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https://github.com/coq-community/buchberger
Verified implementation in Coq of Buchberger's algorithm for computing Gröbner bases [maintainer=@palmskog]
https://github.com/coq-community/buchberger
buchberger-algorithm coq coq-extraction docker-coq-action grobner-basis nix-action
Last synced: about 1 month ago
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Verified implementation in Coq of Buchberger's algorithm for computing Gröbner bases [maintainer=@palmskog]
- Host: GitHub
- URL: https://github.com/coq-community/buchberger
- Owner: coq-community
- License: lgpl-2.1
- Created: 2016-04-26T09:57:37.000Z (over 8 years ago)
- Default Branch: master
- Last Pushed: 2023-12-30T09:36:17.000Z (about 1 year ago)
- Last Synced: 2024-04-22T06:26:29.402Z (9 months ago)
- Topics: buchberger-algorithm, coq, coq-extraction, docker-coq-action, grobner-basis, nix-action
- Language: Coq
- Homepage:
- Size: 272 KB
- Stars: 8
- Watchers: 11
- Forks: 1
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- License: LICENSE
Awesome Lists containing this project
README
# Buchberger
[![Docker CI][docker-action-shield]][docker-action-link]
[![Nix CI][nix-action-shield]][nix-action-link]
[![Contributing][contributing-shield]][contributing-link]
[![Code of Conduct][conduct-shield]][conduct-link]
[![Zulip][zulip-shield]][zulip-link]
[docker-action-shield]: https://github.com/coq-community/buchberger/actions/workflows/docker-action.yml/badge.svg?branch=master
[docker-action-link]: https://github.com/coq-community/buchberger/actions/workflows/docker-action.yml
[nix-action-shield]: https://github.com/coq-community/buchberger/actions/workflows/nix-action.yml/badge.svg?branch=master
[nix-action-link]: https://github.com/coq-community/buchberger/actions/workflows/nix-action.yml
[contributing-shield]: https://img.shields.io/badge/contributions-welcome-%23f7931e.svg
[contributing-link]: https://github.com/coq-community/manifesto/blob/master/CONTRIBUTING.md
[conduct-shield]: https://img.shields.io/badge/%E2%9D%A4-code%20of%20conduct-%23f15a24.svg
[conduct-link]: https://github.com/coq-community/manifesto/blob/master/CODE_OF_CONDUCT.md
[zulip-shield]: https://img.shields.io/badge/chat-on%20zulip-%23c1272d.svg
[zulip-link]: https://coq.zulipchat.com/#narrow/stream/237663-coq-community-devs.20.26.20users
A verified implementation of Buchberger's algorithm in Coq,
which computes the Gröbner basis associated with a polynomial ideal.
Also includes a constructive proof of Dickson's lemma.
## Meta
- Author(s):
- Laurent Théry (initial)
- Henrik Persson (initial)
- Coq-community maintainer(s):
- Karl Palmskog ([**@palmskog**](https://github.com/palmskog))
- License: [GNU Lesser General Public License v2.1 or later](LICENSE)
- Compatible Coq versions: 8.17 or later
- Additional dependencies: none
- Coq namespace: `Buchberger`
- Related publication(s):
- [A machine checked implementation of Buchberger's algorithm](https://link.springer.com/article/10.1023/A:1026518331905) doi:[10.1023/A:1026518331905](https://doi.org/10.1023/A:1026518331905)
- [An Integrated Development of Buchberger's Algorithm in Coq](https://hal.inria.fr/inria-00072316/)
- [Gröbner Bases in Type Theory](https://link.springer.com/chapter/10.1007/3-540-48167-2_3) doi:[10.1007/3-540-48167-2_3](https://doi.org/10.1007/3-540-48167-2_3)
## Building and installation instructions
The easiest way to install the latest released version of Buchberger
is via [OPAM](https://opam.ocaml.org/doc/Install.html):
```shell
opam repo add coq-released https://coq.inria.fr/opam/released
opam install coq-buchberger
```
To instead build and install manually, do:
``` shell
git clone https://github.com/coq-community/buchberger.git
cd buchberger
make # or make -j
make install
```
## Documentation
This project contains a Coq formalization of Buchberger's algorithm.
It is composed of:
- A proof of correctness of the algorithm as described in
[A machine checked implementation of Buchberger's algorithm][jar-url],
Journal of Automated Reasoning, January 2001.
- An implementation of the algorithm. With respect to the paper,
terms are not abstracted but built directly from coef and monomials.
- A constructive proof of Dickson's lemma due to Henrik Persson.
In the file `Extract.v`, it is explained how the extracted code found in
`sin_num.ml` can be used to compute Gröbner bases.
## Related work
An alternative formalization of Gröbner bases in Coq using the SSReflect
proof language and the Mathematical Components library is available
[elsewhere][grobner-url].
[jar-url]: https://link.springer.com/article/10.1023/A:1026518331905
[grobner-url]: https://github.com/thery/grobner