Illinois Journal of Mathematics

Newton’s lemma for differential equations

Fuensanta Aroca and Giovanna Ilardi

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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.

Article information

Source
Illinois J. Math., Volume 60, Number 3-4 (2016), 859-867.

Dates
Received: 10 January 2017
Revised: 18 April 2017
First available in Project Euclid: 22 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1506067296

Digital Object Identifier
doi:10.1215/ijm/1506067296

Mathematical Reviews number (MathSciNet)
MR3705449

Zentralblatt MATH identifier
06790332

Subjects
Primary: 14J17: Singularities [See also 14B05, 14E15] 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx] 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx] 14Q15: Higher-dimensional varieties 13P99: None of the above, but in this section

Citation

Aroca, Fuensanta; Ilardi, Giovanna. Newton’s lemma for differential equations. Illinois J. Math. 60 (2016), no. 3-4, 859--867. doi:10.1215/ijm/1506067296. https://projecteuclid.org/euclid.ijm/1506067296


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