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7.7.12.0. IntersectWithSub
Procedure from library ncdecomp.lib (see ncdecomp_lib).
- Usage:
- IntersectWithSub(M,Z), M an ideal, Z an ideal
- Assume:
- Z consists of pairwise commutative elements
- Return:
- ideal of two-sided generators, not a Groebner basis
- Purpose:
- computes the intersection of M with the subalgebra, generated by Z
- Note:
- usually Z consists of generators of the center
The function central from central.lib may be used to obtain the center Z, if needed.
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;
def r = nc_algebra(1,@d); setring r; // 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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