[ab547e2] | 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 | * @internal @version \$Id$ |
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| 11 | * |
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| 12 | **/ |
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| 13 | /*****************************************************************************/ |
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| 14 | |
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| 15 | #ifndef FAC_FACTORIZE_H |
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| 16 | #define FAC_FACTORIZE_H |
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| 17 | |
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[e4fe2b] | 18 | // #include "config.h" |
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[ab547e2] | 19 | |
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| 20 | #include "facBivar.h" |
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| 21 | #include "facFqBivarUtil.h" |
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| 22 | |
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| 23 | /// Factorization over Q (a) |
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| 24 | /// |
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| 25 | /// @return @a multiFactorize returns a factorization of F |
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| 26 | CFList |
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| 27 | multiFactorize (const CanonicalForm& F, ///< [in] poly to be factored |
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| 28 | const Variable& v ///< [in] some algebraic variable |
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| 29 | ); |
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| 30 | |
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| 31 | /// factorize a squarefree multivariate polynomial over \f$ Q(\alpha) \f$ |
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| 32 | /// |
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| 33 | /// @return @a ratSqrfFactorize returns a list of monic factors, the first |
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| 34 | /// element is the leading coefficient. |
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[d990001] | 35 | #ifdef HAVE_NTL |
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[ab547e2] | 36 | inline |
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[f9b796e] | 37 | CFList |
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[530295] | 38 | ratSqrfFactorize (const CanonicalForm & G, ///<[in] a multivariate poly |
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| 39 | const Variable& v= Variable (1) ///<[in] algebraic variable |
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[f9b796e] | 40 | ) |
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[ab547e2] | 41 | { |
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[5f9b47] | 42 | if (getNumVars (G) == 2) |
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| 43 | return ratBiSqrfFactorize (G, v); |
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| 44 | CanonicalForm F= G; |
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| 45 | if (isOn (SW_RATIONAL)) |
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| 46 | F *= bCommonDen (F); |
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[ab547e2] | 47 | CFList result= multiFactorize (F, v); |
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| 48 | if (isOn (SW_RATIONAL)) |
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| 49 | { |
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| 50 | normalize (result); |
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| 51 | result.insert (Lc(F)); |
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| 52 | } |
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| 53 | return result; |
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| 54 | } |
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| 55 | |
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| 56 | /// factorize a multivariate polynomial over \f$ Q(\alpha) \f$ |
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| 57 | /// |
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| 58 | /// @return @a ratFactorize returns a list of monic factors with |
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| 59 | /// multiplicity, the first element is the leading coefficient. |
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| 60 | inline |
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[f9b796e] | 61 | CFFList |
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[530295] | 62 | ratFactorize (const CanonicalForm& G, ///<[in] a multivariate poly |
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| 63 | const Variable& v= Variable (1), ///<[in] algebraic variable |
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| 64 | bool substCheck= true ///<[in] enables substitute check |
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[f9b796e] | 65 | ) |
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[ab547e2] | 66 | { |
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[5f9b47] | 67 | if (getNumVars (G) == 2) |
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[ab547e2] | 68 | { |
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[5f9b47] | 69 | CFFList result= ratBiFactorize (G,v); |
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[ab547e2] | 70 | return result; |
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| 71 | } |
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[5f9b47] | 72 | CanonicalForm F= G; |
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[f9b796e] | 73 | |
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| 74 | if (substCheck) |
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| 75 | { |
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| 76 | bool foundOne= false; |
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| 77 | int * substDegree= new int [F.level()]; |
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| 78 | for (int i= 1; i <= F.level(); i++) |
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| 79 | { |
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| 80 | if (degree (F, i) > 0) |
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| 81 | { |
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| 82 | substDegree[i-1]= substituteCheck (F, Variable (i)); |
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| 83 | if (substDegree [i-1] > 1) |
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| 84 | { |
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| 85 | foundOne= true; |
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| 86 | subst (F, F, substDegree[i-1], Variable (i)); |
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| 87 | } |
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| 88 | } |
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| 89 | else |
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| 90 | substDegree[i-1]= -1; |
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| 91 | } |
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| 92 | if (foundOne) |
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| 93 | { |
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| 94 | CFFList result= ratFactorize (F, v, false); |
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| 95 | CFFList newResult, tmp; |
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| 96 | CanonicalForm tmp2; |
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| 97 | newResult.insert (result.getFirst()); |
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| 98 | result.removeFirst(); |
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| 99 | for (CFFListIterator i= result; i.hasItem(); i++) |
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| 100 | { |
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| 101 | tmp2= i.getItem().factor(); |
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| 102 | for (int j= 1; j <= G.level(); j++) |
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| 103 | { |
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| 104 | if (substDegree[j-1] > 1) |
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| 105 | tmp2= reverseSubst (tmp2, substDegree[j-1], Variable (j)); |
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| 106 | } |
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| 107 | tmp= ratFactorize (tmp2, v, false); |
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| 108 | tmp.removeFirst(); |
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| 109 | for (CFFListIterator j= tmp; j.hasItem(); j++) |
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| 110 | newResult.append (CFFactor (j.getItem().factor(), |
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| 111 | j.getItem().exp()*i.getItem().exp())); |
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| 112 | } |
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| 113 | delete [] substDegree; |
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| 114 | return newResult; |
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| 115 | } |
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| 116 | delete [] substDegree; |
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| 117 | } |
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| 118 | |
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[ab547e2] | 119 | CanonicalForm LcF= Lc (F); |
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[5f9b47] | 120 | if (isOn (SW_RATIONAL)) |
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| 121 | F *= bCommonDen (F); |
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[ab547e2] | 122 | |
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| 123 | CFFList result; |
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[5f9b47] | 124 | CFFList sqrfFactors= sqrFree (F); |
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| 125 | for (CFFListIterator i= sqrfFactors; i.hasItem(); i++) |
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| 126 | { |
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| 127 | CFList tmp= ratSqrfFactorize (i.getItem().factor(), v); |
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| 128 | for (CFListIterator j= tmp; j.hasItem(); j++) |
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| 129 | { |
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| 130 | if (j.getItem().inCoeffDomain()) continue; |
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| 131 | result.append (CFFactor (j.getItem(), i.getItem().exp())); |
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| 132 | } |
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| 133 | } |
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[ab547e2] | 134 | if (isOn (SW_RATIONAL)) |
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| 135 | { |
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| 136 | normalize (result); |
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[a8a93f] | 137 | if (v.level() == 1) |
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| 138 | { |
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| 139 | for (CFFListIterator i= result; i.hasItem(); i++) |
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| 140 | { |
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| 141 | LcF /= bCommonDen (i.getItem().factor()); |
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| 142 | i.getItem()= CFFactor (i.getItem().factor()* |
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| 143 | bCommonDen(i.getItem().factor()), i.getItem().exp()); |
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| 144 | } |
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| 145 | } |
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[ab547e2] | 146 | result.insert (CFFactor (LcF, 1)); |
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| 147 | } |
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| 148 | return result; |
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| 149 | } |
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[d990001] | 150 | #endif |
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[ab547e2] | 151 | |
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| 152 | #endif |
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| 153 | |
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