Abstract
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.
Citation
Fuensanta Aroca. Giovanna Ilardi. "Newton’s lemma for differential equations." Illinois J. Math. 60 (3-4) 859 - 867, Fall and Winter 2016. https://doi.org/10.1215/ijm/1506067296
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