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

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3 original generators of the toric ring
3 Hilbert basis elements
3 Hilbert basis elements of degree 1
2 extreme rays
1 module generators over original monoid
2 support hyperplanes

embedding dimension = 2
rank = 2 (maximal)
external index = 2
internal index = 1
original monoid is integrally closed

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

grading:
1 1 
with denominator = 2

degrees of extreme rays:
1: 2  

Hilbert basis elements are of degree 1

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

3 original generators:
 0 2
 1 1
 2 0

3 Hilbert basis elements of degree 1:
 0 2
 1 1
 2 0

0 further Hilbert basis elements of higher degree:

2 extreme rays:
 0 2
 2 0

1 module generators over original monoid:
 0 0

2 support hyperplanes:
 0 1
 1 0

1 congruences:
 1 1 2

2 basis elements of lattice:
 1 1
 0 2