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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
rank of class group = 17
class group is free
***********************************************************************
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
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