mode456.ref

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

embedding dimension = 3
rank = 2
external index = 5

size of triangulation   = 1
resulting sum of |det|s = 40

grading:
-1 -1 -1 

degrees of extreme rays:
5: 1  15: 1  

multiplicity = 8/15

Hilbert series:
1 0 0 1 0 1 0 0 2 0 1 0 0 1 0 1 
denominator with 2 factors:
1: 1  15: 1  

degree of Hilbert Series as rational function = -1

Hilbert series with cyclotomic denominator:
1 0 0 1 0 1 0 0 2 0 1 0 0 1 0 1 
cyclotomic denominator:
1: 2  3: 1  5: 1  15: 1  

Hilbert quasi-polynomial of period 15:
  0:   15 8
  1:    7 8
  2:   -1 8
  3:    6 8
  4:   -2 8
  5:    5 8
  6:   -3 8
  7:  -11 8
  8:   11 8
  9:    3 8
 10:   10 8
 11:    2 8
 12:   -6 8
 13:    1 8
 14:   -7 8
with common denominator = 15

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

4 further Hilbert basis elements of higher degree:
   5  -8 0
  10 -15 0
  -5  -3 0
 -10  -5 0

2 extreme rays:
  10 -15 0
 -10  -5 0

2 support hyperplanes:
 -3 -2 0
  1 -2 0

1 equations:
 0 0 1

1 congruences:
 4 0 0 5

2 basis elements of lattice:
 5 0 0
 0 1 0