SFB Coordination and Service Project [SFB F1301-3]

Project Lead

Project Duration

01/04/2004 - 30/09/2008

Project URL

Project Website

Publications

2017

Rogers-Ramanujan Functions, Modular Functions, and Computer Algebra

Peter Paule, Cristian-Silviu Radu

In: Advances in Computer Algebra - In Honour of Sergei Abramov's 70th Birthday, C. Schneider and E. Zima. (ed.), pp. 1-41. 2017. Springer, 1019-7168 . [pdf]
[bib]
@incollection{RISC5475,
author = {Peter Paule and Cristian-Silviu Radu},
title = {{Rogers-Ramanujan Functions, Modular Functions, and Computer Algebra}},
booktitle = {{Advances in Computer Algebra - In Honour of Sergei Abramov's 70th Birthday}},
language = {english},
pages = {1--41},
publisher = {Springer},
isbn_issn = {1019-7168 },
year = {2017},
editor = {C. Schneider and E. Zima.},
refereed = {yes},
length = {41}
}

2016

Workshop on Symbolic Combinatorics and Algorithmic Differential Algebra

Manuel Kauers, Peter Paule, Greg Reid

ACM Communications in Computer Algebra 50(Issue 1), pp. 27-34. March 2016. 1932-2240. [pdf]
[bib]
@article{RISC5284,
author = {Manuel Kauers and Peter Paule and Greg Reid},
title = {{Workshop on Symbolic Combinatorics and Algorithmic Differential Algebra}},
language = {english},
journal = {ACM Communications in Computer Algebra},
volume = {50},
number = {Issue 1},
pages = {27--34},
isbn_issn = {1932-2240},
year = {2016},
month = {March},
refereed = {no},
length = {8}
}

A New Witness Identity for $11|p(11n+6)$

Peter Paule, Cristian-Silviu Radu

In: status submitted, , pp. -. 2016. [pdf]
[bib]
@inproceedings{RISC5329,
author = {Peter Paule and Cristian-Silviu Radu},
title = {{A New Witness Identity for $11|p(11n+6)$}},
booktitle = {{status submitted}},
language = {english},
pages = {--},
isbn_issn = { },
year = {2016},
editor = { },
refereed = {yes},
length = {11}
}

2014

Relativistic Coulomb Integrals and Zeilberger's Holonomic Systems Approach II

Christoph Koutschan, Peter Paule, Sergei K. Suslov

In: Algebraic and Algorithmic Aspects of Differential and Integral Operators, Moulay Barkatou and Thomas Cluzeau and Georg Regensburger and Markus Rosenkranz (ed.), Lecture Notes in Computer Science 8372, pp. 135-145. 2014. Springer, Berlin Heidelberg, ISBN 978-3-642-54478-1. [pdf]
[bib]
@incollection{RISC4847,
author = {Christoph Koutschan and Peter Paule and Sergei K. Suslov},
title = {{Relativistic Coulomb Integrals and Zeilberger's Holonomic Systems Approach II}},
booktitle = {{Algebraic and Algorithmic Aspects of Differential and Integral Operators}},
language = {english},
abstract = {We derive the recurrence relations for relativistic Coulomb integrals directly from the integral representations with the help of computer algebra methods. In order to manage the computational complexity of this problem, we employ holonomic closure properties in a sophisticated way.},
series = {Lecture Notes in Computer Science},
volume = {8372},
pages = {135--145},
publisher = {Springer},
address = {Berlin Heidelberg},
isbn_issn = {ISBN 978-3-642-54478-1},
year = {2014},
editor = {Moulay Barkatou and Thomas Cluzeau and Georg Regensburger and Markus Rosenkranz},
refereed = {yes},
length = {11}
}

2013

Relativistic Coulomb Integrals and Zeilbergers Holonomic Systems Approach. I.

Peter Paule, Sergei K. Suslov

In: Computer Algebra in Quantum Field Theory, Texts and Monographs in Symbolic Computation, Springer, 2013, Carsten Schneider, Johannes Blümlein (ed.), pp. 225-241. 2013. Springer, 978-3-7091-1615-9.
[bib]
@incollection{RISC4718,
author = {Peter Paule and Sergei K. Suslov},
title = {{Relativistic Coulomb Integrals and Zeilbergers Holonomic Systems Approach. I.}},
booktitle = {{Computer Algebra in Quantum Field Theory, Texts and Monographs in Symbolic Computation, Springer, 2013}},
language = {english},
pages = {225--241},
publisher = {Springer},
isbn_issn = {978-3-7091-1615-9},
year = {2013},
editor = {Carsten Schneider and Johannes Blümlein},
refereed = {no},
length = {17}
}

Mathematics, Computer Science and Logic - A Never Ending Story The Bruno Buchberger Festschrift

Peter Paule

1st edition, 2013. Springer, 978-3-319-00965-0.
[bib]
@booklet{RISC4850,
author = {Peter Paule},
title = {{Mathematics, Computer Science and Logic - A Never Ending Story The Bruno Buchberger Festschrift}},
language = {english},
publisher = {Springer},
isbn_issn = {978-3-319-00965-0},
year = {2013},
edition = {1st},
translation = {0},
length = {113}
}

Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order

S. Gerhold, M. Kauers, C. Koutschan, P. Paule, C. Schneider, B. Zimmermann

In: Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions, C. Schneider, J. Bluemlein (ed.), Texts and Monographs in Symbolic Computation , pp. 75-96. 2013. Springer, ISBN-13: 978-3709116159. arXiv:1305.4818 [cs.SC]. [url]
[bib]
@incollection{RISC4721,
author = {S. Gerhold and M. Kauers and C. Koutschan and P. Paule and C. Schneider and B. Zimmermann},
title = {{Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order}},
booktitle = {{Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions}},
language = {english},
series = {Texts and Monographs in Symbolic Computation},
pages = {75--96},
publisher = {Springer},
isbn_issn = {ISBN-13: 978-3709116159},
year = {2013},
note = {arXiv:1305.4818 [cs.SC]},
editor = {C. Schneider and J. Bluemlein},
refereed = {no},
length = {22},
url = {http://arxiv.org/abs/1305.4818}
}

2012

MacMahon's Dream

George E. Andrews and Peter Paule

In: Partitions, q-Series, and Modular Forms, K. Alladi and F. Garvan (ed.), Developments in Mathematics 23, pp. 1-12. 2012. Springer, 978-1-4614-0028-8.
[bib]
@incollection{RISC5157,
author = {George E. Andrews and Peter Paule},
title = {{MacMahon's Dream}},
booktitle = {{Partitions, q-Series, and Modular Forms}},
language = {english},
series = {Developments in Mathematics},
volume = {23},
pages = {1--12},
publisher = {Springer},
isbn_issn = {978-1-4614-0028-8},
year = {2012},
editor = {K. Alladi and F. Garvan},
refereed = {yes},
length = {12}
}

A Symbolic Summation Approach to Feynman Integral Calculus

J. Bluemlein, S. Klein, C. Schneider, F. Stan

J. Symbolic Comput. 47, pp. 1267-1289. 2012. ISSN 0747-7171. [pdf]
[bib]
@article{RISC4400,
author = {J. Bluemlein and S. Klein and C. Schneider and F. Stan},
title = {{A Symbolic Summation Approach to Feynman Integral Calculus}},
language = {english},
journal = {J. Symbolic Comput.},
volume = {47},
pages = { 1267--1289},
isbn_issn = {ISSN 0747-7171},
year = {2012},
refereed = {yes},
length = {23}
}

2011

The Concrete Tetrahedron

Manuel Kauers, Peter Paule

Text and Monographs in Symbolic Computation 1st edition, 2011. Springer Wien, 978-3-7091-0444-6.
[bib]
@book{RISC4162,
author = {Manuel Kauers and Peter Paule},
title = {{The Concrete Tetrahedron}},
language = {english},
series = {Text and Monographs in Symbolic Computation},
publisher = {Springer Wien},
isbn_issn = {978-3-7091-0444-6},
year = {2011},
edition = {1st},
translation = {0},
length = {210}
}

Dominance in the Family of Sugeno-Weber t-norms

Manuel Kauers, Veronika Pillwein, Susanne Saminger-Platz

Fuzzy Sets and Systems 181(1), pp. 74-87. October 2011. ISSN 0165-0114. [ps] [pdf]
[bib]
@article{RISC4328,
author = {Manuel Kauers and Veronika Pillwein and Susanne Saminger-Platz},
title = {{Dominance in the Family of Sugeno-Weber t-norms}},
language = {english},
abstract = {The dominance relationship between two members of the family of Sugeno Weber t-norms is proven by using a quantifer elimination algorithm. Further it is shown that dominance is a transitive, and therefore also an order relation, on this family of t-norms.},
journal = {Fuzzy Sets and Systems},
volume = {181},
number = {1},
pages = {74--87},
isbn_issn = {ISSN 0165-0114},
year = {2011},
month = {October},
refereed = {yes},
length = {14}
}

Automatic Improvements of Wallis' Inequality

P. Paule, V. Pillwein

In: SYNASC 2010, 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, T. Ida and others (ed.), pp. 12-16. 2011. IEEE Computer Society, 0. [pdf]
[bib]
@inproceedings{RISC4297,
author = {P. Paule and V. Pillwein},
title = {{Automatic Improvements of Wallis' Inequality}},
booktitle = {{SYNASC 2010, 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing}},
language = {english},
pages = {12--16},
publisher = {IEEE Computer Society},
isbn_issn = {0},
year = {2011},
editor = {T.~Ida and others},
refereed = {no},
length = {5}
}

Sparsity optimized high order finite element functions on simplices

S. Beuchler, V. Pillwein, J. Schoeberl and S. Zaglmayr

In: Numerical and Symbolic Scientific Computing: Progress and Prospects, Ulrich Langer and Peter Paule (ed.), pp. 21-44. 2011. Springer, Wien, [pdf]
[bib]
@incollection{RISC4253,
author = {S. Beuchler and V. Pillwein and J. Schoeberl and S. Zaglmayr },
title = {{Sparsity optimized high order finite element functions on simplices}},
booktitle = {{Numerical and Symbolic Scientific Computing: Progress and Prospects}},
language = {english},
pages = {21--44},
publisher = {Springer},
address = {Wien},
isbn_issn = {?},
year = {2011},
editor = {Ulrich Langer and Peter Paule},
refereed = {yes},
length = {24}
}

2010

When can we detect that a P-finite sequence is positive?

Manuel Kauers, Veronika Pillwein

In: Proceedings of ISSAC'10, Stephen Watt (ed.), pp. 195-202. 2010. 978-1-4503-0150-3. [pdf] [ps]
[bib]
@inproceedings{RISC4022,
author = {Manuel Kauers and Veronika Pillwein},
title = {{When can we detect that a P-finite sequence is positive?}},
booktitle = {{Proceedings of ISSAC'10}},
language = {english},
abstract = {We consider two algorithms which can be used for proving positivity ofsequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed on a greatmany examples, there is no guarantee for them to terminate, and theydo in fact not terminate for every input.For some restricted classes of P-finite recurrence equations of order up to three we provide a priori criteria that assert the termination of the algorithms.},
pages = {195--202},
isbn_issn = {978-1-4503-0150-3},
year = {2010},
editor = {Stephen Watt},
refereed = {yes},
length = {7}
}

Infinite Families of Strange Partition Congruences for Broken 2-Diamonds

Peter Paule, Silviu Radu

The Ramanujan Journal 23, pp. 409-416. 2010. ISSN 1382-4090. [pdf]
[bib]
@article{RISC4294,
author = {Peter Paule and Silviu Radu},
title = {{Infinite Families of Strange Partition Congruences for Broken 2-Diamonds }},
language = {english},
journal = {The Ramanujan Journal},
volume = {23},
pages = {409--416},
isbn_issn = {ISSN 1382-4090},
year = {2010},
refereed = {yes},
length = {8}
}

Henrici's Friendly Monster Identity Revisited

Peter Paule

In: "Advances in Combinatorial Mathematics", Proceedings of the Waterloo Workshop in Computer Algebra 2008, Kotsireas, Ilias S.; Zima, Eugene V. (ed.), pp. 155-163. 2010. Springer, 978-3-642-03561-6.
[bib]
@inproceedings{RISC4864,
author = {Peter Paule},
title = {{Henrici's Friendly Monster Identity Revisited}},
booktitle = {{"Advances in Combinatorial Mathematics", Proceedings of the Waterloo Workshop in Computer Algebra 2008}},
language = {english},
pages = {155--163},
publisher = {Springer},
isbn_issn = {978-3-642-03561-6},
year = {2010},
editor = {Kotsireas and Ilias S.; Zima and Eugene V.},
refereed = {yes},
length = {9}
}

Chapter Computer Algebra

F. Chyzak and P. Paule

In: NIST's Digital Library of Mathematical Foundations, F. Olver et al. (ed.), pp. 0-0. 2010. 0.
[bib]
@incollection{RISC5622,
author = {F. Chyzak and P. Paule},
title = {{Chapter Computer Algebra}},
booktitle = {{NIST's Digital Library of Mathematical Foundations}},
language = {english},
pages = {0--0},
publisher = {?},
isbn_issn = {0},
year = {2010},
editor = {F. Olver et al.},
refereed = {no},
length = {40}
}

On Recurrences for Ising Integrals

Flavia Stan

Adv. in Appl. Math. 45(3), pp. 334-345. 2010. Elsevier, ISSN 0196-8858. [pdf]
[bib]
@article{RISC4016,
author = {Flavia Stan},
title = {{On Recurrences for Ising Integrals}},
language = {english},
journal = {Adv. in Appl. Math.},
volume = {45},
number = {3},
pages = {334--345},
publisher = {Elsevier},
isbn_issn = {ISSN 0196-8858},
year = {2010},
refereed = {yes},
length = {12}
}

Algorithms for Special Functions: Computer Algebra and Analytical Aspects

Flavia Stan

RISC, Johannes Kepler University Linz. PhD Thesis. June 2010. RISC technical report 10-19. [pdf]
[bib]
@phdthesis{RISC4045,
author = {Flavia Stan},
title = {{Algorithms for Special Functions: Computer Algebra and Analytical Aspects}},
language = {english},
year = {2010},
month = {June},
note = {RISC technical report 10-19},
translation = {0},
school = {RISC, Johannes Kepler University Linz},
keywords = {symbolic summation, special functions, recurrences, integral transforms, Mellin-Barnes integrals, Feynman integrals},
length = {106}
}

An Algorithmic Approach to the Mellin Transform Method

Karen T. Kohl and Flavia Stan

In: Gems in Experimental Mathematics, T. Amdeberhan, L. A. Medina, V. H. Moll (ed.), Contemporary Mathematics 517, pp. 207-218. 2010. AMS, ISBN 978-0-8218-4869-2. [pdf]
[bib]
@inproceedings{RISC4048,
author = {Karen T. Kohl and Flavia Stan},
title = {{An Algorithmic Approach to the Mellin Transform Method}},
booktitle = {{Gems in Experimental Mathematics}},
language = {english},
series = {Contemporary Mathematics},
volume = {517},
pages = {207--218},
publisher = {AMS},
isbn_issn = {ISBN 978-0-8218-4869-2},
year = {2010},
editor = {T. Amdeberhan and L. A. Medina and V. H. Moll},
refereed = {yes},
length = {12}
}

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