[6c44098] | 1 | /*****************************************************************************\ |
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| 2 | * Computer Algebra System SINGULAR |
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| 3 | \*****************************************************************************/ |
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| 4 | /** @file facBivar.h |
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| 5 | * |
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| 6 | * bivariate 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_BIVAR_H |
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| 16 | #define FAC_BIVAR_H |
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| 17 | |
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[d990001] | 18 | #include <config.h> |
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[6c44098] | 19 | |
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| 20 | #include "assert.h" |
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| 21 | |
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| 22 | #include "facFqBivarUtil.h" |
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| 23 | #include "DegreePattern.h" |
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| 24 | #include "cf_util.h" |
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| 25 | #include "facFqSquarefree.h" |
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| 26 | #include "cf_map.h" |
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| 27 | #include "cfNewtonPolygon.h" |
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| 28 | #include "algext.h" |
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| 29 | |
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| 30 | /// @return @a biFactorize returns a list of factors of F. If F is not monic |
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| 31 | /// its leading coefficient is not outputted. |
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| 32 | CFList |
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| 33 | biFactorize (const CanonicalForm& F, ///< [in] a bivariate poly |
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| 34 | const Variable& v ///< [in] some algebraic variable |
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| 35 | ); |
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| 36 | |
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| 37 | /// factorize a squarefree bivariate polynomial over \f$ Q(\alpha) \f$. |
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| 38 | /// |
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| 39 | /// @ return @a ratBiSqrfFactorize returns a list of monic factors, the first |
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| 40 | /// element is the leading coefficient. |
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[d990001] | 41 | #ifdef HAVE_NTL |
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[6c44098] | 42 | inline |
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[f9b796e] | 43 | CFList |
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[530295] | 44 | ratBiSqrfFactorize (const CanonicalForm & G, ///< [in] a bivariate poly |
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| 45 | const Variable& v= Variable (1) ///< [in] algebraic variable |
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[f9b796e] | 46 | ) |
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[6c44098] | 47 | { |
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| 48 | CFMap N; |
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| 49 | CanonicalForm F= compress (G, N); |
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| 50 | CanonicalForm contentX= content (F, 1); |
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| 51 | CanonicalForm contentY= content (F, 2); |
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| 52 | F /= (contentX*contentY); |
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| 53 | CFFList contentXFactors, contentYFactors; |
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[530295] | 54 | if (v.level() != 1) |
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| 55 | { |
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| 56 | contentXFactors= factorize (contentX, v); |
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| 57 | contentYFactors= factorize (contentY, v); |
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| 58 | } |
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| 59 | else |
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| 60 | { |
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| 61 | contentXFactors= factorize (contentX); |
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| 62 | contentYFactors= factorize (contentY); |
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| 63 | } |
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[6c44098] | 64 | if (contentXFactors.getFirst().factor().inCoeffDomain()) |
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| 65 | contentXFactors.removeFirst(); |
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| 66 | if (contentYFactors.getFirst().factor().inCoeffDomain()) |
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| 67 | contentYFactors.removeFirst(); |
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| 68 | if (F.inCoeffDomain()) |
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| 69 | { |
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| 70 | CFList result; |
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| 71 | for (CFFListIterator i= contentXFactors; i.hasItem(); i++) |
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| 72 | result.append (N (i.getItem().factor())); |
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| 73 | for (CFFListIterator i= contentYFactors; i.hasItem(); i++) |
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| 74 | result.append (N (i.getItem().factor())); |
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| 75 | if (isOn (SW_RATIONAL)) |
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| 76 | { |
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| 77 | normalize (result); |
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| 78 | result.insert (Lc (G)); |
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| 79 | } |
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| 80 | return result; |
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| 81 | } |
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| 82 | mat_ZZ M; |
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| 83 | vec_ZZ S; |
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| 84 | F= compress (F, M, S); |
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| 85 | CFList result= biFactorize (F, v); |
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| 86 | for (CFListIterator i= result; i.hasItem(); i++) |
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| 87 | i.getItem()= N (decompress (i.getItem(), M, S)); |
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| 88 | for (CFFListIterator i= contentXFactors; i.hasItem(); i++) |
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| 89 | result.append (N(i.getItem().factor())); |
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| 90 | for (CFFListIterator i= contentYFactors; i.hasItem(); i++) |
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| 91 | result.append (N (i.getItem().factor())); |
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| 92 | if (isOn (SW_RATIONAL)) |
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| 93 | { |
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| 94 | normalize (result); |
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| 95 | result.insert (Lc (G)); |
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| 96 | } |
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| 97 | return result; |
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| 98 | } |
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| 99 | |
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| 100 | /// factorize a bivariate polynomial over \f$ Q(\alpha) \f$ |
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| 101 | /// |
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| 102 | /// @return @a ratBiFactorize returns a list of monic factors with |
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| 103 | /// multiplicity, the first element is the leading coefficient. |
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| 104 | inline |
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[f9b796e] | 105 | CFFList |
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[530295] | 106 | ratBiFactorize (const CanonicalForm & G, ///< [in] a bivariate poly |
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| 107 | const Variable& v= Variable (1), ///< [in] algebraic variable |
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| 108 | bool substCheck= true ///< [in] enables substitute check |
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[f9b796e] | 109 | ) |
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[6c44098] | 110 | { |
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| 111 | CFMap N; |
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| 112 | CanonicalForm F= compress (G, N); |
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[f9b796e] | 113 | |
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| 114 | if (substCheck) |
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| 115 | { |
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| 116 | bool foundOne= false; |
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| 117 | int * substDegree= new int [F.level()]; |
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| 118 | for (int i= 1; i <= F.level(); i++) |
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| 119 | { |
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| 120 | substDegree[i-1]= substituteCheck (F, Variable (i)); |
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| 121 | if (substDegree [i-1] > 1) |
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| 122 | { |
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| 123 | foundOne= true; |
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| 124 | subst (F, F, substDegree[i-1], Variable (i)); |
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| 125 | } |
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| 126 | } |
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| 127 | if (foundOne) |
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| 128 | { |
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| 129 | CFFList result= ratBiFactorize (F, v, false); |
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| 130 | CFFList newResult, tmp; |
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| 131 | CanonicalForm tmp2; |
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| 132 | newResult.insert (result.getFirst()); |
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| 133 | result.removeFirst(); |
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| 134 | for (CFFListIterator i= result; i.hasItem(); i++) |
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| 135 | { |
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| 136 | tmp2= i.getItem().factor(); |
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| 137 | for (int j= 1; j <= F.level(); j++) |
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| 138 | { |
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| 139 | if (substDegree[j-1] > 1) |
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| 140 | tmp2= reverseSubst (tmp2, substDegree[j-1], Variable (j)); |
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| 141 | } |
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| 142 | tmp= ratBiFactorize (tmp2, v, false); |
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| 143 | tmp.removeFirst(); |
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| 144 | for (CFFListIterator j= tmp; j.hasItem(); j++) |
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| 145 | newResult.append (CFFactor (j.getItem().factor(), |
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| 146 | j.getItem().exp()*i.getItem().exp())); |
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| 147 | } |
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| 148 | decompress (newResult, N); |
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| 149 | delete [] substDegree; |
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| 150 | return newResult; |
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| 151 | } |
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| 152 | delete [] substDegree; |
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| 153 | } |
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| 154 | |
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[6c44098] | 155 | CanonicalForm LcF= Lc (F); |
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| 156 | CanonicalForm contentX= content (F, 1); |
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| 157 | CanonicalForm contentY= content (F, 2); |
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| 158 | F /= (contentX*contentY); |
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| 159 | CFFList contentXFactors, contentYFactors; |
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[530295] | 160 | if (v.level() != 1) |
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| 161 | { |
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| 162 | contentXFactors= factorize (contentX, v); |
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| 163 | contentYFactors= factorize (contentY, v); |
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| 164 | } |
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| 165 | else |
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| 166 | { |
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| 167 | contentXFactors= factorize (contentX); |
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| 168 | contentYFactors= factorize (contentY); |
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| 169 | } |
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[6c44098] | 170 | if (contentXFactors.getFirst().factor().inCoeffDomain()) |
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| 171 | contentXFactors.removeFirst(); |
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| 172 | if (contentYFactors.getFirst().factor().inCoeffDomain()) |
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| 173 | contentYFactors.removeFirst(); |
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| 174 | decompress (contentXFactors, N); |
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| 175 | decompress (contentYFactors, N); |
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| 176 | CFFList result, resultRoot; |
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| 177 | if (F.inCoeffDomain()) |
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| 178 | { |
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| 179 | result= Union (contentXFactors, contentYFactors); |
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| 180 | if (isOn (SW_RATIONAL)) |
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| 181 | { |
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| 182 | normalize (result); |
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| 183 | result.insert (CFFactor (LcF, 1)); |
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| 184 | } |
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| 185 | return result; |
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| 186 | } |
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| 187 | mat_ZZ M; |
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| 188 | vec_ZZ S; |
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| 189 | F= compress (F, M, S); |
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[5f9b47] | 190 | CFFList sqrfFactors= sqrFree (F); |
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| 191 | for (CFFListIterator i= sqrfFactors; i.hasItem(); i++) |
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| 192 | { |
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| 193 | CFList tmp= ratBiSqrfFactorize (i.getItem().factor(), v); |
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| 194 | for (CFListIterator j= tmp; j.hasItem(); j++) |
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| 195 | { |
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| 196 | if (j.getItem().inCoeffDomain()) continue; |
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| 197 | result.append (CFFactor (N (decompress (j.getItem(), M, S)), i.getItem().exp())); |
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| 198 | } |
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| 199 | } |
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[6c44098] | 200 | result= Union (result, contentXFactors); |
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| 201 | result= Union (result, contentYFactors); |
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| 202 | if (isOn (SW_RATIONAL)) |
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| 203 | { |
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| 204 | normalize (result); |
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| 205 | result.insert (CFFactor (LcF, 1)); |
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| 206 | } |
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| 207 | return result; |
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| 208 | } |
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| 209 | |
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[d990001] | 210 | #endif |
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| 211 | |
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[6c44098] | 212 | /// convert a CFFList to a CFList by dropping the multiplicity |
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| 213 | CFList conv (const CFFList& L ///< [in] a CFFList |
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| 214 | ); |
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| 215 | |
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| 216 | #endif |
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| 217 | |
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