decompose(WitnessSet) -- decompose a witness set into irreducibles

i1 : R = CC[x,y]

o1 = R

o1 : PolynomialRing

i2 : F = {x^2+y^2-1, x*y};

i3 : W = first components regeneration F 

o3 = W

o3 : WitnessSet

i4 : decompose W

o4 = {(dim=0,deg=1), (dim=0,deg=1), (dim=0,deg=1), (dim=0,deg=1)}

o4 : List

i5 : R = CC[x,y,z]

o5 = R

o5 : PolynomialRing

i6 : sph = (x^2+y^2+z^2-1); 

i7 : decompose \ components regeneration {sph*(x-1)*(y-x^2), sph*(y-2)*(z-x^3)}

o7 = {{(dim=1,deg=1), (dim=1,deg=1), (dim=1,deg=1), (dim=1,deg=1),
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     (dim=1,deg=3)}, {(dim=2,deg=2)}}

o7 : List