Gröbner bases and logarithmic -modules

• Autores: José María Ucha Enríquez , Francisco Jesús Castro Jiménez
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 41, Nº 3, 2006, págs. 317-335
• Idioma: inglés
• DOI: 10.1016/j.jsc.2004.04.011
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• Resumen

  • Let be the ring of polynomials with complex coefficients and An the Weyl algebra of order n over . Elements in An are linear differential operators with polynomial coefficients. For each polynomial f, the ring of rational functions with poles along f has a natural structure of a left An-module which is finitely generated by a classical result of I.N. Bernstein. A central problem in this context is how to find a finite presentation of M starting from the input f. In this paper we use Gröbner base theory in the non-commutative frame of the ring An to compare M to some other An-modules arising in Singularity Theory as the so-called logarithmic An-modules. We also show how the analytic case can be treated with computations in the Weyl algebra if the input data f is a polynomial.