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NumericalAlgebraicGeometry :: numericalIrreducibleDecomposition(Ideal)

numericalIrreducibleDecomposition(Ideal) -- constructs a numerical variety defined by the given ideal

Synopsis

Description

The witness sets of the numerical varietyV are in one-to-one correspondence with irreducible components of the variety defined by I.
i1 : setRandomSeed 1

o1 = 1
i2 : R = CC[x,y,z]

o2 = R

o2 : PolynomialRing
i3 : sph = (x^2+y^2+z^2-1); 
i4 : I = ideal {sph*(x-1)*(y-x^2), sph*(y-2)*(z-x^3)};

o4 : Ideal of R
i5 : V = numericalIrreducibleDecomposition I 

o5 = V

o5 : NumericalVariety
i6 : peek V

o6 = NumericalVariety{1 => {(dim=1,deg=1), (dim=1,deg=1), (dim=1,deg=1),
                      2 => {(dim=2,deg=2)}
     ------------------------------------------------------------------------
     (dim=1,deg=1), (dim=1,deg=3)}}

Caveat

This function is under development. It may not work well if the input represents a nonreduced scheme.

See also