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

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

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

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

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Fork of saschatimme/MixedSubdivisions.jl
Created over 4 years ago · Last pushed over 4 years ago

https://github.com/blegat/MixedSubdivisions.jl/blob/master/

# 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/BernsteinKushnirenko_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

Owner

  • Name: Benoît Legat
  • Login: blegat
  • Kind: user
  • Location: Boston, MA, USA
  • Company: LIDS, MIT

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