A computable extension for D-finite functions: DD-finite functions

Jiménez-Pastor, Antonio; Pillwein, Veronika

doi:10.1016/j.jsc.2018.07.002

Cited by 13 publications

(13 citation statements)

References 5 publications

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“…We also extend this theory to the general case of differentially definable functions [10]. In particular, we extend the result for Dfinite functions.…”

Section: Introductionmentioning

confidence: 65%

“…When we consider = \ {0} this definition yields the usual differentially definable elements over . It is known that differentially definable elements can be characterized with finite dimensional vector spaces [12]. A similar characterization can be proven for the -simple differentially definable elements by using finitely generated -modules instead.…”

Section: Definition 23 ([2 Chapter 3])mentioning

confidence: 92%

“…In [10], the concept of differentially definable elements was given. Namely, if ( , ) is a differential integral domain and a differential extension, we say that ∈ is differentially definable over if there is A ∈ [ ] \ {0} such that A • = 0.…”

Section: Definition 23 ([2 Chapter 3])mentioning

confidence: 99%

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Simple Differentially Definable Functions

Jiménez-Pastor

2021

Proceedings of the 2021 International Symposium on Symbolic and Algebraic Computation

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D-finite functions satisfy linear differential equations with polynomial coefficients. The solutions to this type of equations may have singularities determined by the zeros of their leading coefficient. There are algorithms to desingularize the equations, i.e., remove singularities from the equation that do not appear in its solutions. However, classical computations of closure properties (such as addition, multiplication, etc.) with D-finite functions return equations with extra zeros in the leading coefficient. In this paper we present theory and algorithms based on linear algebra to control the leading coefficients when computing these closure properties and we also extend this theory to the more general class of differentially definable functions. CCS CONCEPTS• Mathematics of computing → Mathematical software; Generating functions; Ordinary differential equations.

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“…We also extend this theory to the general case of differentially definable functions [10]. In particular, we extend the result for Dfinite functions.…”

Section: Introductionmentioning

confidence: 65%

Section: Definition 23 ([2 Chapter 3])mentioning

confidence: 92%

See 1 more Smart Citation

Simple Differentially Definable Functions

Jiménez-Pastor

2021

Proceedings of the 2021 International Symposium on Symbolic and Algebraic Computation

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“…Many generating functions in combinatorics and many special functions in mathematical physics are D-finite [2,9]. DD-finite series and more generally D n -finite series are larger classes of power series, recently introduced in [13]. DD-finite power series satisfy linear differential equations, whose coefficients are themselves D-finite power series.…”

Section: Context and Main Resultsmentioning

confidence: 99%

On the exponential generating function of labelled trees

Bostan¹,

Jiménez-Pastor²

2021

Comptes Rendus. Mathématique

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“…This could shed more light on whether these D-algebraic functions of combinatorial origin belong to more structured subclasses: are they quotients of D-finite functions? are they more complicated DD-finite functions [11]? We also intend to complete and enhance the tests and the documentation of the package.…”

Section: T 'X' and 'Y'mentioning

confidence: 99%