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

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10 module generators
4 Hilbert basis elements of recession monoid
4 vertices of polyhedron
4 extreme rays of recession cone
6 support hyperplanes of polyhedron (homogenized)

embedding dimension = 6
affine dimension of the polyhedron = 3
rank of recession monoid = 3

dehomogenization:
0 0 0 0 0 1 


module rank = 1

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

10 module generators:
  0 6 0 3 1 1
  1 3 2 1 0 1
  1 6 1 0 3 1
  2 5 1 2 1 1
  2 8 0 1 4 1
  3 2 3 0 0 1
  4 6 0 5 0 1
  6 5 1 4 0 1
 14 1 5 0 0 1
 25 0 7 0 0 1

4 Hilbert basis elements of recession monoid:
  3 1 0 0 1 0
  7 1 0 2 0 0
  9 0 1 1 0 0
 14 0 2 0 1 0

4 vertices of polyhedron:
  0 16  0  0 9  2
  0 25 27  0 0 11
  0 38  0 27 0  7
 25  0  7  0 0  1

4 extreme rays of recession cone:
  3 1 0 0 1 0
  7 1 0 2 0 0
  9 0 1 1 0 0
 14 0 2 0 1 0

6 support hyperplanes of polyhedron (homogenized):
 -3  23  28 0 -14 -121
  0   0   0 0   0    1
  0   1   0 0   0    0
  1  -7  -8 0   4   38
  1   0   0 0   0    0
  2 -14 -18 0   9   76

2 equations:
 1 -1 -6 -3 -2 17
 0  2  1 -1 -2 -7

4 basis elements of lattice:
 1 0  1  -3  2  0
 0 1 -1 -10  9 -1
 0 0  2   5 -5  1
 0 0 -4  14 -9  0