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7.7.4.0. operatorModulo
Procedure from library dmod.lib (see dmod_lib).
- Usage:
- operatorModulo(f,I,b); f a poly, I an ideal, b a poly
- Return:
- poly
- Purpose:
- compute the B-operator from the polynomial f,
ideal I = Ann f^s and Bernstein-Sato polynomial b
using modulo i.e. kernel of module homomorphism
- Note:
- The computations take place in the ring, similar to the one
returned by Sannfs procedure.
Note, that operator is not completely reduced wrt Ann f^{s+1}.
If printlevel=1, progress debug messages will be printed,
if printlevel>=2, all the debug messages will be printed.
Example:
| | LIB "dmod.lib";
// LIB "dmod.lib"; option(prot); option(mem);
ring r = 0,(x,y),Dp;
poly F = x^3+y^3+x*y^3;
def A = Sannfs(F); // here we get LD = ann f^s
setring A;
poly F = imap(r,F);
def B = annfs0(LD,F); // to obtain BS polynomial
list BS = imap(B,BS); poly bs = fl2poly(BS,"s");
poly PS = operatorModulo(F,LD,bs);
LD = groebner(LD);
PS = NF(PS,subst(LD,s,s+1));; // reduction modulo Ann s^{s+1}
==> // ** _ is no standard basis
size(PS);
==> 56
lead(PS);
==> -2/243*y^3*Dx*Dy^3
reduce(PS*F-bs,LD); // check the defining property of PS
==> 0
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