7.8.15 vdim (letterplace)

Syntax:

vdim ( ideal_expression )

Type:

int

Purpose:

computes the vector space dimension respective to the ground field of the ring modulo the ideal, generated by the leading terms of the given generators. If the generators form a standard basis, this is the same as the vector space dimension of the ring, resp. free module, modulo the ideal, resp. module.
If the ideal is not finite dimensional over the ground field, -1 is returned.
The non-commutative analog of the kbase command is lpMonomialBasis from fpadim_lib.

Example:

LIB "fpadim.lib"; ring r = 0,(x,y),dp; ring R = freeAlgebra(r,5); ideal I = x*x + x, y*y+y, x*y*x + x; ideal G = twostd(I); G; ==> G[1]=y*y+y ==> G[2]=x*x+x ==> G[3]=x*y*x+x vdim(G); // 6 ==> 6 lpMonomialBasis(5,0,G); // lists the K-basis explicitly ==> _[1]=1 ==> _[2]=x ==> _[3]=y ==> _[4]=y*x ==> _[5]=x*y ==> _[6]=y*x*y