knapsack_11_60_test2.ref

6 Hilbert basis elements of degree 1
7 extreme rays
8 support hyperplanes

embedding dimension = 5
rank = 5 (maximal)
external index = 1
internal index = 2

size of triangulation   = 4
resulting sum of |det|s = 14

grading:
0 0 0 0 1 

degrees of extreme rays:
1: 5  2: 1  3: 1  

multiplicity = 10/3

Hilbert series:
1 2 4 3 4 2 4 
denominator with 5 factors:
1: 4  6: 1  

degree of Hilbert Series as rational function = -4

Hilbert series with cyclotomic denominator:
-1 -3 -6 -6 -4 
cyclotomic denominator:
1: 5  2: 1  3: 1  

Hilbert quasi-polynomial of period 6:
 0:  72 150 139 62 10
 1:  71 150 139 62 10
 2:  72 150 139 62 10
 3:  63 150 139 62 10
 4:  80 150 139 62 10
 5:  63 150 139 62 10
with common denominator = 72

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6 Hilbert basis elements of degree 1:
 0 1 1 0 1
 0 2 0 0 1
 2 0 1 0 1
 2 1 0 0 1
 3 1 0 0 1
 4 0 0 0 1

7 extreme rays:
 0 1 1 0 1
 0 2 0 0 1
 2 0 1 0 1
 3 1 0 0 1
 4 0 0 0 1
 0 4 1 0 2
 0 0 0 2 3

8 support hyperplanes:
 -3 -5 -8 -21 14
 -1 -3  0  -9  6
 -1 -2 -4  -9  6
 -1 -1 -2  -6  4
  0  0  0   1  0
  0  0  1   0  0
  1  0  0   0  0
  1  2  2   6 -4