{"id":25059877,"url":"https://github.com/stla/jackpy","last_synced_at":"2025-04-14T14:24:34.266Z","repository":{"id":73101551,"uuid":"427952879","full_name":"stla/jackpy","owner":"stla","description":"Jack polynomials with Python.","archived":false,"fork":false,"pushed_at":"2024-05-15T22:59:48.000Z","size":274,"stargazers_count":4,"open_issues_count":0,"forks_count":0,"subscribers_count":3,"default_branch":"main","last_synced_at":"2025-04-08T04:17:36.209Z","etag":null,"topics":["jack-polynomials","schur-polynomials","zonal-polynomials"],"latest_commit_sha":null,"homepage":"https://jackpy.readthedocs.io/en/latest/","language":"Python","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/stla.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":"2021-11-14T14:36:35.000Z","updated_at":"2024-05-15T22:59:51.000Z","dependencies_parsed_at":"2025-02-06T15:55:39.131Z","dependency_job_id":"a79cf234-1cd2-4f42-82ee-d1eeba5bdf7e","html_url":"https://github.com/stla/jackpy","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/stla%2Fjackpy","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stla%2Fjackpy/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stla%2Fjackpy/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stla%2Fjackpy/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/stla","download_url":"https://codeload.github.com/stla/jackpy/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":248895490,"owners_count":21179245,"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":["jack-polynomials","schur-polynomials","zonal-polynomials"],"created_at":"2025-02-06T15:55:31.076Z","updated_at":"2025-04-14T14:24:34.220Z","avatar_url":"https://github.com/stla.png","language":"Python","funding_links":[],"categories":[],"sub_categories":[],"readme":"# jackpolynomials\n\n\u003c!-- badges: start --\u003e\n[![Documentation status](https://readthedocs.org/projects/jackpy/badge/)](http://jackpy.readthedocs.io)\n\u003c!-- badges: end --\u003e\n\n***Jack, zonal, and Schur polynomials with Python.***\n\nSchur polynomials have applications in combinatorics and zonal polynomials have\napplications in multivariate statistics. They are particular cases of\n[Jack polynomials](https://en.wikipedia.org/wiki/Jack_function). This package\nallows to get these polynomials.\n\n___\n\nThe Jack polynomial in three variables of the integer partition $(2,1)$, with \nparameter $3/2$:\n\n```python\n\u003e\u003e\u003e from gmpy2 import mpq\n\u003e\u003e\u003e from jackpy.jack import JackPol\n\u003e\u003e\u003e\n\u003e\u003e\u003e poly = JackPol(3, [2, 1], alpha = mpq(3, 2))\n\u003e\u003e\u003e print(poly)\nPoly(7/2*x_1**2*x_2 + 7/2*x_1**2*x_3 + 7/2*x_1*x_2**2 + 6*x_1*x_2*x_3 \n + 7/2*x_1*x_3**2 + 7/2*x_2**2*x_3 + 7/2*x_2*x_3**2, x_1, x_2, x_3, domain='QQ')\n```\n\nBy default, `JackPol` returns the Jack $J$-polynomial. It can also return \nthe Jack $C$-polynomial, the Jack $P$-polynomial, and the Jack $Q$-polynomial,\nby using the `which` argument.\n\nThe expression of a Jack polynomial can be long. Since a Jack polynomial is \nsymmetric, it is possible to write it as a linear combination of some \nmonomial symmetric polynomials, and this gives a shorter expression.\n\n```python\n\u003e\u003e\u003e from jackpy.jack import JackPol\n\u003e\u003e\u003e from jackpy.monomial_symmetric_polynomials import msp_combination_expr\n\u003e\u003e\u003e poly = JackPol(4, [2, 2], alpha = 5)\n\u003e\u003e\u003e print(poly)\nPoly(84*x_1**2*x_2**2 + 28*x_1**2*x_2*x_3 + 28*x_1**2*x_2*x_4\n + 84*x_1**2*x_3**2 + 28*x_1**2*x_3*x_4 + 84*x_1**2*x_4**2\n + 28*x_1*x_2**2*x_3 + 28*x_1*x_2**2*x_4 + 28*x_1*x_2*x_3**2\n + 24*x_1*x_2*x_3*x_4 + 28*x_1*x_2*x_4**2 + 28*x_1*x_3**2*x_4 \n + 28*x_1*x_3*x_4**2 + 84*x_2**2*x_3**2 + 28*x_2**2*x_3*x_4 \n + 84*x_2**2*x_4**2 + 28*x_2*x_3**2*x_4 + 28*x_2*x_3*x_4**2 \n + 84*x_3**2*x_4**2, x_1, x_2, x_3, x_4, domain='QQ')\n\u003e\u003e\u003e expr = msp_combination_expr(poly)\n\u003e\u003e\u003e print(expr)\n24*M[1;1;1;1] + 28*M[2;1;1] + 84*M[2;2]\n```\n\nHere the symbol `M[1;1;1;1]` represents the monomial symmetric polynomial of \nthe integer partition $(1,1,1,1)$.\n\nAs of the development version `0.1.0.9000`, it is possible to get Jack polynomials with a symbolic \nJack parameter. These polynomials have domain `'QQ(alpha)'`, where `alpha` is\nthe Jack parameter.\n\n```python\n\u003e\u003e\u003e from jackpy.jack import JackSymbolicPol\n\u003e\u003e\u003e\n\u003e\u003e\u003e poly = JackSymbolicPol(3, [2, 2])\n\u003e\u003e\u003e print(poly)\nPoly((2*alpha**2 + 6*alpha + 4)*x_1**2*x_2**2 \n + (4*alpha + 8)*x_1**2*x_2*x_3 \n + (2*alpha**2 + 6*alpha + 4)*x_1**2*x_3**2 \n + (4*alpha + 8)*x_1*x_2**2*x_3 \n + (4*alpha + 8)*x_1*x_2*x_3**2 \n + (2*alpha**2 + 6*alpha + 4)*x_2**2*x_3**2, \n x_1, x_2, x_3, domain='QQ(alpha)')\n```\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstla%2Fjackpy","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fstla%2Fjackpy","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstla%2Fjackpy/lists"}