# Package sagbi/SB.GetHS

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< Package sagbi

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

## SB.GetHS

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

### Syntax

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

### Description

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`

#### Example

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.GetTruncSAGBI