Extension of Algorithms for D-finite functions [DK15]

Project Lead

Project Duration

01/10/2014 - 30/06/2022

Project URL

Go to Website

Publications

2020

[AUTHOR]

The Sage Package Comb_walks for Walks in the Quarter Plane

Antonio Jiménez-Pastor, Alin Bostan, Frédéric Chyzak, Pierre Lairez

ACM Commun. Comput. Algebra 54(2), pp. 30-38. sep 2020. Association for Computing Machinery, New York, NY, USA, 1932-2240. [url]
[bib]
@article{RISC6282,
author = {Antonio Jiménez-Pastor and Alin Bostan and Frédéric Chyzak and Pierre Lairez},
title = {{The Sage Package Comb_walks for Walks in the Quarter Plane}},
language = {english},
abstract = {We present in this extended abstract a new software designed to work with generating functions that count walks in the quarter plane. With this software we offer a cohesive package that brings together all the required procedures for manipulating these generating functions, as well as a unified interface to deal with them. We also display results that this package offers on a public webpage.},
journal = {ACM Commun. Comput. Algebra},
volume = {54},
number = {2},
pages = {30--38},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
isbn_issn = {1932-2240},
year = {2020},
month = {sep},
refereed = {yes},
keywords = {Sage, D-algebraic functions, generating functions, elliptic functions, lattice walks},
length = {9},
url = {https://doi.org/10.1145/3427218.3427220}
}
[Jimenez Pastor]

Some structural results on D^n finite functions

A. Jimenez-Pastor, V. Pillwein, M.F. Singer

Advances in Applied Mathematics 117, pp. 0-0. June 2020. Elsevier, 0196-8858. [url] [pdf]
[bib]
@article{RISC6077,
author = {A. Jimenez-Pastor and V. Pillwein and M.F. Singer},
title = {{Some structural results on D^n finite functions}},
language = {english},
abstract = {D-finite (or holonomic) functions satisfy linear differential equations with polynomial coefficients. They form a large class of functions that appear in many applications in Mathematics or Physics. It is well-known that these functions are closed under certain operations and these closure properties can be executed algorithmically. Recently, the notion of D-finite functions has been generalized to differentially definable or Dn-finite functions. Also these functions are closed under operations such as forming (anti)derivative, addition or multiplication and, again, these can be implemented. In this paper we investigate how Dn-finite functions behave under composition and how they are related to algebraic and differentially algebraic functions.},
journal = {Advances in Applied Mathematics},
volume = {117},
pages = {0--0},
publisher = {Elsevier},
isbn_issn = {0196-8858},
year = {2020},
month = {June},
refereed = {yes},
length = {0},
url = {https://doi.org/10.1016/j.aam.2020.102027}
}
[Jimenez Pastor]

On the exponential generating function of labelled trees

Alin Bostan, Antonio Jiménez-Pastor

Comptes Rendus. Mathématique 358(9-10), pp. 1005-1009. 2020. Académie des sciences, Paris, 1631-0721. [url]
[bib]
@article{RISC6281,
author = {Alin Bostan and Antonio Jiménez-Pastor},
title = {{On the exponential generating function of labelled trees}},
language = {english},
journal = {Comptes Rendus. Mathématique},
volume = {358},
number = {9-10},
pages = {1005--1009},
publisher = {Académie des sciences, Paris},
isbn_issn = {1631-0721},
year = {2020},
refereed = {yes},
length = {5},
url = {https://doi.org/10.5802/crmath.108}
}
[Jimenez Pastor]

The Sage Package Comb_walks for Walks in the Quarter Plane

Antonio Jiménez-Pastor, Alin Bostan, Frédéric Chyzak, Pierre Lairez

ACM Commun. Comput. Algebra 54(2), pp. 30-38. sep 2020. Association for Computing Machinery, New York, NY, USA, 1932-2240. [url]
[bib]
@article{RISC6283,
author = {Antonio Jiménez-Pastor and Alin Bostan and Frédéric Chyzak and Pierre Lairez},
title = {{The Sage Package Comb_walks for Walks in the Quarter Plane}},
language = {english},
abstract = {We present in this extended abstract a new software designed to work with generating functions that count walks in the quarter plane. With this software we offer a cohesive package that brings together all the required procedures for manipulating these generating functions, as well as a unified interface to deal with them. We also display results that this package offers on a public webpage.},
journal = {ACM Commun. Comput. Algebra},
volume = {54},
number = {2},
pages = {30--38},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
isbn_issn = {1932-2240},
year = {2020},
month = {sep},
refereed = {yes},
keywords = {Sage, D-algebraic functions, generating functions, elliptic functions, lattice walks},
length = {9},
url = {https://doi.org/10.1145/3427218.3427220}
}
[Pillwein]

A sequence of polynomials generated by a Kapteyn series of the second kind

D. Dominici, V. Pillwein

In: Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra, in Honour of Peter Paule on his 60th Birthday, V. Pillwein and C. Schneider (ed.), Texts and Monographs in Symbolic Computuation, in press , pp. ?-?. 2020. Springer, arXiv:1607.05314 [math.CO]. [url] [pdf]
[bib]
@incollection{RISC6078,
author = {D. Dominici and V. Pillwein},
title = {{A sequence of polynomials generated by a Kapteyn series of the second kind}},
booktitle = {{Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra, in Honour of Peter Paule on his 60th Birthday}},
language = {english},
series = {Texts and Monographs in Symbolic Computuation, in press},
pages = {?--?},
publisher = {Springer},
isbn_issn = {?},
year = {2020},
note = {arXiv:1607.05314 [math.CO]},
editor = {V. Pillwein and C. Schneider},
refereed = {yes},
length = {0},
url = {https://www.dk-compmath.jku.at/publications/dk-reports/2019-05-28/view}
}

2019

[Jimenez Pastor]

A Computable Extension for Holonomic Functions: DD-Finite Functions

Jiménez-Pastor Antonio, Pillwein Veronika

Journal of Symbolic Computation 94, pp. 90-104. September-October 2019. ISSN 0747-7171. [url]
[bib]
@article{RISC5831,
author = {Jiménez-Pastor Antonio and Pillwein Veronika},
title = {{A Computable Extension for Holonomic Functions: DD-Finite Functions}},
language = {english},
abstract = {Differentiably finite (D-finite) formal power series form a large class of useful functions for which a variety of symbolic algorithms exists. Among these methods are several closure properties that can be carried out automatically. We introduce a natural extension of these functions to a larger class of computable objects for which we prove closure properties. These are again algorithmic. This extension can be iterated constructively preserving the closure properties},
journal = {Journal of Symbolic Computation},
volume = {94},
pages = {90--104},
isbn_issn = {ISSN 0747-7171},
year = {2019},
month = {September-October},
refereed = {yes},
length = {15},
url = {https://doi.org/10.1016/j.jsc.2018.07.002}
}

2018

[Jimenez Pastor]

Algorithmic Arithmetics with DD-Finite Functions

Jiménez-Pastor Antonio, Pillwein Veronika

In: Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation, Arreche Carlos (ed.), ISSAC '18 , pp. 231-237. 2018. ACM, New York, NY, USA, ISBN 978-1-4503-5550-6. [url]
[bib]
@inproceedings{RISC5730,
author = {Jiménez-Pastor Antonio and Pillwein Veronika},
title = {{Algorithmic Arithmetics with DD-Finite Functions}},
booktitle = {{Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation}},
language = {english},
series = {ISSAC '18},
pages = {231--237},
publisher = {ACM},
address = {New York, NY, USA},
isbn_issn = {ISBN 978-1-4503-5550-6},
year = {2018},
editor = {Arreche Carlos},
refereed = {yes},
keywords = {algorithms, closure properties, holonomic functions},
length = {7},
url = {http://doi.acm.org/10.1145/3208976.3209009}
}
[Pillwein]

Positivity of the Gillis-Reznick-Zeilberger rational function

V. Pillwein

Technical report no. 18-05 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 2018. [pdf]
[bib]
@techreport{RISC5612,
author = {V. Pillwein},
title = {{Positivity of the Gillis-Reznick-Zeilberger rational function}},
language = {english},
number = {18-05},
year = {2018},
length = {12},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}
[Pillwein]

Difference equation satisfied by the Stieltjes transform of a sequence

D. Dominici, V. Pillwein

Doctoral Program "Computational Mathematics". Technical report no. DK Report 2018-11, 2018. [url] [pdf]
[bib]
@techreport{RISC5827,
author = {D. Dominici and V. Pillwein},
title = {{Difference equation satisfied by the Stieltjes transform of a sequence}},
language = {english},
number = {DK Report 2018-11},
year = {2018},
institution = {Doctoral Program "Computational Mathematics"},
length = {13},
url = {https://www.dk-compmath.jku.at/publications/dk-reports/2018-12-12/}
}

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