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B.6.0.4 IntersectWithSub

Procedure from library ncdecomp.lib (see ncdecomp_lib).

Usage:
IntersectWithSub(M,Z), M an ideal, Z an ideal of pairwise commutative elements

Purpose:
computes an intersection of M with the subalgebra, generated by Z

Return:
ideal (of two--sided generators, not a Groebner basis!)

Note:
usually one puts generators of the center into Z

Example:
 
LIB "ncdecomp.lib";
ring r=(0,a),(e,f,h),Dp;
matrix @d[3][3];
@d[1,2]=-h;
@d[1,3]=2e;
@d[2,3]=-2f;
ncalgebra(1,@d); // parametric U(sl_2)
ideal I = e,h-a;
ideal C;
C[1] = h^2-2*h+4*e*f; // the center of U(sl_2)
ideal X = IntersectWithSub(I,C);
X;
==> X[1]=4*ef+h2-2*h+(-a2-2a)
ideal G = e*f, h; // the biggest comm. subalgebra of U(sl_2)
ideal Y = IntersectWithSub(I,G);
Y;
==> Y[1]=h+(-a)
==> Y[2]=ef+(-a)


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