graal.lib - a Singular library for computing in localizations at prime ideals. ”graal.lib” is a Singular library for a computational treatment of localizations at prime ideals and their associated graded rings based on a work of Mora. Not only does it construct a ring isomorphic to the localization of an affine coordinate ring at a prime ideal, the algorithms in this library aim to exploit the topology in the localization by computing first and foremost in the associated graded ring and lifting the result to the localization afterwards. Features include a check for regularity and the resolution of ideals.

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  1. Marais, Magdaleen S.; Ren, Yue: Mora’s holy graal: algorithms for computing in localizations at prime ideals (2015)