Gröbner bases and logarithmic D-modules
|Author/s||Castro Jiménez, Francisco Jesús
Ucha Enríquez, José María
|Department||Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Universidad de Sevilla. Departamento de álgebra
|Abstract||Let C[x] = C[x1, . . . , xn] be the ring of polynomials with complex coefficients and An the Weyl
algebra of order n over C. Elements in An are linear differential operators with polynomial coefficients.
For each polynomial ...
Let C[x] = C[x1, . . . , xn] be the ring of polynomials with complex coefficients and An the Weyl algebra of order n over C. Elements in An are linear differential operators with polynomial coefficients. For each polynomial f , the ring M = C[x] f 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 Gr¨obner 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.
|Citation||Castro Jiménez, F.J. y Ucha Enríquez, J.M. (2006). Gröbner bases and logarithmic D-modules. Journal of Symbolic Computation, 41 (3-4), 317-335.|
|Gröbner bases and logarithmic ...||445.0Kb||[PDF]||View/|