## Ongoing Projects

### Security and Safety for Shared AI by Deep Model Design (scch)

Project Lead: Josef Schicho

### European Network GRAPES: learninG, pRocessing And oPtimizing shapES [GRAPES]

Project Lead: Josef Schicho

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

Project Lead: Josef Schicho

### Die Algebra der dreidimensionalen Bewegungen

Project Lead: Josef Schicho

## Publications

### 2020

[Grasegger]

### 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]@

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}

}

**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}

}

[Grasegger]

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

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

arXiv. Technical report, 2020. [url]@

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}

}

**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}

}

[Grasegger]

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

#### G. Grasegger, J. Legerský

arXiv. Technical report, 2020. [url]@

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}

}

**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}

}

[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]

### 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}

}

[Schicho]

### 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.@

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}

}

**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

[Capco]

### Sum of Squares over Rationals

#### J. Capco, C. Scheiderer

RISC. Technical report, 2019. [url] [pdf]@

author = {J. Capco and C. Scheiderer},

title = {{Sum of Squares over Rationals}},

language = {english},

abstract = {Recently it has been shown that a multivariate (homogeneous) polynomialwith rational coefficients that can be written as a sum of squares offorms with real coefficients, is not necessarily a sum of squares offorms with rational coefficients. Essentially, only one constructionfor such forms is known, namely taking the $K/\Q$-norm of a sufficientlygeneral form with coefficients in a number field $K$. Whether thisconstruction yields a form with the desired properties depends onGalois-theoretic properties of $K$ that are not yet well understood.We construct new families of examples, and we shed new light on somewell-known open questions.},

year = {2019},

institution = {RISC},

length = {0},

url = {https://www3.risc.jku.at/~jcapco/public_files/ss18/sosq.html}

}

**techreport**{RISC5884,author = {J. Capco and C. Scheiderer},

title = {{Sum of Squares over Rationals}},

language = {english},

abstract = {Recently it has been shown that a multivariate (homogeneous) polynomialwith rational coefficients that can be written as a sum of squares offorms with real coefficients, is not necessarily a sum of squares offorms with rational coefficients. Essentially, only one constructionfor such forms is known, namely taking the $K/\Q$-norm of a sufficientlygeneral form with coefficients in a number field $K$. Whether thisconstruction yields a form with the desired properties depends onGalois-theoretic properties of $K$ that are not yet well understood.We construct new families of examples, and we shed new light on somewell-known open questions.},

year = {2019},

institution = {RISC},

length = {0},

url = {https://www3.risc.jku.at/~jcapco/public_files/ss18/sosq.html}

}

[Grasegger]

### 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]@

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}

}

**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}

}

[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}

}

[Legersky]

### Flexible and Rigid Labelings of Graphs

#### Jan Legerský

Research Institute for Symbolic Computation, Johannes Kepler University Linz. PhD Thesis. 2019. [url] [pdf]@

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/}

}

**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/}

}

[Legersky]

### 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]@

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}

}

**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}

}

[Schicho]

### 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.@

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}

}

**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}

}

### 2018

[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}

}

[Koutschan]

### 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]@

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}

}

**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}

}

[Legersky]

### 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]@

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}

}

**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}

}

[Legersky]

### Minimal non-integer alphabets allowing parallel addition

#### J. Legerský

Acta Polytechnica, Journal of Advanced Engineering 58(5), pp. 285-291. 2018. ISSN 1805-2363. [url]@

author = {J. Legerský},

title = {{Minimal non-integer alphabets allowing parallel addition}},

language = {english},

journal = {Acta Polytechnica, Journal of Advanced Engineering},

volume = {58},

number = {5},

pages = {285--291},

isbn_issn = {ISSN 1805-2363},

year = {2018},

refereed = {yes},

length = {7},

url = {https://doi.org/10.14311/AP.2018.58.0285}

}

**article**{RISC5807,author = {J. Legerský},

title = {{Minimal non-integer alphabets allowing parallel addition}},

language = {english},

journal = {Acta Polytechnica, Journal of Advanced Engineering},

volume = {58},

number = {5},

pages = {285--291},

isbn_issn = {ISSN 1805-2363},

year = {2018},

refereed = {yes},

length = {7},

url = {https://doi.org/10.14311/AP.2018.58.0285}

}

[Schicho]

### On sets defining few ordinary circles

#### A. Lin, M. Makhul, H. N. Mojarrad, J. Schicho, K. Swanepoel, F. de Zeeuw

Discrete and Computational Geometry 59, pp. 59-87. 2018. 0179-5376.@

author = {A. Lin and M. Makhul and H. N. Mojarrad and J. Schicho and K. Swanepoel and F. de Zeeuw},

title = {{On sets defining few ordinary circles}},

language = {english},

journal = {Discrete and Computational Geometry},

volume = {59},

pages = {59--87},

isbn_issn = {0179-5376},

year = {2018},

refereed = {yes},

length = {29}

}

**article**{RISC5535,author = {A. Lin and M. Makhul and H. N. Mojarrad and J. Schicho and K. Swanepoel and F. de Zeeuw},

title = {{On sets defining few ordinary circles}},

language = {english},

journal = {Discrete and Computational Geometry},

volume = {59},

pages = {59--87},

isbn_issn = {0179-5376},

year = {2018},

refereed = {yes},

length = {29}

}

[Schicho]

### Kinematic generation of Darboux cyclides

#### N. Lubbes, J. Schicho

Comp. Aided Geom. Des. 64, pp. -. 2018. 0167-8396.@

author = {N. Lubbes and J. Schicho},

title = {{Kinematic generation of Darboux cyclides}},

language = {english},

journal = {Comp. Aided Geom. Des.},

volume = {64},

pages = {--},

isbn_issn = {0167-8396},

year = {2018},

refereed = {yes},

length = {0}

}

**article**{RISC5876,author = {N. Lubbes and J. Schicho},

title = {{Kinematic generation of Darboux cyclides}},

language = {english},

journal = {Comp. Aided Geom. Des.},

volume = {64},

pages = {--},

isbn_issn = {0167-8396},

year = {2018},

refereed = {yes},

length = {0}

}

[Schicho]

### Kempe's Universality Theorem for Rational Space Curves

#### Z. Li, J. Schicho, H.-P. Schröcker

Found. Comp. Math. 18, pp. 509-536. 2018. 1615-3375.@

author = {Z. Li and J. Schicho and H.-P. Schröcker},

title = {{Kempe's Universality Theorem for Rational Space Curves}},

language = {english},

journal = {Found. Comp. Math.},

volume = {18},

pages = {509--536},

isbn_issn = {1615-3375},

year = {2018},

refereed = {yes},

length = {28}

}

**article**{RISC5879,author = {Z. Li and J. Schicho and H.-P. Schröcker},

title = {{Kempe's Universality Theorem for Rational Space Curves}},

language = {english},

journal = {Found. Comp. Math.},

volume = {18},

pages = {509--536},

isbn_issn = {1615-3375},

year = {2018},

refereed = {yes},

length = {28}

}