Pilotprojekt “Projektentwicklung u. Durchführung eines Referenzprojektes f. d. SWCCH”
Project Description
Projektnummer: GZ 60.195/1-V/B/9/97 (A-924)
Project Lead
Project Duration
01/09/1997 - 30/09/1998Publications
2024
[Schneider]
Representation of hypergeometric products of higher nesting depths in difference rings
E.D. Ocansey, C. Schneider
J. Symb. Comput. 120, pp. 1-50. 2024. ISSN: 0747-7171. arXiv:2011.08775 [cs.SC]. [doi]@article{RISC6688,
author = {E.D. Ocansey and C. Schneider},
title = {{Representation of hypergeometric products of higher nesting depths in difference rings}},
language = {english},
journal = {J. Symb. Comput.},
volume = {120},
pages = {1--50},
isbn_issn = {ISSN: 0747-7171},
year = {2024},
note = {arXiv:2011.08775 [cs.SC]},
refereed = {yes},
length = {50},
url = {https://doi.org/10.1016/j.jsc.2023.03.002}
}
author = {E.D. Ocansey and C. Schneider},
title = {{Representation of hypergeometric products of higher nesting depths in difference rings}},
language = {english},
journal = {J. Symb. Comput.},
volume = {120},
pages = {1--50},
isbn_issn = {ISSN: 0747-7171},
year = {2024},
note = {arXiv:2011.08775 [cs.SC]},
refereed = {yes},
length = {50},
url = {https://doi.org/10.1016/j.jsc.2023.03.002}
}
2023
[Banerjee]
Positivity of the second shifted difference of partitions and overpartitions: a combinatorial approach
Koustav Banerjee
Enumerative Combinatorics and Applications 3, pp. 1-4. 2023. ISSN 2710-2335. [doi]@article{RISC6701,
author = {Koustav Banerjee},
title = {{Positivity of the second shifted difference of partitions and overpartitions: a combinatorial approach}},
language = {english},
journal = {Enumerative Combinatorics and Applications},
volume = {3},
pages = {1--4},
isbn_issn = {ISSN 2710-2335},
year = {2023},
refereed = {yes},
length = {5},
url = {https://doi.org/10.54550/ECA2023V3S2R12}
}
author = {Koustav Banerjee},
title = {{Positivity of the second shifted difference of partitions and overpartitions: a combinatorial approach}},
language = {english},
journal = {Enumerative Combinatorics and Applications},
volume = {3},
pages = {1--4},
isbn_issn = {ISSN 2710-2335},
year = {2023},
refereed = {yes},
length = {5},
url = {https://doi.org/10.54550/ECA2023V3S2R12}
}
[Banerjee]
Inequalities for the modified Bessel function of first kind of non-negative order
K. Banerjee
Journal of Mathematical Analysis and Applications 524, pp. 1-28. 2023. Elsevier, ISSN 1096-0813. [doi]@article{RISC6700,
author = {K. Banerjee},
title = {{Inequalities for the modified Bessel function of first kind of non-negative order}},
language = {english},
journal = {Journal of Mathematical Analysis and Applications},
volume = {524},
pages = {1--28},
publisher = {Elsevier},
isbn_issn = {ISSN 1096-0813},
year = {2023},
refereed = {yes},
length = {28},
url = {https://doi.org/10.1016/j.jmaa.2023.127082}
}
author = {K. Banerjee},
title = {{Inequalities for the modified Bessel function of first kind of non-negative order}},
language = {english},
journal = {Journal of Mathematical Analysis and Applications},
volume = {524},
pages = {1--28},
publisher = {Elsevier},
isbn_issn = {ISSN 1096-0813},
year = {2023},
refereed = {yes},
length = {28},
url = {https://doi.org/10.1016/j.jmaa.2023.127082}
}
[Buchberger]
Is ChatGPT Smarter Than Master’s Applicants?
Bruno Buchberger
Technical report no. 23-04 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). January 2023. Licensed under CC BY 4.0 International. [doi] [pdf]@techreport{RISC6684,
author = {Bruno Buchberger},
title = {{Is ChatGPT Smarter Than Master’s Applicants?}},
language = {English},
abstract = {During the selection procedure for a particular informatics fellowship program sponsored by Upper Austrian companies, I ask the applicants a couple of simple technical questions about programming, etc., in a Zoom meeting. I put the same questions to the dialogue system ChatGPT, [ChatGPT]. The result surprised me: Nearly all answers of ChatGPT were totally correct and nicely explained. Also, in the dialogues to clarify some critical points in the answers, the explanations by ChatGPT were amazingly clear and goal-oriented.In comparison: I tried out the same questions in the personal Zoom interviews with approximately 30 applicants from five countries. Only the top three candidates (with a GPA of 1.0, i.e., the highest possible GPA in their bachelor’s study) performed approximately equally well in the interview. All the others performed (far) worse than ChatGPT. And, of course, all answers from ChatGPT came within 1 to 10 seconds, whereas most of the human applicants' answers needed lengthy and arduous dialogues.I am particularly impressed by the ability of ChatGPT to extract meaningful and well-structured programs from problem specifications in natural language. In this experiment, I also added some questions that ask for proofs for simple statements in natural language, which I do not ask in the student's interviews. The performance of ChatGPT was quite impressive as far as formalization and propositional logic are concerned. In examples where predicate logic reasoning is necessary, the ChatGPT answers are not (yet?) perfect. I am pleased to see that ChatGPT tries to present the proofs in a “natural style” This is something that I had as one of my main goals when I initiated the Theorema project in 1995. I think we already achieved this in the early stage of Theorema, and we performed this slightly better and more systematically than ChatGPT does.I also tried to develop a natural language input facility for Theorema in 2017, i.e., a tool to formalize natural language statements in predicate logic. However, I could not continue this research for a couple of reasons. Now I see that ChatGPT achieved this goal. Thus, I think that the following combination of methods could result in a significant leap forward:- the “natural style” proving methods that we developed within Theorema (for the automated generation of programs from specifications, the automated verification of programs in the frame of knowledge, and the automated proof of theorems in theories), in particular, my “Lazy Thinking Method” for algorithm synthesis from specifications- and the natural language formalization techniques of ChatGPT.I propose this as a research project topic and invite colleagues and students to contact me and join me in this effort: Buchberger.bruno@gmail.com.},
number = {23-04},
year = {2023},
month = {January},
keywords = {ChatGPT, automated programming, program synthesis, automated proving, formalization of natural language, master's screening},
length = {30},
license = {CC BY 4.0 International},
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)}
}
author = {Bruno Buchberger},
title = {{Is ChatGPT Smarter Than Master’s Applicants?}},
language = {English},
abstract = {During the selection procedure for a particular informatics fellowship program sponsored by Upper Austrian companies, I ask the applicants a couple of simple technical questions about programming, etc., in a Zoom meeting. I put the same questions to the dialogue system ChatGPT, [ChatGPT]. The result surprised me: Nearly all answers of ChatGPT were totally correct and nicely explained. Also, in the dialogues to clarify some critical points in the answers, the explanations by ChatGPT were amazingly clear and goal-oriented.In comparison: I tried out the same questions in the personal Zoom interviews with approximately 30 applicants from five countries. Only the top three candidates (with a GPA of 1.0, i.e., the highest possible GPA in their bachelor’s study) performed approximately equally well in the interview. All the others performed (far) worse than ChatGPT. And, of course, all answers from ChatGPT came within 1 to 10 seconds, whereas most of the human applicants' answers needed lengthy and arduous dialogues.I am particularly impressed by the ability of ChatGPT to extract meaningful and well-structured programs from problem specifications in natural language. In this experiment, I also added some questions that ask for proofs for simple statements in natural language, which I do not ask in the student's interviews. The performance of ChatGPT was quite impressive as far as formalization and propositional logic are concerned. In examples where predicate logic reasoning is necessary, the ChatGPT answers are not (yet?) perfect. I am pleased to see that ChatGPT tries to present the proofs in a “natural style” This is something that I had as one of my main goals when I initiated the Theorema project in 1995. I think we already achieved this in the early stage of Theorema, and we performed this slightly better and more systematically than ChatGPT does.I also tried to develop a natural language input facility for Theorema in 2017, i.e., a tool to formalize natural language statements in predicate logic. However, I could not continue this research for a couple of reasons. Now I see that ChatGPT achieved this goal. Thus, I think that the following combination of methods could result in a significant leap forward:- the “natural style” proving methods that we developed within Theorema (for the automated generation of programs from specifications, the automated verification of programs in the frame of knowledge, and the automated proof of theorems in theories), in particular, my “Lazy Thinking Method” for algorithm synthesis from specifications- and the natural language formalization techniques of ChatGPT.I propose this as a research project topic and invite colleagues and students to contact me and join me in this effort: Buchberger.bruno@gmail.com.},
number = {23-04},
year = {2023},
month = {January},
keywords = {ChatGPT, automated programming, program synthesis, automated proving, formalization of natural language, master's screening},
length = {30},
license = {CC BY 4.0 International},
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)}
}
[Dominici]
Linear functionals and $Delta$- coherent pairs of the second kind
Diego Dominici and Francisco Marcellan
Technical report no. 23-02 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). February 2023. Licensed under CC BY 4.0 International. [doi] [pdf]@techreport{RISC6677,
author = {Diego Dominici and Francisco Marcellan},
title = {{Linear functionals and $Delta$- coherent pairs of the second kind}},
language = {english},
abstract = {We classify all the emph{$Delta$-}coherent pairs of measures of the secondkind on the real line. We obtain $5$ cases, corresponding to all the familiesof discrete semiclassical orthogonal polynomials of class $sleq1.$},
number = {23-02},
year = {2023},
month = {February},
keywords = { Discrete orthogonal polynomials, discrete semiclassical functionals, discrete Sobolev inner products, coherent pairs of discrete measures, coherent pairs of second kind for discrete measures.},
length = {24},
license = {CC BY 4.0 International},
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)}
}
author = {Diego Dominici and Francisco Marcellan},
title = {{Linear functionals and $Delta$- coherent pairs of the second kind}},
language = {english},
abstract = {We classify all the emph{$Delta$-}coherent pairs of measures of the secondkind on the real line. We obtain $5$ cases, corresponding to all the familiesof discrete semiclassical orthogonal polynomials of class $sleq1.$},
number = {23-02},
year = {2023},
month = {February},
keywords = { Discrete orthogonal polynomials, discrete semiclassical functionals, discrete Sobolev inner products, coherent pairs of discrete measures, coherent pairs of second kind for discrete measures.},
length = {24},
license = {CC BY 4.0 International},
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)}
}
[Dominici]
Recurrence relations for the moments of discrete semiclassical functionals of class $sleq2.$
Diego Dominici
Technical report no. 23-05 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). March 2023. Licensed under CC BY 4.0 International. [doi] [pdf]@techreport{RISC6687,
author = {Diego Dominici },
title = {{Recurrence relations for the moments of discrete semiclassical functionals of class $sleq2.$}},
language = {english},
abstract = {We study recurrence relations satisfied by the moments $lambda_{n}left(zright) $ of discrete linear functionals whose first moment satisfies aholonomic differential equation. We consider all cases when the order of theODE is less or equal than $3$.},
number = {23-05},
year = {2023},
month = {March},
keywords = {Discrete orthogonal polynomials, discrete semiclassical functionals, moments.},
length = {81},
license = {CC BY 4.0 International},
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)}
}
author = {Diego Dominici },
title = {{Recurrence relations for the moments of discrete semiclassical functionals of class $sleq2.$}},
language = {english},
abstract = {We study recurrence relations satisfied by the moments $lambda_{n}left(zright) $ of discrete linear functionals whose first moment satisfies aholonomic differential equation. We consider all cases when the order of theODE is less or equal than $3$.},
number = {23-05},
year = {2023},
month = {March},
keywords = {Discrete orthogonal polynomials, discrete semiclassical functionals, moments.},
length = {81},
license = {CC BY 4.0 International},
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)}
}
[Jimenez Pastor]
An extension of holonomic sequences: $C^2$-finite sequences
A. Jimenez-Pastor, P. Nuspl, V. Pillwein
Journal of Symbolic Computation 116, pp. 400-424. 2023. ISSN: 0747-7171.@article{RISC6636,
author = {A. Jimenez-Pastor and P. Nuspl and V. Pillwein},
title = {{An extension of holonomic sequences: $C^2$-finite sequences}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {116},
pages = {400--424},
isbn_issn = {ISSN: 0747-7171},
year = {2023},
refereed = {yes},
length = {25}
}
author = {A. Jimenez-Pastor and P. Nuspl and V. Pillwein},
title = {{An extension of holonomic sequences: $C^2$-finite sequences}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {116},
pages = {400--424},
isbn_issn = {ISSN: 0747-7171},
year = {2023},
refereed = {yes},
length = {25}
}
[Kauers]
Order bounds for $C^2$-finite sequences
M. Kauers, P. Nuspl, V. Pillwein
Technical report no. 23-03 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). February 2023. Licensed under CC BY 4.0 International. [doi] [pdf]@techreport{RISC6683,
author = {M. Kauers and P. Nuspl and V. Pillwein},
title = {{Order bounds for $C^2$-finite sequences}},
language = {english},
abstract = {A sequence is called $C$-finite if it satisfies a linear recurrence with constant coefficients. We study sequences which satisfy a linear recurrence with $C$-finite coefficients. Recently, it was shown that such $C^2$-finite sequences satisfy similar closure properties as $C$-finite sequences. In particular, they form a difference ring. In this paper we present new techniques for performing these closure properties of $C^2$-finite sequences. These methods also allow us to derive order bounds which were not known before. Additionally, they provide more insight in the effectiveness of these computations. The results are based on the exponent lattice of algebraic numbers. We present an iterative algorithm which can be used to compute bases of such lattices.},
number = {23-03},
year = {2023},
month = {February},
keywords = {Difference equations, holonomic sequences, closure properties, algorithms},
length = {16},
license = {CC BY 4.0 International},
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)}
}
author = {M. Kauers and P. Nuspl and V. Pillwein},
title = {{Order bounds for $C^2$-finite sequences}},
language = {english},
abstract = {A sequence is called $C$-finite if it satisfies a linear recurrence with constant coefficients. We study sequences which satisfy a linear recurrence with $C$-finite coefficients. Recently, it was shown that such $C^2$-finite sequences satisfy similar closure properties as $C$-finite sequences. In particular, they form a difference ring. In this paper we present new techniques for performing these closure properties of $C^2$-finite sequences. These methods also allow us to derive order bounds which were not known before. Additionally, they provide more insight in the effectiveness of these computations. The results are based on the exponent lattice of algebraic numbers. We present an iterative algorithm which can be used to compute bases of such lattices.},
number = {23-03},
year = {2023},
month = {February},
keywords = {Difference equations, holonomic sequences, closure properties, algorithms},
length = {16},
license = {CC BY 4.0 International},
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)}
}
[Mitteramskogler]
The algebro-geometric method: Solving algebraic differential equations by parametrizations
S. Falkensteiner, J.J. Mitteramskogler, R. Sendra, F. Winkler
Bulletin of the American Mathematical Society, pp. 1-41. 2023. ISSN 0273-0979.@article{RISC6507,
author = {S. Falkensteiner and J.J. Mitteramskogler and R. Sendra and F. Winkler},
title = {{The algebro-geometric method: Solving algebraic differential equations by parametrizations}},
language = {english},
journal = {Bulletin of the American Mathematical Society},
pages = {1--41},
isbn_issn = {ISSN 0273-0979},
year = {2023},
refereed = {yes},
length = {41}
}
author = {S. Falkensteiner and J.J. Mitteramskogler and R. Sendra and F. Winkler},
title = {{The algebro-geometric method: Solving algebraic differential equations by parametrizations}},
language = {english},
journal = {Bulletin of the American Mathematical Society},
pages = {1--41},
isbn_issn = {ISSN 0273-0979},
year = {2023},
refereed = {yes},
length = {41}
}
[Mitteramskogler]
General solutions of first-order algebraic ODEs in simple constant extensions
J. J. Mitteramskogler, F. Winkler
Journal of Systems Science and Complexity (JSSC), pp. 0-0. 2023. 1009-6124.@article{RISC6674,
author = {J. J. Mitteramskogler and F. Winkler},
title = {{General solutions of first-order algebraic ODEs in simple constant extensions}},
language = {english},
journal = {Journal of Systems Science and Complexity (JSSC)},
pages = {0--0},
isbn_issn = {1009-6124},
year = {2023},
refereed = {yes},
length = {0}
}
author = {J. J. Mitteramskogler and F. Winkler},
title = {{General solutions of first-order algebraic ODEs in simple constant extensions}},
language = {english},
journal = {Journal of Systems Science and Complexity (JSSC)},
pages = {0--0},
isbn_issn = {1009-6124},
year = {2023},
refereed = {yes},
length = {0}
}
[Paule]
Ramanujan and Computer Algebra
Peter Paule
In: Srinivasa Ramanujan: His Life, Legacy, and Mathematical Influence, K. Alladi, G.E. Andrews, B. Berndt, F. Garvan, K. Ono, P. Paule, S. Ole Warnaar, Ae Ja Yee (ed.), pp. -. 2023. Springer, ISBN x. [pdf]@incollection{RISC6678,
author = {Peter Paule},
title = {{Ramanujan and Computer Algebra}},
booktitle = {{Srinivasa Ramanujan: His Life, Legacy, and Mathematical Influence}},
language = {english},
pages = {--},
publisher = {Springer},
isbn_issn = {ISBN x},
year = {2023},
editor = {K. Alladi and G.E. Andrews and B. Berndt and F. Garvan and K. Ono and P. Paule and S. Ole Warnaar and Ae Ja Yee },
refereed = {yes},
length = {0}
}
author = {Peter Paule},
title = {{Ramanujan and Computer Algebra}},
booktitle = {{Srinivasa Ramanujan: His Life, Legacy, and Mathematical Influence}},
language = {english},
pages = {--},
publisher = {Springer},
isbn_issn = {ISBN x},
year = {2023},
editor = {K. Alladi and G.E. Andrews and B. Berndt and F. Garvan and K. Ono and P. Paule and S. Ole Warnaar and Ae Ja Yee },
refereed = {yes},
length = {0}
}
[Paule]
Interview with Peter Paule
Toufik Mansour and Peter Paule
Enumerative Combinatorics and Applications ECA 3:1(#S3I1), pp. -. 2023. ISSN 2710-2335. [doi]@article{RISC6679,
author = {Toufik Mansour and Peter Paule},
title = {{Interview with Peter Paule}},
language = {english},
journal = {Enumerative Combinatorics and Applications },
volume = {ECA 3:1},
number = {#S3I1},
pages = {--},
isbn_issn = {ISSN 2710-2335},
year = {2023},
refereed = {yes},
length = {0},
url = {http://doi.org/10.54550/ECA2023V3S1I1}
}
author = {Toufik Mansour and Peter Paule},
title = {{Interview with Peter Paule}},
language = {english},
journal = {Enumerative Combinatorics and Applications },
volume = {ECA 3:1},
number = {#S3I1},
pages = {--},
isbn_issn = {ISSN 2710-2335},
year = {2023},
refereed = {yes},
length = {0},
url = {http://doi.org/10.54550/ECA2023V3S1I1}
}
[Schneider]
Hypergeometric Structures in Feynman Integrals
J. Blümlein, C. Schneider, M. Saragnese
Annals of Mathematics and Artificial Intelligence, Special issue on " Symbolic Computation in Software Science" to appear, pp. ?-?. 2023. ISSN 1573-7470. arXiv:2111.15501 [math-ph]. [doi]@article{RISC6643,
author = {J. Blümlein and C. Schneider and M. Saragnese},
title = {{Hypergeometric Structures in Feynman Integrals}},
language = {english},
abstract = {Hypergeometric structures in single and multiscale Feynman integrals emerge in a wide class of topologies. Using integration-by-parts relations, associated master or scalar integrals have to be calculated. For this purpose it appears useful to devise an automated method which recognizes the respective (partial) differential equations related to the corresponding higher transcendental functions. We solve these equations through associated recursions of the expansion coefficient of the multivalued formal Taylor series. The expansion coefficients can be determined using either the package {tt Sigma} in the case of linear difference equations or by applying heuristic methods in the case of partial linear difference equations. In the present context a new type of sums occurs, the Hurwitz harmonic sums, and generalized versions of them. The code {tt HypSeries} transforming classes of differential equations into analytic series expansions is described. Also partial difference equations having rational solutions and rational function solutions of Pochhammer symbols are considered, for which the code {tt solvePartialLDE} is designed. Generalized hypergeometric functions, Appell-,~Kamp'e de F'eriet-, Horn-, Lauricella-Saran-, Srivasta-, and Exton--type functions are considered. We illustrate the algorithms by examples.},
journal = {Annals of Mathematics and Artificial Intelligence, Special issue on " Symbolic Computation in Software Science"},
volume = {to appear},
pages = {?--?},
isbn_issn = {ISSN 1573-7470},
year = {2023},
note = {arXiv:2111.15501 [math-ph]},
refereed = {yes},
keywords = {hypergeometric functions, symbolic summation, expansion, partial linear difference equations, partial linear differential equations},
length = {55},
url = {https://doi.org/10.1007/s10472-023-09831-8}
}
author = {J. Blümlein and C. Schneider and M. Saragnese},
title = {{Hypergeometric Structures in Feynman Integrals}},
language = {english},
abstract = {Hypergeometric structures in single and multiscale Feynman integrals emerge in a wide class of topologies. Using integration-by-parts relations, associated master or scalar integrals have to be calculated. For this purpose it appears useful to devise an automated method which recognizes the respective (partial) differential equations related to the corresponding higher transcendental functions. We solve these equations through associated recursions of the expansion coefficient of the multivalued formal Taylor series. The expansion coefficients can be determined using either the package {tt Sigma} in the case of linear difference equations or by applying heuristic methods in the case of partial linear difference equations. In the present context a new type of sums occurs, the Hurwitz harmonic sums, and generalized versions of them. The code {tt HypSeries} transforming classes of differential equations into analytic series expansions is described. Also partial difference equations having rational solutions and rational function solutions of Pochhammer symbols are considered, for which the code {tt solvePartialLDE} is designed. Generalized hypergeometric functions, Appell-,~Kamp'e de F'eriet-, Horn-, Lauricella-Saran-, Srivasta-, and Exton--type functions are considered. We illustrate the algorithms by examples.},
journal = {Annals of Mathematics and Artificial Intelligence, Special issue on " Symbolic Computation in Software Science"},
volume = {to appear},
pages = {?--?},
isbn_issn = {ISSN 1573-7470},
year = {2023},
note = {arXiv:2111.15501 [math-ph]},
refereed = {yes},
keywords = {hypergeometric functions, symbolic summation, expansion, partial linear difference equations, partial linear differential equations},
length = {55},
url = {https://doi.org/10.1007/s10472-023-09831-8}
}
[Schneider]
Refined telescoping algorithms in $RPiSigma$-extensions to reduce the degrees of the denominators
C. Schneider
In: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation (Proc. ISSAC 23), Gabriela Jeronimo (ed.), to appear , pp. ?-?. February 2023. arXiv:2302.03563 [cs.SC]. [doi]@inproceedings{RISC6699,
author = {C. Schneider},
title = {{Refined telescoping algorithms in $RPiSigma$-extensions to reduce the degrees of the denominators}},
booktitle = {{Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation (Proc. ISSAC 23)}},
language = {english},
abstract = {We present a general framework in the setting of difference ring extensions that enables one to find improved representations of indefinite nested sums such that the arising denominators within the summands have reduced degrees. The underlying (parameterized) telescoping algorithms can be executed in $RPiSigma$-ring extensions that are built over general $PiSigma$-fields. An important application of this toolbox is the simplification of d'Alembertian and Liouvillian solutions coming from recurrence relations where the denominators of the arising sums do not factor nicely.},
series = {to appear},
pages = {?--?},
isbn_issn = {?},
year = {2023},
month = {February},
note = {arXiv:2302.03563 [cs.SC]},
editor = {Gabriela Jeronimo},
refereed = {yes},
keywords = {telescoping, difference rings, reduced denominators, nested sums},
length = {9},
url = {https://doi.org/10.35011/risc.23-01}
}
author = {C. Schneider},
title = {{Refined telescoping algorithms in $RPiSigma$-extensions to reduce the degrees of the denominators}},
booktitle = {{Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation (Proc. ISSAC 23)}},
language = {english},
abstract = {We present a general framework in the setting of difference ring extensions that enables one to find improved representations of indefinite nested sums such that the arising denominators within the summands have reduced degrees. The underlying (parameterized) telescoping algorithms can be executed in $RPiSigma$-ring extensions that are built over general $PiSigma$-fields. An important application of this toolbox is the simplification of d'Alembertian and Liouvillian solutions coming from recurrence relations where the denominators of the arising sums do not factor nicely.},
series = {to appear},
pages = {?--?},
isbn_issn = {?},
year = {2023},
month = {February},
note = {arXiv:2302.03563 [cs.SC]},
editor = {Gabriela Jeronimo},
refereed = {yes},
keywords = {telescoping, difference rings, reduced denominators, nested sums},
length = {9},
url = {https://doi.org/10.35011/risc.23-01}
}
[Schneider]
Error bounds for the asymptotic expansion of the partition function
Koustav Banerjee, Peter Paule, Cristian-Silviu Radu, Carsten Schneider
Rocky Mt J Math to appear, pp. ?-?. 2023. ISSN: 357596. arXiv:2209.07887 [math.NT]. [doi]@article{RISC6710,
author = {Koustav Banerjee and Peter Paule and Cristian-Silviu Radu and Carsten Schneider},
title = {{Error bounds for the asymptotic expansion of the partition function}},
language = {english},
abstract = {Asymptotic study on the partition function $p(n)$ began with the work of Hardy and Ramanujan. Later Rademacher obtained a convergent series for $p(n)$ and an error bound was given by Lehmer. Despite having this, a full asymptotic expansion for $p(n)$ with an explicit error bound is not known. Recently O'Sullivan studied the asymptotic expansion of $p^{k}(n)$-partitions into $k$th powers, initiated by Wright, and consequently obtained an asymptotic expansion for $p(n)$ along with a concise description of the coefficients involved in the expansion but without any estimation of the error term. Here we consider a detailed and comprehensive analysis on an estimation of the error term obtained by truncating the asymptotic expansion for $p(n)$ at any positive integer $n$. This gives rise to an infinite family of inequalities for $p(n)$ which finally answers to a question proposed by Chen. Our error term estimation predominantly relies on applications of algorithmic methods from symbolic summation. },
journal = {Rocky Mt J Math },
volume = {to appear},
pages = {?--?},
isbn_issn = {ISSN: 357596},
year = {2023},
note = {arXiv:2209.07887 [math.NT]},
refereed = {yes},
keywords = {partition function, asymptotic expansion, error bounds, symbolic summation},
length = {43},
url = {https://doi.org/10.35011/risc.22-13}
}
author = {Koustav Banerjee and Peter Paule and Cristian-Silviu Radu and Carsten Schneider},
title = {{Error bounds for the asymptotic expansion of the partition function}},
language = {english},
abstract = {Asymptotic study on the partition function $p(n)$ began with the work of Hardy and Ramanujan. Later Rademacher obtained a convergent series for $p(n)$ and an error bound was given by Lehmer. Despite having this, a full asymptotic expansion for $p(n)$ with an explicit error bound is not known. Recently O'Sullivan studied the asymptotic expansion of $p^{k}(n)$-partitions into $k$th powers, initiated by Wright, and consequently obtained an asymptotic expansion for $p(n)$ along with a concise description of the coefficients involved in the expansion but without any estimation of the error term. Here we consider a detailed and comprehensive analysis on an estimation of the error term obtained by truncating the asymptotic expansion for $p(n)$ at any positive integer $n$. This gives rise to an infinite family of inequalities for $p(n)$ which finally answers to a question proposed by Chen. Our error term estimation predominantly relies on applications of algorithmic methods from symbolic summation. },
journal = {Rocky Mt J Math },
volume = {to appear},
pages = {?--?},
isbn_issn = {ISSN: 357596},
year = {2023},
note = {arXiv:2209.07887 [math.NT]},
refereed = {yes},
keywords = {partition function, asymptotic expansion, error bounds, symbolic summation},
length = {43},
url = {https://doi.org/10.35011/risc.22-13}
}
[Schreiner]
Concrete Abstractions
Wolfgang Schreiner
Texts & Monographs in Symbolic Computation 1st edition, 2023. Springer, Cham, Switzerland, Hardcover ISBN 978-3-031-24933-4, Softcover ISBN 978-3-031-24936-5, eBook ISBN 978-3-031-24934-1. [doi]@book{RISC6698,
author = {Wolfgang Schreiner},
title = {{Concrete Abstractions}},
language = {english},
series = {Texts & Monographs in Symbolic Computation},
publisher = {Springer},
address = {Cham, Switzerland},
isbn_issn = {Hardcover ISBN 978-3-031-24933-4, Softcover ISBN 978-3-031-24936-5, eBook ISBN 978-3-031-24934-1},
year = {2023},
edition = {1st},
translation = {0},
keywords = {logic in computer science, model checking, formal modeling and reasoning, program specification and verification, discrete structures and algorithms, nondeterminism and concurrency},
length = {270},
url = {https://doi.org/10.1007/978-3-031-24934-1}
}
author = {Wolfgang Schreiner},
title = {{Concrete Abstractions}},
language = {english},
series = {Texts & Monographs in Symbolic Computation},
publisher = {Springer},
address = {Cham, Switzerland},
isbn_issn = {Hardcover ISBN 978-3-031-24933-4, Softcover ISBN 978-3-031-24936-5, eBook ISBN 978-3-031-24934-1},
year = {2023},
edition = {1st},
translation = {0},
keywords = {logic in computer science, model checking, formal modeling and reasoning, program specification and verification, discrete structures and algorithms, nondeterminism and concurrency},
length = {270},
url = {https://doi.org/10.1007/978-3-031-24934-1}
}
[Smoot]
A Congruence Family For 2-Elongated Plane Partitions: An Application of the Localization Method
N. Smoot
Journal of Number Theory 242, pp. 112-153. January 2023. ISSN 1096-1658. [doi]@article{RISC6661,
author = {N. Smoot},
title = {{A Congruence Family For 2-Elongated Plane Partitions: An Application of the Localization Method}},
language = {english},
abstract = {George Andrews and Peter Paule have recently conjectured an infinite family of congruences modulo powers of 3 for the 2-elongated plane partition function $d_2(n)$. This congruence family appears difficult to prove by classical methods. We prove a refined form of this conjecture by expressing the associated generating functions as elements of a ring of modular functions isomorphic to a localization of $mathbb{Z}[X]$.},
journal = {Journal of Number Theory},
volume = {242},
pages = {112--153},
isbn_issn = {ISSN 1096-1658},
year = {2023},
month = {January},
refereed = {yes},
length = {42},
url = {https://doi.org/10.1016/j.jnt.2022.07.014}
}
author = {N. Smoot},
title = {{A Congruence Family For 2-Elongated Plane Partitions: An Application of the Localization Method}},
language = {english},
abstract = {George Andrews and Peter Paule have recently conjectured an infinite family of congruences modulo powers of 3 for the 2-elongated plane partition function $d_2(n)$. This congruence family appears difficult to prove by classical methods. We prove a refined form of this conjecture by expressing the associated generating functions as elements of a ring of modular functions isomorphic to a localization of $mathbb{Z}[X]$.},
journal = {Journal of Number Theory},
volume = {242},
pages = {112--153},
isbn_issn = {ISSN 1096-1658},
year = {2023},
month = {January},
refereed = {yes},
length = {42},
url = {https://doi.org/10.1016/j.jnt.2022.07.014}
}
[STUDENT]
Formalisation of Relational Algebra and a SQL-like Language with the RISCAL Model Checker
Joachim Borya
Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. Bachelor Thesis. May 2023. Also available as RISC Report 23-06. [doi] [pdf]@misc{RISC6707,
author = {Joachim Borya},
title = {{Formalisation of Relational Algebra and a SQL-like Language with the RISCAL Model Checker}},
language = {english},
abstract = {The relational database model is based on the mathematical concept of relational algebra.Query languages have been developed to make data available quickly without creatingdedicated access procedures that depend on the internal representation of the data. SQL(structured query language) can be seen as a quasi-standard for this. This thesis dealswith the formalization and verification of relational algebra and a small but elementarysubset of SQL with the help of the RISCAL model checker, a software tool for the formalspecification and verification of mathematical theories and algorithms.},
year = {2023},
month = {May},
note = {Also available as RISC Report 23-06},
translation = {0},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria},
keywords = {formal methods, program verification, model checking, automated theorem proving},
length = {77},
url = {https://doi.org/10.35011/risc.23-06}
}
author = {Joachim Borya},
title = {{Formalisation of Relational Algebra and a SQL-like Language with the RISCAL Model Checker}},
language = {english},
abstract = {The relational database model is based on the mathematical concept of relational algebra.Query languages have been developed to make data available quickly without creatingdedicated access procedures that depend on the internal representation of the data. SQL(structured query language) can be seen as a quasi-standard for this. This thesis dealswith the formalization and verification of relational algebra and a small but elementarysubset of SQL with the help of the RISCAL model checker, a software tool for the formalspecification and verification of mathematical theories and algorithms.},
year = {2023},
month = {May},
note = {Also available as RISC Report 23-06},
translation = {0},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria},
keywords = {formal methods, program verification, model checking, automated theorem proving},
length = {77},
url = {https://doi.org/10.35011/risc.23-06}
}
[STUDENT]
Model Checking Concurrent Systems Under Fairness Constraints in RISCAL
Ágoston Sütő
Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. Master Thesis. May 2023. Also available as RISC Report 23-07. Master's thesis. [doi] [pdf]@misc{RISC6709,
author = {Ágoston Sütő},
title = {{Model Checking Concurrent Systems Under Fairness Constraints in RISCAL}},
language = {english},
abstract = {Model checking is a method for verifying that a program satisfies certain desirable properties formalised using mathematical logic. It is a rigorous method, similar to theorem proving, but it is generally applied when theorem proving would be too difficult due to the complexity of the algorithm, such as in concurrent systems. Model checking is used in the software industry. RISCAL (RISC Algorithm Language) is a language and software system that can be used to describe algorithms over a finite domain, specify their behaviour and then validate the specification. While it mainly focuses on deterministic algorithms, it has limited support for non-deterministic systems as well.The thesis extends the support for non-deterministic systems in RISCAL by allowing the user to specify complex properties about their behaviour in the language of Linear Temporal Logic (LTL) and then to validate them. The core contribution is a model checker implemented in Java using the so-called automaton-based explicit state model checking approach. The software is capable of verifying certain properties that could not be handled by a well-known model checker used in the industry. While in most cases it has underperformed its competitors, our implementation is promising, especially when it comes to properties with certain side conditions, called fairness constraints. The majority of the thesis is be concerned with the theoretical aspects of the automaton-based model checking approach, which is followed by a description of the implementation and various benchmarks.},
year = {2023},
month = {May},
note = {Also available as RISC Report 23-07},
translation = {0},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria},
keywords = {formal methods, model checking, concurrent systems, nondeterminism, linear temporal logic},
sponsor = {Supported by Aktion Österreich–Slowakei project grant Nr. 2019-10-15-003 “Semantic Modeling of Component-Based Program Systems”},
length = {102},
url = {https://doi.org/10.35011/risc.23-07},
type = {Master's thesis}
}
author = {Ágoston Sütő},
title = {{Model Checking Concurrent Systems Under Fairness Constraints in RISCAL}},
language = {english},
abstract = {Model checking is a method for verifying that a program satisfies certain desirable properties formalised using mathematical logic. It is a rigorous method, similar to theorem proving, but it is generally applied when theorem proving would be too difficult due to the complexity of the algorithm, such as in concurrent systems. Model checking is used in the software industry. RISCAL (RISC Algorithm Language) is a language and software system that can be used to describe algorithms over a finite domain, specify their behaviour and then validate the specification. While it mainly focuses on deterministic algorithms, it has limited support for non-deterministic systems as well.The thesis extends the support for non-deterministic systems in RISCAL by allowing the user to specify complex properties about their behaviour in the language of Linear Temporal Logic (LTL) and then to validate them. The core contribution is a model checker implemented in Java using the so-called automaton-based explicit state model checking approach. The software is capable of verifying certain properties that could not be handled by a well-known model checker used in the industry. While in most cases it has underperformed its competitors, our implementation is promising, especially when it comes to properties with certain side conditions, called fairness constraints. The majority of the thesis is be concerned with the theoretical aspects of the automaton-based model checking approach, which is followed by a description of the implementation and various benchmarks.},
year = {2023},
month = {May},
note = {Also available as RISC Report 23-07},
translation = {0},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria},
keywords = {formal methods, model checking, concurrent systems, nondeterminism, linear temporal logic},
sponsor = {Supported by Aktion Österreich–Slowakei project grant Nr. 2019-10-15-003 “Semantic Modeling of Component-Based Program Systems”},
length = {102},
url = {https://doi.org/10.35011/risc.23-07},
type = {Master's thesis}
}
2022
[Banerjee]
Hook Type enumeration and parity of parts in partitions
K. Banerjee, M. G. Dastidar
Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6596, 2022. [pdf]@techreport{RISC6596,
author = {K. Banerjee and M. G. Dastidar},
title = {{Hook Type enumeration and parity of parts in partitions}},
language = {english},
abstract = {This paper is devoted to study an association between hook type enumeration and counting integer partitions subject to parity of its parts. We shall primarily focus on a result of Andrews in two possible direction. First, we confirm a conjecture of Rubey and secondly, we extend the theorem of Andrews in a more general set up. },
number = {RISC6596},
year = {2022},
institution = {Research Institute for Symbolic Computation, JKU, Linz},
length = {8}
}
author = {K. Banerjee and M. G. Dastidar},
title = {{Hook Type enumeration and parity of parts in partitions}},
language = {english},
abstract = {This paper is devoted to study an association between hook type enumeration and counting integer partitions subject to parity of its parts. We shall primarily focus on a result of Andrews in two possible direction. First, we confirm a conjecture of Rubey and secondly, we extend the theorem of Andrews in a more general set up. },
number = {RISC6596},
year = {2022},
institution = {Research Institute for Symbolic Computation, JKU, Linz},
length = {8}
}