Members
Bruno Buchberger: Founding Chairman 1987-1998
Günter Landsmann
Johann Mitteramskogler
Josef Schicho
Franz Winkler: Chairman 1999-2009
Ongoing Projects
Algebraic Solutions of Fuchsian Differential Equations
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 ...
FirstOrderSolve
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 ...
Publications
2023
Automated Programming, Symbolic computation, Machine Learning: My Personal View
Bruno Buchberger
Ann. Math. Artif. Intell. 91(5), pp. 569-589. 2023. 1012-2443.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}
}
International Young Talents Hotspot Austria
Bruno Buchberger
In: Ideen, die gehen!, W. Schüssel, G. Kneifel (ed.), pp. 37-39. 2023. Edition Kleine Zeitung, 20234.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}
}
Wissenschaft und Meditation: Auf dem Weg zur bewussten Naturgesellschaft
Bruno Buchberger
1st edition, December 2023. Amazon, 979-8868299117.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}
}
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.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}
}
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.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
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]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}
}
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]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}
}
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]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}
}
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.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}
}
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]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
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]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}
}
Combinatorics of Bricard's octahedra
M. Gallet, G. Grasegger, J. Legerský, J. Schicho
Comptes Rendus. Mathématique 359(1), pp. 7-38. 2021. Académie des sciences, Paris, ISSN 1631-073X. [doi]author = {M. Gallet and G. Grasegger and J. Legerský and J. Schicho},
title = {{Combinatorics of Bricard's octahedra}},
language = {english},
journal = {Comptes Rendus. Mathématique},
volume = {359},
number = {1},
pages = {7--38},
publisher = {Académie des sciences, Paris},
isbn_issn = {ISSN 1631-073X},
year = {2021},
refereed = {yes},
length = {32},
url = {https://doi.org/10.5802/crmath.132}
}
On the Existence of Paradoxical Motions of Generically Rigid Graphs on the Sphere
M. Gallet, G. Grasegger, J. Legerský, J. Schicho
SIAM Journal on Discrete Mathematics 35(1), pp. 325-361. 2021. ISSN 0895-4801. [doi]author = {M. Gallet and G. Grasegger and J. Legerský and J. Schicho},
title = {{On the Existence of Paradoxical Motions of Generically Rigid Graphs on the Sphere}},
language = {english},
journal = {SIAM Journal on Discrete Mathematics},
volume = {35},
number = {1},
pages = {325--361},
isbn_issn = {ISSN 0895-4801},
year = {2021},
refereed = {yes},
length = {37},
url = {https://doi.org/10.1137/19M1289467}
}
General solutions of first-order algebraic ODEs in simple constant extensions
Johann J. Mitteramskogler, Franz Winkler
Technical report no. 21-18 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). September 2021. Licensed under CC BY 4.0 International. [doi] [pdf]author = {Johann J. Mitteramskogler and Franz Winkler},
title = {{General solutions of first-order algebraic ODEs in simple constant extensions}},
language = {english},
abstract = {If a first-order algebraic ODE is defined over a certain differential field, then the most elementary solution class, in which one can hope to find a general solution, is given by the adjunction of a single arbitrary constant to this field. Solutions of this type give rise to a particular kind of generic point—a rational parametrization—of an algebraic curve which is associated in a natural way to the ODE’s defining polynomial. As for the opposite direction, we show that a suitable rational parametrization of the associated curve can be extended to a general solution of the ODE if and only if one can find a certain automorphism of the solution field. These automorphisms are determined by linear rational functions, i.e. Möbius transformations. Intrinsic properties of rational parametrizations, in combination with the particular shape of such automorphisms, lead to a number of necessary conditions on the existence of general solutions in this solution class. Furthermore, the desired linear rational function can be determined by solving a simple differential system over the ODE’s field of definition. All results are derived in a purely algebraic fashion and apply to any differential field of characteristic zero with arbitrary derivative operator.},
number = {21-18},
year = {2021},
month = {September},
keywords = {Algebraic ordinary differential equation, general solution, algebraic curve, rational parametrization},
length = {17},
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)}
}
Existence and convergence of Puiseux series solutions for first order autonomous differential equations
J. Cano, S. Falkensteiner, R. Sendra
Journal of Symbolic Computation 108, pp. 137-151. 2021. ISSN 0747-7171. [doi]author = {J. Cano and S. Falkensteiner and R. Sendra},
title = {{Existence and convergence of Puiseux series solutions for first order autonomous differential equations}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {108},
pages = {137--151},
isbn_issn = {ISSN 0747-7171},
year = {2021},
refereed = {yes},
keywords = {Algebraic differential equation, Algebraic curve, Place, Formal Puiseux series solution, Convergent solution},
length = {15},
url = {http://doi.org/10.1016/j.jsc.2020.06.010}
}
Puiseux Series and Algebraic Solutions of First Order Autonomous AODEs - A MAPLE Package
F. Boulier, J. Cano, S. Falkensteiner, R. Sendra
In: Communications in Computer and Information Science, Rob Corless, Jürgen Gerhard and Ilias Kotsireas (ed.), Proceedings of Maple Conference 20201414, pp. 89-103. 2021. Springer, Cham, ISSN 1865-0929. [url]author = {F. Boulier and J. Cano and S. Falkensteiner and R. Sendra},
title = {{Puiseux Series and Algebraic Solutions of First Order Autonomous AODEs - A MAPLE Package}},
booktitle = {{Communications in Computer and Information Science}},
language = {english},
volume = {1414},
pages = {89--103},
publisher = {Springer, Cham},
isbn_issn = {ISSN 1865-0929},
year = {2021},
editor = {Rob Corless and Jürgen Gerhard and Ilias Kotsireas},
refereed = {yes},
keywords = {Maple, Symbolic computation, Algebraic differential equation, Formal Puiseux series solution, Algebraic solution},
length = {15},
conferencename = {Maple Conference 2020},
url = {doi.org/10.1007/978-3-030-81698-8_7}
}
My Life in Computer Algebra
F. Winkler
Technical report no. 21-12 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). June 2021. Licensed under CC BY 4.0 International. [doi] [pdf]author = {F. Winkler},
title = {{My Life in Computer Algebra}},
language = {english},
abstract = {After having spent more than 40 years in Mathematics, and in particular in Computer Algebra, I recollect stages in my scientific career and I explain the connections between my different areas of interest.},
number = {21-12},
year = {2021},
month = {June},
keywords = {computer algebra, biography},
length = {19},
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)}
}
2020
The Sage Package Comb_walks for Walks in the Quarter Plane
Antonio Jiménez-Pastor, Alin Bostan, Frédéric Chyzak, Pierre Lairez
ACM Commun. Comput. Algebra 54(2), pp. 30-38. sep 2020. Association for Computing Machinery, New York, NY, USA, 1932-2240. [doi]author = {Antonio Jiménez-Pastor and Alin Bostan and Frédéric Chyzak and Pierre Lairez},
title = {{The Sage Package Comb_walks for Walks in the Quarter Plane}},
language = {english},
abstract = {We present in this extended abstract a new software designed to work with generating functions that count walks in the quarter plane. With this software we offer a cohesive package that brings together all the required procedures for manipulating these generating functions, as well as a unified interface to deal with them. We also display results that this package offers on a public webpage.},
journal = {ACM Commun. Comput. Algebra},
volume = {54},
number = {2},
pages = {30--38},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
isbn_issn = {1932-2240},
year = {2020},
month = {sep},
refereed = {yes},
keywords = {Sage, D-algebraic functions, generating functions, elliptic functions, lattice walks},
length = {9},
url = {https://doi.org/10.1145/3427218.3427220}
}
Two remarks on sums of squares with rational coefficients
Jose Capco, Claus Scheiderer
Banach Center Publications 121, pp. 25-36. 2020. 0137-6934. [doi]author = {Jose Capco and Claus Scheiderer},
title = {{ Two remarks on sums of squares with rational coefficients}},
language = {english},
journal = {Banach Center Publications},
volume = {121},
pages = {25--36},
isbn_issn = {0137-6934},
year = {2020},
refereed = {yes},
length = {11},
url = {https://doi.org/10.4064/bc121-2}
}
Power Series Solutions of AODEs - Existence, Uniqueness, Convergence and Computation
S. Falkensteiner
RISC Hagenberg, Johannes Kepler University Linz. PhD Thesis. June 2020. Also available as RISC report no. 20-13. [pdf]author = {S. Falkensteiner},
title = {{Power Series Solutions of AODEs - Existence, Uniqueness, Convergence and Computation}},
language = {english},
year = {2020},
month = {June},
note = {Also available as RISC report no. 20-13},
translation = {0},
school = {RISC Hagenberg, Johannes Kepler University Linz},
length = {146}
}