{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T05:18:01Z","timestamp":1672291081223},"reference-count":0,"publisher":"Association for Computing Machinery (ACM)","issue":"3","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGSAM Bull."],"published-print":{"date-parts":[[2005,9]]},"abstract":"The program CRACK is a computer algebra package written in\nREDUCE for the solution of over-determined systems of algebraic,\nordinary or partial differential equations with at most polynomial\nnon-linearity. It is available as part of version 3.8 of the REDUCE\nsystem (dated April 2004) and the latest development version can be\ndownloaded from http:\/\/lie.math.brocku.ca\/crack\/.<\/jats:p>\n The purpose of this poster is to accompany a software\ndemonstration of CRACK at ISSAC 2005. The poster is supposed to\ngive a graphical overview of CRACK, emphasizing features which are\nspecial to the package. Those are<\/jats:p>\n • a rich interface, with visualization aids for\ninspecting large systems, including<\/jats:p>\n - for each equation its properties, history and investigations\nthat have already been done with the equation,<\/jats:p>\n - the occurrence of all derivatives of selected functions in any\nequation,<\/jats:p>\n - a statistical overview of the system (number of equations and\nfunctions in dependence of number of independent variables),<\/jats:p>\n - a matrix display of occurrences of unknown constants\/functions\nin all equations,<\/jats:p>\n - a count of the total number of appearances of each\nunknown,<\/jats:p>\n - the determination of not under-determined subsystems,<\/jats:p>\n - a listing of all sub- and sub-sub-.. cases investigated so\nfar, with their assumptions, number of steps and number of\nsolutions,<\/jats:p>\n - graphical displays of size related measures of the computation\ndone so far;<\/jats:p>\n • a discussion of possibilities to trade interactively\nor automatically the speed of the solution process versus safety\n(avoidance of expression swell):<\/jats:p>\n - only length-reducing versus complete Gröbner basis\ncomputation steps.<\/jats:p>\n - substitutions in shorter equations only, i.e. only in a\nsub-system versus substitutions in the complete system,<\/jats:p>\n - growth bounded substitutions versus general substitutions,<\/jats:p>\n - case splittings (induced by factorizations, substitutions with\npotentially vanishing coefficients or adhoc case distinctions)\nversus Gröbner basis steps,<\/jats:p>\n - an investment in the length reduction of equations to reach\nsparse systems with multiple benefits;<\/jats:p>\n • algorithmic extensions which include<\/jats:p>\n - the ability to collect and apply syzygies which result as a\nby-product in the process of computing a differential\nGröbner basis to integrate linear PDEs.<\/jats:p>\n - the treatment of inequalities: their usage, active collection\nand derivation, and their constant update in an ongoing reduction\nprocess based on newly derived equations.<\/jats:p>\n - the capability added by Winfried Neun (ZIB Berlin) to run in a\ntruly parallel mode on a beowulf cluster, recently also ported to\n64bit AMD processors.<\/jats:p>\n - post-computation procedures, especially the possibility to\nmerge solutions of parametric linear algebraic systems and to\nautomate the production of web-pages for solutions that are\nfound.<\/jats:p>\n - the ability to separate expressions with respect to\nindependent variables which occur polynomially but with variable\nexponents, leading to automatically investigated case distinctions\nof exponents being equal or not;<\/jats:p>\n • safety enhancing measures as<\/jats:p>\n - the ability to backup and re-load the whole session,<\/jats:p>\n - the automatic storing of the complete keyboard input during a\nsession with the opportunity to feed this stored input into a new\nsession,<\/jats:p>\n - the possibility to impose time restrictions of notoriously\nslow sub-steps, like factorizations and sometimes the computation\nand reduction of S-polynomials in a Gröbner basis\ncomputations,<\/jats:p>\n - a method to interrupt an ongoing automatic computation and\nchange it to interactive mode<\/jats:p>\n The poster in landscape format will display the above four\ntopics in boxes. For some of the sub-items above a screen output\nwill give a visual impression, like the matrix indicating\noccurrences of unknowns in equations. In the following publications\nthe solution of large overdetermined systems was a crucial\ningredient:<\/jats:p>\n • the solution of large bi-linear algebraic systems and\nautomatic merging of obtained solutions:<\/jats:p>\n - Wolf, T., Efimovskaya, O. V.: Classification of integrable\nquadratic Hamiltonians on e(3), Regular and Chaotic Dynamics, vol\n8, no 2 (2003), p 155--162.<\/jats:p>\n - Sokolov, V. V., Wolf, T.: Classification of integrable\npolynomial vector evolution equations, J. Phys. A: Math. Gen. 34\n(2001) 11139--11148.<\/jats:p>\n - Tsuchida, T. and Wolf, T.: Classification of integrable\ncoupled systems with one scalar and one vector unknown, preprint\nnlin.SI\/0412003 (2004) 60 pages, to appear in J. Phys. A: Math.\nGen.<\/jats:p>\n - Sokolov, V. V. and Wolf, T.: Integrable quadratic Hamiltonians\non <i>so<\/i>(4) and <i>so<\/i>(3, 1),\npreprint (2004) 16 pages, nlin.SI\/0405066.<\/jats:p>\n - Kiselev, A. and Wolf, T.: New recursive chains of N=1\nhomogeneous superequations, to appear in proceedings of \"Symmetry\nin Nonlinear Mathematical Physics\", Kyiv 2005.<\/jats:p>\n • the solution of extensive overdetermined\nODE\/PDE-systems:<\/jats:p>\n - Anco, S. and Wolf, T.: Some symmetry classifications of\nhyperbolic vector evolution equations, nlin.SI\/0412015, JNMP,\nVolume 12, Supplement 1 (2005), p 13--31.<\/jats:p>","DOI":"10.1145\/1113439.1113455","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"95-96","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["The package CRACK for solving large overdetermined systems"],"prefix":"10.1145","volume":"39","author":[{"given":"Thomas","family":"Wolf","sequence":"first","affiliation":[{"name":"Brock University, Saint Catharines, Canada"}]}],"member":"320","published-online":{"date-parts":[[2005,9]]},"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1113439.1113455","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T14:40:38Z","timestamp":1672238438000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1113439.1113455"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,9]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2005,9]]}},"alternative-id":["10.1145\/1113439.1113455"],"URL":"http:\/\/dx.doi.org\/10.1145\/1113439.1113455","relation":{},"ISSN":["0163-5824"],"issn-type":[{"value":"0163-5824","type":"print"}],"subject":[],"published":{"date-parts":[[2005,9]]},"assertion":[{"value":"2005-09-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}