{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:50:47Z","timestamp":1776844247239,"version":"3.51.2"},"reference-count":32,"publisher":"Wiley","license":[{"start":{"date-parts":[[2012,8,1]],"date-time":"2012-08-01T00:00:00Z","timestamp":1343779200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce the computer algebra package PyCox, written entirely in the Python language. It implements a set of algorithms, in a spirit similar to the older CHEVIE system, for working with Coxeter groups and Hecke algebras. This includes a new variation of the traditional algorithm for computing Kazhdan\u2013Lusztig cells and<jats:italic>W<\/jats:italic>-graphs, which works efficiently for all finite groups of rank \u22648 (except<jats:italic>E<\/jats:italic><jats:sub>8<\/jats:sub>). We also discuss the computation of Lusztig\u2019s leading coefficients of character values and distinguished involutions (which works for<jats:italic>E<\/jats:italic><jats:sub>8<\/jats:sub>as well). Our experiments suggest a re-definition of Lusztig\u2019s \u2018special\u2019 representations which, conjecturally, should also apply to the unequal parameter case. Supplementary materials are available with this article.<\/jats:p>","DOI":"10.1112\/s1461157012001064","type":"journal-article","created":{"date-parts":[[2012,9,11]],"date-time":"2012-09-11T07:31:27Z","timestamp":1347348687000},"page":"231-256","source":"Crossref","is-referenced-by-count":17,"title":["PyCox: computing with (finite) Coxeter groups and Iwahori\u2013Hecke algebras"],"prefix":"10.1112","volume":"15","author":[{"given":"Meinolf","family":"Geck","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2012,8,1]]},"reference":[{"key":"S1461157012001064_ref30","volume-title":"GAP \u2013 Groups, Algorithms, and Programming","author":"Sch\u00f6nert","year":"1994"},{"key":"S1461157012001064_ref31","unstructured":"[31] Stein W. A. et al., Sage Mathematics Software (Version 4.7.1) (The Sage Development Team, 2011, see http:\/\/www.sagemath.org)."},{"key":"S1461157012001064_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/s00209-003-0507-1"},{"key":"S1461157012001064_ref2","doi-asserted-by":"publisher","DOI":"10.1090\/S1088-4165-00-00052-2"},{"key":"S1461157012001064_ref7","doi-asserted-by":"publisher","DOI":"10.1112\/S0024609303002236"},{"key":"S1461157012001064_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/S1385-7258(79)80026-8"},{"key":"S1461157012001064_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190330"},{"key":"S1461157012001064_ref19","doi-asserted-by":"publisher","DOI":"10.1007\/BF01390031"},{"key":"S1461157012001064_ref3","doi-asserted-by":"publisher","DOI":"10.1080\/00927879208826378"},{"key":"S1461157012001064_ref28","unstructured":"[28] Lusztig G. and Vogan D. A. Jr. , \u2018Hecke algebras and involutions in Weyl groups\u2019, Bull. Inst. Math. Acad. Sin. (N.S.), to appear, arXiv:1109.4606."},{"key":"S1461157012001064_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2004.07.029"},{"key":"S1461157012001064_ref20","doi-asserted-by":"publisher","DOI":"10.1090\/S1088-4165-00-00050-9"},{"key":"S1461157012001064_ref24","doi-asserted-by":"crossref","first-page":"255","DOI":"10.2969\/aspm\/00610255","volume-title":"Algebraic groups and related topics","author":"Lusztig","year":"1985"},{"key":"S1461157012001064_ref23","doi-asserted-by":"publisher","DOI":"10.1515\/9781400881772"},{"key":"S1461157012001064_ref17","doi-asserted-by":"publisher","DOI":"10.1007\/s00229-004-0508-3"},{"key":"S1461157012001064_ref27","doi-asserted-by":"publisher","DOI":"10.1090\/crmm\/018"},{"key":"S1461157012001064_ref26","first-page":"235","volume-title":"Leading coefficients of character values of Hecke algebras","author":"Lusztig","year":"1987"},{"key":"S1461157012001064_ref5","unstructured":"[5] DuCloux F. , \u2018Coxeter: software for Kazhdan\u2013Lusztig polynomials for Coxeter groups\u2019; available at http:\/\/www.liegroups.org\/coxeter\/coxeter3\/english."},{"key":"S1461157012001064_ref32","doi-asserted-by":"publisher","DOI":"10.1007\/s00229-006-0022-x"},{"key":"S1461157012001064_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(87)90082-2"},{"key":"S1461157012001064_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0071433"},{"key":"S1461157012001064_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2005.10.004"},{"key":"S1461157012001064_ref11","doi-asserted-by":"crossref","first-page":"64","DOI":"10.37193\/CJM.2011.01.07","article-title":"Some applications of CHEVIE to the theory of algebraic groups","volume":"27","author":"Geck","year":"2011","journal-title":"Carpathuian. Math."},{"key":"S1461157012001064_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2008.12.018"},{"key":"S1461157012001064_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-85729-716-7"},{"key":"S1461157012001064_ref15","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198502500.001.0001","volume-title":"Characters of finite Coxeter groups and Iwahori\u2013Hecke algebras","author":"Geck","year":"2000"},{"key":"S1461157012001064_ref12","doi-asserted-by":"crossref","unstructured":"[12] Geck M. , \u2018Kazhdan\u2013Lusztig cells and the Frobenius\u2013Schur indicator\u2019, Preprint, 2011, arXiv:1110.5672.","DOI":"10.1007\/978-0-85729-716-7_2"},{"key":"S1461157012001064_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190329"},{"key":"S1461157012001064_ref9","doi-asserted-by":"publisher","DOI":"10.1090\/S1088-4165-06-00287-1"},{"key":"S1461157012001064_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(87)90154-2"},{"key":"S1461157012001064_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091508000394"},{"key":"S1461157012001064_ref29","unstructured":"[29] van Rossum G. et al., Python Language Website, 1990\u20132012 (Python Software Foundation, see http:\/\/www.python.org\/)."}],"container-title":["LMS Journal of Computation and Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1461157012001064","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,29]],"date-time":"2024-04-29T03:28:18Z","timestamp":1714361298000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1461157012001064\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,1]]},"references-count":32,"alternative-id":["S1461157012001064"],"URL":"https:\/\/doi.org\/10.1112\/s1461157012001064","relation":{},"ISSN":["1461-1570"],"issn-type":[{"value":"1461-1570","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,8,1]]}}}