[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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| 65 | if (L.length() == 1) |
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| 66 | return L.getFirst(); |
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| 67 | if (L.length() == 2) |
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[04cdf06] | 68 | return gcd (L.getFirst(), L.getLast()); |
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[7bf145] | 69 | else |
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| 70 | { |
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| 71 | CFList lHi, lLo; |
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| 72 | CanonicalForm resultHi, resultLo; |
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| 73 | int length= L.length()/2; |
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| 74 | int j= 0; |
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| 75 | for (CFListIterator i= L; j < length; i++, j++) |
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[44651b] | 76 | lHi.append (i.getItem()); |
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[7bf145] | 77 | lLo= Difference (L, lHi); |
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| 78 | resultHi= listGCD (lHi); |
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| 79 | resultLo= listGCD (lLo); |
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| 80 | if (resultHi.isOne() || resultLo.isOne()) |
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| 81 | return 1; |
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[04cdf06] | 82 | return gcd (resultHi, resultLo); |
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[7bf145] | 83 | } |
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| 84 | } |
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| 85 | |
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| 86 | static inline |
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| 87 | CanonicalForm |
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| 88 | myContent (const CanonicalForm& F, const Variable& x) |
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| 89 | { |
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| 90 | if (degree (F, x) <= 0) |
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| 91 | return 1; |
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| 92 | CanonicalForm G= F; |
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| 93 | bool swap= false; |
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| 94 | if (x != F.mvar()) |
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| 95 | { |
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| 96 | swap= true; |
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| 97 | G= swapvar (F, x, F.mvar()); |
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| 98 | } |
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| 99 | CFList L; |
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| 100 | Variable alpha; |
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| 101 | for (CFIterator i= G; i.hasTerms(); i++) |
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| 102 | L.append (i.coeff()); |
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| 103 | if (L.length() == 2) |
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| 104 | { |
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[04cdf06] | 105 | if (swap) |
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| 106 | return swapvar (gcd (L.getFirst(), L.getLast()), F.mvar(), x); |
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[7bf145] | 107 | else |
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[04cdf06] | 108 | return gcd (L.getFirst(), L.getLast()); |
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[7bf145] | 109 | } |
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| 110 | if (L.length() == 1) |
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| 111 | { |
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| 112 | return LC (F, x); |
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| 113 | } |
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| 114 | if (swap) |
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| 115 | return swapvar (listGCD (L), F.mvar(), x); |
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| 116 | else |
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| 117 | return listGCD (L); |
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| 118 | } |
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| 119 | |
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| 120 | CanonicalForm myCompress (const CanonicalForm& F, CFMap& N) |
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| 121 | { |
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| 122 | int n= F.level(); |
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| 123 | int * degsf= new int [n + 1]; |
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| 124 | int ** swap; |
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| 125 | swap= new int* [n + 1]; |
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[44651b] | 126 | for (int i= 0; i <= n; i++) |
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[7bf145] | 127 | { |
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| 128 | degsf[i]= 0; |
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| 129 | swap [i]= new int [2]; |
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[44651b] | 130 | swap [i] [0]= 0; |
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[7bf145] | 131 | swap [i] [1]= 0; |
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| 132 | } |
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| 133 | int i= 1; |
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[44651b] | 134 | n= 1; |
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[7bf145] | 135 | degsf= degrees (F, degsf); |
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| 136 | |
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| 137 | CanonicalForm result= F; |
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[44651b] | 138 | while ( i <= F.level() ) |
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[7bf145] | 139 | { |
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| 140 | while( degsf[i] == 0 ) i++; |
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[44651b] | 141 | swap[n][0]= i; |
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[4fee0ed] | 142 | swap[n][1]= size (LC (F,i)); |
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[7bf145] | 143 | if (i != n) |
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| 144 | result= swapvar (result, Variable (n), Variable(i)); |
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| 145 | n++; i++; |
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| 146 | } |
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| 147 | |
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| 148 | int buf1, buf2; |
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| 149 | n--; |
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| 150 | |
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[44651b] | 151 | for (i= 1; i < n; i++) |
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[7bf145] | 152 | { |
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[44651b] | 153 | for (int j= 1; j < n - i + 1; j++) |
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[7bf145] | 154 | { |
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[4fee0ed] | 155 | if (swap[j][1] > swap[j + 1][1]) |
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[7bf145] | 156 | { |
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[44651b] | 157 | buf1= swap [j + 1] [0]; |
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| 158 | buf2= swap [j + 1] [1]; |
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| 159 | swap[j + 1] [0]= swap[j] [0]; |
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[7bf145] | 160 | swap[j + 1] [1]= swap[j] [1]; |
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[44651b] | 161 | swap[j][0]= buf1; |
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| 162 | swap[j][1]= buf2; |
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[7bf145] | 163 | result= swapvar (result, Variable (j + 1), Variable (j)); |
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[44651b] | 164 | } |
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[7bf145] | 165 | } |
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| 166 | } |
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| 167 | |
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[44651b] | 168 | for (i= n; i > 0; i--) |
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[7bf145] | 169 | { |
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[44651b] | 170 | if (i != swap[i] [0]) |
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| 171 | N.newpair (Variable (i), Variable (swap[i] [0])); |
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[7bf145] | 172 | } |
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| 173 | |
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| 174 | for (i= 0; i <= n; i++) |
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| 175 | delete [] swap[i]; |
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| 176 | delete [] swap; |
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| 177 | |
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| 178 | delete [] degsf; |
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| 179 | |
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| 180 | return result; |
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| 181 | } |
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[44651b] | 182 | |
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| 183 | CFList |
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| 184 | extFactorRecombination (const CFList& factors, const CanonicalForm& F, |
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| 185 | const CFList& M, const ExtensionInfo& info, |
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[7bf145] | 186 | const CFList& evaluation) |
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[44651b] | 187 | { |
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[7bf145] | 188 | Variable alpha= info.getAlpha(); |
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| 189 | Variable beta= info.getBeta(); |
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| 190 | CanonicalForm gamma= info.getGamma(); |
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| 191 | CanonicalForm delta= info.getDelta(); |
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| 192 | int k= info.getGFDegree(); |
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| 193 | CFList source, dest; |
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[44651b] | 194 | if (factors.length() == 1) |
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[7bf145] | 195 | { |
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| 196 | CanonicalForm buf= reverseShift (F, evaluation); |
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[44651b] | 197 | return CFList (mapDown (buf, info, source, dest)); |
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| 198 | } |
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[7bf145] | 199 | if (factors.length() < 1) |
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| 200 | return CFList(); |
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| 201 | |
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[ac8e1a] | 202 | int degMipoBeta= 1; |
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| 203 | if (!k && beta.level() != 1) |
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[7bf145] | 204 | degMipoBeta= degree (getMipo (beta)); |
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| 205 | |
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| 206 | CFList T, S; |
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| 207 | T= factors; |
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| 208 | |
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| 209 | int s= 1; |
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| 210 | CFList result; |
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| 211 | CanonicalForm buf; |
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[ccd1b0] | 212 | |
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| 213 | buf= F; |
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[7bf145] | 214 | |
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[a54114] | 215 | Variable x= Variable (1); |
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| 216 | CanonicalForm g, LCBuf= LC (buf, x); |
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[21b8f4] | 217 | CanonicalForm buf2, quot; |
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[1673386] | 218 | int * v= new int [T.length()]; |
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[7bf145] | 219 | for (int i= 0; i < T.length(); i++) |
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| 220 | v[i]= 0; |
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| 221 | bool noSubset= false; |
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| 222 | CFArray TT; |
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[44651b] | 223 | TT= copy (factors); |
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[7bf145] | 224 | bool recombination= false; |
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[93134c] | 225 | bool trueFactor= false; |
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[44651b] | 226 | while (T.length() >= 2*s) |
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[7bf145] | 227 | { |
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[44651b] | 228 | while (noSubset == false) |
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[7bf145] | 229 | { |
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[44651b] | 230 | if (T.length() == s) |
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[7bf145] | 231 | { |
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[1673386] | 232 | delete [] v; |
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[7bf145] | 233 | if (recombination) |
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| 234 | { |
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| 235 | T.insert (LCBuf); |
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| 236 | g= prodMod (T, M); |
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| 237 | T.removeFirst(); |
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| 238 | result.append (g/myContent (g)); |
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| 239 | g= reverseShift (g, evaluation); |
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| 240 | g /= Lc (g); |
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| 241 | appendTestMapDown (result, g, info, source, dest); |
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| 242 | return result; |
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| 243 | } |
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| 244 | else |
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| 245 | { |
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| 246 | buf= reverseShift (buf, evaluation); |
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| 247 | return CFList (buf); |
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| 248 | } |
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| 249 | } |
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| 250 | |
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| 251 | S= subset (v, s, TT, noSubset); |
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| 252 | if (noSubset) break; |
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| 253 | |
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| 254 | S.insert (LCBuf); |
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| 255 | g= prodMod (S, M); |
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| 256 | S.removeFirst(); |
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| 257 | g /= myContent (g); |
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[21b8f4] | 258 | if (fdivides (g, buf, quot)) |
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[7bf145] | 259 | { |
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[44651b] | 260 | buf2= reverseShift (g, evaluation); |
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[7bf145] | 261 | buf2 /= Lc (buf2); |
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[a54114] | 262 | if (!k && beta == x) |
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[44651b] | 263 | { |
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| 264 | if (degree (buf2, alpha) < degMipoBeta) |
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| 265 | { |
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| 266 | appendTestMapDown (result, buf2, info, source, dest); |
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[21b8f4] | 267 | buf= quot; |
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[a54114] | 268 | LCBuf= LC (buf, x); |
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[44651b] | 269 | recombination= true; |
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[93134c] | 270 | trueFactor= true; |
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[44651b] | 271 | } |
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| 272 | } |
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| 273 | else |
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| 274 | { |
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[f876a66] | 275 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
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[44651b] | 276 | { |
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| 277 | appendTestMapDown (result, buf2, info, source, dest); |
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| 278 | buf /= g; |
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[a54114] | 279 | LCBuf= LC (buf, x); |
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[44651b] | 280 | recombination= true; |
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[93134c] | 281 | trueFactor= true; |
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[44651b] | 282 | } |
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| 283 | } |
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| 284 | |
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[93134c] | 285 | if (trueFactor) |
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[44651b] | 286 | { |
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[93134c] | 287 | T= Difference (T, S); |
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| 288 | |
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| 289 | if (T.length() < 2*s || T.length() == s) |
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| 290 | { |
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| 291 | buf= reverseShift (buf, evaluation); |
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| 292 | buf /= Lc (buf); |
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| 293 | appendTestMapDown (result, buf, info, source, dest); |
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[1673386] | 294 | delete [] v; |
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[93134c] | 295 | return result; |
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| 296 | } |
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| 297 | trueFactor= false; |
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| 298 | TT= copy (T); |
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| 299 | indexUpdate (v, s, T.length(), noSubset); |
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| 300 | if (noSubset) break; |
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[44651b] | 301 | } |
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[7bf145] | 302 | } |
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| 303 | } |
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| 304 | s++; |
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[44651b] | 305 | if (T.length() < 2*s || T.length() == s) |
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[7bf145] | 306 | { |
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| 307 | buf= reverseShift (buf, evaluation); |
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| 308 | appendTestMapDown (result, buf, info, source, dest); |
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[1673386] | 309 | delete [] v; |
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[7bf145] | 310 | return result; |
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| 311 | } |
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| 312 | for (int i= 0; i < T.length(); i++) |
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| 313 | v[i]= 0; |
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| 314 | noSubset= false; |
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| 315 | } |
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| 316 | if (T.length() < 2*s) |
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| 317 | { |
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[44651b] | 318 | buf= reverseShift (F, evaluation); |
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| 319 | appendMapDown (result, buf, info, source, dest); |
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[7bf145] | 320 | } |
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| 321 | |
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[1673386] | 322 | delete [] v; |
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[44651b] | 323 | return result; |
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| 324 | } |
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[7bf145] | 325 | |
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[44651b] | 326 | CFList |
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| 327 | factorRecombination (const CanonicalForm& F, const CFList& factors, |
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[7bf145] | 328 | const CFList& M) |
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| 329 | { |
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[44651b] | 330 | if (factors.length() == 1) |
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[7bf145] | 331 | return CFList(F); |
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| 332 | if (factors.length() < 1) |
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| 333 | return CFList(); |
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| 334 | |
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| 335 | CFList T, S; |
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| 336 | |
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| 337 | T= factors; |
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| 338 | |
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| 339 | int s= 1; |
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| 340 | CFList result; |
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| 341 | CanonicalForm LCBuf= LC (F, Variable (1)); |
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| 342 | CanonicalForm g, buf= F; |
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[1673386] | 343 | int * v= new int [T.length()]; |
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[7bf145] | 344 | for (int i= 0; i < T.length(); i++) |
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| 345 | v[i]= 0; |
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| 346 | bool noSubset= false; |
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| 347 | CFArray TT; |
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[44651b] | 348 | TT= copy (factors); |
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[7bf145] | 349 | Variable y= F.level() - 1; |
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| 350 | bool recombination= false; |
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[21b8f4] | 351 | CanonicalForm h, quot; |
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[44651b] | 352 | while (T.length() >= 2*s) |
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[7bf145] | 353 | { |
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[44651b] | 354 | while (noSubset == false) |
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[7bf145] | 355 | { |
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[44651b] | 356 | if (T.length() == s) |
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[7bf145] | 357 | { |
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[1673386] | 358 | delete [] v; |
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[7bf145] | 359 | if (recombination) |
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| 360 | { |
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| 361 | T.insert (LC (buf)); |
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| 362 | g= prodMod (T, M); |
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| 363 | result.append (g/myContent (g)); |
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| 364 | return result; |
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| 365 | } |
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| 366 | else |
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| 367 | return CFList (F); |
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| 368 | } |
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| 369 | S= subset (v, s, TT, noSubset); |
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| 370 | if (noSubset) break; |
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| 371 | S.insert (LCBuf); |
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| 372 | g= prodMod (S, M); |
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| 373 | S.removeFirst(); |
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| 374 | g /= myContent (g); |
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[21b8f4] | 375 | if (fdivides (g, buf, quot)) |
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[7bf145] | 376 | { |
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| 377 | recombination= true; |
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| 378 | result.append (g); |
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[21b8f4] | 379 | buf= quot; |
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[7bf145] | 380 | LCBuf= LC (buf, Variable(1)); |
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| 381 | T= Difference (T, S); |
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[44651b] | 382 | if (T.length() < 2*s || T.length() == s) |
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[7bf145] | 383 | { |
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[44651b] | 384 | result.append (buf); |
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[1673386] | 385 | delete [] v; |
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[44651b] | 386 | return result; |
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| 387 | } |
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| 388 | TT= copy (T); |
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| 389 | indexUpdate (v, s, T.length(), noSubset); |
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| 390 | if (noSubset) break; |
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[7bf145] | 391 | } |
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| 392 | } |
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| 393 | s++; |
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[44651b] | 394 | if (T.length() < 2*s || T.length() == s) |
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[7bf145] | 395 | { |
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| 396 | result.append (buf); |
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[1673386] | 397 | delete [] v; |
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[7bf145] | 398 | return result; |
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| 399 | } |
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| 400 | for (int i= 0; i < T.length(); i++) |
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| 401 | v[i]= 0; |
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| 402 | noSubset= false; |
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| 403 | } |
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[44651b] | 404 | if (T.length() < 2*s) |
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[7bf145] | 405 | result.append (F); |
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| 406 | |
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[1673386] | 407 | delete [] v; |
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[44651b] | 408 | return result; |
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[7bf145] | 409 | } |
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| 410 | |
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| 411 | int |
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| 412 | liftBoundAdaption (const CanonicalForm& F, const CFList& factors, bool& |
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| 413 | success, const int deg, const CFList& MOD, const int bound) |
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| 414 | { |
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| 415 | int adaptedLiftBound= 0; |
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| 416 | CanonicalForm buf= F; |
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| 417 | Variable y= F.mvar(); |
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[a54114] | 418 | Variable x= Variable (1); |
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| 419 | CanonicalForm LCBuf= LC (buf, x); |
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[21b8f4] | 420 | CanonicalForm g, quot; |
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[7bf145] | 421 | CFList M= MOD; |
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| 422 | M.append (power (y, deg)); |
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| 423 | int d= bound; |
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| 424 | int e= 0; |
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| 425 | int nBuf; |
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[44651b] | 426 | for (CFListIterator i= factors; i.hasItem(); i++) |
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[7bf145] | 427 | { |
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[44651b] | 428 | g= mulMod (i.getItem(), LCBuf, M); |
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[7bf145] | 429 | g /= myContent (g); |
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[21b8f4] | 430 | if (fdivides (g, buf, quot)) |
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[7bf145] | 431 | { |
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| 432 | nBuf= degree (g, y) + degree (LC (g, 1), y); |
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| 433 | d -= nBuf; |
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| 434 | e= tmax (e, nBuf); |
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[21b8f4] | 435 | buf= quot; |
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[a54114] | 436 | LCBuf= LC (buf, x); |
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[7bf145] | 437 | } |
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| 438 | } |
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| 439 | adaptedLiftBound= d; |
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| 440 | |
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[44651b] | 441 | if (adaptedLiftBound < deg) |
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| 442 | { |
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[7bf145] | 443 | if (adaptedLiftBound < degree (F) + 1) |
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| 444 | { |
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| 445 | if (d == 1) |
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| 446 | { |
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| 447 | if (e + 1 > deg) |
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| 448 | { |
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| 449 | adaptedLiftBound= deg; |
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| 450 | success= false; |
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| 451 | } |
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[44651b] | 452 | else |
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[7bf145] | 453 | { |
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| 454 | success= true; |
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| 455 | if (e + 1 < degree (F) + 1) |
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| 456 | adaptedLiftBound= deg; |
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| 457 | else |
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| 458 | adaptedLiftBound= e + 1; |
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| 459 | } |
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| 460 | } |
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| 461 | else |
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| 462 | { |
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| 463 | success= true; |
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[44651b] | 464 | adaptedLiftBound= deg; |
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[7bf145] | 465 | } |
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| 466 | } |
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| 467 | else |
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| 468 | { |
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| 469 | success= true; |
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| 470 | } |
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| 471 | } |
---|
| 472 | return adaptedLiftBound; |
---|
| 473 | } |
---|
| 474 | |
---|
[44651b] | 475 | int |
---|
| 476 | extLiftBoundAdaption (const CanonicalForm& F, const CFList& factors, bool& |
---|
| 477 | success, const ExtensionInfo& info, const CFList& eval, |
---|
[7bf145] | 478 | const int deg, const CFList& MOD, const int bound) |
---|
| 479 | { |
---|
| 480 | Variable alpha= info.getAlpha(); |
---|
| 481 | Variable beta= info.getBeta(); |
---|
| 482 | CanonicalForm gamma= info.getGamma(); |
---|
| 483 | CanonicalForm delta= info.getDelta(); |
---|
| 484 | int k= info.getGFDegree(); |
---|
| 485 | int adaptedLiftBound= 0; |
---|
| 486 | CanonicalForm buf= F; |
---|
| 487 | Variable y= F.mvar(); |
---|
[a54114] | 488 | Variable x= Variable (1); |
---|
| 489 | CanonicalForm LCBuf= LC (buf, x); |
---|
[21b8f4] | 490 | CanonicalForm g, gg, quot; |
---|
[7bf145] | 491 | CFList M= MOD; |
---|
| 492 | M.append (power (y, deg)); |
---|
| 493 | adaptedLiftBound= 0; |
---|
| 494 | int d= bound; |
---|
[44651b] | 495 | int e= 0; |
---|
[7bf145] | 496 | int nBuf; |
---|
[ac8e1a] | 497 | int degMipoBeta= 1; |
---|
| 498 | if (!k && beta.level() != 1) |
---|
[7bf145] | 499 | degMipoBeta= degree (getMipo (beta)); |
---|
| 500 | |
---|
[f876a66] | 501 | CFList source, dest; |
---|
[44651b] | 502 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
[7bf145] | 503 | { |
---|
| 504 | g= mulMod (i.getItem(), LCBuf, M); |
---|
| 505 | g /= myContent (g); |
---|
[21b8f4] | 506 | if (fdivides (g, buf, quot)) |
---|
[7bf145] | 507 | { |
---|
| 508 | gg= reverseShift (g, eval); |
---|
| 509 | gg /= Lc (gg); |
---|
[a54114] | 510 | if (!k && beta == x) |
---|
[7bf145] | 511 | { |
---|
| 512 | if (degree (gg, alpha) < degMipoBeta) |
---|
[44651b] | 513 | { |
---|
[21b8f4] | 514 | buf= quot; |
---|
[a54114] | 515 | nBuf= degree (g, y) + degree (LC (g, x), y); |
---|
[7bf145] | 516 | d -= nBuf; |
---|
| 517 | e= tmax (e, nBuf); |
---|
[a54114] | 518 | LCBuf= LC (buf, x); |
---|
[7bf145] | 519 | } |
---|
| 520 | } |
---|
[44651b] | 521 | else |
---|
[7bf145] | 522 | { |
---|
[f876a66] | 523 | if (!isInExtension (gg, gamma, k, delta, source, dest)) |
---|
[7bf145] | 524 | { |
---|
[21b8f4] | 525 | buf= quot; |
---|
[a54114] | 526 | nBuf= degree (g, y) + degree (LC (g, x), y); |
---|
[7bf145] | 527 | d -= nBuf; |
---|
| 528 | e= tmax (e, nBuf); |
---|
[a54114] | 529 | LCBuf= LC (buf, x); |
---|
[7bf145] | 530 | } |
---|
| 531 | } |
---|
[44651b] | 532 | } |
---|
[7bf145] | 533 | } |
---|
| 534 | adaptedLiftBound= d; |
---|
| 535 | |
---|
| 536 | if (adaptedLiftBound < deg) |
---|
| 537 | { |
---|
| 538 | if (adaptedLiftBound < degree (F) + 1) |
---|
| 539 | { |
---|
| 540 | if (d == 1) |
---|
| 541 | { |
---|
| 542 | if (e + 1 > deg) |
---|
| 543 | { |
---|
| 544 | adaptedLiftBound= deg; |
---|
| 545 | success= false; |
---|
| 546 | } |
---|
[44651b] | 547 | else |
---|
[7bf145] | 548 | { |
---|
| 549 | success= true; |
---|
| 550 | if (e + 1 < degree (F) + 1) |
---|
| 551 | adaptedLiftBound= deg; |
---|
| 552 | else |
---|
| 553 | adaptedLiftBound= e + 1; |
---|
| 554 | } |
---|
| 555 | } |
---|
[44651b] | 556 | else |
---|
[7bf145] | 557 | { |
---|
| 558 | success= true; |
---|
[44651b] | 559 | adaptedLiftBound= deg; |
---|
[7bf145] | 560 | } |
---|
| 561 | } |
---|
| 562 | else |
---|
| 563 | { |
---|
| 564 | success= true; |
---|
| 565 | } |
---|
| 566 | } |
---|
| 567 | |
---|
| 568 | return adaptedLiftBound; |
---|
| 569 | } |
---|
| 570 | |
---|
[44651b] | 571 | CFList |
---|
[7bf145] | 572 | earlyFactorDetect (CanonicalForm& F, CFList& factors, int& adaptedLiftBound, |
---|
[44651b] | 573 | bool& success, const int deg, const CFList& MOD, |
---|
[7bf145] | 574 | const int bound) |
---|
| 575 | { |
---|
| 576 | CFList result; |
---|
| 577 | CFList T= factors; |
---|
| 578 | CanonicalForm buf= F; |
---|
| 579 | Variable y= F.mvar(); |
---|
[a54114] | 580 | Variable x= Variable (1); |
---|
| 581 | CanonicalForm LCBuf= LC (buf, x); |
---|
[21b8f4] | 582 | CanonicalForm g, quot; |
---|
[7bf145] | 583 | CFList M= MOD; |
---|
| 584 | M.append (power (y, deg)); |
---|
| 585 | adaptedLiftBound= 0; |
---|
| 586 | int d= bound; |
---|
| 587 | int e= 0; |
---|
| 588 | int nBuf; |
---|
[44651b] | 589 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
[7bf145] | 590 | { |
---|
| 591 | g= mulMod (i.getItem(), LCBuf, M); |
---|
| 592 | g /= myContent (g); |
---|
[21b8f4] | 593 | if (fdivides (g, buf, quot)) |
---|
[7bf145] | 594 | { |
---|
| 595 | result.append (g); |
---|
[a54114] | 596 | nBuf= degree (g, y) + degree (LC (g, x), y); |
---|
[7bf145] | 597 | d -= nBuf; |
---|
| 598 | e= tmax (e, nBuf); |
---|
[21b8f4] | 599 | buf= quot; |
---|
[a54114] | 600 | LCBuf= LC (buf, x); |
---|
[7bf145] | 601 | T= Difference (T, CFList (i.getItem())); |
---|
| 602 | } |
---|
| 603 | } |
---|
| 604 | adaptedLiftBound= d; |
---|
| 605 | |
---|
[44651b] | 606 | if (adaptedLiftBound < deg) |
---|
[7bf145] | 607 | { |
---|
| 608 | if (adaptedLiftBound < degree (F) + 1) |
---|
| 609 | { |
---|
| 610 | if (d == 1) |
---|
| 611 | adaptedLiftBound= tmin (e + 1, deg); |
---|
| 612 | else |
---|
[44651b] | 613 | adaptedLiftBound= deg; |
---|
[7bf145] | 614 | } |
---|
| 615 | factors= T; |
---|
| 616 | F= buf; |
---|
| 617 | success= true; |
---|
| 618 | } |
---|
| 619 | return result; |
---|
| 620 | } |
---|
| 621 | |
---|
[44651b] | 622 | CFList |
---|
[7bf145] | 623 | extEarlyFactorDetect (CanonicalForm& F, CFList& factors, int& adaptedLiftBound, |
---|
[44651b] | 624 | bool& success, const ExtensionInfo& info, const CFList& |
---|
[7bf145] | 625 | eval, const int deg, const CFList& MOD, const int bound) |
---|
| 626 | { |
---|
| 627 | Variable alpha= info.getAlpha(); |
---|
| 628 | Variable beta= info.getBeta(); |
---|
| 629 | CanonicalForm gamma= info.getGamma(); |
---|
| 630 | CanonicalForm delta= info.getDelta(); |
---|
| 631 | int k= info.getGFDegree(); |
---|
| 632 | CFList result; |
---|
| 633 | CFList T= factors; |
---|
| 634 | CanonicalForm buf= F; |
---|
| 635 | Variable y= F.mvar(); |
---|
[a54114] | 636 | Variable x= Variable (1); |
---|
| 637 | CanonicalForm LCBuf= LC (buf, x); |
---|
[21b8f4] | 638 | CanonicalForm g, gg, quot; |
---|
[7bf145] | 639 | CFList M= MOD; |
---|
| 640 | M.append (power (y, deg)); |
---|
| 641 | adaptedLiftBound= 0; |
---|
| 642 | int d= bound; |
---|
| 643 | int e= 0; |
---|
| 644 | int nBuf; |
---|
| 645 | CFList source, dest; |
---|
| 646 | |
---|
[ac8e1a] | 647 | int degMipoBeta= 1; |
---|
| 648 | if (!k && beta.level() != 1) |
---|
[7bf145] | 649 | degMipoBeta= degree (getMipo (beta)); |
---|
| 650 | |
---|
[44651b] | 651 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
[7bf145] | 652 | { |
---|
| 653 | g= mulMod (i.getItem(), LCBuf, M); |
---|
| 654 | g /= myContent (g); |
---|
[21b8f4] | 655 | if (fdivides (g, buf, quot)) |
---|
[7bf145] | 656 | { |
---|
| 657 | gg= reverseShift (g, eval); |
---|
| 658 | gg /= Lc (gg); |
---|
[a54114] | 659 | if (!k && beta == x) |
---|
[93134c] | 660 | { |
---|
| 661 | if (degree (gg, alpha) < degMipoBeta) |
---|
| 662 | { |
---|
| 663 | appendTestMapDown (result, gg, info, source, dest); |
---|
[21b8f4] | 664 | buf= quot; |
---|
[a54114] | 665 | nBuf= degree (g, y) + degree (LC (g, x), y); |
---|
[93134c] | 666 | d -= nBuf; |
---|
| 667 | e= tmax (e, nBuf); |
---|
[a54114] | 668 | LCBuf= LC (buf, x); |
---|
[93134c] | 669 | T= Difference (T, CFList (i.getItem())); |
---|
| 670 | } |
---|
| 671 | } |
---|
| 672 | else |
---|
| 673 | { |
---|
[f876a66] | 674 | if (!isInExtension (gg, gamma, k, delta, source, dest)) |
---|
[93134c] | 675 | { |
---|
| 676 | appendTestMapDown (result, gg, info, source, dest); |
---|
[21b8f4] | 677 | buf= quot; |
---|
[a54114] | 678 | nBuf= degree (g, y) + degree (LC (g, x), y); |
---|
[93134c] | 679 | d -= nBuf; |
---|
| 680 | e= tmax (e, nBuf); |
---|
[a54114] | 681 | LCBuf= LC (buf, x); |
---|
[93134c] | 682 | T= Difference (T, CFList (i.getItem())); |
---|
| 683 | } |
---|
| 684 | } |
---|
[7bf145] | 685 | } |
---|
| 686 | } |
---|
| 687 | adaptedLiftBound= d; |
---|
| 688 | |
---|
| 689 | if (adaptedLiftBound < deg) |
---|
| 690 | { |
---|
| 691 | if (adaptedLiftBound < degree (F) + 1) |
---|
| 692 | { |
---|
| 693 | if (d == 1) |
---|
| 694 | adaptedLiftBound= tmin (e + 1, deg); |
---|
| 695 | else |
---|
[44651b] | 696 | adaptedLiftBound= deg; |
---|
[7bf145] | 697 | } |
---|
| 698 | success= true; |
---|
| 699 | factors= T; |
---|
| 700 | F= buf; |
---|
| 701 | } |
---|
| 702 | return result; |
---|
| 703 | } |
---|
| 704 | |
---|
[44651b] | 705 | CFList |
---|
[7bf145] | 706 | evalPoints (const CanonicalForm& F, CFList & eval, const Variable& alpha, |
---|
[44651b] | 707 | CFList& list, const bool& GF, bool& fail) |
---|
| 708 | { |
---|
[7bf145] | 709 | int k= F.level() - 1; |
---|
| 710 | Variable x= Variable (1); |
---|
| 711 | CFList result; |
---|
| 712 | FFRandom genFF; |
---|
| 713 | GFRandom genGF; |
---|
| 714 | int p= getCharacteristic (); |
---|
[44651b] | 715 | double bound; |
---|
[a54114] | 716 | if (alpha != x) |
---|
[7bf145] | 717 | { |
---|
| 718 | bound= pow ((double) p, (double) degree (getMipo(alpha))); |
---|
| 719 | bound= pow ((double) bound, (double) k); |
---|
| 720 | } |
---|
[44651b] | 721 | else if (GF) |
---|
[7bf145] | 722 | { |
---|
| 723 | bound= pow ((double) p, (double) getGFDegree()); |
---|
| 724 | bound= pow ((double) bound, (double) k); |
---|
| 725 | } |
---|
| 726 | else |
---|
| 727 | bound= pow ((double) p, (double) k); |
---|
| 728 | |
---|
| 729 | CanonicalForm random; |
---|
| 730 | CanonicalForm deriv_x, gcd_deriv; |
---|
[44651b] | 731 | do |
---|
[7bf145] | 732 | { |
---|
| 733 | random= 0; |
---|
| 734 | // possible overflow if list.length() does not fit into a int |
---|
[44651b] | 735 | if (list.length() >= bound) |
---|
| 736 | { |
---|
[7bf145] | 737 | fail= true; |
---|
| 738 | break; |
---|
| 739 | } |
---|
[44651b] | 740 | for (int i= 0; i < k; i++) |
---|
| 741 | { |
---|
[8db258] | 742 | if (list.isEmpty()) |
---|
| 743 | result.append (0); |
---|
| 744 | else if (GF) |
---|
[7bf145] | 745 | { |
---|
| 746 | result.append (genGF.generate()); |
---|
| 747 | random += result.getLast()*power (x, i); |
---|
| 748 | } |
---|
[1372ae] | 749 | else if (alpha.level() != 1) |
---|
[44651b] | 750 | { |
---|
[7bf145] | 751 | AlgExtRandomF genAlgExt (alpha); |
---|
| 752 | result.append (genAlgExt.generate()); |
---|
[44651b] | 753 | random += result.getLast()*power (x, i); |
---|
[7bf145] | 754 | } |
---|
[44651b] | 755 | else |
---|
| 756 | { |
---|
[7bf145] | 757 | result.append (genFF.generate()); |
---|
| 758 | random += result.getLast()*power (x, i); |
---|
[44651b] | 759 | } |
---|
[7bf145] | 760 | } |
---|
[44651b] | 761 | if (find (list, random)) |
---|
[7bf145] | 762 | { |
---|
| 763 | result= CFList(); |
---|
| 764 | continue; |
---|
| 765 | } |
---|
| 766 | int l= F.level(); |
---|
| 767 | eval.insert (F); |
---|
[ccd1b0] | 768 | bool bad= false; |
---|
[44651b] | 769 | for (CFListIterator i= result; i.hasItem(); i++, l--) |
---|
[ccd1b0] | 770 | { |
---|
[7bf145] | 771 | eval.insert (eval.getFirst()(i.getItem(), l)); |
---|
[ccd1b0] | 772 | if (degree (eval.getFirst(), l - 1) != degree (F, l - 1)) |
---|
| 773 | { |
---|
| 774 | if (!find (list, random)) |
---|
| 775 | list.append (random); |
---|
| 776 | result= CFList(); |
---|
| 777 | eval= CFList(); |
---|
| 778 | bad= true; |
---|
| 779 | break; |
---|
| 780 | } |
---|
| 781 | } |
---|
| 782 | |
---|
| 783 | if (bad) |
---|
| 784 | continue; |
---|
[7bf145] | 785 | |
---|
[44651b] | 786 | if (degree (eval.getFirst()) != degree (F, 1)) |
---|
[7bf145] | 787 | { |
---|
| 788 | if (!find (list, random)) |
---|
| 789 | list.append (random); |
---|
| 790 | result= CFList(); |
---|
| 791 | eval= CFList(); |
---|
| 792 | continue; |
---|
[44651b] | 793 | } |
---|
| 794 | |
---|
[7bf145] | 795 | deriv_x= deriv (eval.getFirst(), x); |
---|
| 796 | gcd_deriv= gcd (eval.getFirst(), deriv_x); |
---|
[44651b] | 797 | if (degree (gcd_deriv) > 0) |
---|
| 798 | { |
---|
[7bf145] | 799 | if (!find (list, random)) |
---|
| 800 | list.append (random); |
---|
| 801 | result= CFList(); |
---|
| 802 | eval= CFList(); |
---|
| 803 | continue; |
---|
| 804 | } |
---|
| 805 | CFListIterator i= eval; |
---|
| 806 | i++; |
---|
| 807 | CanonicalForm contentx= content (i.getItem(), x); |
---|
| 808 | if (degree (contentx) > 0) |
---|
| 809 | { |
---|
| 810 | if (!find (list, random)) |
---|
| 811 | list.append (random); |
---|
| 812 | result= CFList(); |
---|
| 813 | eval= CFList(); |
---|
| 814 | continue; |
---|
| 815 | } |
---|
| 816 | |
---|
[44651b] | 817 | if (list.length() >= bound) |
---|
[7bf145] | 818 | { |
---|
| 819 | fail= true; |
---|
| 820 | break; |
---|
| 821 | } |
---|
| 822 | } while (find (list, random)); |
---|
| 823 | |
---|
[44651b] | 824 | if (!eval.isEmpty()) |
---|
[7bf145] | 825 | eval.removeFirst(); |
---|
| 826 | |
---|
| 827 | return result; |
---|
| 828 | } |
---|
| 829 | |
---|
[44651b] | 830 | static inline |
---|
[7bf145] | 831 | int newMainVariableSearch (CanonicalForm& A, CFList& Aeval, CFList& |
---|
[ccd1b0] | 832 | evaluation, const Variable& alpha, const int lev, |
---|
| 833 | CanonicalForm& g |
---|
| 834 | ) |
---|
[44651b] | 835 | { |
---|
[7bf145] | 836 | Variable x= Variable (1); |
---|
| 837 | CanonicalForm derivI, buf; |
---|
| 838 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
| 839 | int swapLevel= 0; |
---|
| 840 | CFList list; |
---|
| 841 | bool fail= false; |
---|
| 842 | buf= A; |
---|
| 843 | Aeval= CFList(); |
---|
| 844 | evaluation= CFList(); |
---|
[44651b] | 845 | for (int i= lev; i <= A.level(); i++) |
---|
[7bf145] | 846 | { |
---|
| 847 | derivI= deriv (buf, Variable (i)); |
---|
| 848 | if (!derivI.isZero()) |
---|
| 849 | { |
---|
[ccd1b0] | 850 | g= gcd (buf, derivI); |
---|
| 851 | if (degree (g) > 0) |
---|
| 852 | return -1; |
---|
| 853 | |
---|
[44651b] | 854 | buf= swapvar (buf, x, Variable (i)); |
---|
[7bf145] | 855 | Aeval= CFList(); |
---|
| 856 | evaluation= CFList(); |
---|
| 857 | fail= false; |
---|
| 858 | evaluation= evalPoints (buf, Aeval, alpha, list, GF, fail); |
---|
[44651b] | 859 | if (!fail) |
---|
[7bf145] | 860 | { |
---|
[44651b] | 861 | A= buf; |
---|
| 862 | swapLevel= i; |
---|
| 863 | break; |
---|
[7bf145] | 864 | } |
---|
[44651b] | 865 | else |
---|
[7bf145] | 866 | buf= A; |
---|
| 867 | } |
---|
| 868 | } |
---|
| 869 | return swapLevel; |
---|
| 870 | } |
---|
| 871 | |
---|
[44651b] | 872 | CanonicalForm lcmContent (const CanonicalForm& A, CFList& contentAi) |
---|
[7bf145] | 873 | { |
---|
| 874 | int i= A.level(); |
---|
| 875 | contentAi.append (myContent (A, i)); |
---|
| 876 | contentAi.append (myContent (A, i - 1)); |
---|
[04cdf06] | 877 | CanonicalForm result= lcm (contentAi.getFirst(), contentAi.getLast()); |
---|
[44651b] | 878 | for (i= i - 2; i > 0; i--) |
---|
[7bf145] | 879 | { |
---|
| 880 | contentAi.append (content (A, i)); |
---|
[04cdf06] | 881 | result= lcm (result, contentAi.getLast()); |
---|
[7bf145] | 882 | } |
---|
| 883 | return result; |
---|
[44651b] | 884 | } |
---|
| 885 | |
---|
[7bf145] | 886 | CFList |
---|
| 887 | henselLiftAndEarly (CanonicalForm& A, CFList& MOD, int*& liftBounds, bool& |
---|
| 888 | earlySuccess, CFList& earlyFactors, const CFList& Aeval, |
---|
[44651b] | 889 | const CFList& biFactors, const CFList& evaluation, |
---|
[7bf145] | 890 | const ExtensionInfo& info) |
---|
| 891 | { |
---|
| 892 | bool extension= info.isInExtension(); |
---|
[44651b] | 893 | CFList bufFactors= biFactors; |
---|
[7bf145] | 894 | bufFactors.insert (LC (Aeval.getFirst(), 1)); |
---|
| 895 | |
---|
| 896 | sortList (bufFactors, Variable (1)); |
---|
| 897 | |
---|
| 898 | CFList diophant; |
---|
| 899 | CFArray Pi; |
---|
| 900 | int smallFactorDeg= 11; //tunable parameter |
---|
[44651b] | 901 | CFList result; |
---|
[7bf145] | 902 | int adaptedLiftBound= 0; |
---|
| 903 | int liftBound= liftBounds[1]; |
---|
| 904 | |
---|
| 905 | earlySuccess= false; |
---|
| 906 | CFList earlyReconstFactors; |
---|
| 907 | CFListIterator j= Aeval; |
---|
| 908 | j++; |
---|
| 909 | CanonicalForm buf= j.getItem(); |
---|
| 910 | CFMatrix Mat= CFMatrix (liftBound, bufFactors.length() - 1); |
---|
| 911 | MOD= CFList (power (Variable (2), liftBounds[0])); |
---|
| 912 | if (smallFactorDeg >= liftBound) |
---|
| 913 | { |
---|
| 914 | result= henselLift23 (Aeval, bufFactors, liftBounds, diophant, Pi, Mat); |
---|
| 915 | } |
---|
| 916 | else if (smallFactorDeg >= degree (buf) + 1) |
---|
| 917 | { |
---|
| 918 | liftBounds[1]= degree (buf) + 1; |
---|
| 919 | result= henselLift23 (Aeval, bufFactors, liftBounds, diophant, Pi, Mat); |
---|
| 920 | if (Aeval.length() == 2) |
---|
| 921 | { |
---|
| 922 | if (!extension) |
---|
[44651b] | 923 | earlyFactors= earlyFactorDetect |
---|
[7bf145] | 924 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
| 925 | degree (buf) + 1, MOD, liftBound); |
---|
| 926 | else |
---|
[44651b] | 927 | earlyFactors= extEarlyFactorDetect |
---|
[7bf145] | 928 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
[44651b] | 929 | info, evaluation, degree |
---|
[7bf145] | 930 | (buf) + 1, MOD, liftBound); |
---|
| 931 | } |
---|
| 932 | else |
---|
| 933 | { |
---|
| 934 | if (!extension) |
---|
| 935 | adaptedLiftBound= liftBoundAdaption (buf, result, earlySuccess, |
---|
| 936 | degree (buf) + 1, MOD, liftBound); |
---|
| 937 | else |
---|
| 938 | adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, info, |
---|
| 939 | evaluation, degree (buf) + 1, |
---|
[44651b] | 940 | MOD, liftBound); |
---|
[7bf145] | 941 | } |
---|
| 942 | if (!earlySuccess) |
---|
| 943 | { |
---|
| 944 | result.insert (LC (buf, 1)); |
---|
| 945 | liftBounds[1]= adaptedLiftBound; |
---|
| 946 | liftBound= adaptedLiftBound; |
---|
[44651b] | 947 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
[7bf145] | 948 | Pi, diophant, Mat, MOD); |
---|
[44651b] | 949 | } |
---|
[7bf145] | 950 | else |
---|
| 951 | liftBounds[1]= adaptedLiftBound; |
---|
| 952 | } |
---|
| 953 | else if (smallFactorDeg < degree (buf) + 1) |
---|
| 954 | { |
---|
| 955 | liftBounds[1]= smallFactorDeg; |
---|
| 956 | result= henselLift23 (Aeval, bufFactors, liftBounds, diophant, Pi, Mat); |
---|
| 957 | if (Aeval.length() == 2) |
---|
| 958 | { |
---|
| 959 | if (!extension) |
---|
[44651b] | 960 | earlyFactors= earlyFactorDetect (buf, result, adaptedLiftBound, |
---|
[7bf145] | 961 | earlySuccess, smallFactorDeg, MOD, |
---|
| 962 | liftBound); |
---|
[44651b] | 963 | else |
---|
[7bf145] | 964 | earlyFactors= extEarlyFactorDetect (buf, result, adaptedLiftBound, |
---|
| 965 | earlySuccess, info, evaluation, |
---|
| 966 | smallFactorDeg, MOD, liftBound); |
---|
| 967 | } |
---|
| 968 | else |
---|
| 969 | { |
---|
| 970 | if (!extension) |
---|
| 971 | adaptedLiftBound= liftBoundAdaption (buf, result, earlySuccess, |
---|
| 972 | smallFactorDeg, MOD, liftBound); |
---|
| 973 | else |
---|
| 974 | adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, info, |
---|
[44651b] | 975 | evaluation, smallFactorDeg, MOD, |
---|
[7bf145] | 976 | liftBound); |
---|
| 977 | } |
---|
| 978 | |
---|
| 979 | if (!earlySuccess) |
---|
| 980 | { |
---|
| 981 | result.insert (LC (buf, 1)); |
---|
[44651b] | 982 | henselLiftResume (buf, result, smallFactorDeg, degree (buf) + 1, |
---|
[7bf145] | 983 | Pi, diophant, Mat, MOD); |
---|
| 984 | if (Aeval.length() == 2) |
---|
| 985 | { |
---|
| 986 | if (!extension) |
---|
| 987 | earlyFactors= earlyFactorDetect (buf, result, adaptedLiftBound, |
---|
| 988 | earlySuccess, degree (buf) + 1, |
---|
| 989 | MOD, liftBound); |
---|
| 990 | else |
---|
| 991 | earlyFactors= extEarlyFactorDetect (buf, result, adaptedLiftBound, |
---|
| 992 | earlySuccess, info, evaluation, |
---|
[44651b] | 993 | degree (buf) + 1, MOD, |
---|
[7bf145] | 994 | liftBound); |
---|
| 995 | } |
---|
[44651b] | 996 | else |
---|
[7bf145] | 997 | { |
---|
| 998 | if (!extension) |
---|
| 999 | adaptedLiftBound= liftBoundAdaption (buf, result, earlySuccess, |
---|
[44651b] | 1000 | degree (buf) + 1, MOD,liftBound); |
---|
[7bf145] | 1001 | else |
---|
[44651b] | 1002 | adaptedLiftBound= extLiftBoundAdaption (buf, result, earlySuccess, |
---|
[7bf145] | 1003 | info, evaluation, |
---|
| 1004 | degree (buf) + 1, MOD, |
---|
| 1005 | liftBound); |
---|
| 1006 | } |
---|
| 1007 | if (!earlySuccess) |
---|
| 1008 | { |
---|
| 1009 | result.insert (LC (buf, 1)); |
---|
| 1010 | liftBounds[1]= adaptedLiftBound; |
---|
| 1011 | liftBound= adaptedLiftBound; |
---|
[44651b] | 1012 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
[7bf145] | 1013 | Pi, diophant, Mat, MOD); |
---|
| 1014 | } |
---|
| 1015 | else |
---|
| 1016 | liftBounds[1]= adaptedLiftBound; |
---|
| 1017 | } |
---|
| 1018 | else |
---|
| 1019 | liftBounds[1]= adaptedLiftBound; |
---|
| 1020 | } |
---|
| 1021 | |
---|
| 1022 | MOD.append (power (Variable (3), liftBounds[1])); |
---|
| 1023 | |
---|
| 1024 | if (Aeval.length() > 2) |
---|
| 1025 | { |
---|
| 1026 | CFListIterator j= Aeval; |
---|
| 1027 | j++; |
---|
| 1028 | CFList bufEval; |
---|
| 1029 | bufEval.append (j.getItem()); |
---|
| 1030 | j++; |
---|
| 1031 | int liftBoundsLength= Aeval.getLast().level() - 1; |
---|
| 1032 | for (int i= 2; i <= liftBoundsLength && j.hasItem(); i++, j++) |
---|
[44651b] | 1033 | { |
---|
[7bf145] | 1034 | earlySuccess= false; |
---|
| 1035 | result.insert (LC (bufEval.getFirst(), 1)); |
---|
| 1036 | bufEval.append (j.getItem()); |
---|
| 1037 | liftBound= liftBounds[i]; |
---|
| 1038 | Mat= CFMatrix (liftBounds[i], result.length() - 1); |
---|
| 1039 | |
---|
| 1040 | buf= j.getItem(); |
---|
| 1041 | if (smallFactorDeg >= liftBound) |
---|
| 1042 | result= henselLift (bufEval, result, MOD, diophant, Pi, Mat, |
---|
[44651b] | 1043 | liftBounds[i - 1], liftBounds[i]); |
---|
[7bf145] | 1044 | else if (smallFactorDeg >= degree (buf) + 1) |
---|
| 1045 | { |
---|
[44651b] | 1046 | result= henselLift (bufEval, result, MOD, diophant, Pi, Mat, |
---|
| 1047 | liftBounds[i - 1], degree (buf) + 1); |
---|
[7bf145] | 1048 | |
---|
[44651b] | 1049 | if (Aeval.length() == i + 1) |
---|
| 1050 | { |
---|
| 1051 | if (!extension) |
---|
| 1052 | earlyFactors= earlyFactorDetect |
---|
[7bf145] | 1053 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
| 1054 | degree (buf) + 1, MOD, liftBound); |
---|
[44651b] | 1055 | else |
---|
| 1056 | earlyFactors= extEarlyFactorDetect |
---|
[7bf145] | 1057 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
| 1058 | info, evaluation, degree (buf) + 1, MOD, liftBound); |
---|
[44651b] | 1059 | } |
---|
| 1060 | else |
---|
| 1061 | { |
---|
| 1062 | if (!extension) |
---|
| 1063 | adaptedLiftBound= liftBoundAdaption |
---|
[7bf145] | 1064 | (buf, result, earlySuccess, degree (buf) |
---|
| 1065 | + 1, MOD, liftBound); |
---|
[44651b] | 1066 | else |
---|
| 1067 | adaptedLiftBound= extLiftBoundAdaption |
---|
| 1068 | (buf, result, earlySuccess, info, evaluation, |
---|
| 1069 | degree (buf) + 1, MOD, liftBound); |
---|
| 1070 | } |
---|
| 1071 | |
---|
| 1072 | if (!earlySuccess) |
---|
| 1073 | { |
---|
| 1074 | result.insert (LC (buf, 1)); |
---|
[7bf145] | 1075 | liftBounds[i]= adaptedLiftBound; |
---|
| 1076 | liftBound= adaptedLiftBound; |
---|
[44651b] | 1077 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
| 1078 | Pi, diophant, Mat, MOD); |
---|
| 1079 | } |
---|
| 1080 | else |
---|
| 1081 | { |
---|
| 1082 | liftBounds[i]= adaptedLiftBound; |
---|
| 1083 | } |
---|
[7bf145] | 1084 | } |
---|
| 1085 | else if (smallFactorDeg < degree (buf) + 1) |
---|
| 1086 | { |
---|
[44651b] | 1087 | result= henselLift (bufEval, result, MOD, diophant, Pi, Mat, |
---|
| 1088 | liftBounds[i - 1], smallFactorDeg); |
---|
[7bf145] | 1089 | |
---|
[44651b] | 1090 | if (Aeval.length() == i + 1) |
---|
| 1091 | { |
---|
| 1092 | if (!extension) |
---|
| 1093 | earlyFactors= earlyFactorDetect |
---|
[7bf145] | 1094 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
| 1095 | smallFactorDeg, MOD, liftBound); |
---|
[44651b] | 1096 | else |
---|
| 1097 | earlyFactors= extEarlyFactorDetect |
---|
[7bf145] | 1098 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
| 1099 | info, evaluation, smallFactorDeg, MOD, liftBound); |
---|
[44651b] | 1100 | } |
---|
| 1101 | else |
---|
| 1102 | { |
---|
| 1103 | if (!extension) |
---|
| 1104 | adaptedLiftBound= liftBoundAdaption |
---|
[7bf145] | 1105 | (buf, result, earlySuccess, |
---|
| 1106 | smallFactorDeg, MOD, liftBound); |
---|
[44651b] | 1107 | else |
---|
| 1108 | adaptedLiftBound= extLiftBoundAdaption |
---|
[7bf145] | 1109 | (buf, result, earlySuccess, info, evaluation, |
---|
[44651b] | 1110 | smallFactorDeg, MOD, liftBound); |
---|
| 1111 | } |
---|
[7bf145] | 1112 | |
---|
[44651b] | 1113 | if (!earlySuccess) |
---|
| 1114 | { |
---|
| 1115 | result.insert (LC (buf, 1)); |
---|
| 1116 | henselLiftResume (buf, result, smallFactorDeg, |
---|
[7bf145] | 1117 | degree (buf) + 1, Pi, diophant, Mat, MOD); |
---|
[44651b] | 1118 | if (Aeval.length() == i + 1) |
---|
| 1119 | { |
---|
| 1120 | if (!extension) |
---|
| 1121 | earlyFactors= earlyFactorDetect |
---|
[7bf145] | 1122 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
| 1123 | degree (buf) + 1, MOD, liftBound); |
---|
[44651b] | 1124 | else |
---|
| 1125 | earlyFactors= extEarlyFactorDetect |
---|
[7bf145] | 1126 | (buf, result, adaptedLiftBound, earlySuccess, |
---|
[44651b] | 1127 | info, evaluation, degree (buf) + 1, MOD, |
---|
[7bf145] | 1128 | liftBound); |
---|
[44651b] | 1129 | } |
---|
| 1130 | else |
---|
| 1131 | { |
---|
| 1132 | if (!extension) |
---|
| 1133 | adaptedLiftBound= liftBoundAdaption |
---|
[7bf145] | 1134 | (buf, result, earlySuccess, degree |
---|
| 1135 | (buf) + 1, MOD, liftBound); |
---|
[44651b] | 1136 | else |
---|
| 1137 | adaptedLiftBound= extLiftBoundAdaption |
---|
| 1138 | (buf, result, earlySuccess, info, evaluation, |
---|
| 1139 | degree (buf) + 1, MOD, liftBound); |
---|
| 1140 | } |
---|
| 1141 | |
---|
| 1142 | if (!earlySuccess) |
---|
| 1143 | { |
---|
| 1144 | result.insert (LC (buf, 1)); |
---|
[7bf145] | 1145 | liftBounds[i]= adaptedLiftBound; |
---|
| 1146 | liftBound= adaptedLiftBound; |
---|
[44651b] | 1147 | henselLiftResume (buf, result, degree (buf) + 1, liftBound, |
---|
| 1148 | Pi, diophant, Mat, MOD); |
---|
| 1149 | } |
---|
| 1150 | else |
---|
| 1151 | liftBounds[i]= adaptedLiftBound; |
---|
| 1152 | } |
---|
| 1153 | else |
---|
| 1154 | liftBounds[i]= adaptedLiftBound; |
---|
[7bf145] | 1155 | } |
---|
| 1156 | MOD.append (power (Variable (i + 2), liftBounds[i])); |
---|
| 1157 | bufEval.removeFirst(); |
---|
| 1158 | } |
---|
| 1159 | bufFactors= result; |
---|
| 1160 | } |
---|
| 1161 | else |
---|
| 1162 | bufFactors= result; |
---|
| 1163 | |
---|
| 1164 | if (earlySuccess) |
---|
| 1165 | A= buf; |
---|
| 1166 | return result; |
---|
| 1167 | } |
---|
| 1168 | |
---|
[ccd1b0] | 1169 | void |
---|
| 1170 | gcdFreeBasis (CFFList& factors1, CFFList& factors2) |
---|
| 1171 | { |
---|
| 1172 | CanonicalForm g; |
---|
| 1173 | int k= factors1.length(); |
---|
| 1174 | int l= factors2.length(); |
---|
| 1175 | int n= 1; |
---|
| 1176 | int m; |
---|
[38ffb7] | 1177 | CFFListIterator j; |
---|
| 1178 | for (CFFListIterator i= factors1; (n < k && i.hasItem()); i++, n++) |
---|
[ccd1b0] | 1179 | { |
---|
| 1180 | m= 1; |
---|
[38ffb7] | 1181 | for (j= factors2; (m < l && j.hasItem()); j++, m++) |
---|
[ccd1b0] | 1182 | { |
---|
[38ffb7] | 1183 | g= gcd (i.getItem().factor(), j.getItem().factor()); |
---|
[8256fd] | 1184 | if (degree (g,1) > 0) |
---|
[ccd1b0] | 1185 | { |
---|
| 1186 | j.getItem()= CFFactor (j.getItem().factor()/g, j.getItem().exp()); |
---|
| 1187 | i.getItem()= CFFactor (i.getItem().factor()/g, i.getItem().exp()); |
---|
| 1188 | factors1.append (CFFactor (g, i.getItem().exp())); |
---|
| 1189 | factors2.append (CFFactor (g, j.getItem().exp())); |
---|
| 1190 | } |
---|
| 1191 | } |
---|
| 1192 | } |
---|
| 1193 | } |
---|
| 1194 | |
---|
| 1195 | CFList |
---|
| 1196 | distributeContent (const CFList& L, const CFList* differentSecondVarFactors, |
---|
[8c1a84] | 1197 | int length |
---|
[ccd1b0] | 1198 | ) |
---|
| 1199 | { |
---|
| 1200 | CFList l= L; |
---|
| 1201 | CanonicalForm content= l.getFirst(); |
---|
| 1202 | |
---|
| 1203 | if (content.inCoeffDomain()) |
---|
| 1204 | return l; |
---|
| 1205 | |
---|
| 1206 | if (l.length() == 1) |
---|
| 1207 | { |
---|
| 1208 | CFList result; |
---|
| 1209 | for (int i= 0; i < length; i++) |
---|
| 1210 | { |
---|
| 1211 | if (differentSecondVarFactors[i].isEmpty()) |
---|
| 1212 | continue; |
---|
| 1213 | if (result.isEmpty()) |
---|
| 1214 | { |
---|
| 1215 | result= differentSecondVarFactors[i]; |
---|
| 1216 | for (CFListIterator iter= result; iter.hasItem(); iter++) |
---|
| 1217 | content /= iter.getItem(); |
---|
| 1218 | } |
---|
| 1219 | else |
---|
| 1220 | { |
---|
| 1221 | CFListIterator iter1= result; |
---|
[8a30b1] | 1222 | for (CFListIterator iter2= differentSecondVarFactors[i];iter2.hasItem(); |
---|
[ccd1b0] | 1223 | iter2++, iter1++) |
---|
| 1224 | { |
---|
| 1225 | iter1.getItem() *= iter2.getItem(); |
---|
| 1226 | content /= iter2.getItem(); |
---|
| 1227 | } |
---|
| 1228 | } |
---|
| 1229 | } |
---|
| 1230 | result.insert (content); |
---|
| 1231 | return result; |
---|
| 1232 | } |
---|
| 1233 | |
---|
[38ffb7] | 1234 | Variable v; |
---|
[8a30b1] | 1235 | CFListIterator iter1, iter2; |
---|
[38ffb7] | 1236 | CanonicalForm tmp, g; |
---|
[8a30b1] | 1237 | CFList multiplier; |
---|
[ccd1b0] | 1238 | for (int i= 0; i < length; i++) |
---|
| 1239 | { |
---|
| 1240 | if (differentSecondVarFactors[i].isEmpty()) |
---|
| 1241 | continue; |
---|
[38ffb7] | 1242 | iter1= l; |
---|
[ccd1b0] | 1243 | iter1++; |
---|
| 1244 | |
---|
[38ffb7] | 1245 | v= Variable (i + 3); |
---|
[8a30b1] | 1246 | tmp= 1; |
---|
| 1247 | for (iter2= differentSecondVarFactors[i]; iter2.hasItem(); |
---|
[ccd1b0] | 1248 | iter2++, iter1++) |
---|
| 1249 | { |
---|
| 1250 | if (degree (iter2.getItem(),v) == degree (iter1.getItem(),v)) |
---|
| 1251 | { |
---|
[8a30b1] | 1252 | multiplier.append (1); |
---|
| 1253 | continue; |
---|
[ccd1b0] | 1254 | } |
---|
[38ffb7] | 1255 | g= gcd (iter2.getItem(), content); |
---|
[8a30b1] | 1256 | if (!g.inCoeffDomain()) |
---|
[ccd1b0] | 1257 | { |
---|
[8a30b1] | 1258 | tmp *= g; |
---|
| 1259 | multiplier.append (g); |
---|
[ccd1b0] | 1260 | } |
---|
[8a30b1] | 1261 | else |
---|
| 1262 | multiplier.append (1); |
---|
| 1263 | } |
---|
| 1264 | if (!tmp.isOne() && fdivides (tmp, content)) |
---|
| 1265 | { |
---|
| 1266 | iter1= l; |
---|
| 1267 | iter1++; |
---|
| 1268 | content /= tmp; |
---|
| 1269 | for (iter2= multiplier; iter2.hasItem(); iter1++, iter2++) |
---|
| 1270 | iter1.getItem() *= iter2.getItem(); |
---|
[ccd1b0] | 1271 | } |
---|
[8a30b1] | 1272 | multiplier= CFList(); |
---|
[ccd1b0] | 1273 | } |
---|
| 1274 | |
---|
| 1275 | l.removeFirst(); |
---|
| 1276 | l.insert (content); |
---|
| 1277 | return l; |
---|
| 1278 | } |
---|
| 1279 | |
---|
| 1280 | CFList evaluateAtZero (const CanonicalForm& F) |
---|
| 1281 | { |
---|
| 1282 | CFList result; |
---|
| 1283 | CanonicalForm buf= F; |
---|
| 1284 | result.insert (buf); |
---|
| 1285 | for (int i= F.level(); i > 2; i--) |
---|
| 1286 | { |
---|
| 1287 | buf= buf (0, i); |
---|
| 1288 | result.insert (buf); |
---|
| 1289 | } |
---|
| 1290 | return result; |
---|
| 1291 | } |
---|
| 1292 | |
---|
[eefc3a] | 1293 | CFList evaluateAtEval (const CanonicalForm& F, const CFArray& eval) |
---|
| 1294 | { |
---|
| 1295 | CFList result; |
---|
| 1296 | CanonicalForm buf= F; |
---|
| 1297 | result.insert (buf); |
---|
| 1298 | int k= eval.size(); |
---|
| 1299 | for (int i= 1; i < k; i++) |
---|
| 1300 | { |
---|
| 1301 | buf= buf (eval[i], i + 2); |
---|
| 1302 | result.insert (buf); |
---|
| 1303 | } |
---|
| 1304 | return result; |
---|
| 1305 | } |
---|
| 1306 | |
---|
| 1307 | CFList evaluateAtEval (const CanonicalForm& F, const CFList& evaluation, int l) |
---|
| 1308 | { |
---|
| 1309 | CFList result; |
---|
| 1310 | CanonicalForm buf= F; |
---|
| 1311 | result.insert (buf); |
---|
| 1312 | int k= evaluation.length() + l - 1; |
---|
| 1313 | CFListIterator j= evaluation; |
---|
| 1314 | for (int i= k; j.hasItem() && i > l; i--, j++) |
---|
| 1315 | { |
---|
| 1316 | if (F.level() < i) |
---|
| 1317 | continue; |
---|
| 1318 | buf= buf (j.getItem(), i); |
---|
| 1319 | result.insert (buf); |
---|
| 1320 | } |
---|
| 1321 | return result; |
---|
| 1322 | } |
---|
| 1323 | |
---|
[ccd1b0] | 1324 | int |
---|
| 1325 | testFactors (const CanonicalForm& G, const CFList& uniFactors, |
---|
| 1326 | const Variable& alpha, CanonicalForm& sqrfPartF, CFList& factors, |
---|
[eefc3a] | 1327 | CFFList*& bufSqrfFactors, CFList& evalSqrfPartF, |
---|
| 1328 | const CFArray& evalPoint) |
---|
[ccd1b0] | 1329 | { |
---|
[38ffb7] | 1330 | CanonicalForm tmp; |
---|
| 1331 | CFListIterator j; |
---|
[ccd1b0] | 1332 | for (CFListIterator i= uniFactors; i.hasItem(); i++) |
---|
| 1333 | { |
---|
[38ffb7] | 1334 | tmp= i.getItem(); |
---|
[ccd1b0] | 1335 | if (i.hasItem()) |
---|
| 1336 | i++; |
---|
| 1337 | else |
---|
| 1338 | break; |
---|
[38ffb7] | 1339 | for (j= i; j.hasItem(); j++) |
---|
[ccd1b0] | 1340 | { |
---|
| 1341 | if (tmp == j.getItem()) |
---|
| 1342 | return 0; |
---|
| 1343 | } |
---|
| 1344 | } |
---|
| 1345 | |
---|
| 1346 | CanonicalForm F= G; |
---|
| 1347 | CFFList sqrfFactorization= squarefreeFactorization (F, alpha); |
---|
| 1348 | |
---|
| 1349 | sqrfPartF= 1; |
---|
| 1350 | for (CFFListIterator i= sqrfFactorization; i.hasItem(); i++) |
---|
| 1351 | sqrfPartF *= i.getItem().factor(); |
---|
| 1352 | |
---|
[eefc3a] | 1353 | evalSqrfPartF= evaluateAtEval (sqrfPartF, evalPoint); |
---|
[ccd1b0] | 1354 | |
---|
[eefc3a] | 1355 | CanonicalForm test= evalSqrfPartF.getFirst() (evalPoint[0], 2); |
---|
[ccd1b0] | 1356 | |
---|
| 1357 | if (degree (test) != degree (sqrfPartF, 1)) |
---|
| 1358 | return 0; |
---|
| 1359 | |
---|
| 1360 | CFFList sqrfFactors; |
---|
| 1361 | CFList tmp2; |
---|
| 1362 | int k= 0; |
---|
| 1363 | factors= uniFactors; |
---|
[38ffb7] | 1364 | CFFListIterator iter; |
---|
[ccd1b0] | 1365 | for (CFListIterator i= factors; i.hasItem(); i++, k++) |
---|
| 1366 | { |
---|
[38ffb7] | 1367 | tmp= 1; |
---|
[ccd1b0] | 1368 | sqrfFactors= squarefreeFactorization (i.getItem(), alpha); |
---|
| 1369 | |
---|
[38ffb7] | 1370 | for (iter= sqrfFactors; iter.hasItem(); iter++) |
---|
[ccd1b0] | 1371 | { |
---|
[38ffb7] | 1372 | tmp2.append (iter.getItem().factor()); |
---|
| 1373 | tmp *= iter.getItem().factor(); |
---|
[ccd1b0] | 1374 | } |
---|
| 1375 | i.getItem()= tmp/Lc(tmp); |
---|
| 1376 | bufSqrfFactors [k]= sqrfFactors; |
---|
| 1377 | } |
---|
| 1378 | |
---|
| 1379 | for (int i= 0; i < factors.length() - 1; i++) |
---|
| 1380 | { |
---|
[38ffb7] | 1381 | for (k= i + 1; k < factors.length(); k++) |
---|
[ccd1b0] | 1382 | { |
---|
| 1383 | gcdFreeBasis (bufSqrfFactors [i], bufSqrfFactors[k]); |
---|
| 1384 | } |
---|
| 1385 | } |
---|
| 1386 | |
---|
| 1387 | factors= CFList(); |
---|
| 1388 | for (int i= 0; i < uniFactors.length(); i++) |
---|
| 1389 | { |
---|
| 1390 | if (i == 0) |
---|
| 1391 | { |
---|
[38ffb7] | 1392 | for (iter= bufSqrfFactors [i]; iter.hasItem(); iter++) |
---|
[ccd1b0] | 1393 | { |
---|
[327efa2] | 1394 | if (iter.getItem().factor().inCoeffDomain()) |
---|
| 1395 | continue; |
---|
[38ffb7] | 1396 | iter.getItem()= CFFactor (iter.getItem().factor()/ |
---|
| 1397 | Lc (iter.getItem().factor()), |
---|
| 1398 | iter.getItem().exp()); |
---|
| 1399 | factors.append (iter.getItem().factor()); |
---|
[ccd1b0] | 1400 | } |
---|
| 1401 | } |
---|
| 1402 | else |
---|
| 1403 | { |
---|
[38ffb7] | 1404 | for (iter= bufSqrfFactors [i]; iter.hasItem(); iter++) |
---|
[ccd1b0] | 1405 | { |
---|
[327efa2] | 1406 | if (iter.getItem().factor().inCoeffDomain()) |
---|
| 1407 | continue; |
---|
[38ffb7] | 1408 | iter.getItem()= CFFactor (iter.getItem().factor()/ |
---|
| 1409 | Lc (iter.getItem().factor()), |
---|
| 1410 | iter.getItem().exp()); |
---|
| 1411 | if (!find (factors, iter.getItem().factor())) |
---|
| 1412 | factors.append (iter.getItem().factor()); |
---|
[ccd1b0] | 1413 | } |
---|
| 1414 | } |
---|
| 1415 | } |
---|
| 1416 | |
---|
| 1417 | test= prod (factors); |
---|
[eefc3a] | 1418 | tmp= evalSqrfPartF.getFirst() (evalPoint[0],2); |
---|
[ccd1b0] | 1419 | if (test/Lc (test) != tmp/Lc (tmp)) |
---|
| 1420 | return 0; |
---|
| 1421 | else |
---|
| 1422 | return 1; |
---|
| 1423 | } |
---|
| 1424 | |
---|
| 1425 | CFList |
---|
| 1426 | precomputeLeadingCoeff (const CanonicalForm& LCF, const CFList& LCFFactors, |
---|
| 1427 | const Variable& alpha, const CFList& evaluation, |
---|
[eefc3a] | 1428 | CFList* & differentSecondVarLCs, int lSecondVarLCs, |
---|
[ccd1b0] | 1429 | Variable& y |
---|
| 1430 | ) |
---|
| 1431 | { |
---|
| 1432 | y= Variable (1); |
---|
| 1433 | if (LCF.inCoeffDomain()) |
---|
| 1434 | { |
---|
| 1435 | CFList result; |
---|
| 1436 | for (int i= 1; i <= LCFFactors.length() + 1; i++) |
---|
| 1437 | result.append (1); |
---|
| 1438 | return result; |
---|
| 1439 | } |
---|
| 1440 | |
---|
[8256fd] | 1441 | CFMap N, M; |
---|
[8a30b1] | 1442 | CFArray dummy= CFArray (2); |
---|
[8256fd] | 1443 | dummy [0]= LCF; |
---|
[8a30b1] | 1444 | dummy [1]= Variable (2); |
---|
[8256fd] | 1445 | compress (dummy, M, N); |
---|
| 1446 | CanonicalForm F= M (LCF); |
---|
[ccd1b0] | 1447 | if (LCF.isUnivariate()) |
---|
| 1448 | { |
---|
| 1449 | CFList result; |
---|
| 1450 | int LCFLevel= LCF.level(); |
---|
| 1451 | bool found= false; |
---|
| 1452 | if (LCFLevel == 2) |
---|
| 1453 | { |
---|
| 1454 | //bivariate leading coefficients are already the true leading coefficients |
---|
| 1455 | result= LCFFactors; |
---|
| 1456 | found= true; |
---|
| 1457 | } |
---|
| 1458 | else |
---|
| 1459 | { |
---|
[38ffb7] | 1460 | CFListIterator j; |
---|
[eefc3a] | 1461 | for (int i= 0; i < lSecondVarLCs; i++) |
---|
[ccd1b0] | 1462 | { |
---|
[38ffb7] | 1463 | for (j= differentSecondVarLCs[i]; j.hasItem(); j++) |
---|
[ccd1b0] | 1464 | { |
---|
| 1465 | if (j.getItem().level() == LCFLevel) |
---|
| 1466 | { |
---|
| 1467 | found= true; |
---|
| 1468 | break; |
---|
| 1469 | } |
---|
| 1470 | } |
---|
| 1471 | if (found) |
---|
| 1472 | { |
---|
| 1473 | result= differentSecondVarLCs [i]; |
---|
| 1474 | break; |
---|
| 1475 | } |
---|
| 1476 | } |
---|
| 1477 | if (!found) |
---|
| 1478 | result= LCFFactors; |
---|
| 1479 | } |
---|
| 1480 | if (found) |
---|
| 1481 | result.insert (Lc (LCF)); |
---|
| 1482 | else |
---|
| 1483 | result.append (LCF); |
---|
| 1484 | return result; |
---|
| 1485 | } |
---|
| 1486 | |
---|
| 1487 | CFList factors= LCFFactors; |
---|
| 1488 | |
---|
| 1489 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
[8256fd] | 1490 | i.getItem()= M (i.getItem()); |
---|
[ccd1b0] | 1491 | |
---|
| 1492 | CanonicalForm sqrfPartF; |
---|
| 1493 | CFFList * bufSqrfFactors= new CFFList [factors.length()]; |
---|
[eefc3a] | 1494 | CFList evalSqrfPartF, bufFactors; |
---|
| 1495 | CFArray evalPoint= CFArray (evaluation.length() - 1); |
---|
[8a30b1] | 1496 | CFArray buf= CFArray (evaluation.length()); |
---|
| 1497 | CFArray swap= CFArray (evaluation.length()); |
---|
[eefc3a] | 1498 | CFListIterator iter= evaluation; |
---|
[8a30b1] | 1499 | CanonicalForm vars=getVars (LCF); |
---|
| 1500 | for (int i= evaluation.length() +1; i > 1; i--, iter++) |
---|
| 1501 | { |
---|
| 1502 | buf[i-2]=iter.getItem(); |
---|
| 1503 | if (degree (vars, i) > 0) |
---|
| 1504 | swap[M(Variable (i)).level()-1]=buf[i-2]; |
---|
| 1505 | } |
---|
| 1506 | buf= swap; |
---|
| 1507 | for (int i= 0; i < evaluation.length() - 1; i++) |
---|
| 1508 | evalPoint[i]= buf[i+1]; |
---|
[eefc3a] | 1509 | |
---|
[ccd1b0] | 1510 | int pass= testFactors (F, factors, alpha, sqrfPartF, |
---|
[eefc3a] | 1511 | bufFactors, bufSqrfFactors, evalSqrfPartF, evalPoint); |
---|
[ccd1b0] | 1512 | |
---|
| 1513 | bool foundDifferent= false; |
---|
[eefc3a] | 1514 | Variable z, x= y; |
---|
[ccd1b0] | 1515 | int j= 0; |
---|
| 1516 | if (!pass) |
---|
| 1517 | { |
---|
[7a1151] | 1518 | int lev= 0; |
---|
[ccd1b0] | 1519 | // LCF is non-constant here |
---|
[38ffb7] | 1520 | CFList bufBufFactors; |
---|
[8a30b1] | 1521 | CanonicalForm bufF; |
---|
[eefc3a] | 1522 | for (int i= 0; i < lSecondVarLCs; i++) |
---|
[ccd1b0] | 1523 | { |
---|
| 1524 | if (!differentSecondVarLCs [i].isEmpty()) |
---|
| 1525 | { |
---|
| 1526 | bool allConstant= true; |
---|
[38ffb7] | 1527 | for (iter= differentSecondVarLCs[i]; iter.hasItem(); iter++) |
---|
[ccd1b0] | 1528 | { |
---|
| 1529 | if (!iter.getItem().inCoeffDomain()) |
---|
| 1530 | { |
---|
| 1531 | allConstant= false; |
---|
| 1532 | y= Variable (iter.getItem().level()); |
---|
[8256fd] | 1533 | lev= M(y).level(); |
---|
[ccd1b0] | 1534 | } |
---|
| 1535 | } |
---|
| 1536 | if (allConstant) |
---|
| 1537 | continue; |
---|
| 1538 | |
---|
| 1539 | bufFactors= differentSecondVarLCs [i]; |
---|
[38ffb7] | 1540 | for (iter= bufFactors; iter.hasItem(); iter++) |
---|
[ccd1b0] | 1541 | iter.getItem()= swapvar (iter.getItem(), x, y); |
---|
[38ffb7] | 1542 | bufF= F; |
---|
[8256fd] | 1543 | z= Variable (lev); |
---|
[ccd1b0] | 1544 | bufF= swapvar (bufF, x, z); |
---|
[38ffb7] | 1545 | bufBufFactors= bufFactors; |
---|
[eefc3a] | 1546 | evalPoint= CFArray (evaluation.length() - 1); |
---|
[8a30b1] | 1547 | for (int k= 0; k < evaluation.length()-1; k++) |
---|
[eefc3a] | 1548 | { |
---|
[8a30b1] | 1549 | if (k+1 != lev) |
---|
| 1550 | evalPoint[k]= buf[k+1]; |
---|
| 1551 | else |
---|
| 1552 | evalPoint[k]= buf[0]; |
---|
[eefc3a] | 1553 | } |
---|
[ccd1b0] | 1554 | pass= testFactors (bufF, bufBufFactors, alpha, sqrfPartF, bufFactors, |
---|
[eefc3a] | 1555 | bufSqrfFactors, evalSqrfPartF, evalPoint); |
---|
[ccd1b0] | 1556 | if (pass) |
---|
| 1557 | { |
---|
| 1558 | foundDifferent= true; |
---|
| 1559 | F= bufF; |
---|
| 1560 | CFList l= factors; |
---|
[38ffb7] | 1561 | for (iter= l; iter.hasItem(); iter++) |
---|
[ccd1b0] | 1562 | iter.getItem()= swapvar (iter.getItem(), x, y); |
---|
| 1563 | differentSecondVarLCs [i]= l; |
---|
| 1564 | j= i; |
---|
| 1565 | break; |
---|
| 1566 | } |
---|
[eefc3a] | 1567 | if (!pass && i == lSecondVarLCs - 1) |
---|
[ccd1b0] | 1568 | { |
---|
| 1569 | CFList result; |
---|
| 1570 | result.append (LCF); |
---|
| 1571 | for (int k= 1; k <= factors.length(); k++) |
---|
| 1572 | result.append (LCF); |
---|
| 1573 | y= Variable (1); |
---|
[229530] | 1574 | delete [] bufSqrfFactors; |
---|
[ccd1b0] | 1575 | return result; |
---|
| 1576 | } |
---|
| 1577 | } |
---|
| 1578 | } |
---|
| 1579 | } |
---|
| 1580 | if (!pass) |
---|
| 1581 | { |
---|
| 1582 | CFList result; |
---|
| 1583 | result.append (LCF); |
---|
| 1584 | for (int k= 1; k <= factors.length(); k++) |
---|
| 1585 | result.append (LCF); |
---|
| 1586 | y= Variable (1); |
---|
[229530] | 1587 | delete [] bufSqrfFactors; |
---|
[ccd1b0] | 1588 | return result; |
---|
| 1589 | } |
---|
| 1590 | else |
---|
| 1591 | factors= bufFactors; |
---|
| 1592 | |
---|
[327efa2] | 1593 | bufFactors= factors; |
---|
[eefc3a] | 1594 | CFList evaluation2; |
---|
[8a30b1] | 1595 | for (int i= 0; i < F.level()-1; i++) |
---|
| 1596 | evaluation2.insert (evalPoint[i]); |
---|
[327efa2] | 1597 | |
---|
[ec16f0] | 1598 | CFList interMedResult; |
---|
| 1599 | CanonicalForm oldSqrfPartF= sqrfPartF; |
---|
[8a30b1] | 1600 | sqrfPartF= shift2Zero (sqrfPartF, evalSqrfPartF, evaluation2); |
---|
[327efa2] | 1601 | if (factors.length() > 1) |
---|
| 1602 | { |
---|
[ec16f0] | 1603 | CanonicalForm LC1= LC (oldSqrfPartF, 1); |
---|
| 1604 | CFList leadingCoeffs; |
---|
[327efa2] | 1605 | for (int i= 0; i < factors.length(); i++) |
---|
[ec16f0] | 1606 | leadingCoeffs.append (LC1); |
---|
| 1607 | |
---|
[8a30b1] | 1608 | CFList LC1eval= evaluateAtEval (LC1, evaluation2, 2); |
---|
[ec16f0] | 1609 | CFList oldFactors= factors; |
---|
| 1610 | for (CFListIterator i= oldFactors; i.hasItem(); i++) |
---|
| 1611 | i.getItem() *= LC1eval.getFirst()/Lc (i.getItem()); |
---|
[eefc3a] | 1612 | |
---|
[ec16f0] | 1613 | bool success= false; |
---|
[64b824] | 1614 | CanonicalForm oldSqrfPartFPowLC= oldSqrfPartF*power(LC1,factors.length()-1); |
---|
| 1615 | if (size (oldSqrfPartFPowLC)/getNumVars (oldSqrfPartFPowLC) < 500 && |
---|
| 1616 | LucksWangSparseHeuristic (oldSqrfPartFPowLC, |
---|
[8a30b1] | 1617 | oldFactors, 2, leadingCoeffs, factors)) |
---|
[eefc3a] | 1618 | { |
---|
[ec16f0] | 1619 | interMedResult= recoverFactors (oldSqrfPartF, factors); |
---|
| 1620 | if (oldFactors.length() == interMedResult.length()) |
---|
| 1621 | success= true; |
---|
[eefc3a] | 1622 | } |
---|
[ec16f0] | 1623 | if (!success) |
---|
| 1624 | { |
---|
| 1625 | LC1= LC (evalSqrfPartF.getFirst(), 1); |
---|
[ccd1b0] | 1626 | |
---|
[ec16f0] | 1627 | CFArray leadingCoeffs= CFArray (factors.length()); |
---|
| 1628 | for (int i= 0; i < factors.length(); i++) |
---|
| 1629 | leadingCoeffs[i]= LC1; |
---|
[ccd1b0] | 1630 | |
---|
[ec16f0] | 1631 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
| 1632 | i.getItem() *= LC1 (0,2)/Lc (i.getItem()); |
---|
| 1633 | factors.insert (1); |
---|
[ccd1b0] | 1634 | |
---|
[ec16f0] | 1635 | CanonicalForm |
---|
| 1636 | newSqrfPartF= evalSqrfPartF.getFirst()*power (LC1, factors.length() - 2); |
---|
[327efa2] | 1637 | |
---|
[ec16f0] | 1638 | int liftBound= degree (newSqrfPartF,2) + 1; |
---|
| 1639 | |
---|
| 1640 | CFMatrix M= CFMatrix (liftBound, factors.length() - 1); |
---|
| 1641 | CFArray Pi; |
---|
| 1642 | CFList diophant; |
---|
[81d96c] | 1643 | nonMonicHenselLift12 (newSqrfPartF, factors, liftBound, Pi, diophant, M, |
---|
| 1644 | leadingCoeffs, false); |
---|
[ec16f0] | 1645 | |
---|
| 1646 | if (sqrfPartF.level() > 2) |
---|
[327efa2] | 1647 | { |
---|
[ec16f0] | 1648 | int* liftBounds= new int [sqrfPartF.level() - 1]; |
---|
| 1649 | liftBounds [0]= liftBound; |
---|
| 1650 | bool noOneToOne= false; |
---|
| 1651 | CFList *leadingCoeffs2= new CFList [sqrfPartF.level()-2]; |
---|
| 1652 | LC1= LC (evalSqrfPartF.getLast(), 1); |
---|
| 1653 | CFList LCs; |
---|
| 1654 | for (int i= 0; i < factors.length(); i++) |
---|
| 1655 | LCs.append (LC1); |
---|
| 1656 | leadingCoeffs2 [sqrfPartF.level() - 3]= LCs; |
---|
| 1657 | for (int i= sqrfPartF.level() - 1; i > 2; i--) |
---|
| 1658 | { |
---|
| 1659 | for (CFListIterator j= LCs; j.hasItem(); j++) |
---|
| 1660 | j.getItem()= j.getItem() (0, i + 1); |
---|
| 1661 | leadingCoeffs2 [i - 3]= LCs; |
---|
| 1662 | } |
---|
| 1663 | sqrfPartF *= power (LC1, factors.length()-1); |
---|
| 1664 | |
---|
| 1665 | int liftBoundsLength= sqrfPartF.level() - 1; |
---|
| 1666 | for (int i= 1; i < liftBoundsLength; i++) |
---|
| 1667 | liftBounds [i]= degree (sqrfPartF, i + 2) + 1; |
---|
| 1668 | evalSqrfPartF= evaluateAtZero (sqrfPartF); |
---|
| 1669 | evalSqrfPartF.removeFirst(); |
---|
| 1670 | factors= nonMonicHenselLift (evalSqrfPartF, factors, leadingCoeffs2, |
---|
| 1671 | diophant, Pi, liftBounds, sqrfPartF.level() - 1, noOneToOne); |
---|
| 1672 | delete [] leadingCoeffs2; |
---|
| 1673 | delete [] liftBounds; |
---|
[327efa2] | 1674 | } |
---|
[ec16f0] | 1675 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
[8a30b1] | 1676 | iter.getItem()= reverseShift (iter.getItem(), evaluation2); |
---|
[ec16f0] | 1677 | |
---|
| 1678 | interMedResult= |
---|
[8a30b1] | 1679 | recoverFactors (reverseShift(evalSqrfPartF.getLast(),evaluation2), |
---|
[ec16f0] | 1680 | factors); |
---|
[327efa2] | 1681 | } |
---|
| 1682 | } |
---|
| 1683 | else |
---|
[ec16f0] | 1684 | { |
---|
[8256fd] | 1685 | CanonicalForm contF=content (oldSqrfPartF,1); |
---|
| 1686 | factors= CFList (oldSqrfPartF/contF); |
---|
[ec16f0] | 1687 | interMedResult= recoverFactors (oldSqrfPartF, factors); |
---|
| 1688 | } |
---|
[ccd1b0] | 1689 | |
---|
| 1690 | CFList result; |
---|
[38ffb7] | 1691 | CFFListIterator k; |
---|
[ccd1b0] | 1692 | for (int i= 0; i < LCFFactors.length(); i++) |
---|
| 1693 | { |
---|
| 1694 | CanonicalForm tmp= 1; |
---|
[38ffb7] | 1695 | for (k= bufSqrfFactors[i]; k.hasItem(); k++) |
---|
[ccd1b0] | 1696 | { |
---|
| 1697 | int pos= findItem (bufFactors, k.getItem().factor()); |
---|
| 1698 | if (pos) |
---|
| 1699 | tmp *= power (getItem (interMedResult, pos), k.getItem().exp()); |
---|
| 1700 | } |
---|
| 1701 | result.append (tmp); |
---|
| 1702 | } |
---|
| 1703 | |
---|
| 1704 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
| 1705 | { |
---|
| 1706 | F /= i.getItem(); |
---|
| 1707 | if (foundDifferent) |
---|
| 1708 | i.getItem()= swapvar (i.getItem(), x, z); |
---|
| 1709 | i.getItem()= N (i.getItem()); |
---|
| 1710 | } |
---|
| 1711 | |
---|
| 1712 | if (foundDifferent) |
---|
| 1713 | { |
---|
| 1714 | CFList l= differentSecondVarLCs [j]; |
---|
| 1715 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 1716 | i.getItem()= swapvar (i.getItem(), y, z); |
---|
| 1717 | differentSecondVarLCs [j]= l; |
---|
| 1718 | F= swapvar (F, x, z); |
---|
| 1719 | } |
---|
| 1720 | |
---|
| 1721 | result.insert (N (F)); |
---|
| 1722 | |
---|
[eefc3a] | 1723 | result= distributeContent (result, differentSecondVarLCs, lSecondVarLCs); |
---|
[ccd1b0] | 1724 | |
---|
| 1725 | if (!result.getFirst().inCoeffDomain()) |
---|
| 1726 | { |
---|
| 1727 | CFListIterator i= result; |
---|
| 1728 | CanonicalForm tmp; |
---|
| 1729 | if (foundDifferent) |
---|
| 1730 | i.getItem()= swapvar (i.getItem(), Variable (2), y); |
---|
| 1731 | |
---|
| 1732 | tmp= i.getItem(); |
---|
| 1733 | |
---|
| 1734 | i++; |
---|
| 1735 | for (; i.hasItem(); i++) |
---|
| 1736 | { |
---|
| 1737 | if (foundDifferent) |
---|
| 1738 | i.getItem()= swapvar (i.getItem(), Variable (2), y)*tmp; |
---|
| 1739 | else |
---|
| 1740 | i.getItem() *= tmp; |
---|
| 1741 | } |
---|
| 1742 | } |
---|
| 1743 | else |
---|
| 1744 | y= Variable (1); |
---|
| 1745 | |
---|
[229530] | 1746 | delete [] bufSqrfFactors; |
---|
| 1747 | |
---|
[ccd1b0] | 1748 | return result; |
---|
| 1749 | } |
---|
| 1750 | |
---|
| 1751 | void |
---|
| 1752 | evaluationWRTDifferentSecondVars (CFList*& Aeval, const CFList& evaluation, |
---|
| 1753 | const CanonicalForm& A) |
---|
| 1754 | { |
---|
[38ffb7] | 1755 | CanonicalForm tmp; |
---|
| 1756 | CFList tmp2; |
---|
| 1757 | CFListIterator iter; |
---|
[ccd1b0] | 1758 | for (int i= A.level(); i > 2; i--) |
---|
| 1759 | { |
---|
[38ffb7] | 1760 | tmp= A; |
---|
| 1761 | tmp2= CFList(); |
---|
| 1762 | iter= evaluation; |
---|
[ccd1b0] | 1763 | bool preserveDegree= true; |
---|
| 1764 | for (int j= A.level(); j > 1; j--, iter++) |
---|
| 1765 | { |
---|
| 1766 | if (j == i) |
---|
| 1767 | continue; |
---|
| 1768 | else |
---|
| 1769 | { |
---|
| 1770 | tmp= tmp (iter.getItem(), j); |
---|
| 1771 | tmp2.insert (tmp); |
---|
| 1772 | if ((degree (tmp, i) != degree (A, i)) || |
---|
| 1773 | (degree (tmp, 1) != degree (A, 1))) |
---|
| 1774 | { |
---|
| 1775 | preserveDegree= false; |
---|
| 1776 | break; |
---|
| 1777 | } |
---|
| 1778 | if (!content(tmp).inCoeffDomain() || !content(tmp,1).inCoeffDomain()) |
---|
| 1779 | { |
---|
| 1780 | preserveDegree= false; |
---|
| 1781 | break; |
---|
| 1782 | } |
---|
| 1783 | } |
---|
| 1784 | } |
---|
| 1785 | if (preserveDegree) |
---|
| 1786 | Aeval [i - 3]= tmp2; |
---|
| 1787 | else |
---|
| 1788 | Aeval [i - 3]= CFList(); |
---|
| 1789 | } |
---|
| 1790 | } |
---|
| 1791 | |
---|
[6f6320] | 1792 | #endif |
---|
| 1793 | |
---|
[ccd1b0] | 1794 | static inline |
---|
| 1795 | CanonicalForm prodEval (const CFList& l, const CanonicalForm& evalPoint, |
---|
| 1796 | const Variable& v) |
---|
| 1797 | { |
---|
| 1798 | CanonicalForm result= 1; |
---|
| 1799 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
| 1800 | result *= i.getItem() (evalPoint, v); |
---|
| 1801 | return result; |
---|
| 1802 | } |
---|
| 1803 | |
---|
| 1804 | //recombine bivariate factors in case one bivariate factorization yields less |
---|
| 1805 | // factors than the other |
---|
| 1806 | CFList |
---|
| 1807 | recombination (const CFList& factors1, const CFList& factors2, int s, int thres, |
---|
| 1808 | const CanonicalForm& evalPoint, const Variable& x) |
---|
| 1809 | { |
---|
| 1810 | CFList T, S; |
---|
| 1811 | |
---|
| 1812 | T= factors1; |
---|
| 1813 | CFList result; |
---|
| 1814 | CanonicalForm buf; |
---|
| 1815 | int * v= new int [T.length()]; |
---|
| 1816 | for (int i= 0; i < T.length(); i++) |
---|
| 1817 | v[i]= 0; |
---|
| 1818 | bool nosubset= false; |
---|
| 1819 | CFArray TT; |
---|
| 1820 | TT= copy (factors1); |
---|
| 1821 | while (T.length() >= 2*s && s <= thres) |
---|
| 1822 | { |
---|
[a30a5fc] | 1823 | while (nosubset == false) |
---|
[ccd1b0] | 1824 | { |
---|
[a30a5fc] | 1825 | if (T.length() == s) |
---|
[ccd1b0] | 1826 | { |
---|
| 1827 | delete [] v; |
---|
| 1828 | result.append (prod (T)); |
---|
| 1829 | return result; |
---|
| 1830 | } |
---|
| 1831 | S= subset (v, s, TT, nosubset); |
---|
| 1832 | if (nosubset) break; |
---|
| 1833 | buf= prodEval (S, evalPoint, x); |
---|
| 1834 | buf /= Lc (buf); |
---|
| 1835 | if (find (factors2, buf)) |
---|
| 1836 | { |
---|
| 1837 | T= Difference (T, S); |
---|
| 1838 | result.append (prod (S)); |
---|
| 1839 | TT= copy (T); |
---|
| 1840 | indexUpdate (v, s, T.length(), nosubset); |
---|
| 1841 | if (nosubset) break; |
---|
| 1842 | } |
---|
| 1843 | } |
---|
| 1844 | s++; |
---|
| 1845 | if (T.length() < 2*s || T.length() == s) |
---|
| 1846 | { |
---|
| 1847 | delete [] v; |
---|
| 1848 | result.append (prod (T)); |
---|
| 1849 | return result; |
---|
| 1850 | } |
---|
| 1851 | for (int i= 0; i < T.length(); i++) |
---|
| 1852 | v[i]= 0; |
---|
| 1853 | nosubset= false; |
---|
| 1854 | } |
---|
| 1855 | |
---|
| 1856 | delete [] v; |
---|
| 1857 | if (T.length() < 2*s) |
---|
| 1858 | { |
---|
| 1859 | result.append (prod (T)); |
---|
| 1860 | return result; |
---|
| 1861 | } |
---|
| 1862 | |
---|
| 1863 | return result; |
---|
| 1864 | } |
---|
| 1865 | |
---|
[6f6320] | 1866 | #ifdef HAVE_NTL |
---|
[ccd1b0] | 1867 | void |
---|
| 1868 | factorizationWRTDifferentSecondVars (const CanonicalForm& A, CFList*& Aeval, |
---|
| 1869 | const ExtensionInfo& info, |
---|
| 1870 | int& minFactorsLength, bool& irred) |
---|
| 1871 | { |
---|
| 1872 | Variable x= Variable (1); |
---|
| 1873 | minFactorsLength= 0; |
---|
| 1874 | irred= false; |
---|
[38ffb7] | 1875 | CFList factors; |
---|
| 1876 | Variable v; |
---|
[ccd1b0] | 1877 | for (int j= 0; j < A.level() - 2; j++) |
---|
| 1878 | { |
---|
| 1879 | if (!Aeval[j].isEmpty()) |
---|
| 1880 | { |
---|
[38ffb7] | 1881 | v= Variable (Aeval[j].getFirst().level()); |
---|
[ccd1b0] | 1882 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
| 1883 | factors= GFBiSqrfFactorize (Aeval[j].getFirst()); |
---|
| 1884 | else if (info.getAlpha().level() == 1) |
---|
| 1885 | factors= FpBiSqrfFactorize (Aeval[j].getFirst()); |
---|
| 1886 | else |
---|
| 1887 | factors= FqBiSqrfFactorize (Aeval[j].getFirst(), info.getAlpha()); |
---|
| 1888 | |
---|
| 1889 | factors.removeFirst(); |
---|
| 1890 | if (minFactorsLength == 0) |
---|
| 1891 | minFactorsLength= factors.length(); |
---|
| 1892 | else |
---|
| 1893 | minFactorsLength= tmin (minFactorsLength, factors.length()); |
---|
| 1894 | |
---|
| 1895 | if (factors.length() == 1) |
---|
| 1896 | { |
---|
| 1897 | irred= true; |
---|
| 1898 | return; |
---|
| 1899 | } |
---|
| 1900 | sortList (factors, x); |
---|
| 1901 | Aeval [j]= factors; |
---|
| 1902 | } |
---|
| 1903 | } |
---|
| 1904 | } |
---|
| 1905 | |
---|
[8a30b1] | 1906 | CFList conv (const CFArray & A) |
---|
| 1907 | { |
---|
| 1908 | CFList result; |
---|
| 1909 | for (int i= A.max(); i >= A.min(); i--) |
---|
| 1910 | result.insert (A[i]); |
---|
| 1911 | return result; |
---|
| 1912 | } |
---|
| 1913 | |
---|
[ccd1b0] | 1914 | void getLeadingCoeffs (const CanonicalForm& A, CFList*& Aeval, |
---|
| 1915 | const CFList& uniFactors, const CFList& evaluation |
---|
| 1916 | ) |
---|
| 1917 | { |
---|
[38ffb7] | 1918 | CanonicalForm evalPoint; |
---|
| 1919 | int i; |
---|
| 1920 | CFListIterator iter, iter2; |
---|
| 1921 | Variable v; |
---|
[8a30b1] | 1922 | CFList LCs, buf; |
---|
| 1923 | CFArray l; |
---|
| 1924 | int pos, index; |
---|
[ccd1b0] | 1925 | for (int j= 0; j < A.level() - 2; j++) |
---|
| 1926 | { |
---|
| 1927 | if (!Aeval[j].isEmpty()) |
---|
| 1928 | { |
---|
[38ffb7] | 1929 | i= A.level(); |
---|
| 1930 | for (iter= evaluation; iter.hasItem(); iter++, i--) |
---|
[ccd1b0] | 1931 | { |
---|
| 1932 | if (i == Aeval[j].getFirst().level()) |
---|
| 1933 | { |
---|
| 1934 | evalPoint= iter.getItem(); |
---|
| 1935 | break; |
---|
| 1936 | } |
---|
| 1937 | } |
---|
| 1938 | |
---|
[38ffb7] | 1939 | v= Variable (i); |
---|
[ccd1b0] | 1940 | if (Aeval[j].length() > uniFactors.length()) |
---|
| 1941 | Aeval[j]= recombination (Aeval[j], uniFactors, 1, |
---|
| 1942 | Aeval[j].length() - uniFactors.length() + 1, |
---|
| 1943 | evalPoint, v); |
---|
| 1944 | |
---|
[eefc3a] | 1945 | buf= buildUniFactors (Aeval[j], evalPoint, v); |
---|
[8a30b1] | 1946 | l= CFArray (uniFactors.length()); |
---|
| 1947 | index= 1; |
---|
| 1948 | for (iter= buf; iter.hasItem(); iter++, index++) |
---|
[ccd1b0] | 1949 | { |
---|
[8a30b1] | 1950 | pos= findItem (uniFactors, iter.getItem()); |
---|
[eefc3a] | 1951 | if (pos) |
---|
[8a30b1] | 1952 | l[pos-1]= getItem (Aeval[j], index); |
---|
[ccd1b0] | 1953 | } |
---|
[8a30b1] | 1954 | buf= conv (l); |
---|
| 1955 | Aeval [j]= buf; |
---|
[ccd1b0] | 1956 | |
---|
[8a30b1] | 1957 | buf= buildUniFactors (Aeval[j], evalPoint, v); |
---|
[38ffb7] | 1958 | LCs= CFList(); |
---|
| 1959 | for (iter= Aeval[j]; iter.hasItem(); iter++) |
---|
[eefc3a] | 1960 | LCs.append (LC (iter.getItem(), 1)); |
---|
[8a30b1] | 1961 | //normalize (LCs); |
---|
[ccd1b0] | 1962 | Aeval[j]= LCs; |
---|
| 1963 | } |
---|
| 1964 | } |
---|
| 1965 | } |
---|
| 1966 | |
---|
| 1967 | CFList |
---|
| 1968 | buildUniFactors (const CFList& biFactors, const CanonicalForm& evalPoint, |
---|
| 1969 | const Variable& y) |
---|
| 1970 | { |
---|
| 1971 | CFList result; |
---|
| 1972 | CanonicalForm tmp; |
---|
| 1973 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
| 1974 | { |
---|
| 1975 | tmp= mod (i.getItem(), y - evalPoint); |
---|
| 1976 | tmp /= Lc (tmp); |
---|
| 1977 | result.append (tmp); |
---|
| 1978 | } |
---|
| 1979 | return result; |
---|
| 1980 | } |
---|
| 1981 | |
---|
| 1982 | void refineBiFactors (const CanonicalForm& A, CFList& biFactors, |
---|
| 1983 | CFList* const& Aeval, const CFList& evaluation, |
---|
| 1984 | int minFactorsLength) |
---|
| 1985 | { |
---|
[38ffb7] | 1986 | CFListIterator iter; |
---|
| 1987 | CanonicalForm evalPoint; |
---|
| 1988 | int i; |
---|
| 1989 | Variable v; |
---|
| 1990 | Variable y= Variable (2); |
---|
| 1991 | CFList list; |
---|
[ccd1b0] | 1992 | for (int j= 0; j < A.level() - 2; j++) |
---|
| 1993 | { |
---|
| 1994 | if (Aeval[j].length() == minFactorsLength) |
---|
| 1995 | { |
---|
[38ffb7] | 1996 | i= A.level(); |
---|
| 1997 | |
---|
| 1998 | for (iter= evaluation; iter.hasItem(); iter++, i--) |
---|
[ccd1b0] | 1999 | { |
---|
| 2000 | if (i == Aeval[j].getFirst().level()) |
---|
| 2001 | { |
---|
| 2002 | evalPoint= iter.getItem(); |
---|
| 2003 | break; |
---|
| 2004 | } |
---|
| 2005 | } |
---|
| 2006 | |
---|
[38ffb7] | 2007 | v= Variable (i); |
---|
| 2008 | list= buildUniFactors (Aeval[j], evalPoint, v); |
---|
[ccd1b0] | 2009 | |
---|
| 2010 | biFactors= recombination (biFactors, list, 1, |
---|
| 2011 | biFactors.length() - list.length() + 1, |
---|
| 2012 | evaluation.getLast(), y); |
---|
| 2013 | return; |
---|
| 2014 | } |
---|
| 2015 | } |
---|
| 2016 | } |
---|
| 2017 | |
---|
| 2018 | void prepareLeadingCoeffs (CFList*& LCs, int n, const CFList& leadingCoeffs, |
---|
[eefc3a] | 2019 | const CFList& biFactors, const CFList& evaluation) |
---|
[ccd1b0] | 2020 | { |
---|
| 2021 | CFList l= leadingCoeffs; |
---|
| 2022 | LCs [n-3]= l; |
---|
[38ffb7] | 2023 | CFListIterator j; |
---|
[eefc3a] | 2024 | CFListIterator iter= evaluation; |
---|
| 2025 | for (int i= n - 1; i > 2; i--, iter++) |
---|
[ccd1b0] | 2026 | { |
---|
[38ffb7] | 2027 | for (j= l; j.hasItem(); j++) |
---|
[eefc3a] | 2028 | j.getItem()= j.getItem() (iter.getItem(), i + 1); |
---|
[ccd1b0] | 2029 | LCs [i - 3]= l; |
---|
| 2030 | } |
---|
| 2031 | l= LCs [0]; |
---|
| 2032 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
[eefc3a] | 2033 | i.getItem()= i.getItem() (iter.getItem(), 3); |
---|
[ccd1b0] | 2034 | CFListIterator ii= biFactors; |
---|
| 2035 | CFList normalizeFactor; |
---|
| 2036 | for (CFListIterator i= l; i.hasItem(); i++, ii++) |
---|
| 2037 | normalizeFactor.append (Lc (LC (ii.getItem(), 1))/Lc (i.getItem())); |
---|
| 2038 | for (int i= 0; i < n-2; i++) |
---|
| 2039 | { |
---|
| 2040 | ii= normalizeFactor; |
---|
[38ffb7] | 2041 | for (j= LCs [i]; j.hasItem(); j++, ii++) |
---|
[ccd1b0] | 2042 | j.getItem() *= ii.getItem(); |
---|
| 2043 | } |
---|
| 2044 | } |
---|
| 2045 | |
---|
| 2046 | CFList recoverFactors (const CanonicalForm& F, const CFList& factors) |
---|
| 2047 | { |
---|
| 2048 | CFList result; |
---|
[09723d] | 2049 | CanonicalForm tmp, tmp2; |
---|
| 2050 | CanonicalForm G= F; |
---|
[ccd1b0] | 2051 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
| 2052 | { |
---|
[09723d] | 2053 | tmp= i.getItem()/content (i.getItem(), 1); |
---|
| 2054 | if (fdivides (tmp, G, tmp2)) |
---|
| 2055 | { |
---|
| 2056 | G= tmp2; |
---|
[ccd1b0] | 2057 | result.append (tmp); |
---|
[09723d] | 2058 | } |
---|
[ccd1b0] | 2059 | } |
---|
| 2060 | return result; |
---|
| 2061 | } |
---|
| 2062 | |
---|
[c79a9d] | 2063 | CFList recoverFactors (const CanonicalForm& F, const CFList& factors, |
---|
| 2064 | const CFList& evaluation) |
---|
| 2065 | { |
---|
| 2066 | CFList result; |
---|
| 2067 | CanonicalForm tmp, tmp2; |
---|
| 2068 | CanonicalForm G= F; |
---|
| 2069 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
| 2070 | { |
---|
| 2071 | tmp= reverseShift (i.getItem(), evaluation); |
---|
| 2072 | tmp /= content (tmp, 1); |
---|
| 2073 | if (fdivides (tmp, G, tmp2)) |
---|
| 2074 | { |
---|
| 2075 | G= tmp2; |
---|
| 2076 | result.append (tmp); |
---|
| 2077 | } |
---|
| 2078 | } |
---|
| 2079 | return result; |
---|
| 2080 | } |
---|
| 2081 | |
---|
[8267b8] | 2082 | CFList recoverFactors (CanonicalForm& F, const CFList& factors, int* index) |
---|
| 2083 | { |
---|
| 2084 | CFList result; |
---|
| 2085 | CanonicalForm tmp, tmp2; |
---|
| 2086 | CanonicalForm G= F; |
---|
| 2087 | int j= 0; |
---|
| 2088 | for (CFListIterator i= factors; i.hasItem(); i++, j++) |
---|
| 2089 | { |
---|
| 2090 | if (i.getItem().isZero()) |
---|
| 2091 | { |
---|
| 2092 | index[j]= 0; |
---|
| 2093 | continue; |
---|
| 2094 | } |
---|
| 2095 | tmp= i.getItem(); |
---|
| 2096 | if (fdivides (tmp, G, tmp2)) |
---|
| 2097 | { |
---|
| 2098 | G= tmp2; |
---|
| 2099 | tmp /=content (tmp, 1); |
---|
| 2100 | result.append (tmp); |
---|
| 2101 | index[j]= 1; |
---|
| 2102 | } |
---|
| 2103 | else |
---|
| 2104 | index[j]= 0; |
---|
| 2105 | } |
---|
| 2106 | F= G; |
---|
| 2107 | return result; |
---|
| 2108 | } |
---|
| 2109 | |
---|
[ccd1b0] | 2110 | CFList |
---|
| 2111 | extNonMonicFactorRecombination (const CFList& factors, const CanonicalForm& F, |
---|
[c79a9d] | 2112 | const ExtensionInfo& info) |
---|
[ccd1b0] | 2113 | { |
---|
| 2114 | Variable alpha= info.getAlpha(); |
---|
| 2115 | Variable beta= info.getBeta(); |
---|
| 2116 | CanonicalForm gamma= info.getGamma(); |
---|
| 2117 | CanonicalForm delta= info.getDelta(); |
---|
| 2118 | int k= info.getGFDegree(); |
---|
| 2119 | CFList source, dest; |
---|
| 2120 | |
---|
| 2121 | int degMipoBeta= 1; |
---|
| 2122 | if (!k && beta != Variable(1)) |
---|
| 2123 | degMipoBeta= degree (getMipo (beta)); |
---|
| 2124 | |
---|
| 2125 | CFList T, S; |
---|
| 2126 | T= factors; |
---|
| 2127 | int s= 1; |
---|
| 2128 | CFList result; |
---|
[21b8f4] | 2129 | CanonicalForm quot, buf= F; |
---|
[ccd1b0] | 2130 | |
---|
| 2131 | CanonicalForm g; |
---|
| 2132 | CanonicalForm buf2; |
---|
| 2133 | int * v= new int [T.length()]; |
---|
| 2134 | for (int i= 0; i < T.length(); i++) |
---|
| 2135 | v[i]= 0; |
---|
| 2136 | bool noSubset= false; |
---|
| 2137 | CFArray TT; |
---|
| 2138 | TT= copy (factors); |
---|
| 2139 | bool recombination= false; |
---|
| 2140 | bool trueFactor= false; |
---|
| 2141 | while (T.length() >= 2*s) |
---|
| 2142 | { |
---|
| 2143 | while (noSubset == false) |
---|
| 2144 | { |
---|
| 2145 | if (T.length() == s) |
---|
| 2146 | { |
---|
| 2147 | delete [] v; |
---|
| 2148 | if (recombination) |
---|
| 2149 | { |
---|
| 2150 | g= prod (T); |
---|
| 2151 | T.removeFirst(); |
---|
| 2152 | result.append (g/myContent (g)); |
---|
| 2153 | g /= Lc (g); |
---|
| 2154 | appendTestMapDown (result, g, info, source, dest); |
---|
| 2155 | return result; |
---|
| 2156 | } |
---|
| 2157 | else |
---|
[dc390c] | 2158 | return CFList (buf/myContent(buf)); |
---|
[ccd1b0] | 2159 | } |
---|
| 2160 | |
---|
| 2161 | S= subset (v, s, TT, noSubset); |
---|
| 2162 | if (noSubset) break; |
---|
| 2163 | |
---|
| 2164 | g= prod (S); |
---|
| 2165 | g /= myContent (g); |
---|
[21b8f4] | 2166 | if (fdivides (g, buf, quot)) |
---|
[ccd1b0] | 2167 | { |
---|
[c79a9d] | 2168 | buf2= g; |
---|
[ccd1b0] | 2169 | buf2 /= Lc (buf2); |
---|
[a54114] | 2170 | if (!k && beta.level() == 1) |
---|
[ccd1b0] | 2171 | { |
---|
| 2172 | if (degree (buf2, alpha) < degMipoBeta) |
---|
| 2173 | { |
---|
| 2174 | appendTestMapDown (result, buf2, info, source, dest); |
---|
[21b8f4] | 2175 | buf= quot; |
---|
[ccd1b0] | 2176 | recombination= true; |
---|
| 2177 | trueFactor= true; |
---|
| 2178 | } |
---|
| 2179 | } |
---|
| 2180 | else |
---|
| 2181 | { |
---|
| 2182 | if (!isInExtension (buf2, gamma, k, delta, source, dest)) |
---|
| 2183 | { |
---|
| 2184 | appendTestMapDown (result, buf2, info, source, dest); |
---|
[21b8f4] | 2185 | buf= quot; |
---|
[ccd1b0] | 2186 | recombination= true; |
---|
| 2187 | trueFactor= true; |
---|
| 2188 | } |
---|
| 2189 | } |
---|
| 2190 | if (trueFactor) |
---|
| 2191 | { |
---|
| 2192 | T= Difference (T, S); |
---|
| 2193 | |
---|
| 2194 | if (T.length() < 2*s || T.length() == s) |
---|
| 2195 | { |
---|
| 2196 | delete [] v; |
---|
[dc390c] | 2197 | buf /= myContent (buf); |
---|
[ccd1b0] | 2198 | buf /= Lc (buf); |
---|
| 2199 | appendTestMapDown (result, buf, info, source, dest); |
---|
| 2200 | return result; |
---|
| 2201 | } |
---|
| 2202 | trueFactor= false; |
---|
| 2203 | TT= copy (T); |
---|
| 2204 | indexUpdate (v, s, T.length(), noSubset); |
---|
| 2205 | if (noSubset) break; |
---|
| 2206 | } |
---|
| 2207 | } |
---|
| 2208 | } |
---|
| 2209 | s++; |
---|
| 2210 | if (T.length() < 2*s || T.length() == s) |
---|
| 2211 | { |
---|
| 2212 | delete [] v; |
---|
[dc390c] | 2213 | appendTestMapDown (result, buf/myContent(buf), info, source, dest); |
---|
[ccd1b0] | 2214 | return result; |
---|
| 2215 | } |
---|
| 2216 | for (int i= 0; i < T.length(); i++) |
---|
| 2217 | v[i]= 0; |
---|
| 2218 | noSubset= false; |
---|
| 2219 | } |
---|
| 2220 | if (T.length() < 2*s) |
---|
[dc390c] | 2221 | appendMapDown (result, F/myContent(F), info, source, dest); |
---|
[ccd1b0] | 2222 | |
---|
| 2223 | delete [] v; |
---|
| 2224 | return result; |
---|
| 2225 | } |
---|
| 2226 | |
---|
| 2227 | CFList |
---|
| 2228 | extFactorize (const CanonicalForm& F, const ExtensionInfo& info); |
---|
| 2229 | |
---|
| 2230 | CFList |
---|
| 2231 | multiFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
| 2232 | { |
---|
| 2233 | |
---|
| 2234 | if (F.inCoeffDomain()) |
---|
| 2235 | return CFList (F); |
---|
| 2236 | |
---|
| 2237 | // compress and find main Variable |
---|
| 2238 | CFMap N; |
---|
| 2239 | CanonicalForm A= myCompress (F, N); |
---|
| 2240 | |
---|
| 2241 | A /= Lc (A); // make monic |
---|
| 2242 | |
---|
| 2243 | Variable alpha= info.getAlpha(); |
---|
| 2244 | Variable beta= info.getBeta(); |
---|
| 2245 | CanonicalForm gamma= info.getGamma(); |
---|
| 2246 | CanonicalForm delta= info.getDelta(); |
---|
| 2247 | bool extension= info.isInExtension(); |
---|
| 2248 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
| 2249 | //univariate case |
---|
| 2250 | if (F.isUnivariate()) |
---|
| 2251 | { |
---|
| 2252 | if (extension == false) |
---|
| 2253 | return uniFactorizer (F, alpha, GF); |
---|
| 2254 | else |
---|
[44651b] | 2255 | { |
---|
[7bf145] | 2256 | CFList source, dest; |
---|
| 2257 | A= mapDown (F, info, source, dest); |
---|
| 2258 | return uniFactorizer (A, beta, GF); |
---|
| 2259 | } |
---|
| 2260 | } |
---|
| 2261 | |
---|
| 2262 | //bivariate case |
---|
[44651b] | 2263 | if (A.level() == 2) |
---|
[7bf145] | 2264 | { |
---|
[44651b] | 2265 | CFList buf= biFactorize (F, info); |
---|
[7bf145] | 2266 | return buf; |
---|
| 2267 | } |
---|
[44651b] | 2268 | |
---|
[7bf145] | 2269 | Variable x= Variable (1); |
---|
| 2270 | Variable y= Variable (2); |
---|
[44651b] | 2271 | |
---|
[7bf145] | 2272 | // remove content |
---|
| 2273 | CFList contentAi; |
---|
| 2274 | CanonicalForm lcmCont= lcmContent (A, contentAi); |
---|
[44651b] | 2275 | A /= lcmCont; |
---|
[7bf145] | 2276 | |
---|
| 2277 | // trivial after content removal |
---|
| 2278 | CFList contentAFactors; |
---|
[44651b] | 2279 | if (A.inCoeffDomain()) |
---|
| 2280 | { |
---|
| 2281 | for (CFListIterator i= contentAi; i.hasItem(); i++) |
---|
[7bf145] | 2282 | { |
---|
| 2283 | if (i.getItem().inCoeffDomain()) |
---|
| 2284 | continue; |
---|
[44651b] | 2285 | else |
---|
[7bf145] | 2286 | { |
---|
| 2287 | lcmCont /= i.getItem(); |
---|
[44651b] | 2288 | contentAFactors= |
---|
| 2289 | Union (multiFactorize (lcmCont, info), |
---|
[7bf145] | 2290 | multiFactorize (i.getItem(), info)); |
---|
| 2291 | break; |
---|
| 2292 | } |
---|
| 2293 | } |
---|
| 2294 | decompress (contentAFactors, N); |
---|
| 2295 | normalize (contentAFactors); |
---|
| 2296 | return contentAFactors; |
---|
| 2297 | } |
---|
| 2298 | |
---|
| 2299 | // factorize content |
---|
[44651b] | 2300 | contentAFactors= multiFactorize (lcmCont, info); |
---|
[7bf145] | 2301 | |
---|
| 2302 | // univariate after content removal |
---|
| 2303 | CFList factors; |
---|
[44651b] | 2304 | if (A.isUnivariate ()) |
---|
[7bf145] | 2305 | { |
---|
| 2306 | factors= uniFactorizer (A, alpha, GF); |
---|
| 2307 | append (factors, contentAFactors); |
---|
| 2308 | decompress (factors, N); |
---|
| 2309 | return factors; |
---|
| 2310 | } |
---|
| 2311 | |
---|
| 2312 | // check main variable |
---|
| 2313 | int swapLevel= 0; |
---|
| 2314 | CanonicalForm derivZ; |
---|
| 2315 | CanonicalForm gcdDerivZ; |
---|
| 2316 | CanonicalForm bufA= A; |
---|
| 2317 | Variable z; |
---|
| 2318 | for (int i= 1; i <= A.level(); i++) |
---|
[44651b] | 2319 | { |
---|
[7bf145] | 2320 | z= Variable (i); |
---|
| 2321 | derivZ= deriv (bufA, z); |
---|
| 2322 | if (derivZ.isZero()) |
---|
| 2323 | { |
---|
| 2324 | if (i == 1) |
---|
| 2325 | swapLevel= 1; |
---|
| 2326 | else |
---|
| 2327 | continue; |
---|
| 2328 | } |
---|
| 2329 | else |
---|
| 2330 | { |
---|
| 2331 | if (swapLevel == 1) |
---|
| 2332 | { |
---|
| 2333 | swapLevel= i; |
---|
[ccd1b0] | 2334 | bufA= swapvar (A, x, z); |
---|
[7bf145] | 2335 | } |
---|
[04cdf06] | 2336 | gcdDerivZ= gcd (bufA, derivZ); |
---|
[44651b] | 2337 | if (degree (gcdDerivZ) > 0 && !derivZ.isZero()) |
---|
[7bf145] | 2338 | { |
---|
| 2339 | CanonicalForm g= bufA/gcdDerivZ; |
---|
[44651b] | 2340 | CFList factorsG= |
---|
[7bf145] | 2341 | Union (multiFactorize (g, info), |
---|
| 2342 | multiFactorize (gcdDerivZ, info)); |
---|
| 2343 | appendSwapDecompress (factorsG, contentAFactors, N, swapLevel, x); |
---|
| 2344 | normalize (factorsG); |
---|
| 2345 | return factorsG; |
---|
| 2346 | } |
---|
[ccd1b0] | 2347 | else |
---|
| 2348 | { |
---|
| 2349 | A= bufA; |
---|
| 2350 | break; |
---|
| 2351 | } |
---|
[7bf145] | 2352 | } |
---|
| 2353 | } |
---|
| 2354 | |
---|
| 2355 | |
---|
| 2356 | CFList Aeval, list, evaluation, bufEvaluation, bufAeval; |
---|
| 2357 | bool fail= false; |
---|
| 2358 | int swapLevel2= 0; |
---|
| 2359 | int level; |
---|
| 2360 | int factorNums= 3; |
---|
| 2361 | CanonicalForm bivarEval; |
---|
| 2362 | CFList biFactors, bufBiFactors; |
---|
| 2363 | CanonicalForm evalPoly; |
---|
| 2364 | int lift, bufLift; |
---|
[fd5b3a] | 2365 | double logarithm= (double) ilog2 (totaldegree (A)); |
---|
| 2366 | logarithm /= log2exp; |
---|
| 2367 | logarithm= ceil (logarithm); |
---|
| 2368 | if (factorNums < (int) logarithm) |
---|
| 2369 | factorNums= (int) logarithm; |
---|
[ccd1b0] | 2370 | CFList* bufAeval2= new CFList [A.level() - 2]; |
---|
| 2371 | CFList* Aeval2= new CFList [A.level() - 2]; |
---|
| 2372 | int counter; |
---|
| 2373 | int differentSecondVar= 0; |
---|
[44651b] | 2374 | // several bivariate factorizations |
---|
| 2375 | for (int i= 0; i < factorNums; i++) |
---|
[7bf145] | 2376 | { |
---|
[ccd1b0] | 2377 | counter= 0; |
---|
[7bf145] | 2378 | bufA= A; |
---|
| 2379 | bufAeval= CFList(); |
---|
| 2380 | bufEvaluation= evalPoints (bufA, bufAeval, alpha, list, GF, fail); |
---|
[44651b] | 2381 | evalPoly= 0; |
---|
[7bf145] | 2382 | |
---|
[44651b] | 2383 | if (fail && (i == 0)) |
---|
[7bf145] | 2384 | { |
---|
| 2385 | if (!swapLevel) |
---|
[44651b] | 2386 | level= 2; |
---|
| 2387 | else |
---|
| 2388 | level= swapLevel + 1; |
---|
[7bf145] | 2389 | |
---|
[ccd1b0] | 2390 | CanonicalForm g; |
---|
| 2391 | swapLevel2= newMainVariableSearch (A, Aeval, evaluation, alpha, level, g); |
---|
[7bf145] | 2392 | |
---|
| 2393 | if (!swapLevel2) // need to pass to an extension |
---|
[44651b] | 2394 | { |
---|
| 2395 | factors= extFactorize (A, info); |
---|
| 2396 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, x); |
---|
| 2397 | normalize (factors); |
---|
[ccd1b0] | 2398 | delete [] bufAeval2; |
---|
| 2399 | delete [] Aeval2; |
---|
[44651b] | 2400 | return factors; |
---|
[7bf145] | 2401 | } |
---|
| 2402 | else |
---|
| 2403 | { |
---|
[ccd1b0] | 2404 | if (swapLevel2 == -1) |
---|
| 2405 | { |
---|
| 2406 | CFList factorsG= |
---|
| 2407 | Union (multiFactorize (g, info), |
---|
| 2408 | multiFactorize (A/g, info)); |
---|
| 2409 | appendSwapDecompress (factorsG, contentAFactors, N, swapLevel, x); |
---|
| 2410 | normalize (factorsG); |
---|
| 2411 | delete [] bufAeval2; |
---|
| 2412 | delete [] Aeval2; |
---|
| 2413 | return factorsG; |
---|
| 2414 | } |
---|
[7bf145] | 2415 | fail= false; |
---|
| 2416 | bufAeval= Aeval; |
---|
| 2417 | bufA= A; |
---|
[44651b] | 2418 | bufEvaluation= evaluation; |
---|
[7bf145] | 2419 | } |
---|
| 2420 | } |
---|
| 2421 | else if (fail && (i > 0)) |
---|
| 2422 | break; |
---|
| 2423 | |
---|
| 2424 | bivarEval= bufEvaluation.getLast(); |
---|
[ccd1b0] | 2425 | |
---|
| 2426 | evaluationWRTDifferentSecondVars (bufAeval2, bufEvaluation, A); |
---|
| 2427 | |
---|
[c79a9d] | 2428 | for (int j= 0; j < A.level() - 2; j++) |
---|
[ccd1b0] | 2429 | { |
---|
| 2430 | if (!bufAeval2[j].isEmpty()) |
---|
| 2431 | counter++; |
---|
| 2432 | } |
---|
[7bf145] | 2433 | |
---|
| 2434 | bufLift= degree (A, y) + 1 + degree (LC(A, x), y); |
---|
| 2435 | |
---|
[978ce3] | 2436 | TIMING_START (fac_fq_bi_factorizer); |
---|
[ccd1b0] | 2437 | if (!GF && alpha.level() == 1) |
---|
| 2438 | bufBiFactors= FpBiSqrfFactorize (bufAeval.getFirst()); |
---|
| 2439 | else if (GF) |
---|
| 2440 | bufBiFactors= GFBiSqrfFactorize (bufAeval.getFirst()); |
---|
| 2441 | else |
---|
| 2442 | bufBiFactors= FqBiSqrfFactorize (bufAeval.getFirst(), alpha); |
---|
[978ce3] | 2443 | TIMING_END_AND_PRINT (fac_fq_bi_factorizer, |
---|
[44651b] | 2444 | "time for bivariate factorization: "); |
---|
[ccd1b0] | 2445 | bufBiFactors.removeFirst(); |
---|
[7bf145] | 2446 | |
---|
[44651b] | 2447 | if (bufBiFactors.length() == 1) |
---|
[7bf145] | 2448 | { |
---|
[44651b] | 2449 | if (extension) |
---|
[7bf145] | 2450 | { |
---|
[44651b] | 2451 | CFList source, dest; |
---|
| 2452 | A= mapDown (A, info, source, dest); |
---|
[7bf145] | 2453 | } |
---|
| 2454 | factors.append (A); |
---|
| 2455 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, |
---|
[44651b] | 2456 | swapLevel2, x); |
---|
[7bf145] | 2457 | normalize (factors); |
---|
[ccd1b0] | 2458 | delete [] bufAeval2; |
---|
| 2459 | delete [] Aeval2; |
---|
[7bf145] | 2460 | return factors; |
---|
| 2461 | } |
---|
| 2462 | |
---|
| 2463 | if (i == 0) |
---|
| 2464 | { |
---|
| 2465 | Aeval= bufAeval; |
---|
| 2466 | evaluation= bufEvaluation; |
---|
| 2467 | biFactors= bufBiFactors; |
---|
| 2468 | lift= bufLift; |
---|
[ccd1b0] | 2469 | for (int j= 0; j < A.level() - 2; j++) |
---|
| 2470 | Aeval2 [j]= bufAeval2 [j]; |
---|
| 2471 | differentSecondVar= counter; |
---|
[7bf145] | 2472 | } |
---|
| 2473 | else |
---|
| 2474 | { |
---|
[44651b] | 2475 | if (bufBiFactors.length() < biFactors.length() || |
---|
[ccd1b0] | 2476 | ((bufLift < lift) && (bufBiFactors.length() == biFactors.length())) || |
---|
| 2477 | counter > differentSecondVar) |
---|
[7bf145] | 2478 | { |
---|
| 2479 | Aeval= bufAeval; |
---|
| 2480 | evaluation= bufEvaluation; |
---|
| 2481 | biFactors= bufBiFactors; |
---|
| 2482 | lift= bufLift; |
---|
[ccd1b0] | 2483 | for (int j= 0; j < A.level() - 2; j++) |
---|
| 2484 | Aeval2 [j]= bufAeval2 [j]; |
---|
| 2485 | differentSecondVar= counter; |
---|
[7bf145] | 2486 | } |
---|
| 2487 | } |
---|
| 2488 | int k= 0; |
---|
| 2489 | for (CFListIterator j= bufEvaluation; j.hasItem(); j++, k++) |
---|
| 2490 | evalPoly += j.getItem()*power (x, k); |
---|
[44651b] | 2491 | list.append (evalPoly); |
---|
[7bf145] | 2492 | } |
---|
| 2493 | |
---|
[ccd1b0] | 2494 | delete [] bufAeval2; |
---|
| 2495 | |
---|
| 2496 | sortList (biFactors, x); |
---|
| 2497 | |
---|
| 2498 | int minFactorsLength; |
---|
| 2499 | bool irred= false; |
---|
| 2500 | factorizationWRTDifferentSecondVars (A, Aeval2, info, minFactorsLength, irred); |
---|
| 2501 | |
---|
| 2502 | if (irred) |
---|
| 2503 | { |
---|
| 2504 | if (extension) |
---|
| 2505 | { |
---|
| 2506 | CFList source, dest; |
---|
| 2507 | A= mapDown (A, info, source, dest); |
---|
| 2508 | } |
---|
| 2509 | factors.append (A); |
---|
| 2510 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, |
---|
| 2511 | swapLevel2, x); |
---|
| 2512 | normalize (factors); |
---|
| 2513 | delete [] Aeval2; |
---|
| 2514 | return factors; |
---|
| 2515 | } |
---|
| 2516 | |
---|
| 2517 | if (minFactorsLength == 0) |
---|
| 2518 | minFactorsLength= biFactors.length(); |
---|
| 2519 | else if (biFactors.length() > minFactorsLength) |
---|
| 2520 | refineBiFactors (A, biFactors, Aeval2, evaluation, minFactorsLength); |
---|
[6036d90] | 2521 | minFactorsLength= tmin (minFactorsLength, biFactors.length()); |
---|
| 2522 | |
---|
| 2523 | if (differentSecondVar == A.level() - 2) |
---|
| 2524 | { |
---|
| 2525 | bool zeroOccured= false; |
---|
| 2526 | for (CFListIterator iter= evaluation; iter.hasItem(); iter++) |
---|
| 2527 | { |
---|
| 2528 | if (iter.getItem().isZero()) |
---|
| 2529 | { |
---|
| 2530 | zeroOccured= true; |
---|
| 2531 | break; |
---|
| 2532 | } |
---|
| 2533 | } |
---|
| 2534 | if (!zeroOccured) |
---|
| 2535 | { |
---|
| 2536 | factors= sparseHeuristic (A, biFactors, Aeval2, evaluation, minFactorsLength); |
---|
| 2537 | if (factors.length() == biFactors.length()) |
---|
| 2538 | { |
---|
| 2539 | if (extension) |
---|
| 2540 | factors= extNonMonicFactorRecombination (factors, A, info); |
---|
| 2541 | |
---|
| 2542 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, |
---|
| 2543 | swapLevel2, x); |
---|
| 2544 | normalize (factors); |
---|
| 2545 | delete [] Aeval2; |
---|
| 2546 | return factors; |
---|
| 2547 | } |
---|
| 2548 | else |
---|
| 2549 | factors= CFList(); |
---|
| 2550 | //TODO case where factors.length() > 0 |
---|
| 2551 | } |
---|
| 2552 | } |
---|
[ccd1b0] | 2553 | |
---|
| 2554 | CFList uniFactors= buildUniFactors (biFactors, evaluation.getLast(), y); |
---|
| 2555 | |
---|
| 2556 | CFList * oldAeval= new CFList [A.level() - 2]; //TODO use bufAeval2 for this |
---|
| 2557 | for (int i= 0; i < A.level() - 2; i++) |
---|
| 2558 | oldAeval[i]= Aeval2[i]; |
---|
| 2559 | |
---|
| 2560 | getLeadingCoeffs (A, Aeval2, uniFactors, evaluation); |
---|
| 2561 | |
---|
| 2562 | CFList biFactorsLCs; |
---|
| 2563 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
| 2564 | biFactorsLCs.append (LC (i.getItem(), 1)); |
---|
| 2565 | |
---|
| 2566 | Variable v; |
---|
| 2567 | CFList leadingCoeffs= precomputeLeadingCoeff (LC (A, 1), biFactorsLCs, alpha, |
---|
| 2568 | evaluation, Aeval2, A.level() - 2, v); |
---|
| 2569 | |
---|
| 2570 | if (v.level() != 1) |
---|
[7bf145] | 2571 | { |
---|
[ccd1b0] | 2572 | A= swapvar (A, y, v); |
---|
| 2573 | int i= A.level(); |
---|
| 2574 | CanonicalForm evalPoint; |
---|
| 2575 | for (CFListIterator iter= evaluation; iter.hasItem(); iter++, i--) |
---|
| 2576 | { |
---|
| 2577 | if (i == v.level()) |
---|
| 2578 | { |
---|
| 2579 | evalPoint= iter.getItem(); |
---|
| 2580 | iter.getItem()= evaluation.getLast(); |
---|
| 2581 | evaluation.removeLast(); |
---|
| 2582 | evaluation.append (evalPoint); |
---|
| 2583 | break; |
---|
| 2584 | } |
---|
| 2585 | } |
---|
[8256fd] | 2586 | for (i= 0; i < A.level() - 2; i++) |
---|
| 2587 | { |
---|
| 2588 | if (oldAeval[i].isEmpty()) |
---|
| 2589 | continue; |
---|
| 2590 | if (oldAeval[i].getFirst().level() == v.level()) |
---|
| 2591 | { |
---|
| 2592 | CFArray tmp= copy (oldAeval[i]); |
---|
| 2593 | for (int ii= 0; ii < tmp.size(); ii++) |
---|
| 2594 | tmp[ii]= swapvar (tmp[ii], v, y); |
---|
| 2595 | CFArray tmp2= CFArray (tmp.size()); |
---|
| 2596 | CanonicalForm buf; |
---|
| 2597 | for (int ii= 0; ii < tmp.size(); ii++) |
---|
| 2598 | { |
---|
| 2599 | buf= tmp[ii] (evaluation.getLast(),y); |
---|
| 2600 | buf /= Lc (buf); |
---|
| 2601 | tmp2[findItem (uniFactors, buf)-1]=tmp[ii]; |
---|
| 2602 | } |
---|
| 2603 | biFactors= CFList(); |
---|
| 2604 | for (int j= 0; j < tmp2.size(); j++) |
---|
| 2605 | biFactors.append (tmp2[j]); |
---|
| 2606 | } |
---|
| 2607 | } |
---|
[7bf145] | 2608 | } |
---|
[ccd1b0] | 2609 | |
---|
[eefc3a] | 2610 | CFListIterator iter; |
---|
[ccd1b0] | 2611 | CanonicalForm oldA= A; |
---|
| 2612 | CFList oldBiFactors= biFactors; |
---|
| 2613 | if (!leadingCoeffs.getFirst().inCoeffDomain()) |
---|
| 2614 | { |
---|
| 2615 | CanonicalForm tmp= power (leadingCoeffs.getFirst(), biFactors.length() - 1); |
---|
| 2616 | A *= tmp; |
---|
| 2617 | tmp= leadingCoeffs.getFirst(); |
---|
[eefc3a] | 2618 | iter= evaluation; |
---|
| 2619 | for (int i= A.level(); i > 2; i--, iter++) |
---|
| 2620 | tmp= tmp (iter.getItem(), i); |
---|
[ccd1b0] | 2621 | if (!tmp.inCoeffDomain()) |
---|
| 2622 | { |
---|
| 2623 | for (CFListIterator i= biFactors; i.hasItem(); i++) |
---|
| 2624 | { |
---|
| 2625 | i.getItem() *= tmp/LC (i.getItem(), 1); |
---|
| 2626 | i.getItem() /= Lc (i.getItem()); |
---|
| 2627 | } |
---|
| 2628 | } |
---|
| 2629 | } |
---|
| 2630 | |
---|
| 2631 | leadingCoeffs.removeFirst(); |
---|
| 2632 | |
---|
| 2633 | //prepare leading coefficients |
---|
| 2634 | CFList* leadingCoeffs2= new CFList [A.level() - 2]; |
---|
[eefc3a] | 2635 | prepareLeadingCoeffs (leadingCoeffs2, A.level(), leadingCoeffs, biFactors, |
---|
| 2636 | evaluation); |
---|
| 2637 | |
---|
| 2638 | Aeval= evaluateAtEval (A, evaluation, 2); |
---|
| 2639 | CanonicalForm hh= Lc (Aeval.getFirst()); |
---|
| 2640 | for (iter= Aeval; iter.hasItem(); iter++) |
---|
| 2641 | iter.getItem() /= hh; |
---|
| 2642 | |
---|
| 2643 | A /= hh; |
---|
| 2644 | |
---|
[64b824] | 2645 | if (size (A)/getNumVars (A) < 500 && |
---|
| 2646 | LucksWangSparseHeuristic (A, biFactors, 2, leadingCoeffs2 [A.level() - 3], |
---|
| 2647 | factors)) |
---|
[4fe8a3] | 2648 | { |
---|
| 2649 | int check= factors.length(); |
---|
| 2650 | factors= recoverFactors (A, factors); |
---|
| 2651 | |
---|
| 2652 | if (check == factors.length()) |
---|
| 2653 | { |
---|
| 2654 | if (extension) |
---|
| 2655 | factors= extNonMonicFactorRecombination (factors, A, info); |
---|
| 2656 | |
---|
[dc390c] | 2657 | if (v.level() != 1) |
---|
| 2658 | { |
---|
| 2659 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
| 2660 | iter.getItem()= swapvar (iter.getItem(), v, y); |
---|
| 2661 | } |
---|
[4fe8a3] | 2662 | appendSwapDecompress (factors, contentAFactors, N, swapLevel, |
---|
| 2663 | swapLevel2, x); |
---|
| 2664 | normalize (factors); |
---|
| 2665 | delete [] Aeval2; |
---|
| 2666 | return factors; |
---|
| 2667 | } |
---|
| 2668 | else |
---|
| 2669 | factors= CFList(); |
---|
| 2670 | //TODO handle this case |
---|
| 2671 | } |
---|
| 2672 | |
---|
[eefc3a] | 2673 | A= shift2Zero (A, Aeval, evaluation); |
---|
| 2674 | |
---|
| 2675 | for (iter= biFactors; iter.hasItem(); iter++) |
---|
| 2676 | iter.getItem()= iter.getItem () (y + evaluation.getLast(), y); |
---|
| 2677 | |
---|
| 2678 | for (int i= 0; i < A.level() - 2; i++) |
---|
| 2679 | { |
---|
| 2680 | if (i != A.level() - 3) |
---|
| 2681 | leadingCoeffs2[i]= CFList(); |
---|
| 2682 | } |
---|
| 2683 | for (iter= leadingCoeffs2[A.level() - 3]; iter.hasItem(); iter++) |
---|
| 2684 | { |
---|
| 2685 | iter.getItem()= shift2Zero (iter.getItem(), list, evaluation); |
---|
| 2686 | for (int i= A.level() - 4; i > -1; i--) |
---|
| 2687 | { |
---|
| 2688 | if (i + 1 == A.level() - 3) |
---|
| 2689 | leadingCoeffs2[i].append (iter.getItem() (0, i + 4)); |
---|
| 2690 | else |
---|
| 2691 | leadingCoeffs2[i].append (leadingCoeffs2[i+1].getLast() (0, i + 4)); |
---|
| 2692 | } |
---|
| 2693 | } |
---|
[ccd1b0] | 2694 | |
---|
| 2695 | CFArray Pi; |
---|
| 2696 | CFList diophant; |
---|
| 2697 | int* liftBounds= new int [A.level() - 1]; |
---|
| 2698 | int liftBoundsLength= A.level() - 1; |
---|
| 2699 | for (int i= 0; i < liftBoundsLength; i++) |
---|
| 2700 | liftBounds [i]= degree (A, i + 2) + 1; |
---|
| 2701 | |
---|
| 2702 | Aeval.removeFirst(); |
---|
| 2703 | bool noOneToOne= false; |
---|
| 2704 | factors= nonMonicHenselLift (Aeval, biFactors, leadingCoeffs2, diophant, |
---|
| 2705 | Pi, liftBounds, liftBoundsLength, noOneToOne); |
---|
| 2706 | |
---|
| 2707 | if (!noOneToOne) |
---|
[7bf145] | 2708 | { |
---|
[ccd1b0] | 2709 | int check= factors.length(); |
---|
[eefc3a] | 2710 | A= oldA; |
---|
[c79a9d] | 2711 | factors= recoverFactors (A, factors, evaluation); |
---|
[ccd1b0] | 2712 | if (check != factors.length()) |
---|
| 2713 | noOneToOne= true; |
---|
| 2714 | |
---|
| 2715 | if (extension && !noOneToOne) |
---|
[c79a9d] | 2716 | factors= extNonMonicFactorRecombination (factors, A, info); |
---|
[7bf145] | 2717 | } |
---|
[ccd1b0] | 2718 | if (noOneToOne) |
---|
| 2719 | { |
---|
[eefc3a] | 2720 | A= shift2Zero (oldA, Aeval, evaluation); |
---|
[ccd1b0] | 2721 | biFactors= oldBiFactors; |
---|
[eefc3a] | 2722 | for (iter= biFactors; iter.hasItem(); iter++) |
---|
| 2723 | iter.getItem()= iter.getItem () (y + evaluation.getLast(), y); |
---|
[ccd1b0] | 2724 | CanonicalForm LCA= LC (Aeval.getFirst(), 1); |
---|
| 2725 | CanonicalForm yToLift= power (y, lift); |
---|
| 2726 | CFListIterator i= biFactors; |
---|
| 2727 | lift= degree (i.getItem(), 2) + degree (LC (i.getItem(), 1)) + 1; |
---|
| 2728 | i++; |
---|
[7bf145] | 2729 | |
---|
[ccd1b0] | 2730 | for (; i.hasItem(); i++) |
---|
| 2731 | lift= tmax (lift, degree (i.getItem(), 2) + degree (LC (i.getItem(), 1)) + 1); |
---|
| 2732 | |
---|
| 2733 | lift= tmax (degree (Aeval.getFirst() , 2) + 1, lift); |
---|
| 2734 | |
---|
| 2735 | i= biFactors; |
---|
| 2736 | yToLift= power (y, lift); |
---|
| 2737 | CanonicalForm dummy; |
---|
| 2738 | for (; i.hasItem(); i++) |
---|
| 2739 | { |
---|
| 2740 | LCA= LC (i.getItem(), 1); |
---|
| 2741 | extgcd (LCA, yToLift, LCA, dummy); |
---|
| 2742 | i.getItem()= mod (i.getItem()*LCA, yToLift); |
---|
| 2743 | } |
---|
| 2744 | |
---|
| 2745 | liftBoundsLength= F.level() - 1; |
---|
| 2746 | liftBounds= liftingBounds (A, lift); |
---|
| 2747 | |
---|
| 2748 | CFList MOD; |
---|
| 2749 | bool earlySuccess; |
---|
[0b618a7] | 2750 | CFList earlyFactors, liftedFactors; |
---|
[978ce3] | 2751 | TIMING_START (fac_fq_hensel_lift); |
---|
[0b618a7] | 2752 | liftedFactors= henselLiftAndEarly |
---|
| 2753 | (A, MOD, liftBounds, earlySuccess, earlyFactors, |
---|
| 2754 | Aeval, biFactors, evaluation, info); |
---|
[978ce3] | 2755 | TIMING_END_AND_PRINT (fac_fq_hensel_lift, "time for hensel lifting: "); |
---|
[ccd1b0] | 2756 | |
---|
| 2757 | if (!extension) |
---|
| 2758 | { |
---|
[978ce3] | 2759 | TIMING_START (fac_fq_factor_recombination); |
---|
[ccd1b0] | 2760 | factors= factorRecombination (A, liftedFactors, MOD); |
---|
[978ce3] | 2761 | TIMING_END_AND_PRINT (fac_fq_factor_recombination, |
---|
[ccd1b0] | 2762 | "time for factor recombination: "); |
---|
| 2763 | } |
---|
| 2764 | else |
---|
| 2765 | { |
---|
[978ce3] | 2766 | TIMING_START (fac_fq_factor_recombination); |
---|
[ccd1b0] | 2767 | factors= extFactorRecombination (liftedFactors, A, MOD, info, evaluation); |
---|
[978ce3] | 2768 | TIMING_END_AND_PRINT (fac_fq_factor_recombination, |
---|
[ccd1b0] | 2769 | "time for factor recombination: "); |
---|
| 2770 | } |
---|
| 2771 | |
---|
| 2772 | if (earlySuccess) |
---|
| 2773 | factors= Union (factors, earlyFactors); |
---|
[c79a9d] | 2774 | if (!extension) |
---|
[7bf145] | 2775 | { |
---|
[c79a9d] | 2776 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
[7bf145] | 2777 | { |
---|
[c79a9d] | 2778 | int kk= Aeval.getLast().level(); |
---|
| 2779 | for (CFListIterator j= evaluation; j.hasItem(); j++, kk--) |
---|
| 2780 | { |
---|
| 2781 | if (i.getItem().level() < kk) |
---|
| 2782 | continue; |
---|
| 2783 | i.getItem()= i.getItem() (Variable (kk) - j.getItem(), kk); |
---|
| 2784 | } |
---|
[7bf145] | 2785 | } |
---|
| 2786 | } |
---|
| 2787 | } |
---|
| 2788 | |
---|
[ccd1b0] | 2789 | if (v.level() != 1) |
---|
| 2790 | { |
---|
| 2791 | for (CFListIterator iter= factors; iter.hasItem(); iter++) |
---|
| 2792 | iter.getItem()= swapvar (iter.getItem(), v, y); |
---|
| 2793 | } |
---|
| 2794 | |
---|
[44651b] | 2795 | swap (factors, swapLevel, swapLevel2, x); |
---|
[7bf145] | 2796 | append (factors, contentAFactors); |
---|
| 2797 | decompress (factors, N); |
---|
| 2798 | normalize (factors); |
---|
| 2799 | |
---|
| 2800 | delete[] liftBounds; |
---|
| 2801 | |
---|
| 2802 | return factors; |
---|
| 2803 | } |
---|
| 2804 | |
---|
| 2805 | /// multivariate factorization over an extension of the initial field |
---|
[44651b] | 2806 | CFList |
---|
| 2807 | extFactorize (const CanonicalForm& F, const ExtensionInfo& info) |
---|
[7bf145] | 2808 | { |
---|
| 2809 | CanonicalForm A= F; |
---|
| 2810 | |
---|
| 2811 | Variable alpha= info.getAlpha(); |
---|
| 2812 | Variable beta= info.getBeta(); |
---|
| 2813 | int k= info.getGFDegree(); |
---|
| 2814 | char cGFName= info.getGFName(); |
---|
| 2815 | CanonicalForm delta= info.getDelta(); |
---|
| 2816 | bool GF= (CFFactory::gettype() == GaloisFieldDomain); |
---|
| 2817 | Variable w= Variable (1); |
---|
| 2818 | |
---|
| 2819 | CFList factors; |
---|
| 2820 | if (!GF && alpha == w) // we are in F_p |
---|
| 2821 | { |
---|
| 2822 | CFList factors; |
---|
[44651b] | 2823 | bool extension= true; |
---|
[7bf145] | 2824 | int p= getCharacteristic(); |
---|
| 2825 | if (p*p < (1<<16)) // pass to GF if possible |
---|
[44651b] | 2826 | { |
---|
[7bf145] | 2827 | setCharacteristic (getCharacteristic(), 2, 'Z'); |
---|
| 2828 | ExtensionInfo info= ExtensionInfo (extension); |
---|
| 2829 | A= A.mapinto(); |
---|
| 2830 | factors= multiFactorize (A, info); |
---|
| 2831 | |
---|
[0a7d0ca] | 2832 | CanonicalForm mipo= gf_mipo; |
---|
[7bf145] | 2833 | setCharacteristic (getCharacteristic()); |
---|
[0a7d0ca] | 2834 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
[44651b] | 2835 | for (CFListIterator j= factors; j.hasItem(); j++) |
---|
| 2836 | j.getItem()= GF2FalphaRep (j.getItem(), vBuf); |
---|
[7bf145] | 2837 | } |
---|
| 2838 | else // not able to pass to GF, pass to F_p(\alpha) |
---|
| 2839 | { |
---|
[a54114] | 2840 | CanonicalForm mipo= randomIrredpoly (2, w); |
---|
[11bf82] | 2841 | Variable v= rootOf (mipo); |
---|
[ccd1b0] | 2842 | ExtensionInfo info= ExtensionInfo (v); |
---|
[7bf145] | 2843 | factors= multiFactorize (A, info); |
---|
| 2844 | } |
---|
| 2845 | return factors; |
---|
| 2846 | } |
---|
| 2847 | else if (!GF && (alpha != w)) // we are in F_p(\alpha) |
---|
[44651b] | 2848 | { |
---|
[7bf145] | 2849 | if (k == 1) // need factorization over F_p |
---|
| 2850 | { |
---|
| 2851 | int extDeg= degree (getMipo (alpha)); |
---|
[44651b] | 2852 | extDeg++; |
---|
[a54114] | 2853 | CanonicalForm mipo= randomIrredpoly (extDeg + 1, w); |
---|
[7bf145] | 2854 | Variable v= rootOf (mipo); |
---|
| 2855 | ExtensionInfo info= ExtensionInfo (v); |
---|
[4e17e7] | 2856 | factors= multiFactorize (A, info); |
---|
[7bf145] | 2857 | } |
---|
[44651b] | 2858 | else |
---|
[7bf145] | 2859 | { |
---|
[a54114] | 2860 | if (beta == w) |
---|
[7bf145] | 2861 | { |
---|
[11bf82] | 2862 | Variable v= chooseExtension (alpha, beta, k); |
---|
[7bf145] | 2863 | CanonicalForm primElem, imPrimElem; |
---|
| 2864 | bool primFail= false; |
---|
| 2865 | Variable vBuf; |
---|
| 2866 | primElem= primitiveElement (alpha, vBuf, primFail); |
---|
| 2867 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
| 2868 | if (primFail) |
---|
| 2869 | ; //ERROR |
---|
| 2870 | else |
---|
[ccd1b0] | 2871 | imPrimElem= mapPrimElem (primElem, vBuf, v); |
---|
[7bf145] | 2872 | |
---|
| 2873 | CFList source, dest; |
---|
[44651b] | 2874 | CanonicalForm bufA= mapUp (A, alpha, v, primElem, imPrimElem, |
---|
[7bf145] | 2875 | source, dest); |
---|
| 2876 | ExtensionInfo info= ExtensionInfo (v, alpha, imPrimElem, primElem); |
---|
[4e17e7] | 2877 | factors= multiFactorize (bufA, info); |
---|
[7bf145] | 2878 | } |
---|
| 2879 | else |
---|
| 2880 | { |
---|
[11bf82] | 2881 | Variable v= chooseExtension (alpha, beta, k); |
---|
[7bf145] | 2882 | CanonicalForm primElem, imPrimElem; |
---|
| 2883 | bool primFail= false; |
---|
| 2884 | Variable vBuf; |
---|
| 2885 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
| 2886 | if (primFail) |
---|
| 2887 | ; //ERROR |
---|
| 2888 | else |
---|
[618da5] | 2889 | imPrimElem= mapPrimElem (delta, beta, v); |
---|
[7bf145] | 2890 | |
---|
| 2891 | CFList source, dest; |
---|
| 2892 | CanonicalForm bufA= mapDown (A, info, source, dest); |
---|
| 2893 | source= CFList(); |
---|
| 2894 | dest= CFList(); |
---|
| 2895 | bufA= mapUp (bufA, beta, v, delta, imPrimElem, source, dest); |
---|
| 2896 | ExtensionInfo info= ExtensionInfo (v, beta, imPrimElem, delta); |
---|
[4e17e7] | 2897 | factors= multiFactorize (bufA, info); |
---|
[7bf145] | 2898 | } |
---|
| 2899 | } |
---|
| 2900 | return factors; |
---|
| 2901 | } |
---|
| 2902 | else // we are in GF (p^k) |
---|
[44651b] | 2903 | { |
---|
[7bf145] | 2904 | int p= getCharacteristic(); |
---|
| 2905 | int extensionDeg= getGFDegree(); |
---|
| 2906 | bool extension= true; |
---|
| 2907 | if (k == 1) // need factorization over F_p |
---|
[44651b] | 2908 | { |
---|
[7bf145] | 2909 | extensionDeg++; |
---|
[44651b] | 2910 | if (pow ((double) p, (double) extensionDeg) < (1<<16)) |
---|
[7bf145] | 2911 | // pass to GF(p^k+1) |
---|
[44651b] | 2912 | { |
---|
[0a7d0ca] | 2913 | CanonicalForm mipo= gf_mipo; |
---|
[7bf145] | 2914 | setCharacteristic (p); |
---|
[0a7d0ca] | 2915 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
[44651b] | 2916 | A= GF2FalphaRep (A, vBuf); |
---|
| 2917 | setCharacteristic (p, extensionDeg, 'Z'); |
---|
[7bf145] | 2918 | ExtensionInfo info= ExtensionInfo (extension); |
---|
[44651b] | 2919 | factors= multiFactorize (A.mapinto(), info); |
---|
[7bf145] | 2920 | } |
---|
| 2921 | else // not able to pass to another GF, pass to F_p(\alpha) |
---|
[44651b] | 2922 | { |
---|
[0a7d0ca] | 2923 | CanonicalForm mipo= gf_mipo; |
---|
[44651b] | 2924 | setCharacteristic (p); |
---|
[0a7d0ca] | 2925 | Variable vBuf= rootOf (mipo.mapinto()); |
---|
[44651b] | 2926 | A= GF2FalphaRep (A, vBuf); |
---|
[11bf82] | 2927 | Variable v= chooseExtension (vBuf, beta, k); |
---|
[7bf145] | 2928 | ExtensionInfo info= ExtensionInfo (v, extension); |
---|
[44651b] | 2929 | factors= multiFactorize (A, info); |
---|
[7bf145] | 2930 | } |
---|
| 2931 | } |
---|
| 2932 | else // need factorization over GF (p^k) |
---|
| 2933 | { |
---|
[44651b] | 2934 | if (pow ((double) p, (double) 2*extensionDeg) < (1<<16)) |
---|
[7bf145] | 2935 | // pass to GF(p^2k) |
---|
[44651b] | 2936 | { |
---|
| 2937 | setCharacteristic (p, 2*extensionDeg, 'Z'); |
---|
[7bf145] | 2938 | ExtensionInfo info= ExtensionInfo (k, cGFName, extension); |
---|
[44651b] | 2939 | factors= multiFactorize (GFMapUp (A, extensionDeg), info); |
---|
| 2940 | setCharacteristic (p, extensionDeg, cGFName); |
---|
[7bf145] | 2941 | } |
---|
| 2942 | else // not able to pass to GF (p^2k), pass to F_p (\alpha) |
---|
[44651b] | 2943 | { |
---|
[0a7d0ca] | 2944 | CanonicalForm mipo= gf_mipo; |
---|
[44651b] | 2945 | setCharacteristic (p); |
---|
[0a7d0ca] | 2946 | Variable v1= rootOf (mipo.mapinto()); |
---|
[44651b] | 2947 | A= GF2FalphaRep (A, v1); |
---|
[11bf82] | 2948 | Variable v2= chooseExtension (v1, v1, k); |
---|
[7bf145] | 2949 | CanonicalForm primElem, imPrimElem; |
---|
| 2950 | bool primFail= false; |
---|
| 2951 | Variable vBuf; |
---|
[11bf82] | 2952 | primElem= primitiveElement (v1, v1, primFail); |
---|
[7bf145] | 2953 | if (primFail) |
---|
| 2954 | ; //ERROR |
---|
| 2955 | else |
---|
[618da5] | 2956 | imPrimElem= mapPrimElem (primElem, v1, v2); |
---|
[7bf145] | 2957 | CFList source, dest; |
---|
[618da5] | 2958 | CanonicalForm bufA= mapUp (A, v1, v2, primElem, imPrimElem, |
---|
[7bf145] | 2959 | source, dest); |
---|
| 2960 | ExtensionInfo info= ExtensionInfo (v2, v1, imPrimElem, primElem); |
---|
[44651b] | 2961 | factors= multiFactorize (bufA, info); |
---|
| 2962 | setCharacteristic (p, k, cGFName); |
---|
| 2963 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
| 2964 | i.getItem()= Falpha2GFRep (i.getItem()); |
---|
[7bf145] | 2965 | } |
---|
| 2966 | } |
---|
| 2967 | return factors; |
---|
| 2968 | } |
---|
| 2969 | } |
---|
| 2970 | |
---|
| 2971 | #endif |
---|
| 2972 | /* HAVE_NTL */ |
---|
| 2973 | |
---|