ApCoCoA-1:Num.RatPoints

Num.RatPoints

Computes a set of points, which are the zeros of an exact border basis. This border basis is close to an approximate border basis.

Syntax

Num.RatPoints(AppBB: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 points is represented as one matrix, in which each column represents one point. 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.

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([
  [<quotes>0.66</quotes>, <quotes>0.00</quotes>, <quotes>-0.00</quotes>],
  [<quotes>0</quotes>, <quotes>0</quotes>, <quotes>1.00</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

Introduction to CoCoAServer