{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T20:32:50Z","timestamp":1648758770411},"reference-count":3,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2015,11]]},"abstract":"<jats:p> This paper discusses a computational treatment of the localization [Formula: see text] of an affine coordinate ring [Formula: see text] at a prime ideal [Formula: see text] and its associated graded algebra [Formula: see text] with the means of computer algebra. Building on Mora\u2019s paper [T. Mora, La queste del Saint [Formula: see text]: A computational approach to local algebra, Discrete Appl. Math. 33 (1991) 161\u2013190], we present shorter proofs on two of the central statements and expand on the applications touched by Mora: resolutions of ideals, systems of parameters and Hilbert polynomials, as well as dimension and regularity of [Formula: see text]. All algorithms are implemented in the library graal.lib for the computer algebra system Singular. <\/jats:p>","DOI":"10.1142\/s0218196715500332","type":"journal-article","created":{"date-parts":[[2015,10,7]],"date-time":"2015-10-07T02:42:54Z","timestamp":1444185774000},"page":"1125-1143","source":"Crossref","is-referenced-by-count":1,"title":["Mora\u2019s holy graal: Algorithms for computing in localizations at prime ideals"],"prefix":"10.1142","volume":"25","author":[{"given":"Magdaleen S.","family":"Marais","sequence":"first","affiliation":[{"name":"Department of Mathematics and Applied Mathematics, African Institute for Mathematical Sciences, University of Pretoria, 0002 Pretoria, South Africa"}]},{"given":"Yue","family":"Ren","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Kaiserslautern, Erwin-Schr\u00f6dinger-Str., 67663 Kaiserslautern, Germany"}]}],"member":"219","published-online":{"date-parts":[[2015,12,8]]},"reference":[{"key":"S0218196715500332BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5350-1"},{"key":"S0218196715500332BIB003","volume-title":"A Singular Introduction to Commutative Algebra","author":"Greuel G.-M.","year":"2008","edition":"2"},{"key":"S0218196715500332BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(91)90114-C"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196715500332","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T17:37:39Z","timestamp":1565199459000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196715500332"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11]]},"references-count":3,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2015,12,8]]},"published-print":{"date-parts":[[2015,11]]}},"alternative-id":["10.1142\/S0218196715500332"],"URL":"https:\/\/doi.org\/10.1142\/s0218196715500332","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11]]}}}