Monodromy driven decomposition is followed by the linear trace test.
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 : W = first regeneration F
o4 = [dim=0,deg=4]
o4 : WitnessSet
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i5 : decompose W
o5 = {(dim=0,deg=1), (dim=0,deg=1), (dim=0,deg=1), (dim=0,deg=1)}
o5 : List
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i6 : R = CC[x,y,z]
o6 = R
o6 : PolynomialRing
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i7 : sph = (x^2+y^2+z^2-1);
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i8 : 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)};
o8 : Ideal of R
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i9 : regeneration I_* / decompose
o9 = {{(dim=0,deg=1), (dim=0,deg=1), (dim=0,deg=1)}, {(dim=1,deg=1),
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(dim=1,deg=3)}, {(dim=2,deg=2)}}
o9 : List
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