Members
Bruno Buchberger: Founding Chairman 1987-1998
Günter Landsmann
Josef Schicho
Franz Winkler: Chairman 1999-2009
Software
AGADE
A Maple package for computing rational general solutions of first-order algebraic ODEs
The Maple package AGADE implements several methods for computing rational general solutions of first-order algebraic ordinary differential equations and planar rational systems. An advantage of these methods, compared to the standard dsolve-routine in Maple, is that the implemented algorithms provide ...
Authors: Johann Mitteramskogler
MoreSoftware WebsiteFirstOrderSolve
A Maple package for computing local and algebraic solutions of first order autonomous AODEs
This Maple package computes power series, Puiseux series and algebraic solutions of first order autonomous ordinary differential equations where the unknown function and its derivative fulfill a polynomial equation. The standard commands of Maple might not find these solutions and ...
Authors: Sebastian Falkensteiner
MoreSoftware WebsitePublications
2026
[Raab]
Universal truth of operator statements via ideal membership
Georg Regensburger, Clemens Hofstadler, Clemens Raab
Journal of Pure and Applied Algebra 230(108221), pp. 0-0. 2026. 0022-4049. [doi]@article{RISC7252,
author = {Georg Regensburger and Clemens Hofstadler and Clemens Raab},
title = {{Universal truth of operator statements via ideal membership}},
language = {english},
abstract = {We introduce a framework for proving statements about linear operators by verification of ideal membership in a free algebra. More specifically, arbitrary first-order statements about identities of morphisms in preadditive semicategories can be treated. We present a semi-decision procedure for validity of such formulas based on computations with noncommutative polynomials. These algebraic computations automatically incorporate linearity and benefit from efficient ideal membership procedures.In the framework, domains and codomains of operators are modelled using many-sorted first-order logic. To eliminate quantifiers and function symbols from logical formulas, we apply Herbrand's theorem and Ackermann's reduction. The validity of the resulting formulas is shown to be equivalent to finitely many ideal memberships of noncommutative polynomials. We explain all relevant concepts and discuss computational aspects. Furthermore, we illustrate our framework by proving concrete operator statements assisted by our computer algebra software.},
journal = {Journal of Pure and Applied Algebra},
volume = {230},
number = {108221},
pages = {0--0},
isbn_issn = {0022-4049},
year = {2026},
refereed = {yes},
length = {40},
url = {https://doi.org/10.1016/j.jpaa.2026.108221}
}
author = {Georg Regensburger and Clemens Hofstadler and Clemens Raab},
title = {{Universal truth of operator statements via ideal membership}},
language = {english},
abstract = {We introduce a framework for proving statements about linear operators by verification of ideal membership in a free algebra. More specifically, arbitrary first-order statements about identities of morphisms in preadditive semicategories can be treated. We present a semi-decision procedure for validity of such formulas based on computations with noncommutative polynomials. These algebraic computations automatically incorporate linearity and benefit from efficient ideal membership procedures.In the framework, domains and codomains of operators are modelled using many-sorted first-order logic. To eliminate quantifiers and function symbols from logical formulas, we apply Herbrand's theorem and Ackermann's reduction. The validity of the resulting formulas is shown to be equivalent to finitely many ideal memberships of noncommutative polynomials. We explain all relevant concepts and discuss computational aspects. Furthermore, we illustrate our framework by proving concrete operator statements assisted by our computer algebra software.},
journal = {Journal of Pure and Applied Algebra},
volume = {230},
number = {108221},
pages = {0--0},
isbn_issn = {0022-4049},
year = {2026},
refereed = {yes},
length = {40},
url = {https://doi.org/10.1016/j.jpaa.2026.108221}
}
[Regensburger]
Refuting noncommutative ideal memberschip via matrix certificates
Georg Regensburger, Clemens Hofstadler, Peter Krug
In: Proceedings of ISSAC 2026, Christoph Koutschan, Alin Bostan, Clement pernet, Thi Xuan Vu (ed.), pp. 209-218. 2026. 979-8-4007-2595-1. [doi]@inproceedings{RISC7251,
author = {Georg Regensburger and Clemens Hofstadler and Peter Krug},
title = {{Refuting noncommutative ideal memberschip via matrix certificates}},
booktitle = {{Proceedings of ISSAC 2026}},
language = {english},
abstract = {The ideal membership problem in free algebras is undecidable in general. More precisely, while membership can always be verified in finite time (e.g., via noncommutative Gröbner bases), non-membership is undecidable in general.In this work, we introduce matrix certificates for refuting ideal membership of (commutative and) noncommutative polynomials. Such certificates are matrix evaluations that vanish on the generators of an ideal but not on a given candidate polynomial. For commutative polynomials, a perfect Nullstellensatz guarantees the existence of such certificates with commuting square matrices. For noncommutative polynomials, certificates may require non-square matrices or may not exist at all. To handle evaluations on non-square matrices, we use quivers and their matrix representations.We have implemented an approach for finding matrix certificates by ansatz in SageMath and demonstrate its effectiveness on different examples. Our method relies on the ability to efficiently find one (simple) solution to a system of commutative polynomial equations, which we do by combining SAT solving with Hensel lifting. Our experiments suggest that, in practice, ideal (non-)membership can be efficiently decided and certified.},
pages = {209--218},
isbn_issn = {979-8-4007-2595-1},
year = {2026},
editor = {Christoph Koutschan and Alin Bostan and Clement pernet and Thi Xuan Vu},
refereed = {yes},
length = {10},
url = {https://dl.acm.org/doi/10.1145/3815436.3815447}
}
author = {Georg Regensburger and Clemens Hofstadler and Peter Krug},
title = {{Refuting noncommutative ideal memberschip via matrix certificates}},
booktitle = {{Proceedings of ISSAC 2026}},
language = {english},
abstract = {The ideal membership problem in free algebras is undecidable in general. More precisely, while membership can always be verified in finite time (e.g., via noncommutative Gröbner bases), non-membership is undecidable in general.In this work, we introduce matrix certificates for refuting ideal membership of (commutative and) noncommutative polynomials. Such certificates are matrix evaluations that vanish on the generators of an ideal but not on a given candidate polynomial. For commutative polynomials, a perfect Nullstellensatz guarantees the existence of such certificates with commuting square matrices. For noncommutative polynomials, certificates may require non-square matrices or may not exist at all. To handle evaluations on non-square matrices, we use quivers and their matrix representations.We have implemented an approach for finding matrix certificates by ansatz in SageMath and demonstrate its effectiveness on different examples. Our method relies on the ability to efficiently find one (simple) solution to a system of commutative polynomial equations, which we do by combining SAT solving with Hensel lifting. Our experiments suggest that, in practice, ideal (non-)membership can be efficiently decided and certified.},
pages = {209--218},
isbn_issn = {979-8-4007-2595-1},
year = {2026},
editor = {Christoph Koutschan and Alin Bostan and Clement pernet and Thi Xuan Vu},
refereed = {yes},
length = {10},
url = {https://dl.acm.org/doi/10.1145/3815436.3815447}
}
[Regensburger]
Parametrized systems of generalized polynomial inequalities via linear algebra and convex geometry
Georg Regensburger, Stefan Müller
Positivity 30(4), pp. 0-0. 2026. 1385-1292. [url]@article{RISC7253,
author = {Georg Regensburger and Stefan Müller},
title = {{Parametrized systems of generalized polynomial inequalities via linear algebra and convex geometry}},
language = {english},
abstract = {We provide fundamental results on positive solutions to parametrized systems of generalized polynomial inequalities (with real exponents and positive parameters), including generalized polynomial equations. In doing so, we also offer a new perspective on fewnomials and (generalized) mass-action systems. We find that geometric objects, rather than matrices, determine generalized polynomial systems: a bounded set/“polytope” P (arising from the coefficient matrix) and two subspaces representing monomial differences and dependencies (arising from the exponent matrix). The dimension of the latter subspace, the monomial dependency d, is crucial. As our main result, we rewrite polynomial inequalities in terms of d binomial equations on P, involving d monomials in the parameters. In particular, we establish an explicit bijection between the original solution set and the solution set on P via exponentiation. (i) Our results apply to any generalized polynomial system. (ii) The dependency d and the dimension of P indicate the complexity of a system. (iii) Our results are based on methods from linear algebra and convex/polyhedral geometry, and the solution set on P can be further studied using methods from analysis such as sign-characteristic functions (introduced in this work). We illustrate our results (in particular, the relevant geometric objects) through three examples from real fewnomial and reaction network theory. For two mass-action systems, we parametrize the set of equilibria and the region for multistationarity, respectively, and even for univariate trinomials, we offer new insights: We provide a “solution formula” involving discriminants and “roots”.},
journal = {Positivity},
volume = {30},
number = {4},
pages = {0--0},
isbn_issn = {1385-1292},
year = {2026},
refereed = {yes},
length = {26},
url = {https://link.springer.com/article/10.1007/s11117-025-01158-4}
}
author = {Georg Regensburger and Stefan Müller},
title = {{Parametrized systems of generalized polynomial inequalities via linear algebra and convex geometry}},
language = {english},
abstract = {We provide fundamental results on positive solutions to parametrized systems of generalized polynomial inequalities (with real exponents and positive parameters), including generalized polynomial equations. In doing so, we also offer a new perspective on fewnomials and (generalized) mass-action systems. We find that geometric objects, rather than matrices, determine generalized polynomial systems: a bounded set/“polytope” P (arising from the coefficient matrix) and two subspaces representing monomial differences and dependencies (arising from the exponent matrix). The dimension of the latter subspace, the monomial dependency d, is crucial. As our main result, we rewrite polynomial inequalities in terms of d binomial equations on P, involving d monomials in the parameters. In particular, we establish an explicit bijection between the original solution set and the solution set on P via exponentiation. (i) Our results apply to any generalized polynomial system. (ii) The dependency d and the dimension of P indicate the complexity of a system. (iii) Our results are based on methods from linear algebra and convex/polyhedral geometry, and the solution set on P can be further studied using methods from analysis such as sign-characteristic functions (introduced in this work). We illustrate our results (in particular, the relevant geometric objects) through three examples from real fewnomial and reaction network theory. For two mass-action systems, we parametrize the set of equilibria and the region for multistationarity, respectively, and even for univariate trinomials, we offer new insights: We provide a “solution formula” involving discriminants and “roots”.},
journal = {Positivity},
volume = {30},
number = {4},
pages = {0--0},
isbn_issn = {1385-1292},
year = {2026},
refereed = {yes},
length = {26},
url = {https://link.springer.com/article/10.1007/s11117-025-01158-4}
}
[Schneider]
The $q$-extension of iterated integrals and nested sums in quantum field theory
J. Bluemlein, A.M. Gavrilik, O. Mykhailiv, C. Schneider
Technical report no. 26-11 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). August 2026. arXiv:2608.02702[math-ph]. Licensed under CC BY 4.0 International. [doi] [pdf]@techreport{RISC7257,
author = {J. Bluemlein and A.M. Gavrilik and O. Mykhailiv and C. Schneider},
title = {{The $q$-extension of iterated integrals and nested sums in quantum field theory}},
language = {english},
abstract = {Analytic calculations of zero- and single-scale quantities in perturbative quantum fieldtheory result into special numbers and functions, the first of which have been revealed during the last decades. These are generalizations of the polylogarithm in form of Kummer-Poincar'e iterative integrals over special alphabets and extensions thereof.With growing order in the coupling constant, the polylogarithms, Nielsen integrals, the iterated integrals over linear denominator terms, cyclotomic letters, letters induced by quadratic forms, square-root valued letters, and more general functions contribute. For the nested sums we consider nested harmonic sums, generalized harmonic sums,nested sums implied by quadratic forms, cyclotomic harmonic sums, and nested sumscontaining central binomials. We construct the $q$-extensions of these special functions and of the nested sums, which are associated to them by the series expansion at $x=0$, and their Mellin transform in the $q$-free case. These functions are expected to play a role in perturbative calculations in the case of $q$-deformed commutation relations. For the simpler function spaces closed form solutions are presented. For more involvedalphabets we present the algorithmic steps leading to the $q$-extension for the individual cases. We also derive the determining differential and difference equations of these higher transcendental functions. The $q$-extended special functions arequite different form the corresponding $mu$-extended functions.},
number = {26-11},
year = {2026},
month = {August},
note = {arXiv:2608.02702[math-ph]},
keywords = {q-difference equations, q-differential eqations, q-iterative integrals, q-iterative sums, holonomic closure properties, recurrence solving, quantum field theory},
length = {40},
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 = {J. Bluemlein and A.M. Gavrilik and O. Mykhailiv and C. Schneider},
title = {{The $q$-extension of iterated integrals and nested sums in quantum field theory}},
language = {english},
abstract = {Analytic calculations of zero- and single-scale quantities in perturbative quantum fieldtheory result into special numbers and functions, the first of which have been revealed during the last decades. These are generalizations of the polylogarithm in form of Kummer-Poincar'e iterative integrals over special alphabets and extensions thereof.With growing order in the coupling constant, the polylogarithms, Nielsen integrals, the iterated integrals over linear denominator terms, cyclotomic letters, letters induced by quadratic forms, square-root valued letters, and more general functions contribute. For the nested sums we consider nested harmonic sums, generalized harmonic sums,nested sums implied by quadratic forms, cyclotomic harmonic sums, and nested sumscontaining central binomials. We construct the $q$-extensions of these special functions and of the nested sums, which are associated to them by the series expansion at $x=0$, and their Mellin transform in the $q$-free case. These functions are expected to play a role in perturbative calculations in the case of $q$-deformed commutation relations. For the simpler function spaces closed form solutions are presented. For more involvedalphabets we present the algorithmic steps leading to the $q$-extension for the individual cases. We also derive the determining differential and difference equations of these higher transcendental functions. The $q$-extended special functions arequite different form the corresponding $mu$-extended functions.},
number = {26-11},
year = {2026},
month = {August},
note = {arXiv:2608.02702[math-ph]},
keywords = {q-difference equations, q-differential eqations, q-iterative integrals, q-iterative sums, holonomic closure properties, recurrence solving, quantum field theory},
length = {40},
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)}
}
2025
[Chen]
A Unified Reduction for Hypergeometric and $q$-Hypergeometric Creative Telescoping
Shaoshi Chen, Hao Du, Yiman Gao, Hui Huang, Ziming Li
The Ramanujan J. 68(14), pp. 1-39. 2025. ISSN 1572-9303. arXiv:2501.03837 [cs.SC]. [doi] [pdf]@article{RISC7154,
author = {Shaoshi Chen and Hao Du and Yiman Gao and Hui Huang and Ziming Li},
title = {{A Unified Reduction for Hypergeometric and $q$-Hypergeometric Creative Telescoping}},
language = {english},
journal = {The Ramanujan J.},
volume = {68},
number = {14},
pages = {1--39},
isbn_issn = {ISSN 1572-9303},
year = {2025},
note = {arXiv:2501.03837 [cs.SC]},
refereed = {yes},
length = {39},
url = {https://doi.org/10.1007/s11139-025-01164-w}
}
author = {Shaoshi Chen and Hao Du and Yiman Gao and Hui Huang and Ziming Li},
title = {{A Unified Reduction for Hypergeometric and $q$-Hypergeometric Creative Telescoping}},
language = {english},
journal = {The Ramanujan J.},
volume = {68},
number = {14},
pages = {1--39},
isbn_issn = {ISSN 1572-9303},
year = {2025},
note = {arXiv:2501.03837 [cs.SC]},
refereed = {yes},
length = {39},
url = {https://doi.org/10.1007/s11139-025-01164-w}
}
2024
[Buchberger]
Science and Meditation: Creating the Future (English Translation of "Wissenschaft und Meditation")
Bruno Buchberger
1st edition, 2024. Amazon, 979-8332230837.@book{RISC7102,
author = {Bruno Buchberger},
title = {{Science and Meditation: Creating the Future (English Translation of "Wissenschaft und Meditation")}},
language = {english},
publisher = {Amazon},
isbn_issn = { 979-8332230837},
year = {2024},
edition = {1st},
translation = {0},
length = {153}
}
author = {Bruno Buchberger},
title = {{Science and Meditation: Creating the Future (English Translation of "Wissenschaft und Meditation")}},
language = {english},
publisher = {Amazon},
isbn_issn = { 979-8332230837},
year = {2024},
edition = {1st},
translation = {0},
length = {153}
}
[Raab]
The fundamental theorem of calculus in differential rings
Georg Regensburger, Clemens Raab
Advances in Mathematics 447(109676), pp. 0-50. 2024. 0001-8708. [url]@article{RISC7255,
author = {Georg Regensburger and Clemens Raab},
title = {{The fundamental theorem of calculus in differential rings}},
language = {english},
abstract = {In this paper, we study the consequences of the fundamental theorem of calculus from an algebraic point of view. For functions with singularities, this leads to a generalized notion of evaluation. We investigate properties of such integro-differential rings and discuss many examples. We also construct corresponding integro-differential operators and provide normal forms via rewrite rules. They are then used to derive several identities and properties in a purely algebraic way, generalizing well-known results from analysis. In identities like shuffle relations for nested integrals and the Taylor formula, additional terms are obtained that take singularities into account. Another focus lies on treating basics of linear ODEs in this framework of integro-differential operators. These operators can have matrix coefficients, which allow to treat systems of arbitrary size in a unified way. In the appendix, using tensor reduction systems, we give the technical details of normal forms and prove them for operators including other functionals besides evaluation.},
journal = {Advances in Mathematics},
volume = {447},
number = {109676},
pages = {0--50},
isbn_issn = {0001-8708},
year = {2024},
refereed = {yes},
length = {50},
url = {https://www.sciencedirect.com/science/article/pii/S0001870824001919?via%3Dihub}
}
author = {Georg Regensburger and Clemens Raab},
title = {{The fundamental theorem of calculus in differential rings}},
language = {english},
abstract = {In this paper, we study the consequences of the fundamental theorem of calculus from an algebraic point of view. For functions with singularities, this leads to a generalized notion of evaluation. We investigate properties of such integro-differential rings and discuss many examples. We also construct corresponding integro-differential operators and provide normal forms via rewrite rules. They are then used to derive several identities and properties in a purely algebraic way, generalizing well-known results from analysis. In identities like shuffle relations for nested integrals and the Taylor formula, additional terms are obtained that take singularities into account. Another focus lies on treating basics of linear ODEs in this framework of integro-differential operators. These operators can have matrix coefficients, which allow to treat systems of arbitrary size in a unified way. In the appendix, using tensor reduction systems, we give the technical details of normal forms and prove them for operators including other functionals besides evaluation.},
journal = {Advances in Mathematics},
volume = {447},
number = {109676},
pages = {0--50},
isbn_issn = {0001-8708},
year = {2024},
refereed = {yes},
length = {50},
url = {https://www.sciencedirect.com/science/article/pii/S0001870824001919?via%3Dihub}
}
[Regensburger]
A SageMath Package for elementary and sign vectors with applications to chemical reaction networks
Georg Regensburger, Marcus S. Aichmayr, Stefan Müller
In: Proceedings of ICMS 2024, K. Buzzard, A. Dickenstein, B. Eick, A. Leykin, Y. Ren (ed.), Proceedings of ICMS 202414749, pp. 155-164. 2024. Springer, Cham, 978-3-031-64528-0. [url]@inproceedings{RISC7254,
author = {Georg Regensburger and Marcus S. Aichmayr and Stefan Müller},
title = {{A SageMath Package for elementary and sign vectors with applications to chemical reaction networks}},
booktitle = {{Proceedings of ICMS 2024}},
language = {english},
volume = {14749},
pages = {155--164},
publisher = {Springer, Cham},
isbn_issn = {978-3-031-64528-0},
year = {2024},
editor = {K. Buzzard and A. Dickenstein and B. Eick and A. Leykin and Y. Ren},
refereed = {yes},
length = {10},
conferencename = {ICMS 2024},
url = {https://link.springer.com/chapter/10.1007/978-3-031-64529-7_17}
}
author = {Georg Regensburger and Marcus S. Aichmayr and Stefan Müller},
title = {{A SageMath Package for elementary and sign vectors with applications to chemical reaction networks}},
booktitle = {{Proceedings of ICMS 2024}},
language = {english},
volume = {14749},
pages = {155--164},
publisher = {Springer, Cham},
isbn_issn = {978-3-031-64528-0},
year = {2024},
editor = {K. Buzzard and A. Dickenstein and B. Eick and A. Leykin and Y. Ren},
refereed = {yes},
length = {10},
conferencename = {ICMS 2024},
url = {https://link.springer.com/chapter/10.1007/978-3-031-64529-7_17}
}
[Regensburger]
Sufficient Conditions for Linear Stability of Complex-Balanced Equilibria in Generalized Mass-Action Systems
Georg Regensburger, Stefan Müller
SIAM Journal on Applied Dynamical Systems 23, pp. 325-357. 2024. 1536-0040. [doi]@article{RISC7256,
author = {Georg Regensburger and Stefan Müller},
title = {{Sufficient Conditions for Linear Stability of Complex-Balanced Equilibria in Generalized Mass-Action Systems}},
language = {english},
abstract = {Generalized mass-action systems are power-law dynamical systems arising from chemical reaction networks. Essentially, every nonnegative ODE model used in chemistry and biology (for example, in ecology and epidemiology) and even in economics and engineering can be written in this form. Previous results have focused on existence and uniqueness of special steady states (complex-balanced equilibria) for all rate constants, thereby ruling out multiple (special) steady states. Recently, necessary conditions for linear stability have been obtained. In this work, we provide sufficient conditions for the linear stability of complex-balanced equilibria for all rate constants (and also for the nonexistence of other steady states). In particular, via sign vector conditions (on the stoichiometric coefficients and kinetic orders), we guarantee that the Jacobian matrix is a (P)-matrix. Technically, we use a new decomposition of the graph Laplacian which allows us to consider orders of (generalized) monomials. Alternatively, we use cycle decomposition which allows a linear parametrization of all Jacobian matrices. In any case, we guarantee stability without explicit computation of steady states. We illustrate our results in examples from chemistry and biology: generalized Lotka–Volterra systems and SIR models, a two-component signaling system, and an enzymatic futile cycle.},
journal = {SIAM Journal on Applied Dynamical Systems},
volume = {23},
pages = {325--357},
isbn_issn = {1536-0040},
year = {2024},
refereed = {yes},
length = {33},
url = {https://epubs.siam.org/doi/10.1137/22M154260X}
}
author = {Georg Regensburger and Stefan Müller},
title = {{Sufficient Conditions for Linear Stability of Complex-Balanced Equilibria in Generalized Mass-Action Systems}},
language = {english},
abstract = {Generalized mass-action systems are power-law dynamical systems arising from chemical reaction networks. Essentially, every nonnegative ODE model used in chemistry and biology (for example, in ecology and epidemiology) and even in economics and engineering can be written in this form. Previous results have focused on existence and uniqueness of special steady states (complex-balanced equilibria) for all rate constants, thereby ruling out multiple (special) steady states. Recently, necessary conditions for linear stability have been obtained. In this work, we provide sufficient conditions for the linear stability of complex-balanced equilibria for all rate constants (and also for the nonexistence of other steady states). In particular, via sign vector conditions (on the stoichiometric coefficients and kinetic orders), we guarantee that the Jacobian matrix is a (P)-matrix. Technically, we use a new decomposition of the graph Laplacian which allows us to consider orders of (generalized) monomials. Alternatively, we use cycle decomposition which allows a linear parametrization of all Jacobian matrices. In any case, we guarantee stability without explicit computation of steady states. We illustrate our results in examples from chemistry and biology: generalized Lotka–Volterra systems and SIR models, a two-component signaling system, and an enzymatic futile cycle.},
journal = {SIAM Journal on Applied Dynamical Systems},
volume = {23},
pages = {325--357},
isbn_issn = {1536-0040},
year = {2024},
refereed = {yes},
length = {33},
url = {https://epubs.siam.org/doi/10.1137/22M154260X}
}
2023
[Buchberger]
Automated Programming, Symbolic computation, Machine Learning: My Personal View
Bruno Buchberger
Ann. Math. Artif. Intell. 91(5), pp. 569-589. 2023. 1012-2443.@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}
}
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.@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}
}
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.@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}
}
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}
}
[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}
}
2022
[Falkensteiner]
On Initials and the Fundamental Theorem of Tropical Partial Differential Geometry
S. Falkensteiner, C. Garay-Lopez, M. Haiech, M. P. Noordman, F. Boulier, Z. Toghani
Journal of Symbolic Computation 115, pp. 53-73. 2022. ISSN: 0747-7171. [doi]@article{RISC6335,
author = {S. Falkensteiner and C. Garay-Lopez and M. Haiech and M. P. Noordman and F. Boulier and Z. Toghani},
title = {{On Initials and the Fundamental Theorem of Tropical Partial Differential Geometry}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {115},
pages = {53--73},
isbn_issn = {ISSN: 0747-7171},
year = {2022},
refereed = {yes},
keywords = {Differential Algebra, Tropical Differential Algebraic Geometry, Power Series Solutions, Newton Polyhedra, Arc Spaces, Tropical Differential Equations, Initial forms of Differential Polynomials},
length = {21},
url = {https://doi.org/10.1016/j.jsc.2022.08.005}
}
author = {S. Falkensteiner and C. Garay-Lopez and M. Haiech and M. P. Noordman and F. Boulier and Z. Toghani},
title = {{On Initials and the Fundamental Theorem of Tropical Partial Differential Geometry}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {115},
pages = {53--73},
isbn_issn = {ISSN: 0747-7171},
year = {2022},
refereed = {yes},
keywords = {Differential Algebra, Tropical Differential Algebraic Geometry, Power Series Solutions, Newton Polyhedra, Arc Spaces, Tropical Differential Equations, Initial forms of Differential Polynomials},
length = {21},
url = {https://doi.org/10.1016/j.jsc.2022.08.005}
}
[Falkensteiner]
On Formal Power Series Solutions of Algebraic Ordinary Differential Equations
S. Falkensteiner, Yi Zhang, N. Thieu Vo
Mediterranean Journal of Mathematics 19(74), pp. 1-16. March 2022. ISSN 1660-5446. [doi]@article{RISC6490,
author = {S. Falkensteiner and Yi Zhang and N. Thieu Vo},
title = {{On Formal Power Series Solutions of Algebraic Ordinary Differential Equations}},
language = {english},
journal = {Mediterranean Journal of Mathematics},
volume = {19},
number = {74},
pages = {1--16},
isbn_issn = {ISSN 1660-5446},
year = {2022},
month = {March},
refereed = {yes},
keywords = {Formal power series, algebraic differential equation.},
length = {16},
url = {https://doi.org/10.1007/s00009-022-01984-w}
}
author = {S. Falkensteiner and Yi Zhang and N. Thieu Vo},
title = {{On Formal Power Series Solutions of Algebraic Ordinary Differential Equations}},
language = {english},
journal = {Mediterranean Journal of Mathematics},
volume = {19},
number = {74},
pages = {1--16},
isbn_issn = {ISSN 1660-5446},
year = {2022},
month = {March},
refereed = {yes},
keywords = {Formal power series, algebraic differential equation.},
length = {16},
url = {https://doi.org/10.1007/s00009-022-01984-w}
}
[Falkensteiner]
Puiseux Series Solutions with Real or Rational Coefficients of First Order Autonomous AODEs
S. Falkensteiner
In: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, Amir Hashemi (ed.), Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC), ISSAC '22 , pp. 63-71. 2022. Association for Computing Machinery, ISBN 9781450386883. [doi]@inproceedings{RISC6585,
author = {S. Falkensteiner},
title = {{Puiseux Series Solutions with Real or Rational Coefficients of First Order Autonomous AODEs}},
booktitle = {{Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation}},
language = {english},
series = {ISSAC '22},
pages = {63--71},
publisher = {Association for Computing Machinery},
isbn_issn = {ISBN 9781450386883},
year = {2022},
editor = {Amir Hashemi},
refereed = {yes},
length = {9},
conferencename = {International Symposium on Symbolic and Algebraic Computation (ISSAC)},
url = {https://doi.org/10.1145/3476446.3536185}
}
author = {S. Falkensteiner},
title = {{Puiseux Series Solutions with Real or Rational Coefficients of First Order Autonomous AODEs}},
booktitle = {{Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation}},
language = {english},
series = {ISSAC '22},
pages = {63--71},
publisher = {Association for Computing Machinery},
isbn_issn = {ISBN 9781450386883},
year = {2022},
editor = {Amir Hashemi},
refereed = {yes},
length = {9},
conferencename = {International Symposium on Symbolic and Algebraic Computation (ISSAC)},
url = {https://doi.org/10.1145/3476446.3536185}
}
[Mitteramskogler]
Symbolic solutions of algebraic ODEs - A comparison of methods
J. J. Mitteramskogler, F. Winkler
Publicationes Mathematicae Debrecen 100(1-2), pp. 143-166. 2022. 0033-3883.@article{RISC6673,
author = {J. J. Mitteramskogler and F. Winkler},
title = {{Symbolic solutions of algebraic ODEs -- A comparison of methods}},
language = {english},
journal = {Publicationes Mathematicae Debrecen},
volume = {100},
number = {1-2},
pages = {143--166},
isbn_issn = {0033-3883},
year = {2022},
refereed = {yes},
length = {23}
}
author = {J. J. Mitteramskogler and F. Winkler},
title = {{Symbolic solutions of algebraic ODEs -- A comparison of methods}},
language = {english},
journal = {Publicationes Mathematicae Debrecen},
volume = {100},
number = {1-2},
pages = {143--166},
isbn_issn = {0033-3883},
year = {2022},
refereed = {yes},
length = {23}
}
[Sendra]
Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables
J. Cano, S. Falkensteiner, D. Robertz, R. Sendra
Journal of Symbolic Computation 114, pp. 1-17. 2022. ISSN 1095-855X. [doi]@article{RISC6501,
author = {J. Cano and S. Falkensteiner and D. Robertz and R. Sendra},
title = {{Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {114},
pages = {1--17},
isbn_issn = {ISSN 1095-855X},
year = {2022},
refereed = {yes},
length = {17},
url = {http://doi.org/10.1016/j.jsc.2022.04.012}
}
author = {J. Cano and S. Falkensteiner and D. Robertz and R. Sendra},
title = {{Algebraic and Puiseux series solutions of systems of autonomous algebraic ODEs of dimension one in several variables}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {114},
pages = {1--17},
isbn_issn = {ISSN 1095-855X},
year = {2022},
refereed = {yes},
length = {17},
url = {http://doi.org/10.1016/j.jsc.2022.04.012}
}
2021
[Falkensteiner]
On The Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry
F. Boulier, S. Falkensteiner, M.P. Noordman, O.L. Sanchez
In: International Workshop on Computer Algebra in Scientific Computing, F. Boulier, M. England, T. Sadykov, E. Vorozhtsov (ed.), Proceedings of Computer Algebra in Scientific Computing, pp. 62-77. 2021. Springer, ISSN 0302-9743. [doi]@inproceedings{RISC6337,
author = {F. Boulier and S. Falkensteiner and M.P. Noordman and O.L. Sanchez},
title = {{On The Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry}},
booktitle = {{International Workshop on Computer Algebra in Scientific Computing}},
language = {english},
pages = {62--77},
publisher = {Springer},
isbn_issn = {ISSN 0302-9743},
year = {2021},
editor = {F. Boulier and M. England and T. Sadykov and E. Vorozhtsov},
refereed = {yes},
length = {16},
conferencename = {Computer Algebra in Scientific Computing},
url = {https://doi.org/10.1007/978-3-030-85165-1_5}
}
author = {F. Boulier and S. Falkensteiner and M.P. Noordman and O.L. Sanchez},
title = {{On The Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry}},
booktitle = {{International Workshop on Computer Algebra in Scientific Computing}},
language = {english},
pages = {62--77},
publisher = {Springer},
isbn_issn = {ISSN 0302-9743},
year = {2021},
editor = {F. Boulier and M. England and T. Sadykov and E. Vorozhtsov},
refereed = {yes},
length = {16},
conferencename = {Computer Algebra in Scientific Computing},
url = {https://doi.org/10.1007/978-3-030-85165-1_5}
}