Macaulay2 » Documentation
Packages » NumericalImplicitization :: isOnImage
next | previous | forward | backward | up | index | toc

isOnImage -- tests whether a point lies on the image of a variety



This method determines if a point in the ambient target space lies on the image of a variety. This is done via computing a pseudo-witness set for the image.

If a pseudo-witness set has already been computed, then to avoid repetitive calculation one may run this function with the pseudo-witness set as input.

The following example determines whether a point lies on the Grassmannian $Gr(2,4)$ of $P^1$'s in $P^3$, under its Plücker embedding in $P^5$.

i1 : R = CC[x_(1,1)..x_(2,4)]; I = ideal 0_R;

o2 : Ideal of R
i3 : F = (minors(2, genericMatrix(R, 2, 4)))_*;
i4 : W = pseudoWitnessSet(F, I, Repeats => 2, Verbose => false);
i5 : q = first numericalImageSample(F, I)

o5 = q

o5 : Point
i6 : isOnImage(W, q)

o6 = true
i7 : isOnImage(W, point random(CC^1, CC^#F))

o7 = false
i8 : isOnImage(W, point{{1_CC,0,0,0,0,0}})

o8 = true

See also

Ways to use isOnImage :

For the programmer

The object isOnImage is a method function with options.