## 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

### 2020

### 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}

}

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

#### G. Grasegger, J. Legerský

arXiv. Technical report, 2020. [url]**techreport**{RISC6090,

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

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

language = {english},

year = {2020},

institution = {arXiv},

length = {9},

url = {https://arxiv.org/abs/2003.12029}

}

### 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}

}

### 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}

}

### Graphs with Flexible Labelings allowing Injective Realizations

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

Discrete Mathematics, pp. -. 2019. 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},

pages = {--},

isbn_issn = {ISSN 0012-365X},

year = {2019},

refereed = {yes},

length = {14},

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

}

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

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

Advances in Applied Mathematics, pp. 0-0. 2019. Accepted. [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},

journal = {Advances in Applied Mathematics},

pages = {0--0},

isbn_issn = {?},

year = {2019},

note = {Accepted},

refereed = {yes},

length = {0}

}

### 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/}

}

### 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, pp. -. 2019. 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},

pages = {--},

isbn_issn = {ISSN 0747-7171},

year = {2019},

refereed = {yes},

length = {20},

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

}

### 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}

}

### Deciding the existence of rational general solutions for first-order algebraic ODEs

#### N.T. Vo, G. Grasegger, F. Winkler

Journal of Symbolic Computation(87), pp. 127-139. 2018. ISSN 0747-7171. [pdf]**article**{RISC5838,

author = {N.T. Vo and G. Grasegger and F. Winkler},

title = {{Deciding the existence of rational general solutions for first-order algebraic ODEs}},

language = {english},

journal = {Journal of Symbolic Computation},

number = {87},

pages = {127--139},

isbn_issn = {ISSN 0747-7171},

year = {2018},

refereed = {yes},

length = {13}

}

### The Number of Realizations of a Laman Graph

#### Jose Capco, Matteo Gallet, Georg Grasegger, Christoph Koutschan, Niels Lubbes, Josef Schicho

SIAM Journal on Applied Algebra and Geometry 2(1), pp. 94-125. 2018. 2470-6566. [url]**article**{RISC5700,

author = {Jose Capco and Matteo Gallet and Georg Grasegger and Christoph Koutschan and Niels Lubbes and Josef Schicho},

title = {{The Number of Realizations of a Laman Graph}},

language = {english},

journal = {SIAM Journal on Applied Algebra and Geometry},

volume = {2},

number = {1},

pages = {94--125},

isbn_issn = {2470-6566},

year = {2018},

refereed = {yes},

length = {32},

url = {https://doi.org/10.1137/17M1118312}

}

### On the Maximal Number of Real Embeddings of Spatial Minimally Rigid Graphs

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

In: ISSAC '18 Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation, C. Arreche (ed.), Proceedings of International Symposium on Symbolic and Algebraic Computation 2018, pp. 55-62. 2018. 978-1-4503-5550-6. [url]**inproceedings**{RISC5804,

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

title = {{On the Maximal Number of Real Embeddings of Spatial Minimally Rigid Graphs}},

booktitle = {{ISSAC '18 Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation}},

language = {english},

pages = {55--62},

isbn_issn = {978-1-4503-5550-6},

year = {2018},

editor = {C. Arreche},

refereed = {yes},

length = {8},

conferencename = {International Symposium on Symbolic and Algebraic Computation 2018},

url = {https://doi.org/10.1145/3208976.3208994}

}

### Resultants: Algebraic and Differential

#### S. McCallum, F. Winkler

Technical report no. 18-08 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. August 2018. [pdf]**techreport**{RISC5735,

author = {S. McCallum and F. Winkler},

title = {{Resultants: Algebraic and Differential}},

language = {english},

abstract = {This report summarises ongoing discussions of the authors on the topic of differential resultantswhich have three goals in mind. First, we aim to try to understand existing literature on thetopic. Second, we wish to formulate some interesting questions and research goals based on ourunderstanding of the literature. Third, we would like to advance the subject in one or moredirections, by pursuing some of these questions and research goals. Both authors have somewhatmore background in nondifferential, as distinct from differential, computational algebra. For thisreason, our approach to learning about differential resultants has started with a careful review ofthe corresponding theory of resultants in the purely algebraic (polynomial) case. We try, as faras possible, to adapt and extend our knowledge of purely algebraic resultants to the differentialcase. Overall, we have the hope of helping to clarify, unify and further develop the computationaltheory of differential resultants.},

number = {18-08},

year = {2018},

month = {August},

length = {21},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}