# Package sagbi/SB.IsInSA SAGBI

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< Package sagbi

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

## SB.IsInSA

This function tests whether a polynomial is in a given standard-graded subalgebra.

### Syntax

SB.IsInSA(f: RINGELEM,S: TAGGED("$apcocoa/sagbi.Subalgebra")): BOOL

### Description

This function takes a polynomial *f* and a subalgebra *S* and tests whether *f* is an element of *S* using truncated SAGBI bases.

@param

*f*A polynomial@param

*S*A standard-graded subalgebra, i.e. of type*TAGGED("$apcocoa/sagbi.Subalgebra")*and the generators of f are homogeneous polynomials with respect to the standard grading.@return

*true*if*f*is an element of*S*and*false*if not.

#### Example

Use R ::= QQ[x,y,z]; S := SB.Subalgebra(R,[x^2,y+z]); f := x^4 +2*x^3*y +x^2*y^2 +x^2 +2*x*y +y^2; SB.IsInSA_SAGBI(f,S); -- true

### See also

Package sagbi/SB.IsInSubalgebra

Package sagbi/SB.IsInSubalgebra_SAGBI