• DOI:10.1142/9789814383462_0003
Corpus ID: 119178068

Computing localizations iteratively

@article{CastroJimnez2011ComputingLI,
  title={Computing localizations iteratively},
  author={F. Castro-Jim{\'e}nez and A. Leykin},
  journal={arXiv: Algebraic Geometry},
  year={2011}
}

F. Castro-Jiménez, A. Leykin

Published 2011

Mathematics

arXiv: Algebraic Geometry

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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.