Regeneration is a blackbox method that obtains a numerical describtion of an algebraic variety. Note that
to decompose into irreducibles.
i1 : setRandomSeed 7
o1 = 7
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i2 : R = CC[x,y]
o2 = R
o2 : PolynomialRing
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i3 : F = {x^2+y^2-1, x*y};
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i4 : regeneration F
o4 = {[dim=0,deg=4]}
o4 : List
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i5 : R = CC[x,y,z]
o5 = R
o5 : PolynomialRing
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i6 : sph = (x^2+y^2+z^2-1);
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i7 : I = ideal {sph*(x-0.5)*(y-x^2), sph*(y-0.5)*(z-x^3), sph*(z-0.5)*(z-x^3)*(y-x^3)};
o7 : Ideal of R
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i8 : cs = regeneration I_*
o8 = {[dim=0,deg=3], [dim=1,deg=7], [dim=2,deg=2]}
o8 : List
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