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5 Hilbert basis elements
1 lattice points in polytope (Hilbert basis elements of degree 1)
2 extreme rays
2 support hyperplanes
embedding dimension = 3
rank = 2
external index = 5
size of triangulation = 1
resulting sum of |det|s = 40
grading:
-1 -1 -1
degrees of extreme rays:
5:1 15:1
multiplicity = 8/15
multiplicity (float) = 0.533333333333
Hilbert series:
1 0 0 1 0 1 0 0 2 0 1 0 0 1 0 1
denominator with 2 factors:
1:1 15:1
degree of Hilbert Series as rational function = -1
Hilbert series with cyclotomic denominator:
1 0 0 1 0 1 0 0 2 0 1 0 0 1 0 1
cyclotomic denominator:
1:2 3:1 5:1 15:1
Hilbert quasi-polynomial of period 15:
0: 15 8
1: 7 8
2: -1 8
3: 6 8
4: -2 8
5: 5 8
6: -3 8
7: -11 8
8: 11 8
9: 3 8
10: 10 8
11: 2 8
12: -6 8
13: 1 8
14: -7 8
with common denominator = 15
rank of class group = 0
finite cyclic summands:
40:1
***********************************************************************
1 lattice points in polytope (Hilbert basis elements of degree 1):
0 -1 0
4 further Hilbert basis elements of higher degree:
5 -8 0
10 -15 0
-5 -3 0
-10 -5 0
2 extreme rays:
10 -15 0
-10 -5 0
2 support hyperplanes:
-3 -2 0
1 -2 0
1 equations:
0 0 1
1 congruences:
4 0 0 5
2 basis elements of generated lattice:
5 0 0
0 1 0
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