File: [local] / OpenXM_contrib2 / asir2000 / lib / bfct (download)
Revision 1.5, Mon Dec 11 02:00:42 2000 UTC (23 years, 6 months ago) by noro
Branch: MAIN
Changes since 1.4: +14 -2
lines
Defined a new monomial ordering. (ord=10 : 'reverse elimination order')
Modified 'lib/bfct' as follows.
1. bfct() now uses the trace lifting.
2. The Groebner basis check is replaced by another Groebner basis computation.
(See Algorithm 11.25 in the text book in OpenXM/doc/compalg.)
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/*
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* $OpenXM: OpenXM_contrib2/asir2000/lib/bfct,v 1.5 2000/12/11 02:00:42 noro Exp $
*/
/* requires 'primdec' */
/* annihilating ideal of F^s ? */
def ann(F)
{
V = vars(F);
W = append([y1,y2,t],V);
N = length(V);
B = [1-y1*y2,t-y1*F];
for ( I = N-1, DV = []; I >= 0; I-- )
DV = cons(strtov("d"+rtostr(V[I])),DV);
DW = append([dy1,dy2,dt],DV);
for ( I = 0; I < N; I++ ) {
B = cons(DV[I]+y1*diff(F,V[I])*dt,B);
}
dp_nelim(2);
G0 = dp_weyl_gr_main(B,append(W,DW),0,0,6);
G1 = [];
for ( T = G0; T != []; T = cdr(T) ) {
E = car(T); VL = vars(E);
if ( !member(y1,VL) && !member(y2,VL) )
G1 = cons(E,G1);
}
G2 = map(subst,G1,dt,1);
G3 = map(b_subst,G2,t);
G4 = map(subst,G3,t,-1-s);
return G4;
}
/* b-function of F ? */
def bfct(F)
{
G4 = ann(F);
V = vars(F);
N = length(V);
for ( I = N-1, DV = []; I >= 0; I-- )
DV = cons(strtov("d"+rtostr(V[I])),DV);
N1 = 2*(N+1);
M = newmat(N1+1,N1);
for ( J = N+1; J < N1; J++ )
M[0][J] = 1;
for ( J = 0; J < N+1; J++ )
M[1][J] = 1;
#if 0
for ( I = 0; I < N+1; I++ )
M[I+2][N-I] = -1;
for ( I = 0; I < N; I++ )
M[I+2+N+1][N1-1-I] = -1;
#elif 1
for ( I = 0; I < N1-1; I++ )
M[I+2][N1-I-1] = 1;
#else
for ( I = 0; I < N1-1; I++ )
M[I+2][I] = 1;
#endif
V1 = cons(s,V); DV1 = cons(ds,DV);
dp_nelim(0);
/* G4 = dp_weyl_gr_main(G4,append(V1,DV1),0,0,10); */
for ( PrimeIndex = 0; ; PrimeIndex++ ) {
Prime = lprime(PrimeIndex);
dp_nelim(0); /* XXX */
Success = dp_weyl_gr_main(cons(F,G4),append(V1,DV1),0,Prime,10);
if ( !Success )
continue;
dp_nelim(N+1);
G5 = dp_weyl_gr_main(cons(F,G4),append(V1,DV1),0,-Prime,10);
if ( G5 )
break;
}
for ( T = G5, G6 = []; T != []; T = cdr(T) ) {
E = car(T);
if ( intersection(vars(E),DV1) == [] )
G6 = cons(E,G6);
}
G6_0 = remove_zero(map(z_subst,G6,V));
F0 = flatmf(cdr(fctr(dp_gr_main(G6_0,[s],0,0,0)[0])));
for ( T = F0, BF = []; T != []; T = cdr(T) ) {
FI = car(T);
for ( J = 1; ; J++ ) {
S = map(srem,map(z_subst,idealquo(G6,[FI^J],V1,0),V),FI);
for ( ; S != [] && !car(S); S = cdr(S) );
if ( S != [] )
break;
}
BF = cons([FI,J],BF);
}
return BF;
}
def remove_zero(L)
{
for ( R = []; L != []; L = cdr(L) )
if ( car(L) )
R = cons(car(L),R);
return R;
}
def z_subst(F,V)
{
for ( ; V != []; V = cdr(V) )
F = subst(F,car(V),0);
return F;
}
def flatmf(L) {
for ( S = []; L != []; L = cdr(L) )
if ( type(F=car(car(L))) != NUM )
S = append(S,[F]);
return S;
}
def member(A,L) {
for ( ; L != []; L = cdr(L) )
if ( A == car(L) )
return 1;
return 0;
}
def intersection(A,B)
{
for ( L = []; A != []; A = cdr(A) )
if ( member(car(A),B) )
L = cons(car(A),L);
return L;
}
def b_subst(F,V)
{
D = deg(F,V);
C = newvect(D+1);
for ( I = D; I >= 0; I-- )
C[I] = coef(F,I,V);
for ( I = 0, R = 0; I <= D; I++ )
if ( C[I] )
R += C[I]*v_factorial(V,I);
return R;
}
def v_factorial(V,N)
{
for ( J = N-1, R = 1; J >= 0; J-- )
R *= V-J;
return R;
}
end$