1 | /*****************************************************************************\ |
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2 | * Computer Algebra System SINGULAR |
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3 | \*****************************************************************************/ |
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4 | /** @file facAbsBiFact.cc |
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5 | * |
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6 | * @author Martin Lee |
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7 | * |
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8 | **/ |
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9 | /*****************************************************************************/ |
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10 | |
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11 | #ifdef HAVE_CONFIG_H |
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12 | #include "config.h" |
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13 | #endif /* HAVE_CONFIG_H */ |
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14 | |
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15 | #include "timing.h" |
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16 | #include "debug.h" |
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17 | |
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18 | #include "facAbsBiFact.h" |
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19 | #include "facBivar.h" |
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20 | #include "facFqBivar.h" |
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21 | #include "cf_reval.h" |
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22 | #include "cf_primes.h" |
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23 | #include "cf_algorithm.h" |
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24 | #ifdef HAVE_FLINT |
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25 | #include "FLINTconvert.h" |
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26 | #include <flint/fmpz_poly_factor.h> |
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27 | #endif |
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28 | #ifdef HAVE_NTL |
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29 | #include "NTLconvert.h" |
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30 | #include <NTL/LLL.h> |
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31 | #endif |
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32 | |
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33 | #ifdef HAVE_NTL |
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34 | |
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35 | TIMING_DEFINE_PRINT(fac_Qa_factorize) |
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36 | TIMING_DEFINE_PRINT(fac_evalpoint) |
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37 | |
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38 | CFAFList uniAbsFactorize (const CanonicalForm& F, bool full) |
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39 | { |
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40 | CFAFList result; |
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41 | if (degree (F) == 1) |
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42 | { |
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43 | bool isRat= isOn (SW_RATIONAL); |
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44 | On (SW_RATIONAL); |
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45 | result= CFAFList (CFAFactor (F/Lc(F), 1, 1)); |
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46 | result.insert (CFAFactor (Lc (F), 1, 1)); |
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47 | if (!isRat) |
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48 | Off (SW_RATIONAL); |
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49 | return result; |
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50 | } |
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51 | CanonicalForm LcF= 1; |
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52 | Variable alpha; |
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53 | CFFList QaFactors; |
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54 | CFFListIterator iter; |
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55 | alpha= rootOf (F); |
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56 | QaFactors= factorize (F, alpha); |
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57 | iter= QaFactors; |
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58 | if (iter.getItem().factor().inCoeffDomain()) |
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59 | { |
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60 | LcF = iter.getItem().factor(); |
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61 | iter++; |
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62 | } |
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63 | for (;iter.hasItem(); iter++) |
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64 | { |
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65 | if (full) |
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66 | result.append (CFAFactor (iter.getItem().factor(), getMipo (alpha), |
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67 | iter.getItem().exp())); |
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68 | if (!full && degree (iter.getItem().factor()) == 1) |
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69 | { |
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70 | result.append (CFAFactor (iter.getItem().factor(), getMipo (alpha), |
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71 | iter.getItem().exp())); |
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72 | break; |
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73 | } |
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74 | } |
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75 | result.insert (CFAFactor (LcF, 1, 1)); |
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76 | return result; |
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77 | } |
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78 | |
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79 | //TODO optimize choice of p -> choose p as large as possible (better than small p since factorization mod p does not require field extension, also less lifting) |
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80 | int |
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81 | choosePoint (const CanonicalForm& F, int tdegF, CFArray& eval, bool rec, |
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82 | int absValue) |
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83 | { |
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84 | REvaluation E1 (1, 1, IntRandom (absValue)); |
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85 | REvaluation E2 (2, 2, IntRandom (absValue)); |
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86 | if (rec) |
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87 | { |
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88 | E1.nextpoint(); |
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89 | E2.nextpoint(); |
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90 | } |
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91 | |
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92 | CanonicalForm f, f1, f2, Fp; |
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93 | int i, p; |
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94 | CFFList f1Factors, f2Factors; |
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95 | CFFListIterator iter; |
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96 | int count= 0; |
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97 | while (1) |
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98 | { |
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99 | count++; |
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100 | f1= E1 (F); |
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101 | if (!f1.isZero() && degree (f1) == degree (F,2)) |
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102 | { |
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103 | f1Factors= factorize (f1); |
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104 | if (f1Factors.getFirst().factor().inCoeffDomain()) |
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105 | f1Factors.removeFirst(); |
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106 | if (f1Factors.length() == 1 && f1Factors.getFirst().exp() == 1) |
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107 | { |
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108 | f= E2(f1); |
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109 | f2= E2 (F); |
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110 | f2Factors= factorize (f2); |
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111 | Off (SW_RATIONAL); |
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112 | if (f2Factors.getFirst().factor().inCoeffDomain()) |
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113 | f2Factors.removeFirst(); |
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114 | if (f2Factors.length() == 1 && f2Factors.getFirst().exp() == 1) |
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115 | { |
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116 | ZZX NTLf1= convertFacCF2NTLZZX (f1); |
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117 | ZZX NTLf2= convertFacCF2NTLZZX (f2); |
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118 | ZZ NTLD1= discriminant (NTLf1); |
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119 | ZZ NTLD2= discriminant (NTLf2); |
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120 | CanonicalForm D1= convertZZ2CF (NTLD1); |
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121 | CanonicalForm D2= convertZZ2CF (NTLD2); |
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122 | if ((!f.isZero()) && |
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123 | (abs(f)>cf_getSmallPrime (cf_getNumSmallPrimes()-1))) |
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124 | { |
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125 | for (i= cf_getNumPrimes()-1; i >= 0; i--) |
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126 | { |
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127 | if (f % CanonicalForm (cf_getPrime (i)) == 0) |
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128 | { |
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129 | p= cf_getPrime(i); |
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130 | Fp= mod (F,p); |
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131 | if (totaldegree (Fp) == tdegF && |
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132 | degree (mod (f2,p), 1) == degree (F,1) && |
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133 | degree (mod (f1, p),2) == degree (F,2)) |
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134 | { |
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135 | if (mod (D1, p) != 0 && mod (D2, p) != 0) |
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136 | { |
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137 | eval[0]= E1[1]; |
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138 | eval[1]= E2[2]; |
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139 | return p; |
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140 | } |
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141 | } |
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142 | } |
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143 | } |
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144 | } |
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145 | else if (!f.isZero()) |
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146 | { |
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147 | for (i= cf_getNumSmallPrimes()-1; i >= 0; i--) |
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148 | { |
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149 | if (f % CanonicalForm (cf_getSmallPrime (i)) == 0) |
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150 | { |
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151 | p= cf_getSmallPrime (i); |
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152 | Fp= mod (F,p); |
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153 | if (totaldegree (Fp) == tdegF && |
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154 | degree (mod (f2, p),1) == degree (F,1) && |
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155 | degree (mod (f1,p),2) == degree (F,2)) |
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156 | { |
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157 | if (mod (D1, p) != 0 && mod (D2, p) != 0) |
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158 | { |
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159 | eval[0]= E1[1]; |
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160 | eval[1]= E2[2]; |
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161 | return p; |
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162 | } |
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163 | } |
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164 | } |
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165 | } |
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166 | } |
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167 | } |
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168 | E2.nextpoint(); |
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169 | On (SW_RATIONAL); |
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170 | } |
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171 | } |
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172 | E1.nextpoint(); |
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173 | if (count == 2) |
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174 | { |
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175 | count= 0; |
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176 | absValue++; |
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177 | E1=REvaluation (1, 1, IntRandom (absValue)); |
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178 | E2=REvaluation (2, 2, IntRandom (absValue)); |
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179 | E1.nextpoint(); |
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180 | E2.nextpoint(); |
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181 | } |
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182 | } |
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183 | return 0; |
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184 | } |
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185 | |
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186 | //G is assumed to be bivariate, irreducible over Q, primitive wrt x and y, compressed |
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187 | CFAFList absBiFactorizeMain (const CanonicalForm& G, bool full) |
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188 | { |
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189 | CanonicalForm F= bCommonDen (G)*G; |
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190 | bool isRat= isOn (SW_RATIONAL); |
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191 | Off (SW_RATIONAL); |
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192 | F /= icontent (F); |
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193 | On (SW_RATIONAL); |
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194 | |
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195 | mpz_t * M=new mpz_t [4]; |
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196 | mpz_init (M[0]); |
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197 | mpz_init (M[1]); |
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198 | mpz_init (M[2]); |
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199 | mpz_init (M[3]); |
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200 | |
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201 | mpz_t * S=new mpz_t [2]; |
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202 | mpz_init (S[0]); |
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203 | mpz_init (S[1]); |
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204 | |
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205 | F= compress (F, M, S); |
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206 | |
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207 | if (F.isUnivariate()) |
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208 | { |
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209 | if (degree (F) == 1) |
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210 | { |
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211 | mpz_clear (M[0]); |
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212 | mpz_clear (M[1]); |
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213 | mpz_clear (M[2]); |
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214 | mpz_clear (M[3]); |
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215 | delete [] M; |
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216 | |
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217 | mpz_clear (S[0]); |
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218 | mpz_clear (S[1]); |
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219 | delete [] S; |
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220 | if (!isRat) |
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221 | Off (SW_RATIONAL); |
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222 | return CFAFList (CFAFactor (G, 1, 1)); |
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223 | } |
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224 | CFAFList result= uniAbsFactorize (F, full); |
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225 | if (result.getFirst().factor().inCoeffDomain()) |
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226 | result.removeFirst(); |
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227 | for (CFAFListIterator iter=result; iter.hasItem(); iter++) |
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228 | iter.getItem()= CFAFactor (decompress (iter.getItem().factor(), M, S), |
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229 | iter.getItem().minpoly(),iter.getItem().exp()); |
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230 | mpz_clear (M[0]); |
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231 | mpz_clear (M[1]); |
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232 | mpz_clear (M[2]); |
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233 | mpz_clear (M[3]); |
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234 | delete [] M; |
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235 | |
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236 | mpz_clear (S[0]); |
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237 | mpz_clear (S[1]); |
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238 | delete [] S; |
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239 | if (!isRat) |
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240 | Off (SW_RATIONAL); |
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241 | return result; |
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242 | } |
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243 | |
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244 | if (degree (F, 1) == 1 || degree (F, 2) == 1) |
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245 | { |
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246 | mpz_clear (M[0]); |
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247 | mpz_clear (M[1]); |
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248 | mpz_clear (M[2]); |
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249 | mpz_clear (M[3]); |
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250 | delete [] M; |
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251 | |
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252 | mpz_clear (S[0]); |
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253 | mpz_clear (S[1]); |
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254 | delete [] S; |
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255 | if (!isRat) |
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256 | Off (SW_RATIONAL); |
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257 | return CFAFList (CFAFactor (G, 1, 1)); |
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258 | } |
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259 | int minTdeg, tdegF= totaldegree (F); |
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260 | CanonicalForm Fp, smallestFactor; |
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261 | int p; |
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262 | CFFList factors; |
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263 | Variable alpha; |
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264 | bool rec= false; |
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265 | Variable x= Variable (1); |
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266 | Variable y= Variable (2); |
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267 | CanonicalForm bufF= F; |
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268 | CFFListIterator iter; |
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269 | CFArray eval= CFArray (2); |
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270 | int absValue= 1; |
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271 | differentevalpoint: |
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272 | while (1) |
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273 | { |
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274 | TIMING_START (fac_evalpoint); |
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275 | p= choosePoint (F, tdegF, eval, rec, absValue); |
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276 | TIMING_END_AND_PRINT (fac_evalpoint, "time to find eval point: "); |
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277 | |
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278 | //after here isOn (SW_RATIONAL)==false |
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279 | setCharacteristic (p); |
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280 | Fp=F.mapinto(); |
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281 | factors= factorize (Fp); |
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282 | |
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283 | if (factors.getFirst().factor().inCoeffDomain()) |
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284 | factors.removeFirst(); |
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285 | |
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286 | if (factors.length() == 1 && factors.getFirst().exp() == 1) |
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287 | { |
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288 | if (absIrredTest (Fp)) |
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289 | { |
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290 | if (isRat) |
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291 | On (SW_RATIONAL); |
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292 | setCharacteristic(0); |
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293 | mpz_clear (M[0]); |
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294 | mpz_clear (M[1]); |
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295 | mpz_clear (M[2]); |
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296 | mpz_clear (M[3]); |
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297 | delete [] M; |
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298 | |
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299 | mpz_clear (S[0]); |
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300 | mpz_clear (S[1]); |
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301 | delete [] S; |
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302 | return CFAFList (CFAFactor (G, 1, 1)); |
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303 | } |
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304 | else |
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305 | { |
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306 | setCharacteristic (0); |
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307 | if (modularIrredTestWithShift (F)) |
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308 | { |
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309 | if (isRat) |
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310 | On (SW_RATIONAL); |
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311 | mpz_clear (M[0]); |
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312 | mpz_clear (M[1]); |
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313 | mpz_clear (M[2]); |
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314 | mpz_clear (M[3]); |
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315 | delete [] M; |
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316 | |
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317 | mpz_clear (S[0]); |
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318 | mpz_clear (S[1]); |
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319 | delete [] S; |
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320 | return CFAFList (CFAFactor (G, 1, 1)); |
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321 | } |
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322 | rec= true; |
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323 | continue; |
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324 | } |
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325 | } |
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326 | iter= factors; |
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327 | smallestFactor= iter.getItem().factor(); |
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328 | while (smallestFactor.isUnivariate() && iter.hasItem()) |
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329 | { |
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330 | iter++; |
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331 | if (!iter.hasItem()) |
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332 | break; |
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333 | smallestFactor= iter.getItem().factor(); |
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334 | } |
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335 | |
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336 | minTdeg= totaldegree (smallestFactor); |
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337 | if (iter.hasItem()) |
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338 | iter++; |
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339 | for (; iter.hasItem(); iter++) |
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340 | { |
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341 | if (!iter.getItem().factor().isUnivariate() && |
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342 | (totaldegree (iter.getItem().factor()) < minTdeg)) |
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343 | { |
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344 | smallestFactor= iter.getItem().factor(); |
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345 | minTdeg= totaldegree (smallestFactor); |
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346 | } |
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347 | } |
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348 | if (tdegF % minTdeg == 0) |
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349 | break; |
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350 | setCharacteristic(0); |
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351 | rec=true; |
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352 | } |
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353 | CanonicalForm Gp= Fp/smallestFactor; |
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354 | Gp= Gp /Lc (Gp); |
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355 | |
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356 | CanonicalForm Gpy= Gp (eval[0].mapinto(), 1); |
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357 | CanonicalForm smallestFactorEvaly= smallestFactor (eval[0].mapinto(),1); |
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358 | CanonicalForm Gpx= Gp (eval[1].mapinto(), 2); |
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359 | CanonicalForm smallestFactorEvalx= smallestFactor (eval[1].mapinto(),2); |
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360 | |
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361 | bool xValid= !(Gpx.inCoeffDomain() || smallestFactorEvalx.inCoeffDomain() || |
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362 | !gcd (Gpx, smallestFactorEvalx).inCoeffDomain()); |
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363 | bool yValid= !(Gpy.inCoeffDomain() || smallestFactorEvaly.inCoeffDomain() || |
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364 | !gcd (Gpy, smallestFactorEvaly).inCoeffDomain()); |
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365 | if (!xValid || !yValid) |
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366 | { |
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367 | rec= true; |
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368 | setCharacteristic (0); |
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369 | goto differentevalpoint; |
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370 | } |
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371 | |
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372 | setCharacteristic (0); |
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373 | |
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374 | CanonicalForm mipo; |
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375 | |
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376 | CFArray mipos= CFArray (2); |
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377 | CFFList mipoFactors; |
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378 | for (int i= 1; i < 3; i++) |
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379 | { |
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380 | CanonicalForm Fi= F(eval[i-1],i); |
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381 | |
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382 | int s= tdegF/minTdeg + 1; |
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383 | CanonicalForm bound= power (maxNorm (Fi), 2*(s-1)); |
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384 | bound *= power (CanonicalForm (s),s-1); |
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385 | bound *= power (CanonicalForm (2), ((s-1)*(s-1))/2); //possible int overflow |
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386 | |
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387 | CanonicalForm B = p; |
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388 | long k = 1L; |
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389 | while ( B < bound ) { |
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390 | B *= p; |
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391 | k++; |
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392 | } |
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393 | |
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394 | //TODO take floor (log2(k)) |
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395 | k= k+1; |
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396 | #ifdef HAVE_FLINT |
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397 | fmpz_poly_t FLINTFi; |
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398 | convertFacCF2Fmpz_poly_t (FLINTFi, Fi); |
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399 | setCharacteristic (p); |
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400 | nmod_poly_t FLINTFpi, FLINTGpi; |
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401 | if (i == 2) |
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402 | { |
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403 | convertFacCF2nmod_poly_t (FLINTFpi, |
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404 | smallestFactorEvalx/lc (smallestFactorEvalx)); |
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405 | convertFacCF2nmod_poly_t (FLINTGpi, Gpx/lc (Gpx)); |
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406 | } |
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407 | else |
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408 | { |
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409 | convertFacCF2nmod_poly_t (FLINTFpi, |
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410 | smallestFactorEvaly/lc (smallestFactorEvaly)); |
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411 | convertFacCF2nmod_poly_t (FLINTGpi, Gpy/lc (Gpy)); |
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412 | } |
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413 | nmod_poly_factor_t nmodFactors; |
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414 | nmod_poly_factor_init (nmodFactors); |
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415 | nmod_poly_factor_insert (nmodFactors, FLINTFpi, 1L); |
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416 | nmod_poly_factor_insert (nmodFactors, FLINTGpi, 1L); |
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417 | |
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418 | // the following fix is due to interface changes from FLINT 2.3 -> FLINT 2.4 |
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419 | # ifndef slong |
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420 | # define slong long |
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421 | # endif |
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422 | |
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423 | slong * link= new slong [2]; |
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424 | fmpz_poly_t *v= new fmpz_poly_t[2]; |
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425 | fmpz_poly_t *w= new fmpz_poly_t[2]; |
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426 | fmpz_poly_init(v[0]); |
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427 | fmpz_poly_init(v[1]); |
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428 | fmpz_poly_init(w[0]); |
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429 | fmpz_poly_init(w[1]); |
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430 | |
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431 | fmpz_poly_factor_t liftedFactors; |
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432 | fmpz_poly_factor_init (liftedFactors); |
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433 | _fmpz_poly_hensel_start_lift (liftedFactors, link, v, w, FLINTFi, |
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434 | nmodFactors, k); |
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435 | |
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436 | nmod_poly_factor_clear (nmodFactors); |
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437 | nmod_poly_clear (FLINTFpi); |
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438 | nmod_poly_clear (FLINTGpi); |
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439 | |
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440 | setCharacteristic(0); |
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441 | CanonicalForm liftedSmallestFactor= |
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442 | convertFmpz_poly_t2FacCF ((fmpz_poly_t &)liftedFactors->p[0],x); |
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443 | |
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444 | CanonicalForm otherFactor= |
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445 | convertFmpz_poly_t2FacCF ((fmpz_poly_t &)liftedFactors->p[1],x); |
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446 | modpk pk= modpk (p, k); |
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447 | #else |
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448 | modpk pk= modpk (p, k); |
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449 | ZZX NTLFi=convertFacCF2NTLZZX (pk (Fi*pk.inverse (lc(Fi)))); |
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450 | setCharacteristic (p); |
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451 | |
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452 | if (fac_NTL_char != p) |
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453 | { |
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454 | fac_NTL_char= p; |
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455 | zz_p::init (p); |
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456 | } |
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457 | zz_pX NTLFpi, NTLGpi; |
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458 | if (i == 2) |
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459 | { |
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460 | NTLFpi=convertFacCF2NTLzzpX (smallestFactorEvalx/lc(smallestFactorEvalx)); |
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461 | NTLGpi=convertFacCF2NTLzzpX (Gpx/lc (Gpx)); |
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462 | } |
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463 | else |
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464 | { |
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465 | NTLFpi=convertFacCF2NTLzzpX (smallestFactorEvaly/lc(smallestFactorEvaly)); |
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466 | NTLGpi=convertFacCF2NTLzzpX (Gpy/lc (Gpy)); |
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467 | } |
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468 | vec_zz_pX modFactors; |
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469 | modFactors.SetLength(2); |
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470 | modFactors[0]= NTLFpi; |
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471 | modFactors[1]= NTLGpi; |
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472 | vec_ZZX liftedFactors; |
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473 | MultiLift (liftedFactors, modFactors, NTLFi, (long) k); |
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474 | setCharacteristic(0); |
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475 | CanonicalForm liftedSmallestFactor= |
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476 | convertNTLZZX2CF (liftedFactors[0], x); |
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477 | |
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478 | CanonicalForm otherFactor= |
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479 | convertNTLZZX2CF (liftedFactors[1], x); |
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480 | #endif |
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481 | |
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482 | Off (SW_SYMMETRIC_FF); |
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483 | liftedSmallestFactor= pk (liftedSmallestFactor); |
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484 | if (i == 2) |
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485 | liftedSmallestFactor= liftedSmallestFactor (eval[0],1); |
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486 | else |
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487 | liftedSmallestFactor= liftedSmallestFactor (eval[1],1); |
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488 | |
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489 | On (SW_SYMMETRIC_FF); |
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490 | CFMatrix *M= new CFMatrix (s, s); |
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491 | (*M)(s,s)= power (CanonicalForm (p), k); |
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492 | for (int j= 1; j < s; j++) |
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493 | { |
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494 | (*M) (j,j)= 1; |
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495 | (*M) (j+1,j)= -liftedSmallestFactor; |
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496 | } |
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497 | |
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498 | mat_ZZ * NTLM= convertFacCFMatrix2NTLmat_ZZ (*M); |
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499 | |
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500 | ZZ det; |
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501 | |
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502 | transpose (*NTLM, *NTLM); |
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503 | (void) LLL (det, *NTLM, 1L, 1L); //use floating point LLL ? |
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504 | transpose (*NTLM, *NTLM); |
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505 | delete M; |
---|
506 | M= convertNTLmat_ZZ2FacCFMatrix (*NTLM); |
---|
507 | delete NTLM; |
---|
508 | |
---|
509 | mipo= 0; |
---|
510 | for (int j= 1; j <= s; j++) |
---|
511 | mipo += (*M) (j,1)*power (x,s-j); |
---|
512 | |
---|
513 | delete M; |
---|
514 | mipoFactors= factorize (mipo); |
---|
515 | if (mipoFactors.getFirst().factor().inCoeffDomain()) |
---|
516 | mipoFactors.removeFirst(); |
---|
517 | |
---|
518 | #ifdef HAVE_FLINT |
---|
519 | fmpz_poly_clear (v[0]); |
---|
520 | fmpz_poly_clear (v[1]); |
---|
521 | fmpz_poly_clear (w[0]); |
---|
522 | fmpz_poly_clear (w[1]); |
---|
523 | delete [] v; |
---|
524 | delete [] w; |
---|
525 | delete [] link; |
---|
526 | fmpz_poly_factor_clear (liftedFactors); |
---|
527 | #endif |
---|
528 | |
---|
529 | if (mipoFactors.length() > 1 || |
---|
530 | (mipoFactors.length() == 1 && mipoFactors.getFirst().exp() > 1) || |
---|
531 | mipo.inCoeffDomain()) |
---|
532 | { |
---|
533 | rec=true; |
---|
534 | goto differentevalpoint; |
---|
535 | } |
---|
536 | else |
---|
537 | mipos[i-1]= mipo; |
---|
538 | } |
---|
539 | |
---|
540 | if (degree (mipos[0]) != degree (mipos[1])) |
---|
541 | { |
---|
542 | rec=true; |
---|
543 | goto differentevalpoint; |
---|
544 | } |
---|
545 | |
---|
546 | On (SW_RATIONAL); |
---|
547 | if (maxNorm (mipos[0]) < maxNorm (mipos[1])) |
---|
548 | alpha= rootOf (mipos[0]); |
---|
549 | else |
---|
550 | alpha= rootOf (mipos[1]); |
---|
551 | |
---|
552 | int wrongMipo= 0; |
---|
553 | |
---|
554 | Variable beta; |
---|
555 | if (maxNorm (mipos[0]) < maxNorm (mipos[1])) |
---|
556 | { |
---|
557 | mipoFactors= factorize (mipos[1], alpha); |
---|
558 | if (mipoFactors.getFirst().factor().inCoeffDomain()) |
---|
559 | mipoFactors.removeFirst(); |
---|
560 | for (iter= mipoFactors; iter.hasItem(); iter++) |
---|
561 | { |
---|
562 | if (degree (iter.getItem().factor()) > 1) |
---|
563 | wrongMipo++; |
---|
564 | } |
---|
565 | if (wrongMipo == mipoFactors.length()) |
---|
566 | { |
---|
567 | rec=true; |
---|
568 | goto differentevalpoint; |
---|
569 | } |
---|
570 | wrongMipo= 0; |
---|
571 | beta= rootOf (mipos[1]); |
---|
572 | mipoFactors= factorize (mipos[0], beta); |
---|
573 | if (mipoFactors.getFirst().factor().inCoeffDomain()) |
---|
574 | mipoFactors.removeFirst(); |
---|
575 | for (iter= mipoFactors; iter.hasItem(); iter++) |
---|
576 | { |
---|
577 | if (degree (iter.getItem().factor()) > 1) |
---|
578 | wrongMipo++; |
---|
579 | } |
---|
580 | if (wrongMipo == mipoFactors.length()) |
---|
581 | { |
---|
582 | rec=true; |
---|
583 | goto differentevalpoint; |
---|
584 | } |
---|
585 | } |
---|
586 | else |
---|
587 | { |
---|
588 | mipoFactors= factorize (mipos[0], alpha); |
---|
589 | if (mipoFactors.getFirst().factor().inCoeffDomain()) |
---|
590 | mipoFactors.removeFirst(); |
---|
591 | for (iter= mipoFactors; iter.hasItem(); iter++) |
---|
592 | { |
---|
593 | if (degree (iter.getItem().factor()) > 1) |
---|
594 | wrongMipo++; |
---|
595 | } |
---|
596 | if (wrongMipo == mipoFactors.length()) |
---|
597 | { |
---|
598 | rec=true; |
---|
599 | goto differentevalpoint; |
---|
600 | } |
---|
601 | wrongMipo= 0; |
---|
602 | beta= rootOf (mipos[0]); |
---|
603 | mipoFactors= factorize (mipos[1], beta); |
---|
604 | if (mipoFactors.getFirst().factor().inCoeffDomain()) |
---|
605 | mipoFactors.removeFirst(); |
---|
606 | for (iter= mipoFactors; iter.hasItem(); iter++) |
---|
607 | { |
---|
608 | if (degree (iter.getItem().factor()) > 1) |
---|
609 | wrongMipo++; |
---|
610 | } |
---|
611 | if (wrongMipo == mipoFactors.length()) |
---|
612 | { |
---|
613 | rec=true; |
---|
614 | goto differentevalpoint; |
---|
615 | } |
---|
616 | } |
---|
617 | |
---|
618 | |
---|
619 | CanonicalForm F1; |
---|
620 | if (degree (F,1) > minTdeg) |
---|
621 | F1= F (eval[1], 2); |
---|
622 | else |
---|
623 | F1= F (eval[0], 1); |
---|
624 | |
---|
625 | CFFList QaF1Factors; |
---|
626 | bool swap= false; |
---|
627 | if (F1.level() == 2) |
---|
628 | { |
---|
629 | swap= true; |
---|
630 | F1=swapvar (F1, x, y); |
---|
631 | F= swapvar (F, x, y); |
---|
632 | } |
---|
633 | |
---|
634 | wrongMipo= 0; |
---|
635 | QaF1Factors= factorize (F1, alpha); |
---|
636 | if (QaF1Factors.getFirst().factor().inCoeffDomain()) |
---|
637 | QaF1Factors.removeFirst(); |
---|
638 | for (iter= QaF1Factors; iter.hasItem(); iter++) |
---|
639 | { |
---|
640 | if (degree (iter.getItem().factor()) > minTdeg) |
---|
641 | wrongMipo++; |
---|
642 | } |
---|
643 | |
---|
644 | if (wrongMipo == QaF1Factors.length()) |
---|
645 | { |
---|
646 | rec= true; |
---|
647 | F= bufF; |
---|
648 | goto differentevalpoint; |
---|
649 | } |
---|
650 | |
---|
651 | CanonicalForm evaluation; |
---|
652 | if (swap) |
---|
653 | evaluation= eval[0]; |
---|
654 | else |
---|
655 | evaluation= eval[1]; |
---|
656 | |
---|
657 | F *= bCommonDen (F); |
---|
658 | F= F (y + evaluation, y); |
---|
659 | |
---|
660 | int liftBound= degree (F,y) + 1; |
---|
661 | |
---|
662 | modpk b= modpk(); |
---|
663 | |
---|
664 | CanonicalForm den= 1; |
---|
665 | |
---|
666 | mipo= getMipo (alpha); |
---|
667 | |
---|
668 | CFList uniFactors; |
---|
669 | for (iter=QaF1Factors; iter.hasItem(); iter++) |
---|
670 | uniFactors.append (iter.getItem().factor()); |
---|
671 | |
---|
672 | F /= Lc (F1); |
---|
673 | ZZX NTLmipo= convertFacCF2NTLZZX (mipo); |
---|
674 | ZZX NTLLcf= convertFacCF2NTLZZX (Lc (F*bCommonDen (F))); |
---|
675 | ZZ NTLf= resultant (NTLmipo, NTLLcf); |
---|
676 | ZZ NTLD= discriminant (NTLmipo); |
---|
677 | den= abs (convertZZ2CF (NTLD*NTLf)); |
---|
678 | |
---|
679 | // make factors elements of Z(a)[x] disable for modularDiophant |
---|
680 | CanonicalForm multiplier= 1; |
---|
681 | for (CFListIterator i= uniFactors; i.hasItem(); i++) |
---|
682 | { |
---|
683 | multiplier *= bCommonDen (i.getItem()); |
---|
684 | i.getItem()= i.getItem()*bCommonDen(i.getItem()); |
---|
685 | } |
---|
686 | F *= multiplier; |
---|
687 | F *= bCommonDen (F); |
---|
688 | |
---|
689 | Off (SW_RATIONAL); |
---|
690 | int ii= 0; |
---|
691 | CanonicalForm discMipo= convertZZ2CF (NTLD); |
---|
692 | findGoodPrime (bufF*discMipo,ii); |
---|
693 | findGoodPrime (F1*discMipo,ii); |
---|
694 | findGoodPrime (F*discMipo,ii); |
---|
695 | |
---|
696 | int pp=cf_getBigPrime(ii); |
---|
697 | b = coeffBound( F, pp, mipo ); |
---|
698 | modpk bb= coeffBound (F1, pp, mipo); |
---|
699 | if (bb.getk() > b.getk() ) b=bb; |
---|
700 | bb= coeffBound (F, pp, mipo); |
---|
701 | if (bb.getk() > b.getk() ) b=bb; |
---|
702 | |
---|
703 | ExtensionInfo dummy= ExtensionInfo (alpha, false); |
---|
704 | DegreePattern degs= DegreePattern (uniFactors); |
---|
705 | |
---|
706 | bool earlySuccess= false; |
---|
707 | CFList earlyFactors; |
---|
708 | uniFactors= henselLiftAndEarly |
---|
709 | (F, earlySuccess, earlyFactors, degs, liftBound, |
---|
710 | uniFactors, dummy, evaluation, b, den); |
---|
711 | |
---|
712 | DEBOUTLN (cerr, "lifted factors= " << uniFactors); |
---|
713 | |
---|
714 | CanonicalForm MODl= power (y, liftBound); |
---|
715 | |
---|
716 | On (SW_RATIONAL); |
---|
717 | F *= bCommonDen (F); |
---|
718 | Off (SW_RATIONAL); |
---|
719 | |
---|
720 | CFList biFactors; |
---|
721 | |
---|
722 | biFactors= factorRecombination (uniFactors, F, MODl, degs, evaluation, 1, |
---|
723 | uniFactors.length()/2, b, den); |
---|
724 | |
---|
725 | On (SW_RATIONAL); |
---|
726 | |
---|
727 | if (earlySuccess) |
---|
728 | biFactors= Union (earlyFactors, biFactors); |
---|
729 | else if (!earlySuccess && degs.getLength() == 1) |
---|
730 | biFactors= earlyFactors; |
---|
731 | |
---|
732 | bool swap2= false; |
---|
733 | appendSwapDecompress (biFactors, CFList(), CFList(), swap, swap2, CFMap()); |
---|
734 | if (isOn (SW_RATIONAL)) |
---|
735 | normalize (biFactors); |
---|
736 | |
---|
737 | CFAFList result; |
---|
738 | bool found= false; |
---|
739 | |
---|
740 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
741 | { |
---|
742 | if (full) |
---|
743 | result.append (CFAFactor (decompress (i.getItem(), M, S), |
---|
744 | getMipo (alpha), 1)); |
---|
745 | |
---|
746 | if (totaldegree (i.getItem()) == minTdeg) |
---|
747 | { |
---|
748 | if (!full) |
---|
749 | result= CFAFList (CFAFactor (decompress (i.getItem(), M, S), |
---|
750 | getMipo (alpha), 1)); |
---|
751 | found= true; |
---|
752 | |
---|
753 | if (!full) |
---|
754 | break; |
---|
755 | } |
---|
756 | } |
---|
757 | |
---|
758 | if (!found) |
---|
759 | { |
---|
760 | rec= true; |
---|
761 | F= bufF; |
---|
762 | goto differentevalpoint; |
---|
763 | } |
---|
764 | |
---|
765 | if (isRat) |
---|
766 | On (SW_RATIONAL); |
---|
767 | else |
---|
768 | Off (SW_RATIONAL); |
---|
769 | |
---|
770 | mpz_clear (M[0]); |
---|
771 | mpz_clear (M[1]); |
---|
772 | mpz_clear (M[2]); |
---|
773 | mpz_clear (M[3]); |
---|
774 | delete [] M; |
---|
775 | |
---|
776 | mpz_clear (S[0]); |
---|
777 | mpz_clear (S[1]); |
---|
778 | delete [] S; |
---|
779 | |
---|
780 | return result; |
---|
781 | } |
---|
782 | |
---|
783 | #endif |
---|
784 | |
---|
785 | |
---|