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

o7 : 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