[ad3c3ff] | 1 | /*****************************************************************************\ |
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[806c18] | 2 | * Computer Algebra System SINGULAR |
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[ad3c3ff] | 3 | \*****************************************************************************/ |
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| 4 | /** @file facHensel.cc |
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[806c18] | 5 | * |
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| 6 | * This file implements functions to lift factors via Hensel lifting and |
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[ad3c3ff] | 7 | * functions for modular multiplication and division with remainder. |
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[806c18] | 8 | * |
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| 9 | * ABSTRACT: Hensel lifting is described in "Efficient Multivariate |
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| 10 | * Factorization over Finite Fields" by L. Bernardin & M. Monagon. Division with |
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| 11 | * remainder is described in "Fast Recursive Division" by C. Burnikel and |
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| 12 | * J. Ziegler. Karatsuba multiplication is described in "Modern Computer |
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| 13 | * Algebra" by J. von zur Gathen and J. Gerhard. |
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[ad3c3ff] | 14 | * |
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| 15 | * @author Martin Lee |
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| 16 | * |
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| 17 | * @internal @version \$Id$ |
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| 18 | * |
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| 19 | **/ |
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| 20 | /*****************************************************************************/ |
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| 21 | |
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[e4fe2b] | 22 | #include "config.h" |
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| 23 | |
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[650f2d8] | 24 | #include "cf_assert.h" |
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[ad3c3ff] | 25 | #include "debug.h" |
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| 26 | #include "timing.h" |
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| 27 | |
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| 28 | #include "facHensel.h" |
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| 29 | #include "cf_util.h" |
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[08daea] | 30 | #include "fac_util.h" |
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| 31 | #include "cf_algorithm.h" |
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[4a05ed] | 32 | #include "cf_primes.h" |
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[ad3c3ff] | 33 | |
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| 34 | #ifdef HAVE_NTL |
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| 35 | #include <NTL/lzz_pEX.h> |
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| 36 | #include "NTLconvert.h" |
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| 37 | |
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[4a05ed] | 38 | static |
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| 39 | CFList productsNTL (const CFList& factors, const CanonicalForm& M) |
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| 40 | { |
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| 41 | zz_p::init (getCharacteristic()); |
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| 42 | zz_pX NTLMipo= convertFacCF2NTLzzpX (M); |
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| 43 | zz_pE::init (NTLMipo); |
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| 44 | zz_pEX prod; |
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| 45 | vec_zz_pEX v; |
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| 46 | v.SetLength (factors.length()); |
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| 47 | int j= 0; |
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| 48 | for (CFListIterator i= factors; i.hasItem(); i++, j++) |
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| 49 | { |
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| 50 | if (i.getItem().inCoeffDomain()) |
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| 51 | v[j]= to_zz_pEX (to_zz_pE (convertFacCF2NTLzzpX (i.getItem()))); |
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| 52 | else |
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| 53 | v[j]= convertFacCF2NTLzz_pEX (i.getItem(), NTLMipo); |
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| 54 | } |
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| 55 | CFList result; |
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| 56 | Variable x= Variable (1); |
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| 57 | for (int j= 0; j < factors.length(); j++) |
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| 58 | { |
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| 59 | int k= 0; |
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| 60 | set(prod); |
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| 61 | for (int i= 0; i < factors.length(); i++, k++) |
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| 62 | { |
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| 63 | if (k == j) |
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| 64 | continue; |
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| 65 | prod *= v[i]; |
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| 66 | } |
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| 67 | result.append (convertNTLzz_pEX2CF (prod, x, M.mvar())); |
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| 68 | } |
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| 69 | return result; |
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| 70 | } |
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| 71 | |
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| 72 | static |
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| 73 | void tryDiophantine (CFList& result, const CanonicalForm& F, |
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| 74 | const CFList& factors, const CanonicalForm& M, bool& fail) |
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| 75 | { |
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| 76 | ASSERT (M.isUnivariate(), "expected univariate poly"); |
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| 77 | |
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| 78 | CFList bufFactors= factors; |
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| 79 | bufFactors.removeFirst(); |
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| 80 | bufFactors.insert (factors.getFirst () (0,2)); |
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| 81 | CanonicalForm inv, leadingCoeff= Lc (F); |
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| 82 | CFListIterator i= bufFactors; |
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| 83 | if (bufFactors.getFirst().inCoeffDomain()) |
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| 84 | { |
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| 85 | if (i.hasItem()) |
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| 86 | i++; |
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| 87 | } |
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| 88 | for (; i.hasItem(); i++) |
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| 89 | { |
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| 90 | tryInvert (Lc (i.getItem()), M, inv ,fail); |
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| 91 | if (fail) |
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| 92 | return; |
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| 93 | i.getItem()= reduce (i.getItem()*inv, M); |
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| 94 | } |
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| 95 | bufFactors= productsNTL (bufFactors, M); |
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| 96 | |
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| 97 | CanonicalForm buf1, buf2, buf3, S, T; |
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| 98 | i= bufFactors; |
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| 99 | if (i.hasItem()) |
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| 100 | i++; |
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| 101 | buf1= bufFactors.getFirst(); |
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| 102 | buf2= i.getItem(); |
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| 103 | tryExtgcd (buf1, buf2, M, buf3, S, T, fail); |
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| 104 | if (fail) |
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| 105 | return; |
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| 106 | result.append (S); |
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| 107 | result.append (T); |
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| 108 | if (i.hasItem()) |
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| 109 | i++; |
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| 110 | for (; i.hasItem(); i++) |
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| 111 | { |
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| 112 | buf1= i.getItem(); |
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| 113 | tryExtgcd (buf3, buf1, M, buf3, S, T, fail); |
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| 114 | if (fail) |
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| 115 | return; |
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| 116 | CFListIterator k= factors; |
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| 117 | for (CFListIterator j= result; j.hasItem(); j++, k++) |
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| 118 | { |
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| 119 | j.getItem() *= S; |
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| 120 | j.getItem()= mod (j.getItem(), k.getItem()); |
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| 121 | j.getItem()= reduce (j.getItem(), M); |
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| 122 | } |
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| 123 | result.append (T); |
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| 124 | } |
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| 125 | } |
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| 126 | |
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| 127 | static inline |
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| 128 | CFList mapinto (const CFList& L) |
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| 129 | { |
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| 130 | CFList result; |
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| 131 | for (CFListIterator i= L; i.hasItem(); i++) |
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| 132 | result.append (mapinto (i.getItem())); |
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| 133 | return result; |
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| 134 | } |
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| 135 | |
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| 136 | static inline |
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| 137 | int mod (const CFList& L, const CanonicalForm& p) |
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| 138 | { |
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| 139 | for (CFListIterator i= L; i.hasItem(); i++) |
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| 140 | { |
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| 141 | if (mod (i.getItem(), p) == 0) |
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| 142 | return 0; |
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| 143 | } |
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| 144 | return 1; |
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| 145 | } |
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| 146 | |
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| 147 | |
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| 148 | static inline void |
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| 149 | chineseRemainder (const CFList & x1, const CanonicalForm & q1, |
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| 150 | const CFList & x2, const CanonicalForm & q2, |
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| 151 | CFList & xnew, CanonicalForm & qnew) |
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| 152 | { |
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| 153 | ASSERT (x1.length() == x2.length(), "expected lists of equal length"); |
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| 154 | CanonicalForm tmp1, tmp2; |
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| 155 | CFListIterator j= x2; |
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| 156 | for (CFListIterator i= x1; i.hasItem() && j.hasItem(); i++, j++) |
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| 157 | { |
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| 158 | chineseRemainder (i.getItem(), q1, j.getItem(), q2, tmp1, tmp2); |
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| 159 | xnew.append (tmp1); |
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| 160 | } |
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| 161 | qnew= tmp2; |
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| 162 | } |
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| 163 | |
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| 164 | static inline |
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| 165 | CFList Farey (const CFList& L, const CanonicalForm& q) |
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| 166 | { |
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| 167 | CFList result; |
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| 168 | for (CFListIterator i= L; i.hasItem(); i++) |
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| 169 | result.append (Farey (i.getItem(), q)); |
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| 170 | return result; |
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| 171 | } |
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| 172 | |
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| 173 | static inline |
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| 174 | CFList replacevar (const CFList& L, const Variable& a, const Variable& b) |
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| 175 | { |
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| 176 | CFList result; |
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| 177 | for (CFListIterator i= L; i.hasItem(); i++) |
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| 178 | result.append (replacevar (i.getItem(), a, b)); |
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| 179 | return result; |
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| 180 | } |
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| 181 | |
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| 182 | CFList |
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| 183 | modularDiophant (const CanonicalForm& f, const CFList& factors, |
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| 184 | const CanonicalForm& M) |
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| 185 | { |
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| 186 | bool save_rat=!isOn (SW_RATIONAL); |
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| 187 | On (SW_RATIONAL); |
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| 188 | CanonicalForm F= f*bCommonDen (f); |
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| 189 | CFList products= factors; |
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| 190 | for (CFListIterator i= products; i.hasItem(); i++) |
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[9b2c8a] | 191 | { |
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| 192 | if (products.getFirst().level() == 1) |
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| 193 | i.getItem() /= Lc (i.getItem()); |
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[4a05ed] | 194 | i.getItem() *= bCommonDen (i.getItem()); |
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[9b2c8a] | 195 | } |
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[4a05ed] | 196 | if (products.getFirst().level() == 1) |
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| 197 | products.insert (Lc (F)); |
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| 198 | CanonicalForm bound= maxNorm (F); |
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| 199 | CFList leadingCoeffs; |
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| 200 | leadingCoeffs.append (lc (F)); |
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| 201 | CanonicalForm dummy; |
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| 202 | for (CFListIterator i= products; i.hasItem(); i++) |
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| 203 | { |
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| 204 | leadingCoeffs.append (lc (i.getItem())); |
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| 205 | dummy= maxNorm (i.getItem()); |
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| 206 | bound= (dummy > bound) ? dummy : bound; |
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| 207 | } |
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| 208 | bound *= maxNorm (Lc (F))*maxNorm (Lc(F))*bound; |
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| 209 | bound *= bound*bound; |
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| 210 | bound= power (bound, degree (M)); |
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| 211 | bound *= power (CanonicalForm (2),degree (f)); |
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| 212 | CanonicalForm bufBound= bound; |
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| 213 | int i = cf_getNumBigPrimes() - 1; |
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| 214 | int p; |
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| 215 | CFList resultModP, result, newResult; |
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| 216 | CanonicalForm q (0), newQ; |
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| 217 | bool fail= false; |
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| 218 | Variable a= M.mvar(); |
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| 219 | Variable b= Variable (2); |
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| 220 | setReduce (M.mvar(), false); |
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| 221 | CanonicalForm mipo= bCommonDen (M)*M; |
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| 222 | Off (SW_RATIONAL); |
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| 223 | CanonicalForm modMipo; |
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| 224 | leadingCoeffs.append (lc (mipo)); |
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| 225 | CFList tmp1, tmp2; |
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| 226 | bool equal= false; |
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| 227 | int count= 0; |
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| 228 | do |
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| 229 | { |
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| 230 | p = cf_getBigPrime( i ); |
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| 231 | i--; |
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| 232 | while ( i >= 0 && mod( leadingCoeffs, p ) == 0) |
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| 233 | { |
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| 234 | p = cf_getBigPrime( i ); |
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| 235 | i--; |
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| 236 | } |
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| 237 | |
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| 238 | ASSERT (i >= 0, "ran out of primes"); //sic |
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| 239 | |
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| 240 | setCharacteristic (p); |
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| 241 | modMipo= mapinto (mipo); |
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| 242 | modMipo /= lc (modMipo); |
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| 243 | resultModP= CFList(); |
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| 244 | tryDiophantine (resultModP, mapinto (F), mapinto (products), modMipo, fail); |
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| 245 | setCharacteristic (0); |
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| 246 | if (fail) |
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| 247 | { |
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| 248 | fail= false; |
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| 249 | continue; |
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| 250 | } |
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| 251 | |
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| 252 | if ( q.isZero() ) |
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| 253 | { |
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| 254 | result= replacevar (mapinto(resultModP), a, b); |
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| 255 | q= p; |
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| 256 | } |
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| 257 | else |
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| 258 | { |
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| 259 | result= replacevar (result, a, b); |
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| 260 | newResult= CFList(); |
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| 261 | chineseRemainder( result, q, replacevar (mapinto (resultModP), a, b), |
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| 262 | p, newResult, newQ ); |
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| 263 | q= newQ; |
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| 264 | result= newResult; |
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| 265 | if (newQ > bound) |
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| 266 | { |
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| 267 | count++; |
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| 268 | tmp1= replacevar (Farey (result, q), b, a); |
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| 269 | if (tmp2.isEmpty()) |
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| 270 | tmp2= tmp1; |
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| 271 | else |
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| 272 | { |
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| 273 | equal= true; |
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| 274 | CFListIterator k= tmp1; |
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| 275 | for (CFListIterator j= tmp2; j.hasItem(); j++, k++) |
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| 276 | { |
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| 277 | if (j.getItem() != k.getItem()) |
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| 278 | equal= false; |
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| 279 | } |
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| 280 | if (!equal) |
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| 281 | tmp2= tmp1; |
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| 282 | } |
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| 283 | if (count > 2) |
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| 284 | { |
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| 285 | bound *= bufBound; |
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| 286 | equal= false; |
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| 287 | count= 0; |
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| 288 | } |
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| 289 | } |
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| 290 | if (newQ > bound && equal) |
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| 291 | { |
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| 292 | On( SW_RATIONAL ); |
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| 293 | CFList bufResult= result; |
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[9b2c8a] | 294 | result= tmp2; |
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[4a05ed] | 295 | setReduce (M.mvar(), true); |
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| 296 | if (factors.getFirst().level() == 1) |
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| 297 | { |
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| 298 | result.removeFirst(); |
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| 299 | CFListIterator j= factors; |
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| 300 | CanonicalForm denf= bCommonDen (f); |
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| 301 | for (CFListIterator i= result; i.hasItem(); i++, j++) |
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| 302 | i.getItem() *= Lc (j.getItem())*denf; |
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| 303 | } |
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| 304 | if (factors.getFirst().level() != 1 && |
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| 305 | !bCommonDen (factors.getFirst()).isOne()) |
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| 306 | { |
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| 307 | CanonicalForm denFirst= bCommonDen (factors.getFirst()); |
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| 308 | for (CFListIterator i= result; i.hasItem(); i++) |
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| 309 | i.getItem() *= denFirst; |
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| 310 | } |
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| 311 | |
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| 312 | CanonicalForm test= 0; |
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| 313 | CFListIterator jj= factors; |
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| 314 | for (CFListIterator ii= result; ii.hasItem(); ii++, jj++) |
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| 315 | test += ii.getItem()*(f/jj.getItem()); |
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| 316 | if (!test.isOne()) |
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| 317 | { |
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| 318 | bound *= bufBound; |
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| 319 | equal= false; |
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| 320 | count= 0; |
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| 321 | setReduce (M.mvar(), false); |
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| 322 | result= bufResult; |
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| 323 | Off (SW_RATIONAL); |
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| 324 | } |
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| 325 | else |
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| 326 | break; |
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| 327 | } |
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| 328 | } |
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| 329 | } while (1); |
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| 330 | if (save_rat) Off(SW_RATIONAL); |
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| 331 | return result; |
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| 332 | } |
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| 333 | |
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[ad3c3ff] | 334 | CanonicalForm |
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| 335 | mulNTL (const CanonicalForm& F, const CanonicalForm& G) |
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| 336 | { |
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[64e7cb] | 337 | if (F.inCoeffDomain() || G.inCoeffDomain() || getCharacteristic() == 0) |
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[ad3c3ff] | 338 | return F*G; |
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| 339 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
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| 340 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
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| 341 | if (CFFactory::gettype() == GaloisFieldDomain) |
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| 342 | return F*G; |
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| 343 | zz_p::init (getCharacteristic()); |
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| 344 | Variable alpha; |
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| 345 | CanonicalForm result; |
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| 346 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
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| 347 | { |
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| 348 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
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| 349 | zz_pE::init (NTLMipo); |
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| 350 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
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| 351 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
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| 352 | mul (NTLF, NTLF, NTLG); |
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| 353 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
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| 354 | } |
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| 355 | else |
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| 356 | { |
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| 357 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
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| 358 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
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| 359 | mul (NTLF, NTLF, NTLG); |
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| 360 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
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| 361 | } |
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| 362 | return result; |
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| 363 | } |
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| 364 | |
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| 365 | CanonicalForm |
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| 366 | modNTL (const CanonicalForm& F, const CanonicalForm& G) |
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| 367 | { |
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| 368 | if (F.inCoeffDomain() && G.isUnivariate()) |
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| 369 | return F; |
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| 370 | else if (F.inCoeffDomain() && G.inCoeffDomain()) |
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| 371 | return mod (F, G); |
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| 372 | else if (F.isUnivariate() && G.inCoeffDomain()) |
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| 373 | return mod (F,G); |
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[806c18] | 374 | |
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[64e7cb] | 375 | if (getCharacteristic() == 0) |
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| 376 | return mod (F, G); |
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| 377 | |
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[ad3c3ff] | 378 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
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| 379 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
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| 380 | if (CFFactory::gettype() == GaloisFieldDomain) |
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| 381 | return mod (F, G); |
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| 382 | zz_p::init (getCharacteristic()); |
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| 383 | Variable alpha; |
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| 384 | CanonicalForm result; |
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| 385 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
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| 386 | { |
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| 387 | zz_pX NTLMipo= convertFacCF2NTLzzpX(getMipo (alpha)); |
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| 388 | zz_pE::init (NTLMipo); |
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| 389 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
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| 390 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
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| 391 | rem (NTLF, NTLF, NTLG); |
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| 392 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
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| 393 | } |
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| 394 | else |
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| 395 | { |
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| 396 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
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| 397 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
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| 398 | rem (NTLF, NTLF, NTLG); |
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| 399 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
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| 400 | } |
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| 401 | return result; |
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| 402 | } |
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| 403 | |
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| 404 | CanonicalForm |
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| 405 | divNTL (const CanonicalForm& F, const CanonicalForm& G) |
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| 406 | { |
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| 407 | if (F.inCoeffDomain() && G.isUnivariate()) |
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| 408 | return F; |
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| 409 | else if (F.inCoeffDomain() && G.inCoeffDomain()) |
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| 410 | return div (F, G); |
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| 411 | else if (F.isUnivariate() && G.inCoeffDomain()) |
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| 412 | return div (F,G); |
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| 413 | |
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[64e7cb] | 414 | if (getCharacteristic() == 0) |
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| 415 | return div (F, G); |
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| 416 | |
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[ad3c3ff] | 417 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
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| 418 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
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| 419 | if (CFFactory::gettype() == GaloisFieldDomain) |
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| 420 | return div (F, G); |
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| 421 | zz_p::init (getCharacteristic()); |
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| 422 | Variable alpha; |
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| 423 | CanonicalForm result; |
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| 424 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
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| 425 | { |
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| 426 | zz_pX NTLMipo= convertFacCF2NTLzzpX(getMipo (alpha)); |
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| 427 | zz_pE::init (NTLMipo); |
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| 428 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
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| 429 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
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| 430 | div (NTLF, NTLF, NTLG); |
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| 431 | result= convertNTLzz_pEX2CF(NTLF, F.mvar(), alpha); |
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| 432 | } |
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| 433 | else |
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| 434 | { |
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| 435 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
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| 436 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
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| 437 | div (NTLF, NTLF, NTLG); |
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| 438 | result= convertNTLzzpX2CF(NTLF, F.mvar()); |
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| 439 | } |
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| 440 | return result; |
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| 441 | } |
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| 442 | |
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[11bf82] | 443 | /* |
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[ad3c3ff] | 444 | void |
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[806c18] | 445 | divremNTL (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
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[ad3c3ff] | 446 | CanonicalForm& R) |
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| 447 | { |
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| 448 | if (F.inCoeffDomain() && G.isUnivariate()) |
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| 449 | { |
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| 450 | R= F; |
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| 451 | Q= 0; |
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| 452 | } |
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| 453 | else if (F.inCoeffDomain() && G.inCoeffDomain()) |
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| 454 | { |
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| 455 | divrem (F, G, Q, R); |
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| 456 | return; |
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| 457 | } |
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| 458 | else if (F.isUnivariate() && G.inCoeffDomain()) |
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| 459 | { |
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| 460 | divrem (F, G, Q, R); |
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| 461 | return; |
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| 462 | } |
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| 463 | |
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| 464 | ASSERT (F.isUnivariate() && G.isUnivariate(), "expected univariate polys"); |
---|
| 465 | ASSERT (F.level() == G.level(), "expected polys of same level"); |
---|
| 466 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
| 467 | { |
---|
| 468 | divrem (F, G, Q, R); |
---|
| 469 | return; |
---|
| 470 | } |
---|
| 471 | zz_p::init (getCharacteristic()); |
---|
| 472 | Variable alpha; |
---|
| 473 | CanonicalForm result; |
---|
| 474 | if (hasFirstAlgVar (F, alpha) || hasFirstAlgVar (G, alpha)) |
---|
| 475 | { |
---|
| 476 | zz_pX NTLMipo= convertFacCF2NTLzzpX(getMipo (alpha)); |
---|
| 477 | zz_pE::init (NTLMipo); |
---|
| 478 | zz_pEX NTLF= convertFacCF2NTLzz_pEX (F, NTLMipo); |
---|
| 479 | zz_pEX NTLG= convertFacCF2NTLzz_pEX (G, NTLMipo); |
---|
[806c18] | 480 | zz_pEX NTLQ; |
---|
[ad3c3ff] | 481 | zz_pEX NTLR; |
---|
| 482 | DivRem (NTLQ, NTLR, NTLF, NTLG); |
---|
| 483 | Q= convertNTLzz_pEX2CF(NTLQ, F.mvar(), alpha); |
---|
| 484 | R= convertNTLzz_pEX2CF(NTLR, F.mvar(), alpha); |
---|
| 485 | return; |
---|
| 486 | } |
---|
| 487 | else |
---|
| 488 | { |
---|
| 489 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
| 490 | zz_pX NTLG= convertFacCF2NTLzzpX (G); |
---|
[806c18] | 491 | zz_pX NTLQ; |
---|
[ad3c3ff] | 492 | zz_pX NTLR; |
---|
| 493 | DivRem (NTLQ, NTLR, NTLF, NTLG); |
---|
| 494 | Q= convertNTLzzpX2CF(NTLQ, F.mvar()); |
---|
| 495 | R= convertNTLzzpX2CF(NTLR, F.mvar()); |
---|
| 496 | return; |
---|
| 497 | } |
---|
| 498 | }*/ |
---|
| 499 | |
---|
[806c18] | 500 | CanonicalForm mod (const CanonicalForm& F, const CFList& M) |
---|
[ad3c3ff] | 501 | { |
---|
| 502 | CanonicalForm A= F; |
---|
[806c18] | 503 | for (CFListIterator i= M; i.hasItem(); i++) |
---|
[ad3c3ff] | 504 | A= mod (A, i.getItem()); |
---|
| 505 | return A; |
---|
| 506 | } |
---|
| 507 | |
---|
[dd2a9b3] | 508 | zz_pX kronSubFp (const CanonicalForm& A, int d) |
---|
| 509 | { |
---|
| 510 | int degAy= degree (A); |
---|
| 511 | zz_pX result; |
---|
| 512 | result.rep.SetLength (d*(degAy + 1)); |
---|
| 513 | |
---|
| 514 | zz_p *resultp; |
---|
| 515 | resultp= result.rep.elts(); |
---|
| 516 | zz_pX buf; |
---|
| 517 | zz_p *bufp; |
---|
| 518 | |
---|
| 519 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 520 | { |
---|
| 521 | if (i.coeff().inCoeffDomain()) |
---|
| 522 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
| 523 | else |
---|
| 524 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
| 525 | |
---|
| 526 | int k= i.exp()*d; |
---|
| 527 | bufp= buf.rep.elts(); |
---|
| 528 | int bufRepLength= (int) buf.rep.length(); |
---|
| 529 | for (int j= 0; j < bufRepLength; j++) |
---|
| 530 | resultp [j + k]= bufp [j]; |
---|
| 531 | } |
---|
| 532 | result.normalize(); |
---|
| 533 | |
---|
| 534 | return result; |
---|
| 535 | } |
---|
| 536 | |
---|
| 537 | zz_pEX kronSub (const CanonicalForm& A, int d, const Variable& alpha) |
---|
| 538 | { |
---|
| 539 | int degAy= degree (A); |
---|
| 540 | zz_pEX result; |
---|
| 541 | result.rep.SetLength (d*(degAy + 1)); |
---|
| 542 | |
---|
| 543 | Variable v; |
---|
| 544 | zz_pE *resultp; |
---|
| 545 | resultp= result.rep.elts(); |
---|
| 546 | zz_pEX buf1; |
---|
| 547 | zz_pE *buf1p; |
---|
| 548 | zz_pX buf2; |
---|
| 549 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 550 | |
---|
| 551 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 552 | { |
---|
| 553 | if (i.coeff().inCoeffDomain()) |
---|
| 554 | { |
---|
| 555 | buf2= convertFacCF2NTLzzpX (i.coeff()); |
---|
| 556 | buf1= to_zz_pEX (to_zz_pE (buf2)); |
---|
| 557 | } |
---|
| 558 | else |
---|
| 559 | buf1= convertFacCF2NTLzz_pEX (i.coeff(), NTLMipo); |
---|
| 560 | |
---|
| 561 | int k= i.exp()*d; |
---|
| 562 | buf1p= buf1.rep.elts(); |
---|
| 563 | int buf1RepLength= (int) buf1.rep.length(); |
---|
| 564 | for (int j= 0; j < buf1RepLength; j++) |
---|
| 565 | resultp [j + k]= buf1p [j]; |
---|
| 566 | } |
---|
| 567 | result.normalize(); |
---|
| 568 | |
---|
| 569 | return result; |
---|
| 570 | } |
---|
| 571 | |
---|
| 572 | void |
---|
| 573 | kronSubRecipro (zz_pEX& subA1, zz_pEX& subA2,const CanonicalForm& A, int d, |
---|
| 574 | const Variable& alpha) |
---|
| 575 | { |
---|
| 576 | int degAy= degree (A); |
---|
[96f9fdf] | 577 | subA1.rep.SetLength ((long) d*(degAy + 2)); |
---|
| 578 | subA2.rep.SetLength ((long) d*(degAy + 2)); |
---|
[dd2a9b3] | 579 | |
---|
| 580 | Variable v; |
---|
| 581 | zz_pE *subA1p; |
---|
| 582 | zz_pE *subA2p; |
---|
| 583 | subA1p= subA1.rep.elts(); |
---|
| 584 | subA2p= subA2.rep.elts(); |
---|
| 585 | zz_pEX buf; |
---|
| 586 | zz_pE *bufp; |
---|
| 587 | zz_pX buf2; |
---|
| 588 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 589 | |
---|
| 590 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 591 | { |
---|
| 592 | if (i.coeff().inCoeffDomain()) |
---|
| 593 | { |
---|
| 594 | buf2= convertFacCF2NTLzzpX (i.coeff()); |
---|
| 595 | buf= to_zz_pEX (to_zz_pE (buf2)); |
---|
| 596 | } |
---|
| 597 | else |
---|
| 598 | buf= convertFacCF2NTLzz_pEX (i.coeff(), NTLMipo); |
---|
| 599 | |
---|
| 600 | int k= i.exp()*d; |
---|
| 601 | int kk= (degAy - i.exp())*d; |
---|
| 602 | bufp= buf.rep.elts(); |
---|
| 603 | int bufRepLength= (int) buf.rep.length(); |
---|
| 604 | for (int j= 0; j < bufRepLength; j++) |
---|
| 605 | { |
---|
[96f9fdf] | 606 | subA1p [j + k] += bufp [j]; |
---|
| 607 | subA2p [j + kk] += bufp [j]; |
---|
[dd2a9b3] | 608 | } |
---|
| 609 | } |
---|
| 610 | subA1.normalize(); |
---|
| 611 | subA2.normalize(); |
---|
| 612 | } |
---|
| 613 | |
---|
| 614 | void |
---|
| 615 | kronSubRecipro (zz_pX& subA1, zz_pX& subA2,const CanonicalForm& A, int d) |
---|
| 616 | { |
---|
| 617 | int degAy= degree (A); |
---|
[96f9fdf] | 618 | subA1.rep.SetLength ((long) d*(degAy + 2)); |
---|
| 619 | subA2.rep.SetLength ((long) d*(degAy + 2)); |
---|
[dd2a9b3] | 620 | |
---|
| 621 | zz_p *subA1p; |
---|
| 622 | zz_p *subA2p; |
---|
| 623 | subA1p= subA1.rep.elts(); |
---|
| 624 | subA2p= subA2.rep.elts(); |
---|
| 625 | zz_pX buf; |
---|
| 626 | zz_p *bufp; |
---|
| 627 | |
---|
| 628 | for (CFIterator i= A; i.hasTerms(); i++) |
---|
| 629 | { |
---|
| 630 | buf= convertFacCF2NTLzzpX (i.coeff()); |
---|
| 631 | |
---|
| 632 | int k= i.exp()*d; |
---|
| 633 | int kk= (degAy - i.exp())*d; |
---|
| 634 | bufp= buf.rep.elts(); |
---|
| 635 | int bufRepLength= (int) buf.rep.length(); |
---|
| 636 | for (int j= 0; j < bufRepLength; j++) |
---|
| 637 | { |
---|
[96f9fdf] | 638 | subA1p [j + k] += bufp [j]; |
---|
| 639 | subA2p [j + kk] += bufp [j]; |
---|
[dd2a9b3] | 640 | } |
---|
| 641 | } |
---|
| 642 | subA1.normalize(); |
---|
| 643 | subA2.normalize(); |
---|
| 644 | } |
---|
| 645 | |
---|
| 646 | CanonicalForm |
---|
| 647 | reverseSubst (const zz_pEX& F, const zz_pEX& G, int d, int k, |
---|
| 648 | const Variable& alpha) |
---|
| 649 | { |
---|
| 650 | Variable y= Variable (2); |
---|
| 651 | Variable x= Variable (1); |
---|
| 652 | |
---|
| 653 | zz_pEX f= F; |
---|
| 654 | zz_pEX g= G; |
---|
| 655 | int degf= deg(f); |
---|
| 656 | int degg= deg(g); |
---|
| 657 | |
---|
| 658 | zz_pEX buf1; |
---|
| 659 | zz_pEX buf2; |
---|
| 660 | zz_pEX buf3; |
---|
| 661 | |
---|
| 662 | zz_pE *buf1p; |
---|
| 663 | zz_pE *buf2p; |
---|
| 664 | zz_pE *buf3p; |
---|
| 665 | if (f.rep.length() < (long) d*(k+1)) //zero padding |
---|
| 666 | f.rep.SetLength ((long)d*(k+1)); |
---|
| 667 | |
---|
| 668 | zz_pE *gp= g.rep.elts(); |
---|
| 669 | zz_pE *fp= f.rep.elts(); |
---|
| 670 | CanonicalForm result= 0; |
---|
| 671 | int i= 0; |
---|
| 672 | int lf= 0; |
---|
| 673 | int lg= d*k; |
---|
| 674 | int degfSubLf= degf; |
---|
| 675 | int deggSubLg= degg-lg; |
---|
| 676 | int repLengthBuf2; |
---|
| 677 | int repLengthBuf1; |
---|
| 678 | zz_pE zzpEZero= zz_pE(); |
---|
| 679 | |
---|
| 680 | while (degf >= lf || lg >= 0) |
---|
| 681 | { |
---|
| 682 | if (degfSubLf >= d) |
---|
| 683 | repLengthBuf1= d; |
---|
| 684 | else if (degfSubLf < 0) |
---|
| 685 | repLengthBuf1= 0; |
---|
| 686 | else |
---|
| 687 | repLengthBuf1= degfSubLf + 1; |
---|
| 688 | buf1.rep.SetLength((long) repLengthBuf1); |
---|
| 689 | |
---|
| 690 | buf1p= buf1.rep.elts(); |
---|
| 691 | for (int ind= 0; ind < repLengthBuf1; ind++) |
---|
| 692 | buf1p [ind]= fp [ind + lf]; |
---|
| 693 | buf1.normalize(); |
---|
| 694 | |
---|
| 695 | repLengthBuf1= buf1.rep.length(); |
---|
| 696 | |
---|
| 697 | if (deggSubLg >= d - 1) |
---|
| 698 | repLengthBuf2= d - 1; |
---|
| 699 | else if (deggSubLg < 0) |
---|
| 700 | repLengthBuf2= 0; |
---|
| 701 | else |
---|
| 702 | repLengthBuf2= deggSubLg + 1; |
---|
| 703 | |
---|
| 704 | buf2.rep.SetLength ((long) repLengthBuf2); |
---|
| 705 | buf2p= buf2.rep.elts(); |
---|
| 706 | for (int ind= 0; ind < repLengthBuf2; ind++) |
---|
| 707 | { |
---|
| 708 | buf2p [ind]= gp [ind + lg]; |
---|
| 709 | } |
---|
| 710 | buf2.normalize(); |
---|
| 711 | |
---|
| 712 | repLengthBuf2= buf2.rep.length(); |
---|
| 713 | |
---|
| 714 | buf3.rep.SetLength((long) repLengthBuf2 + d); |
---|
| 715 | buf3p= buf3.rep.elts(); |
---|
| 716 | buf2p= buf2.rep.elts(); |
---|
| 717 | buf1p= buf1.rep.elts(); |
---|
| 718 | for (int ind= 0; ind < repLengthBuf1; ind++) |
---|
| 719 | buf3p [ind]= buf1p [ind]; |
---|
| 720 | for (int ind= repLengthBuf1; ind < d; ind++) |
---|
| 721 | buf3p [ind]= zzpEZero; |
---|
| 722 | for (int ind= 0; ind < repLengthBuf2; ind++) |
---|
| 723 | buf3p [ind + d]= buf2p [ind]; |
---|
| 724 | buf3.normalize(); |
---|
| 725 | |
---|
| 726 | result += convertNTLzz_pEX2CF (buf3, x, alpha)*power (y, i); |
---|
| 727 | i++; |
---|
| 728 | |
---|
| 729 | |
---|
| 730 | lf= i*d; |
---|
| 731 | degfSubLf= degf - lf; |
---|
| 732 | |
---|
| 733 | lg= d*(k-i); |
---|
| 734 | deggSubLg= degg - lg; |
---|
| 735 | |
---|
| 736 | buf1p= buf1.rep.elts(); |
---|
| 737 | |
---|
| 738 | if (lg >= 0 && deggSubLg > 0) |
---|
| 739 | { |
---|
| 740 | if (repLengthBuf2 > degfSubLf + 1) |
---|
| 741 | degfSubLf= repLengthBuf2 - 1; |
---|
[96f9fdf] | 742 | int tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
[dd2a9b3] | 743 | for (int ind= 0; ind < tmp; ind++) |
---|
| 744 | gp [ind + lg] -= buf1p [ind]; |
---|
| 745 | } |
---|
| 746 | |
---|
| 747 | if (lg < 0) |
---|
| 748 | break; |
---|
| 749 | |
---|
| 750 | buf2p= buf2.rep.elts(); |
---|
| 751 | if (degfSubLf >= 0) |
---|
| 752 | { |
---|
| 753 | for (int ind= 0; ind < repLengthBuf2; ind++) |
---|
| 754 | fp [ind + lf] -= buf2p [ind]; |
---|
| 755 | } |
---|
| 756 | } |
---|
| 757 | |
---|
| 758 | return result; |
---|
| 759 | } |
---|
| 760 | |
---|
| 761 | CanonicalForm |
---|
| 762 | reverseSubst (const zz_pX& F, const zz_pX& G, int d, int k) |
---|
| 763 | { |
---|
| 764 | Variable y= Variable (2); |
---|
| 765 | Variable x= Variable (1); |
---|
| 766 | |
---|
| 767 | zz_pX f= F; |
---|
| 768 | zz_pX g= G; |
---|
| 769 | int degf= deg(f); |
---|
| 770 | int degg= deg(g); |
---|
| 771 | |
---|
| 772 | zz_pX buf1; |
---|
| 773 | zz_pX buf2; |
---|
| 774 | zz_pX buf3; |
---|
| 775 | |
---|
| 776 | zz_p *buf1p; |
---|
| 777 | zz_p *buf2p; |
---|
| 778 | zz_p *buf3p; |
---|
| 779 | |
---|
| 780 | if (f.rep.length() < (long) d*(k+1)) //zero padding |
---|
| 781 | f.rep.SetLength ((long)d*(k+1)); |
---|
| 782 | |
---|
| 783 | zz_p *gp= g.rep.elts(); |
---|
| 784 | zz_p *fp= f.rep.elts(); |
---|
| 785 | CanonicalForm result= 0; |
---|
| 786 | int i= 0; |
---|
| 787 | int lf= 0; |
---|
| 788 | int lg= d*k; |
---|
| 789 | int degfSubLf= degf; |
---|
| 790 | int deggSubLg= degg-lg; |
---|
| 791 | int repLengthBuf2; |
---|
| 792 | int repLengthBuf1; |
---|
| 793 | zz_p zzpZero= zz_p(); |
---|
| 794 | while (degf >= lf || lg >= 0) |
---|
| 795 | { |
---|
| 796 | if (degfSubLf >= d) |
---|
| 797 | repLengthBuf1= d; |
---|
| 798 | else if (degfSubLf < 0) |
---|
| 799 | repLengthBuf1= 0; |
---|
| 800 | else |
---|
| 801 | repLengthBuf1= degfSubLf + 1; |
---|
| 802 | buf1.rep.SetLength((long) repLengthBuf1); |
---|
| 803 | |
---|
| 804 | buf1p= buf1.rep.elts(); |
---|
| 805 | for (int ind= 0; ind < repLengthBuf1; ind++) |
---|
| 806 | buf1p [ind]= fp [ind + lf]; |
---|
| 807 | buf1.normalize(); |
---|
| 808 | |
---|
| 809 | repLengthBuf1= buf1.rep.length(); |
---|
[c1b9927] | 810 | |
---|
[dd2a9b3] | 811 | if (deggSubLg >= d - 1) |
---|
| 812 | repLengthBuf2= d - 1; |
---|
| 813 | else if (deggSubLg < 0) |
---|
| 814 | repLengthBuf2= 0; |
---|
| 815 | else |
---|
| 816 | repLengthBuf2= deggSubLg + 1; |
---|
| 817 | |
---|
| 818 | buf2.rep.SetLength ((long) repLengthBuf2); |
---|
| 819 | buf2p= buf2.rep.elts(); |
---|
| 820 | for (int ind= 0; ind < repLengthBuf2; ind++) |
---|
| 821 | buf2p [ind]= gp [ind + lg]; |
---|
| 822 | |
---|
| 823 | buf2.normalize(); |
---|
| 824 | |
---|
| 825 | repLengthBuf2= buf2.rep.length(); |
---|
| 826 | |
---|
| 827 | |
---|
| 828 | buf3.rep.SetLength((long) repLengthBuf2 + d); |
---|
| 829 | buf3p= buf3.rep.elts(); |
---|
| 830 | buf2p= buf2.rep.elts(); |
---|
| 831 | buf1p= buf1.rep.elts(); |
---|
| 832 | for (int ind= 0; ind < repLengthBuf1; ind++) |
---|
| 833 | buf3p [ind]= buf1p [ind]; |
---|
| 834 | for (int ind= repLengthBuf1; ind < d; ind++) |
---|
| 835 | buf3p [ind]= zzpZero; |
---|
| 836 | for (int ind= 0; ind < repLengthBuf2; ind++) |
---|
| 837 | buf3p [ind + d]= buf2p [ind]; |
---|
| 838 | buf3.normalize(); |
---|
| 839 | |
---|
| 840 | result += convertNTLzzpX2CF (buf3, x)*power (y, i); |
---|
| 841 | i++; |
---|
| 842 | |
---|
| 843 | |
---|
| 844 | lf= i*d; |
---|
| 845 | degfSubLf= degf - lf; |
---|
| 846 | |
---|
| 847 | lg= d*(k-i); |
---|
| 848 | deggSubLg= degg - lg; |
---|
| 849 | |
---|
| 850 | buf1p= buf1.rep.elts(); |
---|
| 851 | |
---|
| 852 | if (lg >= 0 && deggSubLg > 0) |
---|
| 853 | { |
---|
| 854 | if (repLengthBuf2 > degfSubLf + 1) |
---|
| 855 | degfSubLf= repLengthBuf2 - 1; |
---|
[96f9fdf] | 856 | int tmp= tmin (repLengthBuf1, deggSubLg + 1); |
---|
[dd2a9b3] | 857 | for (int ind= 0; ind < tmp; ind++) |
---|
| 858 | gp [ind + lg] -= buf1p [ind]; |
---|
| 859 | } |
---|
| 860 | if (lg < 0) |
---|
| 861 | break; |
---|
| 862 | |
---|
| 863 | buf2p= buf2.rep.elts(); |
---|
| 864 | if (degfSubLf >= 0) |
---|
| 865 | { |
---|
| 866 | for (int ind= 0; ind < repLengthBuf2; ind++) |
---|
| 867 | fp [ind + lf] -= buf2p [ind]; |
---|
| 868 | } |
---|
| 869 | } |
---|
| 870 | |
---|
| 871 | return result; |
---|
| 872 | } |
---|
| 873 | |
---|
| 874 | CanonicalForm reverseSubst (const zz_pEX& F, int d, const Variable& alpha) |
---|
| 875 | { |
---|
| 876 | Variable y= Variable (2); |
---|
| 877 | Variable x= Variable (1); |
---|
| 878 | |
---|
| 879 | zz_pEX f= F; |
---|
| 880 | zz_pE *fp= f.rep.elts(); |
---|
| 881 | |
---|
| 882 | zz_pEX buf; |
---|
| 883 | zz_pE *bufp; |
---|
| 884 | CanonicalForm result= 0; |
---|
| 885 | int i= 0; |
---|
| 886 | int degf= deg(f); |
---|
| 887 | int k= 0; |
---|
| 888 | int degfSubK; |
---|
| 889 | int repLength; |
---|
| 890 | while (degf >= k) |
---|
| 891 | { |
---|
| 892 | degfSubK= degf - k; |
---|
| 893 | if (degfSubK >= d) |
---|
| 894 | repLength= d; |
---|
| 895 | else |
---|
| 896 | repLength= degfSubK + 1; |
---|
| 897 | |
---|
| 898 | buf.rep.SetLength ((long) repLength); |
---|
| 899 | bufp= buf.rep.elts(); |
---|
| 900 | for (int j= 0; j < repLength; j++) |
---|
| 901 | bufp [j]= fp [j + k]; |
---|
| 902 | buf.normalize(); |
---|
| 903 | |
---|
| 904 | result += convertNTLzz_pEX2CF (buf, x, alpha)*power (y, i); |
---|
| 905 | i++; |
---|
| 906 | k= d*i; |
---|
| 907 | } |
---|
| 908 | |
---|
| 909 | return result; |
---|
| 910 | } |
---|
| 911 | |
---|
| 912 | CanonicalForm reverseSubstFp (const zz_pX& F, int d) |
---|
| 913 | { |
---|
| 914 | Variable y= Variable (2); |
---|
| 915 | Variable x= Variable (1); |
---|
| 916 | |
---|
| 917 | zz_pX f= F; |
---|
| 918 | zz_p *fp= f.rep.elts(); |
---|
| 919 | |
---|
| 920 | zz_pX buf; |
---|
| 921 | zz_p *bufp; |
---|
| 922 | CanonicalForm result= 0; |
---|
| 923 | int i= 0; |
---|
| 924 | int degf= deg(f); |
---|
| 925 | int k= 0; |
---|
| 926 | int degfSubK; |
---|
| 927 | int repLength; |
---|
| 928 | while (degf >= k) |
---|
| 929 | { |
---|
| 930 | degfSubK= degf - k; |
---|
| 931 | if (degfSubK >= d) |
---|
| 932 | repLength= d; |
---|
| 933 | else |
---|
| 934 | repLength= degfSubK + 1; |
---|
| 935 | |
---|
| 936 | buf.rep.SetLength ((long) repLength); |
---|
| 937 | bufp= buf.rep.elts(); |
---|
| 938 | for (int j= 0; j < repLength; j++) |
---|
| 939 | bufp [j]= fp [j + k]; |
---|
| 940 | buf.normalize(); |
---|
| 941 | |
---|
| 942 | result += convertNTLzzpX2CF (buf, x)*power (y, i); |
---|
| 943 | i++; |
---|
| 944 | k= d*i; |
---|
| 945 | } |
---|
| 946 | |
---|
| 947 | return result; |
---|
| 948 | } |
---|
| 949 | |
---|
| 950 | // assumes input to be reduced mod M and to be an element of Fq not Fp |
---|
| 951 | CanonicalForm |
---|
[c1b9927] | 952 | mulMod2NTLFpReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
[dd2a9b3] | 953 | CanonicalForm& M) |
---|
| 954 | { |
---|
[96f9fdf] | 955 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
| 956 | d1 /= 2; |
---|
| 957 | d1 += 1; |
---|
[dd2a9b3] | 958 | |
---|
| 959 | zz_pX F1, F2; |
---|
| 960 | kronSubRecipro (F1, F2, F, d1); |
---|
| 961 | zz_pX G1, G2; |
---|
| 962 | kronSubRecipro (G1, G2, G, d1); |
---|
| 963 | |
---|
| 964 | int k= d1*degree (M); |
---|
| 965 | MulTrunc (F1, F1, G1, (long) k); |
---|
| 966 | |
---|
[96f9fdf] | 967 | int degtailF= degree (tailcoeff (F), 1); |
---|
| 968 | int degtailG= degree (tailcoeff (G), 1); |
---|
| 969 | int taildegF= taildegree (F); |
---|
| 970 | int taildegG= taildegree (G); |
---|
| 971 | int b= k + degtailF + degtailG - d1*(2+taildegF+taildegG); |
---|
| 972 | |
---|
| 973 | reverse (F2, F2); |
---|
| 974 | reverse (G2, G2); |
---|
| 975 | MulTrunc (F2, F2, G2, b + 1); |
---|
| 976 | reverse (F2, F2, b); |
---|
[dd2a9b3] | 977 | |
---|
[96f9fdf] | 978 | int d2= tmax (deg (F2)/d1, deg (F1)/d1); |
---|
[dd2a9b3] | 979 | return reverseSubst (F1, F2, d1, d2); |
---|
| 980 | } |
---|
| 981 | |
---|
| 982 | //Kronecker substitution |
---|
| 983 | CanonicalForm |
---|
| 984 | mulMod2NTLFp (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 985 | CanonicalForm& M) |
---|
| 986 | { |
---|
| 987 | CanonicalForm A= F; |
---|
| 988 | CanonicalForm B= G; |
---|
| 989 | |
---|
| 990 | int degAx= degree (A, 1); |
---|
| 991 | int degAy= degree (A, 2); |
---|
| 992 | int degBx= degree (B, 1); |
---|
| 993 | int degBy= degree (B, 2); |
---|
| 994 | int d1= degAx + 1 + degBx; |
---|
[96f9fdf] | 995 | int d2= tmax (degAy, degBy); |
---|
[dd2a9b3] | 996 | |
---|
[fd803bc] | 997 | if (d1 > 128 && d2 > 160 && (degAy == degBy) && (2*degAy > degree (M))) |
---|
[dd2a9b3] | 998 | return mulMod2NTLFpReci (A, B, M); |
---|
| 999 | |
---|
| 1000 | zz_pX NTLA= kronSubFp (A, d1); |
---|
| 1001 | zz_pX NTLB= kronSubFp (B, d1); |
---|
| 1002 | |
---|
| 1003 | int k= d1*degree (M); |
---|
| 1004 | MulTrunc (NTLA, NTLA, NTLB, (long) k); |
---|
| 1005 | |
---|
| 1006 | A= reverseSubstFp (NTLA, d1); |
---|
| 1007 | |
---|
| 1008 | return A; |
---|
| 1009 | } |
---|
| 1010 | |
---|
| 1011 | // assumes input to be reduced mod M and to be an element of Fq not Fp |
---|
| 1012 | CanonicalForm |
---|
[c1b9927] | 1013 | mulMod2NTLFqReci (const CanonicalForm& F, const CanonicalForm& G, const |
---|
[dd2a9b3] | 1014 | CanonicalForm& M, const Variable& alpha) |
---|
| 1015 | { |
---|
[96f9fdf] | 1016 | int d1= degree (F, 1) + degree (G, 1) + 1; |
---|
| 1017 | d1 /= 2; |
---|
| 1018 | d1 += 1; |
---|
[dd2a9b3] | 1019 | |
---|
| 1020 | zz_pEX F1, F2; |
---|
| 1021 | kronSubRecipro (F1, F2, F, d1, alpha); |
---|
| 1022 | zz_pEX G1, G2; |
---|
| 1023 | kronSubRecipro (G1, G2, G, d1, alpha); |
---|
| 1024 | |
---|
[fd803bc] | 1025 | int k= d1*degree (M); |
---|
| 1026 | MulTrunc (F1, F1, G1, (long) k); |
---|
[dd2a9b3] | 1027 | |
---|
[96f9fdf] | 1028 | int degtailF= degree (tailcoeff (F), 1); |
---|
| 1029 | int degtailG= degree (tailcoeff (G), 1); |
---|
| 1030 | int taildegF= taildegree (F); |
---|
| 1031 | int taildegG= taildegree (G); |
---|
| 1032 | int b= k + degtailF + degtailG - d1*(2+taildegF+taildegG); |
---|
[dd2a9b3] | 1033 | |
---|
[96f9fdf] | 1034 | reverse (F2, F2); |
---|
| 1035 | reverse (G2, G2); |
---|
| 1036 | MulTrunc (F2, F2, G2, b + 1); |
---|
| 1037 | reverse (F2, F2, b); |
---|
[dd2a9b3] | 1038 | |
---|
[96f9fdf] | 1039 | int d2= tmax (deg (F2)/d1, deg (F1)/d1); |
---|
| 1040 | return reverseSubst (F1, F2, d1, d2, alpha); |
---|
[dd2a9b3] | 1041 | } |
---|
| 1042 | |
---|
| 1043 | CanonicalForm |
---|
| 1044 | mulMod2NTLFq (const CanonicalForm& F, const CanonicalForm& G, const |
---|
| 1045 | CanonicalForm& M) |
---|
| 1046 | { |
---|
| 1047 | Variable alpha; |
---|
| 1048 | CanonicalForm A= F; |
---|
| 1049 | CanonicalForm B= G; |
---|
| 1050 | |
---|
| 1051 | if (hasFirstAlgVar (A, alpha) || hasFirstAlgVar (B, alpha)) |
---|
| 1052 | { |
---|
| 1053 | int degAx= degree (A, 1); |
---|
| 1054 | int degAy= degree (A, 2); |
---|
| 1055 | int degBx= degree (B, 1); |
---|
| 1056 | int degBy= degree (B, 2); |
---|
| 1057 | int d1= degAx + degBx + 1; |
---|
[96f9fdf] | 1058 | int d2= tmax (degAy, degBy); |
---|
[dd2a9b3] | 1059 | zz_p::init (getCharacteristic()); |
---|
| 1060 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
| 1061 | zz_pE::init (NTLMipo); |
---|
| 1062 | |
---|
| 1063 | int degMipo= degree (getMipo (alpha)); |
---|
[fd803bc] | 1064 | if ((d1 > 128/degMipo) && (d2 > 160/degMipo) && (degAy == degBy) && |
---|
| 1065 | (2*degAy > degree (M))) |
---|
[dd2a9b3] | 1066 | return mulMod2NTLFqReci (A, B, M, alpha); |
---|
| 1067 | |
---|
| 1068 | zz_pEX NTLA= kronSub (A, d1, alpha); |
---|
| 1069 | zz_pEX NTLB= kronSub (B, d1, alpha); |
---|
| 1070 | |
---|
| 1071 | int k= d1*degree (M); |
---|
| 1072 | |
---|
| 1073 | MulTrunc (NTLA, NTLA, NTLB, (long) k); |
---|
| 1074 | |
---|
| 1075 | A= reverseSubst (NTLA, d1, alpha); |
---|
| 1076 | |
---|
| 1077 | return A; |
---|
| 1078 | } |
---|
| 1079 | else |
---|
| 1080 | return mulMod2NTLFp (A, B, M); |
---|
| 1081 | } |
---|
| 1082 | |
---|
[806c18] | 1083 | CanonicalForm mulMod2 (const CanonicalForm& A, const CanonicalForm& B, |
---|
[ad3c3ff] | 1084 | const CanonicalForm& M) |
---|
| 1085 | { |
---|
| 1086 | if (A.isZero() || B.isZero()) |
---|
| 1087 | return 0; |
---|
| 1088 | |
---|
| 1089 | ASSERT (M.isUnivariate(), "M must be univariate"); |
---|
| 1090 | |
---|
| 1091 | CanonicalForm F= mod (A, M); |
---|
| 1092 | CanonicalForm G= mod (B, M); |
---|
| 1093 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
---|
| 1094 | return F*G; |
---|
| 1095 | Variable y= M.mvar(); |
---|
| 1096 | int degF= degree (F, y); |
---|
| 1097 | int degG= degree (G, y); |
---|
| 1098 | |
---|
[c1b9927] | 1099 | if ((degF < 1 && degG < 1) && (F.isUnivariate() && G.isUnivariate()) && |
---|
[ad3c3ff] | 1100 | (F.level() == G.level())) |
---|
[c1b9927] | 1101 | { |
---|
[ad3c3ff] | 1102 | CanonicalForm result= mulNTL (F, G); |
---|
| 1103 | return mod (result, M); |
---|
| 1104 | } |
---|
| 1105 | else if (degF <= 1 && degG <= 1) |
---|
[c1b9927] | 1106 | { |
---|
[ad3c3ff] | 1107 | CanonicalForm result= F*G; |
---|
| 1108 | return mod (result, M); |
---|
| 1109 | } |
---|
[806c18] | 1110 | |
---|
[dd2a9b3] | 1111 | int sizeF= size (F); |
---|
| 1112 | int sizeG= size (G); |
---|
[c1b9927] | 1113 | |
---|
[dd2a9b3] | 1114 | int fallBackToNaive= 50; |
---|
| 1115 | if (sizeF < fallBackToNaive || sizeG < fallBackToNaive) |
---|
| 1116 | return mod (F*G, M); |
---|
| 1117 | |
---|
[64e7cb] | 1118 | if (getCharacteristic() > 0 && CFFactory::gettype() != GaloisFieldDomain && |
---|
[dd2a9b3] | 1119 | (((degF-degG) < 50 && degF > degG) || ((degG-degF) < 50 && degF <= degG))) |
---|
| 1120 | return mulMod2NTLFq (F, G, M); |
---|
| 1121 | |
---|
[ad3c3ff] | 1122 | int m= (int) ceil (degree (M)/2.0); |
---|
| 1123 | if (degF >= m || degG >= m) |
---|
| 1124 | { |
---|
| 1125 | CanonicalForm MLo= power (y, m); |
---|
| 1126 | CanonicalForm MHi= power (y, degree (M) - m); |
---|
| 1127 | CanonicalForm F0= mod (F, MLo); |
---|
| 1128 | CanonicalForm F1= div (F, MLo); |
---|
| 1129 | CanonicalForm G0= mod (G, MLo); |
---|
| 1130 | CanonicalForm G1= div (G, MLo); |
---|
| 1131 | CanonicalForm F0G1= mulMod2 (F0, G1, MHi); |
---|
| 1132 | CanonicalForm F1G0= mulMod2 (F1, G0, MHi); |
---|
| 1133 | CanonicalForm F0G0= mulMod2 (F0, G0, M); |
---|
| 1134 | return F0G0 + MLo*(F0G1 + F1G0); |
---|
| 1135 | } |
---|
| 1136 | else |
---|
| 1137 | { |
---|
| 1138 | m= (int) ceil (tmax (degF, degG)/2.0); |
---|
| 1139 | CanonicalForm yToM= power (y, m); |
---|
| 1140 | CanonicalForm F0= mod (F, yToM); |
---|
| 1141 | CanonicalForm F1= div (F, yToM); |
---|
| 1142 | CanonicalForm G0= mod (G, yToM); |
---|
| 1143 | CanonicalForm G1= div (G, yToM); |
---|
| 1144 | CanonicalForm H00= mulMod2 (F0, G0, M); |
---|
| 1145 | CanonicalForm H11= mulMod2 (F1, G1, M); |
---|
| 1146 | CanonicalForm H01= mulMod2 (F0 + F1, G0 + G1, M); |
---|
| 1147 | return H11*yToM*yToM + (H01 - H11 - H00)*yToM + H00; |
---|
[806c18] | 1148 | } |
---|
[ad3c3ff] | 1149 | DEBOUTLN (cerr, "fatal end in mulMod2"); |
---|
| 1150 | } |
---|
| 1151 | |
---|
[806c18] | 1152 | CanonicalForm mulMod (const CanonicalForm& A, const CanonicalForm& B, |
---|
[ad3c3ff] | 1153 | const CFList& MOD) |
---|
| 1154 | { |
---|
| 1155 | if (A.isZero() || B.isZero()) |
---|
| 1156 | return 0; |
---|
| 1157 | |
---|
| 1158 | if (MOD.length() == 1) |
---|
| 1159 | return mulMod2 (A, B, MOD.getLast()); |
---|
| 1160 | |
---|
| 1161 | CanonicalForm M= MOD.getLast(); |
---|
| 1162 | CanonicalForm F= mod (A, M); |
---|
| 1163 | CanonicalForm G= mod (B, M); |
---|
| 1164 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
---|
| 1165 | return F*G; |
---|
| 1166 | Variable y= M.mvar(); |
---|
| 1167 | int degF= degree (F, y); |
---|
| 1168 | int degG= degree (G, y); |
---|
| 1169 | |
---|
[806c18] | 1170 | if ((degF <= 1 && F.level() <= M.level()) && |
---|
[ad3c3ff] | 1171 | (degG <= 1 && G.level() <= M.level())) |
---|
| 1172 | { |
---|
| 1173 | CFList buf= MOD; |
---|
| 1174 | buf.removeLast(); |
---|
| 1175 | if (degF == 1 && degG == 1) |
---|
| 1176 | { |
---|
| 1177 | CanonicalForm F0= mod (F, y); |
---|
| 1178 | CanonicalForm F1= div (F, y); |
---|
| 1179 | CanonicalForm G0= mod (G, y); |
---|
| 1180 | CanonicalForm G1= div (G, y); |
---|
| 1181 | if (degree (M) > 2) |
---|
| 1182 | { |
---|
| 1183 | CanonicalForm H00= mulMod (F0, G0, buf); |
---|
| 1184 | CanonicalForm H11= mulMod (F1, G1, buf); |
---|
| 1185 | CanonicalForm H01= mulMod (F0 + F1, G0 + G1, buf); |
---|
| 1186 | return H11*y*y + (H01 - H00 - H11)*y + H00; |
---|
| 1187 | } |
---|
| 1188 | else //here degree (M) == 2 |
---|
| 1189 | { |
---|
| 1190 | buf.append (y); |
---|
| 1191 | CanonicalForm F0G1= mulMod (F0, G1, buf); |
---|
| 1192 | CanonicalForm F1G0= mulMod (F1, G0, buf); |
---|
| 1193 | CanonicalForm F0G0= mulMod (F0, G0, MOD); |
---|
| 1194 | CanonicalForm result= F0G0 + y*(F0G1 + F1G0); |
---|
| 1195 | return result; |
---|
| 1196 | } |
---|
| 1197 | } |
---|
| 1198 | else if (degF == 1 && degG == 0) |
---|
| 1199 | return mulMod (div (F, y), G, buf)*y + mulMod (mod (F, y), G, buf); |
---|
| 1200 | else if (degF == 0 && degG == 1) |
---|
| 1201 | return mulMod (div (G, y), F, buf)*y + mulMod (mod (G, y), F, buf); |
---|
| 1202 | else |
---|
| 1203 | return mulMod (F, G, buf); |
---|
| 1204 | } |
---|
| 1205 | int m= (int) ceil (degree (M)/2.0); |
---|
| 1206 | if (degF >= m || degG >= m) |
---|
| 1207 | { |
---|
| 1208 | CanonicalForm MLo= power (y, m); |
---|
| 1209 | CanonicalForm MHi= power (y, degree (M) - m); |
---|
| 1210 | CanonicalForm F0= mod (F, MLo); |
---|
| 1211 | CanonicalForm F1= div (F, MLo); |
---|
| 1212 | CanonicalForm G0= mod (G, MLo); |
---|
| 1213 | CanonicalForm G1= div (G, MLo); |
---|
| 1214 | CFList buf= MOD; |
---|
| 1215 | buf.removeLast(); |
---|
| 1216 | buf.append (MHi); |
---|
| 1217 | CanonicalForm F0G1= mulMod (F0, G1, buf); |
---|
| 1218 | CanonicalForm F1G0= mulMod (F1, G0, buf); |
---|
| 1219 | CanonicalForm F0G0= mulMod (F0, G0, MOD); |
---|
| 1220 | return F0G0 + MLo*(F0G1 + F1G0); |
---|
| 1221 | } |
---|
| 1222 | else |
---|
| 1223 | { |
---|
| 1224 | m= (int) ceil (tmax (degF, degG)/2.0); |
---|
| 1225 | CanonicalForm yToM= power (y, m); |
---|
| 1226 | CanonicalForm F0= mod (F, yToM); |
---|
| 1227 | CanonicalForm F1= div (F, yToM); |
---|
| 1228 | CanonicalForm G0= mod (G, yToM); |
---|
| 1229 | CanonicalForm G1= div (G, yToM); |
---|
| 1230 | CanonicalForm H00= mulMod (F0, G0, MOD); |
---|
| 1231 | CanonicalForm H11= mulMod (F1, G1, MOD); |
---|
| 1232 | CanonicalForm H01= mulMod (F0 + F1, G0 + G1, MOD); |
---|
| 1233 | return H11*yToM*yToM + (H01 - H11 - H00)*yToM + H00; |
---|
[806c18] | 1234 | } |
---|
[ad3c3ff] | 1235 | DEBOUTLN (cerr, "fatal end in mulMod"); |
---|
| 1236 | } |
---|
| 1237 | |
---|
[806c18] | 1238 | CanonicalForm prodMod (const CFList& L, const CanonicalForm& M) |
---|
[ad3c3ff] | 1239 | { |
---|
| 1240 | if (L.isEmpty()) |
---|
| 1241 | return 1; |
---|
| 1242 | int l= L.length(); |
---|
| 1243 | if (l == 1) |
---|
| 1244 | return mod (L.getFirst(), M); |
---|
| 1245 | else if (l == 2) { |
---|
| 1246 | CanonicalForm result= mulMod2 (L.getFirst(), L.getLast(), M); |
---|
| 1247 | return result; |
---|
| 1248 | } |
---|
| 1249 | else |
---|
| 1250 | { |
---|
| 1251 | l /= 2; |
---|
| 1252 | CFList tmp1, tmp2; |
---|
| 1253 | CFListIterator i= L; |
---|
| 1254 | CanonicalForm buf1, buf2; |
---|
[806c18] | 1255 | for (int j= 1; j <= l; j++, i++) |
---|
[ad3c3ff] | 1256 | tmp1.append (i.getItem()); |
---|
| 1257 | tmp2= Difference (L, tmp1); |
---|
| 1258 | buf1= prodMod (tmp1, M); |
---|
| 1259 | buf2= prodMod (tmp2, M); |
---|
| 1260 | CanonicalForm result= mulMod2 (buf1, buf2, M); |
---|
| 1261 | return result; |
---|
[806c18] | 1262 | } |
---|
[ad3c3ff] | 1263 | } |
---|
| 1264 | |
---|
[806c18] | 1265 | CanonicalForm prodMod (const CFList& L, const CFList& M) |
---|
[ad3c3ff] | 1266 | { |
---|
| 1267 | if (L.isEmpty()) |
---|
| 1268 | return 1; |
---|
| 1269 | else if (L.length() == 1) |
---|
| 1270 | return L.getFirst(); |
---|
| 1271 | else if (L.length() == 2) |
---|
| 1272 | return mulMod (L.getFirst(), L.getLast(), M); |
---|
| 1273 | else |
---|
| 1274 | { |
---|
| 1275 | int l= L.length()/2; |
---|
| 1276 | CFListIterator i= L; |
---|
| 1277 | CFList tmp1, tmp2; |
---|
| 1278 | CanonicalForm buf1, buf2; |
---|
[806c18] | 1279 | for (int j= 1; j <= l; j++, i++) |
---|
[ad3c3ff] | 1280 | tmp1.append (i.getItem()); |
---|
| 1281 | tmp2= Difference (L, tmp1); |
---|
| 1282 | buf1= prodMod (tmp1, M); |
---|
| 1283 | buf2= prodMod (tmp2, M); |
---|
| 1284 | return mulMod (buf1, buf2, M); |
---|
| 1285 | } |
---|
| 1286 | } |
---|
| 1287 | |
---|
[c9b1d66] | 1288 | |
---|
| 1289 | CanonicalForm reverse (const CanonicalForm& F, int d) |
---|
| 1290 | { |
---|
| 1291 | if (d == 0) |
---|
| 1292 | return F; |
---|
| 1293 | CanonicalForm A= F; |
---|
[dd2a9b3] | 1294 | Variable y= Variable (2); |
---|
[c9b1d66] | 1295 | Variable x= Variable (1); |
---|
[dd2a9b3] | 1296 | if (degree (A, x) > 0) |
---|
| 1297 | { |
---|
| 1298 | A= swapvar (A, x, y); |
---|
| 1299 | CanonicalForm result= 0; |
---|
| 1300 | CFIterator i= A; |
---|
| 1301 | while (d - i.exp() < 0) |
---|
| 1302 | i++; |
---|
[c9b1d66] | 1303 | |
---|
[dd2a9b3] | 1304 | for (; i.hasTerms() && (d - i.exp() >= 0); i++) |
---|
| 1305 | result += swapvar (i.coeff(),x,y)*power (x, d - i.exp()); |
---|
| 1306 | return result; |
---|
| 1307 | } |
---|
| 1308 | else |
---|
| 1309 | return A*power (x, d); |
---|
[c9b1d66] | 1310 | } |
---|
| 1311 | |
---|
| 1312 | CanonicalForm |
---|
| 1313 | newtonInverse (const CanonicalForm& F, const int n, const CanonicalForm& M) |
---|
| 1314 | { |
---|
| 1315 | int l= ilog2(n); |
---|
| 1316 | |
---|
| 1317 | CanonicalForm g= mod (F, M)[0] [0]; |
---|
| 1318 | |
---|
| 1319 | ASSERT (!g.isZero(), "expected a unit"); |
---|
| 1320 | |
---|
| 1321 | Variable alpha; |
---|
| 1322 | |
---|
| 1323 | if (!g.isOne()) |
---|
| 1324 | g = 1/g; |
---|
| 1325 | Variable x= Variable (1); |
---|
| 1326 | CanonicalForm result; |
---|
| 1327 | int exp= 0; |
---|
| 1328 | if (n & 1) |
---|
| 1329 | { |
---|
| 1330 | result= g; |
---|
| 1331 | exp= 1; |
---|
| 1332 | } |
---|
| 1333 | CanonicalForm h; |
---|
| 1334 | |
---|
| 1335 | for (int i= 1; i <= l; i++) |
---|
| 1336 | { |
---|
| 1337 | h= mulMod2 (g, mod (F, power (x, (1 << i))), M); |
---|
| 1338 | h= mod (h, power (x, (1 << i)) - 1); |
---|
| 1339 | h= div (h, power (x, (1 << (i - 1)))); |
---|
| 1340 | h= mod (h, M); |
---|
| 1341 | g -= power (x, (1 << (i - 1)))* |
---|
| 1342 | mod (mulMod2 (g, h, M), power (x, (1 << (i - 1)))); |
---|
| 1343 | |
---|
| 1344 | if (n & (1 << i)) |
---|
| 1345 | { |
---|
| 1346 | if (exp) |
---|
| 1347 | { |
---|
| 1348 | h= mulMod2 (result, mod (F, power (x, exp + (1 << i))), M); |
---|
| 1349 | h= mod (h, power (x, exp + (1 << i)) - 1); |
---|
| 1350 | h= div (h, power (x, exp)); |
---|
| 1351 | h= mod (h, M); |
---|
| 1352 | result -= power(x, exp)*mod (mulMod2 (g, h, M), |
---|
| 1353 | power (x, (1 << i))); |
---|
| 1354 | exp += (1 << i); |
---|
| 1355 | } |
---|
| 1356 | else |
---|
| 1357 | { |
---|
| 1358 | exp= (1 << i); |
---|
| 1359 | result= g; |
---|
| 1360 | } |
---|
| 1361 | } |
---|
| 1362 | } |
---|
| 1363 | |
---|
| 1364 | return result; |
---|
| 1365 | } |
---|
| 1366 | |
---|
| 1367 | CanonicalForm |
---|
| 1368 | newtonDiv (const CanonicalForm& F, const CanonicalForm& G, const CanonicalForm& |
---|
| 1369 | M) |
---|
| 1370 | { |
---|
| 1371 | ASSERT (getCharacteristic() > 0, "positive characteristic expected"); |
---|
| 1372 | ASSERT (CFFactory::gettype() != GaloisFieldDomain, "no GF expected"); |
---|
| 1373 | |
---|
| 1374 | CanonicalForm A= mod (F, M); |
---|
| 1375 | CanonicalForm B= mod (G, M); |
---|
| 1376 | |
---|
| 1377 | Variable x= Variable (1); |
---|
| 1378 | int degA= degree (A, x); |
---|
| 1379 | int degB= degree (B, x); |
---|
| 1380 | int m= degA - degB; |
---|
| 1381 | if (m < 0) |
---|
| 1382 | return 0; |
---|
| 1383 | |
---|
[3426de2] | 1384 | Variable v; |
---|
[c9b1d66] | 1385 | CanonicalForm Q; |
---|
[dd2a9b3] | 1386 | if (degB <= 1 || CFFactory::gettype() == GaloisFieldDomain) |
---|
[c9b1d66] | 1387 | { |
---|
| 1388 | CanonicalForm R; |
---|
| 1389 | divrem2 (A, B, Q, R, M); |
---|
| 1390 | } |
---|
| 1391 | else |
---|
| 1392 | { |
---|
[3426de2] | 1393 | if (hasFirstAlgVar (A, v) || hasFirstAlgVar (B, v)) |
---|
| 1394 | { |
---|
| 1395 | CanonicalForm R= reverse (A, degA); |
---|
| 1396 | CanonicalForm revB= reverse (B, degB); |
---|
| 1397 | revB= newtonInverse (revB, m + 1, M); |
---|
| 1398 | Q= mulMod2 (R, revB, M); |
---|
| 1399 | Q= mod (Q, power (x, m + 1)); |
---|
| 1400 | Q= reverse (Q, m); |
---|
| 1401 | } |
---|
| 1402 | else |
---|
| 1403 | { |
---|
| 1404 | zz_pX mipo= convertFacCF2NTLzzpX (M); |
---|
| 1405 | Variable y= Variable (2); |
---|
| 1406 | zz_pEX NTLA, NTLB; |
---|
| 1407 | NTLA= convertFacCF2NTLzz_pEX (swapvar (A, x, y), mipo); |
---|
| 1408 | NTLB= convertFacCF2NTLzz_pEX (swapvar (B, x, y), mipo); |
---|
| 1409 | div (NTLA, NTLA, NTLB); |
---|
| 1410 | Q= convertNTLzz_pEX2CF (NTLA, x, y); |
---|
| 1411 | } |
---|
[c9b1d66] | 1412 | } |
---|
| 1413 | |
---|
| 1414 | return Q; |
---|
| 1415 | } |
---|
| 1416 | |
---|
| 1417 | void |
---|
| 1418 | newtonDivrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
| 1419 | CanonicalForm& R, const CanonicalForm& M) |
---|
| 1420 | { |
---|
| 1421 | CanonicalForm A= mod (F, M); |
---|
| 1422 | CanonicalForm B= mod (G, M); |
---|
| 1423 | Variable x= Variable (1); |
---|
| 1424 | int degA= degree (A, x); |
---|
| 1425 | int degB= degree (B, x); |
---|
| 1426 | int m= degA - degB; |
---|
| 1427 | |
---|
| 1428 | if (m < 0) |
---|
| 1429 | { |
---|
| 1430 | R= A; |
---|
| 1431 | Q= 0; |
---|
| 1432 | return; |
---|
| 1433 | } |
---|
| 1434 | |
---|
[3426de2] | 1435 | Variable v; |
---|
[dd2a9b3] | 1436 | if (degB <= 1 || CFFactory::gettype() == GaloisFieldDomain) |
---|
[c9b1d66] | 1437 | { |
---|
| 1438 | divrem2 (A, B, Q, R, M); |
---|
| 1439 | } |
---|
| 1440 | else |
---|
| 1441 | { |
---|
[3426de2] | 1442 | if (hasFirstAlgVar (A, v) || hasFirstAlgVar (B, v)) |
---|
| 1443 | { |
---|
| 1444 | R= reverse (A, degA); |
---|
[c9b1d66] | 1445 | |
---|
[3426de2] | 1446 | CanonicalForm revB= reverse (B, degB); |
---|
| 1447 | revB= newtonInverse (revB, m + 1, M); |
---|
| 1448 | Q= mulMod2 (R, revB, M); |
---|
[c9b1d66] | 1449 | |
---|
[3426de2] | 1450 | Q= mod (Q, power (x, m + 1)); |
---|
| 1451 | Q= reverse (Q, m); |
---|
[c9b1d66] | 1452 | |
---|
[3426de2] | 1453 | R= A - mulMod2 (Q, B, M); |
---|
| 1454 | } |
---|
| 1455 | else |
---|
| 1456 | { |
---|
| 1457 | zz_pX mipo= convertFacCF2NTLzzpX (M); |
---|
| 1458 | Variable y= Variable (2); |
---|
| 1459 | zz_pEX NTLA, NTLB; |
---|
| 1460 | NTLA= convertFacCF2NTLzz_pEX (swapvar (A, x, y), mipo); |
---|
| 1461 | NTLB= convertFacCF2NTLzz_pEX (swapvar (B, x, y), mipo); |
---|
| 1462 | zz_pEX NTLQ, NTLR; |
---|
| 1463 | DivRem (NTLQ, NTLR, NTLA, NTLB); |
---|
| 1464 | Q= convertNTLzz_pEX2CF (NTLQ, x, y); |
---|
| 1465 | R= convertNTLzz_pEX2CF (NTLR, x, y); |
---|
| 1466 | } |
---|
[c9b1d66] | 1467 | } |
---|
| 1468 | } |
---|
| 1469 | |
---|
[ad3c3ff] | 1470 | static inline |
---|
[806c18] | 1471 | CFList split (const CanonicalForm& F, const int m, const Variable& x) |
---|
[ad3c3ff] | 1472 | { |
---|
| 1473 | CanonicalForm A= F; |
---|
| 1474 | CanonicalForm buf= 0; |
---|
| 1475 | bool swap= false; |
---|
| 1476 | if (degree (A, x) <= 0) |
---|
| 1477 | return CFList(A); |
---|
| 1478 | else if (x.level() != A.level()) |
---|
| 1479 | { |
---|
| 1480 | swap= true; |
---|
| 1481 | A= swapvar (A, x, A.mvar()); |
---|
| 1482 | } |
---|
| 1483 | |
---|
| 1484 | int j= (int) floor ((double) degree (A)/ m); |
---|
[806c18] | 1485 | CFList result; |
---|
[ad3c3ff] | 1486 | CFIterator i= A; |
---|
| 1487 | for (; j >= 0; j--) |
---|
| 1488 | { |
---|
[806c18] | 1489 | while (i.hasTerms() && i.exp() - j*m >= 0) |
---|
[ad3c3ff] | 1490 | { |
---|
| 1491 | if (swap) |
---|
| 1492 | buf += i.coeff()*power (A.mvar(), i.exp() - j*m); |
---|
| 1493 | else |
---|
| 1494 | buf += i.coeff()*power (x, i.exp() - j*m); |
---|
| 1495 | i++; |
---|
| 1496 | } |
---|
| 1497 | if (swap) |
---|
| 1498 | result.append (swapvar (buf, x, F.mvar())); |
---|
| 1499 | else |
---|
[806c18] | 1500 | result.append (buf); |
---|
[ad3c3ff] | 1501 | buf= 0; |
---|
| 1502 | } |
---|
[806c18] | 1503 | return result; |
---|
[ad3c3ff] | 1504 | } |
---|
| 1505 | |
---|
| 1506 | static inline |
---|
[806c18] | 1507 | void divrem32 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
[ad3c3ff] | 1508 | CanonicalForm& R, const CFList& M); |
---|
| 1509 | |
---|
[806c18] | 1510 | static inline |
---|
| 1511 | void divrem21 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
[ad3c3ff] | 1512 | CanonicalForm& R, const CFList& M) |
---|
| 1513 | { |
---|
| 1514 | CanonicalForm A= mod (F, M); |
---|
| 1515 | CanonicalForm B= mod (G, M); |
---|
| 1516 | Variable x= Variable (1); |
---|
| 1517 | int degB= degree (B, x); |
---|
| 1518 | int degA= degree (A, x); |
---|
| 1519 | if (degA < degB) |
---|
| 1520 | { |
---|
| 1521 | Q= 0; |
---|
| 1522 | R= A; |
---|
| 1523 | return; |
---|
| 1524 | } |
---|
| 1525 | ASSERT (2*degB > degA, "expected degree (F, 1) < 2*degree (G, 1)"); |
---|
| 1526 | if (degB < 1) |
---|
| 1527 | { |
---|
| 1528 | divrem (A, B, Q, R); |
---|
| 1529 | Q= mod (Q, M); |
---|
| 1530 | R= mod (R, M); |
---|
| 1531 | return; |
---|
| 1532 | } |
---|
[806c18] | 1533 | |
---|
| 1534 | int m= (int) ceil ((double) (degB + 1)/2.0) + 1; |
---|
[ad3c3ff] | 1535 | CFList splitA= split (A, m, x); |
---|
| 1536 | if (splitA.length() == 3) |
---|
| 1537 | splitA.insert (0); |
---|
| 1538 | if (splitA.length() == 2) |
---|
| 1539 | { |
---|
| 1540 | splitA.insert (0); |
---|
| 1541 | splitA.insert (0); |
---|
[806c18] | 1542 | } |
---|
[ad3c3ff] | 1543 | if (splitA.length() == 1) |
---|
| 1544 | { |
---|
| 1545 | splitA.insert (0); |
---|
| 1546 | splitA.insert (0); |
---|
| 1547 | splitA.insert (0); |
---|
| 1548 | } |
---|
| 1549 | |
---|
| 1550 | CanonicalForm xToM= power (x, m); |
---|
| 1551 | |
---|
| 1552 | CFListIterator i= splitA; |
---|
| 1553 | CanonicalForm H= i.getItem(); |
---|
| 1554 | i++; |
---|
| 1555 | H *= xToM; |
---|
| 1556 | H += i.getItem(); |
---|
| 1557 | i++; |
---|
| 1558 | H *= xToM; |
---|
| 1559 | H += i.getItem(); |
---|
| 1560 | i++; |
---|
| 1561 | |
---|
| 1562 | divrem32 (H, B, Q, R, M); |
---|
| 1563 | |
---|
| 1564 | CFList splitR= split (R, m, x); |
---|
| 1565 | if (splitR.length() == 1) |
---|
| 1566 | splitR.insert (0); |
---|
| 1567 | |
---|
| 1568 | H= splitR.getFirst(); |
---|
| 1569 | H *= xToM; |
---|
| 1570 | H += splitR.getLast(); |
---|
| 1571 | H *= xToM; |
---|
| 1572 | H += i.getItem(); |
---|
| 1573 | |
---|
| 1574 | CanonicalForm bufQ; |
---|
| 1575 | divrem32 (H, B, bufQ, R, M); |
---|
| 1576 | |
---|
| 1577 | Q *= xToM; |
---|
| 1578 | Q += bufQ; |
---|
| 1579 | return; |
---|
| 1580 | } |
---|
| 1581 | |
---|
| 1582 | static inline |
---|
[806c18] | 1583 | void divrem32 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
| 1584 | CanonicalForm& R, const CFList& M) |
---|
[ad3c3ff] | 1585 | { |
---|
| 1586 | CanonicalForm A= mod (F, M); |
---|
| 1587 | CanonicalForm B= mod (G, M); |
---|
| 1588 | Variable x= Variable (1); |
---|
| 1589 | int degB= degree (B, x); |
---|
| 1590 | int degA= degree (A, x); |
---|
[806c18] | 1591 | if (degA < degB) |
---|
[ad3c3ff] | 1592 | { |
---|
| 1593 | Q= 0; |
---|
| 1594 | R= A; |
---|
| 1595 | return; |
---|
| 1596 | } |
---|
| 1597 | ASSERT (3*(degB/2) > degA, "expected degree (F, 1) < 3*(degree (G, 1)/2)"); |
---|
| 1598 | if (degB < 1) |
---|
| 1599 | { |
---|
| 1600 | divrem (A, B, Q, R); |
---|
| 1601 | Q= mod (Q, M); |
---|
| 1602 | R= mod (R, M); |
---|
| 1603 | return; |
---|
| 1604 | } |
---|
| 1605 | int m= (int) ceil ((double) (degB + 1)/ 2.0); |
---|
| 1606 | |
---|
| 1607 | CFList splitA= split (A, m, x); |
---|
| 1608 | CFList splitB= split (B, m, x); |
---|
| 1609 | |
---|
| 1610 | if (splitA.length() == 2) |
---|
| 1611 | { |
---|
| 1612 | splitA.insert (0); |
---|
| 1613 | } |
---|
| 1614 | if (splitA.length() == 1) |
---|
| 1615 | { |
---|
| 1616 | splitA.insert (0); |
---|
| 1617 | splitA.insert (0); |
---|
| 1618 | } |
---|
| 1619 | CanonicalForm xToM= power (x, m); |
---|
| 1620 | |
---|
| 1621 | CanonicalForm H; |
---|
| 1622 | CFListIterator i= splitA; |
---|
| 1623 | i++; |
---|
| 1624 | |
---|
| 1625 | if (degree (splitA.getFirst(), x) < degree (splitB.getFirst(), x)) |
---|
| 1626 | { |
---|
| 1627 | H= splitA.getFirst()*xToM + i.getItem(); |
---|
| 1628 | divrem21 (H, splitB.getFirst(), Q, R, M); |
---|
| 1629 | } |
---|
[806c18] | 1630 | else |
---|
[ad3c3ff] | 1631 | { |
---|
[806c18] | 1632 | R= splitA.getFirst()*xToM + i.getItem() + splitB.getFirst() - |
---|
[ad3c3ff] | 1633 | splitB.getFirst()*xToM; |
---|
| 1634 | Q= xToM - 1; |
---|
| 1635 | } |
---|
| 1636 | |
---|
| 1637 | H= mulMod (Q, splitB.getLast(), M); |
---|
| 1638 | |
---|
| 1639 | R= R*xToM + splitA.getLast() - H; |
---|
| 1640 | |
---|
| 1641 | while (degree (R, x) >= degB) |
---|
| 1642 | { |
---|
| 1643 | xToM= power (x, degree (R, x) - degB); |
---|
| 1644 | Q += LC (R, x)*xToM; |
---|
| 1645 | R -= mulMod (LC (R, x), B, M)*xToM; |
---|
| 1646 | Q= mod (Q, M); |
---|
| 1647 | R= mod (R, M); |
---|
| 1648 | } |
---|
| 1649 | |
---|
| 1650 | return; |
---|
| 1651 | } |
---|
| 1652 | |
---|
| 1653 | void divrem2 (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
[806c18] | 1654 | CanonicalForm& R, const CanonicalForm& M) |
---|
[ad3c3ff] | 1655 | { |
---|
| 1656 | CanonicalForm A= mod (F, M); |
---|
| 1657 | CanonicalForm B= mod (G, M); |
---|
[e368746] | 1658 | |
---|
| 1659 | if (B.inCoeffDomain()) |
---|
| 1660 | { |
---|
| 1661 | divrem (A, B, Q, R); |
---|
| 1662 | return; |
---|
| 1663 | } |
---|
| 1664 | if (A.inCoeffDomain() && !B.inCoeffDomain()) |
---|
| 1665 | { |
---|
| 1666 | Q= 0; |
---|
| 1667 | R= A; |
---|
| 1668 | return; |
---|
| 1669 | } |
---|
| 1670 | |
---|
| 1671 | if (B.level() < A.level()) |
---|
| 1672 | { |
---|
| 1673 | divrem (A, B, Q, R); |
---|
| 1674 | return; |
---|
| 1675 | } |
---|
| 1676 | if (A.level() > B.level()) |
---|
| 1677 | { |
---|
| 1678 | R= A; |
---|
| 1679 | Q= 0; |
---|
| 1680 | return; |
---|
| 1681 | } |
---|
| 1682 | if (B.level() == 1 && B.isUnivariate()) |
---|
| 1683 | { |
---|
| 1684 | divrem (A, B, Q, R); |
---|
| 1685 | return; |
---|
| 1686 | } |
---|
| 1687 | if (!(B.level() == 1 && B.isUnivariate()) && (A.level() == 1 && A.isUnivariate())) |
---|
| 1688 | { |
---|
| 1689 | Q= 0; |
---|
| 1690 | R= A; |
---|
| 1691 | return; |
---|
| 1692 | } |
---|
| 1693 | |
---|
[ad3c3ff] | 1694 | Variable x= Variable (1); |
---|
| 1695 | int degB= degree (B, x); |
---|
[806c18] | 1696 | if (degB > degree (A, x)) |
---|
[ad3c3ff] | 1697 | { |
---|
| 1698 | Q= 0; |
---|
| 1699 | R= A; |
---|
| 1700 | return; |
---|
| 1701 | } |
---|
| 1702 | |
---|
| 1703 | CFList splitA= split (A, degB, x); |
---|
| 1704 | |
---|
| 1705 | CanonicalForm xToDegB= power (x, degB); |
---|
| 1706 | CanonicalForm H, bufQ; |
---|
| 1707 | Q= 0; |
---|
| 1708 | CFListIterator i= splitA; |
---|
| 1709 | H= i.getItem()*xToDegB; |
---|
| 1710 | i++; |
---|
| 1711 | H += i.getItem(); |
---|
| 1712 | CFList buf; |
---|
[806c18] | 1713 | while (i.hasItem()) |
---|
[ad3c3ff] | 1714 | { |
---|
| 1715 | buf= CFList (M); |
---|
| 1716 | divrem21 (H, B, bufQ, R, buf); |
---|
| 1717 | i++; |
---|
| 1718 | if (i.hasItem()) |
---|
| 1719 | H= R*xToDegB + i.getItem(); |
---|
| 1720 | Q *= xToDegB; |
---|
[806c18] | 1721 | Q += bufQ; |
---|
[ad3c3ff] | 1722 | } |
---|
| 1723 | return; |
---|
| 1724 | } |
---|
| 1725 | |
---|
| 1726 | void divrem (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& Q, |
---|
| 1727 | CanonicalForm& R, const CFList& MOD) |
---|
| 1728 | { |
---|
| 1729 | CanonicalForm A= mod (F, MOD); |
---|
| 1730 | CanonicalForm B= mod (G, MOD); |
---|
| 1731 | Variable x= Variable (1); |
---|
| 1732 | int degB= degree (B, x); |
---|
[806c18] | 1733 | if (degB > degree (A, x)) |
---|
[ad3c3ff] | 1734 | { |
---|
| 1735 | Q= 0; |
---|
| 1736 | R= A; |
---|
| 1737 | return; |
---|
| 1738 | } |
---|
| 1739 | |
---|
[d80a1a] | 1740 | if (degB <= 0) |
---|
[ad3c3ff] | 1741 | { |
---|
| 1742 | divrem (A, B, Q, R); |
---|
| 1743 | Q= mod (Q, MOD); |
---|
| 1744 | R= mod (R, MOD); |
---|
| 1745 | return; |
---|
| 1746 | } |
---|
| 1747 | CFList splitA= split (A, degB, x); |
---|
| 1748 | |
---|
| 1749 | CanonicalForm xToDegB= power (x, degB); |
---|
| 1750 | CanonicalForm H, bufQ; |
---|
| 1751 | Q= 0; |
---|
| 1752 | CFListIterator i= splitA; |
---|
| 1753 | H= i.getItem()*xToDegB; |
---|
| 1754 | i++; |
---|
| 1755 | H += i.getItem(); |
---|
[806c18] | 1756 | while (i.hasItem()) |
---|
[ad3c3ff] | 1757 | { |
---|
| 1758 | divrem21 (H, B, bufQ, R, MOD); |
---|
| 1759 | i++; |
---|
| 1760 | if (i.hasItem()) |
---|
| 1761 | H= R*xToDegB + i.getItem(); |
---|
| 1762 | Q *= xToDegB; |
---|
[806c18] | 1763 | Q += bufQ; |
---|
[ad3c3ff] | 1764 | } |
---|
| 1765 | return; |
---|
| 1766 | } |
---|
| 1767 | |
---|
[806c18] | 1768 | void sortList (CFList& list, const Variable& x) |
---|
| 1769 | { |
---|
[ad3c3ff] | 1770 | int l= 1; |
---|
| 1771 | int k= 1; |
---|
| 1772 | CanonicalForm buf; |
---|
| 1773 | CFListIterator m; |
---|
[806c18] | 1774 | for (CFListIterator i= list; l <= list.length(); i++, l++) |
---|
[ad3c3ff] | 1775 | { |
---|
[806c18] | 1776 | for (CFListIterator j= list; k <= list.length() - l; k++) |
---|
[ad3c3ff] | 1777 | { |
---|
| 1778 | m= j; |
---|
| 1779 | m++; |
---|
[806c18] | 1780 | if (degree (j.getItem(), x) > degree (m.getItem(), x)) |
---|
[ad3c3ff] | 1781 | { |
---|
| 1782 | buf= m.getItem(); |
---|
| 1783 | m.getItem()= j.getItem(); |
---|
| 1784 | j.getItem()= buf; |
---|
| 1785 | j++; |
---|
| 1786 | j.getItem()= m.getItem(); |
---|
[806c18] | 1787 | } |
---|
[ad3c3ff] | 1788 | else |
---|
| 1789 | j++; |
---|
| 1790 | } |
---|
| 1791 | k= 1; |
---|
| 1792 | } |
---|
| 1793 | } |
---|
| 1794 | |
---|
| 1795 | static inline |
---|
[806c18] | 1796 | CFList diophantine (const CanonicalForm& F, const CFList& factors) |
---|
[ad3c3ff] | 1797 | { |
---|
[4a05ed] | 1798 | if (getCharacteristic() == 0) |
---|
| 1799 | { |
---|
| 1800 | Variable v; |
---|
| 1801 | bool hasAlgVar= hasFirstAlgVar (F, v); |
---|
| 1802 | for (CFListIterator i= factors; i.hasItem() && !hasAlgVar; i++) |
---|
| 1803 | hasAlgVar= hasFirstAlgVar (i.getItem(), v); |
---|
| 1804 | if (hasAlgVar) |
---|
| 1805 | { |
---|
| 1806 | CFList result= modularDiophant (F, factors, getMipo (v)); |
---|
| 1807 | return result; |
---|
| 1808 | } |
---|
| 1809 | } |
---|
| 1810 | |
---|
[ad3c3ff] | 1811 | CanonicalForm buf1, buf2, buf3, S, T; |
---|
| 1812 | CFListIterator i= factors; |
---|
| 1813 | CFList result; |
---|
| 1814 | if (i.hasItem()) |
---|
| 1815 | i++; |
---|
[806c18] | 1816 | buf1= F/factors.getFirst(); |
---|
[ad3c3ff] | 1817 | buf2= divNTL (F, i.getItem()); |
---|
| 1818 | buf3= extgcd (buf1, buf2, S, T); |
---|
| 1819 | result.append (S); |
---|
| 1820 | result.append (T); |
---|
| 1821 | if (i.hasItem()) |
---|
| 1822 | i++; |
---|
| 1823 | for (; i.hasItem(); i++) |
---|
| 1824 | { |
---|
| 1825 | buf1= divNTL (F, i.getItem()); |
---|
| 1826 | buf3= extgcd (buf3, buf1, S, T); |
---|
| 1827 | CFListIterator k= factors; |
---|
| 1828 | for (CFListIterator j= result; j.hasItem(); j++, k++) |
---|
| 1829 | { |
---|
| 1830 | j.getItem()= mulNTL (j.getItem(), S); |
---|
| 1831 | j.getItem()= modNTL (j.getItem(), k.getItem()); |
---|
| 1832 | } |
---|
| 1833 | result.append (T); |
---|
| 1834 | } |
---|
| 1835 | return result; |
---|
| 1836 | } |
---|
| 1837 | |
---|
[806c18] | 1838 | void |
---|
| 1839 | henselStep12 (const CanonicalForm& F, const CFList& factors, |
---|
[ad3c3ff] | 1840 | CFArray& bufFactors, const CFList& diophant, CFMatrix& M, |
---|
| 1841 | CFArray& Pi, int j) |
---|
| 1842 | { |
---|
| 1843 | CanonicalForm E; |
---|
| 1844 | CanonicalForm xToJ= power (F.mvar(), j); |
---|
| 1845 | Variable x= F.mvar(); |
---|
| 1846 | // compute the error |
---|
| 1847 | if (j == 1) |
---|
[806c18] | 1848 | E= F[j]; |
---|
[ad3c3ff] | 1849 | else |
---|
| 1850 | { |
---|
[806c18] | 1851 | if (degree (Pi [factors.length() - 2], x) > 0) |
---|
[ad3c3ff] | 1852 | E= F[j] - Pi [factors.length() - 2] [j]; |
---|
| 1853 | else |
---|
[806c18] | 1854 | E= F[j]; |
---|
[ad3c3ff] | 1855 | } |
---|
| 1856 | |
---|
| 1857 | CFArray buf= CFArray (diophant.length()); |
---|
| 1858 | bufFactors[0]= mod (factors.getFirst(), power (F.mvar(), j + 1)); |
---|
| 1859 | int k= 0; |
---|
| 1860 | CanonicalForm remainder; |
---|
| 1861 | // actual lifting |
---|
[806c18] | 1862 | for (CFListIterator i= diophant; i.hasItem(); i++, k++) |
---|
[ad3c3ff] | 1863 | { |
---|
| 1864 | if (degree (bufFactors[k], x) > 0) |
---|
| 1865 | { |
---|
| 1866 | if (k > 0) |
---|
| 1867 | remainder= modNTL (E, bufFactors[k] [0]); |
---|
| 1868 | else |
---|
| 1869 | remainder= E; |
---|
| 1870 | } |
---|
| 1871 | else |
---|
| 1872 | remainder= modNTL (E, bufFactors[k]); |
---|
| 1873 | |
---|
| 1874 | buf[k]= mulNTL (i.getItem(), remainder); |
---|
| 1875 | if (degree (bufFactors[k], x) > 0) |
---|
| 1876 | buf[k]= modNTL (buf[k], bufFactors[k] [0]); |
---|
[806c18] | 1877 | else |
---|
| 1878 | buf[k]= modNTL (buf[k], bufFactors[k]); |
---|
[ad3c3ff] | 1879 | } |
---|
| 1880 | for (k= 1; k < factors.length(); k++) |
---|
| 1881 | bufFactors[k] += xToJ*buf[k]; |
---|
| 1882 | |
---|
| 1883 | // update Pi [0] |
---|
| 1884 | int degBuf0= degree (bufFactors[0], x); |
---|
| 1885 | int degBuf1= degree (bufFactors[1], x); |
---|
| 1886 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 1887 | M (j + 1, 1)= mulNTL (bufFactors[0] [j], bufFactors[1] [j]); |
---|
| 1888 | CanonicalForm uIZeroJ; |
---|
| 1889 | if (j == 1) |
---|
| 1890 | { |
---|
| 1891 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 1892 | uIZeroJ= mulNTL ((bufFactors[0] [0] + bufFactors[0] [j]), |
---|
| 1893 | (bufFactors[1] [0] + buf[1])) - M(1, 1) - M(j + 1, 1); |
---|
| 1894 | else if (degBuf0 > 0) |
---|
| 1895 | uIZeroJ= mulNTL (bufFactors[0] [j], bufFactors[1]); |
---|
| 1896 | else if (degBuf1 > 0) |
---|
| 1897 | uIZeroJ= mulNTL (bufFactors[0], buf[1]); |
---|
| 1898 | else |
---|
| 1899 | uIZeroJ= 0; |
---|
[806c18] | 1900 | Pi [0] += xToJ*uIZeroJ; |
---|
| 1901 | } |
---|
[ad3c3ff] | 1902 | else |
---|
| 1903 | { |
---|
| 1904 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 1905 | uIZeroJ= mulNTL ((bufFactors[0] [0] + bufFactors[0] [j]), |
---|
| 1906 | (bufFactors[1] [0] + buf[1])) - M(1, 1) - M(j + 1, 1); |
---|
| 1907 | else if (degBuf0 > 0) |
---|
| 1908 | uIZeroJ= mulNTL (bufFactors[0] [j], bufFactors[1]); |
---|
| 1909 | else if (degBuf1 > 0) |
---|
| 1910 | uIZeroJ= mulNTL (bufFactors[0], buf[1]); |
---|
| 1911 | else |
---|
| 1912 | uIZeroJ= 0; |
---|
[806c18] | 1913 | Pi [0] += xToJ*uIZeroJ; |
---|
[ad3c3ff] | 1914 | } |
---|
| 1915 | CFArray tmp= CFArray (factors.length() - 1); |
---|
| 1916 | for (k= 0; k < factors.length() - 1; k++) |
---|
| 1917 | tmp[k]= 0; |
---|
| 1918 | CFIterator one, two; |
---|
| 1919 | one= bufFactors [0]; |
---|
| 1920 | two= bufFactors [1]; |
---|
| 1921 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 1922 | { |
---|
| 1923 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
[806c18] | 1924 | { |
---|
[ad3c3ff] | 1925 | if (k != j - k + 1) |
---|
| 1926 | { |
---|
[e368746] | 1927 | if ((one.hasTerms() && one.exp() == j - k + 1) && (two.hasTerms() && two.exp() == j - k + 1)) |
---|
[806c18] | 1928 | { |
---|
| 1929 | tmp[0] += mulNTL ((bufFactors[0] [k] + one.coeff()), (bufFactors[1] [k] + |
---|
[ad3c3ff] | 1930 | two.coeff())) - M (k + 1, 1) - M (j - k + 2, 1); |
---|
[806c18] | 1931 | one++; |
---|
| 1932 | two++; |
---|
| 1933 | } |
---|
[e368746] | 1934 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
[806c18] | 1935 | { |
---|
| 1936 | tmp[0] += mulNTL ((bufFactors[0] [k] + one.coeff()), bufFactors[1] [k]) - |
---|
[ad3c3ff] | 1937 | M (k + 1, 1); |
---|
[806c18] | 1938 | one++; |
---|
| 1939 | } |
---|
[e368746] | 1940 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
[806c18] | 1941 | { |
---|
| 1942 | tmp[0] += mulNTL (bufFactors[0] [k], (bufFactors[1] [k] + two.coeff())) - |
---|
[ad3c3ff] | 1943 | M (k + 1, 1); |
---|
[806c18] | 1944 | two++; |
---|
| 1945 | } |
---|
[ad3c3ff] | 1946 | } |
---|
| 1947 | else |
---|
| 1948 | { |
---|
[806c18] | 1949 | tmp[0] += M (k + 1, 1); |
---|
[ad3c3ff] | 1950 | } |
---|
| 1951 | } |
---|
| 1952 | } |
---|
| 1953 | Pi [0] += tmp[0]*xToJ*F.mvar(); |
---|
| 1954 | |
---|
[806c18] | 1955 | // update Pi [l] |
---|
[ad3c3ff] | 1956 | int degPi, degBuf; |
---|
[806c18] | 1957 | for (int l= 1; l < factors.length() - 1; l++) |
---|
[ad3c3ff] | 1958 | { |
---|
| 1959 | degPi= degree (Pi [l - 1], x); |
---|
| 1960 | degBuf= degree (bufFactors[l + 1], x); |
---|
| 1961 | if (degPi > 0 && degBuf > 0) |
---|
[806c18] | 1962 | M (j + 1, l + 1)= mulNTL (Pi [l - 1] [j], bufFactors[l + 1] [j]); |
---|
[ad3c3ff] | 1963 | if (j == 1) |
---|
| 1964 | { |
---|
| 1965 | if (degPi > 0 && degBuf > 0) |
---|
| 1966 | Pi [l] += xToJ*(mulNTL (Pi [l - 1] [0] + Pi [l - 1] [j], |
---|
[806c18] | 1967 | bufFactors[l + 1] [0] + buf[l + 1]) - M (j + 1, l +1) - |
---|
[ad3c3ff] | 1968 | M (1, l + 1)); |
---|
| 1969 | else if (degPi > 0) |
---|
| 1970 | Pi [l] += xToJ*(mulNTL (Pi [l - 1] [j], bufFactors[l + 1])); |
---|
| 1971 | else if (degBuf > 0) |
---|
| 1972 | Pi [l] += xToJ*(mulNTL (Pi [l - 1], buf[l + 1])); |
---|
| 1973 | } |
---|
| 1974 | else |
---|
| 1975 | { |
---|
| 1976 | if (degPi > 0 && degBuf > 0) |
---|
| 1977 | { |
---|
| 1978 | uIZeroJ= mulNTL (uIZeroJ, bufFactors [l + 1] [0]); |
---|
[806c18] | 1979 | uIZeroJ += mulNTL (Pi [l - 1] [0], buf [l + 1]); |
---|
[ad3c3ff] | 1980 | } |
---|
| 1981 | else if (degPi > 0) |
---|
| 1982 | uIZeroJ= mulNTL (uIZeroJ, bufFactors [l + 1]); |
---|
| 1983 | else if (degBuf > 0) |
---|
| 1984 | { |
---|
| 1985 | uIZeroJ= mulNTL (uIZeroJ, bufFactors [l + 1] [0]); |
---|
| 1986 | uIZeroJ += mulNTL (Pi [l - 1], buf[l + 1]); |
---|
| 1987 | } |
---|
| 1988 | Pi[l] += xToJ*uIZeroJ; |
---|
| 1989 | } |
---|
| 1990 | one= bufFactors [l + 1]; |
---|
| 1991 | two= Pi [l - 1]; |
---|
[e368746] | 1992 | if (two.hasTerms() && two.exp() == j + 1) |
---|
[ad3c3ff] | 1993 | { |
---|
| 1994 | if (degBuf > 0 && degPi > 0) |
---|
| 1995 | { |
---|
[806c18] | 1996 | tmp[l] += mulNTL (two.coeff(), bufFactors[l + 1][0]); |
---|
| 1997 | two++; |
---|
[ad3c3ff] | 1998 | } |
---|
| 1999 | else if (degPi > 0) |
---|
[806c18] | 2000 | { |
---|
| 2001 | tmp[l] += mulNTL (two.coeff(), bufFactors[l + 1]); |
---|
| 2002 | two++; |
---|
| 2003 | } |
---|
[ad3c3ff] | 2004 | } |
---|
[806c18] | 2005 | if (degBuf > 0 && degPi > 0) |
---|
[ad3c3ff] | 2006 | { |
---|
| 2007 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
[806c18] | 2008 | { |
---|
| 2009 | if (k != j - k + 1) |
---|
| 2010 | { |
---|
[c1b9927] | 2011 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
[e368746] | 2012 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
[806c18] | 2013 | { |
---|
| 2014 | tmp[l] += mulNTL ((bufFactors[l + 1] [k] + one.coeff()), (Pi[l - 1] [k] + |
---|
[ad3c3ff] | 2015 | two.coeff())) - M (k + 1, l + 1) - M (j - k + 2, l + 1); |
---|
[806c18] | 2016 | one++; |
---|
| 2017 | two++; |
---|
| 2018 | } |
---|
[e368746] | 2019 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
[806c18] | 2020 | { |
---|
| 2021 | tmp[l] += mulNTL ((bufFactors[l + 1] [k] + one.coeff()), Pi[l - 1] [k]) - |
---|
| 2022 | M (k + 1, l + 1); |
---|
| 2023 | one++; |
---|
| 2024 | } |
---|
[e368746] | 2025 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
[806c18] | 2026 | { |
---|
| 2027 | tmp[l] += mulNTL (bufFactors[l + 1] [k], (Pi[l - 1] [k] + two.coeff())) - |
---|
[ad3c3ff] | 2028 | M (k + 1, l + 1); |
---|
[806c18] | 2029 | two++; |
---|
| 2030 | } |
---|
| 2031 | } |
---|
| 2032 | else |
---|
| 2033 | tmp[l] += M (k + 1, l + 1); |
---|
| 2034 | } |
---|
| 2035 | } |
---|
[ad3c3ff] | 2036 | Pi[l] += tmp[l]*xToJ*F.mvar(); |
---|
| 2037 | } |
---|
| 2038 | return; |
---|
| 2039 | } |
---|
| 2040 | |
---|
[806c18] | 2041 | void |
---|
| 2042 | henselLift12 (const CanonicalForm& F, CFList& factors, int l, CFArray& Pi, |
---|
[e368746] | 2043 | CFList& diophant, CFMatrix& M, bool sort) |
---|
[ad3c3ff] | 2044 | { |
---|
[e368746] | 2045 | if (sort) |
---|
| 2046 | sortList (factors, Variable (1)); |
---|
[ad3c3ff] | 2047 | Pi= CFArray (factors.length() - 1); |
---|
| 2048 | CFListIterator j= factors; |
---|
| 2049 | diophant= diophantine (F[0], factors); |
---|
| 2050 | DEBOUTLN (cerr, "diophant= " << diophant); |
---|
| 2051 | j++; |
---|
| 2052 | Pi [0]= mulNTL (j.getItem(), mod (factors.getFirst(), F.mvar())); |
---|
| 2053 | M (1, 1)= Pi [0]; |
---|
| 2054 | int i= 1; |
---|
| 2055 | if (j.hasItem()) |
---|
| 2056 | j++; |
---|
[c1b9927] | 2057 | for (; j.hasItem(); j++, i++) |
---|
[ad3c3ff] | 2058 | { |
---|
| 2059 | Pi [i]= mulNTL (Pi [i - 1], j.getItem()); |
---|
| 2060 | M (1, i + 1)= Pi [i]; |
---|
| 2061 | } |
---|
| 2062 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 2063 | i= 0; |
---|
| 2064 | for (CFListIterator k= factors; k.hasItem(); i++, k++) |
---|
| 2065 | { |
---|
| 2066 | if (i == 0) |
---|
| 2067 | bufFactors[i]= mod (k.getItem(), F.mvar()); |
---|
| 2068 | else |
---|
| 2069 | bufFactors[i]= k.getItem(); |
---|
| 2070 | } |
---|
| 2071 | for (i= 1; i < l; i++) |
---|
| 2072 | henselStep12 (F, factors, bufFactors, diophant, M, Pi, i); |
---|
| 2073 | |
---|
| 2074 | CFListIterator k= factors; |
---|
| 2075 | for (i= 0; i < factors.length (); i++, k++) |
---|
| 2076 | k.getItem()= bufFactors[i]; |
---|
| 2077 | factors.removeFirst(); |
---|
| 2078 | return; |
---|
| 2079 | } |
---|
| 2080 | |
---|
[806c18] | 2081 | void |
---|
[ad3c3ff] | 2082 | henselLiftResume12 (const CanonicalForm& F, CFList& factors, int start, int |
---|
| 2083 | end, CFArray& Pi, const CFList& diophant, CFMatrix& M) |
---|
| 2084 | { |
---|
| 2085 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 2086 | int i= 0; |
---|
| 2087 | CanonicalForm xToStart= power (F.mvar(), start); |
---|
| 2088 | for (CFListIterator k= factors; k.hasItem(); k++, i++) |
---|
| 2089 | { |
---|
| 2090 | if (i == 0) |
---|
| 2091 | bufFactors[i]= mod (k.getItem(), xToStart); |
---|
| 2092 | else |
---|
| 2093 | bufFactors[i]= k.getItem(); |
---|
| 2094 | } |
---|
| 2095 | for (i= start; i < end; i++) |
---|
[806c18] | 2096 | henselStep12 (F, factors, bufFactors, diophant, M, Pi, i); |
---|
| 2097 | |
---|
[ad3c3ff] | 2098 | CFListIterator k= factors; |
---|
| 2099 | for (i= 0; i < factors.length(); k++, i++) |
---|
| 2100 | k.getItem()= bufFactors [i]; |
---|
| 2101 | factors.removeFirst(); |
---|
[806c18] | 2102 | return; |
---|
| 2103 | } |
---|
[ad3c3ff] | 2104 | |
---|
| 2105 | static inline |
---|
| 2106 | CFList |
---|
| 2107 | biDiophantine (const CanonicalForm& F, const CFList& factors, const int d) |
---|
| 2108 | { |
---|
| 2109 | Variable y= F.mvar(); |
---|
| 2110 | CFList result; |
---|
| 2111 | if (y.level() == 1) |
---|
| 2112 | { |
---|
| 2113 | result= diophantine (F, factors); |
---|
| 2114 | return result; |
---|
| 2115 | } |
---|
| 2116 | else |
---|
| 2117 | { |
---|
| 2118 | CFList buf= factors; |
---|
| 2119 | for (CFListIterator i= buf; i.hasItem(); i++) |
---|
| 2120 | i.getItem()= mod (i.getItem(), y); |
---|
| 2121 | CanonicalForm A= mod (F, y); |
---|
| 2122 | int bufD= 1; |
---|
| 2123 | CFList recResult= biDiophantine (A, buf, bufD); |
---|
| 2124 | CanonicalForm e= 1; |
---|
| 2125 | CFList p; |
---|
| 2126 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 2127 | CanonicalForm yToD= power (y, d); |
---|
| 2128 | int k= 0; |
---|
| 2129 | for (CFListIterator i= factors; i.hasItem(); i++, k++) |
---|
| 2130 | { |
---|
| 2131 | bufFactors [k]= i.getItem(); |
---|
| 2132 | } |
---|
[21b8f4c] | 2133 | CanonicalForm b, quot; |
---|
[ad3c3ff] | 2134 | for (k= 0; k < factors.length(); k++) //TODO compute b's faster |
---|
| 2135 | { |
---|
| 2136 | b= 1; |
---|
[21b8f4c] | 2137 | if (fdivides (bufFactors[k], F, quot)) |
---|
| 2138 | b= quot; |
---|
[806c18] | 2139 | else |
---|
[ad3c3ff] | 2140 | { |
---|
[806c18] | 2141 | for (int l= 0; l < factors.length(); l++) |
---|
| 2142 | { |
---|
| 2143 | if (l == k) |
---|
| 2144 | continue; |
---|
| 2145 | else |
---|
| 2146 | { |
---|
| 2147 | b= mulMod2 (b, bufFactors[l], yToD); |
---|
| 2148 | } |
---|
| 2149 | } |
---|
[ad3c3ff] | 2150 | } |
---|
| 2151 | p.append (b); |
---|
[806c18] | 2152 | } |
---|
[ad3c3ff] | 2153 | |
---|
| 2154 | CFListIterator j= p; |
---|
| 2155 | for (CFListIterator i= recResult; i.hasItem(); i++, j++) |
---|
| 2156 | e -= i.getItem()*j.getItem(); |
---|
| 2157 | |
---|
| 2158 | if (e.isZero()) |
---|
[806c18] | 2159 | return recResult; |
---|
[ad3c3ff] | 2160 | CanonicalForm coeffE; |
---|
| 2161 | CFList s; |
---|
| 2162 | result= recResult; |
---|
| 2163 | CanonicalForm g; |
---|
| 2164 | for (int i= 1; i < d; i++) |
---|
| 2165 | { |
---|
| 2166 | if (degree (e, y) > 0) |
---|
| 2167 | coeffE= e[i]; |
---|
| 2168 | else |
---|
| 2169 | coeffE= 0; |
---|
| 2170 | if (!coeffE.isZero()) |
---|
| 2171 | { |
---|
[806c18] | 2172 | CFListIterator k= result; |
---|
| 2173 | CFListIterator l= p; |
---|
[ad3c3ff] | 2174 | int ii= 0; |
---|
[806c18] | 2175 | j= recResult; |
---|
| 2176 | for (; j.hasItem(); j++, k++, l++, ii++) |
---|
| 2177 | { |
---|
| 2178 | g= coeffE*j.getItem(); |
---|
[ad3c3ff] | 2179 | if (degree (bufFactors[ii], y) <= 0) |
---|
| 2180 | g= mod (g, bufFactors[ii]); |
---|
| 2181 | else |
---|
| 2182 | g= mod (g, bufFactors[ii][0]); |
---|
[806c18] | 2183 | k.getItem() += g*power (y, i); |
---|
| 2184 | e -= mulMod2 (g*power(y, i), l.getItem(), yToD); |
---|
| 2185 | DEBOUTLN (cerr, "mod (e, power (y, i + 1))= " << |
---|
[ad3c3ff] | 2186 | mod (e, power (y, i + 1))); |
---|
[806c18] | 2187 | } |
---|
| 2188 | } |
---|
[ad3c3ff] | 2189 | if (e.isZero()) |
---|
| 2190 | break; |
---|
| 2191 | } |
---|
| 2192 | |
---|
| 2193 | DEBOUTLN (cerr, "mod (e, y)= " << mod (e, y)); |
---|
| 2194 | |
---|
| 2195 | #ifdef DEBUGOUTPUT |
---|
| 2196 | CanonicalForm test= 0; |
---|
[806c18] | 2197 | j= p; |
---|
[ad3c3ff] | 2198 | for (CFListIterator i= result; i.hasItem(); i++, j++) |
---|
| 2199 | test += mod (i.getItem()*j.getItem(), power (y, d)); |
---|
| 2200 | DEBOUTLN (cerr, "test= " << test); |
---|
| 2201 | #endif |
---|
| 2202 | return result; |
---|
| 2203 | } |
---|
| 2204 | } |
---|
| 2205 | |
---|
| 2206 | static inline |
---|
| 2207 | CFList |
---|
[806c18] | 2208 | multiRecDiophantine (const CanonicalForm& F, const CFList& factors, |
---|
[ad3c3ff] | 2209 | const CFList& recResult, const CFList& M, const int d) |
---|
| 2210 | { |
---|
| 2211 | Variable y= F.mvar(); |
---|
| 2212 | CFList result; |
---|
| 2213 | CFListIterator i; |
---|
| 2214 | CanonicalForm e= 1; |
---|
| 2215 | CFListIterator j= factors; |
---|
| 2216 | CFList p; |
---|
| 2217 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 2218 | CanonicalForm yToD= power (y, d); |
---|
| 2219 | int k= 0; |
---|
| 2220 | for (CFListIterator i= factors; i.hasItem(); i++, k++) |
---|
| 2221 | bufFactors [k]= i.getItem(); |
---|
[21b8f4c] | 2222 | CanonicalForm b, quot; |
---|
[ad3c3ff] | 2223 | CFList buf= M; |
---|
| 2224 | buf.removeLast(); |
---|
| 2225 | buf.append (yToD); |
---|
| 2226 | for (k= 0; k < factors.length(); k++) //TODO compute b's faster |
---|
| 2227 | { |
---|
| 2228 | b= 1; |
---|
[21b8f4c] | 2229 | if (fdivides (bufFactors[k], F, quot)) |
---|
| 2230 | b= quot; |
---|
[806c18] | 2231 | else |
---|
[ad3c3ff] | 2232 | { |
---|
| 2233 | for (int l= 0; l < factors.length(); l++) |
---|
| 2234 | { |
---|
[806c18] | 2235 | if (l == k) |
---|
| 2236 | continue; |
---|
| 2237 | else |
---|
| 2238 | { |
---|
| 2239 | b= mulMod (b, bufFactors[l], buf); |
---|
| 2240 | } |
---|
[ad3c3ff] | 2241 | } |
---|
| 2242 | } |
---|
| 2243 | p.append (b); |
---|
[806c18] | 2244 | } |
---|
[ad3c3ff] | 2245 | j= p; |
---|
| 2246 | for (CFListIterator i= recResult; i.hasItem(); i++, j++) |
---|
| 2247 | e -= mulMod (i.getItem(), j.getItem(), M); |
---|
| 2248 | |
---|
| 2249 | if (e.isZero()) |
---|
[806c18] | 2250 | return recResult; |
---|
[ad3c3ff] | 2251 | CanonicalForm coeffE; |
---|
| 2252 | CFList s; |
---|
| 2253 | result= recResult; |
---|
| 2254 | CanonicalForm g; |
---|
| 2255 | for (int i= 1; i < d; i++) |
---|
| 2256 | { |
---|
| 2257 | if (degree (e, y) > 0) |
---|
| 2258 | coeffE= e[i]; |
---|
| 2259 | else |
---|
| 2260 | coeffE= 0; |
---|
| 2261 | if (!coeffE.isZero()) |
---|
| 2262 | { |
---|
| 2263 | CFListIterator k= result; |
---|
| 2264 | CFListIterator l= p; |
---|
| 2265 | j= recResult; |
---|
| 2266 | int ii= 0; |
---|
| 2267 | CanonicalForm dummy; |
---|
| 2268 | for (; j.hasItem(); j++, k++, l++, ii++) |
---|
| 2269 | { |
---|
[806c18] | 2270 | g= mulMod (coeffE, j.getItem(), M); |
---|
| 2271 | if (degree (bufFactors[ii], y) <= 0) |
---|
| 2272 | divrem (g, mod (bufFactors[ii], Variable (y.level() - 1)), dummy, |
---|
[ad3c3ff] | 2273 | g, M); |
---|
[806c18] | 2274 | else |
---|
| 2275 | divrem (g, bufFactors[ii][0], dummy, g, M); |
---|
| 2276 | k.getItem() += g*power (y, i); |
---|
| 2277 | e -= mulMod (g*power (y, i), l.getItem(), M); |
---|
| 2278 | } |
---|
[ad3c3ff] | 2279 | } |
---|
[806c18] | 2280 | |
---|
[ad3c3ff] | 2281 | if (e.isZero()) |
---|
| 2282 | break; |
---|
| 2283 | } |
---|
| 2284 | |
---|
| 2285 | #ifdef DEBUGOUTPUT |
---|
| 2286 | CanonicalForm test= 0; |
---|
[806c18] | 2287 | j= p; |
---|
[ad3c3ff] | 2288 | for (CFListIterator i= result; i.hasItem(); i++, j++) |
---|
| 2289 | test += mod (i.getItem()*j.getItem(), power (y, d)); |
---|
| 2290 | DEBOUTLN (cerr, "test= " << test); |
---|
| 2291 | #endif |
---|
| 2292 | return result; |
---|
| 2293 | } |
---|
| 2294 | |
---|
| 2295 | static inline |
---|
[806c18] | 2296 | void |
---|
| 2297 | henselStep (const CanonicalForm& F, const CFList& factors, CFArray& bufFactors, |
---|
| 2298 | const CFList& diophant, CFMatrix& M, CFArray& Pi, int j, |
---|
| 2299 | const CFList& MOD) |
---|
[ad3c3ff] | 2300 | { |
---|
[c4f4fd] | 2301 | CanonicalForm E; |
---|
| 2302 | CanonicalForm xToJ= power (F.mvar(), j); |
---|
| 2303 | Variable x= F.mvar(); |
---|
| 2304 | // compute the error |
---|
| 2305 | if (j == 1) |
---|
[ad3c3ff] | 2306 | { |
---|
[c4f4fd] | 2307 | E= F[j]; |
---|
[806c18] | 2308 | #ifdef DEBUGOUTPUT |
---|
[c4f4fd] | 2309 | CanonicalForm test= 1; |
---|
| 2310 | for (int i= 0; i < factors.length(); i++) |
---|
[ad3c3ff] | 2311 | { |
---|
[c4f4fd] | 2312 | if (i == 0) |
---|
| 2313 | test= mulMod (test, mod (bufFactors [i], xToJ), MOD); |
---|
| 2314 | else |
---|
| 2315 | test= mulMod (test, bufFactors[i], MOD); |
---|
[ad3c3ff] | 2316 | } |
---|
[c4f4fd] | 2317 | CanonicalForm test2= mod (F-test, xToJ); |
---|
[139b67] | 2318 | |
---|
[c4f4fd] | 2319 | test2= mod (test2, MOD); |
---|
| 2320 | DEBOUTLN (cerr, "test= " << test2); |
---|
| 2321 | #endif |
---|
[806c18] | 2322 | } |
---|
[c4f4fd] | 2323 | else |
---|
[ad3c3ff] | 2324 | { |
---|
[806c18] | 2325 | #ifdef DEBUGOUTPUT |
---|
[c4f4fd] | 2326 | CanonicalForm test= 1; |
---|
| 2327 | for (int i= 0; i < factors.length(); i++) |
---|
[ad3c3ff] | 2328 | { |
---|
[c4f4fd] | 2329 | if (i == 0) |
---|
| 2330 | test *= mod (bufFactors [i], power (x, j)); |
---|
| 2331 | else |
---|
| 2332 | test *= bufFactors[i]; |
---|
[ad3c3ff] | 2333 | } |
---|
[c4f4fd] | 2334 | test= mod (test, power (x, j)); |
---|
| 2335 | test= mod (test, MOD); |
---|
| 2336 | CanonicalForm test2= mod (F, power (x, j - 1)) - mod (test, power (x, j-1)); |
---|
| 2337 | DEBOUTLN (cerr, "test= " << test2); |
---|
| 2338 | #endif |
---|
| 2339 | |
---|
| 2340 | if (degree (Pi [factors.length() - 2], x) > 0) |
---|
| 2341 | E= F[j] - Pi [factors.length() - 2] [j]; |
---|
| 2342 | else |
---|
| 2343 | E= F[j]; |
---|
[139b67] | 2344 | } |
---|
| 2345 | |
---|
| 2346 | CFArray buf= CFArray (diophant.length()); |
---|
| 2347 | bufFactors[0]= mod (factors.getFirst(), power (F.mvar(), j + 1)); |
---|
| 2348 | int k= 0; |
---|
| 2349 | // actual lifting |
---|
| 2350 | CanonicalForm dummy, rest1; |
---|
[806c18] | 2351 | for (CFListIterator i= diophant; i.hasItem(); i++, k++) |
---|
[139b67] | 2352 | { |
---|
[ad3c3ff] | 2353 | if (degree (bufFactors[k], x) > 0) |
---|
| 2354 | { |
---|
| 2355 | if (k > 0) |
---|
| 2356 | divrem (E, bufFactors[k] [0], dummy, rest1, MOD); |
---|
| 2357 | else |
---|
| 2358 | rest1= E; |
---|
| 2359 | } |
---|
| 2360 | else |
---|
| 2361 | divrem (E, bufFactors[k], dummy, rest1, MOD); |
---|
| 2362 | |
---|
| 2363 | buf[k]= mulMod (i.getItem(), rest1, MOD); |
---|
| 2364 | |
---|
| 2365 | if (degree (bufFactors[k], x) > 0) |
---|
| 2366 | divrem (buf[k], bufFactors[k] [0], dummy, buf[k], MOD); |
---|
[806c18] | 2367 | else |
---|
[ad3c3ff] | 2368 | divrem (buf[k], bufFactors[k], dummy, buf[k], MOD); |
---|
| 2369 | } |
---|
| 2370 | for (k= 1; k < factors.length(); k++) |
---|
| 2371 | bufFactors[k] += xToJ*buf[k]; |
---|
| 2372 | |
---|
| 2373 | // update Pi [0] |
---|
| 2374 | int degBuf0= degree (bufFactors[0], x); |
---|
| 2375 | int degBuf1= degree (bufFactors[1], x); |
---|
| 2376 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 2377 | M (j + 1, 1)= mulMod (bufFactors[0] [j], bufFactors[1] [j], MOD); |
---|
| 2378 | CanonicalForm uIZeroJ; |
---|
| 2379 | if (j == 1) |
---|
| 2380 | { |
---|
| 2381 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 2382 | uIZeroJ= mulMod ((bufFactors[0] [0] + bufFactors[0] [j]), |
---|
| 2383 | (bufFactors[1] [0] + buf[1]), MOD) - M(1, 1) - M(j + 1, 1); |
---|
| 2384 | else if (degBuf0 > 0) |
---|
| 2385 | uIZeroJ= mulMod (bufFactors[0] [j], bufFactors[1], MOD); |
---|
| 2386 | else if (degBuf1 > 0) |
---|
| 2387 | uIZeroJ= mulMod (bufFactors[0], buf[1], MOD); |
---|
| 2388 | else |
---|
| 2389 | uIZeroJ= 0; |
---|
[806c18] | 2390 | Pi [0] += xToJ*uIZeroJ; |
---|
| 2391 | } |
---|
[ad3c3ff] | 2392 | else |
---|
| 2393 | { |
---|
| 2394 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
[806c18] | 2395 | uIZeroJ= mulMod ((bufFactors[0] [0] + bufFactors[0] [j]), |
---|
[ad3c3ff] | 2396 | (bufFactors[1] [0] + buf[1]), MOD) - M(1, 1) - M(j + 1, 1); |
---|
| 2397 | else if (degBuf0 > 0) |
---|
| 2398 | uIZeroJ= mulMod (bufFactors[0] [j], bufFactors[1], MOD); |
---|
| 2399 | else if (degBuf1 > 0) |
---|
| 2400 | uIZeroJ= mulMod (bufFactors[0], buf[1], MOD); |
---|
| 2401 | else |
---|
| 2402 | uIZeroJ= 0; |
---|
[806c18] | 2403 | Pi [0] += xToJ*uIZeroJ; |
---|
[ad3c3ff] | 2404 | } |
---|
| 2405 | |
---|
| 2406 | CFArray tmp= CFArray (factors.length() - 1); |
---|
| 2407 | for (k= 0; k < factors.length() - 1; k++) |
---|
| 2408 | tmp[k]= 0; |
---|
| 2409 | CFIterator one, two; |
---|
| 2410 | one= bufFactors [0]; |
---|
| 2411 | two= bufFactors [1]; |
---|
| 2412 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 2413 | { |
---|
| 2414 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
[806c18] | 2415 | { |
---|
[ad3c3ff] | 2416 | if (k != j - k + 1) |
---|
| 2417 | { |
---|
[c1b9927] | 2418 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
[e368746] | 2419 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
[806c18] | 2420 | { |
---|
| 2421 | tmp[0] += mulMod ((bufFactors[0] [k] + one.coeff()), |
---|
| 2422 | (bufFactors[1] [k] + two.coeff()), MOD) - M (k + 1, 1) - |
---|
[ad3c3ff] | 2423 | M (j - k + 2, 1); |
---|
[806c18] | 2424 | one++; |
---|
| 2425 | two++; |
---|
| 2426 | } |
---|
[e368746] | 2427 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
[806c18] | 2428 | { |
---|
| 2429 | tmp[0] += mulMod ((bufFactors[0] [k] + one.coeff()), |
---|
[ad3c3ff] | 2430 | bufFactors[1] [k], MOD) - M (k + 1, 1); |
---|
[806c18] | 2431 | one++; |
---|
| 2432 | } |
---|
[e368746] | 2433 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
[806c18] | 2434 | { |
---|
| 2435 | tmp[0] += mulMod (bufFactors[0] [k], (bufFactors[1] [k] + |
---|
[ad3c3ff] | 2436 | two.coeff()), MOD) - M (k + 1, 1); |
---|
[806c18] | 2437 | two++; |
---|
| 2438 | } |
---|
[ad3c3ff] | 2439 | } |
---|
| 2440 | else |
---|
| 2441 | { |
---|
[806c18] | 2442 | tmp[0] += M (k + 1, 1); |
---|
[ad3c3ff] | 2443 | } |
---|
| 2444 | } |
---|
| 2445 | } |
---|
| 2446 | Pi [0] += tmp[0]*xToJ*F.mvar(); |
---|
| 2447 | |
---|
[806c18] | 2448 | // update Pi [l] |
---|
[ad3c3ff] | 2449 | int degPi, degBuf; |
---|
[806c18] | 2450 | for (int l= 1; l < factors.length() - 1; l++) |
---|
[ad3c3ff] | 2451 | { |
---|
| 2452 | degPi= degree (Pi [l - 1], x); |
---|
| 2453 | degBuf= degree (bufFactors[l + 1], x); |
---|
| 2454 | if (degPi > 0 && degBuf > 0) |
---|
[806c18] | 2455 | M (j + 1, l + 1)= mulMod (Pi [l - 1] [j], bufFactors[l + 1] [j], MOD); |
---|
[ad3c3ff] | 2456 | if (j == 1) |
---|
| 2457 | { |
---|
| 2458 | if (degPi > 0 && degBuf > 0) |
---|
[806c18] | 2459 | Pi [l] += xToJ*(mulMod ((Pi [l - 1] [0] + Pi [l - 1] [j]), |
---|
| 2460 | (bufFactors[l + 1] [0] + buf[l + 1]), MOD) - M (j + 1, l +1)- |
---|
[ad3c3ff] | 2461 | M (1, l + 1)); |
---|
| 2462 | else if (degPi > 0) |
---|
| 2463 | Pi [l] += xToJ*(mulMod (Pi [l - 1] [j], bufFactors[l + 1], MOD)); |
---|
| 2464 | else if (degBuf > 0) |
---|
| 2465 | Pi [l] += xToJ*(mulMod (Pi [l - 1], buf[l + 1], MOD)); |
---|
| 2466 | } |
---|
| 2467 | else |
---|
| 2468 | { |
---|
| 2469 | if (degPi > 0 && degBuf > 0) |
---|
| 2470 | { |
---|
| 2471 | uIZeroJ= mulMod (uIZeroJ, bufFactors [l + 1] [0], MOD); |
---|
[806c18] | 2472 | uIZeroJ += mulMod (Pi [l - 1] [0], buf [l + 1], MOD); |
---|
[ad3c3ff] | 2473 | } |
---|
| 2474 | else if (degPi > 0) |
---|
| 2475 | uIZeroJ= mulMod (uIZeroJ, bufFactors [l + 1], MOD); |
---|
| 2476 | else if (degBuf > 0) |
---|
| 2477 | { |
---|
| 2478 | uIZeroJ= mulMod (uIZeroJ, bufFactors [l + 1] [0], MOD); |
---|
| 2479 | uIZeroJ += mulMod (Pi [l - 1], buf[l + 1], MOD); |
---|
| 2480 | } |
---|
| 2481 | Pi[l] += xToJ*uIZeroJ; |
---|
| 2482 | } |
---|
| 2483 | one= bufFactors [l + 1]; |
---|
| 2484 | two= Pi [l - 1]; |
---|
[e368746] | 2485 | if (two.hasTerms() && two.exp() == j + 1) |
---|
[ad3c3ff] | 2486 | { |
---|
| 2487 | if (degBuf > 0 && degPi > 0) |
---|
| 2488 | { |
---|
[806c18] | 2489 | tmp[l] += mulMod (two.coeff(), bufFactors[l + 1][0], MOD); |
---|
| 2490 | two++; |
---|
[ad3c3ff] | 2491 | } |
---|
| 2492 | else if (degPi > 0) |
---|
[806c18] | 2493 | { |
---|
| 2494 | tmp[l] += mulMod (two.coeff(), bufFactors[l + 1], MOD); |
---|
| 2495 | two++; |
---|
| 2496 | } |
---|
[ad3c3ff] | 2497 | } |
---|
[806c18] | 2498 | if (degBuf > 0 && degPi > 0) |
---|
[ad3c3ff] | 2499 | { |
---|
| 2500 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
[806c18] | 2501 | { |
---|
| 2502 | if (k != j - k + 1) |
---|
| 2503 | { |
---|
[c1b9927] | 2504 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
[e368746] | 2505 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
[806c18] | 2506 | { |
---|
| 2507 | tmp[l] += mulMod ((bufFactors[l + 1] [k] + one.coeff()), |
---|
| 2508 | (Pi[l - 1] [k] + two.coeff()), MOD) - M (k + 1, l + 1) - |
---|
[ad3c3ff] | 2509 | M (j - k + 2, l + 1); |
---|
[806c18] | 2510 | one++; |
---|
| 2511 | two++; |
---|
| 2512 | } |
---|
[e368746] | 2513 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
[806c18] | 2514 | { |
---|
| 2515 | tmp[l] += mulMod ((bufFactors[l + 1] [k] + one.coeff()), |
---|
| 2516 | Pi[l - 1] [k], MOD) - M (k + 1, l + 1); |
---|
| 2517 | one++; |
---|
| 2518 | } |
---|
[e368746] | 2519 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
[806c18] | 2520 | { |
---|
| 2521 | tmp[l] += mulMod (bufFactors[l + 1] [k], |
---|
[ad3c3ff] | 2522 | (Pi[l - 1] [k] + two.coeff()), MOD) - M (k + 1, l + 1); |
---|
[806c18] | 2523 | two++; |
---|
| 2524 | } |
---|
| 2525 | } |
---|
| 2526 | else |
---|
| 2527 | tmp[l] += M (k + 1, l + 1); |
---|
| 2528 | } |
---|
| 2529 | } |
---|
[ad3c3ff] | 2530 | Pi[l] += tmp[l]*xToJ*F.mvar(); |
---|
| 2531 | } |
---|
| 2532 | |
---|
| 2533 | return; |
---|
| 2534 | } |
---|
| 2535 | |
---|
[806c18] | 2536 | CFList |
---|
[ad3c3ff] | 2537 | henselLift23 (const CFList& eval, const CFList& factors, const int* l, CFList& |
---|
| 2538 | diophant, CFArray& Pi, CFMatrix& M) |
---|
| 2539 | { |
---|
| 2540 | CFList buf= factors; |
---|
| 2541 | int k= 0; |
---|
| 2542 | int liftBoundBivar= l[k]; |
---|
| 2543 | diophant= biDiophantine (eval.getFirst(), buf, liftBoundBivar); |
---|
| 2544 | CFList MOD; |
---|
| 2545 | MOD.append (power (Variable (2), liftBoundBivar)); |
---|
| 2546 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 2547 | k= 0; |
---|
| 2548 | CFListIterator j= eval; |
---|
| 2549 | j++; |
---|
| 2550 | buf.removeFirst(); |
---|
| 2551 | buf.insert (LC (j.getItem(), 1)); |
---|
| 2552 | for (CFListIterator i= buf; i.hasItem(); i++, k++) |
---|
| 2553 | bufFactors[k]= i.getItem(); |
---|
| 2554 | Pi= CFArray (factors.length() - 1); |
---|
| 2555 | CFListIterator i= buf; |
---|
| 2556 | i++; |
---|
| 2557 | Variable y= j.getItem().mvar(); |
---|
| 2558 | Pi [0]= mulMod (i.getItem(), mod (buf.getFirst(), y), MOD); |
---|
| 2559 | M (1, 1)= Pi [0]; |
---|
| 2560 | k= 1; |
---|
| 2561 | if (i.hasItem()) |
---|
| 2562 | i++; |
---|
[c1b9927] | 2563 | for (; i.hasItem(); i++, k++) |
---|
[ad3c3ff] | 2564 | { |
---|
| 2565 | Pi [k]= mulMod (Pi [k - 1], i.getItem(), MOD); |
---|
| 2566 | M (1, k + 1)= Pi [k]; |
---|
| 2567 | } |
---|
| 2568 | |
---|
| 2569 | for (int d= 1; d < l[1]; d++) |
---|
| 2570 | henselStep (j.getItem(), buf, bufFactors, diophant, M, Pi, d, MOD); |
---|
| 2571 | CFList result; |
---|
| 2572 | for (k= 1; k < factors.length(); k++) |
---|
| 2573 | result.append (bufFactors[k]); |
---|
| 2574 | return result; |
---|
[806c18] | 2575 | } |
---|
[ad3c3ff] | 2576 | |
---|
[806c18] | 2577 | void |
---|
| 2578 | henselLiftResume (const CanonicalForm& F, CFList& factors, int start, int end, |
---|
| 2579 | CFArray& Pi, const CFList& diophant, CFMatrix& M, |
---|
[ad3c3ff] | 2580 | const CFList& MOD) |
---|
| 2581 | { |
---|
| 2582 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 2583 | int i= 0; |
---|
| 2584 | CanonicalForm xToStart= power (F.mvar(), start); |
---|
| 2585 | for (CFListIterator k= factors; k.hasItem(); k++, i++) |
---|
| 2586 | { |
---|
| 2587 | if (i == 0) |
---|
| 2588 | bufFactors[i]= mod (k.getItem(), xToStart); |
---|
| 2589 | else |
---|
| 2590 | bufFactors[i]= k.getItem(); |
---|
| 2591 | } |
---|
| 2592 | for (i= start; i < end; i++) |
---|
[806c18] | 2593 | henselStep (F, factors, bufFactors, diophant, M, Pi, i, MOD); |
---|
| 2594 | |
---|
[ad3c3ff] | 2595 | CFListIterator k= factors; |
---|
| 2596 | for (i= 0; i < factors.length(); k++, i++) |
---|
| 2597 | k.getItem()= bufFactors [i]; |
---|
| 2598 | factors.removeFirst(); |
---|
[806c18] | 2599 | return; |
---|
| 2600 | } |
---|
[ad3c3ff] | 2601 | |
---|
| 2602 | CFList |
---|
| 2603 | henselLift (const CFList& F, const CFList& factors, const CFList& MOD, CFList& |
---|
| 2604 | diophant, CFArray& Pi, CFMatrix& M, const int lOld, const int |
---|
| 2605 | lNew) |
---|
| 2606 | { |
---|
| 2607 | diophant= multiRecDiophantine (F.getFirst(), factors, diophant, MOD, lOld); |
---|
| 2608 | int k= 0; |
---|
| 2609 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 2610 | for (CFListIterator i= factors; i.hasItem(); i++, k++) |
---|
| 2611 | { |
---|
| 2612 | if (k == 0) |
---|
| 2613 | bufFactors[k]= LC (F.getLast(), 1); |
---|
| 2614 | else |
---|
| 2615 | bufFactors[k]= i.getItem(); |
---|
| 2616 | } |
---|
| 2617 | CFList buf= factors; |
---|
| 2618 | buf.removeFirst(); |
---|
| 2619 | buf.insert (LC (F.getLast(), 1)); |
---|
| 2620 | CFListIterator i= buf; |
---|
| 2621 | i++; |
---|
| 2622 | Variable y= F.getLast().mvar(); |
---|
| 2623 | Variable x= F.getFirst().mvar(); |
---|
| 2624 | CanonicalForm xToLOld= power (x, lOld); |
---|
| 2625 | Pi [0]= mod (Pi[0], xToLOld); |
---|
| 2626 | M (1, 1)= Pi [0]; |
---|
| 2627 | k= 1; |
---|
| 2628 | if (i.hasItem()) |
---|
| 2629 | i++; |
---|
[c1b9927] | 2630 | for (; i.hasItem(); i++, k++) |
---|
[ad3c3ff] | 2631 | { |
---|
| 2632 | Pi [k]= mod (Pi [k], xToLOld); |
---|
| 2633 | M (1, k + 1)= Pi [k]; |
---|
| 2634 | } |
---|
| 2635 | |
---|
| 2636 | for (int d= 1; d < lNew; d++) |
---|
| 2637 | henselStep (F.getLast(), buf, bufFactors, diophant, M, Pi, d, MOD); |
---|
| 2638 | CFList result; |
---|
| 2639 | for (k= 1; k < factors.length(); k++) |
---|
| 2640 | result.append (bufFactors[k]); |
---|
| 2641 | return result; |
---|
| 2642 | } |
---|
| 2643 | |
---|
| 2644 | CFList |
---|
| 2645 | henselLift (const CFList& eval, const CFList& factors, const int* l, const int |
---|
[e368746] | 2646 | lLength, bool sort) |
---|
[ad3c3ff] | 2647 | { |
---|
[806c18] | 2648 | CFList diophant; |
---|
| 2649 | CFList buf= factors; |
---|
[ad3c3ff] | 2650 | buf.insert (LC (eval.getFirst(), 1)); |
---|
[e368746] | 2651 | if (sort) |
---|
| 2652 | sortList (buf, Variable (1)); |
---|
[ad3c3ff] | 2653 | CFArray Pi; |
---|
| 2654 | CFMatrix M= CFMatrix (l[1], factors.length()); |
---|
| 2655 | CFList result= henselLift23 (eval, buf, l, diophant, Pi, M); |
---|
| 2656 | if (eval.length() == 2) |
---|
| 2657 | return result; |
---|
| 2658 | CFList MOD; |
---|
| 2659 | for (int i= 0; i < 2; i++) |
---|
| 2660 | MOD.append (power (Variable (i + 2), l[i])); |
---|
| 2661 | CFListIterator j= eval; |
---|
| 2662 | j++; |
---|
| 2663 | CFList bufEval; |
---|
| 2664 | bufEval.append (j.getItem()); |
---|
| 2665 | j++; |
---|
[806c18] | 2666 | |
---|
[ea88e0] | 2667 | for (int i= 2; i < lLength && j.hasItem(); i++, j++) |
---|
[ad3c3ff] | 2668 | { |
---|
| 2669 | result.insert (LC (bufEval.getFirst(), 1)); |
---|
| 2670 | bufEval.append (j.getItem()); |
---|
| 2671 | M= CFMatrix (l[i], factors.length()); |
---|
| 2672 | result= henselLift (bufEval, result, MOD, diophant, Pi, M, l[i - 1], l[i]); |
---|
| 2673 | MOD.append (power (Variable (i + 2), l[i])); |
---|
| 2674 | bufEval.removeFirst(); |
---|
| 2675 | } |
---|
[806c18] | 2676 | return result; |
---|
[ad3c3ff] | 2677 | } |
---|
| 2678 | |
---|
[08daea] | 2679 | void |
---|
| 2680 | henselStep122 (const CanonicalForm& F, const CFList& factors, |
---|
| 2681 | CFArray& bufFactors, const CFList& diophant, CFMatrix& M, |
---|
| 2682 | CFArray& Pi, int j, const CFArray& LCs) |
---|
| 2683 | { |
---|
| 2684 | Variable x= F.mvar(); |
---|
| 2685 | CanonicalForm xToJ= power (x, j); |
---|
| 2686 | |
---|
| 2687 | CanonicalForm E; |
---|
| 2688 | // compute the error |
---|
| 2689 | if (degree (Pi [factors.length() - 2], x) > 0) |
---|
| 2690 | E= F[j] - Pi [factors.length() - 2] [j]; |
---|
| 2691 | else |
---|
| 2692 | E= F[j]; |
---|
| 2693 | |
---|
| 2694 | CFArray buf= CFArray (diophant.length()); |
---|
| 2695 | |
---|
| 2696 | int k= 0; |
---|
| 2697 | CanonicalForm remainder; |
---|
| 2698 | // actual lifting |
---|
| 2699 | for (CFListIterator i= diophant; i.hasItem(); i++, k++) |
---|
| 2700 | { |
---|
| 2701 | if (degree (bufFactors[k], x) > 0) |
---|
| 2702 | remainder= modNTL (E, bufFactors[k] [0]); |
---|
| 2703 | else |
---|
| 2704 | remainder= modNTL (E, bufFactors[k]); |
---|
| 2705 | buf[k]= mulNTL (i.getItem(), remainder); |
---|
| 2706 | if (degree (bufFactors[k], x) > 0) |
---|
| 2707 | buf[k]= modNTL (buf[k], bufFactors[k] [0]); |
---|
| 2708 | else |
---|
[c1b9927] | 2709 | buf[k]= modNTL (buf[k], bufFactors[k]); |
---|
[08daea] | 2710 | } |
---|
| 2711 | |
---|
| 2712 | for (k= 0; k < factors.length(); k++) |
---|
| 2713 | bufFactors[k] += xToJ*buf[k]; |
---|
| 2714 | |
---|
| 2715 | // update Pi [0] |
---|
| 2716 | int degBuf0= degree (bufFactors[0], x); |
---|
| 2717 | int degBuf1= degree (bufFactors[1], x); |
---|
| 2718 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 2719 | { |
---|
| 2720 | M (j + 1, 1)= mulNTL (bufFactors[0] [j], bufFactors[1] [j]); |
---|
| 2721 | if (j + 2 <= M.rows()) |
---|
| 2722 | M (j + 2, 1)= mulNTL (bufFactors[0] [j + 1], bufFactors[1] [j + 1]); |
---|
| 2723 | } |
---|
| 2724 | CanonicalForm uIZeroJ; |
---|
| 2725 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 2726 | uIZeroJ= mulNTL(bufFactors[0][0],buf[1])+mulNTL (bufFactors[1][0], buf[0]); |
---|
| 2727 | else if (degBuf0 > 0) |
---|
| 2728 | uIZeroJ= mulNTL (buf[0], bufFactors[1]); |
---|
| 2729 | else if (degBuf1 > 0) |
---|
| 2730 | uIZeroJ= mulNTL (bufFactors[0], buf [1]); |
---|
| 2731 | else |
---|
| 2732 | uIZeroJ= 0; |
---|
| 2733 | Pi [0] += xToJ*uIZeroJ; |
---|
| 2734 | |
---|
| 2735 | CFArray tmp= CFArray (factors.length() - 1); |
---|
| 2736 | for (k= 0; k < factors.length() - 1; k++) |
---|
| 2737 | tmp[k]= 0; |
---|
| 2738 | CFIterator one, two; |
---|
| 2739 | one= bufFactors [0]; |
---|
| 2740 | two= bufFactors [1]; |
---|
| 2741 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 2742 | { |
---|
[1b8e048] | 2743 | while (one.hasTerms() && one.exp() > j) one++; |
---|
| 2744 | while (two.hasTerms() && two.exp() > j) two++; |
---|
[08daea] | 2745 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
| 2746 | { |
---|
[e368746] | 2747 | if (one.hasTerms() && two.hasTerms()) |
---|
[08daea] | 2748 | { |
---|
[e368746] | 2749 | if (k != j - k + 1) |
---|
| 2750 | { |
---|
| 2751 | if ((one.hasTerms() && one.exp() == j - k + 1) && + |
---|
| 2752 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
[08daea] | 2753 | { |
---|
| 2754 | tmp[0] += mulNTL ((bufFactors[0][k]+one.coeff()),(bufFactors[1][k] + |
---|
| 2755 | two.coeff())) - M (k + 1, 1) - M (j - k + 2, 1); |
---|
| 2756 | one++; |
---|
| 2757 | two++; |
---|
| 2758 | } |
---|
[e368746] | 2759 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
[08daea] | 2760 | { |
---|
| 2761 | tmp[0] += mulNTL ((bufFactors[0][k]+one.coeff()), bufFactors[1] [k]) - |
---|
| 2762 | M (k + 1, 1); |
---|
| 2763 | one++; |
---|
| 2764 | } |
---|
[e368746] | 2765 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
[08daea] | 2766 | { |
---|
| 2767 | tmp[0] += mulNTL (bufFactors[0][k],(bufFactors[1][k] + two.coeff())) - |
---|
| 2768 | M (k + 1, 1); |
---|
| 2769 | two++; |
---|
| 2770 | } |
---|
| 2771 | } |
---|
| 2772 | else |
---|
| 2773 | tmp[0] += M (k + 1, 1); |
---|
[e368746] | 2774 | } |
---|
[08daea] | 2775 | } |
---|
[1b8e048] | 2776 | } |
---|
[08daea] | 2777 | |
---|
[1b8e048] | 2778 | if (degBuf0 >= j + 1 && degBuf1 >= j + 1) |
---|
| 2779 | { |
---|
[08daea] | 2780 | if (j + 2 <= M.rows()) |
---|
[1b8e048] | 2781 | tmp [0] += mulNTL ((bufFactors [0] [j + 1]+ bufFactors [0] [0]), |
---|
| 2782 | (bufFactors [1] [j + 1] + bufFactors [1] [0])) |
---|
| 2783 | - M(1,1) - M (j + 2,1); |
---|
| 2784 | } |
---|
| 2785 | else if (degBuf0 >= j + 1) |
---|
| 2786 | { |
---|
| 2787 | if (degBuf1 > 0) |
---|
| 2788 | tmp[0] += mulNTL (bufFactors [0] [j+1], bufFactors [1] [0]); |
---|
| 2789 | else |
---|
| 2790 | tmp[0] += mulNTL (bufFactors [0] [j+1], bufFactors [1]); |
---|
| 2791 | } |
---|
| 2792 | else if (degBuf1 >= j + 1) |
---|
| 2793 | { |
---|
| 2794 | if (degBuf0 > 0) |
---|
| 2795 | tmp[0] += mulNTL (bufFactors [0] [0], bufFactors [1] [j + 1]); |
---|
| 2796 | else |
---|
| 2797 | tmp[0] += mulNTL (bufFactors [0], bufFactors [1] [j + 1]); |
---|
[08daea] | 2798 | } |
---|
[1b8e048] | 2799 | |
---|
[08daea] | 2800 | Pi [0] += tmp[0]*xToJ*F.mvar(); |
---|
[327efa2] | 2801 | |
---|
| 2802 | int degPi, degBuf; |
---|
| 2803 | for (int l= 1; l < factors.length() - 1; l++) |
---|
| 2804 | { |
---|
| 2805 | degPi= degree (Pi [l - 1], x); |
---|
| 2806 | degBuf= degree (bufFactors[l + 1], x); |
---|
| 2807 | if (degPi > 0 && degBuf > 0) |
---|
| 2808 | { |
---|
| 2809 | M (j + 1, l + 1)= mulNTL (Pi [l - 1] [j], bufFactors[l + 1] [j]); |
---|
| 2810 | if (j + 2 <= M.rows()) |
---|
| 2811 | M (j + 2, l + 1)= mulNTL (Pi [l - 1][j + 1], bufFactors[l + 1] [j + 1]); |
---|
| 2812 | } |
---|
| 2813 | |
---|
| 2814 | if (degPi > 0 && degBuf > 0) |
---|
| 2815 | uIZeroJ= mulNTL (Pi[l -1] [0], buf[l + 1]) + |
---|
| 2816 | mulNTL (uIZeroJ, bufFactors[l+1] [0]); |
---|
| 2817 | else if (degPi > 0) |
---|
| 2818 | uIZeroJ= mulNTL (uIZeroJ, bufFactors[l + 1]); |
---|
| 2819 | else if (degBuf > 0) |
---|
| 2820 | uIZeroJ= mulNTL (Pi[l - 1], buf[1]); |
---|
| 2821 | else |
---|
| 2822 | uIZeroJ= 0; |
---|
| 2823 | |
---|
| 2824 | Pi [l] += xToJ*uIZeroJ; |
---|
| 2825 | |
---|
| 2826 | one= bufFactors [l + 1]; |
---|
| 2827 | two= Pi [l - 1]; |
---|
| 2828 | if (degBuf > 0 && degPi > 0) |
---|
| 2829 | { |
---|
| 2830 | while (one.hasTerms() && one.exp() > j) one++; |
---|
| 2831 | while (two.hasTerms() && two.exp() > j) two++; |
---|
| 2832 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
| 2833 | { |
---|
| 2834 | if (k != j - k + 1) |
---|
| 2835 | { |
---|
| 2836 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
| 2837 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
| 2838 | { |
---|
| 2839 | tmp[l] += mulNTL ((bufFactors[l + 1] [k] + one.coeff()), |
---|
| 2840 | (Pi[l - 1] [k] + two.coeff())) - M (k + 1, l + 1) - |
---|
| 2841 | M (j - k + 2, l + 1); |
---|
| 2842 | one++; |
---|
| 2843 | two++; |
---|
| 2844 | } |
---|
| 2845 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
| 2846 | { |
---|
| 2847 | tmp[l] += mulNTL ((bufFactors[l + 1] [k] + one.coeff()), |
---|
| 2848 | Pi[l - 1] [k]) - M (k + 1, l + 1); |
---|
| 2849 | one++; |
---|
| 2850 | } |
---|
| 2851 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
| 2852 | { |
---|
| 2853 | tmp[l] += mulNTL (bufFactors[l + 1] [k], |
---|
| 2854 | (Pi[l - 1] [k] + two.coeff())) - M (k + 1, l + 1); |
---|
| 2855 | two++; |
---|
| 2856 | } |
---|
| 2857 | } |
---|
| 2858 | else |
---|
| 2859 | tmp[l] += M (k + 1, l + 1); |
---|
| 2860 | } |
---|
| 2861 | } |
---|
| 2862 | |
---|
| 2863 | if (degPi >= j + 1 && degBuf >= j + 1) |
---|
| 2864 | { |
---|
| 2865 | if (j + 2 <= M.rows()) |
---|
| 2866 | tmp [l] += mulNTL ((Pi [l - 1] [j + 1]+ Pi [l - 1] [0]), |
---|
| 2867 | (bufFactors [l + 1] [j + 1] + bufFactors [l + 1] [0]) |
---|
| 2868 | ) - M(1,l+1) - M (j + 2,l+1); |
---|
| 2869 | } |
---|
| 2870 | else if (degPi >= j + 1) |
---|
| 2871 | { |
---|
| 2872 | if (degBuf > 0) |
---|
| 2873 | tmp[l] += mulNTL (Pi [l - 1] [j+1], bufFactors [l + 1] [0]); |
---|
| 2874 | else |
---|
| 2875 | tmp[l] += mulNTL (Pi [l - 1] [j+1], bufFactors [l + 1]); |
---|
| 2876 | } |
---|
| 2877 | else if (degBuf >= j + 1) |
---|
| 2878 | { |
---|
| 2879 | if (degPi > 0) |
---|
| 2880 | tmp[l] += mulNTL (Pi [l - 1] [0], bufFactors [l + 1] [j + 1]); |
---|
| 2881 | else |
---|
| 2882 | tmp[l] += mulNTL (Pi [l - 1], bufFactors [l + 1] [j + 1]); |
---|
| 2883 | } |
---|
| 2884 | |
---|
| 2885 | Pi[l] += tmp[l]*xToJ*F.mvar(); |
---|
| 2886 | } |
---|
[08daea] | 2887 | return; |
---|
| 2888 | } |
---|
| 2889 | |
---|
| 2890 | void |
---|
| 2891 | henselLift122 (const CanonicalForm& F, CFList& factors, int l, CFArray& Pi, |
---|
| 2892 | CFList& diophant, CFMatrix& M, const CFArray& LCs, bool sort) |
---|
| 2893 | { |
---|
| 2894 | if (sort) |
---|
| 2895 | sortList (factors, Variable (1)); |
---|
| 2896 | Pi= CFArray (factors.length() - 2); |
---|
| 2897 | CFList bufFactors2= factors; |
---|
| 2898 | bufFactors2.removeFirst(); |
---|
[327efa2] | 2899 | diophant= diophantine (F[0], bufFactors2); |
---|
[08daea] | 2900 | DEBOUTLN (cerr, "diophant= " << diophant); |
---|
| 2901 | |
---|
| 2902 | CFArray bufFactors= CFArray (bufFactors2.length()); |
---|
| 2903 | int i= 0; |
---|
| 2904 | for (CFListIterator k= bufFactors2; k.hasItem(); i++, k++) |
---|
| 2905 | bufFactors[i]= replaceLc (k.getItem(), LCs [i]); |
---|
| 2906 | |
---|
| 2907 | Variable x= F.mvar(); |
---|
| 2908 | if (degree (bufFactors[0], x) > 0 && degree (bufFactors [1], x) > 0) |
---|
| 2909 | { |
---|
| 2910 | M (1, 1)= mulNTL (bufFactors [0] [0], bufFactors[1] [0]); |
---|
| 2911 | Pi [0]= M (1, 1) + (mulNTL (bufFactors [0] [1], bufFactors[1] [0]) + |
---|
| 2912 | mulNTL (bufFactors [0] [0], bufFactors [1] [1]))*x; |
---|
| 2913 | } |
---|
| 2914 | else if (degree (bufFactors[0], x) > 0) |
---|
| 2915 | { |
---|
| 2916 | M (1, 1)= mulNTL (bufFactors [0] [0], bufFactors[1]); |
---|
| 2917 | Pi [0]= M (1, 1) + |
---|
| 2918 | mulNTL (bufFactors [0] [1], bufFactors[1])*x; |
---|
| 2919 | } |
---|
| 2920 | else if (degree (bufFactors[1], x) > 0) |
---|
| 2921 | { |
---|
| 2922 | M (1, 1)= mulNTL (bufFactors [0], bufFactors[1] [0]); |
---|
| 2923 | Pi [0]= M (1, 1) + |
---|
| 2924 | mulNTL (bufFactors [0], bufFactors[1] [1])*x; |
---|
| 2925 | } |
---|
| 2926 | else |
---|
| 2927 | { |
---|
| 2928 | M (1, 1)= mulNTL (bufFactors [0], bufFactors[1]); |
---|
| 2929 | Pi [0]= M (1, 1); |
---|
| 2930 | } |
---|
| 2931 | |
---|
[327efa2] | 2932 | for (i= 1; i < Pi.size(); i++) |
---|
| 2933 | { |
---|
| 2934 | if (degree (Pi[i-1], x) > 0 && degree (bufFactors [i+1], x) > 0) |
---|
| 2935 | { |
---|
| 2936 | M (1,i+1)= mulNTL (Pi[i-1] [0], bufFactors[i+1] [0]); |
---|
| 2937 | Pi [i]= M (1,i+1) + (mulNTL (Pi[i-1] [1], bufFactors[i+1] [0]) + |
---|
| 2938 | mulNTL (Pi[i-1] [0], bufFactors [i+1] [1]))*x; |
---|
| 2939 | } |
---|
| 2940 | else if (degree (Pi[i-1], x) > 0) |
---|
| 2941 | { |
---|
| 2942 | M (1,i+1)= mulNTL (Pi[i-1] [0], bufFactors [i+1]); |
---|
| 2943 | Pi [i]= M(1,i+1) + mulNTL (Pi[i-1] [1], bufFactors[i+1])*x; |
---|
| 2944 | } |
---|
| 2945 | else if (degree (bufFactors[i+1], x) > 0) |
---|
| 2946 | { |
---|
| 2947 | M (1,i+1)= mulNTL (Pi[i-1], bufFactors [i+1] [0]); |
---|
| 2948 | Pi [i]= M (1,i+1) + mulNTL (Pi[i-1], bufFactors[i+1] [1])*x; |
---|
| 2949 | } |
---|
| 2950 | else |
---|
| 2951 | { |
---|
| 2952 | M (1,i+1)= mulNTL (Pi [i-1], bufFactors [i+1]); |
---|
| 2953 | Pi [i]= M (1,i+1); |
---|
| 2954 | } |
---|
| 2955 | } |
---|
| 2956 | |
---|
[08daea] | 2957 | for (i= 1; i < l; i++) |
---|
| 2958 | henselStep122 (F, bufFactors2, bufFactors, diophant, M, Pi, i, LCs); |
---|
| 2959 | |
---|
| 2960 | factors= CFList(); |
---|
| 2961 | for (i= 0; i < bufFactors.size(); i++) |
---|
| 2962 | factors.append (bufFactors[i]); |
---|
| 2963 | return; |
---|
| 2964 | } |
---|
| 2965 | |
---|
[327efa2] | 2966 | |
---|
[c1b9927] | 2967 | /// solve \f$ E=sum_{i= 1}^{r}{\sigma_{i}prod_{j=1, j\neq i}^{r}{f_{i}}}\f$ |
---|
[08daea] | 2968 | /// mod M, products contains \f$ prod_{j=1, j\neq i}^{r}{f_{i}}} \f$ |
---|
| 2969 | static inline |
---|
| 2970 | CFList |
---|
[c1b9927] | 2971 | diophantine (const CFList& recResult, const CFList& factors, |
---|
[e368746] | 2972 | const CFList& products, const CFList& M, const CanonicalForm& E, |
---|
| 2973 | bool& bad) |
---|
[08daea] | 2974 | { |
---|
| 2975 | if (M.isEmpty()) |
---|
| 2976 | { |
---|
| 2977 | CFList result; |
---|
| 2978 | CFListIterator j= factors; |
---|
| 2979 | CanonicalForm buf; |
---|
| 2980 | for (CFListIterator i= recResult; i.hasItem(); i++, j++) |
---|
| 2981 | { |
---|
| 2982 | ASSERT (E.isUnivariate() || E.inCoeffDomain(), |
---|
| 2983 | "constant or univariate poly expected"); |
---|
| 2984 | ASSERT (i.getItem().isUnivariate() || i.getItem().inCoeffDomain(), |
---|
| 2985 | "constant or univariate poly expected"); |
---|
| 2986 | ASSERT (j.getItem().isUnivariate() || j.getItem().inCoeffDomain(), |
---|
| 2987 | "constant or univariate poly expected"); |
---|
| 2988 | buf= mulNTL (E, i.getItem()); |
---|
| 2989 | result.append (modNTL (buf, j.getItem())); |
---|
| 2990 | } |
---|
| 2991 | return result; |
---|
| 2992 | } |
---|
| 2993 | Variable y= M.getLast().mvar(); |
---|
| 2994 | CFList bufFactors= factors; |
---|
| 2995 | for (CFListIterator i= bufFactors; i.hasItem(); i++) |
---|
| 2996 | i.getItem()= mod (i.getItem(), y); |
---|
| 2997 | CFList bufProducts= products; |
---|
| 2998 | for (CFListIterator i= bufProducts; i.hasItem(); i++) |
---|
| 2999 | i.getItem()= mod (i.getItem(), y); |
---|
| 3000 | CFList buf= M; |
---|
| 3001 | buf.removeLast(); |
---|
| 3002 | CanonicalForm bufE= mod (E, y); |
---|
| 3003 | CFList recDiophantine= diophantine (recResult, bufFactors, bufProducts, buf, |
---|
[e368746] | 3004 | bufE, bad); |
---|
| 3005 | |
---|
| 3006 | if (bad) |
---|
| 3007 | return CFList(); |
---|
[08daea] | 3008 | |
---|
| 3009 | CanonicalForm e= E; |
---|
| 3010 | CFListIterator j= products; |
---|
| 3011 | for (CFListIterator i= recDiophantine; i.hasItem(); i++, j++) |
---|
[e368746] | 3012 | e -= i.getItem()*j.getItem(); |
---|
[08daea] | 3013 | |
---|
| 3014 | CFList result= recDiophantine; |
---|
| 3015 | int d= degree (M.getLast()); |
---|
| 3016 | CanonicalForm coeffE; |
---|
| 3017 | for (int i= 1; i < d; i++) |
---|
| 3018 | { |
---|
| 3019 | if (degree (e, y) > 0) |
---|
| 3020 | coeffE= e[i]; |
---|
| 3021 | else |
---|
| 3022 | coeffE= 0; |
---|
| 3023 | if (!coeffE.isZero()) |
---|
| 3024 | { |
---|
| 3025 | CFListIterator k= result; |
---|
| 3026 | recDiophantine= diophantine (recResult, bufFactors, bufProducts, buf, |
---|
[e368746] | 3027 | coeffE, bad); |
---|
| 3028 | if (bad) |
---|
| 3029 | return CFList(); |
---|
[08daea] | 3030 | CFListIterator l= products; |
---|
| 3031 | for (j= recDiophantine; j.hasItem(); j++, k++, l++) |
---|
| 3032 | { |
---|
| 3033 | k.getItem() += j.getItem()*power (y, i); |
---|
[e368746] | 3034 | e -= j.getItem()*power (y, i)*l.getItem(); |
---|
[08daea] | 3035 | } |
---|
| 3036 | } |
---|
| 3037 | if (e.isZero()) |
---|
| 3038 | break; |
---|
| 3039 | } |
---|
[e368746] | 3040 | if (!e.isZero()) |
---|
[08daea] | 3041 | { |
---|
[e368746] | 3042 | bad= true; |
---|
| 3043 | return CFList(); |
---|
[08daea] | 3044 | } |
---|
| 3045 | return result; |
---|
| 3046 | } |
---|
| 3047 | |
---|
| 3048 | static inline |
---|
| 3049 | void |
---|
| 3050 | henselStep2 (const CanonicalForm& F, const CFList& factors, CFArray& bufFactors, |
---|
| 3051 | const CFList& diophant, CFMatrix& M, CFArray& Pi, |
---|
[e368746] | 3052 | const CFList& products, int j, const CFList& MOD, bool& noOneToOne) |
---|
[08daea] | 3053 | { |
---|
| 3054 | CanonicalForm E; |
---|
| 3055 | CanonicalForm xToJ= power (F.mvar(), j); |
---|
| 3056 | Variable x= F.mvar(); |
---|
| 3057 | |
---|
| 3058 | // compute the error |
---|
| 3059 | #ifdef DEBUGOUTPUT |
---|
| 3060 | CanonicalForm test= 1; |
---|
| 3061 | for (int i= 0; i < factors.length(); i++) |
---|
| 3062 | { |
---|
| 3063 | if (i == 0) |
---|
| 3064 | test *= mod (bufFactors [i], power (x, j)); |
---|
| 3065 | else |
---|
| 3066 | test *= bufFactors[i]; |
---|
| 3067 | } |
---|
| 3068 | test= mod (test, power (x, j)); |
---|
| 3069 | test= mod (test, MOD); |
---|
| 3070 | CanonicalForm test2= mod (F, power (x, j - 1)) - mod (test, power (x, j-1)); |
---|
| 3071 | DEBOUTLN (cerr, "test= " << test2); |
---|
| 3072 | #endif |
---|
| 3073 | |
---|
| 3074 | if (degree (Pi [factors.length() - 2], x) > 0) |
---|
| 3075 | E= F[j] - Pi [factors.length() - 2] [j]; |
---|
| 3076 | else |
---|
| 3077 | E= F[j]; |
---|
| 3078 | |
---|
| 3079 | CFArray buf= CFArray (diophant.length()); |
---|
| 3080 | |
---|
| 3081 | // actual lifting |
---|
[e368746] | 3082 | CFList diophantine2= diophantine (diophant, factors, products, MOD, E, |
---|
| 3083 | noOneToOne); |
---|
| 3084 | |
---|
| 3085 | if (noOneToOne) |
---|
| 3086 | return; |
---|
[08daea] | 3087 | |
---|
| 3088 | int k= 0; |
---|
| 3089 | for (CFListIterator i= diophantine2; k < factors.length(); k++, i++) |
---|
| 3090 | { |
---|
| 3091 | buf[k]= i.getItem(); |
---|
| 3092 | bufFactors[k] += xToJ*i.getItem(); |
---|
| 3093 | } |
---|
| 3094 | |
---|
| 3095 | // update Pi [0] |
---|
| 3096 | int degBuf0= degree (bufFactors[0], x); |
---|
| 3097 | int degBuf1= degree (bufFactors[1], x); |
---|
| 3098 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 3099 | { |
---|
| 3100 | M (j + 1, 1)= mulMod (bufFactors[0] [j], bufFactors[1] [j], MOD); |
---|
| 3101 | if (j + 2 <= M.rows()) |
---|
| 3102 | M (j + 2, 1)= mulMod (bufFactors[0] [j + 1], bufFactors[1] [j + 1], MOD); |
---|
| 3103 | } |
---|
| 3104 | CanonicalForm uIZeroJ; |
---|
| 3105 | |
---|
[1b8e048] | 3106 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 3107 | uIZeroJ= mulMod (bufFactors[0] [0], buf[1], MOD) + |
---|
| 3108 | mulMod (bufFactors[1] [0], buf[0], MOD); |
---|
| 3109 | else if (degBuf0 > 0) |
---|
| 3110 | uIZeroJ= mulMod (buf[0], bufFactors[1], MOD); |
---|
| 3111 | else if (degBuf1 > 0) |
---|
| 3112 | uIZeroJ= mulMod (bufFactors[0], buf[1], MOD); |
---|
| 3113 | else |
---|
| 3114 | uIZeroJ= 0; |
---|
[c1b9927] | 3115 | Pi [0] += xToJ*uIZeroJ; |
---|
[08daea] | 3116 | |
---|
| 3117 | CFArray tmp= CFArray (factors.length() - 1); |
---|
| 3118 | for (k= 0; k < factors.length() - 1; k++) |
---|
| 3119 | tmp[k]= 0; |
---|
| 3120 | CFIterator one, two; |
---|
| 3121 | one= bufFactors [0]; |
---|
| 3122 | two= bufFactors [1]; |
---|
| 3123 | if (degBuf0 > 0 && degBuf1 > 0) |
---|
| 3124 | { |
---|
[1b8e048] | 3125 | while (one.hasTerms() && one.exp() > j) one++; |
---|
| 3126 | while (two.hasTerms() && two.exp() > j) two++; |
---|
[08daea] | 3127 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
| 3128 | { |
---|
| 3129 | if (k != j - k + 1) |
---|
| 3130 | { |
---|
[c1b9927] | 3131 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
[e368746] | 3132 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
[08daea] | 3133 | { |
---|
| 3134 | tmp[0] += mulMod ((bufFactors[0] [k] + one.coeff()), |
---|
| 3135 | (bufFactors[1] [k] + two.coeff()), MOD) - M (k + 1, 1) - |
---|
| 3136 | M (j - k + 2, 1); |
---|
| 3137 | one++; |
---|
| 3138 | two++; |
---|
| 3139 | } |
---|
[e368746] | 3140 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
[08daea] | 3141 | { |
---|
| 3142 | tmp[0] += mulMod ((bufFactors[0] [k] + one.coeff()), |
---|
| 3143 | bufFactors[1] [k], MOD) - M (k + 1, 1); |
---|
| 3144 | one++; |
---|
| 3145 | } |
---|
[e368746] | 3146 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
[08daea] | 3147 | { |
---|
| 3148 | tmp[0] += mulMod (bufFactors[0] [k], (bufFactors[1] [k] + |
---|
| 3149 | two.coeff()), MOD) - M (k + 1, 1); |
---|
| 3150 | two++; |
---|
| 3151 | } |
---|
| 3152 | } |
---|
| 3153 | else |
---|
| 3154 | { |
---|
| 3155 | tmp[0] += M (k + 1, 1); |
---|
| 3156 | } |
---|
| 3157 | } |
---|
[1b8e048] | 3158 | } |
---|
[08daea] | 3159 | |
---|
[1b8e048] | 3160 | if (degBuf0 >= j + 1 && degBuf1 >= j + 1) |
---|
| 3161 | { |
---|
[08daea] | 3162 | if (j + 2 <= M.rows()) |
---|
[1b8e048] | 3163 | tmp [0] += mulMod ((bufFactors [0] [j + 1]+ bufFactors [0] [0]), |
---|
| 3164 | (bufFactors [1] [j + 1] + bufFactors [1] [0]), MOD) |
---|
| 3165 | - M(1,1) - M (j + 2,1); |
---|
| 3166 | } |
---|
| 3167 | else if (degBuf0 >= j + 1) |
---|
| 3168 | { |
---|
| 3169 | if (degBuf1 > 0) |
---|
| 3170 | tmp[0] += mulMod (bufFactors [0] [j+1], bufFactors [1] [0], MOD); |
---|
| 3171 | else |
---|
| 3172 | tmp[0] += mulMod (bufFactors [0] [j+1], bufFactors [1], MOD); |
---|
| 3173 | } |
---|
| 3174 | else if (degBuf1 >= j + 1) |
---|
| 3175 | { |
---|
| 3176 | if (degBuf0 > 0) |
---|
| 3177 | tmp[0] += mulMod (bufFactors [0] [0], bufFactors [1] [j + 1], MOD); |
---|
| 3178 | else |
---|
| 3179 | tmp[0] += mulMod (bufFactors [0], bufFactors [1] [j + 1], MOD); |
---|
[08daea] | 3180 | } |
---|
| 3181 | Pi [0] += tmp[0]*xToJ*F.mvar(); |
---|
| 3182 | |
---|
| 3183 | // update Pi [l] |
---|
| 3184 | int degPi, degBuf; |
---|
| 3185 | for (int l= 1; l < factors.length() - 1; l++) |
---|
| 3186 | { |
---|
| 3187 | degPi= degree (Pi [l - 1], x); |
---|
| 3188 | degBuf= degree (bufFactors[l + 1], x); |
---|
| 3189 | if (degPi > 0 && degBuf > 0) |
---|
| 3190 | { |
---|
[e368746] | 3191 | M (j + 1, l + 1)= mulMod (Pi [l - 1] [j], bufFactors[l + 1] [j], MOD); |
---|
| 3192 | if (j + 2 <= M.rows()) |
---|
| 3193 | M (j + 2, l + 1)= mulMod (Pi [l - 1] [j + 1], bufFactors[l + 1] [j + 1], |
---|
| 3194 | MOD); |
---|
[08daea] | 3195 | } |
---|
[e368746] | 3196 | |
---|
| 3197 | if (degPi > 0 && degBuf > 0) |
---|
| 3198 | uIZeroJ= mulMod (Pi[l -1] [0], buf[l + 1], MOD) + |
---|
| 3199 | mulMod (uIZeroJ, bufFactors[l+1] [0], MOD); |
---|
| 3200 | else if (degPi > 0) |
---|
| 3201 | uIZeroJ= mulMod (uIZeroJ, bufFactors[l + 1], MOD); |
---|
| 3202 | else if (degBuf > 0) |
---|
| 3203 | uIZeroJ= mulMod (Pi[l - 1], buf[1], MOD); |
---|
[08daea] | 3204 | else |
---|
[e368746] | 3205 | uIZeroJ= 0; |
---|
| 3206 | |
---|
| 3207 | Pi [l] += xToJ*uIZeroJ; |
---|
| 3208 | |
---|
[08daea] | 3209 | one= bufFactors [l + 1]; |
---|
| 3210 | two= Pi [l - 1]; |
---|
| 3211 | if (degBuf > 0 && degPi > 0) |
---|
| 3212 | { |
---|
[e368746] | 3213 | while (one.hasTerms() && one.exp() > j) one++; |
---|
| 3214 | while (two.hasTerms() && two.exp() > j) two++; |
---|
[08daea] | 3215 | for (k= 1; k <= (int) ceil (j/2.0); k++) |
---|
| 3216 | { |
---|
| 3217 | if (k != j - k + 1) |
---|
| 3218 | { |
---|
[e368746] | 3219 | if ((one.hasTerms() && one.exp() == j - k + 1) && |
---|
| 3220 | (two.hasTerms() && two.exp() == j - k + 1)) |
---|
[08daea] | 3221 | { |
---|
| 3222 | tmp[l] += mulMod ((bufFactors[l + 1] [k] + one.coeff()), |
---|
| 3223 | (Pi[l - 1] [k] + two.coeff()), MOD) - M (k + 1, l + 1) - |
---|
| 3224 | M (j - k + 2, l + 1); |
---|
| 3225 | one++; |
---|
| 3226 | two++; |
---|
| 3227 | } |
---|
[e368746] | 3228 | else if (one.hasTerms() && one.exp() == j - k + 1) |
---|
[08daea] | 3229 | { |
---|
| 3230 | tmp[l] += mulMod ((bufFactors[l + 1] [k] + one.coeff()), |
---|
| 3231 | Pi[l - 1] [k], MOD) - M (k + 1, l + 1); |
---|
| 3232 | one++; |
---|
| 3233 | } |
---|
[e368746] | 3234 | else if (two.hasTerms() && two.exp() == j - k + 1) |
---|
[08daea] | 3235 | { |
---|
[c1b9927] | 3236 | tmp[l] += mulMod (bufFactors[l + 1] [k], |
---|
[08daea] | 3237 | (Pi[l - 1] [k] + two.coeff()), MOD) - M (k + 1, l + 1); |
---|
| 3238 | two++; |
---|
[e368746] | 3239 | } |
---|
[08daea] | 3240 | } |
---|
| 3241 | else |
---|
| 3242 | tmp[l] += M (k + 1, l + 1); |
---|
| 3243 | } |
---|
| 3244 | } |
---|
[e368746] | 3245 | |
---|
| 3246 | if (degPi >= j + 1 && degBuf >= j + 1) |
---|
| 3247 | { |
---|
| 3248 | if (j + 2 <= M.rows()) |
---|
| 3249 | tmp [l] += mulMod ((Pi [l - 1] [j + 1]+ Pi [l - 1] [0]), |
---|
| 3250 | (bufFactors [l + 1] [j + 1] + bufFactors [l + 1] [0]) |
---|
| 3251 | , MOD) - M(1,l+1) - M (j + 2,l+1); |
---|
| 3252 | } |
---|
| 3253 | else if (degPi >= j + 1) |
---|
| 3254 | { |
---|
| 3255 | if (degBuf > 0) |
---|
| 3256 | tmp[l] += mulMod (Pi [l - 1] [j+1], bufFactors [l + 1] [0], MOD); |
---|
| 3257 | else |
---|
| 3258 | tmp[l] += mulMod (Pi [l - 1] [j+1], bufFactors [l + 1], MOD); |
---|
| 3259 | } |
---|
| 3260 | else if (degBuf >= j + 1) |
---|
| 3261 | { |
---|
| 3262 | if (degPi > 0) |
---|
| 3263 | tmp[l] += mulMod (Pi [l - 1] [0], bufFactors [l + 1] [j + 1], MOD); |
---|
| 3264 | else |
---|
| 3265 | tmp[l] += mulMod (Pi [l - 1], bufFactors [l + 1] [j + 1], MOD); |
---|
| 3266 | } |
---|
| 3267 | |
---|
[08daea] | 3268 | Pi[l] += tmp[l]*xToJ*F.mvar(); |
---|
| 3269 | } |
---|
| 3270 | return; |
---|
| 3271 | } |
---|
| 3272 | |
---|
| 3273 | // wrt. Variable (1) |
---|
| 3274 | CanonicalForm replaceLC (const CanonicalForm& F, const CanonicalForm& c) |
---|
| 3275 | { |
---|
| 3276 | if (degree (F, 1) <= 0) |
---|
| 3277 | return c; |
---|
| 3278 | else |
---|
| 3279 | { |
---|
| 3280 | CanonicalForm result= swapvar (F, Variable (F.level() + 1), Variable (1)); |
---|
| 3281 | result += (swapvar (c, Variable (F.level() + 1), Variable (1)) |
---|
| 3282 | - LC (result))*power (result.mvar(), degree (result)); |
---|
| 3283 | return swapvar (result, Variable (F.level() + 1), Variable (1)); |
---|
| 3284 | } |
---|
| 3285 | } |
---|
| 3286 | |
---|
| 3287 | CFList |
---|
| 3288 | henselLift232 (const CFList& eval, const CFList& factors, int* l, CFList& |
---|
| 3289 | diophant, CFArray& Pi, CFMatrix& M, const CFList& LCs1, |
---|
[e368746] | 3290 | const CFList& LCs2, bool& bad) |
---|
[08daea] | 3291 | { |
---|
| 3292 | CFList buf= factors; |
---|
| 3293 | int k= 0; |
---|
| 3294 | int liftBoundBivar= l[k]; |
---|
| 3295 | CFList bufbuf= factors; |
---|
| 3296 | Variable v= Variable (2); |
---|
| 3297 | |
---|
| 3298 | CFList MOD; |
---|
| 3299 | MOD.append (power (Variable (2), liftBoundBivar)); |
---|
| 3300 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 3301 | k= 0; |
---|
| 3302 | CFListIterator j= eval; |
---|
| 3303 | j++; |
---|
| 3304 | CFListIterator iter1= LCs1; |
---|
| 3305 | CFListIterator iter2= LCs2; |
---|
| 3306 | iter1++; |
---|
| 3307 | iter2++; |
---|
| 3308 | bufFactors[0]= replaceLC (buf.getFirst(), iter1.getItem()); |
---|
| 3309 | bufFactors[1]= replaceLC (buf.getLast(), iter2.getItem()); |
---|
| 3310 | |
---|
| 3311 | CFListIterator i= buf; |
---|
| 3312 | i++; |
---|
| 3313 | Variable y= j.getItem().mvar(); |
---|
| 3314 | if (y.level() != 3) |
---|
| 3315 | y= Variable (3); |
---|
| 3316 | |
---|
| 3317 | Pi[0]= mod (Pi[0], power (v, liftBoundBivar)); |
---|
| 3318 | M (1, 1)= Pi[0]; |
---|
| 3319 | if (degree (bufFactors[0], y) > 0 && degree (bufFactors [1], y) > 0) |
---|
| 3320 | Pi [0] += (mulMod (bufFactors [0] [1], bufFactors[1] [0], MOD) + |
---|
| 3321 | mulMod (bufFactors [0] [0], bufFactors [1] [1], MOD))*y; |
---|
| 3322 | else if (degree (bufFactors[0], y) > 0) |
---|
| 3323 | Pi [0] += mulMod (bufFactors [0] [1], bufFactors[1], MOD)*y; |
---|
| 3324 | else if (degree (bufFactors[1], y) > 0) |
---|
| 3325 | Pi [0] += mulMod (bufFactors [0], bufFactors[1] [1], MOD)*y; |
---|
| 3326 | |
---|
| 3327 | CFList products; |
---|
| 3328 | for (int i= 0; i < bufFactors.size(); i++) |
---|
| 3329 | { |
---|
| 3330 | if (degree (bufFactors[i], y) > 0) |
---|
[e368746] | 3331 | products.append (eval.getFirst()/bufFactors[i] [0]); |
---|
[08daea] | 3332 | else |
---|
[e368746] | 3333 | products.append (eval.getFirst()/bufFactors[i]); |
---|
[08daea] | 3334 | } |
---|
| 3335 | |
---|
| 3336 | for (int d= 1; d < l[1]; d++) |
---|
[e368746] | 3337 | { |
---|
| 3338 | henselStep2 (j.getItem(), buf, bufFactors, diophant, M, Pi, products, d, MOD, bad); |
---|
| 3339 | if (bad) |
---|
| 3340 | return CFList(); |
---|
| 3341 | } |
---|
[08daea] | 3342 | CFList result; |
---|
| 3343 | for (k= 0; k < factors.length(); k++) |
---|
| 3344 | result.append (bufFactors[k]); |
---|
| 3345 | return result; |
---|
| 3346 | } |
---|
| 3347 | |
---|
| 3348 | |
---|
| 3349 | CFList |
---|
| 3350 | henselLift2 (const CFList& F, const CFList& factors, const CFList& MOD, CFList& |
---|
| 3351 | diophant, CFArray& Pi, CFMatrix& M, const int lOld, int& |
---|
[e368746] | 3352 | lNew, const CFList& LCs1, const CFList& LCs2, bool& bad) |
---|
[08daea] | 3353 | { |
---|
| 3354 | int k= 0; |
---|
| 3355 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 3356 | bufFactors[0]= replaceLC (factors.getFirst(), LCs1.getLast()); |
---|
| 3357 | bufFactors[1]= replaceLC (factors.getLast(), LCs2.getLast()); |
---|
| 3358 | CFList buf= factors; |
---|
| 3359 | Variable y= F.getLast().mvar(); |
---|
| 3360 | Variable x= F.getFirst().mvar(); |
---|
| 3361 | CanonicalForm xToLOld= power (x, lOld); |
---|
| 3362 | Pi [0]= mod (Pi[0], xToLOld); |
---|
| 3363 | M (1, 1)= Pi [0]; |
---|
| 3364 | |
---|
| 3365 | if (degree (bufFactors[0], y) > 0 && degree (bufFactors [1], y) > 0) |
---|
[c1b9927] | 3366 | Pi [0] += (mulMod (bufFactors [0] [1], bufFactors[1] [0], MOD) + |
---|
[08daea] | 3367 | mulMod (bufFactors [0] [0], bufFactors [1] [1], MOD))*y; |
---|
| 3368 | else if (degree (bufFactors[0], y) > 0) |
---|
| 3369 | Pi [0] += mulMod (bufFactors [0] [1], bufFactors[1], MOD)*y; |
---|
| 3370 | else if (degree (bufFactors[1], y) > 0) |
---|
| 3371 | Pi [0] += mulMod (bufFactors [0], bufFactors[1] [1], MOD)*y; |
---|
| 3372 | |
---|
| 3373 | CFList products; |
---|
[21b8f4c] | 3374 | CanonicalForm quot; |
---|
[08daea] | 3375 | for (int i= 0; i < bufFactors.size(); i++) |
---|
| 3376 | { |
---|
| 3377 | if (degree (bufFactors[i], y) > 0) |
---|
| 3378 | { |
---|
[21b8f4c] | 3379 | if (!fdivides (bufFactors[i] [0], F.getFirst(), quot)) |
---|
[e368746] | 3380 | { |
---|
| 3381 | bad= true; |
---|
| 3382 | return CFList(); |
---|
| 3383 | } |
---|
[21b8f4c] | 3384 | products.append (quot); |
---|
[08daea] | 3385 | } |
---|
| 3386 | else |
---|
| 3387 | { |
---|
[21b8f4c] | 3388 | if (!fdivides (bufFactors[i], F.getFirst(), quot)) |
---|
[e368746] | 3389 | { |
---|
| 3390 | bad= true; |
---|
| 3391 | return CFList(); |
---|
| 3392 | } |
---|
[21b8f4c] | 3393 | products.append (quot); |
---|
[08daea] | 3394 | } |
---|
| 3395 | } |
---|
| 3396 | |
---|
| 3397 | for (int d= 1; d < lNew; d++) |
---|
[e368746] | 3398 | { |
---|
| 3399 | henselStep2 (F.getLast(), buf, bufFactors, diophant, M, Pi, products, d, MOD, bad); |
---|
| 3400 | if (bad) |
---|
| 3401 | return CFList(); |
---|
| 3402 | } |
---|
[08daea] | 3403 | |
---|
| 3404 | CFList result; |
---|
| 3405 | for (k= 0; k < factors.length(); k++) |
---|
| 3406 | result.append (bufFactors[k]); |
---|
| 3407 | return result; |
---|
| 3408 | } |
---|
| 3409 | |
---|
| 3410 | CFList |
---|
| 3411 | henselLift2 (const CFList& eval, const CFList& factors, int* l, const int |
---|
| 3412 | lLength, bool sort, const CFList& LCs1, const CFList& LCs2, |
---|
[e368746] | 3413 | const CFArray& Pi, const CFList& diophant, bool& bad) |
---|
[08daea] | 3414 | { |
---|
| 3415 | CFList bufDiophant= diophant; |
---|
| 3416 | CFList buf= factors; |
---|
| 3417 | if (sort) |
---|
| 3418 | sortList (buf, Variable (1)); |
---|
| 3419 | CFArray bufPi= Pi; |
---|
| 3420 | CFMatrix M= CFMatrix (l[1], factors.length()); |
---|
[e368746] | 3421 | CFList result= henselLift232(eval, buf, l, bufDiophant, bufPi, M, LCs1, LCs2, |
---|
| 3422 | bad); |
---|
| 3423 | if (bad) |
---|
| 3424 | return CFList(); |
---|
| 3425 | |
---|
[08daea] | 3426 | if (eval.length() == 2) |
---|
| 3427 | return result; |
---|
| 3428 | CFList MOD; |
---|
| 3429 | for (int i= 0; i < 2; i++) |
---|
| 3430 | MOD.append (power (Variable (i + 2), l[i])); |
---|
| 3431 | CFListIterator j= eval; |
---|
| 3432 | j++; |
---|
| 3433 | CFList bufEval; |
---|
| 3434 | bufEval.append (j.getItem()); |
---|
| 3435 | j++; |
---|
| 3436 | CFListIterator jj= LCs1; |
---|
| 3437 | CFListIterator jjj= LCs2; |
---|
| 3438 | CFList bufLCs1, bufLCs2; |
---|
| 3439 | jj++, jjj++; |
---|
| 3440 | bufLCs1.append (jj.getItem()); |
---|
| 3441 | bufLCs2.append (jjj.getItem()); |
---|
| 3442 | jj++, jjj++; |
---|
| 3443 | |
---|
[ea88e0] | 3444 | for (int i= 2; i < lLength && j.hasItem(); i++, j++, jj++, jjj++) |
---|
[08daea] | 3445 | { |
---|
| 3446 | bufEval.append (j.getItem()); |
---|
| 3447 | bufLCs1.append (jj.getItem()); |
---|
| 3448 | bufLCs2.append (jjj.getItem()); |
---|
| 3449 | M= CFMatrix (l[i], factors.length()); |
---|
| 3450 | result= henselLift2 (bufEval, result, MOD, bufDiophant, bufPi, M, l[i - 1], |
---|
[e368746] | 3451 | l[i], bufLCs1, bufLCs2, bad); |
---|
| 3452 | if (bad) |
---|
| 3453 | return CFList(); |
---|
[08daea] | 3454 | MOD.append (power (Variable (i + 2), l[i])); |
---|
| 3455 | bufEval.removeFirst(); |
---|
| 3456 | bufLCs1.removeFirst(); |
---|
| 3457 | bufLCs2.removeFirst(); |
---|
| 3458 | } |
---|
| 3459 | return result; |
---|
| 3460 | } |
---|
| 3461 | |
---|
[e368746] | 3462 | CFList |
---|
[c1b9927] | 3463 | nonMonicHenselLift23 (const CanonicalForm& F, const CFList& factors, const |
---|
[e368746] | 3464 | CFList& LCs, CFList& diophant, CFArray& Pi, int liftBound, |
---|
| 3465 | int bivarLiftBound, bool& bad) |
---|
| 3466 | { |
---|
| 3467 | CFList bufFactors2= factors; |
---|
| 3468 | |
---|
| 3469 | Variable y= Variable (2); |
---|
| 3470 | for (CFListIterator i= bufFactors2; i.hasItem(); i++) |
---|
| 3471 | i.getItem()= mod (i.getItem(), y); |
---|
| 3472 | |
---|
| 3473 | CanonicalForm bufF= F; |
---|
| 3474 | bufF= mod (bufF, y); |
---|
| 3475 | bufF= mod (bufF, Variable (3)); |
---|
| 3476 | |
---|
| 3477 | diophant= diophantine (bufF, bufFactors2); |
---|
| 3478 | |
---|
| 3479 | CFMatrix M= CFMatrix (liftBound, bufFactors2.length() - 1); |
---|
| 3480 | |
---|
| 3481 | Pi= CFArray (bufFactors2.length() - 1); |
---|
| 3482 | |
---|
| 3483 | CFArray bufFactors= CFArray (bufFactors2.length()); |
---|
| 3484 | CFListIterator j= LCs; |
---|
| 3485 | int i= 0; |
---|
| 3486 | for (CFListIterator k= factors; k.hasItem(); j++, k++, i++) |
---|
| 3487 | bufFactors[i]= replaceLC (k.getItem(), j.getItem()); |
---|
| 3488 | |
---|
| 3489 | //initialise Pi |
---|
| 3490 | Variable v= Variable (3); |
---|
| 3491 | CanonicalForm yToL= power (y, bivarLiftBound); |
---|
| 3492 | if (degree (bufFactors[0], v) > 0 && degree (bufFactors [1], v) > 0) |
---|
| 3493 | { |
---|
| 3494 | M (1, 1)= mulMod2 (bufFactors [0] [0], bufFactors[1] [0], yToL); |
---|
[c1b9927] | 3495 | Pi [0]= M (1,1) + (mulMod2 (bufFactors [0] [1], bufFactors[1] [0], yToL) + |
---|
[e368746] | 3496 | mulMod2 (bufFactors [0] [0], bufFactors [1] [1], yToL))*v; |
---|
| 3497 | } |
---|
| 3498 | else if (degree (bufFactors[0], v) > 0) |
---|
| 3499 | { |
---|
| 3500 | M (1,1)= mulMod2 (bufFactors [0] [0], bufFactors [1], yToL); |
---|
| 3501 | Pi [0]= M(1,1) + mulMod2 (bufFactors [0] [1], bufFactors[1], yToL)*v; |
---|
| 3502 | } |
---|
| 3503 | else if (degree (bufFactors[1], v) > 0) |
---|
| 3504 | { |
---|
| 3505 | M (1,1)= mulMod2 (bufFactors [0], bufFactors [1] [0], yToL); |
---|
| 3506 | Pi [0]= M (1,1) + mulMod2 (bufFactors [0], bufFactors[1] [1], yToL)*v; |
---|
| 3507 | } |
---|
| 3508 | else |
---|
| 3509 | { |
---|
| 3510 | M (1,1)= mulMod2 (bufFactors [0], bufFactors [1], yToL); |
---|
| 3511 | Pi [0]= M (1,1); |
---|
| 3512 | } |
---|
| 3513 | |
---|
| 3514 | for (i= 1; i < Pi.size(); i++) |
---|
| 3515 | { |
---|
| 3516 | if (degree (Pi[i-1], v) > 0 && degree (bufFactors [i+1], v) > 0) |
---|
| 3517 | { |
---|
| 3518 | M (1,i+1)= mulMod2 (Pi[i-1] [0], bufFactors[i+1] [0], yToL); |
---|
[c1b9927] | 3519 | Pi [i]= M (1,i+1) + (mulMod2 (Pi[i-1] [1], bufFactors[i+1] [0], yToL) + |
---|
[e368746] | 3520 | mulMod2 (Pi[i-1] [0], bufFactors [i+1] [1], yToL))*v; |
---|
| 3521 | } |
---|
| 3522 | else if (degree (Pi[i-1], v) > 0) |
---|
| 3523 | { |
---|
| 3524 | M (1,i+1)= mulMod2 (Pi[i-1] [0], bufFactors [i+1], yToL); |
---|
| 3525 | Pi [i]= M(1,i+1) + mulMod2 (Pi[i-1] [1], bufFactors[i+1], yToL)*v; |
---|
| 3526 | } |
---|
| 3527 | else if (degree (bufFactors[i+1], v) > 0) |
---|
| 3528 | { |
---|
| 3529 | M (1,i+1)= mulMod2 (Pi[i-1], bufFactors [i+1] [0], yToL); |
---|
| 3530 | Pi [i]= M (1,i+1) + mulMod2 (Pi[i-1], bufFactors[i+1] [1], yToL)*v; |
---|
| 3531 | } |
---|
| 3532 | else |
---|
| 3533 | { |
---|
| 3534 | M (1,i+1)= mulMod2 (Pi [i-1], bufFactors [i+1], yToL); |
---|
| 3535 | Pi [i]= M (1,i+1); |
---|
| 3536 | } |
---|
| 3537 | } |
---|
| 3538 | |
---|
| 3539 | CFList products; |
---|
| 3540 | bufF= mod (F, Variable (3)); |
---|
| 3541 | for (CFListIterator k= factors; k.hasItem(); k++) |
---|
| 3542 | products.append (bufF/k.getItem()); |
---|
| 3543 | |
---|
| 3544 | CFList MOD= CFList (power (v, liftBound)); |
---|
| 3545 | MOD.insert (yToL); |
---|
| 3546 | for (int d= 1; d < liftBound; d++) |
---|
| 3547 | { |
---|
| 3548 | henselStep2 (F, factors, bufFactors, diophant, M, Pi, products, d, MOD, bad); |
---|
| 3549 | if (bad) |
---|
| 3550 | return CFList(); |
---|
| 3551 | } |
---|
| 3552 | |
---|
| 3553 | CFList result; |
---|
| 3554 | for (i= 0; i < factors.length(); i++) |
---|
| 3555 | result.append (bufFactors[i]); |
---|
| 3556 | return result; |
---|
| 3557 | } |
---|
| 3558 | |
---|
| 3559 | CFList |
---|
| 3560 | nonMonicHenselLift (const CFList& F, const CFList& factors, const CFList& LCs, |
---|
| 3561 | CFList& diophant, CFArray& Pi, CFMatrix& M, const int lOld, |
---|
| 3562 | int& lNew, const CFList& MOD, bool& noOneToOne |
---|
| 3563 | ) |
---|
| 3564 | { |
---|
| 3565 | |
---|
| 3566 | int k= 0; |
---|
| 3567 | CFArray bufFactors= CFArray (factors.length()); |
---|
| 3568 | CFListIterator j= LCs; |
---|
| 3569 | for (CFListIterator i= factors; i.hasItem(); i++, j++, k++) |
---|
| 3570 | bufFactors [k]= replaceLC (i.getItem(), j.getItem()); |
---|
| 3571 | |
---|
| 3572 | Variable y= F.getLast().mvar(); |
---|
| 3573 | Variable x= F.getFirst().mvar(); |
---|
| 3574 | CanonicalForm xToLOld= power (x, lOld); |
---|
| 3575 | |
---|
| 3576 | Pi [0]= mod (Pi[0], xToLOld); |
---|
| 3577 | M (1, 1)= Pi [0]; |
---|
| 3578 | |
---|
| 3579 | if (degree (bufFactors[0], y) > 0 && degree (bufFactors [1], y) > 0) |
---|
[c1b9927] | 3580 | Pi [0] += (mulMod (bufFactors [0] [1], bufFactors[1] [0], MOD) + |
---|
[e368746] | 3581 | mulMod (bufFactors [0] [0], bufFactors [1] [1], MOD))*y; |
---|
| 3582 | else if (degree (bufFactors[0], y) > 0) |
---|
| 3583 | Pi [0] += mulMod (bufFactors [0] [1], bufFactors[1], MOD)*y; |
---|
| 3584 | else if (degree (bufFactors[1], y) > 0) |
---|
| 3585 | Pi [0] += mulMod (bufFactors [0], bufFactors[1] [1], MOD)*y; |
---|
| 3586 | |
---|
| 3587 | for (int i= 1; i < Pi.size(); i++) |
---|
| 3588 | { |
---|
| 3589 | Pi [i]= mod (Pi [i], xToLOld); |
---|
| 3590 | M (1, i + 1)= Pi [i]; |
---|
| 3591 | |
---|
| 3592 | if (degree (Pi[i-1], y) > 0 && degree (bufFactors [i+1], y) > 0) |
---|
| 3593 | Pi [i] += (mulMod (Pi[i-1] [1], bufFactors[i+1] [0], MOD) + |
---|
| 3594 | mulMod (Pi[i-1] [0], bufFactors [i+1] [1], MOD))*y; |
---|
| 3595 | else if (degree (Pi[i-1], y) > 0) |
---|
| 3596 | Pi [i] += mulMod (Pi[i-1] [1], bufFactors[i+1], MOD)*y; |
---|
| 3597 | else if (degree (bufFactors[i+1], y) > 0) |
---|
| 3598 | Pi [i] += mulMod (Pi[i-1], bufFactors[i+1] [1], MOD)*y; |
---|
| 3599 | } |
---|
| 3600 | |
---|
| 3601 | CFList products; |
---|
[21b8f4c] | 3602 | CanonicalForm quot, bufF= F.getFirst(); |
---|
[e368746] | 3603 | |
---|
| 3604 | for (int i= 0; i < bufFactors.size(); i++) |
---|
| 3605 | { |
---|
| 3606 | if (degree (bufFactors[i], y) > 0) |
---|
| 3607 | { |
---|
[21b8f4c] | 3608 | if (!fdivides (bufFactors[i] [0], bufF, quot)) |
---|
[e368746] | 3609 | { |
---|
| 3610 | noOneToOne= true; |
---|
| 3611 | return factors; |
---|
| 3612 | } |
---|
[21b8f4c] | 3613 | products.append (quot); |
---|
[e368746] | 3614 | } |
---|
| 3615 | else |
---|
| 3616 | { |
---|
[21b8f4c] | 3617 | if (!fdivides (bufFactors[i], bufF, quot)) |
---|
[e368746] | 3618 | { |
---|
| 3619 | noOneToOne= true; |
---|
| 3620 | return factors; |
---|
| 3621 | } |
---|
[21b8f4c] | 3622 | products.append (quot); |
---|
[e368746] | 3623 | } |
---|
| 3624 | } |
---|
| 3625 | |
---|
| 3626 | for (int d= 1; d < lNew; d++) |
---|
| 3627 | { |
---|
| 3628 | henselStep2 (F.getLast(), factors, bufFactors, diophant, M, Pi, products, d, |
---|
| 3629 | MOD, noOneToOne); |
---|
| 3630 | if (noOneToOne) |
---|
| 3631 | return CFList(); |
---|
| 3632 | } |
---|
| 3633 | |
---|
| 3634 | CFList result; |
---|
| 3635 | for (k= 0; k < factors.length(); k++) |
---|
| 3636 | result.append (bufFactors[k]); |
---|
| 3637 | return result; |
---|
| 3638 | } |
---|
| 3639 | |
---|
| 3640 | CFList |
---|
| 3641 | nonMonicHenselLift (const CFList& eval, const CFList& factors, |
---|
| 3642 | CFList* const& LCs, CFList& diophant, CFArray& Pi, |
---|
| 3643 | int* liftBound, int length, bool& noOneToOne |
---|
| 3644 | ) |
---|
| 3645 | { |
---|
| 3646 | CFList bufDiophant= diophant; |
---|
| 3647 | CFList buf= factors; |
---|
| 3648 | CFArray bufPi= Pi; |
---|
| 3649 | CFMatrix M= CFMatrix (liftBound[1], factors.length() - 1); |
---|
| 3650 | int k= 0; |
---|
| 3651 | |
---|
| 3652 | CFList result= |
---|
| 3653 | nonMonicHenselLift23 (eval.getFirst(), factors, LCs [0], diophant, bufPi, |
---|
| 3654 | liftBound[1], liftBound[0], noOneToOne); |
---|
| 3655 | |
---|
| 3656 | if (noOneToOne) |
---|
| 3657 | return CFList(); |
---|
| 3658 | |
---|
| 3659 | if (eval.length() == 1) |
---|
| 3660 | return result; |
---|
| 3661 | |
---|
| 3662 | k++; |
---|
| 3663 | CFList MOD; |
---|
| 3664 | for (int i= 0; i < 2; i++) |
---|
| 3665 | MOD.append (power (Variable (i + 2), liftBound[i])); |
---|
| 3666 | |
---|
| 3667 | CFListIterator j= eval; |
---|
| 3668 | CFList bufEval; |
---|
| 3669 | bufEval.append (j.getItem()); |
---|
| 3670 | j++; |
---|
| 3671 | |
---|
| 3672 | for (int i= 2; i <= length && j.hasItem(); i++, j++, k++) |
---|
| 3673 | { |
---|
| 3674 | bufEval.append (j.getItem()); |
---|
| 3675 | M= CFMatrix (liftBound[i], factors.length() - 1); |
---|
| 3676 | result= nonMonicHenselLift (bufEval, result, LCs [i-1], diophant, bufPi, M, |
---|
| 3677 | liftBound[i-1], liftBound[i], MOD, noOneToOne); |
---|
| 3678 | if (noOneToOne) |
---|
| 3679 | return result; |
---|
| 3680 | MOD.append (power (Variable (i + 2), liftBound[i])); |
---|
| 3681 | bufEval.removeFirst(); |
---|
| 3682 | } |
---|
| 3683 | |
---|
| 3684 | return result; |
---|
| 3685 | } |
---|
| 3686 | |
---|
[ad3c3ff] | 3687 | #endif |
---|
| 3688 | /* HAVE_NTL */ |
---|
| 3689 | |
---|