# ApCoCoA-1:Num.RatPoints

## Num.RatPoints

Computes the zero set of an exact zero dimensional border basis. The zeros are computed approximately using the eigenvalues of the transposed multiplication matrices.

### Syntax

Num.RatPoints(BB:LIST, OrderIdeal:LIST)):LIST of 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.

This command computes a set of points, which are the zeros of an exact border basis. This border basis is close to the approximate border basis `AppBB`. The set of (complex) points is represented as two matrices. The `j`-th column of the first matrix gives the real part of a point and the `j`-th column of the second matrix gives the imaginary part. For computation the function is using the Num.EigenValues command.

@param

*AppBB*An approximate border basis.@param

*OrderIdeal*The associated order ideal@return A set of points in matrix form described above.

#### Example

Use P::=QQ[x,y,z]; Points := Mat([[2/3,0,0],[0,10,0],[0,0,1/3]]); R:=Num.ABM(Points, 0); Dec(Num.RatPoints(R[1],R[2]),2); -- CoCoAServer: computing Cpu Time = 0 ------------------------------- -- CoCoAServer: computing Cpu Time = 0.016 ------------------------------- [Mat([ [<quotes>0.66</quotes>, <quotes>0.00</quotes>, <quotes>0</quotes>], [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>10</quotes>], [<quotes>0</quotes>, <quotes>0.33</quotes>, <quotes>0</quotes>] ]), Mat([ [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>0</quotes>], [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>0</quotes>], [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>0</quotes>] ])] -------------------------------

### See also