[7bf145] | 1 | /*****************************************************************************\ |
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[44651b] | 2 | * Computer Algebra System SINGULAR |
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[7bf145] | 3 | \*****************************************************************************/ |
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| 4 | /** @file facFqFactorize.cc |
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[44651b] | 5 | * |
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[7bf145] | 6 | * This file implements functions for factoring a multivariate polynomial over |
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[44651b] | 7 | * a finite field. |
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| 8 | * |
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| 9 | * ABSTRACT: "Efficient Multivariate Factorization over Finite Fields" by |
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[8c1a84] | 10 | * L. Bernardin & M. Monagon. Precomputation of leading coefficients is |
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| 11 | * described in "Sparse Hensel lifting" by E. Kaltofen |
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[7bf145] | 12 | * |
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| 13 | * @author Martin Lee |
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| 14 | * |
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| 15 | **/ |
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| 16 | /*****************************************************************************/ |
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| 17 | |
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[e4fe2b] | 18 | #include "config.h" |
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[7bf145] | 19 | |
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[650f2d8] | 20 | #include "cf_assert.h" |
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[7bf145] | 21 | #include "debug.h" |
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| 22 | #include "timing.h" |
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| 23 | |
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| 24 | #include "facFqFactorizeUtil.h" |
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| 25 | #include "facFqFactorize.h" |
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| 26 | #include "cf_random.h" |
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| 27 | #include "facHensel.h" |
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| 28 | #include "cf_gcd_smallp.h" |
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[fecc08] | 29 | #include "cf_map_ext.h" |
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[7bf145] | 30 | #include "algext.h" |
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[91788c0] | 31 | #include "facSparseHensel.h" |
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[0e2e23] | 32 | #include "facMul.h" |
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[7bf145] | 33 | |
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| 34 | #ifdef HAVE_NTL |
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| 35 | #include "NTLconvert.h" |
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| 36 | |
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[978ce3] | 37 | TIMING_DEFINE_PRINT(fac_fq_bi_factorizer) |
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| 38 | TIMING_DEFINE_PRINT(fac_fq_hensel_lift) |
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| 39 | TIMING_DEFINE_PRINT(fac_fq_factor_recombination) |
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[7bf145] | 40 | |
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| 41 | static inline |
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[44651b] | 42 | CanonicalForm |
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[7bf145] | 43 | listGCD (const CFList& L); |
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| 44 | |
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| 45 | static inline |
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[44651b] | 46 | CanonicalForm |
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[7bf145] | 47 | myContent (const CanonicalForm& F) |
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| 48 | { |
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[a54114] | 49 | Variable x= Variable (1); |
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| 50 | CanonicalForm G= swapvar (F, F.mvar(), x); |
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[7bf145] | 51 | CFList L; |
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| 52 | for (CFIterator i= G; i.hasTerms(); i++) |
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| 53 | L.append (i.coeff()); |
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| 54 | if (L.length() == 2) |
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[a54114] | 55 | return swapvar (gcd (L.getFirst(), L.getLast()), F.mvar(), x); |
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[7bf145] | 56 | if (L.length() == 1) |
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[a54114] | 57 | return LC (F, x); |
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| 58 | return swapvar (listGCD (L), F.mvar(), x); |
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[7bf145] | 59 | } |
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| 60 | |
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| 61 | static inline |
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[44651b] | 62 | CanonicalForm |
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[7bf145] | 63 | listGCD (const CFList& L) |
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| 64 | { |
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[27e0172] | 65 | if (L.length() == 0) |
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| 66 | return 0; |
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[7bf145] | 67 | if (L.length() == 1) |
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| 68 | return L.getFirst(); |
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| 69 | if (L.length() == 2) |
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[04cdf06] | 70 | return gcd (L.getFirst(), L.getLast()); |
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[7bf145] | 71 | else |
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| 72 | { |
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| 73 | CFList lHi, lLo; |
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| 74 | CanonicalForm resultHi, resultLo; |
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| 75 | int length= L.length()/2; |
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| 76 | int j= 0; |
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| 77 | for (CFListIterator i= L; j < length; i++, j++) |
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[44651b] | 78 | lHi.append (i.getItem()); |
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[7bf145] | 79 | lLo= Difference (L, lHi); |
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| 80 | resultHi= listGCD (lHi); |
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| 81 | resultLo= listGCD (lLo); |
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| 82 | if (resultHi.isOne() || resultLo.isOne()) |
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| 83 | return 1; |
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[04cdf06] | 84 | return gcd (resultHi, resultLo); |
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[7bf145] | 85 | } |
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| 86 | } |
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| 87 | |
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| 88 | static inline |
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| 89 | CanonicalForm |
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| 90 | myContent (const CanonicalForm& F, const Variable& x) |
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| 91 | { |
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| 92 | if (degree (F, x) <= 0) |
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| 93 | return 1; |
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| 94 | CanonicalForm G= F; |
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| 95 | bool swap= false; |
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| 96 | if (x != F.mvar()) |
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| 97 | { |
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| 98 | swap= true; |
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| 99 | G= swapvar (F, x, F.mvar()); |
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| 100 | } |
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| 101 | CFList L; |
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| 102 | Variable alpha; |
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| 103 | for (CFIterator i= G; i.hasTerms(); i++) |
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| 104 | L.append (i.coeff()); |
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| 105 | if (L.length() == 2) |
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| 106 | { |
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[04cdf06] | 107 | if (swap) |
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| 108 | return swapvar (gcd (L.getFirst(), L.getLast()), F.mvar(), x); |
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[7bf145] | 109 | else |
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[04cdf06] | 110 | return gcd (L.getFirst(), L.getLast()); |
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[7bf145] | 111 | } |
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| 112 | if (L.length() == 1) |
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| 113 | { |
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| 114 | return LC (F, x); |
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| 115 | } |
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| 116 | if (swap) |
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| 117 | return swapvar (listGCD (L), F.mvar(), x); |
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| 118 | else |
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| 119 | return listGCD (L); |
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| 120 | } |
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| 121 | |
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| 122 | CanonicalForm myCompress (const CanonicalForm& F, CFMap& N) |
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| 123 | { |
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| 124 | int n= F.level(); |
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| 125 | int * degsf= new int [n + 1]; |
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| 126 | int ** swap; |
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| 127 | swap= new int* [n + 1]; |
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[44651b] | 128 | for (int i= 0; i <= n; i++) |
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[7bf145] | 129 | { |
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| 130 | degsf[i]= 0; |
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| 131 | swap [i]= new int [2]; |
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[44651b] | 132 | swap [i] [0]= 0; |
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[7bf145] | 133 | swap [i] [1]= 0; |
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| 134 | } |
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| 135 | int i= 1; |
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[44651b] | 136 | n= 1; |
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[7bf145] | 137 | degsf= degrees (F, degsf); |
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| 138 | |
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| 139 | CanonicalForm result= F; |
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[44651b] | 140 | while ( i <= F.level() ) |
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[7bf145] | 141 | { |
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| 142 | while( degsf[i] == 0 ) i++; |
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[44651b] | 143 | swap[n][0]= i; |
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[4fee0ed] | 144 | swap[n][1]= size (LC (F,i)); |
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[7bf145] | 145 | if (i != n) |
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| 146 | result= swapvar (result, Variable (n), Variable(i)); |
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| 147 | n++; i++; |
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| 148 | } |
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| 149 | |
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| 150 | int buf1, buf2; |
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| 151 | n--; |
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| 152 | |
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[44651b] | 153 | for (i= 1; i < n; i++) |
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[7bf145] | 154 | { |
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[44651b] | 155 | for (int j= 1; j < n - i + 1; j++) |
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[7bf145] | 156 | { |
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[4fee0ed] | 157 | if (swap[j][1] > swap[j + 1][1]) |
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[7bf145] | 158 | { |
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[44651b] | 159 | buf1= swap [j + 1] [0]; |
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| 160 | buf2= swap [j + 1] [1]; |
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| 161 | swap[j + 1] [0]= swap[j] [0]; |
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[7bf145] | 162 | swap[j + 1] [1]= swap[j] [1]; |
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[44651b] | 163 | swap[j][0]= buf1; |
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| 164 | swap[j][1]= buf2; |
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[7bf145] | 165 | result= swapvar (result, Variable (j + 1), Variable (j)); |
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[44651b] | 166 | } |
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[7bf145] | 167 | } |
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| 168 | } |
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| 169 | |
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[44651b] | 170 | for (i= n; i > 0; i--) |
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[7bf145] | 171 | { |
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[44651b] | 172 | if (i != swap[i] [0]) |
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| 173 | N.newpair (Variable (i), Variable (swap[i] [0])); |
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[7bf145] | 174 | } |
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| 175 | |
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| 176 | for (i= 0; i <= n; i++) |
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| 177 | delete [] swap[i]; |
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| 178 | delete [] swap; |
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| 179 | |
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| 180 | delete [] degsf; |
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| 181 | |
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| 182 | return result; |
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| 183 | } |
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[44651b] | 184 | |
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| 185 | CFList |
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| 186 | extFactorRecombination (const CFList& factors, const CanonicalForm& F, |
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| 187 | const CFList& M, const ExtensionInfo& info, |
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[7bf145] | 188 | const CFList& evaluation) |
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[44651b] | 189 | { |
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[7bf145] | 190 | Variable alpha= info.getAlpha(); |
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| 191 | Variable beta= info.getBeta(); |
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| 192 | CanonicalForm gamma= info.getGamma(); |
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| 193 | CanonicalForm delta= info.getDelta(); |
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| 194 | int k= info.getGFDegree(); |
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| 195 | CFList source, dest; |
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[44651b] | 196 | if (factors.length() == 1) |
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[7bf145] | 197 | { |
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| 198 | CanonicalForm buf= reverseShift (F, evaluation); |
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[44651b] | 199 | return CFList (mapDown (buf, info, source, dest)); |
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| 200 | } |
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[7bf145] | 201 | if (factors.length() < 1) |
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| 202 | return CFList(); |
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| 203 | |
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[ac8e1a] | 204 | int degMipoBeta= 1; |
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| 205 | if (!k && beta.level() != 1) |
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[7bf145] | 206 | degMipoBeta= degree (getMipo (beta)); |
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| 207 | |
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| 208 | CFList T, S; |
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| 209 | T= factors; |
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| 210 | |
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| 211 | int s= 1; |
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| 212 | CFList result; |
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| 213 | CanonicalForm buf; |
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[ccd1b0] | 214 | |
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| 215 | buf= F; |
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[7bf145] | 216 | |
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[a54114] | 217 | Variable x= Variable (1); |
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| 218 | CanonicalForm g, LCBuf= LC (buf, x); |
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[21b8f4c] | 219 | CanonicalForm buf2, quot; |
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[1673386] | 220 | int * v= new int [T.length()]; |
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[7bf145] | 221 | for (int i= 0; i < T.length(); i++) |
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| 222 | v[i]= 0; |
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| 223 | bool noSubset= false; |
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| 224 | CFArray TT; |
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[44651b] | 225 | TT= copy (factors); |
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[7bf145] | 226 | bool recombination= false; |
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[93134c] | 227 | bool trueFactor= false; |
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[44651b] | 228 | while (T.length() >= 2*s) |
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[7bf145] | 229 | { |
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[44651b] | 230 | while (noSubset == false) |
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[7bf145] | 231 | { |
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[44651b] | 232 | if (T.length() == s) |
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[7bf145] | 233 | { |
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[1673386] | 234 | delete [] v; |
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[7bf145] | 235 | if (recombination) |
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| 236 | { |
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| 237 | T.insert (LCBuf); |
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| 238 | g= prodMod (T, M); |
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| 239 | T.removeFirst(); |
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| 240 | result.append (g/myContent (g)); |
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| 241 | g= reverseShift (g, evaluation); |
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| 242 | g /= Lc (g); |
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| 243 | appendTestMapDown (result, g, info, source, dest); |
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| 244 | return result; |
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| 245 | } |
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| 246 | else |
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| 247 | { |
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| 248 | buf= reverseShift (buf, evaluation); |
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| 249 | return CFList (buf); |
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| 250 | } |
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| 251 | } |
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| 252 | |
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| 253 | S= subset (v, s, TT, noSubset); |
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| 254 | if (noSubset) break; |
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| 255 | |
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| 256 | S.insert (LCBuf); |
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| 257 | g= prodMod (S, M); |
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| 258 | S.removeFirst(); |
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| 259 | g /= myContent (g); |
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[21b8f4c] | 260 | if (fdivides (g, buf, quot)) |
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[7bf145] | 261 | { |
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[44651b] | 262 | buf2= reverseShift (g, evaluation); |
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[7bf145] | 263 | buf2 /= Lc (buf2); |
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[a54114] | 264 | if (!k && beta == x) |
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[44651b] | 265 | { |
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| 266 | if (degree (buf2, alpha) < degMipoBeta) |
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| 267 | { |
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| 268 | appendTestMapDown (result, buf2, info, source, dest); |
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[21b8f4c] | 269 | buf= quot; |
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[a54114] | 270 | LCBuf= LC (buf, x); |
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[44651b] | 271 | recombination= true; |
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[93134c] | 272 | trueFactor= true; |
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[44651b] | 273 | } |
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| 274 | } |
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| 275 | else |
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| 276 | { |
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[f876a66] | 277 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
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[44651b] | 278 | { |
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| 279 | appendTestMapDown (result, buf2, info, source, dest); |
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| 280 | buf /= g; |
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[a54114] | 281 | LCBuf= LC (buf, x); |
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[44651b] | 282 | recombination= true; |
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[93134c] | 283 | trueFactor= true; |
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[44651b] | 284 | } |
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| 285 | } |
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| 286 | |
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[93134c] | 287 | if (trueFactor) |
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[44651b] | 288 | { |
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[93134c] | 289 | T= Difference (T, S); |
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| 290 | |
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| 291 | if (T.length() < 2*s || T.length() == s) |
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| 292 | { |
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| 293 | buf= reverseShift (buf, evaluation); |
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| 294 | buf /= Lc (buf); |
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| 295 | appendTestMapDown (result, buf, info, source, dest); |
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[1673386] | 296 | delete [] v; |
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[93134c] | 297 | return result; |
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| 298 | } |
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| 299 | trueFactor= false; |
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| 300 | TT= copy (T); |
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| 301 | indexUpdate (v, s, T.length(), noSubset); |
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| 302 | if (noSubset) break; |
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[44651b] | 303 | } |
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[7bf145] | 304 | } |
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| 305 | } |
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| 306 | s++; |
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[44651b] | 307 | if (T.length() < 2*s || T.length() == s) |
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[7bf145] | 308 | { |
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| 309 | buf= reverseShift (buf, evaluation); |
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| 310 | appendTestMapDown (result, buf, info, source, dest); |
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[1673386] | 311 | delete [] v; |
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[7bf145] | 312 | return result; |
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| 313 | } |
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| 314 | for (int i= 0; i < T.length(); i++) |
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| 315 | v[i]= 0; |
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| 316 | noSubset= false; |
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| 317 | } |
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| 318 | if (T.length() < 2*s) |
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| 319 | { |
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[44651b] | 320 | buf= reverseShift (F, evaluation); |
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| 321 | appendMapDown (result, buf, info, source, dest); |
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[7bf145] | 322 | } |
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| 323 | |
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[1673386] | 324 | delete [] v; |
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[44651b] | 325 | return result; |
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| 326 | } |
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[7bf145] | 327 | |
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[44651b] | 328 | CFList |
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| 329 | factorRecombination (const CanonicalForm& F, const CFList& factors, |
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[7bf145] | 330 | const CFList& M) |
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| 331 | { |
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[44651b] | 332 | if (factors.length() == 1) |
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[7bf145] | 333 | return CFList(F); |
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| 334 | if (factors.length() < 1) |
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| 335 | return CFList(); |
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| 336 | |
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| 337 | CFList T, S; |
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| 338 | |
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| 339 | T= factors; |
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| 340 | |
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| 341 | int s= 1; |
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| 342 | CFList result; |
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| 343 | CanonicalForm LCBuf= LC (F, Variable (1)); |
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| 344 | CanonicalForm g, buf= F; |
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[1673386] | 345 | int * v= new int [T.length()]; |
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[7bf145] | 346 | for (int i= 0; i < T.length(); i++) |
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| 347 | v[i]= 0; |
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| 348 | bool noSubset= false; |
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| 349 | CFArray TT; |
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[44651b] | 350 | TT= copy (factors); |
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[7bf145] | 351 | Variable y= F.level() - 1; |
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| 352 | bool recombination= false; |
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[21b8f4c] | 353 | CanonicalForm h, quot; |
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[44651b] | 354 | while (T.length() >= 2*s) |
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[7bf145] | 355 | { |
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[44651b] | 356 | while (noSubset == false) |
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[7bf145] | 357 | { |
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[44651b] | 358 | if (T.length() == s) |
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[7bf145] | 359 | { |
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[1673386] | 360 | delete [] v; |
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[7bf145] | 361 | if (recombination) |
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| 362 | { |
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| 363 | T.insert (LC (buf)); |
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| 364 | g= prodMod (T, M); |
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| 365 | result.append (g/myContent (g)); |
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| 366 | return result; |
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| 367 | } |
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| 368 | else |
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| 369 | return CFList (F); |
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| 370 | } |
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| 371 | S= subset (v, s, TT, noSubset); |
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| 372 | if (noSubset) break; |
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| 373 | S.insert (LCBuf); |
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| 374 | g= prodMod (S, M); |
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| 375 | S.removeFirst(); |
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| 376 | g /= myContent (g); |
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[21b8f4c] | 377 | if (fdivides (g, buf, quot)) |
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[7bf145] | 378 | { |
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| 379 | recombination= true; |
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| 380 | result.append (g); |
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[21b8f4c] | 381 | buf= quot; |
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[7bf145] | 382 | LCBuf= LC (buf, Variable(1)); |
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| 383 | T= Difference (T, S); |
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[44651b] | 384 | if (T.length() < 2*s || T.length() == s) |
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[7bf145] | 385 | { |
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[44651b] | 386 | result.append (buf); |
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[1673386] | 387 | delete [] v; |
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[44651b] | 388 | return result; |
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| 389 | } |
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| 390 | TT= copy (T); |
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| 391 | indexUpdate (v, s, T.length(), noSubset); |
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| 392 | if (noSubset) break; |
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[7bf145] | 393 | } |
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| 394 | } |
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| 395 | s++; |
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[44651b] | 396 | if (T.length() < 2*s || T.length() == s) |
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[7bf145] | 397 | { |
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| 398 | result.append (buf); |
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[1673386] | 399 | delete [] v; |
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[7bf145] | 400 | return result; |
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| 401 | } |
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| 402 | for (int i= 0; i < T.length(); i++) |
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| 403 | v[i]= 0; |
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| 404 | noSubset= false; |
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| 405 | } |
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[44651b] | 406 | if (T.length() < 2*s) |
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[7bf145] | 407 | result.append (F); |
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| 408 | |
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[1673386] | 409 | delete [] v; |
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[44651b] | 410 | return result; |
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[7bf145] | 411 | } |
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| 412 | |
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| 413 | int |
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| 414 | liftBoundAdaption (const CanonicalForm& F, const CFList& factors, bool& |
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| 415 | success, const int deg, const CFList& MOD, const int bound) |
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| 416 | { |
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| 417 | int adaptedLiftBound= 0; |
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| 418 | CanonicalForm buf= F; |
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| 419 | Variable y= F.mvar(); |
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[a54114] | 420 | Variable x= Variable (1); |
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| 421 | CanonicalForm LCBuf= LC (buf, x); |
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[21b8f4c] | 422 | CanonicalForm g, quot; |
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[7bf145] | 423 | CFList M= MOD; |
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| 424 | M.append (power (y, deg)); |
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| 425 | int d= bound; |
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| 426 | int e= 0; |
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| 427 | int nBuf; |
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[44651b] | 428 | for (CFListIterator i= factors; i.hasItem(); i++) |
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[7bf145] | 429 | { |
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[44651b] | 430 | g= mulMod (i.getItem(), LCBuf, M); |
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[7bf145] | 431 | g /= myContent (g); |
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[21b8f4c] | 432 | if (fdivides (g, buf, quot)) |
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[7bf145] | 433 | { |
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| 434 | nBuf= degree (g, y) + degree (LC (g, 1), y); |
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| 435 | d -= nBuf; |
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| 436 | e= tmax (e, nBuf); |
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[21b8f4c] | 437 | buf= quot; |
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[a54114] | 438 | LCBuf= LC (buf, x); |
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[7bf145] | 439 | } |
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| 440 | } |
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| 441 | adaptedLiftBound= d; |
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| 442 | |
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[44651b] | 443 | if (adaptedLiftBound < deg) |
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| 444 | { |
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[7bf145] | 445 | if (adaptedLiftBound < degree (F) + 1) |
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| 446 | { |
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| 447 | if (d == 1) |
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| 448 | { |
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| 449 | if (e + 1 > deg) |
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| 450 | { |
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| 451 | adaptedLiftBound= deg; |
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| 452 | success= false; |
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| 453 | } |
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[44651b] | 454 | else |
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[7bf145] | 455 | { |
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| 456 | success= true; |
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| 457 | if (e + 1 < degree (F) + 1) |
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| 458 | adaptedLiftBound= deg; |
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| 459 | else |
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| 460 | adaptedLiftBound= e + 1; |
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| 461 | } |
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| 462 | } |
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| 463 | else |
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| 464 | { |
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| 465 | success= true; |
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[44651b] | 466 | adaptedLiftBound= deg; |
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[7bf145] | 467 | } |
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| 468 | } |
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| 469 | else |
---|
| 470 | { |
---|
| 471 | success= true; |
---|
| 472 | } |
---|
| 473 | } |
---|
| 474 | return adaptedLiftBound; |
---|
| 475 | } |
---|
| 476 | |
---|
[44651b] | 477 | int |
---|
| 478 | extLiftBoundAdaption (const CanonicalForm& F, const CFList& factors, bool& |
---|
| 479 | success, const ExtensionInfo& info, const CFList& eval, |
---|
[7bf145] | 480 | const int deg, const CFList& MOD, const int bound) |
---|
| 481 | { |
---|
| 482 | Variable alpha= info.getAlpha(); |
---|
| 483 | Variable beta= info.getBeta(); |
---|
| 484 | CanonicalForm gamma= info.getGamma(); |
---|
| 485 | CanonicalForm delta= info.getDelta(); |
---|
| 486 | int k= info.getGFDegree(); |
---|
| 487 | int adaptedLiftBound= 0; |
---|
| 488 | CanonicalForm buf= F; |
---|
| 489 | Variable y= F.mvar(); |
---|
[a54114] | 490 | Variable x= Variable (1); |
---|
| 491 | CanonicalForm LCBuf= LC (buf, x); |
---|
[21b8f4c] | 492 | CanonicalForm g, gg, quot; |
---|
[7bf145] | 493 | CFList M= MOD; |
---|
| 494 | M.append (power (y, deg)); |
---|
| 495 | adaptedLiftBound= 0; |
---|
| 496 | int d= bound; |
---|
[44651b] | 497 | int e= 0; |
---|
[7bf145] | 498 | int nBuf; |
---|
[ac8e1a] | 499 | int degMipoBeta= 1; |
---|
| 500 | if (!k && beta.level() != 1) |
---|
[7bf145] | 501 | degMipoBeta= degree (getMipo (beta)); |
---|
| 502 | |
---|
[f876a66] | 503 | CFList source, dest; |
---|
[44651b] | 504 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
[7bf145] | 505 | { |
---|
| 506 | g= mulMod (i.getItem(), LCBuf, M); |
---|
| 507 | g /= myContent (g); |
---|
[21b8f4c] | 508 | if (fdivides (g, buf, quot)) |
---|
[7bf145] | 509 | { |
---|
| 510 | gg= reverseShift (g, eval); |
---|
| 511 | gg /= Lc (gg); |
---|
[a54114] | 512 | if (!k && beta == x) |
---|
[7bf145] | 513 | { |
---|
| 514 | if (degree (gg, alpha) < degMipoBeta) |
---|
[44651b] | 515 | { |
---|
[21b8f4c] | 516 | buf= quot; |
---|
[a54114] | 517 | nBuf= degree (g, y) + degree (LC (g, x), y); |
---|
[7bf145] | 518 | d -= nBuf; |
---|
| 519 | e= tmax (e, nBuf); |
---|
[a54114] | 520 | LCBuf= LC (buf, x); |
---|
[7bf145] | 521 | } |
---|
| 522 | } |
---|
[44651b] | 523 | else |
---|
[7bf145] | 524 | { |
---|
[f876a66] | 525 | if (!isInExtension (gg, gamma, k, delta, source, dest)) |
---|
[7bf145] | 526 | { |
---|
[21b8f4c] | 527 | buf= quot; |
---|
[a54114] | 528 | nBuf= degree (g, y) + degree (LC (g, x), y); |
---|
[7bf145] | 529 | d -= nBuf; |
---|
| 530 | e= tmax (e, nBuf); |
---|
[a54114] | 531 | LCBuf= LC (buf, x); |
---|
[7bf145] | 532 | } |
---|
| 533 | } |
---|
[44651b] | 534 | } |
---|
[7bf145] | 535 | } |
---|
| 536 | adaptedLiftBound= d; |
---|
| 537 | |
---|
| 538 | if (adaptedLiftBound < deg) |
---|
| 539 | { |
---|
| 540 | if (adaptedLiftBound < degree (F) + 1) |
---|
| 541 | { |
---|
| 542 | if (d == 1) |
---|
| 543 | { |
---|
| 544 | if (e + 1 > deg) |
---|
| 545 | { |
---|
| 546 | adaptedLiftBound= deg; |
---|
| 547 | success= false; |
---|
| 548 | } |
---|
[44651b] | 549 | else |
---|
[7bf145] | 550 | { |
---|
| 551 | success= true; |
---|
| 552 | if (e + 1 < degree (F) + 1) |
---|
| 553 | adaptedLiftBound= deg; |
---|
| 554 | else |
---|
| 555 | adaptedLiftBound= e + 1; |
---|
| 556 | } |
---|
| 557 | } |
---|
[44651b] | 558 | else |
---|
[7bf145] | 559 | { |
---|
| 560 | success= true; |
---|
[44651b] | 561 | adaptedLiftBound= deg; |
---|
[7bf145] | 562 | } |
---|
| 563 | } |
---|
| 564 | else |
---|
| 565 | { |
---|
| 566 | success= true; |
---|
| 567 | } |
---|
| 568 | } |
---|
| 569 | |
---|
| 570 | return adaptedLiftBound; |
---|
| 571 | } |
---|
| 572 | |
---|
[44651b] | 573 | CFList |
---|
[7bf145] | 574 | earlyFactorDetect (CanonicalForm& F, CFList& factors, int& adaptedLiftBound, |
---|
[44651b] | 575 | bool& success, const int deg, const CFList& MOD, |
---|
[7bf145] | 576 | const int bound) |
---|
| 577 | { |
---|
| 578 | CFList result; |
---|
| 579 | CFList T= factors; |
---|
| 580 | CanonicalForm buf= F; |
---|
| 581 | Variable y= F.mvar(); |
---|
[a54114] | 582 | Variable x= Variable (1); |
---|
| 583 | CanonicalForm LCBuf= LC (buf, x); |
---|
[21b8f4c] | 584 | CanonicalForm g, quot; |
---|
[7bf145] | 585 | CFList M= MOD; |
---|
| 586 | M.append (power (y, deg)); |
---|
| 587 | adaptedLiftBound= 0; |
---|
| 588 | int d= bound; |
---|
| 589 | int e= 0; |
---|
| 590 | int nBuf; |
---|
[44651b] | 591 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
[7bf145] | 592 | { |
---|
| 593 | g= mulMod (i.getItem(), LCBuf, M); |
---|
| 594 | g /= myContent (g); |
---|
[21b8f4c] | 595 | if (fdivides (g, buf, quot)) |
---|
[7bf145] | 596 | { |
---|
| 597 | result.append (g); |
---|
[a54114] | 598 | nBuf= degree (g, y) + degree (LC (g, x), y); |
---|
[7bf145] | 599 | d -= nBuf; |
---|
| 600 | e= tmax (e, nBuf); |
---|
[21b8f4c] | 601 | buf= quot; |
---|
[a54114] | 602 | LCBuf= LC (buf, x); |
---|
[7bf145] | 603 | T= Difference (T, CFList (i.getItem())); |
---|
| 604 | } |
---|
| 605 | } |
---|
| 606 | adaptedLiftBound= d; |
---|
| 607 | |
---|
[44651b] | 608 | if (adaptedLiftBound < deg) |
---|
[7bf145] | 609 | { |
---|
| 610 | if (adaptedLiftBound < degree (F) + 1) |
---|
| 611 | { |
---|
| 612 | if (d == 1) |
---|
| 613 | adaptedLiftBound= tmin (e + 1, deg); |
---|
| 614 | else |
---|
[44651b] | 615 | adaptedLiftBound= deg; |
---|
[7bf145] | 616 | } |
---|
| 617 | factors= T; |
---|
| 618 | F= buf; |
---|
| 619 | success= true; |
---|
| 620 | } |
---|
| 621 | return result; |
---|
| 622 | } |
---|
| 623 | |
---|
[44651b] | 624 | CFList |
---|
[7bf145] | 625 | extEarlyFactorDetect (CanonicalForm& F, CFList& factors, int& adaptedLiftBound, |
---|
[44651b] | 626 | bool& success, const ExtensionInfo& info, const CFList& |
---|
[7bf145] | 627 | eval, const int deg, const CFList& MOD, const int bound) |
---|
| 628 | { |
---|
| 629 | Variable alpha= info.getAlpha(); |
---|
| 630 | Variable beta= info.getBeta(); |
---|
| 631 | CanonicalForm gamma= info.getGamma(); |
---|
| 632 | CanonicalForm delta= info.getDelta(); |
---|
| 633 | int k= info.getGFDegree(); |
---|
| 634 | CFList result; |
---|
| 635 | CFList T= factors; |
---|
| 636 | CanonicalForm buf= F; |
---|
| 637 | Variable y= F.mvar(); |
---|
[a54114] | 638 | Variable x= Variable (1); |
---|
| 639 | CanonicalForm LCBuf= LC (buf, x); |
---|
[21b8f4c] | 640 | CanonicalForm g, gg, quot; |
---|
[7bf145] | 641 | CFList M= MOD; |
---|
| 642 | M.append (power (y, deg)); |
---|
| 643 | adaptedLiftBound= 0; |
---|
| 644 | int d= bound; |
---|
| 645 | int e= 0; |
---|
| 646 | int nBuf; |
---|
| 647 | CFList source, dest; |
---|
| 648 | |
---|
[ac8e1a] | 649 | int degMipoBeta= 1; |
---|
| 650 | if (!k && beta.level() != 1) |
---|
[7bf145] | 651 | degMipoBeta= degree (getMipo (beta)); |
---|
| 652 | |
---|
[44651b] | 653 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
[7bf145] | 654 | { |
---|
| 655 | g= mulMod (i.getItem(), LCBuf, M); |
---|
| 656 | g /= myContent (g); |
---|
[21b8f4c] | 657 | if (fdivides (g, buf, quot)) |
---|
[7bf145] | 658 | { |
---|
| 659 | gg= reverseShift (g, eval); |
---|
| 660 | gg /= Lc (gg); |
---|
[a54114] | 661 | if (!k && beta == x) |
---|
[93134c] | 662 | { |
---|
| 663 | if (degree (gg, alpha) < degMipoBeta) |
---|
| 664 | { |
---|
| 665 | appendTestMapDown (result, gg, info, source, dest); |
---|
[21b8f4c] | 666 | buf= quot; |
---|
[a54114] | 667 | nBuf= degree (g, y) + degree (LC (g, x), y); |
---|
[93134c] | 668 | d -= nBuf; |
---|
| 669 | e= tmax (e, nBuf); |
---|
[a54114] | 670 | LCBuf= LC (buf, x); |
---|
[93134c] | 671 | T= Difference (T, CFList (i.getItem())); |
---|
| 672 | } |
---|
| 673 | } |
---|
| 674 | else |
---|
| 675 | { |
---|
[f876a66] | 676 | if (!isInExtension (gg, gamma, k, delta, source, dest)) |
---|
[93134c] | 677 | { |
---|
| 678 | appendTestMapDown (result, gg, info, source, dest); |
---|
[21b8f4c] | 679 | buf= quot; |
---|
[a54114] | 680 | nBuf= degree (g, y) + degree (LC (g, x), y); |
---|
[93134c] | 681 | d -= nBuf; |
---|
| 682 | e= tmax (e, nBuf); |
---|
[a54114] | 683 | LCBuf= LC (buf, x); |
---|
[93134c] | 684 | T= Difference (T, CFList (i.getItem())); |
---|
| 685 | } |
---|
| 686 | } |
---|
[7bf145] | 687 | } |
---|
| 688 | } |
---|
| 689 | adaptedLiftBound= d; |
---|
| 690 | |
---|
| 691 | if (adaptedLiftBound < deg) |
---|
| 692 | { |
---|
| 693 | if (adaptedLiftBound < degree (F) + 1) |
---|
| 694 | { |
---|
| 695 | if (d == 1) |
---|
| 696 | adaptedLiftBound= tmin (e + 1, deg); |
---|
| 697 | else |
---|
[44651b] | 698 | adaptedLiftBound= deg; |
---|
[7bf145] | 699 | } |
---|
| 700 | success= true; |
---|
| 701 | factors= T; |
---|
| 702 | F= buf; |
---|
| 703 | } |
---|
| 704 | return result; |
---|
| 705 | } |
---|
| 706 | |
---|
[44651b] | 707 | CFList |
---|
[7bf145] | 708 | evalPoints (const CanonicalForm& F, CFList & eval, const Variable& alpha, |
---|
[44651b] | 709 | CFList& list, const bool& GF, bool& fail) |
---|
| 710 | { |
---|
[7bf145] | 711 | int k= F.level() - 1; |
---|
| 712 | Variable x= Variable (1); |
---|
| 713 | CFList result; |
---|
| 714 | FFRandom genFF; |
---|
| 715 | GFRandom genGF; |
---|
| 716 | int p= getCharacteristic (); |
---|
[44651b] | 717 | double bound; |
---|
[a54114] | 718 | if (alpha != x) |
---|
[7bf145] | 719 | { |
---|
| 720 | bound= pow ((double) p, (double) degree (getMipo(alpha))); |
---|
[e3cb321] | 721 | bound *= (double) k; |
---|
[7bf145] | 722 | } |
---|
[44651b] | 723 | else if (GF) |
---|
[7bf145] | 724 | { |
---|
| 725 | bound= pow ((double) p, (double) getGFDegree()); |
---|
[e3cb321] | 726 | bound *= (double) k; |
---|
[7bf145] | 727 | } |
---|
| 728 | else |
---|
| 729 | bound= pow ((double) p, (double) k); |
---|
| 730 | |
---|
| 731 | CanonicalForm random; |
---|
| 732 | CanonicalForm deriv_x, gcd_deriv; |
---|
[44651b] | 733 | do |
---|
[7bf145] | 734 | { |
---|
| 735 | random= 0; |
---|
| 736 | // possible overflow if list.length() does not fit into a int |
---|
[44651b] | 737 | if (list.length() >= bound) |
---|
| 738 | { |
---|
[7bf145] | 739 | fail= true; |
---|
| 740 | break; |
---|
| 741 | } |
---|
[44651b] | 742 | for (int i= 0; i < k; i++) |
---|
| 743 | { |
---|
[8db258] | 744 | if (list.isEmpty()) |
---|
| 745 | result.append (0); |
---|
| 746 | else if (GF) |
---|
[7bf145] | 747 | { |
---|
| 748 | result.append (genGF.generate()); |
---|
| 749 | random += result.getLast()*power (x, i); |
---|
| 750 | } |
---|
[1372ae] | 751 | else if (alpha.level() != 1) |
---|
[44651b] | 752 | { |
---|
[7bf145] | 753 | AlgExtRandomF genAlgExt (alpha); |
---|
| 754 | result.append (genAlgExt.generate()); |
---|
[44651b] | 755 | random += result.getLast()*power (x, i); |
---|
[7bf145] | 756 | } |
---|
[44651b] | 757 | else |
---|
| 758 | { |
---|
[7bf145] | 759 | result.append (genFF.generate()); |
---|
| 760 | random += result.getLast()*power (x, i); |
---|
[44651b] | 761 | } |
---|
[7bf145] | 762 | } |
---|
[44651b] | 763 | if (find (list, random)) |
---|
[7bf145] | 764 | { |
---|
| 765 | result= CFList(); |
---|
| 766 | continue; |
---|
| 767 | } |
---|
| 768 | int l= F.level(); |
---|
| 769 | eval.insert (F); |
---|
[ccd1b0] | 770 | bool bad= false; |
---|
[44651b] | 771 | for (CFListIterator i= result; i.hasItem(); i++, l--) |
---|
[ccd1b0] | 772 | { |
---|
[7bf145] | 773 | eval.insert (eval.getFirst()(i.getItem(), l)); |
---|
[ccd1b0] | 774 | if (degree (eval.getFirst(), l - 1) != degree (F, l - 1)) |
---|
| 775 | { |
---|
| 776 | if (!find (list, random)) |
---|
| 777 | list.append (random); |
---|
| 778 | result= CFList(); |
---|
| 779 | eval= CFList(); |
---|
| 780 | bad= true; |
---|
| 781 | break; |
---|
| 782 | } |
---|
| 783 | } |
---|
| 784 | |
---|
| 785 | if (bad) |
---|
| 786 | continue; |
---|
[7bf145] | 787 | |
---|
[44651b] | 788 | if (degree (eval.getFirst()) != degree (F, 1)) |
---|
[7bf145] | 789 | { |
---|
| 790 | if (!find (list, random)) |
---|
| 791 | list.append (random); |
---|
| 792 | result= CFList(); |
---|
| 793 | eval= CFList(); |
---|
| 794 | continue; |
---|
[44651b] | 795 | } |
---|
| 796 | |
---|
[7bf145] | 797 | deriv_x= deriv (eval.getFirst(), x); |
---|
| 798 | gcd_deriv= gcd (eval.getFirst(), deriv_x); |
---|
[44651b] | 799 | if (degree (gcd_deriv) > 0) |
---|
| 800 | { |
---|
[7bf145] | 801 | if (!find (list, random)) |
---|
| 802 | list.append (random); |
---|
| 803 | result= CFList(); |
---|
| 804 | eval= CFList(); |
---|
| 805 | continue; |
---|
| 806 | } |
---|
| 807 | CFListIterator i= eval; |
---|
| 808 | i++; |
---|
| 809 | CanonicalForm contentx= content (i.getItem(), x); |
---|
| 810 | if (degree (contentx) > 0) |
---|
| 811 | { |
---|
| 812 | if (!find (list, random)) |
---|
| 813 | list.append (random); |
---|
| 814 | result= CFList(); |
---|
| 815 | eval= CFList(); |
---|
| 816 | continue; |
---|
| 817 | } |
---|
| 818 | |
---|
[44651b] | 819 | if (list.length() >= bound) |
---|
[7bf145] | 820 | { |
---|
| 821 | fail= true; |
---|
| 822 | break; |
---|
| 823 | } |
---|
| 824 | } while (find (list, random)); |
---|
| 825 | |
---|
[44651b] | 826 | if (!eval.isEmpty()) |
---|
[7bf145] | 827 | eval.removeFirst(); |
---|
| 828 | |
---|
| 829 | return result; |
---|
| 830 | } |
---|
| 831 | |
---|
[44651b] | 832 | static inline |
---|
[7bf145] | 833 | int newMainVariableSearch (CanonicalForm& A, CFList& Aeval, CFList& |
---|
[ccd1b0] | 834 | evaluation, const Variable& alpha, const int lev, |
---|
| 835 | CanonicalForm& g |
---|
| 836 | ) |
---|
[44651b] | 837 | { |
---|
[7bf145] | 838 | Variable x= Variable (1); |
---|
| 839 | CanonicalForm derivI, buf; |
---|
| 840 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
| 841 | int swapLevel= 0; |
---|
| 842 | CFList list; |
---|
| 843 | bool fail= false; |
---|
| 844 | buf= A; |
---|
| 845 | Aeval= CFList(); |
---|
| 846 | evaluation= CFList(); |
---|
[44651b] | 847 | for (int i= lev; i <= A.level(); i++) |
---|
[7bf145] | 848 | { |
---|
| 849 | derivI= deriv (buf, Variable (i)); |
---|
| 850 | if (!derivI.isZero()) |
---|
| 851 | { |
---|
[ccd1b0] | 852 | g= gcd (buf, derivI); |
---|
| 853 | if (degree (g) > 0) |
---|
| 854 | return -1; |
---|
| 855 | |
---|
[44651b] | 856 | buf= swapvar (buf, x, Variable (i)); |
---|
[7bf145] | 857 | Aeval= CFList(); |
---|
| 858 | evaluation= CFList(); |
---|
| 859 | fail= false; |
---|
| 860 | evaluation= evalPoints (buf, Aeval, alpha, list, GF, fail); |
---|
[44651b] | 861 | if (!fail) |
---|
[7bf145] | 862 | { |
---|
[44651b] | 863 | A= buf; |
---|
| 864 | swapLevel= i; |
---|
| 865 | break; |
---|
[7bf145] | 866 | } |
---|
[44651b] | 867 | else |
---|
[7bf145] | 868 | buf= A; |
---|
| 869 | } |
---|
| 870 | } |
---|
| 871 | return swapLevel; |
---|
| 872 | } |
---|
| 873 | |
---|
[44651b] | 874 | CanonicalForm lcmContent (const CanonicalForm& A, CFList& contentAi) |
---|
[7bf145] | 875 | { |
---|
| 876 | int i= A.level(); |
---|
| 877 | contentAi.append (myContent (A, i)); |
---|
| 878 | contentAi.append (myContent (A, i - 1)); |
---|
[04cdf06] | 879 | CanonicalForm result= lcm (contentAi.getFirst(), contentAi.getLast()); |
---|
[44651b] | 880 | for (i= i - 2; i > 0; i--) |
---|
[7bf145] | 881 | { |
---|
| 882 | contentAi.append (content (A, i)); |
---|
[04cdf06] | 883 | result= lcm (result, contentAi.getLast()); |
---|
[7bf145] | 884 | } |
---|
| 885 | return result; |
---|
[44651b] | 886 | } |
---|
| 887 | |
---|
[7bf145] | 888 | CFList |
---|
| 889 | henselLiftAndEarly (CanonicalForm& A, CFList& MOD, int*& liftBounds, bool& |
---|
| 890 | earlySuccess, CFList& earlyFactors, const CFList& Aeval, |
---|
[44651b] | 891 | const CFList& biFactors, const CFList& evaluation, |
---|
[7bf145] | 892 | const ExtensionInfo& info) |
---|
| 893 | { |
---|
| 894 | bool extension= info.isInExtension(); |
---|
[44651b] | 895 | CFList bufFactors= biFactors; |
---|
[7bf145] | 896 | bufFactors.insert (LC (Aeval.getFirst(), 1)); |
---|
| 897 | |
---|
| 898 | sortList (bufFactors, Variable (1)); |
---|
| 899 | |
---|
| 900 | CFList diophant; |
---|
| 901 | CFArray Pi; |
---|
| 902 | int smallFactorDeg= 11; //tunable parameter |
---|
[44651b] | 903 | CFList result; |
---|
[7bf145] | 904 | int adaptedLiftBound= 0; |
---|
| 905 | int liftBound= liftBounds[1]; |
---|
| 906 | |
---|
| 907 | earlySuccess= false; |
---|
| 908 | CFList earlyReconstFactors; |
---|
| 909 | CFListIterator j= Aeval; |
---|
| 910 | j++; |
---|
| 911 | CanonicalForm buf= j.getItem(); |
---|
| 912 | CFMatrix Mat= CFMatrix (liftBound, bufFactors.length() - 1); |
---|
| 913 | MOD= CFList (power (Variable (2), liftBounds[0])); |
---|
| 914 | if (smallFactorDeg >= liftBound) |
---|
| 915 | { |
---|
| 916 | result= henselLift23 (Aeval, bufFactors, liftBounds, diophant, Pi, Mat); |
---|
| 917 | } |
---|
| 918 | else if (smallFactorDeg >= degree (buf) + 1) |
---|
| 919 | { |
---|
| 920 | liftBounds[1]= degree (buf) + 1; |
---|
| 921 | result= henselLift23 (Aeval, bufFactors, liftBounds, diophant, Pi, Mat); |
---|
| 922 | if (Aeval.length() == 2) |
---|
| 923 | { |
---|
| 924 | if (!extension) |
---|
[44651b] | 925 | earlyFactors= earlyFactorDetect |
---|
[7bf145] | 926 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
| 927 | degree (buf) + 1, MOD, liftBound); |
---|
| 928 | else |
---|
[44651b] | 929 | earlyFactors= extEarlyFactorDetect |
---|
[7bf145] | 930 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
[44651b] | 931 | info, evaluation, degree |
---|
[7bf145] | 932 | (buf) + 1, MOD, liftBound); |
---|
| 933 | } |
---|
| 934 | else |
---|
| 935 | { |
---|
| 936 | if (!extension) |
---|
| 937 | adaptedLiftBound= liftBoundAdaption (buf, result, earlySuccess, |
---|
| 938 | degree (buf) + 1, MOD, liftBound); |
---|
| 939 | else |
---|
| 940 | adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, info, |
---|
| 941 | evaluation, degree (buf) + 1, |
---|
[44651b] | 942 | MOD, liftBound); |
---|
[7bf145] | 943 | } |
---|
| 944 | if (!earlySuccess) |
---|
| 945 | { |
---|
| 946 | result.insert (LC (buf, 1)); |
---|
| 947 | liftBounds[1]= adaptedLiftBound; |
---|
| 948 | liftBound= adaptedLiftBound; |
---|
[44651b] | 949 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
[7bf145] | 950 | Pi, diophant, Mat, MOD); |
---|
[44651b] | 951 | } |
---|
[7bf145] | 952 | else |
---|
| 953 | liftBounds[1]= adaptedLiftBound; |
---|
| 954 | } |
---|
| 955 | else if (smallFactorDeg < degree (buf) + 1) |
---|
| 956 | { |
---|
| 957 | liftBounds[1]= smallFactorDeg; |
---|
| 958 | result= henselLift23 (Aeval, bufFactors, liftBounds, diophant, Pi, Mat); |
---|
| 959 | if (Aeval.length() == 2) |
---|
| 960 | { |
---|
| 961 | if (!extension) |
---|
[44651b] | 962 | earlyFactors= earlyFactorDetect (buf, result, adaptedLiftBound, |
---|
[7bf145] | 963 | earlySuccess, smallFactorDeg, MOD, |
---|
| 964 | liftBound); |
---|
[44651b] | 965 | else |
---|
[7bf145] | 966 | earlyFactors= extEarlyFactorDetect (buf, result, adaptedLiftBound, |
---|
| 967 | earlySuccess, info, evaluation, |
---|
| 968 | smallFactorDeg, MOD, liftBound); |
---|
| 969 | } |
---|
| 970 | else |
---|
| 971 | { |
---|
| 972 | if (!extension) |
---|
| 973 | adaptedLiftBound= liftBoundAdaption (buf, result, earlySuccess, |
---|
| 974 | smallFactorDeg, MOD, liftBound); |
---|
| 975 | else |
---|
| 976 | adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, info, |
---|
[44651b] | 977 | evaluation, smallFactorDeg, MOD, |
---|
[7bf145] | 978 | liftBound); |
---|
| 979 | } |
---|
| 980 | |
---|
| 981 | if (!earlySuccess) |
---|
| 982 | { |
---|
| 983 | result.insert (LC (buf, 1)); |
---|
[44651b] | 984 | henselLiftResume (buf, result, smallFactorDeg, degree (buf) + 1, |
---|
[7bf145] | 985 | Pi, diophant, Mat, MOD); |
---|
| 986 | if (Aeval.length() == 2) |
---|
| 987 | { |
---|
| 988 | if (!extension) |
---|
| 989 | earlyFactors= earlyFactorDetect (buf, result, adaptedLiftBound, |
---|
| 990 | earlySuccess, degree (buf) + 1, |
---|
| 991 | MOD, liftBound); |
---|
| 992 | else |
---|
| 993 | earlyFactors= extEarlyFactorDetect (buf, result, adaptedLiftBound, |
---|
| 994 | earlySuccess, info, evaluation, |
---|
[44651b] | 995 | degree (buf) + 1, MOD, |
---|
[7bf145] | 996 | liftBound); |
---|
| 997 | } |
---|
[44651b] | 998 | else |
---|
[7bf145] | 999 | { |
---|
| 1000 | if (!extension) |
---|
| 1001 | adaptedLiftBound= liftBoundAdaption (buf, result, earlySuccess, |
---|
[44651b] | 1002 | degree (buf) + 1, MOD,liftBound); |
---|
[7bf145] | 1003 | else |
---|
[44651b] | 1004 | adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, |
---|
[7bf145] | 1005 | info, evaluation, |
---|
| 1006 | degree (buf) + 1, MOD, |
---|
| 1007 | liftBound); |
---|
| 1008 | } |
---|
| 1009 | if (!earlySuccess) |
---|
| 1010 | { |
---|
| 1011 | result.insert (LC (buf, 1)); |
---|
| 1012 | liftBounds[1]= adaptedLiftBound; |
---|
| 1013 | liftBound= adaptedLiftBound; |
---|
[44651b] | 1014 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
[7bf145] | 1015 | Pi, diophant, Mat, MOD); |
---|
| 1016 | } |
---|
| 1017 | else |
---|
| 1018 | liftBounds[1]= adaptedLiftBound; |
---|
| 1019 | } |
---|
| 1020 | else |
---|
| 1021 | liftBounds[1]= adaptedLiftBound; |
---|
| 1022 | } |
---|
| 1023 | |
---|
| 1024 | MOD.append (power (Variable (3), liftBounds[1])); |
---|
| 1025 | |
---|
| 1026 | if (Aeval.length() > 2) |
---|
| 1027 | { |
---|
| 1028 | CFListIterator j= Aeval; |
---|
| 1029 | j++; |
---|
| 1030 | CFList bufEval; |
---|
| 1031 | bufEval.append (j.getItem()); |
---|
| 1032 | j++; |
---|
| 1033 | int liftBoundsLength= Aeval.getLast().level() - 1; |
---|
| 1034 | for (int i= 2; i <= liftBoundsLength && j.hasItem(); i++, j++) |
---|
[44651b] | 1035 | { |
---|
[7bf145] | 1036 | earlySuccess= false; |
---|
| 1037 | result.insert (LC (bufEval.getFirst(), 1)); |
---|
| 1038 | bufEval.append (j.getItem()); |
---|
| 1039 | liftBound= liftBounds[i]; |
---|
| 1040 | Mat= CFMatrix (liftBounds[i], result.length() - 1); |
---|
| 1041 | |
---|
| 1042 | buf= j.getItem(); |
---|
| 1043 | if (smallFactorDeg >= liftBound) |
---|
| 1044 | result= henselLift (bufEval, result, MOD, diophant, Pi, Mat, |
---|
[44651b] | 1045 | liftBounds[i - 1], liftBounds[i]); |
---|
[7bf145] | 1046 | else if (smallFactorDeg >= degree (buf) + 1) |
---|
| 1047 | { |
---|
[44651b] | 1048 | result= henselLift (bufEval, result, MOD, diophant, Pi, Mat, |
---|
| 1049 | liftBounds[i - 1], degree (buf) + 1); |
---|
[7bf145] | 1050 | |
---|
[44651b] | 1051 | if (Aeval.length() == i + 1) |
---|
| 1052 | { |
---|
| 1053 | if (!extension) |
---|
| 1054 | earlyFactors= earlyFactorDetect |
---|
[7bf145] | 1055 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
| 1056 | degree (buf) + 1, MOD, liftBound); |
---|
[44651b] | 1057 | else |
---|
| 1058 | earlyFactors= extEarlyFactorDetect |
---|
[7bf145] | 1059 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
| 1060 | info, evaluation, degree (buf) + 1, MOD, liftBound); |
---|
[44651b] | 1061 | } |
---|
| 1062 | else |
---|
| 1063 | { |
---|
| 1064 | if (!extension) |
---|
| 1065 | adaptedLiftBound= liftBoundAdaption |
---|
[7bf145] | 1066 | (buf, result, earlySuccess, degree (buf) |
---|
| 1067 | + 1, MOD, liftBound); |
---|
[44651b] | 1068 | else |
---|
| 1069 | adaptedLiftBound= extLiftBoundAdaption |
---|
| 1070 | (buf, result, earlySuccess, info, evaluation, |
---|
| 1071 | degree (buf) + 1, MOD, liftBound); |
---|
| 1072 | } |
---|
| 1073 | |
---|
| 1074 | if (!earlySuccess) |
---|
| 1075 | { |
---|
| 1076 | result.insert (LC (buf, 1)); |
---|
[7bf145] | 1077 | liftBounds[i]= adaptedLiftBound; |
---|
| 1078 | liftBound= adaptedLiftBound; |
---|
[44651b] | 1079 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
| 1080 | Pi, diophant, Mat, MOD); |
---|
| 1081 | } |
---|
| 1082 | else |
---|
| 1083 | { |
---|
| 1084 | liftBounds[i]= adaptedLiftBound; |
---|
| 1085 | } |
---|
[7bf145] | 1086 | } |
---|
| 1087 | else if (smallFactorDeg < degree (buf) + 1) |
---|
| 1088 | { |
---|
[44651b] | 1089 | result= henselLift (bufEval, result, MOD, diophant, Pi, Mat, |
---|
| 1090 | liftBounds[i - 1], smallFactorDeg); |
---|
[7bf145] | 1091 | |
---|
[44651b] | 1092 | if (Aeval.length() == i + 1) |
---|
| 1093 | { |
---|
| 1094 | if (!extension) |
---|
| 1095 | earlyFactors= earlyFactorDetect |
---|
[7bf145] | 1096 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
| 1097 | smallFactorDeg, MOD, liftBound); |
---|
[44651b] | 1098 | else |
---|
| 1099 | earlyFactors= extEarlyFactorDetect |
---|
[7bf145] | 1100 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
| 1101 | info, evaluation, smallFactorDeg, MOD, liftBound); |
---|
[44651b] | 1102 | } |
---|
| 1103 | else |
---|
| 1104 | { |
---|
| 1105 | if (!extension) |
---|
| 1106 | adaptedLiftBound= liftBoundAdaption |
---|
[7bf145] | 1107 | (buf, result, earlySuccess, |
---|
| 1108 | smallFactorDeg, MOD, liftBound); |
---|
[44651b] | 1109 | else |
---|
| 1110 | adaptedLiftBound= extLiftBoundAdaption |
---|
[7bf145] | 1111 | (buf, result, earlySuccess, info, evaluation, |
---|
[44651b] | 1112 | smallFactorDeg, MOD, liftBound); |
---|
| 1113 | } |
---|
[7bf145] | 1114 | |
---|
[44651b] | 1115 | if (!earlySuccess) |
---|
| 1116 | { |
---|
| 1117 | result.insert (LC (buf, 1)); |
---|
| 1118 | henselLiftResume (buf, result, smallFactorDeg, |
---|
[7bf145] | 1119 | degree (buf) + 1, Pi, diophant, Mat, MOD); |
---|
[44651b] | 1120 | if (Aeval.length() == i + 1) |
---|
| 1121 | { |
---|
| 1122 | if (!extension) |
---|
| 1123 | earlyFactors= earlyFactorDetect |
---|
[7bf145] | 1124 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
| 1125 | degree (buf) + 1, MOD, liftBound); |
---|
[44651b] | 1126 | else |
---|
| 1127 | earlyFactors= extEarlyFactorDetect |
---|
[7bf145] | 1128 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
[44651b] | 1129 | info, evaluation, degree (buf) + 1, MOD, |
---|
[7bf145] | 1130 | liftBound); |
---|
[44651b] | 1131 | } |
---|
| 1132 | else |
---|
| 1133 | { |
---|
| 1134 | if (!extension) |
---|
| 1135 | adaptedLiftBound= liftBoundAdaption |
---|
[7bf145] | 1136 | (buf, result, earlySuccess, degree |
---|
| 1137 | (buf) + 1, MOD, liftBound); |
---|
[44651b] | 1138 | else |
---|
| 1139 | adaptedLiftBound= extLiftBoundAdaption |
---|
| 1140 | (buf, result, earlySuccess, info, evaluation, |
---|
| 1141 | degree (buf) + 1, MOD, liftBound); |
---|
| 1142 | } |
---|
| 1143 | |
---|
| 1144 | if (!earlySuccess) |
---|
| 1145 | { |
---|
| 1146 | result.insert (LC (buf, 1)); |
---|
[7bf145] | 1147 | liftBounds[i]= adaptedLiftBound; |
---|
| 1148 | liftBound= adaptedLiftBound; |
---|
[44651b] | 1149 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
| 1150 | Pi, diophant, Mat, MOD); |
---|
| 1151 | } |
---|
| 1152 | else |
---|
| 1153 | liftBounds[i]= adaptedLiftBound; |
---|
| 1154 | } |
---|
| 1155 | else |
---|
| 1156 | liftBounds[i]= adaptedLiftBound; |
---|
[7bf145] | 1157 | } |
---|
| 1158 | MOD.append (power (Variable (i + 2), liftBounds[i])); |
---|
| 1159 | bufEval.removeFirst(); |
---|
| 1160 | } |
---|
| 1161 | bufFactors= result; |
---|
| 1162 | } |
---|
| 1163 | else |
---|
| 1164 | bufFactors= result; |
---|
| 1165 | |
---|
| 1166 | if (earlySuccess) |
---|
| 1167 | A= buf; |
---|
| 1168 | return result; |
---|
| 1169 | } |
---|
| 1170 | |
---|
[ccd1b0] | 1171 | void |
---|
| 1172 | gcdFreeBasis (CFFList& factors1, CFFList& factors2) |
---|
| 1173 | { |
---|
| 1174 | CanonicalForm g; |
---|
| 1175 | int k= factors1.length(); |
---|
| 1176 | int l= factors2.length(); |
---|
| 1177 | int n= 1; |
---|
| 1178 | int m; |
---|
[38ffb7] | 1179 | CFFListIterator j; |
---|
| 1180 | for (CFFListIterator i= factors1; (n < k && i.hasItem()); i++, n++) |
---|
[ccd1b0] | 1181 | { |
---|
| 1182 | m= 1; |
---|
[38ffb7] | 1183 | for (j= factors2; (m < l && j.hasItem()); j++, m++) |
---|
[ccd1b0] | 1184 | { |
---|
[38ffb7] | 1185 | g= gcd (i.getItem().factor(), j.getItem().factor()); |
---|
[8256fd] | 1186 | if (degree (g,1) > 0) |
---|
[ccd1b0] | 1187 | { |
---|
| 1188 | j.getItem()= CFFactor (j.getItem().factor()/g, j.getItem().exp()); |
---|
| 1189 | i.getItem()= CFFactor (i.getItem().factor()/g, i.getItem().exp()); |
---|
| 1190 | factors1.append (CFFactor (g, i.getItem().exp())); |
---|
| 1191 | factors2.append (CFFactor (g, j.getItem().exp())); |
---|
| 1192 | } |
---|
| 1193 | } |
---|
| 1194 | } |
---|
| 1195 | } |
---|
| 1196 | |
---|
| 1197 | CFList |
---|
| 1198 | distributeContent (const CFList& L, const CFList* differentSecondVarFactors, |
---|
[8c1a84] | 1199 | int length |
---|
[ccd1b0] | 1200 | ) |
---|
| 1201 | { |
---|
| 1202 | CFList l= L; |
---|
| 1203 | CanonicalForm content= l.getFirst(); |
---|
| 1204 | |
---|
| 1205 | if (content.inCoeffDomain()) |
---|
| 1206 | return l; |
---|
| 1207 | |
---|
| 1208 | if (l.length() == 1) |
---|
| 1209 | { |
---|
| 1210 | CFList result; |
---|
| 1211 | for (int i= 0; i < length; i++) |
---|
| 1212 | { |
---|
| 1213 | if (differentSecondVarFactors[i].isEmpty()) |
---|
| 1214 | continue; |
---|
| 1215 | if (result.isEmpty()) |
---|
| 1216 | { |
---|
| 1217 | result= differentSecondVarFactors[i]; |
---|
| 1218 | for (CFListIterator iter= result; iter.hasItem(); iter++) |
---|
| 1219 | content /= iter.getItem(); |
---|
| 1220 | } |
---|
| 1221 | else |
---|
| 1222 | { |
---|
| 1223 | CFListIterator iter1= result; |
---|
[8a30b1] | 1224 | for (CFListIterator iter2= differentSecondVarFactors[i];iter2.hasItem(); |
---|
[ccd1b0] | 1225 | iter2++, iter1++) |
---|
| 1226 | { |
---|
| 1227 | iter1.getItem() *= iter2.getItem(); |
---|
| 1228 | content /= iter2.getItem(); |
---|
| 1229 | } |
---|
| 1230 | } |
---|
| 1231 | } |
---|
| 1232 | result.insert (content); |
---|
| 1233 | return result; |
---|
| 1234 | } |
---|
| 1235 | |
---|
[38ffb7] | 1236 | Variable v; |
---|
[8a30b1] | 1237 | CFListIterator iter1, iter2; |
---|
[38ffb7] | 1238 | CanonicalForm tmp, g; |
---|
[8a30b1] | 1239 | CFList multiplier; |
---|
[ccd1b0] | 1240 | for (int i= 0; i < length; i++) |
---|
| 1241 | { |
---|
| 1242 | if (differentSecondVarFactors[i].isEmpty()) |
---|
| 1243 | continue; |
---|
[38ffb7] | 1244 | iter1= l; |
---|
[ccd1b0] | 1245 | iter1++; |
---|
| 1246 | |
---|
[8a30b1] | 1247 | tmp= 1; |
---|
| 1248 | for (iter2= differentSecondVarFactors[i]; iter2.hasItem(); |
---|
[ccd1b0] | 1249 | iter2++, iter1++) |
---|
| 1250 | { |
---|
[935632] | 1251 | if (iter2.getItem().inCoeffDomain()) |
---|
| 1252 | { |
---|
| 1253 | multiplier.append (1); |
---|
| 1254 | continue; |
---|
| 1255 | } |
---|
| 1256 | v= iter2.getItem().mvar(); |
---|
| 1257 | if (degree (iter2.getItem()) == degree (iter1.getItem(),v)) |
---|
[ccd1b0] | 1258 | { |
---|
[8a30b1] | 1259 | multiplier.append (1); |
---|
| 1260 | continue; |
---|
[ccd1b0] | 1261 | } |
---|
[38ffb7] | 1262 | g= gcd (iter2.getItem(), content); |
---|
[8a30b1] | 1263 | if (!g.inCoeffDomain()) |
---|
[ccd1b0] | 1264 | { |
---|
[8a30b1] | 1265 | tmp *= g; |
---|
| 1266 | multiplier.append (g); |
---|
[ccd1b0] | 1267 | } |
---|
[8a30b1] | 1268 | else |
---|
| 1269 | multiplier.append (1); |
---|
| 1270 | } |
---|
| 1271 | if (!tmp.isOne() && fdivides (tmp, content)) |
---|
| 1272 | { |
---|
| 1273 | iter1= l; |
---|
| 1274 | iter1++; |
---|
| 1275 | content /= tmp; |
---|
| 1276 | for (iter2= multiplier; iter2.hasItem(); iter1++, iter2++) |
---|
| 1277 | iter1.getItem() *= iter2.getItem(); |
---|
[ccd1b0] | 1278 | } |
---|
[8a30b1] | 1279 | multiplier= CFList(); |
---|
[ccd1b0] | 1280 | } |
---|
| 1281 | |
---|
| 1282 | l.removeFirst(); |
---|
| 1283 | l.insert (content); |
---|
| 1284 | return l; |
---|
| 1285 | } |
---|
| 1286 | |
---|
| 1287 | int |
---|
| 1288 | testFactors (const CanonicalForm& G, const CFList& uniFactors, |
---|
| 1289 | const Variable& alpha, CanonicalForm& sqrfPartF, CFList& factors, |
---|
[eefc3a] | 1290 | CFFList*& bufSqrfFactors, CFList& evalSqrfPartF, |
---|
| 1291 | const CFArray& evalPoint) |
---|
[ccd1b0] | 1292 | { |
---|
[38ffb7] | 1293 | CanonicalForm tmp; |
---|
| 1294 | CFListIterator j; |
---|
[ccd1b0] | 1295 | for (CFListIterator i= uniFactors; i.hasItem(); i++) |
---|
| 1296 | { |
---|
[38ffb7] | 1297 | tmp= i.getItem(); |
---|
[ccd1b0] | 1298 | if (i.hasItem()) |
---|
| 1299 | i++; |
---|
| 1300 | else |
---|
| 1301 | break; |
---|
[38ffb7] | 1302 | for (j= i; j.hasItem(); j++) |
---|
[ccd1b0] | 1303 | { |
---|
| 1304 | if (tmp == j.getItem()) |
---|
| 1305 | return 0; |
---|
| 1306 | } |
---|
| 1307 | } |
---|
| 1308 | |
---|
| 1309 | CanonicalForm F= G; |
---|
| 1310 | CFFList sqrfFactorization= squarefreeFactorization (F, alpha); |
---|
| 1311 | |
---|
| 1312 | sqrfPartF= 1; |
---|
| 1313 | for (CFFListIterator i= sqrfFactorization; i.hasItem(); i++) |
---|
| 1314 | sqrfPartF *= i.getItem().factor(); |
---|
| 1315 | |
---|
[eefc3a] | 1316 | evalSqrfPartF= evaluateAtEval (sqrfPartF, evalPoint); |
---|
[ccd1b0] | 1317 | |
---|
[eefc3a] | 1318 | CanonicalForm test= evalSqrfPartF.getFirst() (evalPoint[0], 2); |
---|
[ccd1b0] | 1319 | |
---|
[9dacf3f] | 1320 | if (degree (test) != degree (sqrfPartF, 1) || test.inCoeffDomain()) |
---|
[ccd1b0] | 1321 | return 0; |
---|
| 1322 | |
---|
| 1323 | CFFList sqrfFactors; |
---|
| 1324 | CFList tmp2; |
---|
| 1325 | int k= 0; |
---|
| 1326 | factors= uniFactors; |
---|
[38ffb7] | 1327 | CFFListIterator iter; |
---|
[ccd1b0] | 1328 | for (CFListIterator i= factors; i.hasItem(); i++, k++) |
---|
| 1329 | { |
---|
[38ffb7] | 1330 | tmp= 1; |
---|
[ccd1b0] | 1331 | sqrfFactors= squarefreeFactorization (i.getItem(), alpha); |
---|
| 1332 | |
---|
[38ffb7] | 1333 | for (iter= sqrfFactors; iter.hasItem(); iter++) |
---|
[ccd1b0] | 1334 | { |
---|
[38ffb7] | 1335 | tmp2.append (iter.getItem().factor()); |
---|
| 1336 | tmp *= iter.getItem().factor(); |
---|
[ccd1b0] | 1337 | } |
---|
| 1338 | i.getItem()= tmp/Lc(tmp); |
---|
| 1339 | bufSqrfFactors [k]= sqrfFactors; |
---|
| 1340 | } |
---|
| 1341 | |
---|
| 1342 | for (int i= 0; i < factors.length() - 1; i++) |
---|
| 1343 | { |
---|
[38ffb7] | 1344 | for (k= i + 1; k < factors.length(); k++) |
---|
[ccd1b0] | 1345 | { |
---|
| 1346 | gcdFreeBasis (bufSqrfFactors [i], bufSqrfFactors[k]); |
---|
| 1347 | } |
---|
| 1348 | } |
---|
| 1349 | |
---|
| 1350 | factors= CFList(); |
---|
| 1351 | for (int i= 0; i < uniFactors.length(); i++) |
---|
| 1352 | { |
---|
| 1353 | if (i == 0) |
---|
| 1354 | { |
---|
[38ffb7] | 1355 | for (iter= bufSqrfFactors [i]; iter.hasItem(); iter++) |
---|
[ccd1b0] | 1356 | { |
---|
[327efa2] | 1357 | if (iter.getItem().factor().inCoeffDomain()) |
---|
| 1358 | continue; |
---|
[38ffb7] | 1359 | iter.getItem()= CFFactor (iter.getItem().factor()/ |
---|
| 1360 | Lc (iter.getItem().factor()), |
---|
| 1361 | iter.getItem().exp()); |
---|
| 1362 | factors.append (iter.getItem().factor()); |
---|
[ccd1b0] | 1363 | } |
---|
| 1364 | } |
---|
| 1365 | else |
---|
| 1366 | { |
---|
[38ffb7] | 1367 | for (iter= bufSqrfFactors [i]; iter.hasItem(); iter++) |
---|
[ccd1b0] | 1368 | { |
---|
[327efa2] | 1369 | if (iter.getItem().factor().inCoeffDomain()) |
---|
| 1370 | continue; |
---|
[38ffb7] | 1371 | iter.getItem()= CFFactor (iter.getItem().factor()/ |
---|
| 1372 | Lc (iter.getItem().factor()), |
---|
| 1373 | iter.getItem().exp()); |
---|
| 1374 | if (!find (factors, iter.getItem().factor())) |
---|
| 1375 | factors.append (iter.getItem().factor()); |
---|
[ccd1b0] | 1376 | } |
---|
| 1377 | } |
---|
| 1378 | } |
---|
| 1379 | |
---|
| 1380 | test= prod (factors); |
---|
[eefc3a] | 1381 | tmp= evalSqrfPartF.getFirst() (evalPoint[0],2); |
---|
[ccd1b0] | 1382 | if (test/Lc (test) != tmp/Lc (tmp)) |
---|
| 1383 | return 0; |
---|
| 1384 | else |
---|
| 1385 | return 1; |
---|
| 1386 | } |
---|
| 1387 | |
---|
| 1388 | CFList |
---|
| 1389 | precomputeLeadingCoeff (const CanonicalForm& LCF, const CFList& LCFFactors, |
---|
| 1390 | const Variable& alpha, const CFList& evaluation, |
---|
[eefc3a] | 1391 | CFList* & differentSecondVarLCs, int lSecondVarLCs, |
---|
[ccd1b0] | 1392 | Variable& y |
---|
| 1393 | ) |
---|
| 1394 | { |
---|
| 1395 | y= Variable (1); |
---|
| 1396 | if (LCF.inCoeffDomain()) |
---|
| 1397 | { |
---|
| 1398 | CFList result; |
---|
| 1399 | for (int i= 1; i <= LCFFactors.length() + 1; i++) |
---|
| 1400 | result.append (1); |
---|
| 1401 | return result; |
---|
| 1402 | } |
---|
| 1403 | |
---|
[8256fd] | 1404 | CFMap N, M; |
---|
[8a30b1] | 1405 | CFArray dummy= CFArray (2); |
---|
[8256fd] | 1406 | dummy [0]= LCF; |
---|
[8a30b1] | 1407 | dummy [1]= Variable (2); |
---|
[8256fd] | 1408 | compress (dummy, M, N); |
---|
| 1409 | CanonicalForm F= M (LCF); |
---|
[ccd1b0] | 1410 | if (LCF.isUnivariate()) |
---|
| 1411 | { |
---|
| 1412 | CFList result; |
---|
| 1413 | int LCFLevel= LCF.level(); |
---|
| 1414 | bool found= false; |
---|
| 1415 | if (LCFLevel == 2) |
---|
| 1416 | { |
---|
| 1417 | //bivariate leading coefficients are already the true leading coefficients |
---|
| 1418 | result= LCFFactors; |
---|
| 1419 | found= true; |
---|
| 1420 | } |
---|
| 1421 | else |
---|
| 1422 | { |
---|
[38ffb7] | 1423 | CFListIterator j; |
---|
[eefc3a] | 1424 | for (int i= 0; i < lSecondVarLCs; i++) |
---|
[ccd1b0] | 1425 | { |
---|
[38ffb7] | 1426 | for (j= differentSecondVarLCs[i]; j.hasItem(); j++) |
---|
[ccd1b0] | 1427 | { |
---|
| 1428 | if (j.getItem().level() == LCFLevel) |
---|
| 1429 | { |
---|
| 1430 | found= true; |
---|
| 1431 | break; |
---|
| 1432 | } |
---|
| 1433 | } |
---|
| 1434 | if (found) |
---|
| 1435 | { |
---|
| 1436 | result= differentSecondVarLCs [i]; |
---|
| 1437 | break; |
---|
| 1438 | } |
---|
| 1439 | } |
---|
| 1440 | if (!found) |
---|
| 1441 | result= LCFFactors; |
---|
| 1442 | } |
---|
| 1443 | if (found) |
---|
| 1444 | result.insert (Lc (LCF)); |
---|
| 1445 | else |
---|
[41e77d] | 1446 | { |
---|
| 1447 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
| 1448 | i.getItem() *= LCF; |
---|
| 1449 | result.insert (LCF); |
---|
| 1450 | } |
---|
[ccd1b0] | 1451 | return result; |
---|
| 1452 | } |
---|
| 1453 | |
---|
| 1454 | CFList factors= LCFFactors; |
---|
| 1455 | |
---|
| 1456 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
[8256fd] | 1457 | i.getItem()= M (i.getItem()); |
---|
[ccd1b0] | 1458 | |
---|
| 1459 | CanonicalForm sqrfPartF; |
---|
| 1460 | CFFList * bufSqrfFactors= new CFFList [factors.length()]; |
---|
[eefc3a] | 1461 | CFList evalSqrfPartF, bufFactors; |
---|
| 1462 | CFArray evalPoint= CFArray (evaluation.length() - 1); |
---|
[8a30b1] | 1463 | CFArray buf= CFArray (evaluation.length()); |
---|
| 1464 | CFArray swap= CFArray (evaluation.length()); |
---|
[eefc3a] | 1465 | CFListIterator iter= evaluation; |
---|
[9dacf3f] | 1466 | CanonicalForm vars=getVars (LCF)*Variable (2); |
---|
[8a30b1] | 1467 | for (int i= evaluation.length() +1; i > 1; i--, iter++) |
---|
| 1468 | { |
---|
| 1469 | buf[i-2]=iter.getItem(); |
---|
| 1470 | if (degree (vars, i) > 0) |
---|
| 1471 | swap[M(Variable (i)).level()-1]=buf[i-2]; |
---|
| 1472 | } |
---|
| 1473 | buf= swap; |
---|
| 1474 | for (int i= 0; i < evaluation.length() - 1; i++) |
---|
| 1475 | evalPoint[i]= buf[i+1]; |
---|
[eefc3a] | 1476 | |
---|
[ccd1b0] | 1477 | int pass= testFactors (F, factors, alpha, sqrfPartF, |
---|
[eefc3a] | 1478 | bufFactors, bufSqrfFactors, evalSqrfPartF, evalPoint); |
---|
[ccd1b0] | 1479 | |
---|
| 1480 | bool foundDifferent= false; |
---|
[eefc3a] | 1481 | Variable z, x= y; |
---|
[ccd1b0] | 1482 | int j= 0; |
---|
| 1483 | if (!pass) |
---|
| 1484 | { |
---|
[7a1151] | 1485 | int lev= 0; |
---|
[ccd1b0] | 1486 | // LCF is non-constant here |
---|
[38ffb7] | 1487 | CFList bufBufFactors; |
---|
[8a30b1] | 1488 | CanonicalForm bufF; |
---|
[eefc3a] | 1489 | for (int i= 0; i < lSecondVarLCs; i++) |
---|
[ccd1b0] | 1490 | { |
---|
| 1491 | if (!differentSecondVarLCs [i].isEmpty()) |
---|
| 1492 | { |
---|
| 1493 | bool allConstant= true; |
---|
[38ffb7] | 1494 | for (iter= differentSecondVarLCs[i]; iter.hasItem(); iter++) |
---|
[ccd1b0] | 1495 | { |
---|
| 1496 | if (!iter.getItem().inCoeffDomain()) |
---|
| 1497 | { |
---|
| 1498 | allConstant= false; |
---|
| 1499 | y= Variable (iter.getItem().level()); |
---|
[8256fd] | 1500 | lev= M(y).level(); |
---|
[ccd1b0] | 1501 | } |
---|
| 1502 | } |
---|
| 1503 | if (allConstant) |
---|
| 1504 | continue; |
---|
| 1505 | |
---|
| 1506 | bufFactors= differentSecondVarLCs [i]; |
---|
[38ffb7] | 1507 | for (iter= bufFactors; iter.hasItem(); iter++) |
---|
[ccd1b0] | 1508 | iter.getItem()= swapvar (iter.getItem(), x, y); |
---|
[38ffb7] | 1509 | bufF= F; |
---|
[8256fd] | 1510 | z= Variable (lev); |
---|
[ccd1b0] | 1511 | bufF= swapvar (bufF, x, z); |
---|
[38ffb7] | 1512 | bufBufFactors= bufFactors; |
---|
[eefc3a] | 1513 | evalPoint= CFArray (evaluation.length() - 1); |
---|
[8a30b1] | 1514 | for (int k= 0; k < evaluation.length()-1; k++) |
---|
[eefc3a] | 1515 | { |
---|
[9dacf3f] | 1516 | if (N (Variable (k+1)).level() != y.level()) |
---|
[8a30b1] | 1517 | evalPoint[k]= buf[k+1]; |
---|
| 1518 | else |
---|
| 1519 | evalPoint[k]= buf[0]; |
---|
[eefc3a] | 1520 | } |
---|
[ccd1b0] | 1521 | pass= testFactors (bufF, bufBufFactors, alpha, sqrfPartF, bufFactors, |
---|
[eefc3a] | 1522 | bufSqrfFactors, evalSqrfPartF, evalPoint); |
---|
[ccd1b0] | 1523 | if (pass) |
---|
| 1524 | { |
---|
| 1525 | foundDifferent= true; |
---|
| 1526 | F= bufF; |
---|
| 1527 | CFList l= factors; |
---|
[38ffb7] | 1528 | for (iter= l; iter.hasItem(); iter++) |
---|
[ccd1b0] | 1529 | iter.getItem()= swapvar (iter.getItem(), x, y); |
---|
| 1530 | differentSecondVarLCs [i]= l; |
---|
| 1531 | j= i; |
---|
| 1532 | break; |
---|
| 1533 | } |
---|
[eefc3a] | 1534 | if (!pass && i == lSecondVarLCs - 1) |
---|
[ccd1b0] | 1535 | { |
---|
| 1536 | CFList result; |
---|
| 1537 | result.append (LCF); |
---|
| 1538 | for (int k= 1; k <= factors.length(); k++) |
---|
| 1539 | result.append (LCF); |
---|
| 1540 | y= Variable (1); |
---|
[229530] | 1541 | delete [] bufSqrfFactors; |
---|
[ccd1b0] | 1542 | return result; |
---|
| 1543 | } |
---|
| 1544 | } |
---|
| 1545 | } |
---|
| 1546 | } |
---|
| 1547 | if (!pass) |
---|
| 1548 | { |
---|
| 1549 | CFList result; |
---|
| 1550 | result.append (LCF); |
---|
| 1551 | for (int k= 1; k <= factors.length(); k++) |
---|
| 1552 | result.append (LCF); |
---|
| 1553 | y= Variable (1); |
---|
[229530] | 1554 | delete [] bufSqrfFactors; |
---|
[ccd1b0] | 1555 | return result; |
---|
| 1556 | } |
---|
| 1557 | else |
---|
| 1558 | factors= bufFactors; |
---|
| 1559 | |
---|
[327efa2] | 1560 | bufFactors= factors; |
---|
[1a2d66] | 1561 | |
---|
| 1562 | CFMap MM, NN; |
---|
| 1563 | dummy [0]= sqrfPartF; |
---|
| 1564 | dummy [1]= 1; |
---|
| 1565 | compress (dummy, MM, NN); |
---|
| 1566 | sqrfPartF= MM (sqrfPartF); |
---|
| 1567 | CanonicalForm varsSqrfPartF= getVars (sqrfPartF); |
---|
| 1568 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
| 1569 | iter.getItem()= MM (iter.getItem()); |
---|
| 1570 | |
---|
[eefc3a] | 1571 | CFList evaluation2; |
---|
[1a2d66] | 1572 | for (int i= 2; i <= varsSqrfPartF.level(); i++) |
---|
| 1573 | evaluation2.insert (evalPoint[NN (Variable (i)).level()-2]); |
---|
[327efa2] | 1574 | |
---|
[ec16f0] | 1575 | CFList interMedResult; |
---|
| 1576 | CanonicalForm oldSqrfPartF= sqrfPartF; |
---|
[8a30b1] | 1577 | sqrfPartF= shift2Zero (sqrfPartF, evalSqrfPartF, evaluation2); |
---|
[327efa2] | 1578 | if (factors.length() > 1) |
---|
| 1579 | { |
---|
[ec16f0] | 1580 | CanonicalForm LC1= LC (oldSqrfPartF, 1); |
---|
| 1581 | CFList leadingCoeffs; |
---|
[327efa2] | 1582 | for (int i= 0; i < factors.length(); i++) |
---|
[ec16f0] | 1583 | leadingCoeffs.append (LC1); |
---|
| 1584 | |
---|
[8a30b1] | 1585 | CFList LC1eval= evaluateAtEval (LC1, evaluation2, 2); |
---|
[ec16f0] | 1586 | CFList oldFactors= factors; |
---|
| 1587 | for (CFListIterator i= oldFactors; i.hasItem(); i++) |
---|
| 1588 | i.getItem() *= LC1eval.getFirst()/Lc (i.getItem()); |
---|
[eefc3a] | 1589 | |
---|
[ec16f0] | 1590 | bool success= false; |
---|
[64b824] | 1591 | CanonicalForm oldSqrfPartFPowLC= oldSqrfPartF*power(LC1,factors.length()-1); |
---|
[589ef64] | 1592 | CFList heuResult; |
---|
[64b824] | 1593 | if (size (oldSqrfPartFPowLC)/getNumVars (oldSqrfPartFPowLC) < 500 && |
---|
| 1594 | LucksWangSparseHeuristic (oldSqrfPartFPowLC, |
---|
[589ef64] | 1595 | oldFactors, 2, leadingCoeffs, heuResult)) |
---|
[eefc3a] | 1596 | { |
---|
[589ef64] | 1597 | interMedResult= recoverFactors (oldSqrfPartF, heuResult); |
---|
[ec16f0] | 1598 | if (oldFactors.length() == interMedResult.length()) |
---|
| 1599 | success= true; |
---|
[eefc3a] | 1600 | } |
---|
[ec16f0] | 1601 | if (!success) |
---|
| 1602 | { |
---|
| 1603 | LC1= LC (evalSqrfPartF.getFirst(), 1); |
---|
[ccd1b0] | 1604 | |
---|
[ec16f0] | 1605 | CFArray leadingCoeffs= CFArray (factors.length()); |
---|
| 1606 | for (int i= 0; i < factors.length(); i++) |
---|
| 1607 | leadingCoeffs[i]= LC1; |
---|
[ccd1b0] | 1608 | |
---|
[ec16f0] | 1609 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
| 1610 | i.getItem() *= LC1 (0,2)/Lc (i.getItem()); |
---|
| 1611 | factors.insert (1); |
---|
[ccd1b0] | 1612 | |
---|
[ec16f0] | 1613 | CanonicalForm |
---|
| 1614 | newSqrfPartF= evalSqrfPartF.getFirst()*power (LC1, factors.length() - 2); |
---|
[327efa2] | 1615 | |
---|
[ec16f0] | 1616 | int liftBound= degree (newSqrfPartF,2) + 1; |
---|
| 1617 | |
---|
| 1618 | CFMatrix M= CFMatrix (liftBound, factors.length() - 1); |
---|
| 1619 | CFArray Pi; |
---|
| 1620 | CFList diophant; |
---|
[81d96c] | 1621 | nonMonicHenselLift12 (newSqrfPartF, factors, liftBound, Pi, diophant, M, |
---|
| 1622 | leadingCoeffs, false); |
---|
[ec16f0] | 1623 | |
---|
| 1624 | if (sqrfPartF.level() > 2) |
---|
[327efa2] | 1625 | { |
---|
[ec16f0] | 1626 | int* liftBounds= new int [sqrfPartF.level() - 1]; |
---|
| 1627 | liftBounds [0]= liftBound; |
---|
| 1628 | bool noOneToOne= false; |
---|
| 1629 | CFList *leadingCoeffs2= new CFList [sqrfPartF.level()-2]; |
---|
| 1630 | LC1= LC (evalSqrfPartF.getLast(), 1); |
---|
| 1631 | CFList LCs; |
---|
| 1632 | for (int i= 0; i < factors.length(); i++) |
---|
| 1633 | LCs.append (LC1); |
---|
| 1634 | leadingCoeffs2 [sqrfPartF.level() - 3]= LCs; |
---|
| 1635 | for (int i= sqrfPartF.level() - 1; i > 2; i--) |
---|
| 1636 | { |
---|
| 1637 | for (CFListIterator j= LCs; j.hasItem(); j++) |
---|
| 1638 | j.getItem()= j.getItem() (0, i + 1); |
---|
| 1639 | leadingCoeffs2 [i - 3]= LCs; |
---|
| 1640 | } |
---|
| 1641 | sqrfPartF *= power (LC1, factors.length()-1); |
---|
| 1642 | |
---|
| 1643 | int liftBoundsLength= sqrfPartF.level() - 1; |
---|
| 1644 | for (int i= 1; i < liftBoundsLength; i++) |
---|
| 1645 | liftBounds [i]= degree (sqrfPartF, i + 2) + 1; |
---|
| 1646 | evalSqrfPartF= evaluateAtZero (sqrfPartF); |
---|
| 1647 | evalSqrfPartF.removeFirst(); |
---|
| 1648 | factors= nonMonicHenselLift (evalSqrfPartF, factors, leadingCoeffs2, |
---|
| 1649 | diophant, Pi, liftBounds, sqrfPartF.level() - 1, noOneToOne); |
---|
| 1650 | delete [] leadingCoeffs2; |
---|
| 1651 | delete [] liftBounds; |
---|
[327efa2] | 1652 | } |
---|
[ec16f0] | 1653 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
[8a30b1] | 1654 | iter.getItem()= reverseShift (iter.getItem(), evaluation2); |
---|
[ec16f0] | 1655 | |
---|
| 1656 | interMedResult= |
---|
[8a30b1] | 1657 | recoverFactors (reverseShift(evalSqrfPartF.getLast(),evaluation2), |
---|
[ec16f0] | 1658 | factors); |
---|
[327efa2] | 1659 | } |
---|
| 1660 | } |
---|
| 1661 | else |
---|
[ec16f0] | 1662 | { |
---|
[8256fd] | 1663 | CanonicalForm contF=content (oldSqrfPartF,1); |
---|
| 1664 | factors= CFList (oldSqrfPartF/contF); |
---|
[ec16f0] | 1665 | interMedResult= recoverFactors (oldSqrfPartF, factors); |
---|
| 1666 | } |
---|
[ccd1b0] | 1667 | |
---|
[1a2d66] | 1668 | for (CFListIterator iter= interMedResult; iter.hasItem(); iter++) |
---|
| 1669 | iter.getItem()= NN (iter.getItem()); |
---|
| 1670 | |
---|
[ccd1b0] | 1671 | CFList result; |
---|
[38ffb7] | 1672 | CFFListIterator k; |
---|
[ccd1b0] | 1673 | for (int i= 0; i < LCFFactors.length(); i++) |
---|
| 1674 | { |
---|
| 1675 | CanonicalForm tmp= 1; |
---|
[38ffb7] | 1676 | for (k= bufSqrfFactors[i]; k.hasItem(); k++) |
---|
[ccd1b0] | 1677 | { |
---|
| 1678 | int pos= findItem (bufFactors, k.getItem().factor()); |
---|
| 1679 | if (pos) |
---|
| 1680 | tmp *= power (getItem (interMedResult, pos), k.getItem().exp()); |
---|
| 1681 | } |
---|
| 1682 | result.append (tmp); |
---|
| 1683 | } |
---|
| 1684 | |
---|
| 1685 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
| 1686 | { |
---|
| 1687 | F /= i.getItem(); |
---|
| 1688 | if (foundDifferent) |
---|
| 1689 | i.getItem()= swapvar (i.getItem(), x, z); |
---|
| 1690 | i.getItem()= N (i.getItem()); |
---|
| 1691 | } |
---|
| 1692 | |
---|
| 1693 | if (foundDifferent) |
---|
| 1694 | { |
---|
| 1695 | CFList l= differentSecondVarLCs [j]; |
---|
| 1696 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 1697 | i.getItem()= swapvar (i.getItem(), y, z); |
---|
| 1698 | differentSecondVarLCs [j]= l; |
---|
| 1699 | F= swapvar (F, x, z); |
---|
| 1700 | } |
---|
| 1701 | |
---|
| 1702 | result.insert (N (F)); |
---|
| 1703 | |
---|
[eefc3a] | 1704 | result= distributeContent (result, differentSecondVarLCs, lSecondVarLCs); |
---|
[ccd1b0] | 1705 | |
---|
| 1706 | if (!result.getFirst().inCoeffDomain()) |
---|
| 1707 | { |
---|
| 1708 | CFListIterator i= result; |
---|
| 1709 | CanonicalForm tmp; |
---|
| 1710 | if (foundDifferent) |
---|
| 1711 | i.getItem()= swapvar (i.getItem(), Variable (2), y); |
---|
| 1712 | |
---|
| 1713 | tmp= i.getItem(); |
---|
| 1714 | |
---|
| 1715 | i++; |
---|
| 1716 | for (; i.hasItem(); i++) |
---|
| 1717 | { |
---|
| 1718 | if (foundDifferent) |
---|
| 1719 | i.getItem()= swapvar (i.getItem(), Variable (2), y)*tmp; |
---|
| 1720 | else |
---|
| 1721 | i.getItem() *= tmp; |
---|
| 1722 | } |
---|
| 1723 | } |
---|
| 1724 | else |
---|
| 1725 | y= Variable (1); |
---|
| 1726 | |
---|
[229530] | 1727 | delete [] bufSqrfFactors; |
---|
| 1728 | |
---|
[ccd1b0] | 1729 | return result; |
---|
| 1730 | } |
---|
| 1731 | |
---|
| 1732 | void |
---|
| 1733 | evaluationWRTDifferentSecondVars (CFList*& Aeval, const CFList& evaluation, |
---|
| 1734 | const CanonicalForm& A) |
---|
| 1735 | { |
---|
[38ffb7] | 1736 | CanonicalForm tmp; |
---|
| 1737 | CFList tmp2; |
---|
| 1738 | CFListIterator iter; |
---|
[c7b56e2] | 1739 | bool preserveDegree= true; |
---|
| 1740 | int j; |
---|
[ccd1b0] | 1741 | for (int i= A.level(); i > 2; i--) |
---|
| 1742 | { |
---|
[38ffb7] | 1743 | tmp= A; |
---|
| 1744 | tmp2= CFList(); |
---|
| 1745 | iter= evaluation; |
---|
[c7b56e2] | 1746 | preserveDegree= true; |
---|
| 1747 | for (j= A.level(); j > 1; j--, iter++) |
---|
[ccd1b0] | 1748 | { |
---|
| 1749 | if (j == i) |
---|
| 1750 | continue; |
---|
| 1751 | else |
---|
| 1752 | { |
---|
| 1753 | tmp= tmp (iter.getItem(), j); |
---|
| 1754 | tmp2.insert (tmp); |
---|
| 1755 | if ((degree (tmp, i) != degree (A, i)) || |
---|
| 1756 | (degree (tmp, 1) != degree (A, 1))) |
---|
| 1757 | { |
---|
| 1758 | preserveDegree= false; |
---|
| 1759 | break; |
---|
| 1760 | } |
---|
| 1761 | if (!content(tmp).inCoeffDomain() || !content(tmp,1).inCoeffDomain()) |
---|
| 1762 | { |
---|
| 1763 | preserveDegree= false; |
---|
| 1764 | break; |
---|
| 1765 | } |
---|
| 1766 | } |
---|
| 1767 | } |
---|
| 1768 | if (preserveDegree) |
---|
| 1769 | Aeval [i - 3]= tmp2; |
---|
| 1770 | else |
---|
| 1771 | Aeval [i - 3]= CFList(); |
---|
| 1772 | } |
---|
| 1773 | } |
---|
| 1774 | |
---|
[6f6320] | 1775 | #endif |
---|
| 1776 | |
---|
[ccd1b0] | 1777 | static inline |
---|
| 1778 | CanonicalForm prodEval (const CFList& l, const CanonicalForm& evalPoint, |
---|
| 1779 | const Variable& v) |
---|
| 1780 | { |
---|
| 1781 | CanonicalForm result= 1; |
---|
| 1782 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 1783 | result *= i.getItem() (evalPoint, v); |
---|
| 1784 | return result; |
---|
| 1785 | } |
---|
| 1786 | |
---|
| 1787 | //recombine bivariate factors in case one bivariate factorization yields less |
---|
| 1788 | // factors than the other |
---|
| 1789 | CFList |
---|
| 1790 | recombination (const CFList& factors1, const CFList& factors2, int s, int thres, |
---|
| 1791 | const CanonicalForm& evalPoint, const Variable& x) |
---|
| 1792 | { |
---|
| 1793 | CFList T, S; |
---|
| 1794 | |
---|
| 1795 | T= factors1; |
---|
| 1796 | CFList result; |
---|
| 1797 | CanonicalForm buf; |
---|
| 1798 | int * v= new int [T.length()]; |
---|
| 1799 | for (int i= 0; i < T.length(); i++) |
---|
| 1800 | v[i]= 0; |
---|
| 1801 | bool nosubset= false; |
---|
| 1802 | CFArray TT; |
---|
| 1803 | TT= copy (factors1); |
---|
| 1804 | while (T.length() >= 2*s && s <= thres) |
---|
| 1805 | { |
---|
[a30a5fc] | 1806 | while (nosubset == false) |
---|
[ccd1b0] | 1807 | { |
---|
[a30a5fc] | 1808 | if (T.length() == s) |
---|
[ccd1b0] | 1809 | { |
---|
| 1810 | delete [] v; |
---|
| 1811 | result.append (prod (T)); |
---|
| 1812 | return result; |
---|
| 1813 | } |
---|
| 1814 | S= subset (v, s, TT, nosubset); |
---|
| 1815 | if (nosubset) break; |
---|
| 1816 | buf= prodEval (S, evalPoint, x); |
---|
| 1817 | buf /= Lc (buf); |
---|
| 1818 | if (find (factors2, buf)) |
---|
| 1819 | { |
---|
| 1820 | T= Difference (T, S); |
---|
| 1821 | result.append (prod (S)); |
---|
| 1822 | TT= copy (T); |
---|
| 1823 | indexUpdate (v, s, T.length(), nosubset); |
---|
| 1824 | if (nosubset) break; |
---|
| 1825 | } |
---|
| 1826 | } |
---|
| 1827 | s++; |
---|
| 1828 | if (T.length() < 2*s || T.length() == s) |
---|
| 1829 | { |
---|
| 1830 | delete [] v; |
---|
| 1831 | result.append (prod (T)); |
---|
| 1832 | return result; |
---|
| 1833 | } |
---|
| 1834 | for (int i= 0; i < T.length(); i++) |
---|
| 1835 | v[i]= 0; |
---|
| 1836 | nosubset= false; |
---|
| 1837 | } |
---|
| 1838 | |
---|
| 1839 | delete [] v; |
---|
| 1840 | if (T.length() < 2*s) |
---|
| 1841 | { |
---|
| 1842 | result.append (prod (T)); |
---|
| 1843 | return result; |
---|
| 1844 | } |
---|
| 1845 | |
---|
| 1846 | return result; |
---|
| 1847 | } |
---|
| 1848 | |
---|
[6f6320] | 1849 | #ifdef HAVE_NTL |
---|
[ccd1b0] | 1850 | void |
---|
| 1851 | factorizationWRTDifferentSecondVars (const CanonicalForm& A, CFList*& Aeval, |
---|
| 1852 | const ExtensionInfo& info, |
---|
| 1853 | int& minFactorsLength, bool& irred) |
---|
| 1854 | { |
---|
| 1855 | Variable x= Variable (1); |
---|
| 1856 | minFactorsLength= 0; |
---|
| 1857 | irred= false; |
---|
[38ffb7] | 1858 | CFList factors; |
---|
| 1859 | Variable v; |
---|
[ccd1b0] | 1860 | for (int j= 0; j < A.level() - 2; j++) |
---|
| 1861 | { |
---|
| 1862 | if (!Aeval[j].isEmpty()) |
---|
| 1863 | { |
---|
[38ffb7] | 1864 | v= Variable (Aeval[j].getFirst().level()); |
---|
[ccd1b0] | 1865 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
| 1866 | factors= GFBiSqrfFactorize (Aeval[j].getFirst()); |
---|
| 1867 | else if (info.getAlpha().level() == 1) |
---|
| 1868 | factors= FpBiSqrfFactorize (Aeval[j].getFirst()); |
---|
| 1869 | else |
---|
| 1870 | factors= FqBiSqrfFactorize (Aeval[j].getFirst(), info.getAlpha()); |
---|
| 1871 | |
---|
| 1872 | factors.removeFirst(); |
---|
| 1873 | if (minFactorsLength == 0) |
---|
| 1874 | minFactorsLength= factors.length(); |
---|
| 1875 | else |
---|
| 1876 | minFactorsLength= tmin (minFactorsLength, factors.length()); |
---|
| 1877 | |
---|
| 1878 | if (factors.length() == 1) |
---|
| 1879 | { |
---|
| 1880 | irred= true; |
---|
| 1881 | return; |
---|
| 1882 | } |
---|
| 1883 | sortList (factors, x); |
---|
| 1884 | Aeval [j]= factors; |
---|
| 1885 | } |
---|
| 1886 | } |
---|
| 1887 | } |
---|
| 1888 | |
---|
[8a30b1] | 1889 | CFList conv (const CFArray & A) |
---|
| 1890 | { |
---|
| 1891 | CFList result; |
---|
| 1892 | for (int i= A.max(); i >= A.min(); i--) |
---|
| 1893 | result.insert (A[i]); |
---|
| 1894 | return result; |
---|
| 1895 | } |
---|
| 1896 | |
---|
[772056] | 1897 | |
---|
[ccd1b0] | 1898 | void getLeadingCoeffs (const CanonicalForm& A, CFList*& Aeval, |
---|
| 1899 | const CFList& uniFactors, const CFList& evaluation |
---|
| 1900 | ) |
---|
[772056] | 1901 | { |
---|
| 1902 | CFListIterator iter; |
---|
| 1903 | CFList LCs; |
---|
| 1904 | for (int j= 0; j < A.level() - 2; j++) |
---|
| 1905 | { |
---|
| 1906 | if (!Aeval[j].isEmpty()) |
---|
| 1907 | { |
---|
| 1908 | LCs= CFList(); |
---|
| 1909 | for (iter= Aeval[j]; iter.hasItem(); iter++) |
---|
| 1910 | LCs.append (LC (iter.getItem(), 1)); |
---|
| 1911 | //normalize (LCs); |
---|
| 1912 | Aeval[j]= LCs; |
---|
| 1913 | } |
---|
| 1914 | } |
---|
| 1915 | } |
---|
| 1916 | |
---|
| 1917 | void sortByUniFactors (CFList*& Aeval, int AevalLength, |
---|
| 1918 | const CFList& uniFactors, const CFList& evaluation |
---|
| 1919 | ) |
---|
[ccd1b0] | 1920 | { |
---|
[38ffb7] | 1921 | CanonicalForm evalPoint; |
---|
| 1922 | int i; |
---|
| 1923 | CFListIterator iter, iter2; |
---|
| 1924 | Variable v; |
---|
[8a30b1] | 1925 | CFList LCs, buf; |
---|
| 1926 | CFArray l; |
---|
| 1927 | int pos, index; |
---|
[772056] | 1928 | for (int j= 0; j < AevalLength; j++) |
---|
[ccd1b0] | 1929 | { |
---|
| 1930 | if (!Aeval[j].isEmpty()) |
---|
| 1931 | { |
---|
[772056] | 1932 | i= evaluation.length() + 1; |
---|
[38ffb7] | 1933 | for (iter= evaluation; iter.hasItem(); iter++, i--) |
---|
[ccd1b0] | 1934 | { |
---|
| 1935 | if (i == Aeval[j].getFirst().level()) |
---|
| 1936 | { |
---|
| 1937 | evalPoint= iter.getItem(); |
---|
| 1938 | break; |
---|
| 1939 | } |
---|
| 1940 | } |
---|
| 1941 | |
---|
[38ffb7] | 1942 | v= Variable (i); |
---|
[ccd1b0] | 1943 | if (Aeval[j].length() > uniFactors.length()) |
---|
| 1944 | Aeval[j]= recombination (Aeval[j], uniFactors, 1, |
---|
| 1945 | Aeval[j].length() - uniFactors.length() + 1, |
---|
| 1946 | evalPoint, v); |
---|
| 1947 | |
---|
[eefc3a] | 1948 | buf= buildUniFactors (Aeval[j], evalPoint, v); |
---|
[8a30b1] | 1949 | l= CFArray (uniFactors.length()); |
---|
| 1950 | index= 1; |
---|
| 1951 | for (iter= buf; iter.hasItem(); iter++, index++) |
---|
[ccd1b0] | 1952 | { |
---|
[8a30b1] | 1953 | pos= findItem (uniFactors, iter.getItem()); |
---|
[eefc3a] | 1954 | if (pos) |
---|
[8a30b1] | 1955 | l[pos-1]= getItem (Aeval[j], index); |
---|
[ccd1b0] | 1956 | } |
---|
[8a30b1] | 1957 | buf= conv (l); |
---|
| 1958 | Aeval [j]= buf; |
---|
[ccd1b0] | 1959 | |
---|
[8a30b1] | 1960 | buf= buildUniFactors (Aeval[j], evalPoint, v); |
---|
[ccd1b0] | 1961 | } |
---|
| 1962 | } |
---|
| 1963 | } |
---|
| 1964 | |
---|
| 1965 | CFList |
---|
| 1966 | buildUniFactors (const CFList& biFactors, const CanonicalForm& evalPoint, |
---|
| 1967 | const Variable& y) |
---|
| 1968 | { |
---|
| 1969 | CFList result; |
---|
| 1970 | CanonicalForm tmp; |
---|
| 1971 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
| 1972 | { |
---|
| 1973 | tmp= mod (i.getItem(), y - evalPoint); |
---|
| 1974 | tmp /= Lc (tmp); |
---|
| 1975 | result.append (tmp); |
---|
| 1976 | } |
---|
| 1977 | return result; |
---|
| 1978 | } |
---|
| 1979 | |
---|
| 1980 | void refineBiFactors (const CanonicalForm& A, CFList& biFactors, |
---|
| 1981 | CFList* const& Aeval, const CFList& evaluation, |
---|
| 1982 | int minFactorsLength) |
---|
| 1983 | { |
---|
[38ffb7] | 1984 | CFListIterator iter; |
---|
| 1985 | CanonicalForm evalPoint; |
---|
| 1986 | int i; |
---|
| 1987 | Variable v; |
---|
| 1988 | Variable y= Variable (2); |
---|
| 1989 | CFList list; |
---|
[ccd1b0] | 1990 | for (int j= 0; j < A.level() - 2; j++) |
---|
| 1991 | { |
---|
| 1992 | if (Aeval[j].length() == minFactorsLength) |
---|
| 1993 | { |
---|
[38ffb7] | 1994 | i= A.level(); |
---|
| 1995 | |
---|
| 1996 | for (iter= evaluation; iter.hasItem(); iter++, i--) |
---|
[ccd1b0] | 1997 | { |
---|
| 1998 | if (i == Aeval[j].getFirst().level()) |
---|
| 1999 | { |
---|
| 2000 | evalPoint= iter.getItem(); |
---|
| 2001 | break; |
---|
| 2002 | } |
---|
| 2003 | } |
---|
| 2004 | |
---|
[38ffb7] | 2005 | v= Variable (i); |
---|
| 2006 | list= buildUniFactors (Aeval[j], evalPoint, v); |
---|
[ccd1b0] | 2007 | |
---|
| 2008 | biFactors= recombination (biFactors, list, 1, |
---|
| 2009 | biFactors.length() - list.length() + 1, |
---|
| 2010 | evaluation.getLast(), y); |
---|
| 2011 | return; |
---|
| 2012 | } |
---|
| 2013 | } |
---|
| 2014 | } |
---|
| 2015 | |
---|
| 2016 | void prepareLeadingCoeffs (CFList*& LCs, int n, const CFList& leadingCoeffs, |
---|
[eefc3a] | 2017 | const CFList& biFactors, const CFList& evaluation) |
---|
[ccd1b0] | 2018 | { |
---|
| 2019 | CFList l= leadingCoeffs; |
---|
| 2020 | LCs [n-3]= l; |
---|
[38ffb7] | 2021 | CFListIterator j; |
---|
[eefc3a] | 2022 | CFListIterator iter= evaluation; |
---|
| 2023 | for (int i= n - 1; i > 2; i--, iter++) |
---|
[ccd1b0] | 2024 | { |
---|
[38ffb7] | 2025 | for (j= l; j.hasItem(); j++) |
---|
[eefc3a] | 2026 | j.getItem()= j.getItem() (iter.getItem(), i + 1); |
---|
[ccd1b0] | 2027 | LCs [i - 3]= l; |
---|
| 2028 | } |
---|
| 2029 | l= LCs [0]; |
---|
| 2030 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
[eefc3a] | 2031 | i.getItem()= i.getItem() (iter.getItem(), 3); |
---|
[ccd1b0] | 2032 | CFListIterator ii= biFactors; |
---|
| 2033 | CFList normalizeFactor; |
---|
| 2034 | for (CFListIterator i= l; i.hasItem(); i++, ii++) |
---|
| 2035 | normalizeFactor.append (Lc (LC (ii.getItem(), 1))/Lc (i.getItem())); |
---|
| 2036 | for (int i= 0; i < n-2; i++) |
---|
| 2037 | { |
---|
| 2038 | ii= normalizeFactor; |
---|
[38ffb7] | 2039 | for (j= LCs [i]; j.hasItem(); j++, ii++) |
---|
[ccd1b0] | 2040 | j.getItem() *= ii.getItem(); |
---|
| 2041 | } |
---|
| 2042 | } |
---|
| 2043 | |
---|
| 2044 | CFList |
---|
| 2045 | extNonMonicFactorRecombination (const CFList& factors, const CanonicalForm& F, |
---|
[c79a9d] | 2046 | const ExtensionInfo& info) |
---|
[ccd1b0] | 2047 | { |
---|
| 2048 | Variable alpha= info.getAlpha(); |
---|
| 2049 | Variable beta= info.getBeta(); |
---|
| 2050 | CanonicalForm gamma= info.getGamma(); |
---|
| 2051 | CanonicalForm delta= info.getDelta(); |
---|
| 2052 | int k= info.getGFDegree(); |
---|
| 2053 | CFList source, dest; |
---|
| 2054 | |
---|
| 2055 | int degMipoBeta= 1; |
---|
| 2056 | if (!k && beta != Variable(1)) |
---|
| 2057 | degMipoBeta= degree (getMipo (beta)); |
---|
| 2058 | |
---|
| 2059 | CFList T, S; |
---|
| 2060 | T= factors; |
---|
| 2061 | int s= 1; |
---|
| 2062 | CFList result; |
---|
[21b8f4c] | 2063 | CanonicalForm quot, buf= F; |
---|
[ccd1b0] | 2064 | |
---|
| 2065 | CanonicalForm g; |
---|
| 2066 | CanonicalForm buf2; |
---|
| 2067 | int * v= new int [T.length()]; |
---|
| 2068 | for (int i= 0; i < T.length(); i++) |
---|
| 2069 | v[i]= 0; |
---|
| 2070 | bool noSubset= false; |
---|
| 2071 | CFArray TT; |
---|
| 2072 | TT= copy (factors); |
---|
| 2073 | bool recombination= false; |
---|
| 2074 | bool trueFactor= false; |
---|
| 2075 | while (T.length() >= 2*s) |
---|
| 2076 | { |
---|
| 2077 | while (noSubset == false) |
---|
| 2078 | { |
---|
| 2079 | if (T.length() == s) |
---|
| 2080 | { |
---|
| 2081 | delete [] v; |
---|
| 2082 | if (recombination) |
---|
| 2083 | { |
---|
| 2084 | g= prod (T); |
---|
| 2085 | T.removeFirst(); |
---|
| 2086 | result.append (g/myContent (g)); |
---|
| 2087 | g /= Lc (g); |
---|
| 2088 | appendTestMapDown (result, g, info, source, dest); |
---|
| 2089 | return result; |
---|
| 2090 | } |
---|
| 2091 | else |
---|
[dc390c] | 2092 | return CFList (buf/myContent(buf)); |
---|
[ccd1b0] | 2093 | } |
---|
| 2094 | |
---|
| 2095 | S= subset (v, s, TT, noSubset); |
---|
| 2096 | if (noSubset) break; |
---|
| 2097 | |
---|
| 2098 | g= prod (S); |
---|
| 2099 | g /= myContent (g); |
---|
[21b8f4c] | 2100 | if (fdivides (g, buf, quot)) |
---|
[ccd1b0] | 2101 | { |
---|
[c79a9d] | 2102 | buf2= g; |
---|
[ccd1b0] | 2103 | buf2 /= Lc (buf2); |
---|
[a54114] | 2104 | if (!k && beta.level() == 1) |
---|
[ccd1b0] | 2105 | { |
---|
| 2106 | if (degree (buf2, alpha) < degMipoBeta) |
---|
| 2107 | { |
---|
| 2108 | appendTestMapDown (result, buf2, info, source, dest); |
---|
[21b8f4c] | 2109 | buf= quot; |
---|
[ccd1b0] | 2110 | recombination= true; |
---|
| 2111 | trueFactor= true; |
---|
| 2112 | } |
---|
| 2113 | } |
---|
| 2114 | else |
---|
| 2115 | { |
---|
| 2116 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
| 2117 | { |
---|
| 2118 | appendTestMapDown (result, buf2, info, source, dest); |
---|
[21b8f4c] | 2119 | buf= quot; |
---|
[ccd1b0] | 2120 | recombination= true; |
---|
| 2121 | trueFactor= true; |
---|
| 2122 | } |
---|
| 2123 | } |
---|
| 2124 | if (trueFactor) |
---|
| 2125 | { |
---|
| 2126 | T= Difference (T, S); |
---|
| 2127 | |
---|
| 2128 | if (T.length() < 2*s || T.length() == s) |
---|
| 2129 | { |
---|
| 2130 | delete [] v; |
---|
[dc390c] | 2131 | buf /= myContent (buf); |
---|
[ccd1b0] | 2132 | buf /= Lc (buf); |
---|
| 2133 | appendTestMapDown (result, buf, info, source, dest); |
---|
| 2134 | return result; |
---|
| 2135 | } |
---|
| 2136 | trueFactor= false; |
---|
| 2137 | TT= copy (T); |
---|
| 2138 | indexUpdate (v, s, T.length(), noSubset); |
---|
| 2139 | if (noSubset) break; |
---|
| 2140 | } |
---|
| 2141 | } |
---|
| 2142 | } |
---|
| 2143 | s++; |
---|
| 2144 | if (T.length() < 2*s || T.length() == s) |
---|
| 2145 | { |
---|
| 2146 | delete [] v; |
---|
[dc390c] | 2147 | appendTestMapDown (result, buf/myContent(buf), info, source, dest); |
---|
[ccd1b0] | 2148 | return result; |
---|
| 2149 | } |
---|
| 2150 | for (int i= 0; i < T.length(); i++) |
---|
| 2151 | v[i]= 0; |
---|
| 2152 | noSubset= false; |
---|
| 2153 | } |
---|
| 2154 | if (T.length() < 2*s) |
---|
[dc390c] | 2155 | appendMapDown (result, F/myContent(F), info, source, dest); |
---|
[ccd1b0] | 2156 | |
---|
| 2157 | delete [] v; |
---|
| 2158 | return result; |
---|
| 2159 | } |
---|
| 2160 | |
---|
| 2161 | CFList |
---|
| 2162 | extFactorize (const CanonicalForm& F, const ExtensionInfo& info); |
---|
| 2163 | |
---|
| 2164 | CFList |
---|
| 2165 | multiFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
| 2166 | { |
---|
| 2167 | |
---|
| 2168 | if (F.inCoeffDomain()) |
---|
| 2169 | return CFList (F); |
---|
| 2170 | |
---|
| 2171 | // compress and find main Variable |
---|
| 2172 | CFMap N; |
---|
| 2173 | CanonicalForm A= myCompress (F, N); |
---|
| 2174 | |
---|
| 2175 | A /= Lc (A); // make monic |
---|
| 2176 | |
---|
| 2177 | Variable alpha= info.getAlpha(); |
---|
| 2178 | Variable beta= info.getBeta(); |
---|
| 2179 | CanonicalForm gamma= info.getGamma(); |
---|
| 2180 | CanonicalForm delta= info.getDelta(); |
---|
| 2181 | bool extension= info.isInExtension(); |
---|
| 2182 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
| 2183 | //univariate case |
---|
| 2184 | if (F.isUnivariate()) |
---|
| 2185 | { |
---|
| 2186 | if (extension == false) |
---|
| 2187 | return uniFactorizer (F, alpha, GF); |
---|
| 2188 | else |
---|
[44651b] | 2189 | { |
---|
[7bf145] | 2190 | CFList source, dest; |
---|
| 2191 | A= mapDown (F, info, source, dest); |
---|
| 2192 | return uniFactorizer (A, beta, GF); |
---|
| 2193 | } |
---|
| 2194 | } |
---|
| 2195 | |
---|
| 2196 | //bivariate case |
---|
[44651b] | 2197 | if (A.level() == 2) |
---|
[7bf145] | 2198 | { |
---|
[44651b] | 2199 | CFList buf= biFactorize (F, info); |
---|
[7bf145] | 2200 | return buf; |
---|
| 2201 | } |
---|
[44651b] | 2202 | |
---|
[7bf145] | 2203 | Variable x= Variable (1); |
---|
| 2204 | Variable y= Variable (2); |
---|
[44651b] | 2205 | |
---|
[7bf145] | 2206 | // remove content |
---|
| 2207 | CFList contentAi; |
---|
| 2208 | CanonicalForm lcmCont= lcmContent (A, contentAi); |
---|
[44651b] | 2209 | A /= lcmCont; |
---|
[7bf145] | 2210 | |
---|
| 2211 | // trivial after content removal |
---|
| 2212 | CFList contentAFactors; |
---|
[44651b] | 2213 | if (A.inCoeffDomain()) |
---|
| 2214 | { |
---|
| 2215 | for (CFListIterator i= contentAi; i.hasItem(); i++) |
---|
[7bf145] | 2216 | { |
---|
| 2217 | if (i.getItem().inCoeffDomain()) |
---|
| 2218 | continue; |
---|
[44651b] | 2219 | else |
---|
[7bf145] | 2220 | { |
---|
| 2221 | lcmCont /= i.getItem(); |
---|
[44651b] | 2222 | contentAFactors= |
---|
| 2223 | Union (multiFactorize (lcmCont, info), |
---|
[7bf145] | 2224 | multiFactorize (i.getItem(), info)); |
---|
| 2225 | break; |
---|
| 2226 | } |
---|
| 2227 | } |
---|
| 2228 | decompress (contentAFactors, N); |
---|
[41e77d] | 2229 | if (!extension) |
---|
| 2230 | normalize (contentAFactors); |
---|
[7bf145] | 2231 | return contentAFactors; |
---|
| 2232 | } |
---|
| 2233 | |
---|
| 2234 | // factorize content |
---|
[44651b] | 2235 | contentAFactors= multiFactorize (lcmCont, info); |
---|
[7bf145] | 2236 | |
---|
| 2237 | // univariate after content removal |
---|
| 2238 | CFList factors; |
---|
[44651b] | 2239 | if (A.isUnivariate ()) |
---|
[7bf145] | 2240 | { |
---|
| 2241 | factors= uniFactorizer (A, alpha, GF); |
---|
| 2242 | append (factors, contentAFactors); |
---|
| 2243 | decompress (factors, N); |
---|
| 2244 | return factors; |
---|
| 2245 | } |
---|
| 2246 | |
---|
| 2247 | // check main variable |
---|
| 2248 | int swapLevel= 0; |
---|
| 2249 | CanonicalForm derivZ; |
---|
| 2250 | CanonicalForm gcdDerivZ; |
---|
| 2251 | CanonicalForm bufA= A; |
---|
| 2252 | Variable z; |
---|
| 2253 | for (int i= 1; i <= A.level(); i++) |
---|
[44651b] | 2254 | { |
---|
[7bf145] | 2255 | z= Variable (i); |
---|
| 2256 | derivZ= deriv (bufA, z); |
---|
| 2257 | if (derivZ.isZero()) |
---|
| 2258 | { |
---|
| 2259 | if (i == 1) |
---|
| 2260 | swapLevel= 1; |
---|
| 2261 | else |
---|
| 2262 | continue; |
---|
| 2263 | } |
---|
| 2264 | else |
---|
| 2265 | { |
---|
| 2266 | if (swapLevel == 1) |
---|
| 2267 | { |
---|
| 2268 | swapLevel= i; |
---|
[ccd1b0] | 2269 | bufA= swapvar (A, x, z); |
---|
[7bf145] | 2270 | } |
---|
[04cdf06] | 2271 | gcdDerivZ= gcd (bufA, derivZ); |
---|
[44651b] | 2272 | if (degree (gcdDerivZ) > 0 && !derivZ.isZero()) |
---|
[7bf145] | 2273 | { |
---|
| 2274 | CanonicalForm g= bufA/gcdDerivZ; |
---|
[44651b] | 2275 | CFList factorsG= |
---|
[7bf145] | 2276 | Union (multiFactorize (g, info), |
---|
| 2277 | multiFactorize (gcdDerivZ, info)); |
---|
| 2278 | appendSwapDecompress (factorsG, contentAFactors, N, swapLevel, x); |
---|
[41e77d] | 2279 | if (!extension) |
---|
| 2280 | normalize (factorsG); |
---|
[7bf145] | 2281 | return factorsG; |
---|
| 2282 | } |
---|
[ccd1b0] | 2283 | else |
---|
| 2284 | { |
---|
| 2285 | A= bufA; |
---|
| 2286 | break; |
---|
| 2287 | } |
---|
[7bf145] | 2288 | } |
---|
| 2289 | } |
---|
| 2290 | |
---|
| 2291 | |
---|
| 2292 | CFList Aeval, list, evaluation, bufEvaluation, bufAeval; |
---|
| 2293 | bool fail= false; |
---|
| 2294 | int swapLevel2= 0; |
---|
| 2295 | int level; |
---|
| 2296 | int factorNums= 3; |
---|
| 2297 | CanonicalForm bivarEval; |
---|
| 2298 | CFList biFactors, bufBiFactors; |
---|
| 2299 | CanonicalForm evalPoly; |
---|
[c89740] | 2300 | int lift, bufLift, lengthAeval2= A.level()-2; |
---|
[fd5b3a] | 2301 | double logarithm= (double) ilog2 (totaldegree (A)); |
---|
| 2302 | logarithm /= log2exp; |
---|
| 2303 | logarithm= ceil (logarithm); |
---|
| 2304 | if (factorNums < (int) logarithm) |
---|
| 2305 | factorNums= (int) logarithm; |
---|
[c89740] | 2306 | CFList* bufAeval2= new CFList [lengthAeval2]; |
---|
| 2307 | CFList* Aeval2= new CFList [lengthAeval2]; |
---|
[ccd1b0] | 2308 | int counter; |
---|
| 2309 | int differentSecondVar= 0; |
---|
[44651b] | 2310 | // several bivariate factorizations |
---|
| 2311 | for (int i= 0; i < factorNums; i++) |
---|
[7bf145] | 2312 | { |
---|
[ccd1b0] | 2313 | counter= 0; |
---|
[7bf145] | 2314 | bufA= A; |
---|
| 2315 | bufAeval= CFList(); |
---|
| 2316 | bufEvaluation= evalPoints (bufA, bufAeval, alpha, list, GF, fail); |
---|
[44651b] | 2317 | evalPoly= 0; |
---|
[7bf145] | 2318 | |
---|
[44651b] | 2319 | if (fail && (i == 0)) |
---|
[7bf145] | 2320 | { |
---|
| 2321 | if (!swapLevel) |
---|
[44651b] | 2322 | level= 2; |
---|
| 2323 | else |
---|
| 2324 | level= swapLevel + 1; |
---|
[7bf145] | 2325 | |
---|
[ccd1b0] | 2326 | CanonicalForm g; |
---|
| 2327 | swapLevel2= newMainVariableSearch (A, Aeval, evaluation, alpha, level, g); |
---|
[7bf145] | 2328 | |
---|
| 2329 | if (!swapLevel2) // need to pass to an extension |
---|
[44651b] | 2330 | { |
---|
| 2331 | factors= extFactorize (A, info); |
---|
| 2332 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, x); |
---|
| 2333 | normalize (factors); |
---|
[ccd1b0] | 2334 | delete [] bufAeval2; |
---|
| 2335 | delete [] Aeval2; |
---|
[44651b] | 2336 | return factors; |
---|
[7bf145] | 2337 | } |
---|
| 2338 | else |
---|
| 2339 | { |
---|
[ccd1b0] | 2340 | if (swapLevel2 == -1) |
---|
| 2341 | { |
---|
| 2342 | CFList factorsG= |
---|
| 2343 | Union (multiFactorize (g, info), |
---|
| 2344 | multiFactorize (A/g, info)); |
---|
| 2345 | appendSwapDecompress (factorsG, contentAFactors, N, swapLevel, x); |
---|
[41e77d] | 2346 | if (!extension) |
---|
| 2347 | normalize (factorsG); |
---|
[ccd1b0] | 2348 | delete [] bufAeval2; |
---|
| 2349 | delete [] Aeval2; |
---|
| 2350 | return factorsG; |
---|
| 2351 | } |
---|
[7bf145] | 2352 | fail= false; |
---|
| 2353 | bufAeval= Aeval; |
---|
| 2354 | bufA= A; |
---|
[44651b] | 2355 | bufEvaluation= evaluation; |
---|
[7bf145] | 2356 | } |
---|
| 2357 | } |
---|
| 2358 | else if (fail && (i > 0)) |
---|
| 2359 | break; |
---|
| 2360 | |
---|
| 2361 | bivarEval= bufEvaluation.getLast(); |
---|
[ccd1b0] | 2362 | |
---|
| 2363 | evaluationWRTDifferentSecondVars (bufAeval2, bufEvaluation, A); |
---|
| 2364 | |
---|
[c89740] | 2365 | for (int j= 0; j < lengthAeval2; j++) |
---|
[ccd1b0] | 2366 | { |
---|
| 2367 | if (!bufAeval2[j].isEmpty()) |
---|
| 2368 | counter++; |
---|
| 2369 | } |
---|
[7bf145] | 2370 | |
---|
| 2371 | bufLift= degree (A, y) + 1 + degree (LC(A, x), y); |
---|
| 2372 | |
---|
[978ce3] | 2373 | TIMING_START (fac_fq_bi_factorizer); |
---|
[ccd1b0] | 2374 | if (!GF && alpha.level() == 1) |
---|
| 2375 | bufBiFactors= FpBiSqrfFactorize (bufAeval.getFirst()); |
---|
| 2376 | else if (GF) |
---|
| 2377 | bufBiFactors= GFBiSqrfFactorize (bufAeval.getFirst()); |
---|
| 2378 | else |
---|
| 2379 | bufBiFactors= FqBiSqrfFactorize (bufAeval.getFirst(), alpha); |
---|
[978ce3] | 2380 | TIMING_END_AND_PRINT (fac_fq_bi_factorizer, |
---|
[44651b] | 2381 | "time for bivariate factorization: "); |
---|
[ccd1b0] | 2382 | bufBiFactors.removeFirst(); |
---|
[7bf145] | 2383 | |
---|
[44651b] | 2384 | if (bufBiFactors.length() == 1) |
---|
[7bf145] | 2385 | { |
---|
[44651b] | 2386 | if (extension) |
---|
[7bf145] | 2387 | { |
---|
[44651b] | 2388 | CFList source, dest; |
---|
| 2389 | A= mapDown (A, info, source, dest); |
---|
[7bf145] | 2390 | } |
---|
| 2391 | factors.append (A); |
---|
| 2392 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, |
---|
[44651b] | 2393 | swapLevel2, x); |
---|
[41e77d] | 2394 | if (!extension) |
---|
| 2395 | normalize (factors); |
---|
[ccd1b0] | 2396 | delete [] bufAeval2; |
---|
| 2397 | delete [] Aeval2; |
---|
[7bf145] | 2398 | return factors; |
---|
| 2399 | } |
---|
| 2400 | |
---|
| 2401 | if (i == 0) |
---|
| 2402 | { |
---|
| 2403 | Aeval= bufAeval; |
---|
| 2404 | evaluation= bufEvaluation; |
---|
| 2405 | biFactors= bufBiFactors; |
---|
| 2406 | lift= bufLift; |
---|
[c89740] | 2407 | for (int j= 0; j < lengthAeval2; j++) |
---|
[ccd1b0] | 2408 | Aeval2 [j]= bufAeval2 [j]; |
---|
| 2409 | differentSecondVar= counter; |
---|
[7bf145] | 2410 | } |
---|
| 2411 | else |
---|
| 2412 | { |
---|
[44651b] | 2413 | if (bufBiFactors.length() < biFactors.length() || |
---|
[ccd1b0] | 2414 | ((bufLift < lift) && (bufBiFactors.length() == biFactors.length())) || |
---|
| 2415 | counter > differentSecondVar) |
---|
[7bf145] | 2416 | { |
---|
| 2417 | Aeval= bufAeval; |
---|
| 2418 | evaluation= bufEvaluation; |
---|
| 2419 | biFactors= bufBiFactors; |
---|
| 2420 | lift= bufLift; |
---|
[c89740] | 2421 | for (int j= 0; j < lengthAeval2; j++) |
---|
[ccd1b0] | 2422 | Aeval2 [j]= bufAeval2 [j]; |
---|
| 2423 | differentSecondVar= counter; |
---|
[7bf145] | 2424 | } |
---|
| 2425 | } |
---|
| 2426 | int k= 0; |
---|
| 2427 | for (CFListIterator j= bufEvaluation; j.hasItem(); j++, k++) |
---|
| 2428 | evalPoly += j.getItem()*power (x, k); |
---|
[44651b] | 2429 | list.append (evalPoly); |
---|
[7bf145] | 2430 | } |
---|
| 2431 | |
---|
[ccd1b0] | 2432 | delete [] bufAeval2; |
---|
| 2433 | |
---|
| 2434 | sortList (biFactors, x); |
---|
| 2435 | |
---|
| 2436 | int minFactorsLength; |
---|
| 2437 | bool irred= false; |
---|
[c7b56e2] | 2438 | factorizationWRTDifferentSecondVars (A, Aeval2, info, minFactorsLength,irred); |
---|
[ccd1b0] | 2439 | |
---|
| 2440 | if (irred) |
---|
| 2441 | { |
---|
| 2442 | if (extension) |
---|
| 2443 | { |
---|
| 2444 | CFList source, dest; |
---|
| 2445 | A= mapDown (A, info, source, dest); |
---|
| 2446 | } |
---|
| 2447 | factors.append (A); |
---|
| 2448 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, |
---|
| 2449 | swapLevel2, x); |
---|
[41e77d] | 2450 | if (!extension) |
---|
| 2451 | normalize (factors); |
---|
[ccd1b0] | 2452 | delete [] Aeval2; |
---|
| 2453 | return factors; |
---|
| 2454 | } |
---|
| 2455 | |
---|
| 2456 | if (minFactorsLength == 0) |
---|
| 2457 | minFactorsLength= biFactors.length(); |
---|
| 2458 | else if (biFactors.length() > minFactorsLength) |
---|
| 2459 | refineBiFactors (A, biFactors, Aeval2, evaluation, minFactorsLength); |
---|
[6036d90] | 2460 | minFactorsLength= tmin (minFactorsLength, biFactors.length()); |
---|
| 2461 | |
---|
[c89740] | 2462 | if (differentSecondVar == lengthAeval2) |
---|
[6036d90] | 2463 | { |
---|
| 2464 | bool zeroOccured= false; |
---|
| 2465 | for (CFListIterator iter= evaluation; iter.hasItem(); iter++) |
---|
| 2466 | { |
---|
| 2467 | if (iter.getItem().isZero()) |
---|
| 2468 | { |
---|
| 2469 | zeroOccured= true; |
---|
| 2470 | break; |
---|
| 2471 | } |
---|
| 2472 | } |
---|
| 2473 | if (!zeroOccured) |
---|
| 2474 | { |
---|
[c7b56e2] | 2475 | factors= sparseHeuristic (A, biFactors, Aeval2, evaluation, |
---|
| 2476 | minFactorsLength); |
---|
[6036d90] | 2477 | if (factors.length() == biFactors.length()) |
---|
| 2478 | { |
---|
| 2479 | if (extension) |
---|
| 2480 | factors= extNonMonicFactorRecombination (factors, A, info); |
---|
| 2481 | |
---|
| 2482 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, |
---|
| 2483 | swapLevel2, x); |
---|
[41e77d] | 2484 | if (!extension) |
---|
| 2485 | normalize (factors); |
---|
[6036d90] | 2486 | delete [] Aeval2; |
---|
| 2487 | return factors; |
---|
| 2488 | } |
---|
| 2489 | else |
---|
| 2490 | factors= CFList(); |
---|
| 2491 | //TODO case where factors.length() > 0 |
---|
| 2492 | } |
---|
| 2493 | } |
---|
[ccd1b0] | 2494 | |
---|
| 2495 | CFList uniFactors= buildUniFactors (biFactors, evaluation.getLast(), y); |
---|
| 2496 | |
---|
[c89740] | 2497 | sortByUniFactors (Aeval2, lengthAeval2, uniFactors, evaluation); |
---|
[fce807] | 2498 | |
---|
[c89740] | 2499 | CFList * oldAeval= new CFList [lengthAeval2]; //TODO use bufAeval2 for this |
---|
| 2500 | for (int i= 0; i < lengthAeval2; i++) |
---|
[ccd1b0] | 2501 | oldAeval[i]= Aeval2[i]; |
---|
| 2502 | |
---|
| 2503 | getLeadingCoeffs (A, Aeval2, uniFactors, evaluation); |
---|
| 2504 | |
---|
| 2505 | CFList biFactorsLCs; |
---|
| 2506 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
| 2507 | biFactorsLCs.append (LC (i.getItem(), 1)); |
---|
| 2508 | |
---|
| 2509 | Variable v; |
---|
| 2510 | CFList leadingCoeffs= precomputeLeadingCoeff (LC (A, 1), biFactorsLCs, alpha, |
---|
[c89740] | 2511 | evaluation, Aeval2, lengthAeval2, v); |
---|
[ccd1b0] | 2512 | |
---|
| 2513 | if (v.level() != 1) |
---|
[7bf145] | 2514 | { |
---|
[ccd1b0] | 2515 | A= swapvar (A, y, v); |
---|
| 2516 | int i= A.level(); |
---|
| 2517 | CanonicalForm evalPoint; |
---|
| 2518 | for (CFListIterator iter= evaluation; iter.hasItem(); iter++, i--) |
---|
| 2519 | { |
---|
| 2520 | if (i == v.level()) |
---|
| 2521 | { |
---|
| 2522 | evalPoint= iter.getItem(); |
---|
| 2523 | iter.getItem()= evaluation.getLast(); |
---|
| 2524 | evaluation.removeLast(); |
---|
| 2525 | evaluation.append (evalPoint); |
---|
| 2526 | break; |
---|
| 2527 | } |
---|
| 2528 | } |
---|
[c89740] | 2529 | for (i= 0; i < lengthAeval2; i++) |
---|
[8256fd] | 2530 | { |
---|
| 2531 | if (oldAeval[i].isEmpty()) |
---|
| 2532 | continue; |
---|
| 2533 | if (oldAeval[i].getFirst().level() == v.level()) |
---|
| 2534 | { |
---|
| 2535 | CFArray tmp= copy (oldAeval[i]); |
---|
[753fb61] | 2536 | oldAeval[i]= biFactors; |
---|
| 2537 | for (CFListIterator iter= oldAeval[i]; iter.hasItem(); iter++) |
---|
| 2538 | iter.getItem()= swapvar (iter.getItem(), v, y); |
---|
[8256fd] | 2539 | for (int ii= 0; ii < tmp.size(); ii++) |
---|
| 2540 | tmp[ii]= swapvar (tmp[ii], v, y); |
---|
| 2541 | CFArray tmp2= CFArray (tmp.size()); |
---|
| 2542 | CanonicalForm buf; |
---|
| 2543 | for (int ii= 0; ii < tmp.size(); ii++) |
---|
| 2544 | { |
---|
| 2545 | buf= tmp[ii] (evaluation.getLast(),y); |
---|
| 2546 | buf /= Lc (buf); |
---|
| 2547 | tmp2[findItem (uniFactors, buf)-1]=tmp[ii]; |
---|
| 2548 | } |
---|
| 2549 | biFactors= CFList(); |
---|
| 2550 | for (int j= 0; j < tmp2.size(); j++) |
---|
| 2551 | biFactors.append (tmp2[j]); |
---|
| 2552 | } |
---|
| 2553 | } |
---|
[7bf145] | 2554 | } |
---|
[ccd1b0] | 2555 | |
---|
[eefc3a] | 2556 | CFListIterator iter; |
---|
[ccd1b0] | 2557 | CanonicalForm oldA= A; |
---|
| 2558 | CFList oldBiFactors= biFactors; |
---|
| 2559 | if (!leadingCoeffs.getFirst().inCoeffDomain()) |
---|
| 2560 | { |
---|
| 2561 | CanonicalForm tmp= power (leadingCoeffs.getFirst(), biFactors.length() - 1); |
---|
| 2562 | A *= tmp; |
---|
| 2563 | tmp= leadingCoeffs.getFirst(); |
---|
[eefc3a] | 2564 | iter= evaluation; |
---|
| 2565 | for (int i= A.level(); i > 2; i--, iter++) |
---|
| 2566 | tmp= tmp (iter.getItem(), i); |
---|
[ccd1b0] | 2567 | if (!tmp.inCoeffDomain()) |
---|
| 2568 | { |
---|
| 2569 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
| 2570 | { |
---|
| 2571 | i.getItem() *= tmp/LC (i.getItem(), 1); |
---|
| 2572 | i.getItem() /= Lc (i.getItem()); |
---|
| 2573 | } |
---|
| 2574 | } |
---|
| 2575 | } |
---|
| 2576 | |
---|
[c89740] | 2577 | CanonicalForm LCmultiplier= leadingCoeffs.getFirst(); |
---|
| 2578 | bool LCmultiplierIsConst= LCmultiplier.inCoeffDomain(); |
---|
[ccd1b0] | 2579 | leadingCoeffs.removeFirst(); |
---|
| 2580 | |
---|
| 2581 | //prepare leading coefficients |
---|
[c89740] | 2582 | CFList* leadingCoeffs2= new CFList [lengthAeval2]; |
---|
[eefc3a] | 2583 | prepareLeadingCoeffs (leadingCoeffs2, A.level(), leadingCoeffs, biFactors, |
---|
| 2584 | evaluation); |
---|
| 2585 | |
---|
| 2586 | Aeval= evaluateAtEval (A, evaluation, 2); |
---|
| 2587 | CanonicalForm hh= Lc (Aeval.getFirst()); |
---|
| 2588 | for (iter= Aeval; iter.hasItem(); iter++) |
---|
| 2589 | iter.getItem() /= hh; |
---|
| 2590 | |
---|
| 2591 | A /= hh; |
---|
| 2592 | |
---|
[c89740] | 2593 | CFListIterator iter2; |
---|
| 2594 | CFList bufLeadingCoeffs2= leadingCoeffs2[lengthAeval2-1]; |
---|
| 2595 | bufBiFactors= biFactors; |
---|
| 2596 | bufA= A; |
---|
| 2597 | CanonicalForm bufLCmultiplier= LCmultiplier; |
---|
| 2598 | CanonicalForm testVars; |
---|
| 2599 | if (!LCmultiplierIsConst) |
---|
| 2600 | { |
---|
| 2601 | testVars= Variable (2); |
---|
| 2602 | for (int i= 0; i < lengthAeval2; i++) |
---|
| 2603 | { |
---|
| 2604 | if (!oldAeval[i].isEmpty()) |
---|
| 2605 | testVars *= oldAeval[i].getFirst().mvar(); |
---|
| 2606 | } |
---|
| 2607 | } |
---|
[5079887] | 2608 | CFList bufFactors= CFList(); |
---|
[c89740] | 2609 | bool LCheuristic= false; |
---|
[b30017] | 2610 | if (LucksWangSparseHeuristic (A, biFactors, 2, leadingCoeffs2[lengthAeval2-1], |
---|
[5079887] | 2611 | factors)) |
---|
[4fe8a3] | 2612 | { |
---|
[5079887] | 2613 | int check= biFactors.length(); |
---|
| 2614 | int * index= new int [factors.length()]; |
---|
| 2615 | CFList oldFactors= factors; |
---|
| 2616 | factors= recoverFactors (A, factors, index); |
---|
[4fe8a3] | 2617 | |
---|
| 2618 | if (check == factors.length()) |
---|
| 2619 | { |
---|
| 2620 | if (extension) |
---|
[b30017] | 2621 | factors= extNonMonicFactorRecombination (factors, bufA, info); |
---|
[4fe8a3] | 2622 | |
---|
[dc390c] | 2623 | if (v.level() != 1) |
---|
| 2624 | { |
---|
[5079887] | 2625 | for (iter= factors; iter.hasItem(); iter++) |
---|
[dc390c] | 2626 | iter.getItem()= swapvar (iter.getItem(), v, y); |
---|
| 2627 | } |
---|
[5079887] | 2628 | |
---|
[4fe8a3] | 2629 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, |
---|
| 2630 | swapLevel2, x); |
---|
[41e77d] | 2631 | if (!extension) |
---|
| 2632 | normalize (factors); |
---|
[5079887] | 2633 | delete [] index; |
---|
[4fe8a3] | 2634 | delete [] Aeval2; |
---|
| 2635 | return factors; |
---|
| 2636 | } |
---|
[5079887] | 2637 | else if (factors.length() > 0) |
---|
| 2638 | { |
---|
| 2639 | int oneCount= 0; |
---|
| 2640 | CFList l; |
---|
| 2641 | for (int i= 0; i < check; i++) |
---|
| 2642 | { |
---|
| 2643 | if (index[i] == 1) |
---|
| 2644 | { |
---|
| 2645 | iter=biFactors; |
---|
| 2646 | for (int j=1; j <= i-oneCount; j++) |
---|
| 2647 | iter++; |
---|
| 2648 | iter.remove (1); |
---|
[c89740] | 2649 | for (int j= 0; j < lengthAeval2; j++) |
---|
[5079887] | 2650 | { |
---|
| 2651 | l= leadingCoeffs2[j]; |
---|
| 2652 | iter= l; |
---|
| 2653 | for (int k=1; k <= i-oneCount; k++) |
---|
| 2654 | iter++; |
---|
| 2655 | iter.remove (1); |
---|
| 2656 | leadingCoeffs2[j]=l; |
---|
| 2657 | } |
---|
| 2658 | oneCount++; |
---|
| 2659 | } |
---|
| 2660 | } |
---|
| 2661 | bufFactors= factors; |
---|
| 2662 | factors= CFList(); |
---|
| 2663 | } |
---|
[b30017] | 2664 | else if (!LCmultiplierIsConst && factors.length() == 0) |
---|
| 2665 | { |
---|
| 2666 | LCheuristic= true; |
---|
| 2667 | factors= oldFactors; |
---|
| 2668 | CanonicalForm cont; |
---|
| 2669 | CFList contents, LCs; |
---|
| 2670 | int index=1; |
---|
| 2671 | bool foundTrueMultiplier= false; |
---|
| 2672 | for (iter= factors; iter.hasItem(); iter++, index++) |
---|
| 2673 | { |
---|
| 2674 | cont= content (iter.getItem(), 1); |
---|
| 2675 | cont= gcd (cont , LCmultiplier); |
---|
| 2676 | contents.append (cont); |
---|
| 2677 | if (cont.inCoeffDomain()) // trivial content->LCmultiplier needs to go there |
---|
| 2678 | { |
---|
| 2679 | foundTrueMultiplier= true; |
---|
| 2680 | int index2= 1; |
---|
| 2681 | for (iter2= leadingCoeffs2[lengthAeval2-1]; iter2.hasItem(); iter2++, |
---|
| 2682 | index2++) |
---|
| 2683 | { |
---|
| 2684 | if (index2 == index) |
---|
| 2685 | continue; |
---|
| 2686 | iter2.getItem() /= LCmultiplier; |
---|
| 2687 | } |
---|
| 2688 | A= oldA; |
---|
| 2689 | leadingCoeffs= leadingCoeffs2[lengthAeval2-1]; |
---|
| 2690 | for (int i= lengthAeval2-1; i > -1; i--) |
---|
| 2691 | leadingCoeffs2[i]= CFList(); |
---|
| 2692 | prepareLeadingCoeffs (leadingCoeffs2, A.level(), leadingCoeffs, |
---|
| 2693 | biFactors, evaluation ); |
---|
| 2694 | Aeval= evaluateAtEval (A, evaluation, 2); |
---|
| 2695 | |
---|
| 2696 | hh= Lc (Aeval.getFirst()); |
---|
| 2697 | |
---|
| 2698 | for (iter2= Aeval; iter2.hasItem(); iter2++) |
---|
| 2699 | iter2.getItem() /= hh; |
---|
| 2700 | |
---|
| 2701 | A /= hh; |
---|
| 2702 | break; |
---|
| 2703 | } |
---|
| 2704 | else |
---|
| 2705 | LCs.append (LC (iter.getItem()/cont, 1)); |
---|
| 2706 | } |
---|
| 2707 | if (!foundTrueMultiplier) |
---|
| 2708 | { |
---|
| 2709 | index= 1; |
---|
| 2710 | iter2= factors; |
---|
| 2711 | bool foundMultiplier= false; |
---|
| 2712 | for (iter= contents; iter.hasItem(); iter++, iter2++, index++) |
---|
| 2713 | { |
---|
| 2714 | if (fdivides (iter.getItem(), LCmultiplier)) |
---|
| 2715 | { |
---|
| 2716 | if ((LCmultiplier/iter.getItem()).inCoeffDomain() && |
---|
| 2717 | !isOnlyLeadingCoeff(iter2.getItem())) //content divides LCmultiplier completely and factor consists of more terms than just the leading coeff |
---|
| 2718 | { |
---|
| 2719 | int index2= 1; |
---|
| 2720 | for (CFListIterator iter3= leadingCoeffs2[lengthAeval2-1]; |
---|
| 2721 | iter3.hasItem(); iter3++, index2++) |
---|
| 2722 | { |
---|
| 2723 | if (index2 == index) |
---|
| 2724 | { |
---|
| 2725 | iter3.getItem() /= LCmultiplier; |
---|
| 2726 | break; |
---|
| 2727 | } |
---|
| 2728 | } |
---|
| 2729 | A /= LCmultiplier; |
---|
| 2730 | foundMultiplier= true; |
---|
| 2731 | iter.getItem()= 1; |
---|
| 2732 | } |
---|
| 2733 | } |
---|
| 2734 | } |
---|
| 2735 | // coming from above: divide out more LCmultiplier if possible |
---|
| 2736 | if (foundMultiplier) |
---|
| 2737 | { |
---|
| 2738 | foundMultiplier= false; |
---|
| 2739 | index=1; |
---|
| 2740 | iter2= factors; |
---|
| 2741 | for (iter= contents; iter.hasItem(); iter++, iter2++, index++) |
---|
| 2742 | { |
---|
| 2743 | if (!iter.getItem().isOne() && |
---|
| 2744 | fdivides (iter.getItem(), LCmultiplier)) |
---|
| 2745 | { |
---|
| 2746 | if (!isOnlyLeadingCoeff (iter2.getItem())) // factor is more than just leading coeff |
---|
| 2747 | { |
---|
| 2748 | int index2= 1; |
---|
| 2749 | for (iter2= leadingCoeffs2[lengthAeval2-1]; iter2.hasItem(); |
---|
| 2750 | iter2++, index2++) |
---|
| 2751 | { |
---|
| 2752 | if (index2 == index) |
---|
| 2753 | { |
---|
| 2754 | iter2.getItem() /= iter.getItem(); |
---|
| 2755 | foundMultiplier= true; |
---|
| 2756 | break; |
---|
| 2757 | } |
---|
| 2758 | } |
---|
| 2759 | A /= iter.getItem(); |
---|
| 2760 | LCmultiplier /= iter.getItem(); |
---|
| 2761 | iter.getItem()= 1; |
---|
| 2762 | } |
---|
| 2763 | else if (fdivides (getVars (LCmultiplier), testVars))//factor consists of just leading coeff |
---|
| 2764 | { |
---|
| 2765 | //TODO maybe use a sqrffree decomposition of LCmultiplier as below |
---|
| 2766 | Variable xx= Variable (2); |
---|
| 2767 | CanonicalForm vars; |
---|
| 2768 | vars= power (xx, degree (LC (getItem(oldBiFactors, index),1), |
---|
| 2769 | xx)); |
---|
| 2770 | for (int i= 0; i < lengthAeval2; i++) |
---|
| 2771 | { |
---|
| 2772 | if (oldAeval[i].isEmpty()) |
---|
| 2773 | continue; |
---|
| 2774 | xx= oldAeval[i].getFirst().mvar(); |
---|
| 2775 | vars *= power (xx, degree (LC (getItem(oldAeval[i], index),1), |
---|
| 2776 | xx)); |
---|
| 2777 | } |
---|
| 2778 | if (myGetVars(content(getItem(leadingCoeffs2[lengthAeval2-1],index),1)) |
---|
| 2779 | /myGetVars (LCmultiplier) == vars) |
---|
| 2780 | { |
---|
| 2781 | int index2= 1; |
---|
| 2782 | for (iter2= leadingCoeffs2[lengthAeval2-1]; iter2.hasItem(); |
---|
| 2783 | iter2++, index2++) |
---|
| 2784 | { |
---|
| 2785 | if (index2 == index) |
---|
| 2786 | { |
---|
| 2787 | iter2.getItem() /= LCmultiplier; |
---|
| 2788 | foundMultiplier= true; |
---|
| 2789 | break; |
---|
| 2790 | } |
---|
| 2791 | } |
---|
| 2792 | A /= LCmultiplier; |
---|
| 2793 | iter.getItem()= 1; |
---|
| 2794 | } |
---|
| 2795 | } |
---|
| 2796 | } |
---|
| 2797 | } |
---|
| 2798 | } |
---|
| 2799 | else |
---|
| 2800 | { |
---|
| 2801 | CanonicalForm pLCs= prod (LCs); |
---|
| 2802 | if (fdivides (pLCs, LC (oldA,1)) && (LC(oldA,1)/pLCs).inCoeffDomain()) // check if the product of the lead coeffs of the primitive factors equals the lead coeff of the old A |
---|
| 2803 | { |
---|
| 2804 | A= oldA; |
---|
| 2805 | iter2= leadingCoeffs2[lengthAeval2-1]; |
---|
| 2806 | for (iter= contents; iter.hasItem(); iter++, iter2++) |
---|
| 2807 | iter2.getItem() /= iter.getItem(); |
---|
| 2808 | foundMultiplier= true; |
---|
| 2809 | } |
---|
| 2810 | if (!foundMultiplier && fdivides (getVars (LCmultiplier), testVars)) |
---|
| 2811 | { |
---|
| 2812 | Variable xx; |
---|
| 2813 | CFList vars1; |
---|
| 2814 | CFFList sqrfMultiplier= sqrFree (LCmultiplier); |
---|
| 2815 | if (sqrfMultiplier.getFirst().factor().inCoeffDomain()) |
---|
| 2816 | sqrfMultiplier.removeFirst(); |
---|
| 2817 | sqrfMultiplier= sortCFFListByNumOfVars (sqrfMultiplier); |
---|
| 2818 | xx= Variable (2); |
---|
| 2819 | for (iter= oldBiFactors; iter.hasItem(); iter++) |
---|
| 2820 | vars1.append (power (xx, degree (LC (iter.getItem(),1), xx))); |
---|
| 2821 | for (int i= 0; i < lengthAeval2; i++) |
---|
| 2822 | { |
---|
| 2823 | if (oldAeval[i].isEmpty()) |
---|
| 2824 | continue; |
---|
| 2825 | xx= oldAeval[i].getFirst().mvar(); |
---|
| 2826 | iter2= vars1; |
---|
| 2827 | for (iter= oldAeval[i]; iter.hasItem(); iter++, iter2++) |
---|
| 2828 | iter2.getItem() *= power(xx,degree (LC (iter.getItem(),1), xx)); |
---|
| 2829 | } |
---|
| 2830 | CanonicalForm tmp; |
---|
| 2831 | iter2= vars1; |
---|
| 2832 | for (iter= leadingCoeffs2[lengthAeval2-1]; iter.hasItem(); iter++, |
---|
| 2833 | iter2++) |
---|
| 2834 | { |
---|
| 2835 | tmp= iter.getItem()/LCmultiplier; |
---|
| 2836 | for (int i=1; i <= tmp.level(); i++) |
---|
| 2837 | { |
---|
[bed38b] | 2838 | if (degree(tmp,i) > 0 && |
---|
| 2839 | (degree(iter2.getItem(),i) > degree (tmp,i))) |
---|
[b30017] | 2840 | iter2.getItem() /= power (Variable (i), degree (tmp,i)); |
---|
| 2841 | } |
---|
| 2842 | } |
---|
| 2843 | int multi; |
---|
| 2844 | for (CFFListIterator ii= sqrfMultiplier; ii.hasItem(); ii++) |
---|
| 2845 | { |
---|
| 2846 | multi= 0; |
---|
| 2847 | for (iter= vars1; iter.hasItem(); iter++) |
---|
| 2848 | { |
---|
| 2849 | tmp= iter.getItem(); |
---|
| 2850 | while (fdivides (myGetVars (ii.getItem().factor()), tmp)) |
---|
| 2851 | { |
---|
| 2852 | multi++; |
---|
| 2853 | tmp /= myGetVars (ii.getItem().factor()); |
---|
| 2854 | } |
---|
| 2855 | } |
---|
| 2856 | if (multi == ii.getItem().exp()) |
---|
| 2857 | { |
---|
| 2858 | index= 1; |
---|
| 2859 | for (iter= vars1; iter.hasItem(); iter++, index++) |
---|
| 2860 | { |
---|
| 2861 | while (fdivides (myGetVars(ii.getItem().factor()), |
---|
| 2862 | iter.getItem() |
---|
| 2863 | ) |
---|
| 2864 | ) |
---|
| 2865 | { |
---|
| 2866 | int index2= 1; |
---|
| 2867 | for (iter2= leadingCoeffs2[lengthAeval2-1]; iter2.hasItem(); |
---|
| 2868 | iter2++, index2++) |
---|
| 2869 | { |
---|
| 2870 | if (index2 == index) |
---|
| 2871 | continue; |
---|
| 2872 | else |
---|
| 2873 | { |
---|
| 2874 | tmp= ii.getItem().factor(); |
---|
| 2875 | iter2.getItem() /= tmp; |
---|
| 2876 | CFListIterator iter3= evaluation; |
---|
| 2877 | for (int jj= A.level(); jj > 2; jj--, iter3++) |
---|
| 2878 | tmp= tmp (iter3.getItem(), jj); |
---|
| 2879 | if (!tmp.inCoeffDomain()) |
---|
| 2880 | { |
---|
| 2881 | int index3= 1; |
---|
| 2882 | for (iter3= biFactors; iter3.hasItem(); iter3++, |
---|
| 2883 | index3++) |
---|
| 2884 | { |
---|
| 2885 | if (index3 == index2) |
---|
| 2886 | { |
---|
| 2887 | iter3.getItem() /= tmp; |
---|
| 2888 | iter3.getItem() /= Lc (iter3.getItem()); |
---|
| 2889 | break; |
---|
| 2890 | } |
---|
| 2891 | } |
---|
| 2892 | } |
---|
| 2893 | A /= ii.getItem().factor(); |
---|
| 2894 | } |
---|
| 2895 | } |
---|
| 2896 | iter.getItem() /= getVars (ii.getItem().factor()); |
---|
| 2897 | } |
---|
| 2898 | } |
---|
| 2899 | } |
---|
| 2900 | else |
---|
| 2901 | { |
---|
| 2902 | index= 1; |
---|
| 2903 | for (iter= vars1; iter.hasItem(); iter++, index++) |
---|
| 2904 | { |
---|
| 2905 | if (!fdivides (myGetVars (ii.getItem().factor()), |
---|
| 2906 | iter.getItem() |
---|
| 2907 | ) |
---|
| 2908 | ) |
---|
| 2909 | { |
---|
| 2910 | int index2= 1; |
---|
| 2911 | for (iter2= leadingCoeffs2[lengthAeval2-1]; iter2.hasItem(); |
---|
| 2912 | iter2++, index2++) |
---|
| 2913 | { |
---|
| 2914 | if (index2 == index) |
---|
| 2915 | { |
---|
| 2916 | tmp= power (ii.getItem().factor(), ii.getItem().exp()); |
---|
| 2917 | iter2.getItem() /= tmp; |
---|
| 2918 | A /= tmp; |
---|
| 2919 | CFListIterator iter3= evaluation; |
---|
| 2920 | for (int jj= A.level(); jj > 2; jj--, iter3++) |
---|
| 2921 | tmp= tmp (iter3.getItem(), jj); |
---|
| 2922 | if (!tmp.inCoeffDomain()) |
---|
| 2923 | { |
---|
| 2924 | int index3= 1; |
---|
| 2925 | for (iter3= biFactors; iter3.hasItem(); iter3++, |
---|
| 2926 | index3++) |
---|
| 2927 | { |
---|
| 2928 | if (index3 == index2) |
---|
| 2929 | { |
---|
| 2930 | iter3.getItem() /= tmp; |
---|
| 2931 | iter3.getItem() /= Lc (iter3.getItem()); |
---|
| 2932 | break; |
---|
| 2933 | } |
---|
| 2934 | } |
---|
| 2935 | } |
---|
| 2936 | } |
---|
| 2937 | } |
---|
| 2938 | } |
---|
| 2939 | } |
---|
| 2940 | } |
---|
| 2941 | } |
---|
| 2942 | } |
---|
| 2943 | } |
---|
| 2944 | |
---|
| 2945 | // patch everything together again |
---|
| 2946 | leadingCoeffs= leadingCoeffs2[lengthAeval2-1]; |
---|
| 2947 | for (int i= lengthAeval2-1; i > -1; i--) |
---|
| 2948 | leadingCoeffs2[i]= CFList(); |
---|
| 2949 | prepareLeadingCoeffs (leadingCoeffs2,A.level(),leadingCoeffs, biFactors, |
---|
| 2950 | evaluation); |
---|
| 2951 | Aeval= evaluateAtEval (A, evaluation, 2); |
---|
| 2952 | |
---|
| 2953 | hh= Lc (Aeval.getFirst()); |
---|
| 2954 | |
---|
| 2955 | for (CFListIterator i= Aeval; i.hasItem(); i++) |
---|
| 2956 | i.getItem() /= hh; |
---|
| 2957 | |
---|
| 2958 | A /= hh; |
---|
| 2959 | } |
---|
| 2960 | factors= CFList(); |
---|
| 2961 | if (!fdivides (LC (oldA,1),prod (leadingCoeffs2[lengthAeval2-1]))) |
---|
| 2962 | { |
---|
| 2963 | LCheuristic= false; |
---|
| 2964 | A= bufA; |
---|
| 2965 | biFactors= bufBiFactors; |
---|
| 2966 | leadingCoeffs2[lengthAeval2-1]= bufLeadingCoeffs2; |
---|
| 2967 | LCmultiplier= bufLCmultiplier; |
---|
| 2968 | } |
---|
| 2969 | } |
---|
[4fe8a3] | 2970 | else |
---|
| 2971 | factors= CFList(); |
---|
[5079887] | 2972 | delete [] index; |
---|
[4fe8a3] | 2973 | } |
---|
| 2974 | |
---|
[b30017] | 2975 | if (!LCheuristic && !LCmultiplierIsConst && bufFactors.isEmpty() |
---|
| 2976 | && fdivides (getVars (LCmultiplier), testVars)) |
---|
| 2977 | { |
---|
[41e77d] | 2978 | LCheuristic= true; |
---|
[b30017] | 2979 | int index; |
---|
| 2980 | Variable xx; |
---|
| 2981 | CFList vars1; |
---|
| 2982 | CFFList sqrfMultiplier= sqrFree (LCmultiplier); |
---|
| 2983 | if (sqrfMultiplier.getFirst().factor().inCoeffDomain()) |
---|
| 2984 | sqrfMultiplier.removeFirst(); |
---|
| 2985 | sqrfMultiplier= sortCFFListByNumOfVars (sqrfMultiplier); |
---|
| 2986 | xx= Variable (2); |
---|
| 2987 | for (iter= oldBiFactors; iter.hasItem(); iter++) |
---|
| 2988 | vars1.append (power (xx, degree (LC (iter.getItem(),1), xx))); |
---|
| 2989 | for (int i= 0; i < lengthAeval2; i++) |
---|
| 2990 | { |
---|
| 2991 | if (oldAeval[i].isEmpty()) |
---|
| 2992 | continue; |
---|
| 2993 | xx= oldAeval[i].getFirst().mvar(); |
---|
| 2994 | iter2= vars1; |
---|
| 2995 | for (iter= oldAeval[i]; iter.hasItem(); iter++, iter2++) |
---|
| 2996 | iter2.getItem() *= power (xx, degree (LC (iter.getItem(),1), xx)); |
---|
| 2997 | } |
---|
| 2998 | CanonicalForm tmp; |
---|
| 2999 | iter2= vars1; |
---|
| 3000 | for (iter= leadingCoeffs2[lengthAeval2-1]; iter.hasItem(); iter++, iter2++) |
---|
| 3001 | { |
---|
| 3002 | tmp= iter.getItem()/LCmultiplier; |
---|
| 3003 | for (int i=1; i <= tmp.level(); i++) |
---|
| 3004 | { |
---|
[bed38b] | 3005 | if (degree (tmp,i) > 0 && (degree (iter2.getItem(),i) > degree (tmp,i))) |
---|
[b30017] | 3006 | iter2.getItem() /= power (Variable (i), degree (tmp,i)); |
---|
| 3007 | } |
---|
| 3008 | } |
---|
| 3009 | int multi; |
---|
| 3010 | for (CFFListIterator ii= sqrfMultiplier; ii.hasItem(); ii++) |
---|
| 3011 | { |
---|
| 3012 | multi= 0; |
---|
| 3013 | for (iter= vars1; iter.hasItem(); iter++) |
---|
| 3014 | { |
---|
| 3015 | tmp= iter.getItem(); |
---|
| 3016 | while (fdivides (myGetVars (ii.getItem().factor()), tmp)) |
---|
| 3017 | { |
---|
| 3018 | multi++; |
---|
| 3019 | tmp /= myGetVars (ii.getItem().factor()); |
---|
| 3020 | } |
---|
| 3021 | } |
---|
| 3022 | if (multi == ii.getItem().exp()) |
---|
| 3023 | { |
---|
| 3024 | index= 1; |
---|
| 3025 | for (iter= vars1; iter.hasItem(); iter++, index++) |
---|
| 3026 | { |
---|
| 3027 | while (fdivides (myGetVars (ii.getItem().factor()), iter.getItem())) |
---|
| 3028 | { |
---|
| 3029 | int index2= 1; |
---|
| 3030 | for (iter2= leadingCoeffs2[lengthAeval2-1]; iter2.hasItem();iter2++, |
---|
| 3031 | index2++) |
---|
| 3032 | { |
---|
| 3033 | if (index2 == index) |
---|
| 3034 | continue; |
---|
| 3035 | else |
---|
| 3036 | { |
---|
| 3037 | tmp= ii.getItem().factor(); |
---|
| 3038 | iter2.getItem() /= tmp; |
---|
| 3039 | CFListIterator iter3= evaluation; |
---|
| 3040 | for (int jj= A.level(); jj > 2; jj--, iter3++) |
---|
| 3041 | tmp= tmp (iter3.getItem(), jj); |
---|
| 3042 | if (!tmp.inCoeffDomain()) |
---|
| 3043 | { |
---|
| 3044 | int index3= 1; |
---|
| 3045 | for (iter3= biFactors; iter3.hasItem(); iter3++, index3++) |
---|
| 3046 | { |
---|
| 3047 | if (index3 == index2) |
---|
| 3048 | { |
---|
| 3049 | iter3.getItem() /= tmp; |
---|
| 3050 | iter3.getItem() /= Lc (iter3.getItem()); |
---|
| 3051 | break; |
---|
| 3052 | } |
---|
| 3053 | } |
---|
| 3054 | } |
---|
| 3055 | A /= ii.getItem().factor(); |
---|
| 3056 | } |
---|
| 3057 | } |
---|
| 3058 | iter.getItem() /= getVars (ii.getItem().factor()); |
---|
| 3059 | } |
---|
| 3060 | } |
---|
| 3061 | } |
---|
| 3062 | else |
---|
| 3063 | { |
---|
| 3064 | index= 1; |
---|
| 3065 | for (iter= vars1; iter.hasItem(); iter++, index++) |
---|
| 3066 | { |
---|
| 3067 | if (!fdivides (myGetVars (ii.getItem().factor()), iter.getItem())) |
---|
| 3068 | { |
---|
| 3069 | int index2= 1; |
---|
| 3070 | for (iter2= leadingCoeffs2[lengthAeval2-1];iter2.hasItem();iter2++, |
---|
| 3071 | index2++) |
---|
| 3072 | { |
---|
| 3073 | if (index2 == index) |
---|
| 3074 | { |
---|
| 3075 | tmp= power (ii.getItem().factor(), ii.getItem().exp()); |
---|
| 3076 | iter2.getItem() /= tmp; |
---|
| 3077 | A /= tmp; |
---|
| 3078 | CFListIterator iter3= evaluation; |
---|
| 3079 | for (int jj= A.level(); jj > 2; jj--, iter3++) |
---|
| 3080 | tmp= tmp (iter3.getItem(), jj); |
---|
| 3081 | if (!tmp.inCoeffDomain()) |
---|
| 3082 | { |
---|
| 3083 | int index3= 1; |
---|
| 3084 | for (iter3= biFactors; iter3.hasItem(); iter3++, index3++) |
---|
| 3085 | { |
---|
| 3086 | if (index3 == index2) |
---|
| 3087 | { |
---|
| 3088 | iter3.getItem() /= tmp; |
---|
| 3089 | iter3.getItem() /= Lc (iter3.getItem()); |
---|
| 3090 | break; |
---|
| 3091 | } |
---|
| 3092 | } |
---|
| 3093 | } |
---|
| 3094 | } |
---|
| 3095 | } |
---|
| 3096 | } |
---|
| 3097 | } |
---|
| 3098 | } |
---|
| 3099 | } |
---|
| 3100 | |
---|
| 3101 | leadingCoeffs= leadingCoeffs2[lengthAeval2-1]; |
---|
| 3102 | for (int i= lengthAeval2-1; i > -1; i--) |
---|
| 3103 | leadingCoeffs2[i]= CFList(); |
---|
| 3104 | prepareLeadingCoeffs (leadingCoeffs2,A.level(),leadingCoeffs, biFactors, |
---|
| 3105 | evaluation); |
---|
| 3106 | Aeval= evaluateAtEval (A, evaluation, 2); |
---|
| 3107 | |
---|
| 3108 | hh= Lc (Aeval.getFirst()); |
---|
| 3109 | |
---|
| 3110 | for (CFListIterator i= Aeval; i.hasItem(); i++) |
---|
| 3111 | i.getItem() /= hh; |
---|
| 3112 | |
---|
| 3113 | A /= hh; |
---|
| 3114 | } |
---|
| 3115 | |
---|
| 3116 | tryAgainWithoutHeu: |
---|
[eefc3a] | 3117 | A= shift2Zero (A, Aeval, evaluation); |
---|
| 3118 | |
---|
| 3119 | for (iter= biFactors; iter.hasItem(); iter++) |
---|
| 3120 | iter.getItem()= iter.getItem () (y + evaluation.getLast(), y); |
---|
| 3121 | |
---|
[c89740] | 3122 | for (int i= 0; i < lengthAeval2-1; i++) |
---|
[464b18] | 3123 | leadingCoeffs2[i]= CFList(); |
---|
[c89740] | 3124 | for (iter= leadingCoeffs2[lengthAeval2-1]; iter.hasItem(); iter++) |
---|
[eefc3a] | 3125 | { |
---|
| 3126 | iter.getItem()= shift2Zero (iter.getItem(), list, evaluation); |
---|
| 3127 | for (int i= A.level() - 4; i > -1; i--) |
---|
| 3128 | { |
---|
[c89740] | 3129 | if (i + 1 == lengthAeval2-1) |
---|
[eefc3a] | 3130 | leadingCoeffs2[i].append (iter.getItem() (0, i + 4)); |
---|
| 3131 | else |
---|
| 3132 | leadingCoeffs2[i].append (leadingCoeffs2[i+1].getLast() (0, i + 4)); |
---|
| 3133 | } |
---|
| 3134 | } |
---|
[ccd1b0] | 3135 | |
---|
| 3136 | CFArray Pi; |
---|
| 3137 | CFList diophant; |
---|
| 3138 | int* liftBounds= new int [A.level() - 1]; |
---|
| 3139 | int liftBoundsLength= A.level() - 1; |
---|
| 3140 | for (int i= 0; i < liftBoundsLength; i++) |
---|
| 3141 | liftBounds [i]= degree (A, i + 2) + 1; |
---|
| 3142 | |
---|
| 3143 | Aeval.removeFirst(); |
---|
| 3144 | bool noOneToOne= false; |
---|
| 3145 | factors= nonMonicHenselLift (Aeval, biFactors, leadingCoeffs2, diophant, |
---|
| 3146 | Pi, liftBounds, liftBoundsLength, noOneToOne); |
---|
| 3147 | |
---|
| 3148 | if (!noOneToOne) |
---|
[7bf145] | 3149 | { |
---|
[ccd1b0] | 3150 | int check= factors.length(); |
---|
[eefc3a] | 3151 | A= oldA; |
---|
[c79a9d] | 3152 | factors= recoverFactors (A, factors, evaluation); |
---|
[ccd1b0] | 3153 | if (check != factors.length()) |
---|
| 3154 | noOneToOne= true; |
---|
[5079887] | 3155 | else |
---|
| 3156 | factors= Union (factors, bufFactors); |
---|
[ccd1b0] | 3157 | |
---|
| 3158 | if (extension && !noOneToOne) |
---|
[c79a9d] | 3159 | factors= extNonMonicFactorRecombination (factors, A, info); |
---|
[7bf145] | 3160 | } |
---|
[ccd1b0] | 3161 | if (noOneToOne) |
---|
| 3162 | { |
---|
[b30017] | 3163 | |
---|
| 3164 | if (!LCmultiplierIsConst && LCheuristic) |
---|
| 3165 | { |
---|
| 3166 | A= bufA; |
---|
| 3167 | biFactors= bufBiFactors; |
---|
| 3168 | leadingCoeffs2[lengthAeval2-1]= bufLeadingCoeffs2; |
---|
| 3169 | delete [] liftBounds; |
---|
| 3170 | LCheuristic= false; |
---|
| 3171 | goto tryAgainWithoutHeu; |
---|
| 3172 | //something probably went wrong in the heuristic |
---|
| 3173 | } |
---|
| 3174 | |
---|
[eefc3a] | 3175 | A= shift2Zero (oldA, Aeval, evaluation); |
---|
[ccd1b0] | 3176 | biFactors= oldBiFactors; |
---|
[eefc3a] | 3177 | for (iter= biFactors; iter.hasItem(); iter++) |
---|
| 3178 | iter.getItem()= iter.getItem () (y + evaluation.getLast(), y); |
---|
[ccd1b0] | 3179 | CanonicalForm LCA= LC (Aeval.getFirst(), 1); |
---|
| 3180 | CanonicalForm yToLift= power (y, lift); |
---|
| 3181 | CFListIterator i= biFactors; |
---|
| 3182 | lift= degree (i.getItem(), 2) + degree (LC (i.getItem(), 1)) + 1; |
---|
| 3183 | i++; |
---|
[7bf145] | 3184 | |
---|
[ccd1b0] | 3185 | for (; i.hasItem(); i++) |
---|
[c7b56e2] | 3186 | lift= tmax (lift, |
---|
| 3187 | degree (i.getItem(), 2) + degree (LC (i.getItem(), 1)) + 1); |
---|
[ccd1b0] | 3188 | |
---|
| 3189 | lift= tmax (degree (Aeval.getFirst() , 2) + 1, lift); |
---|
| 3190 | |
---|
| 3191 | i= biFactors; |
---|
| 3192 | yToLift= power (y, lift); |
---|
| 3193 | CanonicalForm dummy; |
---|
| 3194 | for (; i.hasItem(); i++) |
---|
| 3195 | { |
---|
| 3196 | LCA= LC (i.getItem(), 1); |
---|
| 3197 | extgcd (LCA, yToLift, LCA, dummy); |
---|
| 3198 | i.getItem()= mod (i.getItem()*LCA, yToLift); |
---|
| 3199 | } |
---|
| 3200 | |
---|
| 3201 | liftBoundsLength= F.level() - 1; |
---|
| 3202 | liftBounds= liftingBounds (A, lift); |
---|
| 3203 | |
---|
| 3204 | CFList MOD; |
---|
| 3205 | bool earlySuccess; |
---|
[0b618a7] | 3206 | CFList earlyFactors, liftedFactors; |
---|
[978ce3] | 3207 | TIMING_START (fac_fq_hensel_lift); |
---|
[0b618a7] | 3208 | liftedFactors= henselLiftAndEarly |
---|
| 3209 | (A, MOD, liftBounds, earlySuccess, earlyFactors, |
---|
| 3210 | Aeval, biFactors, evaluation, info); |
---|
[978ce3] | 3211 | TIMING_END_AND_PRINT (fac_fq_hensel_lift, "time for hensel lifting: "); |
---|
[ccd1b0] | 3212 | |
---|
| 3213 | if (!extension) |
---|
| 3214 | { |
---|
[978ce3] | 3215 | TIMING_START (fac_fq_factor_recombination); |
---|
[ccd1b0] | 3216 | factors= factorRecombination (A, liftedFactors, MOD); |
---|
[978ce3] | 3217 | TIMING_END_AND_PRINT (fac_fq_factor_recombination, |
---|
[ccd1b0] | 3218 | "time for factor recombination: "); |
---|
| 3219 | } |
---|
| 3220 | else |
---|
| 3221 | { |
---|
[978ce3] | 3222 | TIMING_START (fac_fq_factor_recombination); |
---|
[ccd1b0] | 3223 | factors= extFactorRecombination (liftedFactors, A, MOD, info, evaluation); |
---|
[978ce3] | 3224 | TIMING_END_AND_PRINT (fac_fq_factor_recombination, |
---|
[ccd1b0] | 3225 | "time for factor recombination: "); |
---|
| 3226 | } |
---|
| 3227 | |
---|
| 3228 | if (earlySuccess) |
---|
| 3229 | factors= Union (factors, earlyFactors); |
---|
[c79a9d] | 3230 | if (!extension) |
---|
[7bf145] | 3231 | { |
---|
[c79a9d] | 3232 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
[7bf145] | 3233 | { |
---|
[c79a9d] | 3234 | int kk= Aeval.getLast().level(); |
---|
| 3235 | for (CFListIterator j= evaluation; j.hasItem(); j++, kk--) |
---|
| 3236 | { |
---|
| 3237 | if (i.getItem().level() < kk) |
---|
| 3238 | continue; |
---|
| 3239 | i.getItem()= i.getItem() (Variable (kk) - j.getItem(), kk); |
---|
| 3240 | } |
---|
[7bf145] | 3241 | } |
---|
| 3242 | } |
---|
| 3243 | } |
---|
| 3244 | |
---|
[ccd1b0] | 3245 | if (v.level() != 1) |
---|
| 3246 | { |
---|
| 3247 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
| 3248 | iter.getItem()= swapvar (iter.getItem(), v, y); |
---|
| 3249 | } |
---|
| 3250 | |
---|
[44651b] | 3251 | swap (factors, swapLevel, swapLevel2, x); |
---|
[7bf145] | 3252 | append (factors, contentAFactors); |
---|
| 3253 | decompress (factors, N); |
---|
[41e77d] | 3254 | if (!extension) |
---|
| 3255 | normalize (factors); |
---|
[7bf145] | 3256 | |
---|
| 3257 | delete[] liftBounds; |
---|
| 3258 | |
---|
| 3259 | return factors; |
---|
| 3260 | } |
---|
| 3261 | |
---|
| 3262 | /// multivariate factorization over an extension of the initial field |
---|
[44651b] | 3263 | CFList |
---|
| 3264 | extFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
[7bf145] | 3265 | { |
---|
| 3266 | CanonicalForm A= F; |
---|
| 3267 | |
---|
| 3268 | Variable alpha= info.getAlpha(); |
---|
| 3269 | Variable beta= info.getBeta(); |
---|
| 3270 | int k= info.getGFDegree(); |
---|
| 3271 | char cGFName= info.getGFName(); |
---|
| 3272 | CanonicalForm delta= info.getDelta(); |
---|
| 3273 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
| 3274 | Variable w= Variable (1); |
---|
| 3275 | |
---|
| 3276 | CFList factors; |
---|
| 3277 | if (!GF && alpha == w) // we are in F_p |
---|
| 3278 | { |
---|
| 3279 | CFList factors; |
---|
[44651b] | 3280 | bool extension= true; |
---|
[7bf145] | 3281 | int p= getCharacteristic(); |
---|
| 3282 | if (p*p < (1<<16)) // pass to GF if possible |
---|
[44651b] | 3283 | { |
---|
[7bf145] | 3284 | setCharacteristic (getCharacteristic(), 2, 'Z'); |
---|
| 3285 | ExtensionInfo info= ExtensionInfo (extension); |
---|
| 3286 | A= A.mapinto(); |
---|
| 3287 | factors= multiFactorize (A, info); |
---|
| 3288 | |
---|
[0a7d0ca] | 3289 | CanonicalForm mipo= gf_mipo; |
---|
[7bf145] | 3290 | setCharacteristic (getCharacteristic()); |
---|
[0a7d0ca] | 3291 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
[44651b] | 3292 | for (CFListIterator j= factors; j.hasItem(); j++) |
---|
| 3293 | j.getItem()= GF2FalphaRep (j.getItem(), vBuf); |
---|
[7bf145] | 3294 | } |
---|
| 3295 | else // not able to pass to GF, pass to F_p(\alpha) |
---|
| 3296 | { |
---|
[a54114] | 3297 | CanonicalForm mipo= randomIrredpoly (2, w); |
---|
[11bf82] | 3298 | Variable v= rootOf (mipo); |
---|
[ccd1b0] | 3299 | ExtensionInfo info= ExtensionInfo (v); |
---|
[7bf145] | 3300 | factors= multiFactorize (A, info); |
---|
| 3301 | } |
---|
| 3302 | return factors; |
---|
| 3303 | } |
---|
| 3304 | else if (!GF && (alpha != w)) // we are in F_p(\alpha) |
---|
[44651b] | 3305 | { |
---|
[7bf145] | 3306 | if (k == 1) // need factorization over F_p |
---|
| 3307 | { |
---|
| 3308 | int extDeg= degree (getMipo (alpha)); |
---|
[44651b] | 3309 | extDeg++; |
---|
[a54114] | 3310 | CanonicalForm mipo= randomIrredpoly (extDeg + 1, w); |
---|
[7bf145] | 3311 | Variable v= rootOf (mipo); |
---|
| 3312 | ExtensionInfo info= ExtensionInfo (v); |
---|
[4e17e7] | 3313 | factors= multiFactorize (A, info); |
---|
[7bf145] | 3314 | } |
---|
[44651b] | 3315 | else |
---|
[7bf145] | 3316 | { |
---|
[a54114] | 3317 | if (beta == w) |
---|
[7bf145] | 3318 | { |
---|
[11bf82] | 3319 | Variable v= chooseExtension (alpha, beta, k); |
---|
[7bf145] | 3320 | CanonicalForm primElem, imPrimElem; |
---|
| 3321 | bool primFail= false; |
---|
| 3322 | Variable vBuf; |
---|
| 3323 | primElem= primitiveElement (alpha, vBuf, primFail); |
---|
| 3324 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
| 3325 | if (primFail) |
---|
| 3326 | ; //ERROR |
---|
| 3327 | else |
---|
[ccd1b0] | 3328 | imPrimElem= mapPrimElem (primElem, vBuf, v); |
---|
[7bf145] | 3329 | |
---|
| 3330 | CFList source, dest; |
---|
[44651b] | 3331 | CanonicalForm bufA= mapUp (A, alpha, v, primElem, imPrimElem, |
---|
[7bf145] | 3332 | source, dest); |
---|
| 3333 | ExtensionInfo info= ExtensionInfo (v, alpha, imPrimElem, primElem); |
---|
[4e17e7] | 3334 | factors= multiFactorize (bufA, info); |
---|
[7bf145] | 3335 | } |
---|
| 3336 | else |
---|
| 3337 | { |
---|
[11bf82] | 3338 | Variable v= chooseExtension (alpha, beta, k); |
---|
[7bf145] | 3339 | CanonicalForm primElem, imPrimElem; |
---|
| 3340 | bool primFail= false; |
---|
| 3341 | Variable vBuf; |
---|
| 3342 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
| 3343 | if (primFail) |
---|
| 3344 | ; //ERROR |
---|
| 3345 | else |
---|
[618da5] | 3346 | imPrimElem= mapPrimElem (delta, beta, v); |
---|
[7bf145] | 3347 | |
---|
| 3348 | CFList source, dest; |
---|
| 3349 | CanonicalForm bufA= mapDown (A, info, source, dest); |
---|
| 3350 | source= CFList(); |
---|
| 3351 | dest= CFList(); |
---|
| 3352 | bufA= mapUp (bufA, beta, v, delta, imPrimElem, source, dest); |
---|
| 3353 | ExtensionInfo info= ExtensionInfo (v, beta, imPrimElem, delta); |
---|
[4e17e7] | 3354 | factors= multiFactorize (bufA, info); |
---|
[7bf145] | 3355 | } |
---|
| 3356 | } |
---|
| 3357 | return factors; |
---|
| 3358 | } |
---|
| 3359 | else // we are in GF (p^k) |
---|
[44651b] | 3360 | { |
---|
[7bf145] | 3361 | int p= getCharacteristic(); |
---|
| 3362 | int extensionDeg= getGFDegree(); |
---|
| 3363 | bool extension= true; |
---|
| 3364 | if (k == 1) // need factorization over F_p |
---|
[44651b] | 3365 | { |
---|
[7bf145] | 3366 | extensionDeg++; |
---|
[44651b] | 3367 | if (pow ((double) p, (double) extensionDeg) < (1<<16)) |
---|
[7bf145] | 3368 | // pass to GF(p^k+1) |
---|
[44651b] | 3369 | { |
---|
[0a7d0ca] | 3370 | CanonicalForm mipo= gf_mipo; |
---|
[7bf145] | 3371 | setCharacteristic (p); |
---|
[0a7d0ca] | 3372 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
[44651b] | 3373 | A= GF2FalphaRep (A, vBuf); |
---|
| 3374 | setCharacteristic (p, extensionDeg, 'Z'); |
---|
[7bf145] | 3375 | ExtensionInfo info= ExtensionInfo (extension); |
---|
[44651b] | 3376 | factors= multiFactorize (A.mapinto(), info); |
---|
[7bf145] | 3377 | } |
---|
| 3378 | else // not able to pass to another GF, pass to F_p(\alpha) |
---|
[44651b] | 3379 | { |
---|
[0a7d0ca] | 3380 | CanonicalForm mipo= gf_mipo; |
---|
[44651b] | 3381 | setCharacteristic (p); |
---|
[0a7d0ca] | 3382 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
[44651b] | 3383 | A= GF2FalphaRep (A, vBuf); |
---|
[11bf82] | 3384 | Variable v= chooseExtension (vBuf, beta, k); |
---|
[7bf145] | 3385 | ExtensionInfo info= ExtensionInfo (v, extension); |
---|
[44651b] | 3386 | factors= multiFactorize (A, info); |
---|
[7bf145] | 3387 | } |
---|
| 3388 | } |
---|
| 3389 | else // need factorization over GF (p^k) |
---|
| 3390 | { |
---|
[44651b] | 3391 | if (pow ((double) p, (double) 2*extensionDeg) < (1<<16)) |
---|
[7bf145] | 3392 | // pass to GF(p^2k) |
---|
[44651b] | 3393 | { |
---|
| 3394 | setCharacteristic (p, 2*extensionDeg, 'Z'); |
---|
[7bf145] | 3395 | ExtensionInfo info= ExtensionInfo (k, cGFName, extension); |
---|
[44651b] | 3396 | factors= multiFactorize (GFMapUp (A, extensionDeg), info); |
---|
| 3397 | setCharacteristic (p, extensionDeg, cGFName); |
---|
[7bf145] | 3398 | } |
---|
| 3399 | else // not able to pass to GF (p^2k), pass to F_p (\alpha) |
---|
[44651b] | 3400 | { |
---|
[0a7d0ca] | 3401 | CanonicalForm mipo= gf_mipo; |
---|
[44651b] | 3402 | setCharacteristic (p); |
---|
[0a7d0ca] | 3403 | Variable v1= rootOf (mipo.mapinto()); |
---|
[44651b] | 3404 | A= GF2FalphaRep (A, v1); |
---|
[11bf82] | 3405 | Variable v2= chooseExtension (v1, v1, k); |
---|
[7bf145] | 3406 | CanonicalForm primElem, imPrimElem; |
---|
| 3407 | bool primFail= false; |
---|
| 3408 | Variable vBuf; |
---|
[11bf82] | 3409 | primElem= primitiveElement (v1, v1, primFail); |
---|
[7bf145] | 3410 | if (primFail) |
---|
| 3411 | ; //ERROR |
---|
| 3412 | else |
---|
[618da5] | 3413 | imPrimElem= mapPrimElem (primElem, v1, v2); |
---|
[7bf145] | 3414 | CFList source, dest; |
---|
[618da5] | 3415 | CanonicalForm bufA= mapUp (A, v1, v2, primElem, imPrimElem, |
---|
[7bf145] | 3416 | source, dest); |
---|
| 3417 | ExtensionInfo info= ExtensionInfo (v2, v1, imPrimElem, primElem); |
---|
[44651b] | 3418 | factors= multiFactorize (bufA, info); |
---|
| 3419 | setCharacteristic (p, k, cGFName); |
---|
| 3420 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
| 3421 | i.getItem()= Falpha2GFRep (i.getItem()); |
---|
[7bf145] | 3422 | } |
---|
| 3423 | } |
---|
| 3424 | return factors; |
---|
| 3425 | } |
---|
| 3426 | } |
---|
| 3427 | |
---|
| 3428 | #endif |
---|
| 3429 | /* HAVE_NTL */ |
---|
| 3430 | |
---|