CanonicalForm gcdDerivZ; |
---|
2278 | CanonicalForm bufA= A; |
---|
2279 | Variable z; |
---|
2280 | for (int i= 1; i <= A.level(); i++) |
---|
2281 | { |
---|
2282 | z= Variable (i); |
---|
2283 | derivZ= deriv (bufA, z); |
---|
2284 | if (derivZ.isZero()) |
---|
2285 | { |
---|
2286 | if (i == 1) |
---|
2287 | swapLevel= 1; |
---|
2288 | else |
---|
2289 | continue; |
---|
2290 | } |
---|
2291 | else |
---|
2292 | { |
---|
2293 | if (swapLevel == 1) |
---|
2294 | { |
---|
2295 | swapLevel= i; |
---|
2296 | bufA= swapvar (A, x, z); |
---|
2297 | } |
---|
2298 | gcdDerivZ= gcd (bufA, derivZ); |
---|
2299 | if (degree (gcdDerivZ) > 0 && !derivZ.isZero()) |
---|
2300 | { |
---|
2301 | CanonicalForm g= bufA/gcdDerivZ; |
---|
2302 | CFList factorsG= |
---|
2303 | Union (multiFactorize (g, info), |
---|
2304 | multiFactorize (gcdDerivZ, info)); |
---|
2305 | appendSwapDecompress (factorsG, contentAFactors, N, swapLevel, x); |
---|
2306 | if (!extension) |
---|
2307 | normalize (factorsG); |
---|
2308 | return factorsG; |
---|
2309 | } |
---|
2310 | else |
---|
2311 | { |
---|
2312 | A= bufA; |
---|
2313 | break; |
---|
2314 | } |
---|
2315 | } |
---|
2316 | } |
---|
2317 | |
---|
2318 | |
---|
2319 | CFList Aeval, list, evaluation, bufEvaluation, bufAeval; |
---|
2320 | bool fail= false; |
---|
2321 | int swapLevel2= 0; |
---|
2322 | int level; |
---|
2323 | int factorNums= 3; |
---|
2324 | CFList biFactors, bufBiFactors; |
---|
2325 | CanonicalForm evalPoly; |
---|
2326 | int lift, bufLift, lengthAeval2= A.level()-2; |
---|
2327 | double logarithm= (double) ilog2 (totaldegree (A)); |
---|
2328 | logarithm /= log2exp; |
---|
2329 | logarithm= ceil (logarithm); |
---|
2330 | if (factorNums < (int) logarithm) |
---|
2331 | factorNums= (int) logarithm; |
---|
2332 | CFList* bufAeval2= new CFList [lengthAeval2]; |
---|
2333 | CFList* Aeval2= new CFList [lengthAeval2]; |
---|
2334 | int counter; |
---|
2335 | int differentSecondVar= 0; |
---|
2336 | // several bivariate factorizations |
---|
2337 | for (int i= 0; i < factorNums; i++) |
---|
2338 | { |
---|
2339 | counter= 0; |
---|
2340 | bufA= A; |
---|
2341 | bufAeval= CFList(); |
---|
2342 | bufEvaluation= evalPoints (bufA, bufAeval, alpha, list, GF, fail); |
---|
2343 | evalPoly= 0; |
---|
2344 | |
---|
2345 | if (fail && (i == 0)) |
---|
2346 | { |
---|
2347 | if (!swapLevel) |
---|
2348 | level= 2; |
---|
2349 | else |
---|
2350 | level= swapLevel + 1; |
---|
2351 | |
---|
2352 | CanonicalForm g; |
---|
2353 | swapLevel2= newMainVariableSearch (A, Aeval, evaluation, alpha, level, g); |
---|
2354 | |
---|
2355 | if (!swapLevel2) // need to pass to an extension |
---|
2356 | { |
---|
2357 | factors= extFactorize (A, info); |
---|
2358 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, x); |
---|
2359 | normalize (factors); |
---|
2360 | delete [] bufAeval2; |
---|
2361 | delete [] Aeval2; |
---|
2362 | return factors; |
---|
2363 | } |
---|
2364 | else |
---|
2365 | { |
---|
2366 | if (swapLevel2 == -1) |
---|
2367 | { |
---|
2368 | CFList factorsG= |
---|
2369 | Union (multiFactorize (g, info), |
---|
2370 | multiFactorize (A/g, info)); |
---|
2371 | appendSwapDecompress (factorsG, contentAFactors, N, swapLevel, x); |
---|
2372 | if (!extension) |
---|
2373 | normalize (factorsG); |
---|
2374 | delete [] bufAeval2; |
---|
2375 | delete [] Aeval2; |
---|
2376 | return factorsG; |
---|
2377 | } |
---|
2378 | fail= false; |
---|
2379 | bufAeval= Aeval; |
---|
2380 | bufA= A; |
---|
2381 | bufEvaluation= evaluation; |
---|
2382 | } |
---|
2383 | } |
---|
2384 | else if (fail && (i > 0)) |
---|
2385 | break; |
---|
2386 | |
---|
2387 | evaluationWRTDifferentSecondVars (bufAeval2, bufEvaluation, A); |
---|
2388 | |
---|
2389 | for (int j= 0; j < lengthAeval2; j++) |
---|
2390 | { |
---|
2391 | if (!bufAeval2[j].isEmpty()) |
---|
2392 | counter++; |
---|
2393 | } |
---|
2394 | |
---|
2395 | bufLift= degree (A, y) + 1 + degree (LC(A, x), y); |
---|
2396 | |
---|
2397 | TIMING_START (fac_fq_bi_factorizer); |
---|
2398 | if (!GF && alpha.level() == 1) |
---|
2399 | bufBiFactors= FpBiSqrfFactorize (bufAeval.getFirst()); |
---|
2400 | else if (GF) |
---|
2401 | bufBiFactors= GFBiSqrfFactorize (bufAeval.getFirst()); |
---|
2402 | else |
---|
2403 | bufBiFactors= FqBiSqrfFactorize (bufAeval.getFirst(), alpha); |
---|
2404 | TIMING_END_AND_PRINT (fac_fq_bi_factorizer, |
---|
2405 | "time for bivariate factorization: "); |
---|
2406 | bufBiFactors.removeFirst(); |
---|
2407 | |
---|
2408 | if (bufBiFactors.length() == 1) |
---|
2409 | { |
---|
2410 | if (extension) |
---|
2411 | { |
---|
2412 | CFList source, dest; |
---|
2413 | A= mapDown (A, info, source, dest); |
---|
2414 | } |
---|
2415 | factors.append (A); |
---|
2416 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, |
---|
2417 | swapLevel2, x); |
---|
2418 | if (!extension) |
---|
2419 | normalize (factors); |
---|
2420 | delete [] bufAeval2; |
---|
2421 | delete [] Aeval2; |
---|
2422 | return factors; |
---|
2423 | } |
---|
2424 | |
---|
2425 | if (i == 0) |
---|
2426 | { |
---|
2427 | Aeval= bufAeval; |
---|
2428 | evaluation= bufEvaluation; |
---|
2429 | biFactors= bufBiFactors; |
---|
2430 | lift= bufLift; |
---|
2431 | for (int j= 0; j < lengthAeval2; j++) |
---|
2432 | Aeval2 [j]= bufAeval2 [j]; |
---|
2433 | differentSecondVar= counter; |
---|
2434 | } |
---|
2435 | else |
---|
2436 | { |
---|
2437 | if (bufBiFactors.length() < biFactors.length() || |
---|
2438 | ((bufLift < lift) && (bufBiFactors.length() == biFactors.length())) || |
---|
2439 | counter > differentSecondVar) |
---|
2440 | { |
---|
2441 | Aeval= bufAeval; |
---|
2442 | evaluation= bufEvaluation; |
---|
2443 | biFactors= bufBiFactors; |
---|
2444 | lift= bufLift; |
---|
2445 | for (int j= 0; j < lengthAeval2; j++) |
---|
2446 | Aeval2 [j]= bufAeval2 [j]; |
---|
2447 | differentSecondVar= counter; |
---|
2448 | } |
---|
2449 | } |
---|
2450 | int k= 0; |
---|
2451 | for (CFListIterator j= bufEvaluation; j.hasItem(); j++, k++) |
---|
2452 | evalPoly += j.getItem()*power (x, k); |
---|
2453 | list.append (evalPoly); |
---|
2454 | } |
---|
2455 | |
---|
2456 | delete [] bufAeval2; |
---|
2457 | |
---|
2458 | sortList (biFactors, x); |
---|
2459 | |
---|
2460 | int minFactorsLength; |
---|
2461 | bool irred= false; |
---|
2462 | factorizationWRTDifferentSecondVars (A, Aeval2, info, minFactorsLength,irred); |
---|
2463 | |
---|
2464 | if (irred) |
---|
2465 | { |
---|
2466 | if (extension) |
---|
2467 | { |
---|
2468 | CFList source, dest; |
---|
2469 | A= mapDown (A, info, source, dest); |
---|
2470 | } |
---|
2471 | factors.append (A); |
---|
2472 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, |
---|
2473 | swapLevel2, x); |
---|
2474 | if (!extension) |
---|
2475 | normalize (factors); |
---|
2476 | delete [] Aeval2; |
---|
2477 | return factors; |
---|
2478 | } |
---|
2479 | |
---|
2480 | if (minFactorsLength == 0) |
---|
2481 | minFactorsLength= biFactors.length(); |
---|
2482 | else if (biFactors.length() > minFactorsLength) |
---|
2483 | refineBiFactors (A, biFactors, Aeval2, evaluation, minFactorsLength); |
---|
2484 | minFactorsLength= tmin (minFactorsLength, biFactors.length()); |
---|
2485 | |
---|
2486 | if (differentSecondVar == lengthAeval2) |
---|
2487 | { |
---|
2488 | bool zeroOccured= false; |
---|
2489 | for (CFListIterator iter= evaluation; iter.hasItem(); iter++) |
---|
2490 | { |
---|
2491 | if (iter.getItem().isZero()) |
---|
2492 | { |
---|
2493 | zeroOccured= true; |
---|
2494 | break; |
---|
2495 | } |
---|
2496 | } |
---|
2497 | if (!zeroOccured) |
---|
2498 | { |
---|
2499 | factors= sparseHeuristic (A, biFactors, Aeval2, evaluation, |
---|
2500 | minFactorsLength); |
---|
2501 | if (factors.length() == biFactors.length()) |
---|
2502 | { |
---|
2503 | if (extension) |
---|
2504 | factors= extNonMonicFactorRecombination (factors, A, info); |
---|
2505 | |
---|
2506 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, |
---|
2507 | swapLevel2, x); |
---|
2508 | if (!extension) |
---|
2509 | normalize (factors); |
---|
2510 | delete [] Aeval2; |
---|
2511 | return factors; |
---|
2512 | } |
---|
2513 | else |
---|
2514 | factors= CFList(); |
---|
2515 | //TODO case where factors.length() > 0 |
---|
2516 | } |
---|
2517 | } |
---|
2518 | |
---|
2519 | CFList uniFactors= buildUniFactors (biFactors, evaluation.getLast(), y); |
---|
2520 | |
---|
2521 | sortByUniFactors (Aeval2, lengthAeval2, uniFactors, evaluation); |
---|
2522 | |
---|
2523 | CFList * oldAeval= new CFList [lengthAeval2]; //TODO use bufAeval2 for this |
---|
2524 | for (int i= 0; i < lengthAeval2; i++) |
---|
2525 | oldAeval[i]= Aeval2[i]; |
---|
2526 | |
---|
2527 | getLeadingCoeffs (A, Aeval2, uniFactors, evaluation); |
---|
2528 | |
---|
2529 | CFList biFactorsLCs; |
---|
2530 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
2531 | biFactorsLCs.append (LC (i.getItem(), 1)); |
---|
2532 | |
---|
2533 | Variable v; |
---|
2534 | CFList leadingCoeffs= precomputeLeadingCoeff (LC (A, 1), biFactorsLCs, alpha, |
---|
2535 | evaluation, Aeval2, lengthAeval2, v); |
---|
2536 | |
---|
2537 | if (v.level() != 1) |
---|
2538 | { |
---|
2539 | A= swapvar (A, y, v); |
---|
2540 | int i= A.level(); |
---|
2541 | CanonicalForm evalPoint; |
---|
2542 | for (CFListIterator iter= evaluation; iter.hasItem(); iter++, i--) |
---|
2543 | { |
---|
2544 | if (i == v.level()) |
---|
2545 | { |
---|
2546 | evalPoint= iter.getItem(); |
---|
2547 | iter.getItem()= evaluation.getLast(); |
---|
2548 | evaluation.removeLast(); |
---|
2549 | evaluation.append (evalPoint); |
---|
2550 | break; |
---|
2551 | } |
---|
2552 | } |
---|
2553 | for (i= 0; i < lengthAeval2; i++) |
---|
2554 | { |
---|
2555 | if (oldAeval[i].isEmpty()) |
---|
2556 | continue; |
---|
2557 | if (oldAeval[i].getFirst().level() == v.level()) |
---|
2558 | { |
---|
2559 | CFArray tmp= copy (oldAeval[i]); |
---|
2560 | oldAeval[i]= biFactors; |
---|
2561 | for (CFListIterator iter= oldAeval[i]; iter.hasItem(); iter++) |
---|
2562 | iter.getItem()= swapvar (iter.getItem(), v, y); |
---|
2563 | for (int ii= 0; ii < tmp.size(); ii++) |
---|
2564 | tmp[ii]= swapvar (tmp[ii], v, y); |
---|
2565 | CFArray tmp2= CFArray (tmp.size()); |
---|
2566 | CanonicalForm buf; |
---|
2567 | for (int ii= 0; ii < tmp.size(); ii++) |
---|
2568 | { |
---|
2569 | buf= tmp[ii] (evaluation.getLast(),y); |
---|
2570 | buf /= Lc (buf); |
---|
2571 | tmp2[findItem (uniFactors, buf)-1]=tmp[ii]; |
---|
2572 | } |
---|
2573 | biFactors= CFList(); |
---|
2574 | for (int j= 0; j < tmp2.size(); j++) |
---|
2575 | biFactors.append (tmp2[j]); |
---|
2576 | } |
---|
2577 | } |
---|
2578 | } |
---|
2579 | |
---|
2580 | CFListIterator iter; |
---|
2581 | CanonicalForm oldA= A; |
---|
2582 | CFList oldBiFactors= biFactors; |
---|
2583 | if (!leadingCoeffs.getFirst().inCoeffDomain()) |
---|
2584 | { |
---|
2585 | CanonicalForm tmp= power (leadingCoeffs.getFirst(), biFactors.length() - 1); |
---|
2586 | A *= tmp; |
---|
2587 | tmp= leadingCoeffs.getFirst(); |
---|
2588 | iter= evaluation; |
---|
2589 | for (int i= A.level(); i > 2; i--, iter++) |
---|
2590 | tmp= tmp (iter.getItem(), i); |
---|
2591 | if (!tmp.inCoeffDomain()) |
---|
2592 | { |
---|
2593 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
2594 | { |
---|
2595 | i.getItem() *= tmp/LC (i.getItem(), 1); |
---|
2596 | i.getItem() /= Lc (i.getItem()); |
---|
2597 | } |
---|
2598 | } |
---|
2599 | } |
---|
2600 | |
---|
2601 | CanonicalForm LCmultiplier= leadingCoeffs.getFirst(); |
---|
2602 | bool LCmultiplierIsConst= LCmultiplier.inCoeffDomain(); |
---|
2603 | leadingCoeffs.removeFirst(); |
---|
2604 | |
---|
2605 | //prepare leading coefficients |
---|
2606 | CFList* leadingCoeffs2= new CFList [lengthAeval2]; |
---|
2607 | prepareLeadingCoeffs (leadingCoeffs2, A.level(), leadingCoeffs, biFactors, |
---|
2608 | evaluation); |
---|
2609 | |
---|
2610 | Aeval= evaluateAtEval (A, evaluation, 2); |
---|
2611 | CanonicalForm hh= 1/Lc (Aeval.getFirst()); |
---|
2612 | for (iter= Aeval; iter.hasItem(); iter++) |
---|
2613 | iter.getItem() *= hh; |
---|
2614 | |
---|
2615 | A *= hh; |
---|
2616 | |
---|
2617 | |
---|
2618 | CFListIterator iter2; |
---|
2619 | CFList bufLeadingCoeffs2= leadingCoeffs2[lengthAeval2-1]; |
---|
2620 | bufBiFactors= biFactors; |
---|
2621 | bufA= A; |
---|
2622 | CanonicalForm bufLCmultiplier= LCmultiplier; |
---|
2623 | CanonicalForm testVars; |
---|
2624 | if (!LCmultiplierIsConst) |
---|
2625 | { |
---|
2626 | testVars= Variable (2); |
---|
2627 | for (int i= 0; i < lengthAeval2; i++) |
---|
2628 | { |
---|
2629 | if (!oldAeval[i].isEmpty()) |
---|
2630 | testVars *= oldAeval[i].getFirst().mvar(); |
---|
2631 | } |
---|
2632 | } |
---|
2633 | CFList bufFactors= CFList(); |
---|
2634 | bool LCheuristic= false; |
---|
2635 | if (LucksWangSparseHeuristic (A, biFactors, 2, leadingCoeffs2[lengthAeval2-1], |
---|
2636 | factors)) |
---|
2637 | { |
---|
2638 | int check= biFactors.length(); |
---|
2639 | int * index= new int [factors.length()]; |
---|
2640 | CFList oldFactors= factors; |
---|
2641 | factors= recoverFactors (A, factors, index); |
---|
2642 | |
---|
2643 | if (check == factors.length()) |
---|
2644 | { |
---|
2645 | if (extension) |
---|
2646 | factors= extNonMonicFactorRecombination (factors, bufA, info); |
---|
2647 | |
---|
2648 | if (v.level() != 1) |
---|
2649 | { |
---|
2650 | for (iter= factors; iter.hasItem(); iter++) |
---|
2651 | iter.getItem()= swapvar (iter.getItem(), v, y); |
---|
2652 | } |
---|
2653 | |
---|
2654 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, |
---|
2655 | swapLevel2, x); |
---|
2656 | if (!extension) |
---|
2657 | normalize (factors); |
---|
2658 | delete [] index; |
---|
2659 | delete [] Aeval2; |
---|
2660 | return factors; |
---|
2661 | } |
---|
2662 | else if (factors.length() > 0) |
---|
2663 | { |
---|
2664 | int oneCount= 0; |
---|
2665 | CFList l; |
---|
2666 | for (int i= 0; i < check; i++) |
---|
2667 | { |
---|
2668 | if (index[i] == 1) |
---|
2669 | { |
---|
2670 | iter=biFactors; |
---|
2671 | for (int j=1; j <= i-oneCount; j++) |
---|
2672 | iter++; |
---|
2673 | iter.remove (1); |
---|
2674 | for (int j= 0; j < lengthAeval2; j++) |
---|
2675 | { |
---|
2676 | l= leadingCoeffs2[j]; |
---|
2677 | iter= l; |
---|
2678 | for (int k=1; k <= i-oneCount; k++) |
---|
2679 | iter++; |
---|
2680 | iter.remove (1); |
---|
2681 | leadingCoeffs2[j]=l; |
---|
2682 | } |
---|
2683 | oneCount++; |
---|
2684 | } |
---|
2685 | } |
---|
2686 | bufFactors= factors; |
---|
2687 | factors= CFList(); |
---|
2688 | } |
---|
2689 | else if (!LCmultiplierIsConst && factors.length() == 0) |
---|
2690 | { |
---|
2691 | LCheuristic= true; |
---|
2692 | factors= oldFactors; |
---|
2693 | CanonicalForm cont; |
---|
2694 | CFList contents, LCs; |
---|
2695 | int index=1; |
---|
2696 | bool foundTrueMultiplier= false; |
---|
2697 | for (iter= factors; iter.hasItem(); iter++, index++) |
---|
2698 | { |
---|
2699 | cont= content (iter.getItem(), 1); |
---|
2700 | cont= gcd (cont , LCmultiplier); |
---|
2701 | contents.append (cont); |
---|
2702 | if (cont.inCoeffDomain()) // trivial content->LCmultiplier needs to go there |
---|
2703 | { |
---|
2704 | foundTrueMultiplier= true; |
---|
2705 | int index2= 1; |
---|
2706 | for (iter2= leadingCoeffs2[lengthAeval2-1]; iter2.hasItem(); iter2++, |
---|
2707 | index2++) |
---|
2708 | { |
---|
2709 | if (index2 == index) |
---|
2710 | continue; |
---|
2711 | iter2.getItem() /= LCmultiplier; |
---|
2712 | } |
---|
2713 | A= oldA; |
---|
2714 | leadingCoeffs= leadingCoeffs2[lengthAeval2-1]; |
---|
2715 | for (int i= lengthAeval2-1; i > -1; i--) |
---|
2716 | leadingCoeffs2[i]= CFList(); |
---|
2717 | prepareLeadingCoeffs (leadingCoeffs2, A.level(), leadingCoeffs, |
---|
2718 | biFactors, evaluation ); |
---|
2719 | Aeval= evaluateAtEval (A, evaluation, 2); |
---|
2720 | |
---|
2721 | hh= 1/Lc (Aeval.getFirst()); |
---|
2722 | |
---|
2723 | for (iter2= Aeval; iter2.hasItem(); iter2++) |
---|
2724 | iter2.getItem() *= hh; |
---|
2725 | |
---|
2726 | A *= hh; |
---|
2727 | break; |
---|
2728 | } |
---|
2729 | else |
---|
2730 | LCs.append (LC (iter.getItem()/cont, 1)); |
---|
2731 | } |
---|
2732 | if (!foundTrueMultiplier) |
---|
2733 | { |
---|
2734 | index= 1; |
---|
2735 | iter2= factors; |
---|
2736 | bool foundMultiplier= false; |
---|
2737 | for (iter= contents; iter.hasItem(); iter++, iter2++, index++) |
---|
2738 | { |
---|
2739 | if (fdivides (iter.getItem(), LCmultiplier)) |
---|
2740 | { |
---|
2741 | if ((LCmultiplier/iter.getItem()).inCoeffDomain() && |
---|
2742 | !isOnlyLeadingCoeff(iter2.getItem())) //content divides LCmultiplier completely and factor consists of more terms than just the leading coeff |
---|
2743 | { |
---|
2744 | int index2= 1; |
---|
2745 | for (CFListIterator iter3= leadingCoeffs2[lengthAeval2-1]; |
---|
2746 | iter3.hasItem(); iter3++, index2++) |
---|
2747 | { |
---|
2748 | if (index2 == index) |
---|
2749 | { |
---|
2750 | iter3.getItem() /= LCmultiplier; |
---|
2751 | break; |
---|
2752 | } |
---|
2753 | } |
---|
2754 | A /= LCmultiplier; |
---|
2755 | foundMultiplier= true; |
---|
2756 | iter.getItem()= 1; |
---|
2757 | } |
---|
2758 | } |
---|
2759 | } |
---|
2760 | // coming from above: divide out more LCmultiplier if possible |
---|
2761 | if (foundMultiplier) |
---|
2762 | { |
---|
2763 | foundMultiplier= false; |
---|
2764 | index=1; |
---|
2765 | iter2= factors; |
---|
2766 | for (iter= contents; iter.hasItem(); iter++, iter2++, index++) |
---|
2767 | { |
---|
2768 | if (!iter.getItem().isOne() && |
---|
2769 | fdivides (iter.getItem(), LCmultiplier)) |
---|
2770 | { |
---|
2771 | if (!isOnlyLeadingCoeff (iter2.getItem())) // factor is more than just leading coeff |
---|
2772 | { |
---|
2773 | int index2= 1; |
---|
2774 | for (iter2= leadingCoeffs2[lengthAeval2-1]; iter2.hasItem(); |
---|
2775 | iter2++, index2++) |
---|
2776 | { |
---|
2777 | if (index2 == index) |
---|
2778 | { |
---|
2779 | iter2.getItem() /= iter.getItem(); |
---|
2780 | foundMultiplier= true; |
---|
2781 | break; |
---|
2782 | } |
---|
2783 | } |
---|
2784 | A /= iter.getItem(); |
---|
2785 | LCmultiplier /= iter.getItem(); |
---|
2786 | iter.getItem()= 1; |
---|
2787 | } |
---|
2788 | else if (fdivides (getVars (LCmultiplier), testVars))//factor consists of just leading coeff |
---|
2789 | { |
---|
2790 | //TODO maybe use a sqrffree decomposition of LCmultiplier as below |
---|
2791 | Variable xx= Variable (2); |
---|
2792 | CanonicalForm vars; |
---|
2793 | vars= power (xx, degree (LC (getItem(oldBiFactors, index),1), |
---|
2794 | xx)); |
---|
2795 | for (int i= 0; i < lengthAeval2; i++) |
---|
2796 | { |
---|
2797 | if (oldAeval[i].isEmpty()) |
---|
2798 | continue; |
---|
2799 | xx= oldAeval[i].getFirst().mvar(); |
---|
2800 | vars *= power (xx, degree (LC (getItem(oldAeval[i], index),1), |
---|
2801 | xx)); |
---|
2802 | } |
---|
2803 | if (myGetVars(content(getItem(leadingCoeffs2[lengthAeval2-1],index),1)) |
---|
2804 | /myGetVars (LCmultiplier) == vars) |
---|
2805 | { |
---|
2806 | int index2= 1; |
---|
2807 | for (iter2= leadingCoeffs2[lengthAeval2-1]; iter2.hasItem(); |
---|
2808 | iter2++, index2++) |
---|
2809 | { |
---|
2810 | if (index2 == index) |
---|
2811 | { |
---|
2812 | iter2.getItem() /= LCmultiplier; |
---|
2813 | foundMultiplier= true; |
---|
2814 | break; |
---|
2815 | } |
---|
2816 | } |
---|
2817 | A /= LCmultiplier; |
---|
2818 | iter.getItem()= 1; |
---|
2819 | } |
---|
2820 | } |
---|
2821 | } |
---|
2822 | } |
---|
2823 | } |
---|
2824 | else |
---|
2825 | { |
---|
2826 | CanonicalForm pLCs= prod (LCs); |
---|
2827 | if (fdivides (pLCs, LC (oldA,1)) && (LC(oldA,1)/pLCs).inCoeffDomain()) // check if the product of the lead coeffs of the primitive factors equals the lead coeff of the old A |
---|
2828 | { |
---|
2829 | A= oldA; |
---|
2830 | iter2= leadingCoeffs2[lengthAeval2-1]; |
---|
2831 | for (iter= contents; iter.hasItem(); iter++, iter2++) |
---|
2832 | iter2.getItem() /= iter.getItem(); |
---|
2833 | foundMultiplier= true; |
---|
2834 | } |
---|
2835 | if (!foundMultiplier && fdivides (getVars (LCmultiplier), testVars)) |
---|
2836 | { |
---|
2837 | Variable xx; |
---|
2838 | CFList vars1; |
---|
2839 | CFFList sqrfMultiplier= sqrFree (LCmultiplier); |
---|
2840 | if (sqrfMultiplier.getFirst().factor().inCoeffDomain()) |
---|
2841 | sqrfMultiplier.removeFirst(); |
---|
2842 | sqrfMultiplier= sortCFFListByNumOfVars (sqrfMultiplier); |
---|
2843 | xx= Variable (2); |
---|
2844 | for (iter= oldBiFactors; iter.hasItem(); iter++) |
---|
2845 | vars1.append (power (xx, degree (LC (iter.getItem(),1), xx))); |
---|
2846 | for (int i= 0; i < lengthAeval2; i++) |
---|
2847 | { |
---|
2848 | if (oldAeval[i].isEmpty()) |
---|
2849 | continue; |
---|
2850 | xx= oldAeval[i].getFirst().mvar(); |
---|
2851 | iter2= vars1; |
---|
2852 | for (iter= oldAeval[i]; iter.hasItem(); iter++, iter2++) |
---|
2853 | iter2.getItem() *= power(xx,degree (LC (iter.getItem(),1), xx)); |
---|
2854 | } |
---|
2855 | CanonicalForm tmp; |
---|
2856 | iter2= vars1; |
---|
2857 | for (iter= leadingCoeffs2[lengthAeval2-1]; iter.hasItem(); iter++, |
---|
2858 | iter2++) |
---|
2859 | { |
---|
2860 | tmp= iter.getItem()/LCmultiplier; |
---|
2861 | for (int i=1; i <= tmp.level(); i++) |
---|
2862 | { |
---|
2863 | if (degree(tmp,i) > 0 && |
---|
2864 | (degree(iter2.getItem(),i) > degree (tmp,i))) |
---|
2865 | iter2.getItem() /= power (Variable (i), degree (tmp,i)); |
---|
2866 | } |
---|
2867 | } |
---|
2868 | int multi; |
---|
2869 | for (CFFListIterator ii= sqrfMultiplier; ii.hasItem(); ii++) |
---|
2870 | { |
---|
2871 | multi= 0; |
---|
2872 | for (iter= vars1; iter.hasItem(); iter++) |
---|
2873 | { |
---|
2874 | tmp= iter.getItem(); |
---|
2875 | while (fdivides (myGetVars (ii.getItem().factor()), tmp)) |
---|
2876 | { |
---|
2877 | multi++; |
---|
2878 | tmp /= myGetVars (ii.getItem().factor()); |
---|
2879 | } |
---|
2880 | } |
---|
2881 | if (multi == ii.getItem().exp()) |
---|
2882 | { |
---|
2883 | index= 1; |
---|
2884 | for (iter= vars1; iter.hasItem(); iter++, index++) |
---|
2885 | { |
---|
2886 | while (fdivides (myGetVars(ii.getItem().factor()), |
---|
2887 | iter.getItem() |
---|
2888 | ) |
---|
2889 | ) |
---|
2890 | { |
---|
2891 | int index2= 1; |
---|
2892 | for (iter2= leadingCoeffs2[lengthAeval2-1]; iter2.hasItem(); |
---|
2893 | iter2++, index2++) |
---|
2894 | { |
---|
2895 | if (index2 == index) |
---|
2896 | continue; |
---|
2897 | else |
---|
2898 | { |
---|
2899 | tmp= ii.getItem().factor(); |
---|
2900 | iter2.getItem() /= tmp; |
---|
2901 | CFListIterator iter3= evaluation; |
---|
2902 | for (int jj= A.level(); jj > 2; jj--, iter3++) |
---|
2903 | tmp= tmp (iter3.getItem(), jj); |
---|
2904 | if (!tmp.inCoeffDomain()) |
---|
2905 | { |
---|
2906 | int index3= 1; |
---|
2907 | for (iter3= biFactors; iter3.hasItem(); iter3++, |
---|
2908 | index3++) |
---|
2909 | { |
---|
2910 | if (index3 == index2) |
---|
2911 | { |
---|
2912 | iter3.getItem() /= tmp; |
---|
2913 | iter3.getItem() /= Lc (iter3.getItem()); |
---|
2914 | break; |
---|
2915 | } |
---|
2916 | } |
---|
2917 | } |
---|
2918 | A /= ii.getItem().factor(); |
---|
2919 | } |
---|
2920 | } |
---|
2921 | iter.getItem() /= getVars (ii.getItem().factor()); |
---|
2922 | } |
---|
2923 | } |
---|
2924 | } |
---|
2925 | else |
---|
2926 | { |
---|
2927 | index= 1; |
---|
2928 | for (iter= vars1; iter.hasItem(); iter++, index++) |
---|
2929 | { |
---|
2930 | if (!fdivides (myGetVars (ii.getItem().factor()), |
---|
2931 | iter.getItem() |
---|
2932 | ) |
---|
2933 | ) |
---|
2934 | { |
---|
2935 | int index2= 1; |
---|
2936 | for (iter2= leadingCoeffs2[lengthAeval2-1]; iter2.hasItem(); |
---|
2937 | iter2++, index2++) |
---|
2938 | { |
---|
2939 | if (index2 == index) |
---|
2940 | { |
---|
2941 | tmp= power (ii.getItem().factor(), ii.getItem().exp()); |
---|
2942 | iter2.getItem() /= tmp; |
---|
2943 | A /= tmp; |
---|
2944 | CFListIterator iter3= evaluation; |
---|
2945 | for (int jj= A.level(); jj > 2; jj--, iter3++) |
---|
2946 | tmp= tmp (iter3.getItem(), jj); |
---|
2947 | if (!tmp.inCoeffDomain()) |
---|
2948 | { |
---|
2949 | int index3= 1; |
---|
2950 | for (iter3= biFactors; iter3.hasItem(); iter3++, |
---|
2951 | index3++) |
---|
2952 | { |
---|
2953 | if (index3 == index2) |
---|
2954 | { |
---|
2955 | iter3.getItem() /= tmp; |
---|
2956 | iter3.getItem() /= Lc (iter3.getItem()); |
---|
2957 | break; |
---|
2958 | } |
---|
2959 | } |
---|
2960 | } |
---|
2961 | } |
---|
2962 | } |
---|
2963 | } |
---|
2964 | } |
---|
2965 | } |
---|
2966 | } |
---|
2967 | } |
---|
2968 | } |
---|
2969 | |
---|
2970 | // patch everything together again |
---|
2971 | leadingCoeffs= leadingCoeffs2[lengthAeval2-1]; |
---|
2972 | for (int i= lengthAeval2-1; i > -1; i--) |
---|
2973 | leadingCoeffs2[i]= CFList(); |
---|
2974 | prepareLeadingCoeffs (leadingCoeffs2,A.level(),leadingCoeffs, biFactors, |
---|
2975 | evaluation); |
---|
2976 | Aeval= evaluateAtEval (A, evaluation, 2); |
---|
2977 | |
---|
2978 | hh= 1/Lc (Aeval.getFirst()); |
---|
2979 | |
---|
2980 | for (CFListIterator i= Aeval; i.hasItem(); i++) |
---|
2981 | i.getItem() *= hh; |
---|
2982 | |
---|
2983 | A *= hh; |
---|
2984 | } |
---|
2985 | factors= CFList(); |
---|
2986 | if (!fdivides (LC (oldA,1),prod (leadingCoeffs2[lengthAeval2-1]))) |
---|
2987 | { |
---|
2988 | LCheuristic= false; |
---|
2989 | A= bufA; |
---|
2990 | biFactors= bufBiFactors; |
---|
2991 | leadingCoeffs2[lengthAeval2-1]= bufLeadingCoeffs2; |
---|
2992 | LCmultiplier= bufLCmultiplier; |
---|
2993 | } |
---|
2994 | } |
---|
2995 | else |
---|
2996 | factors= CFList(); |
---|
2997 | delete [] index; |
---|
2998 | } |
---|
2999 | |
---|
3000 | if (!LCheuristic && !LCmultiplierIsConst && bufFactors.isEmpty() |
---|
3001 | && fdivides (getVars (LCmultiplier), testVars)) |
---|
3002 | { |
---|
3003 | LCheuristic= true; |
---|
3004 | int index; |
---|
3005 | Variable xx; |
---|
3006 | CFList vars1; |
---|
3007 | CFFList sqrfMultiplier= sqrFree (LCmultiplier); |
---|
3008 | if (sqrfMultiplier.getFirst().factor().inCoeffDomain()) |
---|
3009 | sqrfMultiplier.removeFirst(); |
---|
3010 | sqrfMultiplier= sortCFFListByNumOfVars (sqrfMultiplier); |
---|
3011 | xx= Variable (2); |
---|
3012 | for (iter= oldBiFactors; iter.hasItem(); iter++) |
---|
3013 | vars1.append (power (xx, degree (LC (iter.getItem(),1), xx))); |
---|
3014 | for (int i= 0; i < lengthAeval2; i++) |
---|
3015 | { |
---|
3016 | if (oldAeval[i].isEmpty()) |
---|
3017 | continue; |
---|
3018 | xx= oldAeval[i].getFirst().mvar(); |
---|
3019 | iter2= vars1; |
---|
3020 | for (iter= oldAeval[i]; iter.hasItem(); iter++, iter2++) |
---|
3021 | iter2.getItem() *= power (xx, degree (LC (iter.getItem(),1), xx)); |
---|
3022 | } |
---|
3023 | CanonicalForm tmp; |
---|
3024 | iter2= vars1; |
---|
3025 | for (iter= leadingCoeffs2[lengthAeval2-1]; iter.hasItem(); iter++, iter2++) |
---|
3026 | { |
---|
3027 | tmp= iter.getItem()/LCmultiplier; |
---|
3028 | for (int i=1; i <= tmp.level(); i++) |
---|
3029 | { |
---|
3030 | if (degree (tmp,i) > 0 && (degree (iter2.getItem(),i) > degree (tmp,i))) |
---|
3031 | iter2.getItem() /= power (Variable (i), degree (tmp,i)); |
---|
3032 | } |
---|
3033 | } |
---|
3034 | int multi; |
---|
3035 | for (CFFListIterator ii= sqrfMultiplier; ii.hasItem(); ii++) |
---|
3036 | { |
---|
3037 | multi= 0; |
---|
3038 | for (iter= vars1; iter.hasItem(); iter++) |
---|
3039 | { |
---|
3040 | tmp= iter.getItem(); |
---|
3041 | while (fdivides (myGetVars (ii.getItem().factor()), tmp)) |
---|
3042 | { |
---|
3043 | multi++; |
---|
3044 | tmp /= myGetVars (ii.getItem().factor()); |
---|
3045 | } |
---|
3046 | } |
---|
3047 | if (multi == ii.getItem().exp()) |
---|
3048 | { |
---|
3049 | index= 1; |
---|
3050 | for (iter= vars1; iter.hasItem(); iter++, index++) |
---|
3051 | { |
---|
3052 | while (fdivides (myGetVars (ii.getItem().factor()), iter.getItem())) |
---|
3053 | { |
---|
3054 | int index2= 1; |
---|
3055 | for (iter2= leadingCoeffs2[lengthAeval2-1]; iter2.hasItem();iter2++, |
---|
3056 | index2++) |
---|
3057 | { |
---|
3058 | if (index2 == index) |
---|
3059 | continue; |
---|
3060 | else |
---|
3061 | { |
---|
3062 | tmp= ii.getItem().factor(); |
---|
3063 | iter2.getItem() /= tmp; |
---|
3064 | CFListIterator iter3= evaluation; |
---|
3065 | for (int jj= A.level(); jj > 2; jj--, iter3++) |
---|
3066 | tmp= tmp (iter3.getItem(), jj); |
---|
3067 | if (!tmp.inCoeffDomain()) |
---|
3068 | { |
---|
3069 | int index3= 1; |
---|
3070 | for (iter3= biFactors; iter3.hasItem(); iter3++, index3++) |
---|
3071 | { |
---|
3072 | if (index3 == index2) |
---|
3073 | { |
---|
3074 | iter3.getItem() /= tmp; |
---|
3075 | iter3.getItem() /= Lc (iter3.getItem()); |
---|
3076 | break; |
---|
3077 | } |
---|
3078 | } |
---|
3079 | } |
---|
3080 | A /= ii.getItem().factor(); |
---|
3081 | } |
---|
3082 | } |
---|
3083 | iter.getItem() /= getVars (ii.getItem().factor()); |
---|
3084 | } |
---|
3085 | } |
---|
3086 | } |
---|
3087 | else |
---|
3088 | { |
---|
3089 | index= 1; |
---|
3090 | for (iter= vars1; iter.hasItem(); iter++, index++) |
---|
3091 | { |
---|
3092 | if (!fdivides (myGetVars (ii.getItem().factor()), iter.getItem())) |
---|
3093 | { |
---|
3094 | int index2= 1; |
---|
3095 | for (iter2= leadingCoeffs2[lengthAeval2-1];iter2.hasItem();iter2++, |
---|
3096 | index2++) |
---|
3097 | { |
---|
3098 | if (index2 == index) |
---|
3099 | { |
---|
3100 | tmp= power (ii.getItem().factor(), ii.getItem().exp()); |
---|
3101 | iter2.getItem() /= tmp; |
---|
3102 | A /= tmp; |
---|
3103 | CFListIterator iter3= evaluation; |
---|
3104 | for (int jj= A.level(); jj > 2; jj--, iter3++) |
---|
3105 | tmp= tmp (iter3.getItem(), jj); |
---|
3106 | if (!tmp.inCoeffDomain()) |
---|
3107 | { |
---|
3108 | int index3= 1; |
---|
3109 | for (iter3= biFactors; iter3.hasItem(); iter3++, index3++) |
---|
3110 | { |
---|
3111 | if (index3 == index2) |
---|
3112 | { |
---|
3113 | iter3.getItem() /= tmp; |
---|
3114 | iter3.getItem() /= Lc (iter3.getItem()); |
---|
3115 | break; |
---|
3116 | } |
---|
3117 | } |
---|
3118 | } |
---|
3119 | } |
---|
3120 | } |
---|
3121 | } |
---|
3122 | } |
---|
3123 | } |
---|
3124 | } |
---|
3125 | |
---|
3126 | leadingCoeffs= leadingCoeffs2[lengthAeval2-1]; |
---|
3127 | for (int i= lengthAeval2-1; i > -1; i--) |
---|
3128 | leadingCoeffs2[i]= CFList(); |
---|
3129 | prepareLeadingCoeffs (leadingCoeffs2,A.level(),leadingCoeffs, biFactors, |
---|
3130 | evaluation); |
---|
3131 | Aeval= evaluateAtEval (A, evaluation, 2); |
---|
3132 | |
---|
3133 | hh= 1/Lc (Aeval.getFirst()); |
---|
3134 | |
---|
3135 | for (CFListIterator i= Aeval; i.hasItem(); i++) |
---|
3136 | i.getItem() *= hh; |
---|
3137 | |
---|
3138 | A *= hh; |
---|
3139 | |
---|
3140 | if (!fdivides (LC (oldA,1),prod (leadingCoeffs2[lengthAeval2-1]))) |
---|
3141 | { |
---|
3142 | LCheuristic= false; |
---|
3143 | A= bufA; |
---|
3144 | biFactors= bufBiFactors; |
---|
3145 | leadingCoeffs2[lengthAeval2-1]= bufLeadingCoeffs2; |
---|
3146 | LCmultiplier= bufLCmultiplier; |
---|
3147 | } |
---|
3148 | } |
---|
3149 | |
---|
3150 | tryAgainWithoutHeu: |
---|
3151 | A= shift2Zero (A, Aeval, evaluation); |
---|
3152 | |
---|
3153 | for (iter= biFactors; iter.hasItem(); iter++) |
---|
3154 | iter.getItem()= iter.getItem () (y + evaluation.getLast(), y); |
---|
3155 | |
---|
3156 | for (int i= 0; i < lengthAeval2-1; i++) |
---|
3157 | leadingCoeffs2[i]= CFList(); |
---|
3158 | for (iter= leadingCoeffs2[lengthAeval2-1]; iter.hasItem(); iter++) |
---|
3159 | { |
---|
3160 | iter.getItem()= shift2Zero (iter.getItem(), list, evaluation); |
---|
3161 | for (int i= A.level() - 4; i > -1; i--) |
---|
3162 | { |
---|
3163 | if (i + 1 == lengthAeval2-1) |
---|
3164 | leadingCoeffs2[i].append (iter.getItem() (0, i + 4)); |
---|
3165 | else |
---|
3166 | leadingCoeffs2[i].append (leadingCoeffs2[i+1].getLast() (0, i + 4)); |
---|
3167 | } |
---|
3168 | } |
---|
3169 | |
---|
3170 | CFArray Pi; |
---|
3171 | CFList diophant; |
---|
3172 | int* liftBounds= new int [A.level() - 1]; |
---|
3173 | int liftBoundsLength= A.level() - 1; |
---|
3174 | for (int i= 0; i < liftBoundsLength; i++) |
---|
3175 | liftBounds [i]= degree (A, i + 2) + 1; |
---|
3176 | |
---|
3177 | Aeval.removeFirst(); |
---|
3178 | bool noOneToOne= false; |
---|
3179 | factors= nonMonicHenselLift (Aeval, biFactors, leadingCoeffs2, diophant, |
---|
3180 | Pi, liftBounds, liftBoundsLength, noOneToOne); |
---|
3181 | |
---|
3182 | if (!noOneToOne) |
---|
3183 | { |
---|
3184 | int check= factors.length(); |
---|
3185 | A= oldA; |
---|
3186 | factors= recoverFactors (A, factors, evaluation); |
---|
3187 | if (check != factors.length()) |
---|
3188 | noOneToOne= true; |
---|
3189 | else |
---|
3190 | factors= Union (factors, bufFactors); |
---|
3191 | |
---|
3192 | if (extension && !noOneToOne) |
---|
3193 | factors= extNonMonicFactorRecombination (factors, A, info); |
---|
3194 | } |
---|
3195 | if (noOneToOne) |
---|
3196 | { |
---|
3197 | |
---|
3198 | if (!LCmultiplierIsConst && LCheuristic) |
---|
3199 | { |
---|
3200 | A= bufA; |
---|
3201 | biFactors= bufBiFactors; |
---|
3202 | leadingCoeffs2[lengthAeval2-1]= bufLeadingCoeffs2; |
---|
3203 | delete [] liftBounds; |
---|
3204 | LCheuristic= false; |
---|
3205 | goto tryAgainWithoutHeu; |
---|
3206 | //something probably went wrong in the heuristic |
---|
3207 | } |
---|
3208 | |
---|
3209 | A= shift2Zero (oldA, Aeval, evaluation); |
---|
3210 | biFactors= oldBiFactors; |
---|
3211 | for (iter= biFactors; iter.hasItem(); iter++) |
---|
3212 | iter.getItem()= iter.getItem () (y + evaluation.getLast(), y); |
---|
3213 | CanonicalForm LCA= LC (Aeval.getFirst(), 1); |
---|
3214 | CanonicalForm yToLift= power (y, lift); |
---|
3215 | CFListIterator i= biFactors; |
---|
3216 | lift= degree (i.getItem(), 2) + degree (LC (i.getItem(), 1)) + 1; |
---|
3217 | i++; |
---|
3218 | |
---|
3219 | for (; i.hasItem(); i++) |
---|
3220 | lift= tmax (lift, |
---|
3221 | degree (i.getItem(), 2) + degree (LC (i.getItem(), 1)) + 1); |
---|
3222 | |
---|
3223 | lift= tmax (degree (Aeval.getFirst() , 2) + 1, lift); |
---|
3224 | |
---|
3225 | i= biFactors; |
---|
3226 | yToLift= power (y, lift); |
---|
3227 | CanonicalForm dummy; |
---|
3228 | for (; i.hasItem(); i++) |
---|
3229 | { |
---|
3230 | LCA= LC (i.getItem(), 1); |
---|
3231 | extgcd (LCA, yToLift, LCA, dummy); |
---|
3232 | i.getItem()= mod (i.getItem()*LCA, yToLift); |
---|
3233 | } |
---|
3234 | |
---|
3235 | liftBoundsLength= F.level() - 1; |
---|
3236 | liftBounds= liftingBounds (A, lift); |
---|
3237 | |
---|
3238 | CFList MOD; |
---|
3239 | bool earlySuccess; |
---|
3240 | CFList earlyFactors, liftedFactors; |
---|
3241 | TIMING_START (fac_fq_hensel_lift); |
---|
3242 | liftedFactors= henselLiftAndEarly |
---|
3243 | (A, MOD, liftBounds, earlySuccess, earlyFactors, |
---|
3244 | Aeval, biFactors, evaluation, info); |
---|
3245 | TIMING_END_AND_PRINT (fac_fq_hensel_lift, "time for hensel lifting: "); |
---|
3246 | |
---|
3247 | if (!extension) |
---|
3248 | { |
---|
3249 | TIMING_START (fac_fq_factor_recombination); |
---|
3250 | factors= factorRecombination (A, liftedFactors, MOD); |
---|
3251 | TIMING_END_AND_PRINT (fac_fq_factor_recombination, |
---|
3252 | "time for factor recombination: "); |
---|
3253 | } |
---|
3254 | else |
---|
3255 | { |
---|
3256 | TIMING_START (fac_fq_factor_recombination); |
---|
3257 | factors= extFactorRecombination (liftedFactors, A, MOD, info, evaluation); |
---|
3258 | TIMING_END_AND_PRINT (fac_fq_factor_recombination, |
---|
3259 | "time for factor recombination: "); |
---|
3260 | } |
---|
3261 | |
---|
3262 | if (earlySuccess) |
---|
3263 | factors= Union (factors, earlyFactors); |
---|
3264 | if (!extension) |
---|
3265 | { |
---|
3266 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
3267 | { |
---|
3268 | int kk= Aeval.getLast().level(); |
---|
3269 | for (CFListIterator j= evaluation; j.hasItem(); j++, kk--) |
---|
3270 | { |
---|
3271 | if (i.getItem().level() < kk) |
---|
3272 | continue; |
---|
3273 | i.getItem()= i.getItem() (Variable (kk) - j.getItem(), kk); |
---|
3274 | } |
---|
3275 | } |
---|
3276 | } |
---|
3277 | } |
---|
3278 | |
---|
3279 | if (v.level() != 1) |
---|
3280 | { |
---|
3281 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
3282 | iter.getItem()= swapvar (iter.getItem(), v, y); |
---|
3283 | } |
---|
3284 | |
---|
3285 | swap (factors, swapLevel, swapLevel2, x); |
---|
3286 | append (factors, contentAFactors); |
---|
3287 | decompress (factors, N); |
---|
3288 | if (!extension) |
---|
3289 | normalize (factors); |
---|
3290 | |
---|
3291 | delete[] liftBounds; |
---|
3292 | |
---|
3293 | return factors; |
---|
3294 | } |
---|
3295 | |
---|
3296 | /// multivariate factorization over an extension of the initial field |
---|
3297 | CFList |
---|
3298 | extFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
3299 | { |
---|
3300 | CanonicalForm A= F; |
---|
3301 | |
---|
3302 | Variable alpha= info.getAlpha(); |
---|
3303 | Variable beta= info.getBeta(); |
---|
3304 | int k= info.getGFDegree(); |
---|
3305 | char cGFName= info.getGFName(); |
---|
3306 | CanonicalForm delta= info.getDelta(); |
---|
3307 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
3308 | Variable w= Variable (1); |
---|
3309 | |
---|
3310 | CFList factors; |
---|
3311 | if (!GF && alpha == w) // we are in F_p |
---|
3312 | { |
---|
3313 | CFList factors; |
---|
3314 | bool extension= true; |
---|
3315 | int p= getCharacteristic(); |
---|
3316 | if (p < 7) |
---|
3317 | { |
---|
3318 | if (p == 2) |
---|
3319 | setCharacteristic (getCharacteristic(), 6, 'Z'); |
---|
3320 | else if (p == 3) |
---|
3321 | setCharacteristic (getCharacteristic(), 4, 'Z'); |
---|
3322 | else if (p == 5) |
---|
3323 | setCharacteristic (getCharacteristic(), 3, 'Z'); |
---|
3324 | ExtensionInfo info= ExtensionInfo (extension); |
---|
3325 | A= A.mapinto(); |
---|
3326 | factors= multiFactorize (A, info); |
---|
3327 | |
---|
3328 | CanonicalForm mipo= gf_mipo; |
---|
3329 | setCharacteristic (getCharacteristic()); |
---|
3330 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
3331 | for (CFListIterator j= factors; j.hasItem(); j++) |
---|
3332 | j.getItem()= GF2FalphaRep (j.getItem(), vBuf); |
---|
3333 | } |
---|
3334 | else if (p >= 7 && p*p < (1<<16)) // pass to GF if possible |
---|
3335 | { |
---|
3336 | setCharacteristic (getCharacteristic(), 2, 'Z'); |
---|
3337 | ExtensionInfo info= ExtensionInfo (extension); |
---|
3338 | A= A.mapinto(); |
---|
3339 | factors= multiFactorize (A, info); |
---|
3340 | |
---|
3341 | CanonicalForm mipo= gf_mipo; |
---|
3342 | setCharacteristic (getCharacteristic()); |
---|
3343 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
3344 | for (CFListIterator j= factors; j.hasItem(); j++) |
---|
3345 | j.getItem()= GF2FalphaRep (j.getItem(), vBuf); |
---|
3346 | } |
---|
3347 | else // not able to pass to GF, pass to F_p(\alpha) |
---|
3348 | { |
---|
3349 | CanonicalForm mipo= randomIrredpoly (2, w); |
---|
3350 | Variable v= rootOf (mipo); |
---|
3351 | ExtensionInfo info= ExtensionInfo (v); |
---|
3352 | factors= multiFactorize (A, info); |
---|
3353 | } |
---|
3354 | return factors; |
---|
3355 | } |
---|
3356 | else if (!GF && (alpha != w)) // we are in F_p(\alpha) |
---|
3357 | { |
---|
3358 | if (k == 1) // need factorization over F_p |
---|
3359 | { |
---|
3360 | int extDeg= degree (getMipo (alpha)); |
---|
3361 | extDeg++; |
---|
3362 | CanonicalForm mipo= randomIrredpoly (extDeg + 1, w); |
---|
3363 | Variable v= rootOf (mipo); |
---|
3364 | ExtensionInfo info= ExtensionInfo (v); |
---|
3365 | factors= multiFactorize (A, info); |
---|
3366 | } |
---|
3367 | else |
---|
3368 | { |
---|
3369 | if (beta == w) |
---|
3370 | { |
---|
3371 | Variable v= chooseExtension (alpha, beta, k); |
---|
3372 | CanonicalForm primElem, imPrimElem; |
---|
3373 | bool primFail= false; |
---|
3374 | Variable vBuf; |
---|
3375 | primElem= primitiveElement (alpha, vBuf, primFail); |
---|
3376 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
3377 | if (primFail) |
---|
3378 | ; //ERROR |
---|
3379 | else |
---|
3380 | imPrimElem= mapPrimElem (primElem, vBuf, v); |
---|
3381 | |
---|
3382 | CFList source, dest; |
---|
3383 | CanonicalForm bufA= mapUp (A, alpha, v, primElem, imPrimElem, |
---|
3384 | source, dest); |
---|
3385 | ExtensionInfo info= ExtensionInfo (v, alpha, imPrimElem, primElem); |
---|
3386 | factors= multiFactorize (bufA, info); |
---|
3387 | } |
---|
3388 | else |
---|
3389 | { |
---|
3390 | Variable v= chooseExtension (alpha, beta, k); |
---|
3391 | CanonicalForm primElem, imPrimElem; |
---|
3392 | bool primFail= false; |
---|
3393 | Variable vBuf; |
---|
3394 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
3395 | if (primFail) |
---|
3396 | ; //ERROR |
---|
3397 | else |
---|
3398 | imPrimElem= mapPrimElem (delta, beta, v); |
---|
3399 | |
---|
3400 | CFList source, dest; |
---|
3401 | CanonicalForm bufA= mapDown (A, info, source, dest); |
---|
3402 | source= CFList(); |
---|
3403 | dest= CFList(); |
---|
3404 | bufA= mapUp (bufA, beta, v, delta, imPrimElem, source, dest); |
---|
3405 | ExtensionInfo info= ExtensionInfo (v, beta, imPrimElem, delta); |
---|
3406 | factors= multiFactorize (bufA, info); |
---|
3407 | } |
---|
3408 | } |
---|
3409 | return factors; |
---|
3410 | } |
---|
3411 | else // we are in GF (p^k) |
---|
3412 | { |
---|
3413 | int p= getCharacteristic(); |
---|
3414 | int extensionDeg= getGFDegree(); |
---|
3415 | bool extension= true; |
---|
3416 | if (k == 1) // need factorization over F_p |
---|
3417 | { |
---|
3418 | extensionDeg++; |
---|
3419 | if (pow ((double) p, (double) extensionDeg) < (1<<16)) |
---|
3420 | // pass to GF(p^k+1) |
---|
3421 | { |
---|
3422 | CanonicalForm mipo= gf_mipo; |
---|
3423 | setCharacteristic (p); |
---|
3424 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
3425 | A= GF2FalphaRep (A, vBuf); |
---|
3426 | setCharacteristic (p, extensionDeg, 'Z'); |
---|
3427 | ExtensionInfo info= ExtensionInfo (extension); |
---|
3428 | factors= multiFactorize (A.mapinto(), info); |
---|
3429 | } |
---|
3430 | else // not able to pass to another GF, pass to F_p(\alpha) |
---|
3431 | { |
---|
3432 | CanonicalForm mipo= gf_mipo; |
---|
3433 | setCharacteristic (p); |
---|
3434 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
3435 | A= GF2FalphaRep (A, vBuf); |
---|
3436 | Variable v= chooseExtension (vBuf, beta, k); |
---|
3437 | ExtensionInfo info= ExtensionInfo (v, extension); |
---|
3438 | factors= multiFactorize (A, info); |
---|
3439 | } |
---|
3440 | } |
---|
3441 | else // need factorization over GF (p^k) |
---|
3442 | { |
---|
3443 | if (pow ((double) p, (double) 2*extensionDeg) < (1<<16)) |
---|
3444 | // pass to GF(p^2k) |
---|
3445 | { |
---|
3446 | setCharacteristic (p, 2*extensionDeg, 'Z'); |
---|
3447 | ExtensionInfo info= ExtensionInfo (k, cGFName, extension); |
---|
3448 | factors= multiFactorize (GFMapUp (A, extensionDeg), info); |
---|
3449 | setCharacteristic (p, extensionDeg, cGFName); |
---|
3450 | } |
---|
3451 | else // not able to pass to GF (p^2k), pass to F_p (\alpha) |
---|
3452 | { |
---|
3453 | CanonicalForm mipo= gf_mipo; |
---|
3454 | setCharacteristic (p); |
---|
3455 | Variable v1= rootOf (mipo.mapinto()); |
---|
3456 | A= GF2FalphaRep (A, v1); |
---|
3457 | Variable v2= chooseExtension (v1, v1, k); |
---|
3458 | CanonicalForm primElem, imPrimElem; |
---|
3459 | bool primFail= false; |
---|
3460 | Variable vBuf; |
---|
3461 | primElem= primitiveElement (v1, v1, primFail); |
---|
3462 | if (primFail) |
---|
3463 | ; //ERROR |
---|
3464 | else |
---|
3465 | imPrimElem= mapPrimElem (primElem, v1, v2); |
---|
3466 | CFList source, dest; |
---|
3467 | CanonicalForm bufA= mapUp (A, v1, v2, primElem, imPrimElem, |
---|
3468 | source, dest); |
---|
3469 | ExtensionInfo info= ExtensionInfo (v2, v1, imPrimElem, primElem); |
---|
3470 | factors= multiFactorize (bufA, info); |
---|
3471 | setCharacteristic (p, k, cGFName); |
---|
3472 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
3473 | i.getItem()= Falpha2GFRep (i.getItem()); |
---|
3474 | } |
---|
3475 | } |
---|
3476 | return factors; |
---|
3477 | } |
---|
3478 | } |
---|
3479 | |
---|
3480 | #endif |
---|
3481 | /* HAVE_NTL */ |
---|
3482 | |
---|