[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 | **/ |
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| 11 | /*****************************************************************************/ |
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| 12 | |
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[e4fe2b] | 13 | #include "config.h" |
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[ab547e2] | 14 | |
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| 15 | #include "assert.h" |
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| 16 | #include "debug.h" |
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| 17 | #include "timing.h" |
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| 18 | |
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[d990001] | 19 | #include "cf_algorithm.h" |
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[ab547e2] | 20 | #include "facFqFactorizeUtil.h" |
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| 21 | #include "facFactorize.h" |
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| 22 | #include "facFqFactorize.h" |
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| 23 | #include "cf_random.h" |
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| 24 | #include "facHensel.h" |
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| 25 | #include "cf_gcd_smallp.h" |
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| 26 | #include "cf_map_ext.h" |
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| 27 | #include "algext.h" |
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| 28 | #include "cf_reval.h" |
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[91788c0] | 29 | #include "facSparseHensel.h" |
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[ab547e2] | 30 | |
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[ec664a2] | 31 | TIMING_DEFINE_PRINT(fac_bi_factorize) |
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| 32 | TIMING_DEFINE_PRINT(fac_hensel_lift) |
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| 33 | TIMING_DEFINE_PRINT(fac_factor_recombination) |
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[0b618a7] | 34 | |
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[d990001] | 35 | #ifdef HAVE_NTL |
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[ab547e2] | 36 | CFList evalPoints (const CanonicalForm& F, CFList& eval, Evaluation& E) |
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| 37 | { |
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| 38 | CFList result; |
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| 39 | Variable x= Variable (1); |
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| 40 | |
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| 41 | bool found= false; |
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| 42 | CanonicalForm deriv_x, gcd_deriv; |
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[38ffb7] | 43 | CFListIterator iter; |
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[ab547e2] | 44 | do |
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| 45 | { |
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| 46 | eval.insert (F); |
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| 47 | bool bad= false; |
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| 48 | for (int i= E.max(); i >= E.min(); i--) |
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| 49 | { |
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| 50 | eval.insert (eval.getFirst()( E [i], i)); |
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| 51 | result.append (E[i]); |
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| 52 | if (degree (eval.getFirst(), i - 1) != degree (F, i - 1)) |
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| 53 | { |
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| 54 | result= CFList(); |
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| 55 | eval= CFList(); |
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| 56 | bad= true; |
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| 57 | break; |
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| 58 | } |
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| 59 | } |
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| 60 | |
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| 61 | if (bad) |
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| 62 | { |
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| 63 | E.nextpoint(); |
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| 64 | continue; |
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| 65 | } |
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| 66 | |
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| 67 | if (degree (eval.getFirst()) != degree (F, 1)) |
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| 68 | { |
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| 69 | result= CFList(); |
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| 70 | eval= CFList(); |
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| 71 | E.nextpoint(); |
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| 72 | continue; |
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| 73 | } |
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| 74 | |
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| 75 | deriv_x= deriv (eval.getFirst(), x); |
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| 76 | gcd_deriv= gcd (eval.getFirst(), deriv_x); |
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| 77 | if (degree (gcd_deriv) > 0) |
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| 78 | { |
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| 79 | result= CFList(); |
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| 80 | eval= CFList(); |
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| 81 | E.nextpoint(); |
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| 82 | continue; |
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| 83 | } |
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[38ffb7] | 84 | iter= eval; |
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| 85 | iter++; |
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| 86 | CanonicalForm contentx= content (iter.getItem(), x); |
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[ab547e2] | 87 | if (degree (contentx) > 0) |
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| 88 | { |
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| 89 | result= CFList(); |
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| 90 | eval= CFList(); |
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| 91 | E.nextpoint(); |
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| 92 | continue; |
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| 93 | } |
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| 94 | found= true; |
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| 95 | } |
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| 96 | while (!found); |
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| 97 | |
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| 98 | if (!eval.isEmpty()) |
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| 99 | eval.removeFirst(); |
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| 100 | return result; |
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| 101 | } |
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| 102 | |
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| 103 | void |
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| 104 | factorizationWRTDifferentSecondVars (const CanonicalForm& A, CFList*& Aeval, |
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| 105 | int& minFactorsLength, bool& irred, |
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| 106 | const Variable& w) |
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| 107 | { |
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| 108 | Variable x= Variable (1); |
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| 109 | minFactorsLength= 0; |
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| 110 | irred= false; |
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[38ffb7] | 111 | Variable v; |
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| 112 | CFList factors; |
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[afb6a6] | 113 | CanonicalForm LCA= LC (A,1); |
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| 114 | if (!LCA.inCoeffDomain()) |
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[ab547e2] | 115 | { |
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[afb6a6] | 116 | for (int j= 0; j < A.level() - 2; j++) |
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[ab547e2] | 117 | { |
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[afb6a6] | 118 | if (!Aeval[j].isEmpty() && (degree (LCA, j+3) > 0)) |
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| 119 | { |
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| 120 | v= Variable (Aeval[j].getFirst().level()); |
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[ab547e2] | 121 | |
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[afb6a6] | 122 | factors= ratBiSqrfFactorize (Aeval[j].getFirst(), w); |
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[ab547e2] | 123 | |
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[afb6a6] | 124 | if (factors.getFirst().inCoeffDomain()) |
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| 125 | factors.removeFirst(); |
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[ab547e2] | 126 | |
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[afb6a6] | 127 | if (minFactorsLength == 0) |
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| 128 | minFactorsLength= factors.length(); |
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| 129 | else |
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| 130 | minFactorsLength= tmin (minFactorsLength, factors.length()); |
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[ab547e2] | 131 | |
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[afb6a6] | 132 | if (factors.length() == 1) |
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| 133 | { |
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| 134 | irred= true; |
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| 135 | return; |
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| 136 | } |
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| 137 | sortList (factors, x); |
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| 138 | Aeval [j]= factors; |
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| 139 | } |
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| 140 | else if (!Aeval[j].isEmpty()) |
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[ab547e2] | 141 | { |
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[afb6a6] | 142 | Aeval[j]=CFList(); |
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[ab547e2] | 143 | } |
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| 144 | } |
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| 145 | } |
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[afb6a6] | 146 | else |
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| 147 | { |
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| 148 | for (int j= 0; j < A.level() - 2; j++) |
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| 149 | Aeval[j]= CFList(); |
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| 150 | } |
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[ab547e2] | 151 | } |
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| 152 | |
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| 153 | int |
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| 154 | testFactors (const CanonicalForm& G, const CFList& uniFactors, |
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| 155 | CanonicalForm& sqrfPartF, CFList& factors, |
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[eefc3a] | 156 | CFFList*& bufSqrfFactors, CFList& evalSqrfPartF, |
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| 157 | const CFArray& evalPoint) |
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[ab547e2] | 158 | { |
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[38ffb7] | 159 | CanonicalForm tmp; |
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| 160 | CFListIterator j; |
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[ab547e2] | 161 | for (CFListIterator i= uniFactors; i.hasItem(); i++) |
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| 162 | { |
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[38ffb7] | 163 | tmp= i.getItem(); |
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[ab547e2] | 164 | if (i.hasItem()) |
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| 165 | i++; |
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| 166 | else |
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| 167 | break; |
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[38ffb7] | 168 | for (j= i; j.hasItem(); j++) |
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[ab547e2] | 169 | { |
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| 170 | if (tmp == j.getItem()) |
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| 171 | return 0; |
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| 172 | } |
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| 173 | } |
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| 174 | |
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| 175 | CanonicalForm F= G; |
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| 176 | CFFList sqrfFactorization= sqrFree (F); |
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| 177 | |
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| 178 | sqrfPartF= 1; |
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| 179 | for (CFFListIterator i= sqrfFactorization; i.hasItem(); i++) |
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| 180 | sqrfPartF *= i.getItem().factor(); |
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| 181 | |
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[eefc3a] | 182 | evalSqrfPartF= evaluateAtEval (sqrfPartF, evalPoint); |
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[ab547e2] | 183 | |
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[eefc3a] | 184 | CanonicalForm test= evalSqrfPartF.getFirst() (evalPoint[0], 2); |
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[ab547e2] | 185 | |
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| 186 | if (degree (test) != degree (sqrfPartF, 1)) |
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| 187 | return 0; |
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| 188 | |
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| 189 | CFFList sqrfFactors; |
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| 190 | CFList tmp2; |
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| 191 | int k= 0; |
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| 192 | factors= uniFactors; |
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[38ffb7] | 193 | CFFListIterator iter; |
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[ab547e2] | 194 | for (CFListIterator i= factors; i.hasItem(); i++, k++) |
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| 195 | { |
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[38ffb7] | 196 | tmp= 1; |
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[ab547e2] | 197 | sqrfFactors= sqrFree (i.getItem()); |
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| 198 | |
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[38ffb7] | 199 | for (iter= sqrfFactors; iter.hasItem(); iter++) |
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[ab547e2] | 200 | { |
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[38ffb7] | 201 | tmp2.append (iter.getItem().factor()); |
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| 202 | tmp *= iter.getItem().factor(); |
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[ab547e2] | 203 | } |
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| 204 | i.getItem()= tmp/Lc(tmp); |
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| 205 | bufSqrfFactors [k]= sqrfFactors; |
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| 206 | } |
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| 207 | |
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| 208 | for (int i= 0; i < factors.length() - 1; i++) |
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| 209 | { |
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| 210 | for (int k= i + 1; k < factors.length(); k++) |
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| 211 | { |
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| 212 | gcdFreeBasis (bufSqrfFactors [i], bufSqrfFactors[k]); |
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| 213 | } |
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| 214 | } |
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| 215 | |
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| 216 | factors= CFList(); |
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| 217 | for (int i= 0; i < uniFactors.length(); i++) |
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| 218 | { |
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| 219 | if (i == 0) |
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| 220 | { |
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[38ffb7] | 221 | for (iter= bufSqrfFactors [i]; iter.hasItem(); iter++) |
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[ab547e2] | 222 | { |
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[327efa2] | 223 | if (iter.getItem().factor().inCoeffDomain()) |
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| 224 | continue; |
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[38ffb7] | 225 | iter.getItem()= CFFactor (iter.getItem().factor()/ |
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| 226 | Lc (iter.getItem().factor()), |
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| 227 | iter.getItem().exp()); |
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| 228 | factors.append (iter.getItem().factor()); |
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[ab547e2] | 229 | } |
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| 230 | } |
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| 231 | else |
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| 232 | { |
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[38ffb7] | 233 | for (iter= bufSqrfFactors [i]; iter.hasItem(); iter++) |
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[ab547e2] | 234 | { |
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[327efa2] | 235 | if (iter.getItem().factor().inCoeffDomain()) |
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| 236 | continue; |
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[38ffb7] | 237 | iter.getItem()= CFFactor (iter.getItem().factor()/ |
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| 238 | Lc (iter.getItem().factor()), |
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| 239 | iter.getItem().exp()); |
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| 240 | if (!find (factors, iter.getItem().factor())) |
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| 241 | factors.append (iter.getItem().factor()); |
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[ab547e2] | 242 | } |
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| 243 | } |
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| 244 | } |
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| 245 | |
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| 246 | test= prod (factors); |
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[eefc3a] | 247 | tmp= evalSqrfPartF.getFirst() (evalPoint[0],2); |
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[ab547e2] | 248 | if (test/Lc (test) != tmp/Lc (tmp)) |
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| 249 | return 0; |
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| 250 | else |
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| 251 | return 1; |
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| 252 | } |
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| 253 | |
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| 254 | CFList |
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| 255 | precomputeLeadingCoeff (const CanonicalForm& LCF, const CFList& LCFFactors, |
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| 256 | const CFList& evaluation,CFList*& differentSecondVarLCs, |
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| 257 | int length, Variable& y |
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| 258 | ) |
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| 259 | { |
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| 260 | y= Variable (1); |
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| 261 | if (LCF.inCoeffDomain()) |
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| 262 | { |
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| 263 | CFList result; |
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| 264 | for (int i= 1; i <= LCFFactors.length() + 1; i++) |
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| 265 | result.append (1); |
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| 266 | return result; |
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| 267 | } |
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| 268 | |
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[8256fd] | 269 | CFMap N, M; |
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[8a30b1] | 270 | CFArray dummy= CFArray (2); |
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[8256fd] | 271 | dummy [0]= LCF; |
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[8a30b1] | 272 | dummy [1]= Variable (2); |
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[8256fd] | 273 | compress (dummy, M, N); |
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| 274 | CanonicalForm F= M (LCF); |
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[ab547e2] | 275 | if (LCF.isUnivariate()) |
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| 276 | { |
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| 277 | CFList result; |
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| 278 | int LCFLevel= LCF.level(); |
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| 279 | bool found= false; |
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| 280 | if (LCFLevel == 2) |
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| 281 | { |
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| 282 | //bivariate leading coefficients are already the true leading coefficients |
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| 283 | result= LCFFactors; |
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| 284 | found= true; |
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| 285 | } |
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| 286 | else |
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| 287 | { |
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[38ffb7] | 288 | CFListIterator j; |
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[ab547e2] | 289 | for (int i= 0; i < length; i++) |
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| 290 | { |
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[38ffb7] | 291 | for (j= differentSecondVarLCs[i]; j.hasItem(); j++) |
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[ab547e2] | 292 | { |
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| 293 | if (j.getItem().level() == LCFLevel) |
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| 294 | { |
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| 295 | found= true; |
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| 296 | break; |
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| 297 | } |
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| 298 | } |
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| 299 | if (found) |
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| 300 | { |
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| 301 | result= differentSecondVarLCs [i]; |
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| 302 | break; |
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| 303 | } |
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| 304 | } |
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| 305 | if (!found) |
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| 306 | result= LCFFactors; |
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| 307 | } |
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| 308 | if (found) |
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| 309 | result.insert (Lc (LCF)); |
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| 310 | else |
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| 311 | result.append (LCF); |
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| 312 | return result; |
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| 313 | } |
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| 314 | |
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| 315 | CFList factors= LCFFactors; |
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| 316 | |
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| 317 | for (CFListIterator i= factors; i.hasItem(); i++) |
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[8256fd] | 318 | i.getItem()= M (i.getItem()); |
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[ab547e2] | 319 | |
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| 320 | CanonicalForm sqrfPartF; |
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| 321 | CFFList * bufSqrfFactors= new CFFList [factors.length()]; |
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[eefc3a] | 322 | CFList evalSqrfPartF, bufFactors; |
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| 323 | CFArray evalPoint= CFArray (evaluation.length() - 1); |
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[8a30b1] | 324 | CFArray buf= CFArray (evaluation.length()); |
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| 325 | CFArray swap= CFArray (evaluation.length()); |
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[eefc3a] | 326 | CFListIterator iter= evaluation; |
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[8a30b1] | 327 | CanonicalForm vars=getVars (LCF); |
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| 328 | for (int i= evaluation.length() +1; i > 1; i--, iter++) |
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| 329 | { |
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| 330 | buf[i-2]=iter.getItem(); |
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| 331 | if (degree (vars, i) > 0) |
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| 332 | swap[M(Variable (i)).level()-1]=buf[i-2]; |
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| 333 | } |
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| 334 | buf= swap; |
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| 335 | for (int i= 0; i < evaluation.length() - 1; i++) |
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| 336 | evalPoint[i]= buf[i+1]; |
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| 337 | |
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[ab547e2] | 338 | //TODO sqrfPartF einmal berechnen nicht stÀndig |
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| 339 | int pass= testFactors (F, factors, sqrfPartF, |
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[eefc3a] | 340 | bufFactors, bufSqrfFactors, evalSqrfPartF, evalPoint); |
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[ab547e2] | 341 | |
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| 342 | bool foundDifferent= false; |
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| 343 | Variable z; |
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| 344 | Variable x= y; |
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| 345 | int j= 0; |
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| 346 | if (!pass) |
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| 347 | { |
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[7a1151] | 348 | int lev= 0; |
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[8a30b1] | 349 | CanonicalForm bufF; |
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| 350 | CFList bufBufFactors; |
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[ab547e2] | 351 | for (int i= 0; i < length; i++) |
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| 352 | { |
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| 353 | if (!differentSecondVarLCs [i].isEmpty()) |
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| 354 | { |
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| 355 | bool allConstant= true; |
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[38ffb7] | 356 | for (iter= differentSecondVarLCs[i]; iter.hasItem(); iter++) |
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[ab547e2] | 357 | { |
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| 358 | if (!iter.getItem().inCoeffDomain()) |
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| 359 | { |
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| 360 | allConstant= false; |
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| 361 | y= Variable (iter.getItem().level()); |
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[8256fd] | 362 | lev= M(y).level(); |
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[ab547e2] | 363 | } |
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| 364 | } |
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| 365 | if (allConstant) |
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| 366 | continue; |
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| 367 | |
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| 368 | bufFactors= differentSecondVarLCs [i]; |
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[38ffb7] | 369 | for (iter= bufFactors; iter.hasItem(); iter++) |
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[ab547e2] | 370 | iter.getItem()= swapvar (iter.getItem(), x, y); |
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[38ffb7] | 371 | bufF= F; |
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[8256fd] | 372 | z= Variable (lev); |
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[ab547e2] | 373 | bufF= swapvar (bufF, x, z); |
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[38ffb7] | 374 | bufBufFactors= bufFactors; |
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[eefc3a] | 375 | evalPoint= CFArray (evaluation.length() - 1); |
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[8a30b1] | 376 | for (int k= 0; k < evaluation.length()-1; k++) |
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[eefc3a] | 377 | { |
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[8a30b1] | 378 | if (k+1 != lev) |
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| 379 | evalPoint[k]= buf[k+1]; |
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| 380 | else |
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| 381 | evalPoint[k]= buf[0]; |
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[eefc3a] | 382 | } |
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[ab547e2] | 383 | pass= testFactors (bufF, bufBufFactors, sqrfPartF, bufFactors, |
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[eefc3a] | 384 | bufSqrfFactors, evalSqrfPartF, evalPoint); |
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[ab547e2] | 385 | if (pass) |
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| 386 | { |
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| 387 | foundDifferent= true; |
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| 388 | F= bufF; |
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| 389 | CFList l= factors; |
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[38ffb7] | 390 | for (iter= l; iter.hasItem(); iter++) |
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[ab547e2] | 391 | iter.getItem()= swapvar (iter.getItem(), x, y); |
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| 392 | differentSecondVarLCs [i]= l; |
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| 393 | j= i; |
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| 394 | break; |
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| 395 | } |
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| 396 | if (!pass && i == length - 1) |
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| 397 | { |
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| 398 | CFList result; |
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| 399 | result.append (LCF); |
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| 400 | for (int j= 1; j <= factors.length(); j++) |
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| 401 | result.append (LCF); |
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| 402 | y= Variable (1); |
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[229530] | 403 | delete [] bufSqrfFactors; |
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[ab547e2] | 404 | return result; |
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| 405 | } |
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| 406 | } |
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| 407 | } |
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| 408 | } |
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| 409 | if (!pass) |
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| 410 | { |
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| 411 | CFList result; |
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| 412 | result.append (LCF); |
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| 413 | for (int j= 1; j <= factors.length(); j++) |
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| 414 | result.append (LCF); |
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| 415 | y= Variable (1); |
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[229530] | 416 | delete [] bufSqrfFactors; |
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[ab547e2] | 417 | return result; |
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| 418 | } |
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| 419 | else |
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| 420 | factors= bufFactors; |
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| 421 | |
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| 422 | |
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| 423 | bufFactors= factors; |
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[eefc3a] | 424 | CFList evaluation2; |
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[8a30b1] | 425 | for (int i= 0; i < F.level()-1; i++) |
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| 426 | evaluation2.insert (evalPoint[i]); |
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[327efa2] | 427 | |
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[ec16f0] | 428 | CFList interMedResult; |
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| 429 | CanonicalForm oldSqrfPartF= sqrfPartF; |
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[8a30b1] | 430 | sqrfPartF= shift2Zero (sqrfPartF, evalSqrfPartF, evaluation2); |
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[327efa2] | 431 | if (factors.length() > 1) |
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| 432 | { |
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[ec16f0] | 433 | CanonicalForm LC1= LC (oldSqrfPartF, 1); |
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| 434 | CFList leadingCoeffs; |
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[327efa2] | 435 | for (int i= 0; i < factors.length(); i++) |
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[ec16f0] | 436 | leadingCoeffs.append (LC1); |
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| 437 | |
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[8a30b1] | 438 | CFList LC1eval= evaluateAtEval (LC1, evaluation2,2); |
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[ec16f0] | 439 | CFList oldFactors= factors; |
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| 440 | for (CFListIterator i= oldFactors; i.hasItem(); i++) |
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| 441 | i.getItem() *= LC1eval.getFirst()/Lc (i.getItem()); |
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| 442 | |
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| 443 | bool success= false; |
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[64b824] | 444 | CanonicalForm oldSqrfPartFPowLC= oldSqrfPartF*power(LC1,factors.length()-1); |
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| 445 | if (size (oldSqrfPartFPowLC)/getNumVars (oldSqrfPartFPowLC) < 500 && |
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| 446 | LucksWangSparseHeuristic (oldSqrfPartFPowLC, |
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[8a30b1] | 447 | oldFactors, 2, leadingCoeffs, factors)) |
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[eefc3a] | 448 | { |
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[ec16f0] | 449 | interMedResult= recoverFactors (oldSqrfPartF, factors); |
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| 450 | if (oldFactors.length() == interMedResult.length()) |
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| 451 | success= true; |
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[eefc3a] | 452 | } |
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[ec16f0] | 453 | if (!success) |
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| 454 | { |
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| 455 | LC1= LC (evalSqrfPartF.getFirst(), 1); |
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[327efa2] | 456 | |
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[ec16f0] | 457 | CFArray leadingCoeffs= CFArray (factors.length()); |
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| 458 | for (int i= 0; i < factors.length(); i++) |
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| 459 | leadingCoeffs[i]= LC1; |
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[327efa2] | 460 | |
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[ec16f0] | 461 | for (CFListIterator i= factors; i.hasItem(); i++) |
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| 462 | i.getItem() *= LC1 (0,2)/Lc (i.getItem()); |
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| 463 | factors.insert (1); |
---|
[327efa2] | 464 | |
---|
[ec16f0] | 465 | CanonicalForm |
---|
| 466 | newSqrfPartF= evalSqrfPartF.getFirst()*power (LC1, factors.length() - 2); |
---|
[327efa2] | 467 | |
---|
[ec16f0] | 468 | int liftBound= degree (newSqrfPartF,2) + 1; |
---|
| 469 | |
---|
| 470 | CFMatrix M= CFMatrix (liftBound, factors.length() - 1); |
---|
| 471 | CFArray Pi; |
---|
| 472 | CFList diophant; |
---|
[81d96c] | 473 | nonMonicHenselLift12 (newSqrfPartF, factors, liftBound, Pi, diophant, M, |
---|
| 474 | leadingCoeffs, false); |
---|
[ec16f0] | 475 | |
---|
| 476 | if (sqrfPartF.level() > 2) |
---|
[327efa2] | 477 | { |
---|
[ec16f0] | 478 | int* liftBounds= new int [sqrfPartF.level() - 1]; |
---|
| 479 | liftBounds [0]= liftBound; |
---|
| 480 | bool noOneToOne= false; |
---|
| 481 | CFList *leadingCoeffs2= new CFList [sqrfPartF.level()-2]; |
---|
| 482 | LC1= LC (evalSqrfPartF.getLast(), 1); |
---|
| 483 | CFList LCs; |
---|
| 484 | for (int i= 0; i < factors.length(); i++) |
---|
| 485 | LCs.append (LC1); |
---|
| 486 | leadingCoeffs2 [sqrfPartF.level() - 3]= LCs; |
---|
| 487 | for (int i= sqrfPartF.level() - 1; i > 2; i--) |
---|
| 488 | { |
---|
| 489 | for (CFListIterator j= LCs; j.hasItem(); j++) |
---|
| 490 | j.getItem()= j.getItem() (0, i + 1); |
---|
| 491 | leadingCoeffs2 [i - 3]= LCs; |
---|
| 492 | } |
---|
| 493 | sqrfPartF *= power (LC1, factors.length()-1); |
---|
| 494 | |
---|
| 495 | int liftBoundsLength= sqrfPartF.level() - 1; |
---|
| 496 | for (int i= 1; i < liftBoundsLength; i++) |
---|
| 497 | liftBounds [i]= degree (sqrfPartF, i + 2) + 1; |
---|
| 498 | evalSqrfPartF= evaluateAtZero (sqrfPartF); |
---|
| 499 | evalSqrfPartF.removeFirst(); |
---|
| 500 | factors= nonMonicHenselLift (evalSqrfPartF, factors, leadingCoeffs2, |
---|
| 501 | diophant, Pi, liftBounds, sqrfPartF.level() - 1, noOneToOne); |
---|
| 502 | delete [] leadingCoeffs2; |
---|
| 503 | delete [] liftBounds; |
---|
[327efa2] | 504 | } |
---|
[ec16f0] | 505 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
[8a30b1] | 506 | iter.getItem()= reverseShift (iter.getItem(), evaluation2); |
---|
[ec16f0] | 507 | |
---|
| 508 | interMedResult= |
---|
[8a30b1] | 509 | recoverFactors (reverseShift(evalSqrfPartF.getLast(),evaluation2), |
---|
[ec16f0] | 510 | factors); |
---|
[327efa2] | 511 | } |
---|
| 512 | } |
---|
| 513 | else |
---|
[ec16f0] | 514 | { |
---|
[8256fd] | 515 | CanonicalForm contF=content (oldSqrfPartF,1); |
---|
| 516 | factors= CFList (oldSqrfPartF/contF); |
---|
[ec16f0] | 517 | interMedResult= recoverFactors (oldSqrfPartF, factors); |
---|
| 518 | } |
---|
[ab547e2] | 519 | |
---|
| 520 | CFList result; |
---|
[38ffb7] | 521 | CFFListIterator k; |
---|
| 522 | CanonicalForm tmp; |
---|
[ab547e2] | 523 | for (int i= 0; i < LCFFactors.length(); i++) |
---|
| 524 | { |
---|
[38ffb7] | 525 | tmp= 1; |
---|
| 526 | for (k= bufSqrfFactors[i]; k.hasItem(); k++) |
---|
[ab547e2] | 527 | { |
---|
| 528 | int pos= findItem (bufFactors, k.getItem().factor()); |
---|
| 529 | if (pos) |
---|
| 530 | tmp *= power (getItem (interMedResult, pos), k.getItem().exp()); |
---|
| 531 | } |
---|
| 532 | result.append (tmp); |
---|
| 533 | } |
---|
| 534 | |
---|
| 535 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
| 536 | { |
---|
| 537 | F /= i.getItem(); |
---|
| 538 | if (foundDifferent) |
---|
| 539 | i.getItem()= swapvar (i.getItem(), x, z); |
---|
| 540 | i.getItem()= N (i.getItem()); |
---|
| 541 | } |
---|
| 542 | |
---|
| 543 | if (foundDifferent) |
---|
| 544 | { |
---|
| 545 | CFList l= differentSecondVarLCs [j]; |
---|
| 546 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 547 | i.getItem()= swapvar (i.getItem(), y, z); |
---|
| 548 | differentSecondVarLCs [j]= l; |
---|
| 549 | F= swapvar (F, x, z); |
---|
| 550 | } |
---|
| 551 | |
---|
| 552 | result.insert (N (F)); |
---|
| 553 | |
---|
| 554 | result= distributeContent (result, differentSecondVarLCs, length); |
---|
| 555 | |
---|
| 556 | if (!result.getFirst().inCoeffDomain()) |
---|
| 557 | { |
---|
| 558 | CFListIterator i= result; |
---|
| 559 | CanonicalForm tmp; |
---|
| 560 | if (foundDifferent) |
---|
| 561 | i.getItem()= swapvar (i.getItem(), Variable (2), y); |
---|
| 562 | |
---|
| 563 | tmp= i.getItem(); |
---|
| 564 | |
---|
| 565 | i++; |
---|
| 566 | for (; i.hasItem(); i++) |
---|
| 567 | { |
---|
| 568 | if (foundDifferent) |
---|
| 569 | i.getItem()= swapvar (i.getItem(), Variable (2), y)*tmp; |
---|
| 570 | else |
---|
| 571 | i.getItem() *= tmp; |
---|
| 572 | } |
---|
| 573 | } |
---|
| 574 | else |
---|
| 575 | y= Variable (1); |
---|
| 576 | |
---|
[229530] | 577 | delete [] bufSqrfFactors; |
---|
| 578 | |
---|
[ab547e2] | 579 | return result; |
---|
| 580 | } |
---|
| 581 | |
---|
| 582 | |
---|
| 583 | CFList |
---|
| 584 | multiFactorize (const CanonicalForm& F, const Variable& v) |
---|
| 585 | { |
---|
| 586 | if (F.inCoeffDomain()) |
---|
| 587 | return CFList (F); |
---|
| 588 | |
---|
| 589 | // compress and find main Variable |
---|
| 590 | CFMap N; |
---|
| 591 | CanonicalForm A= myCompress (F, N); |
---|
| 592 | |
---|
| 593 | //univariate case |
---|
| 594 | if (F.isUnivariate()) |
---|
| 595 | { |
---|
[0e6668] | 596 | CFList result; |
---|
| 597 | if (v.level() != 1) |
---|
| 598 | result= conv (factorize (F, v)); |
---|
| 599 | else |
---|
| 600 | result= conv (factorize (F,true)); |
---|
[ab547e2] | 601 | if (result.getFirst().inCoeffDomain()) |
---|
| 602 | result.removeFirst(); |
---|
| 603 | return result; |
---|
| 604 | } |
---|
| 605 | |
---|
| 606 | //bivariate case |
---|
| 607 | if (A.level() == 2) |
---|
| 608 | { |
---|
| 609 | CFList buf= biFactorize (F, v); |
---|
| 610 | return buf; |
---|
| 611 | } |
---|
| 612 | |
---|
| 613 | Variable x= Variable (1); |
---|
| 614 | Variable y= Variable (2); |
---|
| 615 | |
---|
| 616 | // remove content |
---|
| 617 | CFList contentAi; |
---|
| 618 | CanonicalForm lcmCont= lcmContent (A, contentAi); |
---|
| 619 | A /= lcmCont; |
---|
| 620 | |
---|
| 621 | // trivial after content removal |
---|
| 622 | CFList contentAFactors; |
---|
| 623 | if (A.inCoeffDomain()) |
---|
| 624 | { |
---|
| 625 | for (CFListIterator i= contentAi; i.hasItem(); i++) |
---|
| 626 | { |
---|
| 627 | if (i.getItem().inCoeffDomain()) |
---|
| 628 | continue; |
---|
| 629 | else |
---|
| 630 | { |
---|
| 631 | lcmCont /= i.getItem(); |
---|
| 632 | contentAFactors= |
---|
| 633 | Union (multiFactorize (lcmCont, v), |
---|
| 634 | multiFactorize (i.getItem(), v)); |
---|
| 635 | break; |
---|
| 636 | } |
---|
| 637 | } |
---|
| 638 | decompress (contentAFactors, N); |
---|
| 639 | if (isOn (SW_RATIONAL)) |
---|
| 640 | normalize (contentAFactors); |
---|
| 641 | return contentAFactors; |
---|
| 642 | } |
---|
| 643 | |
---|
| 644 | // factorize content |
---|
| 645 | contentAFactors= multiFactorize (lcmCont, v); |
---|
| 646 | |
---|
| 647 | // univariate after content removal |
---|
| 648 | CFList factors; |
---|
| 649 | if (A.isUnivariate ()) |
---|
| 650 | { |
---|
[0e6668] | 651 | if (v.level() != 1) |
---|
| 652 | factors= conv (factorize (A, v)); |
---|
| 653 | else |
---|
| 654 | factors= conv (factorize (A,true)); |
---|
[ab547e2] | 655 | append (factors, contentAFactors); |
---|
| 656 | decompress (factors, N); |
---|
| 657 | return factors; |
---|
| 658 | } |
---|
| 659 | |
---|
| 660 | // check main variable |
---|
| 661 | CFList Aeval, list, evaluation, bufEvaluation, bufAeval; |
---|
| 662 | int factorNums= 3; |
---|
| 663 | CanonicalForm bivarEval; |
---|
| 664 | CFList biFactors, bufBiFactors; |
---|
| 665 | CanonicalForm evalPoly; |
---|
| 666 | int lift, bufLift; |
---|
| 667 | CFList* bufAeval2= new CFList [A.level() - 2]; |
---|
| 668 | CFList* Aeval2= new CFList [A.level() - 2]; |
---|
| 669 | int counter; |
---|
| 670 | int differentSecondVar= 0; |
---|
| 671 | CanonicalForm bufA; |
---|
| 672 | // several bivariate factorizations |
---|
| 673 | REvaluation E (2, A.level(), IntRandom (25)); |
---|
| 674 | for (int i= 0; i < factorNums; i++) |
---|
| 675 | { |
---|
| 676 | counter= 0; |
---|
| 677 | bufA= A; |
---|
| 678 | bufAeval= CFList(); |
---|
| 679 | bufEvaluation= evalPoints (bufA, bufAeval, E); |
---|
| 680 | E.nextpoint(); |
---|
| 681 | evalPoly= 0; |
---|
| 682 | |
---|
| 683 | bivarEval= bufEvaluation.getLast(); |
---|
| 684 | |
---|
| 685 | evaluationWRTDifferentSecondVars (bufAeval2, bufEvaluation, A); |
---|
| 686 | |
---|
| 687 | for (int j= 0; j < A.level() - 1; j++) |
---|
| 688 | { |
---|
| 689 | if (!bufAeval2[j].isEmpty()) |
---|
| 690 | counter++; |
---|
| 691 | } |
---|
| 692 | |
---|
| 693 | bufLift= degree (A, y) + 1 + degree (LC(A, x), y); |
---|
| 694 | |
---|
[ec664a2] | 695 | TIMING_START (fac_bi_factorize); |
---|
[ab547e2] | 696 | bufBiFactors= ratBiSqrfFactorize (bufAeval.getFirst(), v); |
---|
[ec664a2] | 697 | TIMING_END_AND_PRINT (fac_bi_factorize, |
---|
[ab547e2] | 698 | "time for bivariate factorization: "); |
---|
| 699 | bufBiFactors.removeFirst(); |
---|
| 700 | |
---|
| 701 | if (bufBiFactors.length() == 1) |
---|
| 702 | { |
---|
| 703 | factors.append (A); |
---|
| 704 | appendSwapDecompress (factors, contentAFactors, N, 0, 0, x); |
---|
| 705 | if (isOn (SW_RATIONAL)) |
---|
| 706 | normalize (factors); |
---|
| 707 | delete [] bufAeval2; |
---|
| 708 | delete [] Aeval2; |
---|
| 709 | return factors; |
---|
| 710 | } |
---|
| 711 | |
---|
| 712 | if (i == 0) |
---|
| 713 | { |
---|
| 714 | Aeval= bufAeval; |
---|
| 715 | evaluation= bufEvaluation; |
---|
| 716 | biFactors= bufBiFactors; |
---|
| 717 | lift= bufLift; |
---|
| 718 | for (int j= 0; j < A.level() - 2; j++) |
---|
| 719 | Aeval2 [j]= bufAeval2 [j]; |
---|
| 720 | differentSecondVar= counter; |
---|
| 721 | } |
---|
| 722 | else |
---|
| 723 | { |
---|
| 724 | if (bufBiFactors.length() < biFactors.length() || |
---|
| 725 | ((bufLift < lift) && (bufBiFactors.length() == biFactors.length())) || |
---|
| 726 | counter > differentSecondVar) |
---|
| 727 | { |
---|
| 728 | Aeval= bufAeval; |
---|
| 729 | evaluation= bufEvaluation; |
---|
| 730 | biFactors= bufBiFactors; |
---|
| 731 | lift= bufLift; |
---|
| 732 | for (int j= 0; j < A.level() - 2; j++) |
---|
| 733 | Aeval2 [j]= bufAeval2 [j]; |
---|
| 734 | differentSecondVar= counter; |
---|
| 735 | } |
---|
| 736 | } |
---|
| 737 | int k= 0; |
---|
| 738 | for (CFListIterator j= bufEvaluation; j.hasItem(); j++, k++) |
---|
| 739 | evalPoly += j.getItem()*power (x, k); |
---|
| 740 | list.append (evalPoly); |
---|
| 741 | } |
---|
| 742 | |
---|
| 743 | delete [] bufAeval2; |
---|
| 744 | |
---|
| 745 | sortList (biFactors, x); |
---|
| 746 | |
---|
| 747 | int minFactorsLength; |
---|
| 748 | bool irred= false; |
---|
| 749 | factorizationWRTDifferentSecondVars (A, Aeval2, minFactorsLength, irred, v); |
---|
| 750 | |
---|
| 751 | if (irred) |
---|
| 752 | { |
---|
| 753 | factors.append (A); |
---|
| 754 | appendSwapDecompress (factors, contentAFactors, N, 0, 0, x); |
---|
| 755 | if (isOn (SW_RATIONAL)) |
---|
| 756 | normalize (factors); |
---|
| 757 | delete [] Aeval2; |
---|
| 758 | return factors; |
---|
| 759 | } |
---|
| 760 | |
---|
| 761 | if (minFactorsLength == 0) |
---|
| 762 | minFactorsLength= biFactors.length(); |
---|
| 763 | else if (biFactors.length() > minFactorsLength) |
---|
| 764 | refineBiFactors (A, biFactors, Aeval2, evaluation, minFactorsLength); |
---|
| 765 | |
---|
[8681bf] | 766 | if (differentSecondVar == A.level() - 2 && getNumVars(LC(A,1)) == A.level()-1) |
---|
[6036d90] | 767 | { |
---|
| 768 | bool zeroOccured= false; |
---|
| 769 | for (CFListIterator iter= evaluation; iter.hasItem(); iter++) |
---|
| 770 | { |
---|
| 771 | if (iter.getItem().isZero()) |
---|
| 772 | { |
---|
| 773 | zeroOccured= true; |
---|
| 774 | break; |
---|
| 775 | } |
---|
| 776 | } |
---|
| 777 | if (!zeroOccured) |
---|
| 778 | { |
---|
[8256fd] | 779 | factors= sparseHeuristic (A, biFactors, Aeval2, evaluation, |
---|
| 780 | minFactorsLength); |
---|
[6036d90] | 781 | if (factors.length() == biFactors.length()) |
---|
| 782 | { |
---|
| 783 | appendSwapDecompress (factors, contentAFactors, N, 0, 0, x); |
---|
| 784 | normalize (factors); |
---|
| 785 | delete [] Aeval2; |
---|
| 786 | return factors; |
---|
| 787 | } |
---|
| 788 | else |
---|
| 789 | factors= CFList(); |
---|
| 790 | //TODO case where factors.length() > 0 |
---|
| 791 | } |
---|
| 792 | } |
---|
| 793 | |
---|
[ab547e2] | 794 | CFList uniFactors= buildUniFactors (biFactors, evaluation.getLast(), y); |
---|
| 795 | |
---|
| 796 | CFList * oldAeval= new CFList [A.level() - 2]; |
---|
| 797 | for (int i= 0; i < A.level() - 2; i++) |
---|
| 798 | oldAeval[i]= Aeval2[i]; |
---|
| 799 | |
---|
| 800 | getLeadingCoeffs (A, Aeval2, uniFactors, evaluation); |
---|
| 801 | |
---|
| 802 | CFList biFactorsLCs; |
---|
| 803 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
| 804 | biFactorsLCs.append (LC (i.getItem(), 1)); |
---|
| 805 | |
---|
| 806 | Variable w; |
---|
| 807 | CFList leadingCoeffs= precomputeLeadingCoeff (LC (A, 1), biFactorsLCs, |
---|
| 808 | evaluation, Aeval2, A.level() - 2, w); |
---|
| 809 | |
---|
| 810 | if (w.level() != 1) |
---|
| 811 | { |
---|
| 812 | A= swapvar (A, y, w); |
---|
| 813 | int i= A.level(); |
---|
| 814 | CanonicalForm evalPoint; |
---|
| 815 | for (CFListIterator iter= evaluation; iter.hasItem(); iter++, i--) |
---|
| 816 | { |
---|
| 817 | if (i == w.level()) |
---|
| 818 | { |
---|
| 819 | evalPoint= iter.getItem(); |
---|
| 820 | iter.getItem()= evaluation.getLast(); |
---|
| 821 | evaluation.removeLast(); |
---|
| 822 | evaluation.append (evalPoint); |
---|
| 823 | break; |
---|
| 824 | } |
---|
| 825 | } |
---|
[8256fd] | 826 | for (i= 0; i < A.level() - 2; i++) |
---|
| 827 | { |
---|
| 828 | if (oldAeval[i].isEmpty()) |
---|
| 829 | continue; |
---|
| 830 | if (oldAeval[i].getFirst().level() == w.level()) |
---|
| 831 | { |
---|
| 832 | CFArray tmp= copy (oldAeval[i]); |
---|
| 833 | for (int ii= 0; ii < tmp.size(); ii++) |
---|
| 834 | tmp[ii]= swapvar (tmp[ii], w, y); |
---|
| 835 | CFArray tmp2= CFArray (tmp.size()); |
---|
| 836 | CanonicalForm buf; |
---|
| 837 | for (int ii= 0; ii < tmp.size(); ii++) |
---|
| 838 | { |
---|
| 839 | buf= tmp[ii] (evaluation.getLast(),y); |
---|
| 840 | buf /= Lc (buf); |
---|
| 841 | tmp2[findItem (uniFactors, buf)-1]=tmp[ii]; |
---|
| 842 | } |
---|
| 843 | biFactors= CFList(); |
---|
| 844 | for (int j= 0; j < tmp2.size(); j++) |
---|
| 845 | biFactors.append (tmp2[j]); |
---|
| 846 | } |
---|
| 847 | } |
---|
[ab547e2] | 848 | } |
---|
| 849 | |
---|
[eefc3a] | 850 | CFListIterator iter; |
---|
[ab547e2] | 851 | CanonicalForm oldA= A; |
---|
| 852 | CFList oldBiFactors= biFactors; |
---|
| 853 | if (!leadingCoeffs.getFirst().inCoeffDomain()) |
---|
| 854 | { |
---|
| 855 | CanonicalForm tmp= power (leadingCoeffs.getFirst(), biFactors.length() - 1); |
---|
| 856 | A *= tmp; |
---|
| 857 | Aeval= evaluateAtZero (A); |
---|
| 858 | tmp= leadingCoeffs.getFirst(); |
---|
[eefc3a] | 859 | iter= evaluation; |
---|
| 860 | for (int i= A.level(); i > 2; i--, iter++) |
---|
| 861 | tmp= tmp (iter.getItem(), i); |
---|
[ab547e2] | 862 | if (!tmp.inCoeffDomain()) |
---|
| 863 | { |
---|
| 864 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
| 865 | { |
---|
| 866 | i.getItem() *= tmp/LC (i.getItem(), 1); |
---|
| 867 | i.getItem() /= Lc (i.getItem()); |
---|
| 868 | } |
---|
| 869 | } |
---|
| 870 | } |
---|
| 871 | |
---|
| 872 | leadingCoeffs.removeFirst(); |
---|
| 873 | |
---|
| 874 | //prepare leading coefficients |
---|
| 875 | CFList* leadingCoeffs2= new CFList [A.level() - 2]; |
---|
[eefc3a] | 876 | prepareLeadingCoeffs (leadingCoeffs2, A.level(), leadingCoeffs, biFactors, |
---|
| 877 | evaluation); |
---|
| 878 | |
---|
| 879 | |
---|
| 880 | Aeval= evaluateAtEval (A, evaluation, 2); |
---|
| 881 | |
---|
| 882 | CanonicalForm hh= Lc (Aeval.getFirst()); |
---|
| 883 | |
---|
| 884 | for (CFListIterator i= Aeval; i.hasItem(); i++) |
---|
| 885 | i.getItem() /= hh; |
---|
| 886 | |
---|
| 887 | A /= hh; |
---|
| 888 | |
---|
[64b824] | 889 | if (size (A)/getNumVars (A) < 500 && |
---|
| 890 | LucksWangSparseHeuristic (A, biFactors, 2, leadingCoeffs2 [A.level() - 3], |
---|
| 891 | factors)) |
---|
[4fe8a3] | 892 | { |
---|
| 893 | int check= factors.length(); |
---|
| 894 | factors= recoverFactors (A, factors); |
---|
| 895 | |
---|
| 896 | if (check == factors.length()) |
---|
| 897 | { |
---|
[8256fd] | 898 | |
---|
| 899 | if (w.level() != 1) |
---|
| 900 | { |
---|
| 901 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
| 902 | iter.getItem()= swapvar (iter.getItem(), w, y); |
---|
| 903 | } |
---|
| 904 | |
---|
[4fe8a3] | 905 | appendSwapDecompress (factors, contentAFactors, N, 0, 0, x); |
---|
| 906 | normalize (factors); |
---|
| 907 | delete [] Aeval2; |
---|
| 908 | return factors; |
---|
| 909 | } |
---|
| 910 | else |
---|
| 911 | factors= CFList(); |
---|
[64b824] | 912 | } |
---|
[4fe8a3] | 913 | |
---|
| 914 | |
---|
[eefc3a] | 915 | //shifting to zero |
---|
| 916 | A= shift2Zero (A, Aeval, evaluation); |
---|
| 917 | |
---|
| 918 | for (iter= biFactors; iter.hasItem(); iter++) |
---|
| 919 | iter.getItem()= iter.getItem () (y + evaluation.getLast(), y); |
---|
| 920 | |
---|
| 921 | for (int i= 0; i < A.level() - 2; i++) |
---|
| 922 | { |
---|
| 923 | if (i != A.level() - 3) |
---|
| 924 | leadingCoeffs2[i]= CFList(); |
---|
| 925 | } |
---|
| 926 | for (iter= leadingCoeffs2[A.level() - 3]; iter.hasItem(); iter++) |
---|
| 927 | { |
---|
| 928 | iter.getItem()= shift2Zero (iter.getItem(), list, evaluation); |
---|
| 929 | for (int i= A.level() - 4; i > -1; i--) |
---|
| 930 | { |
---|
| 931 | if (i + 1 == A.level() - 3) |
---|
| 932 | leadingCoeffs2[i].append (iter.getItem() (0, i + 4)); |
---|
| 933 | else |
---|
| 934 | leadingCoeffs2[i].append (leadingCoeffs2[i+1].getLast() (0, i + 4)); |
---|
| 935 | } |
---|
| 936 | } |
---|
[ab547e2] | 937 | |
---|
| 938 | CFArray Pi; |
---|
| 939 | CFList diophant; |
---|
| 940 | int* liftBounds= new int [A.level() - 1]; |
---|
| 941 | int liftBoundsLength= A.level() - 1; |
---|
| 942 | for (int i= 0; i < liftBoundsLength; i++) |
---|
| 943 | liftBounds [i]= degree (A, i + 2) + 1; |
---|
| 944 | |
---|
| 945 | Aeval.removeFirst(); |
---|
| 946 | bool noOneToOne= false; |
---|
| 947 | |
---|
| 948 | factors= nonMonicHenselLift (Aeval, biFactors, leadingCoeffs2, diophant, |
---|
| 949 | Pi, liftBounds, liftBoundsLength, noOneToOne); |
---|
| 950 | |
---|
| 951 | if (!noOneToOne) |
---|
| 952 | { |
---|
| 953 | int check= factors.length(); |
---|
[eefc3a] | 954 | A= oldA; |
---|
| 955 | factors= recoverFactors (A, factors, evaluation); |
---|
[ab547e2] | 956 | if (check != factors.length()) |
---|
| 957 | noOneToOne= true; |
---|
| 958 | } |
---|
| 959 | if (noOneToOne) |
---|
| 960 | { |
---|
[eefc3a] | 961 | A= shift2Zero (oldA, Aeval, evaluation); |
---|
[ab547e2] | 962 | biFactors= oldBiFactors; |
---|
[eefc3a] | 963 | for (iter= biFactors; iter.hasItem(); iter++) |
---|
| 964 | iter.getItem()= iter.getItem () (y + evaluation.getLast(), y); |
---|
[ab547e2] | 965 | CanonicalForm LCA= LC (Aeval.getFirst(), 1); |
---|
| 966 | CanonicalForm yToLift= power (y, lift); |
---|
| 967 | CFListIterator i= biFactors; |
---|
| 968 | lift= degree (i.getItem(), 2) + degree (LC (i.getItem(), 1)) + 1; |
---|
| 969 | i++; |
---|
| 970 | |
---|
| 971 | for (; i.hasItem(); i++) |
---|
| 972 | lift= tmax (lift, degree (i.getItem(), 2)+degree (LC (i.getItem(), 1))+1); |
---|
| 973 | |
---|
| 974 | lift= tmax (degree (Aeval.getFirst() , 2) + 1, lift); |
---|
| 975 | |
---|
| 976 | i= biFactors; |
---|
| 977 | yToLift= power (y, lift); |
---|
| 978 | CanonicalForm dummy; |
---|
| 979 | for (; i.hasItem(); i++) |
---|
| 980 | { |
---|
| 981 | LCA= LC (i.getItem(), 1); |
---|
| 982 | extgcd (LCA, yToLift, LCA, dummy); |
---|
| 983 | i.getItem()= mod (i.getItem()*LCA, yToLift); |
---|
| 984 | } |
---|
| 985 | |
---|
| 986 | liftBoundsLength= F.level() - 1; |
---|
| 987 | liftBounds= liftingBounds (A, lift); |
---|
| 988 | |
---|
| 989 | CFList MOD; |
---|
| 990 | bool earlySuccess; |
---|
| 991 | CFList earlyFactors; |
---|
| 992 | ExtensionInfo info= ExtensionInfo (false); |
---|
[0b618a7] | 993 | CFList liftedFactors; |
---|
[ec664a2] | 994 | TIMING_START (fac_hensel_lift); |
---|
[0b618a7] | 995 | liftedFactors= henselLiftAndEarly |
---|
| 996 | (A, MOD, liftBounds, earlySuccess, earlyFactors, |
---|
| 997 | Aeval, biFactors, evaluation, info); |
---|
[ec664a2] | 998 | TIMING_END_AND_PRINT (fac_hensel_lift, "time for hensel lifting: "); |
---|
[0b618a7] | 999 | |
---|
[ec664a2] | 1000 | TIMING_START (fac_factor_recombination); |
---|
[ab547e2] | 1001 | factors= factorRecombination (A, liftedFactors, MOD); |
---|
[ec664a2] | 1002 | TIMING_END_AND_PRINT (fac_factor_recombination, |
---|
[ab547e2] | 1003 | "time for factor recombination: "); |
---|
| 1004 | |
---|
| 1005 | if (earlySuccess) |
---|
| 1006 | factors= Union (factors, earlyFactors); |
---|
| 1007 | |
---|
[c79a9d] | 1008 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
[ab547e2] | 1009 | { |
---|
[c79a9d] | 1010 | int kk= Aeval.getLast().level(); |
---|
| 1011 | for (CFListIterator j= evaluation; j.hasItem(); j++, kk--) |
---|
| 1012 | { |
---|
| 1013 | if (i.getItem().level() < kk) |
---|
| 1014 | continue; |
---|
| 1015 | i.getItem()= i.getItem() (Variable (kk) - j.getItem(), kk); |
---|
| 1016 | } |
---|
[ab547e2] | 1017 | } |
---|
| 1018 | } |
---|
| 1019 | |
---|
| 1020 | if (w.level() != 1) |
---|
| 1021 | { |
---|
| 1022 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
| 1023 | iter.getItem()= swapvar (iter.getItem(), w, y); |
---|
| 1024 | } |
---|
| 1025 | |
---|
| 1026 | swap (factors, 0, 0, x); |
---|
| 1027 | append (factors, contentAFactors); |
---|
| 1028 | decompress (factors, N); |
---|
| 1029 | if (isOn (SW_RATIONAL)) |
---|
| 1030 | normalize (factors); |
---|
| 1031 | |
---|
[229530] | 1032 | delete [] leadingCoeffs2; |
---|
| 1033 | delete [] oldAeval; |
---|
| 1034 | delete [] Aeval2; |
---|
[ab547e2] | 1035 | delete[] liftBounds; |
---|
| 1036 | |
---|
| 1037 | return factors; |
---|
| 1038 | } |
---|
[d990001] | 1039 | |
---|
| 1040 | #endif |
---|