# ApCoCoA-1:Num.RatPoints

From ApCoCoAWiki

## 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"] ])] -------------------------------

### See also