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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 support hyperplanes

embedding dimension = 2
rank = 2 (maximal)
external index = 1
dimension of maximal subspace = 1

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

grading:
1 0 

degrees of extreme rays:
1: 1  

Hilbert basis elements are of degree 1

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

1 Hilbert basis elements of degree 1:
 1 0

0 further Hilbert basis elements of higher degree:

1 extreme rays:
 1 0

1 basis elements of maximal subspace:
 0 1

1 support hyperplanes:
 1 0