Additive Normal Forms and Integration of Differential Fractions
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 non integrable 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.
Domains
Symbolic Computation [cs.SC]
Origin : Files produced by the author(s)
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