# Package sagbi/SB.GetSAGBI

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< Package sagbi

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

## SB.GetSAGBI

This function returns the reduced SAGBI basis of a given subalgebra.

### Syntax

SB.GetSAGBI(ref S: TAGGED("$apcocoa/sagbi.Subalgebra"): LIST of POLY

### Description

This function takes a subalgebra `S` as a reference, computes its unique reduced SAGBI basis, returns it and saves it into `S` if the function wasn't called previously. If the function was called previously on the same subalgebra, then it just returns the reduced SAGBI basis of `S`. If no finite SAGBI basis is found after 120 seconds, the function stops and returns an error.

@param

`S`A subalgebra@return The reduced SAGBI basis of S

#### 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); PrintLn SB.GetSAGBI(ref S); -- [x^2 -y^2, x^2*y, x^2*y^2 -y^4, y^6, x^2*y^4]

### See also

Package sagbi/SB.GetTruncSAGBI