[ab547e2] | 1 | /*****************************************************************************\ |
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| 2 | * Computer Algebra System SINGULAR |
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| 3 | \*****************************************************************************/ |
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| 4 | /** @file facFqFactorize.cc |
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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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[e4fe2b] | 15 | #include "config.h" |
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[ab547e2] | 16 | |
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| 17 | #include "assert.h" |
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| 18 | #include "debug.h" |
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| 19 | #include "timing.h" |
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| 20 | |
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[d990001] | 21 | #include "cf_algorithm.h" |
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[ab547e2] | 22 | #include "facFqFactorizeUtil.h" |
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| 23 | #include "facFactorize.h" |
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| 24 | #include "facFqFactorize.h" |
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| 25 | #include "cf_random.h" |
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| 26 | #include "facHensel.h" |
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| 27 | #include "cf_gcd_smallp.h" |
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| 28 | #include "cf_map_ext.h" |
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| 29 | #include "algext.h" |
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| 30 | #include "cf_reval.h" |
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[91788c0] | 31 | #include "facSparseHensel.h" |
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[ab547e2] | 32 | |
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[0b618a7] | 33 | TIMING_DEFINE_PRINT(bi_factorize) |
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| 34 | TIMING_DEFINE_PRINT(hensel_lift) |
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| 35 | TIMING_DEFINE_PRINT(factor_recombination) |
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| 36 | |
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[d990001] | 37 | #ifdef HAVE_NTL |
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[ab547e2] | 38 | CFList evalPoints (const CanonicalForm& F, CFList& eval, Evaluation& E) |
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| 39 | { |
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| 40 | CFList result; |
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| 41 | Variable x= Variable (1); |
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| 42 | |
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| 43 | bool found= false; |
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| 44 | CanonicalForm deriv_x, gcd_deriv; |
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[38ffb7] | 45 | CFListIterator iter; |
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[ab547e2] | 46 | do |
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| 47 | { |
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| 48 | eval.insert (F); |
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| 49 | bool bad= false; |
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| 50 | for (int i= E.max(); i >= E.min(); i--) |
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| 51 | { |
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| 52 | eval.insert (eval.getFirst()( E [i], i)); |
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| 53 | result.append (E[i]); |
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| 54 | if (degree (eval.getFirst(), i - 1) != degree (F, i - 1)) |
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| 55 | { |
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| 56 | result= CFList(); |
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| 57 | eval= CFList(); |
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| 58 | bad= true; |
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| 59 | break; |
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| 60 | } |
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| 61 | } |
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| 62 | |
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| 63 | if (bad) |
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| 64 | { |
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| 65 | E.nextpoint(); |
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| 66 | continue; |
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| 67 | } |
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| 68 | |
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| 69 | if (degree (eval.getFirst()) != degree (F, 1)) |
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| 70 | { |
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| 71 | result= CFList(); |
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| 72 | eval= CFList(); |
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| 73 | E.nextpoint(); |
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| 74 | continue; |
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| 75 | } |
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| 76 | |
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| 77 | deriv_x= deriv (eval.getFirst(), x); |
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| 78 | gcd_deriv= gcd (eval.getFirst(), deriv_x); |
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| 79 | if (degree (gcd_deriv) > 0) |
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| 80 | { |
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| 81 | result= CFList(); |
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| 82 | eval= CFList(); |
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| 83 | E.nextpoint(); |
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| 84 | continue; |
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| 85 | } |
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[38ffb7] | 86 | iter= eval; |
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| 87 | iter++; |
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| 88 | CanonicalForm contentx= content (iter.getItem(), x); |
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[ab547e2] | 89 | if (degree (contentx) > 0) |
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| 90 | { |
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| 91 | result= CFList(); |
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| 92 | eval= CFList(); |
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| 93 | E.nextpoint(); |
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| 94 | continue; |
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| 95 | } |
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| 96 | found= true; |
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| 97 | } |
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| 98 | while (!found); |
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| 99 | |
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| 100 | if (!eval.isEmpty()) |
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| 101 | eval.removeFirst(); |
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| 102 | return result; |
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| 103 | } |
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| 104 | |
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| 105 | void |
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| 106 | factorizationWRTDifferentSecondVars (const CanonicalForm& A, CFList*& Aeval, |
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| 107 | int& minFactorsLength, bool& irred, |
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| 108 | const Variable& w) |
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| 109 | { |
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| 110 | Variable x= Variable (1); |
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| 111 | minFactorsLength= 0; |
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| 112 | irred= false; |
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[38ffb7] | 113 | Variable v; |
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| 114 | CFList factors; |
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[ab547e2] | 115 | for (int j= 0; j < A.level() - 2; j++) |
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| 116 | { |
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| 117 | if (!Aeval[j].isEmpty()) |
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| 118 | { |
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[38ffb7] | 119 | v= Variable (Aeval[j].getFirst().level()); |
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[ab547e2] | 120 | |
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[38ffb7] | 121 | factors= ratBiSqrfFactorize (Aeval[j].getFirst(), w); |
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[ab547e2] | 122 | |
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| 123 | if (factors.getFirst().inCoeffDomain()) |
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| 124 | factors.removeFirst(); |
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| 125 | |
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| 126 | if (minFactorsLength == 0) |
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| 127 | minFactorsLength= factors.length(); |
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| 128 | else |
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| 129 | minFactorsLength= tmin (minFactorsLength, factors.length()); |
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| 130 | |
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| 131 | if (factors.length() == 1) |
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| 132 | { |
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| 133 | irred= true; |
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| 134 | return; |
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| 135 | } |
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| 136 | sortList (factors, x); |
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| 137 | Aeval [j]= factors; |
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| 138 | } |
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| 139 | } |
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| 140 | } |
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| 141 | |
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| 142 | int |
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| 143 | testFactors (const CanonicalForm& G, const CFList& uniFactors, |
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| 144 | CanonicalForm& sqrfPartF, CFList& factors, |
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[eefc3a] | 145 | CFFList*& bufSqrfFactors, CFList& evalSqrfPartF, |
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| 146 | const CFArray& evalPoint) |
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[ab547e2] | 147 | { |
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[38ffb7] | 148 | CanonicalForm tmp; |
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| 149 | CFListIterator j; |
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[ab547e2] | 150 | for (CFListIterator i= uniFactors; i.hasItem(); i++) |
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| 151 | { |
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[38ffb7] | 152 | tmp= i.getItem(); |
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[ab547e2] | 153 | if (i.hasItem()) |
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| 154 | i++; |
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| 155 | else |
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| 156 | break; |
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[38ffb7] | 157 | for (j= i; j.hasItem(); j++) |
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[ab547e2] | 158 | { |
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| 159 | if (tmp == j.getItem()) |
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| 160 | return 0; |
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| 161 | } |
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| 162 | } |
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| 163 | |
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| 164 | CanonicalForm F= G; |
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| 165 | CFFList sqrfFactorization= sqrFree (F); |
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| 166 | |
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| 167 | sqrfPartF= 1; |
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| 168 | for (CFFListIterator i= sqrfFactorization; i.hasItem(); i++) |
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| 169 | sqrfPartF *= i.getItem().factor(); |
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| 170 | |
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[eefc3a] | 171 | evalSqrfPartF= evaluateAtEval (sqrfPartF, evalPoint); |
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[ab547e2] | 172 | |
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[eefc3a] | 173 | CanonicalForm test= evalSqrfPartF.getFirst() (evalPoint[0], 2); |
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[ab547e2] | 174 | |
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| 175 | if (degree (test) != degree (sqrfPartF, 1)) |
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| 176 | return 0; |
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| 177 | |
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| 178 | CFFList sqrfFactors; |
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| 179 | CFList tmp2; |
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| 180 | int k= 0; |
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| 181 | factors= uniFactors; |
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[38ffb7] | 182 | CFFListIterator iter; |
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[ab547e2] | 183 | for (CFListIterator i= factors; i.hasItem(); i++, k++) |
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| 184 | { |
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[38ffb7] | 185 | tmp= 1; |
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[ab547e2] | 186 | sqrfFactors= sqrFree (i.getItem()); |
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| 187 | |
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[38ffb7] | 188 | for (iter= sqrfFactors; iter.hasItem(); iter++) |
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[ab547e2] | 189 | { |
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[38ffb7] | 190 | tmp2.append (iter.getItem().factor()); |
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| 191 | tmp *= iter.getItem().factor(); |
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[ab547e2] | 192 | } |
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| 193 | i.getItem()= tmp/Lc(tmp); |
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| 194 | bufSqrfFactors [k]= sqrfFactors; |
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| 195 | } |
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| 196 | |
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| 197 | for (int i= 0; i < factors.length() - 1; i++) |
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| 198 | { |
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| 199 | for (int k= i + 1; k < factors.length(); k++) |
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| 200 | { |
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| 201 | gcdFreeBasis (bufSqrfFactors [i], bufSqrfFactors[k]); |
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| 202 | } |
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| 203 | } |
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| 204 | |
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| 205 | factors= CFList(); |
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| 206 | for (int i= 0; i < uniFactors.length(); i++) |
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| 207 | { |
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| 208 | if (i == 0) |
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| 209 | { |
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[38ffb7] | 210 | for (iter= bufSqrfFactors [i]; iter.hasItem(); iter++) |
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[ab547e2] | 211 | { |
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[327efa2] | 212 | if (iter.getItem().factor().inCoeffDomain()) |
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| 213 | continue; |
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[38ffb7] | 214 | iter.getItem()= CFFactor (iter.getItem().factor()/ |
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| 215 | Lc (iter.getItem().factor()), |
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| 216 | iter.getItem().exp()); |
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| 217 | factors.append (iter.getItem().factor()); |
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[ab547e2] | 218 | } |
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| 219 | } |
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| 220 | else |
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| 221 | { |
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[38ffb7] | 222 | for (iter= bufSqrfFactors [i]; iter.hasItem(); iter++) |
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[ab547e2] | 223 | { |
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[327efa2] | 224 | if (iter.getItem().factor().inCoeffDomain()) |
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| 225 | continue; |
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[38ffb7] | 226 | iter.getItem()= CFFactor (iter.getItem().factor()/ |
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| 227 | Lc (iter.getItem().factor()), |
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| 228 | iter.getItem().exp()); |
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| 229 | if (!find (factors, iter.getItem().factor())) |
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| 230 | factors.append (iter.getItem().factor()); |
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[ab547e2] | 231 | } |
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| 232 | } |
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| 233 | } |
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| 234 | |
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| 235 | test= prod (factors); |
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[eefc3a] | 236 | tmp= evalSqrfPartF.getFirst() (evalPoint[0],2); |
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[ab547e2] | 237 | if (test/Lc (test) != tmp/Lc (tmp)) |
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| 238 | return 0; |
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| 239 | else |
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| 240 | return 1; |
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| 241 | } |
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| 242 | |
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| 243 | CFList |
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| 244 | precomputeLeadingCoeff (const CanonicalForm& LCF, const CFList& LCFFactors, |
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| 245 | const CFList& evaluation,CFList*& differentSecondVarLCs, |
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| 246 | int length, Variable& y |
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| 247 | ) |
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| 248 | { |
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| 249 | y= Variable (1); |
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| 250 | if (LCF.inCoeffDomain()) |
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| 251 | { |
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| 252 | CFList result; |
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| 253 | for (int i= 1; i <= LCFFactors.length() + 1; i++) |
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| 254 | result.append (1); |
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| 255 | return result; |
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| 256 | } |
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| 257 | |
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| 258 | CFMap N; |
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| 259 | CanonicalForm F= compress (LCF, N); |
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| 260 | if (LCF.isUnivariate()) |
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| 261 | { |
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| 262 | CFList result; |
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| 263 | int LCFLevel= LCF.level(); |
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| 264 | bool found= false; |
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| 265 | if (LCFLevel == 2) |
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| 266 | { |
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| 267 | //bivariate leading coefficients are already the true leading coefficients |
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| 268 | result= LCFFactors; |
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| 269 | found= true; |
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| 270 | } |
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| 271 | else |
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| 272 | { |
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[38ffb7] | 273 | CFListIterator j; |
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[ab547e2] | 274 | for (int i= 0; i < length; i++) |
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| 275 | { |
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[38ffb7] | 276 | for (j= differentSecondVarLCs[i]; j.hasItem(); j++) |
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[ab547e2] | 277 | { |
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| 278 | if (j.getItem().level() == LCFLevel) |
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| 279 | { |
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| 280 | found= true; |
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| 281 | break; |
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| 282 | } |
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| 283 | } |
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| 284 | if (found) |
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| 285 | { |
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| 286 | result= differentSecondVarLCs [i]; |
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| 287 | break; |
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| 288 | } |
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| 289 | } |
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| 290 | if (!found) |
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| 291 | result= LCFFactors; |
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| 292 | } |
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| 293 | if (found) |
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| 294 | result.insert (Lc (LCF)); |
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| 295 | else |
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| 296 | result.append (LCF); |
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| 297 | return result; |
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| 298 | } |
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| 299 | |
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| 300 | CFList factors= LCFFactors; |
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| 301 | |
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| 302 | CFMap dummy; |
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| 303 | for (CFListIterator i= factors; i.hasItem(); i++) |
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| 304 | i.getItem()= compress (i.getItem(), dummy); |
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| 305 | |
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| 306 | CanonicalForm sqrfPartF; |
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| 307 | CFFList * bufSqrfFactors= new CFFList [factors.length()]; |
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[eefc3a] | 308 | CFList evalSqrfPartF, bufFactors; |
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| 309 | CFArray evalPoint= CFArray (evaluation.length() - 1); |
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| 310 | CFListIterator iter= evaluation; |
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| 311 | for (int i= evaluation.length() - 2; i > -1; i--, iter++) |
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| 312 | evalPoint[i]= iter.getItem(); |
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[ab547e2] | 313 | //TODO sqrfPartF einmal berechnen nicht stÀndig |
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| 314 | int pass= testFactors (F, factors, sqrfPartF, |
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[eefc3a] | 315 | bufFactors, bufSqrfFactors, evalSqrfPartF, evalPoint); |
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[ab547e2] | 316 | |
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| 317 | bool foundDifferent= false; |
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| 318 | Variable z; |
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| 319 | Variable x= y; |
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| 320 | int j= 0; |
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| 321 | if (!pass) |
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| 322 | { |
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[7a1151] | 323 | int lev= 0; |
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[ab547e2] | 324 | for (int i= 1; i <= LCF.level(); i++) |
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| 325 | { |
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| 326 | if(degree (LCF, i) > 0) |
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| 327 | { |
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| 328 | lev= i - 1; |
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| 329 | break; |
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| 330 | } |
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| 331 | } |
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| 332 | for (int i= 0; i < length; i++) |
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| 333 | { |
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[eefc3a] | 334 | CanonicalForm bufF, swap; |
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[38ffb7] | 335 | CFList bufBufFactors; |
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[eefc3a] | 336 | CFArray buf; |
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[ab547e2] | 337 | if (!differentSecondVarLCs [i].isEmpty()) |
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| 338 | { |
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| 339 | bool allConstant= true; |
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[38ffb7] | 340 | for (iter= differentSecondVarLCs[i]; iter.hasItem(); iter++) |
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[ab547e2] | 341 | { |
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| 342 | if (!iter.getItem().inCoeffDomain()) |
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| 343 | { |
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| 344 | allConstant= false; |
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| 345 | y= Variable (iter.getItem().level()); |
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| 346 | } |
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| 347 | } |
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| 348 | if (allConstant) |
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| 349 | continue; |
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| 350 | |
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| 351 | bufFactors= differentSecondVarLCs [i]; |
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[38ffb7] | 352 | for (iter= bufFactors; iter.hasItem(); iter++) |
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[ab547e2] | 353 | iter.getItem()= swapvar (iter.getItem(), x, y); |
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[38ffb7] | 354 | bufF= F; |
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[ab547e2] | 355 | z= Variable (y.level() - lev); |
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| 356 | bufF= swapvar (bufF, x, z); |
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[38ffb7] | 357 | bufBufFactors= bufFactors; |
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[eefc3a] | 358 | evalPoint= CFArray (evaluation.length() - 1); |
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| 359 | buf= CFArray (evaluation.length()); |
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| 360 | iter= evaluation; |
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| 361 | int k= evaluation.length() - 1; |
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| 362 | for (; iter.hasItem(); iter++, k--) |
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| 363 | buf[k]= iter.getItem(); |
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| 364 | swap= buf[z.level() - 1]; |
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| 365 | buf[z.level() - 1]= buf[0]; |
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| 366 | buf[0]= 0; |
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| 367 | int l= 0; |
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| 368 | for (k= 0; k < evaluation.length(); k++) |
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| 369 | { |
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| 370 | if (buf[k].isZero()) |
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| 371 | continue; |
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| 372 | evalPoint[l]= buf[k]; |
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| 373 | l++; |
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| 374 | } |
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[ab547e2] | 375 | pass= testFactors (bufF, bufBufFactors, sqrfPartF, bufFactors, |
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[eefc3a] | 376 | bufSqrfFactors, evalSqrfPartF, evalPoint); |
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[ab547e2] | 377 | if (pass) |
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| 378 | { |
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| 379 | foundDifferent= true; |
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| 380 | F= bufF; |
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| 381 | CFList l= factors; |
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[38ffb7] | 382 | for (iter= l; iter.hasItem(); iter++) |
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[ab547e2] | 383 | iter.getItem()= swapvar (iter.getItem(), x, y); |
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| 384 | differentSecondVarLCs [i]= l; |
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| 385 | j= i; |
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| 386 | break; |
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| 387 | } |
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| 388 | if (!pass && i == length - 1) |
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| 389 | { |
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| 390 | CFList result; |
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| 391 | result.append (LCF); |
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| 392 | for (int j= 1; j <= factors.length(); j++) |
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| 393 | result.append (LCF); |
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| 394 | y= Variable (1); |
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[229530] | 395 | delete [] bufSqrfFactors; |
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[ab547e2] | 396 | return result; |
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| 397 | } |
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| 398 | } |
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| 399 | } |
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| 400 | } |
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| 401 | if (!pass) |
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| 402 | { |
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| 403 | CFList result; |
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| 404 | result.append (LCF); |
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| 405 | for (int j= 1; j <= factors.length(); j++) |
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| 406 | result.append (LCF); |
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| 407 | y= Variable (1); |
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[229530] | 408 | delete [] bufSqrfFactors; |
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[ab547e2] | 409 | return result; |
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| 410 | } |
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| 411 | else |
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| 412 | factors= bufFactors; |
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| 413 | |
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| 414 | |
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| 415 | bufFactors= factors; |
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[eefc3a] | 416 | CFList evaluation2; |
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| 417 | if (y == x) |
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| 418 | evaluation2= evaluation; |
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| 419 | else |
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| 420 | { |
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| 421 | CanonicalForm tmp; |
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| 422 | evaluation2= evaluation; |
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| 423 | int i= evaluation.length() + 1; |
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| 424 | for (CFListIterator iter= evaluation2; iter.hasItem(); iter++, i--) |
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| 425 | { |
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| 426 | if (i == y.level()) |
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| 427 | { |
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| 428 | tmp= iter.getItem(); |
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| 429 | iter.getItem()= evaluation2.getLast(); |
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| 430 | evaluation2.removeLast(); |
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| 431 | evaluation2.append (tmp); |
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| 432 | break; |
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| 433 | } |
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| 434 | } |
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| 435 | } |
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[327efa2] | 436 | |
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[ec16f0] | 437 | CFList interMedResult; |
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| 438 | CanonicalForm oldSqrfPartF= sqrfPartF; |
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[eefc3a] | 439 | sqrfPartF= shift2Zero (sqrfPartF, evalSqrfPartF, evaluation2, 1); |
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[327efa2] | 440 | if (factors.length() > 1) |
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| 441 | { |
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[ec16f0] | 442 | CanonicalForm LC1= LC (oldSqrfPartF, 1); |
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| 443 | CFList leadingCoeffs; |
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[327efa2] | 444 | for (int i= 0; i < factors.length(); i++) |
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[ec16f0] | 445 | leadingCoeffs.append (LC1); |
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| 446 | |
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| 447 | CFList LC1eval= evaluateAtEval (LC1, evaluation2, 1); |
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| 448 | CFList oldFactors= factors; |
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| 449 | for (CFListIterator i= oldFactors; i.hasItem(); i++) |
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| 450 | i.getItem() *= LC1eval.getFirst()/Lc (i.getItem()); |
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| 451 | |
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| 452 | bool success= false; |
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[64b824] | 453 | CanonicalForm oldSqrfPartFPowLC= oldSqrfPartF*power(LC1,factors.length()-1); |
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| 454 | if (size (oldSqrfPartFPowLC)/getNumVars (oldSqrfPartFPowLC) < 500 && |
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| 455 | LucksWangSparseHeuristic (oldSqrfPartFPowLC, |
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[ec16f0] | 456 | oldFactors, 1, leadingCoeffs, factors)) |
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[eefc3a] | 457 | { |
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[ec16f0] | 458 | interMedResult= recoverFactors (oldSqrfPartF, factors); |
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| 459 | if (oldFactors.length() == interMedResult.length()) |
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| 460 | success= true; |
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[eefc3a] | 461 | } |
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[ec16f0] | 462 | if (!success) |
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| 463 | { |
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| 464 | LC1= LC (evalSqrfPartF.getFirst(), 1); |
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[327efa2] | 465 | |
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[ec16f0] | 466 | CFArray leadingCoeffs= CFArray (factors.length()); |
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| 467 | for (int i= 0; i < factors.length(); i++) |
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| 468 | leadingCoeffs[i]= LC1; |
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[327efa2] | 469 | |
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[ec16f0] | 470 | for (CFListIterator i= factors; i.hasItem(); i++) |
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| 471 | { |
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| 472 | i.getItem()= i.getItem() (x + evaluation2.getLast(), x); |
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| 473 | i.getItem() *= LC1 (0,2)/Lc (i.getItem()); |
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| 474 | } |
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| 475 | factors.insert (1); |
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[327efa2] | 476 | |
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[ec16f0] | 477 | CanonicalForm |
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| 478 | newSqrfPartF= evalSqrfPartF.getFirst()*power (LC1, factors.length() - 2); |
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[327efa2] | 479 | |
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[ec16f0] | 480 | int liftBound= degree (newSqrfPartF,2) + 1; |
---|
| 481 | |
---|
| 482 | CFMatrix M= CFMatrix (liftBound, factors.length() - 1); |
---|
| 483 | CFArray Pi; |
---|
| 484 | CFList diophant; |
---|
[81d96c] | 485 | nonMonicHenselLift12 (newSqrfPartF, factors, liftBound, Pi, diophant, M, |
---|
| 486 | leadingCoeffs, false); |
---|
[ec16f0] | 487 | |
---|
| 488 | if (sqrfPartF.level() > 2) |
---|
[327efa2] | 489 | { |
---|
[ec16f0] | 490 | int* liftBounds= new int [sqrfPartF.level() - 1]; |
---|
| 491 | liftBounds [0]= liftBound; |
---|
| 492 | bool noOneToOne= false; |
---|
| 493 | CFList *leadingCoeffs2= new CFList [sqrfPartF.level()-2]; |
---|
| 494 | LC1= LC (evalSqrfPartF.getLast(), 1); |
---|
| 495 | CFList LCs; |
---|
| 496 | for (int i= 0; i < factors.length(); i++) |
---|
| 497 | LCs.append (LC1); |
---|
| 498 | leadingCoeffs2 [sqrfPartF.level() - 3]= LCs; |
---|
| 499 | for (int i= sqrfPartF.level() - 1; i > 2; i--) |
---|
| 500 | { |
---|
| 501 | for (CFListIterator j= LCs; j.hasItem(); j++) |
---|
| 502 | j.getItem()= j.getItem() (0, i + 1); |
---|
| 503 | leadingCoeffs2 [i - 3]= LCs; |
---|
| 504 | } |
---|
| 505 | sqrfPartF *= power (LC1, factors.length()-1); |
---|
| 506 | |
---|
| 507 | int liftBoundsLength= sqrfPartF.level() - 1; |
---|
| 508 | for (int i= 1; i < liftBoundsLength; i++) |
---|
| 509 | liftBounds [i]= degree (sqrfPartF, i + 2) + 1; |
---|
| 510 | evalSqrfPartF= evaluateAtZero (sqrfPartF); |
---|
| 511 | evalSqrfPartF.removeFirst(); |
---|
| 512 | factors= nonMonicHenselLift (evalSqrfPartF, factors, leadingCoeffs2, |
---|
| 513 | diophant, Pi, liftBounds, sqrfPartF.level() - 1, noOneToOne); |
---|
| 514 | delete [] leadingCoeffs2; |
---|
| 515 | delete [] liftBounds; |
---|
[327efa2] | 516 | } |
---|
[ec16f0] | 517 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
| 518 | iter.getItem()= reverseShift (iter.getItem(), evaluation2, 1); |
---|
| 519 | |
---|
| 520 | interMedResult= |
---|
| 521 | recoverFactors (reverseShift(evalSqrfPartF.getLast(),evaluation2,1), |
---|
| 522 | factors); |
---|
[327efa2] | 523 | } |
---|
| 524 | } |
---|
| 525 | else |
---|
[ec16f0] | 526 | { |
---|
| 527 | factors= CFList (oldSqrfPartF); |
---|
| 528 | interMedResult= recoverFactors (oldSqrfPartF, factors); |
---|
| 529 | } |
---|
[ab547e2] | 530 | |
---|
| 531 | CFList result; |
---|
[38ffb7] | 532 | CFFListIterator k; |
---|
| 533 | CanonicalForm tmp; |
---|
[ab547e2] | 534 | for (int i= 0; i < LCFFactors.length(); i++) |
---|
| 535 | { |
---|
[38ffb7] | 536 | tmp= 1; |
---|
| 537 | for (k= bufSqrfFactors[i]; k.hasItem(); k++) |
---|
[ab547e2] | 538 | { |
---|
| 539 | int pos= findItem (bufFactors, k.getItem().factor()); |
---|
| 540 | if (pos) |
---|
| 541 | tmp *= power (getItem (interMedResult, pos), k.getItem().exp()); |
---|
| 542 | } |
---|
| 543 | result.append (tmp); |
---|
| 544 | } |
---|
| 545 | |
---|
| 546 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
| 547 | { |
---|
| 548 | F /= i.getItem(); |
---|
| 549 | if (foundDifferent) |
---|
| 550 | i.getItem()= swapvar (i.getItem(), x, z); |
---|
| 551 | i.getItem()= N (i.getItem()); |
---|
| 552 | } |
---|
| 553 | |
---|
| 554 | if (foundDifferent) |
---|
| 555 | { |
---|
| 556 | CFList l= differentSecondVarLCs [j]; |
---|
| 557 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 558 | i.getItem()= swapvar (i.getItem(), y, z); |
---|
| 559 | differentSecondVarLCs [j]= l; |
---|
| 560 | F= swapvar (F, x, z); |
---|
| 561 | } |
---|
| 562 | |
---|
| 563 | result.insert (N (F)); |
---|
| 564 | |
---|
| 565 | result= distributeContent (result, differentSecondVarLCs, length); |
---|
| 566 | |
---|
| 567 | if (!result.getFirst().inCoeffDomain()) |
---|
| 568 | { |
---|
| 569 | CFListIterator i= result; |
---|
| 570 | CanonicalForm tmp; |
---|
| 571 | if (foundDifferent) |
---|
| 572 | i.getItem()= swapvar (i.getItem(), Variable (2), y); |
---|
| 573 | |
---|
| 574 | tmp= i.getItem(); |
---|
| 575 | |
---|
| 576 | i++; |
---|
| 577 | for (; i.hasItem(); i++) |
---|
| 578 | { |
---|
| 579 | if (foundDifferent) |
---|
| 580 | i.getItem()= swapvar (i.getItem(), Variable (2), y)*tmp; |
---|
| 581 | else |
---|
| 582 | i.getItem() *= tmp; |
---|
| 583 | } |
---|
| 584 | } |
---|
| 585 | else |
---|
| 586 | y= Variable (1); |
---|
| 587 | |
---|
[229530] | 588 | delete [] bufSqrfFactors; |
---|
| 589 | |
---|
[ab547e2] | 590 | return result; |
---|
| 591 | } |
---|
| 592 | |
---|
| 593 | |
---|
| 594 | CFList |
---|
| 595 | multiFactorize (const CanonicalForm& F, const Variable& v) |
---|
| 596 | { |
---|
| 597 | if (F.inCoeffDomain()) |
---|
| 598 | return CFList (F); |
---|
| 599 | |
---|
| 600 | // compress and find main Variable |
---|
| 601 | CFMap N; |
---|
| 602 | CanonicalForm A= myCompress (F, N); |
---|
| 603 | |
---|
| 604 | //univariate case |
---|
| 605 | if (F.isUnivariate()) |
---|
| 606 | { |
---|
[0e6668] | 607 | CFList result; |
---|
| 608 | if (v.level() != 1) |
---|
| 609 | result= conv (factorize (F, v)); |
---|
| 610 | else |
---|
| 611 | result= conv (factorize (F,true)); |
---|
[ab547e2] | 612 | if (result.getFirst().inCoeffDomain()) |
---|
| 613 | result.removeFirst(); |
---|
| 614 | return result; |
---|
| 615 | } |
---|
| 616 | |
---|
| 617 | //bivariate case |
---|
| 618 | if (A.level() == 2) |
---|
| 619 | { |
---|
| 620 | CFList buf= biFactorize (F, v); |
---|
| 621 | return buf; |
---|
| 622 | } |
---|
| 623 | |
---|
| 624 | Variable x= Variable (1); |
---|
| 625 | Variable y= Variable (2); |
---|
| 626 | |
---|
| 627 | // remove content |
---|
| 628 | CFList contentAi; |
---|
| 629 | CanonicalForm lcmCont= lcmContent (A, contentAi); |
---|
| 630 | A /= lcmCont; |
---|
| 631 | |
---|
| 632 | // trivial after content removal |
---|
| 633 | CFList contentAFactors; |
---|
| 634 | if (A.inCoeffDomain()) |
---|
| 635 | { |
---|
| 636 | for (CFListIterator i= contentAi; i.hasItem(); i++) |
---|
| 637 | { |
---|
| 638 | if (i.getItem().inCoeffDomain()) |
---|
| 639 | continue; |
---|
| 640 | else |
---|
| 641 | { |
---|
| 642 | lcmCont /= i.getItem(); |
---|
| 643 | contentAFactors= |
---|
| 644 | Union (multiFactorize (lcmCont, v), |
---|
| 645 | multiFactorize (i.getItem(), v)); |
---|
| 646 | break; |
---|
| 647 | } |
---|
| 648 | } |
---|
| 649 | decompress (contentAFactors, N); |
---|
| 650 | if (isOn (SW_RATIONAL)) |
---|
| 651 | normalize (contentAFactors); |
---|
| 652 | return contentAFactors; |
---|
| 653 | } |
---|
| 654 | |
---|
| 655 | // factorize content |
---|
| 656 | contentAFactors= multiFactorize (lcmCont, v); |
---|
| 657 | |
---|
| 658 | // univariate after content removal |
---|
| 659 | CFList factors; |
---|
| 660 | if (A.isUnivariate ()) |
---|
| 661 | { |
---|
[0e6668] | 662 | if (v.level() != 1) |
---|
| 663 | factors= conv (factorize (A, v)); |
---|
| 664 | else |
---|
| 665 | factors= conv (factorize (A,true)); |
---|
[ab547e2] | 666 | append (factors, contentAFactors); |
---|
| 667 | decompress (factors, N); |
---|
| 668 | return factors; |
---|
| 669 | } |
---|
| 670 | |
---|
| 671 | // check main variable |
---|
| 672 | CFList Aeval, list, evaluation, bufEvaluation, bufAeval; |
---|
| 673 | int factorNums= 3; |
---|
| 674 | CanonicalForm bivarEval; |
---|
| 675 | CFList biFactors, bufBiFactors; |
---|
| 676 | CanonicalForm evalPoly; |
---|
| 677 | int lift, bufLift; |
---|
| 678 | CFList* bufAeval2= new CFList [A.level() - 2]; |
---|
| 679 | CFList* Aeval2= new CFList [A.level() - 2]; |
---|
| 680 | int counter; |
---|
| 681 | int differentSecondVar= 0; |
---|
| 682 | CanonicalForm bufA; |
---|
| 683 | // several bivariate factorizations |
---|
| 684 | REvaluation E (2, A.level(), IntRandom (25)); |
---|
| 685 | for (int i= 0; i < factorNums; i++) |
---|
| 686 | { |
---|
| 687 | counter= 0; |
---|
| 688 | bufA= A; |
---|
| 689 | bufAeval= CFList(); |
---|
| 690 | bufEvaluation= evalPoints (bufA, bufAeval, E); |
---|
| 691 | E.nextpoint(); |
---|
| 692 | evalPoly= 0; |
---|
| 693 | |
---|
| 694 | bivarEval= bufEvaluation.getLast(); |
---|
| 695 | |
---|
| 696 | evaluationWRTDifferentSecondVars (bufAeval2, bufEvaluation, A); |
---|
| 697 | |
---|
| 698 | for (int j= 0; j < A.level() - 1; j++) |
---|
| 699 | { |
---|
| 700 | if (!bufAeval2[j].isEmpty()) |
---|
| 701 | counter++; |
---|
| 702 | } |
---|
| 703 | |
---|
| 704 | bufLift= degree (A, y) + 1 + degree (LC(A, x), y); |
---|
| 705 | |
---|
[0b618a7] | 706 | TIMING_START (bi_factorize); |
---|
[ab547e2] | 707 | bufBiFactors= ratBiSqrfFactorize (bufAeval.getFirst(), v); |
---|
[0b618a7] | 708 | TIMING_END_AND_PRINT (bi_factorize, |
---|
[ab547e2] | 709 | "time for bivariate factorization: "); |
---|
| 710 | bufBiFactors.removeFirst(); |
---|
| 711 | |
---|
| 712 | if (bufBiFactors.length() == 1) |
---|
| 713 | { |
---|
| 714 | factors.append (A); |
---|
| 715 | appendSwapDecompress (factors, contentAFactors, N, 0, 0, x); |
---|
| 716 | if (isOn (SW_RATIONAL)) |
---|
| 717 | normalize (factors); |
---|
| 718 | delete [] bufAeval2; |
---|
| 719 | delete [] Aeval2; |
---|
| 720 | return factors; |
---|
| 721 | } |
---|
| 722 | |
---|
| 723 | if (i == 0) |
---|
| 724 | { |
---|
| 725 | Aeval= bufAeval; |
---|
| 726 | evaluation= bufEvaluation; |
---|
| 727 | biFactors= bufBiFactors; |
---|
| 728 | lift= bufLift; |
---|
| 729 | for (int j= 0; j < A.level() - 2; j++) |
---|
| 730 | Aeval2 [j]= bufAeval2 [j]; |
---|
| 731 | differentSecondVar= counter; |
---|
| 732 | } |
---|
| 733 | else |
---|
| 734 | { |
---|
| 735 | if (bufBiFactors.length() < biFactors.length() || |
---|
| 736 | ((bufLift < lift) && (bufBiFactors.length() == biFactors.length())) || |
---|
| 737 | counter > differentSecondVar) |
---|
| 738 | { |
---|
| 739 | Aeval= bufAeval; |
---|
| 740 | evaluation= bufEvaluation; |
---|
| 741 | biFactors= bufBiFactors; |
---|
| 742 | lift= bufLift; |
---|
| 743 | for (int j= 0; j < A.level() - 2; j++) |
---|
| 744 | Aeval2 [j]= bufAeval2 [j]; |
---|
| 745 | differentSecondVar= counter; |
---|
| 746 | } |
---|
| 747 | } |
---|
| 748 | int k= 0; |
---|
| 749 | for (CFListIterator j= bufEvaluation; j.hasItem(); j++, k++) |
---|
| 750 | evalPoly += j.getItem()*power (x, k); |
---|
| 751 | list.append (evalPoly); |
---|
| 752 | } |
---|
| 753 | |
---|
| 754 | delete [] bufAeval2; |
---|
| 755 | |
---|
| 756 | sortList (biFactors, x); |
---|
| 757 | |
---|
| 758 | int minFactorsLength; |
---|
| 759 | bool irred= false; |
---|
| 760 | factorizationWRTDifferentSecondVars (A, Aeval2, minFactorsLength, irred, v); |
---|
| 761 | |
---|
| 762 | if (irred) |
---|
| 763 | { |
---|
| 764 | factors.append (A); |
---|
| 765 | appendSwapDecompress (factors, contentAFactors, N, 0, 0, x); |
---|
| 766 | if (isOn (SW_RATIONAL)) |
---|
| 767 | normalize (factors); |
---|
| 768 | delete [] Aeval2; |
---|
| 769 | return factors; |
---|
| 770 | } |
---|
| 771 | |
---|
| 772 | if (minFactorsLength == 0) |
---|
| 773 | minFactorsLength= biFactors.length(); |
---|
| 774 | else if (biFactors.length() > minFactorsLength) |
---|
| 775 | refineBiFactors (A, biFactors, Aeval2, evaluation, minFactorsLength); |
---|
| 776 | |
---|
[6036d90] | 777 | if (differentSecondVar == A.level() - 2) |
---|
| 778 | { |
---|
| 779 | bool zeroOccured= false; |
---|
| 780 | for (CFListIterator iter= evaluation; iter.hasItem(); iter++) |
---|
| 781 | { |
---|
| 782 | if (iter.getItem().isZero()) |
---|
| 783 | { |
---|
| 784 | zeroOccured= true; |
---|
| 785 | break; |
---|
| 786 | } |
---|
| 787 | } |
---|
| 788 | if (!zeroOccured) |
---|
| 789 | { |
---|
| 790 | factors= sparseHeuristic (A, biFactors, Aeval2, evaluation, minFactorsLength); |
---|
| 791 | if (factors.length() == biFactors.length()) |
---|
| 792 | { |
---|
| 793 | appendSwapDecompress (factors, contentAFactors, N, 0, 0, x); |
---|
| 794 | normalize (factors); |
---|
| 795 | delete [] Aeval2; |
---|
| 796 | return factors; |
---|
| 797 | } |
---|
| 798 | else |
---|
| 799 | factors= CFList(); |
---|
| 800 | //TODO case where factors.length() > 0 |
---|
| 801 | } |
---|
| 802 | } |
---|
| 803 | |
---|
[ab547e2] | 804 | CFList uniFactors= buildUniFactors (biFactors, evaluation.getLast(), y); |
---|
| 805 | |
---|
| 806 | CFList * oldAeval= new CFList [A.level() - 2]; |
---|
| 807 | for (int i= 0; i < A.level() - 2; i++) |
---|
| 808 | oldAeval[i]= Aeval2[i]; |
---|
| 809 | |
---|
| 810 | getLeadingCoeffs (A, Aeval2, uniFactors, evaluation); |
---|
| 811 | |
---|
| 812 | CFList biFactorsLCs; |
---|
| 813 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
| 814 | biFactorsLCs.append (LC (i.getItem(), 1)); |
---|
| 815 | |
---|
| 816 | Variable w; |
---|
| 817 | CFList leadingCoeffs= precomputeLeadingCoeff (LC (A, 1), biFactorsLCs, |
---|
| 818 | evaluation, Aeval2, A.level() - 2, w); |
---|
| 819 | |
---|
| 820 | if (w.level() != 1) |
---|
| 821 | { |
---|
| 822 | A= swapvar (A, y, w); |
---|
| 823 | for (int i= 0; i < A.level() - 2; i++) |
---|
| 824 | { |
---|
| 825 | if (oldAeval[i].isEmpty()) |
---|
| 826 | continue; |
---|
| 827 | if (oldAeval[i].getFirst().level() == w.level()) |
---|
| 828 | { |
---|
| 829 | biFactors= CFList(); |
---|
| 830 | for (CFListIterator iter= oldAeval [i]; iter.hasItem(); iter++) |
---|
| 831 | biFactors.append (swapvar (iter.getItem(), w, y)); |
---|
| 832 | } |
---|
| 833 | } |
---|
| 834 | int i= A.level(); |
---|
| 835 | CanonicalForm evalPoint; |
---|
| 836 | for (CFListIterator iter= evaluation; iter.hasItem(); iter++, i--) |
---|
| 837 | { |
---|
| 838 | if (i == w.level()) |
---|
| 839 | { |
---|
| 840 | evalPoint= iter.getItem(); |
---|
| 841 | iter.getItem()= evaluation.getLast(); |
---|
| 842 | evaluation.removeLast(); |
---|
| 843 | evaluation.append (evalPoint); |
---|
| 844 | break; |
---|
| 845 | } |
---|
| 846 | } |
---|
| 847 | } |
---|
| 848 | |
---|
[eefc3a] | 849 | CFListIterator iter; |
---|
[ab547e2] | 850 | CanonicalForm oldA= A; |
---|
| 851 | CFList oldBiFactors= biFactors; |
---|
| 852 | if (!leadingCoeffs.getFirst().inCoeffDomain()) |
---|
| 853 | { |
---|
| 854 | CanonicalForm tmp= power (leadingCoeffs.getFirst(), biFactors.length() - 1); |
---|
| 855 | A *= tmp; |
---|
| 856 | Aeval= evaluateAtZero (A); |
---|
| 857 | tmp= leadingCoeffs.getFirst(); |
---|
[eefc3a] | 858 | iter= evaluation; |
---|
| 859 | for (int i= A.level(); i > 2; i--, iter++) |
---|
| 860 | tmp= tmp (iter.getItem(), i); |
---|
[ab547e2] | 861 | if (!tmp.inCoeffDomain()) |
---|
| 862 | { |
---|
| 863 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
| 864 | { |
---|
| 865 | i.getItem() *= tmp/LC (i.getItem(), 1); |
---|
| 866 | i.getItem() /= Lc (i.getItem()); |
---|
| 867 | } |
---|
| 868 | } |
---|
| 869 | } |
---|
| 870 | |
---|
| 871 | leadingCoeffs.removeFirst(); |
---|
| 872 | |
---|
| 873 | //prepare leading coefficients |
---|
| 874 | CFList* leadingCoeffs2= new CFList [A.level() - 2]; |
---|
[eefc3a] | 875 | prepareLeadingCoeffs (leadingCoeffs2, A.level(), leadingCoeffs, biFactors, |
---|
| 876 | evaluation); |
---|
| 877 | |
---|
| 878 | |
---|
| 879 | Aeval= evaluateAtEval (A, evaluation, 2); |
---|
| 880 | |
---|
| 881 | CanonicalForm hh= Lc (Aeval.getFirst()); |
---|
| 882 | |
---|
| 883 | for (CFListIterator i= Aeval; i.hasItem(); i++) |
---|
| 884 | i.getItem() /= hh; |
---|
| 885 | |
---|
| 886 | A /= hh; |
---|
| 887 | |
---|
[64b824] | 888 | if (size (A)/getNumVars (A) < 500 && |
---|
| 889 | LucksWangSparseHeuristic (A, biFactors, 2, leadingCoeffs2 [A.level() - 3], |
---|
| 890 | factors)) |
---|
[4fe8a3] | 891 | { |
---|
| 892 | int check= factors.length(); |
---|
| 893 | factors= recoverFactors (A, factors); |
---|
| 894 | |
---|
| 895 | if (check == factors.length()) |
---|
| 896 | { |
---|
| 897 | appendSwapDecompress (factors, contentAFactors, N, 0, 0, x); |
---|
| 898 | normalize (factors); |
---|
| 899 | delete [] Aeval2; |
---|
| 900 | return factors; |
---|
| 901 | } |
---|
| 902 | else |
---|
| 903 | factors= CFList(); |
---|
[64b824] | 904 | } |
---|
[4fe8a3] | 905 | |
---|
| 906 | |
---|
[eefc3a] | 907 | //shifting to zero |
---|
| 908 | A= shift2Zero (A, Aeval, evaluation); |
---|
| 909 | |
---|
| 910 | for (iter= biFactors; iter.hasItem(); iter++) |
---|
| 911 | iter.getItem()= iter.getItem () (y + evaluation.getLast(), y); |
---|
| 912 | |
---|
| 913 | for (int i= 0; i < A.level() - 2; i++) |
---|
| 914 | { |
---|
| 915 | if (i != A.level() - 3) |
---|
| 916 | leadingCoeffs2[i]= CFList(); |
---|
| 917 | } |
---|
| 918 | for (iter= leadingCoeffs2[A.level() - 3]; iter.hasItem(); iter++) |
---|
| 919 | { |
---|
| 920 | iter.getItem()= shift2Zero (iter.getItem(), list, evaluation); |
---|
| 921 | for (int i= A.level() - 4; i > -1; i--) |
---|
| 922 | { |
---|
| 923 | if (i + 1 == A.level() - 3) |
---|
| 924 | leadingCoeffs2[i].append (iter.getItem() (0, i + 4)); |
---|
| 925 | else |
---|
| 926 | leadingCoeffs2[i].append (leadingCoeffs2[i+1].getLast() (0, i + 4)); |
---|
| 927 | } |
---|
| 928 | } |
---|
[ab547e2] | 929 | |
---|
| 930 | CFArray Pi; |
---|
| 931 | CFList diophant; |
---|
| 932 | int* liftBounds= new int [A.level() - 1]; |
---|
| 933 | int liftBoundsLength= A.level() - 1; |
---|
| 934 | for (int i= 0; i < liftBoundsLength; i++) |
---|
| 935 | liftBounds [i]= degree (A, i + 2) + 1; |
---|
| 936 | |
---|
| 937 | Aeval.removeFirst(); |
---|
| 938 | bool noOneToOne= false; |
---|
| 939 | |
---|
| 940 | factors= nonMonicHenselLift (Aeval, biFactors, leadingCoeffs2, diophant, |
---|
| 941 | Pi, liftBounds, liftBoundsLength, noOneToOne); |
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| 942 | |
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| 943 | if (!noOneToOne) |
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| 944 | { |
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| 945 | int check= factors.length(); |
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[eefc3a] | 946 | A= oldA; |
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| 947 | factors= recoverFactors (A, factors, evaluation); |
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[ab547e2] | 948 | if (check != factors.length()) |
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| 949 | noOneToOne= true; |
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| 950 | } |
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| 951 | if (noOneToOne) |
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| 952 | { |
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[eefc3a] | 953 | A= shift2Zero (oldA, Aeval, evaluation); |
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[ab547e2] | 954 | biFactors= oldBiFactors; |
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[eefc3a] | 955 | for (iter= biFactors; iter.hasItem(); iter++) |
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| 956 | iter.getItem()= iter.getItem () (y + evaluation.getLast(), y); |
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[ab547e2] | 957 | CanonicalForm LCA= LC (Aeval.getFirst(), 1); |
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| 958 | CanonicalForm yToLift= power (y, lift); |
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| 959 | CFListIterator i= biFactors; |
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| 960 | lift= degree (i.getItem(), 2) + degree (LC (i.getItem(), 1)) + 1; |
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| 961 | i++; |
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| 962 | |
---|
| 963 | for (; i.hasItem(); i++) |
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| 964 | lift= tmax (lift, degree (i.getItem(), 2)+degree (LC (i.getItem(), 1))+1); |
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| 965 | |
---|
| 966 | lift= tmax (degree (Aeval.getFirst() , 2) + 1, lift); |
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| 967 | |
---|
| 968 | i= biFactors; |
---|
| 969 | yToLift= power (y, lift); |
---|
| 970 | CanonicalForm dummy; |
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| 971 | for (; i.hasItem(); i++) |
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| 972 | { |
---|
| 973 | LCA= LC (i.getItem(), 1); |
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| 974 | extgcd (LCA, yToLift, LCA, dummy); |
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| 975 | i.getItem()= mod (i.getItem()*LCA, yToLift); |
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| 976 | } |
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| 977 | |
---|
| 978 | liftBoundsLength= F.level() - 1; |
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| 979 | liftBounds= liftingBounds (A, lift); |
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| 980 | |
---|
| 981 | CFList MOD; |
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| 982 | bool earlySuccess; |
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| 983 | CFList earlyFactors; |
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| 984 | ExtensionInfo info= ExtensionInfo (false); |
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[0b618a7] | 985 | CFList liftedFactors; |
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| 986 | TIMING_START (hensel_lift); |
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| 987 | liftedFactors= henselLiftAndEarly |
---|
| 988 | (A, MOD, liftBounds, earlySuccess, earlyFactors, |
---|
| 989 | Aeval, biFactors, evaluation, info); |
---|
| 990 | TIMING_END_AND_PRINT (hensel_lift, "time for hensel lifting: "); |
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| 991 | |
---|
| 992 | TIMING_START (factor_recombination); |
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[ab547e2] | 993 | factors= factorRecombination (A, liftedFactors, MOD); |
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[0b618a7] | 994 | TIMING_END_AND_PRINT (factor_recombination, |
---|
[ab547e2] | 995 | "time for factor recombination: "); |
---|
| 996 | |
---|
| 997 | if (earlySuccess) |
---|
| 998 | factors= Union (factors, earlyFactors); |
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| 999 | |
---|
[c79a9d] | 1000 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
[ab547e2] | 1001 | { |
---|
[c79a9d] | 1002 | int kk= Aeval.getLast().level(); |
---|
| 1003 | for (CFListIterator j= evaluation; j.hasItem(); j++, kk--) |
---|
| 1004 | { |
---|
| 1005 | if (i.getItem().level() < kk) |
---|
| 1006 | continue; |
---|
| 1007 | i.getItem()= i.getItem() (Variable (kk) - j.getItem(), kk); |
---|
| 1008 | } |
---|
[ab547e2] | 1009 | } |
---|
| 1010 | } |
---|
| 1011 | |
---|
| 1012 | if (w.level() != 1) |
---|
| 1013 | { |
---|
| 1014 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
| 1015 | iter.getItem()= swapvar (iter.getItem(), w, y); |
---|
| 1016 | } |
---|
| 1017 | |
---|
| 1018 | swap (factors, 0, 0, x); |
---|
| 1019 | append (factors, contentAFactors); |
---|
| 1020 | decompress (factors, N); |
---|
| 1021 | if (isOn (SW_RATIONAL)) |
---|
| 1022 | normalize (factors); |
---|
| 1023 | |
---|
[229530] | 1024 | delete [] leadingCoeffs2; |
---|
| 1025 | delete [] oldAeval; |
---|
| 1026 | delete [] Aeval2; |
---|
[ab547e2] | 1027 | delete[] liftBounds; |
---|
| 1028 | |
---|
| 1029 | return factors; |
---|
| 1030 | } |
---|
[d990001] | 1031 | |
---|
| 1032 | #endif |
---|