Linear Differential Operators for Polynomial Equations |
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| Affiliation: | 1. IRMAR, Université de Rennes 1, F-35042 Rennes Cedex, France;2. Department of Mathematics, Box 8205, NC State University, Raleigh, NC 27695-8205, U.S.A.;3. IBM TJ Watson Research Ctr. PO Box 218, Yorktown Heights, NY 10598, U.S.A. |
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| Abstract: | Given a squarefree polynomial P ∈ k0 x,y ], k0a 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 overk0 (x). |
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