Added a test notebook for the 2 step Homotopy

[bestlerm]

We tried to test the implementation of the two step Homotopy as a part of the Hackathon. For reference, this was the task:

Current homotopy methods are not tailored to any system in particular. This results in a significant overhead in the "warm-up" step, where roots are deformed from a polynomial system with many roots into a generic system with less roots that serves as the start system. We could however gain efficiency by directly input a start system where the number of solutions is exactly an upper bound for the target system to solve. A (known) [https://www.sciencedirect.com/science/article/pii/S0021782423001563] example, for N linearly coupled parametric oscillators with coupling J is the system with J=0, which saturates at 5^N solutions.
The goal is to implement and test this homotopy, analyzing how big with N can we get.

We tried by setting J=0 at the warm up step, but the warm up is still very slow for large systems (8 oscillators). For small systems, it appears as this warm up works and gives all real solutions of the problem in the second step. Only the 0 solution seems to get lost at times, but that should be easy to recover.

We therefore suggest to try solving the warmup for every oscillator individually, then constructing the warmup solution through combinatorics from the individual solution and finally doing the second step.

[jkosata]

Nice stuff, but there is a separate repo for test notebooks, the main repo should really just be the codebase.

[oameye]

@jkosata This was a result of a hackathon session. Later this PR will be turned into a HarmonicBalanceMethod