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Applicable Algebra in Engineering, Communication and Computing
Published in: Applicable Algebra in Engineering, Communication and Computing 1/2019

03-05-2018 | Original Paper

Computing with D-algebraic power series

Author: Joris van der Hoeven

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 1/2019

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Abstract

In this paper, we will present several algorithms for computing with D-algebraic power series. Such power series are specified by one or more algebraic differential equations and a sufficient number of initial conditions. The emphasis is not on the efficient computation of coefficients of such power series (various techniques are known for that), but rather on the ability to decide whether expressions involving D-algebraic power series are zero. We will both consider univariate and multivariate series and, besides the usual ring operations and differentiation, we will also consider composition, implicitly determined power series and monomial transformations.
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Metadata
Title
Computing with D-algebraic power series
Author
Joris van der Hoeven
Publication date
03-05-2018
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 1/2019
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-018-0358-y

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