3x3_sign2.ref

6 Hilbert basis elements
6 Hilbert basis elements of degree 1
5 extreme rays
5 support hyperplanes

embedding dimension = 9
rank = 3
external index = 1

size of triangulation   = 3
resulting sum of |det|s = 5

grading:
0 0 0 0 1 0 0 0 0 

degrees of extreme rays:
1: 5  

Hilbert basis elements are of degree 1

multiplicity = 5

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

degree of Hilbert Series as rational function = -1

The numerator of the Hilbert Series is symmetric.

Hilbert polynomial:
2 5 5 
with common denominator = 2

rank of class group = 2
class group is free

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6 Hilbert basis elements of degree 1:
 0  2 1 2 1 0 1 0 2
 1  0 2 2 1 0 0 2 1
 1  1 1 1 1 1 1 1 1
 1  2 0 0 1 2 2 0 1
 2 -1 2 1 1 1 0 3 0
 2  0 1 0 1 2 1 2 0

0 further Hilbert basis elements of higher degree:

5 extreme rays:
 0  2 1 2 1 0 1 0 2
 1  0 2 2 1 0 0 2 1
 1  2 0 0 1 2 2 0 1
 2 -1 2 1 1 1 0 3 0
 2  0 1 0 1 2 1 2 0

5 support hyperplanes:
 -2 -1 0 0  4 0 0 0 0
 -1  0 0 0  2 0 0 0 0
  0 -1 0 0  2 0 0 0 0
  1  1 0 0 -1 0 0 0 0
  2  1 0 0 -2 0 0 0 0

6 equations:
 1 0 0 0 0  1 -2 -1  1
 0 1 0 0 0  1 -2  0  0
 0 0 1 0 0  1 -1 -1  0
 0 0 0 1 0 -1  2  0 -2
 0 0 0 0 1 -1  1  0 -1
 0 0 0 0 0  3 -4 -1  2

3 basis elements of lattice:
 1 0 -1 -2 0  2  1  0 -1
 0 1 -1 -1 0  1  1 -1  0
 0 0  3  4 1 -2 -1  2  2