## Ongoing Projects

### Artin Approximation, Arc-Räume, Auflösung von Singularitäten

### Symbolic-Numeric Techniques for Genus Computation and Parametrization [DK9]

## Software

desing homepage ...

CASA is a special-purpose system for computational algebra and constructive algebraic geometry. The system has been developed since 1990, and is the ongoing product of the Computer Algebra Group under the direction of Prof. Winkler. It is built on the ...

CharSet is an Aldor package written by Christian Aistleitner for differential characteristic set computations. CharSet comes with generic implementations of reduction, Gröbner bases, and differential characteristic set algorithms. Interfaces to the command line, Mathematica and Maple are included. ...

PGB is a software package for computing parametric Gröbner bases and related objects in several domains. It is implemented in the computer algebra system Risa/Asir by Katsusuke Nabeshima. ...

## Publications

### 2021

### On the maximal number of real embeddings of minimally rigid graphs in R2, R3 and S2

#### E. Bartzos, I.Z. Emiris, J. Legerský, E. Tsigaridas

Journal of Symbolic Computation 102, pp. 189-208. 2021. ISSN 0747-7171. [url]**article**{RISC5992,

author = {E. Bartzos and I.Z. Emiris and J. Legerský and E. Tsigaridas},

title = {{On the maximal number of real embeddings of minimally rigid graphs in R2, R3 and S2}},

language = {english},

journal = {Journal of Symbolic Computation},

volume = {102},

pages = {189--208},

isbn_issn = {ISSN 0747-7171},

year = {2021},

refereed = {yes},

length = {20},

url = {https://doi.org/10.1016/j.jsc.2019.10.015}

}

### 2020

### Computing Animations of Linkages with Rotational Symmetry (Media Exposition)

#### Sean Dewar, Georg Grasegger, Jan Legerský

In: 36th International Symposium on Computational Geometry (SoCG 2020), Sergio Cabello and Danny Z. Chen (ed.), Leibniz International Proceedings in Informatics (LIPIcs) 164, pp. 77:1-77:4. 2020. Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, Germany, ISBN 978-3-95977-143-6. [url]**inproceedings**{RISC6128,

author = {Sean Dewar and Georg Grasegger and Jan Legerský},

title = {{Computing Animations of Linkages with Rotational Symmetry (Media Exposition)}},

booktitle = {{36th International Symposium on Computational Geometry (SoCG 2020)}},

language = {english},

series = {Leibniz International Proceedings in Informatics (LIPIcs)},

volume = {164},

pages = {77:1--77:4},

publisher = {Schloss Dagstuhl--Leibniz-Zentrum für Informatik},

address = {Dagstuhl, Germany},

isbn_issn = {ISBN 978-3-95977-143-6},

year = {2020},

editor = {Sergio Cabello and Danny Z. Chen},

refereed = {no},

length = {4},

url = {https://doi.org/10.4230/LIPIcs.SoCG.2020.77}

}

### Graphs with Flexible Labelings allowing Injective Realizations

#### G. Grasegger, J. Legerský, J. Schicho

Discrete Mathematics 343(6), pp. Art. 111713-. 2020. ISSN 0012-365X. [url]**article**{RISC6012,

author = {G. Grasegger and J. Legerský and J. Schicho},

title = {{Graphs with Flexible Labelings allowing Injective Realizations}},

language = {english},

journal = {Discrete Mathematics},

volume = {343},

number = {6},

pages = {Art. 111713--},

isbn_issn = {ISSN 0012-365X},

year = {2020},

refereed = {yes},

length = {14},

url = {https://doi.org/10.1016/j.disc.2019.111713}

}

### On the Classification of Motions of Paradoxically Movable Graphs

#### G. Grasegger, J. Legerský, J. Schicho

arXiv. Technical report, 2020. [url]**techreport**{RISC6092,

author = {G. Grasegger and J. Legerský and J. Schicho},

title = {{On the Classification of Motions of Paradoxically Movable Graphs}},

language = {english},

year = {2020},

institution = {arXiv},

length = {27},

url = {https://arxiv.org/abs/2003.11416}

}

### Flexible placements of graphs with rotational symmetry

#### S.Dewar, G. Grasegger, J. Legerský

arXiv. Technical report, 2020. [url]**techreport**{RISC6091,

author = {S.Dewar and G. Grasegger and J. Legerský},

title = {{Flexible placements of graphs with rotational symmetry}},

language = {english},

year = {2020},

institution = {arXiv},

length = {9},

url = {https://arxiv.org/abs/2003.09328}

}

### Combinatorics of Bricard’s octahedra

#### M. Gallet, G. Grasegger, J. Legerský, J. Schicho

arXiv. Technical report, 2020. [url]**techreport**{RISC6095,

author = {M. Gallet and G. Grasegger and J. Legerský and J. Schicho},

title = {{Combinatorics of Bricard’s octahedra}},

language = {english},

year = {2020},

institution = {arXiv},

length = {40},

url = {https://arxiv.org/pdf/2004.01236.pdf}

}

### FlexRiLoG - A SageMath Package for Motions of Graphs

#### G. Grasegger, J. Legerský

In: Mathematical Software – ICMS 2020, Bigatti A., Carette J., Davenport J., Joswig M., de Wolff T. (ed.), Proceedings of ICMS 2020, Lecture Notes in Computer Science 12097, pp. 442-450. 2020. Springer, Cham, ISBN 978-3-030-52199-8. [url]**inproceedings**{RISC6182,

author = {G. Grasegger and J. Legerský},

title = {{FlexRiLoG - A SageMath Package for Motions of Graphs}},

booktitle = {{ Mathematical Software – ICMS 2020}},

language = {english},

series = {Lecture Notes in Computer Science},

volume = {12097},

pages = {442--450},

publisher = {Springer, Cham},

isbn_issn = {ISBN 978-3-030-52199-8},

year = {2020},

editor = {Bigatti A. and Carette J. and Davenport J. and Joswig M. and de Wolff T.},

refereed = {no},

length = {9},

conferencename = {ICMS 2020},

url = {https://doi.org/10.1007/978-3-030-52200-1_44}

}

### Bracing frameworks consisting of parallelograms

#### G. Grasegger, J. Legerský

arXiv. Technical report, 2020. [url]**techreport**{RISC6203,

author = {G. Grasegger and J. Legerský},

title = {{Bracing frameworks consisting of parallelograms}},

language = {english},

year = {2020},

institution = {arXiv},

length = {20},

url = {https://arxiv.org/abs/2008.11521}

}

### Some structural results on D^n finite functions

#### A. Jimenez-Pastor, V. Pillwein, M.F. Singer

Advances in Applied Mathematics 117, pp. 0-0. June 2020. Elsevier, 0196-8858. [url] [pdf]**article**{RISC6077,

author = {A. Jimenez-Pastor and V. Pillwein and M.F. Singer},

title = {{Some structural results on D^n finite functions}},

language = {english},

abstract = {D-finite (or holonomic) functions satisfy linear differential equations with polynomial coefficients. They form a large class of functions that appear in many applications in Mathematics or Physics. It is well-known that these functions are closed under certain operations and these closure properties can be executed algorithmically. Recently, the notion of D-finite functions has been generalized to differentially definable or Dn-finite functions. Also these functions are closed under operations such as forming (anti)derivative, addition or multiplication and, again, these can be implemented. In this paper we investigate how Dn-finite functions behave under composition and how they are related to algebraic and differentially algebraic functions.},

journal = {Advances in Applied Mathematics},

volume = {117},

pages = {0--0},

publisher = {Elsevier},

isbn_issn = {0196-8858},

year = {2020},

month = {June},

refereed = {yes},

length = {0},

url = {https://doi.org/10.1016/j.aam.2020.102027}

}

### A Reduction Theorem of Certain Relations Modulo p Involving Modular Forms

#### Radu, Cristian-Silviu

In: Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra, in Honour of Peter Paule on his 60th Birthday, V. Pillwein, C. Schneider (ed.), pp. 1-15. 2020. Springer, 978-3-030-44558-4. [pdf]**incollection**{RISC6110,

author = {Radu and Cristian-Silviu},

title = {{A Reduction Theorem of Certain Relations Modulo p Involving Modular Forms}},

booktitle = {{Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra, in Honour of Peter Paule on his 60th Birthday}},

language = {english},

pages = {1--15},

publisher = {Springer},

isbn_issn = {978-3-030-44558-4},

year = {2020},

editor = {V. Pillwein and C. Schneider},

refereed = {yes},

length = {15}

}

### Probabilities of incidence between lines and a plane curve over finite field

#### M. Gallet, M. Makhul, J. Schicho

Finite Fields and Their Applications 61, pp. 1-22. 2020. 1071-5797.**article**{RISC6073,

author = {M. Gallet and M. Makhul and J. Schicho},

title = {{Probabilities of incidence between lines and a plane curve over finite field}},

language = {english},

journal = {Finite Fields and Their Applications},

volume = {61},

pages = {1--22},

isbn_issn = {1071-5797},

year = {2020},

refereed = {yes},

length = {22}

}

### 2019

### Graphs with Flexible Labelings

#### G. Grasegger, J. Legerský, J. Schicho

Discrete & Computational Geometry 62(2), pp. 461-480. 2019. 1432-0444. arXiv:1708.05298. [url]**article**{RISC5803,

author = {G. Grasegger and J. Legerský and J. Schicho},

title = {{Graphs with Flexible Labelings}},

language = {english},

journal = {Discrete & Computational Geometry},

volume = {62},

number = {2},

pages = {461--480},

isbn_issn = {1432-0444},

year = {2019},

note = {arXiv:1708.05298},

refereed = {yes},

length = {20},

url = {https://doi.org/10.1007/s00454-018-0026-9}

}

### On the existence of paradoxical motions of generically rigid graphs on the sphere

#### M. Gallet, G. Grasegger, J. Legerský, J. Schicho

arXiv. Technical report, 2019. [url]**techreport**{RISC5977,

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},

year = {2019},

institution = {arXiv},

length = {40},

url = {https://arxiv.org/abs/1908.00467}

}

### Flexible and Rigid Labelings of Graphs

#### Jan Legerský

Research Institute for Symbolic Computation, Johannes Kepler University Linz. PhD Thesis. 2019. [url] [pdf]**phdthesis**{RISC5941,

author = {Jan Legerský},

title = {{Flexible and Rigid Labelings of Graphs}},

language = {english},

year = {2019},

translation = {0},

school = {Research Institute for Symbolic Computation, Johannes Kepler University Linz},

length = {108},

url = {https://jan.legersky.cz/project/movablegraphs/}

}

### Projective and affine symmetries and equivalences of rational and polynomial surfaces

#### M. Hauer, B. Jüttler, J. Schicho

J. Comp. Appl. Math. 349, pp. 424-437. 2019. 0377-0427.**article**{RISC5875,

author = {M. Hauer and B. Jüttler and J. Schicho},

title = {{Projective and affine symmetries and equivalences of rational and polynomial surfaces}},

language = {english},

journal = {J. Comp. Appl. Math.},

volume = {349},

pages = {424--437},

isbn_issn = {0377-0427},

year = {2019},

refereed = {yes},

length = {14}

}

### The Algebro-Geometric Method for Solving Algebraic Differential Equations - A Survey

#### Franz Winkler

Journal of System Science and Complexity 32, pp. 256-270. 2019. 1009-6124.**article**{RISC6027,

author = {Franz Winkler},

title = {{The Algebro-Geometric Method for Solving Algebraic Differential Equations -- A Survey}},

language = {english},

journal = {Journal of System Science and Complexity},

volume = {32},

pages = {256--270},

isbn_issn = {1009-6124},

year = {2019},

refereed = {yes},

length = {15}

}

### The algebro-geometric solution method for algebraic differential equations - An introduction by examples

#### J.R. Sendra, Franz Winkler

In: Complex Differential and Difference Equations, Proceedings of the School and Conference CDDE, held at Bedlewo, Poland, deGruyter (ed.), pp. 129-146. 2019. Polish Academy of Sciences, deGruyter, 978-3-11-061142-7.**inproceedings**{RISC6033,

author = {J.R. Sendra and Franz Winkler},

title = {{The algebro-geometric solution method for algebraic differential equations -- An introduction by examples}},

booktitle = {{Complex Differential and Difference Equations, Proceedings of the School and Conference CDDE, held at Bedlewo, Poland}},

language = {english},

pages = {129--146},

publisher = {Polish Academy of Sciences, deGruyter},

isbn_issn = {978-3-11-061142-7},

year = {2019},

editor = {deGruyter},

refereed = {yes},

length = {18}

}

### 2018

### Varieties of apolar subschemes of toric surfaces

#### Gallet Matteo, Ranestad Kristian, Villamizar Nelly

Ark. Mat. 56(1), pp. 73-99. 2018. ISSN 0004-2080. [url]**article**{RISC5796,

author = {Gallet Matteo and Ranestad Kristian and Villamizar Nelly},

title = {{Varieties of apolar subschemes of toric surfaces}},

language = {english},

journal = {Ark. Mat.},

volume = {56},

number = {1},

pages = {73--99},

isbn_issn = { ISSN 0004-2080},

year = {2018},

refereed = {yes},

length = {27},

url = {https://doi.org/10.4310/ARKIV.2018.v56.n1.a6}

}

### Rational General Solutions of Systems of First-Order Partial Differential Equations

#### Georg Grasegger, Alberto Lastra, J. Rafael Sendra, Franz Winkler

Journal of Computational and Applied Mathematics 331, pp. 88-103. 2018. ISSN: 0377-0427.**article**{RISC5509,

author = {Georg Grasegger and Alberto Lastra and J. Rafael Sendra and Franz Winkler},

title = {{Rational General Solutions of Systems of First-Order Partial Differential Equations}},

language = {english},

journal = {Journal of Computational and Applied Mathematics},

volume = {331},

pages = {88--103},

isbn_issn = {ISSN: 0377-0427},

year = {2018},

refereed = {yes},

length = {16}

}

### Rational general solutions of systems of first-order algebraic partial differential equations

#### G. Grasegger, A. Lastra, J.R. Sendra, F. Winkler

J. Computational and Applied Mathematics(331), pp. 88-103. 2018. ISSN 0377-0427. [pdf]**article**{RISC5837,

author = {G. Grasegger and A. Lastra and J.R. Sendra and F. Winkler},

title = {{Rational general solutions of systems of first-order algebraic partial differential equations}},

language = {english},

journal = {J. Computational and Applied Mathematics},

number = {331},

pages = {88--103},

isbn_issn = {ISSN 0377-0427},

year = {2018},

refereed = {yes},

length = {16}

}