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 "assert.h" |
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18 | |
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19 | #include "canonicalform.h" |
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20 | #include "cf_map.h" |
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21 | #include "cfNewtonPolygon.h" |
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22 | |
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23 | CFAFList absFactorizeMain (const CanonicalForm& F); |
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24 | |
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25 | static inline |
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26 | void normalize (CFAFList & L) |
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27 | { |
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28 | for (CFAFListIterator i= L; i.hasItem(); i++) |
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29 | i.getItem()= CFAFactor (i.getItem().factor()/Lc (i.getItem().factor()), |
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30 | i.getItem().minpoly(), i.getItem().exp()); |
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31 | } |
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32 | |
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33 | static inline |
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34 | CFAFList uniAbsFactorize (const CanonicalForm& F) |
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35 | { |
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36 | CFFList rationalFactors= factorize (F); |
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37 | CFFListIterator i= rationalFactors; |
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38 | i++; |
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39 | Variable alpha; |
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40 | CFAFList result; |
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41 | CFFList QaFactors; |
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42 | CFFListIterator iter; |
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43 | for (; i.hasItem(); i++) |
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44 | { |
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45 | if (degree (i.getItem().factor()) == 1) |
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46 | { |
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47 | alpha= rootOf (Variable (1)); |
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48 | result.append (CFAFactor (i.getItem().factor(), getMipo (alpha), |
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49 | i.getItem().exp())); |
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50 | continue; |
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51 | } |
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52 | alpha= rootOf (i.getItem().factor()); |
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53 | QaFactors= factorize (i.getItem().factor(), alpha); |
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54 | iter= QaFactors; |
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55 | if (iter.getItem().factor().inCoeffDomain()) |
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56 | iter++; |
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57 | for (;iter.hasItem(); iter++) |
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58 | { |
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59 | if (degree (iter.getItem().factor()) == 1) |
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60 | { |
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61 | result.append (CFAFactor (iter.getItem().factor(), getMipo (alpha), |
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62 | i.getItem().exp())); |
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63 | break; |
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64 | } |
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65 | } |
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66 | } |
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67 | result.insert (CFAFactor (rationalFactors.getFirst().factor(), 1, 1)); |
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68 | return result; |
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69 | } |
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70 | |
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71 | /*BEGINPUBLIC*/ |
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72 | |
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73 | CFAFList absFactorize (const CanonicalForm& G); |
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74 | |
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75 | /*ENDPUBLIC*/ |
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76 | |
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77 | CFAFList absFactorize (const CanonicalForm& G) |
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78 | { |
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79 | //TODO handle homogeneous input |
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80 | ASSERT (getNumVars (F) == 2, "expected bivariate input"); |
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81 | ASSERT (getCharacteristic() == 0 && isOn (SW_RATIONAL), |
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82 | "expected poly over Q"); |
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83 | |
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84 | CFMap N; |
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85 | CanonicalForm F= compress (G, N); |
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86 | bool isRat= isOn (SW_RATIONAL); |
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87 | if (isRat) |
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88 | F *= bCommonDen (F); |
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89 | |
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90 | Off (SW_RATIONAL); |
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91 | F /= icontent (F); |
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92 | if (isRat) |
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93 | On (SW_RATIONAL); |
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94 | |
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95 | CanonicalForm contentX= content (F, 1); |
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96 | CanonicalForm contentY= content (F, 2); |
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97 | F /= (contentX*contentY); |
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98 | CFAFList contentXFactors, contentYFactors; |
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99 | contentXFactors= uniAbsFactorize (contentX); |
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100 | contentYFactors= uniAbsFactorize (contentY); |
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101 | |
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102 | if (contentXFactors.getFirst().factor().inCoeffDomain()) |
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103 | contentXFactors.removeFirst(); |
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104 | if (contentYFactors.getFirst().factor().inCoeffDomain()) |
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105 | contentYFactors.removeFirst(); |
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106 | if (F.inCoeffDomain()) |
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107 | { |
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108 | CFAFList result; |
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109 | for (CFAFListIterator i= contentXFactors; i.hasItem(); i++) |
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110 | result.append (CFAFactor (N (i.getItem().factor()), i.getItem().minpoly(), |
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111 | i.getItem().exp())); |
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112 | for (CFAFListIterator i= contentYFactors; i.hasItem(); i++) |
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113 | result.append (CFAFactor (N (i.getItem().factor()),i.getItem().minpoly(), |
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114 | i.getItem().exp())); |
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115 | normalize (result); |
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116 | result.insert (CFAFactor (Lc (G), 1, 1)); |
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117 | return result; |
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118 | } |
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119 | CFFList rationalFactors= factorize (F); |
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120 | |
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121 | CFAFList result, resultBuf; |
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122 | |
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123 | CFAFListIterator iter; |
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124 | CFFListIterator i= rationalFactors; |
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125 | i++; |
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126 | for (; i.hasItem(); i++) |
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127 | { |
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128 | resultBuf= absFactorizeMain (i.getItem().factor()); |
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129 | for (iter= resultBuf; iter.hasItem(); iter++) |
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130 | iter.getItem()= CFAFactor (iter.getItem().factor(), |
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131 | iter.getItem().minpoly(), i.getItem().exp()); |
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132 | result= Union (result, resultBuf); |
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133 | } |
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134 | |
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135 | for (CFAFListIterator i= result; i.hasItem(); i++) |
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136 | i.getItem()= CFAFactor (N (i.getItem().factor()), i.getItem().minpoly(), |
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137 | i.getItem().exp()); |
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138 | for (CFAFListIterator i= contentXFactors; i.hasItem(); i++) |
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139 | result.append (CFAFactor (N(i.getItem().factor()), i.getItem().minpoly(), |
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140 | i.getItem().exp())); |
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141 | for (CFAFListIterator i= contentYFactors; i.hasItem(); i++) |
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142 | result.append (CFAFactor (N(i.getItem().factor()), i.getItem().minpoly(), |
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143 | i.getItem().exp())); |
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144 | normalize (result); |
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145 | result.insert (CFAFactor (Lc(G), 1, 1)); |
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146 | |
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147 | return result; |
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148 | } |
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149 | |
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150 | #endif |
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