## Members

## Sebastian Falkensteiner

## Günter Landsmann

## Johannes Middeke

## Johann Mitteramskogler

## Markus Rosenkranz

## Franz Winkler

## Ongoing Projects

### Symbolic Solutions of Algebraic Differential Equations [ADE-solve]

Project Lead: Franz Winkler

## Publications

### 2020

[Falkensteiner]

### 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}

}

**phdthesis**{RISC6120,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}

}

[Grasegger]

### 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]@

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}

}

**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}

}

[Grasegger]

### Flexible placements of graphs with rotational symmetry

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

arXiv. Technical report, 2020. [url]@

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}

}

**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}

}

[Grasegger]

### Combinatorics of Bricard’s octahedra

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

arXiv. Technical report, 2020. [url]@

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}

}

**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}

}

[Grasegger]

### 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]@

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}

}

**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}

}

[Grasegger]

### Bracing frameworks consisting of parallelograms

#### G. Grasegger, J. Legerský

arXiv. Technical report, 2020. [url]@

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}

}

**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}

}

[Grasegger]

### Zero-sum cycles in flexible polyhedra

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

arXiv. Technical report, 2020. [url]@

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

title = {{Zero-sum cycles in flexible polyhedra}},

language = {english},

year = {2020},

institution = {arXiv},

length = {16},

url = {https://arxiv.org/abs/2009.14041}

}

**techreport**{RISC6211,author = {M. Gallet and G. Grasegger and J. Legerský and J. Schicho},

title = {{Zero-sum cycles in flexible polyhedra}},

language = {english},

year = {2020},

institution = {arXiv},

length = {16},

url = {https://arxiv.org/abs/2009.14041}

}

[Grasegger]

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

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

Journal of Computational Geometry 11(1), pp. 548-575. 2020. ISSN: 1920-180X. [url]@

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

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

language = {english},

journal = {Journal of Computational Geometry},

volume = {11},

number = {1},

pages = {548--575},

isbn_issn = {ISSN: 1920-180X},

year = {2020},

refereed = {yes},

length = {27},

url = {https://journals.carleton.ca/jocg/index.php/jocg/article/view/495}

}

**article**{RISC6239,author = {G. Grasegger and J. Legerský and J. Schicho},

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

language = {english},

journal = {Journal of Computational Geometry},

volume = {11},

number = {1},

pages = {548--575},

isbn_issn = {ISSN: 1920-180X},

year = {2020},

refereed = {yes},

length = {27},

url = {https://journals.carleton.ca/jocg/index.php/jocg/article/view/495}

}

[Grasegger]

### Counting realizations of {L}aman graphs on the sphere

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

Electronic Journal of Combinatorics 27(2), pp. 1-18. 2020. 1077-8926 . [url]@

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

title = {{Counting realizations of {L}aman graphs on the sphere}},

language = {english},

journal = {Electronic Journal of Combinatorics},

volume = {27},

number = {2},

pages = {1--18},

isbn_issn = {1077-8926 },

year = {2020},

refereed = {yes},

length = {18},

url = {https://arxiv.org/abs/1903.01145}

}

**article**{RISC6243,author = {M. Gallet and G. Grasegger and J. Schicho},

title = {{Counting realizations of {L}aman graphs on the sphere}},

language = {english},

journal = {Electronic Journal of Combinatorics},

volume = {27},

number = {2},

pages = {1--18},

isbn_issn = {1077-8926 },

year = {2020},

refereed = {yes},

length = {18},

url = {https://arxiv.org/abs/1903.01145}

}

[Jimenez Pastor]

### 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]@

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}

}

**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}

}

[Mitteramskogler]

### A comparison of methods for computing rational general solutions of algebraic ODEs

#### Johann J. Mitteramskogler, Franz Winkler

Technical report no. 20-11 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 2020. [pdf]@

author = {Johann J. Mitteramskogler and Franz Winkler},

title = {{A comparison of methods for computing rational general solutions of algebraic ODEs}},

language = {english},

number = {20-11},

year = {2020},

length = {21},

type = {RISC Report Series},

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

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

**techreport**{RISC6135,author = {Johann J. Mitteramskogler and Franz Winkler},

title = {{A comparison of methods for computing rational general solutions of algebraic ODEs}},

language = {english},

number = {20-11},

year = {2020},

length = {21},

type = {RISC Report Series},

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

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}

}

[Mitteramskogler]

### Symbolic solutions of algebraic ODEs - A comparison of methods

#### Franz Winkler, Johann Mitteramskogler

Publications Mathemticae Debrecen, pp. 0-0. 2020. 0.@

author = {Franz Winkler and Johann Mitteramskogler},

title = {{Symbolic solutions of algebraic ODEs -- A comparison of methods}},

language = {english},

journal = {Publications Mathemticae Debrecen},

pages = {0--0},

isbn_issn = {0},

year = {2020},

refereed = {yes},

length = {0}

}

**article**{RISC6253,author = {Franz Winkler and Johann Mitteramskogler},

title = {{Symbolic solutions of algebraic ODEs -- A comparison of methods}},

language = {english},

journal = {Publications Mathemticae Debrecen},

pages = {0--0},

isbn_issn = {0},

year = {2020},

refereed = {yes},

length = {0}

}

[Winkler]

### Symbolic computation in algebra, geometry, and differential equations

#### Franz Winkler

In: Proceedings CAI-2019, , Special issue of "Information and Computation" , pp. 0-0. 2020. 0.@

author = {Franz Winkler},

title = {{Symbolic computation in algebra, geometry, and differential equations}},

booktitle = {{Proceedings CAI-2019}},

language = {english},

series = {Special issue of "Information and Computation"},

pages = {0--0},

isbn_issn = {0},

year = {2020},

editor = {?},

refereed = {yes},

length = {0}

}

**inproceedings**{RISC6252,author = {Franz Winkler},

title = {{Symbolic computation in algebra, geometry, and differential equations}},

booktitle = {{Proceedings CAI-2019}},

language = {english},

series = {Special issue of "Information and Computation"},

pages = {0--0},

isbn_issn = {0},

year = {2020},

editor = {?},

refereed = {yes},

length = {0}

}

### 2019

[Grasegger]

### 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]@

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}

}

**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}

}

[Sendra]

### Solving First Order Autonomous Algebraic Ordinary Differential Equations by Places

#### S. Falkensteiner, R. Sendra

Mathematics in Computer Science 14, pp. 327-337. 12 2019. ISSN 1661-8289. [url]@

author = {S. Falkensteiner and R. Sendra},

title = {{Solving First Order Autonomous Algebraic Ordinary Differential Equations by Places}},

language = {english},

journal = {Mathematics in Computer Science},

volume = {14},

pages = {327--337},

isbn_issn = {ISSN 1661-8289},

year = {2019},

month = {12},

refereed = {yes},

keywords = {Algebraic autonomous differential equation, Algebraic curve, Local parametrization, Place, Formal power series solution, Analytic solution},

length = {11},

url = {https://doi.org/10.1007/s11786-019-00431-6}

}

**article**{RISC6035,author = {S. Falkensteiner and R. Sendra},

title = {{Solving First Order Autonomous Algebraic Ordinary Differential Equations by Places}},

language = {english},

journal = {Mathematics in Computer Science},

volume = {14},

pages = {327--337},

isbn_issn = {ISSN 1661-8289},

year = {2019},

month = {12},

refereed = {yes},

keywords = {Algebraic autonomous differential equation, Algebraic curve, Local parametrization, Place, Formal power series solution, Analytic solution},

length = {11},

url = {https://doi.org/10.1007/s11786-019-00431-6}

}

[Winkler]

### 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.@

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}

}

**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}

}

[Winkler]

### 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.@

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}

}

**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

[Grasegger]

### 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]@

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}

}

**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}

}

[Grasegger]

### 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.@

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}

}

**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}

}

[Grasegger]

### 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]@

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}

}

**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}

}