HomotopyContinuation.jl is a Julia package for solving systems of polynomial equations by numerical homotopy continuation.

HomotopyContinuation.jl aims at having easy-to-understand top-level commands. Here is a simple example:

using HomotopyContinuation
@var x y; # declare the variables x and y
F = System([x^2+2y, y^2-2])
result = solve(F)

Result with 4 solutions
==================================
• 4 non-singular solutions (2 real)
• 0 singular solutions (0 real)
• 4 paths tracked
• random seed: 902575

For more see our user guides.

If you find HomotopyContinuation.jl useful in your work, we kindly request that you cite the following paper:

@inproceedings{HomotopyContinuation.jl,
  title={{H}omotopy{C}ontinuation.jl: {A} {P}ackage for {H}omotopy {C}ontinuation in {J}ulia},
  author={Breiding, Paul and Timme, Sascha},
  booktitle={International Congress on Mathematical Software},
  pages={458--465},
  year={2018},
  organization={Springer}
}

A preprint of this paper is freely available.