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33 Hilbert basis elements
19 lattice points in polytope (Hilbert basis elements of degree 1)
19 extreme rays
134 support hyperplanes
embedding dimension = 9
rank = 9 (maximal)
external index = 4
internal index = 1
original monoid is not integrally closed in chosen lattice
size of triangulation = 281
resulting sum of |det|s = 425
grading:
1 1 1 1 1 1 1 1 1
with denominator = 4
degrees of extreme rays:
1:19
Hilbert basis elements are not of degree 1
multiplicity = 425
Hilbert series:
1 10 49 137 161 63 4
denominator with 9 factors:
1:9
degree of Hilbert Series as rational function = -3
Hilbert polynomial:
40320 142512 216092 191156 112105 46088 14098 3284 425
with common denominator = 40320
rank of class group = 125
class group is free
***********************************************************************
19 lattice points in polytope (Hilbert basis elements of degree 1):
0 0 0 0 1 1 1 0 1
0 0 1 1 1 1 0 0 0
0 1 0 0 1 1 1 0 0
0 1 0 1 1 0 0 0 1
0 1 0 1 1 1 0 0 0
0 1 1 0 1 0 1 0 0
0 1 1 0 1 1 0 0 0
0 1 1 1 0 0 1 0 0
0 1 1 1 1 0 0 0 0
1 0 0 1 0 1 1 0 0
1 0 0 1 1 1 0 0 0
1 0 1 0 0 0 0 1 1
1 0 1 0 0 1 0 1 0
1 0 1 1 1 0 0 0 0
1 1 0 0 0 1 0 0 1
1 1 0 0 1 0 1 0 0
1 1 0 1 0 0 0 1 0
1 1 1 0 1 0 0 0 0
1 1 1 1 0 0 0 0 0
14 further Hilbert basis elements of higher degree:
1 1 0 1 1 2 1 0 1
1 1 0 1 2 1 1 0 1
2 1 1 1 1 1 0 1 0
1 3 1 1 2 1 2 0 1
2 2 0 2 2 2 1 0 1
2 2 1 1 1 1 1 1 2
2 2 1 1 1 2 1 1 1
2 2 2 2 1 0 1 1 1
2 2 2 2 2 0 0 1 1
3 1 1 1 1 2 1 1 1
3 2 1 1 1 1 1 1 1
3 2 2 1 1 1 0 1 1
2 3 1 2 2 1 2 1 2
3 3 2 3 2 0 1 1 1
19 extreme rays:
0 0 0 0 1 1 1 0 1
0 0 1 1 1 1 0 0 0
0 1 0 0 1 1 1 0 0
0 1 0 1 1 0 0 0 1
0 1 0 1 1 1 0 0 0
0 1 1 0 1 0 1 0 0
0 1 1 0 1 1 0 0 0
0 1 1 1 0 0 1 0 0
0 1 1 1 1 0 0 0 0
1 0 0 1 0 1 1 0 0
1 0 0 1 1 1 0 0 0
1 0 1 0 0 0 0 1 1
1 0 1 0 0 1 0 1 0
1 0 1 1 1 0 0 0 0
1 1 0 0 0 1 0 0 1
1 1 0 0 1 0 1 0 0
1 1 0 1 0 0 0 1 0
1 1 1 0 1 0 0 0 0
1 1 1 1 0 0 0 0 0
134 support hyperplanes:
-11 5 9 -3 5 13 1 9 -7
-7 -3 1 9 17 5 -7 1 5
-7 1 5 1 1 9 5 5 -3
-7 1 9 -3 13 17 -7 9 -11
-5 3 5 -1 1 5 1 3 -3
-3 1 -3 5 5 1 -3 5 1
-3 1 1 1 1 1 1 1 1
-3 1 3 -1 1 3 1 3 -1
-3 1 3 1 -1 3 3 1 -1
-3 3 -1 1 3 5 -3 -1 5
-3 5 -3 5 1 -3 1 9 1
-3 5 -3 5 1 1 -3 5 1
-1 -5 -1 7 7 3 -1 -1 3
-1 -3 1 3 5 -1 -1 1 5
-1 -1 -1 3 3 -1 -1 3 3
-1 -1 1 1 1 -1 1 1 3
-1 -1 2 0 0 1 2 2 1
-1 -1 3 -1 -1 3 3 3 3
-1 -1 3 -1 1 1 1 3 1
-1 0 1 0 0 1 1 1 0
-1 1 -1 1 1 -1 1 3 1
-1 1 -1 1 1 1 -1 1 1
-1 1 -1 1 1 1 -1 3 -1
-1 1 -1 1 1 3 -1 -1 3
-1 1 -1 1 1 3 -1 5 -3
-1 1 -1 2 1 0 -1 2 0
-1 1 -1 3 1 -1 -1 3 1
-1 1 0 0 1 2 -1 3 -2
-1 1 0 1 0 0 0 1 0
-1 1 0 2 0 -1 0 2 1
-1 1 1 -1 1 1 1 1 -1
-1 1 1 -1 1 3 -1 1 -1
-1 1 1 0 0 1 0 1 -1
-1 1 1 1 -1 1 1 1 -1
-1 1 2 0 0 1 0 0 -1
-1 1 2 1 0 0 0 -1 0
-1 1 4 2 0 -1 0 -2 1
-1 3 -5 3 3 -1 -1 7 -1
-1 3 -1 -1 3 -1 3 3 -1
-1 3 -1 1 1 -1 1 3 -1
-1 3 -1 3 -1 -1 -1 3 3
-1 3 -1 3 -1 -1 3 3 -1
-1 3 3 -1 -1 3 -1 -1 -1
0 -2 3 -1 2 1 0 3 1
0 -1 0 1 1 0 0 0 1
0 -1 1 0 1 0 0 1 1
0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 1 0 0
0 0 0 0 0 1 0 0 0
0 0 0 0 1 -1 1 1 1
0 0 0 1 0 0 0 0 0
0 0 0 1 1 0 -1 0 0
0 0 1 -1 0 1 0 1 1
0 0 1 0 0 0 0 0 0
0 0 1 0 1 1 -1 0 -1
0 0 1 1 -1 0 1 -1 0
0 0 1 1 1 0 -1 -1 0
0 1 0 -1 1 0 1 0 0
0 1 0 -1 1 0 1 1 -1
0 1 0 0 0 1 -1 -1 1
0 1 0 1 -1 0 2 1 -1
0 2 0 -1 1 0 1 2 -2
0 2 1 0 -1 1 -1 -2 1
1 -7 1 5 5 9 1 1 -3
1 -3 -1 3 3 1 1 -1 1
1 -3 1 1 1 1 1 1 1
1 -3 1 1 5 -3 1 1 5
1 -3 1 5 1 1 1 -3 1
1 -3 1 5 5 1 -3 -3 1
1 -3 5 -1 3 1 -1 3 1
1 -3 5 9 13 1 -11 -7 1
1 -1 -1 1 1 1 1 -1 1
1 -1 0 1 1 0 0 -1 0
1 -1 1 1 1 1 -1 -1 -1
1 -1 1 3 -1 1 1 -1 -1
1 -1 3 0 2 1 -2 0 -1
1 -1 3 3 5 1 -5 -3 -1
1 0 0 -1 2 -1 1 0 0
1 0 0 0 0 0 0 -1 0
1 0 0 0 1 -1 0 0 0
1 1 -3 1 1 1 1 1 1
1 1 -3 1 1 1 1 5 -3
1 1 -3 1 1 5 1 -3 5
1 1 -3 5 5 -3 -3 5 1
1 1 -1 -1 1 1 1 -1 1
1 1 -1 1 1 -1 -1 1 1
1 1 1 -3 1 1 1 1 1
1 1 1 -3 3 -1 3 1 -1
1 1 1 -3 5 -3 5 1 1
1 1 1 -1 -1 1 -1 -1 1
1 1 1 -1 1 -1 1 -1 -1
1 1 1 1 -3 1 1 -3 1
1 1 1 1 -1 -1 3 -1 -1
1 1 1 1 1 -3 1 1 1
1 1 1 1 1 1 -3 -3 1
1 1 5 1 1 -3 1 -3 1
1 2 0 -3 2 1 1 0 -1
1 2 1 -1 -1 3 -2 -2 0
1 3 -1 -3 3 1 1 -1 1
1 3 1 -5 5 -1 5 1 -3
1 3 1 -1 -1 1 -1 -3 1
1 3 1 -1 -1 3 -3 -3 1
1 5 -3 -3 5 1 1 9 -7
1 5 1 -7 5 1 5 1 -3
1 5 1 -7 9 -3 9 1 -3
1 5 3 -3 -1 7 -5 -3 -1
2 -1 0 1 1 0 0 -1 -1
2 1 0 -3 4 -1 2 0 -2
3 -5 -1 3 3 3 3 -1 -1
3 -5 3 7 -1 3 3 -5 -1
3 -1 -1 -1 3 -1 3 -1 -1
3 -1 -1 -1 7 -5 3 3 3
3 -1 -1 3 3 -1 -1 -1 -1
3 -1 3 -1 3 -1 -1 -1 -1
3 -1 3 3 7 -1 -5 -5 -1
3 1 1 -1 1 -1 -1 -3 1
3 3 -1 -5 3 3 3 -1 -1
3 3 -1 -1 -1 3 -1 -5 3
3 3 1 -1 -1 1 -3 -5 3
3 3 3 -1 -1 -1 -1 -5 3
3 7 3 -5 -1 3 -1 -5 -1
3 7 3 -1 -5 3 -5 -9 7
3 11 3 -1 -5 7 -9 -13 7
5 1 1 -7 9 -3 5 1 -3
5 1 1 -3 5 -3 1 -3 -3
5 5 1 -3 -3 5 -3 -7 1
5 9 1 -3 -3 5 -7 -11 5
7 -1 3 -1 7 -5 -1 -5 -1
7 3 -1 -9 15 -5 7 -1 -5
7 11 3 -9 -1 7 -5 -9 -1
9 -7 1 5 5 1 1 -7 -3
9 -3 1 1 5 -3 1 -7 -3
11 -1 -1 -1 7 -5 3 -5 -5
1 congruences:
1 1 1 1 1 1 1 1 1 4
9 basis elements of generated lattice:
1 0 0 0 0 0 0 0 -1
0 1 0 0 0 0 0 0 -1
0 0 1 0 0 0 0 0 -1
0 0 0 1 0 0 0 0 -1
0 0 0 0 1 0 0 0 -1
0 0 0 0 0 1 0 0 -1
0 0 0 0 0 0 1 0 -1
0 0 0 0 0 0 0 1 -1
0 0 0 0 0 0 0 0 4
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