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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

See also ideal (plural); kbase (plural); std (plural).


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