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arXiv · 1110.0182

Computing localizations iteratively

Francisco-Jesús Castro-Jiménez·Anton Leykin
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Abstract

Let $R=\bC[\bfx]$ be a polynomial ring with complex coefficients and $\Dx = \bC $ be the Weyl algebra. Describing the localization $R_f = R[f^{-1}]$ for nonzero $f\in R$ as a $\Dx$-module amounts to computing the annihilator $A = \Ann(f^a)\subset \Dx$ of the cyclic generator $f^{a}$ for a suitable negative integer $a$. We construct an iterative algorithm that uses truncated annihilators to build $A$ for planar curves.

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Francisco-Jesús Castro-Jiménez, Anton Leykin. 2011-11-22. Computing localizations iteratively. https://arxiv.org/abs/1110.0182

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