https://github.com/thery/twosquare

A proof of Fermat's theorem on sum of two squares with mathcom using gaussian integers.
https://github.com/thery/twosquare

coq coq-formalization fermat-theorem sum-of-squares

Last synced: 8 days ago
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A proof of Fermat's theorem on sum of two squares with mathcom using gaussian integers.

• Host: GitHub
• URL: https://github.com/thery/twosquare
• Owner: thery
• Created: 2016-02-18T14:34:45.000Z (over 8 years ago)
• Default Branch: master
• Last Pushed: 2023-11-02T12:46:08.000Z (about 1 year ago)
• Last Synced: 2024-10-11T21:51:48.728Z (about 1 month ago)
• Topics: coq, coq-formalization, fermat-theorem, sum-of-squares
• Language: Coq
• Size: 135 KB
• Stars: 4
• Watchers: 2
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        

# twoSquare

[![Docker CI][docker-action-shield]][docker-action-link]

[docker-action-shield]: https://github.com/thery/twoSquare/workflows/Docker%20CI/badge.svg?branch=master

[docker-action-link]: https://github.com/thery/twoSquare/actions?query=workflow:"Docker%20CI"

A proof of Fermat's theorem on sum of two squares.

It is the proof that uses gaussian integers. This is done in ssreflect.

It contains two files :

********************************

gauss_int.v : the definition of gaussian integers

fermat2.v : the proof of Fermat's theorem

********************************

The final statement reads:

From mathcomp.contrib.sum_of_two_square

Require Import fermat2.

Check sum2stest.

sum2stest :

reflect

    (forall p,  prime p -> odd p -> p %| n -> odd (logn p n) -> p %% 4 = 1)

    (n is a sum_of_two_square).

## Meta

- Author(s):

  - Laurent Théry

- License: [MIT License](LICENSE)

- Compatible Coq versions: 8.18 or later

- Additional dependencies:

  - [MathComp ssreflect 2.1 or later](https://math-comp.github.io)

  - [MathComp algebra 2.1 or later](https://math-comp.github.io)

  - [MathComp field 2.1 or later](https://math-comp.github.io)

- Coq namespace: `twoSquare`

- Related publication(s): none

## Building and installation instructions

To build and install manually, do:

``` shell

git clone https://github.com/thery/twoSquare.git

cd twoSquare

make   # or make -j  

make install

```