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fullname: Apery
shortname: apery
organization: coq-community
opam_name: coq-mathcomp-apery
community: true
action: true
coqdoc: false
synopsis: >-
A formally verified proof in Coq, by computer algebra, that ζ(3) is irrational
description: |-
This project contains a formal proof that the real number ζ(3),
also known as Apéry's constant, is irrational. It follows roughly
Apéry's original sketch of a proof. However, the recurrence
relations constituting the crux of the proof have been guessed by a
computer algebra program (in this case in Maple/Algolib). These
relations are formally checked a posteriori, so that Coq's kernel
remains the sole trusted code base.
publications:
- pub_url: https://arxiv.org/abs/1912.06611
pub_title: A Formal Proof of the Irrationality of ζ(3)
- pub_url: https://hal.inria.fr/hal-00984057
pub_title: A Computer-Algebra-Based Formal Proof of the Irrationality of ζ(3)
pub_doi: 10.1007/978-3-319-08970-6_11
- pub_url: https://drops.dagstuhl.de/opus/volltexte/2022/16738/pdf/LIPIcs-ITP-2022-29.pdf
pub_title: Reflexive tactics for algebra, revisited
pub_doi: 10.4230/LIPIcs.ITP.2022.29
authors:
- name: Frédéric Chyzak
initial: true
- name: Assia Mahboubi
initial: true
- name: Thomas Sibut-Pinote
initial: true
maintainers:
- name: Assia Mahboubi
nickname: amahboubi
- name: Kazuhiko Sakaguchi
nickname: pi8027
opam-file-maintainer: assia.mahboubi@inria.fr
opam-file-version: dev
license:
fullname: CeCILL-C
identifier: CECILL-C
supported_coq_versions:
text: 8.20 or later
opam: '{>= "8.20"}'
tested_coq_opam_versions:
- version: '2.3.0-coq-8.20'
repo: 'mathcomp/mathcomp'
- version: '2.4.0-coq-8.20'
repo: 'mathcomp/mathcomp'
- version: '2.4.0-rocq-prover-9.0'
repo: 'mathcomp/mathcomp'
- version: '2.4.0-rocq-prover-dev'
repo: 'mathcomp/mathcomp'
- version: 'coq-8.20'
repo: 'mathcomp/mathcomp-dev'
- version: 'rocq-prover-9.0'
repo: 'mathcomp/mathcomp-dev'
- version: 'rocq-prover-dev'
repo: 'mathcomp/mathcomp-dev'
dependencies:
- opam:
name: coq-mathcomp-ssreflect
version: '{>= "2.3"}'
description: |-
[MathComp ssreflect](https://math-comp.github.io) 2.3 or later
- opam:
name: coq-mathcomp-algebra
description: |-
[MathComp algebra](https://math-comp.github.io)
- opam:
name: coq-mathcomp-field
description: |-
[MathComp field](https://math-comp.github.io)
- opam:
name: coq-coqeal
version: '{>= "2.1.0"}'
description: |-
[CoqEAL](https://github.com/coq-community/coqeal) 2.1.0 or later
- opam:
name: coq-mathcomp-real-closed
description: |-
[MathComp real closed fields](https://github.com/math-comp/real-closed)
- opam:
name: coq-mathcomp-bigenough
version: '{>= "1.0.1"}'
description: |-
[MathComp bigenough](https://github.com/math-comp/bigenough) 1.0.1 or later
- opam:
name: coq-mathcomp-zify
description: |-
[Mczify](https://github.com/math-comp/mczify)
- opam:
name: coq-mathcomp-algebra-tactics
description: |-
[Algebra Tactics](https://github.com/math-comp/algebra-tactics)
namespace: mathcomp.apery
keywords:
- name: apery recurrence
- name: irrationality
- name: creative telescoping
categories:
- name: Mathematics/Arithmetic and Number Theory/Number theory