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Session S24 - Symbolic Computation: Theory, Algorithms and Applications

Tuesday, July 13, 12:00 ~ 12:25 UTC-3

Newton's Lemma for differential equations

Fuensanta Aroca

Universidad Nacional Autónoma de México, México   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The Newton method for plane algebraic curves is based on the following remark: the first term of a series, root of a polynomial with coefficients in the ring of series in one variable, is a solution of an initial equation that can be determined by the Newton polygon. Given a monomial ordering in the ring of polynomials in several variables, we describe the systems of initial equations that satisfy the first terms of the solutions of a system of partial differential equations. As a consequence, we extend Mora and Robbiano’s Groebner fan to differential ideals.

Joint work with Giovanna Ilardi (Universidad de Nápoles).

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