Singular

7.7.13.0. CentralQuot

Usage:

CentralQuot(M, G), M a module, G an ideal

Assume:

G is an ideal in the center of the base ring

Return:

module

Purpose:

compute the central quotient M:G

Theory:

for an ideal G of the center of an algebra and a submodule M of A^n,
the central quotient of M by G is defined to be
M:G := { v in A^n | z*v in M, for all z in G }.

Note:

the output module is not necessarily given in a Groebner basis

LIB "ncdecomp.lib";
option(returnSB);
def a = makeUsl2();
setring a;
ideal I = e3,f3,h3-4*h;
I = std(I);
poly C=4*e*f+h^2-2*h;  // C in Z(U(sl2)), the central element
ideal G = (C-8)*(C-24);  // G normal factor in Z(U(sl2)) as an ideal in the center
ideal R = CentralQuot(I,G);  // same as I:G
R;
==> R[1]=h
==> R[2]=f
==> R[3]=e