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7.8.1 dim (letterplace)

Syntax:
dim( ideal_expression)
Type:
int
Purpose:
Compute the Gelfand-Kirillov dimension of the algebra basering/(input ideal). Uses Ufnarovskij graph for computations.
Note:
the input ideal must be given as a two-sided Groebner basis.
Example:
 
LIB "freegb.lib";
ring r = 0,(x,y,z),dp;
ring R = freeAlgebra(r, 5);
ideal I = z;
dim(twostd(I)); // GK dimension is infinite
==> -1
I = x,y,z;
dim(twostd(I));
==> 0
I = x*y, x*z, z*y, z*z;
dim(twostd(I));
==> 2
I = y*x - x*y, z*x - x*z, z*y - y*z;
I = twostd(I); I;
==> I[1]=z*y-y*z
==> I[2]=z*x-x*z
==> I[3]=y*x-x*y
dim(I); // 3, as expected for R/I = K[x,y,z]
==> 3
See fpadim_lib.


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