# Package sagbi/SB.SAGBI

From ApCoCoAWiki

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

## SB.SAGBI

Computes a finite SAGBI-basis of a subalgebra if existing.

### Syntax

SB.SAGBI(G:LIST of POLY):LIST of POLY

### Description

This function computes a finite SAGBI-basis of a subalgebra `S` generated by the polynomials of the list `G`, if a finite SAGBI-basis of `S` is existing. Then a list of polynomials is returned which form a SAGBI-basis of `S`. Otherwise the computation runs until it is interrupted.

@param

*G*A list of polynomials which generates a subalgebra.@return A list of polynomials which form a finite SAGBI-basis of the subalgebra generated by

`G`.

#### Example

Use QQ[x[1..3]]; S := SB.SAGBI([x[1]^2-x[3]^2,x[1]*x[2]+x[3]^2,x[2]^2-2*x[3]^2]); indent(S); ----------------------------------------------------------------------------- [ x[2]^2 -2*x[3]^2, x[1]*x[2] +x[3]^2, x[1]^2 -x[3]^2, x[1]^2*x[3]^2 +x[1]*x[2]*x[3]^2 +(1/2)*x[2]^2*x[3]^2 +(-1/2)*x[3]^4 ]