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NumericalImplicitization :: numericalImageDegree

numericalImageDegree -- computes the degree of the image of a variety



This method computes the degree of the image of a variety, by computing a pseudo-witness set for the image (cf. pseudo-witness set for more on the techniques and options used).

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 the degree of 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 : numericalImageDegree(F, I, Repeats => 2, Verbose => false)

o4 = 2

See also

Ways to use numericalImageDegree :

For the programmer

The object numericalImageDegree is a method function with options.