7.3.30 vdim (plural)

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:

In the non-commutative case, a ring modulo an ideal has a ring stucture 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; def RS=nc_algebra(1,d); //U(sl_2) setring RS; option(redSB); option(redTail); 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