[24b338] | 1 | /*****************************************************************************\ |
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[806c18] | 2 | * Computer Algebra System SINGULAR |
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[24b338] | 3 | \*****************************************************************************/ |
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| 4 | /** @file facFqSquarefree.h |
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[806c18] | 5 | * |
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[24b338] | 6 | * This file provides functions for squarefrees factorizing over |
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[806c18] | 7 | * \f$ F_{p} \f$ , \f$ F_{p}(\alpha ) \f$ or GF. |
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[24b338] | 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_FQ_SQUAREFREE_H |
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| 15 | #define FAC_FQ_SQUAREFREE_H |
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| 16 | |
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[650f2d8] | 17 | #include "cf_assert.h" |
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[eacb7aa] | 18 | #include "cf_factory.h" |
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[6caa2a6] | 19 | #include "fac_sqrfree.h" |
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[72f1e4b] | 20 | #include "cf_factory.h" |
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[24b338] | 21 | |
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| 22 | /// squarefree factorization over a finite field |
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| 23 | /// @a return a list of squarefree factors with multiplicity |
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[806c18] | 24 | CFFList |
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| 25 | squarefreeFactorization |
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[24b338] | 26 | (const CanonicalForm & F, ///<[in] a poly |
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[806c18] | 27 | const Variable & alpha ///<[in] either an algebraic variable, |
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[24b338] | 28 | ///< i.e. we are over some F_p (alpha) |
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| 29 | ///< or a variable of level 1, i.e. |
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[806c18] | 30 | ///< we are F_p or GF |
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[24b338] | 31 | ); |
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| 32 | |
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| 33 | /// squarefree factorization over \f$ F_{p} \f$. |
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| 34 | /// If input is not monic, the leading coefficient is dropped |
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| 35 | /// |
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| 36 | /// @return a list of squarefree factors with multiplicity |
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| 37 | inline |
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[6caa2a6] | 38 | CFFList FpSqrf (const CanonicalForm& F, ///< [in] a poly |
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| 39 | bool sort= true ///< [in] sort factors by exponent? |
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[806c18] | 40 | ) |
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[24b338] | 41 | { |
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| 42 | Variable a= 1; |
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[6caa2a6] | 43 | int n= F.level(); |
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| 44 | CanonicalForm cont, bufF= F; |
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| 45 | CFFList bufResult; |
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| 46 | |
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| 47 | CFFList result; |
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| 48 | for (int i= n; i >= 1; i++) |
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| 49 | { |
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| 50 | cont= content (bufF, i); |
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| 51 | bufResult= squarefreeFactorization (cont, a); |
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| 52 | if (bufResult.getFirst().factor().inCoeffDomain()) |
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| 53 | bufResult.removeFirst(); |
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| 54 | result= Union (result, bufResult); |
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| 55 | bufF /= cont; |
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| 56 | if (bufF.inCoeffDomain()) |
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| 57 | break; |
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| 58 | } |
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| 59 | if (!bufF.inCoeffDomain()) |
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| 60 | { |
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| 61 | bufResult= squarefreeFactorization (bufF, a); |
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| 62 | if (bufResult.getFirst().factor().inCoeffDomain()) |
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| 63 | bufResult.removeFirst(); |
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| 64 | result= Union (result, bufResult); |
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| 65 | } |
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| 66 | if (sort) |
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| 67 | result= sortCFFList (result); |
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[24b338] | 68 | result.insert (CFFactor (Lc(F), 1)); |
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| 69 | return result; |
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| 70 | } |
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| 71 | |
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| 72 | /// squarefree factorization over \f$ F_{p}(\alpha ) \f$. |
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| 73 | /// If input is not monic, the leading coefficient is dropped |
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| 74 | /// |
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| 75 | /// @return a list of squarefree factors with multiplicity |
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| 76 | inline |
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| 77 | CFFList FqSqrf (const CanonicalForm& F, ///< [in] a poly |
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[6caa2a6] | 78 | const Variable& alpha, ///< [in] algebraic variable |
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| 79 | bool sort= true ///< [in] sort factors by exponent? |
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[24b338] | 80 | ) |
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| 81 | { |
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[6caa2a6] | 82 | int n= F.level(); |
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| 83 | CanonicalForm cont, bufF= F; |
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| 84 | CFFList bufResult; |
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| 85 | |
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| 86 | CFFList result; |
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| 87 | for (int i= n; i >= 1; i++) |
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| 88 | { |
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| 89 | cont= content (bufF, i); |
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| 90 | bufResult= squarefreeFactorization (cont, alpha); |
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| 91 | if (bufResult.getFirst().factor().inCoeffDomain()) |
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| 92 | bufResult.removeFirst(); |
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| 93 | result= Union (result, bufResult); |
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| 94 | bufF /= cont; |
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| 95 | if (bufF.inCoeffDomain()) |
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| 96 | break; |
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| 97 | } |
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| 98 | if (!bufF.inCoeffDomain()) |
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| 99 | { |
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| 100 | bufResult= squarefreeFactorization (bufF, alpha); |
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| 101 | if (bufResult.getFirst().factor().inCoeffDomain()) |
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| 102 | bufResult.removeFirst(); |
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| 103 | result= Union (result, bufResult); |
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| 104 | } |
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| 105 | if (sort) |
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| 106 | result= sortCFFList (result); |
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[24b338] | 107 | result.insert (CFFactor (Lc(F), 1)); |
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| 108 | return result; |
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[806c18] | 109 | } |
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[24b338] | 110 | |
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[806c18] | 111 | /// squarefree factorization over GF. |
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[24b338] | 112 | /// If input is not monic, the leading coefficient is dropped |
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| 113 | /// |
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| 114 | /// @return a list of squarefree factors with multiplicity |
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| 115 | inline |
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[6caa2a6] | 116 | CFFList GFSqrf (const CanonicalForm& F, ///< [in] a poly |
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| 117 | bool sort= true ///< [in] sort factors by exponent? |
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[806c18] | 118 | ) |
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[24b338] | 119 | { |
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[806c18] | 120 | ASSERT (CFFactory::gettype() == GaloisFieldDomain, |
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[24b338] | 121 | "GF as base field expected"); |
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[6caa2a6] | 122 | return FpSqrf (F, sort); |
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[24b338] | 123 | } |
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| 124 | |
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[806c18] | 125 | /// squarefree part of @a F/g, where g is the product of those squarefree |
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| 126 | /// factors whose multiplicity is 0 mod p, if @a F a pth power pthPower= F. |
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[24b338] | 127 | /// |
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[806c18] | 128 | /// @return @a sqrfPart returns 1, if F is a pthPower, else it returns the |
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| 129 | /// squarefree part of @a F/g, where g is the product of those |
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| 130 | /// squarefree factors whose multiplicity is 0 mod p |
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| 131 | CanonicalForm |
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| 132 | sqrfPart (const CanonicalForm& F, ///< [in] a poly |
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| 133 | CanonicalForm& pthPower, ///< [in,out] returns F is F is a pthPower |
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[24b338] | 134 | const Variable& alpha ///< [in] algebraic variable |
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| 135 | ); |
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| 136 | |
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| 137 | /// p^l-th root extraction, where l is maximal |
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| 138 | /// |
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| 139 | /// @return @a maxpthRoot returns a p^l-th root of @a F, where @a l is maximal |
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[806c18] | 140 | /// @sa pthRoot() |
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[24b338] | 141 | CanonicalForm |
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| 142 | maxpthRoot (const CanonicalForm & F, ///< [in] a poly which is a pth power |
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| 143 | const int & q, ///< [in] size of the field |
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| 144 | int& l ///< [in,out] @a l maximal, s.t. @a F is |
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[806c18] | 145 | ///< a p^l-th power |
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[24b338] | 146 | ); |
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| 147 | |
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| 148 | #endif |
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| 149 | /* FAC_FQ_SQUAREFREE_H */ |
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| 150 | |
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