solve(f) return only “true” solutions of
f. But when tracking towards
f paths might diverge to infinity (solutions at infinity describe solutions of the homogenization of
f which are no solutions of
To save the results of all paths, one has to use
solve(f, save_all_paths = true)
Here is an example that has solutions at infinity.
julia> using HomotopyContinuation julia> @polyvar x y julia> f = [x^2 - y^2 - 1, x - y] julia> solve(f, save_all_paths = true) Result with 0 solutions ================================== • 0 non-singular solutions (0 real) • 0 singular solutions (0 real) • 2 solutions at infinity • 2 paths tracked • random seed: 229664