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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

embedding dimension = 6

dehomogenization:
0 0 0 0 0 1 


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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