File: simple_grading.ref

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normaliz 3.1.1%2Bds-1
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3 Hilbert basis elements
0 Hilbert basis elements of degree 1
2 extreme rays
2 support hyperplanes

embedding dimension = 2
rank = 2 (maximal)
external index = 1
internal index = 1
original monoid is integrally closed

size of triangulation   = 2
resulting sum of |det|s = 2

grading:
1 1 

degrees of extreme rays:
3: 2  

multiplicity = 1/3

Hilbert series:
1 -1 1 
denominator with 2 factors:
1: 1  3: 1  

degree of Hilbert Series as rational function = -2

Hilbert series with cyclotomic denominator:
1 -1 1 
cyclotomic denominator:
1: 2  3: 1  

Hilbert quasi-polynomial of period 3:
 0:   3 1
 1:  -1 1
 2:   1 1
with common denominator = 3

rank of class group = 0
finite cyclic summands:
3: 1  

***********************************************************************

0 Hilbert basis elements of degree 1:

3 further Hilbert basis elements of higher degree:
 1 1
 1 2
 2 1

2 extreme rays:
 1 2
 2 1

2 support hyperplanes:
 -1  2
  2 -1