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Num.SubEXTABM

Computes a border basis of an almost vanishing sub-ideal for a set of points and an ideal using the Num.EXTABM algorithm.
Syntax
          
Num.SubEXTABM(Points:MAT, Val:MAT, Epsilon:RAT, Basis:LIST):Object
Num.SubEXTABM(Points:MAT, Val:MAT, Epsilon:RAT, Basis:LIST, 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 sub-ideal for a set of points and an ideal using the Num.EXTABM algorithm.

The current ring has to be a ring over the rational numbers with a standard-degree compatible term-ordering. Each row in the matrix Points represents one point, 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([[1,2,3],[4,5,6],[7,11,12]]);
Val := Mat([[1],[0.1],[0.2]]);
R:=Num.SubEXTABM(Points,Val, 0.1, [x]);

Dec(-Eval(R[1],Points[1]),3);
Dec(-Eval(R[1],Points[2]),3);
Dec(-Eval(R[1],Points[3]),3);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
["1.000", "0.999", "1.000", "0.999", "0.999", "1.000"]
-------------------------------
["0.099", "0.100", "0.100", "0.099", "0.099", "0.100"]
-------------------------------
["0.200", "0.200", "0.200", "0.199", "0.199", "0.199"]
-------------------------------


See Also