| Linear Differential Operators for Polynomial Equations (2008) | |||||||||||||||
Abstract | |||||||||||||||
| Given a squarefree polynomial P k 0 [x, y], k 0 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 k 0 , and calculate information concerning the Galois group of P over k 0 (x) as well as over k 0 (x). | |||||||||||||||
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