{"id":18024497,"url":"https://github.com/thofma/tropical.jl","last_synced_at":"2026-01-19T03:32:47.882Z","repository":{"id":93280188,"uuid":"410040620","full_name":"thofma/Tropical.jl","owner":"thofma","description":"Tropical geometry in Oscar","archived":false,"fork":false,"pushed_at":"2021-09-26T13:37:05.000Z","size":20,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":4,"default_branch":"master","last_synced_at":"2025-02-10T03:44:49.848Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":null,"language":"Julia","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/thofma.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":"2021-09-24T17:01:05.000Z","updated_at":"2025-01-08T08:53:34.000Z","dependencies_parsed_at":"2023-03-15T16:00:30.470Z","dependency_job_id":null,"html_url":"https://github.com/thofma/Tropical.jl","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/thofma%2FTropical.jl","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/thofma%2FTropical.jl/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/thofma%2FTropical.jl/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/thofma%2FTropical.jl/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/thofma","download_url":"https://codeload.github.com/thofma/Tropical.jl/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":247228602,"owners_count":20904901,"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":[],"created_at":"2024-10-30T07:12:59.848Z","updated_at":"2026-01-19T03:32:47.874Z","avatar_url":"https://github.com/thofma.png","language":"Julia","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Tropical\n\n[![Build Status](https://github.com/thofma/Tropical.jl/workflows/Run%20tests/badge.svg)](https://github.com/thofma/Tropical.jl/actions?query=workflow%3A%22Run%20tests%22+branch%3Amaster)\n\n## Installation\n\nIn the REPL type\n\n```julia\n]add https://github.com/thofma/Tropical.jl\n```\n\nIf you want to play with the package and make changes, type\n\n```julia\n]dev https://github.com/thofma/Tropical.jl\n```\n\n## Summary\n\nFirst stab at tropical rings in Oscar. This implementation\ninserts tropical rings and their elements into the Oscar\nhierarchy as a *ring* and *ring elements*, making all the ring\nfunctionality available. Here is a quick example:\n\n```julia\njulia\u003e T = tropical_ring(min)\nTropical ring (min)\n\njulia\u003e T(2) * T(3)\n(5)\n\njulia\u003e T(2) + T(0)\n(0)\n\njulia\u003e one(T)\n(0)\n\njulia\u003e zero(T)\n∞\n\njulia\u003e Tx, x = T[\"x\"]\n(Univariate Polynomial Ring in x over Tropical ring (min), x)\n\njulia\u003e x^2 + x\nx^2 + x\n```\n\nTo create tropical polynomials, there is also a `@tropical` macro.\n\n```julia\njulia\u003e T = tropical_ring(min)\nTropical ring (min)\n\njulia\u003e Tx, x = PolynomialRing(T, \"x\" =\u003e 1:3);\n\njulia\u003e @tropical min(1, x[1], x[2], 2*x[3])\nx[1] + x[2] + x[3]^2 + (1)\n```\n\nFor more examples see `test/runtests.jl`.\n\n## More details\n\nInternally, a tropical ring element is either a rational number\n(of type `fmpq`) or infinity. To accommodate both conventions (min/max),\nthe types are parameterized by `T`, which is either `typeof(min)` or\n`typeof(max)`. All this is hidden behind `+` and `*`.\n\nAt certain places Oscar (or the packages Oscar is built upon) assumes\nthat `R(1)` is the one of the ring `R` (and similar for zero). For this\nreason we have to implement our own version of various functions, for\nexample printing of polynomials or zero/one of polynomial rings.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fthofma%2Ftropical.jl","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fthofma%2Ftropical.jl","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fthofma%2Ftropical.jl/lists"}