Package sagbi/SB.SubalgebraHS

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This article is about a function from ApCoCoA-2.


This function computes the Hilbert series of the subalgebra generated by a given set of homogeneous polynomials.


SB.SubalgebraHS(G: LIST of POLY): TAGGED("$hp.PSeries")


This function takes a list of polynomials G all of the same polynomial ring R over the field K and computes the Hilbert series of the subalgebra S = K[g | g in G] of R. Note that the polynomials in G all have to be homogeneous such that the subalgebra S is standard-graded and its Hilbert series is well-defined.

  • @param G A list of polynomials

  • @return The Hilbert series of the subalgebra K[g | g in G] of R


Use QQ[x,y];
G := [x^2*y,  x^2 -y^2,  x^2*y^2 -y^4,  x^2*y^4];
---  Non-simplified HilbertPoincare' Series  ---
(1 - t^8 - t^10 - t^12 + t^14 + t^16) / ( (1-t^3)*(1-t^2)*(1-t^4)*(1-t^6) )

See also

Package sagbi/SB.GetHS

Package sagbi/SB.IsGraded

Package sagbi/SB.TorRingHS