{"id":20600407,"url":"https://github.com/defeo/ffisom","last_synced_at":"2025-04-15T00:42:09.296Z","repository":{"id":9477458,"uuid":"11363898","full_name":"defeo/ffisom","owner":"defeo","description":"A research project on isomorphisms of finite fields","archived":false,"fork":false,"pushed_at":"2018-06-15T03:23:45.000Z","size":37803,"stargazers_count":16,"open_issues_count":0,"forks_count":5,"subscribers_count":10,"default_branch":"master","last_synced_at":"2025-04-15T00:41:41.470Z","etag":null,"topics":["algorithms","finite-fields","isomorphism","research-paper"],"latest_commit_sha":null,"homepage":"https://arxiv.org/abs/1705.01221","language":"Jupyter Notebook","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/defeo.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null}},"created_at":"2013-07-12T08:11:56.000Z","updated_at":"2023-11-01T05:44:19.000Z","dependencies_parsed_at":"2022-09-15T22:12:12.418Z","dependency_job_id":null,"html_url":"https://github.com/defeo/ffisom","commit_stats":null,"previous_names":[],"tags_count":5,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/defeo%2Fffisom","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/defeo%2Fffisom/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/defeo%2Fffisom/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/defeo%2Fffisom/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/defeo","download_url":"https://codeload.github.com/defeo/ffisom/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":248986271,"owners_count":21194024,"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":["algorithms","finite-fields","isomorphism","research-paper"],"created_at":"2024-11-16T08:38:12.150Z","updated_at":"2025-04-15T00:42:09.281Z","avatar_url":"https://github.com/defeo.png","language":"Jupyter Notebook","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Computing isomorphisms and embeddings of finite fields\n\n*a research project in Computer Algebra*\n\nby [Ludovic Brieulle](https://github.com/brieulle/), [Luca De\nFeo](http://defeo.lu/), [Javad\nDoliskani](https://github.com/javad-doliskani), [Jean-Pierre\nFlori](https://github.com/jpf-anssi/) and [Éric\nSchost](http://www.csd.uwo.ca/~eschost/).\n\n#### Abstract\n\nLet *𝔽\u003csub\u003eq\u003c/sub\u003e* be a finite field.  Given two irreducible\npolynomials *f*, *g* over *𝔽\u003csub\u003eq\u003c/sub\u003e*, with deg *f* dividing deg\n*g*, the finite field embedding problem asks to compute an explicit\ndescription of a field embedding of *𝔽\u003csub\u003eq\u003c/sub\u003e[X]/f(X)* into\n*𝔽\u003csub\u003eq\u003c/sub\u003e[Y]/g(Y)*.  When deg *f* = deg *g*, this is also known\nas the isomorphism problem.\n\nThis problem, a special instance of polynomial factorization, plays a\ncentral role in computer algebra software.  We review previous\nalgorithms, due to Lenstra, Allombert, Rains, and Narayanan, and\npropose improvements and generalizations.  Our detailed complexity\nanalysis shows that our newly proposed variants are at least as\nefficient as previously known algorithms, and in many cases\nsignificantly better.\n\nWe also implement most of the presented algorithms, compare them with\nthe state of the art computer algebra software, and make the code\navailable as open source.  Our experiments show that our new variants\nconsistently outperform available software.\n\n\n## Research paper\n\nThe research paper has been submitted for publication in [AMS\nMathematics of\nComputation](http://www.ams.org/publications/journals/journalsframework/mcom).\n\nA preprint version is available at \u003chttps://arxiv.org/abs/1705.01221\u003e.\n\nThe LaTeX sources to the paper can be found in the [`paper`](paper)\nfolder.  They are subject to the copying restriction enforced by the\neditor.\n\n\n## Software [![launch binder](https://mybinder.org/badge.svg)](https://mybinder.org/v2/gh/defeo/ffisom/master?filepath=notebooks)\n\nThe [`implementation`](implementation) folder contains source code for\nthe algorithms implemented by the project. See the folder `README.md`\nfor instructions on compiling and running the software on your own\nmachine.\n\nThe [`notebooks`](notebooks) folder contains Jupyter notebooks showing\nsample usage of the software and benchmarks. Notebooks can be\nstatically viewed on GitHub, or **executed** in\n[Binder](https://mybinder.org/v2/gh/defeo/ffisom/master?filepath=notebooks),\nthus saving you the time to compile and install the software.\n\nAll source code is distributed under the MIT license.\n\n\n## Related material\n\nThe [`misc`](misc) folder contains material related to the project,\nsuch as\n\n- conference posters,\n- presentation slides,\n- experimental data gathered on the conjecture formulated in the\n  paper.\n\n\n## Contributing\n\nWe do not accept pull requests, but if you see any problem with this\nrepository, plese open an issue.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdefeo%2Fffisom","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fdefeo%2Fffisom","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdefeo%2Fffisom/lists"}