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7.5.9.0. GKdim
Procedure from library gkdim.lib (see gkdim_lib).
- Usage:
- GKdim(L); L is a left ideal/module/matrix
- Return:
- int
- Purpose:
- compute the Gelfand-Kirillov dimension of the factor-module, whose presentation is given by L, e.g. R^r/L
- Note:
- if the factor-module is zero, -1 is returned
Example:
| | LIB "gkdim.lib";
ring R = 0,(x,y,z),Dp;
matrix C[3][3]=0,1,1,0,0,-1,0,0,0;
matrix D[3][3]=0,0,0,0,0,x;
def r = nc_algebra(C,D); setring r;
r;
==> // coefficients: QQ
==> // number of vars : 3
==> // block 1 : ordering Dp
==> // : names x y z
==> // block 2 : ordering C
==> // noncommutative relations:
==> // zy=-yz+x
ideal I=x;
GKdim(I);
==> 2
ideal J=x2,y;
GKdim(J);
==> 1
module M=[x2,y,1],[x,y2,0];
GKdim(M);
==> 3
ideal A = x,y,z;
GKdim(A);
==> 0
ideal B = 1;
GKdim(B);
==> -1
GKdim(ideal(0)) == nvars(basering); // should be true, i.e., evaluated to 1
==> 1
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