[91788c0] | 1 | /*****************************************************************************\ |
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| 2 | * Computer Algebra System SINGULAR |
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| 3 | \*****************************************************************************/ |
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| 4 | /** @file facSparseHensel.cc |
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| 5 | * |
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| 6 | * This file implements functions for sparse heuristic Hensel lifting |
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| 7 | * |
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| 8 | * ABSTRACT: "A fast implementation of polynomial factorization" by M. Lucks and |
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| 9 | * "Effective polynomial computation" by R. Zippel |
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| 10 | * |
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| 11 | * @author Martin Lee |
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| 12 | * |
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| 13 | **/ |
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| 14 | /*****************************************************************************/ |
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| 15 | |
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[ce21bd8] | 16 | #include "config.h" |
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| 17 | #include "cf_assert.h" |
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[91788c0] | 18 | #include "facSparseHensel.h" |
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| 19 | #include "cf_algorithm.h" |
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| 20 | #include "cf_gcd_smallp.h" |
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| 21 | #include "facFqFactorize.h" |
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| 22 | |
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| 23 | bool |
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| 24 | LucksWangSparseHeuristic (const CanonicalForm& F, const CFList& factors, |
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| 25 | int level, const CFList& leadingCoeffs, CFList& result) |
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| 26 | { |
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| 27 | CFArray* monoms= new CFArray [factors.length()]; |
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| 28 | int i= 0; |
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| 29 | int num= 0; |
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| 30 | for (CFListIterator iter= factors; iter.hasItem(); iter++, i++) |
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| 31 | { |
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| 32 | monoms[i]= getTerms (iter.getItem()); |
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| 33 | num += monoms [i].size(); |
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| 34 | sort (monoms [i]); |
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| 35 | } |
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| 36 | |
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| 37 | i= 0; |
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| 38 | CFArray* monomsLead= new CFArray [leadingCoeffs.length()]; |
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| 39 | for (CFListIterator iter= leadingCoeffs; iter.hasItem(); iter++, i++) |
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| 40 | { |
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| 41 | monomsLead[i]= getTerms (iter.getItem()); |
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| 42 | sort (monomsLead [i]); |
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| 43 | groupTogether (monomsLead [i], level); |
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| 44 | strip (monomsLead [i], level); |
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| 45 | } |
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| 46 | |
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| 47 | CFArray solution= CFArray (num); |
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| 48 | int k, d, count, j= F.level() + 1; |
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| 49 | num= 0; |
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| 50 | i= 0; |
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| 51 | for (CFListIterator iter= factors; iter.hasItem(); i++, iter++) |
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| 52 | { |
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| 53 | d= degree (iter.getItem(), 1); |
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| 54 | count= 0; |
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| 55 | for (k= 0; k < monoms[i].size(); k++, j++, num++) |
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| 56 | { |
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| 57 | monoms [i][k] *= Variable (j); |
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| 58 | if (degree (monoms[i][k], 1) == d) |
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| 59 | { |
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| 60 | solution[num]= monomsLead [i] [count]; |
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| 61 | count++; |
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| 62 | } |
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| 63 | } |
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| 64 | } |
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| 65 | |
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| 66 | delete [] monomsLead; |
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| 67 | |
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| 68 | CFArray termsF= getTerms (F); |
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| 69 | sort (termsF); |
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| 70 | |
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| 71 | CFList tmp; |
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| 72 | CFArray* stripped2= new CFArray [factors.length()]; |
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| 73 | for (i= factors.length() - 1; i > -1; i--) |
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| 74 | { |
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| 75 | tmp.insert (buildPolyFromArray (monoms [i])); |
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| 76 | strip (monoms[i], stripped2 [i], level); |
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| 77 | } |
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| 78 | delete [] monoms; |
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| 79 | |
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| 80 | CanonicalForm H= prod (tmp); |
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| 81 | CFArray monomsH= getMonoms (H); |
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| 82 | sort (monomsH); |
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| 83 | |
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| 84 | groupTogether (termsF, level); |
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| 85 | groupTogether (monomsH, F.level()); |
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| 86 | |
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| 87 | if (monomsH.size() != termsF.size()) |
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| 88 | { |
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| 89 | delete [] stripped2; |
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| 90 | return false; |
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| 91 | } |
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| 92 | |
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| 93 | CFArray strippedH; |
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| 94 | strip (monomsH, strippedH, level); |
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| 95 | CFArray strippedF; |
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| 96 | strip (termsF, strippedF, level); |
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| 97 | |
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| 98 | if (!isEqual (strippedH, strippedF)) |
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| 99 | { |
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| 100 | delete [] stripped2; |
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| 101 | return false; |
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| 102 | } |
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| 103 | |
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| 104 | CFArray A= getEquations (monomsH, termsF); |
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| 105 | CFArray newSolution= CFArray (solution.size()); |
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| 106 | do |
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| 107 | { |
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| 108 | evaluate (A, solution, F.level() + 1); |
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| 109 | if (isZero (A)) |
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| 110 | break; |
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| 111 | if (!simplify (A, newSolution, F.level() + 1)) |
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| 112 | { |
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| 113 | delete [] stripped2; |
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| 114 | return false; |
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| 115 | } |
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| 116 | if (isZero (newSolution)) |
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| 117 | { |
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| 118 | delete [] stripped2; |
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| 119 | return false; |
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| 120 | } |
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| 121 | if (!merge (solution, newSolution)) |
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| 122 | { |
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| 123 | delete [] stripped2; |
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| 124 | return false; |
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| 125 | } |
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| 126 | } while (1); |
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| 127 | |
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| 128 | |
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| 129 | result= CFList(); |
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| 130 | CanonicalForm factor; |
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| 131 | num= 0; |
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| 132 | for (i= 0; i < factors.length(); i++) |
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| 133 | { |
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| 134 | k= stripped2[i].size(); |
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| 135 | factor= 0; |
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| 136 | for (j= 0; j < k; j++, num++) |
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| 137 | factor += solution [num]*stripped2[i][j]; |
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| 138 | result.append (factor); |
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| 139 | } |
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| 140 | |
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| 141 | delete [] stripped2; |
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| 142 | return true; |
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| 143 | } |
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| 144 | |
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| 145 | CFList |
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| 146 | sparseHeuristic (const CanonicalForm& A, const CFList& biFactors, |
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| 147 | CFList*& moreBiFactors, const CFList& evaluation, |
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| 148 | int minFactorsLength) |
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| 149 | { |
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| 150 | int j= A.level() - 1; |
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| 151 | int i; |
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| 152 | |
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| 153 | //initialize storage |
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| 154 | CFArray *** storeFactors= new CFArray** [j]; |
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| 155 | for (i= 0; i < j; i++) |
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| 156 | storeFactors [i]= new CFArray* [2]; |
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| 157 | |
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| 158 | CFArray eval= CFArray (j); |
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| 159 | i= j - 1; |
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| 160 | for (CFListIterator iter= evaluation; iter.hasItem(); iter++,i--) |
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| 161 | eval[i]= iter.getItem(); |
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| 162 | storeFactors [0] [0]= new CFArray [minFactorsLength]; |
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| 163 | storeFactors [0] [1]= new CFArray [minFactorsLength]; |
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| 164 | for (i= 1; i < j; i++) |
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| 165 | { |
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| 166 | storeFactors[i] [0]= new CFArray [minFactorsLength]; |
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| 167 | storeFactors[i] [1]= new CFArray [minFactorsLength]; |
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| 168 | } |
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| 169 | // |
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| 170 | |
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| 171 | CFList * normalizingFactors= new CFList [j]; |
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| 172 | CFList uniFactors; |
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| 173 | normalizingFactors [0]= findNormalizingFactor1 (biFactors, |
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| 174 | evaluation.getLast(), uniFactors); |
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| 175 | for (i= j - 1; i > 0; i--) |
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| 176 | { |
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| 177 | if (moreBiFactors[i-1].length() != minFactorsLength) |
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| 178 | { |
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| 179 | moreBiFactors[i-1]= |
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| 180 | recombination (moreBiFactors [i-1], uniFactors, 1, |
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| 181 | moreBiFactors[i-1].length()-uniFactors.length()+1, |
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| 182 | eval[i], Variable (i + 2) |
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| 183 | ); |
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| 184 | } |
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| 185 | normalizingFactors [i]= findNormalizingFactor2 (moreBiFactors [i - 1], |
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| 186 | eval[i], uniFactors); |
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| 187 | } |
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| 188 | |
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| 189 | CFList tmp; |
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| 190 | tmp= normalize (biFactors, normalizingFactors[0]); |
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| 191 | getTerms2 (tmp, storeFactors [0] [0]); |
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| 192 | storeFactors [0] [1]= evaluate (storeFactors [0] [0], minFactorsLength, |
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| 193 | evaluation.getLast(), Variable (2)); |
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| 194 | for (i= j - 1; i > 0; i--) |
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| 195 | { |
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| 196 | tmp= normalize (moreBiFactors [i-1], normalizingFactors [i]); |
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| 197 | getTerms2 (tmp, storeFactors [i] [0]); |
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| 198 | storeFactors [i] [1]= evaluate (storeFactors [i] [0], minFactorsLength, |
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| 199 | eval[i], Variable (i + 2)); |
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| 200 | } |
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| 201 | |
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| 202 | |
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| 203 | int k, l, m, mm, count, sizeOfUniFactors= 0; |
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| 204 | int*** seperator= new int** [j]; |
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| 205 | Variable x= Variable (1); |
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| 206 | |
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| 207 | for (i= 0; i < j; i++) |
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| 208 | seperator [i]= new int* [minFactorsLength]; |
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| 209 | for (k= 0; k < minFactorsLength; k++) |
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| 210 | { |
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| 211 | for (i= 0; i < j; i++) |
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| 212 | { |
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| 213 | count= 0; |
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| 214 | for (l= 0; l < storeFactors [i][0][k].size() - 1; l++) |
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| 215 | { |
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| 216 | if (degree (storeFactors[i][0][k][l], x) < |
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| 217 | degree (storeFactors[i][0][k][l+1], x)) |
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| 218 | count++; |
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| 219 | } |
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| 220 | if (i == 0) |
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| 221 | sizeOfUniFactors= count; |
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| 222 | else if (sizeOfUniFactors != count) |
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| 223 | { |
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| 224 | for (m= 0; m < j; m++) |
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| 225 | { |
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| 226 | delete [] storeFactors [m] [0]; |
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| 227 | delete [] storeFactors [m] [1]; |
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| 228 | delete [] storeFactors [m]; |
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| 229 | for (mm= 0; mm < k; mm++) |
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| 230 | delete [] seperator [m][mm]; |
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| 231 | delete [] seperator [m]; |
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| 232 | } |
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| 233 | delete [] storeFactors; |
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| 234 | delete [] seperator; |
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| 235 | return CFList(); |
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| 236 | } |
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| 237 | seperator [i][k]= new int [count + 3]; |
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| 238 | seperator [i][k][0]= count + 1; |
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| 239 | seperator [i][k][1]= 0; |
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| 240 | count= 2; |
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| 241 | for (l= 0; l < storeFactors [i][0][k].size() - 1; l++) |
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| 242 | { |
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| 243 | if (degree (storeFactors[i][0][k][l], x) < |
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| 244 | degree (storeFactors[i][0][k][l+1], x)) |
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| 245 | { |
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| 246 | seperator[i][k][count]=l + 1; |
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| 247 | count++; |
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| 248 | } |
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| 249 | } |
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| 250 | seperator [i][k][count]= storeFactors[i][0][k].size(); |
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| 251 | } |
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| 252 | } |
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| 253 | |
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| 254 | CanonicalForm tmp1, factor, quot; |
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| 255 | CanonicalForm B= A; |
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| 256 | CFList result; |
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| 257 | int maxTerms, n, index1, index2, mmm, found, columns, oneCount; |
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| 258 | int ** mat; |
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| 259 | |
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| 260 | for (k= 0; k < minFactorsLength; k++) |
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| 261 | { |
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| 262 | factor= 0; |
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| 263 | sizeOfUniFactors= seperator [0][k][0]; |
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| 264 | for (n= 1; n <= sizeOfUniFactors; n++) |
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| 265 | { |
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| 266 | columns= 0; |
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| 267 | maxTerms= 1; |
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| 268 | index1= j - 1; |
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| 269 | for (i= j - 1; i >= 0; i--) |
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| 270 | { |
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| 271 | if (maxTerms < seperator[i][k][n+1]-seperator[i][k][n]) |
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| 272 | { |
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| 273 | maxTerms= seperator[i][k][n + 1]-seperator[i][k][n]; |
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| 274 | index1= i; |
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| 275 | } |
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| 276 | } |
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| 277 | for (i= j - 1; i >= 0; i--) |
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| 278 | { |
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| 279 | if (i == index1) |
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| 280 | continue; |
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| 281 | columns += seperator [i][k][n+1]-seperator[i][k][n]; |
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| 282 | } |
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| 283 | mat= new int *[maxTerms]; |
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| 284 | mm= 0; |
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| 285 | for (m= seperator[index1][k][n]; m < seperator[index1][k][n+1]; m++, mm++) |
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| 286 | { |
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| 287 | tmp1= storeFactors [index1][1][k][m]; |
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| 288 | mat[mm]= new int [columns]; |
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| 289 | for (i= 0; i < columns; i++) |
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| 290 | mat[mm][i]= 0; |
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| 291 | index2= 0; |
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| 292 | for (i= j - 1; i >= 0; i--) |
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| 293 | { |
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| 294 | if (i == index1) |
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| 295 | continue; |
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| 296 | found= -1; |
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| 297 | if ((found= search (storeFactors[i][1][k], tmp1, |
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| 298 | seperator[i][k][n], seperator[i][k][n+1])) >= 0) |
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| 299 | mat[mm][index2 + found - seperator [i][k][n]]= 1; |
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| 300 | index2 += seperator [i][k][n+1]-seperator[i][k][n]; |
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| 301 | } |
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| 302 | } |
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| 303 | |
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| 304 | index2= 0; |
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| 305 | for (i= j - 1; i >= 0; i--) |
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| 306 | { |
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| 307 | if (i == index1) |
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| 308 | continue; |
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| 309 | oneCount= 0; |
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| 310 | for (mm= 0; mm < seperator [i][k][n + 1] - seperator [i][k][n]; mm++) |
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| 311 | { |
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| 312 | for (m= 0; m < maxTerms; m++) |
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| 313 | { |
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| 314 | if (mat[m][mm+index2] == 1) |
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| 315 | oneCount++; |
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| 316 | } |
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| 317 | } |
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| 318 | if (oneCount == seperator [i][k][n+1]-seperator[i][k][n] - 1) |
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| 319 | { |
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| 320 | for (mm= 0; mm < seperator [i][k][n+1]-seperator[i][k][n]; mm++) |
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| 321 | { |
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| 322 | oneCount= 0; |
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| 323 | for (m= 0; m < maxTerms; m++) |
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| 324 | if (mat[m][mm+index2] == 1) |
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| 325 | oneCount++; |
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| 326 | if (oneCount > 0) |
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| 327 | continue; |
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| 328 | for (m= 0; m < maxTerms; m++) |
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| 329 | { |
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| 330 | oneCount= 0; |
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| 331 | for (mmm= 0; mmm < seperator[i][k][n+1]-seperator[i][k][n]; mmm++) |
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| 332 | { |
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| 333 | if (mat[m][mmm+index2] == 1) |
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| 334 | oneCount++; |
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| 335 | } |
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| 336 | if (oneCount > 0) |
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| 337 | continue; |
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| 338 | mat[m][mm+index2]= 1; |
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| 339 | } |
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| 340 | } |
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| 341 | } |
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| 342 | index2 += seperator [i][k][n+1] - seperator [i][k][n]; |
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| 343 | } |
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| 344 | |
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| 345 | //read off solution |
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| 346 | mm= 0; |
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| 347 | for (m= seperator[index1][k][n]; m < seperator[index1][k][n+1]; m++, mm++) |
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| 348 | { |
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| 349 | tmp1= storeFactors [index1][0][k][m]; |
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| 350 | index2= 0; |
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| 351 | for (i= j - 1; i > -1; i--) |
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| 352 | { |
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| 353 | if (i == index1) |
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| 354 | continue; |
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| 355 | for (mmm= 0; mmm < seperator [i][k][n+1]-seperator[i][k][n]; mmm++) |
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| 356 | if (mat[mm][mmm+index2] == 1) |
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| 357 | tmp1= patch (tmp1, storeFactors[i][0][k][seperator[i][k][n]+mmm], |
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| 358 | eval[i]); |
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| 359 | index2 += seperator [i][k][n+1]-seperator[i][k][n]; |
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| 360 | } |
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| 361 | factor += tmp1; |
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| 362 | } |
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| 363 | |
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| 364 | for (m= 0; m < maxTerms; m++) |
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| 365 | delete [] mat [m]; |
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| 366 | delete [] mat; |
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| 367 | } |
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| 368 | |
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| 369 | if (fdivides (factor, B, quot)) |
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| 370 | { |
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| 371 | result.append (factor); |
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| 372 | B= quot; |
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| 373 | if (result.length() == biFactors.length() - 1) |
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| 374 | { |
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| 375 | result.append (quot); |
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| 376 | break; |
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| 377 | } |
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| 378 | } |
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| 379 | } |
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| 380 | |
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| 381 | //delete |
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| 382 | for (i= 0; i < j; i++) |
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| 383 | { |
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| 384 | delete [] storeFactors [i] [0]; |
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| 385 | delete [] storeFactors [i] [1]; |
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| 386 | delete [] storeFactors [i]; |
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| 387 | for (k= 0; k < minFactorsLength; k++) |
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| 388 | delete [] seperator [i][k]; |
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| 389 | delete [] seperator [i]; |
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| 390 | } |
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| 391 | delete [] seperator; |
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| 392 | delete [] storeFactors; |
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| 393 | // |
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| 394 | |
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| 395 | return result; |
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| 396 | } |
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