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

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

1 excluded faces

embedding dimension = 3
rank = 3 (maximal)
external index = 1
internal index = 2
original monoid is not integrally closed

size of partial triangulation   = 1
resulting sum of |det|s = 2

grading:
0 0 1 

degrees of extreme rays:
1: 4  

Hilbert basis elements are of degree 1

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

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

0 further Hilbert basis elements of higher degree:

4 extreme rays:
 -1  0 1
  0 -1 1
  0  1 1
  1  0 1

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

4 support hyperplanes:
 -1 -1 1
 -1  1 1
  1 -1 1
  1  1 1

1 excluded faces:
 -1 -1 1