# Package sagbi/SB.ReductionStep

From ApCoCoAWiki

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

## SB.ReductionStep

This function computes a polynomial to which the given polynomial reduces in one step.

### Syntax

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

### Description

This function takes a polynomial `f` and a list of polynomials `G` and computes a polynomial `g` such that `f` reduces to `g` in one step with respect to the Subalgebra rewrite relation defined by `G`, see Package sagbi. If there is no such polynomial `g`, then `f` is returned.

@param

`f`A polynomial@param

`G`A list of polynomials@return see description above

#### Example

Use QQ[x,y], DegRevLex; f := x^4*y^2 + x^2*y^4; G := [x^2-1, y^2-1]; SB.ReductionStep(f,G); -- x^4*y^3 +2*x^2*y^2 +y^4 -x^2 -2*y^2 +1

#### Example

Use QQ[x,y], DegRevLex; f := x^4*y^3 + x^2*y^3; G := [x^2-1, y^2-1]; SB.ReductionStep(f,G); -- x^4*y^3 +x^2*y^3

### See also

Package sagbi/SB.FindLTRepr_glpk