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 juliahomotopycontinuation.org 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
@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
``` html
For more see [our user guides](https://www.juliahomotopycontinuation.org/guides/).

## Citing HomotopyContinuation.jl
If you find HomotopyContinuation.jl useful in your work, we kindly request that you cite the [following paper](https://link.springer.com/chapter/10.1007/978-3-319-96418-8_54):

@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](https://arxiv.org/abs/1711.10911).

[docs-stable-img]: https://img.shields.io/badge/docs-online-blue.svg
[docs-stable-url]: https://www.juliahomotopycontinuation.org/HomotopyContinuation.jl/stable

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