{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T17:40:36Z","timestamp":1776793236621,"version":"3.51.2"},"reference-count":13,"publisher":"American Mathematical Society (AMS)","issue":"274","license":[{"start":{"date-parts":[[2011,11,1]],"date-time":"2011-11-01T00:00:00Z","timestamp":1320105600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>In modeling physical systems, it is sometimes useful to construct border bases of 0-dimensional polynomial ideals which are contained in the ideal generated by a given set of polynomials. We define and construct such subideal border bases, provide some basic properties and generalize a suitable variant of the Buchberger-M\u00f6ller algorithm as well as the AVI-algorithm of\u00a0Heldt, Kreuzer, Pokutta, and Poulisse to the subideal setting. The subideal version of the AVI-algorithm is then applied to an actual industrial problem.<\/p>","DOI":"10.1090\/s0025-5718-2010-02432-9","type":"journal-article","created":{"date-parts":[[2010,12,29]],"date-time":"2010-12-29T14:39:46Z","timestamp":1293633586000},"page":"1135-1154","source":"Crossref","is-referenced-by-count":6,"title":["Subideal border bases"],"prefix":"10.1090","volume":"80","author":[{"given":"Martin","family":"Kreuzer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Henk","family":"Poulisse","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2010,11,1]]},"reference":[{"issue":"12","key":"1","doi-asserted-by":"publisher","first-page":"883","DOI":"10.1016\/j.jsc.2008.05.002","article-title":"Stable border bases for ideals of points","volume":"43","author":"Abbott, John","year":"2008","journal-title":"J. Symbolic Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0747-7171","issn-type":"print"},{"key":"2","unstructured":"The Algebraic Oil Research Project, see http:\/\/www.fim.uni-passau.de\/algebraic-oil"},{"key":"3","unstructured":"\\apcocoa: Applied Computations in Commutative Algebra, see http:\/\/www.apcocoa.org"},{"key":"4","isbn-type":"print","first-page":"24","article-title":"The construction of multivariate polynomials with preassigned zeros","author":"M\u00f6ller, H. M.","year":"1982","ISBN":"https:\/\/id.crossref.org\/isbn\/3540116079"},{"issue":"11","key":"5","doi-asserted-by":"publisher","first-page":"1566","DOI":"10.1016\/j.jsc.2008.11.010","article-title":"Approximate computation of zero-dimensional polynomial ideals","volume":"44","author":"Heldt, Daniel","year":"2009","journal-title":"J. Symbolic Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0747-7171","issn-type":"print"},{"issue":"2-3","key":"6","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1016\/j.jpaa.2004.08.028","article-title":"Characterizations of border bases","volume":"196","author":"Kehrein, Achim","year":"2005","journal-title":"J. Pure Appl. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0022-4049","issn-type":"print"},{"key":"7","isbn-type":"print","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1007\/3-540-27357-3_4","article-title":"An algebraist\u2019s view on border bases","author":"Kehrein, Achim","year":"2005","ISBN":"https:\/\/id.crossref.org\/isbn\/9783540243267"},{"key":"8","doi-asserted-by":"crossref","unstructured":"M. Kreuzer, H. Poulisse, and L. Robbiano, From oil fields to Hilbert schemes, in: J. Abbott, L. Robbiano (eds.), Approximate Commutative Algebra, Springer-Verlag, Vienna, 2009, pp. 1\u201354.","DOI":"10.1007\/978-3-211-99314-9_1"},{"key":"9","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-70628-1","volume-title":"Computational commutative algebra. 1","author":"Kreuzer, Martin","year":"2000","ISBN":"https:\/\/id.crossref.org\/isbn\/354067733X"},{"key":"10","isbn-type":"print","volume-title":"Computational commutative algebra. 2","author":"Kreuzer, Martin","year":"2005","ISBN":"https:\/\/id.crossref.org\/isbn\/9783540255277"},{"issue":"3","key":"11","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1007\/BF03191188","article-title":"Deformations of border bases","volume":"59","author":"Kreuzer, Martin","year":"2008","journal-title":"Collect. 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Symbolic Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0747-7171","issn-type":"print"},{"key":"13","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717976","volume-title":"Numerical polynomial algebra","author":"Stetter, Hans J.","year":"2004","ISBN":"https:\/\/id.crossref.org\/isbn\/0898715571"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2011-80-274\/S0025-5718-2010-02432-9\/S0025-5718-2010-02432-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2011-80-274\/S0025-5718-2010-02432-9\/S0025-5718-2010-02432-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:48:06Z","timestamp":1776790086000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2011-80-274\/S0025-5718-2010-02432-9\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,11,1]]},"references-count":13,"journal-issue":{"issue":"274","published-print":{"date-parts":[[2011,4]]}},"alternative-id":["S0025-5718-2010-02432-9"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-2010-02432-9","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2010,11,1]]}}}