[493c477] | 1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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[341696] | 2 | /* $Id$ */ |
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[2dd068] | 3 | |
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[e4fe2b] | 4 | #include "config.h" |
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[173e86] | 5 | |
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[650f2d8] | 6 | #include "cf_assert.h" |
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[83452f] | 7 | |
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[2dd068] | 8 | #include "cf_defs.h" |
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[7b4bfe6] | 9 | #include "canonicalform.h" |
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| 10 | #include "cf_iter.h" |
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[2dd068] | 11 | #include "fac_util.h" |
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| 12 | |
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| 13 | static CanonicalForm PK, PKHALF; |
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| 14 | |
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| 15 | static CanonicalForm mappk ( const CanonicalForm& ); |
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| 16 | |
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| 17 | static CanonicalForm mappksymmetric ( const CanonicalForm& ); |
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| 18 | |
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| 19 | |
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| 20 | modpk::modpk() |
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| 21 | { |
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[667ba1] | 22 | p = 0; |
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| 23 | k = 0; |
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| 24 | pk = 1; |
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| 25 | pkhalf = 0; |
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[2dd068] | 26 | } |
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| 27 | |
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| 28 | modpk::modpk( int q, int l ) |
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| 29 | { |
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| 30 | p = q; |
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| 31 | k = l; |
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| 32 | pk = power( CanonicalForm( p ), k ); |
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| 33 | pkhalf = pk / 2; |
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| 34 | } |
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| 35 | |
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| 36 | modpk::modpk( const modpk & m ) |
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| 37 | { |
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| 38 | p = m.p; |
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| 39 | k = m.k; |
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| 40 | pk = m.pk; |
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| 41 | pkhalf = m.pkhalf; |
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| 42 | } |
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| 43 | |
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| 44 | modpk& |
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| 45 | modpk::operator= ( const modpk & m ) |
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| 46 | { |
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| 47 | if ( this != &m ) { |
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[412bedd] | 48 | p = m.p; |
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| 49 | k = m.k; |
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| 50 | pk = m.pk; |
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| 51 | pkhalf = m.pkhalf; |
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[2dd068] | 52 | } |
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| 53 | return *this; |
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| 54 | } |
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| 55 | |
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| 56 | CanonicalForm |
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| 57 | modpk::inverse( const CanonicalForm & f, bool symmetric ) const |
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| 58 | { |
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| 59 | CanonicalForm u, r0 = this->operator()( f, false ), r1 = pk, q0 = 1, q1 = 0; |
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| 60 | while ( ( r0 > 0 ) && ( r1 > 0 ) ) { |
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[412bedd] | 61 | u = r0 / r1; |
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| 62 | r0 = r0 % r1; |
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| 63 | q0 = u*q1 + q0; |
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| 64 | if ( r0 > 0 ) { |
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| 65 | u = r1 / r0; |
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| 66 | r1 = r1 % r0; |
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| 67 | q1 = u*q0 + q1; |
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| 68 | } |
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[2dd068] | 69 | } |
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| 70 | if ( r0 == 0 ) |
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[412bedd] | 71 | return this->operator()( pk-q1, symmetric ); |
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[2dd068] | 72 | else |
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[412bedd] | 73 | return this->operator()( q0, symmetric ); |
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[83452f] | 74 | } |
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[2dd068] | 75 | |
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| 76 | CanonicalForm |
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| 77 | modpk::operator() ( const CanonicalForm & f, bool symmetric ) const |
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| 78 | { |
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| 79 | PKHALF = pkhalf; |
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| 80 | PK = pk; |
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| 81 | if ( symmetric ) |
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[412bedd] | 82 | return mapdomain( f, mappksymmetric ); |
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[2dd068] | 83 | else |
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[412bedd] | 84 | return mapdomain( f, mappk ); |
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[e76d7a6] | 85 | } |
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[2dd068] | 86 | |
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| 87 | CanonicalForm |
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| 88 | replaceLc( const CanonicalForm & f, const CanonicalForm & c ) |
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| 89 | { |
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| 90 | if ( f.inCoeffDomain() ) |
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[412bedd] | 91 | return c; |
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[2dd068] | 92 | else |
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[412bedd] | 93 | return f + ( c - LC( f ) ) * power( f.mvar(), degree( f ) ); |
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[2dd068] | 94 | } |
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| 95 | |
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| 96 | CanonicalForm |
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| 97 | remainder( const CanonicalForm & f, const CanonicalForm & g, const modpk & pk ) |
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| 98 | { |
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| 99 | 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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| 100 | if ( f.inCoeffDomain() ) |
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[412bedd] | 101 | if ( g.inCoeffDomain() ) |
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| 102 | return pk( f % g ); |
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| 103 | else |
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| 104 | return pk( f ); |
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[2dd068] | 105 | else { |
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[412bedd] | 106 | Variable x = f.mvar(); |
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| 107 | CanonicalForm result = f; |
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| 108 | int degg = g.degree(); |
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| 109 | CanonicalForm invlcg = pk.inverse( g.lc() ); |
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| 110 | CanonicalForm gg = pk( g*invlcg ); |
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| 111 | if((gg.lc().isOne())) |
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| 112 | { |
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| 113 | while ( result.degree() >= degg ) |
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| 114 | { |
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| 115 | result -= pk(lc( result ) * gg) * power( x, result.degree() - degg ); |
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| 116 | result=pk(result); |
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| 117 | } |
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| 118 | } |
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[806c18] | 119 | else |
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| 120 | // no inverse found |
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[412bedd] | 121 | { |
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| 122 | CanonicalForm ic=icontent(g); |
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| 123 | if (!ic.isOne()) |
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| 124 | { |
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| 125 | gg=g/ic; |
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| 126 | return remainder(f,gg,pk); |
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| 127 | } |
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| 128 | while ( result.degree() >= degg ) |
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| 129 | { |
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[806c18] | 130 | if (gg.lc().isZero()) return result; |
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[412bedd] | 131 | CanonicalForm lcgf = result.lc() / gg.lc(); |
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| 132 | if (lcgf.inZ()) |
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| 133 | gg = pk( g*lcgf ); |
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| 134 | else |
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| 135 | { |
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| 136 | //printf("!\n\n"); |
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| 137 | return result; |
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| 138 | } |
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| 139 | result -= gg * power( x, result.degree() - degg ); |
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| 140 | result=pk(result); |
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| 141 | } |
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| 142 | } |
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| 143 | return result; |
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[2dd068] | 144 | } |
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| 145 | } |
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| 146 | |
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[fcae67] | 147 | void |
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| 148 | divremainder( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & quot, CanonicalForm & rem, const modpk & pk ) |
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| 149 | { |
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| 150 | 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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| 151 | if ( f.inCoeffDomain() ) |
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[412bedd] | 152 | if ( g.inCoeffDomain() ) { |
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| 153 | divrem( f, g, quot, rem ); |
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| 154 | quot = pk( quot ); |
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| 155 | rem = pk( rem ); |
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| 156 | } |
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| 157 | else { |
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| 158 | quot = 0; |
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| 159 | rem = pk( f ); |
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| 160 | } |
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[fcae67] | 161 | else { |
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[412bedd] | 162 | Variable x = f.mvar(); |
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| 163 | CanonicalForm invlcg = pk.inverse( g.lc() ); |
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| 164 | rem = f; |
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| 165 | int degg = g.degree(); |
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| 166 | while ( rem.degree() >= degg ) { |
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| 167 | quot += pk( lc( rem ) * invlcg ) * power( x, rem.degree() - degg ); |
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| 168 | rem = pk( rem - lc( rem ) * invlcg * g * power( x, rem.degree() - degg ) ); |
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| 169 | } |
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[fcae67] | 170 | } |
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| 171 | } |
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| 172 | |
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[2dd068] | 173 | CanonicalForm |
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| 174 | mappksymmetric ( const CanonicalForm & f ) |
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| 175 | { |
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| 176 | CanonicalForm result = mod( f, PK ); |
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| 177 | if ( result > PKHALF ) |
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[412bedd] | 178 | return result - PK; |
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[2dd068] | 179 | else |
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[412bedd] | 180 | return result; |
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[2dd068] | 181 | } |
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| 182 | |
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| 183 | CanonicalForm |
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| 184 | mappk ( const CanonicalForm & f ) |
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| 185 | { |
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| 186 | return mod( f, PK ); |
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| 187 | } |
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[7b4bfe6] | 188 | |
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| 189 | void |
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| 190 | extgcd ( const CanonicalForm & a, const CanonicalForm & b, CanonicalForm & S, CanonicalForm & T, const modpk & pk ) |
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| 191 | { |
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| 192 | int p = pk.getp(), k = pk.getk(), j; |
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| 193 | CanonicalForm amodp, bmodp, smodp, tmodp, s, t, sigma, tau, e; |
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| 194 | CanonicalForm modulus = p, sigmat, taut, q; |
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| 195 | |
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| 196 | setCharacteristic( p ); |
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| 197 | { |
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[412bedd] | 198 | amodp = mapinto( a ); bmodp = mapinto( b ); |
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| 199 | (void)extgcd( amodp, bmodp, smodp, tmodp ); |
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[7b4bfe6] | 200 | } |
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| 201 | setCharacteristic( 0 ); |
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| 202 | s = mapinto( smodp ); t = mapinto( tmodp ); |
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| 203 | |
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| 204 | for ( j = 1; j < k; j++ ) { |
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[412bedd] | 205 | e = ( 1 - s * a - t * b ) / modulus; |
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| 206 | setCharacteristic( p ); |
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| 207 | { |
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| 208 | e = mapinto( e ); |
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| 209 | sigmat = smodp * e; |
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| 210 | taut = tmodp * e; |
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| 211 | divrem( sigmat, bmodp, q, sigma ); |
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| 212 | tau = taut + q * amodp; |
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| 213 | } |
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| 214 | setCharacteristic( 0 ); |
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| 215 | s += mapinto( sigma ) * modulus; |
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| 216 | t += mapinto( tau ) * modulus; |
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| 217 | modulus *= p; |
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[7b4bfe6] | 218 | } |
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| 219 | S = s; T = t; |
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| 220 | } |
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| 221 | |
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[70161e] | 222 | CanonicalForm |
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| 223 | sum ( const CFArray & a, int f, int l ) |
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| 224 | { |
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| 225 | if ( f < a.min() ) f = a.min(); |
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| 226 | if ( l > a.max() ) l = a.max(); |
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| 227 | CanonicalForm s = 0; |
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| 228 | for ( int i = f; i <= l; i++ ) |
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[412bedd] | 229 | s += a[i]; |
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[70161e] | 230 | return s; |
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| 231 | } |
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| 232 | |
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| 233 | CanonicalForm |
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| 234 | prod ( const CFArray & a, int f, int l ) |
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| 235 | { |
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| 236 | if ( f < a.min() ) f = a.min(); |
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| 237 | if ( l > a.max() ) l = a.max(); |
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| 238 | CanonicalForm p = 1; |
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| 239 | for ( int i = f; i <= l; i++ ) |
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[412bedd] | 240 | p *= a[i]; |
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[70161e] | 241 | return p; |
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| 242 | } |
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| 243 | |
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| 244 | CanonicalForm |
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| 245 | sum ( const CFArray & a ) |
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| 246 | { |
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| 247 | return sum( a, a.min(), a.max() ); |
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| 248 | } |
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| 249 | |
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| 250 | CanonicalForm |
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| 251 | prod ( const CFArray & a ) |
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| 252 | { |
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| 253 | return prod( a, a.min(), a.max() ); |
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| 254 | } |
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| 255 | |
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| 256 | CanonicalForm |
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| 257 | crossprod ( const CFArray & a, const CFArray & b ) |
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| 258 | { |
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[83452f] | 259 | ASSERT( a.size() == b.size(), "array size mismatch" ); |
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[70161e] | 260 | CanonicalForm s = 0; |
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| 261 | int fa = a.min(); |
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| 262 | int fb = b.min(); |
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| 263 | int n = a.max(); |
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| 264 | for ( ; fa <= n; fa++, fb++ ) |
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[412bedd] | 265 | s += a[fa] * b[fb]; |
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[70161e] | 266 | return s; |
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| 267 | } |
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