[493c477] | 1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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[ba1fde] | 2 | |
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[e4fe2b] | 3 | #include "config.h" |
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[b973c0] | 4 | |
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[650f2d8] | 5 | #include "cf_assert.h" |
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[4393f6] | 6 | #include "debug.h" |
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| 7 | |
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[ba1fde] | 8 | #include "cf_defs.h" |
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| 9 | #include "canonicalform.h" |
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[6746a4] | 10 | #include "cf_algorithm.h" |
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[ba1fde] | 11 | #include "cf_iter.h" |
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| 12 | #include "fac_util.h" |
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| 13 | |
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| 14 | bool |
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| 15 | nonDivisors ( CanonicalForm omega, CanonicalForm delta, const CFArray & F, CFArray & d ) |
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| 16 | { |
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| 17 | DEBINCLEVEL( cerr, "nonDivisors" ); |
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| 18 | CanonicalForm q, r; |
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| 19 | int k = F.size(); |
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| 20 | d = CFArray( 0, k ); |
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| 21 | d[0] = delta * omega; |
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[df95e6] | 22 | for ( int i = 1; i <= k; i++ ) |
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| 23 | { |
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[cae0b6] | 24 | q = abs(F[i]); |
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[df95e6] | 25 | for ( int j = i-1; j >= 0; j-- ) |
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| 26 | { |
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[cae0b6] | 27 | r = d[j]; |
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[df95e6] | 28 | do |
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| 29 | { |
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[cae0b6] | 30 | r = gcd( r, q ); |
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| 31 | q = q / r; |
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[df95e6] | 32 | } while ( !r.isOne() ); |
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| 33 | if ( q == 1 ) |
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| 34 | { |
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[cae0b6] | 35 | DEBDECLEVEL( cerr, "nonDivisors" ); |
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| 36 | return false; |
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| 37 | } |
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| 38 | } |
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| 39 | d[i] = q; |
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[ba1fde] | 40 | } |
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| 41 | DEBDECLEVEL( cerr, "nonDivisors" ); |
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| 42 | return true; |
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| 43 | } |
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| 44 | |
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| 45 | bool |
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| 46 | checkEvaluation ( const CanonicalForm & U, const CanonicalForm & lcU, const CanonicalForm & omega, const CFFList & F, const Evaluation & A, CanonicalForm & delta ) |
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| 47 | { |
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| 48 | CanonicalForm Vn, U0 = A( U ); |
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| 49 | CFFListIterator I; |
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| 50 | int j; |
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| 51 | CFArray FF = CFArray( 1, F.length() ); |
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| 52 | CFArray D; |
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| 53 | Vn = A( lcU ); |
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| 54 | if ( Vn.isZero() ) |
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[cae0b6] | 55 | return false; |
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[ba1fde] | 56 | delta = content( U0 ); |
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| 57 | for ( I = F, j = 1; I.hasItem(); I++, j++ ) |
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[cae0b6] | 58 | FF[j] = A( I.getItem().factor() ); |
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[ba1fde] | 59 | return nonDivisors( omega, delta, FF, D ); |
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| 60 | } |
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| 61 | |
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| 62 | bool |
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| 63 | distributeLeadingCoeffs ( CanonicalForm & U, CFArray & G, CFArray & lcG, const CFFList & F, const CFArray & D, CanonicalForm & delta, CanonicalForm & omega, const Evaluation & A, int r ) |
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| 64 | { |
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| 65 | DEBINCLEVEL( cerr, "distributeLeadingCoeffs" ); |
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| 66 | CanonicalForm ut, gt, d, ft; |
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[21b8f4c] | 67 | CanonicalForm dd, quot; |
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[ba1fde] | 68 | CFFListIterator I; |
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| 69 | int m, j, i; |
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| 70 | lcG = CFArray( 1, r ); |
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| 71 | for ( j = 1; j <= r; j ++ ) |
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[cae0b6] | 72 | lcG[j] = 1; |
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[4393f6] | 73 | |
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[df95e6] | 74 | for ( I = F, i = 1; I.hasItem(); I++, i++ ) |
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| 75 | { |
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[cae0b6] | 76 | ft = I.getItem().factor(); |
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| 77 | m = I.getItem().exp(); |
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| 78 | DEBOUTLN( cerr, "trying to distribute " << ft ); |
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| 79 | DEBOUTLN( cerr, "which is tested with " << D[i] ); |
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| 80 | DEBOUTLN( cerr, "and contained to the power of " << m ); |
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| 81 | j = 1; |
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[df95e6] | 82 | while ( m > 0 && j <= r ) |
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| 83 | { |
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[cae0b6] | 84 | ut = lc( G[j] ); |
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| 85 | DEBOUTLN( cerr, "checking with " << ut ); |
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[21b8f4c] | 86 | while ( m > 0 && fdivides( D[i], ut, quot ) ) |
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[df95e6] | 87 | { |
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[cae0b6] | 88 | DEBOUTLN( cerr, "match found" ); |
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[21b8f4c] | 89 | m--; ut= quot; |
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[cae0b6] | 90 | lcG[j] *= ft; |
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| 91 | } |
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| 92 | j++; |
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| 93 | } |
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[df95e6] | 94 | if (m != 0) |
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| 95 | { |
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[cae0b6] | 96 | DEBDECLEVEL( cerr, "distributeLeadingCoeffs" ); |
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| 97 | return false; |
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| 98 | } |
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[ba1fde] | 99 | } |
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[160f8f7] | 100 | DEBOUTLN( cerr, "the leading coeffs before omega and delta correction: " << lcG ); |
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[df95e6] | 101 | if ( !omega.isOne() ) |
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| 102 | { |
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| 103 | for ( j = 1; j <= r; j++ ) |
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| 104 | { |
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[cae0b6] | 105 | // G[j] *= omega; |
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| 106 | lcG[j] *= omega; |
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[df95e6] | 107 | if(lc( G[j] ).isZero()) return false; |
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[cae0b6] | 108 | G[j] = G[j] * ( A( lcG[j] ) / lc( G[j] ) ); |
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| 109 | } |
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| 110 | U *= power( omega, r-1 ); |
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[ba1fde] | 111 | } |
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[df95e6] | 112 | if ( !delta.isOne() ) |
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| 113 | { |
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| 114 | for ( j = 1; j <= r; j++ ) |
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| 115 | { |
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[cae0b6] | 116 | lcG[j] *= delta; |
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[df95e6] | 117 | if(lc( G[j] ).isZero()) return false; |
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[cae0b6] | 118 | G[j] = G[j] * ( A( lcG[j] ) / lc( G[j] ) ); |
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| 119 | } |
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| 120 | U *= power( delta, r ); |
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[ba1fde] | 121 | } |
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| 122 | DEBDECLEVEL( cerr, "distributeLeadingCoeffs" ); |
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| 123 | return true; |
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| 124 | } |
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| 125 | |
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| 126 | |
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| 127 | static void |
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| 128 | gfbAdjoin ( const CanonicalForm & F, CFList & L ) |
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| 129 | { |
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| 130 | if ( F.isOne() ) |
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[cae0b6] | 131 | return; |
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[df95e6] | 132 | if ( L.isEmpty() ) |
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| 133 | { |
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[cae0b6] | 134 | L.append( F ); |
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| 135 | return; |
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[ba1fde] | 136 | } |
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[21b8f4c] | 137 | CanonicalForm h, quot, f = F; |
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[ba1fde] | 138 | CFListIterator i, j; |
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[df95e6] | 139 | for ( i = L; i.hasItem() && ! f.isOne(); ) |
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| 140 | { |
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[cae0b6] | 141 | h = gcd( f, i.getItem() ); |
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[df95e6] | 142 | if ( h.isOne() ) |
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| 143 | { |
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[cae0b6] | 144 | i++; |
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| 145 | continue; |
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| 146 | } |
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[21b8f4c] | 147 | while ( fdivides( h, f, quot ) ) |
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| 148 | f= quot; |
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[cae0b6] | 149 | CFList D( h ); |
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| 150 | gfbAdjoin( i.getItem() / h, D ); |
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| 151 | for ( j = D; j.hasItem(); j++ ) |
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| 152 | i.append( j.getItem() ); |
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| 153 | i.remove( true ); |
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[ba1fde] | 154 | } |
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| 155 | if ( ! f.isOne() ) |
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[cae0b6] | 156 | L.append( f ); |
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[ba1fde] | 157 | } |
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| 158 | |
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| 159 | |
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| 160 | CFList |
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| 161 | gcdFreeBasis ( const CFList L ) |
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| 162 | { |
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| 163 | CFListIterator i; |
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| 164 | CFList R; |
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| 165 | for ( i = L; i.hasItem(); i++ ) |
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[cae0b6] | 166 | gfbAdjoin( i.getItem(), R ); |
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[ba1fde] | 167 | return R; |
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| 168 | } |
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| 169 | |
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| 170 | bool |
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| 171 | Univar2Bivar(const CanonicalForm & U, CFArray & G, const Evaluation & A, const modpk & bound, const Variable & x ) |
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| 172 | { |
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| 173 | CanonicalForm l = LC( U, Variable(1) ); |
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| 174 | int n = G.size(); |
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| 175 | CFArray lcG(1,n); |
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[df95e6] | 176 | for ( int i = 1; i <= n; i++ ) |
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| 177 | { |
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[cae0b6] | 178 | G[i] *= A(l)/lc(G[i]); |
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| 179 | lcG[i] = l; |
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[ba1fde] | 180 | } |
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| 181 | return Hensel( U * power( l, n-1 ), G, lcG, A, bound, x ); |
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| 182 | } |
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| 183 | |
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| 184 | bool |
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| 185 | Hensel2 ( const CanonicalForm & U, CFArray & G, const Evaluation & A, const modpk & bound, const Variable & x ) |
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| 186 | { |
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| 187 | int i,n = G.size(); // n is number of factors of U |
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| 188 | CFArray TrueLcs(1, n); |
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| 189 | for (i=1; i <= n; i++) |
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[cae0b6] | 190 | TrueLcs[i] = 1; |
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[ba1fde] | 191 | Variable y; |
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| 192 | CanonicalForm lcU = LC ( U, Variable(1) ); |
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| 193 | while (! lcU.inCoeffDomain()) |
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| 194 | { |
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[cae0b6] | 195 | y = lcU.mvar(); // should make a more intelligent choice |
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| 196 | CanonicalForm BivariateU = A ( U, 2, y.level() - 1 ); |
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| 197 | CFArray BivariateFactors = G; |
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| 198 | CFArray lcFactors(1,n); |
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| 199 | Univar2Bivar(BivariateU, BivariateFactors, A, bound, y); |
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| 200 | for (i = 1; i <= n; i++) |
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| 201 | { |
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| 202 | BivariateFactors[i] /= content(BivariateFactors[i]); |
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| 203 | lcFactors[i] = LC(BivariateFactors[i],Variable(1)); |
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| 204 | } |
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| 205 | // GFB = GcdFreeBasis(lcFactors); // this is not right... should probably make everything squarefree |
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| 206 | // Hensel2(lcU, GFB, A, bound, y); |
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[ba1fde] | 207 | } |
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| 208 | for (i = 1; i <= n; i++) |
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[cae0b6] | 209 | G[i] *= A(TrueLcs[i])/lc(G[i]); |
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[ba1fde] | 210 | return Hensel(U, G, TrueLcs, A, bound, x); |
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| 211 | } |
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