# Package sagbi/SB.SDA

From ApCoCoAWiki

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

## SB.SDA

This function is an implementation of the Subalgebra Division Algorithm.

### Syntax

SB.SDA(f: POLY, G: LIST of POLY): POLY

### Description

The function takes a polynomial `f` and a list of polynomials `G` all of the same ring `RingOf(f)` and performs the Subalgebra Division Algoritm on `f` and `G`. Note that this algorithm is different from the Subduction algorithm written by Robbiano and Sweedler, for more informations see Package sagbi.

@param

`f`A polynomial@param

`G`A list of polynomials@return A polynomial

`g`such that`f`Subalgebra reduces (with respect to`G`) to`g`and`g`is irreducible with respect to the rewrite relation defined by`G`.

#### Example

Use QQ[x,y], DegRevLex; f := x^4*y^2 + x^2*y^4+1; G := [x^2-1, y^2-1]; SB.SDA(f,G); -- 0

### See also

Package sagbi/SB.ReductionStep

Package sagbi/SB.IsInSubalgebra_SAGBI