# ApCoCoA-1:SB.IsSagbi

## SB.IsSagbi

Checks if a set of polynomials is a SAGBI-basis.

### Syntax

```SB.IsSagbi(G:LIST of POLY):BOOL
```

### Description

This function checks if the given list of polynomials G is a SAGBI-basis, i.e. if the conditions of a SAGBI-basis are fulfilled. Then the corresponding boolean value will be returned.

• @param G A list of polynomials.

• @return The corresponding boolean value.

#### Example

```Use R::=QQ[x,y];

G:=[x-y,x+y];
SB.IsSagbi(G);
SB.Sagbi(G);

-------------------------------------------------------
-- output:

FALSE
-------------------------------

-- The result is correct, because a SAGBI-basis of G is the following:
[
x - y,
x + y,
y]
-------------------------------
-- Done.
-------------------------------
```

#### Example

```Use R::=QQ[x[1..6]];

Generators:=[-x - x, -x, x^2 + x^2,
-4x^2 - 5/2x^2 + 2xx - 4x^2,
-2xxx + x^2x - x^2x + 2xxx,
-x^2x + x^2x - 2xxx + x^2x - x^2x];

SB.IsSagbi(Generators);

-- Computation of a SAGBI-basis
Basis:=SB.Sagbi(Generators);
SB.IsSagbi(Basis);

-------------------------------------------------------
-- output:

FALSE
-------------------------------

-- Of course the test passes now because the computed SAGBI-basis is
-- indeed a SAGBI-basis.
TRUE
-------------------------------
-- Done.
-------------------------------
```