# Package sagbi/SB.IsInSubalgebra 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-1:SB.IsInSubalgebra. |

## SB.IsInSubalgebra_SAGBI

Tests whether a polynomial is in a standard-graded subalgebra using SAGBI bases.

### Syntax

SB.IsInSubalgebra_SAGBI(f:POLY, G:LIST of POLY):BOOL

### Description

This function takes a polynomials `f` and a list of homogeneous polynomials `G` and checks whether `F` is in the algebra generated by the polynomials in `G` using truncated SAGBI bases.

@param

*f*A polynomial.@param

*G*A list of homogeneous polynomials which generate a subalgebra.@return

`true`if`f`is in the subalgebra generated by`G`,`false`elsewise.

#### Example

Use QQ[x[1..2]]; G := [x[1]-x[2], x[1]*x[2]-x[2]^2, x[1]*x[2]^2]; SB.IsInSubalgebra_SAGBI(x[1]*x[2]^4-x[2]^5, G); -- true

#### Example

Use QQ[y[1..3]]; G := [y[1]^2-y[3]^2, y[1]*y[2]+y[3]^2, y[2]^2-2*y[3]^2]; SB.IsInSubalgebra_SAGBI(y[3]^4, G); -- false

### See also

Package sagbi/SB.IsInSubalgebra

Package sagbi/SB.IsInToricRing