Description
Regeneration is a blackbox method that obtains a numerical description of an algebraic variety. Note that
Ws are not necessarily irreducible witness sets; use
decompose(WitnessSet) to decompose into irreducibles.
i1 : R = CC[x,y]
o1 = R
o1 : PolynomialRing

i2 : F = {x^2+y^21, x*y};

i3 : regeneration F
o3 = a numerical variety with components in
dim 0: [dim=0,deg=4]*may be reducible*
o3 : NumericalVariety

i4 : R = CC[x,y,z]
o4 = R
o4 : PolynomialRing

i5 : sph = (x^2+y^2+z^21);

i6 : regeneration {sph*(x1)*(yx^2), sph*(y2)*(zx^3)}
o6 = a numerical variety with components in
dim 1: [dim=1,deg=7]*may be reducible*
dim 2: [dim=2,deg=2]*may be reducible*
o6 : NumericalVariety

Caveat
This function is under development. It may not work well if the input represents a nonreduced scheme.The (temporary) option
Output can take two values:
Regular (default) and
Singular. It specifies whether the algorithm attempts to keep singular points.