[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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[015711] | 29 | #include "fac_util.h" |
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[6c44098] | 30 | |
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| 31 | /// @return @a biFactorize returns a list of factors of F. If F is not monic |
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| 32 | /// its leading coefficient is not outputted. |
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| 33 | CFList |
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| 34 | biFactorize (const CanonicalForm& F, ///< [in] a bivariate poly |
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| 35 | const Variable& v ///< [in] some algebraic variable |
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| 36 | ); |
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| 37 | |
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| 38 | /// factorize a squarefree bivariate polynomial over \f$ Q(\alpha) \f$. |
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| 39 | /// |
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| 40 | /// @ return @a ratBiSqrfFactorize returns a list of monic factors, the first |
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| 41 | /// element is the leading coefficient. |
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[d990001] | 42 | #ifdef HAVE_NTL |
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[6c44098] | 43 | inline |
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[f9b796e] | 44 | CFList |
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[530295] | 45 | ratBiSqrfFactorize (const CanonicalForm & G, ///< [in] a bivariate poly |
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| 46 | const Variable& v= Variable (1) ///< [in] algebraic variable |
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[f9b796e] | 47 | ) |
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[6c44098] | 48 | { |
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| 49 | CFMap N; |
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| 50 | CanonicalForm F= compress (G, N); |
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| 51 | CanonicalForm contentX= content (F, 1); |
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| 52 | CanonicalForm contentY= content (F, 2); |
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| 53 | F /= (contentX*contentY); |
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| 54 | CFFList contentXFactors, contentYFactors; |
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[530295] | 55 | if (v.level() != 1) |
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| 56 | { |
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| 57 | contentXFactors= factorize (contentX, v); |
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| 58 | contentYFactors= factorize (contentY, v); |
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| 59 | } |
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| 60 | else |
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| 61 | { |
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| 62 | contentXFactors= factorize (contentX); |
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| 63 | contentYFactors= factorize (contentY); |
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| 64 | } |
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[6c44098] | 65 | if (contentXFactors.getFirst().factor().inCoeffDomain()) |
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| 66 | contentXFactors.removeFirst(); |
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| 67 | if (contentYFactors.getFirst().factor().inCoeffDomain()) |
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| 68 | contentYFactors.removeFirst(); |
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| 69 | if (F.inCoeffDomain()) |
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| 70 | { |
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| 71 | CFList result; |
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| 72 | for (CFFListIterator i= contentXFactors; i.hasItem(); i++) |
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| 73 | result.append (N (i.getItem().factor())); |
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| 74 | for (CFFListIterator i= contentYFactors; i.hasItem(); i++) |
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| 75 | result.append (N (i.getItem().factor())); |
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| 76 | if (isOn (SW_RATIONAL)) |
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| 77 | { |
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| 78 | normalize (result); |
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| 79 | result.insert (Lc (G)); |
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| 80 | } |
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| 81 | return result; |
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| 82 | } |
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| 83 | mat_ZZ M; |
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| 84 | vec_ZZ S; |
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| 85 | F= compress (F, M, S); |
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[f9da5e] | 86 | CFList result= biFactorize (F, v); |
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| 87 | for (CFListIterator i= result; i.hasItem(); i++) |
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| 88 | i.getItem()= N (decompress (i.getItem(), M, S)); |
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[6c44098] | 89 | for (CFFListIterator i= contentXFactors; i.hasItem(); i++) |
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| 90 | result.append (N(i.getItem().factor())); |
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| 91 | for (CFFListIterator i= contentYFactors; i.hasItem(); i++) |
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| 92 | result.append (N (i.getItem().factor())); |
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| 93 | if (isOn (SW_RATIONAL)) |
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| 94 | { |
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| 95 | normalize (result); |
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| 96 | result.insert (Lc (G)); |
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| 97 | } |
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| 98 | return result; |
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| 99 | } |
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| 100 | |
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| 101 | /// factorize a bivariate polynomial over \f$ Q(\alpha) \f$ |
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| 102 | /// |
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| 103 | /// @return @a ratBiFactorize returns a list of monic factors with |
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| 104 | /// multiplicity, the first element is the leading coefficient. |
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| 105 | inline |
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[f9b796e] | 106 | CFFList |
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[530295] | 107 | ratBiFactorize (const CanonicalForm & G, ///< [in] a bivariate poly |
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| 108 | const Variable& v= Variable (1), ///< [in] algebraic variable |
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| 109 | bool substCheck= true ///< [in] enables substitute check |
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[f9b796e] | 110 | ) |
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[6c44098] | 111 | { |
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| 112 | CFMap N; |
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| 113 | CanonicalForm F= compress (G, N); |
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[f9b796e] | 114 | |
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| 115 | if (substCheck) |
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| 116 | { |
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| 117 | bool foundOne= false; |
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| 118 | int * substDegree= new int [F.level()]; |
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| 119 | for (int i= 1; i <= F.level(); i++) |
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| 120 | { |
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| 121 | substDegree[i-1]= substituteCheck (F, Variable (i)); |
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| 122 | if (substDegree [i-1] > 1) |
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| 123 | { |
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| 124 | foundOne= true; |
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| 125 | subst (F, F, substDegree[i-1], Variable (i)); |
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| 126 | } |
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| 127 | } |
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| 128 | if (foundOne) |
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| 129 | { |
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| 130 | CFFList result= ratBiFactorize (F, v, false); |
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| 131 | CFFList newResult, tmp; |
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| 132 | CanonicalForm tmp2; |
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| 133 | newResult.insert (result.getFirst()); |
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| 134 | result.removeFirst(); |
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| 135 | for (CFFListIterator i= result; i.hasItem(); i++) |
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| 136 | { |
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| 137 | tmp2= i.getItem().factor(); |
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| 138 | for (int j= 1; j <= F.level(); j++) |
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| 139 | { |
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| 140 | if (substDegree[j-1] > 1) |
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| 141 | tmp2= reverseSubst (tmp2, substDegree[j-1], Variable (j)); |
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| 142 | } |
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| 143 | tmp= ratBiFactorize (tmp2, v, false); |
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| 144 | tmp.removeFirst(); |
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| 145 | for (CFFListIterator j= tmp; j.hasItem(); j++) |
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| 146 | newResult.append (CFFactor (j.getItem().factor(), |
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| 147 | j.getItem().exp()*i.getItem().exp())); |
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| 148 | } |
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| 149 | decompress (newResult, N); |
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| 150 | delete [] substDegree; |
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| 151 | return newResult; |
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| 152 | } |
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| 153 | delete [] substDegree; |
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| 154 | } |
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| 155 | |
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[6c44098] | 156 | CanonicalForm LcF= Lc (F); |
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| 157 | CanonicalForm contentX= content (F, 1); |
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| 158 | CanonicalForm contentY= content (F, 2); |
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| 159 | F /= (contentX*contentY); |
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| 160 | CFFList contentXFactors, contentYFactors; |
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[530295] | 161 | if (v.level() != 1) |
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| 162 | { |
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| 163 | contentXFactors= factorize (contentX, v); |
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| 164 | contentYFactors= factorize (contentY, v); |
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| 165 | } |
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| 166 | else |
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| 167 | { |
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| 168 | contentXFactors= factorize (contentX); |
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| 169 | contentYFactors= factorize (contentY); |
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| 170 | } |
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[6c44098] | 171 | if (contentXFactors.getFirst().factor().inCoeffDomain()) |
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| 172 | contentXFactors.removeFirst(); |
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| 173 | if (contentYFactors.getFirst().factor().inCoeffDomain()) |
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| 174 | contentYFactors.removeFirst(); |
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| 175 | decompress (contentXFactors, N); |
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| 176 | decompress (contentYFactors, N); |
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| 177 | CFFList result, resultRoot; |
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| 178 | if (F.inCoeffDomain()) |
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| 179 | { |
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| 180 | result= Union (contentXFactors, contentYFactors); |
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| 181 | if (isOn (SW_RATIONAL)) |
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| 182 | { |
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| 183 | normalize (result); |
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[a8a93f] | 184 | if (v.level() == 1) |
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| 185 | { |
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| 186 | for (CFFListIterator i= result; i.hasItem(); i++) |
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| 187 | { |
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| 188 | LcF /= bCommonDen (i.getItem().factor()); |
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| 189 | i.getItem()= CFFactor (i.getItem().factor()* |
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| 190 | bCommonDen(i.getItem().factor()), i.getItem().exp()); |
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| 191 | } |
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| 192 | } |
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[6c44098] | 193 | result.insert (CFFactor (LcF, 1)); |
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| 194 | } |
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| 195 | return result; |
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| 196 | } |
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| 197 | mat_ZZ M; |
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| 198 | vec_ZZ S; |
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| 199 | F= compress (F, M, S); |
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[5f9b47] | 200 | CFFList sqrfFactors= sqrFree (F); |
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| 201 | for (CFFListIterator i= sqrfFactors; i.hasItem(); i++) |
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| 202 | { |
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[f9da5e] | 203 | CFList tmp= ratBiSqrfFactorize (i.getItem().factor(), v); |
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| 204 | for (CFListIterator j= tmp; j.hasItem(); j++) |
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[5f9b47] | 205 | { |
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[f9da5e] | 206 | if (j.getItem().inCoeffDomain()) continue; |
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| 207 | result.append (CFFactor (N (decompress (j.getItem(), M, S)), |
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| 208 | i.getItem().exp())); |
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[5f9b47] | 209 | } |
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| 210 | } |
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[6c44098] | 211 | result= Union (result, contentXFactors); |
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| 212 | result= Union (result, contentYFactors); |
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| 213 | if (isOn (SW_RATIONAL)) |
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| 214 | { |
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| 215 | normalize (result); |
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[a8a93f] | 216 | if (v.level() == 1) |
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| 217 | { |
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| 218 | for (CFFListIterator i= result; i.hasItem(); i++) |
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| 219 | { |
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| 220 | LcF /= bCommonDen (i.getItem().factor()); |
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| 221 | i.getItem()= CFFactor (i.getItem().factor()* |
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| 222 | bCommonDen(i.getItem().factor()), i.getItem().exp()); |
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| 223 | } |
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| 224 | } |
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[6c44098] | 225 | result.insert (CFFactor (LcF, 1)); |
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| 226 | } |
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| 227 | return result; |
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| 228 | } |
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| 229 | |
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[d990001] | 230 | #endif |
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| 231 | |
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[6c44098] | 232 | /// convert a CFFList to a CFList by dropping the multiplicity |
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| 233 | CFList conv (const CFFList& L ///< [in] a CFFList |
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| 234 | ); |
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| 235 | |
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[5f92d8] | 236 | modpk |
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| 237 | coeffBound ( const CanonicalForm & f, int p, const CanonicalForm& mipo ); |
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| 238 | |
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| 239 | void findGoodPrime(const CanonicalForm &f, int &start); |
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| 240 | |
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| 241 | modpk |
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| 242 | coeffBound ( const CanonicalForm & f, int p ); |
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| 243 | |
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[6c44098] | 244 | #endif |
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| 245 | |
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