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------------------------------------------------------
-- routines for positive-dimensional solution sets
-- not included in other files
-- (loaded by ../NumericalAlgebraicGeometry.m2)
------------------------------------------------------
isOn (AbstractPoint,NumericalVariety) := o -> (p, V) -> (
o = fillInDefaultOptions o;
if o.Software === BERTINI then #bertiniComponentMemberTest({p},V)>0
else any(keys V, d->any(V#d, C->isOn(p,C,o)))
)
TEST ///
R = CC[x,y]
e = 0.0000001
V = numericalIrreducibleDecomposition ideal (x*(x-1), x*(y-1))
assert isOn( point{{e,random CC}}, V )
assert isOn( point{{1-e,1+e}}, V )
assert not isOn( point{{1,0}}, V )
///
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