# ApCoCoA-1:Num.RatPoints

## Num.RatPoints

Checks if a given set of polynomials vanishes at a given set of points.

### Syntax

```Num.RatPoints(AppBB:LIST, OrderIdeal:LIST)):[MAT];
```

### Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

Calculates a set of points which are the zeros of an exact border basis which is close to AppBB. Uses the eigenvalue methode.

• @param AppBB An approximate border basis.

• @param Points The asscoiated order ideal

• @return A set of points in matrix form.

#### Example

```Use P::=QQ[x,y,z];

Points := Mat([[2/3,0,0],[0,1,0],[0,0,1/3]]);
R:=Num.SubAVI(Points, 0.001, [1]);
Dec(Num.RatPoints(R[1],R[2]),2);

-- CoCoAServer: computing Cpu Time = 0
-------------------------------
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
[Mat([
["0.66", "0.00", "-0.00"],
["0", "0", "1.00"],
["0", "0.33", "0"]
]), Mat([
["0", "0", "0"],
["0", "0", "0"],
["0", "0", "0"]
])]
-------------------------------

```