[图书][B] D-finite Functions
M Kauers - 2023 - Springer
A univariate function is called D-finite if it satisfies a linear differential equation with
polynomial coefficients. The concept of D-finiteness applies more generally to sequences …
polynomial coefficients. The concept of D-finiteness applies more generally to sequences …
[图书][B] Symbolic analysis for boundary problems: From rewriting to parametrized Gröbner bases
M Rosenkranz, G Regensburger, L Tec, B Buchberger - 2012 - Springer
We review our algebraic framework for linear boundary problems (concentrating on ordinary
differential equations). Its starting point is an appropriate algebraization of the domain of …
differential equations). Its starting point is an appropriate algebraization of the domain of …
Some open problems related to creative telescoping
Creative telescoping is the method of choice for obtaining information about definite sums or
integrals. It has been intensively studied since the early 1990s, and can now be considered …
integrals. It has been intensively studied since the early 1990s, and can now be considered …
The algebra of integro-differential operators on a polynomial algebra
VV Bavula - Journal of the London Mathematical Society, 2011 - academic.oup.com
We prove that the algebra of integro-differential operators on a polynomial algebra is a
prime, central, catenary, self-dual, non-Noetherian algebra of classical Krull dimension n …
prime, central, catenary, self-dual, non-Noetherian algebra of classical Krull dimension n …
A computational view on normal forms of matrices of Ore polynomials
J Middeke - ACM Communications in Computer Algebra, 2012 - dl.acm.org
This thesis treats normal forms of matrices over rings of Ore polynomials. The whole thesis is
divided in three parts: First, Ore polynomials are described and basic facts about them are …
divided in three parts: First, Ore polynomials are described and basic facts about them are …
On polynomial solutions of linear integro-differential equations
M Barkatou, T Cluzeau - IFAC-PapersOnLine, 2022 - Elsevier
We develop an efficient algorithm for computing polynomial solutions of linear integro-
differential equations. Considering a linear integro-differential operator written in normal …
differential equations. Considering a linear integro-differential operator written in normal …
The fundamental theorem of calculus in differential rings
CG Raab, G Regensburger - Advances in Mathematics, 2024 - Elsevier
In this paper, we study the consequences of the fundamental theorem of calculus from an
algebraic point of view. For functions with singularities, this leads to a generalized notion of …
algebraic point of view. For functions with singularities, this leads to a generalized notion of …
[HTML][HTML] Algorithmic operator algebras via normal forms in tensor rings
JH Poor, CG Raab, G Regensburger - Journal of Symbolic Computation, 2018 - Elsevier
We propose a general algorithmic approach to noncommutative operator algebras
generated by additive operators using quotients of tensor rings that are defined by tensor …
generated by additive operators using quotients of tensor rings that are defined by tensor …
A constructive algebraic analysis approach to Artstein's reduction of linear time-delay systems
A Quadrat - IFAC-PapersOnLine, 2015 - Elsevier
Artstein's results show that a first-order linear differential system with delayed inputs is
equivalent to a first-order linear differential system without delay under an invertible …
equivalent to a first-order linear differential system without delay under an invertible …
A Maple package for integro-differential operators and boundary problems
A Korporal, G Regensburger… - ACM Communications in …, 2011 - dl.acm.org
Introduction. We present a Maple package for computing in algebras of integro-differential
operators. This provides the appropriate algebraic setting for treating boundary problems [7] …
operators. This provides the appropriate algebraic setting for treating boundary problems [7] …