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3.27 vdim

Syntax:
vdim ( ideal_expression )
vdim ( module_expression )
Type:
int
Purpose:
computes the vector space dimension of the factor-module that equals ring (resp. free module) modulo the ideal (resp. submodule), generated by the leading terms of the given generators.
If the factor-module is not of finite dimension, -1 is returned. If the generators form a Groebner basis, this is the same as the vector space dimension of the factor-module.

Note:
you have the ring structure on the ring modulo the ideal if and only if the ideal is two-sided.

Example:
 
ring R=0,(x,y,z),dp;
matrix d[3][3];
d[1,2]=-z;
d[1,3]=2x;
d[2,3]=-2y;
ncalgebra(1,d); //U(sl_2)
ideal I=x3,y3,z3-z;
I=std(I);
I;
==> I[1]=z3-z
==> I[2]=y3
==> I[3]=x3
==> I[4]=y2z2-y2z
==> I[5]=x2z2+x2z
==> I[6]=x2y2z-2xyz2-2xyz+2z2+2z
vdim(I);
==> 21

See ideal; kbase; std.

see also SINGULAR manual sections dim, degree, mult, kbase.


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            User manual for Singular version 2-1-99, August 2004, generated by texi2html.