Extension of Algorithms for D-finite functions [DK15]

Project Lead

Project Duration

01/10/2014 - 30/06/2022

Project URL

Go to Website

Publications

2021

[Jimenez Pastor]

On C2-Finite Sequences

Antonio Jiménez-Pastor, Philipp Nuspl, Veronika Pillwein

In: Proceedings of the 2021 on International Symposium on Symbolic and Algebraic Computation, Frédéric Chyzak, George Labahn (ed.), ISSAC '21 , pp. 217-224. 2021. Association for Computing Machinery, New York, NY, USA, ISBN 9781450383820. [doi]
[bib]
@inproceedings{RISC6348,
author = {Antonio Jiménez-Pastor and Philipp Nuspl and Veronika Pillwein},
title = {{On C2-Finite Sequences}},
booktitle = {{Proceedings of the 2021 on International Symposium on Symbolic and Algebraic Computation}},
language = {english},
abstract = {Holonomic sequences are widely studied as many objects interesting to mathematiciansand computer scientists are in this class. In the univariate case, these are the sequencessatisfying linear recurrences with polynomial coefficients and also referred to asD-finite sequences. A subclass are C-finite sequences satisfying a linear recurrencewith constant coefficients.We investigate the set of sequences which satisfy linearrecurrence equations with coefficients that are C-finite sequences. These sequencesare a natural generalization of holonomic sequences. In this paper, we show that C2-finitesequences form a difference ring and provide methods to compute in this ring.},
series = {ISSAC '21},
pages = {217--224},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
isbn_issn = {ISBN 9781450383820},
year = {2021},
editor = {Frédéric Chyzak and George Labahn},
refereed = {yes},
keywords = {holonomic sequences, algorithms, closure properties, difference equations},
length = {8},
url = {https://doi.org/10.1145/3452143.3465529}
}

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. [doi]
[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. [doi] [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. [doi]
[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. [doi]
[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. [doi]
[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. [doi]
[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, Austria. ISSN 2791-4267 (online). 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 = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}
[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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