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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 : R = CC[x,y,z]

o1 = R

o1 : PolynomialRing
i2 : sph = (x^2+y^2+z^2-1); 
i3 : I = ideal {sph*(y-x^2), sph*(z-x^3)};

o3 : Ideal of R
i4 : numericalIrreducibleDecomposition I 

o4 = a numerical variety with components in
     dim 1:  (dim=1,deg=3)
     dim 2:  (dim=2,deg=2)

o4 : NumericalVariety

Caveat

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

See also