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: 418384
19 Hilbert basis elements of degree 1
19 extreme rays
134 support hyperplanes

embedding dimension = 9
rank = 9 (maximal)
external index = 4
internal index = 1

size of triangulation   = 281
resulting sum of |det|s = 425

grading:
1 1 1 1 1 1 1 1 1 
with denominator = 4

degrees of extreme rays:
1: 19  

multiplicity = 425

Hilbert series:
1 10 49 137 161 63 4 
denominator with 9 factors:
1: 9  

degree of Hilbert Series as rational function = -3

Hilbert polynomial:
40320 142512 216092 191156 112105 46088 14098 3284 425 
with common denominator = 40320

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

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

19 extreme rays:
 0 0 0 0 1 1 1 0 1
 0 0 1 1 1 1 0 0 0
 0 1 0 0 1 1 1 0 0
 0 1 0 1 1 0 0 0 1
 0 1 0 1 1 1 0 0 0
 0 1 1 0 1 0 1 0 0
 0 1 1 0 1 1 0 0 0
 0 1 1 1 0 0 1 0 0
 0 1 1 1 1 0 0 0 0
 1 0 0 1 0 1 1 0 0
 1 0 0 1 1 1 0 0 0
 1 0 1 0 0 0 0 1 1
 1 0 1 0 0 1 0 1 0
 1 0 1 1 1 0 0 0 0
 1 1 0 0 0 1 0 0 1
 1 1 0 0 1 0 1 0 0
 1 1 0 1 0 0 0 1 0
 1 1 1 0 1 0 0 0 0
 1 1 1 1 0 0 0 0 0

134 support hyperplanes:
 -11  5  9 -3  5 13   1   9  -7
  -7 -3  1  9 17  5  -7   1   5
  -7  1  5  1  1  9   5   5  -3
  -7  1  9 -3 13 17  -7   9 -11
  -5  3  5 -1  1  5   1   3  -3
  -3  1 -3  5  5  1  -3   5   1
  -3  1  1  1  1  1   1   1   1
  -3  1  3 -1  1  3   1   3  -1
  -3  1  3  1 -1  3   3   1  -1
  -3  3 -1  1  3  5  -3  -1   5
  -3  5 -3  5  1 -3   1   9   1
  -3  5 -3  5  1  1  -3   5   1
  -1 -5 -1  7  7  3  -1  -1   3
  -1 -3  1  3  5 -1  -1   1   5
  -1 -1 -1  3  3 -1  -1   3   3
  -1 -1  1  1  1 -1   1   1   3
  -1 -1  2  0  0  1   2   2   1
  -1 -1  3 -1 -1  3   3   3   3
  -1 -1  3 -1  1  1   1   3   1
  -1  0  1  0  0  1   1   1   0
  -1  1 -1  1  1 -1   1   3   1
  -1  1 -1  1  1  1  -1   1   1
  -1  1 -1  1  1  1  -1   3  -1
  -1  1 -1  1  1  3  -1  -1   3
  -1  1 -1  1  1  3  -1   5  -3
  -1  1 -1  2  1  0  -1   2   0
  -1  1 -1  3  1 -1  -1   3   1
  -1  1  0  0  1  2  -1   3  -2
  -1  1  0  1  0  0   0   1   0
  -1  1  0  2  0 -1   0   2   1
  -1  1  1 -1  1  1   1   1  -1
  -1  1  1 -1  1  3  -1   1  -1
  -1  1  1  0  0  1   0   1  -1
  -1  1  1  1 -1  1   1   1  -1
  -1  1  2  0  0  1   0   0  -1
  -1  1  2  1  0  0   0  -1   0
  -1  1  4  2  0 -1   0  -2   1
  -1  3 -5  3  3 -1  -1   7  -1
  -1  3 -1 -1  3 -1   3   3  -1
  -1  3 -1  1  1 -1   1   3  -1
  -1  3 -1  3 -1 -1  -1   3   3
  -1  3 -1  3 -1 -1   3   3  -1
  -1  3  3 -1 -1  3  -1  -1  -1
   0 -2  3 -1  2  1   0   3   1
   0 -1  0  1  1  0   0   0   1
   0 -1  1  0  1  0   0   1   1
   0  0  0  0  0  0   0   0   1
   0  0  0  0  0  0   0   1   0
   0  0  0  0  0  0   1   0   0
   0  0  0  0  0  1   0   0   0
   0  0  0  0  1 -1   1   1   1
   0  0  0  1  0  0   0   0   0
   0  0  0  1  1  0  -1   0   0
   0  0  1 -1  0  1   0   1   1
   0  0  1  0  0  0   0   0   0
   0  0  1  0  1  1  -1   0  -1
   0  0  1  1 -1  0   1  -1   0
   0  0  1  1  1  0  -1  -1   0
   0  1  0 -1  1  0   1   0   0
   0  1  0 -1  1  0   1   1  -1
   0  1  0  0  0  1  -1  -1   1
   0  1  0  1 -1  0   2   1  -1
   0  2  0 -1  1  0   1   2  -2
   0  2  1  0 -1  1  -1  -2   1
   1 -7  1  5  5  9   1   1  -3
   1 -3 -1  3  3  1   1  -1   1
   1 -3  1  1  1  1   1   1   1
   1 -3  1  1  5 -3   1   1   5
   1 -3  1  5  1  1   1  -3   1
   1 -3  1  5  5  1  -3  -3   1
   1 -3  5 -1  3  1  -1   3   1
   1 -3  5  9 13  1 -11  -7   1
   1 -1 -1  1  1  1   1  -1   1
   1 -1  0  1  1  0   0  -1   0
   1 -1  1  1  1  1  -1  -1  -1
   1 -1  1  3 -1  1   1  -1  -1
   1 -1  3  0  2  1  -2   0  -1
   1 -1  3  3  5  1  -5  -3  -1
   1  0  0 -1  2 -1   1   0   0
   1  0  0  0  0  0   0  -1   0
   1  0  0  0  1 -1   0   0   0
   1  1 -3  1  1  1   1   1   1
   1  1 -3  1  1  1   1   5  -3
   1  1 -3  1  1  5   1  -3   5
   1  1 -3  5  5 -3  -3   5   1
   1  1 -1 -1  1  1   1  -1   1
   1  1 -1  1  1 -1  -1   1   1
   1  1  1 -3  1  1   1   1   1
   1  1  1 -3  3 -1   3   1  -1
   1  1  1 -3  5 -3   5   1   1
   1  1  1 -1 -1  1  -1  -1   1
   1  1  1 -1  1 -1   1  -1  -1
   1  1  1  1 -3  1   1  -3   1
   1  1  1  1 -1 -1   3  -1  -1
   1  1  1  1  1 -3   1   1   1
   1  1  1  1  1  1  -3  -3   1
   1  1  5  1  1 -3   1  -3   1
   1  2  0 -3  2  1   1   0  -1
   1  2  1 -1 -1  3  -2  -2   0
   1  3 -1 -3  3  1   1  -1   1
   1  3  1 -5  5 -1   5   1  -3
   1  3  1 -1 -1  1  -1  -3   1
   1  3  1 -1 -1  3  -3  -3   1
   1  5 -3 -3  5  1   1   9  -7
   1  5  1 -7  5  1   5   1  -3
   1  5  1 -7  9 -3   9   1  -3
   1  5  3 -3 -1  7  -5  -3  -1
   2 -1  0  1  1  0   0  -1  -1
   2  1  0 -3  4 -1   2   0  -2
   3 -5 -1  3  3  3   3  -1  -1
   3 -5  3  7 -1  3   3  -5  -1
   3 -1 -1 -1  3 -1   3  -1  -1
   3 -1 -1 -1  7 -5   3   3   3
   3 -1 -1  3  3 -1  -1  -1  -1
   3 -1  3 -1  3 -1  -1  -1  -1
   3 -1  3  3  7 -1  -5  -5  -1
   3  1  1 -1  1 -1  -1  -3   1
   3  3 -1 -5  3  3   3  -1  -1
   3  3 -1 -1 -1  3  -1  -5   3
   3  3  1 -1 -1  1  -3  -5   3
   3  3  3 -1 -1 -1  -1  -5   3
   3  7  3 -5 -1  3  -1  -5  -1
   3  7  3 -1 -5  3  -5  -9   7
   3 11  3 -1 -5  7  -9 -13   7
   5  1  1 -7  9 -3   5   1  -3
   5  1  1 -3  5 -3   1  -3  -3
   5  5  1 -3 -3  5  -3  -7   1
   5  9  1 -3 -3  5  -7 -11   5
   7 -1  3 -1  7 -5  -1  -5  -1
   7  3 -1 -9 15 -5   7  -1  -5
   7 11  3 -9 -1  7  -5  -9  -1
   9 -7  1  5  5  1   1  -7  -3
   9 -3  1  1  5 -3   1  -7  -3
  11 -1 -1 -1  7 -5   3  -5  -5

1 congruences:
 1 1 1 1 1 1 1 1 1 4

9 basis elements of lattice:
 1 0 0 0 0 0 0 0 -1
 0 1 0 0 0 0 0 0 -1
 0 0 1 0 0 0 0 0 -1
 0 0 0 1 0 0 0 0 -1
 0 0 0 0 1 0 0 0 -1
 0 0 0 0 0 1 0 0 -1
 0 0 0 0 0 0 1 0 -1
 0 0 0 0 0 0 0 1 -1
 0 0 0 0 0 0 0 0  4