{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:30:11Z","timestamp":1750307411183,"version":"3.41.0"},"reference-count":0,"publisher":"Association for Computing Machinery (ACM)","issue":"3\/4","license":[{"start":{"date-parts":[[2010,6,24]],"date-time":"2010-06-24T00:00:00Z","timestamp":1277337600000},"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":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2010,6,24]]},"abstract":"<jats:p>This thesis is devoted to the design and implementation of polynomial system solvers based on symbolic computation. Solving systems of non-linear, algebraic or differential equations, is a fundamental problem in mathematical sciences. It has been studied for centuries and still stimulates many research developments, in particular on the front of high-performance computing.<\/jats:p>\n          <jats:p>Triangular decompositions are a highly promising technique with the potential to produce high-performance polynomial system solvers. This thesis makes several contributions to this effort.<\/jats:p>\n          <jats:p>We propose asymptotically fast algorithms for the core operations on which triangular decompositions rely. Complexity results and comparative implementation show that these new algorithms provide substantial performance improvements.<\/jats:p>\n          <jats:p>We present a fundamental software library for polynomial arithmetic in order to support the implementation of high-performance solvers based on triangular decompositions. We investigate strategies for the integration of this library in high-level programming environments where triangular decompositions are usually implemented.<\/jats:p>\n          <jats:p>We obtain a high performance library combining highly optimized C routines and solving procedures written in the Maple computer algebra system. The experimental result shows that our approaches are very effective, since our code often outperforms pre-existing solvers in a significant manner.<\/jats:p>","DOI":"10.1145\/1823931.1823956","type":"journal-article","created":{"date-parts":[[2010,6,29]],"date-time":"2010-06-29T13:02:22Z","timestamp":1277816542000},"page":"120-120","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Toward high-performance polynomial system solvers based on triangular decompositions"],"prefix":"10.1145","volume":"43","author":[{"given":"Xin","family":"Li","sequence":"first","affiliation":[{"name":"Computer Science, UWO, Canada"}]}],"member":"320","published-online":{"date-parts":[[2010,6,24]]},"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1823931.1823956","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1823931.1823956","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T11:39:33Z","timestamp":1750246773000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1823931.1823956"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6,24]]},"references-count":0,"journal-issue":{"issue":"3\/4","published-print":{"date-parts":[[2010,6,24]]}},"alternative-id":["10.1145\/1823931.1823956"],"URL":"https:\/\/doi.org\/10.1145\/1823931.1823956","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2010,6,24]]},"assertion":[{"value":"2010-06-24","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}