[ad3c3ff] | 1 | /*****************************************************************************\ |
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[806c18] | 2 | * Computer Algebra System SINGULAR |
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[ad3c3ff] | 3 | \*****************************************************************************/ |
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| 4 | /** @file facHensel.cc |
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[806c18] | 5 | * |
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| 6 | * This file implements functions to lift factors via Hensel lifting and |
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[ad3c3ff] | 7 | * functions for modular multiplication and division with remainder. |
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[806c18] | 8 | * |
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| 9 | * ABSTRACT: Hensel lifting is described in "Efficient Multivariate |
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| 10 | * Factorization over Finite Fields" by L. Bernardin & M. Monagon. Division with |
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| 11 | * remainder is described in "Fast Recursive Division" by C. Burnikel and |
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| 12 | * J. Ziegler. Karatsuba multiplication is described in "Modern Computer |
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| 13 | * Algebra" by J. von zur Gathen and J. Gerhard. |
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[ad3c3ff] | 14 | * |
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| 15 | * @author Martin Lee |
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| 16 | * |
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| 17 | * @internal @version \$Id$ |
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| 18 | * |
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| 19 | **/ |
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| 20 | /*****************************************************************************/ |
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| 21 | |
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[e4fe2b] | 22 | #include "config.h" |
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| 23 | |
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[650f2d8] | 24 | #include "cf_assert.h" |
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[ad3c3ff] | 25 | #include "debug.h" |
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| 26 | #include "timing.h" |
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| 27 | |
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| 28 | #include "facHensel.h" |
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| 29 | #include "cf_util.h" |
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[08daea] | 30 | #include "fac_util.h" |
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| 31 | #include "cf_algorithm.h" |
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[4a05ed] | 32 | #include "cf_primes.h" |
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[ad3c3ff] | 33 | |
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| 34 | #ifdef HAVE_NTL |
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| 35 | #include <NTL/lzz_pEX.h> |
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| 36 | #include "NTLconvert.h" |
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| 37 | |
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[88408d0] | 38 | #ifdef HAVE_FLINT |
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| 39 | #include "FLINTconvert.h" |
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| 40 | #endif |
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| 41 | |
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| 42 | #ifdef HAVE_FLINT |
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| 43 | void kronSub (fmpz_poly_t result, const CanonicalForm& A, int d) |
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| 44 | { |
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| 45 | int degAy= degree (A); |
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| 46 | fmpz_poly_init2 (result, d*(degAy + 1)); |
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| 47 | _fmpz_poly_set_length (result, d*(degAy + 1)); |
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| 48 | CFIterator j; |
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| 49 | for (CFIterator i= A; i.hasTerms(); i++) |
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| 50 | { |
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| 51 | if (i.coeff().inBaseDomain()) |
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| 52 | convertCF2Fmpz (fmpz_poly_get_coeff_ptr (result, i.exp()*d), i.coeff()); |
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| 53 | else |
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[935e83] | 54 | for (j= i.coeff(); j.hasTerms(); j++) |
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| 55 | convertCF2Fmpz (fmpz_poly_get_coeff_ptr (result, i.exp()*d+j.exp()), |
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| 56 | j.coeff()); |
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[88408d0] | 57 | } |
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| 58 | _fmpz_poly_normalise(result); |
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| 59 | } |
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| 60 | |
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| 61 | |
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[935e83] | 62 | CanonicalForm |
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| 63 | reverseSubst (const fmpz_poly_t F, int d, const Variable& alpha, |
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| 64 | const CanonicalForm& den) |
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[88408d0] | 65 | { |
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| 66 | Variable x= Variable (1); |
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| 67 | |
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| 68 | CanonicalForm result= 0; |
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| 69 | int i= 0; |
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| 70 | int degf= fmpz_poly_degree (F); |
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| 71 | int k= 0; |
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| 72 | int degfSubK; |
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[935e83] | 73 | int repLength, j; |
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[88408d0] | 74 | CanonicalForm coeff; |
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| 75 | fmpz* tmp; |
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| 76 | while (degf >= k) |
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| 77 | { |
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| 78 | coeff= 0; |
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| 79 | degfSubK= degf - k; |
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| 80 | if (degfSubK >= d) |
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| 81 | repLength= d; |
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| 82 | else |
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| 83 | repLength= degfSubK + 1; |
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| 84 | |
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[935e83] | 85 | for (j= 0; j < repLength; j++) |
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[88408d0] | 86 | { |
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| 87 | tmp= fmpz_poly_get_coeff_ptr (F, j+k); |
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| 88 | if (!fmpz_is_zero (tmp)) |
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| 89 | { |
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| 90 | CanonicalForm ff= convertFmpz2CF (tmp)/den; |
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| 91 | coeff += ff*power (alpha, j); |
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| 92 | } |
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| 93 | } |
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| 94 | result += coeff*power (x, i); |
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| 95 | i++; |
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| 96 | k= d*i; |
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| 97 | } |
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| 98 | return result; |
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| 99 | } |
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| 100 | |
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[935e83] | 101 | CanonicalForm |
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| 102 | mulFLINTQa (const CanonicalForm& F, const CanonicalForm& G, |
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| 103 | const Variable& alpha) |
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[88408d0] | 104 | { |
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| 105 | CanonicalForm A= F; |
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| 106 | CanonicalForm B= G; |
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| 107 | |
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| 108 | CanonicalForm denA= bCommonDen (A); |
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| 109 | CanonicalForm denB= bCommonDen (B); |
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| 110 | |
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| 111 | A *= denA; |
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| 112 | B *= denB; |
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| 113 | int degAa= degree (A, alpha); |
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| 114 | int degBa= degree (B, alpha); |
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| 115 | int d= degAa + 1 + degBa; |
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| 116 | |
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| 117 | fmpz_poly_t FLINTA,FLINTB; |
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| 118 | fmpz_poly_init (FLINTA); |
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| 119 | fmpz_poly_init (FLINTB); |
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| 120 | kronSub (FLINTA, A, d); |
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| 121 | kronSub (FLINTB, B, d); |
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| 122 | |
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| 123 | fmpz_poly_mul (FLINTA, FLINTA, FLINTB); |
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| 124 | |
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| 125 | denA *= denB; |
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| 126 | A= reverseSubst (FLINTA, d, alpha, denA); |
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| 127 | |
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| 128 | fmpz_poly_clear (FLINTA); |
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| 129 | fmpz_poly_clear (FLINTB); |
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| 130 | return A; |
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| 131 | } |
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| 132 | |
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| 133 | CanonicalForm |
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| 134 | mulFLINTQ (const CanonicalForm& F, const CanonicalForm& G) |
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| 135 | { |
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| 136 | CanonicalForm A= F; |
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| 137 | CanonicalForm B= G; |
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| 138 | |
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| 139 | CanonicalForm denA= bCommonDen (A); |
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| 140 | CanonicalForm denB= bCommonDen (B); |
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| 141 | |
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| 142 | A *= denA; |
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| 143 | B *= denB; |
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| 144 | fmpz_poly_t FLINTA,FLINTB; |
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| 145 | convertFacCF2Fmpz_poly_t (FLINTA, A); |
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| 146 | convertFacCF2Fmpz_poly_t (FLINTB, B); |
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| 147 | fmpz_poly_mul (FLINTA, FLINTA, FLINTB); |
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| 148 | denA *= denB; |
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| 149 | A= convertFmpz_poly_t2FacCF (FLINTA, F.mvar()); |
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| 150 | A /= denA; |
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| 151 | fmpz_poly_clear (FLINTA); |
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| 152 | fmpz_poly_clear (FLINTB); |
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| 153 | |
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| 154 | return A; |
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| 155 | } |
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| 156 | |
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[935e83] | 157 | /*CanonicalForm |
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[88408d0] | 158 | mulFLINTQ2 (const CanonicalForm& F, const CanonicalForm& G) |
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| 159 | { |
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| 160 | CanonicalForm A= F; |
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| 161 | CanonicalForm B= G; |
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| 162 | |
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| 163 | fmpq_poly_t FLINTA,FLINTB; |
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| 164 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
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| 165 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
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| 166 | |
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| 167 | fmpq_poly_mul (FLINTA, FLINTA, FLINTB); |
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| 168 | A= convertFmpq_poly_t2FacCF (FLINTA, F.mvar()); |
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| 169 | fmpq_poly_clear (FLINTA); |
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| 170 | fmpq_poly_clear (FLINTB); |
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| 171 | return A; |
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[935e83] | 172 | }*/ |
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[88408d0] | 173 | |
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| 174 | CanonicalForm |
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| 175 | divFLINTQ (const CanonicalForm& F, const CanonicalForm& G) |
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| 176 | { |
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| 177 | CanonicalForm A= F; |
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| 178 | CanonicalForm B= G; |
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| 179 | |
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| 180 | fmpq_poly_t FLINTA,FLINTB; |
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| 181 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
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| 182 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
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| 183 | |
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| 184 | fmpq_poly_div (FLINTA, FLINTA, FLINTB); |
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| 185 | A= convertFmpq_poly_t2FacCF (FLINTA, F.mvar()); |
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| 186 | |
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| 187 | fmpq_poly_clear (FLINTA); |
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| 188 | fmpq_poly_clear (FLINTB); |
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| 189 | return A; |
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| 190 | } |
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| 191 | |
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| 192 | CanonicalForm |
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| 193 | modFLINTQ (const CanonicalForm& F, const CanonicalForm& G) |
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| 194 | { |
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| 195 | CanonicalForm A= F; |
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| 196 | CanonicalForm B= G; |
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| 197 | |
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| 198 | fmpq_poly_t FLINTA,FLINTB; |
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| 199 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
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| 200 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
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| 201 | |
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| 202 | fmpq_poly_rem (FLINTA, FLINTA, FLINTB); |
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| 203 | A= convertFmpq_poly_t2FacCF (FLINTA, F.mvar()); |
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| 204 | |
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| 205 | fmpq_poly_clear (FLINTA); |
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| 206 | fmpq_poly_clear (FLINTB); |
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| 207 | return A; |
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| 208 | } |
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| 209 | |
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| 210 | CanonicalForm |
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[935e83] | 211 | mulFLINTQaTrunc (const CanonicalForm& F, const CanonicalForm& G, |
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| 212 | const Variable& alpha, int m) |
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[88408d0] | 213 | { |
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| 214 | CanonicalForm A= F; |
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| 215 | CanonicalForm B= G; |
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| 216 | |
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| 217 | CanonicalForm denA= bCommonDen (A); |
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| 218 | CanonicalForm denB= bCommonDen (B); |
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| 219 | |
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| 220 | A *= denA; |
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| 221 | B *= denB; |
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| 222 | |
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| 223 | int degAa= degree (A, alpha); |
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| 224 | int degBa= degree (B, alpha); |
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| 225 | int d= degAa + 1 + degBa; |
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| 226 | |
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| 227 | fmpz_poly_t FLINTA,FLINTB; |
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| 228 | fmpz_poly_init (FLINTA); |
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| 229 | fmpz_poly_init (FLINTB); |
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| 230 | kronSub (FLINTA, A, d); |
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| 231 | kronSub (FLINTB, B, d); |
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| 232 | |
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| 233 | int k= d*m; |
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| 234 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, k); |
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| 235 | |
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| 236 | denA *= denB; |
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| 237 | A= reverseSubst (FLINTA, d, alpha, denA); |
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| 238 | fmpz_poly_clear (FLINTA); |
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| 239 | fmpz_poly_clear (FLINTB); |
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| 240 | return A; |
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| 241 | } |
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| 242 | |
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[3ef2d6] | 243 | CanonicalForm |
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| 244 | mulFLINTQTrunc (const CanonicalForm& F, const CanonicalForm& G, int m) |
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| 245 | { |
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| 246 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
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| 247 | return mod (F*G, power (Variable (1), m)); |
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| 248 | Variable alpha; |
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| 249 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
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| 250 | return mulFLINTQaTrunc (F, G, alpha, m); |
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| 251 | |
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| 252 | CanonicalForm A= F; |
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| 253 | CanonicalForm B= G; |
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| 254 | |
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| 255 | CanonicalForm denA= bCommonDen (A); |
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| 256 | CanonicalForm denB= bCommonDen (B); |
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| 257 | |
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| 258 | A *= denA; |
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| 259 | B *= denB; |
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| 260 | fmpz_poly_t FLINTA,FLINTB; |
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| 261 | convertFacCF2Fmpz_poly_t (FLINTA, A); |
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| 262 | convertFacCF2Fmpz_poly_t (FLINTB, B); |
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| 263 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, m); |
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| 264 | denA *= denB; |
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| 265 | A= convertFmpz_poly_t2FacCF (FLINTA, F.mvar()); |
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| 266 | A /= denA; |
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| 267 | fmpz_poly_clear (FLINTA); |
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| 268 | fmpz_poly_clear (FLINTB); |
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| 269 | |
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| 270 | return A; |
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| 271 | } |
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| 272 | |
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| 273 | CanonicalForm uniReverse (const CanonicalForm& F, int d) |
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| 274 | { |
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| 275 | if (d == 0) |
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| 276 | return F; |
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| 277 | if (F.inCoeffDomain()) |
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| 278 | return F*power (Variable (1),d); |
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| 279 | Variable x= Variable (1); |
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| 280 | CanonicalForm result= 0; |
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| 281 | CFIterator i= F; |
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| 282 | while (d - i.exp() < 0) |
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| 283 | i++; |
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| 284 | |
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| 285 | for (; i.hasTerms() && (d - i.exp() >= 0); i++) |
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| 286 | result += i.coeff()*power (x, d - i.exp()); |
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| 287 | return result; |
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| 288 | } |
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| 289 | |
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| 290 | CanonicalForm |
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| 291 | newtonInverse (const CanonicalForm& F, const int n) |
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| 292 | { |
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| 293 | int l= ilog2(n); |
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| 294 | |
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| 295 | CanonicalForm g= F [0]; |
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| 296 | |
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| 297 | ASSERT (!g.isZero(), "expected a unit"); |
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| 298 | |
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| 299 | if (!g.isOne()) |
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| 300 | g = 1/g; |
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| 301 | Variable x= Variable (1); |
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| 302 | CanonicalForm result; |
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| 303 | int exp= 0; |
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| 304 | if (n & 1) |
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| 305 | { |
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| 306 | result= g; |
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| 307 | exp= 1; |
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| 308 | } |
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| 309 | CanonicalForm h; |
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| 310 | |
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| 311 | for (int i= 1; i <= l; i++) |
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| 312 | { |
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| 313 | h= mulNTL (g, mod (F, power (x, (1 << i)))); |
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| 314 | h= mod (h, power (x, (1 << i)) - 1); |
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| 315 | h= div (h, power (x, (1 << (i - 1)))); |
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| 316 | g -= power (x, (1 << (i - 1)))* |
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| 317 | mulFLINTQTrunc (g, h, 1 << (i-1)); |
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| 318 | |
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| 319 | if (n & (1 << i)) |
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| 320 | { |
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| 321 | if (exp) |
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| 322 | { |
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| 323 | h= mulNTL (result, mod (F, power (x, exp + (1 << i)))); |
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| 324 | h= mod (h, power (x, exp + (1 << i)) - 1); |
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| 325 | h= div (h, power (x, exp)); |
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| 326 | result -= power(x, exp)*mulFLINTQTrunc (g, h, 1 << i); |
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| 327 | exp += (1 << i); |
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| 328 | } |
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| 329 | else |
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| 330 | { |
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| 331 | exp= (1 << i); |
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| 332 | result= g; |
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| 333 | } |
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| 334 | } |
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| 335 | } |
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| 336 | |
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| 337 | return result; |
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| 338 | } |
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| 339 | |
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| 340 | void |
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| 341 | newtonDivrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
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| 342 | CanonicalForm& R) |
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| 343 | { |
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| 344 | CanonicalForm A= F; |
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| 345 | CanonicalForm B= G; |
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| 346 | Variable x= Variable (1); |
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| 347 | int degA= degree (A, x); |
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| 348 | int degB= degree (B, x); |
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| 349 | int m= degA - degB; |
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| 350 | |
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| 351 | if (m < 0) |
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| 352 | { |
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| 353 | R= A; |
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| 354 | Q= 0; |
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| 355 | return; |
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| 356 | } |
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| 357 | |
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| 358 | if (degB <= 1) |
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| 359 | divrem (A, B, Q, R); |
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| 360 | else |
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| 361 | { |
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| 362 | R= uniReverse (A, degA); |
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| 363 | |
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| 364 | CanonicalForm revB= uniReverse (B, degB); |
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| 365 | CanonicalForm buf= revB; |
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| 366 | revB= newtonInverse (revB, m + 1); |
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| 367 | Q= mulFLINTQTrunc (R, revB, m + 1); |
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| 368 | Q= uniReverse (Q, m); |
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| 369 | |
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| 370 | R= A - mulNTL (Q, B); |
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| 371 | } |
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| 372 | } |
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| 373 | |
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| 374 | void |
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| 375 | newtonDiv (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q) |
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| 376 | { |
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| 377 | CanonicalForm A= F; |
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| 378 | CanonicalForm B= G; |
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| 379 | Variable x= Variable (1); |
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| 380 | int degA= degree (A, x); |
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| 381 | int degB= degree (B, x); |
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| 382 | int m= degA - degB; |
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| 383 | |
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| 384 | if (m < 0) |
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| 385 | { |
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| 386 | Q= 0; |
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| 387 | return; |
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| 388 | } |
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| 389 | |
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| 390 | if (degB <= 1) |
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| 391 | Q= div (A, B); |
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| 392 | else |
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| 393 | { |
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| 394 | CanonicalForm R= uniReverse (A, degA); |
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| 395 | |
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| 396 | CanonicalForm revB= uniReverse (B, degB); |
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| 397 | revB= newtonInverse (revB, m + 1); |
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| 398 | Q= mulFLINTQTrunc (R, revB, m + 1); |
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| 399 | Q= uniReverse (Q, m); |
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| 400 | } |
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| 401 | } |
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| 402 | |
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[88408d0] | 403 | #endif |
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| 404 | |
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[4a05ed] | 405 | static |
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| 406 | CFList productsNTL (const CFList& factors, const CanonicalForm& M) |
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| 407 | { |
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| 408 | zz_p::init (getCharacteristic()); |
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| 409 | zz_pX NTLMipo= convertFacCF2NTLzzpX (M); |
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| 410 | zz_pE::init (NTLMipo); |
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| 411 | zz_pEX prod; |
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| 412 | vec_zz_pEX v; |
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| 413 | v.SetLength (factors.length()); |
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| 414 | int j= 0; |
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| 415 | for (CFListIterator i= factors; i.hasItem(); i++, j++) |
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| 416 | { |
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| 417 | if (i.getItem().inCoeffDomain()) |
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| 418 | v[j]= to_zz_pEX (to_zz_pE (convertFacCF2NTLzzpX (i.getItem()))); |
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| 419 | else |
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| 420 | v[j]= convertFacCF2NTLzz_pEX (i.getItem(), NTLMipo); |
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| 421 | } |
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| 422 | CFList result; |
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| 423 | Variable x= Variable (1); |
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| 424 | for (int j= 0; j < factors.length(); j++) |
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| 425 | { |
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| 426 | int k= 0; |
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| 427 | set(prod); |
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| 428 | for (int i= 0; i < factors.length(); i++, k++) |
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| 429 | { |
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| 430 | if (k == j) |
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| 431 | continue; |
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| 432 | prod *= v[i]; |
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| 433 | } |
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| 434 | result.append (convertNTLzz_pEX2CF (prod, x, M.mvar())); |
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| 435 | } |
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| 436 | return result; |
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| 437 | } |
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| 438 | |
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| 439 | static |
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| 440 | void tryDiophantine (CFList& result, const CanonicalForm& F, |
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| 441 | const CFList& factors, const CanonicalForm& M, bool& fail) |
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| 442 | { |
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| 443 | ASSERT (M.isUnivariate(), "expected univariate poly"); |
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| 444 | |
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| 445 | CFList bufFactors= factors; |
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| 446 | bufFactors.removeFirst(); |
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| 447 | bufFactors.insert (factors.getFirst () (0,2)); |
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| 448 | CanonicalForm inv, leadingCoeff= Lc (F); |
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| 449 | CFListIterator i= bufFactors; |
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| 450 | if (bufFactors.getFirst().inCoeffDomain()) |
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| 451 | { |
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| 452 | if (i.hasItem()) |
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| 453 | i++; |
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| 454 | } |
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| 455 | for (; i.hasItem(); i++) |
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| 456 | { |
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| 457 | tryInvert (Lc (i.getItem()), M, inv ,fail); |
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| 458 | if (fail) |
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| 459 | return; |
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| 460 | i.getItem()= reduce (i.getItem()*inv, M); |
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| 461 | } |
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| 462 | bufFactors= productsNTL (bufFactors, M); |
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| 463 | |
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| 464 | CanonicalForm buf1, buf2, buf3, S, T; |
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| 465 | i= bufFactors; |
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| 466 | if (i.hasItem()) |
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| 467 | i++; |
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| 468 | buf1= bufFactors.getFirst(); |
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| 469 | buf2= i.getItem(); |
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| 470 | tryExtgcd (buf1, buf2, M, buf3, S, T, fail); |
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| 471 | if (fail) |
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| 472 | return; |
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| 473 | result.append (S); |
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| 474 | result.append (T); |
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| 475 | if (i.hasItem()) |
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| 476 | i++; |
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| 477 | for (; i.hasItem(); i++) |
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| 478 | { |
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| 479 | buf1= i.getItem(); |
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| 480 | tryExtgcd (buf3, buf1, M, buf3, S, T, fail); |
---|
| 481 | if (fail) |
---|
| 482 | return; |
---|
| 483 | CFListIterator k= factors; |
---|
| 484 | for (CFListIterator j= result; j.hasItem(); j++, k++) |
---|
| 485 | { |
---|
| 486 | j.getItem() *= S; |
---|
| 487 | j.getItem()= mod (j.getItem(), k.getItem()); |
---|
| 488 | j.getItem()= reduce (j.getItem(), M); |
---|
| 489 | } |
---|
| 490 | result.append (T); |
---|
| 491 | } |
---|
| 492 | } |
---|
| 493 | |
---|
| 494 | static inline |
---|
| 495 | CFList mapinto (const CFList& L) |
---|
| 496 | { |
---|
| 497 | CFList result; |
---|
| 498 | for (CFListIterator i= L; i.hasItem(); i++) |
---|
| 499 | result.append (mapinto (i.getItem())); |
---|
| 500 | return result; |
---|
| 501 | } |
---|
| 502 | |
---|
| 503 | static inline |
---|
| 504 | int mod (const CFList& L, const CanonicalForm& p) |
---|
| 505 | { |
---|
| 506 | for (CFListIterator i= L; i.hasItem(); i++) |
---|
| 507 | { |
---|
| 508 | if (mod (i.getItem(), p) == 0) |
---|
| 509 | return 0; |
---|
| 510 | } |
---|
| 511 | return 1; |
---|
| 512 | } |
---|
| 513 | |
---|
| 514 | |
---|
| 515 | static inline void |
---|
| 516 | chineseRemainder (const CFList & x1, const CanonicalForm & q1, |
---|
| 517 | const CFList & x2, const CanonicalForm & q2, |
---|
| 518 | CFList & xnew, CanonicalForm & qnew) |
---|
| 519 | { |
---|
| 520 | ASSERT (x1.length() == x2.length(), "expected lists of equal length"); |
---|
| 521 | CanonicalForm tmp1, tmp2; |
---|
| 522 | CFListIterator j= x2; |
---|
| 523 | for (CFListIterator i= x1; i.hasItem() && j.hasItem(); i++, j++) |
---|
| 524 | { |
---|
| 525 | chineseRemainder (i.getItem(), q1, j.getItem(), q2, tmp1, tmp2); |
---|
| 526 | xnew.append (tmp1); |
---|
| 527 | } |
---|
| 528 | qnew= tmp2; |
---|
| 529 | } |
---|
| 530 | |
---|
| 531 | static inline |
---|
| 532 | CFList Farey (const CFList& L, const CanonicalForm& q) |
---|
| 533 | { |
---|
| 534 | CFList result; |
---|
| 535 | for (CFListIterator i= L; i.hasItem(); i++) |
---|
| 536 | result.append (Farey (i.getItem(), q)); |
---|
| 537 | return result; |
---|
| 538 | } |
---|
| 539 | |
---|
| 540 | static inline |
---|
| 541 | CFList replacevar (const CFList& L, const Variable& a, const Variable& b) |
---|
| 542 | { |
---|
| 543 | CFList result; |
---|
| 544 | for (CFListIterator i= L; i.hasItem(); i++) |
---|
| 545 | result.append (replacevar (i.getItem(), a, b)); |
---|
| 546 | return result; |
---|
| 547 | } |
---|
| 548 | |
---|
| 549 | CFList |
---|
| 550 | modularDiophant (const CanonicalForm& f, const CFList& factors, |
---|
| 551 | const CanonicalForm& M) |
---|
| 552 | { |
---|
| 553 | bool save_rat=!isOn (SW_RATIONAL); |
---|
| 554 | On (SW_RATIONAL); |
---|
| 555 | CanonicalForm F= f*bCommonDen (f); |
---|
| 556 | CFList products= factors; |
---|
| 557 | for (CFListIterator i= products; i.hasItem(); i++) |
---|
[9b2c8a] | 558 | { |
---|
| 559 | if (products.getFirst().level() == 1) |
---|
| 560 | i.getItem() /= Lc (i.getItem()); |
---|
[4a05ed] | 561 | i.getItem() *= bCommonDen (i.getItem()); |
---|
[9b2c8a] | 562 | } |
---|
[4a05ed] | 563 | if (products.getFirst().level() == 1) |
---|
| 564 | products.insert (Lc (F)); |
---|
| 565 | CanonicalForm bound= maxNorm (F); |
---|
| 566 | CFList leadingCoeffs; |
---|
| 567 | leadingCoeffs.append (lc (F)); |
---|
| 568 | CanonicalForm dummy; |
---|
| 569 | for (CFListIterator i= products; i.hasItem(); i++) |
---|
| 570 | { |
---|
| 571 | leadingCoeffs.append (lc (i.getItem())); |
---|
| 572 | dummy= maxNorm (i.getItem()); |
---|
| 573 | bound= (dummy > bound) ? dummy : bound; |
---|
| 574 | } |
---|
| 575 | bound *= maxNorm (Lc (F))*maxNorm (Lc(F))*bound; |
---|
| 576 | bound *= bound*bound; |
---|
| 577 | bound= power (bound, degree (M)); |
---|
| 578 | bound *= power (CanonicalForm (2),degree (f)); |
---|
| 579 | CanonicalForm bufBound= bound; |
---|
| 580 | int i = cf_getNumBigPrimes() - 1; |
---|
| 581 | int p; |
---|
| 582 | CFList resultModP, result, newResult; |
---|
| 583 | CanonicalForm q (0), newQ; |
---|
| 584 | bool fail= false; |
---|
| 585 | Variable a= M.mvar(); |
---|
| 586 | Variable b= Variable (2); |
---|
| 587 | setReduce (M.mvar(), false); |
---|
| 588 | CanonicalForm mipo= bCommonDen (M)*M; |
---|
| 589 | Off (SW_RATIONAL); |
---|
| 590 | CanonicalForm modMipo; |
---|
| 591 | leadingCoeffs.append (lc (mipo)); |
---|
| 592 | CFList tmp1, tmp2; |
---|
| 593 | bool equal= false; |
---|
| 594 | int count= 0; |
---|
| 595 | do |
---|
| 596 | { |
---|
| 597 | p = cf_getBigPrime( i ); |
---|
| 598 | i--; |
---|
| 599 | while ( i >= 0 && mod( leadingCoeffs, p ) == 0) |
---|
| 600 | { |
---|
| 601 | p = cf_getBigPrime( i ); |
---|
| 602 | i--; |
---|
| 603 | } |
---|
| 604 | |
---|
| 605 | ASSERT (i >= 0, "ran out of primes"); //sic |
---|
| 606 | |
---|
| 607 | setCharacteristic (p); |
---|
| 608 | modMipo= mapinto (mipo); |
---|
| 609 | modMipo /= lc (modMipo); |
---|
| 610 | resultModP= CFList(); |
---|
| 611 | tryDiophantine (resultModP, mapinto (F), mapinto (products), modMipo, fail); |
---|
| 612 | setCharacteristic (0); |
---|
| 613 | if (fail) |
---|
| 614 | { |
---|
| 615 | fail= false; |
---|
| 616 | continue; |
---|
| 617 | } |
---|
| 618 | |
---|
| 619 | if ( q.isZero() ) |
---|
| 620 | { |
---|
| 621 | result= replacevar (mapinto(resultModP), a, b); |
---|
| 622 | q= p; |
---|
| 623 | } |
---|
| 624 | else |
---|
| 625 | { |
---|
| 626 | result= replacevar (result, a, b); |
---|
| 627 | newResult= CFList(); |
---|
| 628 | chineseRemainder( result, q, replacevar (mapinto (resultModP), a, b), |
---|
| 629 | p, newResult, newQ ); |
---|
| 630 | q= newQ; |
---|
| 631 | result= newResult; |
---|
| 632 | if (newQ > bound) |
---|
| 633 | { |
---|
| 634 | count++; |
---|
| 635 | tmp1= replacevar (Farey (result, q), b, a); |
---|
| 636 | if (tmp2.isEmpty()) |
---|
| 637 | tmp2= tmp1; |
---|
| 638 | else |
---|
| 639 | { |
---|
| 640 | equal= true; |
---|
| 641 | CFListIterator k= tmp1; |
---|
| 642 | for (CFListIterator j= tmp2; j.hasItem(); j++, k++) |
---|
| 643 | { |
---|
| 644 | if (j.getItem() != k.getItem()) |
---|
| 645 | equal= false; |
---|
| 646 | } |
---|
| 647 | if (!equal) |
---|
| 648 | tmp2= tmp1; |
---|
| 649 | } |
---|
| 650 | if (count > 2) |
---|
| 651 | { |
---|
| 652 | bound *= bufBound; |
---|
| 653 | equal= false; |
---|
| 654 | count= 0; |
---|
| 655 | } |
---|
| 656 | } |
---|
| 657 | if (newQ > bound && equal) |
---|
| 658 | { |
---|
| 659 | On( SW_RATIONAL ); |
---|
| 660 | CFList bufResult= result; |
---|
[9b2c8a] | 661 | result= tmp2; |
---|
[4a05ed] | 662 | setReduce (M.mvar(), true); |
---|
| 663 | if (factors.getFirst().level() == 1) |
---|
| 664 | { |
---|
| 665 | result.removeFirst(); |
---|
| 666 | CFListIterator j= factors; |
---|
| 667 | CanonicalForm denf= bCommonDen (f); |
---|
| 668 | for (CFListIterator i= result; i.hasItem(); i++, j++) |
---|
| 669 | i.getItem() *= Lc (j.getItem())*denf; |
---|
| 670 | } |
---|
| 671 | if (factors.getFirst().level() != 1 && |
---|
| 672 | !bCommonDen (factors.getFirst()).isOne()) |
---|
| 673 | { |
---|
| 674 | CanonicalForm denFirst= bCommonDen (factors.getFirst()); |
---|
| 675 | for (CFListIterator i= result; i.hasItem(); i++) |
---|
| 676 | i.getItem() *= denFirst; |
---|
| 677 | } |
---|
| 678 | |
---|
| 679 | CanonicalForm test= 0; |
---|
| 680 | CFListIterator jj= factors; |
---|
| 681 | for (CFListIterator ii= result; ii.hasItem(); ii++, jj++) |
---|
| 682 | test += ii.getItem()*(f/jj.getItem()); |
---|
| 683 | if (!test.isOne()) |
---|
| 684 | { |
---|
| 685 | bound *= bufBound; |
---|
| 686 | equal= false; |
---|
| 687 | count= 0; |
---|
| 688 | setReduce (M.mvar(), false); |
---|
| 689 | result= bufResult; |
---|
| 690 | Off (SW_RATIONAL); |
---|
| 691 | } |
---|
| 692 | else |
---|
| 693 | break; |
---|
| 694 | } |
---|
| 695 | } |
---|
| 696 | } while (1); |
---|
| 697 | if (save_rat) Off(SW_RATIONAL); |
---|
| 698 | return result; |
---|
| 699 | } |
---|
| 700 | |
---|
[ad3c3ff] | 701 | CanonicalForm |
---|
| 702 | mulNTL (const CanonicalForm& F, const CanonicalForm& G) |
---|
| 703 | { |
---|
[64e7cb] | 704 | if (F.inCoeffDomain() || G.inCoeffDomain() || getCharacteristic() == 0) |
---|
[88408d0] | 705 | { |
---|
| 706 | Variable alpha; |
---|
| 707 | #ifdef HAVE_FLINT |
---|
[935e83] | 708 | if ((!F.inCoeffDomain() && !G.inCoeffDomain()) && |
---|
| 709 | (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha))) |
---|
[88408d0] | 710 | { |
---|
| 711 | CanonicalForm result= mulFLINTQa (F, G, alpha); |
---|
| 712 | return result; |
---|
| 713 | } |
---|
| 714 | else if (!F.inCoeffDomain() && !G.inCoeffDomain()) |
---|
| 715 | return mulFLINTQ (F, G); |
---|
| 716 | #endif |
---|
[ad3c3ff] | 717 | return F*G; |
---|
[88408d0] | 718 | } |
---|
[ad3c3ff] | 719 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
| 720 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
| 721 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
| 722 | return F*G; |
---|
| 723 | zz_p::init (getCharacteristic()); |
---|
| 724 | Variable alpha; |
---|
| 725 | CanonicalForm result; |
---|
| 726 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
| 727 | { |
---|
| 728 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 729 | zz_pE::init (NTLMipo); |
---|
| 730 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
| 731 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
| 732 | mul (NTLF, NTLF, NTLG); |
---|
| 733 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
---|
| 734 | } |
---|
| 735 | else |
---|
| 736 | { |
---|
[88408d0] | 737 | #ifdef HAVE_FLINT |
---|
| 738 | nmod_poly_t FLINTF, FLINTG; |
---|
| 739 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
| 740 | convertFacCF2nmod_poly_t (FLINTG, G); |
---|
| 741 | nmod_poly_mul (FLINTF, FLINTF, FLINTG); |
---|
| 742 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
---|
| 743 | nmod_poly_clear (FLINTF); |
---|
| 744 | nmod_poly_clear (FLINTG); |
---|
| 745 | #else |
---|
[ad3c3ff] | 746 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
| 747 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
| 748 | mul (NTLF, NTLF, NTLG); |
---|
| 749 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
---|
[88408d0] | 750 | #endif |
---|
[ad3c3ff] | 751 | } |
---|
| 752 | return result; |
---|
| 753 | } |
---|
| 754 | |
---|
| 755 | CanonicalForm |
---|
| 756 | modNTL (const CanonicalForm& F, const CanonicalForm& G) |
---|
| 757 | { |
---|
| 758 | if (F.inCoeffDomain() && G.isUnivariate()) |
---|
| 759 | return F; |
---|
| 760 | else if (F.inCoeffDomain() && G.inCoeffDomain()) |
---|
| 761 | return mod (F, G); |
---|
| 762 | else if (F.isUnivariate() && G.inCoeffDomain()) |
---|
| 763 | return mod (F,G); |
---|
[806c18] | 764 | |
---|
[64e7cb] | 765 | if (getCharacteristic() == 0) |
---|
[88408d0] | 766 | { |
---|
| 767 | #ifdef HAVE_FLINT |
---|
[0e6668] | 768 | Variable alpha; |
---|
| 769 | if (!hasFirstAlgVar (F, alpha) && !hasFirstAlgVar (G, alpha)) |
---|
[84dcd6b] | 770 | return modFLINTQ (F, G); |
---|
[0e6668] | 771 | else |
---|
[3ef2d6] | 772 | { |
---|
| 773 | CanonicalForm Q, R; |
---|
| 774 | newtonDivrem (F, G, Q, R); |
---|
| 775 | return R; |
---|
| 776 | } |
---|
[88408d0] | 777 | #else |
---|
[64e7cb] | 778 | return mod (F, G); |
---|
[88408d0] | 779 | #endif |
---|
| 780 | } |
---|
[64e7cb] | 781 | |
---|
[ad3c3ff] | 782 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
| 783 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
| 784 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
| 785 | return mod (F, G); |
---|
| 786 | zz_p::init (getCharacteristic()); |
---|
| 787 | Variable alpha; |
---|
| 788 | CanonicalForm result; |
---|
| 789 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
| 790 | { |
---|
| 791 | zz_pX NTLMipo= convertFacCF2NTLzzpX(getMipo (alpha)); |
---|
| 792 | zz_pE::init (NTLMipo); |
---|
| 793 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
| 794 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
| 795 | rem (NTLF, NTLF, NTLG); |
---|
| 796 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
---|
| 797 | } |
---|
| 798 | else |
---|
| 799 | { |
---|
[88408d0] | 800 | #ifdef HAVE_FLINT |
---|
| 801 | nmod_poly_t FLINTF, FLINTG; |
---|
| 802 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
| 803 | convertFacCF2nmod_poly_t (FLINTG, G); |
---|
| 804 | nmod_poly_divrem (FLINTG, FLINTF, FLINTF, FLINTG); |
---|
| 805 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
---|
| 806 | nmod_poly_clear (FLINTF); |
---|
| 807 | nmod_poly_clear (FLINTG); |
---|
| 808 | #else |
---|
[ad3c3ff] | 809 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
| 810 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
| 811 | rem (NTLF, NTLF, NTLG); |
---|
| 812 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
---|
[88408d0] | 813 | #endif |
---|
[ad3c3ff] | 814 | } |
---|
| 815 | return result; |
---|
| 816 | } |
---|
| 817 | |
---|
| 818 | CanonicalForm |
---|
| 819 | divNTL (const CanonicalForm& F, const CanonicalForm& G) |
---|
| 820 | { |
---|
| 821 | if (F.inCoeffDomain() && G.isUnivariate()) |
---|
| 822 | return F; |
---|
| 823 | else if (F.inCoeffDomain() && G.inCoeffDomain()) |
---|
| 824 | return div (F, G); |
---|
| 825 | else if (F.isUnivariate() && G.inCoeffDomain()) |
---|
| 826 | return div (F,G); |
---|
| 827 | |
---|
[64e7cb] | 828 | if (getCharacteristic() == 0) |
---|
[88408d0] | 829 | { |
---|
| 830 | #ifdef HAVE_FLINT |
---|
[0e6668] | 831 | Variable alpha; |
---|
| 832 | if (!hasFirstAlgVar (F, alpha) && !hasFirstAlgVar (G, alpha)) |
---|
[84dcd6b] | 833 | return divFLINTQ (F,G); |
---|
[0e6668] | 834 | else |
---|
[3ef2d6] | 835 | { |
---|
| 836 | CanonicalForm Q; |
---|
| 837 | newtonDiv (F, G, Q); |
---|
| 838 | return Q; |
---|
| 839 | } |
---|
[88408d0] | 840 | #else |
---|
[64e7cb] | 841 | return div (F, G); |
---|
[88408d0] | 842 | #endif |
---|
| 843 | } |
---|
[64e7cb] | 844 | |
---|
[ad3c3ff] | 845 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
| 846 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
| 847 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
| 848 | return div (F, G); |
---|
| 849 | zz_p::init (getCharacteristic()); |
---|
| 850 | Variable alpha; |
---|
| 851 | CanonicalForm result; |
---|
| 852 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
| 853 | { |
---|
| 854 | zz_pX NTLMipo= convertFacCF2NTLzzpX(getMipo (alpha)); |
---|
| 855 | zz_pE::init (NTLMipo); |
---|
| 856 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
| 857 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
| 858 | div (NTLF, NTLF, NTLG); |
---|
| 859 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
---|
| 860 | } |
---|
| 861 | else |
---|
| 862 | { |
---|
[88408d0] | 863 | #ifdef HAVE_FLINT |
---|
| 864 | nmod_poly_t FLINTF, FLINTG; |
---|
| 865 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
| 866 | convertFacCF2nmod_poly_t (FLINTG, G); |
---|
| 867 | nmod_poly_div (FLINTF, FLINTF, FLINTG); |
---|
| 868 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
---|
| 869 | nmod_poly_clear (FLINTF); |
---|
| 870 | nmod_poly_clear (FLINTG); |
---|
| 871 | #else |
---|
[ad3c3ff] | 872 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
| 873 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
| 874 | div (NTLF, NTLF, NTLG); |
---|
| 875 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
---|
[88408d0] | 876 | #endif |
---|
[ad3c3ff] | 877 | } |
---|
| 878 | return result; |
---|
| 879 | } |
---|
| 880 | |
---|
[11bf82] | 881 | /* |
---|
[ad3c3ff] | 882 | void |
---|
[806c18] | 883 | divremNTL (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
[ad3c3ff] | 884 | CanonicalForm& R) |
---|
| 885 | { |
---|
| 886 | if (F.inCoeffDomain() && G.isUnivariate()) |
---|
| 887 | { |
---|
| 888 | R= F; |
---|
| 889 | Q= 0; |
---|
| 890 | } |
---|
| 891 | else if (F.inCoeffDomain() && G.inCoeffDomain()) |
---|
| 892 | { |
---|
| 893 | divrem (F, G, Q, R); |
---|
| 894 | return; |
---|
| 895 | } |
---|
| 896 | else if (F.isUnivariate() && G.inCoeffDomain()) |
---|
| 897 | { |
---|
| 898 | divrem (F, G, Q, R); |
---|
| 899 | return; |
---|
| 900 | } |
---|
| 901 | |
---|
| 902 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
| 903 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
| 904 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
| 905 | { |
---|
| 906 | divrem (F, G, Q, R); |
---|
| 907 | return; |
---|
| 908 | } |
---|
| 909 | zz_p::init (getCharacteristic()); |
---|
| 910 | Variable alpha; |
---|
| 911 | CanonicalForm result; |
---|
| 912 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
| 913 | { |
---|
| 914 | zz_pX NTLMipo= convertFacCF2NTLzzpX(getMipo (alpha)); |
---|
| 915 | zz_pE::init (NTLMipo); |
---|
| 916 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
| 917 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
[806c18] | 918 | zz_pEX NTLQ; |
---|
[ad3c3ff] | 919 | zz_pEX NTLR; |
---|
| 920 | DivRem (NTLQ, NTLR, NTLF, NTLG); |
---|
| 921 | Q= convertNTLzz_pEX2CF(NTLQ, F.mvar(), alpha); |
---|
| 922 | R= convertNTLzz_pEX2CF(NTLR, F.mvar(), alpha); |
---|
| 923 | return; |
---|
| 924 | } |
---|
| 925 | else |
---|
| 926 | { |
---|
| 927 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
| 928 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
[806c18] | 929 | zz_pX NTLQ; |
---|
[ad3c3ff] | 930 | zz_pX NTLR; |
---|
| 931 | DivRem (NTLQ, NTLR, NTLF, NTLG); |
---|
| 932 | Q= convertNTLzzpX2CF(NTLQ, F.mvar()); |
---|
| 933 | R= convertNTLzzpX2CF(NTLR, F.mvar()); |
---|
| 934 | return; |
---|
| 935 | } |
---|
| 936 | }*/ |
---|
| 937 | |
---|
[806c18] | 938 | CanonicalForm mod (const CanonicalForm& F, const CFList& M) |
---|
[ad3c3ff] | 939 | { |
---|
| 940 | CanonicalForm A= F; |
---|
[806c18] | 941 | for (CFListIterator i= M; i.hasItem(); i++) |
---|
[ad3c3ff] | 942 | A= mod (A, i.getItem()); |
---|
| 943 | return A; |
---|
| 944 | } |
---|
| 945 | |
---|
[88408d0] | 946 | #ifdef HAVE_FLINT |
---|
| 947 | void kronSubFp (nmod_poly_t result, const CanonicalForm& A, int d) |
---|
| 948 | { |
---|
| 949 | int degAy= degree (A); |
---|
| 950 | nmod_poly_init2 (result, getCharacteristic(), d*(degAy + 1)); |
---|
| 951 | |
---|
| 952 | nmod_poly_t buf; |
---|
| 953 | |
---|
[935e83] | 954 | int j, k, bufRepLength; |
---|
[88408d0] | 955 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 956 | { |
---|
| 957 | convertFacCF2nmod_poly_t (buf, i.coeff()); |
---|
| 958 | |
---|
[935e83] | 959 | k= i.exp()*d; |
---|
| 960 | bufRepLength= (int) nmod_poly_length (buf); |
---|
| 961 | for (j= 0; j < bufRepLength; j++) |
---|
[88408d0] | 962 | nmod_poly_set_coeff_ui (result, j + k, nmod_poly_get_coeff_ui (buf, j)); |
---|
| 963 | nmod_poly_clear (buf); |
---|
| 964 | } |
---|
| 965 | _nmod_poly_normalise (result); |
---|
| 966 | } |
---|
| 967 | |
---|
| 968 | /*void kronSubQ (fmpz_poly_t result, const CanonicalForm& A, int d) |
---|
| 969 | { |
---|
| 970 | int degAy= degree (A); |
---|
| 971 | fmpz_poly_init2 (result, d*(degAy + 1)); |
---|
| 972 | _fmpz_poly_set_length (result, d*(degAy+1)); |
---|
| 973 | |
---|
| 974 | CFIterator j; |
---|
| 975 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 976 | { |
---|
| 977 | if (i.coeff().inBas |
---|
| 978 | convertFacCF2Fmpz_poly_t (buf, i.coeff()); |
---|
| 979 | |
---|
| 980 | int k= i.exp()*d; |
---|
| 981 | int bufRepLength= (int) fmpz_poly_length (buf); |
---|
| 982 | for (int j= 0; j < bufRepLength; j++) |
---|
| 983 | { |
---|
| 984 | fmpz_poly_get_coeff_fmpz (coeff, buf, j); |
---|
| 985 | fmpz_poly_set_coeff_fmpz (result, j + k, coeff); |
---|
| 986 | } |
---|
| 987 | fmpz_poly_clear (buf); |
---|
| 988 | } |
---|
| 989 | fmpz_clear (coeff); |
---|
| 990 | _fmpz_poly_normalise (result); |
---|
| 991 | }*/ |
---|
| 992 | |
---|
| 993 | // A is a bivariate poly over Qa!!!! |
---|
| 994 | // d2= 2*deg_alpha + 1 |
---|
| 995 | // d1= 2*deg_x*d2+1 |
---|
| 996 | void kronSubQa (fmpq_poly_t result, const CanonicalForm& A, int d1, int d2) |
---|
| 997 | { |
---|
| 998 | int degAy= degree (A); |
---|
| 999 | fmpq_poly_init2 (result, d1*(degAy + 1)); |
---|
| 1000 | |
---|
| 1001 | fmpq_poly_t buf; |
---|
| 1002 | fmpq_t coeff; |
---|
| 1003 | |
---|
| 1004 | int k, l, bufRepLength; |
---|
| 1005 | CFIterator j; |
---|
| 1006 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 1007 | { |
---|
| 1008 | if (i.coeff().inCoeffDomain()) |
---|
| 1009 | { |
---|
| 1010 | k= d1*i.exp(); |
---|
| 1011 | convertFacCF2Fmpq_poly_t (buf, i.coeff()); |
---|
| 1012 | bufRepLength= (int) fmpq_poly_length(buf); |
---|
| 1013 | for (l= 0; l < bufRepLength; l++) |
---|
| 1014 | { |
---|
| 1015 | fmpq_poly_get_coeff_fmpq (coeff, buf, l); |
---|
| 1016 | fmpq_poly_set_coeff_fmpq (result, l + k, coeff); |
---|
| 1017 | } |
---|
| 1018 | fmpq_poly_clear (buf); |
---|
| 1019 | } |
---|
| 1020 | else |
---|
| 1021 | { |
---|
| 1022 | for (j= i.coeff(); j.hasTerms(); j++) |
---|
| 1023 | { |
---|
| 1024 | k= d1*i.exp(); |
---|
| 1025 | k += d2*j.exp(); |
---|
| 1026 | convertFacCF2Fmpq_poly_t (buf, j.coeff()); |
---|
| 1027 | bufRepLength= (int) fmpq_poly_length(buf); |
---|
| 1028 | for (l= 0; l < bufRepLength; l++) |
---|
| 1029 | { |
---|
| 1030 | fmpq_poly_get_coeff_fmpq (coeff, buf, l); |
---|
| 1031 | fmpq_poly_set_coeff_fmpq (result, k + l, coeff); |
---|
| 1032 | } |
---|
| 1033 | fmpq_poly_clear (buf); |
---|
| 1034 | } |
---|
| 1035 | } |
---|
| 1036 | } |
---|
| 1037 | fmpq_clear (coeff); |
---|
| 1038 | _fmpq_poly_normalise (result); |
---|
| 1039 | } |
---|
| 1040 | #endif |
---|
| 1041 | |
---|
[dd2a9b3] | 1042 | zz_pX kronSubFp (const CanonicalForm& A, int d) |
---|
| 1043 | { |
---|
| 1044 | int degAy= degree (A); |
---|
| 1045 | zz_pX result; |
---|
| 1046 | result.rep.SetLength (d*(degAy + 1)); |
---|
| 1047 | |
---|
| 1048 | zz_p *resultp; |
---|
| 1049 | resultp= result.rep.elts(); |
---|
| 1050 | zz_pX buf; |
---|
| 1051 | zz_p *bufp; |
---|
[935e83] | 1052 | int j, k, bufRepLength; |
---|
[dd2a9b3] | 1053 | |
---|
| 1054 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 1055 | { |
---|
| 1056 | if (i.coeff().inCoeffDomain()) |
---|
| 1057 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
| 1058 | else |
---|
| 1059 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
| 1060 | |
---|
[935e83] | 1061 | k= i.exp()*d; |
---|
[dd2a9b3] | 1062 | bufp= buf.rep.elts(); |
---|
[935e83] | 1063 | bufRepLength= (int) buf.rep.length(); |
---|
| 1064 | for (j= 0; j < bufRepLength; j++) |
---|
[dd2a9b3] | 1065 | resultp [j + k]= bufp [j]; |
---|
| 1066 | } |
---|
| 1067 | result.normalize(); |
---|
| 1068 | |
---|
| 1069 | return result; |
---|
| 1070 | } |
---|
| 1071 | |
---|
| 1072 | zz_pEX kronSub (const CanonicalForm& A, int d, const Variable& alpha) |
---|
| 1073 | { |
---|
| 1074 | int degAy= degree (A); |
---|
| 1075 | zz_pEX result; |
---|
| 1076 | result.rep.SetLength (d*(degAy + 1)); |
---|
| 1077 | |
---|
| 1078 | Variable v; |
---|
| 1079 | zz_pE *resultp; |
---|
| 1080 | resultp= result.rep.elts(); |
---|
| 1081 | zz_pEX buf1; |
---|
| 1082 | zz_pE *buf1p; |
---|
| 1083 | zz_pX buf2; |
---|
| 1084 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
[935e83] | 1085 | int j, k, buf1RepLength; |
---|
[dd2a9b3] | 1086 | |
---|
| 1087 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 1088 | { |
---|
| 1089 | if (i.coeff().inCoeffDomain()) |
---|
| 1090 | { |
---|
| 1091 | buf2= convertFacCF2NTLzzpX (i.coeff()); |
---|
| 1092 | buf1= to_zz_pEX (to_zz_pE (buf2)); |
---|
| 1093 | } |
---|
| 1094 | else |
---|
| 1095 | buf1= convertFacCF2NTLzz_pEX (i.coeff(), NTLMipo); |
---|
| 1096 | |
---|
[935e83] | 1097 | k= i.exp()*d; |
---|
[dd2a9b3] | 1098 | buf1p= buf1.rep.elts(); |
---|
[935e83] | 1099 | buf1RepLength= (int) buf1.rep.length(); |
---|
| 1100 | for (j= 0; j < buf1RepLength; j++) |
---|
[dd2a9b3] | 1101 | resultp [j + k]= buf1p [j]; |
---|
| 1102 | } |
---|
| 1103 | result.normalize(); |
---|
| 1104 | |
---|
| 1105 | return result; |
---|
| 1106 | } |
---|
| 1107 | |
---|
| 1108 | void |
---|
| 1109 | kronSubRecipro (zz_pEX& subA1, zz_pEX& subA2,const CanonicalForm& A, int d, |
---|
| 1110 | const Variable& alpha) |
---|
| 1111 | { |
---|
| 1112 | int degAy= degree (A); |
---|
[96f9fdf] | 1113 | subA1.rep.SetLength ((long) d*(degAy + 2)); |
---|
| 1114 | subA2.rep.SetLength ((long) d*(degAy + 2)); |
---|
[dd2a9b3] | 1115 | |
---|
| 1116 | Variable v; |
---|
| 1117 | zz_pE *subA1p; |
---|
| 1118 | zz_pE *subA2p; |
---|
| 1119 | subA1p= subA1.rep.elts(); |
---|
| 1120 | subA2p= subA2.rep.elts(); |
---|
| 1121 | zz_pEX buf; |
---|
| 1122 | zz_pE *bufp; |
---|
| 1123 | zz_pX buf2; |
---|
| 1124 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
[935e83] | 1125 | int j, k, kk, bufRepLength; |
---|
[dd2a9b3] | 1126 | |
---|
| 1127 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 1128 | { |
---|
| 1129 | if (i.coeff().inCoeffDomain()) |
---|
| 1130 | { |
---|
| 1131 | buf2= convertFacCF2NTLzzpX (i.coeff()); |
---|
| 1132 | buf= to_zz_pEX (to_zz_pE (buf2)); |
---|
| 1133 | } |
---|
| 1134 | else |
---|
| 1135 | buf= convertFacCF2NTLzz_pEX (i.coeff(), NTLMipo); |
---|
| 1136 | |
---|
[935e83] | 1137 | k= i.exp()*d; |
---|
| 1138 | kk= (degAy - i.exp())*d; |
---|
[dd2a9b3] | 1139 | bufp= buf.rep.elts(); |
---|
[935e83] | 1140 | bufRepLength= (int) buf.rep.length(); |
---|
| 1141 | for (j= 0; j < bufRepLength; j++) |
---|
[dd2a9b3] | 1142 | { |
---|
[96f9fdf] | 1143 | subA1p [j + k] += bufp [j]; |
---|
| 1144 | subA2p [j + kk] += bufp [j]; |
---|
[dd2a9b3] | 1145 | } |
---|
| 1146 | } |
---|
| 1147 | subA1.normalize(); |
---|
| 1148 | subA2.normalize(); |
---|
| 1149 | } |
---|
| 1150 | |
---|
| 1151 | void |
---|
| 1152 | kronSubRecipro (zz_pX& subA1, zz_pX& subA2,const CanonicalForm& A, int d) |
---|
| 1153 | { |
---|
| 1154 | int degAy= degree (A); |
---|
[96f9fdf] | 1155 | subA1.rep.SetLength ((long) d*(degAy + 2)); |
---|
| 1156 | subA2.rep.SetLength ((long) d*(degAy + 2)); |
---|
[dd2a9b3] | 1157 | |
---|
| 1158 | zz_p *subA1p; |
---|
| 1159 | zz_p *subA2p; |
---|
| 1160 | subA1p= subA1.rep.elts(); |
---|
| 1161 | subA2p= subA2.rep.elts(); |
---|
| 1162 | zz_pX buf; |
---|
| 1163 | zz_p *bufp; |
---|
[935e83] | 1164 | int j, k, kk, bufRepLength; |
---|
[dd2a9b3] | 1165 | |
---|
| 1166 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 1167 | { |
---|
| 1168 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
| 1169 | |
---|
[935e83] | 1170 | k= i.exp()*d; |
---|
| 1171 | kk= (degAy - i.exp())*d; |
---|
[dd2a9b3] | 1172 | bufp= buf.rep.elts(); |
---|
[935e83] | 1173 | bufRepLength= (int) buf.rep.length(); |
---|
| 1174 | for (j= 0; j < bufRepLength; j++) |
---|
[dd2a9b3] | 1175 | { |
---|
[96f9fdf] | 1176 | subA1p [j + k] += bufp [j]; |
---|
| 1177 | subA2p [j + kk] += bufp [j]; |
---|
[dd2a9b3] | 1178 | } |
---|
| 1179 | } |
---|
| 1180 | subA1.normalize(); |
---|
| 1181 | subA2.normalize(); |
---|
| 1182 | } |
---|
| 1183 | |
---|
| 1184 | CanonicalForm |
---|
| 1185 | reverseSubst (const zz_pEX& F, const zz_pEX& G, int d, int k, |
---|
| 1186 | const Variable& alpha) |
---|
| 1187 | { |
---|
| 1188 | Variable y= Variable (2); |
---|
| 1189 | Variable x= Variable (1); |
---|
| 1190 | |
---|
| 1191 | zz_pEX f= F; |
---|
| 1192 | zz_pEX g= G; |
---|
| 1193 | int degf= deg(f); |
---|
| 1194 | int degg= deg(g); |
---|
| 1195 | |
---|
| 1196 | zz_pEX buf1; |
---|
| 1197 | zz_pEX buf2; |
---|
| 1198 | zz_pEX buf3; |
---|
| 1199 | |
---|
| 1200 | zz_pE *buf1p; |
---|
| 1201 | zz_pE *buf2p; |
---|
| 1202 | zz_pE *buf3p; |
---|
| 1203 | if (f.rep.length() < (long) d*(k+1)) //zero padding |
---|
| 1204 | f.rep.SetLength ((long)d*(k+1)); |
---|
| 1205 | |
---|
| 1206 | zz_pE *gp= g.rep.elts(); |
---|
| 1207 | zz_pE *fp= f.rep.elts(); |
---|
| 1208 | CanonicalForm result= 0; |
---|
| 1209 | int i= 0; |
---|
| 1210 | int lf= 0; |
---|
| 1211 | int lg= d*k; |
---|
| 1212 | int degfSubLf= degf; |
---|
| 1213 | int deggSubLg= degg-lg; |
---|
[935e83] | 1214 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
[dd2a9b3] | 1215 | zz_pE zzpEZero= zz_pE(); |
---|
| 1216 | |
---|
| 1217 | while (degf >= lf || lg >= 0) |
---|
| 1218 | { |
---|
| 1219 | if (degfSubLf >= d) |
---|
| 1220 | repLengthBuf1= d; |
---|
| 1221 | else if (degfSubLf < 0) |
---|
| 1222 | repLengthBuf1= 0; |
---|
| 1223 | else |
---|
| 1224 | repLengthBuf1= degfSubLf + 1; |
---|
| 1225 | buf1.rep.SetLength((long) repLengthBuf1); |
---|
| 1226 | |
---|
| 1227 | buf1p= buf1.rep.elts(); |
---|
[935e83] | 1228 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
[dd2a9b3] | 1229 | buf1p [ind]= fp [ind + lf]; |
---|
| 1230 | buf1.normalize(); |
---|
| 1231 | |
---|
| 1232 | repLengthBuf1= buf1.rep.length(); |
---|
| 1233 | |
---|
| 1234 | if (deggSubLg >= d - 1) |
---|
| 1235 | repLengthBuf2= d - 1; |
---|
| 1236 | else if (deggSubLg < 0) |
---|
| 1237 | repLengthBuf2= 0; |
---|
| 1238 | else |
---|
| 1239 | repLengthBuf2= deggSubLg + 1; |
---|
| 1240 | |
---|
| 1241 | buf2.rep.SetLength ((long) repLengthBuf2); |
---|
| 1242 | buf2p= buf2.rep.elts(); |
---|
[935e83] | 1243 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[dd2a9b3] | 1244 | buf2p [ind]= gp [ind + lg]; |
---|
| 1245 | buf2.normalize(); |
---|
| 1246 | |
---|
| 1247 | repLengthBuf2= buf2.rep.length(); |
---|
| 1248 | |
---|
| 1249 | buf3.rep.SetLength((long) repLengthBuf2 + d); |
---|
| 1250 | buf3p= buf3.rep.elts(); |
---|
| 1251 | buf2p= buf2.rep.elts(); |
---|
| 1252 | buf1p= buf1.rep.elts(); |
---|
[935e83] | 1253 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
[dd2a9b3] | 1254 | buf3p [ind]= buf1p [ind]; |
---|
[935e83] | 1255 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
[dd2a9b3] | 1256 | buf3p [ind]= zzpEZero; |
---|
[935e83] | 1257 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[dd2a9b3] | 1258 | buf3p [ind + d]= buf2p [ind]; |
---|
| 1259 | buf3.normalize(); |
---|
| 1260 | |
---|
| 1261 | result += convertNTLzz_pEX2CF (buf3, x, alpha)*power (y, i); |
---|
| 1262 | i++; |
---|
| 1263 | |
---|
| 1264 | |
---|
| 1265 | lf= i*d; |
---|
| 1266 | degfSubLf= degf - lf; |
---|
| 1267 | |
---|
| 1268 | lg= d*(k-i); |
---|
| 1269 | deggSubLg= degg - lg; |
---|
| 1270 | |
---|
| 1271 | buf1p= buf1.rep.elts(); |
---|
| 1272 | |
---|
| 1273 | if (lg >= 0 && deggSubLg > 0) |
---|
| 1274 | { |
---|
| 1275 | if (repLengthBuf2 > degfSubLf + 1) |
---|
| 1276 | degfSubLf= repLengthBuf2 - 1; |
---|
[935e83] | 1277 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
| 1278 | for (ind= 0; ind < tmp; ind++) |
---|
[dd2a9b3] | 1279 | gp [ind + lg] -= buf1p [ind]; |
---|
| 1280 | } |
---|
| 1281 | |
---|
| 1282 | if (lg < 0) |
---|
| 1283 | break; |
---|
| 1284 | |
---|
| 1285 | buf2p= buf2.rep.elts(); |
---|
| 1286 | if (degfSubLf >= 0) |
---|
| 1287 | { |
---|
[935e83] | 1288 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[dd2a9b3] | 1289 | fp [ind + lf] -= buf2p [ind]; |
---|
| 1290 | } |
---|
| 1291 | } |
---|
| 1292 | |
---|
| 1293 | return result; |
---|
| 1294 | } |
---|
| 1295 | |
---|
| 1296 | CanonicalForm |
---|
| 1297 | reverseSubst (const zz_pX& F, const zz_pX& G, int d, int k) |
---|
| 1298 | { |
---|
| 1299 | Variable y= Variable (2); |
---|
| 1300 | Variable x= Variable (1); |
---|
| 1301 | |
---|
| 1302 | zz_pX f= F; |
---|
| 1303 | zz_pX g= G; |
---|
| 1304 | int degf= deg(f); |
---|
| 1305 | int degg= deg(g); |
---|
| 1306 | |
---|
| 1307 | zz_pX buf1; |
---|
| 1308 | zz_pX buf2; |
---|
| 1309 | zz_pX buf3; |
---|
| 1310 | |
---|
| 1311 | zz_p *buf1p; |
---|
| 1312 | zz_p *buf2p; |
---|
| 1313 | zz_p *buf3p; |
---|
| 1314 | |
---|
| 1315 | if (f.rep.length() < (long) d*(k+1)) //zero padding |
---|
| 1316 | f.rep.SetLength ((long)d*(k+1)); |
---|
| 1317 | |
---|
| 1318 | zz_p *gp= g.rep.elts(); |
---|
| 1319 | zz_p *fp= f.rep.elts(); |
---|
| 1320 | CanonicalForm result= 0; |
---|
| 1321 | int i= 0; |
---|
| 1322 | int lf= 0; |
---|
| 1323 | int lg= d*k; |
---|
| 1324 | int degfSubLf= degf; |
---|
| 1325 | int deggSubLg= degg-lg; |
---|
[935e83] | 1326 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
[dd2a9b3] | 1327 | zz_p zzpZero= zz_p(); |
---|
| 1328 | while (degf >= lf || lg >= 0) |
---|
| 1329 | { |
---|
| 1330 | if (degfSubLf >= d) |
---|
| 1331 | repLengthBuf1= d; |
---|
| 1332 | else if (degfSubLf < 0) |
---|
| 1333 | repLengthBuf1= 0; |
---|
| 1334 | else |
---|
| 1335 | repLengthBuf1= degfSubLf + 1; |
---|
| 1336 | buf1.rep.SetLength((long) repLengthBuf1); |
---|
| 1337 | |
---|
| 1338 | buf1p= buf1.rep.elts(); |
---|
[935e83] | 1339 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
[dd2a9b3] | 1340 | buf1p [ind]= fp [ind + lf]; |
---|
| 1341 | buf1.normalize(); |
---|
| 1342 | |
---|
| 1343 | repLengthBuf1= buf1.rep.length(); |
---|
[c1b9927] | 1344 | |
---|
[dd2a9b3] | 1345 | if (deggSubLg >= d - 1) |
---|
| 1346 | repLengthBuf2= d - 1; |
---|
| 1347 | else if (deggSubLg < 0) |
---|
| 1348 | repLengthBuf2= 0; |
---|
| 1349 | else |
---|
| 1350 | repLengthBuf2= deggSubLg + 1; |
---|
| 1351 | |
---|
| 1352 | buf2.rep.SetLength ((long) repLengthBuf2); |
---|
| 1353 | buf2p= buf2.rep.elts(); |
---|
[935e83] | 1354 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[dd2a9b3] | 1355 | buf2p [ind]= gp [ind + lg]; |
---|
| 1356 | |
---|
| 1357 | buf2.normalize(); |
---|
| 1358 | |
---|
| 1359 | repLengthBuf2= buf2.rep.length(); |
---|
| 1360 | |
---|
| 1361 | |
---|
| 1362 | buf3.rep.SetLength((long) repLengthBuf2 + d); |
---|
| 1363 | buf3p= buf3.rep.elts(); |
---|
| 1364 | buf2p= buf2.rep.elts(); |
---|
| 1365 | buf1p= buf1.rep.elts(); |
---|
[935e83] | 1366 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
[dd2a9b3] | 1367 | buf3p [ind]= buf1p [ind]; |
---|
[935e83] | 1368 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
[dd2a9b3] | 1369 | buf3p [ind]= zzpZero; |
---|
[935e83] | 1370 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[dd2a9b3] | 1371 | buf3p [ind + d]= buf2p [ind]; |
---|
| 1372 | buf3.normalize(); |
---|
| 1373 | |
---|
| 1374 | result += convertNTLzzpX2CF (buf3, x)*power (y, i); |
---|
| 1375 | i++; |
---|
| 1376 | |
---|
| 1377 | |
---|
| 1378 | lf= i*d; |
---|
| 1379 | degfSubLf= degf - lf; |
---|
| 1380 | |
---|
| 1381 | lg= d*(k-i); |
---|
| 1382 | deggSubLg= degg - lg; |
---|
| 1383 | |
---|
| 1384 | buf1p= buf1.rep.elts(); |
---|
| 1385 | |
---|
| 1386 | if (lg >= 0 && deggSubLg > 0) |
---|
| 1387 | { |
---|
| 1388 | if (repLengthBuf2 > degfSubLf + 1) |
---|
| 1389 | degfSubLf= repLengthBuf2 - 1; |
---|
[935e83] | 1390 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
| 1391 | for (ind= 0; ind < tmp; ind++) |
---|
[dd2a9b3] | 1392 | gp [ind + lg] -= buf1p [ind]; |
---|
| 1393 | } |
---|
| 1394 | if (lg < 0) |
---|
| 1395 | break; |
---|
| 1396 | |
---|
| 1397 | buf2p= buf2.rep.elts(); |
---|
| 1398 | if (degfSubLf >= 0) |
---|
| 1399 | { |
---|
[935e83] | 1400 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[dd2a9b3] | 1401 | fp [ind + lf] -= buf2p [ind]; |
---|
| 1402 | } |
---|
| 1403 | } |
---|
| 1404 | |
---|
| 1405 | return result; |
---|
| 1406 | } |
---|
| 1407 | |
---|
| 1408 | CanonicalForm reverseSubst (const zz_pEX& F, int d, const Variable& alpha) |
---|
| 1409 | { |
---|
| 1410 | Variable y= Variable (2); |
---|
| 1411 | Variable x= Variable (1); |
---|
| 1412 | |
---|
| 1413 | zz_pEX f= F; |
---|
| 1414 | zz_pE *fp= f.rep.elts(); |
---|
| 1415 | |
---|
| 1416 | zz_pEX buf; |
---|
| 1417 | zz_pE *bufp; |
---|
| 1418 | CanonicalForm result= 0; |
---|
| 1419 | int i= 0; |
---|
| 1420 | int degf= deg(f); |
---|
| 1421 | int k= 0; |
---|
[935e83] | 1422 | int degfSubK, repLength, j; |
---|
[dd2a9b3] | 1423 | while (degf >= k) |
---|
| 1424 | { |
---|
| 1425 | degfSubK= degf - k; |
---|
| 1426 | if (degfSubK >= d) |
---|
| 1427 | repLength= d; |
---|
| 1428 | else |
---|
| 1429 | repLength= degfSubK + 1; |
---|
| 1430 | |
---|
| 1431 | buf.rep.SetLength ((long) repLength); |
---|
| 1432 | bufp= buf.rep.elts(); |
---|
[935e83] | 1433 | for (j= 0; j < repLength; j++) |
---|
[dd2a9b3] | 1434 | bufp [j]= fp [j + k]; |
---|
| 1435 | buf.normalize(); |
---|
| 1436 | |
---|
| 1437 | result += convertNTLzz_pEX2CF (buf, x, alpha)*power (y, i); |
---|
| 1438 | i++; |
---|
| 1439 | k= d*i; |
---|
| 1440 | } |
---|
| 1441 | |
---|
| 1442 | return result; |
---|
| 1443 | } |
---|
| 1444 | |
---|
| 1445 | CanonicalForm reverseSubstFp (const zz_pX& F, int d) |
---|
| 1446 | { |
---|
| 1447 | Variable y= Variable (2); |
---|
| 1448 | Variable x= Variable (1); |
---|
| 1449 | |
---|
| 1450 | zz_pX f= F; |
---|
| 1451 | zz_p *fp= f.rep.elts(); |
---|
| 1452 | |
---|
| 1453 | zz_pX buf; |
---|
| 1454 | zz_p *bufp; |
---|
| 1455 | CanonicalForm result= 0; |
---|
| 1456 | int i= 0; |
---|
| 1457 | int degf= deg(f); |
---|
| 1458 | int k= 0; |
---|
[935e83] | 1459 | int degfSubK, repLength, j; |
---|
[dd2a9b3] | 1460 | while (degf >= k) |
---|
| 1461 | { |
---|
| 1462 | degfSubK= degf - k; |
---|
| 1463 | if (degfSubK >= d) |
---|
| 1464 | repLength= d; |
---|
| 1465 | else |
---|
| 1466 | repLength= degfSubK + 1; |
---|
| 1467 | |
---|
| 1468 | buf.rep.SetLength ((long) repLength); |
---|
| 1469 | bufp= buf.rep.elts(); |
---|
[935e83] | 1470 | for (j= 0; j < repLength; j++) |
---|
[dd2a9b3] | 1471 | bufp [j]= fp [j + k]; |
---|
| 1472 | buf.normalize(); |
---|
| 1473 | |
---|
| 1474 | result += convertNTLzzpX2CF (buf, x)*power (y, i); |
---|
| 1475 | i++; |
---|
| 1476 | k= d*i; |
---|
| 1477 | } |
---|
| 1478 | |
---|
| 1479 | return result; |
---|
| 1480 | } |
---|
| 1481 | |
---|
| 1482 | // assumes input to be reduced mod M and to be an element of Fq not Fp |
---|
| 1483 | CanonicalForm |
---|
[c1b9927] | 1484 | mulMod2NTLFpReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
[dd2a9b3] | 1485 | CanonicalForm& M) |
---|
| 1486 | { |
---|
[96f9fdf] | 1487 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
| 1488 | d1 /= 2; |
---|
| 1489 | d1 += 1; |
---|
[dd2a9b3] | 1490 | |
---|
| 1491 | zz_pX F1, F2; |
---|
| 1492 | kronSubRecipro (F1, F2, F, d1); |
---|
| 1493 | zz_pX G1, G2; |
---|
| 1494 | kronSubRecipro (G1, G2, G, d1); |
---|
| 1495 | |
---|
| 1496 | int k= d1*degree (M); |
---|
| 1497 | MulTrunc (F1, F1, G1, (long) k); |
---|
| 1498 | |
---|
[96f9fdf] | 1499 | int degtailF= degree (tailcoeff (F), 1); |
---|
| 1500 | int degtailG= degree (tailcoeff (G), 1); |
---|
| 1501 | int taildegF= taildegree (F); |
---|
| 1502 | int taildegG= taildegree (G); |
---|
| 1503 | int b= k + degtailF + degtailG - d1*(2+taildegF+taildegG); |
---|
| 1504 | |
---|
| 1505 | reverse (F2, F2); |
---|
| 1506 | reverse (G2, G2); |
---|
| 1507 | MulTrunc (F2, F2, G2, b + 1); |
---|
| 1508 | reverse (F2, F2, b); |
---|
[dd2a9b3] | 1509 | |
---|
[96f9fdf] | 1510 | int d2= tmax (deg (F2)/d1, deg (F1)/d1); |
---|
[dd2a9b3] | 1511 | return reverseSubst (F1, F2, d1, d2); |
---|
| 1512 | } |
---|
| 1513 | |
---|
| 1514 | //Kronecker substitution |
---|
| 1515 | CanonicalForm |
---|
| 1516 | mulMod2NTLFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 1517 | CanonicalForm& M) |
---|
| 1518 | { |
---|
| 1519 | CanonicalForm A= F; |
---|
| 1520 | CanonicalForm B= G; |
---|
| 1521 | |
---|
| 1522 | int degAx= degree (A, 1); |
---|
| 1523 | int degAy= degree (A, 2); |
---|
| 1524 | int degBx= degree (B, 1); |
---|
| 1525 | int degBy= degree (B, 2); |
---|
| 1526 | int d1= degAx + 1 + degBx; |
---|
[96f9fdf] | 1527 | int d2= tmax (degAy, degBy); |
---|
[dd2a9b3] | 1528 | |
---|
[fd803bc] | 1529 | if (d1 > 128 && d2 > 160 && (degAy == degBy) && (2*degAy > degree (M))) |
---|
[dd2a9b3] | 1530 | return mulMod2NTLFpReci (A, B, M); |
---|
| 1531 | |
---|
| 1532 | zz_pX NTLA= kronSubFp (A, d1); |
---|
| 1533 | zz_pX NTLB= kronSubFp (B, d1); |
---|
| 1534 | |
---|
| 1535 | int k= d1*degree (M); |
---|
| 1536 | MulTrunc (NTLA, NTLA, NTLB, (long) k); |
---|
| 1537 | |
---|
| 1538 | A= reverseSubstFp (NTLA, d1); |
---|
| 1539 | |
---|
| 1540 | return A; |
---|
| 1541 | } |
---|
| 1542 | |
---|
| 1543 | // assumes input to be reduced mod M and to be an element of Fq not Fp |
---|
| 1544 | CanonicalForm |
---|
[c1b9927] | 1545 | mulMod2NTLFqReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
[dd2a9b3] | 1546 | CanonicalForm& M, const Variable& alpha) |
---|
| 1547 | { |
---|
[96f9fdf] | 1548 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
| 1549 | d1 /= 2; |
---|
| 1550 | d1 += 1; |
---|
[dd2a9b3] | 1551 | |
---|
| 1552 | zz_pEX F1, F2; |
---|
| 1553 | kronSubRecipro (F1, F2, F, d1, alpha); |
---|
| 1554 | zz_pEX G1, G2; |
---|
| 1555 | kronSubRecipro (G1, G2, G, d1, alpha); |
---|
| 1556 | |
---|
[fd803bc] | 1557 | int k= d1*degree (M); |
---|
| 1558 | MulTrunc (F1, F1, G1, (long) k); |
---|
[dd2a9b3] | 1559 | |
---|
[96f9fdf] | 1560 | int degtailF= degree (tailcoeff (F), 1); |
---|
| 1561 | int degtailG= degree (tailcoeff (G), 1); |
---|
| 1562 | int taildegF= taildegree (F); |
---|
| 1563 | int taildegG= taildegree (G); |
---|
| 1564 | int b= k + degtailF + degtailG - d1*(2+taildegF+taildegG); |
---|
[dd2a9b3] | 1565 | |
---|
[96f9fdf] | 1566 | reverse (F2, F2); |
---|
| 1567 | reverse (G2, G2); |
---|
| 1568 | MulTrunc (F2, F2, G2, b + 1); |
---|
| 1569 | reverse (F2, F2, b); |
---|
[dd2a9b3] | 1570 | |
---|
[96f9fdf] | 1571 | int d2= tmax (deg (F2)/d1, deg (F1)/d1); |
---|
| 1572 | return reverseSubst (F1, F2, d1, d2, alpha); |
---|
[dd2a9b3] | 1573 | } |
---|
| 1574 | |
---|
[0e6668] | 1575 | #ifdef HAVE_FLINT |
---|
| 1576 | CanonicalForm |
---|
| 1577 | mulMod2FLINTFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 1578 | CanonicalForm& M); |
---|
| 1579 | #endif |
---|
| 1580 | |
---|
[dd2a9b3] | 1581 | CanonicalForm |
---|
| 1582 | mulMod2NTLFq (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 1583 | CanonicalForm& M) |
---|
| 1584 | { |
---|
| 1585 | Variable alpha; |
---|
| 1586 | CanonicalForm A= F; |
---|
| 1587 | CanonicalForm B= G; |
---|
| 1588 | |
---|
| 1589 | if (hasFirstAlgVar (A, alpha) || hasFirstAlgVar (B, alpha)) |
---|
| 1590 | { |
---|
| 1591 | int degAx= degree (A, 1); |
---|
| 1592 | int degAy= degree (A, 2); |
---|
| 1593 | int degBx= degree (B, 1); |
---|
| 1594 | int degBy= degree (B, 2); |
---|
| 1595 | int d1= degAx + degBx + 1; |
---|
[96f9fdf] | 1596 | int d2= tmax (degAy, degBy); |
---|
[dd2a9b3] | 1597 | zz_p::init (getCharacteristic()); |
---|
| 1598 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 1599 | zz_pE::init (NTLMipo); |
---|
| 1600 | |
---|
| 1601 | int degMipo= degree (getMipo (alpha)); |
---|
[fd803bc] | 1602 | if ((d1 > 128/degMipo) && (d2 > 160/degMipo) && (degAy == degBy) && |
---|
| 1603 | (2*degAy > degree (M))) |
---|
[dd2a9b3] | 1604 | return mulMod2NTLFqReci (A, B, M, alpha); |
---|
| 1605 | |
---|
| 1606 | zz_pEX NTLA= kronSub (A, d1, alpha); |
---|
| 1607 | zz_pEX NTLB= kronSub (B, d1, alpha); |
---|
| 1608 | |
---|
| 1609 | int k= d1*degree (M); |
---|
| 1610 | |
---|
| 1611 | MulTrunc (NTLA, NTLA, NTLB, (long) k); |
---|
| 1612 | |
---|
| 1613 | A= reverseSubst (NTLA, d1, alpha); |
---|
| 1614 | |
---|
| 1615 | return A; |
---|
| 1616 | } |
---|
| 1617 | else |
---|
[0e6668] | 1618 | #ifdef HAVE_FLINT |
---|
| 1619 | return mulMod2FLINTFp (A, B, M); |
---|
| 1620 | #else |
---|
[dd2a9b3] | 1621 | return mulMod2NTLFp (A, B, M); |
---|
[0e6668] | 1622 | #endif |
---|
| 1623 | } |
---|
| 1624 | |
---|
| 1625 | #ifdef HAVE_FLINT |
---|
| 1626 | void |
---|
[935e83] | 1627 | kronSubRecipro (nmod_poly_t subA1, nmod_poly_t subA2, const CanonicalForm& A, |
---|
| 1628 | int d) |
---|
[0e6668] | 1629 | { |
---|
| 1630 | int degAy= degree (A); |
---|
| 1631 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
| 1632 | nmod_poly_init2_preinv (subA1, getCharacteristic(), ninv, d*(degAy + 2)); |
---|
| 1633 | nmod_poly_init2_preinv (subA2, getCharacteristic(), ninv, d*(degAy + 2)); |
---|
| 1634 | |
---|
| 1635 | nmod_poly_t buf; |
---|
| 1636 | |
---|
[935e83] | 1637 | int k, kk, j, bufRepLength; |
---|
[0e6668] | 1638 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 1639 | { |
---|
| 1640 | convertFacCF2nmod_poly_t (buf, i.coeff()); |
---|
| 1641 | |
---|
[935e83] | 1642 | k= i.exp()*d; |
---|
| 1643 | kk= (degAy - i.exp())*d; |
---|
| 1644 | bufRepLength= (int) nmod_poly_length (buf); |
---|
| 1645 | for (j= 0; j < bufRepLength; j++) |
---|
[0e6668] | 1646 | { |
---|
[935e83] | 1647 | nmod_poly_set_coeff_ui (subA1, j + k, |
---|
| 1648 | n_addmod (nmod_poly_get_coeff_ui (subA1, j+k), |
---|
| 1649 | nmod_poly_get_coeff_ui (buf, j), |
---|
| 1650 | getCharacteristic() |
---|
| 1651 | ) |
---|
| 1652 | ); |
---|
| 1653 | nmod_poly_set_coeff_ui (subA2, j + kk, |
---|
| 1654 | n_addmod (nmod_poly_get_coeff_ui (subA2, j + kk), |
---|
| 1655 | nmod_poly_get_coeff_ui (buf, j), |
---|
| 1656 | getCharacteristic() |
---|
| 1657 | ) |
---|
| 1658 | ); |
---|
[0e6668] | 1659 | } |
---|
| 1660 | nmod_poly_clear (buf); |
---|
| 1661 | } |
---|
| 1662 | _nmod_poly_normalise (subA1); |
---|
| 1663 | _nmod_poly_normalise (subA2); |
---|
| 1664 | } |
---|
| 1665 | |
---|
| 1666 | void |
---|
[935e83] | 1667 | kronSubRecipro (fmpz_poly_t subA1, fmpz_poly_t subA2, const CanonicalForm& A, |
---|
| 1668 | int d) |
---|
[0e6668] | 1669 | { |
---|
| 1670 | int degAy= degree (A); |
---|
| 1671 | fmpz_poly_init2 (subA1, d*(degAy + 2)); |
---|
| 1672 | fmpz_poly_init2 (subA2, d*(degAy + 2)); |
---|
| 1673 | |
---|
| 1674 | fmpz_poly_t buf; |
---|
| 1675 | fmpz_t coeff1, coeff2; |
---|
| 1676 | |
---|
[935e83] | 1677 | int k, kk, j, bufRepLength; |
---|
[0e6668] | 1678 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 1679 | { |
---|
| 1680 | convertFacCF2Fmpz_poly_t (buf, i.coeff()); |
---|
| 1681 | |
---|
[935e83] | 1682 | k= i.exp()*d; |
---|
| 1683 | kk= (degAy - i.exp())*d; |
---|
| 1684 | bufRepLength= (int) fmpz_poly_length (buf); |
---|
| 1685 | for (j= 0; j < bufRepLength; j++) |
---|
[0e6668] | 1686 | { |
---|
[935e83] | 1687 | fmpz_poly_get_coeff_fmpz (coeff1, subA1, j+k); |
---|
[0e6668] | 1688 | fmpz_poly_get_coeff_fmpz (coeff2, buf, j); |
---|
| 1689 | fmpz_add (coeff1, coeff1, coeff2); |
---|
| 1690 | fmpz_poly_set_coeff_fmpz (subA1, j + k, coeff1); |
---|
| 1691 | fmpz_poly_get_coeff_fmpz (coeff1, subA2, j + kk); |
---|
| 1692 | fmpz_add (coeff1, coeff1, coeff2); |
---|
| 1693 | fmpz_poly_set_coeff_fmpz (subA2, j + kk, coeff1); |
---|
| 1694 | } |
---|
| 1695 | fmpz_poly_clear (buf); |
---|
| 1696 | } |
---|
| 1697 | fmpz_clear (coeff1); |
---|
| 1698 | fmpz_clear (coeff2); |
---|
| 1699 | _fmpz_poly_normalise (subA1); |
---|
| 1700 | _fmpz_poly_normalise (subA2); |
---|
| 1701 | } |
---|
| 1702 | |
---|
| 1703 | CanonicalForm reverseSubstQ (const fmpz_poly_t F, int d) |
---|
| 1704 | { |
---|
| 1705 | Variable y= Variable (2); |
---|
| 1706 | Variable x= Variable (1); |
---|
| 1707 | |
---|
| 1708 | fmpz_poly_t f; |
---|
| 1709 | fmpz_poly_init (f); |
---|
| 1710 | fmpz_poly_set (f, F); |
---|
| 1711 | |
---|
| 1712 | fmpz_poly_t buf; |
---|
| 1713 | CanonicalForm result= 0; |
---|
| 1714 | int i= 0; |
---|
| 1715 | int degf= fmpz_poly_degree(f); |
---|
| 1716 | int k= 0; |
---|
[935e83] | 1717 | int degfSubK, repLength, j; |
---|
[0e6668] | 1718 | fmpz_t coeff; |
---|
| 1719 | while (degf >= k) |
---|
| 1720 | { |
---|
| 1721 | degfSubK= degf - k; |
---|
| 1722 | if (degfSubK >= d) |
---|
| 1723 | repLength= d; |
---|
| 1724 | else |
---|
| 1725 | repLength= degfSubK + 1; |
---|
| 1726 | |
---|
| 1727 | fmpz_poly_init2 (buf, repLength); |
---|
| 1728 | fmpz_init (coeff); |
---|
[935e83] | 1729 | for (j= 0; j < repLength; j++) |
---|
[0e6668] | 1730 | { |
---|
| 1731 | fmpz_poly_get_coeff_fmpz (coeff, f, j + k); |
---|
| 1732 | fmpz_poly_set_coeff_fmpz (buf, j, coeff); |
---|
| 1733 | } |
---|
| 1734 | _fmpz_poly_normalise (buf); |
---|
| 1735 | |
---|
| 1736 | result += convertFmpz_poly_t2FacCF (buf, x)*power (y, i); |
---|
| 1737 | i++; |
---|
| 1738 | k= d*i; |
---|
| 1739 | fmpz_poly_clear (buf); |
---|
| 1740 | fmpz_clear (coeff); |
---|
| 1741 | } |
---|
| 1742 | fmpz_poly_clear (f); |
---|
| 1743 | |
---|
| 1744 | return result; |
---|
| 1745 | } |
---|
| 1746 | |
---|
| 1747 | CanonicalForm |
---|
| 1748 | reverseSubst (const nmod_poly_t F, const nmod_poly_t G, int d, int k) |
---|
| 1749 | { |
---|
| 1750 | Variable y= Variable (2); |
---|
| 1751 | Variable x= Variable (1); |
---|
| 1752 | |
---|
| 1753 | nmod_poly_t f, g; |
---|
| 1754 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
| 1755 | nmod_poly_init_preinv (f, getCharacteristic(), ninv); |
---|
| 1756 | nmod_poly_init_preinv (g, getCharacteristic(), ninv); |
---|
| 1757 | nmod_poly_set (f, F); |
---|
| 1758 | nmod_poly_set (g, G); |
---|
| 1759 | int degf= nmod_poly_degree(f); |
---|
| 1760 | int degg= nmod_poly_degree(g); |
---|
| 1761 | |
---|
| 1762 | |
---|
| 1763 | nmod_poly_t buf1,buf2, buf3; |
---|
| 1764 | |
---|
| 1765 | if (nmod_poly_length (f) < (long) d*(k+1)) //zero padding |
---|
| 1766 | nmod_poly_fit_length (f,(long)d*(k+1)); |
---|
| 1767 | |
---|
| 1768 | CanonicalForm result= 0; |
---|
| 1769 | int i= 0; |
---|
| 1770 | int lf= 0; |
---|
| 1771 | int lg= d*k; |
---|
| 1772 | int degfSubLf= degf; |
---|
| 1773 | int deggSubLg= degg-lg; |
---|
[935e83] | 1774 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
[0e6668] | 1775 | while (degf >= lf || lg >= 0) |
---|
| 1776 | { |
---|
| 1777 | if (degfSubLf >= d) |
---|
| 1778 | repLengthBuf1= d; |
---|
| 1779 | else if (degfSubLf < 0) |
---|
| 1780 | repLengthBuf1= 0; |
---|
| 1781 | else |
---|
| 1782 | repLengthBuf1= degfSubLf + 1; |
---|
| 1783 | nmod_poly_init2_preinv (buf1, getCharacteristic(), ninv, repLengthBuf1); |
---|
| 1784 | |
---|
[935e83] | 1785 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
[0e6668] | 1786 | nmod_poly_set_coeff_ui (buf1, ind, nmod_poly_get_coeff_ui (f, ind+lf)); |
---|
| 1787 | _nmod_poly_normalise (buf1); |
---|
| 1788 | |
---|
| 1789 | repLengthBuf1= nmod_poly_length (buf1); |
---|
| 1790 | |
---|
| 1791 | if (deggSubLg >= d - 1) |
---|
| 1792 | repLengthBuf2= d - 1; |
---|
| 1793 | else if (deggSubLg < 0) |
---|
| 1794 | repLengthBuf2= 0; |
---|
| 1795 | else |
---|
| 1796 | repLengthBuf2= deggSubLg + 1; |
---|
| 1797 | |
---|
| 1798 | nmod_poly_init2_preinv (buf2, getCharacteristic(), ninv, repLengthBuf2); |
---|
[935e83] | 1799 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[0e6668] | 1800 | nmod_poly_set_coeff_ui (buf2, ind, nmod_poly_get_coeff_ui (g, ind + lg)); |
---|
| 1801 | |
---|
| 1802 | _nmod_poly_normalise (buf2); |
---|
| 1803 | repLengthBuf2= nmod_poly_length (buf2); |
---|
| 1804 | |
---|
| 1805 | nmod_poly_init2_preinv (buf3, getCharacteristic(), ninv, repLengthBuf2 + d); |
---|
[935e83] | 1806 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
[0e6668] | 1807 | nmod_poly_set_coeff_ui (buf3, ind, nmod_poly_get_coeff_ui (buf1, ind)); |
---|
[935e83] | 1808 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
[0e6668] | 1809 | nmod_poly_set_coeff_ui (buf3, ind, 0); |
---|
[935e83] | 1810 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
| 1811 | nmod_poly_set_coeff_ui (buf3, ind+d, nmod_poly_get_coeff_ui (buf2, ind)); |
---|
[0e6668] | 1812 | _nmod_poly_normalise (buf3); |
---|
| 1813 | |
---|
| 1814 | result += convertnmod_poly_t2FacCF (buf3, x)*power (y, i); |
---|
| 1815 | i++; |
---|
| 1816 | |
---|
| 1817 | |
---|
| 1818 | lf= i*d; |
---|
| 1819 | degfSubLf= degf - lf; |
---|
| 1820 | |
---|
| 1821 | lg= d*(k-i); |
---|
| 1822 | deggSubLg= degg - lg; |
---|
| 1823 | |
---|
| 1824 | if (lg >= 0 && deggSubLg > 0) |
---|
| 1825 | { |
---|
| 1826 | if (repLengthBuf2 > degfSubLf + 1) |
---|
| 1827 | degfSubLf= repLengthBuf2 - 1; |
---|
[935e83] | 1828 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
| 1829 | for (ind= 0; ind < tmp; ind++) |
---|
| 1830 | nmod_poly_set_coeff_ui (g, ind + lg, |
---|
| 1831 | n_submod (nmod_poly_get_coeff_ui (g, ind + lg), |
---|
| 1832 | nmod_poly_get_coeff_ui (buf1, ind), |
---|
| 1833 | getCharacteristic() |
---|
| 1834 | ) |
---|
| 1835 | ); |
---|
[0e6668] | 1836 | } |
---|
| 1837 | if (lg < 0) |
---|
| 1838 | { |
---|
| 1839 | nmod_poly_clear (buf1); |
---|
| 1840 | nmod_poly_clear (buf2); |
---|
| 1841 | nmod_poly_clear (buf3); |
---|
| 1842 | break; |
---|
| 1843 | } |
---|
| 1844 | if (degfSubLf >= 0) |
---|
| 1845 | { |
---|
[935e83] | 1846 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
| 1847 | nmod_poly_set_coeff_ui (f, ind + lf, |
---|
| 1848 | n_submod (nmod_poly_get_coeff_ui (f, ind + lf), |
---|
| 1849 | nmod_poly_get_coeff_ui (buf2, ind), |
---|
| 1850 | getCharacteristic() |
---|
| 1851 | ) |
---|
| 1852 | ); |
---|
[0e6668] | 1853 | } |
---|
| 1854 | nmod_poly_clear (buf1); |
---|
| 1855 | nmod_poly_clear (buf2); |
---|
| 1856 | nmod_poly_clear (buf3); |
---|
| 1857 | } |
---|
| 1858 | |
---|
| 1859 | nmod_poly_clear (f); |
---|
| 1860 | nmod_poly_clear (g); |
---|
| 1861 | |
---|
| 1862 | return result; |
---|
| 1863 | } |
---|
| 1864 | |
---|
| 1865 | CanonicalForm |
---|
| 1866 | reverseSubst (const fmpz_poly_t F, const fmpz_poly_t G, int d, int k) |
---|
| 1867 | { |
---|
| 1868 | Variable y= Variable (2); |
---|
| 1869 | Variable x= Variable (1); |
---|
| 1870 | |
---|
| 1871 | fmpz_poly_t f, g; |
---|
| 1872 | fmpz_poly_init (f); |
---|
| 1873 | fmpz_poly_init (g); |
---|
| 1874 | fmpz_poly_set (f, F); |
---|
| 1875 | fmpz_poly_set (g, G); |
---|
| 1876 | int degf= fmpz_poly_degree(f); |
---|
| 1877 | int degg= fmpz_poly_degree(g); |
---|
| 1878 | |
---|
| 1879 | |
---|
| 1880 | fmpz_poly_t buf1,buf2, buf3; |
---|
| 1881 | |
---|
| 1882 | if (fmpz_poly_length (f) < (long) d*(k+1)) //zero padding |
---|
| 1883 | fmpz_poly_fit_length (f,(long)d*(k+1)); |
---|
| 1884 | |
---|
| 1885 | CanonicalForm result= 0; |
---|
| 1886 | int i= 0; |
---|
| 1887 | int lf= 0; |
---|
| 1888 | int lg= d*k; |
---|
| 1889 | int degfSubLf= degf; |
---|
| 1890 | int deggSubLg= degg-lg; |
---|
[935e83] | 1891 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
[0e6668] | 1892 | fmpz_t tmp1, tmp2; |
---|
| 1893 | while (degf >= lf || lg >= 0) |
---|
| 1894 | { |
---|
| 1895 | if (degfSubLf >= d) |
---|
| 1896 | repLengthBuf1= d; |
---|
| 1897 | else if (degfSubLf < 0) |
---|
| 1898 | repLengthBuf1= 0; |
---|
| 1899 | else |
---|
| 1900 | repLengthBuf1= degfSubLf + 1; |
---|
[935e83] | 1901 | |
---|
[0e6668] | 1902 | fmpz_poly_init2 (buf1, repLengthBuf1); |
---|
| 1903 | |
---|
[935e83] | 1904 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
[0e6668] | 1905 | { |
---|
| 1906 | fmpz_poly_get_coeff_fmpz (tmp1, f, ind + lf); |
---|
| 1907 | fmpz_poly_set_coeff_fmpz (buf1, ind, tmp1); |
---|
| 1908 | } |
---|
| 1909 | _fmpz_poly_normalise (buf1); |
---|
| 1910 | |
---|
| 1911 | repLengthBuf1= fmpz_poly_length (buf1); |
---|
| 1912 | |
---|
| 1913 | if (deggSubLg >= d - 1) |
---|
| 1914 | repLengthBuf2= d - 1; |
---|
| 1915 | else if (deggSubLg < 0) |
---|
| 1916 | repLengthBuf2= 0; |
---|
| 1917 | else |
---|
| 1918 | repLengthBuf2= deggSubLg + 1; |
---|
| 1919 | |
---|
| 1920 | fmpz_poly_init2 (buf2, repLengthBuf2); |
---|
[935e83] | 1921 | |
---|
| 1922 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[0e6668] | 1923 | { |
---|
| 1924 | fmpz_poly_get_coeff_fmpz (tmp1, g, ind + lg); |
---|
| 1925 | fmpz_poly_set_coeff_fmpz (buf2, ind, tmp1); |
---|
| 1926 | } |
---|
| 1927 | |
---|
| 1928 | _fmpz_poly_normalise (buf2); |
---|
| 1929 | repLengthBuf2= fmpz_poly_length (buf2); |
---|
| 1930 | |
---|
| 1931 | fmpz_poly_init2 (buf3, repLengthBuf2 + d); |
---|
[935e83] | 1932 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
[0e6668] | 1933 | { |
---|
| 1934 | fmpz_poly_get_coeff_fmpz (tmp1, buf1, ind); //oder fmpz_set (fmpz_poly_get_coeff_ptr (buf3, ind),fmpz_poly_get_coeff_ptr (buf1, ind)) |
---|
| 1935 | fmpz_poly_set_coeff_fmpz (buf3, ind, tmp1); |
---|
| 1936 | } |
---|
[935e83] | 1937 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
[0e6668] | 1938 | fmpz_poly_set_coeff_ui (buf3, ind, 0); |
---|
[935e83] | 1939 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[0e6668] | 1940 | { |
---|
| 1941 | fmpz_poly_get_coeff_fmpz (tmp1, buf2, ind); |
---|
| 1942 | fmpz_poly_set_coeff_fmpz (buf3, ind + d, tmp1); |
---|
| 1943 | } |
---|
| 1944 | _fmpz_poly_normalise (buf3); |
---|
| 1945 | |
---|
| 1946 | result += convertFmpz_poly_t2FacCF (buf3, x)*power (y, i); |
---|
| 1947 | i++; |
---|
| 1948 | |
---|
| 1949 | |
---|
| 1950 | lf= i*d; |
---|
| 1951 | degfSubLf= degf - lf; |
---|
| 1952 | |
---|
| 1953 | lg= d*(k-i); |
---|
| 1954 | deggSubLg= degg - lg; |
---|
| 1955 | |
---|
| 1956 | if (lg >= 0 && deggSubLg > 0) |
---|
| 1957 | { |
---|
| 1958 | if (repLengthBuf2 > degfSubLf + 1) |
---|
| 1959 | degfSubLf= repLengthBuf2 - 1; |
---|
[935e83] | 1960 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
| 1961 | for (ind= 0; ind < tmp; ind++) |
---|
[0e6668] | 1962 | { |
---|
| 1963 | fmpz_poly_get_coeff_fmpz (tmp1, g, ind + lg); |
---|
| 1964 | fmpz_poly_get_coeff_fmpz (tmp2, buf1, ind); |
---|
| 1965 | fmpz_sub (tmp1, tmp1, tmp2); |
---|
| 1966 | fmpz_poly_set_coeff_fmpz (g, ind + lg, tmp1); |
---|
| 1967 | } |
---|
| 1968 | } |
---|
| 1969 | if (lg < 0) |
---|
| 1970 | { |
---|
| 1971 | fmpz_poly_clear (buf1); |
---|
| 1972 | fmpz_poly_clear (buf2); |
---|
| 1973 | fmpz_poly_clear (buf3); |
---|
| 1974 | break; |
---|
| 1975 | } |
---|
| 1976 | if (degfSubLf >= 0) |
---|
| 1977 | { |
---|
[935e83] | 1978 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[0e6668] | 1979 | { |
---|
| 1980 | fmpz_poly_get_coeff_fmpz (tmp1, f, ind + lf); |
---|
| 1981 | fmpz_poly_get_coeff_fmpz (tmp2, buf2, ind); |
---|
| 1982 | fmpz_sub (tmp1, tmp1, tmp2); |
---|
| 1983 | fmpz_poly_set_coeff_fmpz (f, ind + lf, tmp1); |
---|
| 1984 | } |
---|
| 1985 | } |
---|
| 1986 | fmpz_poly_clear (buf1); |
---|
| 1987 | fmpz_poly_clear (buf2); |
---|
| 1988 | fmpz_poly_clear (buf3); |
---|
| 1989 | } |
---|
| 1990 | |
---|
| 1991 | fmpz_poly_clear (f); |
---|
| 1992 | fmpz_poly_clear (g); |
---|
| 1993 | fmpz_clear (tmp1); |
---|
| 1994 | fmpz_clear (tmp2); |
---|
| 1995 | |
---|
| 1996 | return result; |
---|
[dd2a9b3] | 1997 | } |
---|
| 1998 | |
---|
[0e6668] | 1999 | CanonicalForm reverseSubstFp (const nmod_poly_t F, int d) |
---|
| 2000 | { |
---|
| 2001 | Variable y= Variable (2); |
---|
| 2002 | Variable x= Variable (1); |
---|
| 2003 | |
---|
| 2004 | nmod_poly_t f; |
---|
| 2005 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
| 2006 | nmod_poly_init_preinv (f, getCharacteristic(), ninv); |
---|
| 2007 | nmod_poly_set (f, F); |
---|
| 2008 | |
---|
| 2009 | nmod_poly_t buf; |
---|
| 2010 | CanonicalForm result= 0; |
---|
| 2011 | int i= 0; |
---|
| 2012 | int degf= nmod_poly_degree(f); |
---|
| 2013 | int k= 0; |
---|
[935e83] | 2014 | int degfSubK, repLength, j; |
---|
[0e6668] | 2015 | while (degf >= k) |
---|
| 2016 | { |
---|
| 2017 | degfSubK= degf - k; |
---|
| 2018 | if (degfSubK >= d) |
---|
| 2019 | repLength= d; |
---|
| 2020 | else |
---|
| 2021 | repLength= degfSubK + 1; |
---|
| 2022 | |
---|
| 2023 | nmod_poly_init2_preinv (buf, getCharacteristic(), ninv, repLength); |
---|
[935e83] | 2024 | for (j= 0; j < repLength; j++) |
---|
[0e6668] | 2025 | nmod_poly_set_coeff_ui (buf, j, nmod_poly_get_coeff_ui (f, j + k)); |
---|
| 2026 | _nmod_poly_normalise (buf); |
---|
| 2027 | |
---|
| 2028 | result += convertnmod_poly_t2FacCF (buf, x)*power (y, i); |
---|
| 2029 | i++; |
---|
| 2030 | k= d*i; |
---|
| 2031 | nmod_poly_clear (buf); |
---|
| 2032 | } |
---|
| 2033 | nmod_poly_clear (f); |
---|
| 2034 | |
---|
| 2035 | return result; |
---|
| 2036 | } |
---|
| 2037 | |
---|
| 2038 | CanonicalForm |
---|
| 2039 | mulMod2FLINTFpReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 2040 | CanonicalForm& M) |
---|
| 2041 | { |
---|
| 2042 | int d1= tmax (degree (F, 1), degree (G, 1)) + 1; |
---|
| 2043 | d1 /= 2; |
---|
| 2044 | d1 += 1; |
---|
| 2045 | |
---|
| 2046 | nmod_poly_t F1, F2; |
---|
| 2047 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
| 2048 | nmod_poly_init_preinv (F1, getCharacteristic(), ninv); |
---|
| 2049 | nmod_poly_init_preinv (F2, getCharacteristic(), ninv); |
---|
| 2050 | kronSubRecipro (F1, F2, F, d1); |
---|
| 2051 | |
---|
| 2052 | nmod_poly_t G1, G2; |
---|
| 2053 | nmod_poly_init_preinv (G1, getCharacteristic(), ninv); |
---|
| 2054 | nmod_poly_init_preinv (G2, getCharacteristic(), ninv); |
---|
| 2055 | kronSubRecipro (G1, G2, G, d1); |
---|
| 2056 | |
---|
| 2057 | int k= d1*degree (M); |
---|
| 2058 | nmod_poly_mullow (F1, F1, G1, (long) k); |
---|
| 2059 | |
---|
| 2060 | int degtailF= degree (tailcoeff (F), 1);; |
---|
| 2061 | int degtailG= degree (tailcoeff (G), 1); |
---|
| 2062 | int taildegF= taildegree (F); |
---|
| 2063 | int taildegG= taildegree (G); |
---|
| 2064 | |
---|
[935e83] | 2065 | int b= nmod_poly_degree (F2) + nmod_poly_degree (G2) - k - degtailF - degtailG |
---|
| 2066 | + d1*(2+taildegF + taildegG); |
---|
[0e6668] | 2067 | nmod_poly_mulhigh (F2, F2, G2, b); |
---|
| 2068 | nmod_poly_shift_right (F2, F2, b); |
---|
| 2069 | int d2= tmax (nmod_poly_degree (F2)/d1, nmod_poly_degree (F1)/d1); |
---|
| 2070 | |
---|
| 2071 | |
---|
| 2072 | CanonicalForm result= reverseSubst (F1, F2, d1, d2); |
---|
| 2073 | |
---|
| 2074 | nmod_poly_clear (F1); |
---|
| 2075 | nmod_poly_clear (F2); |
---|
| 2076 | nmod_poly_clear (G1); |
---|
| 2077 | nmod_poly_clear (G2); |
---|
| 2078 | return result; |
---|
| 2079 | } |
---|
| 2080 | |
---|
| 2081 | CanonicalForm |
---|
| 2082 | mulMod2FLINTFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 2083 | CanonicalForm& M) |
---|
| 2084 | { |
---|
| 2085 | CanonicalForm A= F; |
---|
| 2086 | CanonicalForm B= G; |
---|
| 2087 | |
---|
| 2088 | int degAx= degree (A, 1); |
---|
| 2089 | int degAy= degree (A, 2); |
---|
| 2090 | int degBx= degree (B, 1); |
---|
| 2091 | int degBy= degree (B, 2); |
---|
| 2092 | int d1= degAx + 1 + degBx; |
---|
| 2093 | int d2= tmax (degAy, degBy); |
---|
| 2094 | |
---|
| 2095 | if (d1 > 128 && d2 > 160 && (degAy == degBy) && (2*degAy > degree (M))) |
---|
| 2096 | return mulMod2FLINTFpReci (A, B, M); |
---|
| 2097 | |
---|
| 2098 | nmod_poly_t FLINTA, FLINTB; |
---|
| 2099 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
| 2100 | nmod_poly_init_preinv (FLINTA, getCharacteristic(), ninv); |
---|
| 2101 | nmod_poly_init_preinv (FLINTB, getCharacteristic(), ninv); |
---|
| 2102 | kronSubFp (FLINTA, A, d1); |
---|
| 2103 | kronSubFp (FLINTB, B, d1); |
---|
| 2104 | |
---|
| 2105 | int k= d1*degree (M); |
---|
| 2106 | nmod_poly_mullow (FLINTA, FLINTA, FLINTB, (long) k); |
---|
| 2107 | |
---|
| 2108 | A= reverseSubstFp (FLINTA, d1); |
---|
| 2109 | |
---|
| 2110 | nmod_poly_clear (FLINTA); |
---|
| 2111 | nmod_poly_clear (FLINTB); |
---|
| 2112 | return A; |
---|
| 2113 | } |
---|
| 2114 | |
---|
| 2115 | CanonicalForm |
---|
| 2116 | mulMod2FLINTQReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 2117 | CanonicalForm& M) |
---|
| 2118 | { |
---|
| 2119 | int d1= tmax (degree (F, 1), degree (G, 1)) + 1; |
---|
| 2120 | d1 /= 2; |
---|
| 2121 | d1 += 1; |
---|
| 2122 | |
---|
| 2123 | fmpz_poly_t F1, F2; |
---|
| 2124 | fmpz_poly_init (F1); |
---|
| 2125 | fmpz_poly_init (F2); |
---|
| 2126 | kronSubRecipro (F1, F2, F, d1); |
---|
| 2127 | |
---|
| 2128 | fmpz_poly_t G1, G2; |
---|
| 2129 | fmpz_poly_init (G1); |
---|
| 2130 | fmpz_poly_init (G2); |
---|
| 2131 | kronSubRecipro (G1, G2, G, d1); |
---|
| 2132 | |
---|
| 2133 | int k= d1*degree (M); |
---|
| 2134 | fmpz_poly_mullow (F1, F1, G1, (long) k); |
---|
| 2135 | |
---|
| 2136 | int degtailF= degree (tailcoeff (F), 1);; |
---|
| 2137 | int degtailG= degree (tailcoeff (G), 1); |
---|
| 2138 | int taildegF= taildegree (F); |
---|
| 2139 | int taildegG= taildegree (G); |
---|
| 2140 | |
---|
[935e83] | 2141 | int b= fmpz_poly_degree (F2) + fmpz_poly_degree (G2) - k - degtailF - degtailG |
---|
| 2142 | + d1*(2+taildegF + taildegG); |
---|
[0e6668] | 2143 | fmpz_poly_mulhigh_n (F2, F2, G2, b); |
---|
| 2144 | fmpz_poly_shift_right (F2, F2, b); |
---|
| 2145 | int d2= tmax (fmpz_poly_degree (F2)/d1, fmpz_poly_degree (F1)/d1); |
---|
| 2146 | |
---|
| 2147 | CanonicalForm result= reverseSubst (F1, F2, d1, d2); |
---|
| 2148 | |
---|
| 2149 | fmpz_poly_clear (F1); |
---|
| 2150 | fmpz_poly_clear (F2); |
---|
| 2151 | fmpz_poly_clear (G1); |
---|
| 2152 | fmpz_poly_clear (G2); |
---|
| 2153 | return result; |
---|
| 2154 | } |
---|
| 2155 | |
---|
| 2156 | CanonicalForm |
---|
| 2157 | mulMod2FLINTQ (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 2158 | CanonicalForm& M) |
---|
| 2159 | { |
---|
| 2160 | CanonicalForm A= F; |
---|
| 2161 | CanonicalForm B= G; |
---|
| 2162 | |
---|
| 2163 | int degAx= degree (A, 1); |
---|
| 2164 | int degBx= degree (B, 1); |
---|
| 2165 | int d1= degAx + 1 + degBx; |
---|
| 2166 | |
---|
| 2167 | CanonicalForm f= bCommonDen (F); |
---|
| 2168 | CanonicalForm g= bCommonDen (G); |
---|
| 2169 | A *= f; |
---|
| 2170 | B *= g; |
---|
| 2171 | |
---|
| 2172 | fmpz_poly_t FLINTA, FLINTB; |
---|
| 2173 | fmpz_poly_init (FLINTA); |
---|
| 2174 | fmpz_poly_init (FLINTB); |
---|
| 2175 | kronSub (FLINTA, A, d1); |
---|
| 2176 | kronSub (FLINTB, B, d1); |
---|
| 2177 | int k= d1*degree (M); |
---|
| 2178 | |
---|
| 2179 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, (long) k); |
---|
| 2180 | A= reverseSubstQ (FLINTA, d1); |
---|
| 2181 | fmpz_poly_clear (FLINTA); |
---|
| 2182 | fmpz_poly_clear (FLINTB); |
---|
| 2183 | return A/(f*g); |
---|
| 2184 | } |
---|
| 2185 | |
---|
| 2186 | #endif |
---|
| 2187 | |
---|
[806c18] | 2188 | CanonicalForm mulMod2 (const CanonicalForm& A, const CanonicalForm& B, |
---|
[ad3c3ff] | 2189 | const CanonicalForm& M) |
---|
| 2190 | { |
---|
| 2191 | if (A.isZero() || B.isZero()) |
---|
| 2192 | return 0; |
---|
| 2193 | |
---|
| 2194 | ASSERT (M.isUnivariate(), "M must be univariate"); |
---|
| 2195 | |
---|
| 2196 | CanonicalForm F= mod (A, M); |
---|
| 2197 | CanonicalForm G= mod (B, M); |
---|
| 2198 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
---|
| 2199 | return F*G; |
---|
| 2200 | Variable y= M.mvar(); |
---|
| 2201 | int degF= degree (F, y); |
---|
| 2202 | int degG= degree (G, y); |
---|
| 2203 | |
---|
[c1b9927] | 2204 | if ((degF < 1 && degG < 1) && (F.isUnivariate() && G.isUnivariate()) && |
---|
[ad3c3ff] | 2205 | (F.level() == G.level())) |
---|
[c1b9927] | 2206 | { |
---|
[ad3c3ff] | 2207 | CanonicalForm result= mulNTL (F, G); |
---|
| 2208 | return mod (result, M); |
---|
| 2209 | } |
---|
| 2210 | else if (degF <= 1 && degG <= 1) |
---|
[c1b9927] | 2211 | { |
---|
[ad3c3ff] | 2212 | CanonicalForm result= F*G; |
---|
| 2213 | return mod (result, M); |
---|
| 2214 | } |
---|
[806c18] | 2215 | |
---|
[dd2a9b3] | 2216 | int sizeF= size (F); |
---|
| 2217 | int sizeG= size (G); |
---|
[c1b9927] | 2218 | |
---|
[dd2a9b3] | 2219 | int fallBackToNaive= 50; |
---|
| 2220 | if (sizeF < fallBackToNaive || sizeG < fallBackToNaive) |
---|
| 2221 | return mod (F*G, M); |
---|
| 2222 | |
---|
[0e6668] | 2223 | #ifdef HAVE_FLINT |
---|
| 2224 | Variable alpha; |
---|
| 2225 | if (getCharacteristic() == 0 && !hasFirstAlgVar (F, alpha) && ! hasFirstAlgVar (G, alpha)) |
---|
[84dcd6b] | 2226 | return mulMod2FLINTQ (F, G, M); |
---|
[0e6668] | 2227 | #endif |
---|
| 2228 | |
---|
[64e7cb] | 2229 | if (getCharacteristic() > 0 && CFFactory::gettype() != GaloisFieldDomain && |
---|
[dd2a9b3] | 2230 | (((degF-degG) < 50 && degF > degG) || ((degG-degF) < 50 && degF <= degG))) |
---|
| 2231 | return mulMod2NTLFq (F, G, M); |
---|
| 2232 | |
---|
[ad3c3ff] | 2233 | int m= (int) ceil (degree (M)/2.0); |
---|
| 2234 | if (degF >= m || degG >= m) |
---|
| 2235 | { |
---|
| 2236 | CanonicalForm MLo= power (y, m); |
---|
| 2237 | CanonicalForm MHi= power (y, degree (M) - m); |
---|
| 2238 | CanonicalForm F0= mod (F, MLo); |
---|
| 2239 | CanonicalForm F1= div (F, MLo); |
---|
| 2240 | CanonicalForm G0= mod (G, MLo); |
---|
| 2241 | CanonicalForm G1= div (G, MLo); |
---|
| 2242 | CanonicalForm F0G1= mulMod2 (F0, G1, MHi); |
---|
| 2243 | CanonicalForm F1G0= mulMod2 (F1, G0, MHi); |
---|
| 2244 | CanonicalForm F0G0= mulMod2 (F0, G0, M); |
---|
| 2245 | return F0G0 + MLo*(F0G1 + F1G0); |
---|
| 2246 | } |
---|
| 2247 | else |
---|
| 2248 | { |
---|
| 2249 | m= (int) ceil (tmax (degF, degG)/2.0); |
---|
| 2250 | CanonicalForm yToM= power (y, m); |
---|
| 2251 | CanonicalForm F0= mod (F, yToM); |
---|
| 2252 | CanonicalForm F1= div (F, yToM); |
---|
| 2253 | CanonicalForm G0= mod (G, yToM); |
---|
| 2254 | CanonicalForm G1= div (G, yToM); |
---|
| 2255 | CanonicalForm H00= mulMod2 (F0, G0, M); |
---|
| 2256 | CanonicalForm H11= mulMod2 (F1, G1, M); |
---|
| 2257 | CanonicalForm H01= mulMod2 (F0 + F1, G0 + G1, M); |
---|
| 2258 | return H11*yToM*yToM + (H01 - H11 - H00)*yToM + H00; |
---|
[806c18] | 2259 | } |
---|
[ad3c3ff] | 2260 | DEBOUTLN (cerr, "fatal end in mulMod2"); |
---|
| 2261 | } |
---|
| 2262 | |
---|
[806c18] | 2263 | CanonicalForm mulMod (const CanonicalForm& A, const CanonicalForm& B, |
---|
[ad3c3ff] | 2264 | const CFList& MOD) |
---|
| 2265 | { |
---|
| 2266 | if (A.isZero() || B.isZero()) |
---|
| 2267 | return 0; |
---|
| 2268 | |
---|
| 2269 | if (MOD.length() == 1) |
---|
| 2270 | return mulMod2 (A, B, MOD.getLast()); |
---|
| 2271 | |
---|
| 2272 | CanonicalForm M= MOD.getLast(); |
---|
| 2273 | CanonicalForm F= mod (A, M); |
---|
| 2274 | CanonicalForm G= mod (B, M); |
---|
| 2275 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
---|
| 2276 | return F*G; |
---|
| 2277 | Variable y= M.mvar(); |
---|
| 2278 | int degF= degree (F, y); |
---|
| 2279 | int degG= degree (G, y); |
---|
| 2280 | |
---|
[806c18] | 2281 | if ((degF <= 1 && F.level() <= M.level()) && |
---|
[ad3c3ff] | 2282 | (degG <= 1 && G.level() <= M.level())) |
---|
| 2283 | { |
---|
| 2284 | CFList buf= MOD; |
---|
| 2285 | buf.removeLast(); |
---|
| 2286 | if (degF == 1 && degG == 1) |
---|
| 2287 | { |
---|
| 2288 | CanonicalForm F0= mod (F, y); |
---|
| 2289 | CanonicalForm F1= div (F, y); |
---|
| 2290 | CanonicalForm G0= mod (G, y); |
---|
| 2291 | CanonicalForm G1= div (G, y); |
---|
| 2292 | if (degree (M) > 2) |
---|
| 2293 | { |
---|
| 2294 | CanonicalForm H00= mulMod (F0, G0, buf); |
---|
| 2295 | CanonicalForm H11= mulMod (F1, G1, buf); |
---|
| 2296 | CanonicalForm H01= mulMod (F0 + F1, G0 + G1, buf); |
---|
| 2297 | return H11*y*y + (H01 - H00 - H11)*y + H00; |
---|
| 2298 | } |
---|
| 2299 | else //here degree (M) == 2 |
---|
| 2300 | { |
---|
| 2301 | buf.append (y); |
---|
| 2302 | CanonicalForm F0G1= mulMod (F0, G1, buf); |
---|
| 2303 | CanonicalForm F1G0= mulMod (F1, G0, buf); |
---|
| 2304 | CanonicalForm F0G0= mulMod (F0, G0, MOD); |
---|
| 2305 | CanonicalForm result= F0G0 + y*(F0G1 + F1G0); |
---|
| 2306 | return result; |
---|
| 2307 | } |
---|
| 2308 | } |
---|
| 2309 | else if (degF == 1 && degG == 0) |
---|
| 2310 | return mulMod (div (F, y), G, buf)*y + mulMod (mod (F, y), G, buf); |
---|
| 2311 | else if (degF == 0 && degG == 1) |
---|
| 2312 | return mulMod (div (G, y), F, buf)*y + mulMod (mod (G, y), F, buf); |
---|
| 2313 | else |
---|
| 2314 | return mulMod (F, G, buf); |
---|
| 2315 | } |
---|
| 2316 | int m= (int) ceil (degree (M)/2.0); |
---|
| 2317 | if (degF >= m || degG >= m) |
---|
| 2318 | { |
---|
| 2319 | CanonicalForm MLo= power (y, m); |
---|
| 2320 | CanonicalForm MHi= power (y, degree (M) - m); |
---|
| 2321 | CanonicalForm F0= mod (F, MLo); |
---|
| 2322 | CanonicalForm F1= div (F, MLo); |
---|
| 2323 | CanonicalForm G0= mod (G, MLo); |
---|
| 2324 | CanonicalForm G1= div (G, MLo); |
---|
| 2325 | CFList buf= MOD; |
---|
| 2326 | buf.removeLast(); |
---|
| 2327 | buf.append (MHi); |
---|
| 2328 | CanonicalForm F0G1= mulMod (F0, G1, buf); |
---|
| 2329 | CanonicalForm F1G0= mulMod (F1, G0, buf); |
---|
| 2330 | CanonicalForm F0G0= mulMod (F0, G0, MOD); |
---|
| 2331 | return F0G0 + MLo*(F0G1 + F1G0); |
---|
| 2332 | } |
---|
| 2333 | else |
---|
| 2334 | { |
---|
| 2335 | m= (int) ceil (tmax (degF, degG)/2.0); |
---|
| 2336 | CanonicalForm yToM= power (y, m); |
---|
| 2337 | CanonicalForm F0= mod (F, yToM); |
---|
| 2338 | CanonicalForm F1= div (F, yToM); |
---|
| 2339 | CanonicalForm G0= mod (G, yToM); |
---|
| 2340 | CanonicalForm G1= div (G, yToM); |
---|
| 2341 | CanonicalForm H00= mulMod (F0, G0, MOD); |
---|
| 2342 | CanonicalForm H11= mulMod (F1, G1, MOD); |
---|
| 2343 | CanonicalForm H01= mulMod (F0 + F1, G0 + G1, MOD); |
---|
| 2344 | return H11*yToM*yToM + (H01 - H11 - H00)*yToM + H00; |
---|
[806c18] | 2345 | } |
---|
[ad3c3ff] | 2346 | DEBOUTLN (cerr, "fatal end in mulMod"); |
---|
| 2347 | } |
---|
| 2348 | |
---|
[806c18] | 2349 | CanonicalForm prodMod (const CFList& L, const CanonicalForm& M) |
---|
[ad3c3ff] | 2350 | { |
---|
| 2351 | if (L.isEmpty()) |
---|
| 2352 | return 1; |
---|
| 2353 | int l= L.length(); |
---|
| 2354 | if (l == 1) |
---|
| 2355 | return mod (L.getFirst(), M); |
---|
| 2356 | else if (l == 2) { |
---|
| 2357 | CanonicalForm result= mulMod2 (L.getFirst(), L.getLast(), M); |
---|
| 2358 | return result; |
---|
| 2359 | } |
---|
| 2360 | else |
---|
| 2361 | { |
---|
| 2362 | l /= 2; |
---|
| 2363 | CFList tmp1, tmp2; |
---|
| 2364 | CFListIterator i= L; |
---|
| 2365 | CanonicalForm buf1, buf2; |
---|
[806c18] | 2366 | for (int j= 1; j <= l; j++, i++) |
---|
[ad3c3ff] | 2367 | tmp1.append (i.getItem()); |
---|
| 2368 | tmp2= Difference (L, tmp1); |
---|
| 2369 | buf1= prodMod (tmp1, M); |
---|
| 2370 | buf2= prodMod (tmp2, M); |
---|
| 2371 | CanonicalForm result= mulMod2 (buf1, buf2, M); |
---|
| 2372 | return result; |
---|
[806c18] | 2373 | } |
---|
[ad3c3ff] | 2374 | } |
---|
| 2375 | |
---|
[806c18] | 2376 | CanonicalForm prodMod (const CFList& L, const CFList& M) |
---|
[ad3c3ff] | 2377 | { |
---|
| 2378 | if (L.isEmpty()) |
---|
| 2379 | return 1; |
---|
| 2380 | else if (L.length() == 1) |
---|
| 2381 | return L.getFirst(); |
---|
| 2382 | else if (L.length() == 2) |
---|
| 2383 | return mulMod (L.getFirst(), L.getLast(), M); |
---|
| 2384 | else |
---|
| 2385 | { |
---|
| 2386 | int l= L.length()/2; |
---|
| 2387 | CFListIterator i= L; |
---|
| 2388 | CFList tmp1, tmp2; |
---|
| 2389 | CanonicalForm buf1, buf2; |
---|
[806c18] | 2390 | for (int j= 1; j <= l; j++, i++) |
---|
[ad3c3ff] | 2391 | tmp1.append (i.getItem()); |
---|
| 2392 | tmp2= Difference (L, tmp1); |
---|
| 2393 | buf1= prodMod (tmp1, M); |
---|
| 2394 | buf2= prodMod (tmp2, M); |
---|
| 2395 | return mulMod (buf1, buf2, M); |
---|
| 2396 | } |
---|
| 2397 | } |
---|
| 2398 | |
---|
[c9b1d66] | 2399 | |
---|
| 2400 | CanonicalForm reverse (const CanonicalForm& F, int d) |
---|
| 2401 | { |
---|
| 2402 | if (d == 0) |
---|
| 2403 | return F; |
---|
| 2404 | CanonicalForm A= F; |
---|
[dd2a9b3] | 2405 | Variable y= Variable (2); |
---|
[c9b1d66] | 2406 | Variable x= Variable (1); |
---|
[dd2a9b3] | 2407 | if (degree (A, x) > 0) |
---|
| 2408 | { |
---|
| 2409 | A= swapvar (A, x, y); |
---|
| 2410 | CanonicalForm result= 0; |
---|
| 2411 | CFIterator i= A; |
---|
| 2412 | while (d - i.exp() < 0) |
---|
| 2413 | i++; |
---|
[c9b1d66] | 2414 | |
---|
[dd2a9b3] | 2415 | for (; i.hasTerms() && (d - i.exp() >= 0); i++) |
---|
| 2416 | result += swapvar (i.coeff(),x,y)*power (x, d - i.exp()); |
---|
| 2417 | return result; |
---|
| 2418 | } |
---|
| 2419 | else |
---|
| 2420 | return A*power (x, d); |
---|
[c9b1d66] | 2421 | } |
---|
| 2422 | |
---|
| 2423 | CanonicalForm |
---|
| 2424 | newtonInverse (const CanonicalForm& F, const int n, const CanonicalForm& M) |
---|
| 2425 | { |
---|
| 2426 | int l= ilog2(n); |
---|
| 2427 | |
---|
| 2428 | CanonicalForm g= mod (F, M)[0] [0]; |
---|
| 2429 | |
---|
| 2430 | ASSERT (!g.isZero(), "expected a unit"); |
---|
| 2431 | |
---|
| 2432 | Variable alpha; |
---|
| 2433 | |
---|
| 2434 | if (!g.isOne()) |
---|
| 2435 | g = 1/g; |
---|
| 2436 | Variable x= Variable (1); |
---|
| 2437 | CanonicalForm result; |
---|
| 2438 | int exp= 0; |
---|
| 2439 | if (n & 1) |
---|
| 2440 | { |
---|
| 2441 | result= g; |
---|
| 2442 | exp= 1; |
---|
| 2443 | } |
---|
| 2444 | CanonicalForm h; |
---|
| 2445 | |
---|
| 2446 | for (int i= 1; i <= l; i++) |
---|
| 2447 | { |
---|
| 2448 | h= mulMod2 (g, mod (F, power (x, (1 << i))), M); |
---|
| 2449 | h= mod (h, power (x, (1 << i)) - 1); |
---|
| 2450 | h= div (h, power (x, (1 << (i - 1)))); |
---|
| 2451 | h= mod (h, M); |
---|
| 2452 | g -= power (x, (1 << (i - 1)))* |
---|
| 2453 | mod (mulMod2 (g, h, M), power (x, (1 << (i - 1)))); |
---|
| 2454 | |
---|
| 2455 | if (n & (1 << i)) |
---|
| 2456 | { |
---|
| 2457 | if (exp) |
---|
| 2458 | { |
---|
| 2459 | h= mulMod2 (result, mod (F, power (x, exp + (1 << i))), M); |
---|
| 2460 | h= mod (h, power (x, exp + (1 << i)) - 1); |
---|
| 2461 | h= div (h, power (x, exp)); |
---|
| 2462 | h= mod (h, M); |
---|
| 2463 | result -= power(x, exp)*mod (mulMod2 (g, h, M), |
---|
| 2464 | power (x, (1 << i))); |
---|
| 2465 | exp += (1 << i); |
---|
| 2466 | } |
---|
| 2467 | else |
---|
| 2468 | { |
---|
| 2469 | exp= (1 << i); |
---|
| 2470 | result= g; |
---|
| 2471 | } |
---|
| 2472 | } |
---|
| 2473 | } |
---|
| 2474 | |
---|
| 2475 | return result; |
---|
| 2476 | } |
---|
| 2477 | |
---|
| 2478 | CanonicalForm |
---|
| 2479 | newtonDiv (const CanonicalForm& F, const CanonicalForm& G, const CanonicalForm& |
---|
| 2480 | M) |
---|
| 2481 | { |
---|
| 2482 | ASSERT (getCharacteristic() > 0, "positive characteristic expected"); |
---|
| 2483 | ASSERT (CFFactory::gettype() != GaloisFieldDomain, "no GF expected"); |
---|
| 2484 | |
---|
| 2485 | CanonicalForm A= mod (F, M); |
---|
| 2486 | CanonicalForm B= mod (G, M); |
---|
| 2487 | |
---|
| 2488 | Variable x= Variable (1); |
---|
| 2489 | int degA= degree (A, x); |
---|
| 2490 | int degB= degree (B, x); |
---|
| 2491 | int m= degA - degB; |
---|
| 2492 | if (m < 0) |
---|
| 2493 | return 0; |
---|
| 2494 | |
---|
[3426de2] | 2495 | Variable v; |
---|
[c9b1d66] | 2496 | CanonicalForm Q; |
---|
[fdae2d] | 2497 | if (degB < 1 || CFFactory::gettype() == GaloisFieldDomain) |
---|
[c9b1d66] | 2498 | { |
---|
| 2499 | CanonicalForm R; |
---|
| 2500 | divrem2 (A, B, Q, R, M); |
---|
| 2501 | } |
---|
| 2502 | else |
---|
| 2503 | { |
---|
[3426de2] | 2504 | if (hasFirstAlgVar (A, v) || hasFirstAlgVar (B, v)) |
---|
| 2505 | { |
---|
| 2506 | CanonicalForm R= reverse (A, degA); |
---|
| 2507 | CanonicalForm revB= reverse (B, degB); |
---|
| 2508 | revB= newtonInverse (revB, m + 1, M); |
---|
| 2509 | Q= mulMod2 (R, revB, M); |
---|
| 2510 | Q= mod (Q, power (x, m + 1)); |
---|
| 2511 | Q= reverse (Q, m); |
---|
| 2512 | } |
---|
| 2513 | else |
---|
| 2514 | { |
---|
| 2515 | zz_pX mipo= convertFacCF2NTLzzpX (M); |
---|
| 2516 | Variable y= Variable (2); |
---|
| 2517 | zz_pEX NTLA, NTLB; |
---|
| 2518 | NTLA= convertFacCF2NTLzz_pEX (swapvar (A, x, y), mipo); |
---|
| 2519 | NTLB= convertFacCF2NTLzz_pEX (swapvar (B, x, y), mipo); |
---|
| 2520 | div (NTLA, NTLA, NTLB); |
---|
| 2521 | Q= convertNTLzz_pEX2CF (NTLA, x, y); |
---|
| 2522 | } |
---|
[c9b1d66] | 2523 | } |
---|
| 2524 | |
---|
| 2525 | return Q; |
---|
| 2526 | } |
---|
| 2527 | |
---|
| 2528 | void |
---|
| 2529 | newtonDivrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
| 2530 | CanonicalForm& R, const CanonicalForm& M) |
---|
| 2531 | { |
---|
| 2532 | CanonicalForm A= mod (F, M); |
---|
| 2533 | CanonicalForm B= mod (G, M); |
---|
| 2534 | Variable x= Variable (1); |
---|
| 2535 | int degA= degree (A, x); |
---|
| 2536 | int degB= degree (B, x); |
---|
| 2537 | int m= degA - degB; |
---|
| 2538 | |
---|
| 2539 | if (m < 0) |
---|
| 2540 | { |
---|
| 2541 | R= A; |
---|
| 2542 | Q= 0; |
---|
| 2543 | return; |
---|
| 2544 | } |
---|
| 2545 | |
---|
[3426de2] | 2546 | Variable v; |
---|
[dd2a9b3] | 2547 | if (degB <= 1 || CFFactory::gettype() == GaloisFieldDomain) |
---|
[c9b1d66] | 2548 | { |
---|
| 2549 | divrem2 (A, B, Q, R, M); |
---|
| 2550 | } |
---|
| 2551 | else |
---|
| 2552 | { |
---|
[3426de2] | 2553 | if (hasFirstAlgVar (A, v) || hasFirstAlgVar (B, v)) |
---|
| 2554 | { |
---|
| 2555 | R= reverse (A, degA); |
---|
[c9b1d66] | 2556 | |
---|
[3426de2] | 2557 | CanonicalForm revB= reverse (B, degB); |
---|
| 2558 | revB= newtonInverse (revB, m + 1, M); |
---|
| 2559 | Q= mulMod2 (R, revB, M); |
---|
[c9b1d66] | 2560 | |
---|
[3426de2] | 2561 | Q= mod (Q, power (x, m + 1)); |
---|
| 2562 | Q= reverse (Q, m); |
---|
[c9b1d66] | 2563 | |
---|
[3426de2] | 2564 | R= A - mulMod2 (Q, B, M); |
---|
| 2565 | } |
---|
| 2566 | else |
---|
| 2567 | { |
---|
| 2568 | zz_pX mipo= convertFacCF2NTLzzpX (M); |
---|
| 2569 | Variable y= Variable (2); |
---|
| 2570 | zz_pEX NTLA, NTLB; |
---|
| 2571 | NTLA= convertFacCF2NTLzz_pEX (swapvar (A, x, y), mipo); |
---|
| 2572 | NTLB= convertFacCF2NTLzz_pEX (swapvar (B, x, y), mipo); |
---|
| 2573 | zz_pEX NTLQ, NTLR; |
---|
| 2574 | DivRem (NTLQ, NTLR, NTLA, NTLB); |
---|
| 2575 | Q= convertNTLzz_pEX2CF (NTLQ, x, y); |
---|
| 2576 | R= convertNTLzz_pEX2CF (NTLR, x, y); |
---|
| 2577 | } |
---|
[c9b1d66] | 2578 | } |
---|
| 2579 | } |
---|
| 2580 | |
---|
[ad3c3ff] | 2581 | static inline |
---|
[806c18] | 2582 | CFList split (const CanonicalForm& F, const int m, const Variable& x) |
---|
[ad3c3ff] | 2583 | { |
---|
| 2584 | CanonicalForm A= F; |
---|
| 2585 | CanonicalForm buf= 0; |
---|
| 2586 | bool swap= false; |
---|
| 2587 | if (degree (A, x) <= 0) |
---|
| 2588 | return CFList(A); |
---|
| 2589 | else if (x.level() != A.level()) |
---|
| 2590 | { |
---|
| 2591 | swap= true; |
---|
| 2592 | A= swapvar (A, x, A.mvar()); |
---|
| 2593 | } |
---|
| 2594 | |
---|
| 2595 | int j= (int) floor ((double) degree (A)/ m); |
---|
[806c18] | 2596 | CFList result; |
---|
[ad3c3ff] | 2597 | CFIterator i= A; |
---|
| 2598 | for (; j >= 0; j--) |
---|
| 2599 | { |
---|
[806c18] | 2600 | while (i.hasTerms() && i.exp() - j*m >= 0) |
---|
[ad3c3ff] | 2601 | { |
---|
| 2602 | if (swap) |
---|
| 2603 | buf += i.coeff()*power (A.mvar(), i.exp() - j*m); |
---|
| 2604 | else |
---|
| 2605 | buf += i.coeff()*power (x, i.exp() - j*m); |
---|
| 2606 | i++; |
---|
| 2607 | } |
---|
| 2608 | if (swap) |
---|
| 2609 | result.append (swapvar (buf, x, F.mvar())); |
---|
| 2610 | else |
---|
[806c18] | 2611 | result.append (buf); |
---|
[ad3c3ff] | 2612 | buf= 0; |
---|
| 2613 | } |
---|
[806c18] | 2614 | return result; |
---|
[ad3c3ff] | 2615 | } |
---|
| 2616 | |
---|
| 2617 | static inline |
---|
[806c18] | 2618 | void divrem32 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
[ad3c3ff] | 2619 | CanonicalForm& R, const CFList& M); |
---|
| 2620 | |
---|
[806c18] | 2621 | static inline |
---|
| 2622 | void divrem21 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
[ad3c3ff] | 2623 | CanonicalForm& R, const CFList& M) |
---|
| 2624 | { |
---|
| 2625 | CanonicalForm A= mod (F, M); |
---|
| 2626 | CanonicalForm B= mod (G, M); |
---|
| 2627 | Variable x= Variable (1); |
---|
| 2628 | int degB= degree (B, x); |
---|
| 2629 | int degA= degree (A, x); |
---|
| 2630 | if (degA < degB) |
---|
| 2631 | { |
---|
| 2632 | Q= 0; |
---|
| 2633 | R= A; |
---|
| 2634 | return; |
---|
| 2635 | } |
---|
| 2636 | ASSERT (2*degB > degA, "expected degree (F, 1) < 2*degree (G, 1)"); |
---|
| 2637 | if (degB < 1) |
---|
| 2638 | { |
---|
| 2639 | divrem (A, B, Q, R); |
---|
| 2640 | Q= mod (Q, M); |
---|
| 2641 | R= mod (R, M); |
---|
| 2642 | return; |
---|
| 2643 | } |
---|
[806c18] | 2644 | |
---|
| 2645 | int m= (int) ceil ((double) (degB + 1)/2.0) + 1; |
---|
[ad3c3ff] | 2646 | CFList splitA= split (A, m, x); |
---|
| 2647 | if (splitA.length() == 3) |
---|
| 2648 | splitA.insert (0); |
---|
| 2649 | if (splitA.length() == 2) |
---|
| 2650 | { |
---|
| 2651 | splitA.insert (0); |
---|
| 2652 | splitA.insert (0); |
---|
[806c18] | 2653 | } |
---|
[ad3c3ff] | 2654 | if (splitA.length() == 1) |
---|
| 2655 | { |
---|
| 2656 | splitA.insert (0); |
---|
| 2657 | splitA.insert (0); |
---|
| 2658 | splitA.insert (0); |
---|
| 2659 | } |
---|
| 2660 | |
---|
| 2661 | CanonicalForm xToM= power (x, m); |
---|
| 2662 | |
---|
| 2663 | CFListIterator i= splitA; |
---|
| 2664 | CanonicalForm H= i.getItem(); |
---|
| 2665 | i++; |
---|
| 2666 | H *= xToM; |
---|
| 2667 | H += i.getItem(); |
---|
| 2668 | i++; |
---|
| 2669 | H *= xToM; |
---|
| 2670 | H += i.getItem(); |
---|
| 2671 | i++; |
---|
| 2672 | |
---|
| 2673 | divrem32 (H, B, Q, R, M); |
---|
| 2674 | |
---|
| 2675 | CFList splitR= split (R, m, x); |
---|
| 2676 | if (splitR.length() == 1) |
---|
| 2677 | splitR.insert (0); |
---|
| 2678 | |
---|
| 2679 | H= splitR.getFirst(); |
---|
| 2680 | H *= xToM; |
---|
| 2681 | H += splitR.getLast(); |
---|
| 2682 | H *= xToM; |
---|
| 2683 | H += i.getItem(); |
---|
| 2684 | |
---|
| 2685 | CanonicalForm bufQ; |
---|
| 2686 | divrem32 (H, B, bufQ, R, M); |
---|
| 2687 | |
---|
| 2688 | Q *= xToM; |
---|
| 2689 | Q += bufQ; |
---|
| 2690 | return; |
---|
| 2691 | } |
---|
| 2692 | |
---|
| 2693 | static inline |
---|
[806c18] | 2694 | void divrem32 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
| 2695 | CanonicalForm& R, const CFList& M) |
---|
[ad3c3ff] | 2696 | { |
---|
| 2697 | CanonicalForm A= mod (F, M); |
---|
| 2698 | CanonicalForm B= mod (G, M); |
---|
| 2699 | Variable x= Variable (1); |
---|
| 2700 | int degB= degree (B, x); |
---|
| 2701 | int degA= degree (A, x); |
---|
[806c18] | 2702 | if (degA < degB) |
---|
[ad3c3ff] | 2703 | { |
---|
| 2704 | Q= 0; |
---|
| 2705 | R= A; |
---|
| 2706 | return; |
---|
| 2707 | } |
---|
| 2708 | ASSERT (3*(degB/2) > degA, "expected degree (F, 1) < 3*(degree (G, 1)/2)"); |
---|
| 2709 | if (degB < 1) |
---|
| 2710 | { |
---|
| 2711 | divrem (A, B, Q, R); |
---|
| 2712 | Q= mod (Q, M); |
---|
| 2713 | R= mod (R, M); |
---|
| 2714 | return; |
---|
| 2715 | } |
---|
| 2716 | int m= (int) ceil ((double) (degB + 1)/ 2.0); |
---|
| 2717 | |
---|
| 2718 | CFList splitA= split (A, m, x); |
---|
| 2719 | CFList splitB= split (B, m, x); |
---|
| 2720 | |
---|
| 2721 | if (splitA.length() == 2) |
---|
| 2722 | { |
---|
| 2723 | splitA.insert (0); |
---|
| 2724 | } |
---|
| 2725 | if (splitA.length() == 1) |
---|
| 2726 | { |
---|
| 2727 | splitA.insert (0); |
---|
| 2728 | splitA.insert (0); |
---|
| 2729 | } |
---|
| 2730 | CanonicalForm xToM= power (x, m); |
---|
| 2731 | |
---|
| 2732 | CanonicalForm H; |
---|
| 2733 | CFListIterator i= splitA; |
---|
| 2734 | i++; |
---|
| 2735 | |
---|
| 2736 | if (degree (splitA.getFirst(), x) < degree (splitB.getFirst(), x)) |
---|
| 2737 | { |
---|
| 2738 | H= splitA.getFirst()*xToM + i.getItem(); |
---|
| 2739 | divrem21 (H, splitB.getFirst(), Q, R, M); |
---|
| 2740 | } |
---|
[806c18] | 2741 | else |
---|
[ad3c3ff] | 2742 | { |
---|
[806c18] | 2743 | R= splitA.getFirst()*xToM + i.getItem() + splitB.getFirst() - |
---|
[ad3c3ff] | 2744 | splitB.getFirst()*xToM; |
---|
| 2745 | Q= xToM - 1; |
---|
| 2746 | } |
---|
| 2747 | |
---|
| 2748 | H= mulMod (Q, splitB.getLast(), M); |
---|
| 2749 | |
---|
| 2750 | R= R*xToM + splitA.getLast() - H; |
---|
| 2751 | |
---|
| 2752 | while (degree (R, x) >= degB) |
---|
| 2753 | { |
---|
| 2754 | xToM= power (x, degree (R, x) - degB); |
---|
| 2755 | Q += LC (R, x)*xToM; |
---|
| 2756 | R -= mulMod (LC (R, x), B, M)*xToM; |
---|
| 2757 | Q= mod (Q, M); |
---|
| 2758 | R= mod (R, M); |
---|
| 2759 | } |
---|
| 2760 | |
---|
| 2761 | return; |
---|
| 2762 | } |
---|
| 2763 | |
---|
| 2764 | void divrem2 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
[806c18] | 2765 | CanonicalForm& R, const CanonicalForm& M) |
---|
[ad3c3ff] | 2766 | { |
---|
| 2767 | CanonicalForm A= mod (F, M); |
---|
| 2768 | CanonicalForm B= mod (G, M); |
---|
[e368746] | 2769 | |
---|
| 2770 | if (B.inCoeffDomain()) |
---|
| 2771 | { |
---|
| 2772 | divrem (A, B, Q, R); |
---|
| 2773 | return; |
---|
| 2774 | } |
---|
| 2775 | if (A.inCoeffDomain() && !B.inCoeffDomain()) |
---|
| 2776 | { |
---|
| 2777 | Q= 0; |
---|
| 2778 | R= A; |
---|
| 2779 | return; |
---|
| 2780 | } |
---|
| 2781 | |
---|
| 2782 | if (B.level() < A.level()) |
---|
| 2783 | { |
---|
| 2784 | divrem (A, B, Q, R); |
---|
| 2785 | return; |
---|
| 2786 | } |
---|
| 2787 | if (A.level() > B.level()) |
---|
| 2788 | { |
---|
| 2789 | R= A; |
---|
| 2790 | Q= 0; |
---|
| 2791 | return; |
---|
| 2792 | } |
---|
| 2793 | if (B.level() == 1 && B.isUnivariate()) |
---|
| 2794 | { |
---|
| 2795 | divrem (A, B, Q, R); |
---|
| 2796 | return; |
---|
| 2797 | } |
---|
| 2798 | if (!(B.level() == 1 && B.isUnivariate()) && (A.level() == 1 && A.isUnivariate())) |
---|
| 2799 | { |
---|
| 2800 | Q= 0; |
---|
| 2801 | R= A; |
---|
| 2802 | return; |
---|
| 2803 | } |
---|
| 2804 | |
---|
[ad3c3ff] | 2805 | Variable x= Variable (1); |
---|
| 2806 | int degB= degree (B, x); |
---|
[806c18] | 2807 | if (degB > degree (A, x)) |
---|
[ad3c3ff] | 2808 | { |
---|
| 2809 | Q= 0; |
---|
| 2810 | R= A; |
---|
| 2811 | return; |
---|
| 2812 | } |
---|
| 2813 | |
---|
| 2814 | CFList splitA= split (A, degB, x); |
---|
| 2815 | |
---|
| 2816 | CanonicalForm xToDegB= power (x, degB); |
---|
| 2817 | CanonicalForm H, bufQ; |
---|
| 2818 | Q= 0; |
---|
| 2819 | CFListIterator i= splitA; |
---|
| 2820 | H= i.getItem()*xToDegB; |
---|
| 2821 | i++; |
---|
| 2822 | H += i.getItem(); |
---|
| 2823 | CFList buf; |
---|
[806c18] | 2824 | while (i.hasItem()) |
---|
[ad3c3ff] | 2825 | { |
---|
| 2826 | buf= CFList (M); |
---|
| 2827 | divrem21 (H, B, bufQ, R, buf); |
---|
| 2828 | i++; |
---|
| 2829 | if (i.hasItem()) |
---|
| 2830 | H= R*xToDegB + i.getItem(); |
---|
| 2831 | Q *= xToDegB; |
---|
[806c18] | 2832 | Q += bufQ; |
---|
[ad3c3ff] | 2833 | } |
---|
| 2834 | return; |
---|
| 2835 | } |
---|
| 2836 | |
---|
| 2837 | void divrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
| 2838 | CanonicalForm& R, const CFList& MOD) |
---|
| 2839 | { |
---|
| 2840 | CanonicalForm A= mod (F, MOD); |
---|
| 2841 | CanonicalForm B= mod (G, MOD); |
---|
| 2842 | Variable x= Variable (1); |
---|
| 2843 | int degB= degree (B, x); |
---|
[806c18] | 2844 | if (degB > degree (A, x)) |
---|
[ad3c3ff] | 2845 | { |
---|
| 2846 | Q= 0; |
---|
| 2847 | R= A; |
---|
| 2848 | return; |
---|
| 2849 | } |
---|
| 2850 | |
---|
[d80a1a] | 2851 | if (degB <= 0) |
---|
[ad3c3ff] | 2852 | { |
---|
| 2853 | divrem (A, B, Q, R); |
---|
| 2854 | Q= mod (Q, MOD); |
---|
| 2855 | R= mod (R, MOD); |
---|
| 2856 | return; |
---|
| 2857 | } |
---|
| 2858 | CFList splitA= split (A, degB, x); |
---|
| 2859 | |
---|
| 2860 | CanonicalForm xToDegB= power (x, degB); |
---|
| 2861 | CanonicalForm H, bufQ; |
---|
| 2862 | Q= 0; |
---|
| 2863 | CFListIterator i= splitA; |
---|
| 2864 | H= i.getItem()*xToDegB; |
---|
| 2865 | i++; |
---|
| 2866 | H += i.getItem(); |
---|
[806c18] | 2867 | while (i.hasItem()) |
---|
[ad3c3ff] | 2868 | { |
---|
| 2869 | divrem21 (H, B, bufQ, R, MOD); |
---|
| 2870 | i++; |
---|
| 2871 | if (i.hasItem()) |
---|
| 2872 | H= R*xToDegB + i.getItem(); |
---|
| 2873 | Q *= xToDegB; |
---|
[806c18] | 2874 | Q += bufQ; |
---|
[ad3c3ff] | 2875 | } |
---|
| 2876 | return; |
---|
| 2877 | } |
---|
| 2878 | |
---|
[806c18] | 2879 | void sortList (CFList& list, const Variable& x) |
---|
| 2880 | { |
---|
[ad3c3ff] | 2881 | int l= 1; |
---|
| 2882 | int k= 1; |
---|
| 2883 | CanonicalForm buf; |
---|
| 2884 | CFListIterator m; |
---|
[806c18] | 2885 | for (CFListIterator i= list; l <= list.length(); i++, l++) |
---|
[ad3c3ff] | 2886 | { |
---|
[806c18] | 2887 | for (CFListIterator j= list; k <= list.length() - l; k++) |
---|
[ad3c3ff] | 2888 | { |
---|
| 2889 | m= j; |
---|
| 2890 | m++; |
---|
[806c18] | 2891 | if (degree (j.getItem(), x) > degree (m.getItem(), x)) |
---|
[ad3c3ff] | 2892 | { |
---|
| 2893 | buf= m.getItem(); |
---|
| 2894 | m.getItem()= j.getItem(); |
---|
| 2895 | j.getItem()= buf; |
---|
| 2896 | j++; |
---|
| 2897 | j.getItem()= m.getItem(); |
---|
[806c18] | 2898 | } |
---|
[ad3c3ff] | 2899 | else |
---|
| 2900 | j++; |
---|
| 2901 | } |
---|
| 2902 | k= 1; |
---|
| 2903 | } |
---|
| 2904 | } |
---|
| 2905 | |
---|
| 2906 | static inline |
---|
[806c18] | 2907 | CFList diophantine (const CanonicalForm& F, const CFList& factors) |
---|
[ad3c3ff] | 2908 | { |
---|
[4a05ed] | 2909 | if (getCharacteristic() == 0) |
---|
| 2910 | { |
---|
| 2911 | Variable v; |
---|
| 2912 | bool hasAlgVar= hasFirstAlgVar (F, v); |
---|
| 2913 | for (CFListIterator i= factors; i.hasItem() && !hasAlgVar; i++) |
---|
| 2914 | hasAlgVar= hasFirstAlgVar (i.getItem(), v); |
---|
| 2915 | if (hasAlgVar) |
---|
| 2916 | { |
---|
| 2917 | CFList result= modularDiophant (F, factors, getMipo (v)); |
---|
| 2918 | return result; |
---|
| 2919 | } |
---|
| 2920 | } |
---|
| 2921 | |
---|
[ad3c3ff] | 2922 | CanonicalForm buf1, buf2, buf3, S, T; |
---|
| 2923 | CFListIterator i= factors; |
---|
| 2924 | CFList result; |
---|
| 2925 | if (i.hasItem()) |
---|
| 2926 | i++; |
---|
[806c18] | 2927 | buf1= F/factors.getFirst(); |
---|
[ad3c3ff] | 2928 | buf2= divNTL (F, i.getItem()); |
---|
| 2929 | buf3= extgcd (buf1, buf2, S, T); |
---|
| 2930 | result.append (S); |
---|
| 2931 | result.append (T); |
---|
| 2932 | if (i.hasItem()) |
---|
| 2933 | i++; |
---|
| 2934 | for (; i.hasItem(); i++) |
---|
| 2935 | { |
---|
| 2936 | buf1= divNTL (F, i.getItem()); |
---|
| 2937 | buf3= extgcd (buf3, buf1, S, T); |
---|
| 2938 | CFListIterator k= factors; |
---|
| 2939 | for (CFListIterator j= result; j.hasItem(); j++, k++) |
---|
| 2940 | { |
---|
| 2941 | j.getItem()= mulNTL (j.getItem(), S); |
---|
| 2942 | j.getItem()= modNTL (j.getItem(), k.getItem()); |
---|
| 2943 | } |
---|
| 2944 | result.append (T); |
---|
| 2945 | } |
---|
| 2946 | return result; |
---|
| 2947 | } |
---|
| 2948 | |
---|
[806c18] | 2949 | void |
---|
| 2950 | henselStep12 (const CanonicalForm& F, const CFList& factors, |
---|
[ad3c3ff] | 2951 | CFArray& bufFactors, const CFList& diophant, CFMatrix& M, |
---|
| 2952 | CFArray& Pi, int j) |
---|
| 2953 | { |
---|
| 2954 | CanonicalForm E; |
---|
| 2955 | CanonicalForm xToJ= power (F.mvar(), j); |
---|
| 2956 | Variable x= F.mvar(); |
---|
| 2957 | // compute the error |
---|
| 2958 | if (j == 1) |
---|
[806c18] | 2959 | E= F[j]; |
---|
[ad3c3ff] | 2960 | else |
---|
| 2961 | { |
---|
[806c18] | 2962 | if (degree (Pi [factors.length() - 2], x) > 0) |
---|
[ad3c3ff] | 2963 | E= F[j] - Pi [factors.length() - 2] [j]; |
---|
| 2964 | else |
---|
[806c18] | 2965 | E= F[j]; |
---|
[ad3c3ff] | 2966 | } |
---|
| 2967 | |
---|
| 2968 | CFArray buf= CFArray (diophant.length()); |
---|
| 2969 | bufFactors[0]= mod (factors.getFirst(), power (F.mvar(), j + 1)); |
---|
| 2970 | int k= 0; |
---|
| 2971 | CanonicalForm remainder; |
---|
| 2972 | // actual lifting |
---|
[806c18] | 2973 | for (CFListIterator i= diophant; i.hasItem(); i++, k++) |
---|
[ad3c3ff] | 2974 | { |
---|
| 2975 | if (degree (bufFactors[k], x) > 0) |
---|
| 2976 | { |
---|
| 2977 | if (k > 0) |
---|
| 2978 | remainder= modNTL (E, bufFactors[k] [0]); |
---|
| 2979 | else |
---|
| 2980 | remainder= E; |
---|
| 2981 | } |
---|
| 2982 | else |
---|
| 2983 | remainder= modNTL (E, bufFactors[k]); |
---|
| 2984 | |
---|
| 2985 | buf[k]= mulNTL (i.getItem(), remainder); |
---|
| 2986 | if (degree (bufFactors[k], x) > 0) |
---|
| 2987 | buf[k]= modNTL (buf[k], bufFactors[k] [0]); |
---|
[806c18] | 2988 | else |
---|
| 2989 | buf[k]= modNTL (buf[k], bufFactors[k]); |
---|
[ad3c3ff] | 2990 | } |
---|
| 2991 | for (k= 1; k < factors.length(); k++) |
---|
| 2992 | bufFactors[k] += xToJ*buf[k]; |
---|
| 2993 | |
---|
| 2994 | // update Pi [0] |
---|
| 2995 | int degBuf0= degree (bufFactors[0], x); |
---|
| 2996 | int degBuf1= degree (bufFactors[1], x); |
---|
| 2997 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 2998 | M (j + 1, 1)= mulNTL (bufFactors[0] [j], bufFactors[1] [j]); |
---|
| 2999 | CanonicalForm uIZeroJ; |
---|
| 3000 | if (j == 1) |
---|
| 3001 | { |
---|
| 3002 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 3003 | uIZeroJ= mulNTL ((bufFactors[0] [0] + bufFactors[0] [j]), |
---|
| 3004 | (bufFactors[1] [0] + buf[1])) - M(1, 1) - M(j + 1, 1); |
---|
| 3005 | else if (degBuf0 > 0) |
---|
| 3006 | uIZeroJ= mulNTL (bufFactors[0] [j], bufFactors[1]); |
---|
| 3007 | else if (degBuf1 > 0) |
---|
| 3008 | uIZeroJ= mulNTL (bufFactors[0], buf[1]); |
---|
| 3009 | else |
---|
| 3010 | uIZeroJ= 0; |
---|
[806c18] | 3011 | Pi [0] += xToJ*uIZeroJ; |
---|
| 3012 | } |
---|
[ad3c3ff] | 3013 | else |
---|
| 3014 | { |
---|
| 3015 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 3016 | uIZeroJ= mulNTL ((bufFactors[0] [0] + bufFactors[0] [j]), |
---|
| 3017 | (bufFactors[1] [0] + buf[1])) - M(1, 1) - M(j + 1, 1); |
---|
| 3018 | else if (degBuf0 > 0) |
---|
| 3019 | uIZeroJ= mulNTL (bufFactors[0] [j], bufFactors[1]); |
---|
| 3020 | else if (degBuf1 > 0) |
---|
| 3021 | uIZeroJ= mulNTL (bufFactors[0], buf[1]); |
---|
| 3022 | else |
---|
| 3023 | uIZeroJ= 0; |
---|
[806c18] | 3024 | Pi [0] += xToJ*uIZeroJ; |
---|
[ad3c3ff] | 3025 | } |
---|
| 3026 | CFArray tmp= CFArray (factors.length() - 1); |
---|
| 3027 | for (k= 0; k < factors.length() - 1; k++) |
---|
| 3028 | tmp[k]= 0; |
---|
| 3029 | CFIterator one, two; |
---|
| 3030 | one= bufFactors [0]; |
---|
| 3031 | two= bufFactors [1]; |
---|
| 3032 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 3033 | { |
---|
| 3034 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
[806c18] | 3035 | { |
---|
[ad3c3ff] | 3036 | if (k != j - k + 1) |
---|
| 3037 | { |
---|
[e368746] | 3038 | if ((one.hasTerms() && one.exp() == j - k + 1) && (two.hasTerms() && two.exp() == j - k + 1)) |
---|
[806c18] | 3039 | { |
---|
| 3040 | tmp[0] += mulNTL ((bufFactors[0] [k] + one.coeff()), (bufFactors[1] [k] + |
---|
[ad3c3ff] | 3041 | two.coeff())) - M (k + 1, 1) - M (j - k + 2, 1); |
---|
[806c18] | 3042 | one++; |
---|
| 3043 | two++; |
---|
| 3044 | } |
---|
[e368746] | 3045 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
[806c18] | 3046 | { |
---|
| 3047 | tmp[0] += mulNTL ((bufFactors[0] [k] + one.coeff()), bufFactors[1] [k]) - |
---|
[ad3c3ff] | 3048 | M (k + 1, 1); |
---|
[806c18] | 3049 | one++; |
---|
| 3050 | } |
---|
[e368746] | 3051 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
[806c18] | 3052 | { |
---|
| 3053 | tmp[0] += mulNTL (bufFactors[0] [k], (bufFactors[1] [k] + two.coeff())) - |
---|
[ad3c3ff] | 3054 | M (k + 1, 1); |
---|
[806c18] | 3055 | two++; |
---|
| 3056 | } |
---|
[ad3c3ff] | 3057 | } |
---|
| 3058 | else |
---|
| 3059 | { |
---|
[806c18] | 3060 | tmp[0] += M (k + 1, 1); |
---|
[ad3c3ff] | 3061 | } |
---|
| 3062 | } |
---|
| 3063 | } |
---|
| 3064 | Pi [0] += tmp[0]*xToJ*F.mvar(); |
---|
| 3065 | |
---|
[806c18] | 3066 | // update Pi [l] |
---|
[ad3c3ff] | 3067 | int degPi, degBuf; |
---|
[806c18] | 3068 | for (int l= 1; l < factors.length() - 1; l++) |
---|
[ad3c3ff] | 3069 | { |
---|
| 3070 | degPi= degree (Pi [l - 1], x); |
---|
| 3071 | degBuf= degree (bufFactors[l + 1], x); |
---|
| 3072 | if (degPi > 0 && degBuf > 0) |
---|
[806c18] | 3073 | M (j + 1, l + 1)= mulNTL (Pi [l - 1] [j], bufFactors[l + 1] [j]); |
---|
[ad3c3ff] | 3074 | if (j == 1) |
---|
| 3075 | { |
---|
| 3076 | if (degPi > 0 && degBuf > 0) |
---|
| 3077 | Pi [l] += xToJ*(mulNTL (Pi [l - 1] [0] + Pi [l - 1] [j], |
---|
[806c18] | 3078 | bufFactors[l + 1] [0] + buf[l + 1]) - M (j + 1, l +1) - |
---|
[ad3c3ff] | 3079 | M (1, l + 1)); |
---|
| 3080 | else if (degPi > 0) |
---|
| 3081 | Pi [l] += xToJ*(mulNTL (Pi [l - 1] [j], bufFactors[l + 1])); |
---|
| 3082 | else if (degBuf > 0) |
---|
| 3083 | Pi [l] += xToJ*(mulNTL (Pi [l - 1], buf[l + 1])); |
---|
| 3084 | } |
---|
| 3085 | else |
---|
| 3086 | { |
---|
| 3087 | if (degPi > 0 && degBuf > 0) |
---|
| 3088 | { |
---|
| 3089 | uIZeroJ= mulNTL (uIZeroJ, bufFactors [l + 1] [0]); |
---|
[806c18] | 3090 | uIZeroJ += mulNTL (Pi [l - 1] [0], buf [l + 1]); |
---|
[ad3c3ff] | 3091 | } |
---|
| 3092 | else if (degPi > 0) |
---|
| 3093 | uIZeroJ= mulNTL (uIZeroJ, bufFactors [l + 1]); |
---|
| 3094 | else if (degBuf > 0) |
---|
| 3095 | { |
---|
| 3096 | uIZeroJ= mulNTL (uIZeroJ, bufFactors [l + 1] [0]); |
---|
| 3097 | uIZeroJ += mulNTL (Pi [l - 1], buf[l + 1]); |
---|
| 3098 | } |
---|
| 3099 | Pi[l] += xToJ*uIZeroJ; |
---|
| 3100 | } |
---|
| 3101 | one= bufFactors [l + 1]; |
---|
| 3102 | two= Pi [l - 1]; |
---|
[e368746] | 3103 | if (two.hasTerms() && two.exp() == j + 1) |
---|
[ad3c3ff] | 3104 | { |
---|
| 3105 | if (degBuf > 0 && degPi > 0) |
---|
| 3106 | { |
---|
[806c18] | 3107 | tmp[l] += mulNTL (two.coeff(), bufFactors[l + 1][0]); |
---|
| 3108 | two++; |
---|
[ad3c3ff] | 3109 | } |
---|
| 3110 | else if (degPi > 0) |
---|
[806c18] | 3111 | { |
---|
| 3112 | tmp[l] += mulNTL (two.coeff(), bufFactors[l + 1]); |
---|
| 3113 | two++; |
---|
| 3114 | } |
---|
[ad3c3ff] | 3115 | } |
---|
[806c18] | 3116 | if (degBuf > 0 && degPi > 0) |
---|
[ad3c3ff] | 3117 | { |
---|
| 3118 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
[806c18] | 3119 | { |
---|
| 3120 | if (k != j - k + 1) |
---|
| 3121 | { |
---|
[c1b9927] | 3122 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
[e368746] | 3123 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
[806c18] | 3124 | { |
---|
| 3125 | tmp[l] += mulNTL ((bufFactors[l + 1] [k] + one.coeff()), (Pi[l - 1] [k] + |
---|
[ad3c3ff] | 3126 | two.coeff())) - M (k + 1, l + 1) - M (j - k + 2, l + 1); |
---|
[806c18] | 3127 | one++; |
---|
| 3128 | two++; |
---|
| 3129 | } |
---|
[e368746] | 3130 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
[806c18] | 3131 | { |
---|
| 3132 | tmp[l] += mulNTL ((bufFactors[l + 1] [k] + one.coeff()), Pi[l - 1] [k]) - |
---|
| 3133 | M (k + 1, l + 1); |
---|
| 3134 | one++; |
---|
| 3135 | } |
---|
[e368746] | 3136 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
[806c18] | 3137 | { |
---|
| 3138 | tmp[l] += mulNTL (bufFactors[l + 1] [k], (Pi[l - 1] [k] + two.coeff())) - |
---|
[ad3c3ff] | 3139 | M (k + 1, l + 1); |
---|
[806c18] | 3140 | two++; |
---|
| 3141 | } |
---|
| 3142 | } |
---|
| 3143 | else |
---|
| 3144 | tmp[l] += M (k + 1, l + 1); |
---|
| 3145 | } |
---|
| 3146 | } |
---|
[ad3c3ff] | 3147 | Pi[l] += tmp[l]*xToJ*F.mvar(); |
---|
| 3148 | } |
---|
| 3149 | return; |
---|
| 3150 | } |
---|
| 3151 | |
---|
[806c18] | 3152 | void |
---|
| 3153 | henselLift12 (const CanonicalForm& F, CFList& factors, int l, CFArray& Pi, |
---|
[e368746] | 3154 | CFList& diophant, CFMatrix& M, bool sort) |
---|
[ad3c3ff] | 3155 | { |
---|
[e368746] | 3156 | if (sort) |
---|
| 3157 | sortList (factors, Variable (1)); |
---|
[ad3c3ff] | 3158 | Pi= CFArray (factors.length() - 1); |
---|
| 3159 | CFListIterator j= factors; |
---|
| 3160 | diophant= diophantine (F[0], factors); |
---|
| 3161 | DEBOUTLN (cerr, "diophant= " << diophant); |
---|
| 3162 | j++; |
---|
| 3163 | Pi [0]= mulNTL (j.getItem(), mod (factors.getFirst(), F.mvar())); |
---|
| 3164 | M (1, 1)= Pi [0]; |
---|
| 3165 | int i= 1; |
---|
| 3166 | if (j.hasItem()) |
---|
| 3167 | j++; |
---|
[c1b9927] | 3168 | for (; j.hasItem(); j++, i++) |
---|
[ad3c3ff] | 3169 | { |
---|
| 3170 | Pi [i]= mulNTL (Pi [i - 1], j.getItem()); |
---|
| 3171 | M (1, i + 1)= Pi [i]; |
---|
| 3172 | } |
---|
| 3173 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 3174 | i= 0; |
---|
| 3175 | for (CFListIterator k= factors; k.hasItem(); i++, k++) |
---|
| 3176 | { |
---|
| 3177 | if (i == 0) |
---|
| 3178 | bufFactors[i]= mod (k.getItem(), F.mvar()); |
---|
| 3179 | else |
---|
| 3180 | bufFactors[i]= k.getItem(); |
---|
| 3181 | } |
---|
| 3182 | for (i= 1; i < l; i++) |
---|
| 3183 | henselStep12 (F, factors, bufFactors, diophant, M, Pi, i); |
---|
| 3184 | |
---|
| 3185 | CFListIterator k= factors; |
---|
| 3186 | for (i= 0; i < factors.length (); i++, k++) |
---|
| 3187 | k.getItem()= bufFactors[i]; |
---|
| 3188 | factors.removeFirst(); |
---|
| 3189 | return; |
---|
| 3190 | } |
---|
| 3191 | |
---|
[806c18] | 3192 | void |
---|
[ad3c3ff] | 3193 | henselLiftResume12 (const CanonicalForm& F, CFList& factors, int start, int |
---|
| 3194 | end, CFArray& Pi, const CFList& diophant, CFMatrix& M) |
---|
| 3195 | { |
---|
| 3196 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 3197 | int i= 0; |
---|
| 3198 | CanonicalForm xToStart= power (F.mvar(), start); |
---|
| 3199 | for (CFListIterator k= factors; k.hasItem(); k++, i++) |
---|
| 3200 | { |
---|
| 3201 | if (i == 0) |
---|
| 3202 | bufFactors[i]= mod (k.getItem(), xToStart); |
---|
| 3203 | else |
---|
| 3204 | bufFactors[i]= k.getItem(); |
---|
| 3205 | } |
---|
| 3206 | for (i= start; i < end; i++) |
---|
[806c18] | 3207 | henselStep12 (F, factors, bufFactors, diophant, M, Pi, i); |
---|
| 3208 | |
---|
[ad3c3ff] | 3209 | CFListIterator k= factors; |
---|
| 3210 | for (i= 0; i < factors.length(); k++, i++) |
---|
| 3211 | k.getItem()= bufFactors [i]; |
---|
| 3212 | factors.removeFirst(); |
---|
[806c18] | 3213 | return; |
---|
| 3214 | } |
---|
[ad3c3ff] | 3215 | |
---|
| 3216 | static inline |
---|
| 3217 | CFList |
---|
| 3218 | biDiophantine (const CanonicalForm& F, const CFList& factors, const int d) |
---|
| 3219 | { |
---|
| 3220 | Variable y= F.mvar(); |
---|
| 3221 | CFList result; |
---|
| 3222 | if (y.level() == 1) |
---|
| 3223 | { |
---|
| 3224 | result= diophantine (F, factors); |
---|
| 3225 | return result; |
---|
| 3226 | } |
---|
| 3227 | else |
---|
| 3228 | { |
---|
| 3229 | CFList buf= factors; |
---|
| 3230 | for (CFListIterator i= buf; i.hasItem(); i++) |
---|
| 3231 | i.getItem()= mod (i.getItem(), y); |
---|
| 3232 | CanonicalForm A= mod (F, y); |
---|
| 3233 | int bufD= 1; |
---|
| 3234 | CFList recResult= biDiophantine (A, buf, bufD); |
---|
| 3235 | CanonicalForm e= 1; |
---|
| 3236 | CFList p; |
---|
| 3237 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 3238 | CanonicalForm yToD= power (y, d); |
---|
| 3239 | int k= 0; |
---|
| 3240 | for (CFListIterator i= factors; i.hasItem(); i++, k++) |
---|
| 3241 | { |
---|
| 3242 | bufFactors [k]= i.getItem(); |
---|
| 3243 | } |
---|
[21b8f4c] | 3244 | CanonicalForm b, quot; |
---|
[ad3c3ff] | 3245 | for (k= 0; k < factors.length(); k++) //TODO compute b's faster |
---|
| 3246 | { |
---|
| 3247 | b= 1; |
---|
[21b8f4c] | 3248 | if (fdivides (bufFactors[k], F, quot)) |
---|
| 3249 | b= quot; |
---|
[806c18] | 3250 | else |
---|
[ad3c3ff] | 3251 | { |
---|
[806c18] | 3252 | for (int l= 0; l < factors.length(); l++) |
---|
| 3253 | { |
---|
| 3254 | if (l == k) |
---|
| 3255 | continue; |
---|
| 3256 | else |
---|
| 3257 | { |
---|
| 3258 | b= mulMod2 (b, bufFactors[l], yToD); |
---|
| 3259 | } |
---|
| 3260 | } |
---|
[ad3c3ff] | 3261 | } |
---|
| 3262 | p.append (b); |
---|
[806c18] | 3263 | } |
---|
[ad3c3ff] | 3264 | |
---|
| 3265 | CFListIterator j= p; |
---|
| 3266 | for (CFListIterator i= recResult; i.hasItem(); i++, j++) |
---|
| 3267 | e -= i.getItem()*j.getItem(); |
---|
| 3268 | |
---|
| 3269 | if (e.isZero()) |
---|
[806c18] | 3270 | return recResult; |
---|
[ad3c3ff] | 3271 | CanonicalForm coeffE; |
---|
| 3272 | CFList s; |
---|
| 3273 | result= recResult; |
---|
| 3274 | CanonicalForm g; |
---|
| 3275 | for (int i= 1; i < d; i++) |
---|
| 3276 | { |
---|
| 3277 | if (degree (e, y) > 0) |
---|
| 3278 | coeffE= e[i]; |
---|
| 3279 | else |
---|
| 3280 | coeffE= 0; |
---|
| 3281 | if (!coeffE.isZero()) |
---|
| 3282 | { |
---|
[806c18] | 3283 | CFListIterator k= result; |
---|
| 3284 | CFListIterator l= p; |
---|
[ad3c3ff] | 3285 | int ii= 0; |
---|
[806c18] | 3286 | j= recResult; |
---|
| 3287 | for (; j.hasItem(); j++, k++, l++, ii++) |
---|
| 3288 | { |
---|
| 3289 | g= coeffE*j.getItem(); |
---|
[ad3c3ff] | 3290 | if (degree (bufFactors[ii], y) <= 0) |
---|
| 3291 | g= mod (g, bufFactors[ii]); |
---|
| 3292 | else |
---|
| 3293 | g= mod (g, bufFactors[ii][0]); |
---|
[806c18] | 3294 | k.getItem() += g*power (y, i); |
---|
| 3295 | e -= mulMod2 (g*power(y, i), l.getItem(), yToD); |
---|
| 3296 | DEBOUTLN (cerr, "mod (e, power (y, i + 1))= " << |
---|
[ad3c3ff] | 3297 | mod (e, power (y, i + 1))); |
---|
[806c18] | 3298 | } |
---|
| 3299 | } |
---|
[ad3c3ff] | 3300 | if (e.isZero()) |
---|
| 3301 | break; |
---|
| 3302 | } |
---|
| 3303 | |
---|
| 3304 | DEBOUTLN (cerr, "mod (e, y)= " << mod (e, y)); |
---|
| 3305 | |
---|
| 3306 | #ifdef DEBUGOUTPUT |
---|
| 3307 | CanonicalForm test= 0; |
---|
[806c18] | 3308 | j= p; |
---|
[ad3c3ff] | 3309 | for (CFListIterator i= result; i.hasItem(); i++, j++) |
---|
| 3310 | test += mod (i.getItem()*j.getItem(), power (y, d)); |
---|
| 3311 | DEBOUTLN (cerr, "test= " << test); |
---|
| 3312 | #endif |
---|
| 3313 | return result; |
---|
| 3314 | } |
---|
| 3315 | } |
---|
| 3316 | |
---|
| 3317 | static inline |
---|
| 3318 | CFList |
---|
[806c18] | 3319 | multiRecDiophantine (const CanonicalForm& F, const CFList& factors, |
---|
[ad3c3ff] | 3320 | const CFList& recResult, const CFList& M, const int d) |
---|
| 3321 | { |
---|
| 3322 | Variable y= F.mvar(); |
---|
| 3323 | CFList result; |
---|
| 3324 | CFListIterator i; |
---|
| 3325 | CanonicalForm e= 1; |
---|
| 3326 | CFListIterator j= factors; |
---|
| 3327 | CFList p; |
---|
| 3328 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 3329 | CanonicalForm yToD= power (y, d); |
---|
| 3330 | int k= 0; |
---|
| 3331 | for (CFListIterator i= factors; i.hasItem(); i++, k++) |
---|
| 3332 | bufFactors [k]= i.getItem(); |
---|
[21b8f4c] | 3333 | CanonicalForm b, quot; |
---|
[ad3c3ff] | 3334 | CFList buf= M; |
---|
| 3335 | buf.removeLast(); |
---|
| 3336 | buf.append (yToD); |
---|
| 3337 | for (k= 0; k < factors.length(); k++) //TODO compute b's faster |
---|
| 3338 | { |
---|
| 3339 | b= 1; |
---|
[21b8f4c] | 3340 | if (fdivides (bufFactors[k], F, quot)) |
---|
| 3341 | b= quot; |
---|
[806c18] | 3342 | else |
---|
[ad3c3ff] | 3343 | { |
---|
| 3344 | for (int l= 0; l < factors.length(); l++) |
---|
| 3345 | { |
---|
[806c18] | 3346 | if (l == k) |
---|
| 3347 | continue; |
---|
| 3348 | else |
---|
| 3349 | { |
---|
| 3350 | b= mulMod (b, bufFactors[l], buf); |
---|
| 3351 | } |
---|
[ad3c3ff] | 3352 | } |
---|
| 3353 | } |
---|
| 3354 | p.append (b); |
---|
[806c18] | 3355 | } |
---|
[ad3c3ff] | 3356 | j= p; |
---|
| 3357 | for (CFListIterator i= recResult; i.hasItem(); i++, j++) |
---|
| 3358 | e -= mulMod (i.getItem(), j.getItem(), M); |
---|
| 3359 | |
---|
| 3360 | if (e.isZero()) |
---|
[806c18] | 3361 | return recResult; |
---|
[ad3c3ff] | 3362 | CanonicalForm coeffE; |
---|
| 3363 | CFList s; |
---|
| 3364 | result= recResult; |
---|
| 3365 | CanonicalForm g; |
---|
| 3366 | for (int i= 1; i < d; i++) |
---|
| 3367 | { |
---|
| 3368 | if (degree (e, y) > 0) |
---|
| 3369 | coeffE= e[i]; |
---|
| 3370 | else |
---|
| 3371 | coeffE= 0; |
---|
| 3372 | if (!coeffE.isZero()) |
---|
| 3373 | { |
---|
| 3374 | CFListIterator k= result; |
---|
| 3375 | CFListIterator l= p; |
---|
| 3376 | j= recResult; |
---|
| 3377 | int ii= 0; |
---|
| 3378 | CanonicalForm dummy; |
---|
| 3379 | for (; j.hasItem(); j++, k++, l++, ii++) |
---|
| 3380 | { |
---|
[806c18] | 3381 | g= mulMod (coeffE, j.getItem(), M); |
---|
| 3382 | if (degree (bufFactors[ii], y) <= 0) |
---|
| 3383 | divrem (g, mod (bufFactors[ii], Variable (y.level() - 1)), dummy, |
---|
[ad3c3ff] | 3384 | g, M); |
---|
[806c18] | 3385 | else |
---|
| 3386 | divrem (g, bufFactors[ii][0], dummy, g, M); |
---|
| 3387 | k.getItem() += g*power (y, i); |
---|
| 3388 | e -= mulMod (g*power (y, i), l.getItem(), M); |
---|
| 3389 | } |
---|
[ad3c3ff] | 3390 | } |
---|
[806c18] | 3391 | |
---|
[ad3c3ff] | 3392 | if (e.isZero()) |
---|
| 3393 | break; |
---|
| 3394 | } |
---|
| 3395 | |
---|
| 3396 | #ifdef DEBUGOUTPUT |
---|
| 3397 | CanonicalForm test= 0; |
---|
[806c18] | 3398 | j= p; |
---|
[ad3c3ff] | 3399 | for (CFListIterator i= result; i.hasItem(); i++, j++) |
---|
| 3400 | test += mod (i.getItem()*j.getItem(), power (y, d)); |
---|
| 3401 | DEBOUTLN (cerr, "test= " << test); |
---|
| 3402 | #endif |
---|
| 3403 | return result; |
---|
| 3404 | } |
---|
| 3405 | |
---|
| 3406 | static inline |
---|
[806c18] | 3407 | void |
---|
| 3408 | henselStep (const CanonicalForm& F, const CFList& factors, CFArray& bufFactors, |
---|
| 3409 | const CFList& diophant, CFMatrix& M, CFArray& Pi, int j, |
---|
| 3410 | const CFList& MOD) |
---|
[ad3c3ff] | 3411 | { |
---|
[c4f4fd] | 3412 | CanonicalForm E; |
---|
| 3413 | CanonicalForm xToJ= power (F.mvar(), j); |
---|
| 3414 | Variable x= F.mvar(); |
---|
| 3415 | // compute the error |
---|
| 3416 | if (j == 1) |
---|
[ad3c3ff] | 3417 | { |
---|
[c4f4fd] | 3418 | E= F[j]; |
---|
[806c18] | 3419 | #ifdef DEBUGOUTPUT |
---|
[c4f4fd] | 3420 | CanonicalForm test= 1; |
---|
| 3421 | for (int i= 0; i < factors.length(); i++) |
---|
[ad3c3ff] | 3422 | { |
---|
[c4f4fd] | 3423 | if (i == 0) |
---|
| 3424 | test= mulMod (test, mod (bufFactors [i], xToJ), MOD); |
---|
| 3425 | else |
---|
| 3426 | test= mulMod (test, bufFactors[i], MOD); |
---|
[ad3c3ff] | 3427 | } |
---|
[c4f4fd] | 3428 | CanonicalForm test2= mod (F-test, xToJ); |
---|
[139b67] | 3429 | |
---|
[c4f4fd] | 3430 | test2= mod (test2, MOD); |
---|
| 3431 | DEBOUTLN (cerr, "test= " << test2); |
---|
| 3432 | #endif |
---|
[806c18] | 3433 | } |
---|
[c4f4fd] | 3434 | else |
---|
[ad3c3ff] | 3435 | { |
---|
[806c18] | 3436 | #ifdef DEBUGOUTPUT |
---|
[c4f4fd] | 3437 | CanonicalForm test= 1; |
---|
| 3438 | for (int i= 0; i < factors.length(); i++) |
---|
[ad3c3ff] | 3439 | { |
---|
[c4f4fd] | 3440 | if (i == 0) |
---|
| 3441 | test *= mod (bufFactors [i], power (x, j)); |
---|
| 3442 | else |
---|
| 3443 | test *= bufFactors[i]; |
---|
[ad3c3ff] | 3444 | } |
---|
[c4f4fd] | 3445 | test= mod (test, power (x, j)); |
---|
| 3446 | test= mod (test, MOD); |
---|
| 3447 | CanonicalForm test2= mod (F, power (x, j - 1)) - mod (test, power (x, j-1)); |
---|
| 3448 | DEBOUTLN (cerr, "test= " << test2); |
---|
| 3449 | #endif |
---|
| 3450 | |
---|
| 3451 | if (degree (Pi [factors.length() - 2], x) > 0) |
---|
| 3452 | E= F[j] - Pi [factors.length() - 2] [j]; |
---|
| 3453 | else |
---|
| 3454 | E= F[j]; |
---|
[139b67] | 3455 | } |
---|
| 3456 | |
---|
| 3457 | CFArray buf= CFArray (diophant.length()); |
---|
| 3458 | bufFactors[0]= mod (factors.getFirst(), power (F.mvar(), j + 1)); |
---|
| 3459 | int k= 0; |
---|
| 3460 | // actual lifting |
---|
| 3461 | CanonicalForm dummy, rest1; |
---|
[806c18] | 3462 | for (CFListIterator i= diophant; i.hasItem(); i++, k++) |
---|
[139b67] | 3463 | { |
---|
[ad3c3ff] | 3464 | if (degree (bufFactors[k], x) > 0) |
---|
| 3465 | { |
---|
| 3466 | if (k > 0) |
---|
| 3467 | divrem (E, bufFactors[k] [0], dummy, rest1, MOD); |
---|
| 3468 | else |
---|
| 3469 | rest1= E; |
---|
| 3470 | } |
---|
| 3471 | else |
---|
| 3472 | divrem (E, bufFactors[k], dummy, rest1, MOD); |
---|
| 3473 | |
---|
| 3474 | buf[k]= mulMod (i.getItem(), rest1, MOD); |
---|
| 3475 | |
---|
| 3476 | if (degree (bufFactors[k], x) > 0) |
---|
| 3477 | divrem (buf[k], bufFactors[k] [0], dummy, buf[k], MOD); |
---|
[806c18] | 3478 | else |
---|
[ad3c3ff] | 3479 | divrem (buf[k], bufFactors[k], dummy, buf[k], MOD); |
---|
| 3480 | } |
---|
| 3481 | for (k= 1; k < factors.length(); k++) |
---|
| 3482 | bufFactors[k] += xToJ*buf[k]; |
---|
| 3483 | |
---|
| 3484 | // update Pi [0] |
---|
| 3485 | int degBuf0= degree (bufFactors[0], x); |
---|
| 3486 | int degBuf1= degree (bufFactors[1], x); |
---|
| 3487 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 3488 | M (j + 1, 1)= mulMod (bufFactors[0] [j], bufFactors[1] [j], MOD); |
---|
| 3489 | CanonicalForm uIZeroJ; |
---|
| 3490 | if (j == 1) |
---|
| 3491 | { |
---|
| 3492 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 3493 | uIZeroJ= mulMod ((bufFactors[0] [0] + bufFactors[0] [j]), |
---|
| 3494 | (bufFactors[1] [0] + buf[1]), MOD) - M(1, 1) - M(j + 1, 1); |
---|
| 3495 | else if (degBuf0 > 0) |
---|
| 3496 | uIZeroJ= mulMod (bufFactors[0] [j], bufFactors[1], MOD); |
---|
| 3497 | else if (degBuf1 > 0) |
---|
| 3498 | uIZeroJ= mulMod (bufFactors[0], buf[1], MOD); |
---|
| 3499 | else |
---|
| 3500 | uIZeroJ= 0; |
---|
[806c18] | 3501 | Pi [0] += xToJ*uIZeroJ; |
---|
| 3502 | } |
---|
[ad3c3ff] | 3503 | else |
---|
| 3504 | { |
---|
| 3505 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
[806c18] | 3506 | uIZeroJ= mulMod ((bufFactors[0] [0] + bufFactors[0] [j]), |
---|
[ad3c3ff] | 3507 | (bufFactors[1] [0] + buf[1]), MOD) - M(1, 1) - M(j + 1, 1); |
---|
| 3508 | else if (degBuf0 > 0) |
---|
| 3509 | uIZeroJ= mulMod (bufFactors[0] [j], bufFactors[1], MOD); |
---|
| 3510 | else if (degBuf1 > 0) |
---|
| 3511 | uIZeroJ= mulMod (bufFactors[0], buf[1], MOD); |
---|
| 3512 | else |
---|
| 3513 | uIZeroJ= 0; |
---|
[806c18] | 3514 | Pi [0] += xToJ*uIZeroJ; |
---|
[ad3c3ff] | 3515 | } |
---|
| 3516 | |
---|
| 3517 | CFArray tmp= CFArray (factors.length() - 1); |
---|
| 3518 | for (k= 0; k < factors.length() - 1; k++) |
---|
| 3519 | tmp[k]= 0; |
---|
| 3520 | CFIterator one, two; |
---|
| 3521 | one= bufFactors [0]; |
---|
| 3522 | two= bufFactors [1]; |
---|
| 3523 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 3524 | { |
---|
| 3525 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
[806c18] | 3526 | { |
---|
[ad3c3ff] | 3527 | if (k != j - k + 1) |
---|
| 3528 | { |
---|
[c1b9927] | 3529 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
[e368746] | 3530 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
[806c18] | 3531 | { |
---|
| 3532 | tmp[0] += mulMod ((bufFactors[0] [k] + one.coeff()), |
---|
| 3533 | (bufFactors[1] [k] + two.coeff()), MOD) - M (k + 1, 1) - |
---|
[ad3c3ff] | 3534 | M (j - k + 2, 1); |
---|
[806c18] | 3535 | one++; |
---|
| 3536 | two++; |
---|
| 3537 | } |
---|
[e368746] | 3538 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
[806c18] | 3539 | { |
---|
| 3540 | tmp[0] += mulMod ((bufFactors[0] [k] + one.coeff()), |
---|
[ad3c3ff] | 3541 | bufFactors[1] [k], MOD) - M (k + 1, 1); |
---|
[806c18] | 3542 | one++; |
---|
| 3543 | } |
---|
[e368746] | 3544 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
[806c18] | 3545 | { |
---|
| 3546 | tmp[0] += mulMod (bufFactors[0] [k], (bufFactors[1] [k] + |
---|
[ad3c3ff] | 3547 | two.coeff()), MOD) - M (k + 1, 1); |
---|
[806c18] | 3548 | two++; |
---|
| 3549 | } |
---|
[ad3c3ff] | 3550 | } |
---|
| 3551 | else |
---|
| 3552 | { |
---|
[806c18] | 3553 | tmp[0] += M (k + 1, 1); |
---|
[ad3c3ff] | 3554 | } |
---|
| 3555 | } |
---|
| 3556 | } |
---|
| 3557 | Pi [0] += tmp[0]*xToJ*F.mvar(); |
---|
| 3558 | |
---|
[806c18] | 3559 | // update Pi [l] |
---|
[ad3c3ff] | 3560 | int degPi, degBuf; |
---|
[806c18] | 3561 | for (int l= 1; l < factors.length() - 1; l++) |
---|
[ad3c3ff] | 3562 | { |
---|
| 3563 | degPi= degree (Pi [l - 1], x); |
---|
| 3564 | degBuf= degree (bufFactors[l + 1], x); |
---|
| 3565 | if (degPi > 0 && degBuf > 0) |
---|
[806c18] | 3566 | M (j + 1, l + 1)= mulMod (Pi [l - 1] [j], bufFactors[l + 1] [j], MOD); |
---|
[ad3c3ff] | 3567 | if (j == 1) |
---|
| 3568 | { |
---|
| 3569 | if (degPi > 0 && degBuf > 0) |
---|
[806c18] | 3570 | Pi [l] += xToJ*(mulMod ((Pi [l - 1] [0] + Pi [l - 1] [j]), |
---|
| 3571 | (bufFactors[l + 1] [0] + buf[l + 1]), MOD) - M (j + 1, l +1)- |
---|
[ad3c3ff] | 3572 | M (1, l + 1)); |
---|
| 3573 | else if (degPi > 0) |
---|
| 3574 | Pi [l] += xToJ*(mulMod (Pi [l - 1] [j], bufFactors[l + 1], MOD)); |
---|
| 3575 | else if (degBuf > 0) |
---|
| 3576 | Pi [l] += xToJ*(mulMod (Pi [l - 1], buf[l + 1], MOD)); |
---|
| 3577 | } |
---|
| 3578 | else |
---|
| 3579 | { |
---|
| 3580 | if (degPi > 0 && degBuf > 0) |
---|
| 3581 | { |
---|
| 3582 | uIZeroJ= mulMod (uIZeroJ, bufFactors [l + 1] [0], MOD); |
---|
[806c18] | 3583 | uIZeroJ += mulMod (Pi [l - 1] [0], buf [l + 1], MOD); |
---|
[ad3c3ff] | 3584 | } |
---|
| 3585 | else if (degPi > 0) |
---|
| 3586 | uIZeroJ= mulMod (uIZeroJ, bufFactors [l + 1], MOD); |
---|
| 3587 | else if (degBuf > 0) |
---|
| 3588 | { |
---|
| 3589 | uIZeroJ= mulMod (uIZeroJ, bufFactors [l + 1] [0], MOD); |
---|
| 3590 | uIZeroJ += mulMod (Pi [l - 1], buf[l + 1], MOD); |
---|
| 3591 | } |
---|
| 3592 | Pi[l] += xToJ*uIZeroJ; |
---|
| 3593 | } |
---|
| 3594 | one= bufFactors [l + 1]; |
---|
| 3595 | two= Pi [l - 1]; |
---|
[e368746] | 3596 | if (two.hasTerms() && two.exp() == j + 1) |
---|
[ad3c3ff] | 3597 | { |
---|
| 3598 | if (degBuf > 0 && degPi > 0) |
---|
| 3599 | { |
---|
[806c18] | 3600 | tmp[l] += mulMod (two.coeff(), bufFactors[l + 1][0], MOD); |
---|
| 3601 | two++; |
---|
[ad3c3ff] | 3602 | } |
---|
| 3603 | else if (degPi > 0) |
---|
[806c18] | 3604 | { |
---|
| 3605 | tmp[l] += mulMod (two.coeff(), bufFactors[l + 1], MOD); |
---|
| 3606 | two++; |
---|
| 3607 | } |
---|
[ad3c3ff] | 3608 | } |
---|
[806c18] | 3609 | if (degBuf > 0 && degPi > 0) |
---|
[ad3c3ff] | 3610 | { |
---|
| 3611 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
[806c18] | 3612 | { |
---|
| 3613 | if (k != j - k + 1) |
---|
| 3614 | { |
---|
[c1b9927] | 3615 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
[e368746] | 3616 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
[806c18] | 3617 | { |
---|
| 3618 | tmp[l] += mulMod ((bufFactors[l + 1] [k] + one.coeff()), |
---|
| 3619 | (Pi[l - 1] [k] + two.coeff()), MOD) - M (k + 1, l + 1) - |
---|
[ad3c3ff] | 3620 | M (j - k + 2, l + 1); |
---|
[806c18] | 3621 | one++; |
---|
| 3622 | two++; |
---|
| 3623 | } |
---|
[e368746] | 3624 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
[806c18] | 3625 | { |
---|
| 3626 | tmp[l] += mulMod ((bufFactors[l + 1] [k] + one.coeff()), |
---|
| 3627 | Pi[l - 1] [k], MOD) - M (k + 1, l + 1); |
---|
| 3628 | one++; |
---|
| 3629 | } |
---|
[e368746] | 3630 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
[806c18] | 3631 | { |
---|
| 3632 | tmp[l] += mulMod (bufFactors[l + 1] [k], |
---|
[ad3c3ff] | 3633 | (Pi[l - 1] [k] + two.coeff()), MOD) - M (k + 1, l + 1); |
---|
[806c18] | 3634 | two++; |
---|
| 3635 | } |
---|
| 3636 | } |
---|
| 3637 | else |
---|
| 3638 | tmp[l] += M (k + 1, l + 1); |
---|
| 3639 | } |
---|
| 3640 | } |
---|
[ad3c3ff] | 3641 | Pi[l] += tmp[l]*xToJ*F.mvar(); |
---|
| 3642 | } |
---|
| 3643 | |
---|
| 3644 | return; |
---|
| 3645 | } |
---|
| 3646 | |
---|
[806c18] | 3647 | CFList |
---|
[ad3c3ff] | 3648 | henselLift23 (const CFList& eval, const CFList& factors, const int* l, CFList& |
---|
| 3649 | diophant, CFArray& Pi, CFMatrix& M) |
---|
| 3650 | { |
---|
| 3651 | CFList buf= factors; |
---|
| 3652 | int k= 0; |
---|
| 3653 | int liftBoundBivar= l[k]; |
---|
| 3654 | diophant= biDiophantine (eval.getFirst(), buf, liftBoundBivar); |
---|
| 3655 | CFList MOD; |
---|
| 3656 | MOD.append (power (Variable (2), liftBoundBivar)); |
---|
| 3657 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 3658 | k= 0; |
---|
| 3659 | CFListIterator j= eval; |
---|
| 3660 | j++; |
---|
| 3661 | buf.removeFirst(); |
---|
| 3662 | buf.insert (LC (j.getItem(), 1)); |
---|
| 3663 | for (CFListIterator i= buf; i.hasItem(); i++, k++) |
---|
| 3664 | bufFactors[k]= i.getItem(); |
---|
| 3665 | Pi= CFArray (factors.length() - 1); |
---|
| 3666 | CFListIterator i= buf; |
---|
| 3667 | i++; |
---|
| 3668 | Variable y= j.getItem().mvar(); |
---|
| 3669 | Pi [0]= mulMod (i.getItem(), mod (buf.getFirst(), y), MOD); |
---|
| 3670 | M (1, 1)= Pi [0]; |
---|
| 3671 | k= 1; |
---|
| 3672 | if (i.hasItem()) |
---|
| 3673 | i++; |
---|
[c1b9927] | 3674 | for (; i.hasItem(); i++, k++) |
---|
[ad3c3ff] | 3675 | { |
---|
| 3676 | Pi [k]= mulMod (Pi [k - 1], i.getItem(), MOD); |
---|
| 3677 | M (1, k + 1)= Pi [k]; |
---|
| 3678 | } |
---|
| 3679 | |
---|
| 3680 | for (int d= 1; d < l[1]; d++) |
---|
| 3681 | henselStep (j.getItem(), buf, bufFactors, diophant, M, Pi, d, MOD); |
---|
| 3682 | CFList result; |
---|
| 3683 | for (k= 1; k < factors.length(); k++) |
---|
| 3684 | result.append (bufFactors[k]); |
---|
| 3685 | return result; |
---|
[806c18] | 3686 | } |
---|
[ad3c3ff] | 3687 | |
---|
[806c18] | 3688 | void |
---|
| 3689 | henselLiftResume (const CanonicalForm& F, CFList& factors, int start, int end, |
---|
| 3690 | CFArray& Pi, const CFList& diophant, CFMatrix& M, |
---|
[ad3c3ff] | 3691 | const CFList& MOD) |
---|
| 3692 | { |
---|
| 3693 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 3694 | int i= 0; |
---|
| 3695 | CanonicalForm xToStart= power (F.mvar(), start); |
---|
| 3696 | for (CFListIterator k= factors; k.hasItem(); k++, i++) |
---|
| 3697 | { |
---|
| 3698 | if (i == 0) |
---|
| 3699 | bufFactors[i]= mod (k.getItem(), xToStart); |
---|
| 3700 | else |
---|
| 3701 | bufFactors[i]= k.getItem(); |
---|
| 3702 | } |
---|
| 3703 | for (i= start; i < end; i++) |
---|
[806c18] | 3704 | henselStep (F, factors, bufFactors, diophant, M, Pi, i, MOD); |
---|
| 3705 | |
---|
[ad3c3ff] | 3706 | CFListIterator k= factors; |
---|
| 3707 | for (i= 0; i < factors.length(); k++, i++) |
---|
| 3708 | k.getItem()= bufFactors [i]; |
---|
| 3709 | factors.removeFirst(); |
---|
[806c18] | 3710 | return; |
---|
| 3711 | } |
---|
[ad3c3ff] | 3712 | |
---|
| 3713 | CFList |
---|
| 3714 | henselLift (const CFList& F, const CFList& factors, const CFList& MOD, CFList& |
---|
| 3715 | diophant, CFArray& Pi, CFMatrix& M, const int lOld, const int |
---|
| 3716 | lNew) |
---|
| 3717 | { |
---|
| 3718 | diophant= multiRecDiophantine (F.getFirst(), factors, diophant, MOD, lOld); |
---|
| 3719 | int k= 0; |
---|
| 3720 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 3721 | for (CFListIterator i= factors; i.hasItem(); i++, k++) |
---|
| 3722 | { |
---|
| 3723 | if (k == 0) |
---|
| 3724 | bufFactors[k]= LC (F.getLast(), 1); |
---|
| 3725 | else |
---|
| 3726 | bufFactors[k]= i.getItem(); |
---|
| 3727 | } |
---|
| 3728 | CFList buf= factors; |
---|
| 3729 | buf.removeFirst(); |
---|
| 3730 | buf.insert (LC (F.getLast(), 1)); |
---|
| 3731 | CFListIterator i= buf; |
---|
| 3732 | i++; |
---|
| 3733 | Variable y= F.getLast().mvar(); |
---|
| 3734 | Variable x= F.getFirst().mvar(); |
---|
| 3735 | CanonicalForm xToLOld= power (x, lOld); |
---|
| 3736 | Pi [0]= mod (Pi[0], xToLOld); |
---|
| 3737 | M (1, 1)= Pi [0]; |
---|
| 3738 | k= 1; |
---|
| 3739 | if (i.hasItem()) |
---|
| 3740 | i++; |
---|
[c1b9927] | 3741 | for (; i.hasItem(); i++, k++) |
---|
[ad3c3ff] | 3742 | { |
---|
| 3743 | Pi [k]= mod (Pi [k], xToLOld); |
---|
| 3744 | M (1, k + 1)= Pi [k]; |
---|
| 3745 | } |
---|
| 3746 | |
---|
| 3747 | for (int d= 1; d < lNew; d++) |
---|
| 3748 | henselStep (F.getLast(), buf, bufFactors, diophant, M, Pi, d, MOD); |
---|
| 3749 | CFList result; |
---|
| 3750 | for (k= 1; k < factors.length(); k++) |
---|
| 3751 | result.append (bufFactors[k]); |
---|
| 3752 | return result; |
---|
| 3753 | } |
---|
| 3754 | |
---|
| 3755 | CFList |
---|
| 3756 | henselLift (const CFList& eval, const CFList& factors, const int* l, const int |
---|
[e368746] | 3757 | lLength, bool sort) |
---|
[ad3c3ff] | 3758 | { |
---|
[806c18] | 3759 | CFList diophant; |
---|
| 3760 | CFList buf= factors; |
---|
[ad3c3ff] | 3761 | buf.insert (LC (eval.getFirst(), 1)); |
---|
[e368746] | 3762 | if (sort) |
---|
| 3763 | sortList (buf, Variable (1)); |
---|
[ad3c3ff] | 3764 | CFArray Pi; |
---|
| 3765 | CFMatrix M= CFMatrix (l[1], factors.length()); |
---|
| 3766 | CFList result= henselLift23 (eval, buf, l, diophant, Pi, M); |
---|
| 3767 | if (eval.length() == 2) |
---|
| 3768 | return result; |
---|
| 3769 | CFList MOD; |
---|
| 3770 | for (int i= 0; i < 2; i++) |
---|
| 3771 | MOD.append (power (Variable (i + 2), l[i])); |
---|
| 3772 | CFListIterator j= eval; |
---|
| 3773 | j++; |
---|
| 3774 | CFList bufEval; |
---|
| 3775 | bufEval.append (j.getItem()); |
---|
| 3776 | j++; |
---|
[806c18] | 3777 | |
---|
[ea88e0] | 3778 | for (int i= 2; i < lLength && j.hasItem(); i++, j++) |
---|
[ad3c3ff] | 3779 | { |
---|
| 3780 | result.insert (LC (bufEval.getFirst(), 1)); |
---|
| 3781 | bufEval.append (j.getItem()); |
---|
| 3782 | M= CFMatrix (l[i], factors.length()); |
---|
| 3783 | result= henselLift (bufEval, result, MOD, diophant, Pi, M, l[i - 1], l[i]); |
---|
| 3784 | MOD.append (power (Variable (i + 2), l[i])); |
---|
| 3785 | bufEval.removeFirst(); |
---|
| 3786 | } |
---|
[806c18] | 3787 | return result; |
---|
[ad3c3ff] | 3788 | } |
---|
| 3789 | |
---|
[08daea] | 3790 | void |
---|
| 3791 | henselStep122 (const CanonicalForm& F, const CFList& factors, |
---|
| 3792 | CFArray& bufFactors, const CFList& diophant, CFMatrix& M, |
---|
[5b8726d] | 3793 | CFArray& Pi, int j, const CFArray& /*LCs*/) |
---|
[08daea] | 3794 | { |
---|
| 3795 | Variable x= F.mvar(); |
---|
| 3796 | CanonicalForm xToJ= power (x, j); |
---|
| 3797 | |
---|
| 3798 | CanonicalForm E; |
---|
| 3799 | // compute the error |
---|
| 3800 | if (degree (Pi [factors.length() - 2], x) > 0) |
---|
| 3801 | E= F[j] - Pi [factors.length() - 2] [j]; |
---|
| 3802 | else |
---|
| 3803 | E= F[j]; |
---|
| 3804 | |
---|
| 3805 | CFArray buf= CFArray (diophant.length()); |
---|
| 3806 | |
---|
| 3807 | int k= 0; |
---|
| 3808 | CanonicalForm remainder; |
---|
| 3809 | // actual lifting |
---|
| 3810 | for (CFListIterator i= diophant; i.hasItem(); i++, k++) |
---|
| 3811 | { |
---|
| 3812 | if (degree (bufFactors[k], x) > 0) |
---|
| 3813 | remainder= modNTL (E, bufFactors[k] [0]); |
---|
| 3814 | else |
---|
| 3815 | remainder= modNTL (E, bufFactors[k]); |
---|
| 3816 | buf[k]= mulNTL (i.getItem(), remainder); |
---|
| 3817 | if (degree (bufFactors[k], x) > 0) |
---|
| 3818 | buf[k]= modNTL (buf[k], bufFactors[k] [0]); |
---|
| 3819 | else |
---|
[c1b9927] | 3820 | buf[k]= modNTL (buf[k], bufFactors[k]); |
---|
[08daea] | 3821 | } |
---|
| 3822 | |
---|
| 3823 | for (k= 0; k < factors.length(); k++) |
---|
| 3824 | bufFactors[k] += xToJ*buf[k]; |
---|
| 3825 | |
---|
| 3826 | // update Pi [0] |
---|
| 3827 | int degBuf0= degree (bufFactors[0], x); |
---|
| 3828 | int degBuf1= degree (bufFactors[1], x); |
---|
| 3829 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 3830 | { |
---|
| 3831 | M (j + 1, 1)= mulNTL (bufFactors[0] [j], bufFactors[1] [j]); |
---|
| 3832 | if (j + 2 <= M.rows()) |
---|
| 3833 | M (j + 2, 1)= mulNTL (bufFactors[0] [j + 1], bufFactors[1] [j + 1]); |
---|
| 3834 | } |
---|
| 3835 | CanonicalForm uIZeroJ; |
---|
| 3836 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 3837 | uIZeroJ= mulNTL(bufFactors[0][0],buf[1])+mulNTL (bufFactors[1][0], buf[0]); |
---|
| 3838 | else if (degBuf0 > 0) |
---|
| 3839 | uIZeroJ= mulNTL (buf[0], bufFactors[1]); |
---|
| 3840 | else if (degBuf1 > 0) |
---|
| 3841 | uIZeroJ= mulNTL (bufFactors[0], buf [1]); |
---|
| 3842 | else |
---|
| 3843 | uIZeroJ= 0; |
---|
| 3844 | Pi [0] += xToJ*uIZeroJ; |
---|
| 3845 | |
---|
| 3846 | CFArray tmp= CFArray (factors.length() - 1); |
---|
| 3847 | for (k= 0; k < factors.length() - 1; k++) |
---|
| 3848 | tmp[k]= 0; |
---|
| 3849 | CFIterator one, two; |
---|
| 3850 | one= bufFactors [0]; |
---|
| 3851 | two= bufFactors [1]; |
---|
| 3852 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 3853 | { |
---|
[1b8e048] | 3854 | while (one.hasTerms() && one.exp() > j) one++; |
---|
| 3855 | while (two.hasTerms() && two.exp() > j) two++; |
---|
[08daea] | 3856 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
| 3857 | { |
---|
[e368746] | 3858 | if (one.hasTerms() && two.hasTerms()) |
---|
[08daea] | 3859 | { |
---|
[e368746] | 3860 | if (k != j - k + 1) |
---|
| 3861 | { |
---|
| 3862 | if ((one.hasTerms() && one.exp() == j - k + 1) && + |
---|
| 3863 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
[08daea] | 3864 | { |
---|
| 3865 | tmp[0] += mulNTL ((bufFactors[0][k]+one.coeff()),(bufFactors[1][k] + |
---|
| 3866 | two.coeff())) - M (k + 1, 1) - M (j - k + 2, 1); |
---|
| 3867 | one++; |
---|
| 3868 | two++; |
---|
| 3869 | } |
---|
[e368746] | 3870 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
[08daea] | 3871 | { |
---|
| 3872 | tmp[0] += mulNTL ((bufFactors[0][k]+one.coeff()), bufFactors[1] [k]) - |
---|
| 3873 | M (k + 1, 1); |
---|
| 3874 | one++; |
---|
| 3875 | } |
---|
[e368746] | 3876 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
[08daea] | 3877 | { |
---|
| 3878 | tmp[0] += mulNTL (bufFactors[0][k],(bufFactors[1][k] + two.coeff())) - |
---|
| 3879 | M (k + 1, 1); |
---|
| 3880 | two++; |
---|
| 3881 | } |
---|
| 3882 | } |
---|
| 3883 | else |
---|
| 3884 | tmp[0] += M (k + 1, 1); |
---|
[e368746] | 3885 | } |
---|
[08daea] | 3886 | } |
---|
[1b8e048] | 3887 | } |
---|
[08daea] | 3888 | |
---|
[1b8e048] | 3889 | if (degBuf0 >= j + 1 && degBuf1 >= j + 1) |
---|
| 3890 | { |
---|
[08daea] | 3891 | if (j + 2 <= M.rows()) |
---|
[1b8e048] | 3892 | tmp [0] += mulNTL ((bufFactors [0] [j + 1]+ bufFactors [0] [0]), |
---|
| 3893 | (bufFactors [1] [j + 1] + bufFactors [1] [0])) |
---|
| 3894 | - M(1,1) - M (j + 2,1); |
---|
| 3895 | } |
---|
| 3896 | else if (degBuf0 >= j + 1) |
---|
| 3897 | { |
---|
| 3898 | if (degBuf1 > 0) |
---|
| 3899 | tmp[0] += mulNTL (bufFactors [0] [j+1], bufFactors [1] [0]); |
---|
| 3900 | else |
---|
| 3901 | tmp[0] += mulNTL (bufFactors [0] [j+1], bufFactors [1]); |
---|
| 3902 | } |
---|
| 3903 | else if (degBuf1 >= j + 1) |
---|
| 3904 | { |
---|
| 3905 | if (degBuf0 > 0) |
---|
| 3906 | tmp[0] += mulNTL (bufFactors [0] [0], bufFactors [1] [j + 1]); |
---|
| 3907 | else |
---|
| 3908 | tmp[0] += mulNTL (bufFactors [0], bufFactors [1] [j + 1]); |
---|
[08daea] | 3909 | } |
---|
[1b8e048] | 3910 | |
---|
[08daea] | 3911 | Pi [0] += tmp[0]*xToJ*F.mvar(); |
---|
[327efa2] | 3912 | |
---|
| 3913 | int degPi, degBuf; |
---|
| 3914 | for (int l= 1; l < factors.length() - 1; l++) |
---|
| 3915 | { |
---|
| 3916 | degPi= degree (Pi [l - 1], x); |
---|
| 3917 | degBuf= degree (bufFactors[l + 1], x); |
---|
| 3918 | if (degPi > 0 && degBuf > 0) |
---|
| 3919 | { |
---|
| 3920 | M (j + 1, l + 1)= mulNTL (Pi [l - 1] [j], bufFactors[l + 1] [j]); |
---|
| 3921 | if (j + 2 <= M.rows()) |
---|
| 3922 | M (j + 2, l + 1)= mulNTL (Pi [l - 1][j + 1], bufFactors[l + 1] [j + 1]); |
---|
| 3923 | } |
---|
| 3924 | |
---|
| 3925 | if (degPi > 0 && degBuf > 0) |
---|
| 3926 | uIZeroJ= mulNTL (Pi[l -1] [0], buf[l + 1]) + |
---|
| 3927 | mulNTL (uIZeroJ, bufFactors[l+1] [0]); |
---|
| 3928 | else if (degPi > 0) |
---|
| 3929 | uIZeroJ= mulNTL (uIZeroJ, bufFactors[l + 1]); |
---|
| 3930 | else if (degBuf > 0) |
---|
| 3931 | uIZeroJ= mulNTL (Pi[l - 1], buf[1]); |
---|
| 3932 | else |
---|
| 3933 | uIZeroJ= 0; |
---|
| 3934 | |
---|
| 3935 | Pi [l] += xToJ*uIZeroJ; |
---|
| 3936 | |
---|
| 3937 | one= bufFactors [l + 1]; |
---|
| 3938 | two= Pi [l - 1]; |
---|
| 3939 | if (degBuf > 0 && degPi > 0) |
---|
| 3940 | { |
---|
| 3941 | while (one.hasTerms() && one.exp() > j) one++; |
---|
| 3942 | while (two.hasTerms() && two.exp() > j) two++; |
---|
| 3943 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
| 3944 | { |
---|
| 3945 | if (k != j - k + 1) |
---|
| 3946 | { |
---|
| 3947 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
| 3948 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
| 3949 | { |
---|
| 3950 | tmp[l] += mulNTL ((bufFactors[l + 1] [k] + one.coeff()), |
---|
| 3951 | (Pi[l - 1] [k] + two.coeff())) - M (k + 1, l + 1) - |
---|
| 3952 | M (j - k + 2, l + 1); |
---|
| 3953 | one++; |
---|
| 3954 | two++; |
---|
| 3955 | } |
---|
| 3956 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
| 3957 | { |
---|
| 3958 | tmp[l] += mulNTL ((bufFactors[l + 1] [k] + one.coeff()), |
---|
| 3959 | Pi[l - 1] [k]) - M (k + 1, l + 1); |
---|
| 3960 | one++; |
---|
| 3961 | } |
---|
| 3962 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
| 3963 | { |
---|
| 3964 | tmp[l] += mulNTL (bufFactors[l + 1] [k], |
---|
| 3965 | (Pi[l - 1] [k] + two.coeff())) - M (k + 1, l + 1); |
---|
| 3966 | two++; |
---|
| 3967 | } |
---|
| 3968 | } |
---|
| 3969 | else |
---|
| 3970 | tmp[l] += M (k + 1, l + 1); |
---|
| 3971 | } |
---|
| 3972 | } |
---|
| 3973 | |
---|
| 3974 | if (degPi >= j + 1 && degBuf >= j + 1) |
---|
| 3975 | { |
---|
| 3976 | if (j + 2 <= M.rows()) |
---|
| 3977 | tmp [l] += mulNTL ((Pi [l - 1] [j + 1]+ Pi [l - 1] [0]), |
---|
| 3978 | (bufFactors [l + 1] [j + 1] + bufFactors [l + 1] [0]) |
---|
| 3979 | ) - M(1,l+1) - M (j + 2,l+1); |
---|
| 3980 | } |
---|
| 3981 | else if (degPi >= j + 1) |
---|
| 3982 | { |
---|
| 3983 | if (degBuf > 0) |
---|
| 3984 | tmp[l] += mulNTL (Pi [l - 1] [j+1], bufFactors [l + 1] [0]); |
---|
| 3985 | else |
---|
| 3986 | tmp[l] += mulNTL (Pi [l - 1] [j+1], bufFactors [l + 1]); |
---|
| 3987 | } |
---|
| 3988 | else if (degBuf >= j + 1) |
---|
| 3989 | { |
---|
| 3990 | if (degPi > 0) |
---|
| 3991 | tmp[l] += mulNTL (Pi [l - 1] [0], bufFactors [l + 1] [j + 1]); |
---|
| 3992 | else |
---|
| 3993 | tmp[l] += mulNTL (Pi [l - 1], bufFactors [l + 1] [j + 1]); |
---|
| 3994 | } |
---|
| 3995 | |
---|
| 3996 | Pi[l] += tmp[l]*xToJ*F.mvar(); |
---|
| 3997 | } |
---|
[08daea] | 3998 | return; |
---|
| 3999 | } |
---|
| 4000 | |
---|
| 4001 | void |
---|
| 4002 | henselLift122 (const CanonicalForm& F, CFList& factors, int l, CFArray& Pi, |
---|
| 4003 | CFList& diophant, CFMatrix& M, const CFArray& LCs, bool sort) |
---|
| 4004 | { |
---|
| 4005 | if (sort) |
---|
| 4006 | sortList (factors, Variable (1)); |
---|
| 4007 | Pi= CFArray (factors.length() - 2); |
---|
| 4008 | CFList bufFactors2= factors; |
---|
| 4009 | bufFactors2.removeFirst(); |
---|
[327efa2] | 4010 | diophant= diophantine (F[0], bufFactors2); |
---|
[08daea] | 4011 | DEBOUTLN (cerr, "diophant= " << diophant); |
---|
| 4012 | |
---|
| 4013 | CFArray bufFactors= CFArray (bufFactors2.length()); |
---|
| 4014 | int i= 0; |
---|
| 4015 | for (CFListIterator k= bufFactors2; k.hasItem(); i++, k++) |
---|
| 4016 | bufFactors[i]= replaceLc (k.getItem(), LCs [i]); |
---|
| 4017 | |
---|
| 4018 | Variable x= F.mvar(); |
---|
| 4019 | if (degree (bufFactors[0], x) > 0 && degree (bufFactors [1], x) > 0) |
---|
| 4020 | { |
---|
| 4021 | M (1, 1)= mulNTL (bufFactors [0] [0], bufFactors[1] [0]); |
---|
| 4022 | Pi [0]= M (1, 1) + (mulNTL (bufFactors [0] [1], bufFactors[1] [0]) + |
---|
| 4023 | mulNTL (bufFactors [0] [0], bufFactors [1] [1]))*x; |
---|
| 4024 | } |
---|
| 4025 | else if (degree (bufFactors[0], x) > 0) |
---|
| 4026 | { |
---|
| 4027 | M (1, 1)= mulNTL (bufFactors [0] [0], bufFactors[1]); |
---|
| 4028 | Pi [0]= M (1, 1) + |
---|
| 4029 | mulNTL (bufFactors [0] [1], bufFactors[1])*x; |
---|
| 4030 | } |
---|
| 4031 | else if (degree (bufFactors[1], x) > 0) |
---|
| 4032 | { |
---|
| 4033 | M (1, 1)= mulNTL (bufFactors [0], bufFactors[1] [0]); |
---|
| 4034 | Pi [0]= M (1, 1) + |
---|
| 4035 | mulNTL (bufFactors [0], bufFactors[1] [1])*x; |
---|
| 4036 | } |
---|
| 4037 | else |
---|
| 4038 | { |
---|
| 4039 | M (1, 1)= mulNTL (bufFactors [0], bufFactors[1]); |
---|
| 4040 | Pi [0]= M (1, 1); |
---|
| 4041 | } |
---|
| 4042 | |
---|
[327efa2] | 4043 | for (i= 1; i < Pi.size(); i++) |
---|
| 4044 | { |
---|
| 4045 | if (degree (Pi[i-1], x) > 0 && degree (bufFactors [i+1], x) > 0) |
---|
| 4046 | { |
---|
| 4047 | M (1,i+1)= mulNTL (Pi[i-1] [0], bufFactors[i+1] [0]); |
---|
| 4048 | Pi [i]= M (1,i+1) + (mulNTL (Pi[i-1] [1], bufFactors[i+1] [0]) + |
---|
| 4049 | mulNTL (Pi[i-1] [0], bufFactors [i+1] [1]))*x; |
---|
| 4050 | } |
---|
| 4051 | else if (degree (Pi[i-1], x) > 0) |
---|
| 4052 | { |
---|
| 4053 | M (1,i+1)= mulNTL (Pi[i-1] [0], bufFactors [i+1]); |
---|
| 4054 | Pi [i]= M(1,i+1) + mulNTL (Pi[i-1] [1], bufFactors[i+1])*x; |
---|
| 4055 | } |
---|
| 4056 | else if (degree (bufFactors[i+1], x) > 0) |
---|
| 4057 | { |
---|
| 4058 | M (1,i+1)= mulNTL (Pi[i-1], bufFactors [i+1] [0]); |
---|
| 4059 | Pi [i]= M (1,i+1) + mulNTL (Pi[i-1], bufFactors[i+1] [1])*x; |
---|
| 4060 | } |
---|
| 4061 | else |
---|
| 4062 | { |
---|
| 4063 | M (1,i+1)= mulNTL (Pi [i-1], bufFactors [i+1]); |
---|
| 4064 | Pi [i]= M (1,i+1); |
---|
| 4065 | } |
---|
| 4066 | } |
---|
| 4067 | |
---|
[08daea] | 4068 | for (i= 1; i < l; i++) |
---|
| 4069 | henselStep122 (F, bufFactors2, bufFactors, diophant, M, Pi, i, LCs); |
---|
| 4070 | |
---|
| 4071 | factors= CFList(); |
---|
| 4072 | for (i= 0; i < bufFactors.size(); i++) |
---|
| 4073 | factors.append (bufFactors[i]); |
---|
| 4074 | return; |
---|
| 4075 | } |
---|
| 4076 | |
---|
[327efa2] | 4077 | |
---|
[c1b9927] | 4078 | /// solve \f$ E=sum_{i= 1}^{r}{\sigma_{i}prod_{j=1, j\neq i}^{r}{f_{i}}}\f$ |
---|
[08daea] | 4079 | /// mod M, products contains \f$ prod_{j=1, j\neq i}^{r}{f_{i}}} \f$ |
---|
| 4080 | static inline |
---|
| 4081 | CFList |
---|
[c1b9927] | 4082 | diophantine (const CFList& recResult, const CFList& factors, |
---|
[e368746] | 4083 | const CFList& products, const CFList& M, const CanonicalForm& E, |
---|
| 4084 | bool& bad) |
---|
[08daea] | 4085 | { |
---|
| 4086 | if (M.isEmpty()) |
---|
| 4087 | { |
---|
| 4088 | CFList result; |
---|
| 4089 | CFListIterator j= factors; |
---|
| 4090 | CanonicalForm buf; |
---|
| 4091 | for (CFListIterator i= recResult; i.hasItem(); i++, j++) |
---|
| 4092 | { |
---|
| 4093 | ASSERT (E.isUnivariate() || E.inCoeffDomain(), |
---|
| 4094 | "constant or univariate poly expected"); |
---|
| 4095 | ASSERT (i.getItem().isUnivariate() || i.getItem().inCoeffDomain(), |
---|
| 4096 | "constant or univariate poly expected"); |
---|
| 4097 | ASSERT (j.getItem().isUnivariate() || j.getItem().inCoeffDomain(), |
---|
| 4098 | "constant or univariate poly expected"); |
---|
| 4099 | buf= mulNTL (E, i.getItem()); |
---|
| 4100 | result.append (modNTL (buf, j.getItem())); |
---|
| 4101 | } |
---|
| 4102 | return result; |
---|
| 4103 | } |
---|
| 4104 | Variable y= M.getLast().mvar(); |
---|
| 4105 | CFList bufFactors= factors; |
---|
| 4106 | for (CFListIterator i= bufFactors; i.hasItem(); i++) |
---|
| 4107 | i.getItem()= mod (i.getItem(), y); |
---|
| 4108 | CFList bufProducts= products; |
---|
| 4109 | for (CFListIterator i= bufProducts; i.hasItem(); i++) |
---|
| 4110 | i.getItem()= mod (i.getItem(), y); |
---|
| 4111 | CFList buf= M; |
---|
| 4112 | buf.removeLast(); |
---|
| 4113 | CanonicalForm bufE= mod (E, y); |
---|
| 4114 | CFList recDiophantine= diophantine (recResult, bufFactors, bufProducts, buf, |
---|
[e368746] | 4115 | bufE, bad); |
---|
| 4116 | |
---|
| 4117 | if (bad) |
---|
| 4118 | return CFList(); |
---|
[08daea] | 4119 | |
---|
| 4120 | CanonicalForm e= E; |
---|
| 4121 | CFListIterator j= products; |
---|
| 4122 | for (CFListIterator i= recDiophantine; i.hasItem(); i++, j++) |
---|
[e368746] | 4123 | e -= i.getItem()*j.getItem(); |
---|
[08daea] | 4124 | |
---|
| 4125 | CFList result= recDiophantine; |
---|
| 4126 | int d= degree (M.getLast()); |
---|
| 4127 | CanonicalForm coeffE; |
---|
| 4128 | for (int i= 1; i < d; i++) |
---|
| 4129 | { |
---|
| 4130 | if (degree (e, y) > 0) |
---|
| 4131 | coeffE= e[i]; |
---|
| 4132 | else |
---|
| 4133 | coeffE= 0; |
---|
| 4134 | if (!coeffE.isZero()) |
---|
| 4135 | { |
---|
| 4136 | CFListIterator k= result; |
---|
| 4137 | recDiophantine= diophantine (recResult, bufFactors, bufProducts, buf, |
---|
[e368746] | 4138 | coeffE, bad); |
---|
| 4139 | if (bad) |
---|
| 4140 | return CFList(); |
---|
[08daea] | 4141 | CFListIterator l= products; |
---|
| 4142 | for (j= recDiophantine; j.hasItem(); j++, k++, l++) |
---|
| 4143 | { |
---|
| 4144 | k.getItem() += j.getItem()*power (y, i); |
---|
[e368746] | 4145 | e -= j.getItem()*power (y, i)*l.getItem(); |
---|
[08daea] | 4146 | } |
---|
| 4147 | } |
---|
| 4148 | if (e.isZero()) |
---|
| 4149 | break; |
---|
| 4150 | } |
---|
[e368746] | 4151 | if (!e.isZero()) |
---|
[08daea] | 4152 | { |
---|
[e368746] | 4153 | bad= true; |
---|
| 4154 | return CFList(); |
---|
[08daea] | 4155 | } |
---|
| 4156 | return result; |
---|
| 4157 | } |
---|
| 4158 | |
---|
| 4159 | static inline |
---|
| 4160 | void |
---|
| 4161 | henselStep2 (const CanonicalForm& F, const CFList& factors, CFArray& bufFactors, |
---|
| 4162 | const CFList& diophant, CFMatrix& M, CFArray& Pi, |
---|
[e368746] | 4163 | const CFList& products, int j, const CFList& MOD, bool& noOneToOne) |
---|
[08daea] | 4164 | { |
---|
| 4165 | CanonicalForm E; |
---|
| 4166 | CanonicalForm xToJ= power (F.mvar(), j); |
---|
| 4167 | Variable x= F.mvar(); |
---|
| 4168 | |
---|
| 4169 | // compute the error |
---|
| 4170 | #ifdef DEBUGOUTPUT |
---|
| 4171 | CanonicalForm test= 1; |
---|
| 4172 | for (int i= 0; i < factors.length(); i++) |
---|
| 4173 | { |
---|
| 4174 | if (i == 0) |
---|
| 4175 | test *= mod (bufFactors [i], power (x, j)); |
---|
| 4176 | else |
---|
| 4177 | test *= bufFactors[i]; |
---|
| 4178 | } |
---|
| 4179 | test= mod (test, power (x, j)); |
---|
| 4180 | test= mod (test, MOD); |
---|
| 4181 | CanonicalForm test2= mod (F, power (x, j - 1)) - mod (test, power (x, j-1)); |
---|
| 4182 | DEBOUTLN (cerr, "test= " << test2); |
---|
| 4183 | #endif |
---|
| 4184 | |
---|
| 4185 | if (degree (Pi [factors.length() - 2], x) > 0) |
---|
| 4186 | E= F[j] - Pi [factors.length() - 2] [j]; |
---|
| 4187 | else |
---|
| 4188 | E= F[j]; |
---|
| 4189 | |
---|
| 4190 | CFArray buf= CFArray (diophant.length()); |
---|
| 4191 | |
---|
| 4192 | // actual lifting |
---|
[e368746] | 4193 | CFList diophantine2= diophantine (diophant, factors, products, MOD, E, |
---|
| 4194 | noOneToOne); |
---|
| 4195 | |
---|
| 4196 | if (noOneToOne) |
---|
| 4197 | return; |
---|
[08daea] | 4198 | |
---|
| 4199 | int k= 0; |
---|
| 4200 | for (CFListIterator i= diophantine2; k < factors.length(); k++, i++) |
---|
| 4201 | { |
---|
| 4202 | buf[k]= i.getItem(); |
---|
| 4203 | bufFactors[k] += xToJ*i.getItem(); |
---|
| 4204 | } |
---|
| 4205 | |
---|
| 4206 | // update Pi [0] |
---|
| 4207 | int degBuf0= degree (bufFactors[0], x); |
---|
| 4208 | int degBuf1= degree (bufFactors[1], x); |
---|
| 4209 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 4210 | { |
---|
| 4211 | M (j + 1, 1)= mulMod (bufFactors[0] [j], bufFactors[1] [j], MOD); |
---|
| 4212 | if (j + 2 <= M.rows()) |
---|
| 4213 | M (j + 2, 1)= mulMod (bufFactors[0] [j + 1], bufFactors[1] [j + 1], MOD); |
---|
| 4214 | } |
---|
| 4215 | CanonicalForm uIZeroJ; |
---|
| 4216 | |
---|
[1b8e048] | 4217 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 4218 | uIZeroJ= mulMod (bufFactors[0] [0], buf[1], MOD) + |
---|
| 4219 | mulMod (bufFactors[1] [0], buf[0], MOD); |
---|
| 4220 | else if (degBuf0 > 0) |
---|
| 4221 | uIZeroJ= mulMod (buf[0], bufFactors[1], MOD); |
---|
| 4222 | else if (degBuf1 > 0) |
---|
| 4223 | uIZeroJ= mulMod (bufFactors[0], buf[1], MOD); |
---|
| 4224 | else |
---|
| 4225 | uIZeroJ= 0; |
---|
[c1b9927] | 4226 | Pi [0] += xToJ*uIZeroJ; |
---|
[08daea] | 4227 | |
---|
| 4228 | CFArray tmp= CFArray (factors.length() - 1); |
---|
| 4229 | for (k= 0; k < factors.length() - 1; k++) |
---|
| 4230 | tmp[k]= 0; |
---|
| 4231 | CFIterator one, two; |
---|
| 4232 | one= bufFactors [0]; |
---|
| 4233 | two= bufFactors [1]; |
---|
| 4234 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 4235 | { |
---|
[1b8e048] | 4236 | while (one.hasTerms() && one.exp() > j) one++; |
---|
| 4237 | while (two.hasTerms() && two.exp() > j) two++; |
---|
[08daea] | 4238 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
| 4239 | { |
---|
| 4240 | if (k != j - k + 1) |
---|
| 4241 | { |
---|
[c1b9927] | 4242 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
[e368746] | 4243 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
[08daea] | 4244 | { |
---|
| 4245 | tmp[0] += mulMod ((bufFactors[0] [k] + one.coeff()), |
---|
| 4246 | (bufFactors[1] [k] + two.coeff()), MOD) - M (k + 1, 1) - |
---|
| 4247 | M (j - k + 2, 1); |
---|
| 4248 | one++; |
---|
| 4249 | two++; |
---|
| 4250 | } |
---|
[e368746] | 4251 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
[08daea] | 4252 | { |
---|
| 4253 | tmp[0] += mulMod ((bufFactors[0] [k] + one.coeff()), |
---|
| 4254 | bufFactors[1] [k], MOD) - M (k + 1, 1); |
---|
| 4255 | one++; |
---|
| 4256 | } |
---|
[e368746] | 4257 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
[08daea] | 4258 | { |
---|
| 4259 | tmp[0] += mulMod (bufFactors[0] [k], (bufFactors[1] [k] + |
---|
| 4260 | two.coeff()), MOD) - M (k + 1, 1); |
---|
| 4261 | two++; |
---|
| 4262 | } |
---|
| 4263 | } |
---|
| 4264 | else |
---|
| 4265 | { |
---|
| 4266 | tmp[0] += M (k + 1, 1); |
---|
| 4267 | } |
---|
| 4268 | } |
---|
[1b8e048] | 4269 | } |
---|
[08daea] | 4270 | |
---|
[1b8e048] | 4271 | if (degBuf0 >= j + 1 && degBuf1 >= j + 1) |
---|
| 4272 | { |
---|
[08daea] | 4273 | if (j + 2 <= M.rows()) |
---|
[1b8e048] | 4274 | tmp [0] += mulMod ((bufFactors [0] [j + 1]+ bufFactors [0] [0]), |
---|
| 4275 | (bufFactors [1] [j + 1] + bufFactors [1] [0]), MOD) |
---|
| 4276 | - M(1,1) - M (j + 2,1); |
---|
| 4277 | } |
---|
| 4278 | else if (degBuf0 >= j + 1) |
---|
| 4279 | { |
---|
| 4280 | if (degBuf1 > 0) |
---|
| 4281 | tmp[0] += mulMod (bufFactors [0] [j+1], bufFactors [1] [0], MOD); |
---|
| 4282 | else |
---|
| 4283 | tmp[0] += mulMod (bufFactors [0] [j+1], bufFactors [1], MOD); |
---|
| 4284 | } |
---|
| 4285 | else if (degBuf1 >= j + 1) |
---|
| 4286 | { |
---|
| 4287 | if (degBuf0 > 0) |
---|
| 4288 | tmp[0] += mulMod (bufFactors [0] [0], bufFactors [1] [j + 1], MOD); |
---|
| 4289 | else |
---|
| 4290 | tmp[0] += mulMod (bufFactors [0], bufFactors [1] [j + 1], MOD); |
---|
[08daea] | 4291 | } |
---|
| 4292 | Pi [0] += tmp[0]*xToJ*F.mvar(); |
---|
| 4293 | |
---|
| 4294 | // update Pi [l] |
---|
| 4295 | int degPi, degBuf; |
---|
| 4296 | for (int l= 1; l < factors.length() - 1; l++) |
---|
| 4297 | { |
---|
| 4298 | degPi= degree (Pi [l - 1], x); |
---|
| 4299 | degBuf= degree (bufFactors[l + 1], x); |
---|
| 4300 | if (degPi > 0 && degBuf > 0) |
---|
| 4301 | { |
---|
[e368746] | 4302 | M (j + 1, l + 1)= mulMod (Pi [l - 1] [j], bufFactors[l + 1] [j], MOD); |
---|
| 4303 | if (j + 2 <= M.rows()) |
---|
| 4304 | M (j + 2, l + 1)= mulMod (Pi [l - 1] [j + 1], bufFactors[l + 1] [j + 1], |
---|
| 4305 | MOD); |
---|
[08daea] | 4306 | } |
---|
[e368746] | 4307 | |
---|
| 4308 | if (degPi > 0 && degBuf > 0) |
---|
| 4309 | uIZeroJ= mulMod (Pi[l -1] [0], buf[l + 1], MOD) + |
---|
| 4310 | mulMod (uIZeroJ, bufFactors[l+1] [0], MOD); |
---|
| 4311 | else if (degPi > 0) |
---|
| 4312 | uIZeroJ= mulMod (uIZeroJ, bufFactors[l + 1], MOD); |
---|
| 4313 | else if (degBuf > 0) |
---|
| 4314 | uIZeroJ= mulMod (Pi[l - 1], buf[1], MOD); |
---|
[08daea] | 4315 | else |
---|
[e368746] | 4316 | uIZeroJ= 0; |
---|
| 4317 | |
---|
| 4318 | Pi [l] += xToJ*uIZeroJ; |
---|
| 4319 | |
---|
[08daea] | 4320 | one= bufFactors [l + 1]; |
---|
| 4321 | two= Pi [l - 1]; |
---|
| 4322 | if (degBuf > 0 && degPi > 0) |
---|
| 4323 | { |
---|
[e368746] | 4324 | while (one.hasTerms() && one.exp() > j) one++; |
---|
| 4325 | while (two.hasTerms() && two.exp() > j) two++; |
---|
[08daea] | 4326 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
| 4327 | { |
---|
| 4328 | if (k != j - k + 1) |
---|
| 4329 | { |
---|
[e368746] | 4330 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
| 4331 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
[08daea] | 4332 | { |
---|
| 4333 | tmp[l] += mulMod ((bufFactors[l + 1] [k] + one.coeff()), |
---|
| 4334 | (Pi[l - 1] [k] + two.coeff()), MOD) - M (k + 1, l + 1) - |
---|
| 4335 | M (j - k + 2, l + 1); |
---|
| 4336 | one++; |
---|
| 4337 | two++; |
---|
| 4338 | } |
---|
[e368746] | 4339 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
[08daea] | 4340 | { |
---|
| 4341 | tmp[l] += mulMod ((bufFactors[l + 1] [k] + one.coeff()), |
---|
| 4342 | Pi[l - 1] [k], MOD) - M (k + 1, l + 1); |
---|
| 4343 | one++; |
---|
| 4344 | } |
---|
[e368746] | 4345 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
[08daea] | 4346 | { |
---|
[c1b9927] | 4347 | tmp[l] += mulMod (bufFactors[l + 1] [k], |
---|
[08daea] | 4348 | (Pi[l - 1] [k] + two.coeff()), MOD) - M (k + 1, l + 1); |
---|
| 4349 | two++; |
---|
[e368746] | 4350 | } |
---|
[08daea] | 4351 | } |
---|
| 4352 | else |
---|
| 4353 | tmp[l] += M (k + 1, l + 1); |
---|
| 4354 | } |
---|
| 4355 | } |
---|
[e368746] | 4356 | |
---|
| 4357 | if (degPi >= j + 1 && degBuf >= j + 1) |
---|
| 4358 | { |
---|
| 4359 | if (j + 2 <= M.rows()) |
---|
| 4360 | tmp [l] += mulMod ((Pi [l - 1] [j + 1]+ Pi [l - 1] [0]), |
---|
| 4361 | (bufFactors [l + 1] [j + 1] + bufFactors [l + 1] [0]) |
---|
| 4362 | , MOD) - M(1,l+1) - M (j + 2,l+1); |
---|
| 4363 | } |
---|
| 4364 | else if (degPi >= j + 1) |
---|
| 4365 | { |
---|
| 4366 | if (degBuf > 0) |
---|
| 4367 | tmp[l] += mulMod (Pi [l - 1] [j+1], bufFactors [l + 1] [0], MOD); |
---|
| 4368 | else |
---|
| 4369 | tmp[l] += mulMod (Pi [l - 1] [j+1], bufFactors [l + 1], MOD); |
---|
| 4370 | } |
---|
| 4371 | else if (degBuf >= j + 1) |
---|
| 4372 | { |
---|
| 4373 | if (degPi > 0) |
---|
| 4374 | tmp[l] += mulMod (Pi [l - 1] [0], bufFactors [l + 1] [j + 1], MOD); |
---|
| 4375 | else |
---|
| 4376 | tmp[l] += mulMod (Pi [l - 1], bufFactors [l + 1] [j + 1], MOD); |
---|
| 4377 | } |
---|
| 4378 | |
---|
[08daea] | 4379 | Pi[l] += tmp[l]*xToJ*F.mvar(); |
---|
| 4380 | } |
---|
| 4381 | return; |
---|
| 4382 | } |
---|
| 4383 | |
---|
| 4384 | // wrt. Variable (1) |
---|
| 4385 | CanonicalForm replaceLC (const CanonicalForm& F, const CanonicalForm& c) |
---|
| 4386 | { |
---|
| 4387 | if (degree (F, 1) <= 0) |
---|
| 4388 | return c; |
---|
| 4389 | else |
---|
| 4390 | { |
---|
| 4391 | CanonicalForm result= swapvar (F, Variable (F.level() + 1), Variable (1)); |
---|
| 4392 | result += (swapvar (c, Variable (F.level() + 1), Variable (1)) |
---|
| 4393 | - LC (result))*power (result.mvar(), degree (result)); |
---|
| 4394 | return swapvar (result, Variable (F.level() + 1), Variable (1)); |
---|
| 4395 | } |
---|
| 4396 | } |
---|
| 4397 | |
---|
| 4398 | CFList |
---|
| 4399 | henselLift232 (const CFList& eval, const CFList& factors, int* l, CFList& |
---|
| 4400 | diophant, CFArray& Pi, CFMatrix& M, const CFList& LCs1, |
---|
[e368746] | 4401 | const CFList& LCs2, bool& bad) |
---|
[08daea] | 4402 | { |
---|
| 4403 | CFList buf= factors; |
---|
| 4404 | int k= 0; |
---|
| 4405 | int liftBoundBivar= l[k]; |
---|
| 4406 | CFList bufbuf= factors; |
---|
| 4407 | Variable v= Variable (2); |
---|
| 4408 | |
---|
| 4409 | CFList MOD; |
---|
| 4410 | MOD.append (power (Variable (2), liftBoundBivar)); |
---|
| 4411 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 4412 | k= 0; |
---|
| 4413 | CFListIterator j= eval; |
---|
| 4414 | j++; |
---|
| 4415 | CFListIterator iter1= LCs1; |
---|
| 4416 | CFListIterator iter2= LCs2; |
---|
| 4417 | iter1++; |
---|
| 4418 | iter2++; |
---|
| 4419 | bufFactors[0]= replaceLC (buf.getFirst(), iter1.getItem()); |
---|
| 4420 | bufFactors[1]= replaceLC (buf.getLast(), iter2.getItem()); |
---|
| 4421 | |
---|
| 4422 | CFListIterator i= buf; |
---|
| 4423 | i++; |
---|
| 4424 | Variable y= j.getItem().mvar(); |
---|
| 4425 | if (y.level() != 3) |
---|
| 4426 | y= Variable (3); |
---|
| 4427 | |
---|
| 4428 | Pi[0]= mod (Pi[0], power (v, liftBoundBivar)); |
---|
| 4429 | M (1, 1)= Pi[0]; |
---|
| 4430 | if (degree (bufFactors[0], y) > 0 && degree (bufFactors [1], y) > 0) |
---|
| 4431 | Pi [0] += (mulMod (bufFactors [0] [1], bufFactors[1] [0], MOD) + |
---|
| 4432 | mulMod (bufFactors [0] [0], bufFactors [1] [1], MOD))*y; |
---|
| 4433 | else if (degree (bufFactors[0], y) > 0) |
---|
| 4434 | Pi [0] += mulMod (bufFactors [0] [1], bufFactors[1], MOD)*y; |
---|
| 4435 | else if (degree (bufFactors[1], y) > 0) |
---|
| 4436 | Pi [0] += mulMod (bufFactors [0], bufFactors[1] [1], MOD)*y; |
---|
| 4437 | |
---|
| 4438 | CFList products; |
---|
| 4439 | for (int i= 0; i < bufFactors.size(); i++) |
---|
| 4440 | { |
---|
| 4441 | if (degree (bufFactors[i], y) > 0) |
---|
[e368746] | 4442 | products.append (eval.getFirst()/bufFactors[i] [0]); |
---|
[08daea] | 4443 | else |
---|
[e368746] | 4444 | products.append (eval.getFirst()/bufFactors[i]); |
---|
[08daea] | 4445 | } |
---|
| 4446 | |
---|
| 4447 | for (int d= 1; d < l[1]; d++) |
---|
[e368746] | 4448 | { |
---|
| 4449 | henselStep2 (j.getItem(), buf, bufFactors, diophant, M, Pi, products, d, MOD, bad); |
---|
| 4450 | if (bad) |
---|
| 4451 | return CFList(); |
---|
| 4452 | } |
---|
[08daea] | 4453 | CFList result; |
---|
| 4454 | for (k= 0; k < factors.length(); k++) |
---|
| 4455 | result.append (bufFactors[k]); |
---|
| 4456 | return result; |
---|
| 4457 | } |
---|
| 4458 | |
---|
| 4459 | |
---|
| 4460 | CFList |
---|
| 4461 | henselLift2 (const CFList& F, const CFList& factors, const CFList& MOD, CFList& |
---|
| 4462 | diophant, CFArray& Pi, CFMatrix& M, const int lOld, int& |
---|
[e368746] | 4463 | lNew, const CFList& LCs1, const CFList& LCs2, bool& bad) |
---|
[08daea] | 4464 | { |
---|
| 4465 | int k= 0; |
---|
| 4466 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 4467 | bufFactors[0]= replaceLC (factors.getFirst(), LCs1.getLast()); |
---|
| 4468 | bufFactors[1]= replaceLC (factors.getLast(), LCs2.getLast()); |
---|
| 4469 | CFList buf= factors; |
---|
| 4470 | Variable y= F.getLast().mvar(); |
---|
| 4471 | Variable x= F.getFirst().mvar(); |
---|
| 4472 | CanonicalForm xToLOld= power (x, lOld); |
---|
| 4473 | Pi [0]= mod (Pi[0], xToLOld); |
---|
| 4474 | M (1, 1)= Pi [0]; |
---|
| 4475 | |
---|
| 4476 | if (degree (bufFactors[0], y) > 0 && degree (bufFactors [1], y) > 0) |
---|
[c1b9927] | 4477 | Pi [0] += (mulMod (bufFactors [0] [1], bufFactors[1] [0], MOD) + |
---|
[08daea] | 4478 | mulMod (bufFactors [0] [0], bufFactors [1] [1], MOD))*y; |
---|
| 4479 | else if (degree (bufFactors[0], y) > 0) |
---|
| 4480 | Pi [0] += mulMod (bufFactors [0] [1], bufFactors[1], MOD)*y; |
---|
| 4481 | else if (degree (bufFactors[1], y) > 0) |
---|
| 4482 | Pi [0] += mulMod (bufFactors [0], bufFactors[1] [1], MOD)*y; |
---|
| 4483 | |
---|
| 4484 | CFList products; |
---|
[21b8f4c] | 4485 | CanonicalForm quot; |
---|
[08daea] | 4486 | for (int i= 0; i < bufFactors.size(); i++) |
---|
| 4487 | { |
---|
| 4488 | if (degree (bufFactors[i], y) > 0) |
---|
| 4489 | { |
---|
[21b8f4c] | 4490 | if (!fdivides (bufFactors[i] [0], F.getFirst(), quot)) |
---|
[e368746] | 4491 | { |
---|
| 4492 | bad= true; |
---|
| 4493 | return CFList(); |
---|
| 4494 | } |
---|
[21b8f4c] | 4495 | products.append (quot); |
---|
[08daea] | 4496 | } |
---|
| 4497 | else |
---|
| 4498 | { |
---|
[21b8f4c] | 4499 | if (!fdivides (bufFactors[i], F.getFirst(), quot)) |
---|
[e368746] | 4500 | { |
---|
| 4501 | bad= true; |
---|
| 4502 | return CFList(); |
---|
| 4503 | } |
---|
[21b8f4c] | 4504 | products.append (quot); |
---|
[08daea] | 4505 | } |
---|
| 4506 | } |
---|
| 4507 | |
---|
| 4508 | for (int d= 1; d < lNew; d++) |
---|
[e368746] | 4509 | { |
---|
| 4510 | henselStep2 (F.getLast(), buf, bufFactors, diophant, M, Pi, products, d, MOD, bad); |
---|
| 4511 | if (bad) |
---|
| 4512 | return CFList(); |
---|
| 4513 | } |
---|
[08daea] | 4514 | |
---|
| 4515 | CFList result; |
---|
| 4516 | for (k= 0; k < factors.length(); k++) |
---|
| 4517 | result.append (bufFactors[k]); |
---|
| 4518 | return result; |
---|
| 4519 | } |
---|
| 4520 | |
---|
| 4521 | CFList |
---|
| 4522 | henselLift2 (const CFList& eval, const CFList& factors, int* l, const int |
---|
| 4523 | lLength, bool sort, const CFList& LCs1, const CFList& LCs2, |
---|
[e368746] | 4524 | const CFArray& Pi, const CFList& diophant, bool& bad) |
---|
[08daea] | 4525 | { |
---|
| 4526 | CFList bufDiophant= diophant; |
---|
| 4527 | CFList buf= factors; |
---|
| 4528 | if (sort) |
---|
| 4529 | sortList (buf, Variable (1)); |
---|
| 4530 | CFArray bufPi= Pi; |
---|
| 4531 | CFMatrix M= CFMatrix (l[1], factors.length()); |
---|
[e368746] | 4532 | CFList result= henselLift232(eval, buf, l, bufDiophant, bufPi, M, LCs1, LCs2, |
---|
| 4533 | bad); |
---|
| 4534 | if (bad) |
---|
| 4535 | return CFList(); |
---|
| 4536 | |
---|
[08daea] | 4537 | if (eval.length() == 2) |
---|
| 4538 | return result; |
---|
| 4539 | CFList MOD; |
---|
| 4540 | for (int i= 0; i < 2; i++) |
---|
| 4541 | MOD.append (power (Variable (i + 2), l[i])); |
---|
| 4542 | CFListIterator j= eval; |
---|
| 4543 | j++; |
---|
| 4544 | CFList bufEval; |
---|
| 4545 | bufEval.append (j.getItem()); |
---|
| 4546 | j++; |
---|
| 4547 | CFListIterator jj= LCs1; |
---|
| 4548 | CFListIterator jjj= LCs2; |
---|
| 4549 | CFList bufLCs1, bufLCs2; |
---|
| 4550 | jj++, jjj++; |
---|
| 4551 | bufLCs1.append (jj.getItem()); |
---|
| 4552 | bufLCs2.append (jjj.getItem()); |
---|
| 4553 | jj++, jjj++; |
---|
| 4554 | |
---|
[ea88e0] | 4555 | for (int i= 2; i < lLength && j.hasItem(); i++, j++, jj++, jjj++) |
---|
[08daea] | 4556 | { |
---|
| 4557 | bufEval.append (j.getItem()); |
---|
| 4558 | bufLCs1.append (jj.getItem()); |
---|
| 4559 | bufLCs2.append (jjj.getItem()); |
---|
| 4560 | M= CFMatrix (l[i], factors.length()); |
---|
| 4561 | result= henselLift2 (bufEval, result, MOD, bufDiophant, bufPi, M, l[i - 1], |
---|
[e368746] | 4562 | l[i], bufLCs1, bufLCs2, bad); |
---|
| 4563 | if (bad) |
---|
| 4564 | return CFList(); |
---|
[08daea] | 4565 | MOD.append (power (Variable (i + 2), l[i])); |
---|
| 4566 | bufEval.removeFirst(); |
---|
| 4567 | bufLCs1.removeFirst(); |
---|
| 4568 | bufLCs2.removeFirst(); |
---|
| 4569 | } |
---|
| 4570 | return result; |
---|
| 4571 | } |
---|
| 4572 | |
---|
[e368746] | 4573 | CFList |
---|
[c1b9927] | 4574 | nonMonicHenselLift23 (const CanonicalForm& F, const CFList& factors, const |
---|
[e368746] | 4575 | CFList& LCs, CFList& diophant, CFArray& Pi, int liftBound, |
---|
| 4576 | int bivarLiftBound, bool& bad) |
---|
| 4577 | { |
---|
| 4578 | CFList bufFactors2= factors; |
---|
| 4579 | |
---|
| 4580 | Variable y= Variable (2); |
---|
| 4581 | for (CFListIterator i= bufFactors2; i.hasItem(); i++) |
---|
| 4582 | i.getItem()= mod (i.getItem(), y); |
---|
| 4583 | |
---|
| 4584 | CanonicalForm bufF= F; |
---|
| 4585 | bufF= mod (bufF, y); |
---|
| 4586 | bufF= mod (bufF, Variable (3)); |
---|
| 4587 | |
---|
| 4588 | diophant= diophantine (bufF, bufFactors2); |
---|
| 4589 | |
---|
| 4590 | CFMatrix M= CFMatrix (liftBound, bufFactors2.length() - 1); |
---|
| 4591 | |
---|
| 4592 | Pi= CFArray (bufFactors2.length() - 1); |
---|
| 4593 | |
---|
| 4594 | CFArray bufFactors= CFArray (bufFactors2.length()); |
---|
| 4595 | CFListIterator j= LCs; |
---|
| 4596 | int i= 0; |
---|
| 4597 | for (CFListIterator k= factors; k.hasItem(); j++, k++, i++) |
---|
| 4598 | bufFactors[i]= replaceLC (k.getItem(), j.getItem()); |
---|
| 4599 | |
---|
| 4600 | //initialise Pi |
---|
| 4601 | Variable v= Variable (3); |
---|
| 4602 | CanonicalForm yToL= power (y, bivarLiftBound); |
---|
| 4603 | if (degree (bufFactors[0], v) > 0 && degree (bufFactors [1], v) > 0) |
---|
| 4604 | { |
---|
| 4605 | M (1, 1)= mulMod2 (bufFactors [0] [0], bufFactors[1] [0], yToL); |
---|
[c1b9927] | 4606 | Pi [0]= M (1,1) + (mulMod2 (bufFactors [0] [1], bufFactors[1] [0], yToL) + |
---|
[e368746] | 4607 | mulMod2 (bufFactors [0] [0], bufFactors [1] [1], yToL))*v; |
---|
| 4608 | } |
---|
| 4609 | else if (degree (bufFactors[0], v) > 0) |
---|
| 4610 | { |
---|
| 4611 | M (1,1)= mulMod2 (bufFactors [0] [0], bufFactors [1], yToL); |
---|
| 4612 | Pi [0]= M(1,1) + mulMod2 (bufFactors [0] [1], bufFactors[1], yToL)*v; |
---|
| 4613 | } |
---|
| 4614 | else if (degree (bufFactors[1], v) > 0) |
---|
| 4615 | { |
---|
| 4616 | M (1,1)= mulMod2 (bufFactors [0], bufFactors [1] [0], yToL); |
---|
| 4617 | Pi [0]= M (1,1) + mulMod2 (bufFactors [0], bufFactors[1] [1], yToL)*v; |
---|
| 4618 | } |
---|
| 4619 | else |
---|
| 4620 | { |
---|
| 4621 | M (1,1)= mulMod2 (bufFactors [0], bufFactors [1], yToL); |
---|
| 4622 | Pi [0]= M (1,1); |
---|
| 4623 | } |
---|
| 4624 | |
---|
| 4625 | for (i= 1; i < Pi.size(); i++) |
---|
| 4626 | { |
---|
| 4627 | if (degree (Pi[i-1], v) > 0 && degree (bufFactors [i+1], v) > 0) |
---|
| 4628 | { |
---|
| 4629 | M (1,i+1)= mulMod2 (Pi[i-1] [0], bufFactors[i+1] [0], yToL); |
---|
[c1b9927] | 4630 | Pi [i]= M (1,i+1) + (mulMod2 (Pi[i-1] [1], bufFactors[i+1] [0], yToL) + |
---|
[e368746] | 4631 | mulMod2 (Pi[i-1] [0], bufFactors [i+1] [1], yToL))*v; |
---|
| 4632 | } |
---|
| 4633 | else if (degree (Pi[i-1], v) > 0) |
---|
| 4634 | { |
---|
| 4635 | M (1,i+1)= mulMod2 (Pi[i-1] [0], bufFactors [i+1], yToL); |
---|
| 4636 | Pi [i]= M(1,i+1) + mulMod2 (Pi[i-1] [1], bufFactors[i+1], yToL)*v; |
---|
| 4637 | } |
---|
| 4638 | else if (degree (bufFactors[i+1], v) > 0) |
---|
| 4639 | { |
---|
| 4640 | M (1,i+1)= mulMod2 (Pi[i-1], bufFactors [i+1] [0], yToL); |
---|
| 4641 | Pi [i]= M (1,i+1) + mulMod2 (Pi[i-1], bufFactors[i+1] [1], yToL)*v; |
---|
| 4642 | } |
---|
| 4643 | else |
---|
| 4644 | { |
---|
| 4645 | M (1,i+1)= mulMod2 (Pi [i-1], bufFactors [i+1], yToL); |
---|
| 4646 | Pi [i]= M (1,i+1); |
---|
| 4647 | } |
---|
| 4648 | } |
---|
| 4649 | |
---|
| 4650 | CFList products; |
---|
| 4651 | bufF= mod (F, Variable (3)); |
---|
| 4652 | for (CFListIterator k= factors; k.hasItem(); k++) |
---|
| 4653 | products.append (bufF/k.getItem()); |
---|
| 4654 | |
---|
| 4655 | CFList MOD= CFList (power (v, liftBound)); |
---|
| 4656 | MOD.insert (yToL); |
---|
| 4657 | for (int d= 1; d < liftBound; d++) |
---|
| 4658 | { |
---|
| 4659 | henselStep2 (F, factors, bufFactors, diophant, M, Pi, products, d, MOD, bad); |
---|
| 4660 | if (bad) |
---|
| 4661 | return CFList(); |
---|
| 4662 | } |
---|
| 4663 | |
---|
| 4664 | CFList result; |
---|
| 4665 | for (i= 0; i < factors.length(); i++) |
---|
| 4666 | result.append (bufFactors[i]); |
---|
| 4667 | return result; |
---|
| 4668 | } |
---|
| 4669 | |
---|
| 4670 | CFList |
---|
| 4671 | nonMonicHenselLift (const CFList& F, const CFList& factors, const CFList& LCs, |
---|
| 4672 | CFList& diophant, CFArray& Pi, CFMatrix& M, const int lOld, |
---|
| 4673 | int& lNew, const CFList& MOD, bool& noOneToOne |
---|
| 4674 | ) |
---|
| 4675 | { |
---|
| 4676 | |
---|
| 4677 | int k= 0; |
---|
| 4678 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 4679 | CFListIterator j= LCs; |
---|
| 4680 | for (CFListIterator i= factors; i.hasItem(); i++, j++, k++) |
---|
| 4681 | bufFactors [k]= replaceLC (i.getItem(), j.getItem()); |
---|
| 4682 | |
---|
| 4683 | Variable y= F.getLast().mvar(); |
---|
| 4684 | Variable x= F.getFirst().mvar(); |
---|
| 4685 | CanonicalForm xToLOld= power (x, lOld); |
---|
| 4686 | |
---|
| 4687 | Pi [0]= mod (Pi[0], xToLOld); |
---|
| 4688 | M (1, 1)= Pi [0]; |
---|
| 4689 | |
---|
| 4690 | if (degree (bufFactors[0], y) > 0 && degree (bufFactors [1], y) > 0) |
---|
[c1b9927] | 4691 | Pi [0] += (mulMod (bufFactors [0] [1], bufFactors[1] [0], MOD) + |
---|
[e368746] | 4692 | mulMod (bufFactors [0] [0], bufFactors [1] [1], MOD))*y; |
---|
| 4693 | else if (degree (bufFactors[0], y) > 0) |
---|
| 4694 | Pi [0] += mulMod (bufFactors [0] [1], bufFactors[1], MOD)*y; |
---|
| 4695 | else if (degree (bufFactors[1], y) > 0) |
---|
| 4696 | Pi [0] += mulMod (bufFactors [0], bufFactors[1] [1], MOD)*y; |
---|
| 4697 | |
---|
| 4698 | for (int i= 1; i < Pi.size(); i++) |
---|
| 4699 | { |
---|
| 4700 | Pi [i]= mod (Pi [i], xToLOld); |
---|
| 4701 | M (1, i + 1)= Pi [i]; |
---|
| 4702 | |
---|
| 4703 | if (degree (Pi[i-1], y) > 0 && degree (bufFactors [i+1], y) > 0) |
---|
| 4704 | Pi [i] += (mulMod (Pi[i-1] [1], bufFactors[i+1] [0], MOD) + |
---|
| 4705 | mulMod (Pi[i-1] [0], bufFactors [i+1] [1], MOD))*y; |
---|
| 4706 | else if (degree (Pi[i-1], y) > 0) |
---|
| 4707 | Pi [i] += mulMod (Pi[i-1] [1], bufFactors[i+1], MOD)*y; |
---|
| 4708 | else if (degree (bufFactors[i+1], y) > 0) |
---|
| 4709 | Pi [i] += mulMod (Pi[i-1], bufFactors[i+1] [1], MOD)*y; |
---|
| 4710 | } |
---|
| 4711 | |
---|
| 4712 | CFList products; |
---|
[21b8f4c] | 4713 | CanonicalForm quot, bufF= F.getFirst(); |
---|
[e368746] | 4714 | |
---|
| 4715 | for (int i= 0; i < bufFactors.size(); i++) |
---|
| 4716 | { |
---|
| 4717 | if (degree (bufFactors[i], y) > 0) |
---|
| 4718 | { |
---|
[21b8f4c] | 4719 | if (!fdivides (bufFactors[i] [0], bufF, quot)) |
---|
[e368746] | 4720 | { |
---|
| 4721 | noOneToOne= true; |
---|
| 4722 | return factors; |
---|
| 4723 | } |
---|
[21b8f4c] | 4724 | products.append (quot); |
---|
[e368746] | 4725 | } |
---|
| 4726 | else |
---|
| 4727 | { |
---|
[21b8f4c] | 4728 | if (!fdivides (bufFactors[i], bufF, quot)) |
---|
[e368746] | 4729 | { |
---|
| 4730 | noOneToOne= true; |
---|
| 4731 | return factors; |
---|
| 4732 | } |
---|
[21b8f4c] | 4733 | products.append (quot); |
---|
[e368746] | 4734 | } |
---|
| 4735 | } |
---|
| 4736 | |
---|
| 4737 | for (int d= 1; d < lNew; d++) |
---|
| 4738 | { |
---|
| 4739 | henselStep2 (F.getLast(), factors, bufFactors, diophant, M, Pi, products, d, |
---|
| 4740 | MOD, noOneToOne); |
---|
| 4741 | if (noOneToOne) |
---|
| 4742 | return CFList(); |
---|
| 4743 | } |
---|
| 4744 | |
---|
| 4745 | CFList result; |
---|
| 4746 | for (k= 0; k < factors.length(); k++) |
---|
| 4747 | result.append (bufFactors[k]); |
---|
| 4748 | return result; |
---|
| 4749 | } |
---|
| 4750 | |
---|
| 4751 | CFList |
---|
| 4752 | nonMonicHenselLift (const CFList& eval, const CFList& factors, |
---|
| 4753 | CFList* const& LCs, CFList& diophant, CFArray& Pi, |
---|
| 4754 | int* liftBound, int length, bool& noOneToOne |
---|
| 4755 | ) |
---|
| 4756 | { |
---|
| 4757 | CFList bufDiophant= diophant; |
---|
| 4758 | CFList buf= factors; |
---|
| 4759 | CFArray bufPi= Pi; |
---|
| 4760 | CFMatrix M= CFMatrix (liftBound[1], factors.length() - 1); |
---|
| 4761 | int k= 0; |
---|
| 4762 | |
---|
| 4763 | CFList result= |
---|
| 4764 | nonMonicHenselLift23 (eval.getFirst(), factors, LCs [0], diophant, bufPi, |
---|
| 4765 | liftBound[1], liftBound[0], noOneToOne); |
---|
| 4766 | |
---|
| 4767 | if (noOneToOne) |
---|
| 4768 | return CFList(); |
---|
| 4769 | |
---|
| 4770 | if (eval.length() == 1) |
---|
| 4771 | return result; |
---|
| 4772 | |
---|
| 4773 | k++; |
---|
| 4774 | CFList MOD; |
---|
| 4775 | for (int i= 0; i < 2; i++) |
---|
| 4776 | MOD.append (power (Variable (i + 2), liftBound[i])); |
---|
| 4777 | |
---|
| 4778 | CFListIterator j= eval; |
---|
| 4779 | CFList bufEval; |
---|
| 4780 | bufEval.append (j.getItem()); |
---|
| 4781 | j++; |
---|
| 4782 | |
---|
| 4783 | for (int i= 2; i <= length && j.hasItem(); i++, j++, k++) |
---|
| 4784 | { |
---|
| 4785 | bufEval.append (j.getItem()); |
---|
| 4786 | M= CFMatrix (liftBound[i], factors.length() - 1); |
---|
| 4787 | result= nonMonicHenselLift (bufEval, result, LCs [i-1], diophant, bufPi, M, |
---|
| 4788 | liftBound[i-1], liftBound[i], MOD, noOneToOne); |
---|
| 4789 | if (noOneToOne) |
---|
| 4790 | return result; |
---|
| 4791 | MOD.append (power (Variable (i + 2), liftBound[i])); |
---|
| 4792 | bufEval.removeFirst(); |
---|
| 4793 | } |
---|
| 4794 | |
---|
| 4795 | return result; |
---|
| 4796 | } |
---|
| 4797 | |
---|
[ad3c3ff] | 4798 | #endif |
---|
| 4799 | /* HAVE_NTL */ |
---|
| 4800 | |
---|