1 | /*****************************************************************************\ |
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2 | * Computer Algebra System SINGULAR |
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3 | \*****************************************************************************/ |
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4 | /** @file facAbsFact.h |
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5 | * |
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6 | * bivariate absolute factorization over Q described in "Modular Las Vegas |
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7 | * Algorithms for Polynomial Absolute Factorization" by Bertone, ChÚze, Galligo |
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8 | * |
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9 | * @author Martin Lee |
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10 | * |
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11 | **/ |
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12 | /*****************************************************************************/ |
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13 | |
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14 | #ifndef FAC_ABS_FACT_H |
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15 | #define FAC_ABS_FACT_H |
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16 | |
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17 | #include "cf_assert.h" |
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18 | |
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19 | #include "cf_algorithm.h" |
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20 | #include "cf_map.h" |
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21 | |
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22 | /// main absolute factorization routine, expects bivariate poly which is |
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23 | /// primitive wrt. any of its variables and irreducible over Q |
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24 | /// |
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25 | /// @return absFactorizeMain returns a list whose entries contain three entities: |
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26 | /// an absolute irreducible factor, an irreducible univariate polynomial |
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27 | /// that defines the minimal field extension over which the irreducible |
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28 | /// factor is defined and the multiplicity of the absolute irreducible |
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29 | /// factor |
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30 | CFAFList absFactorizeMain (const CanonicalForm& F ///<[in] s.a. |
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31 | ); |
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32 | |
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33 | |
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34 | /// normalize factors, i.e. make factors monic |
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35 | static inline |
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36 | void normalize (CFAFList & L) |
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37 | { |
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38 | for (CFAFListIterator i= L; i.hasItem(); i++) |
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39 | i.getItem()= CFAFactor (i.getItem().factor()/Lc (i.getItem().factor()), |
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40 | i.getItem().minpoly(), i.getItem().exp()); |
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41 | } |
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42 | |
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43 | /// univariate absolute factorization over Q |
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44 | /// |
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45 | /// @return uniAbsFactorize returns a list whose entries contain three entities: |
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46 | /// an absolute irreducible factor, an irreducible univariate polynomial |
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47 | /// that defines the minimal field extension over which the irreducible |
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48 | /// factor is defined and the multiplicity of the absolute irreducible |
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49 | /// factor |
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50 | static inline |
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51 | CFAFList uniAbsFactorize (const CanonicalForm& F ///<[in] univariate poly over Q |
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52 | ) |
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53 | { |
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54 | CFFList rationalFactors= factorize (F); |
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55 | CFFListIterator i= rationalFactors; |
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56 | i++; |
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57 | Variable alpha; |
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58 | CFAFList result; |
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59 | CFFList QaFactors; |
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60 | CFFListIterator iter; |
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61 | for (; i.hasItem(); i++) |
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62 | { |
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63 | if (degree (i.getItem().factor()) == 1) |
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64 | { |
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65 | result.append (CFAFactor (i.getItem().factor(), 1, i.getItem().exp())); |
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66 | continue; |
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67 | } |
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68 | alpha= rootOf (i.getItem().factor()); |
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69 | QaFactors= factorize (i.getItem().factor(), alpha); |
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70 | iter= QaFactors; |
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71 | if (iter.getItem().factor().inCoeffDomain()) |
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72 | iter++; |
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73 | for (;iter.hasItem(); iter++) |
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74 | { |
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75 | if (degree (iter.getItem().factor()) == 1) |
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76 | { |
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77 | result.append (CFAFactor (iter.getItem().factor(), getMipo (alpha), |
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78 | i.getItem().exp())); |
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79 | break; |
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80 | } |
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81 | } |
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82 | } |
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83 | result.insert (CFAFactor (rationalFactors.getFirst().factor(), 1, 1)); |
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84 | return result; |
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85 | } |
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86 | |
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87 | /*BEGINPUBLIC*/ |
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88 | |
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89 | CFAFList absFactorize (const CanonicalForm& G); |
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90 | |
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91 | /*ENDPUBLIC*/ |
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92 | |
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93 | /// absolute factorization of bivariate poly over Q |
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94 | /// |
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95 | /// @return absFactorize returns a list whose entries contain three entities: |
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96 | /// an absolute irreducible factor, an irreducible univariate polynomial |
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97 | /// that defines the minimal field extension over which the irreducible |
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98 | /// factor is defined and the multiplicity of the absolute irreducible |
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99 | /// factor |
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100 | CFAFList absFactorize (const CanonicalForm& G ///<[in] bivariate poly over Q |
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101 | ) |
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102 | { |
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103 | //TODO handle homogeneous input |
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104 | ASSERT (getNumVars (F) == 2, "expected bivariate input"); |
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105 | ASSERT (getCharacteristic() == 0 && isOn (SW_RATIONAL), |
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106 | "expected poly over Q"); |
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107 | |
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108 | CFMap N; |
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109 | CanonicalForm F= compress (G, N); |
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110 | bool isRat= isOn (SW_RATIONAL); |
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111 | if (isRat) |
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112 | F *= bCommonDen (F); |
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113 | |
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114 | Off (SW_RATIONAL); |
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115 | F /= icontent (F); |
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116 | if (isRat) |
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117 | On (SW_RATIONAL); |
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118 | |
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119 | CanonicalForm contentX= content (F, 1); |
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120 | CanonicalForm contentY= content (F, 2); |
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121 | F /= (contentX*contentY); |
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122 | CFAFList contentXFactors, contentYFactors; |
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123 | contentXFactors= uniAbsFactorize (contentX); |
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124 | contentYFactors= uniAbsFactorize (contentY); |
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125 | |
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126 | if (contentXFactors.getFirst().factor().inCoeffDomain()) |
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127 | contentXFactors.removeFirst(); |
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128 | if (contentYFactors.getFirst().factor().inCoeffDomain()) |
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129 | contentYFactors.removeFirst(); |
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130 | if (F.inCoeffDomain()) |
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131 | { |
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132 | CFAFList result; |
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133 | for (CFAFListIterator i= contentXFactors; i.hasItem(); i++) |
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134 | result.append (CFAFactor (N (i.getItem().factor()), i.getItem().minpoly(), |
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135 | i.getItem().exp())); |
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136 | for (CFAFListIterator i= contentYFactors; i.hasItem(); i++) |
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137 | result.append (CFAFactor (N (i.getItem().factor()),i.getItem().minpoly(), |
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138 | i.getItem().exp())); |
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139 | normalize (result); |
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140 | result.insert (CFAFactor (Lc (G), 1, 1)); |
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141 | return result; |
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142 | } |
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143 | CFFList rationalFactors= factorize (F); |
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144 | |
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145 | CFAFList result, resultBuf; |
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146 | |
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147 | CFAFListIterator iter; |
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148 | CFFListIterator i= rationalFactors; |
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149 | i++; |
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150 | for (; i.hasItem(); i++) |
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151 | { |
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152 | resultBuf= absFactorizeMain (i.getItem().factor()); |
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153 | for (iter= resultBuf; iter.hasItem(); iter++) |
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154 | iter.getItem()= CFAFactor (iter.getItem().factor(), |
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155 | iter.getItem().minpoly(), i.getItem().exp()); |
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156 | result= Union (result, resultBuf); |
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157 | } |
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158 | |
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159 | for (CFAFListIterator i= result; i.hasItem(); i++) |
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160 | i.getItem()= CFAFactor (N (i.getItem().factor()), i.getItem().minpoly(), |
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161 | i.getItem().exp()); |
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162 | for (CFAFListIterator i= contentXFactors; i.hasItem(); i++) |
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163 | result.append (CFAFactor (N(i.getItem().factor()), i.getItem().minpoly(), |
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164 | i.getItem().exp())); |
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165 | for (CFAFListIterator i= contentYFactors; i.hasItem(); i++) |
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166 | result.append (CFAFactor (N(i.getItem().factor()), i.getItem().minpoly(), |
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167 | i.getItem().exp())); |
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168 | normalize (result); |
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169 | result.insert (CFAFactor (Lc(G), 1, 1)); |
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170 | |
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171 | return result; |
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172 | } |
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173 | |
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174 | #endif |
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