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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 module generators
2 Hilbert basis elements of recession monoid
1 vertices of polyhedron
2 extreme rays of recession cone
6 module generators over original monoid
3 support hyperplanes of polyhedron (homogenized)

embedding dimension = 3
affine dimension of the polyhedron = 2 (maximal)
rank of recession monoid = 2
internal index = 6

size of triangulation   = 1
resulting sum of |det|s = 6

dehomogenization:
0 0 1 


module rank = 1

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1 module generators:
 0 0 1

2 Hilbert basis elements of recession monoid:
 0 1 0
 1 0 0

1 vertices of polyhedron:
 0 0 1

2 extreme rays of recession cone:
 0 1 0
 1 0 0

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

3 support hyperplanes of polyhedron (homogenized):
 0 0 1
 0 1 0
 1 0 0