[0e2e23] | 1 | /*****************************************************************************\ |
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| 2 | * Computer Algebra System SINGULAR |
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| 3 | \*****************************************************************************/ |
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[c2aeb9] | 4 | /** @file facMul.cc |
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[0e2e23] | 5 | * |
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| 6 | * This file implements functions for fast multiplication and division with |
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| 7 | * remainder |
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| 8 | * |
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| 9 | * @author Martin Lee |
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| 10 | * |
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| 11 | **/ |
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| 12 | /*****************************************************************************/ |
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| 13 | |
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| 14 | #include "debug.h" |
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[8944cc] | 15 | #include "config.h" |
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[0e2e23] | 16 | |
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| 17 | #include "canonicalform.h" |
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| 18 | #include "facMul.h" |
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| 19 | #include "algext.h" |
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[81d96c] | 20 | #include "cf_util.h" |
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[0e2e23] | 21 | #include "templates/ftmpl_functions.h" |
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| 22 | |
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| 23 | #ifdef HAVE_NTL |
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| 24 | #include <NTL/lzz_pEX.h> |
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| 25 | #include "NTLconvert.h" |
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| 26 | |
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| 27 | #ifdef HAVE_FLINT |
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| 28 | #include "FLINTconvert.h" |
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| 29 | #endif |
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| 30 | |
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[81d96c] | 31 | // univariate polys |
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| 32 | |
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[0e2e23] | 33 | #ifdef HAVE_FLINT |
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| 34 | void kronSub (fmpz_poly_t result, const CanonicalForm& A, int d) |
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| 35 | { |
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| 36 | int degAy= degree (A); |
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| 37 | fmpz_poly_init2 (result, d*(degAy + 1)); |
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| 38 | _fmpz_poly_set_length (result, d*(degAy + 1)); |
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| 39 | CFIterator j; |
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| 40 | for (CFIterator i= A; i.hasTerms(); i++) |
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| 41 | { |
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| 42 | if (i.coeff().inBaseDomain()) |
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| 43 | convertCF2Fmpz (fmpz_poly_get_coeff_ptr (result, i.exp()*d), i.coeff()); |
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| 44 | else |
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| 45 | for (j= i.coeff(); j.hasTerms(); j++) |
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| 46 | convertCF2Fmpz (fmpz_poly_get_coeff_ptr (result, i.exp()*d+j.exp()), |
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| 47 | j.coeff()); |
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| 48 | } |
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| 49 | _fmpz_poly_normalise(result); |
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| 50 | } |
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| 51 | |
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| 52 | |
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| 53 | CanonicalForm |
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[ca058c] | 54 | reverseSubstQa (const fmpz_poly_t F, int d, const Variable& x, |
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| 55 | const Variable& alpha, const CanonicalForm& den) |
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[0e2e23] | 56 | { |
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| 57 | |
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| 58 | CanonicalForm result= 0; |
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| 59 | int i= 0; |
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| 60 | int degf= fmpz_poly_degree (F); |
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| 61 | int k= 0; |
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| 62 | int degfSubK; |
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| 63 | int repLength, j; |
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[b78a13] | 64 | CanonicalForm coeff, ff; |
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[0e2e23] | 65 | fmpz* tmp; |
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| 66 | while (degf >= k) |
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| 67 | { |
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| 68 | coeff= 0; |
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| 69 | degfSubK= degf - k; |
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| 70 | if (degfSubK >= d) |
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| 71 | repLength= d; |
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| 72 | else |
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| 73 | repLength= degfSubK + 1; |
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| 74 | |
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| 75 | for (j= 0; j < repLength; j++) |
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| 76 | { |
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| 77 | tmp= fmpz_poly_get_coeff_ptr (F, j+k); |
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| 78 | if (!fmpz_is_zero (tmp)) |
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| 79 | { |
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[b78a13] | 80 | ff= convertFmpz2CF (tmp); |
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| 81 | coeff += ff*power (alpha, j); //TODO faster reduction mod alpha |
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[0e2e23] | 82 | } |
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| 83 | } |
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| 84 | result += coeff*power (x, i); |
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| 85 | i++; |
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| 86 | k= d*i; |
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| 87 | } |
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[b78a13] | 88 | result /= den; |
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[0e2e23] | 89 | return result; |
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| 90 | } |
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| 91 | |
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| 92 | CanonicalForm |
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| 93 | mulFLINTQa (const CanonicalForm& F, const CanonicalForm& G, |
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| 94 | const Variable& alpha) |
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| 95 | { |
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| 96 | CanonicalForm A= F; |
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| 97 | CanonicalForm B= G; |
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| 98 | |
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| 99 | CanonicalForm denA= bCommonDen (A); |
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| 100 | CanonicalForm denB= bCommonDen (B); |
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| 101 | |
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| 102 | A *= denA; |
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| 103 | B *= denB; |
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| 104 | int degAa= degree (A, alpha); |
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| 105 | int degBa= degree (B, alpha); |
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| 106 | int d= degAa + 1 + degBa; |
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| 107 | |
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| 108 | fmpz_poly_t FLINTA,FLINTB; |
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| 109 | kronSub (FLINTA, A, d); |
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| 110 | kronSub (FLINTB, B, d); |
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| 111 | |
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| 112 | fmpz_poly_mul (FLINTA, FLINTA, FLINTB); |
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| 113 | |
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| 114 | denA *= denB; |
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[ca058c] | 115 | A= reverseSubstQa (FLINTA, d, F.mvar(), alpha, denA); |
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[0e2e23] | 116 | |
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| 117 | fmpz_poly_clear (FLINTA); |
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| 118 | fmpz_poly_clear (FLINTB); |
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| 119 | return A; |
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| 120 | } |
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| 121 | |
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| 122 | CanonicalForm |
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| 123 | mulFLINTQ (const CanonicalForm& F, const CanonicalForm& G) |
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| 124 | { |
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| 125 | CanonicalForm A= F; |
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| 126 | CanonicalForm B= G; |
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| 127 | |
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| 128 | CanonicalForm denA= bCommonDen (A); |
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| 129 | CanonicalForm denB= bCommonDen (B); |
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| 130 | |
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| 131 | A *= denA; |
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| 132 | B *= denB; |
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| 133 | fmpz_poly_t FLINTA,FLINTB; |
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| 134 | convertFacCF2Fmpz_poly_t (FLINTA, A); |
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| 135 | convertFacCF2Fmpz_poly_t (FLINTB, B); |
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| 136 | fmpz_poly_mul (FLINTA, FLINTA, FLINTB); |
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| 137 | denA *= denB; |
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| 138 | A= convertFmpz_poly_t2FacCF (FLINTA, F.mvar()); |
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| 139 | A /= denA; |
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| 140 | fmpz_poly_clear (FLINTA); |
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| 141 | fmpz_poly_clear (FLINTB); |
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| 142 | |
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| 143 | return A; |
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| 144 | } |
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| 145 | |
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| 146 | /*CanonicalForm |
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| 147 | mulFLINTQ2 (const CanonicalForm& F, const CanonicalForm& G) |
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| 148 | { |
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| 149 | CanonicalForm A= F; |
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| 150 | CanonicalForm B= G; |
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| 151 | |
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| 152 | fmpq_poly_t FLINTA,FLINTB; |
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| 153 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
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| 154 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
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| 155 | |
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| 156 | fmpq_poly_mul (FLINTA, FLINTA, FLINTB); |
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| 157 | A= convertFmpq_poly_t2FacCF (FLINTA, F.mvar()); |
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| 158 | fmpq_poly_clear (FLINTA); |
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| 159 | fmpq_poly_clear (FLINTB); |
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| 160 | return A; |
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| 161 | }*/ |
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| 162 | |
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| 163 | CanonicalForm |
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| 164 | divFLINTQ (const CanonicalForm& F, const CanonicalForm& G) |
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| 165 | { |
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| 166 | CanonicalForm A= F; |
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| 167 | CanonicalForm B= G; |
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| 168 | |
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| 169 | fmpq_poly_t FLINTA,FLINTB; |
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| 170 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
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| 171 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
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| 172 | |
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| 173 | fmpq_poly_div (FLINTA, FLINTA, FLINTB); |
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| 174 | A= convertFmpq_poly_t2FacCF (FLINTA, F.mvar()); |
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| 175 | |
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| 176 | fmpq_poly_clear (FLINTA); |
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| 177 | fmpq_poly_clear (FLINTB); |
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| 178 | return A; |
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| 179 | } |
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| 180 | |
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| 181 | CanonicalForm |
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| 182 | modFLINTQ (const CanonicalForm& F, const CanonicalForm& G) |
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| 183 | { |
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| 184 | CanonicalForm A= F; |
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| 185 | CanonicalForm B= G; |
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| 186 | |
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| 187 | fmpq_poly_t FLINTA,FLINTB; |
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| 188 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
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| 189 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
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| 190 | |
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| 191 | fmpq_poly_rem (FLINTA, FLINTA, FLINTB); |
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| 192 | A= convertFmpq_poly_t2FacCF (FLINTA, F.mvar()); |
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| 193 | |
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| 194 | fmpq_poly_clear (FLINTA); |
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| 195 | fmpq_poly_clear (FLINTB); |
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| 196 | return A; |
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| 197 | } |
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| 198 | |
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| 199 | CanonicalForm |
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| 200 | mulFLINTQaTrunc (const CanonicalForm& F, const CanonicalForm& G, |
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| 201 | const Variable& alpha, int m) |
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| 202 | { |
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| 203 | CanonicalForm A= F; |
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| 204 | CanonicalForm B= G; |
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| 205 | |
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| 206 | CanonicalForm denA= bCommonDen (A); |
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| 207 | CanonicalForm denB= bCommonDen (B); |
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| 208 | |
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| 209 | A *= denA; |
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| 210 | B *= denB; |
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| 211 | |
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| 212 | int degAa= degree (A, alpha); |
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| 213 | int degBa= degree (B, alpha); |
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| 214 | int d= degAa + 1 + degBa; |
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| 215 | |
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| 216 | fmpz_poly_t FLINTA,FLINTB; |
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| 217 | kronSub (FLINTA, A, d); |
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| 218 | kronSub (FLINTB, B, d); |
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| 219 | |
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| 220 | int k= d*m; |
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| 221 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, k); |
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| 222 | |
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| 223 | denA *= denB; |
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[ca058c] | 224 | A= reverseSubstQa (FLINTA, d, F.mvar(), alpha, denA); |
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[0e2e23] | 225 | fmpz_poly_clear (FLINTA); |
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| 226 | fmpz_poly_clear (FLINTB); |
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| 227 | return A; |
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| 228 | } |
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| 229 | |
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| 230 | CanonicalForm |
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| 231 | mulFLINTQTrunc (const CanonicalForm& F, const CanonicalForm& G, int m) |
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| 232 | { |
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| 233 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
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| 234 | return mod (F*G, power (Variable (1), m)); |
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| 235 | Variable alpha; |
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| 236 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
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| 237 | return mulFLINTQaTrunc (F, G, alpha, m); |
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| 238 | |
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| 239 | CanonicalForm A= F; |
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| 240 | CanonicalForm B= G; |
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| 241 | |
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| 242 | CanonicalForm denA= bCommonDen (A); |
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| 243 | CanonicalForm denB= bCommonDen (B); |
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| 244 | |
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| 245 | A *= denA; |
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| 246 | B *= denB; |
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| 247 | fmpz_poly_t FLINTA,FLINTB; |
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| 248 | convertFacCF2Fmpz_poly_t (FLINTA, A); |
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| 249 | convertFacCF2Fmpz_poly_t (FLINTB, B); |
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| 250 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, m); |
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| 251 | denA *= denB; |
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| 252 | A= convertFmpz_poly_t2FacCF (FLINTA, F.mvar()); |
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| 253 | A /= denA; |
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| 254 | fmpz_poly_clear (FLINTA); |
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| 255 | fmpz_poly_clear (FLINTB); |
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| 256 | |
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| 257 | return A; |
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| 258 | } |
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| 259 | |
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| 260 | CanonicalForm uniReverse (const CanonicalForm& F, int d) |
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| 261 | { |
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| 262 | if (d == 0) |
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| 263 | return F; |
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| 264 | if (F.inCoeffDomain()) |
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| 265 | return F*power (Variable (1),d); |
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| 266 | Variable x= Variable (1); |
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| 267 | CanonicalForm result= 0; |
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| 268 | CFIterator i= F; |
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| 269 | while (d - i.exp() < 0) |
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| 270 | i++; |
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| 271 | |
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| 272 | for (; i.hasTerms() && (d - i.exp() >= 0); i++) |
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| 273 | result += i.coeff()*power (x, d - i.exp()); |
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| 274 | return result; |
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| 275 | } |
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| 276 | |
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| 277 | CanonicalForm |
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| 278 | newtonInverse (const CanonicalForm& F, const int n) |
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| 279 | { |
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| 280 | int l= ilog2(n); |
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| 281 | |
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| 282 | CanonicalForm g= F [0]; |
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| 283 | |
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| 284 | ASSERT (!g.isZero(), "expected a unit"); |
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| 285 | |
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| 286 | if (!g.isOne()) |
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| 287 | g = 1/g; |
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| 288 | Variable x= Variable (1); |
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| 289 | CanonicalForm result; |
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| 290 | int exp= 0; |
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| 291 | if (n & 1) |
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| 292 | { |
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| 293 | result= g; |
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| 294 | exp= 1; |
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| 295 | } |
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| 296 | CanonicalForm h; |
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| 297 | |
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| 298 | for (int i= 1; i <= l; i++) |
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| 299 | { |
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| 300 | h= mulNTL (g, mod (F, power (x, (1 << i)))); |
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| 301 | h= mod (h, power (x, (1 << i)) - 1); |
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| 302 | h= div (h, power (x, (1 << (i - 1)))); |
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| 303 | g -= power (x, (1 << (i - 1)))* |
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| 304 | mulFLINTQTrunc (g, h, 1 << (i-1)); |
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| 305 | |
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| 306 | if (n & (1 << i)) |
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| 307 | { |
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| 308 | if (exp) |
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| 309 | { |
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| 310 | h= mulNTL (result, mod (F, power (x, exp + (1 << i)))); |
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| 311 | h= mod (h, power (x, exp + (1 << i)) - 1); |
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| 312 | h= div (h, power (x, exp)); |
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| 313 | result -= power(x, exp)*mulFLINTQTrunc (g, h, 1 << i); |
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| 314 | exp += (1 << i); |
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| 315 | } |
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| 316 | else |
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| 317 | { |
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| 318 | exp= (1 << i); |
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| 319 | result= g; |
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| 320 | } |
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| 321 | } |
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| 322 | } |
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| 323 | |
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| 324 | return result; |
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| 325 | } |
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| 326 | |
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| 327 | void |
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| 328 | newtonDivrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
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| 329 | CanonicalForm& R) |
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| 330 | { |
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| 331 | CanonicalForm A= F; |
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| 332 | CanonicalForm B= G; |
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| 333 | Variable x= Variable (1); |
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| 334 | int degA= degree (A, x); |
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| 335 | int degB= degree (B, x); |
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| 336 | int m= degA - degB; |
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| 337 | |
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| 338 | if (m < 0) |
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| 339 | { |
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| 340 | R= A; |
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| 341 | Q= 0; |
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| 342 | return; |
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| 343 | } |
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| 344 | |
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| 345 | if (degB <= 1) |
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| 346 | divrem (A, B, Q, R); |
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| 347 | else |
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| 348 | { |
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| 349 | R= uniReverse (A, degA); |
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| 350 | |
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| 351 | CanonicalForm revB= uniReverse (B, degB); |
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| 352 | CanonicalForm buf= revB; |
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| 353 | revB= newtonInverse (revB, m + 1); |
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| 354 | Q= mulFLINTQTrunc (R, revB, m + 1); |
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| 355 | Q= uniReverse (Q, m); |
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| 356 | |
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| 357 | R= A - mulNTL (Q, B); |
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| 358 | } |
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| 359 | } |
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| 360 | |
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| 361 | void |
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| 362 | newtonDiv (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q) |
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| 363 | { |
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| 364 | CanonicalForm A= F; |
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| 365 | CanonicalForm B= G; |
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| 366 | Variable x= Variable (1); |
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| 367 | int degA= degree (A, x); |
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| 368 | int degB= degree (B, x); |
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| 369 | int m= degA - degB; |
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| 370 | |
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| 371 | if (m < 0) |
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| 372 | { |
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| 373 | Q= 0; |
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| 374 | return; |
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| 375 | } |
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| 376 | |
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| 377 | if (degB <= 1) |
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| 378 | Q= div (A, B); |
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| 379 | else |
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| 380 | { |
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| 381 | CanonicalForm R= uniReverse (A, degA); |
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| 382 | |
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| 383 | CanonicalForm revB= uniReverse (B, degB); |
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| 384 | revB= newtonInverse (revB, m + 1); |
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| 385 | Q= mulFLINTQTrunc (R, revB, m + 1); |
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| 386 | Q= uniReverse (Q, m); |
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| 387 | } |
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| 388 | } |
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| 389 | |
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| 390 | #endif |
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| 391 | |
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| 392 | CanonicalForm |
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[64c923] | 393 | mulNTL (const CanonicalForm& F, const CanonicalForm& G, const modpk& b) |
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[0e2e23] | 394 | { |
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[ad0177] | 395 | if (CFFactory::gettype() == GaloisFieldDomain) |
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| 396 | return F*G; |
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[f53120] | 397 | if (getCharacteristic() == 0) |
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[0e2e23] | 398 | { |
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| 399 | Variable alpha; |
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| 400 | if ((!F.inCoeffDomain() && !G.inCoeffDomain()) && |
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| 401 | (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha))) |
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| 402 | { |
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[47dc5ea] | 403 | if (b.getp() != 0) |
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| 404 | { |
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| 405 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
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| 406 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
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| 407 | ZZ_pE::init (NTLmipo); |
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| 408 | ZZ_pEX NTLg= convertFacCF2NTLZZ_pEX (G, NTLmipo); |
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| 409 | ZZ_pEX NTLf= convertFacCF2NTLZZ_pEX (F, NTLmipo); |
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| 410 | mul (NTLf, NTLf, NTLg); |
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| 411 | return b (convertNTLZZ_pEX2CF (NTLf, F.mvar(), alpha)); |
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| 412 | } |
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[837495] | 413 | #ifdef HAVE_FLINT |
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[0e2e23] | 414 | CanonicalForm result= mulFLINTQa (F, G, alpha); |
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| 415 | return result; |
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[837495] | 416 | #else |
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| 417 | return F*G; |
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| 418 | #endif |
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[0e2e23] | 419 | } |
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| 420 | else if (!F.inCoeffDomain() && !G.inCoeffDomain()) |
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[f9bd3d] | 421 | { |
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[837495] | 422 | #ifdef HAVE_FLINT |
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[f9bd3d] | 423 | if (b.getp() != 0) |
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[e785e9] | 424 | { |
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| 425 | fmpz_t FLINTpk; |
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[51aa162] | 426 | fmpz_init (FLINTpk); |
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| 427 | convertCF2Fmpz (FLINTpk, b.getpk()); |
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[e785e9] | 428 | fmpz_mod_poly_t FLINTF, FLINTG; |
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| 429 | convertFacCF2Fmpz_mod_poly_t (FLINTF, F, FLINTpk); |
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| 430 | convertFacCF2Fmpz_mod_poly_t (FLINTG, G, FLINTpk); |
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| 431 | fmpz_mod_poly_mul (FLINTF, FLINTF, FLINTG); |
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| 432 | CanonicalForm result= convertFmpz_mod_poly_t2FacCF (FLINTF, F.mvar(), b); |
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| 433 | fmpz_mod_poly_clear (FLINTG); |
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| 434 | fmpz_mod_poly_clear (FLINTF); |
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[51aa162] | 435 | fmpz_clear (FLINTpk); |
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[e785e9] | 436 | return result; |
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| 437 | } |
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[0e2e23] | 438 | return mulFLINTQ (F, G); |
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[837495] | 439 | #else |
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| 440 | if (b.getp() != 0) |
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| 441 | { |
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| 442 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
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| 443 | ZZX ZZf= convertFacCF2NTLZZX (F); |
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| 444 | ZZX ZZg= convertFacCF2NTLZZX (G); |
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| 445 | ZZ_pX NTLf= to_ZZ_pX (ZZf); |
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| 446 | ZZ_pX NTLg= to_ZZ_pX (ZZg); |
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| 447 | mul (NTLf, NTLf, NTLg); |
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| 448 | return b (convertNTLZZX2CF (to_ZZX (NTLf), F.mvar())); |
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| 449 | } |
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| 450 | return F*G; |
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[0e2e23] | 451 | #endif |
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[837495] | 452 | } |
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[f9bd3d] | 453 | if (b.getp() != 0) |
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[47dc5ea] | 454 | { |
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| 455 | if (!F.inBaseDomain() && !G.inBaseDomain()) |
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| 456 | { |
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| 457 | if (hasFirstAlgVar (G, alpha) || hasFirstAlgVar (F, alpha)) |
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| 458 | { |
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| 459 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
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| 460 | if (F.inCoeffDomain() && !G.inCoeffDomain()) |
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| 461 | { |
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| 462 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
---|
| 463 | ZZ_pE::init (NTLmipo); |
---|
| 464 | ZZ_pEX NTLg= convertFacCF2NTLZZ_pEX (G, NTLmipo); |
---|
| 465 | ZZ_pX NTLf= convertFacCF2NTLZZpX (F); |
---|
| 466 | mul (NTLg, to_ZZ_pE (NTLf), NTLg); |
---|
| 467 | return b (convertNTLZZ_pEX2CF (NTLg, G.mvar(), alpha)); |
---|
| 468 | } |
---|
| 469 | else if (!F.inCoeffDomain() && G.inCoeffDomain()) |
---|
| 470 | { |
---|
| 471 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
---|
| 472 | ZZ_pE::init (NTLmipo); |
---|
| 473 | ZZ_pX NTLg= convertFacCF2NTLZZpX (G); |
---|
| 474 | ZZ_pEX NTLf= convertFacCF2NTLZZ_pEX (F, NTLmipo); |
---|
| 475 | mul (NTLf, NTLf, to_ZZ_pE (NTLg)); |
---|
| 476 | return b (convertNTLZZ_pEX2CF (NTLf, F.mvar(), alpha)); |
---|
| 477 | } |
---|
| 478 | else |
---|
| 479 | { |
---|
| 480 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
---|
| 481 | ZZ_pE::init (NTLmipo); |
---|
| 482 | ZZ_pX NTLg= convertFacCF2NTLZZpX (G); |
---|
| 483 | ZZ_pX NTLf= convertFacCF2NTLZZpX (F); |
---|
| 484 | ZZ_pE result; |
---|
| 485 | mul (result, to_ZZ_pE (NTLg), to_ZZ_pE (NTLf)); |
---|
| 486 | return b (convertNTLZZpX2CF (rep (result), alpha)); |
---|
| 487 | } |
---|
| 488 | } |
---|
| 489 | } |
---|
[f9bd3d] | 490 | return b (F*G); |
---|
[47dc5ea] | 491 | } |
---|
[0e2e23] | 492 | return F*G; |
---|
| 493 | } |
---|
[f53120] | 494 | else if (F.inCoeffDomain() || G.inCoeffDomain()) |
---|
| 495 | return F*G; |
---|
[0e2e23] | 496 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
| 497 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
| 498 | zz_p::init (getCharacteristic()); |
---|
| 499 | Variable alpha; |
---|
| 500 | CanonicalForm result; |
---|
| 501 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
| 502 | { |
---|
| 503 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 504 | zz_pE::init (NTLMipo); |
---|
| 505 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
| 506 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
| 507 | mul (NTLF, NTLF, NTLG); |
---|
| 508 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
---|
| 509 | } |
---|
| 510 | else |
---|
| 511 | { |
---|
| 512 | #ifdef HAVE_FLINT |
---|
| 513 | nmod_poly_t FLINTF, FLINTG; |
---|
| 514 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
| 515 | convertFacCF2nmod_poly_t (FLINTG, G); |
---|
| 516 | nmod_poly_mul (FLINTF, FLINTF, FLINTG); |
---|
| 517 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
---|
| 518 | nmod_poly_clear (FLINTF); |
---|
| 519 | nmod_poly_clear (FLINTG); |
---|
| 520 | #else |
---|
| 521 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
| 522 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
| 523 | mul (NTLF, NTLF, NTLG); |
---|
| 524 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
---|
| 525 | #endif |
---|
| 526 | } |
---|
| 527 | return result; |
---|
| 528 | } |
---|
| 529 | |
---|
| 530 | CanonicalForm |
---|
[64c923] | 531 | modNTL (const CanonicalForm& F, const CanonicalForm& G, const modpk& b) |
---|
[0e2e23] | 532 | { |
---|
[ad0177] | 533 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
| 534 | return mod (F, G); |
---|
[ca058c] | 535 | if (F.inCoeffDomain() && G.isUnivariate() && !G.inCoeffDomain()) |
---|
[f9bd3d] | 536 | { |
---|
| 537 | if (b.getp() != 0) |
---|
| 538 | return b(F); |
---|
[0e2e23] | 539 | return F; |
---|
[f9bd3d] | 540 | } |
---|
[0e2e23] | 541 | else if (F.inCoeffDomain() && G.inCoeffDomain()) |
---|
[f9bd3d] | 542 | { |
---|
| 543 | if (b.getp() != 0) |
---|
| 544 | return b(F%G); |
---|
[0e2e23] | 545 | return mod (F, G); |
---|
[f9bd3d] | 546 | } |
---|
[0e2e23] | 547 | else if (F.isUnivariate() && G.inCoeffDomain()) |
---|
[f9bd3d] | 548 | { |
---|
| 549 | if (b.getp() != 0) |
---|
| 550 | return b(F%G); |
---|
[0e2e23] | 551 | return mod (F,G); |
---|
[f9bd3d] | 552 | } |
---|
[0e2e23] | 553 | |
---|
| 554 | if (getCharacteristic() == 0) |
---|
| 555 | { |
---|
| 556 | Variable alpha; |
---|
| 557 | if (!hasFirstAlgVar (F, alpha) && !hasFirstAlgVar (G, alpha)) |
---|
[f9bd3d] | 558 | { |
---|
[837495] | 559 | #ifdef HAVE_FLINT |
---|
[f9bd3d] | 560 | if (b.getp() != 0) |
---|
| 561 | { |
---|
[e785e9] | 562 | fmpz_t FLINTpk; |
---|
[51aa162] | 563 | fmpz_init (FLINTpk); |
---|
| 564 | convertCF2Fmpz (FLINTpk, b.getpk()); |
---|
[e785e9] | 565 | fmpz_mod_poly_t FLINTF, FLINTG; |
---|
| 566 | convertFacCF2Fmpz_mod_poly_t (FLINTF, F, FLINTpk); |
---|
| 567 | convertFacCF2Fmpz_mod_poly_t (FLINTG, G, FLINTpk); |
---|
[c2a8b6] | 568 | fmpz_mod_poly_divrem (FLINTG, FLINTF, FLINTF, FLINTG); |
---|
[e785e9] | 569 | CanonicalForm result= convertFmpz_mod_poly_t2FacCF (FLINTF,F.mvar(),b); |
---|
| 570 | fmpz_mod_poly_clear (FLINTG); |
---|
| 571 | fmpz_mod_poly_clear (FLINTF); |
---|
[51aa162] | 572 | fmpz_clear (FLINTpk); |
---|
[e785e9] | 573 | return result; |
---|
[f9bd3d] | 574 | } |
---|
[0e2e23] | 575 | return modFLINTQ (F, G); |
---|
[837495] | 576 | #else |
---|
| 577 | if (b.getp() != 0) |
---|
| 578 | { |
---|
| 579 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
| 580 | ZZX ZZf= convertFacCF2NTLZZX (F); |
---|
| 581 | ZZX ZZg= convertFacCF2NTLZZX (G); |
---|
| 582 | ZZ_pX NTLf= to_ZZ_pX (ZZf); |
---|
| 583 | ZZ_pX NTLg= to_ZZ_pX (ZZg); |
---|
| 584 | rem (NTLf, NTLf, NTLg); |
---|
| 585 | return b (convertNTLZZX2CF (to_ZZX (NTLf), F.mvar())); |
---|
| 586 | } |
---|
| 587 | return mod (F, G); |
---|
| 588 | #endif |
---|
[f9bd3d] | 589 | } |
---|
[0e2e23] | 590 | else |
---|
| 591 | { |
---|
[47dc5ea] | 592 | if (b.getp() != 0) |
---|
| 593 | { |
---|
| 594 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
| 595 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
---|
| 596 | ZZ_pE::init (NTLmipo); |
---|
| 597 | ZZ_pEX NTLg= convertFacCF2NTLZZ_pEX (G, NTLmipo); |
---|
| 598 | ZZ_pEX NTLf= convertFacCF2NTLZZ_pEX (F, NTLmipo); |
---|
| 599 | rem (NTLf, NTLf, NTLg); |
---|
| 600 | return b (convertNTLZZ_pEX2CF (NTLf, F.mvar(), alpha)); |
---|
| 601 | } |
---|
[837495] | 602 | #ifdef HAVE_FLINT |
---|
[0e2e23] | 603 | CanonicalForm Q, R; |
---|
| 604 | newtonDivrem (F, G, Q, R); |
---|
| 605 | return R; |
---|
| 606 | #else |
---|
[837495] | 607 | return mod (F,G); |
---|
[0e2e23] | 608 | #endif |
---|
[837495] | 609 | } |
---|
[0e2e23] | 610 | } |
---|
| 611 | |
---|
| 612 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
| 613 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
| 614 | zz_p::init (getCharacteristic()); |
---|
| 615 | Variable alpha; |
---|
| 616 | CanonicalForm result; |
---|
| 617 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
| 618 | { |
---|
| 619 | zz_pX NTLMipo= convertFacCF2NTLzzpX(getMipo (alpha)); |
---|
| 620 | zz_pE::init (NTLMipo); |
---|
| 621 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
| 622 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
| 623 | rem (NTLF, NTLF, NTLG); |
---|
| 624 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
---|
| 625 | } |
---|
| 626 | else |
---|
| 627 | { |
---|
| 628 | #ifdef HAVE_FLINT |
---|
| 629 | nmod_poly_t FLINTF, FLINTG; |
---|
| 630 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
| 631 | convertFacCF2nmod_poly_t (FLINTG, G); |
---|
| 632 | nmod_poly_divrem (FLINTG, FLINTF, FLINTF, FLINTG); |
---|
| 633 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
---|
| 634 | nmod_poly_clear (FLINTF); |
---|
| 635 | nmod_poly_clear (FLINTG); |
---|
| 636 | #else |
---|
| 637 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
| 638 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
| 639 | rem (NTLF, NTLF, NTLG); |
---|
| 640 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
---|
| 641 | #endif |
---|
| 642 | } |
---|
| 643 | return result; |
---|
| 644 | } |
---|
| 645 | |
---|
| 646 | CanonicalForm |
---|
[64c923] | 647 | divNTL (const CanonicalForm& F, const CanonicalForm& G, const modpk& b) |
---|
[0e2e23] | 648 | { |
---|
[ad0177] | 649 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
| 650 | return div (F, G); |
---|
[ca058c] | 651 | if (F.inCoeffDomain() && G.isUnivariate() && !G.inCoeffDomain()) |
---|
[f9bd3d] | 652 | { |
---|
[ca058c] | 653 | return 0; |
---|
[f9bd3d] | 654 | } |
---|
[0e2e23] | 655 | else if (F.inCoeffDomain() && G.inCoeffDomain()) |
---|
[f9bd3d] | 656 | { |
---|
| 657 | if (b.getp() != 0) |
---|
[47dc5ea] | 658 | { |
---|
| 659 | if (!F.inBaseDomain() || !G.inBaseDomain()) |
---|
| 660 | { |
---|
| 661 | Variable alpha; |
---|
| 662 | hasFirstAlgVar (F, alpha); |
---|
| 663 | hasFirstAlgVar (G, alpha); |
---|
| 664 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
| 665 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
---|
| 666 | ZZ_pE::init (NTLmipo); |
---|
| 667 | ZZ_pX NTLg= convertFacCF2NTLZZpX (G); |
---|
| 668 | ZZ_pX NTLf= convertFacCF2NTLZZpX (F); |
---|
| 669 | ZZ_pE result; |
---|
[ca058c] | 670 | div (result, to_ZZ_pE (NTLf), to_ZZ_pE (NTLg)); |
---|
[47dc5ea] | 671 | return b (convertNTLZZpX2CF (rep (result), alpha)); |
---|
| 672 | } |
---|
[f9bd3d] | 673 | return b(div (F,G)); |
---|
[47dc5ea] | 674 | } |
---|
[0e2e23] | 675 | return div (F, G); |
---|
[f9bd3d] | 676 | } |
---|
[0e2e23] | 677 | else if (F.isUnivariate() && G.inCoeffDomain()) |
---|
[f9bd3d] | 678 | { |
---|
| 679 | if (b.getp() != 0) |
---|
[47dc5ea] | 680 | { |
---|
| 681 | if (!G.inBaseDomain()) |
---|
| 682 | { |
---|
| 683 | Variable alpha; |
---|
| 684 | hasFirstAlgVar (G, alpha); |
---|
| 685 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
| 686 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
---|
| 687 | ZZ_pE::init (NTLmipo); |
---|
| 688 | ZZ_pX NTLg= convertFacCF2NTLZZpX (G); |
---|
| 689 | ZZ_pEX NTLf= convertFacCF2NTLZZ_pEX (F, NTLmipo); |
---|
| 690 | div (NTLf, NTLf, to_ZZ_pE (NTLg)); |
---|
| 691 | return b (convertNTLZZ_pEX2CF (NTLf, F.mvar(), alpha)); |
---|
| 692 | } |
---|
[f9bd3d] | 693 | return b(div (F,G)); |
---|
[47dc5ea] | 694 | } |
---|
[f9bd3d] | 695 | return div (F, G); |
---|
| 696 | } |
---|
[0e2e23] | 697 | |
---|
| 698 | if (getCharacteristic() == 0) |
---|
| 699 | { |
---|
[837495] | 700 | |
---|
[0e2e23] | 701 | Variable alpha; |
---|
| 702 | if (!hasFirstAlgVar (F, alpha) && !hasFirstAlgVar (G, alpha)) |
---|
[f9bd3d] | 703 | { |
---|
[837495] | 704 | #ifdef HAVE_FLINT |
---|
[f9bd3d] | 705 | if (b.getp() != 0) |
---|
| 706 | { |
---|
[e785e9] | 707 | fmpz_t FLINTpk; |
---|
[51aa162] | 708 | fmpz_init (FLINTpk); |
---|
| 709 | convertCF2Fmpz (FLINTpk, b.getpk()); |
---|
[e785e9] | 710 | fmpz_mod_poly_t FLINTF, FLINTG; |
---|
| 711 | convertFacCF2Fmpz_mod_poly_t (FLINTF, F, FLINTpk); |
---|
| 712 | convertFacCF2Fmpz_mod_poly_t (FLINTG, G, FLINTpk); |
---|
| 713 | fmpz_mod_poly_divrem (FLINTF, FLINTG, FLINTF, FLINTG); |
---|
| 714 | CanonicalForm result= convertFmpz_mod_poly_t2FacCF (FLINTF,F.mvar(),b); |
---|
| 715 | fmpz_mod_poly_clear (FLINTG); |
---|
| 716 | fmpz_mod_poly_clear (FLINTF); |
---|
[51aa162] | 717 | fmpz_clear (FLINTpk); |
---|
[e785e9] | 718 | return result; |
---|
[f9bd3d] | 719 | } |
---|
[0e2e23] | 720 | return divFLINTQ (F,G); |
---|
[837495] | 721 | #else |
---|
| 722 | if (b.getp() != 0) |
---|
| 723 | { |
---|
| 724 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
| 725 | ZZX ZZf= convertFacCF2NTLZZX (F); |
---|
| 726 | ZZX ZZg= convertFacCF2NTLZZX (G); |
---|
| 727 | ZZ_pX NTLf= to_ZZ_pX (ZZf); |
---|
| 728 | ZZ_pX NTLg= to_ZZ_pX (ZZg); |
---|
| 729 | div (NTLf, NTLf, NTLg); |
---|
| 730 | return b (convertNTLZZX2CF (to_ZZX (NTLf), F.mvar())); |
---|
| 731 | } |
---|
| 732 | return div (F, G); |
---|
| 733 | #endif |
---|
[f9bd3d] | 734 | } |
---|
[0e2e23] | 735 | else |
---|
| 736 | { |
---|
[47dc5ea] | 737 | if (b.getp() != 0) |
---|
| 738 | { |
---|
| 739 | ZZ_p::init (convertFacCF2NTLZZ (b.getpk())); |
---|
| 740 | ZZ_pX NTLmipo= to_ZZ_pX (convertFacCF2NTLZZX (getMipo (alpha))); |
---|
| 741 | ZZ_pE::init (NTLmipo); |
---|
| 742 | ZZ_pEX NTLg= convertFacCF2NTLZZ_pEX (G, NTLmipo); |
---|
| 743 | ZZ_pEX NTLf= convertFacCF2NTLZZ_pEX (F, NTLmipo); |
---|
| 744 | div (NTLf, NTLf, NTLg); |
---|
| 745 | return b (convertNTLZZ_pEX2CF (NTLf, F.mvar(), alpha)); |
---|
| 746 | } |
---|
[837495] | 747 | #ifdef HAVE_FLINT |
---|
[0e2e23] | 748 | CanonicalForm Q; |
---|
| 749 | newtonDiv (F, G, Q); |
---|
| 750 | return Q; |
---|
| 751 | #else |
---|
[837495] | 752 | return div (F,G); |
---|
[0e2e23] | 753 | #endif |
---|
[837495] | 754 | } |
---|
[0e2e23] | 755 | } |
---|
| 756 | |
---|
| 757 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
| 758 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
| 759 | zz_p::init (getCharacteristic()); |
---|
| 760 | Variable alpha; |
---|
| 761 | CanonicalForm result; |
---|
| 762 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
| 763 | { |
---|
| 764 | zz_pX NTLMipo= convertFacCF2NTLzzpX(getMipo (alpha)); |
---|
| 765 | zz_pE::init (NTLMipo); |
---|
| 766 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
| 767 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
| 768 | div (NTLF, NTLF, NTLG); |
---|
| 769 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
---|
| 770 | } |
---|
| 771 | else |
---|
| 772 | { |
---|
| 773 | #ifdef HAVE_FLINT |
---|
| 774 | nmod_poly_t FLINTF, FLINTG; |
---|
| 775 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
| 776 | convertFacCF2nmod_poly_t (FLINTG, G); |
---|
| 777 | nmod_poly_div (FLINTF, FLINTF, FLINTG); |
---|
| 778 | result= convertnmod_poly_t2FacCF (FLINTF, F.mvar()); |
---|
| 779 | nmod_poly_clear (FLINTF); |
---|
| 780 | nmod_poly_clear (FLINTG); |
---|
| 781 | #else |
---|
| 782 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
| 783 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
| 784 | div (NTLF, NTLF, NTLG); |
---|
| 785 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
---|
| 786 | #endif |
---|
| 787 | } |
---|
| 788 | return result; |
---|
| 789 | } |
---|
| 790 | |
---|
[81d96c] | 791 | // end univariate polys |
---|
| 792 | //************************* |
---|
| 793 | // bivariate polys |
---|
| 794 | |
---|
[0e2e23] | 795 | #ifdef HAVE_FLINT |
---|
| 796 | void kronSubFp (nmod_poly_t result, const CanonicalForm& A, int d) |
---|
| 797 | { |
---|
| 798 | int degAy= degree (A); |
---|
| 799 | nmod_poly_init2 (result, getCharacteristic(), d*(degAy + 1)); |
---|
| 800 | |
---|
| 801 | nmod_poly_t buf; |
---|
| 802 | |
---|
| 803 | int j, k, bufRepLength; |
---|
| 804 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 805 | { |
---|
| 806 | convertFacCF2nmod_poly_t (buf, i.coeff()); |
---|
| 807 | |
---|
| 808 | k= i.exp()*d; |
---|
| 809 | bufRepLength= (int) nmod_poly_length (buf); |
---|
| 810 | for (j= 0; j < bufRepLength; j++) |
---|
| 811 | nmod_poly_set_coeff_ui (result, j + k, nmod_poly_get_coeff_ui (buf, j)); |
---|
| 812 | nmod_poly_clear (buf); |
---|
| 813 | } |
---|
| 814 | _nmod_poly_normalise (result); |
---|
| 815 | } |
---|
| 816 | |
---|
| 817 | void kronSubQa (fmpq_poly_t result, const CanonicalForm& A, int d1, int d2) |
---|
| 818 | { |
---|
| 819 | int degAy= degree (A); |
---|
| 820 | fmpq_poly_init2 (result, d1*(degAy + 1)); |
---|
| 821 | |
---|
| 822 | fmpq_poly_t buf; |
---|
| 823 | fmpq_t coeff; |
---|
| 824 | |
---|
| 825 | int k, l, bufRepLength; |
---|
| 826 | CFIterator j; |
---|
| 827 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 828 | { |
---|
| 829 | if (i.coeff().inCoeffDomain()) |
---|
| 830 | { |
---|
| 831 | k= d1*i.exp(); |
---|
| 832 | convertFacCF2Fmpq_poly_t (buf, i.coeff()); |
---|
| 833 | bufRepLength= (int) fmpq_poly_length(buf); |
---|
| 834 | for (l= 0; l < bufRepLength; l++) |
---|
| 835 | { |
---|
| 836 | fmpq_poly_get_coeff_fmpq (coeff, buf, l); |
---|
| 837 | fmpq_poly_set_coeff_fmpq (result, l + k, coeff); |
---|
| 838 | } |
---|
| 839 | fmpq_poly_clear (buf); |
---|
| 840 | } |
---|
| 841 | else |
---|
| 842 | { |
---|
| 843 | for (j= i.coeff(); j.hasTerms(); j++) |
---|
| 844 | { |
---|
| 845 | k= d1*i.exp(); |
---|
| 846 | k += d2*j.exp(); |
---|
| 847 | convertFacCF2Fmpq_poly_t (buf, j.coeff()); |
---|
| 848 | bufRepLength= (int) fmpq_poly_length(buf); |
---|
| 849 | for (l= 0; l < bufRepLength; l++) |
---|
| 850 | { |
---|
| 851 | fmpq_poly_get_coeff_fmpq (coeff, buf, l); |
---|
| 852 | fmpq_poly_set_coeff_fmpq (result, k + l, coeff); |
---|
| 853 | } |
---|
| 854 | fmpq_poly_clear (buf); |
---|
| 855 | } |
---|
| 856 | } |
---|
| 857 | } |
---|
| 858 | fmpq_clear (coeff); |
---|
| 859 | _fmpq_poly_normalise (result); |
---|
| 860 | } |
---|
| 861 | |
---|
[81d96c] | 862 | void |
---|
| 863 | kronSubReciproFp (nmod_poly_t subA1, nmod_poly_t subA2, const CanonicalForm& A, |
---|
| 864 | int d) |
---|
[0e2e23] | 865 | { |
---|
| 866 | int degAy= degree (A); |
---|
[81d96c] | 867 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
| 868 | nmod_poly_init2_preinv (subA1, getCharacteristic(), ninv, d*(degAy + 2)); |
---|
| 869 | nmod_poly_init2_preinv (subA2, getCharacteristic(), ninv, d*(degAy + 2)); |
---|
[0e2e23] | 870 | |
---|
[81d96c] | 871 | nmod_poly_t buf; |
---|
[0e2e23] | 872 | |
---|
[81d96c] | 873 | int k, kk, j, bufRepLength; |
---|
[0e2e23] | 874 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 875 | { |
---|
[81d96c] | 876 | convertFacCF2nmod_poly_t (buf, i.coeff()); |
---|
[0e2e23] | 877 | |
---|
| 878 | k= i.exp()*d; |
---|
[81d96c] | 879 | kk= (degAy - i.exp())*d; |
---|
| 880 | bufRepLength= (int) nmod_poly_length (buf); |
---|
[0e2e23] | 881 | for (j= 0; j < bufRepLength; j++) |
---|
| 882 | { |
---|
[81d96c] | 883 | nmod_poly_set_coeff_ui (subA1, j + k, |
---|
| 884 | n_addmod (nmod_poly_get_coeff_ui (subA1, j+k), |
---|
| 885 | nmod_poly_get_coeff_ui (buf, j), |
---|
| 886 | getCharacteristic() |
---|
| 887 | ) |
---|
| 888 | ); |
---|
| 889 | nmod_poly_set_coeff_ui (subA2, j + kk, |
---|
| 890 | n_addmod (nmod_poly_get_coeff_ui (subA2, j + kk), |
---|
| 891 | nmod_poly_get_coeff_ui (buf, j), |
---|
| 892 | getCharacteristic() |
---|
| 893 | ) |
---|
| 894 | ); |
---|
[0e2e23] | 895 | } |
---|
[81d96c] | 896 | nmod_poly_clear (buf); |
---|
[0e2e23] | 897 | } |
---|
[81d96c] | 898 | _nmod_poly_normalise (subA1); |
---|
| 899 | _nmod_poly_normalise (subA2); |
---|
[0e2e23] | 900 | } |
---|
| 901 | |
---|
| 902 | void |
---|
[81d96c] | 903 | kronSubReciproQ (fmpz_poly_t subA1, fmpz_poly_t subA2, const CanonicalForm& A, |
---|
| 904 | int d) |
---|
[0e2e23] | 905 | { |
---|
| 906 | int degAy= degree (A); |
---|
[81d96c] | 907 | fmpz_poly_init2 (subA1, d*(degAy + 2)); |
---|
| 908 | fmpz_poly_init2 (subA2, d*(degAy + 2)); |
---|
[0e2e23] | 909 | |
---|
[81d96c] | 910 | fmpz_poly_t buf; |
---|
| 911 | fmpz_t coeff1, coeff2; |
---|
[0e2e23] | 912 | |
---|
[81d96c] | 913 | int k, kk, j, bufRepLength; |
---|
[0e2e23] | 914 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 915 | { |
---|
[81d96c] | 916 | convertFacCF2Fmpz_poly_t (buf, i.coeff()); |
---|
[0e2e23] | 917 | |
---|
| 918 | k= i.exp()*d; |
---|
| 919 | kk= (degAy - i.exp())*d; |
---|
[81d96c] | 920 | bufRepLength= (int) fmpz_poly_length (buf); |
---|
[0e2e23] | 921 | for (j= 0; j < bufRepLength; j++) |
---|
| 922 | { |
---|
[81d96c] | 923 | fmpz_poly_get_coeff_fmpz (coeff1, subA1, j+k); |
---|
| 924 | fmpz_poly_get_coeff_fmpz (coeff2, buf, j); |
---|
| 925 | fmpz_add (coeff1, coeff1, coeff2); |
---|
| 926 | fmpz_poly_set_coeff_fmpz (subA1, j + k, coeff1); |
---|
| 927 | fmpz_poly_get_coeff_fmpz (coeff1, subA2, j + kk); |
---|
| 928 | fmpz_add (coeff1, coeff1, coeff2); |
---|
| 929 | fmpz_poly_set_coeff_fmpz (subA2, j + kk, coeff1); |
---|
[0e2e23] | 930 | } |
---|
[81d96c] | 931 | fmpz_poly_clear (buf); |
---|
[0e2e23] | 932 | } |
---|
[81d96c] | 933 | fmpz_clear (coeff1); |
---|
| 934 | fmpz_clear (coeff2); |
---|
| 935 | _fmpz_poly_normalise (subA1); |
---|
| 936 | _fmpz_poly_normalise (subA2); |
---|
[0e2e23] | 937 | } |
---|
| 938 | |
---|
[81d96c] | 939 | CanonicalForm reverseSubstQ (const fmpz_poly_t F, int d) |
---|
[0e2e23] | 940 | { |
---|
[81d96c] | 941 | Variable y= Variable (2); |
---|
| 942 | Variable x= Variable (1); |
---|
[0e2e23] | 943 | |
---|
[81d96c] | 944 | fmpz_poly_t f; |
---|
| 945 | fmpz_poly_init (f); |
---|
| 946 | fmpz_poly_set (f, F); |
---|
[0e2e23] | 947 | |
---|
[81d96c] | 948 | fmpz_poly_t buf; |
---|
| 949 | CanonicalForm result= 0; |
---|
| 950 | int i= 0; |
---|
| 951 | int degf= fmpz_poly_degree(f); |
---|
| 952 | int k= 0; |
---|
| 953 | int degfSubK, repLength, j; |
---|
| 954 | fmpz_t coeff; |
---|
| 955 | while (degf >= k) |
---|
[0e2e23] | 956 | { |
---|
[81d96c] | 957 | degfSubK= degf - k; |
---|
| 958 | if (degfSubK >= d) |
---|
| 959 | repLength= d; |
---|
| 960 | else |
---|
| 961 | repLength= degfSubK + 1; |
---|
[0e2e23] | 962 | |
---|
[81d96c] | 963 | fmpz_poly_init2 (buf, repLength); |
---|
| 964 | fmpz_init (coeff); |
---|
| 965 | for (j= 0; j < repLength; j++) |
---|
[0e2e23] | 966 | { |
---|
[81d96c] | 967 | fmpz_poly_get_coeff_fmpz (coeff, f, j + k); |
---|
| 968 | fmpz_poly_set_coeff_fmpz (buf, j, coeff); |
---|
[0e2e23] | 969 | } |
---|
[81d96c] | 970 | _fmpz_poly_normalise (buf); |
---|
| 971 | |
---|
| 972 | result += convertFmpz_poly_t2FacCF (buf, x)*power (y, i); |
---|
| 973 | i++; |
---|
| 974 | k= d*i; |
---|
| 975 | fmpz_poly_clear (buf); |
---|
| 976 | fmpz_clear (coeff); |
---|
[0e2e23] | 977 | } |
---|
[81d96c] | 978 | fmpz_poly_clear (f); |
---|
| 979 | |
---|
| 980 | return result; |
---|
[0e2e23] | 981 | } |
---|
| 982 | |
---|
[67ed74] | 983 | CanonicalForm |
---|
| 984 | reverseSubstQa (const fmpq_poly_t F, int d1, int d2, const Variable& alpha, |
---|
| 985 | const fmpq_poly_t mipo) |
---|
| 986 | { |
---|
| 987 | Variable y= Variable (2); |
---|
| 988 | Variable x= Variable (1); |
---|
| 989 | |
---|
| 990 | fmpq_poly_t f; |
---|
| 991 | fmpq_poly_init (f); |
---|
| 992 | fmpq_poly_set (f, F); |
---|
| 993 | |
---|
| 994 | fmpq_poly_t buf; |
---|
| 995 | CanonicalForm result= 0, result2; |
---|
| 996 | int i= 0; |
---|
| 997 | int degf= fmpq_poly_degree(f); |
---|
| 998 | int k= 0; |
---|
| 999 | int degfSubK; |
---|
| 1000 | int repLength; |
---|
| 1001 | fmpq_t coeff; |
---|
| 1002 | while (degf >= k) |
---|
| 1003 | { |
---|
| 1004 | degfSubK= degf - k; |
---|
| 1005 | if (degfSubK >= d1) |
---|
| 1006 | repLength= d1; |
---|
| 1007 | else |
---|
| 1008 | repLength= degfSubK + 1; |
---|
| 1009 | |
---|
| 1010 | fmpq_init (coeff); |
---|
| 1011 | int j= 0; |
---|
| 1012 | int l; |
---|
| 1013 | result2= 0; |
---|
| 1014 | while (j*d2 < repLength) |
---|
| 1015 | { |
---|
| 1016 | fmpq_poly_init2 (buf, d2); |
---|
| 1017 | for (l= 0; l < d2; l++) |
---|
| 1018 | { |
---|
| 1019 | fmpq_poly_get_coeff_fmpq (coeff, f, k + j*d2 + l); |
---|
| 1020 | fmpq_poly_set_coeff_fmpq (buf, l, coeff); |
---|
| 1021 | } |
---|
| 1022 | _fmpq_poly_normalise (buf); |
---|
| 1023 | fmpq_poly_rem (buf, buf, mipo); |
---|
| 1024 | result2 += convertFmpq_poly_t2FacCF (buf, alpha)*power (x, j); |
---|
| 1025 | j++; |
---|
| 1026 | fmpq_poly_clear (buf); |
---|
| 1027 | } |
---|
| 1028 | if (repLength - j*d2 != 0 && j*d2 - repLength < d2) |
---|
| 1029 | { |
---|
| 1030 | j--; |
---|
| 1031 | repLength -= j*d2; |
---|
| 1032 | fmpq_poly_init2 (buf, repLength); |
---|
| 1033 | j++; |
---|
| 1034 | for (l= 0; l < repLength; l++) |
---|
| 1035 | { |
---|
| 1036 | fmpq_poly_get_coeff_fmpq (coeff, f, k + j*d2 + l); |
---|
| 1037 | fmpq_poly_set_coeff_fmpq (buf, l, coeff); |
---|
| 1038 | } |
---|
| 1039 | _fmpq_poly_normalise (buf); |
---|
| 1040 | fmpq_poly_rem (buf, buf, mipo); |
---|
| 1041 | result2 += convertFmpq_poly_t2FacCF (buf, alpha)*power (x, j); |
---|
| 1042 | fmpq_poly_clear (buf); |
---|
| 1043 | } |
---|
| 1044 | fmpq_clear (coeff); |
---|
| 1045 | |
---|
| 1046 | result += result2*power (y, i); |
---|
| 1047 | i++; |
---|
| 1048 | k= d1*i; |
---|
| 1049 | } |
---|
| 1050 | |
---|
| 1051 | fmpq_poly_clear (f); |
---|
| 1052 | return result; |
---|
| 1053 | } |
---|
| 1054 | |
---|
[0e2e23] | 1055 | CanonicalForm |
---|
[81d96c] | 1056 | reverseSubstReciproFp (const nmod_poly_t F, const nmod_poly_t G, int d, int k) |
---|
[0e2e23] | 1057 | { |
---|
| 1058 | Variable y= Variable (2); |
---|
| 1059 | Variable x= Variable (1); |
---|
| 1060 | |
---|
[81d96c] | 1061 | nmod_poly_t f, g; |
---|
| 1062 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
| 1063 | nmod_poly_init_preinv (f, getCharacteristic(), ninv); |
---|
| 1064 | nmod_poly_init_preinv (g, getCharacteristic(), ninv); |
---|
| 1065 | nmod_poly_set (f, F); |
---|
| 1066 | nmod_poly_set (g, G); |
---|
| 1067 | int degf= nmod_poly_degree(f); |
---|
| 1068 | int degg= nmod_poly_degree(g); |
---|
[0e2e23] | 1069 | |
---|
| 1070 | |
---|
[81d96c] | 1071 | nmod_poly_t buf1,buf2, buf3; |
---|
| 1072 | |
---|
| 1073 | if (nmod_poly_length (f) < (long) d*(k+1)) //zero padding |
---|
| 1074 | nmod_poly_fit_length (f,(long)d*(k+1)); |
---|
[0e2e23] | 1075 | |
---|
| 1076 | CanonicalForm result= 0; |
---|
| 1077 | int i= 0; |
---|
| 1078 | int lf= 0; |
---|
| 1079 | int lg= d*k; |
---|
| 1080 | int degfSubLf= degf; |
---|
| 1081 | int deggSubLg= degg-lg; |
---|
| 1082 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
| 1083 | while (degf >= lf || lg >= 0) |
---|
| 1084 | { |
---|
| 1085 | if (degfSubLf >= d) |
---|
| 1086 | repLengthBuf1= d; |
---|
| 1087 | else if (degfSubLf < 0) |
---|
| 1088 | repLengthBuf1= 0; |
---|
| 1089 | else |
---|
| 1090 | repLengthBuf1= degfSubLf + 1; |
---|
[81d96c] | 1091 | nmod_poly_init2_preinv (buf1, getCharacteristic(), ninv, repLengthBuf1); |
---|
[0e2e23] | 1092 | |
---|
| 1093 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
[81d96c] | 1094 | nmod_poly_set_coeff_ui (buf1, ind, nmod_poly_get_coeff_ui (f, ind+lf)); |
---|
| 1095 | _nmod_poly_normalise (buf1); |
---|
[0e2e23] | 1096 | |
---|
[81d96c] | 1097 | repLengthBuf1= nmod_poly_length (buf1); |
---|
[0e2e23] | 1098 | |
---|
| 1099 | if (deggSubLg >= d - 1) |
---|
| 1100 | repLengthBuf2= d - 1; |
---|
| 1101 | else if (deggSubLg < 0) |
---|
| 1102 | repLengthBuf2= 0; |
---|
| 1103 | else |
---|
| 1104 | repLengthBuf2= deggSubLg + 1; |
---|
| 1105 | |
---|
[81d96c] | 1106 | nmod_poly_init2_preinv (buf2, getCharacteristic(), ninv, repLengthBuf2); |
---|
[0e2e23] | 1107 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[81d96c] | 1108 | nmod_poly_set_coeff_ui (buf2, ind, nmod_poly_get_coeff_ui (g, ind + lg)); |
---|
[0e2e23] | 1109 | |
---|
[81d96c] | 1110 | _nmod_poly_normalise (buf2); |
---|
| 1111 | repLengthBuf2= nmod_poly_length (buf2); |
---|
[0e2e23] | 1112 | |
---|
[81d96c] | 1113 | nmod_poly_init2_preinv (buf3, getCharacteristic(), ninv, repLengthBuf2 + d); |
---|
[0e2e23] | 1114 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
[81d96c] | 1115 | nmod_poly_set_coeff_ui (buf3, ind, nmod_poly_get_coeff_ui (buf1, ind)); |
---|
[0e2e23] | 1116 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
[81d96c] | 1117 | nmod_poly_set_coeff_ui (buf3, ind, 0); |
---|
[0e2e23] | 1118 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[81d96c] | 1119 | nmod_poly_set_coeff_ui (buf3, ind+d, nmod_poly_get_coeff_ui (buf2, ind)); |
---|
| 1120 | _nmod_poly_normalise (buf3); |
---|
[0e2e23] | 1121 | |
---|
[81d96c] | 1122 | result += convertnmod_poly_t2FacCF (buf3, x)*power (y, i); |
---|
[0e2e23] | 1123 | i++; |
---|
| 1124 | |
---|
| 1125 | |
---|
| 1126 | lf= i*d; |
---|
| 1127 | degfSubLf= degf - lf; |
---|
| 1128 | |
---|
| 1129 | lg= d*(k-i); |
---|
| 1130 | deggSubLg= degg - lg; |
---|
| 1131 | |
---|
| 1132 | if (lg >= 0 && deggSubLg > 0) |
---|
| 1133 | { |
---|
| 1134 | if (repLengthBuf2 > degfSubLf + 1) |
---|
| 1135 | degfSubLf= repLengthBuf2 - 1; |
---|
| 1136 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
| 1137 | for (ind= 0; ind < tmp; ind++) |
---|
[81d96c] | 1138 | nmod_poly_set_coeff_ui (g, ind + lg, |
---|
| 1139 | n_submod (nmod_poly_get_coeff_ui (g, ind + lg), |
---|
| 1140 | nmod_poly_get_coeff_ui (buf1, ind), |
---|
| 1141 | getCharacteristic() |
---|
| 1142 | ) |
---|
| 1143 | ); |
---|
[0e2e23] | 1144 | } |
---|
| 1145 | if (lg < 0) |
---|
[81d96c] | 1146 | { |
---|
| 1147 | nmod_poly_clear (buf1); |
---|
| 1148 | nmod_poly_clear (buf2); |
---|
| 1149 | nmod_poly_clear (buf3); |
---|
[0e2e23] | 1150 | break; |
---|
[81d96c] | 1151 | } |
---|
[0e2e23] | 1152 | if (degfSubLf >= 0) |
---|
| 1153 | { |
---|
| 1154 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[81d96c] | 1155 | nmod_poly_set_coeff_ui (f, ind + lf, |
---|
| 1156 | n_submod (nmod_poly_get_coeff_ui (f, ind + lf), |
---|
| 1157 | nmod_poly_get_coeff_ui (buf2, ind), |
---|
| 1158 | getCharacteristic() |
---|
| 1159 | ) |
---|
| 1160 | ); |
---|
[0e2e23] | 1161 | } |
---|
[81d96c] | 1162 | nmod_poly_clear (buf1); |
---|
| 1163 | nmod_poly_clear (buf2); |
---|
| 1164 | nmod_poly_clear (buf3); |
---|
[0e2e23] | 1165 | } |
---|
| 1166 | |
---|
[81d96c] | 1167 | nmod_poly_clear (f); |
---|
| 1168 | nmod_poly_clear (g); |
---|
| 1169 | |
---|
[0e2e23] | 1170 | return result; |
---|
| 1171 | } |
---|
| 1172 | |
---|
| 1173 | CanonicalForm |
---|
[81d96c] | 1174 | reverseSubstReciproQ (const fmpz_poly_t F, const fmpz_poly_t G, int d, int k) |
---|
[0e2e23] | 1175 | { |
---|
| 1176 | Variable y= Variable (2); |
---|
| 1177 | Variable x= Variable (1); |
---|
| 1178 | |
---|
[81d96c] | 1179 | fmpz_poly_t f, g; |
---|
| 1180 | fmpz_poly_init (f); |
---|
| 1181 | fmpz_poly_init (g); |
---|
| 1182 | fmpz_poly_set (f, F); |
---|
| 1183 | fmpz_poly_set (g, G); |
---|
| 1184 | int degf= fmpz_poly_degree(f); |
---|
| 1185 | int degg= fmpz_poly_degree(g); |
---|
[0e2e23] | 1186 | |
---|
| 1187 | |
---|
[81d96c] | 1188 | fmpz_poly_t buf1,buf2, buf3; |
---|
[0e2e23] | 1189 | |
---|
[81d96c] | 1190 | if (fmpz_poly_length (f) < (long) d*(k+1)) //zero padding |
---|
| 1191 | fmpz_poly_fit_length (f,(long)d*(k+1)); |
---|
[0e2e23] | 1192 | |
---|
| 1193 | CanonicalForm result= 0; |
---|
| 1194 | int i= 0; |
---|
| 1195 | int lf= 0; |
---|
| 1196 | int lg= d*k; |
---|
| 1197 | int degfSubLf= degf; |
---|
| 1198 | int deggSubLg= degg-lg; |
---|
| 1199 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
[81d96c] | 1200 | fmpz_t tmp1, tmp2; |
---|
[0e2e23] | 1201 | while (degf >= lf || lg >= 0) |
---|
| 1202 | { |
---|
| 1203 | if (degfSubLf >= d) |
---|
| 1204 | repLengthBuf1= d; |
---|
| 1205 | else if (degfSubLf < 0) |
---|
| 1206 | repLengthBuf1= 0; |
---|
| 1207 | else |
---|
| 1208 | repLengthBuf1= degfSubLf + 1; |
---|
| 1209 | |
---|
[81d96c] | 1210 | fmpz_poly_init2 (buf1, repLengthBuf1); |
---|
| 1211 | |
---|
[0e2e23] | 1212 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
[81d96c] | 1213 | { |
---|
| 1214 | fmpz_poly_get_coeff_fmpz (tmp1, f, ind + lf); |
---|
| 1215 | fmpz_poly_set_coeff_fmpz (buf1, ind, tmp1); |
---|
| 1216 | } |
---|
| 1217 | _fmpz_poly_normalise (buf1); |
---|
[0e2e23] | 1218 | |
---|
[81d96c] | 1219 | repLengthBuf1= fmpz_poly_length (buf1); |
---|
[0e2e23] | 1220 | |
---|
| 1221 | if (deggSubLg >= d - 1) |
---|
| 1222 | repLengthBuf2= d - 1; |
---|
| 1223 | else if (deggSubLg < 0) |
---|
| 1224 | repLengthBuf2= 0; |
---|
| 1225 | else |
---|
| 1226 | repLengthBuf2= deggSubLg + 1; |
---|
| 1227 | |
---|
[81d96c] | 1228 | fmpz_poly_init2 (buf2, repLengthBuf2); |
---|
[0e2e23] | 1229 | |
---|
[81d96c] | 1230 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
| 1231 | { |
---|
| 1232 | fmpz_poly_get_coeff_fmpz (tmp1, g, ind + lg); |
---|
| 1233 | fmpz_poly_set_coeff_fmpz (buf2, ind, tmp1); |
---|
| 1234 | } |
---|
[0e2e23] | 1235 | |
---|
[81d96c] | 1236 | _fmpz_poly_normalise (buf2); |
---|
| 1237 | repLengthBuf2= fmpz_poly_length (buf2); |
---|
[0e2e23] | 1238 | |
---|
[81d96c] | 1239 | fmpz_poly_init2 (buf3, repLengthBuf2 + d); |
---|
[0e2e23] | 1240 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
[81d96c] | 1241 | { |
---|
[e016ba] | 1242 | fmpz_poly_get_coeff_fmpz (tmp1, buf1, ind); |
---|
[81d96c] | 1243 | fmpz_poly_set_coeff_fmpz (buf3, ind, tmp1); |
---|
| 1244 | } |
---|
[0e2e23] | 1245 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
[81d96c] | 1246 | fmpz_poly_set_coeff_ui (buf3, ind, 0); |
---|
[0e2e23] | 1247 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[81d96c] | 1248 | { |
---|
| 1249 | fmpz_poly_get_coeff_fmpz (tmp1, buf2, ind); |
---|
| 1250 | fmpz_poly_set_coeff_fmpz (buf3, ind + d, tmp1); |
---|
| 1251 | } |
---|
| 1252 | _fmpz_poly_normalise (buf3); |
---|
[0e2e23] | 1253 | |
---|
[81d96c] | 1254 | result += convertFmpz_poly_t2FacCF (buf3, x)*power (y, i); |
---|
[0e2e23] | 1255 | i++; |
---|
| 1256 | |
---|
| 1257 | |
---|
| 1258 | lf= i*d; |
---|
| 1259 | degfSubLf= degf - lf; |
---|
| 1260 | |
---|
| 1261 | lg= d*(k-i); |
---|
| 1262 | deggSubLg= degg - lg; |
---|
| 1263 | |
---|
| 1264 | if (lg >= 0 && deggSubLg > 0) |
---|
| 1265 | { |
---|
| 1266 | if (repLengthBuf2 > degfSubLf + 1) |
---|
| 1267 | degfSubLf= repLengthBuf2 - 1; |
---|
| 1268 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
| 1269 | for (ind= 0; ind < tmp; ind++) |
---|
[81d96c] | 1270 | { |
---|
| 1271 | fmpz_poly_get_coeff_fmpz (tmp1, g, ind + lg); |
---|
| 1272 | fmpz_poly_get_coeff_fmpz (tmp2, buf1, ind); |
---|
| 1273 | fmpz_sub (tmp1, tmp1, tmp2); |
---|
| 1274 | fmpz_poly_set_coeff_fmpz (g, ind + lg, tmp1); |
---|
| 1275 | } |
---|
[0e2e23] | 1276 | } |
---|
| 1277 | if (lg < 0) |
---|
[81d96c] | 1278 | { |
---|
| 1279 | fmpz_poly_clear (buf1); |
---|
| 1280 | fmpz_poly_clear (buf2); |
---|
| 1281 | fmpz_poly_clear (buf3); |
---|
[0e2e23] | 1282 | break; |
---|
[81d96c] | 1283 | } |
---|
[0e2e23] | 1284 | if (degfSubLf >= 0) |
---|
| 1285 | { |
---|
| 1286 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[81d96c] | 1287 | { |
---|
| 1288 | fmpz_poly_get_coeff_fmpz (tmp1, f, ind + lf); |
---|
| 1289 | fmpz_poly_get_coeff_fmpz (tmp2, buf2, ind); |
---|
| 1290 | fmpz_sub (tmp1, tmp1, tmp2); |
---|
| 1291 | fmpz_poly_set_coeff_fmpz (f, ind + lf, tmp1); |
---|
| 1292 | } |
---|
[0e2e23] | 1293 | } |
---|
[81d96c] | 1294 | fmpz_poly_clear (buf1); |
---|
| 1295 | fmpz_poly_clear (buf2); |
---|
| 1296 | fmpz_poly_clear (buf3); |
---|
[0e2e23] | 1297 | } |
---|
| 1298 | |
---|
[81d96c] | 1299 | fmpz_poly_clear (f); |
---|
| 1300 | fmpz_poly_clear (g); |
---|
| 1301 | fmpz_clear (tmp1); |
---|
| 1302 | fmpz_clear (tmp2); |
---|
[0e2e23] | 1303 | |
---|
| 1304 | return result; |
---|
| 1305 | } |
---|
| 1306 | |
---|
[81d96c] | 1307 | CanonicalForm reverseSubstFp (const nmod_poly_t F, int d) |
---|
[0e2e23] | 1308 | { |
---|
| 1309 | Variable y= Variable (2); |
---|
| 1310 | Variable x= Variable (1); |
---|
| 1311 | |
---|
[81d96c] | 1312 | nmod_poly_t f; |
---|
| 1313 | mp_limb_t ninv= n_preinvert_limb (getCharacteristic()); |
---|
| 1314 | nmod_poly_init_preinv (f, getCharacteristic(), ninv); |
---|
| 1315 | nmod_poly_set (f, F); |
---|
[0e2e23] | 1316 | |
---|
[81d96c] | 1317 | nmod_poly_t buf; |
---|
[0e2e23] | 1318 | CanonicalForm result= 0; |
---|
| 1319 | int i= 0; |
---|
[81d96c] | 1320 | int degf= nmod_poly_degree(f); |
---|
[0e2e23] | 1321 | int k= 0; |
---|
| 1322 | int degfSubK, repLength, j; |
---|
| 1323 | while (degf >= k) |
---|
| 1324 | { |
---|
| 1325 | degfSubK= degf - k; |
---|
| 1326 | if (degfSubK >= d) |
---|
| 1327 | repLength= d; |
---|
| 1328 | else |
---|
| 1329 | repLength= degfSubK + 1; |
---|
| 1330 | |
---|
[81d96c] | 1331 | nmod_poly_init2_preinv (buf, getCharacteristic(), ninv, repLength); |
---|
[0e2e23] | 1332 | for (j= 0; j < repLength; j++) |
---|
[81d96c] | 1333 | nmod_poly_set_coeff_ui (buf, j, nmod_poly_get_coeff_ui (f, j + k)); |
---|
| 1334 | _nmod_poly_normalise (buf); |
---|
[0e2e23] | 1335 | |
---|
[81d96c] | 1336 | result += convertnmod_poly_t2FacCF (buf, x)*power (y, i); |
---|
[0e2e23] | 1337 | i++; |
---|
| 1338 | k= d*i; |
---|
[81d96c] | 1339 | nmod_poly_clear (buf); |
---|
[0e2e23] | 1340 | } |
---|
[81d96c] | 1341 | nmod_poly_clear (f); |
---|
[0e2e23] | 1342 | |
---|
| 1343 | return result; |
---|
| 1344 | } |
---|
| 1345 | |
---|
| 1346 | CanonicalForm |
---|
[81d96c] | 1347 | mulMod2FLINTFpReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 1348 | CanonicalForm& M) |
---|
[0e2e23] | 1349 | { |
---|
[04cda6a] | 1350 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
[0e2e23] | 1351 | d1 /= 2; |
---|
| 1352 | d1 += 1; |
---|
| 1353 | |
---|
[81d96c] | 1354 | nmod_poly_t F1, F2; |
---|
| 1355 | kronSubReciproFp (F1, F2, F, d1); |
---|
| 1356 | |
---|
| 1357 | nmod_poly_t G1, G2; |
---|
| 1358 | kronSubReciproFp (G1, G2, G, d1); |
---|
[0e2e23] | 1359 | |
---|
| 1360 | int k= d1*degree (M); |
---|
[81d96c] | 1361 | nmod_poly_mullow (F1, F1, G1, (long) k); |
---|
[0e2e23] | 1362 | |
---|
[81d96c] | 1363 | int degtailF= degree (tailcoeff (F), 1);; |
---|
[0e2e23] | 1364 | int degtailG= degree (tailcoeff (G), 1); |
---|
| 1365 | int taildegF= taildegree (F); |
---|
| 1366 | int taildegG= taildegree (G); |
---|
| 1367 | |
---|
[81d96c] | 1368 | int b= nmod_poly_degree (F2) + nmod_poly_degree (G2) - k - degtailF - degtailG |
---|
| 1369 | + d1*(2+taildegF + taildegG); |
---|
| 1370 | nmod_poly_mulhigh (F2, F2, G2, b); |
---|
| 1371 | nmod_poly_shift_right (F2, F2, b); |
---|
| 1372 | int d2= tmax (nmod_poly_degree (F2)/d1, nmod_poly_degree (F1)/d1); |
---|
[0e2e23] | 1373 | |
---|
[81d96c] | 1374 | |
---|
| 1375 | CanonicalForm result= reverseSubstReciproFp (F1, F2, d1, d2); |
---|
| 1376 | |
---|
| 1377 | nmod_poly_clear (F1); |
---|
| 1378 | nmod_poly_clear (F2); |
---|
| 1379 | nmod_poly_clear (G1); |
---|
| 1380 | nmod_poly_clear (G2); |
---|
| 1381 | return result; |
---|
[0e2e23] | 1382 | } |
---|
| 1383 | |
---|
| 1384 | CanonicalForm |
---|
[81d96c] | 1385 | mulMod2FLINTFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 1386 | CanonicalForm& M) |
---|
[0e2e23] | 1387 | { |
---|
| 1388 | CanonicalForm A= F; |
---|
| 1389 | CanonicalForm B= G; |
---|
| 1390 | |
---|
| 1391 | int degAx= degree (A, 1); |
---|
| 1392 | int degAy= degree (A, 2); |
---|
| 1393 | int degBx= degree (B, 1); |
---|
| 1394 | int degBy= degree (B, 2); |
---|
| 1395 | int d1= degAx + 1 + degBx; |
---|
| 1396 | int d2= tmax (degAy, degBy); |
---|
| 1397 | |
---|
| 1398 | if (d1 > 128 && d2 > 160 && (degAy == degBy) && (2*degAy > degree (M))) |
---|
[81d96c] | 1399 | return mulMod2FLINTFpReci (A, B, M); |
---|
[0e2e23] | 1400 | |
---|
[81d96c] | 1401 | nmod_poly_t FLINTA, FLINTB; |
---|
| 1402 | kronSubFp (FLINTA, A, d1); |
---|
| 1403 | kronSubFp (FLINTB, B, d1); |
---|
[0e2e23] | 1404 | |
---|
| 1405 | int k= d1*degree (M); |
---|
[81d96c] | 1406 | nmod_poly_mullow (FLINTA, FLINTA, FLINTB, (long) k); |
---|
[0e2e23] | 1407 | |
---|
[81d96c] | 1408 | A= reverseSubstFp (FLINTA, d1); |
---|
[0e2e23] | 1409 | |
---|
[81d96c] | 1410 | nmod_poly_clear (FLINTA); |
---|
| 1411 | nmod_poly_clear (FLINTB); |
---|
[0e2e23] | 1412 | return A; |
---|
| 1413 | } |
---|
| 1414 | |
---|
| 1415 | CanonicalForm |
---|
[81d96c] | 1416 | mulMod2FLINTQReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 1417 | CanonicalForm& M) |
---|
| 1418 | { |
---|
[04cda6a] | 1419 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
[0e2e23] | 1420 | d1 /= 2; |
---|
| 1421 | d1 += 1; |
---|
| 1422 | |
---|
[81d96c] | 1423 | fmpz_poly_t F1, F2; |
---|
| 1424 | kronSubReciproQ (F1, F2, F, d1); |
---|
| 1425 | |
---|
| 1426 | fmpz_poly_t G1, G2; |
---|
| 1427 | kronSubReciproQ (G1, G2, G, d1); |
---|
[0e2e23] | 1428 | |
---|
| 1429 | int k= d1*degree (M); |
---|
[81d96c] | 1430 | fmpz_poly_mullow (F1, F1, G1, (long) k); |
---|
[0e2e23] | 1431 | |
---|
[81d96c] | 1432 | int degtailF= degree (tailcoeff (F), 1);; |
---|
[0e2e23] | 1433 | int degtailG= degree (tailcoeff (G), 1); |
---|
| 1434 | int taildegF= taildegree (F); |
---|
| 1435 | int taildegG= taildegree (G); |
---|
| 1436 | |
---|
[81d96c] | 1437 | int b= fmpz_poly_degree (F2) + fmpz_poly_degree (G2) - k - degtailF - degtailG |
---|
| 1438 | + d1*(2+taildegF + taildegG); |
---|
| 1439 | fmpz_poly_mulhigh_n (F2, F2, G2, b); |
---|
| 1440 | fmpz_poly_shift_right (F2, F2, b); |
---|
| 1441 | int d2= tmax (fmpz_poly_degree (F2)/d1, fmpz_poly_degree (F1)/d1); |
---|
[0e2e23] | 1442 | |
---|
[81d96c] | 1443 | CanonicalForm result= reverseSubstReciproQ (F1, F2, d1, d2); |
---|
[0e2e23] | 1444 | |
---|
[81d96c] | 1445 | fmpz_poly_clear (F1); |
---|
| 1446 | fmpz_poly_clear (F2); |
---|
| 1447 | fmpz_poly_clear (G1); |
---|
| 1448 | fmpz_poly_clear (G2); |
---|
| 1449 | return result; |
---|
| 1450 | } |
---|
[0e2e23] | 1451 | |
---|
| 1452 | CanonicalForm |
---|
[81d96c] | 1453 | mulMod2FLINTQ (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 1454 | CanonicalForm& M) |
---|
[0e2e23] | 1455 | { |
---|
| 1456 | CanonicalForm A= F; |
---|
| 1457 | CanonicalForm B= G; |
---|
| 1458 | |
---|
[81d96c] | 1459 | int degAx= degree (A, 1); |
---|
| 1460 | int degBx= degree (B, 1); |
---|
| 1461 | int d1= degAx + 1 + degBx; |
---|
[0e2e23] | 1462 | |
---|
[81d96c] | 1463 | CanonicalForm f= bCommonDen (F); |
---|
| 1464 | CanonicalForm g= bCommonDen (G); |
---|
| 1465 | A *= f; |
---|
| 1466 | B *= g; |
---|
[0e2e23] | 1467 | |
---|
[81d96c] | 1468 | fmpz_poly_t FLINTA, FLINTB; |
---|
| 1469 | kronSub (FLINTA, A, d1); |
---|
| 1470 | kronSub (FLINTB, B, d1); |
---|
| 1471 | int k= d1*degree (M); |
---|
[0e2e23] | 1472 | |
---|
[81d96c] | 1473 | fmpz_poly_mullow (FLINTA, FLINTA, FLINTB, (long) k); |
---|
| 1474 | A= reverseSubstQ (FLINTA, d1); |
---|
| 1475 | fmpz_poly_clear (FLINTA); |
---|
| 1476 | fmpz_poly_clear (FLINTB); |
---|
| 1477 | return A/(f*g); |
---|
| 1478 | } |
---|
[0e2e23] | 1479 | |
---|
[67ed74] | 1480 | CanonicalForm |
---|
| 1481 | mulMod2FLINTQa (const CanonicalForm& F, const CanonicalForm& G, |
---|
| 1482 | const CanonicalForm& M) |
---|
| 1483 | { |
---|
| 1484 | Variable a; |
---|
| 1485 | if (!hasFirstAlgVar (F,a) && !hasFirstAlgVar (G, a)) |
---|
| 1486 | return mulMod2FLINTQ (F, G, M); |
---|
| 1487 | CanonicalForm A= F; |
---|
| 1488 | |
---|
| 1489 | int degFx= degree (F, 1); |
---|
| 1490 | int degFa= degree (F, a); |
---|
| 1491 | int degGx= degree (G, 1); |
---|
| 1492 | int degGa= degree (G, a); |
---|
| 1493 | |
---|
| 1494 | int d2= degFa+degGa+1; |
---|
| 1495 | int d1= degFx + 1 + degGx; |
---|
| 1496 | d1 *= d2; |
---|
| 1497 | |
---|
| 1498 | fmpq_poly_t FLINTF, FLINTG; |
---|
| 1499 | kronSubQa (FLINTF, F, d1, d2); |
---|
| 1500 | kronSubQa (FLINTG, G, d1, d2); |
---|
| 1501 | |
---|
| 1502 | fmpq_poly_mullow (FLINTF, FLINTF, FLINTG, d1*degree (M)); |
---|
| 1503 | |
---|
| 1504 | fmpq_poly_t mipo; |
---|
| 1505 | convertFacCF2Fmpq_poly_t (mipo, getMipo (a)); |
---|
| 1506 | CanonicalForm result= reverseSubstQa (FLINTF, d1, d2, a, mipo); |
---|
| 1507 | fmpq_poly_clear (FLINTF); |
---|
| 1508 | fmpq_poly_clear (FLINTG); |
---|
| 1509 | return result; |
---|
| 1510 | } |
---|
| 1511 | |
---|
[0e2e23] | 1512 | #endif |
---|
| 1513 | |
---|
[81d96c] | 1514 | zz_pX kronSubFp (const CanonicalForm& A, int d) |
---|
[0e2e23] | 1515 | { |
---|
| 1516 | int degAy= degree (A); |
---|
[81d96c] | 1517 | zz_pX result; |
---|
| 1518 | result.rep.SetLength (d*(degAy + 1)); |
---|
[0e2e23] | 1519 | |
---|
[81d96c] | 1520 | zz_p *resultp; |
---|
| 1521 | resultp= result.rep.elts(); |
---|
| 1522 | zz_pX buf; |
---|
| 1523 | zz_p *bufp; |
---|
| 1524 | int j, k, bufRepLength; |
---|
[0e2e23] | 1525 | |
---|
| 1526 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 1527 | { |
---|
[81d96c] | 1528 | if (i.coeff().inCoeffDomain()) |
---|
| 1529 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
| 1530 | else |
---|
| 1531 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
[0e2e23] | 1532 | |
---|
| 1533 | k= i.exp()*d; |
---|
[81d96c] | 1534 | bufp= buf.rep.elts(); |
---|
| 1535 | bufRepLength= (int) buf.rep.length(); |
---|
[0e2e23] | 1536 | for (j= 0; j < bufRepLength; j++) |
---|
[81d96c] | 1537 | resultp [j + k]= bufp [j]; |
---|
| 1538 | } |
---|
| 1539 | result.normalize(); |
---|
| 1540 | |
---|
| 1541 | return result; |
---|
| 1542 | } |
---|
| 1543 | |
---|
| 1544 | zz_pEX kronSubFq (const CanonicalForm& A, int d, const Variable& alpha) |
---|
| 1545 | { |
---|
| 1546 | int degAy= degree (A); |
---|
| 1547 | zz_pEX result; |
---|
| 1548 | result.rep.SetLength (d*(degAy + 1)); |
---|
| 1549 | |
---|
| 1550 | Variable v; |
---|
| 1551 | zz_pE *resultp; |
---|
| 1552 | resultp= result.rep.elts(); |
---|
| 1553 | zz_pEX buf1; |
---|
| 1554 | zz_pE *buf1p; |
---|
| 1555 | zz_pX buf2; |
---|
| 1556 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 1557 | int j, k, buf1RepLength; |
---|
| 1558 | |
---|
| 1559 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 1560 | { |
---|
| 1561 | if (i.coeff().inCoeffDomain()) |
---|
[0e2e23] | 1562 | { |
---|
[81d96c] | 1563 | buf2= convertFacCF2NTLzzpX (i.coeff()); |
---|
| 1564 | buf1= to_zz_pEX (to_zz_pE (buf2)); |
---|
[0e2e23] | 1565 | } |
---|
[81d96c] | 1566 | else |
---|
| 1567 | buf1= convertFacCF2NTLzz_pEX (i.coeff(), NTLMipo); |
---|
| 1568 | |
---|
| 1569 | k= i.exp()*d; |
---|
| 1570 | buf1p= buf1.rep.elts(); |
---|
| 1571 | buf1RepLength= (int) buf1.rep.length(); |
---|
| 1572 | for (j= 0; j < buf1RepLength; j++) |
---|
| 1573 | resultp [j + k]= buf1p [j]; |
---|
[0e2e23] | 1574 | } |
---|
[81d96c] | 1575 | result.normalize(); |
---|
| 1576 | |
---|
| 1577 | return result; |
---|
[0e2e23] | 1578 | } |
---|
| 1579 | |
---|
| 1580 | void |
---|
[81d96c] | 1581 | kronSubReciproFq (zz_pEX& subA1, zz_pEX& subA2,const CanonicalForm& A, int d, |
---|
| 1582 | const Variable& alpha) |
---|
[0e2e23] | 1583 | { |
---|
| 1584 | int degAy= degree (A); |
---|
[81d96c] | 1585 | subA1.rep.SetLength ((long) d*(degAy + 2)); |
---|
| 1586 | subA2.rep.SetLength ((long) d*(degAy + 2)); |
---|
[0e2e23] | 1587 | |
---|
[81d96c] | 1588 | Variable v; |
---|
| 1589 | zz_pE *subA1p; |
---|
| 1590 | zz_pE *subA2p; |
---|
| 1591 | subA1p= subA1.rep.elts(); |
---|
| 1592 | subA2p= subA2.rep.elts(); |
---|
| 1593 | zz_pEX buf; |
---|
| 1594 | zz_pE *bufp; |
---|
| 1595 | zz_pX buf2; |
---|
| 1596 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 1597 | int j, k, kk, bufRepLength; |
---|
[0e2e23] | 1598 | |
---|
| 1599 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 1600 | { |
---|
[81d96c] | 1601 | if (i.coeff().inCoeffDomain()) |
---|
| 1602 | { |
---|
| 1603 | buf2= convertFacCF2NTLzzpX (i.coeff()); |
---|
| 1604 | buf= to_zz_pEX (to_zz_pE (buf2)); |
---|
| 1605 | } |
---|
| 1606 | else |
---|
| 1607 | buf= convertFacCF2NTLzz_pEX (i.coeff(), NTLMipo); |
---|
[0e2e23] | 1608 | |
---|
| 1609 | k= i.exp()*d; |
---|
| 1610 | kk= (degAy - i.exp())*d; |
---|
[81d96c] | 1611 | bufp= buf.rep.elts(); |
---|
| 1612 | bufRepLength= (int) buf.rep.length(); |
---|
[0e2e23] | 1613 | for (j= 0; j < bufRepLength; j++) |
---|
| 1614 | { |
---|
[81d96c] | 1615 | subA1p [j + k] += bufp [j]; |
---|
| 1616 | subA2p [j + kk] += bufp [j]; |
---|
[0e2e23] | 1617 | } |
---|
| 1618 | } |
---|
[81d96c] | 1619 | subA1.normalize(); |
---|
| 1620 | subA2.normalize(); |
---|
[0e2e23] | 1621 | } |
---|
| 1622 | |
---|
[81d96c] | 1623 | void |
---|
| 1624 | kronSubReciproFp (zz_pX& subA1, zz_pX& subA2, const CanonicalForm& A, int d) |
---|
[0e2e23] | 1625 | { |
---|
[81d96c] | 1626 | int degAy= degree (A); |
---|
| 1627 | subA1.rep.SetLength ((long) d*(degAy + 2)); |
---|
| 1628 | subA2.rep.SetLength ((long) d*(degAy + 2)); |
---|
[0e2e23] | 1629 | |
---|
[81d96c] | 1630 | zz_p *subA1p; |
---|
| 1631 | zz_p *subA2p; |
---|
| 1632 | subA1p= subA1.rep.elts(); |
---|
| 1633 | subA2p= subA2.rep.elts(); |
---|
| 1634 | zz_pX buf; |
---|
| 1635 | zz_p *bufp; |
---|
| 1636 | int j, k, kk, bufRepLength; |
---|
[0e2e23] | 1637 | |
---|
[81d96c] | 1638 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
[0e2e23] | 1639 | { |
---|
[81d96c] | 1640 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
[0e2e23] | 1641 | |
---|
[81d96c] | 1642 | k= i.exp()*d; |
---|
| 1643 | kk= (degAy - i.exp())*d; |
---|
| 1644 | bufp= buf.rep.elts(); |
---|
| 1645 | bufRepLength= (int) buf.rep.length(); |
---|
| 1646 | for (j= 0; j < bufRepLength; j++) |
---|
[0e2e23] | 1647 | { |
---|
[81d96c] | 1648 | subA1p [j + k] += bufp [j]; |
---|
| 1649 | subA2p [j + kk] += bufp [j]; |
---|
[0e2e23] | 1650 | } |
---|
| 1651 | } |
---|
[81d96c] | 1652 | subA1.normalize(); |
---|
| 1653 | subA2.normalize(); |
---|
[0e2e23] | 1654 | } |
---|
| 1655 | |
---|
| 1656 | CanonicalForm |
---|
[81d96c] | 1657 | reverseSubstReciproFq (const zz_pEX& F, const zz_pEX& G, int d, int k, |
---|
| 1658 | const Variable& alpha) |
---|
[0e2e23] | 1659 | { |
---|
| 1660 | Variable y= Variable (2); |
---|
| 1661 | Variable x= Variable (1); |
---|
| 1662 | |
---|
[81d96c] | 1663 | zz_pEX f= F; |
---|
| 1664 | zz_pEX g= G; |
---|
| 1665 | int degf= deg(f); |
---|
| 1666 | int degg= deg(g); |
---|
[0e2e23] | 1667 | |
---|
[81d96c] | 1668 | zz_pEX buf1; |
---|
| 1669 | zz_pEX buf2; |
---|
| 1670 | zz_pEX buf3; |
---|
[0e2e23] | 1671 | |
---|
[81d96c] | 1672 | zz_pE *buf1p; |
---|
| 1673 | zz_pE *buf2p; |
---|
| 1674 | zz_pE *buf3p; |
---|
| 1675 | if (f.rep.length() < (long) d*(k+1)) //zero padding |
---|
| 1676 | f.rep.SetLength ((long)d*(k+1)); |
---|
[0e2e23] | 1677 | |
---|
[81d96c] | 1678 | zz_pE *gp= g.rep.elts(); |
---|
| 1679 | zz_pE *fp= f.rep.elts(); |
---|
[0e2e23] | 1680 | CanonicalForm result= 0; |
---|
| 1681 | int i= 0; |
---|
| 1682 | int lf= 0; |
---|
| 1683 | int lg= d*k; |
---|
| 1684 | int degfSubLf= degf; |
---|
| 1685 | int deggSubLg= degg-lg; |
---|
| 1686 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
[81d96c] | 1687 | zz_pE zzpEZero= zz_pE(); |
---|
| 1688 | |
---|
[0e2e23] | 1689 | while (degf >= lf || lg >= 0) |
---|
| 1690 | { |
---|
| 1691 | if (degfSubLf >= d) |
---|
| 1692 | repLengthBuf1= d; |
---|
| 1693 | else if (degfSubLf < 0) |
---|
| 1694 | repLengthBuf1= 0; |
---|
| 1695 | else |
---|
| 1696 | repLengthBuf1= degfSubLf + 1; |
---|
[81d96c] | 1697 | buf1.rep.SetLength((long) repLengthBuf1); |
---|
[0e2e23] | 1698 | |
---|
[81d96c] | 1699 | buf1p= buf1.rep.elts(); |
---|
[0e2e23] | 1700 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
[81d96c] | 1701 | buf1p [ind]= fp [ind + lf]; |
---|
| 1702 | buf1.normalize(); |
---|
[0e2e23] | 1703 | |
---|
[81d96c] | 1704 | repLengthBuf1= buf1.rep.length(); |
---|
[0e2e23] | 1705 | |
---|
| 1706 | if (deggSubLg >= d - 1) |
---|
| 1707 | repLengthBuf2= d - 1; |
---|
| 1708 | else if (deggSubLg < 0) |
---|
| 1709 | repLengthBuf2= 0; |
---|
| 1710 | else |
---|
| 1711 | repLengthBuf2= deggSubLg + 1; |
---|
| 1712 | |
---|
[81d96c] | 1713 | buf2.rep.SetLength ((long) repLengthBuf2); |
---|
| 1714 | buf2p= buf2.rep.elts(); |
---|
[0e2e23] | 1715 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[81d96c] | 1716 | buf2p [ind]= gp [ind + lg]; |
---|
| 1717 | buf2.normalize(); |
---|
[0e2e23] | 1718 | |
---|
[81d96c] | 1719 | repLengthBuf2= buf2.rep.length(); |
---|
[0e2e23] | 1720 | |
---|
[81d96c] | 1721 | buf3.rep.SetLength((long) repLengthBuf2 + d); |
---|
| 1722 | buf3p= buf3.rep.elts(); |
---|
| 1723 | buf2p= buf2.rep.elts(); |
---|
| 1724 | buf1p= buf1.rep.elts(); |
---|
[0e2e23] | 1725 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
[81d96c] | 1726 | buf3p [ind]= buf1p [ind]; |
---|
[0e2e23] | 1727 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
[81d96c] | 1728 | buf3p [ind]= zzpEZero; |
---|
[0e2e23] | 1729 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[81d96c] | 1730 | buf3p [ind + d]= buf2p [ind]; |
---|
| 1731 | buf3.normalize(); |
---|
[0e2e23] | 1732 | |
---|
[81d96c] | 1733 | result += convertNTLzz_pEX2CF (buf3, x, alpha)*power (y, i); |
---|
[0e2e23] | 1734 | i++; |
---|
| 1735 | |
---|
| 1736 | |
---|
| 1737 | lf= i*d; |
---|
| 1738 | degfSubLf= degf - lf; |
---|
| 1739 | |
---|
| 1740 | lg= d*(k-i); |
---|
| 1741 | deggSubLg= degg - lg; |
---|
| 1742 | |
---|
[81d96c] | 1743 | buf1p= buf1.rep.elts(); |
---|
| 1744 | |
---|
[0e2e23] | 1745 | if (lg >= 0 && deggSubLg > 0) |
---|
| 1746 | { |
---|
| 1747 | if (repLengthBuf2 > degfSubLf + 1) |
---|
| 1748 | degfSubLf= repLengthBuf2 - 1; |
---|
| 1749 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
| 1750 | for (ind= 0; ind < tmp; ind++) |
---|
[81d96c] | 1751 | gp [ind + lg] -= buf1p [ind]; |
---|
[0e2e23] | 1752 | } |
---|
[81d96c] | 1753 | |
---|
[0e2e23] | 1754 | if (lg < 0) |
---|
| 1755 | break; |
---|
[81d96c] | 1756 | |
---|
| 1757 | buf2p= buf2.rep.elts(); |
---|
[0e2e23] | 1758 | if (degfSubLf >= 0) |
---|
| 1759 | { |
---|
| 1760 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[81d96c] | 1761 | fp [ind + lf] -= buf2p [ind]; |
---|
[0e2e23] | 1762 | } |
---|
| 1763 | } |
---|
| 1764 | |
---|
| 1765 | return result; |
---|
| 1766 | } |
---|
| 1767 | |
---|
| 1768 | CanonicalForm |
---|
[81d96c] | 1769 | reverseSubstReciproFp (const zz_pX& F, const zz_pX& G, int d, int k) |
---|
[0e2e23] | 1770 | { |
---|
| 1771 | Variable y= Variable (2); |
---|
| 1772 | Variable x= Variable (1); |
---|
| 1773 | |
---|
[81d96c] | 1774 | zz_pX f= F; |
---|
| 1775 | zz_pX g= G; |
---|
| 1776 | int degf= deg(f); |
---|
| 1777 | int degg= deg(g); |
---|
[0e2e23] | 1778 | |
---|
[81d96c] | 1779 | zz_pX buf1; |
---|
| 1780 | zz_pX buf2; |
---|
| 1781 | zz_pX buf3; |
---|
[0e2e23] | 1782 | |
---|
[81d96c] | 1783 | zz_p *buf1p; |
---|
| 1784 | zz_p *buf2p; |
---|
| 1785 | zz_p *buf3p; |
---|
[0e2e23] | 1786 | |
---|
[81d96c] | 1787 | if (f.rep.length() < (long) d*(k+1)) //zero padding |
---|
| 1788 | f.rep.SetLength ((long)d*(k+1)); |
---|
[0e2e23] | 1789 | |
---|
[81d96c] | 1790 | zz_p *gp= g.rep.elts(); |
---|
| 1791 | zz_p *fp= f.rep.elts(); |
---|
[0e2e23] | 1792 | CanonicalForm result= 0; |
---|
| 1793 | int i= 0; |
---|
| 1794 | int lf= 0; |
---|
| 1795 | int lg= d*k; |
---|
| 1796 | int degfSubLf= degf; |
---|
| 1797 | int deggSubLg= degg-lg; |
---|
| 1798 | int repLengthBuf2, repLengthBuf1, ind, tmp; |
---|
[81d96c] | 1799 | zz_p zzpZero= zz_p(); |
---|
[0e2e23] | 1800 | while (degf >= lf || lg >= 0) |
---|
| 1801 | { |
---|
| 1802 | if (degfSubLf >= d) |
---|
| 1803 | repLengthBuf1= d; |
---|
| 1804 | else if (degfSubLf < 0) |
---|
| 1805 | repLengthBuf1= 0; |
---|
| 1806 | else |
---|
| 1807 | repLengthBuf1= degfSubLf + 1; |
---|
[81d96c] | 1808 | buf1.rep.SetLength((long) repLengthBuf1); |
---|
[0e2e23] | 1809 | |
---|
[81d96c] | 1810 | buf1p= buf1.rep.elts(); |
---|
[0e2e23] | 1811 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
[81d96c] | 1812 | buf1p [ind]= fp [ind + lf]; |
---|
| 1813 | buf1.normalize(); |
---|
[0e2e23] | 1814 | |
---|
[81d96c] | 1815 | repLengthBuf1= buf1.rep.length(); |
---|
[0e2e23] | 1816 | |
---|
| 1817 | if (deggSubLg >= d - 1) |
---|
| 1818 | repLengthBuf2= d - 1; |
---|
| 1819 | else if (deggSubLg < 0) |
---|
| 1820 | repLengthBuf2= 0; |
---|
| 1821 | else |
---|
| 1822 | repLengthBuf2= deggSubLg + 1; |
---|
| 1823 | |
---|
[81d96c] | 1824 | buf2.rep.SetLength ((long) repLengthBuf2); |
---|
| 1825 | buf2p= buf2.rep.elts(); |
---|
[0e2e23] | 1826 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[81d96c] | 1827 | buf2p [ind]= gp [ind + lg]; |
---|
[0e2e23] | 1828 | |
---|
[81d96c] | 1829 | buf2.normalize(); |
---|
[0e2e23] | 1830 | |
---|
[81d96c] | 1831 | repLengthBuf2= buf2.rep.length(); |
---|
| 1832 | |
---|
| 1833 | |
---|
| 1834 | buf3.rep.SetLength((long) repLengthBuf2 + d); |
---|
| 1835 | buf3p= buf3.rep.elts(); |
---|
| 1836 | buf2p= buf2.rep.elts(); |
---|
| 1837 | buf1p= buf1.rep.elts(); |
---|
[0e2e23] | 1838 | for (ind= 0; ind < repLengthBuf1; ind++) |
---|
[81d96c] | 1839 | buf3p [ind]= buf1p [ind]; |
---|
[0e2e23] | 1840 | for (ind= repLengthBuf1; ind < d; ind++) |
---|
[81d96c] | 1841 | buf3p [ind]= zzpZero; |
---|
[0e2e23] | 1842 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[81d96c] | 1843 | buf3p [ind + d]= buf2p [ind]; |
---|
| 1844 | buf3.normalize(); |
---|
[0e2e23] | 1845 | |
---|
[81d96c] | 1846 | result += convertNTLzzpX2CF (buf3, x)*power (y, i); |
---|
[0e2e23] | 1847 | i++; |
---|
| 1848 | |
---|
| 1849 | |
---|
| 1850 | lf= i*d; |
---|
| 1851 | degfSubLf= degf - lf; |
---|
| 1852 | |
---|
| 1853 | lg= d*(k-i); |
---|
| 1854 | deggSubLg= degg - lg; |
---|
| 1855 | |
---|
[81d96c] | 1856 | buf1p= buf1.rep.elts(); |
---|
| 1857 | |
---|
[0e2e23] | 1858 | if (lg >= 0 && deggSubLg > 0) |
---|
| 1859 | { |
---|
| 1860 | if (repLengthBuf2 > degfSubLf + 1) |
---|
| 1861 | degfSubLf= repLengthBuf2 - 1; |
---|
| 1862 | tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
| 1863 | for (ind= 0; ind < tmp; ind++) |
---|
[81d96c] | 1864 | gp [ind + lg] -= buf1p [ind]; |
---|
[0e2e23] | 1865 | } |
---|
| 1866 | if (lg < 0) |
---|
| 1867 | break; |
---|
[81d96c] | 1868 | |
---|
| 1869 | buf2p= buf2.rep.elts(); |
---|
[0e2e23] | 1870 | if (degfSubLf >= 0) |
---|
| 1871 | { |
---|
| 1872 | for (ind= 0; ind < repLengthBuf2; ind++) |
---|
[81d96c] | 1873 | fp [ind + lf] -= buf2p [ind]; |
---|
[0e2e23] | 1874 | } |
---|
| 1875 | } |
---|
| 1876 | |
---|
[81d96c] | 1877 | return result; |
---|
| 1878 | } |
---|
| 1879 | |
---|
| 1880 | CanonicalForm reverseSubstFq (const zz_pEX& F, int d, const Variable& alpha) |
---|
| 1881 | { |
---|
| 1882 | Variable y= Variable (2); |
---|
| 1883 | Variable x= Variable (1); |
---|
| 1884 | |
---|
| 1885 | zz_pEX f= F; |
---|
| 1886 | zz_pE *fp= f.rep.elts(); |
---|
| 1887 | |
---|
| 1888 | zz_pEX buf; |
---|
| 1889 | zz_pE *bufp; |
---|
| 1890 | CanonicalForm result= 0; |
---|
| 1891 | int i= 0; |
---|
| 1892 | int degf= deg(f); |
---|
| 1893 | int k= 0; |
---|
| 1894 | int degfSubK, repLength, j; |
---|
| 1895 | while (degf >= k) |
---|
| 1896 | { |
---|
| 1897 | degfSubK= degf - k; |
---|
| 1898 | if (degfSubK >= d) |
---|
| 1899 | repLength= d; |
---|
| 1900 | else |
---|
| 1901 | repLength= degfSubK + 1; |
---|
| 1902 | |
---|
| 1903 | buf.rep.SetLength ((long) repLength); |
---|
| 1904 | bufp= buf.rep.elts(); |
---|
| 1905 | for (j= 0; j < repLength; j++) |
---|
| 1906 | bufp [j]= fp [j + k]; |
---|
| 1907 | buf.normalize(); |
---|
| 1908 | |
---|
| 1909 | result += convertNTLzz_pEX2CF (buf, x, alpha)*power (y, i); |
---|
| 1910 | i++; |
---|
| 1911 | k= d*i; |
---|
| 1912 | } |
---|
[0e2e23] | 1913 | |
---|
| 1914 | return result; |
---|
| 1915 | } |
---|
| 1916 | |
---|
[81d96c] | 1917 | CanonicalForm reverseSubstFp (const zz_pX& F, int d) |
---|
[0e2e23] | 1918 | { |
---|
| 1919 | Variable y= Variable (2); |
---|
| 1920 | Variable x= Variable (1); |
---|
| 1921 | |
---|
[81d96c] | 1922 | zz_pX f= F; |
---|
| 1923 | zz_p *fp= f.rep.elts(); |
---|
[0e2e23] | 1924 | |
---|
[81d96c] | 1925 | zz_pX buf; |
---|
| 1926 | zz_p *bufp; |
---|
[0e2e23] | 1927 | CanonicalForm result= 0; |
---|
| 1928 | int i= 0; |
---|
[81d96c] | 1929 | int degf= deg(f); |
---|
[0e2e23] | 1930 | int k= 0; |
---|
| 1931 | int degfSubK, repLength, j; |
---|
| 1932 | while (degf >= k) |
---|
| 1933 | { |
---|
| 1934 | degfSubK= degf - k; |
---|
| 1935 | if (degfSubK >= d) |
---|
| 1936 | repLength= d; |
---|
| 1937 | else |
---|
| 1938 | repLength= degfSubK + 1; |
---|
| 1939 | |
---|
[81d96c] | 1940 | buf.rep.SetLength ((long) repLength); |
---|
| 1941 | bufp= buf.rep.elts(); |
---|
[0e2e23] | 1942 | for (j= 0; j < repLength; j++) |
---|
[81d96c] | 1943 | bufp [j]= fp [j + k]; |
---|
| 1944 | buf.normalize(); |
---|
[0e2e23] | 1945 | |
---|
[81d96c] | 1946 | result += convertNTLzzpX2CF (buf, x)*power (y, i); |
---|
[0e2e23] | 1947 | i++; |
---|
| 1948 | k= d*i; |
---|
| 1949 | } |
---|
| 1950 | |
---|
| 1951 | return result; |
---|
| 1952 | } |
---|
| 1953 | |
---|
[81d96c] | 1954 | // assumes input to be reduced mod M and to be an element of Fq not Fp |
---|
[0e2e23] | 1955 | CanonicalForm |
---|
[81d96c] | 1956 | mulMod2NTLFpReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 1957 | CanonicalForm& M) |
---|
[0e2e23] | 1958 | { |
---|
[81d96c] | 1959 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
[0e2e23] | 1960 | d1 /= 2; |
---|
| 1961 | d1 += 1; |
---|
| 1962 | |
---|
[81d96c] | 1963 | zz_pX F1, F2; |
---|
| 1964 | kronSubReciproFp (F1, F2, F, d1); |
---|
| 1965 | zz_pX G1, G2; |
---|
| 1966 | kronSubReciproFp (G1, G2, G, d1); |
---|
[0e2e23] | 1967 | |
---|
| 1968 | int k= d1*degree (M); |
---|
[81d96c] | 1969 | MulTrunc (F1, F1, G1, (long) k); |
---|
[0e2e23] | 1970 | |
---|
[81d96c] | 1971 | int degtailF= degree (tailcoeff (F), 1); |
---|
[0e2e23] | 1972 | int degtailG= degree (tailcoeff (G), 1); |
---|
| 1973 | int taildegF= taildegree (F); |
---|
| 1974 | int taildegG= taildegree (G); |
---|
[81d96c] | 1975 | int b= k + degtailF + degtailG - d1*(2+taildegF+taildegG); |
---|
[0e2e23] | 1976 | |
---|
[81d96c] | 1977 | reverse (F2, F2); |
---|
| 1978 | reverse (G2, G2); |
---|
| 1979 | MulTrunc (F2, F2, G2, b + 1); |
---|
| 1980 | reverse (F2, F2, b); |
---|
[0e2e23] | 1981 | |
---|
[81d96c] | 1982 | int d2= tmax (deg (F2)/d1, deg (F1)/d1); |
---|
| 1983 | return reverseSubstReciproFp (F1, F2, d1, d2); |
---|
[0e2e23] | 1984 | } |
---|
| 1985 | |
---|
[81d96c] | 1986 | //Kronecker substitution |
---|
[0e2e23] | 1987 | CanonicalForm |
---|
[81d96c] | 1988 | mulMod2NTLFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 1989 | CanonicalForm& M) |
---|
[0e2e23] | 1990 | { |
---|
| 1991 | CanonicalForm A= F; |
---|
| 1992 | CanonicalForm B= G; |
---|
| 1993 | |
---|
| 1994 | int degAx= degree (A, 1); |
---|
| 1995 | int degAy= degree (A, 2); |
---|
| 1996 | int degBx= degree (B, 1); |
---|
| 1997 | int degBy= degree (B, 2); |
---|
| 1998 | int d1= degAx + 1 + degBx; |
---|
| 1999 | int d2= tmax (degAy, degBy); |
---|
| 2000 | |
---|
| 2001 | if (d1 > 128 && d2 > 160 && (degAy == degBy) && (2*degAy > degree (M))) |
---|
[81d96c] | 2002 | return mulMod2NTLFpReci (A, B, M); |
---|
[0e2e23] | 2003 | |
---|
[81d96c] | 2004 | zz_pX NTLA= kronSubFp (A, d1); |
---|
| 2005 | zz_pX NTLB= kronSubFp (B, d1); |
---|
[0e2e23] | 2006 | |
---|
| 2007 | int k= d1*degree (M); |
---|
[81d96c] | 2008 | MulTrunc (NTLA, NTLA, NTLB, (long) k); |
---|
[0e2e23] | 2009 | |
---|
[81d96c] | 2010 | A= reverseSubstFp (NTLA, d1); |
---|
[0e2e23] | 2011 | |
---|
| 2012 | return A; |
---|
| 2013 | } |
---|
| 2014 | |
---|
[81d96c] | 2015 | // assumes input to be reduced mod M and to be an element of Fq not Fp |
---|
[0e2e23] | 2016 | CanonicalForm |
---|
[81d96c] | 2017 | mulMod2NTLFqReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 2018 | CanonicalForm& M, const Variable& alpha) |
---|
[0e2e23] | 2019 | { |
---|
[81d96c] | 2020 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
[0e2e23] | 2021 | d1 /= 2; |
---|
| 2022 | d1 += 1; |
---|
| 2023 | |
---|
[81d96c] | 2024 | zz_pEX F1, F2; |
---|
| 2025 | kronSubReciproFq (F1, F2, F, d1, alpha); |
---|
| 2026 | zz_pEX G1, G2; |
---|
| 2027 | kronSubReciproFq (G1, G2, G, d1, alpha); |
---|
[0e2e23] | 2028 | |
---|
| 2029 | int k= d1*degree (M); |
---|
[81d96c] | 2030 | MulTrunc (F1, F1, G1, (long) k); |
---|
[0e2e23] | 2031 | |
---|
[81d96c] | 2032 | int degtailF= degree (tailcoeff (F), 1); |
---|
[0e2e23] | 2033 | int degtailG= degree (tailcoeff (G), 1); |
---|
| 2034 | int taildegF= taildegree (F); |
---|
| 2035 | int taildegG= taildegree (G); |
---|
[81d96c] | 2036 | int b= k + degtailF + degtailG - d1*(2+taildegF+taildegG); |
---|
[0e2e23] | 2037 | |
---|
[81d96c] | 2038 | reverse (F2, F2); |
---|
| 2039 | reverse (G2, G2); |
---|
| 2040 | MulTrunc (F2, F2, G2, b + 1); |
---|
| 2041 | reverse (F2, F2, b); |
---|
[0e2e23] | 2042 | |
---|
[81d96c] | 2043 | int d2= tmax (deg (F2)/d1, deg (F1)/d1); |
---|
| 2044 | return reverseSubstReciproFq (F1, F2, d1, d2, alpha); |
---|
[0e2e23] | 2045 | } |
---|
| 2046 | |
---|
[81d96c] | 2047 | #ifdef HAVE_FLINT |
---|
[0e2e23] | 2048 | CanonicalForm |
---|
[81d96c] | 2049 | mulMod2FLINTFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 2050 | CanonicalForm& M); |
---|
| 2051 | #endif |
---|
| 2052 | |
---|
| 2053 | CanonicalForm |
---|
| 2054 | mulMod2NTLFq (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 2055 | CanonicalForm& M) |
---|
[0e2e23] | 2056 | { |
---|
[81d96c] | 2057 | Variable alpha; |
---|
[0e2e23] | 2058 | CanonicalForm A= F; |
---|
| 2059 | CanonicalForm B= G; |
---|
| 2060 | |
---|
[81d96c] | 2061 | if (hasFirstAlgVar (A, alpha) || hasFirstAlgVar (B, alpha)) |
---|
| 2062 | { |
---|
| 2063 | int degAx= degree (A, 1); |
---|
| 2064 | int degAy= degree (A, 2); |
---|
| 2065 | int degBx= degree (B, 1); |
---|
| 2066 | int degBy= degree (B, 2); |
---|
| 2067 | int d1= degAx + degBx + 1; |
---|
| 2068 | int d2= tmax (degAy, degBy); |
---|
| 2069 | zz_p::init (getCharacteristic()); |
---|
| 2070 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 2071 | zz_pE::init (NTLMipo); |
---|
[0e2e23] | 2072 | |
---|
[81d96c] | 2073 | int degMipo= degree (getMipo (alpha)); |
---|
| 2074 | if ((d1 > 128/degMipo) && (d2 > 160/degMipo) && (degAy == degBy) && |
---|
| 2075 | (2*degAy > degree (M))) |
---|
| 2076 | return mulMod2NTLFqReci (A, B, M, alpha); |
---|
[0e2e23] | 2077 | |
---|
[81d96c] | 2078 | zz_pEX NTLA= kronSubFq (A, d1, alpha); |
---|
| 2079 | zz_pEX NTLB= kronSubFq (B, d1, alpha); |
---|
[0e2e23] | 2080 | |
---|
[81d96c] | 2081 | int k= d1*degree (M); |
---|
| 2082 | |
---|
| 2083 | MulTrunc (NTLA, NTLA, NTLB, (long) k); |
---|
[0e2e23] | 2084 | |
---|
[81d96c] | 2085 | A= reverseSubstFq (NTLA, d1, alpha); |
---|
| 2086 | |
---|
| 2087 | return A; |
---|
| 2088 | } |
---|
| 2089 | else |
---|
| 2090 | #ifdef HAVE_FLINT |
---|
| 2091 | return mulMod2FLINTFp (A, B, M); |
---|
| 2092 | #else |
---|
| 2093 | return mulMod2NTLFp (A, B, M); |
---|
[0e2e23] | 2094 | #endif |
---|
[81d96c] | 2095 | } |
---|
[0e2e23] | 2096 | |
---|
| 2097 | CanonicalForm mulMod2 (const CanonicalForm& A, const CanonicalForm& B, |
---|
| 2098 | const CanonicalForm& M) |
---|
| 2099 | { |
---|
| 2100 | if (A.isZero() || B.isZero()) |
---|
| 2101 | return 0; |
---|
| 2102 | |
---|
| 2103 | ASSERT (M.isUnivariate(), "M must be univariate"); |
---|
| 2104 | |
---|
| 2105 | CanonicalForm F= mod (A, M); |
---|
| 2106 | CanonicalForm G= mod (B, M); |
---|
| 2107 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
---|
| 2108 | return F*G; |
---|
| 2109 | Variable y= M.mvar(); |
---|
| 2110 | int degF= degree (F, y); |
---|
| 2111 | int degG= degree (G, y); |
---|
| 2112 | |
---|
| 2113 | if ((degF < 1 && degG < 1) && (F.isUnivariate() && G.isUnivariate()) && |
---|
| 2114 | (F.level() == G.level())) |
---|
| 2115 | { |
---|
| 2116 | CanonicalForm result= mulNTL (F, G); |
---|
| 2117 | return mod (result, M); |
---|
| 2118 | } |
---|
| 2119 | else if (degF <= 1 && degG <= 1) |
---|
| 2120 | { |
---|
| 2121 | CanonicalForm result= F*G; |
---|
| 2122 | return mod (result, M); |
---|
| 2123 | } |
---|
| 2124 | |
---|
| 2125 | int sizeF= size (F); |
---|
| 2126 | int sizeG= size (G); |
---|
| 2127 | |
---|
| 2128 | int fallBackToNaive= 50; |
---|
| 2129 | if (sizeF < fallBackToNaive || sizeG < fallBackToNaive) |
---|
| 2130 | return mod (F*G, M); |
---|
| 2131 | |
---|
| 2132 | #ifdef HAVE_FLINT |
---|
[67ed74] | 2133 | if (getCharacteristic() == 0) |
---|
| 2134 | return mulMod2FLINTQa (F, G, M); |
---|
[0e2e23] | 2135 | #endif |
---|
| 2136 | |
---|
| 2137 | if (getCharacteristic() > 0 && CFFactory::gettype() != GaloisFieldDomain && |
---|
| 2138 | (((degF-degG) < 50 && degF > degG) || ((degG-degF) < 50 && degF <= degG))) |
---|
| 2139 | return mulMod2NTLFq (F, G, M); |
---|
| 2140 | |
---|
| 2141 | int m= (int) ceil (degree (M)/2.0); |
---|
| 2142 | if (degF >= m || degG >= m) |
---|
| 2143 | { |
---|
| 2144 | CanonicalForm MLo= power (y, m); |
---|
| 2145 | CanonicalForm MHi= power (y, degree (M) - m); |
---|
| 2146 | CanonicalForm F0= mod (F, MLo); |
---|
| 2147 | CanonicalForm F1= div (F, MLo); |
---|
| 2148 | CanonicalForm G0= mod (G, MLo); |
---|
| 2149 | CanonicalForm G1= div (G, MLo); |
---|
| 2150 | CanonicalForm F0G1= mulMod2 (F0, G1, MHi); |
---|
| 2151 | CanonicalForm F1G0= mulMod2 (F1, G0, MHi); |
---|
| 2152 | CanonicalForm F0G0= mulMod2 (F0, G0, M); |
---|
| 2153 | return F0G0 + MLo*(F0G1 + F1G0); |
---|
| 2154 | } |
---|
| 2155 | else |
---|
| 2156 | { |
---|
| 2157 | m= (int) ceil (tmax (degF, degG)/2.0); |
---|
| 2158 | CanonicalForm yToM= power (y, m); |
---|
| 2159 | CanonicalForm F0= mod (F, yToM); |
---|
| 2160 | CanonicalForm F1= div (F, yToM); |
---|
| 2161 | CanonicalForm G0= mod (G, yToM); |
---|
| 2162 | CanonicalForm G1= div (G, yToM); |
---|
| 2163 | CanonicalForm H00= mulMod2 (F0, G0, M); |
---|
| 2164 | CanonicalForm H11= mulMod2 (F1, G1, M); |
---|
| 2165 | CanonicalForm H01= mulMod2 (F0 + F1, G0 + G1, M); |
---|
| 2166 | return H11*yToM*yToM + (H01 - H11 - H00)*yToM + H00; |
---|
| 2167 | } |
---|
| 2168 | DEBOUTLN (cerr, "fatal end in mulMod2"); |
---|
| 2169 | } |
---|
| 2170 | |
---|
[81d96c] | 2171 | // end bivariate polys |
---|
| 2172 | //********************** |
---|
| 2173 | // multivariate polys |
---|
| 2174 | |
---|
[0e2e23] | 2175 | CanonicalForm mod (const CanonicalForm& F, const CFList& M) |
---|
| 2176 | { |
---|
| 2177 | CanonicalForm A= F; |
---|
| 2178 | for (CFListIterator i= M; i.hasItem(); i++) |
---|
| 2179 | A= mod (A, i.getItem()); |
---|
| 2180 | return A; |
---|
| 2181 | } |
---|
| 2182 | |
---|
| 2183 | CanonicalForm mulMod (const CanonicalForm& A, const CanonicalForm& B, |
---|
| 2184 | const CFList& MOD) |
---|
| 2185 | { |
---|
| 2186 | if (A.isZero() || B.isZero()) |
---|
| 2187 | return 0; |
---|
| 2188 | |
---|
| 2189 | if (MOD.length() == 1) |
---|
| 2190 | return mulMod2 (A, B, MOD.getLast()); |
---|
| 2191 | |
---|
| 2192 | CanonicalForm M= MOD.getLast(); |
---|
| 2193 | CanonicalForm F= mod (A, M); |
---|
| 2194 | CanonicalForm G= mod (B, M); |
---|
| 2195 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
---|
| 2196 | return F*G; |
---|
[67a39b] | 2197 | |
---|
| 2198 | if (size (F) / MOD.length() < 100 || size (G) / MOD.length() < 100) |
---|
| 2199 | return mod (F*G, MOD); |
---|
| 2200 | |
---|
[0e2e23] | 2201 | Variable y= M.mvar(); |
---|
| 2202 | int degF= degree (F, y); |
---|
| 2203 | int degG= degree (G, y); |
---|
| 2204 | |
---|
| 2205 | if ((degF <= 1 && F.level() <= M.level()) && |
---|
| 2206 | (degG <= 1 && G.level() <= M.level())) |
---|
| 2207 | { |
---|
| 2208 | CFList buf= MOD; |
---|
| 2209 | buf.removeLast(); |
---|
| 2210 | if (degF == 1 && degG == 1) |
---|
| 2211 | { |
---|
| 2212 | CanonicalForm F0= mod (F, y); |
---|
| 2213 | CanonicalForm F1= div (F, y); |
---|
| 2214 | CanonicalForm G0= mod (G, y); |
---|
| 2215 | CanonicalForm G1= div (G, y); |
---|
| 2216 | if (degree (M) > 2) |
---|
| 2217 | { |
---|
| 2218 | CanonicalForm H00= mulMod (F0, G0, buf); |
---|
| 2219 | CanonicalForm H11= mulMod (F1, G1, buf); |
---|
| 2220 | CanonicalForm H01= mulMod (F0 + F1, G0 + G1, buf); |
---|
| 2221 | return H11*y*y + (H01 - H00 - H11)*y + H00; |
---|
| 2222 | } |
---|
| 2223 | else //here degree (M) == 2 |
---|
| 2224 | { |
---|
| 2225 | buf.append (y); |
---|
| 2226 | CanonicalForm F0G1= mulMod (F0, G1, buf); |
---|
| 2227 | CanonicalForm F1G0= mulMod (F1, G0, buf); |
---|
| 2228 | CanonicalForm F0G0= mulMod (F0, G0, MOD); |
---|
| 2229 | CanonicalForm result= F0G0 + y*(F0G1 + F1G0); |
---|
| 2230 | return result; |
---|
| 2231 | } |
---|
| 2232 | } |
---|
| 2233 | else if (degF == 1 && degG == 0) |
---|
| 2234 | return mulMod (div (F, y), G, buf)*y + mulMod (mod (F, y), G, buf); |
---|
| 2235 | else if (degF == 0 && degG == 1) |
---|
| 2236 | return mulMod (div (G, y), F, buf)*y + mulMod (mod (G, y), F, buf); |
---|
| 2237 | else |
---|
| 2238 | return mulMod (F, G, buf); |
---|
| 2239 | } |
---|
| 2240 | int m= (int) ceil (degree (M)/2.0); |
---|
| 2241 | if (degF >= m || degG >= m) |
---|
| 2242 | { |
---|
| 2243 | CanonicalForm MLo= power (y, m); |
---|
| 2244 | CanonicalForm MHi= power (y, degree (M) - m); |
---|
| 2245 | CanonicalForm F0= mod (F, MLo); |
---|
| 2246 | CanonicalForm F1= div (F, MLo); |
---|
| 2247 | CanonicalForm G0= mod (G, MLo); |
---|
| 2248 | CanonicalForm G1= div (G, MLo); |
---|
| 2249 | CFList buf= MOD; |
---|
| 2250 | buf.removeLast(); |
---|
| 2251 | buf.append (MHi); |
---|
| 2252 | CanonicalForm F0G1= mulMod (F0, G1, buf); |
---|
| 2253 | CanonicalForm F1G0= mulMod (F1, G0, buf); |
---|
| 2254 | CanonicalForm F0G0= mulMod (F0, G0, MOD); |
---|
| 2255 | return F0G0 + MLo*(F0G1 + F1G0); |
---|
| 2256 | } |
---|
| 2257 | else |
---|
| 2258 | { |
---|
| 2259 | m= (int) ceil (tmax (degF, degG)/2.0); |
---|
| 2260 | CanonicalForm yToM= power (y, m); |
---|
| 2261 | CanonicalForm F0= mod (F, yToM); |
---|
| 2262 | CanonicalForm F1= div (F, yToM); |
---|
| 2263 | CanonicalForm G0= mod (G, yToM); |
---|
| 2264 | CanonicalForm G1= div (G, yToM); |
---|
| 2265 | CanonicalForm H00= mulMod (F0, G0, MOD); |
---|
| 2266 | CanonicalForm H11= mulMod (F1, G1, MOD); |
---|
| 2267 | CanonicalForm H01= mulMod (F0 + F1, G0 + G1, MOD); |
---|
| 2268 | return H11*yToM*yToM + (H01 - H11 - H00)*yToM + H00; |
---|
| 2269 | } |
---|
| 2270 | DEBOUTLN (cerr, "fatal end in mulMod"); |
---|
| 2271 | } |
---|
| 2272 | |
---|
| 2273 | CanonicalForm prodMod (const CFList& L, const CanonicalForm& M) |
---|
| 2274 | { |
---|
| 2275 | if (L.isEmpty()) |
---|
| 2276 | return 1; |
---|
| 2277 | int l= L.length(); |
---|
| 2278 | if (l == 1) |
---|
| 2279 | return mod (L.getFirst(), M); |
---|
| 2280 | else if (l == 2) { |
---|
| 2281 | CanonicalForm result= mulMod2 (L.getFirst(), L.getLast(), M); |
---|
| 2282 | return result; |
---|
| 2283 | } |
---|
| 2284 | else |
---|
| 2285 | { |
---|
| 2286 | l /= 2; |
---|
| 2287 | CFList tmp1, tmp2; |
---|
| 2288 | CFListIterator i= L; |
---|
| 2289 | CanonicalForm buf1, buf2; |
---|
| 2290 | for (int j= 1; j <= l; j++, i++) |
---|
| 2291 | tmp1.append (i.getItem()); |
---|
| 2292 | tmp2= Difference (L, tmp1); |
---|
| 2293 | buf1= prodMod (tmp1, M); |
---|
| 2294 | buf2= prodMod (tmp2, M); |
---|
| 2295 | CanonicalForm result= mulMod2 (buf1, buf2, M); |
---|
| 2296 | return result; |
---|
| 2297 | } |
---|
| 2298 | } |
---|
| 2299 | |
---|
| 2300 | CanonicalForm prodMod (const CFList& L, const CFList& M) |
---|
| 2301 | { |
---|
| 2302 | if (L.isEmpty()) |
---|
| 2303 | return 1; |
---|
| 2304 | else if (L.length() == 1) |
---|
| 2305 | return L.getFirst(); |
---|
| 2306 | else if (L.length() == 2) |
---|
| 2307 | return mulMod (L.getFirst(), L.getLast(), M); |
---|
| 2308 | else |
---|
| 2309 | { |
---|
| 2310 | int l= L.length()/2; |
---|
| 2311 | CFListIterator i= L; |
---|
| 2312 | CFList tmp1, tmp2; |
---|
| 2313 | CanonicalForm buf1, buf2; |
---|
| 2314 | for (int j= 1; j <= l; j++, i++) |
---|
| 2315 | tmp1.append (i.getItem()); |
---|
| 2316 | tmp2= Difference (L, tmp1); |
---|
| 2317 | buf1= prodMod (tmp1, M); |
---|
| 2318 | buf2= prodMod (tmp2, M); |
---|
| 2319 | return mulMod (buf1, buf2, M); |
---|
| 2320 | } |
---|
| 2321 | } |
---|
| 2322 | |
---|
[81d96c] | 2323 | // end multivariate polys |
---|
| 2324 | //*************************** |
---|
| 2325 | // division |
---|
| 2326 | |
---|
[0e2e23] | 2327 | CanonicalForm reverse (const CanonicalForm& F, int d) |
---|
| 2328 | { |
---|
| 2329 | if (d == 0) |
---|
| 2330 | return F; |
---|
| 2331 | CanonicalForm A= F; |
---|
| 2332 | Variable y= Variable (2); |
---|
| 2333 | Variable x= Variable (1); |
---|
| 2334 | if (degree (A, x) > 0) |
---|
| 2335 | { |
---|
| 2336 | A= swapvar (A, x, y); |
---|
| 2337 | CanonicalForm result= 0; |
---|
| 2338 | CFIterator i= A; |
---|
| 2339 | while (d - i.exp() < 0) |
---|
| 2340 | i++; |
---|
| 2341 | |
---|
| 2342 | for (; i.hasTerms() && (d - i.exp() >= 0); i++) |
---|
| 2343 | result += swapvar (i.coeff(),x,y)*power (x, d - i.exp()); |
---|
| 2344 | return result; |
---|
| 2345 | } |
---|
| 2346 | else |
---|
| 2347 | return A*power (x, d); |
---|
| 2348 | } |
---|
| 2349 | |
---|
| 2350 | CanonicalForm |
---|
| 2351 | newtonInverse (const CanonicalForm& F, const int n, const CanonicalForm& M) |
---|
| 2352 | { |
---|
| 2353 | int l= ilog2(n); |
---|
| 2354 | |
---|
| 2355 | CanonicalForm g= mod (F, M)[0] [0]; |
---|
| 2356 | |
---|
| 2357 | ASSERT (!g.isZero(), "expected a unit"); |
---|
| 2358 | |
---|
| 2359 | Variable alpha; |
---|
| 2360 | |
---|
| 2361 | if (!g.isOne()) |
---|
| 2362 | g = 1/g; |
---|
| 2363 | Variable x= Variable (1); |
---|
| 2364 | CanonicalForm result; |
---|
| 2365 | int exp= 0; |
---|
| 2366 | if (n & 1) |
---|
| 2367 | { |
---|
| 2368 | result= g; |
---|
| 2369 | exp= 1; |
---|
| 2370 | } |
---|
| 2371 | CanonicalForm h; |
---|
| 2372 | |
---|
| 2373 | for (int i= 1; i <= l; i++) |
---|
| 2374 | { |
---|
| 2375 | h= mulMod2 (g, mod (F, power (x, (1 << i))), M); |
---|
| 2376 | h= mod (h, power (x, (1 << i)) - 1); |
---|
| 2377 | h= div (h, power (x, (1 << (i - 1)))); |
---|
| 2378 | h= mod (h, M); |
---|
| 2379 | g -= power (x, (1 << (i - 1)))* |
---|
| 2380 | mod (mulMod2 (g, h, M), power (x, (1 << (i - 1)))); |
---|
| 2381 | |
---|
| 2382 | if (n & (1 << i)) |
---|
| 2383 | { |
---|
| 2384 | if (exp) |
---|
| 2385 | { |
---|
| 2386 | h= mulMod2 (result, mod (F, power (x, exp + (1 << i))), M); |
---|
| 2387 | h= mod (h, power (x, exp + (1 << i)) - 1); |
---|
| 2388 | h= div (h, power (x, exp)); |
---|
| 2389 | h= mod (h, M); |
---|
| 2390 | result -= power(x, exp)*mod (mulMod2 (g, h, M), |
---|
| 2391 | power (x, (1 << i))); |
---|
| 2392 | exp += (1 << i); |
---|
| 2393 | } |
---|
| 2394 | else |
---|
| 2395 | { |
---|
| 2396 | exp= (1 << i); |
---|
| 2397 | result= g; |
---|
| 2398 | } |
---|
| 2399 | } |
---|
| 2400 | } |
---|
| 2401 | |
---|
| 2402 | return result; |
---|
| 2403 | } |
---|
| 2404 | |
---|
| 2405 | CanonicalForm |
---|
| 2406 | newtonDiv (const CanonicalForm& F, const CanonicalForm& G, const CanonicalForm& |
---|
| 2407 | M) |
---|
| 2408 | { |
---|
| 2409 | ASSERT (getCharacteristic() > 0, "positive characteristic expected"); |
---|
| 2410 | |
---|
| 2411 | CanonicalForm A= mod (F, M); |
---|
| 2412 | CanonicalForm B= mod (G, M); |
---|
| 2413 | |
---|
| 2414 | Variable x= Variable (1); |
---|
| 2415 | int degA= degree (A, x); |
---|
| 2416 | int degB= degree (B, x); |
---|
| 2417 | int m= degA - degB; |
---|
| 2418 | if (m < 0) |
---|
| 2419 | return 0; |
---|
| 2420 | |
---|
| 2421 | Variable v; |
---|
| 2422 | CanonicalForm Q; |
---|
| 2423 | if (degB < 1 || CFFactory::gettype() == GaloisFieldDomain) |
---|
| 2424 | { |
---|
| 2425 | CanonicalForm R; |
---|
| 2426 | divrem2 (A, B, Q, R, M); |
---|
| 2427 | } |
---|
| 2428 | else |
---|
| 2429 | { |
---|
| 2430 | if (hasFirstAlgVar (A, v) || hasFirstAlgVar (B, v)) |
---|
| 2431 | { |
---|
| 2432 | CanonicalForm R= reverse (A, degA); |
---|
| 2433 | CanonicalForm revB= reverse (B, degB); |
---|
| 2434 | revB= newtonInverse (revB, m + 1, M); |
---|
| 2435 | Q= mulMod2 (R, revB, M); |
---|
| 2436 | Q= mod (Q, power (x, m + 1)); |
---|
| 2437 | Q= reverse (Q, m); |
---|
| 2438 | } |
---|
| 2439 | else |
---|
| 2440 | { |
---|
[53273d] | 2441 | bool zz_pEbak= zz_pE::initialized(); |
---|
| 2442 | zz_pEBak bak; |
---|
| 2443 | if (zz_pEbak) |
---|
| 2444 | bak.save(); |
---|
[0e2e23] | 2445 | zz_pX mipo= convertFacCF2NTLzzpX (M); |
---|
| 2446 | Variable y= Variable (2); |
---|
| 2447 | zz_pEX NTLA, NTLB; |
---|
| 2448 | NTLA= convertFacCF2NTLzz_pEX (swapvar (A, x, y), mipo); |
---|
| 2449 | NTLB= convertFacCF2NTLzz_pEX (swapvar (B, x, y), mipo); |
---|
| 2450 | div (NTLA, NTLA, NTLB); |
---|
| 2451 | Q= convertNTLzz_pEX2CF (NTLA, x, y); |
---|
[53273d] | 2452 | if (zz_pEbak) |
---|
| 2453 | bak.restore(); |
---|
[0e2e23] | 2454 | } |
---|
| 2455 | } |
---|
| 2456 | |
---|
| 2457 | return Q; |
---|
| 2458 | } |
---|
| 2459 | |
---|
| 2460 | void |
---|
| 2461 | newtonDivrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
| 2462 | CanonicalForm& R, const CanonicalForm& M) |
---|
| 2463 | { |
---|
| 2464 | CanonicalForm A= mod (F, M); |
---|
| 2465 | CanonicalForm B= mod (G, M); |
---|
| 2466 | Variable x= Variable (1); |
---|
| 2467 | int degA= degree (A, x); |
---|
| 2468 | int degB= degree (B, x); |
---|
| 2469 | int m= degA - degB; |
---|
| 2470 | |
---|
| 2471 | if (m < 0) |
---|
| 2472 | { |
---|
| 2473 | R= A; |
---|
| 2474 | Q= 0; |
---|
| 2475 | return; |
---|
| 2476 | } |
---|
| 2477 | |
---|
| 2478 | Variable v; |
---|
| 2479 | if (degB <= 1 || CFFactory::gettype() == GaloisFieldDomain) |
---|
| 2480 | { |
---|
| 2481 | divrem2 (A, B, Q, R, M); |
---|
| 2482 | } |
---|
| 2483 | else |
---|
| 2484 | { |
---|
| 2485 | if (hasFirstAlgVar (A, v) || hasFirstAlgVar (B, v)) |
---|
| 2486 | { |
---|
| 2487 | R= reverse (A, degA); |
---|
| 2488 | |
---|
| 2489 | CanonicalForm revB= reverse (B, degB); |
---|
| 2490 | revB= newtonInverse (revB, m + 1, M); |
---|
| 2491 | Q= mulMod2 (R, revB, M); |
---|
| 2492 | |
---|
| 2493 | Q= mod (Q, power (x, m + 1)); |
---|
| 2494 | Q= reverse (Q, m); |
---|
| 2495 | |
---|
| 2496 | R= A - mulMod2 (Q, B, M); |
---|
| 2497 | } |
---|
| 2498 | else |
---|
| 2499 | { |
---|
| 2500 | zz_pX mipo= convertFacCF2NTLzzpX (M); |
---|
| 2501 | Variable y= Variable (2); |
---|
| 2502 | zz_pEX NTLA, NTLB; |
---|
| 2503 | NTLA= convertFacCF2NTLzz_pEX (swapvar (A, x, y), mipo); |
---|
| 2504 | NTLB= convertFacCF2NTLzz_pEX (swapvar (B, x, y), mipo); |
---|
| 2505 | zz_pEX NTLQ, NTLR; |
---|
| 2506 | DivRem (NTLQ, NTLR, NTLA, NTLB); |
---|
| 2507 | Q= convertNTLzz_pEX2CF (NTLQ, x, y); |
---|
| 2508 | R= convertNTLzz_pEX2CF (NTLR, x, y); |
---|
| 2509 | } |
---|
| 2510 | } |
---|
| 2511 | } |
---|
| 2512 | |
---|
| 2513 | static inline |
---|
| 2514 | CFList split (const CanonicalForm& F, const int m, const Variable& x) |
---|
| 2515 | { |
---|
| 2516 | CanonicalForm A= F; |
---|
| 2517 | CanonicalForm buf= 0; |
---|
| 2518 | bool swap= false; |
---|
| 2519 | if (degree (A, x) <= 0) |
---|
| 2520 | return CFList(A); |
---|
| 2521 | else if (x.level() != A.level()) |
---|
| 2522 | { |
---|
| 2523 | swap= true; |
---|
| 2524 | A= swapvar (A, x, A.mvar()); |
---|
| 2525 | } |
---|
| 2526 | |
---|
| 2527 | int j= (int) floor ((double) degree (A)/ m); |
---|
| 2528 | CFList result; |
---|
| 2529 | CFIterator i= A; |
---|
| 2530 | for (; j >= 0; j--) |
---|
| 2531 | { |
---|
| 2532 | while (i.hasTerms() && i.exp() - j*m >= 0) |
---|
| 2533 | { |
---|
| 2534 | if (swap) |
---|
| 2535 | buf += i.coeff()*power (A.mvar(), i.exp() - j*m); |
---|
| 2536 | else |
---|
| 2537 | buf += i.coeff()*power (x, i.exp() - j*m); |
---|
| 2538 | i++; |
---|
| 2539 | } |
---|
| 2540 | if (swap) |
---|
| 2541 | result.append (swapvar (buf, x, F.mvar())); |
---|
| 2542 | else |
---|
| 2543 | result.append (buf); |
---|
| 2544 | buf= 0; |
---|
| 2545 | } |
---|
| 2546 | return result; |
---|
| 2547 | } |
---|
| 2548 | |
---|
| 2549 | static inline |
---|
| 2550 | void divrem32 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
| 2551 | CanonicalForm& R, const CFList& M); |
---|
| 2552 | |
---|
| 2553 | static inline |
---|
| 2554 | void divrem21 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
| 2555 | CanonicalForm& R, const CFList& M) |
---|
| 2556 | { |
---|
| 2557 | CanonicalForm A= mod (F, M); |
---|
| 2558 | CanonicalForm B= mod (G, M); |
---|
| 2559 | Variable x= Variable (1); |
---|
| 2560 | int degB= degree (B, x); |
---|
| 2561 | int degA= degree (A, x); |
---|
| 2562 | if (degA < degB) |
---|
| 2563 | { |
---|
| 2564 | Q= 0; |
---|
| 2565 | R= A; |
---|
| 2566 | return; |
---|
| 2567 | } |
---|
| 2568 | if (degB < 1) |
---|
| 2569 | { |
---|
| 2570 | divrem (A, B, Q, R); |
---|
| 2571 | Q= mod (Q, M); |
---|
| 2572 | R= mod (R, M); |
---|
| 2573 | return; |
---|
| 2574 | } |
---|
| 2575 | int m= (int) ceil ((double) (degB + 1)/2.0) + 1; |
---|
[050d1b] | 2576 | ASSERT (4*m >= degA, "expected degree (F, 1) < 2*degree (G, 1)"); |
---|
[0e2e23] | 2577 | CFList splitA= split (A, m, x); |
---|
| 2578 | if (splitA.length() == 3) |
---|
| 2579 | splitA.insert (0); |
---|
| 2580 | if (splitA.length() == 2) |
---|
| 2581 | { |
---|
| 2582 | splitA.insert (0); |
---|
| 2583 | splitA.insert (0); |
---|
| 2584 | } |
---|
| 2585 | if (splitA.length() == 1) |
---|
| 2586 | { |
---|
| 2587 | splitA.insert (0); |
---|
| 2588 | splitA.insert (0); |
---|
| 2589 | splitA.insert (0); |
---|
| 2590 | } |
---|
| 2591 | |
---|
| 2592 | CanonicalForm xToM= power (x, m); |
---|
| 2593 | |
---|
| 2594 | CFListIterator i= splitA; |
---|
| 2595 | CanonicalForm H= i.getItem(); |
---|
| 2596 | i++; |
---|
| 2597 | H *= xToM; |
---|
| 2598 | H += i.getItem(); |
---|
| 2599 | i++; |
---|
| 2600 | H *= xToM; |
---|
| 2601 | H += i.getItem(); |
---|
| 2602 | i++; |
---|
| 2603 | |
---|
| 2604 | divrem32 (H, B, Q, R, M); |
---|
| 2605 | |
---|
| 2606 | CFList splitR= split (R, m, x); |
---|
| 2607 | if (splitR.length() == 1) |
---|
| 2608 | splitR.insert (0); |
---|
| 2609 | |
---|
| 2610 | H= splitR.getFirst(); |
---|
| 2611 | H *= xToM; |
---|
| 2612 | H += splitR.getLast(); |
---|
| 2613 | H *= xToM; |
---|
| 2614 | H += i.getItem(); |
---|
| 2615 | |
---|
| 2616 | CanonicalForm bufQ; |
---|
| 2617 | divrem32 (H, B, bufQ, R, M); |
---|
| 2618 | |
---|
| 2619 | Q *= xToM; |
---|
| 2620 | Q += bufQ; |
---|
| 2621 | return; |
---|
| 2622 | } |
---|
| 2623 | |
---|
| 2624 | static inline |
---|
| 2625 | void divrem32 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
| 2626 | CanonicalForm& R, const CFList& M) |
---|
| 2627 | { |
---|
| 2628 | CanonicalForm A= mod (F, M); |
---|
| 2629 | CanonicalForm B= mod (G, M); |
---|
| 2630 | Variable x= Variable (1); |
---|
| 2631 | int degB= degree (B, x); |
---|
| 2632 | int degA= degree (A, x); |
---|
| 2633 | if (degA < degB) |
---|
| 2634 | { |
---|
| 2635 | Q= 0; |
---|
| 2636 | R= A; |
---|
| 2637 | return; |
---|
| 2638 | } |
---|
| 2639 | if (degB < 1) |
---|
| 2640 | { |
---|
| 2641 | divrem (A, B, Q, R); |
---|
| 2642 | Q= mod (Q, M); |
---|
| 2643 | R= mod (R, M); |
---|
| 2644 | return; |
---|
| 2645 | } |
---|
| 2646 | int m= (int) ceil ((double) (degB + 1)/ 2.0); |
---|
[050d1b] | 2647 | ASSERT (3*m > degA, "expected degree (F, 1) < 3*degree (G, 1)"); |
---|
[0e2e23] | 2648 | CFList splitA= split (A, m, x); |
---|
| 2649 | CFList splitB= split (B, m, x); |
---|
| 2650 | |
---|
| 2651 | if (splitA.length() == 2) |
---|
| 2652 | { |
---|
| 2653 | splitA.insert (0); |
---|
| 2654 | } |
---|
| 2655 | if (splitA.length() == 1) |
---|
| 2656 | { |
---|
| 2657 | splitA.insert (0); |
---|
| 2658 | splitA.insert (0); |
---|
| 2659 | } |
---|
| 2660 | CanonicalForm xToM= power (x, m); |
---|
| 2661 | |
---|
| 2662 | CanonicalForm H; |
---|
| 2663 | CFListIterator i= splitA; |
---|
| 2664 | i++; |
---|
| 2665 | |
---|
| 2666 | if (degree (splitA.getFirst(), x) < degree (splitB.getFirst(), x)) |
---|
| 2667 | { |
---|
| 2668 | H= splitA.getFirst()*xToM + i.getItem(); |
---|
| 2669 | divrem21 (H, splitB.getFirst(), Q, R, M); |
---|
| 2670 | } |
---|
| 2671 | else |
---|
| 2672 | { |
---|
| 2673 | R= splitA.getFirst()*xToM + i.getItem() + splitB.getFirst() - |
---|
| 2674 | splitB.getFirst()*xToM; |
---|
| 2675 | Q= xToM - 1; |
---|
| 2676 | } |
---|
| 2677 | |
---|
| 2678 | H= mulMod (Q, splitB.getLast(), M); |
---|
| 2679 | |
---|
| 2680 | R= R*xToM + splitA.getLast() - H; |
---|
| 2681 | |
---|
| 2682 | while (degree (R, x) >= degB) |
---|
| 2683 | { |
---|
| 2684 | xToM= power (x, degree (R, x) - degB); |
---|
| 2685 | Q += LC (R, x)*xToM; |
---|
| 2686 | R -= mulMod (LC (R, x), B, M)*xToM; |
---|
| 2687 | Q= mod (Q, M); |
---|
| 2688 | R= mod (R, M); |
---|
| 2689 | } |
---|
| 2690 | |
---|
| 2691 | return; |
---|
| 2692 | } |
---|
| 2693 | |
---|
| 2694 | void divrem2 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
| 2695 | CanonicalForm& R, const CanonicalForm& M) |
---|
| 2696 | { |
---|
| 2697 | CanonicalForm A= mod (F, M); |
---|
| 2698 | CanonicalForm B= mod (G, M); |
---|
| 2699 | |
---|
| 2700 | if (B.inCoeffDomain()) |
---|
| 2701 | { |
---|
| 2702 | divrem (A, B, Q, R); |
---|
| 2703 | return; |
---|
| 2704 | } |
---|
| 2705 | if (A.inCoeffDomain() && !B.inCoeffDomain()) |
---|
| 2706 | { |
---|
| 2707 | Q= 0; |
---|
| 2708 | R= A; |
---|
| 2709 | return; |
---|
| 2710 | } |
---|
| 2711 | |
---|
| 2712 | if (B.level() < A.level()) |
---|
| 2713 | { |
---|
| 2714 | divrem (A, B, Q, R); |
---|
| 2715 | return; |
---|
| 2716 | } |
---|
| 2717 | if (A.level() > B.level()) |
---|
| 2718 | { |
---|
| 2719 | R= A; |
---|
| 2720 | Q= 0; |
---|
| 2721 | return; |
---|
| 2722 | } |
---|
| 2723 | if (B.level() == 1 && B.isUnivariate()) |
---|
| 2724 | { |
---|
| 2725 | divrem (A, B, Q, R); |
---|
| 2726 | return; |
---|
| 2727 | } |
---|
[e016ba] | 2728 | if (!(B.level() == 1 && B.isUnivariate()) && |
---|
| 2729 | (A.level() == 1 && A.isUnivariate())) |
---|
[0e2e23] | 2730 | { |
---|
| 2731 | Q= 0; |
---|
| 2732 | R= A; |
---|
| 2733 | return; |
---|
| 2734 | } |
---|
| 2735 | |
---|
| 2736 | Variable x= Variable (1); |
---|
| 2737 | int degB= degree (B, x); |
---|
| 2738 | if (degB > degree (A, x)) |
---|
| 2739 | { |
---|
| 2740 | Q= 0; |
---|
| 2741 | R= A; |
---|
| 2742 | return; |
---|
| 2743 | } |
---|
| 2744 | |
---|
| 2745 | CFList splitA= split (A, degB, x); |
---|
| 2746 | |
---|
| 2747 | CanonicalForm xToDegB= power (x, degB); |
---|
| 2748 | CanonicalForm H, bufQ; |
---|
| 2749 | Q= 0; |
---|
| 2750 | CFListIterator i= splitA; |
---|
| 2751 | H= i.getItem()*xToDegB; |
---|
| 2752 | i++; |
---|
| 2753 | H += i.getItem(); |
---|
| 2754 | CFList buf; |
---|
| 2755 | while (i.hasItem()) |
---|
| 2756 | { |
---|
| 2757 | buf= CFList (M); |
---|
| 2758 | divrem21 (H, B, bufQ, R, buf); |
---|
| 2759 | i++; |
---|
| 2760 | if (i.hasItem()) |
---|
| 2761 | H= R*xToDegB + i.getItem(); |
---|
| 2762 | Q *= xToDegB; |
---|
| 2763 | Q += bufQ; |
---|
| 2764 | } |
---|
| 2765 | return; |
---|
| 2766 | } |
---|
| 2767 | |
---|
| 2768 | void divrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
| 2769 | CanonicalForm& R, const CFList& MOD) |
---|
| 2770 | { |
---|
| 2771 | CanonicalForm A= mod (F, MOD); |
---|
| 2772 | CanonicalForm B= mod (G, MOD); |
---|
| 2773 | Variable x= Variable (1); |
---|
| 2774 | int degB= degree (B, x); |
---|
| 2775 | if (degB > degree (A, x)) |
---|
| 2776 | { |
---|
| 2777 | Q= 0; |
---|
| 2778 | R= A; |
---|
| 2779 | return; |
---|
| 2780 | } |
---|
| 2781 | |
---|
| 2782 | if (degB <= 0) |
---|
| 2783 | { |
---|
| 2784 | divrem (A, B, Q, R); |
---|
| 2785 | Q= mod (Q, MOD); |
---|
| 2786 | R= mod (R, MOD); |
---|
| 2787 | return; |
---|
| 2788 | } |
---|
| 2789 | CFList splitA= split (A, degB, x); |
---|
| 2790 | |
---|
| 2791 | CanonicalForm xToDegB= power (x, degB); |
---|
| 2792 | CanonicalForm H, bufQ; |
---|
| 2793 | Q= 0; |
---|
| 2794 | CFListIterator i= splitA; |
---|
| 2795 | H= i.getItem()*xToDegB; |
---|
| 2796 | i++; |
---|
| 2797 | H += i.getItem(); |
---|
| 2798 | while (i.hasItem()) |
---|
| 2799 | { |
---|
| 2800 | divrem21 (H, B, bufQ, R, MOD); |
---|
| 2801 | i++; |
---|
| 2802 | if (i.hasItem()) |
---|
| 2803 | H= R*xToDegB + i.getItem(); |
---|
| 2804 | Q *= xToDegB; |
---|
| 2805 | Q += bufQ; |
---|
| 2806 | } |
---|
| 2807 | return; |
---|
| 2808 | } |
---|
| 2809 | |
---|
[c7c7fe4] | 2810 | bool |
---|
| 2811 | uniFdivides (const CanonicalForm& A, const CanonicalForm& B) |
---|
| 2812 | { |
---|
[ad0177] | 2813 | if (B.isZero()) |
---|
| 2814 | return true; |
---|
| 2815 | if (A.isZero()) |
---|
| 2816 | return false; |
---|
| 2817 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
| 2818 | return fdivides (A, B); |
---|
[c7c7fe4] | 2819 | int p= getCharacteristic(); |
---|
[188d2fb] | 2820 | if (A.inCoeffDomain() || B.inCoeffDomain()) |
---|
| 2821 | { |
---|
| 2822 | if (A.inCoeffDomain()) |
---|
| 2823 | return true; |
---|
| 2824 | else |
---|
| 2825 | return false; |
---|
| 2826 | } |
---|
[c7c7fe4] | 2827 | if (p > 0) |
---|
| 2828 | { |
---|
| 2829 | zz_p::init (p); |
---|
| 2830 | Variable alpha; |
---|
| 2831 | if (hasFirstAlgVar (A, alpha) || hasFirstAlgVar (B, alpha)) |
---|
| 2832 | { |
---|
| 2833 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 2834 | zz_pE::init (NTLMipo); |
---|
| 2835 | zz_pEX NTLA= convertFacCF2NTLzz_pEX (A, NTLMipo); |
---|
| 2836 | zz_pEX NTLB= convertFacCF2NTLzz_pEX (B, NTLMipo); |
---|
| 2837 | return divide (NTLB, NTLA); |
---|
| 2838 | } |
---|
| 2839 | #ifdef HAVE_FLINT |
---|
| 2840 | nmod_poly_t FLINTA, FLINTB; |
---|
| 2841 | convertFacCF2nmod_poly_t (FLINTA, A); |
---|
| 2842 | convertFacCF2nmod_poly_t (FLINTB, B); |
---|
[c2a8b6] | 2843 | nmod_poly_divrem (FLINTB, FLINTA, FLINTB, FLINTA); |
---|
[c7c7fe4] | 2844 | bool result= nmod_poly_is_zero (FLINTA); |
---|
| 2845 | nmod_poly_clear (FLINTA); |
---|
| 2846 | nmod_poly_clear (FLINTB); |
---|
| 2847 | return result; |
---|
| 2848 | #else |
---|
| 2849 | zz_pX NTLA= convertFacCF2NTLzzpX (A); |
---|
| 2850 | zz_pX NTLB= convertFacCF2NTLzzpX (B); |
---|
| 2851 | return divide (NTLB, NTLA); |
---|
| 2852 | #endif |
---|
| 2853 | } |
---|
| 2854 | #ifdef HAVE_FLINT |
---|
[e451f48] | 2855 | Variable alpha; |
---|
[ca058c] | 2856 | bool isRat= isOn (SW_RATIONAL); |
---|
| 2857 | if (!isRat) |
---|
| 2858 | On (SW_RATIONAL); |
---|
[e451f48] | 2859 | if (!hasFirstAlgVar (A, alpha) && !hasFirstAlgVar (B, alpha)) |
---|
| 2860 | { |
---|
| 2861 | fmpq_poly_t FLINTA,FLINTB; |
---|
| 2862 | convertFacCF2Fmpq_poly_t (FLINTA, A); |
---|
| 2863 | convertFacCF2Fmpq_poly_t (FLINTB, B); |
---|
| 2864 | fmpq_poly_rem (FLINTA, FLINTB, FLINTA); |
---|
| 2865 | bool result= fmpq_poly_is_zero (FLINTA); |
---|
| 2866 | fmpq_poly_clear (FLINTA); |
---|
| 2867 | fmpq_poly_clear (FLINTB); |
---|
[ca058c] | 2868 | if (!isRat) |
---|
| 2869 | Off (SW_RATIONAL); |
---|
[e451f48] | 2870 | return result; |
---|
| 2871 | } |
---|
[54af8a5] | 2872 | CanonicalForm Q, R; |
---|
| 2873 | Variable x= Variable (1); |
---|
| 2874 | Variable y= Variable (2); |
---|
| 2875 | newtonDivrem (swapvar (B, y, x), swapvar (A, y, x), Q, R); |
---|
| 2876 | if (!isRat) |
---|
| 2877 | Off (SW_RATIONAL); |
---|
| 2878 | return R.isZero(); |
---|
[c7c7fe4] | 2879 | #else |
---|
[ad0177] | 2880 | bool isRat= isOn (SW_RATIONAL); |
---|
| 2881 | if (!isRat) |
---|
| 2882 | On (SW_RATIONAL); |
---|
| 2883 | bool result= fdivides (A, B); |
---|
| 2884 | if (!isRat) |
---|
| 2885 | Off (SW_RATIONAL); |
---|
| 2886 | return result; //maybe NTL? |
---|
[c7c7fe4] | 2887 | #endif |
---|
| 2888 | } |
---|
| 2889 | |
---|
[81d96c] | 2890 | // end division |
---|
| 2891 | |
---|
[0e2e23] | 2892 | #endif |
---|