Symbolic Numerical Computation on Algebraic Curves and Surfaces – Periode I

Project Description

Subprojekt des SFB F-13

Projektnummer: F – 13-14

Project Lead

Project Duration

01/04/1998 - 31/03/2003

Publications

2024

[de Freitas]

The first-order factorizable contributions to the three-loop massive operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$

J. Ablinger, A. Behring, J. Bluemlein, A. De Freitas, A. von Manteuffel, C. Schneider, K. Schoenwald

Nuclear Physics B 999(116427), pp. 1-42. 2024. ISSN 0550-3213. arXiv:2311.00644 [hep-ph]. [doi]
[bib]
@article{RISC6755,
author = {J. Ablinger and A. Behring and J. Bluemlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schoenwald},
title = {{The first--order factorizable contributions to the three--loop massive operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$}},
language = {english},
abstract = {The unpolarized and polarized massive operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$contain first--order factorizable and non--first--order factorizable contributions in the determining difference or differential equations of their master integrals. We compute their first--order factorizable contributions in the single heavy mass case for all contributing Feynman diagrams. Moreover, we present the complete color--$zeta$ factors for the cases in which also non--first--order factorizable contributions emerge in the master integrals, but cancel in the final result as found by using the method of arbitrary high Mellin moments. Individual contributions depend also on generalized harmonic sums and on nested finite binomial and inverse binomial sums in Mellin $N$--space, and correspondingly, on Kummer--Poincar'e and square--root valued alphabets in Bjorken--$x$ space. We present a complete discussion of the possibilities of solving the present problem in $N$--space analytically and we also discuss the limitations in the present case to analytically continue the given $N$--space expressions to $N in mathbb{C}$ by strict methods. The representation through generating functions allows a well synchronized representation of the first--order factorizable results over a 17--letter alphabet. We finally obtain representations in terms of iterated integrals over the corresponding alphabet in $x$--space, also containing up to weight {sf w = 5} special constants, which can be rationalized to Kummer--Poincar'e iterated integrals at special arguments. The analytic $x$--space representation requires separate analyses for the intervals $x in [0,1/4], [1/4,1/2], [1/2,1]$ and $x > 1$. We also derive the small and large $x$ limits of the first--order factorizable contributions. Furthermore, we perform comparisons to a number of known Mellin moments, calculated by a different method for the corresponding subset of Feynman diagrams, and an independent high--precision numerical solution of the problems.},
journal = {Nuclear Physics B},
volume = {999},
number = {116427},
pages = {1--42},
isbn_issn = {ISSN 0550-3213},
year = {2024},
note = {arXiv:2311.00644 [hep-ph]},
refereed = {yes},
keywords = {Feynman diagram, massive operator matrix elements, computer algebra, differential equations, difference equations, coupled systems, nested integrals, nested sums},
length = {42},
url = {https://doi.org/10.1016/j.nuclphysb.2023.116427}
}
[Qi]

A tree-based algorithm for the integration of monomials in the Chow ring of the moduli space of stable marked curves of genus zero

Jiayue Qi

Journal of Symbolic Computation 122(102253), pp. -. 2024. ISSN: 0747-7171. [doi]
[bib]
@article{RISC6774,
author = {Jiayue Qi},
title = {{A tree-based algorithm for the integration of monomials in the Chow ring of the moduli space of stable marked curves of genus zero}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {122},
number = {102253},
pages = {--},
isbn_issn = {ISSN: 0747-7171},
year = {2024},
refereed = {yes},
length = {52},
url = {https://doi.org/10.1016/j.jsc.2023.102253}
}
[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]
[bib]
@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}
}
[Schneider]

Creative Telescoping for Hypergeometric Double Sums

P. Paule, C. Schneider

Technical report no. 24-01 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). January 2024. arXiv:2401.16314 [cs.SC]. Licensed under CC BY 4.0 International. [doi] [pdf]
[bib]
@techreport{RISC6894,
author = {P. Paule and C. Schneider},
title = {{Creative Telescoping for Hypergeometric Double Sums}},
language = {english},
abstract = {We present efficient methods for calculating linear recurrences of hypergeometric double sums and, more generally, of multiple sums. In particular, we supplement this approach with the algorithmic theory of contiguous relations, which guarantees the applicability of our method for many input sums. In addition, we elaborate new techniques to optimize the underlying key task of our method to compute rational solutions of parameterized linear recurrences.},
number = {24-01},
year = {2024},
month = {January},
note = {arXiv:2401.16314 [cs.SC]},
keywords = {creative telescoping; symbolic summation, hypergeometric multi-sums, contiguous relations, parameterized recurrences, rational solutions},
length = {26},
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)}
}

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]
[bib]
@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}
}
[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]
[bib]
@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}
}
[Banerjee]

2-Elongated Plane Partitions and Powers of 7: The Localization Method Applied to a Genus 1 Congruence Family

K. Banerjee, N.A. Smoot

Technical report no. 23-10 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). August 2023. Licensed under CC BY 4.0 International. [doi] [pdf]
[bib]
@techreport{RISC6713,
author = {K. Banerjee and N.A. Smoot},
title = {{2-Elongated Plane Partitions and Powers of 7: The Localization Method Applied to a Genus 1 Congruence Family}},
language = {english},
abstract = {Over the last century, a large variety of infinite congruence families have been discovered and studied, exhibiting a great variety with respect to their difficulty. Major complicating factors arise from the topology of the associated modular curve: classical techniques are sufficient when the associated curve has cusp count 2 and genus 0. Recent work has led to new techniques that have proven useful when the associated curve has cusp count greater than 2 and genus 0. We show here that these techniques may be adapted in the case of positive genus. In particular, we examine a congruence family over the 2-elongated plane partition diamond counting function $d_2(n)$ by powers of 7, for which the associated modular curve has cusp count 4 and genus 1. We compare our method with other techniques for proving genus 1 congruence families, and present a second congruence family by powers of 7 which we conjecture, and which may be amenable to similar techniques.},
number = {23-10},
year = {2023},
month = {August},
keywords = {Partition congruences, infinite congruence family, modular functions, plane partitions, partition analysis, modular curve, Riemann surface},
length = {35},
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)}
}
[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]
[bib]
@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)}
}
[Buchberger]

Automated Programming, Symbolic computation, Machine Learning: My Personal View

Bruno Buchberger

Ann. Math. Artif. Intell. 91(5), pp. 569-589. 2023. 1012-2443.
[bib]
@article{RISC6895,
author = {Bruno Buchberger},
title = {{Automated Programming, Symbolic computation, Machine Learning: My Personal View}},
language = {english},
journal = {Ann. Math. Artif. Intell.},
volume = {91},
number = {5},
pages = {569--589},
isbn_issn = {1012-2443},
year = {2023},
refereed = {yes},
length = {21}
}
[Buchberger]

International Young Talents Hotspot Austria

Bruno Buchberger

In: Ideen, die gehen!, W. Schüssel, G. Kneifel (ed.), pp. 37-39. 2023. Edition Kleine Zeitung, 20234.
[bib]
@incollection{RISC6896,
author = {Bruno Buchberger},
title = {{International Young Talents Hotspot Austria}},
booktitle = {{Ideen, die gehen!}},
language = {english},
pages = {37--39},
publisher = {Edition Kleine Zeitung},
isbn_issn = {20234},
year = {2023},
editor = {W. Schüssel and G. Kneifel},
refereed = {no},
length = {3}
}
[Buchberger]

Wissenschaft und Meditation: Auf dem Weg zur bewussten Naturgesellschaft

Bruno Buchberger

1st edition, December 2023. Amazon, 979-8868299117.
[bib]
@book{RISC6898,
author = {Bruno Buchberger},
title = {{Wissenschaft und Meditation: Auf dem Weg zur bewussten Naturgesellschaft}},
language = {german},
publisher = {Amazon},
isbn_issn = {979-8868299117},
year = {2023},
month = {December},
edition = {1st},
translation = {0},
length = {184}
}
[Cerna]

Anti-unification and Generalization: a Survey

David Cerna, Temur Kutsia

In: Proceedings of IJCAI 2023 - 32nd International Joint Conference on Artifical Intelligence, Edith Elkind (ed.), pp. 6563-6573. 2023. ijcai.org, ISBN 978-1-956792-03-4 . [doi]
[bib]
@inproceedings{RISC6743,
author = {David Cerna and Temur Kutsia},
title = {{Anti-unification and Generalization: a Survey}},
booktitle = {{Proceedings of IJCAI 2023 - 32nd International Joint Conference on Artifical Intelligence}},
language = {english},
pages = {6563--6573},
publisher = {ijcai.org},
isbn_issn = {ISBN 978-1-956792-03-4 },
year = {2023},
editor = {Edith Elkind},
refereed = {yes},
length = {11},
url = {https://doi.org/10.24963/ijcai.2023/736}
}
[Cerna]

Equational Anti-Unification over Absorption Theories

Mauricio Ayala-Rincón, David M. Cerna, Andres Felipe Gonzalez Barragan, Temur Kutsia

arXiv:2310.11136. Technical report, 2023. [doi]
[bib]
@techreport{RISC6884,
author = {Mauricio Ayala-Rincón and David M. Cerna and Andres Felipe Gonzalez Barragan and Temur Kutsia},
title = {{Equational Anti-Unification over Absorption Theories}},
language = {english},
year = {2023},
institution = {arXiv:2310.11136},
length = {23},
url = {https://doi.org/10.48550/arXiv.2310.11136}
}
[de Freitas]

Analytic results on the massive three-loop form factors: quarkonic contributions

J. Bluemlein, A. De Freitas, P. Marquard, N. Rana, C. Schneider

Physical Review D 108(094003), pp. 1-73. 2023. ISSN 2470-0029. arXiv:2307.02983 [hep-ph]. [doi]
[bib]
@article{RISC6742,
author = {J. Bluemlein and A. De Freitas and P. Marquard and N. Rana and C. Schneider},
title = {{Analytic results on the massive three-loop form factors: quarkonic contributions}},
language = {english},
abstract = {The quarkonic contributions to the three--loop heavy-quark form factors for vector, axial-vector, scalar and pseudoscalar currents are described by closed form difference equations for the expansion coefficients in the limit of small virtualities $q^2/m^2$. A part of the contributions can be solved analytically and expressed in terms of harmonic and cyclotomic harmonic polylogarithms and square-root valued iterated integrals. Other contributions obey equations which are not first--order factorizable. For them still infinite series expansions around the singularities of the form factors can be obtained by matching the expansions at intermediate points and using differential equations which are obeyed directly by the form factors and are derived by guessing algorithms. One may determine all expansion coefficients for $q^2/m^2 rightarrow infty$ analytically in terms of multiple zeta values. By expanding around the threshold and pseudo--threshold, the corresponding constants are multiple zeta values supplemented by a finite amount of new constants, which can be computed at high precision. For a part of these coefficients, the infinite series in front of these constants may be even resummed into harmonic polylogarithms. In this way, one obtains a deeper analytic description of the massive form factors, beyond their pure numerical evaluation. The calculations of these analytic results are based on sophisticated computer algebra techniques. We also compare our results with numerical results in the literature.},
journal = {Physical Review D},
volume = {108},
number = {094003},
pages = {1--73},
isbn_issn = {ISSN 2470-0029},
year = {2023},
note = {arXiv:2307.02983 [hep-ph]},
refereed = {yes},
keywords = {form factor, Feynman diagram, computer algebra, holonomic properties, difference equations, differential equations, symbolic summation, numerical matching, analytic continuation, guessing, PSLQ},
length = {92},
url = {https://www.doi.org/10.1103/PhysRevD.108.094003}
}
[de Freitas]

Recent 3-Loop Heavy Flavor Corrections to Deep-Inelastic Scattering

J. Ablinger, A. Behring, J. Bluemlein, A. De Freitas, A. Goedicke, A. von Manteuffel, C. Schneider, K. Schoenwald

In: Proc. of the 16th International Symposium on Radiative Corrections: Applications of Quantum Field Theory to Phenomenology , Giulio Falcioni (ed.), PoS RADCOR2023/046, pp. 1-7. June 2023. ISSN 1824-8039. arXiv:2306.16550 [hep-ph]. [doi]
[bib]
@inproceedings{RISC6748,
author = {J. Ablinger and A. Behring and J. Bluemlein and A. De Freitas and A. Goedicke and A. von Manteuffel and C. Schneider and K. Schoenwald},
title = {{Recent 3-Loop Heavy Flavor Corrections to Deep-Inelastic Scattering}},
booktitle = {{Proc. of the 16th International Symposium on Radiative Corrections: Applications of Quantum Field Theory to Phenomenology }},
language = {english},
abstract = {We report on recent progress in calculating the three loop QCD corrections of the heavy flavor contributions in deep--inelastic scattering and the massive operator matrix elements of the variable flavor number scheme. Notably we deal with the operator matrix elements $A_{gg,Q}^{(3)}$ and $A_{Qg}^{(3)}$ and technical steps to their calculation. In particular, a new method to obtain the inverse Mellin transform without computing the corresponding $N$--space expressions is discussed.},
series = {PoS},
volume = {RADCOR2023},
number = {046},
pages = {1--7},
isbn_issn = {ISSN 1824-8039},
year = {2023},
month = {June},
note = {arXiv:2306.16550 [hep-ph]},
editor = {Giulio Falcioni},
refereed = {no},
keywords = {deep-inelastic scattering, 3-loop Feynman diagrams, (inverse) Mellin transform, binomial sums},
length = {7},
url = { https://doi.org/10.22323/1.432.0046 }
}
[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]
[bib]
@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)}
}
[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]
[bib]
@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)}
}
[Ehling]

Matching in Quantitative Equational Theories

Georg Ehling, Temur Kutsia

In: UNIF 2023 - 37th International Workshop on Unification, Veena Ravishankar and Christophe Ringeissen (ed.), pp. -. 2023. [url]
[bib]
@inproceedings{RISC6885,
author = {Georg Ehling and Temur Kutsia},
title = {{Matching in Quantitative Equational Theories}},
booktitle = {{UNIF 2023 - 37th International Workshop on Unification}},
language = {english},
pages = {--},
isbn_issn = { },
year = {2023},
editor = {Veena Ravishankar and Christophe Ringeissen},
refereed = {yes},
sponsor = {FWF},
length = {7},
url = {https://inria.hal.science/hal-04128216}
}
[Hoxhaj]

Using Algebraic Geometry to Reconstruct a Darboux Cyclide from a Calibrated Camera Picture

E. Hoxhaj, J.-M. Menjanahary, J. Schicho

J. AAECC, pp. -. 2023. 1432-0622. to appear. [doi]
[bib]
@article{RISC6879,
author = {E. Hoxhaj and J.-M. Menjanahary and J. Schicho},
title = {{Using Algebraic Geometry to Reconstruct a Darboux Cyclide from a Calibrated Camera Picture}},
language = {english},
journal = {J. AAECC},
pages = {--},
isbn_issn = {1432-0622},
year = {2023},
note = {to appear},
refereed = {yes},
length = {19},
url = {https://doi.org/10.1007/s00200-023-00600-y}
}
[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.
[bib]
@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}
}

Loading…