Marais, Magdaleen S.Ren, Yue2017-02-072017-02-072015-11Marais, 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. 1125-1143.0218-1967 (print)1793-6500 (online)10.1142/S0218196715500332http://hdl.handle.net/2263/58896This 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© 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.Local ringAssociated graded algebraLocalizationResolutionMora's holy graal : algorithms for computing in localizations at prime idealsPostprint Article