{"id":17766477,"url":"https://github.com/pythonnut/linear-presentation","last_synced_at":"2026-02-14T11:02:29.262Z","repository":{"id":71179823,"uuid":"196785955","full_name":"PythonNut/linear-presentation","owner":"PythonNut","description":"Program to compute the \"linear presentation\" of a knot","archived":false,"fork":false,"pushed_at":"2024-10-30T06:39:16.000Z","size":983,"stargazers_count":2,"open_issues_count":2,"forks_count":0,"subscribers_count":2,"default_branch":"master","last_synced_at":"2025-09-07T12:41:14.820Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":"","language":"Python","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/PythonNut.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,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2019-07-14T02:39:01.000Z","updated_at":"2024-10-02T05:47:52.000Z","dependencies_parsed_at":"2025-02-07T08:43:06.351Z","dependency_job_id":"5440b5fa-7b61-4710-b456-b7ea3cef067b","html_url":"https://github.com/PythonNut/linear-presentation","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/PythonNut/linear-presentation","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/PythonNut%2Flinear-presentation","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/PythonNut%2Flinear-presentation/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/PythonNut%2Flinear-presentation/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/PythonNut%2Flinear-presentation/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/PythonNut","download_url":"https://codeload.github.com/PythonNut/linear-presentation/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/PythonNut%2Flinear-presentation/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":29443446,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-02-14T10:51:12.367Z","status":"ssl_error","status_checked_at":"2026-02-14T10:50:52.088Z","response_time":53,"last_error":"SSL_read: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"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":[],"created_at":"2024-10-26T20:30:27.456Z","updated_at":"2026-02-14T11:02:29.231Z","avatar_url":"https://github.com/PythonNut.png","language":"Python","funding_links":[],"categories":[],"sub_categories":[],"readme":"# A (sort-of) Linear-Time Algorithm for Drawing Linear Knot Diagrams\n## Motivation\nWhen doing work in [Knot\nTheory](https://en.wikipedia.org/wiki/Knot_theory), it is often\nhelpful to use _combinatorial encodings_ such as the [_Gauss\ncode_](http://katlas.math.toronto.edu/wiki/Gauss_Codes) to represent\nour knots (another common encoding is the [_DT\ncode_](http://katlas.org/wiki/DT_%28Dowker-Thistlethwaite%29_Codes),\nbut we won't talk about that today). Such encodings offer computers an\nelegant way of representing / manipulating knots --- indeed, many\ninvariants can be computed directly from combinatorial\nrepresentations.\n\nBasically, the Gauss code is a really elegant tool for applying\nalgebraic/algorithmic techniques to the study of knots. However, it\ncan be challenging to build geometric intuition for how manipulations\nof the Gauss code translate to manipulations of a knot and vice versa.\nThe problem is not the translation process is inherently challenging,\nbut rather that it is tedious and time-consuming.\n\n`linear-presentation` is designed to streamline this process. Given a\nGauss code, it creates a diagram for the associated knot such that\n  (1) all of the crossings are collinear,\n  (2) the over/understrands of each crossing are perpendicular at the\n    crossing point, and\n  (2) the first time a crossing is encountered, the strand is oriented\n    pointing to the right.\nSince Gauss codes are presented as linear strings, there is a sense in\nwhich this feels like the \"natural\" diagram to associate to the code.\nAnd in the other direction: In our personal experience, this\npresentation makes writing down a Gauss code associated to a diagram\nmuch faster than it would otherwise be.\n\n## A Brief Description of the Algorithm\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fpythonnut%2Flinear-presentation","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fpythonnut%2Flinear-presentation","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fpythonnut%2Flinear-presentation/lists"}