{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:20:08Z","timestamp":1787318408169,"version":"3.56.0"},"reference-count":10,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2004,6,1]],"date-time":"2004-06-01T00:00:00Z","timestamp":1086048000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGSAM Bull."],"published-print":{"date-parts":[[2004,6]]},"abstract":"<jats:p>\n                    Algorithms in computer algebra are usually designed for a fixed set of domains. For example, algorithms over the domain of polynomials are not applicable to parameters because the inherent assumption that the indeterminate\n                    <jats:italic>X<\/jats:italic>\n                    bears no algebraic relation to other objects is violated.We propose to use a technique from model theory known as\n                    <jats:italic>constraint programming<\/jats:italic>\n                    to gain more flexibility, and we show how it can be applied to the Gaussian algorithm to be used for parametric systems. Our experiments suggest that in practice this leads to results comparable to the algorithm for parametric linear systems by Sit [9] --- at least if the parameters are sparse.\n                  <\/jats:p>","DOI":"10.1145\/1041791.1041793","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T13:32:02Z","timestamp":1169040722000},"page":"33-46","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":15,"title":["Solving parametric linear systems"],"prefix":"10.1145","volume":"38","author":[{"given":"Clemens","family":"Ballarin","sequence":"first","affiliation":[{"name":"Technische Universit\u00e4t M\u00fcnchen, Garching, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Manuel","family":"Kauers","sequence":"additional","affiliation":[{"name":"RISC-Linz, Johannes-Kepler-Universit\u00e4t, Linz, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2004,6]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","unstructured":"D. Cox J. Little and D. O'Shea. Ideals Varieties and Algorithms. Springer 1992.]]   D. Cox J. Little and D. O'Shea. Ideals Varieties and Algorithms. Springer 1992.]]","DOI":"10.1007\/978-1-4757-2181-2"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61566-5"},{"key":"e_1_2_1_3_1","volume-title":"Computer Algebra: Systems and algorithms for algebraic computation","author":"Davenport J. H.","year":"1993","unstructured":"J. H. Davenport , Y. Siret , and E. Tournier . Computer Algebra: Systems and algorithms for algebraic computation . Academic Press , second edition, 1993 .]] J. H. Davenport, Y. Siret, and E. Tournier. Computer Algebra: Systems and algorithms for algebraic computation. Academic Press, second edition, 1993.]]"},{"key":"e_1_2_1_4_1","volume-title":"Direct Methods for Sparse Matrices","author":"Duff I. S.","year":"1986","unstructured":"I. S. Duff , A. M. Erisman , and J. K. Reid . Direct Methods for Sparse Matrices . Clarendon Press , 1986 .]] I. S. Duff, A. M. Erisman, and J. K. Reid. Direct Methods for Sparse Matrices. Clarendon Press, 1986.]]"},{"key":"e_1_2_1_5_1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-59115-0","volume-title":"Constraint-Programmierung: Grundlagen und Anwendungen","author":"Fr\u00fchwirth Thom","year":"1997","unstructured":"Thom Fr\u00fchwirth and Slim Abdennadher . Constraint-Programmierung: Grundlagen und Anwendungen . Springer-Verlag , 1997 .]] Thom Fr\u00fchwirth and Slim Abdennadher. Constraint-Programmierung: Grundlagen und Anwendungen. Springer-Verlag, 1997.]]"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03241-1"},{"key":"e_1_2_1_7_1","volume-title":"Applied linear algebra","author":"Noble Ben","year":"1988","unstructured":"Ben Noble and James W. Daniel . Applied linear algebra . Prentice-Hall , 3 rd edition, 1988 .]] Ben Noble and James W. Daniel. Applied linear algebra. Prentice-Hall, 3rd edition, 1988.]]","edition":"3"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/321250.321253"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(08)80104-6"},{"key":"e_1_2_1_10_1","first-page":"95","volume-title":"Design and implementation of symbolic computation systems: International Symposium, DISCO '92","author":"Weibel Trudy","year":"1992","unstructured":"Trudy Weibel and Gaston H. Gonnet . An assume facility for CAS, with a sample implementation for Maple . In John Fitch, editor, Design and implementation of symbolic computation systems: International Symposium, DISCO '92 , Bath, U.K. , April 13--15 1992 : proceedings, number 721 in LNCS, pages 95 -- 103 . Springer-Verlag , 1993.]] Trudy Weibel and Gaston H. Gonnet. An assume facility for CAS, with a sample implementation for Maple. In John Fitch, editor, Design and implementation of symbolic computation systems: International Symposium, DISCO '92, Bath, U.K., April 13--15 1992: proceedings, number 721 in LNCS, pages 95--103. Springer-Verlag, 1993.]]"}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1041791.1041793","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1041791.1041793","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T17:14:58Z","timestamp":1750266898000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1041791.1041793"}},"subtitle":["an experiment with constraint algebraic programming"],"short-title":[],"issued":{"date-parts":[[2004,6]]},"references-count":10,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2004,6]]}},"alternative-id":["10.1145\/1041791.1041793"],"URL":"https:\/\/doi.org\/10.1145\/1041791.1041793","relation":{},"ISSN":["0163-5824"],"issn-type":[{"value":"0163-5824","type":"print"}],"subject":[],"published":{"date-parts":[[2004,6]]},"assertion":[{"value":"2004-06-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}