[493c477] | 1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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[2dd068] | 2 | |
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[9f7665] | 3 | |
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[e4fe2b] | 4 | #include "config.h" |
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[9f7665] | 5 | |
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[173e86] | 6 | |
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[650f2d8] | 7 | #include "cf_assert.h" |
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[83452f] | 8 | |
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[2dd068] | 9 | #include "cf_defs.h" |
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[7b4bfe6] | 10 | #include "canonicalform.h" |
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| 11 | #include "cf_iter.h" |
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[2dd068] | 12 | #include "fac_util.h" |
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[564dd8] | 13 | #include "cfUnivarGcd.h" |
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[2dd068] | 14 | |
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[a3f0fea] | 15 | STATIC_INST_VAR CanonicalForm PK, PKHALF; |
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[2dd068] | 16 | |
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| 17 | static CanonicalForm mappk ( const CanonicalForm& ); |
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| 18 | |
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| 19 | static CanonicalForm mappksymmetric ( const CanonicalForm& ); |
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| 20 | |
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| 21 | |
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| 22 | modpk::modpk() |
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| 23 | { |
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[667ba1] | 24 | p = 0; |
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| 25 | k = 0; |
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| 26 | pk = 1; |
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| 27 | pkhalf = 0; |
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[2dd068] | 28 | } |
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| 29 | |
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| 30 | modpk::modpk( int q, int l ) |
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| 31 | { |
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| 32 | p = q; |
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| 33 | k = l; |
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| 34 | pk = power( CanonicalForm( p ), k ); |
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| 35 | pkhalf = pk / 2; |
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| 36 | } |
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| 37 | |
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| 38 | modpk::modpk( const modpk & m ) |
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| 39 | { |
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| 40 | p = m.p; |
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| 41 | k = m.k; |
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| 42 | pk = m.pk; |
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| 43 | pkhalf = m.pkhalf; |
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| 44 | } |
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| 45 | |
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| 46 | modpk& |
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| 47 | modpk::operator= ( const modpk & m ) |
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| 48 | { |
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| 49 | if ( this != &m ) { |
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[412bedd] | 50 | p = m.p; |
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| 51 | k = m.k; |
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| 52 | pk = m.pk; |
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| 53 | pkhalf = m.pkhalf; |
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[2dd068] | 54 | } |
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| 55 | return *this; |
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| 56 | } |
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| 57 | |
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| 58 | CanonicalForm |
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| 59 | modpk::inverse( const CanonicalForm & f, bool symmetric ) const |
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| 60 | { |
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| 61 | CanonicalForm u, r0 = this->operator()( f, false ), r1 = pk, q0 = 1, q1 = 0; |
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| 62 | while ( ( r0 > 0 ) && ( r1 > 0 ) ) { |
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[412bedd] | 63 | u = r0 / r1; |
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| 64 | r0 = r0 % r1; |
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| 65 | q0 = u*q1 + q0; |
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| 66 | if ( r0 > 0 ) { |
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| 67 | u = r1 / r0; |
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| 68 | r1 = r1 % r0; |
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| 69 | q1 = u*q0 + q1; |
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| 70 | } |
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[2dd068] | 71 | } |
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| 72 | if ( r0 == 0 ) |
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[412bedd] | 73 | return this->operator()( pk-q1, symmetric ); |
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[2dd068] | 74 | else |
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[412bedd] | 75 | return this->operator()( q0, symmetric ); |
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[83452f] | 76 | } |
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[2dd068] | 77 | |
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| 78 | CanonicalForm |
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| 79 | modpk::operator() ( const CanonicalForm & f, bool symmetric ) const |
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| 80 | { |
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| 81 | PKHALF = pkhalf; |
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| 82 | PK = pk; |
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| 83 | if ( symmetric ) |
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[412bedd] | 84 | return mapdomain( f, mappksymmetric ); |
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[2dd068] | 85 | else |
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[412bedd] | 86 | return mapdomain( f, mappk ); |
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[e76d7a6] | 87 | } |
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[2dd068] | 88 | |
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| 89 | CanonicalForm |
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| 90 | replaceLc( const CanonicalForm & f, const CanonicalForm & c ) |
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| 91 | { |
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| 92 | if ( f.inCoeffDomain() ) |
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[412bedd] | 93 | return c; |
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[2dd068] | 94 | else |
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[412bedd] | 95 | return f + ( c - LC( f ) ) * power( f.mvar(), degree( f ) ); |
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[2dd068] | 96 | } |
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| 97 | |
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| 98 | CanonicalForm |
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| 99 | mappksymmetric ( const CanonicalForm & f ) |
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| 100 | { |
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| 101 | CanonicalForm result = mod( f, PK ); |
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| 102 | if ( result > PKHALF ) |
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[412bedd] | 103 | return result - PK; |
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[2dd068] | 104 | else |
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[412bedd] | 105 | return result; |
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[2dd068] | 106 | } |
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| 107 | |
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| 108 | CanonicalForm |
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| 109 | mappk ( const CanonicalForm & f ) |
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| 110 | { |
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| 111 | return mod( f, PK ); |
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| 112 | } |
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[7b4bfe6] | 113 | |
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[564dd8] | 114 | CanonicalForm |
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| 115 | remainder( const CanonicalForm & f, const CanonicalForm & g, const modpk & pk ) |
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| 116 | { |
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| 117 | ASSERT( (f.inCoeffDomain() || f.isUnivariate()) && (g.inCoeffDomain() || g.isUnivariate()) && (f.inCoeffDomain() || g.inCoeffDomain() || f.mvar() == g.mvar()), "can not build remainder" ); |
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| 118 | if ( f.inCoeffDomain() ) |
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| 119 | if ( g.inCoeffDomain() ) |
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| 120 | return pk( f % g ); |
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| 121 | else |
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| 122 | return pk( f ); |
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| 123 | else { |
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| 124 | Variable x = f.mvar(); |
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| 125 | CanonicalForm result = f; |
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| 126 | int degg = g.degree(); |
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| 127 | CanonicalForm invlcg = pk.inverse( g.lc() ); |
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| 128 | CanonicalForm gg = pk( g*invlcg ); |
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| 129 | if((gg.lc().isOne())) |
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| 130 | { |
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| 131 | while ( result.degree() >= degg ) |
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| 132 | { |
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| 133 | result -= pk(lc( result ) * gg) * power( x, result.degree() - degg ); |
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| 134 | result=pk(result); |
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| 135 | } |
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| 136 | } |
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| 137 | else |
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| 138 | // no inverse found |
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| 139 | { |
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| 140 | CanonicalForm ic=icontent(g); |
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| 141 | if (!ic.isOne()) |
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| 142 | { |
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| 143 | gg=g/ic; |
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| 144 | return remainder(f,gg,pk); |
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| 145 | } |
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| 146 | while ( result.degree() >= degg ) |
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| 147 | { |
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| 148 | if (gg.lc().isZero()) return result; |
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| 149 | CanonicalForm lcgf = result.lc() / gg.lc(); |
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| 150 | if (lcgf.inZ()) |
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| 151 | gg = pk( g*lcgf ); |
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| 152 | else |
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| 153 | { |
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| 154 | //printf("!\n\n"); |
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| 155 | return result; |
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| 156 | } |
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| 157 | result -= gg * power( x, result.degree() - degg ); |
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| 158 | result=pk(result); |
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| 159 | } |
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| 160 | } |
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| 161 | return result; |
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| 162 | } |
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| 163 | } |
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| 164 | |
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| 165 | CanonicalForm |
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| 166 | prod ( const CFArray & a, int f, int l ) |
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| 167 | { |
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| 168 | if ( f < a.min() ) f = a.min(); |
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| 169 | if ( l > a.max() ) l = a.max(); |
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| 170 | CanonicalForm p = 1; |
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| 171 | for ( int i = f; i <= l; i++ ) |
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| 172 | p *= a[i]; |
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| 173 | return p; |
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| 174 | } |
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| 175 | |
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| 176 | CanonicalForm |
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| 177 | prod ( const CFArray & a ) |
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| 178 | { |
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| 179 | return prod( a, a.min(), a.max() ); |
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[9f48f5] | 180 | } |
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[564dd8] | 181 | |
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| 182 | void |
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| 183 | extgcd ( const CanonicalForm & a, const CanonicalForm & b, CanonicalForm & S, CanonicalForm & T, const modpk & pk ) |
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| 184 | { |
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| 185 | int p = pk.getp(), k = pk.getk(), j; |
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| 186 | CanonicalForm amodp, bmodp, smodp, tmodp, s, t, sigma, tau, e; |
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| 187 | CanonicalForm modulus = p, sigmat, taut, q; |
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| 188 | |
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| 189 | setCharacteristic( p ); |
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| 190 | { |
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| 191 | amodp = mapinto( a ); bmodp = mapinto( b ); |
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| 192 | (void)extgcd( amodp, bmodp, smodp, tmodp ); |
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| 193 | } |
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| 194 | setCharacteristic( 0 ); |
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| 195 | s = mapinto( smodp ); t = mapinto( tmodp ); |
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| 196 | |
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| 197 | for ( j = 1; j < k; j++ ) { |
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| 198 | e = ( 1 - s * a - t * b ) / modulus; |
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| 199 | setCharacteristic( p ); |
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| 200 | { |
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| 201 | e = mapinto( e ); |
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| 202 | sigmat = smodp * e; |
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| 203 | taut = tmodp * e; |
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| 204 | divrem( sigmat, bmodp, q, sigma ); |
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| 205 | tau = taut + q * amodp; |
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| 206 | } |
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| 207 | setCharacteristic( 0 ); |
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| 208 | s += mapinto( sigma ) * modulus; |
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| 209 | t += mapinto( tau ) * modulus; |
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| 210 | modulus *= p; |
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| 211 | } |
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| 212 | S = s; T = t; |
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| 213 | } |
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