lattice_ideal.ref

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

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

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

grading:
1 1 
with denominator = 2

degrees of extreme rays:
1: 2  

Hilbert basis elements are of degree 1

multiplicity = 2

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

degree of Hilbert Series as rational function = -1

The numerator of the Hilbert Series is symmetric.

Hilbert polynomial:
1 2 
with common denominator = 1

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4 original generators:
 0 2
 4 0
 1 1
 3 1

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

2 support hyperplanes:
 0 1
 1 0

1 congruences:
 1 1 2

2 basis elements of lattice:
 1 1
 0 2