Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing Regular Meromorphic Differential Forms via Saito's Logarithmic
  Residues   Logarithmic differential forms and logarithmic vector fields associated to a
hypersurface with an isolated singularity are considered in the context of
computational complex analysis. As applications, based on the concept of
torsion differential forms due to A.G. Aleksandrov, regular meromorphic
differential forms introduced by D. Barlet and M. Kersken, and Brieskorn
formulae on Gauss-Manin connections are investigated. (i) A method is given to
describe singular parts of regular meromorphic differential forms in terms of
non-trivial logarithmic vector fields via Saito's logarithmic residues. The
resulting algorithm is illustrated by using examples. (ii) A new link between
Brieskorn formulae and logarithmic vector fields is discovered and an
expression that rewrites Brieskorn formulae in terms of non-trivial logarithmic
vector fields is presented. A new effective method is described to compute non
trivial logarithmic vector fields which are suitable for the computation of
Gauss-Manin connections. Some examples are given for illustration.

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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph