Univ.-Prof. DI.Dr. Franz Winkler

Research Area

Computer Algebra, Constructive Algebraic Geometry

Office

Schloss Hagenberg
A-4232 Hagenberg im Mühlkreis

Room: 2.5-1

Postal Adress

Research Institute for Symbolic Computation
Johannes Kepler University
Altenberger Straße 69
A-4040 Linz, Austria

Courses

Course Id	Title	Registration	Type	Hours	Teachers	Rhythm
326.007 (2018W)	Computer Algebra Further information	Register	VL	2,0	Franz Winkler	Weekly
326.017 (2018W)	Linear algebra for physicists Further information	Register	VL	4,0	Franz Winkler	Weekly
326.0ZZ (2018W)	Seminar for graduate and doctoral students Winter Semester 2018/19 Further information	Register	SE	2,0	Franz Winkler	Weekly
326.CA1 (2018W)	Seminar symbolic computation Computer-algebra I Further information	Register	SE	2,0	Franz Winkler	Weekly

Content provided by KUSSS, Johannes Kepler University Linz | E-Mail

Software

CASA

Computer Algebra System for Algebraic Geometry

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 ...

Authors: Franz Winkler

More Software Website

Publications

2018

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.

[bib]

@article{RISC5589,
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},
volume = {87},
pages = {127--139},
isbn_issn = {ISSN 0747-7171},
year = {2018},
refereed = {yes},
length = {12}
}

2016

A solution method for autonomous first-order algebraic partial differential equations

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

Journal of Computational and Applied Mathematics 300, pp. 119-133. 2016. 0377-0427. [url]

[bib]

@article{RISC5202,
author = {G. Grasegger and A. Lastra and J.R. Sendra and F. Winkler},
title = {{A solution method for autonomous first-order algebraic partial differential equations}},
language = {english},
journal = {Journal of Computational and Applied Mathematics},
volume = {300},
pages = {119--133},
isbn_issn = {0377-0427},
year = {2016},
refereed = {yes},
length = {15},
url = {http://dx.doi.org/10.1016/j.cam.2015.12.030}
}

A decision algorithm for rational general solutions of first-order algebraic ODEs

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

In: Proceedings XV Encuentro de Algebra Computacional y Aplicaciones (EACA 2016), Universidad de la Rioja, J. Heras and A. Romero (eds.) (ed.), pp. 101-104. 2016. 978-84-608-9024-9.

[bib]

@inproceedings{RISC5400,
author = {G. Grasegger and N.T. Vo and F. Winkler},
title = {{A decision algorithm for rational general solutions of first-order algebraic ODEs}},
booktitle = {{Proceedings XV Encuentro de Algebra Computacional y Aplicaciones (EACA 2016)}},
language = {english},
pages = {101--104},
isbn_issn = {978-84-608-9024-9},
year = {2016},
editor = {Universidad de la Rioja and J. Heras and A. Romero (eds.)},
refereed = {yes},
length = {4}
}

2015

Symbolic Solutions of First-Order Algebraic ODEs

G. Grasegger, F. Winkler

In: Computer algebra and polynomials, J. Gutierrez, J. Schicho, M. Weimann (ed.), Lecture Notes in Computer Science 8942, pp. 94-104. 2015. Springer International Publishing, ISSN 0302-9743. [url]

[bib]

@inproceedings{RISC5018,
author = {G. Grasegger and F. Winkler},
title = {{Symbolic Solutions of First-Order Algebraic ODEs}},
booktitle = {{Computer algebra and polynomials}},
language = {english},
series = {Lecture Notes in Computer Science},
volume = {8942},
pages = {94--104},
publisher = {Springer International Publishing},
isbn_issn = {ISSN 0302-9743},
year = {2015},
editor = {J. Gutierrez and J. Schicho and M. Weimann},
refereed = {yes},
length = {11},
url = {http://dx.doi.org/10.1007/978-3-319-15081-9_5}
}

Algebraic General Solutions of First Order Algebraic ODEs

N. T. Vo, F. Winkler

In: Computer Algebra in Scientific Computing, Vladimir P. Gerdt et. al. (ed.), Lecture Notes in Computer Science 9301, pp. 479-492. 2015. Springer International Publishing, ISSN 0302-9743. [url]

[bib]

@inproceedings{RISC5194,
author = {N. T. Vo and F. Winkler},
title = {{Algebraic General Solutions of First Order Algebraic ODEs}},
booktitle = {{Computer Algebra in Scientific Computing}},
language = {english},
abstract = {In this paper we consider the class of algebraic ordinary differential equations (AODEs), the class of planar rational systems, and discuss their algebraic general solutions. We establish for each parametrizable first order AODE a planar rational system, the associated system, such that one can compute algebraic general solutions of the one from the other and vice versa. For the class of planar rational systems, an algorithm for computing their explicit algebraic general solutions with a given rational first integral is presented. Finally an algorithm for determining an algebraic general solution of degree less than a given positive integer of parametrizable first order AODEs is proposed.},
series = {Lecture Notes in Computer Science},
volume = {9301},
pages = {479--492},
publisher = {Springer International Publishing},
isbn_issn = {ISSN 0302-9743},
year = {2015},
editor = {Vladimir P. Gerdt et. al.},
refereed = {yes},
length = {14},
url = {http://link.springer.com/content/pdf/10.1007%2F978-3-319-24021-3_35.pdf}
}

Rational general solutions of systems of autonomous ordinary differential equations of algebro-geometric dimension one

A. Lastra, J.R. Sendra, L.X.C. Ngô, F. Winkler

Publ.Math.Debrecen(86/1-2), pp. 49-69. 2015. 0033-3883.

[bib]

@article{RISC5204,
author = {A. Lastra and J.R. Sendra and L.X.C. Ngô and F. Winkler},
title = {{Rational general solutions of systems of autonomous ordinary differential equations of algebro-geometric dimension one}},
language = {english},
journal = {Publ.Math.Debrecen},
number = {86/1-2},
pages = {49--69},
isbn_issn = {0033-3883},
year = {2015},
refereed = {yes},
length = {21}
}

Birational transformations preserving rational solutions of algebraic ordinary differential equations

L.X.C. Ngô, J.R. Sendra, F. Winkler

J. Computational and Applied Mathematics(286), pp. 114-127. 2015. 0377-0427.

[bib]

@article{RISC5205,
author = {L.X.C. Ngô and J.R. Sendra and F. Winkler},
title = {{Birational transformations preserving rational solutions of algebraic ordinary differential equations}},
language = {english},
journal = {J. Computational and Applied Mathematics},
number = {286},
pages = {114--127},
isbn_issn = {0377-0427},
year = {2015},
refereed = {yes},
length = {14}
}

2014

On Symbolic Solutions of Algebraic Partial Differential Equations

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

In: Computer Algebra in Scientific Computing, V.P. Gerdt et al. (ed.), Lecture Notes in Computer Science 8660, pp. 111-120. 2014. Springer International Publishing, ISSN 0302-9743. [url]

[bib]

@inproceedings{RISC5017,
author = {G. Grasegger and A. Lastra and J.R. Sendra and F. Winkler},
title = {{On Symbolic Solutions of Algebraic Partial Differential Equations}},
booktitle = {{Computer Algebra in Scientific Computing}},
language = {english},
series = {Lecture Notes in Computer Science},
volume = {8660},
pages = {111--120},
publisher = {Springer International Publishing},
isbn_issn = {ISSN 0302-9743},
year = {2014},
editor = {V.P. Gerdt et al.},
refereed = {yes},
length = {11},
url = {http://link.springer.com/content/pdf/10.1007%2F978-3-319-10515-4_9.pdf}
}

Rational solutions and beyond

Winkler Franz

Southeast Asian Bulletin of Mathematics(38), pp. 153-162. 2014. 0129-2021.

[bib]

@article{RISC5103,
author = {Winkler Franz},
title = {{Rational solutions and beyond}},
language = {english},
journal = {Southeast Asian Bulletin of Mathematics},
number = {38},
pages = {153--162},
isbn_issn = {0129-2021},
year = {2014},
refereed = {yes},
length = {9}
}

2013

Rational general solutions of higher order algebraic ODEs

Y. Huang, L.X.C. Ngo, F. Winkler

J. Systems Science and Complexity (JSSC) 26/2, pp. 261-280. 2013. 1009-6124.

[bib]

@article{RISC4640,
author = {Y. Huang and L.X.C. Ngo and F. Winkler},
title = {{Rational general solutions of higher order algebraic ODEs}},
language = {english},
journal = {J. Systems Science and Complexity (JSSC)},
volume = {26/2},
pages = {261--280},
isbn_issn = {1009-6124},
year = {2013},
refereed = {yes},
length = {20}
}

Rational general solutions of trivariate rational systems of autonomous ODEs

Y. Huang, L.X.C. Ngo, F. Winkler

Mathematics in Computer Science 6/4, pp. 361-374. 2013. 1661-8270.

[bib]

@article{RISC4641,
author = {Y. Huang and L.X.C. Ngo and F. Winkler},
title = {{Rational general solutions of trivariate rational systems of autonomous ODEs}},
language = {english},
journal = {Mathematics in Computer Science},
volume = {6/4},
pages = {361--374},
isbn_issn = {1661-8270},
year = {2013},
refereed = {yes},
length = {14}
}

2012

Classification of algebraic ODEs with respect to rational solvability

L.X.C. Ngo, J.R. Sendra, F. Winkler

Computational Algebraic and Analytic Geometry, Contemporary Mathematics(572), pp. 193-210. 2012. AMS, 0271-4132.

[bib]

@article{RISC4637,
author = {L.X.C. Ngo and J.R. Sendra and F. Winkler},
title = {{Classification of algebraic ODEs with respect to rational solvability}},
language = {english},
journal = {Computational Algebraic and Analytic Geometry, Contemporary Mathematics},
number = {572},
pages = {193--210},
publisher = {AMS},
isbn_issn = {0271-4132},
year = {2012},
refereed = {yes},
length = {18}
}

The role of Symbolic Computation in Mathematics

F. Winkler

In: Proceedings XIII Encuentro de Algebra Computacional y Aplicaciones (EACA 2012), J.R. Sendra and C. Villarino (ed.), pp. 33-34. 2012. 978-84-8138-770-4.

[bib]

@inproceedings{RISC4638,
author = {F. Winkler},
title = {{The role of Symbolic Computation in Mathematics}},
booktitle = {{Proceedings XIII Encuentro de Algebra Computacional y Aplicaciones (EACA 2012)}},
language = {english},
pages = {33--34},
isbn_issn = {978-84-8138-770-4},
year = {2012},
editor = {J.R. Sendra and C. Villarino},
refereed = {yes},
length = {2}
}

Computer algebra methods for pattern recognition: systems with complex order

F. Winkler, M. Hudayberdiev, G. Judakova

In: Proceedings INTELS 2012 (Moscow), - (ed.), Proceedings of INTELS 2012, pp. 148-150. 2012. 978-5-93347-432-6.

[bib]

@inproceedings{RISC4639,
author = {F. Winkler and M. Hudayberdiev and G. Judakova},
title = {{Computer algebra methods for pattern recognition: systems with complex order}},
booktitle = {{Proceedings INTELS 2012 (Moscow)}},
language = {english},
pages = {148--150},
isbn_issn = {978-5-93347-432-6},
year = {2012},
editor = {-},
refereed = {yes},
length = {3},
conferencename = {INTELS 2012}
}

2011

Rational general solutions of planar rational systems of autonomous ODEs

L.X.C Ngo, F. Winkler

Journal of Symbolic Computation 46(10), pp. 1173-1186. 2011. Research Institute for Symbolic Computation, ISSN: 0747-7171. [url]

[bib]

@article{RISC4381,
author = {L.X.C Ngo and F. Winkler},
title = {{Rational general solutions of planar rational systems of autonomous ODEs}},
language = {english},
abstract = {In this paper, we provide an algorithm to compute explicit rational solutions of a rational system of autonomous ordinary differential equations (ODEs) from its rational invariant algebraic curves. The method is based on the proper rational parametrization of these curves and the fact that by linear reparametrizations, we can find the rational solutions of the given system of ODEs. Moreover, if the system has a rational first integral, we can decide whether it has a rational general solution and compute it in the affirmative case.},
journal = {Journal of Symbolic Computation},
volume = {46},
number = {10},
pages = {1173--1186},
isbn_issn = {ISSN: 0747-7171},
year = {2011},
refereed = {yes},
institution = {Research Institute for Symbolic Computation},
sponsor = {FWF Doktoratskolleg W1214},
length = {14},
url = {http://www.sciencedirect.com/science/article/pii/S0747717111000861}
}

Algebraic Informatics

F. Winkler

In: Proceedings of the Forth International Conference on Algebraic Informatics (CAI 2011), Springer Verlag (ed.), Proceedings of 4th International Conference on Algebraic Informatics (CAI 2011), pp. -. 2011. ISSN 0302-9743, ISBN 978-3-642-21492-9.

[bib]

@inproceedings{RISC4430,
author = {F. Winkler},
title = {{Algebraic Informatics}},
booktitle = {{Proceedings of the Forth International Conference on Algebraic Informatics (CAI 2011)}},
language = {english},
pages = {--},
isbn_issn = {ISSN 0302-9743, ISBN 978-3-642-21492-9},
year = {2011},
editor = {Springer Verlag},
refereed = {yes},
sponsor = {FWF},
length = {0},
conferencename = {4th International Conference on Algebraic Informatics (CAI 2011)}
}

Linear partial differential equations and linear partial differential operators in computer algebra

shemyakova, winkler

In: Numerical and Symbolic Scientific Computing - Progress and Prospects, Springer Verlag (ed.), pp. 333-358. 2011. Springer Verlag, ISSN 0943-853X.

[bib]

@incollection{RISC4431,
author = {shemyakova and winkler},
title = {{Linear partial differential equations and linear partial differential operators in computer algebra}},
booktitle = {{Numerical and Symbolic Scientific Computing - Progress and Prospects}},
language = {english},
pages = {333--358},
publisher = {Springer Verlag},
isbn_issn = {ISSN 0943-853X},
year = {2011},
editor = {Springer Verlag },
refereed = {yes},
length = {26}
}

Rational general solutions of parametrizable AODEs

L.X.C. Ngo, F. Winkler

Publicationes Mathematicae Debrecen, pp. 573-587. 2011. ISSN 0033-3883.

[bib]

@article{RISC4439,
author = {L.X.C. Ngo and F. Winkler},
title = {{Rational general solutions of parametrizable AODEs}},
language = {english},
journal = {Publicationes Mathematicae Debrecen},
pages = {573--587},
isbn_issn = {ISSN 0033-3883},
year = {2011},
refereed = {yes},
length = {15}
}

What can Symbolic Computation contribute to Mathematics?

F. Winkler

In: Proceedings SYNASC 2011,, aaa (ed.), pp. 1-14. 2011. 1111.

[bib]

@inproceedings{RISC4440,
author = {F. Winkler},
title = {{What can Symbolic Computation contribute to Mathematics?}},
booktitle = {{Proceedings SYNASC 2011,}},
language = {english},
pages = {1--14},
isbn_issn = {1111},
year = {2011},
editor = {aaa},
refereed = {yes},
length = {15}
}

Rational general solutions of trivariate rational systems of autonomous ODEs

Y. Huang, L.X.C. Ngo, F. Winkler

In: Proceedings Forth Internat. Conf. on Mathematical Aspects of Computer and Information Sciences (MACIS 2011), 111 (ed.), pp. 93-100. 2011. 111.

[bib]

@inproceedings{RISC4441,
author = {Y. Huang and L.X.C. Ngo and F. Winkler},
title = {{Rational general solutions of trivariate rational systems of autonomous ODEs}},
booktitle = {{Proceedings Forth Internat. Conf. on Mathematical Aspects of Computer and Information Sciences (MACIS 2011)}},
language = {english},
pages = {93--100},
isbn_issn = {111},
year = {2011},
editor = {111},
refereed = {yes},
length = {8}
}