[493c477] | 1 | /* emacs edit mode for this file is -*- C++ -*- */ |
---|
[2dd068] | 2 | |
---|
[e4fe2b] | 3 | #include "config.h" |
---|
[173e86] | 4 | |
---|
[650f2d8] | 5 | #include "cf_assert.h" |
---|
[83452f] | 6 | |
---|
[2dd068] | 7 | #include "cf_defs.h" |
---|
[7b4bfe6] | 8 | #include "canonicalform.h" |
---|
| 9 | #include "cf_iter.h" |
---|
[2dd068] | 10 | #include "fac_util.h" |
---|
| 11 | |
---|
| 12 | static CanonicalForm PK, PKHALF; |
---|
| 13 | |
---|
| 14 | static CanonicalForm mappk ( const CanonicalForm& ); |
---|
| 15 | |
---|
| 16 | static CanonicalForm mappksymmetric ( const CanonicalForm& ); |
---|
| 17 | |
---|
| 18 | |
---|
| 19 | modpk::modpk() |
---|
| 20 | { |
---|
[667ba1] | 21 | p = 0; |
---|
| 22 | k = 0; |
---|
| 23 | pk = 1; |
---|
| 24 | pkhalf = 0; |
---|
[2dd068] | 25 | } |
---|
| 26 | |
---|
| 27 | modpk::modpk( int q, int l ) |
---|
| 28 | { |
---|
| 29 | p = q; |
---|
| 30 | k = l; |
---|
| 31 | pk = power( CanonicalForm( p ), k ); |
---|
| 32 | pkhalf = pk / 2; |
---|
| 33 | } |
---|
| 34 | |
---|
| 35 | modpk::modpk( const modpk & m ) |
---|
| 36 | { |
---|
| 37 | p = m.p; |
---|
| 38 | k = m.k; |
---|
| 39 | pk = m.pk; |
---|
| 40 | pkhalf = m.pkhalf; |
---|
| 41 | } |
---|
| 42 | |
---|
| 43 | modpk& |
---|
| 44 | modpk::operator= ( const modpk & m ) |
---|
| 45 | { |
---|
| 46 | if ( this != &m ) { |
---|
[412bedd] | 47 | p = m.p; |
---|
| 48 | k = m.k; |
---|
| 49 | pk = m.pk; |
---|
| 50 | pkhalf = m.pkhalf; |
---|
[2dd068] | 51 | } |
---|
| 52 | return *this; |
---|
| 53 | } |
---|
| 54 | |
---|
| 55 | CanonicalForm |
---|
| 56 | modpk::inverse( const CanonicalForm & f, bool symmetric ) const |
---|
| 57 | { |
---|
| 58 | CanonicalForm u, r0 = this->operator()( f, false ), r1 = pk, q0 = 1, q1 = 0; |
---|
| 59 | while ( ( r0 > 0 ) && ( r1 > 0 ) ) { |
---|
[412bedd] | 60 | u = r0 / r1; |
---|
| 61 | r0 = r0 % r1; |
---|
| 62 | q0 = u*q1 + q0; |
---|
| 63 | if ( r0 > 0 ) { |
---|
| 64 | u = r1 / r0; |
---|
| 65 | r1 = r1 % r0; |
---|
| 66 | q1 = u*q0 + q1; |
---|
| 67 | } |
---|
[2dd068] | 68 | } |
---|
| 69 | if ( r0 == 0 ) |
---|
[412bedd] | 70 | return this->operator()( pk-q1, symmetric ); |
---|
[2dd068] | 71 | else |
---|
[412bedd] | 72 | return this->operator()( q0, symmetric ); |
---|
[83452f] | 73 | } |
---|
[2dd068] | 74 | |
---|
| 75 | CanonicalForm |
---|
| 76 | modpk::operator() ( const CanonicalForm & f, bool symmetric ) const |
---|
| 77 | { |
---|
| 78 | PKHALF = pkhalf; |
---|
| 79 | PK = pk; |
---|
| 80 | if ( symmetric ) |
---|
[412bedd] | 81 | return mapdomain( f, mappksymmetric ); |
---|
[2dd068] | 82 | else |
---|
[412bedd] | 83 | return mapdomain( f, mappk ); |
---|
[e76d7a6] | 84 | } |
---|
[2dd068] | 85 | |
---|
| 86 | CanonicalForm |
---|
| 87 | replaceLc( const CanonicalForm & f, const CanonicalForm & c ) |
---|
| 88 | { |
---|
| 89 | if ( f.inCoeffDomain() ) |
---|
[412bedd] | 90 | return c; |
---|
[2dd068] | 91 | else |
---|
[412bedd] | 92 | return f + ( c - LC( f ) ) * power( f.mvar(), degree( f ) ); |
---|
[2dd068] | 93 | } |
---|
| 94 | |
---|
| 95 | CanonicalForm |
---|
| 96 | remainder( const CanonicalForm & f, const CanonicalForm & g, const modpk & pk ) |
---|
| 97 | { |
---|
| 98 | ASSERT( (f.inCoeffDomain() || f.isUnivariate()) && (g.inCoeffDomain() || g.isUnivariate()) && (f.inCoeffDomain() || g.inCoeffDomain() || f.mvar() == g.mvar()), "can not build remainder" ); |
---|
| 99 | if ( f.inCoeffDomain() ) |
---|
[412bedd] | 100 | if ( g.inCoeffDomain() ) |
---|
| 101 | return pk( f % g ); |
---|
| 102 | else |
---|
| 103 | return pk( f ); |
---|
[2dd068] | 104 | else { |
---|
[412bedd] | 105 | Variable x = f.mvar(); |
---|
| 106 | CanonicalForm result = f; |
---|
| 107 | int degg = g.degree(); |
---|
| 108 | CanonicalForm invlcg = pk.inverse( g.lc() ); |
---|
| 109 | CanonicalForm gg = pk( g*invlcg ); |
---|
| 110 | if((gg.lc().isOne())) |
---|
| 111 | { |
---|
| 112 | while ( result.degree() >= degg ) |
---|
| 113 | { |
---|
| 114 | result -= pk(lc( result ) * gg) * power( x, result.degree() - degg ); |
---|
| 115 | result=pk(result); |
---|
| 116 | } |
---|
| 117 | } |
---|
[806c18] | 118 | else |
---|
| 119 | // no inverse found |
---|
[412bedd] | 120 | { |
---|
| 121 | CanonicalForm ic=icontent(g); |
---|
| 122 | if (!ic.isOne()) |
---|
| 123 | { |
---|
| 124 | gg=g/ic; |
---|
| 125 | return remainder(f,gg,pk); |
---|
| 126 | } |
---|
| 127 | while ( result.degree() >= degg ) |
---|
| 128 | { |
---|
[806c18] | 129 | if (gg.lc().isZero()) return result; |
---|
[412bedd] | 130 | CanonicalForm lcgf = result.lc() / gg.lc(); |
---|
| 131 | if (lcgf.inZ()) |
---|
| 132 | gg = pk( g*lcgf ); |
---|
| 133 | else |
---|
| 134 | { |
---|
| 135 | //printf("!\n\n"); |
---|
| 136 | return result; |
---|
| 137 | } |
---|
| 138 | result -= gg * power( x, result.degree() - degg ); |
---|
| 139 | result=pk(result); |
---|
| 140 | } |
---|
| 141 | } |
---|
| 142 | return result; |
---|
[2dd068] | 143 | } |
---|
| 144 | } |
---|
| 145 | |
---|
[fcae67] | 146 | void |
---|
| 147 | divremainder( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & quot, CanonicalForm & rem, const modpk & pk ) |
---|
| 148 | { |
---|
| 149 | ASSERT( (f.inCoeffDomain() || f.isUnivariate()) && (g.inCoeffDomain() || g.isUnivariate()) && (f.inCoeffDomain() || g.inCoeffDomain() || f.mvar() == g.mvar()), "can not build remainder" ); |
---|
| 150 | if ( f.inCoeffDomain() ) |
---|
[412bedd] | 151 | if ( g.inCoeffDomain() ) { |
---|
| 152 | divrem( f, g, quot, rem ); |
---|
| 153 | quot = pk( quot ); |
---|
| 154 | rem = pk( rem ); |
---|
| 155 | } |
---|
| 156 | else { |
---|
| 157 | quot = 0; |
---|
| 158 | rem = pk( f ); |
---|
| 159 | } |
---|
[fcae67] | 160 | else { |
---|
[412bedd] | 161 | Variable x = f.mvar(); |
---|
| 162 | CanonicalForm invlcg = pk.inverse( g.lc() ); |
---|
| 163 | rem = f; |
---|
| 164 | int degg = g.degree(); |
---|
| 165 | while ( rem.degree() >= degg ) { |
---|
| 166 | quot += pk( lc( rem ) * invlcg ) * power( x, rem.degree() - degg ); |
---|
| 167 | rem = pk( rem - lc( rem ) * invlcg * g * power( x, rem.degree() - degg ) ); |
---|
| 168 | } |
---|
[fcae67] | 169 | } |
---|
| 170 | } |
---|
| 171 | |
---|
[2dd068] | 172 | CanonicalForm |
---|
| 173 | mappksymmetric ( const CanonicalForm & f ) |
---|
| 174 | { |
---|
| 175 | CanonicalForm result = mod( f, PK ); |
---|
| 176 | if ( result > PKHALF ) |
---|
[412bedd] | 177 | return result - PK; |
---|
[2dd068] | 178 | else |
---|
[412bedd] | 179 | return result; |
---|
[2dd068] | 180 | } |
---|
| 181 | |
---|
| 182 | CanonicalForm |
---|
| 183 | mappk ( const CanonicalForm & f ) |
---|
| 184 | { |
---|
| 185 | return mod( f, PK ); |
---|
| 186 | } |
---|
[7b4bfe6] | 187 | |
---|
| 188 | void |
---|
| 189 | extgcd ( const CanonicalForm & a, const CanonicalForm & b, CanonicalForm & S, CanonicalForm & T, const modpk & pk ) |
---|
| 190 | { |
---|
| 191 | int p = pk.getp(), k = pk.getk(), j; |
---|
| 192 | CanonicalForm amodp, bmodp, smodp, tmodp, s, t, sigma, tau, e; |
---|
| 193 | CanonicalForm modulus = p, sigmat, taut, q; |
---|
| 194 | |
---|
| 195 | setCharacteristic( p ); |
---|
| 196 | { |
---|
[412bedd] | 197 | amodp = mapinto( a ); bmodp = mapinto( b ); |
---|
| 198 | (void)extgcd( amodp, bmodp, smodp, tmodp ); |
---|
[7b4bfe6] | 199 | } |
---|
| 200 | setCharacteristic( 0 ); |
---|
| 201 | s = mapinto( smodp ); t = mapinto( tmodp ); |
---|
| 202 | |
---|
| 203 | for ( j = 1; j < k; j++ ) { |
---|
[412bedd] | 204 | e = ( 1 - s * a - t * b ) / modulus; |
---|
| 205 | setCharacteristic( p ); |
---|
| 206 | { |
---|
| 207 | e = mapinto( e ); |
---|
| 208 | sigmat = smodp * e; |
---|
| 209 | taut = tmodp * e; |
---|
| 210 | divrem( sigmat, bmodp, q, sigma ); |
---|
| 211 | tau = taut + q * amodp; |
---|
| 212 | } |
---|
| 213 | setCharacteristic( 0 ); |
---|
| 214 | s += mapinto( sigma ) * modulus; |
---|
| 215 | t += mapinto( tau ) * modulus; |
---|
| 216 | modulus *= p; |
---|
[7b4bfe6] | 217 | } |
---|
| 218 | S = s; T = t; |
---|
| 219 | } |
---|
| 220 | |
---|
[70161e] | 221 | CanonicalForm |
---|
| 222 | sum ( const CFArray & a, int f, int l ) |
---|
| 223 | { |
---|
| 224 | if ( f < a.min() ) f = a.min(); |
---|
| 225 | if ( l > a.max() ) l = a.max(); |
---|
| 226 | CanonicalForm s = 0; |
---|
| 227 | for ( int i = f; i <= l; i++ ) |
---|
[412bedd] | 228 | s += a[i]; |
---|
[70161e] | 229 | return s; |
---|
| 230 | } |
---|
| 231 | |
---|
| 232 | CanonicalForm |
---|
| 233 | prod ( const CFArray & a, int f, int l ) |
---|
| 234 | { |
---|
| 235 | if ( f < a.min() ) f = a.min(); |
---|
| 236 | if ( l > a.max() ) l = a.max(); |
---|
| 237 | CanonicalForm p = 1; |
---|
| 238 | for ( int i = f; i <= l; i++ ) |
---|
[412bedd] | 239 | p *= a[i]; |
---|
[70161e] | 240 | return p; |
---|
| 241 | } |
---|
| 242 | |
---|
| 243 | CanonicalForm |
---|
| 244 | sum ( const CFArray & a ) |
---|
| 245 | { |
---|
| 246 | return sum( a, a.min(), a.max() ); |
---|
| 247 | } |
---|
| 248 | |
---|
| 249 | CanonicalForm |
---|
| 250 | prod ( const CFArray & a ) |
---|
| 251 | { |
---|
| 252 | return prod( a, a.min(), a.max() ); |
---|
| 253 | } |
---|
| 254 | |
---|
| 255 | CanonicalForm |
---|
| 256 | crossprod ( const CFArray & a, const CFArray & b ) |
---|
| 257 | { |
---|
[83452f] | 258 | ASSERT( a.size() == b.size(), "array size mismatch" ); |
---|
[70161e] | 259 | CanonicalForm s = 0; |
---|
| 260 | int fa = a.min(); |
---|
| 261 | int fb = b.min(); |
---|
| 262 | int n = a.max(); |
---|
| 263 | for ( ; fa <= n; fa++, fb++ ) |
---|
[412bedd] | 264 | s += a[fa] * b[fb]; |
---|
[70161e] | 265 | return s; |
---|
| 266 | } |
---|