Linear differential operators for polynomial equations

Authors:
Olivier Cormier;Michael F. Singer;Barry M. Trager;Felix Ulmer
Affiliations:
IRMAR, Université de Rennes 1. F-35042 Rennes Cedex, France;Department of Mathematics, Box 8205, NC State University, Raleigh, NC;IBM TJ Watson Research Ctr., PO Box 218, Yorktown Heights, NY;IRMAR, Université de Rennes 1. F-35042 Rennes Cedex, France
Venue:
Journal of Symbolic Computation
Year:
2002

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Abstract

Given a squarefree polynomial P ∈ k0[x, y], k0 a number field, we construct a linear differential operator that allows one to calculate the genus of the complex curve defined by P = 0 (when P is absolutely irreducible), the absolute factorization of P over the algebraic closure of k0, and calculate information concerning the Galois group of P over k0(x) as well as over k0(x).