Package sagbi/SB.GetHS

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This article is about a function from ApCoCoA-2.


This function returns the Hilbert series of a given standard-graded subalgebra.


SB.GetHS(ref S: TAGGED("$apcocoa/sagbi.Subalgebra")): TAGGED("$hp.PSeries")


This function computes the Hilbert series of S, stores it in S and returns it. If the Hilbert series of S was already computed and stored in S, then it returns the stored Hilbert series.

  • @param ref S A standard-graded subalgebra, i.e. a subalgebra generated by homogeneous polynomials

  • @return The Hilbert series of S


Use R ::= QQ[x,y,z];
S := SB.Subalgebra(R,[x^2,y+z]);
PrintLn SB.GetHS(S);
---  Non-simplified HilbertPoincare' Series  ---
(1) / ( (1-t^2)*(1-t) )

See also


Package sagbi/SB.GetID

Package sagbi/SB.GetRing

Package sagbi/SB.GetGens

Package sagbi/SB.GetCoeffRing

Package sagbi/SB.GetSAGBI

Package sagbi/SB.GetTruncSAGBI

Package sagbi/SB.GetTruncDeg

Package sagbi/SB.GetLTSA

Package sagbi/SB.GetInDeg