# Solutions at infinity

Let solve return the outcomes of all paths

By default, 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 f itself).

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