# Package sagbi/SB.SubalgebraHS

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< Package sagbi

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This article is about a function from ApCoCoA-2. |

## 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) )

### See also