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17 Hilbert basis elements
16 Hilbert basis elements of degree 1
10 generators of integral closure of the ideal
16 extreme rays
24 support hyperplanes
embedding dimension = 7
rank = 7 (maximal)
external index = 1
internal index = 1
original monoid is not integrally closed
size of triangulation = 69
resulting sum of |det|s = 72
grading:
1 1 1 1 1 1 -2
degrees of extreme rays:
1: 16
Hilbert basis elements are not of degree 1
multiplicity = 72
Hilbert series:
1 9 31 25 6
denominator with 7 factors:
1: 7
degree of Hilbert Series as rational function = -3
Hilbert polynomial:
60 194 284 245 130 41 6
with common denominator = 60
ideal is not primary to the ideal generated by the indeterminates
rank of class group = 17
class group is free
***********************************************************************
16 Hilbert basis elements of degree 1:
0 0 0 0 0 1 0
0 0 0 0 1 0 0
0 0 0 1 0 0 0
0 0 1 0 0 0 0
0 0 1 1 0 1 1
0 0 1 1 1 0 1
0 1 0 0 0 0 0
0 1 0 0 1 1 1
0 1 0 1 1 0 1
0 1 1 0 0 1 1
1 0 0 0 0 0 0
1 0 0 0 1 1 1
1 0 0 1 0 1 1
1 0 1 0 1 0 1
1 1 0 1 0 0 1
1 1 1 0 0 0 1
1 further Hilbert basis elements of higher degree:
1 1 1 1 1 1 2
10 generators of integral closure of the ideal:
0 0 1 1 0 1
0 0 1 1 1 0
0 1 0 0 1 1
0 1 0 1 1 0
0 1 1 0 0 1
1 0 0 0 1 1
1 0 0 1 0 1
1 0 1 0 1 0
1 1 0 1 0 0
1 1 1 0 0 0
16 extreme rays:
0 0 0 0 0 1 0
0 0 0 0 1 0 0
0 0 0 1 0 0 0
0 0 1 0 0 0 0
0 0 1 1 0 1 1
0 0 1 1 1 0 1
0 1 0 0 0 0 0
0 1 0 0 1 1 1
0 1 0 1 1 0 1
0 1 1 0 0 1 1
1 0 0 0 0 0 0
1 0 0 0 1 1 1
1 0 0 1 0 1 1
1 0 1 0 1 0 1
1 1 0 1 0 0 1
1 1 1 0 0 0 1
24 support hyperplanes:
0 0 0 0 0 0 1
0 0 0 0 0 1 0
0 0 0 0 1 0 0
0 0 0 1 0 0 0
0 0 1 0 0 0 0
0 0 1 1 0 1 -1
0 0 1 1 1 0 -1
0 1 0 0 0 0 0
0 1 0 0 1 1 -1
0 1 0 1 1 0 -1
0 1 1 0 0 1 -1
0 1 1 1 1 1 -2
1 0 0 0 0 0 0
1 0 0 0 1 1 -1
1 0 0 1 0 1 -1
1 0 1 0 1 0 -1
1 0 1 1 1 1 -2
1 1 0 1 0 0 -1
1 1 0 1 1 1 -2
1 1 1 0 0 0 -1
1 1 1 0 1 1 -2
1 1 1 1 0 1 -2
1 1 1 1 1 0 -2
1 1 1 1 1 1 -3
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