1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
|
17 Hilbert basis elements
16 lattice points in polytope (Hilbert basis elements of degree 1)
16 extreme rays
24 support hyperplanes
embedding dimension = 7
rank = 7 (maximal)
external index = 1
internal index = 1
original monoid is not integrally closed in chosen lattice
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
rank of class group = 17
class group is free
***********************************************************************
16 lattice points in polytope (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
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
|
