CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutSign UpSign In

Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
all in one place.

| Download

GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

Views: 418386
Tweet
Share
Share
17 Hilbert basis elements
1 Hilbert basis elements of degree 1
16 extreme rays
11 support hyperplanes

3 excluded faces

embedding dimension = 8
rank = 8 (maximal)
external index = 1

size of triangulation   = 16
resulting sum of |det|s = 19

grading:
1 1 1 1 1 1 1 1 

degrees of extreme rays:
1: 1  2: 13  4: 2  

multiplicity = 1/8

Hilbert series:
1 0 8 0 14 1 7 0 1 
denominator with 8 factors:
1: 1  2: 6  4: 1  

shift = 1

degree of Hilbert Series as rational function = -8

Hilbert series with cyclotomic denominator:
1 0 8 0 14 1 7 0 1 
cyclotomic denominator:
1: 8  2: 7  4: 1  

Hilbert quasi-polynomial of period 4:
 0:      0  16896  25312  24304 11830 2884 343 16
 1:  80640 209088 210112 108304 31360 5152 448 16
 2:  10080  16896  25312  24304 11830 2884 343 16
 3:  80640 209088 210112 108304 31360 5152 448 16
with common denominator = 645120

rank of class group = 3
class group is free

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

1 Hilbert basis elements of degree 1:
 1 0 0 0 0 0 0 0

16 further Hilbert basis elements of higher degree:
 0 0 0 1 0 0 1 0
 0 0 1 0 0 1 0 0
 0 0 1 1 0 0 0 0
 0 1 0 0 1 0 0 0
 0 1 0 1 0 0 0 0
 0 1 1 0 0 0 0 0
 1 0 0 0 0 0 0 1
 1 0 0 0 0 0 1 0
 1 0 0 0 0 1 0 0
 1 0 0 0 1 0 0 0
 1 0 0 1 0 0 0 0
 1 0 1 0 0 0 0 0
 1 1 0 0 0 0 0 0
 0 1 1 1 0 0 0 0
 0 1 1 1 0 0 0 1
 1 0 0 0 1 1 1 0

16 extreme rays:
 1 0 0 0 0 0 0 0
 0 0 0 1 0 0 1 0
 0 0 1 0 0 1 0 0
 0 0 1 1 0 0 0 0
 0 1 0 0 1 0 0 0
 0 1 0 1 0 0 0 0
 0 1 1 0 0 0 0 0
 1 0 0 0 0 0 0 1
 1 0 0 0 0 0 1 0
 1 0 0 0 0 1 0 0
 1 0 0 0 1 0 0 0
 1 0 0 1 0 0 0 0
 1 0 1 0 0 0 0 0
 1 1 0 0 0 0 0 0
 0 1 1 1 0 0 0 1
 1 0 0 0 1 1 1 0

11 support hyperplanes:
 0  0  0  0  0  0  0  1
 0  0  0  0  0  0  1  0
 0  0  0  0  0  1  0  0
 0  0  0  0  1  0  0  0
 0  0  0  1  0  0  0  0
 0  0  1  0  0  0  0  0
 0  1  0  0  0  0  0  0
 1 -1  1  1  1 -1 -1 -1
 1  0  0  0  0  0  0  0
 1  1 -1  1 -1  1 -1 -1
 1  1  1 -1 -1 -1  1 -1

3 excluded faces:
 1 -1  1  1  1 -1 -1 -1
 1  1 -1  1 -1  1 -1 -1
 1  1  1 -1 -1 -1  1 -1