Computer Algebra for Nested Sums and Products [FWF SFB F050-09]

Project Lead

Project Duration

01/03/2013 - 31/08/2021

Project URL

Go to Website

Software

PLDESolver

The PLDESolver package is a Mathematica package to find solutions of parameterized linear difference equations in difference rings.

The PLDESolver package by Jakob Ablinger and Carsten Schneider is a Mathematica package that allows to compute solutions of non-degenerated linear difference operators in difference rings with zero-divisors by reducing it to finding solutions in difference rings that are integral ...

More

qFunctions

The qFunctions package is a Mathematica package for q-series and partition theory applications.

The qFunctions package by Jakob Ablinger and Ali K. Uncu is a Mathematica package for q-series and partition theory applications. This package includes both experimental and symbolic tools. The experimental set of elements includes guessers for q-shift equations and recurrences ...

More

Publications

2021

[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]

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}
}
[Schneider]

Iterated integrals over letters induced by quadratic forms

J. Ablinger, J. Blümlein, C. Schneider

Physical Review D to appear, pp. -. 2021. ISSN 2470-0029. arXiv:2103.08330 [hep-th]. [url]
[bib]
@article{RISC6294,
author = {J. Ablinger and J. Blümlein and C. Schneider},
title = {{Iterated integrals over letters induced by quadratic forms}},
language = {english},
journal = {Physical Review D },
volume = {to appear},
pages = {--},
isbn_issn = {ISSN 2470-0029},
year = {2021},
note = {arXiv:2103.08330 [hep-th]},
refereed = {yes},
length = {14},
url = {https://arxiv.org/abs/2103.08330}
}
[Uncu]

qFunctions - A Mathematica package for q-series and partition theory applications

J. Ablinger, A. Uncu

Journal of Symbolic Computation 107, pp. 145-166. 2021. ISSN 0747-7171. arXiv:1910.12410. [url]
[bib]
@article{RISC6299,
author = {J. Ablinger and A. Uncu},
title = {{qFunctions -- A Mathematica package for q-series and partition theory applications}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {107},
pages = {145--166},
isbn_issn = {ISSN 0747-7171},
year = {2021},
note = {arXiv:1910.12410},
refereed = {yes},
length = {22},
url = {https://doi.org/10.1016/j.jsc.2021.02.003}
}

2020

[Schneider]

Three loop QCD corrections to heavy quark form factors

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

In: Proc. ACAT 2019, , J. Phys.: Conf. Ser. 1525/012018, pp. 1-10. 2020. ISSN 1742-6596. arXiv:1905.03728 [hep-ph], doi:10.1088/1742-6596/1525/1/012018. [url]
[bib]
@inproceedings{RISC4826,
author = {J. Ablinger and J. Blümlein and P. Marquard and N. Rana and C. Schneider},
title = {{Three loop QCD corrections to heavy quark form factors}},
booktitle = {{Proc. ACAT 2019}},
language = {english},
series = {J. Phys.: Conf. Ser.},
volume = {1525},
number = {012018},
pages = {1--10},
isbn_issn = {ISSN 1742-6596},
year = {2020},
note = {arXiv:1905.03728 [hep-ph], doi:10.1088/1742-6596/1525/1/012018},
editor = {?},
refereed = {yes},
length = {10},
url = {https://iopscience.iop.org/article/10.1088/1742-6596/1525/1/012018/}
}
[Schneider]

Evaluation of binomial double sums involving absolute values

C. Krattenthaler, C. Schneider

In: Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra, in Honour of Peter Paule on his 60th Birthday, V. Pillwein, C. Schneider (ed.), Texts and Monographs in Symbolic Computuation , pp. 249-295. 2020. Springer, ISBN 978-3-030-44558-4. arXiv:1607.05314 [math.CO]. [url]
[bib]
@incollection{RISC5970,
author = {C. Krattenthaler and C. Schneider},
title = {{Evaluation of binomial double sums involving absolute values}},
booktitle = {{Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra, in Honour of Peter Paule on his 60th Birthday}},
language = {english},
series = {Texts and Monographs in Symbolic Computuation},
pages = {249--295},
publisher = {Springer},
isbn_issn = {ISBN 978-3-030-44558-4},
year = {2020},
note = {arXiv:1607.05314 [math.CO]},
editor = {V. Pillwein and C. Schneider},
refereed = {yes},
length = {47},
url = {https://doi.org/10.1007/978-3-030-44559-1_14}
}
[Schneider]

Representation of hypergeometric products of higher nesting depths in difference rings

E.D. Ocansey, C. Schneider

Technical report no. 20-19 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 2020. arXiv:2011.08775 [cs.SC]. [url] [pdf]
[bib]
@techreport{RISC6221,
author = {E.D. Ocansey and C. Schneider},
title = {{Representation of hypergeometric products of higher nesting depths in difference rings}},
language = {english},
number = {20-19},
year = {2020},
note = {arXiv:2011.08775 [cs.SC]},
length = {48},
url = {https://arxiv.org/abs/2011.08775},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

2019

[Ablinger]

Discovering and Proving Infinite Pochhammer Sum Identities

J. Ablinger

Experimental Mathematics, pp. 1-15. 2019. Taylor & Francis, 10.1080/10586458.2019.1627254. [url]
[bib]
@article{RISC5896,
author = {J. Ablinger},
title = {{Discovering and Proving Infinite Pochhammer Sum Identities}},
language = {english},
journal = {Experimental Mathematics},
pages = {1--15},
publisher = {Taylor & Francis},
isbn_issn = {?},
year = {2019},
note = {10.1080/10586458.2019.1627254},
refereed = {yes},
length = {15},
url = {https://doi.org/10.1080/10586458.2019.1627254}
}
[Berkovich]

Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series Identities

Ali Kemal Uncu, Alexander Berkovich

ArXiv e-prints (accepted), pp. 1-10. 2019. N/A. [url]
[bib]
@article{RISC5801,
author = {Ali Kemal Uncu and Alexander Berkovich},
title = {{Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series Identities }},
language = {english},
abstract = {We will prove an identity involving refined q-trinomial coefficients. We then extend this identity to two infinite families of doubly bounded polynomial identities using transformation properties of the refined q-trinomials in an iterative fashion in the spirit of Bailey chains. One of these two hierarchies contains an identity which is equivalent to Capparelli's first Partition Theorem. },
journal = {ArXiv e-prints (accepted)},
pages = {1--10},
isbn_issn = {N/A},
year = {2019},
refereed = {yes},
length = {10},
url = {https://arxiv.org/abs/1810.12048}
}
[Ocansey]

Difference Ring Algorithms for Nested Products

Evans Doe Ocansey

RISC, Johannes Kepler University. PhD Thesis. November 2019. [pdf]
[bib]
@phdthesis{RISC6199,
author = {Evans Doe Ocansey},
title = {{Difference Ring Algorithms for Nested Products}},
language = {english},
year = {2019},
month = {November},
translation = {0},
school = {RISC, Johannes Kepler University},
length = {178}
}
[Ocansey]

Difference Ring Algorithms for Nested Products

Evans Doe Ocansey

Technical report no. 20-08 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. November 2019.
[bib]
@techreport{RISC6200,
author = {Evans Doe Ocansey},
title = {{Difference Ring Algorithms for Nested Products}},
language = {english},
number = {20-08},
year = {2019},
month = {November},
length = {178},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}
[Uncu]

A Polynomial Identity Implying Schur's Partition Theorem

Ali Kemal Uncu

ArXiv e-prints (submitted), pp. 1-11. 2019. N/A. [url]
[bib]
@article{RISC5898,
author = {Ali Kemal Uncu},
title = {{A Polynomial Identity Implying Schur's Partition Theorem }},
language = {english},
abstract = {We propose and prove a new polynomial identity that implies Schur's partition theorem. We give combinatorial interpretations of some of our expressions in the spirit of Kurşungöz. We also present some related polynomial and q-series identities. },
journal = {ArXiv e-prints (submitted)},
pages = {1--11},
isbn_issn = {N/A},
year = {2019},
refereed = {yes},
length = {11},
url = {https://arxiv.org/abs/1903.01157}
}

2018

[Ablinger]

An Improved Method to Compute the Inverse Mellin Transform of Holonomic Sequences

J. Ablinger

In: Proceedings of "Loops and Legs in Quantum Field Theory - LL 2018, J. Blümlein and P. Marquard (ed.), PoS(LL2018) , pp. 1-10. 2018. ISSN 1824-8039. [url]
[bib]
@inproceedings{RISC5789,
author = {J. Ablinger},
title = {{An Improved Method to Compute the Inverse Mellin Transform of Holonomic Sequences}},
booktitle = {{Proceedings of "Loops and Legs in Quantum Field Theory - LL 2018}},
language = {english},
series = {PoS(LL2018)},
pages = {1--10},
isbn_issn = {ISSN 1824-8039},
year = {2018},
editor = {J. Blümlein and P. Marquard},
refereed = {yes},
length = {10},
url = {https://pos.sissa.it/303/063/pdf}
}
[Berkovich]

Elementary Polynomial Identities Involving q-Trinomial Coefficients

Ali Kemal Uncu, Alexander Berkovich

ArXiv e-prints (submitted), pp. -. 2018. N/A. [url]
[bib]
@article{RISC5791,
author = {Ali Kemal Uncu and Alexander Berkovich},
title = {{Elementary Polynomial Identities Involving q-Trinomial Coefficients }},
language = {english},
journal = {ArXiv e-prints (submitted)},
pages = {--},
isbn_issn = {N/A},
year = {2018},
refereed = {yes},
length = {0},
url = {https://arxiv.org/abs/1810.06497}
}
[Jiu]

The Method of Brackets in Experimental Mathematics

Ivan Gonzalez, Karen Kohl, Lin Jiu, and Victor H. Moll

In: Frontiers in Orthogonal Polynomials and q-Series, Xin Li, Zuhair Nashed (ed.), pp. -. 2018. World Scientific Publishing, 978-981-3228-87-0. [url]
[bib]
@incollection{RISC5497,
author = {Ivan Gonzalez and Karen Kohl and Lin Jiu and and Victor H. Moll},
title = {{The Method of Brackets in Experimental Mathematics}},
booktitle = {{Frontiers in Orthogonal Polynomials and q-Series}},
language = {english},
pages = {--},
publisher = {World Scientific Publishing},
isbn_issn = {978-981-3228-87-0},
year = {2018},
editor = {Xin Li and Zuhair Nashed},
refereed = {no},
length = {0},
url = {http://www.worldscientific.com/worldscibooks/10.1142/10677}
}
[Middeke]

Towards a Direct Method for Finding Hypergeometric Solutions of Linear First Order Recurrence Systems

J. Middeke, C. Schneider

To appear in ACM Communications in Computer Algebra, pp. -. 2018. ISSN 1932-2240. Extended abstract of the poster presentation at 43st International Symposium on Symbolic and Algebraic Computation (ISSAC'18). [pdf] [pdf]
[bib]
@article{RISC5736,
author = {J. Middeke and C.~Schneider},
title = {{Towards a Direct Method for Finding Hypergeometric Solutions of Linear First Order Recurrence Systems}},
language = {english},
journal = {To appear in ACM Communications in Computer Algebra},
pages = {--},
isbn_issn = {ISSN 1932-2240},
year = {2018},
note = {Extended abstract of the poster presentation at 43st International Symposium on Symbolic and Algebraic Computation (ISSAC'18)},
refereed = {yes},
length = {0}
}
[Raab]

Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations

J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, E. Imamoglu, M. van Hoeij A. von Manteuffel, C.G. Raab, C.-S. Radu, C. Schneider

In: Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), A. Hoang, C. Schneider (ed.)PoS (RADCOR2017) 069, pp. 1-13. 2018. ISSN 1824-8039. arXiv:1711.09742 [hep-ph]. [url]
[bib]
@inproceedings{RISC5350,
author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and E. Imamoglu and M. van Hoeij A. von Manteuffel and C.G. Raab and C.-S. Radu and C. Schneider},
title = {{Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations}},
booktitle = {{Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)}},
language = {english},
volume = {PoS (RADCOR2017) 069},
pages = {1--13},
isbn_issn = {ISSN 1824-8039},
year = {2018},
note = {arXiv:1711.09742 [hep-ph]},
editor = {A. Hoang and C. Schneider},
refereed = {no},
length = {13},
url = {https://doi.org/10.22323/1.290.0069 }
}
[Schneider]

Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering: Recent Results

J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider

In: Proceedings of QCDEV2017, L. Gamberg, A. Prokudin, J.W. Qiu and A. Radyushkin (ed.)PoS(QCDEV2017)031 , pp. 1-10. 2018. ISSN 1824-8039. arXiv:1711.07957 [hep-ph]. [url]
[bib]
@inproceedings{RISC5506,
author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. von Manteuffel and C. Schneider},
title = {{Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering: Recent Results}},
booktitle = {{Proceedings of QCDEV2017}},
language = {english},
volume = {PoS(QCDEV2017)031 },
pages = {1--10},
isbn_issn = {ISSN 1824-8039},
year = {2018},
note = {arXiv:1711.07957 [hep-ph]},
editor = {L. Gamberg and A. Prokudin and J.W. Qiu and A. Radyushkin},
refereed = {no},
length = {10},
url = {https://doi.org/10.22323/1.308.0031 }
}
[Schneider]

The massive 3-loop operator matrix elements with two masses and the generalized variable flavor number scheme

J. Ablinger, J. Blümlein, A. De Freitas, A. Goedicke, C. Schneider, K. Schönwald, F. Wißbrock

In: Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), A. Hoang, C. Schneider (ed.)PoS (RADCOR2017) 071, pp. 1-20. 2018. ISSN 1824-8039. arXiv:1712.00745 [hep-ph]. [url]
[bib]
@inproceedings{RISC5513,
author = {J. Ablinger and J. Blümlein and A. De Freitas and A. Goedicke and C. Schneider and K. Schönwald and F. Wißbrock},
title = {{The massive 3-loop operator matrix elements with two masses and the generalized variable flavor number scheme}},
booktitle = {{Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)}},
language = {english},
volume = {PoS (RADCOR2017) 071},
pages = {1--20},
isbn_issn = {ISSN 1824-8039},
year = {2018},
note = { arXiv:1712.00745 [hep-ph]},
editor = {A. Hoang and C. Schneider},
refereed = {no},
length = {20},
url = {https://doi.org/10.22323/1.290.0071 }
}
[Schneider]

Special functions, transcendentals and their numerics

Jakob Ablinger, Johannes Blümlein, Mark Round, Carsten Schneider

In: Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), A. Hoang, C. Schneider (ed.)PoS (RADCOR2017) 010, pp. 1-7. 2018. ISSN 1824-8039. arXiv:1712.08541 [hep-th]. [url]
[bib]
@inproceedings{RISC5521,
author = {Jakob Ablinger and Johannes Blümlein and Mark Round and Carsten Schneider},
title = {{Special functions, transcendentals and their numerics}},
booktitle = {{Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)}},
language = {english},
volume = {PoS (RADCOR2017) 010},
pages = {1--7},
isbn_issn = {ISSN 1824-8039},
year = {2018},
note = { arXiv:1712.08541 [hep-th]},
editor = {A. Hoang and C. Schneider},
refereed = {no},
length = {7},
url = {https://doi.org/10.22323/1.290.0010 }
}

Loading…