Top
Back: CenCharDec
Forward: nctools_lib
FastBack: ncalg_lib
FastForward: nctools_lib
Up: ncdecomp_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document
7.5.6.0. 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 an intersection of M with the subalgebra, generated by Z

Note:
usually Z consists of generators of the center

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;
nc_algebra(1,@d); // parametric U(sl_2)
==> //   characteristic : 0
==> //   1 parameter    : a 
==> //   minpoly        : 0
==> //   number of vars : 3
==> //        block   1 : ordering Dp
==> //                  : names    e f h 
==> //        block   2 : ordering C
==> //   noncommutative relations: ...
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


Top Back: CenCharDec Forward: nctools_lib FastBack: ncalg_lib FastForward: nctools_lib Up: ncdecomp_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 3-0-4, Nov 2007, generated by texi2html.