Package sagbi/SB.SubalgebraHS

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SB.SubalgebraHS

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

Syntax

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

Description

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

Example

```Use QQ[x,y];
G := [x^2*y,  x^2 -y^2,  x^2*y^2 -y^4,  x^2*y^4];
SB.SubalgebraHS(G);
-----------------------------------------------------------------------------
---  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) )```