– — Visualization of Homotopy’s and their Properties —

Homotopy continuation, like Newton’s method, is an iterative ap-proach for finding the isolated complex roots of a polynomial. But unlike Newton’s method this process guarantees every isolated root will be found if seeded by a finite number of appropriately chosen starting points. The underlying idea is: 1.Connect the solutions of an exactly solvable system, q(z) = 0 with the solutions of the desired (target) system, p(z) = 0: H(z, t) = tq(z) + (1 − t)p(z). H(z, 1) = q(z) is the start system, e.g. zd − 1. H(z, 0) = p(z) is the target system. 2.Track the solution path as t goes from 1 to 0, using: dH dt = Hz dz d