## View abstract

### 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. document.getElementById('cloakc98d96bc7c7894f380d3968c12290251').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyc98d96bc7c7894f380d3968c12290251 = 'f&#117;&#101;n' + '&#64;'; addyc98d96bc7c7894f380d3968c12290251 = addyc98d96bc7c7894f380d3968c12290251 + '&#105;m' + '&#46;' + '&#117;n&#97;m' + '&#46;' + 'mx'; var addy_textc98d96bc7c7894f380d3968c12290251 = 'f&#117;&#101;n' + '&#64;' + '&#105;m' + '&#46;' + '&#117;n&#97;m' + '&#46;' + 'mx';document.getElementById('cloakc98d96bc7c7894f380d3968c12290251').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyc98d96bc7c7894f380d3968c12290251 + '\'>'+addy_textc98d96bc7c7894f380d3968c12290251+'<\/a>';

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).