rational.ref

1 Hilbert basis elements of degree 1
3 extreme rays
3 support hyperplanes

embedding dimension = 3
rank = 3 (maximal)
external index = 1
internal index = 15

size of triangulation   = 1
resulting sum of |det|s = 15

grading:
0 0 1 

degrees of extreme rays:
2: 1  3: 1  4: 1  

multiplicity = 5/8

Hilbert series:
1 0 0 3 2 -1 2 2 1 1 1 1 2 
denominator with 3 factors:
1: 1  2: 1  12: 1  

degree of Hilbert Series as rational function = -3

Hilbert series with cyclotomic denominator:
-1 -1 -1 -3 -4 -3 -2 
cyclotomic denominator:
1: 3  2: 2  3: 1  4: 1  

Hilbert quasi-polynomial of period 12:
  0:   48 28 15
  1:   11 22 15
  2:  -20 28 15
  3:   39 22 15
  4:   32 28 15
  5:   -5 22 15
  6:   12 28 15
  7:   23 22 15
  8:   16 28 15
  9:   27 22 15
 10:   -4 28 15
 11:    7 22 15
with common denominator = 48

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1 Hilbert basis elements of degree 1:
 0 0 1

3 extreme rays:
  1  1 2
 -1 -1 3
  1 -2 4

3 support hyperplanes:
 -8  2 3
  1 -1 0
  2  7 3