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Num.AVI

Computes a border basis of an almost vanishing ideal for a set of points.
Syntax
          
Num.AVI(Points:MAT, Epsilon:RAT):Object
Num.AVI(Points:MAT, Epsilon:RAT, Delta:RAT, NormalizeType:INT, RREFNormalizeType:INT, RREFUseEps:BOOL, RREFType: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 function computes an approximate border basis of an almost vanishing ideal for a set of points using the AVI algorithm. AVI is an acronym of "Approximate Vanishing Ideal".

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],[0,1,0]]);
Num.AVI(Points,0.001);
-- CoCoAServer: computing Cpu Time = 0
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[[x + y + 4503599627370495/4503599627370496z - 4503599627370497/4503599627370496, xy, y^2 - y, xz, yz, z^2 - z], [1, z, y]]
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See Also