1 | /*****************************************************************************\ |
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2 | * Computer Algebra System SINGULAR |
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3 | \*****************************************************************************/ |
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4 | /** @file facBivar.h |
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5 | * |
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6 | * bivariate factorization over Q(a) |
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7 | * |
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8 | * @author Martin Lee |
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9 | * |
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10 | **/ |
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11 | /*****************************************************************************/ |
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12 | |
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13 | #ifndef FAC_BIVAR_H |
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14 | #define FAC_BIVAR_H |
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15 | |
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16 | // #include "config.h" |
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17 | |
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18 | #include "cf_assert.h" |
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19 | #include "timing.h" |
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20 | |
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21 | #include "facFqBivarUtil.h" |
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22 | #include "DegreePattern.h" |
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23 | #include "cf_util.h" |
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24 | #include "facFqSquarefree.h" |
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25 | #include "cf_map.h" |
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26 | #include "cf_algorithm.h" |
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27 | #include "cfNewtonPolygon.h" |
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28 | #include "fac_util.h" |
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29 | #include "cf_algorithm.h" |
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30 | |
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31 | TIMING_DEFINE_PRINT(fac_bi_sqrf) |
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32 | TIMING_DEFINE_PRINT(fac_bi_factor_sqrf) |
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33 | |
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34 | /// @return @a biFactorize returns a list of factors of F. If F is not monic |
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35 | /// its leading coefficient is not outputted. |
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36 | CFList |
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37 | biFactorize (const CanonicalForm& F, ///< [in] a sqrfree bivariate poly |
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38 | const Variable& v ///< [in] some algebraic variable |
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39 | ); |
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40 | |
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41 | /// factorize a squarefree bivariate polynomial over \f$ Q(\alpha) \f$. |
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42 | /// |
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43 | /// @ return @a ratBiSqrfFactorize returns a list of monic factors, the first |
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44 | /// element is the leading coefficient. |
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45 | inline |
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46 | CFList |
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47 | ratBiSqrfFactorize (const CanonicalForm & G, ///< [in] a bivariate poly |
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48 | const Variable& v= Variable (1) ///< [in] algebraic variable |
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49 | ) |
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50 | { |
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51 | CFMap N; |
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52 | CanonicalForm F= compress (G, N); |
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53 | CanonicalForm contentX= content (F, 1); //erwarte hier primitiven input: primitiv ÃŒber Z bzw. Z[a] |
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54 | CanonicalForm contentY= content (F, 2); |
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55 | F /= (contentX*contentY); |
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56 | CFFList contentXFactors, contentYFactors; |
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57 | if (v.level() != 1) |
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58 | { |
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59 | contentXFactors= factorize (contentX, v); |
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60 | contentYFactors= factorize (contentY, v); |
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61 | } |
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62 | else |
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63 | { |
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64 | contentXFactors= factorize (contentX); |
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65 | contentYFactors= factorize (contentY); |
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66 | } |
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67 | if (contentXFactors.getFirst().factor().inCoeffDomain()) |
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68 | contentXFactors.removeFirst(); |
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69 | if (contentYFactors.getFirst().factor().inCoeffDomain()) |
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70 | contentYFactors.removeFirst(); |
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71 | if (F.inCoeffDomain()) |
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72 | { |
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73 | CFList result; |
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74 | for (CFFListIterator i= contentXFactors; i.hasItem(); i++) |
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75 | result.append (N (i.getItem().factor())); |
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76 | for (CFFListIterator i= contentYFactors; i.hasItem(); i++) |
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77 | result.append (N (i.getItem().factor())); |
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78 | if (isOn (SW_RATIONAL)) |
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79 | { |
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80 | normalize (result); |
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81 | result.insert (Lc (G)); |
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82 | } |
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83 | return result; |
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84 | } |
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85 | |
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86 | mpz_t * M=new mpz_t [4]; |
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87 | mpz_init (M[0]); |
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88 | mpz_init (M[1]); |
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89 | mpz_init (M[2]); |
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90 | mpz_init (M[3]); |
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91 | |
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92 | mpz_t * S=new mpz_t [2]; |
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93 | mpz_init (S[0]); |
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94 | mpz_init (S[1]); |
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95 | |
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96 | F= compress (F, M, S); |
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97 | CFList result= biFactorize (F, v); |
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98 | for (CFListIterator i= result; i.hasItem(); i++) |
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99 | i.getItem()= N (decompress (i.getItem(), M, S)); |
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100 | for (CFFListIterator i= contentXFactors; i.hasItem(); i++) |
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101 | result.append (N(i.getItem().factor())); |
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102 | for (CFFListIterator i= contentYFactors; i.hasItem(); i++) |
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103 | result.append (N (i.getItem().factor())); |
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104 | if (isOn (SW_RATIONAL)) |
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105 | { |
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106 | normalize (result); |
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107 | result.insert (Lc (G)); |
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108 | } |
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109 | |
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110 | mpz_clear (M[0]); |
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111 | mpz_clear (M[1]); |
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112 | mpz_clear (M[2]); |
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113 | mpz_clear (M[3]); |
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114 | delete [] M; |
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115 | |
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116 | mpz_clear (S[0]); |
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117 | mpz_clear (S[1]); |
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118 | delete [] S; |
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119 | |
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120 | return result; |
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121 | } |
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122 | |
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123 | /// factorize a bivariate polynomial over \f$ Q(\alpha) \f$ |
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124 | /// |
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125 | /// @return @a ratBiFactorize returns a list of monic factors with |
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126 | /// multiplicity, the first element is the leading coefficient. |
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127 | inline |
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128 | CFFList |
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129 | ratBiFactorize (const CanonicalForm & G, ///< [in] a bivariate poly |
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130 | const Variable& v= Variable (1), ///< [in] algebraic variable |
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131 | bool substCheck= true ///< [in] enables substitute check |
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132 | ) |
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133 | { |
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134 | CFMap N; |
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135 | CanonicalForm F= compress (G, N); |
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136 | |
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137 | if (substCheck) |
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138 | { |
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139 | bool foundOne= false; |
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140 | int * substDegree= new int [F.level()]; |
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141 | for (int i= 1; i <= F.level(); i++) |
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142 | { |
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143 | substDegree[i-1]= substituteCheck (F, Variable (i)); |
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144 | if (substDegree [i-1] > 1) |
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145 | { |
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146 | foundOne= true; |
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147 | subst (F, F, substDegree[i-1], Variable (i)); |
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148 | } |
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149 | } |
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150 | if (foundOne) |
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151 | { |
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152 | CFFList result= ratBiFactorize (F, v, false); |
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153 | CFFList newResult, tmp; |
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154 | CanonicalForm tmp2; |
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155 | newResult.insert (result.getFirst()); |
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156 | result.removeFirst(); |
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157 | for (CFFListIterator i= result; i.hasItem(); i++) |
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158 | { |
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159 | tmp2= i.getItem().factor(); |
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160 | for (int j= 1; j <= F.level(); j++) |
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161 | { |
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162 | if (substDegree[j-1] > 1) |
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163 | tmp2= reverseSubst (tmp2, substDegree[j-1], Variable (j)); |
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164 | } |
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165 | tmp= ratBiFactorize (tmp2, v, false); |
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166 | tmp.removeFirst(); |
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167 | for (CFFListIterator j= tmp; j.hasItem(); j++) |
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168 | newResult.append (CFFactor (j.getItem().factor(), |
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169 | j.getItem().exp()*i.getItem().exp())); |
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170 | } |
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171 | decompress (newResult, N); |
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172 | delete [] substDegree; |
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173 | return newResult; |
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174 | } |
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175 | delete [] substDegree; |
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176 | } |
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177 | |
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178 | CanonicalForm LcF= Lc (F); |
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179 | CanonicalForm contentX= content (F, 1); |
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180 | CanonicalForm contentY= content (F, 2); |
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181 | F /= (contentX*contentY); |
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182 | CFFList contentXFactors, contentYFactors; |
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183 | if (v.level() != 1) |
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184 | { |
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185 | contentXFactors= factorize (contentX, v); |
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186 | contentYFactors= factorize (contentY, v); |
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187 | } |
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188 | else |
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189 | { |
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190 | contentXFactors= factorize (contentX); |
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191 | contentYFactors= factorize (contentY); |
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192 | } |
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193 | if (contentXFactors.getFirst().factor().inCoeffDomain()) |
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194 | contentXFactors.removeFirst(); |
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195 | if (contentYFactors.getFirst().factor().inCoeffDomain()) |
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196 | contentYFactors.removeFirst(); |
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197 | decompress (contentXFactors, N); |
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198 | decompress (contentYFactors, N); |
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199 | CFFList result, resultRoot; |
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200 | if (F.inCoeffDomain()) |
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201 | { |
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202 | result= Union (contentXFactors, contentYFactors); |
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203 | if (isOn (SW_RATIONAL)) |
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204 | { |
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205 | normalize (result); |
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206 | if (v.level() == 1) |
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207 | { |
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208 | for (CFFListIterator i= result; i.hasItem(); i++) |
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209 | { |
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210 | LcF /= power (bCommonDen (i.getItem().factor()), i.getItem().exp()); |
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211 | i.getItem()= CFFactor (i.getItem().factor()* |
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212 | bCommonDen(i.getItem().factor()), i.getItem().exp()); |
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213 | } |
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214 | } |
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215 | result.insert (CFFactor (LcF, 1)); |
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216 | } |
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217 | return result; |
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218 | } |
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219 | |
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220 | mpz_t * M=new mpz_t [4]; |
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221 | mpz_init (M[0]); |
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222 | mpz_init (M[1]); |
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223 | mpz_init (M[2]); |
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224 | mpz_init (M[3]); |
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225 | |
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226 | mpz_t * S=new mpz_t [2]; |
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227 | mpz_init (S[0]); |
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228 | mpz_init (S[1]); |
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229 | |
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230 | F= compress (F, M, S); |
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231 | TIMING_START (fac_bi_sqrf); |
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232 | CFFList sqrfFactors= sqrFree (F); |
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233 | TIMING_END_AND_PRINT (fac_bi_sqrf, |
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234 | "time for bivariate sqrf factors over Q: "); |
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235 | for (CFFListIterator i= sqrfFactors; i.hasItem(); i++) |
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236 | { |
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237 | TIMING_START (fac_bi_factor_sqrf); |
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238 | CFList tmp= ratBiSqrfFactorize (i.getItem().factor(), v); |
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239 | TIMING_END_AND_PRINT (fac_bi_factor_sqrf, |
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240 | "time to factor bivariate sqrf factors over Q: "); |
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241 | for (CFListIterator j= tmp; j.hasItem(); j++) |
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242 | { |
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243 | if (j.getItem().inCoeffDomain()) continue; |
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244 | result.append (CFFactor (N (decompress (j.getItem(), M, S)), |
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245 | i.getItem().exp())); |
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246 | } |
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247 | } |
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248 | result= Union (result, contentXFactors); |
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249 | result= Union (result, contentYFactors); |
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250 | if (isOn (SW_RATIONAL)) |
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251 | { |
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252 | normalize (result); |
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253 | if (v.level() == 1) |
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254 | { |
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255 | for (CFFListIterator i= result; i.hasItem(); i++) |
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256 | { |
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257 | LcF /= power (bCommonDen (i.getItem().factor()), i.getItem().exp()); |
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258 | i.getItem()= CFFactor (i.getItem().factor()* |
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259 | bCommonDen(i.getItem().factor()), i.getItem().exp()); |
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260 | } |
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261 | } |
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262 | result.insert (CFFactor (LcF, 1)); |
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263 | } |
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264 | |
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265 | mpz_clear (M[0]); |
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266 | mpz_clear (M[1]); |
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267 | mpz_clear (M[2]); |
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268 | mpz_clear (M[3]); |
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269 | delete [] M; |
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270 | |
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271 | mpz_clear (S[0]); |
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272 | mpz_clear (S[1]); |
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273 | delete [] S; |
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274 | |
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275 | return result; |
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276 | } |
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277 | |
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278 | /// convert a CFFList to a CFList by dropping the multiplicity |
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279 | CFList conv (const CFFList& L ///< [in] a CFFList |
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280 | ); |
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281 | |
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282 | /// compute p^k larger than the bound on the coefficients of a factor of @a f |
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283 | /// over Q (mipo) |
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284 | modpk |
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285 | coeffBound (const CanonicalForm & f, ///< [in] poly over Z[a] |
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286 | int p, ///< [in] some positive integer |
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287 | const CanonicalForm& mipo ///< [in] minimal polynomial with |
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288 | ///< denominator 1 |
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289 | ); |
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290 | |
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291 | /// find a big prime p from our tables such that no term of f vanishes mod p |
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292 | void findGoodPrime(const CanonicalForm &f, ///< [in] poly over Z or Z[a] |
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293 | int &start ///< [in,out] index of big prime in |
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294 | /// cf_primetab.h |
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295 | ); |
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296 | |
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297 | /// compute p^k larger than the bound on the coefficients of a factor of @a f |
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298 | /// over Z |
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299 | modpk |
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300 | coeffBound (const CanonicalForm & f, ///< [in] poly over Z |
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301 | int p ///< [in] some positive integer |
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302 | ); |
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303 | |
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304 | #endif |
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305 | |
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