Singular Manual: GKExp

7.5.13.0. GKExp

Procedure from library nchilbert.lib (see nchilbert_lib).

Usage:: GKExp(M); M a module
Return:: int
Purpose:: computes the Gelfand-Kirillov-Dimension of coker(M) via Exp(M)
Assume:: basering is G-Algebra
Note:: for zero module -1 is returned

Example:

LIB "nchilbert.lib";
def A = makeUsl2(); setring A;
ideal I = e,h-1; I = std(I);
GKExp(I); // computes GKdim(A/I), should be 1
==> Warning: the input generators are not a Groebner basis
==> Proceed with Groebner basis computation
==> 1
ideal J = I, f^2; J = std(J);
GKExp(J); // should be 0
==> Warning: the input generators are not a Groebner basis
==> Proceed with Groebner basis computation
==> 0
matrix M[2][4] =
e,h-1,0,0,
0,0,e,h+1;
module G = std(M);
print(G);
==> h-1,0,  e,0,
==> 0,  h+1,0,e 
GKExp(G);
==> 1