{"id":16313467,"url":"https://github.com/hivert/formalpowerseries","last_synced_at":"2025-06-28T10:33:08.464Z","repository":{"id":80684051,"uuid":"208150480","full_name":"hivert/FormalPowerSeries","owner":"hivert","description":"Formal power series in mathomp","archived":false,"fork":false,"pushed_at":"2025-01-08T20:53:04.000Z","size":1506,"stargazers_count":3,"open_issues_count":0,"forks_count":2,"subscribers_count":4,"default_branch":"master","last_synced_at":"2025-01-31T09:04:55.904Z","etag":null,"topics":["combinatorics","coq","formal-power-series","mathcomp","ssreflect"],"latest_commit_sha":null,"homepage":"","language":"Coq","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"gpl-3.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/hivert.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2019-09-12T21:35:58.000Z","updated_at":"2025-01-08T20:03:41.000Z","dependencies_parsed_at":null,"dependency_job_id":"92be4f0e-76e9-4aee-a317-cbc9953e3ffd","html_url":"https://github.com/hivert/FormalPowerSeries","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/hivert%2FFormalPowerSeries","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/hivert%2FFormalPowerSeries/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/hivert%2FFormalPowerSeries/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/hivert%2FFormalPowerSeries/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/hivert","download_url":"https://codeload.github.com/hivert/FormalPowerSeries/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":238183444,"owners_count":19430119,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["combinatorics","coq","formal-power-series","mathcomp","ssreflect"],"created_at":"2024-10-10T21:51:18.228Z","updated_at":"2025-02-10T20:30:55.946Z","avatar_url":"https://github.com/hivert.png","language":"Coq","funding_links":[],"categories":[],"sub_categories":[],"readme":"# FormalPowerSeries\n\n[![Nix CI for bundle\ncoq8.18-mc2.3.0](https://github.com/hivert/FormalPowerSeries/actions/workflows/nix-action-coq8.18-mc2.3.0.yml/badge.svg)](https://github.com/hivert/FormalPowerSeries/actions/workflows/nix-action-coq8.18-mc2.3.0.yml) [![Nix CI for bundle coq8.19-mc2.3.0](https://github.com/hivert/FormalPowerSeries/actions/workflows/nix-action-coq8.19-mc2.3.0.yml/badge.svg)](https://github.com/hivert/FormalPowerSeries/actions/workflows/nix-action-coq8.19-mc2.3.0.yml) [![Nix CI for bundle coq8.20-mc2.3.0](https://github.com/hivert/FormalPowerSeries/actions/workflows/nix-action-coq8.20-mc2.3.0.yml/badge.svg)](https://github.com/hivert/FormalPowerSeries/actions/workflows/nix-action-coq8.20-mc2.3.0.yml)\n\n## Formal power series in Mathematical Components.\n\nThe goal of this project is to formalize the notion of Formal Power\nSeries. I've mainly in view application to enumerative and algebraic\ncombinatorics. They are two different formalization:\n\n1 - an axiom free formalization of Truncated Formal Power Series. It is\nlargely based on the work of Cyril Cohen et al. on Newton Sums.\n\n   https://github.com/math-comp/newtonsums\n\nThe main difference is that they assumed the base ring to be a field whereas I\ntried to use the more general base ring setting to formalize the different\nproperties.\n\n2 - Formal Power Series using classical axioms. These are defined as the\ninverse limit of the truncated power series allowing to transfer easily result\nbetween the two setting.\n\nThe main results are\n- formula for the multiplicative inverse of a series both in a commutative and\n  non-commutative setting;\n- geometric series;\n- formal derivative and primitive (commutative and non-commutative);\n- composition of power series (assuming the inner one has zero constant\n  coefficient);\n- Lagrange inversion formulas (Lagrange-Bürmann theorem);\n- exponential and logarithm series.\n\nAll those results are proved both for truncated and non-trucated series.\n\n\n## Application to combinatorics\n\nTo test the framework I provide 6 proofs of the formula for Catalan\nnumbers. I'm using the following 3 different strategies together with\ntruncated and non-trucated series:\n\n1 - prove the algebraic equation `F = 1 + X F^2` and extract the\ncoefficients using square root and Newton's formula;\n\n2 - Start again from the algebraic equation, extract the coefficients\nusing Lagrange inversion formula;\n\n3 - Transform the algebraic equation into the holonomic differential equation\n `(1 - 2X) F + (1 - 4X) X F' = 1` which give the recursion\n `(n+2) C(n+1) = (4n + 2) C(n)` and solve it.\n\n\nAll these files are still largely experimental\n\nTo compile it I'm using the following opam packages:\n```\ncoq-hierarchy-builder     1.8.0\ncoq-mathcomp-ssreflect    2.3.0\ncoq-mathcomp-algebra      2.3.0\ncoq-mathcomp-multinomials 2.3.0\ncoq-mathcomp-classical    1.8.0\n```\n\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fhivert%2Fformalpowerseries","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fhivert%2Fformalpowerseries","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fhivert%2Fformalpowerseries/lists"}