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arXiv · 1504.01648

Mora's holy grail: Algorithms for computing in localizations at prime ideals

Magdaleen S. Marais·Yue Ren
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Abstract

This article discusses a computational treatment of the localization A_L of an affine coordinate ring A at a prime ideal L and its associated graded ring Gr_a(A_L) 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 A_L. All algorithms are implemented in the library graal.lib for the computer algebra system Singular.

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Magdaleen S. Marais, Yue Ren. 2015-04-07. Mora's holy grail: Algorithms for computing in localizations at prime ideals. https://arxiv.org/abs/1504.01648

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