Opened 13 years ago

Closed 13 years ago

# gkdim is not zero for a zero-dimensional ideal

Reported by: Owned by: Simon King levandov major 3-1-1 dontKnow 3-1-0 gkdim

### Description

```ring r = (3),(b_2_0,b_2_1,b_4_0,b_8_2,b_8_4,c_12_7,a_1_0,a_3_0,a_3_1,a_7_4,a_9_0),(M(2,2,4,8,8,12,1,3,3,7,9,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0),C);
LIB "ncall.lib";
def R = SuperCommutative(7,11);
setring R;
ideal I = a_1_0*a_3_1,b_2_0*b_2_1-b_2_0^2+a_1_0*a_3_0,b_2_0*a_3_1-b_2_0^2*a_1_0,b_2_1*a_3_0-b_2_0*a_3_0,b_2_1*a_3_1-b_2_0^2*a_1_0,b_4_0*a_1_0-b_2_0^2*a_1_0,b_2_0*b_4_0-b_2_0^3+a_3_0*a_3_1,b_2_1*b_4_0-b_2_0^3,a_1_0*a_7_4,b_2_1*a_7_4-b_2_0*a_7_4,b_8_2*a_1_0-b_2_0*a_7_4,b_8_4*a_1_0,a_3_1*a_7_4,b_2_0*b_8_4+a_3_0*a_7_4-b_2_0^3*a_1_0*a_3_0,b_2_1*b_8_2-b_2_0*b_8_2+a_3_0*a_7_4-a_1_0*a_9_0+b_2_0^3*a_1_0*a_3_0,b_2_1*b_8_4-a_1_0*a_9_0,b_8_2*a_3_1+b_4_0*a_7_4+b_2_0^2*a_7_4,b_8_4*a_3_0+b_8_2*a_3_0-b_2_0*a_9_0-b_2_0^2*a_7_4+b_2_0^4*a_3_0,b_8_4*a_3_1-b_4_0*a_7_4+b_2_0^2*a_7_4,b_2_0*a_3_0*a_7_4+b_2_0*a_1_0*a_9_0-b_2_0^4*a_1_0*a_3_0,a_3_0*a_9_0-b_2_0*a_1_0*a_9_0+b_2_0^4*a_1_0*a_3_0,a_3_1*a_9_0-b_2_0*a_1_0*a_9_0,b_4_0*b_8_4+b_4_0*b_8_2-b_2_0^2*b_8_2+b_2_0*a_1_0*a_9_0+b_2_0^4*a_1_0*a_3_0,b_2_0*b_8_2*a_3_0-b_2_0^2*a_9_0-b_2_0^3*a_7_4+b_2_0^5*a_3_0,b_4_0*a_9_0-b_2_0^2*a_9_0,b_8_2*a_7_4-b_2_0^7*a_1_0+c_12_7*a_3_1+b_2_0*c_12_7*a_1_0,b_8_4*a_7_4-c_12_7*a_3_1+b_2_0*c_12_7*a_1_0,a_7_4*a_9_0-b_2_0^3*a_1_0*a_9_0-c_12_7*a_1_0*a_3_0,b_8_2^2-b_2_0^8-b_2_0^6*a_1_0*a_3_0-b_4_0*c_12_7+c_12_7*a_1_0*a_3_0,b_8_2*b_8_4-b_2_0^3*a_1_0*a_9_0+b_4_0*c_12_7-b_2_0^2*c_12_7+c_12_7*a_1_0*a_3_0,b_8_4^2-b_4_0*c_12_7+b_2_0^2*c_12_7+c_12_7*a_1_0*a_3_0,b_8_2*a_9_0-b_2_0^4*a_9_0-b_2_0^5*a_7_4+b_2_0^8*a_1_0-b_2_0*c_12_7*a_3_0+b_2_0^2*c_12_7*a_1_0,b_8_4*a_9_0,c_12_7,b_4_0+b_2_1^2;
I = twostd(I);
> vdim(I);
32
> gkdim(I);
2
```

I could be mistaken, but as much as I know `gkdim(I)` should be zero if `I` has only finitely many standard monomials.

### comment:1 in reply to:  description ; follow-up:  3 Changed 13 years ago by Simon King

gkdim(I);

2

Sorry, according to the manual, the function should be called "GKdim" (not "gkdim"). But the (wrong?) result is the same.

### comment:2 Changed 13 years ago by levandov

Owner: changed from somebody to levandov new → assigned

Hi Simon,

I cannot reproduce this with the version compiled from fresh sources on 19.1.2010. Besides, dim(I) computes now GK dimension as well, thanks to Hannes and Frank! See below.

vdim(I);

32

gkdim(I);

0

dim(I);

0

### comment:3 in reply to:  1 Changed 13 years ago by levandov

Sorry, according to the manual, the function should be called "GKdim" (not "gkdim"). But the (wrong?) result is the same.

well, "gkdim" is just defined as an alias to GKdim, that's the whole mystery.

### comment:4 Changed 13 years ago by Simon King

Resolution: → invalid assigned → closed