Additive Normal Forms and Integration of Differential Fractions

Francois, Boulier, Francois, Lemaire, Joseph, Lallemand, Georg, Regensburger, Markus, Rosenkranz (2016) Additive Normal Forms and Integration of Differential Fractions. Journal of Symbolic Computation, . ISSN 0747-7171. E-ISSN 1095-855X. (doi:10.1016/j.jsc.2016.01.002) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Official URL
http://dx.doi.org/10.1016/j.jsc.2016.01.002

Abstract

This paper presents two new normal forms for fractions of differential polynomials, as well as algorithms for computing them. The first normal form allows to write a fraction as the derivative of a fraction plus a nonintegrable part. The second normal form is an extension of the first one, involving iterated differentiations. The main difficulty in this paper consists in defining normal forms which are linear operations over the field of constants, a property which was missing in our previous works. Our normal forms do not require fractions to be converted into polynomials, a key feature for further problems such as integrating differential fractions, and more generally solving differential equations.

Item Type: Article
DOI/Identification number: 10.1016/j.jsc.2016.01.002
Uncontrolled keywords: Differential algebra; Differential fraction; Integration
Subjects: Q Science > QA Mathematics (inc Computing science) > QA150 Algebra
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Markus Rosenkranz
Date Deposited: 07 Mar 2016 17:43 UTC
Last Modified: 29 May 2019 17:04 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/54451 (The current URI for this page, for reference purposes)
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