# Tracking in affine space or in projective space

Define the space for the paths that are tracked

By default, HomotopyContinuation.jl tracks paths in the complex vector space $\mathbb{C}^n$.

It is also possible to track paths in projective space. This has the advantage that all paths have finite length, because projective space is compact.

One can tell HomotopyContinuation.jl to track over projective space by using the flag projective_tracking = true:

using HomotopyContinuation
@polyvar x y
f = [x^2 + y - 1, y - 4]
solve(f, projective_tracking = true)


This is the same as

using HomotopyContinuation
@polyvar x y
f = [x^2 + y - 1, y - 4]
solve(f, affine_tracking = false)


The flag affine_tracking is dominant; i.e., solve(f, affine_tracking = true, projective_tracking = true) tracks in affine space.