Constructing a Geometric Algorithms Library [CGAL]

Project Description

Forschungsprogramm: FP4-ESPRIT 4

Project Lead

Project Duration

01/09/1996 - 30/06/1998

Partners

Publications

2021

[Ablinger]

Extensions of the AZ-algorithm and the Package MultiIntegrate

J. Ablinger

Technical report no. 21-02 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 2021. [pdf]
[bib]
@techreport{RISC6272,
author = {J. Ablinger},
title = {{Extensions of the AZ-algorithm and the Package MultiIntegrate}},
language = {english},
number = {21-02},
year = {2021},
length = {25},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}
[Dundua]

Variadic equational matching in associative and commutative theories

Besik Dundua, Temur Kutsia, Mircea Marin

Journal of Symbolic Computation 106, pp. 78-109. 2021. Elsevier, ISSN 0747-7171. [url] [pdf]
[bib]
@article{RISC6260,
author = {Besik Dundua and Temur Kutsia and Mircea Marin},
title = {{Variadic equational matching in associative and commutative theories}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {106},
pages = {78--109},
publisher = {Elsevier},
isbn_issn = {ISSN 0747-7171},
year = {2021},
refereed = {yes},
length = {32},
url = {https://doi.org/10.1016/j.jsc.2021.01.001}
}
[Legersky]

On the maximal number of real embeddings of minimally rigid graphs in R2, R3 and S2

E. Bartzos, I.Z. Emiris, J. Legerský, E. Tsigaridas

Journal of Symbolic Computation 102, pp. 189-208. 2021. ISSN 0747-7171. [url]
[bib]
@article{RISC5992,
author = {E. Bartzos and I.Z. Emiris and J. Legerský and E. Tsigaridas},
title = {{On the maximal number of real embeddings of minimally rigid graphs in R2, R3 and S2}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {102},
pages = {189--208},
isbn_issn = {ISSN 0747-7171},
year = {2021},
refereed = {yes},
length = {20},
url = {https://doi.org/10.1016/j.jsc.2019.10.015}
}
[Maletzky]

A generic and executable formalization of signature-based Gröbner basis algorithms

Alexander Maletzky

J. Symb. Comput. 106, pp. 23-47. 2021. Elsevier, ISSN 0747-7171. arXiv:2012.02239 [cs.SC], https://doi.org/10.1016/j.jsc.2020.12.001. [url]
[bib]
@article{RISC6225,
author = {Alexander Maletzky},
title = {{A generic and executable formalization of signature-based Gröbner basis algorithms}},
language = {english},
journal = {J. Symb. Comput.},
volume = {106},
pages = {23--47},
publisher = {Elsevier},
isbn_issn = {ISSN 0747-7171},
year = {2021},
note = {arXiv:2012.02239 [cs.SC], https://doi.org/10.1016/j.jsc.2020.12.001},
refereed = {yes},
length = {25},
url = {https://arxiv.org/abs/2012.02239}
}
[Paule]

An Invitation to Analytic Combinatorics

Peter Paule (ed.), Stephen Melczer

Texts and Monographs in Symbolic Computation 1st edition, 2021. Springer, 978-3-030-67080-1.
[bib]
@book{RISC6277,
author = {Peter Paule (ed.) and Stephen Melczer},
title = {{An Invitation to Analytic Combinatorics}},
language = {english},
series = {Texts and Monographs in Symbolic Computation},
publisher = {Springer},
isbn_issn = {978-3-030-67080-1},
year = {2021},
edition = {1st},
translation = {0},
length = {405}
}
[Schneider]

The Absent-Minded Passengers Problem: A Motivating Challenge Solved by Computer Algebra

C. Schneider

Mathematics in Computer Science , appeared electronically, pp. ?-?. 2021. ISSN 1661-8289. arXiv:2003.01921 [math.CO]. [url]
[bib]
@article{RISC6127,
author = {C. Schneider},
title = {{The Absent-Minded Passengers Problem: A Motivating Challenge Solved by Computer Algebra}},
language = {english},
journal = {Mathematics in Computer Science , appeared electronically},
pages = {?--?},
isbn_issn = {ISSN 1661-8289},
year = {2021},
note = {arXiv:2003.01921 [math.CO]},
refereed = {yes},
length = {12},
url = {https://doi.org/10.1007/s11786-020-00494-w}
}
[Schneider]

Three loop heavy quark form factors and their asymptotic behavior

J. Ablinger, J. Blümlein, P. Marquard, N. Rana, C. Schneider

In: To appear in Proc.of 23rd DAE-BRNS High Energy Physics Symposium 2018, , pp. ?-?. 2021. arXiv:1906.05829 [hep-ph]. [url]
[bib]
@inproceedings{RISC6024,
author = {J. Ablinger and J. Blümlein and P. Marquard and N. Rana and C. Schneider},
title = {{Three loop heavy quark form factors and their asymptotic behavior}},
booktitle = {{To appear in Proc.of 23rd DAE-BRNS High Energy Physics Symposium 2018}},
language = {english},
pages = {?--?},
isbn_issn = {?},
year = {2021},
note = {arXiv:1906.05829 [hep-ph]},
editor = {?},
refereed = {yes},
length = {8},
url = {https://arxiv.org/abs/1906.05829}
}
[Schneider]

A case study for ζ(4)

Carsten Schneider, Wadim Zudilin

In: Proceedings of the conference 'Transient Transcendence in Transylvania', Alin Bostan and Kilian Raschel (ed.), Proceedings in Mathematics & Statistics , pp. ?-?. 2021. Springer, arXiv:2004.08158 [math.NT]. [url]
[bib]
@incollection{RISC6210,
author = {Carsten Schneider and Wadim Zudilin},
title = {{A case study for ζ(4)}},
booktitle = {{Proceedings of the conference 'Transient Transcendence in Transylvania'}},
language = {english},
series = {Proceedings in Mathematics & Statistics},
pages = {?--?},
publisher = {Springer},
isbn_issn = {?},
year = {2021},
note = {arXiv:2004.08158 [math.NT]},
editor = {Alin Bostan and Kilian Raschel},
refereed = {no},
length = {0},
url = {https://arxiv.org/abs/2004.08158}
}
[Schneider]

On Rational and Hypergeometric Solutions of Linear Ordinary Difference Equations in ΠΣ∗-field extensions

Sergei A. Abramov, Manuel Bronstein, Marko Petkovšek, Carsten Schneider

J. Symb. Comput. 107, pp. 23-66. 2021. ISSN 0747-7171. arXiv:2005.04944 [cs.SC]. [url]
[bib]
@article{RISC6224,
author = {Sergei A. Abramov and Manuel Bronstein and Marko Petkovšek and Carsten Schneider},
title = {{On Rational and Hypergeometric Solutions of Linear Ordinary Difference Equations in ΠΣ∗-field extensions}},
language = {english},
journal = {J. Symb. Comput.},
volume = {107},
pages = {23--66},
isbn_issn = {ISSN 0747-7171},
year = {2021},
note = {arXiv:2005.04944 [cs.SC]},
refereed = {yes},
length = {44},
url = {https://doi.org/10.1016/j.jsc.2021.01.002}
}
[Schneider]

The Polarized Transition Matrix Element $A_{g, q}(N)$ of the Variable Flavor Number Scheme at $O(alpha_s^3)$

A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, K. Schönwald, and C. Schneider

Nuclear Physics B 964, pp. 115331-115356. 2021. ISSN 0550-3213. arXiv:2101.05733 [hep-ph]. [url]
[bib]
@article{RISC6278,
author = {A. Behring and J. Blümlein and A. De Freitas and A. von Manteuffel and K. Schönwald and and C. Schneider},
title = {{The Polarized Transition Matrix Element $A_{g,q}(N)$ of the Variable Flavor Number Scheme at $O(alpha_s^3)$}},
language = {english},
journal = {Nuclear Physics B},
volume = {964},
pages = {115331--115356},
isbn_issn = {ISSN 0550-3213},
year = {2021},
note = {arXiv:2101.05733 [hep-ph]},
refereed = {yes},
length = {26},
url = {https://doi.org/10.1016/j.nuclphysb.2021.115331}
}
[Schneider]

Solving linear difference equations with coefficients in rings with idempotent representations

J. Ablinger, C. Schneider

Technical report no. 21-04 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 2021. [pdf]
[bib]
@techreport{RISC6284,
author = {J. Ablinger and C. Schneider},
title = {{Solving linear difference equations with coefficients in rings with idempotent representations}},
language = {english},
number = {21-04},
year = {2021},
length = {8},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}
[Schneider]

Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation

C. Schneider

In: Anti-Differentiation and the Calculation of Feynman Amplitudes, J. Blümlein and C. Schneider (ed.), Texts and Monographs in Symbolic Computuation to appear, pp. ?-?. 2021. Springer, arXiv:2102.01471 [cs.SC], RISC-Linz Report Series No. 21-03. [url]
[bib]
@incollection{RISC6287,
author = {C. Schneider},
title = {{Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation}},
booktitle = {{Anti-Differentiation and the Calculation of Feynman Amplitudes}},
language = {english},
series = {Texts and Monographs in Symbolic Computuation},
volume = {to appear},
pages = {?--?},
publisher = {Springer},
isbn_issn = {?},
year = {2021},
note = {arXiv:2102.01471 [cs.SC], RISC-Linz Report Series No. 21-03},
editor = {J. Blümlein and C. Schneider},
refereed = {yes},
length = {55},
url = {https://arxiv.org/abs/2102.01471}
}

2020

[Ablinger]

Proving Two Conjectural Series for $\zeta(7)$ and Discovering More Series for $\zeta(7)$

J. Ablinger

In: Mathematical Aspects of Computer and Information Science, D. Slamanig, E. Tsigaridas, Z. Zafeirakopoulos (ed.), pp. 42-47. 2020. Springer International Publishing, 978-3-030-43120-4. [url]
[bib]
@inproceedings{RISC6102,
author = {J. Ablinger},
title = {{Proving Two Conjectural Series for $\zeta(7)$ and Discovering More Series for $\zeta(7)$}},
booktitle = {{Mathematical Aspects of Computer and Information Science}},
language = {english},
pages = {42--47},
publisher = {Springer International Publishing},
isbn_issn = {978-3-030-43120-4},
year = {2020},
editor = {D. Slamanig and E. Tsigaridas and Z. Zafeirakopoulos},
refereed = {yes},
length = {6},
url = {https://arxiv.org/abs/1908.06631v1}
}
[Ablinger]

Subleading logarithmic QED initial state corrections to $e^+e^−\to γ^⁎/Z^{0⁎}$ to $O(\alpha^6L^5)$

J. Ablinger, J. Blümlein, A. De Freitas, K. Schönwald

Nuclear Physics B 955, pp. 115045-115045. 2020. ISSN 0550-3213. [url]
[bib]
@article{RISC6111,
author = {J. Ablinger and J. Blümlein and A. De Freitas and K. Schönwald},
title = {{Subleading logarithmic QED initial state corrections to $e^+e^−\to γ^⁎/Z^{0⁎}$ to $O(\alpha^6L^5)$}},
language = {english},
journal = {Nuclear Physics B},
volume = {955},
pages = {115045--115045},
isbn_issn = { ISSN 0550-3213},
year = {2020},
refereed = {yes},
length = {0},
url = {http://www.sciencedirect.com/science/article/pii/S0550321320301310}
}
[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}
}
[Banerjee]

Hook Type Tableaux and Partition Identities

Koustav Banerjee, Manosij Ghosh Dastidar

Research Institute for Symbolic Computation. Technical report, 2020. Preprint. [pdf]
[bib]
@techreport{RISC6118,
author = {Koustav Banerjee and Manosij Ghosh Dastidar},
title = {{Hook Type Tableaux and Partition Identities}},
language = {english},
abstract = {In this paper we exhibit the box-stacking principle (BSP) in conjunction with Young diagrams to prove generalizations of the Stanley’s and Elder’s theorem without the use of partition statistics in general. We explain how the principle can be used to prove another interesting theorem on partitions with parts separated by parity, a special case of which is George Andrews’s result in [2].},
year = {2020},
note = {Preprint},
institution = {Research Institute for Symbolic Computation},
length = {19}
}
[Capco]

Robots, computer algebra and 8 connected components

J. Capco, M. Safey el Din, J. Schicho

In: Proceedings of ISSAC 2020, I. Emiris, L. Zhi (ed.), pp. 62-69. 2020. 978-1-4503-7100-1. [url]
[bib]
@inproceedings{RISC6247,
author = {J. Capco and M. Safey el Din and J. Schicho},
title = {{Robots, computer algebra and 8 connected components}},
booktitle = {{Proceedings of ISSAC 2020}},
language = {english},
pages = {62--69},
isbn_issn = {978-1-4503-7100-1},
year = {2020},
editor = {I. Emiris and L. Zhi},
refereed = {yes},
length = {8},
url = {https://arxiv.org/abs/2008.13392}
}
[Cerna]

Unital Anti-Unification: Type and Algorithms

David M. Cerna, Temur Kutsia

In: Proceedings of the 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020), Zena M. Ariola (ed.), Leibniz International Proceedings in Informatics (LIPIcs) 167, pp. 26:1-26:20. 2020. Schloss Dagstuhl-Leibniz-Zentrum für Informatik, ISBN 978-3-95977-155-9, ISSN 1868-8969. [url]
[bib]
@inproceedings{RISC6132,
author = {David M. Cerna and Temur Kutsia},
title = {{Unital Anti-Unification: Type and Algorithms}},
booktitle = {{Proceedings of the 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)}},
language = {english},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {167},
pages = {26:1--26:20},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum für Informatik},
isbn_issn = {ISBN 978-3-95977-155-9, ISSN 1868-8969},
year = {2020},
editor = {Zena M. Ariola},
refereed = {yes},
length = {20},
url = {https://drops.dagstuhl.de/opus/volltexte/2020/12352/}
}
[Cerna]

Idempotent Anti-unification

David Cerna, Temur Kutsia

ACM Transactions on Computational Logic (TOCL) 21(2), pp. 10:1-10:32. 2020. ACM Press, ISSN 1529-3785. [url] [pdf]
[bib]
@article{RISC6023,
author = {David Cerna and Temur Kutsia},
title = {{Idempotent Anti-unification}},
language = {english},
journal = {ACM Transactions on Computational Logic (TOCL)},
volume = {21},
number = {2},
pages = {10:1--10:32},
publisher = {ACM Press},
isbn_issn = {ISSN 1529-3785},
year = {2020},
refereed = {yes},
length = {32},
url = {https://doi.org/10.1145/3359060}
}
[Cerna]

Aiding an Introduction to Formal Reasoning Within a First-Year Logic Course for CS Majors Using a Mobile Self-Study App

David M. Cerna, Martina Seidl, Wolfgang Schreiner, Wolfgang Windsteiger, Armin Biere

In: ITICSE 2020, ACM (ed.), Proceedings of ITICSE, pp. 61-67. 2020. 9781450368742. [url]
[bib]
@inproceedings{RISC6096,
author = {David M. Cerna and Martina Seidl and Wolfgang Schreiner and Wolfgang Windsteiger and Armin Biere},
title = {{Aiding an Introduction to Formal Reasoning Within a First-Year Logic Course for CS Majors Using a Mobile Self-Study App}},
booktitle = {{ITICSE 2020}},
language = {english},
abstract = {In this paper, we share our experiences concerning the introduc-tion of the Android-based self-study app AXolotl within the first-semester logic course offered at our university. This course is manda-tory for students majoring in Computer Science and Artificial In-telligence. AXolotl was used as part of an optional lab assignmentbridging clausal reasoning and SAT solving with classical reason-ing, proof construction, and first-order logic. The app provides anintuitive interface for proof construction in various logical calculiand aids the students through rule application. The goal of thelab assignment was to help students make a smoother transitionfrom clausal and decompositional reasoning used earlier in thecourse to inferential and contextual reasoning required for proofconstruction and first-order logic. We observed that the lab had apositive influence on students’ understanding and end the paperwith a discussion of these results.},
pages = {61--67},
isbn_issn = {9781450368742},
year = {2020},
editor = {ACM},
refereed = {yes},
length = {7},
conferencename = {ITICSE},
url = {https://dl.acm.org/doi/10.1145/3341525.3387409}
}

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