Mora's holy graal : algorithms for computing in localizations at prime ideals

dc.contributor.authorMarais, Magdaleen S.
dc.contributor.authorRen, Yue
dc.date.accessioned2017-02-07T11:36:23Z
dc.date.available2017-02-07T11:36:23Z
dc.date.issued2015-11
dc.description.abstractThis article discusses a computational treatment of the localization AL of an affine coordinate ring A at a prime ideal L and its associated graded ring Gra(AL) with the means of standard basis techniques. Building on Mora’s work, we present alternative proofs on two of the central statements and expand on the applications mentioned by Mora: resolutions of ideals, systems of parameters and Hilbert polynomials, as well as dimension and regularity of AL. All algorithms are implemented in the library graal.lib for the computer algebra system Singular.en_ZA
dc.description.departmentMathematics and Applied Mathematicsen_ZA
dc.description.librarianhb2017en_ZA
dc.description.sponsorshipThe African Institute for Mathematical Sciences, the Department of Mathematics and Applied Mathematics of the University of Pretoria and a grant awarded by Wolfram Decker.en_ZA
dc.description.urihttp://www.worldscientific.com/worldscinet/ijacen_ZA
dc.identifier.citationMarais, MS & Ren, Y 2015, 'Mora's holy graal : algorithms for computing in localizations at prime ideals', International Journal of Algebra and Computation, vol. 25, no. 7, pp. 1125-1143.en_ZA
dc.identifier.issn0218-1967 (print)
dc.identifier.issn1793-6500 (online)
dc.identifier.other10.1142/S0218196715500332
dc.identifier.urihttp://hdl.handle.net/2263/58896
dc.language.isoenen_ZA
dc.publisherWorld Scientific Publishingen_ZA
dc.rights© 2015 World Scientific Publishing Co. This is an electronic version of an article published in International Journal of Algebra and Computation, vol. 25, no. 7, pp.1125-1143, 2015. doi : 10.1142/S0218196715500332. The original publication is available at : http://www.worldscientific.com/worldscinet/ijac.en_ZA
dc.subjectLocal ringen_ZA
dc.subjectAssociated graded algebraen_ZA
dc.subjectLocalizationen_ZA
dc.subjectResolutionen_ZA
dc.titleMora's holy graal : algorithms for computing in localizations at prime idealsen_ZA
dc.typePostprint Articleen_ZA

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