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NumericalAlgebraicGeometry :: decompose(WitnessSet)

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

Synopsis

Description

Monodromy driven decomposition is followed by the linear trace test.
i1 : setRandomSeed 7

o1 = 7
i2 : R = CC[x,y]

o2 = R

o2 : PolynomialRing
i3 : F = {x^2+y^2-1, x*y};
i4 : W = first regeneration F 

o4 = [dim=0,deg=4]

o4 : WitnessSet
i5 : decompose W

o5 = {(dim=0,deg=1), (dim=0,deg=1), (dim=0,deg=1), (dim=0,deg=1)}

o5 : List
i6 : R = CC[x,y,z]

o6 = R

o6 : PolynomialRing
i7 : sph = (x^2+y^2+z^2-1); 
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
i9 : regeneration I_* / decompose

o9 = {{(dim=0,deg=1), (dim=0,deg=1), (dim=0,deg=1)}, {(dim=1,deg=1),
     ------------------------------------------------------------------------
     (dim=1,deg=3)}, {(dim=2,deg=2)}}

o9 : List

Caveat

This function is under development. It can not decompose nonreduced components at the moment. If monodromy breakup algorithm fails to classify some points, the unnclassified points appear as one witness set (that is not marked as irreducible).

See also