https://github.com/saschatimme/mixedsubdivisions.jl

A Julia package for computing a (fine) mixed subdivision and the mixed volume of lattice polytopes
https://github.com/saschatimme/mixedsubdivisions.jl

Last synced: about 2 months ago
JSON representation

A Julia package for computing a (fine) mixed subdivision and the mixed volume of lattice polytopes

• Host: GitHub
• URL: https://github.com/saschatimme/mixedsubdivisions.jl
• Owner: saschatimme
• License: mit
• Created: 2019-02-21T17:09:03.000Z (almost 6 years ago)
• Default Branch: master
• Last Pushed: 2024-08-16T19:37:40.000Z (5 months ago)
• Last Synced: 2024-08-16T20:38:17.688Z (5 months ago)
• Language: Julia
• Homepage: https://saschatimme.github.io/MixedSubdivisions.jl/stable
• Size: 171 KB
• Stars: 5
• Watchers: 4
• Forks: 4
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

Awesome Lists containing this project

README

        
# MixedSubdivisions.jl

| **Documentation** | **Build Status** |

|:-----------------:|:----------------:|

| [![][docs-stable-img]][docs-stable-url] | ![Run tests](https://github.com/saschatimme/MixedSubdivisions.jl/workflows/Run%20tests/badge.svg) |

| [![][docs-latest-img]][docs-latest-url] | [![Codecov branch][codecov-img]][codecov-url] |

A Julia package for computing a (fine) mixed subdivision and the [mixed volume](https://en.wikipedia.org/wiki/Mixed_volume) of lattice polytopes.

The mixed volume of lattice polytopes arising as Newton polytopes of a polynomial system

gives an upper bound of the number of solutions of the system. This is the celebrated

[BKK-Theorem](https://en.wikipedia.org/wiki/Bernstein–Kushnirenko_theorem).

A (fine) mixed subdivision can be used to efficiently solve sparse polynomial systems as

first described in [A Polyhedral Method for Solving Sparse Polynomial Systems](https://www.jstor.org/stable/2153370)

by Huber and Sturmfels.

There are many algorithms for computing mixed volumes and mixed subdivisions. This implementation

is based on the tropical homotopy continuation algorithm by Anders Jensen described in [arXiv:1601.02818](https://arxiv.org/abs/1601.02818).

## Installation

The package can be installed via the Julia package manager

```julia

pkg> add MixedSubdivisions

```

[docs-stable-img]: https://img.shields.io/badge/docs-stable-blue.svg

[docs-latest-img]: https://img.shields.io/badge/docs-latest-blue.svg

[docs-stable-url]: https://saschatimme.github.io/MixedSubdivisions.jl/stable

[docs-latest-url]: https://saschatimme.github.io/MixedSubdivisions.jl/latest

[codecov-img]: https://codecov.io/gh/saschatimme/MixedSubdivisions.jl/branch/master/graph/badge.svg

[codecov-url]: https://codecov.io/gh/saschatimme/MixedSubdivisions.jl