up previous next
Num.BBABM

Computes the border basis of an almost vanishing ideal for a set of points using the BB ABM algorithm.
Syntax
          
Num.BBABM(Points:MAT, Epsilon:RAT):Object
Num.BBABM(Points:MAT, Epsilon:RAT, Delta:RAT, NormalizeType:INT):Object

          

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 border basis of an almost vanishing ideal for a set of points. In contrast to the ABM algorithm the border polynomials are computed in such a way, that the residual is calculated on polynomials that have leading borderterm coefficient one.

The current ring has to be a ring over the rational numbers with a standard-degree compatible term-ordering. The matrix Points contains the points: each point is a row in the matrix, so the number of columns must equal the number of indeterminates in the current ring. The following parameters are optional:

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

Points := Mat([[1,0,0],[0,0,1],[0,0.99,0]]);
Res := Num.BBABM(Points,0.1);

Dec(Res[1],2);
-- CoCoAServer: computing Cpu Time = 0.015
-------------------------------
["1 x +1.01 y +1 z -0.99  ", "1 z^2 -1 z ", "1 yz ", "1 xz ", "1 y^2 -0.98 y ", "1 xy "]
--------------------------------------------------------------


See Also