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

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

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

grading:
1 1 

degrees of extreme rays:
1: 2  

Hilbert basis elements are of degree 1

multiplicity = 1

Hilbert series:
1 
denominator with 2 factors:
1: 2  

degree of Hilbert Series as rational function = -2

The numerator of the Hilbert Series is symmetric.

Hilbert polynomial:
1 1 
with common denominator = 1

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

5 original generators:
 0 1
 1 0
 1 1
 0 0
 0 0

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

0 further Hilbert basis elements of higher degree:

2 extreme rays:
 0 1
 1 0

2 support hyperplanes:
 0 1
 1 0