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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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1 Hilbert basis elements
1 Hilbert basis elements of degree 1
1 extreme rays
1 module generators over original monoid
1 support hyperplanes

embedding dimension = 5
rank = 5 (maximal)
external index = 1
internal index = 1
dimension of maximal subspace = 4
original monoid is not integrally closed
unit group index = 2

size of partial triangulation   = 0
resulting sum of |det|s = 0

grading:
0 0 0 1 0 

degrees of extreme rays:
1: 1  

Hilbert basis elements are of degree 1

***********************************************************************

1 Hilbert basis elements of degree 1:
 0 0 0 1 0

0 further Hilbert basis elements of higher degree:

1 extreme rays:
 0 0 0 1 0

4 basis elements of maximal subspace:
 1 0 0 0 0
 0 1 0 0 0
 0 0 1 0 0
 0 0 0 0 1

1 module generators over original monoid:
 0 0 0 0 0

1 support hyperplanes:
 0 0 0 1 0