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

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5 Hilbert basis elements of degree 1

embedding dimension = 9

grading:
1 1 1 0 0 0 0 0 0 
with denominator = 3


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5 Hilbert basis elements of degree 1:
 0 2 1 2 1 0 1 0 2
 1 0 2 2 1 0 0 2 1
 1 1 1 1 1 1 1 1 1
 1 2 0 0 1 2 2 0 1
 2 0 1 0 1 2 1 2 0