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
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
|
17 Hilbert basis elements
6 lattice points in polytope (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 in chosen lattice
size of triangulation = 69
resulting sum of |det|s = 72
grading:
1 1 1 1 1 1 0
degrees of extreme rays:
1:6 3:10
multiplicity = 322/243
multiplicity (float) = 1.32510288066
Hilbert series:
1 5 15 39 75 117 166 170 153 119 64 30 11 1
denominator with 7 factors:
1:1 3:6
degree of Hilbert Series as rational function = -6
Hilbert series with cyclotomic denominator:
-1 -5 -15 -39 -75 -117 -166 -170 -153 -119 -64 -30 -11 -1
cyclotomic denominator:
1:7 3:6
Hilbert quasi-polynomial of period 3:
0: 87480 174960 143694 64395 17145 2565 161
1: 104480 189366 146919 64370 17040 2544 161
2: 79280 171012 139674 62305 16725 2523 161
with common denominator = 87480
ideal is not primary to the ideal generated by the indeterminates
***********************************************************************
6 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 1 0 0 0 0 0
1 0 0 0 0 0 0
11 further Hilbert basis elements of higher degree:
0 0 1 1 0 1 1
0 0 1 1 1 0 1
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 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 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 1 0 0 0 0 0
1 0 0 0 0 0 0
0 0 1 1 0 1 1
0 0 1 1 1 0 1
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 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
|
