https://github.com/blegat/mixedsubdivisions.jl
A Julia package for computing a (fine) mixed subdivision and the mixed volume of lattice polytopes
Science Score: 10.0%
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Low similarity (8.3%) to scientific vocabulary
Last synced: 10 months ago
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Repository
A Julia package for computing a (fine) mixed subdivision and the mixed volume of lattice polytopes
Basic Info
- Host: GitHub
- Owner: blegat
- License: mit
- Default Branch: master
- Homepage: https://saschatimme.github.io/MixedSubdivisions.jl/stable
- Size: 143 KB
Statistics
- Stars: 0
- Watchers: 0
- Forks: 0
- Open Issues: 0
- Releases: 0
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] |  | | [![][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
- Website: blegat.github.io
- Repositories: 48
- Profile: https://github.com/blegat