https://github.com/juliahomotopycontinuation/homotopycontinuation.jl

A Julia package for solving systems of polynomials via homotopy continuation.
https://github.com/juliahomotopycontinuation/homotopycontinuation.jl

homotopy-continuation julia nonlinear-algebra numerical-algebraic-geometry polynomial-system-solving polynomial-systems

Last synced: 28 days ago
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A Julia package for solving systems of polynomials via homotopy continuation.

• Host: GitHub
• URL: https://github.com/juliahomotopycontinuation/homotopycontinuation.jl
• Owner: JuliaHomotopyContinuation
• License: mit
• Created: 2017-08-03T11:36:28.000Z (over 7 years ago)
• Default Branch: main
• Last Pushed: 2024-05-23T06:54:10.000Z (12 months ago)
• Last Synced: 2024-05-23T07:25:21.080Z (12 months ago)
• Topics: homotopy-continuation, julia, nonlinear-algebra, numerical-algebraic-geometry, polynomial-system-solving, polynomial-systems
• Language: Julia
• Homepage: https://www.JuliaHomotopyContinuation.org
• Size: 13.3 MB
• Stars: 174
• Watchers: 10
• Forks: 30
• Open Issues: 21
• Metadata Files:
  • Readme: README.md
  • License: LICENSE
  • Code of conduct: CODE_OF_CONDUCT.md

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README

        


[![][docs-stable-img]][docs-stable-url] ![Run tests](https://github.com/JuliaHomotopyContinuation/HomotopyContinuation.jl/workflows/Run%20tests/badge.svg?branch=main)

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

---

### **See [juliahomotopycontinuation.org](https://www.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:

```julia

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](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):

```latex

@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