# Package sagbi/SB.TorRingHS

From ApCoCoAWiki

< Package sagbi

Revision as of 13:23, 29 October 2020 by AndraschkoBot (talk | contribs) (replaced <quotes> tags by real quotes)

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

## SB.TorRingHS

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

### Syntax

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

### Description

This function takes a list of terms `G` all of the same polynomial ring `R` over the field `K` and computes the Hilbert series of the standard-graded subalgebra `S = K[g|g in G]` of `R`.

@param

`G`A list of terms in`R`@return The Hilbert series of the subalgebra

`K[g|g in G]`of`R`

#### Example

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

### See also