1 | /*****************************************************************************\ |
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2 | * Computer Algebra System SINGULAR |
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3 | \*****************************************************************************/ |
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4 | /** @file facFactorize.h |
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5 | * |
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6 | * multivariate 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_FACTORIZE_H |
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14 | #define FAC_FACTORIZE_H |
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15 | |
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16 | // #include "config.h" |
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17 | #include "timing.h" |
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18 | |
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19 | #include "facBivar.h" |
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20 | #include "facFqBivarUtil.h" |
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21 | |
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22 | TIMING_DEFINE_PRINT (fac_squarefree) |
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23 | TIMING_DEFINE_PRINT (fac_factor_squarefree) |
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24 | |
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25 | /// Factorization of A wrt. to different second vars |
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26 | void |
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27 | factorizationWRTDifferentSecondVars ( |
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28 | const CanonicalForm& A, ///<[in] poly |
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29 | CFList*& Aeval, ///<[in,out] A evaluated wrt. |
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30 | ///< different second vars |
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31 | ///< returns bivariate factors |
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32 | int& minFactorsLength, ///<[in,out] minimal length of |
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33 | ///< bivariate factors |
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34 | bool& irred, ///<[in,out] Is A irreducible? |
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35 | const Variable& w ///<[in] alg. variable |
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36 | ); |
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37 | |
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38 | /// Factorization over Q (a) |
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39 | /// |
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40 | /// @return @a multiFactorize returns a factorization of F |
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41 | CFList |
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42 | multiFactorize (const CanonicalForm& F, ///< [in] poly to be factored |
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43 | const Variable& v ///< [in] some algebraic variable |
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44 | ); |
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45 | |
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46 | /// factorize a squarefree multivariate polynomial over \f$ Q(\alpha) \f$ |
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47 | /// |
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48 | /// @return @a ratSqrfFactorize returns a list of monic factors, the first |
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49 | /// element is the leading coefficient. |
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50 | #ifdef HAVE_NTL |
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51 | inline |
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52 | CFList |
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53 | ratSqrfFactorize (const CanonicalForm & G, ///<[in] a multivariate poly |
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54 | const Variable& v= Variable (1) ///<[in] algebraic variable |
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55 | ) |
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56 | { |
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57 | if (getNumVars (G) == 2) |
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58 | return ratBiSqrfFactorize (G, v); |
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59 | CanonicalForm F= G; |
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60 | if (isOn (SW_RATIONAL)) |
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61 | F *= bCommonDen (F); |
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62 | CFList result= multiFactorize (F, v); |
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63 | if (isOn (SW_RATIONAL)) |
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64 | { |
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65 | normalize (result); |
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66 | result.insert (Lc(F)); |
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67 | } |
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68 | return result; |
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69 | } |
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70 | |
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71 | /// factorize a multivariate polynomial over \f$ Q(\alpha) \f$ |
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72 | /// |
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73 | /// @return @a ratFactorize returns a list of monic factors with |
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74 | /// multiplicity, the first element is the leading coefficient. |
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75 | inline |
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76 | CFFList |
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77 | ratFactorize (const CanonicalForm& G, ///<[in] a multivariate poly |
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78 | const Variable& v= Variable (1), ///<[in] algebraic variable |
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79 | bool substCheck= true ///<[in] enables substitute check |
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80 | ) |
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81 | { |
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82 | if (getNumVars (G) == 2) |
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83 | { |
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84 | CFFList result= ratBiFactorize (G,v); |
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85 | return result; |
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86 | } |
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87 | CanonicalForm F= G; |
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88 | |
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89 | if (substCheck) |
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90 | { |
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91 | bool foundOne= false; |
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92 | int * substDegree= new int [F.level()]; |
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93 | for (int i= 1; i <= F.level(); i++) |
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94 | { |
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95 | if (degree (F, i) > 0) |
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96 | { |
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97 | substDegree[i-1]= substituteCheck (F, Variable (i)); |
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98 | if (substDegree [i-1] > 1) |
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99 | { |
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100 | foundOne= true; |
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101 | subst (F, F, substDegree[i-1], Variable (i)); |
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102 | } |
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103 | } |
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104 | else |
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105 | substDegree[i-1]= -1; |
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106 | } |
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107 | if (foundOne) |
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108 | { |
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109 | CFFList result= ratFactorize (F, v, false); |
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110 | CFFList newResult, tmp; |
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111 | CanonicalForm tmp2; |
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112 | newResult.insert (result.getFirst()); |
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113 | result.removeFirst(); |
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114 | for (CFFListIterator i= result; i.hasItem(); i++) |
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115 | { |
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116 | tmp2= i.getItem().factor(); |
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117 | for (int j= 1; j <= G.level(); j++) |
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118 | { |
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119 | if (substDegree[j-1] > 1) |
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120 | tmp2= reverseSubst (tmp2, substDegree[j-1], Variable (j)); |
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121 | } |
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122 | tmp= ratFactorize (tmp2, v, false); |
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123 | tmp.removeFirst(); |
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124 | for (CFFListIterator j= tmp; j.hasItem(); j++) |
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125 | newResult.append (CFFactor (j.getItem().factor(), |
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126 | j.getItem().exp()*i.getItem().exp())); |
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127 | } |
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128 | delete [] substDegree; |
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129 | return newResult; |
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130 | } |
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131 | delete [] substDegree; |
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132 | } |
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133 | |
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134 | CanonicalForm LcF= Lc (F); |
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135 | if (isOn (SW_RATIONAL)) |
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136 | F *= bCommonDen (F); |
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137 | |
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138 | CFFList result; |
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139 | TIMING_START (fac_squarefree); |
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140 | CFFList sqrfFactors= sqrFree (F); |
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141 | TIMING_END_AND_PRINT (fac_squarefree, |
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142 | "time for squarefree factorization over Q: "); |
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143 | |
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144 | CFList tmp; |
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145 | for (CFFListIterator i= sqrfFactors; i.hasItem(); i++) |
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146 | { |
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147 | TIMING_START (fac_factor_squarefree); |
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148 | tmp= ratSqrfFactorize (i.getItem().factor(), v); |
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149 | TIMING_END_AND_PRINT (fac_factor_squarefree, |
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150 | "time to factorize sqrfree factor over Q: "); |
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151 | for (CFListIterator j= tmp; j.hasItem(); j++) |
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152 | { |
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153 | if (j.getItem().inCoeffDomain()) continue; |
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154 | result.append (CFFactor (j.getItem(), i.getItem().exp())); |
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155 | } |
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156 | } |
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157 | if (isOn (SW_RATIONAL)) |
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158 | { |
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159 | normalize (result); |
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160 | if (v.level() == 1) |
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161 | { |
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162 | for (CFFListIterator i= result; i.hasItem(); i++) |
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163 | { |
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164 | LcF /= power (bCommonDen (i.getItem().factor()), i.getItem().exp()); |
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165 | i.getItem()= CFFactor (i.getItem().factor()* |
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166 | bCommonDen(i.getItem().factor()), i.getItem().exp()); |
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167 | } |
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168 | } |
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169 | result.insert (CFFactor (LcF, 1)); |
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170 | } |
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171 | return result; |
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172 | } |
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173 | #endif |
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174 | |
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175 | #endif |
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176 | |
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