# Package sagbi/SB.IsSAGBIOf

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< Package sagbi

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This article is about a function from ApCoCoA-2. If you are looking for the ApCoCoA-1 version of it, see ApCoCoA-1:SB.IsSagbiOf. |

## SB.IsSAGBIOf

This function checks whether a given list of polynomials is a SAGBI basis of a specific subalgebra.

### Syntax

SB.IsSAGBIOf(G: LIST of POLY, S: TAGGED("$apcocoa/sagbi.Subalgebra")): BOOL

### Description

@param

`G`A list of polynomials all of the same ring`R`@param

`S`A subalgebra of`R`@return

`true`if`G`is a SAGBI basis of`S`and false if not.

#### Example

Use R ::= QQ[x,y]; fs := [x^2*y, x^2 -y^2, x^2*y^2 -y^4, x^2*y^4]; S := SB.Subalgebra(R,fs); G := [x^2 -y^2, x^2*y, x^2*y^2 -y^4, y^6, x^2*y^4]; SB.IsSAGBIOf(fs,S); -- false SB.IsSAGBIOf(G,S); -- true

### See also