This method 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 computational 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(3,5) of P2’s in P4, under its Plücker embedding in P9.
i1 : R = CC[x_(1,1)..x_(3,5)]; I = ideal 0_R; o2 : Ideal of R |
i3 : F = (minors(3, genericMatrix(R, 3, 5)))_*; |
i4 : numericalImageDegree(F, I, Repeats => 2, Verbose => false) o4 = 5 |