cross2.ref

5 Hilbert basis elements
5 Hilbert basis elements of degree 1
4 extreme rays
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 triangulation   = 2
resulting sum of |det|s = 4

grading:
0 0 1 

degrees of extreme rays:
1: 4  

Hilbert basis elements are of degree 1

multiplicity = 4

Hilbert series:
3 1 
denominator with 3 factors:
1: 3  

shift = 1

degree of Hilbert Series as rational function = -1

Hilbert polynomial:
0 1 2 
with common denominator = 1

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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

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

1 excluded faces:
 -1 -1 1