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6 Hilbert basis elements
6 lattice points in polytope (Hilbert basis elements of degree 1)
4 generators of integral closure of the ideal
4 extreme rays
4 support hyperplanes
embedding dimension = 3
rank = 3 (maximal)
external index = 1
internal index = 1
original monoid is integrally closed in chosen lattice
size of triangulation = 4
resulting sum of |det|s = 4
grading:
1 1 -2
degrees of extreme rays:
1:4
Hilbert basis elements are of degree 1
multiplicity = 4
Hilbert series:
1 3
denominator with 3 factors:
1:3
degree of Hilbert Series as rational function = -2
Hilbert polynomial:
1 3 2
with common denominator = 1
ideal is primary to the ideal generated by the indeterminates
multiplicity of the ideal = 9
rank of class group = 1
class group is free
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6 lattice points in polytope (Hilbert basis elements of degree 1):
0 1 0
0 3 1
1 0 0
1 2 1
2 1 1
3 0 1
0 further Hilbert basis elements of higher degree:
4 generators of integral closure of the ideal:
0 3
1 2
2 1
3 0
4 extreme rays:
0 1 0
0 3 1
1 0 0
3 0 1
4 support hyperplanes:
0 0 1
0 1 0
1 0 0
1 1 -3
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