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

See for installation instructions, full content overview and detailed documentation.

Basic usage

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

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

Citing HomotopyContinuation.jl

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

  title={HomotopyContinuation.jl: A Package for Homotopy Continuation in Julia},
  author={Breiding, Paul and Timme, Sascha},
  booktitle={International Congress on Mathematical Software},

A preprint of this paper is freely available.

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