Let $R=\bC[\bfx]$ be a polynomial ring with complex coefficients and $\Dx = \bC<bfx,\bfp>$ 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.
Categories: math.AG math.AC