Rational Parametric Algebraic Curves [DK11]

Project Lead

Project Duration

01/10/2011 - 30/09/2014

Project URL

Project Website

Publications

2017

Relative Reduction and Buchberger’s Algorithm in Filtered Free Modules

Christoph Fuerst, Alexander Levin

In: Mathematics in Computer Science, W. Koepf (ed.), pp. 1-11. 2017. 1661-8289.
[bib]
@inproceedings{RISC5432,
author = {Christoph Fuerst and Alexander Levin},
title = {{Relative Reduction and Buchberger’s Algorithm in Filtered Free Modules}},
booktitle = {{Mathematics in Computer Science}},
language = {english},
pages = {1--11},
isbn_issn = {1661-8289},
year = {2017},
editor = {W. Koepf},
refereed = {yes},
length = {11}
}

An Algebraic-Geometric Method for Computing Zolotarev Polynomials

Georg Grasegger, N. Thieu Vo

In: Proceedings of the 2017 international symposium on symbolic and algebraic computation (ISSAC), Burr, M. (ed.), pp. 173-180. 2017. ACM Press, New York, ISBN: 978-1-4503-5064-8.
[bib]
@inproceedings{RISC5510,
author = {Georg Grasegger and N. Thieu Vo},
title = {{An Algebraic-Geometric Method for Computing Zolotarev Polynomials}},
booktitle = {{Proceedings of the 2017 international symposium on symbolic and algebraic computation (ISSAC)}},
language = {english},
pages = {173--180},
publisher = {ACM Press},
address = {New York},
isbn_issn = {ISBN: 978-1-4503-5064-8},
year = {2017},
editor = {Burr and M.},
refereed = {yes},
length = {8}
}

2016

Axiomatic Description of Gröbner Reduction

Christoph Fuerst

RISC, JKU Linz. PhD Thesis. December 2016. [pdf]
[bib]
@phdthesis{RISC5388,
author = {Christoph Fuerst},
title = {{Axiomatic Description of Gröbner Reduction}},
language = {english},
year = {2016},
month = {December},
translation = {0},
school = {RISC, JKU Linz},
length = {154}
}

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

Computation of Dimension in Filtered Free Modules by Gröbner Reduction

Christoph Fuerst, Guenter Landsmann

In: Proceedings of the International Symposium on Symbolic and Algebraic Computation, ACM (ed.), Proceedings of ISSAC '15, pp. 181-188. 2015. 978-1-4503-3435-8. [url]
[bib]
@inproceedings{RISC5154,
author = {Christoph Fuerst and Guenter Landsmann},
title = {{Computation of Dimension in Filtered Free Modules by Gröbner Reduction}},
booktitle = {{Proceedings of the International Symposium on Symbolic and Algebraic Computation}},
language = {english},
pages = {181--188},
isbn_issn = {978-1-4503-3435-8},
year = {2015},
editor = {ACM},
refereed = {yes},
length = {8},
conferencename = {ISSAC '15},
url = {http://doi.acm.org/10.1145/2755996.2756680}
}

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}
}

Symbolic solutions of first-order algebraic differential equations

Georg Grasegger

Johannes Kepler University Linz. PhD Thesis. 06 2015. [url]
[bib]
@phdthesis{RISC5160,
author = {Georg Grasegger},
title = {{Symbolic solutions of first-order algebraic differential equations}},
language = {english},
year = {2015},
month = {06},
translation = {0},
school = {Johannes Kepler University Linz},
length = {154},
url = {http://epub.jku.at/obvulihs/content/titleinfo/753082}
}

2014

Polynomial Equivalence of Finite Rings

G. Grasegger, G. Horváth, K.A. Kearnes

Journal of the Australian Mathematical Society 96(2), pp. 244-257. 2014. 1446-8107. [url]
[bib]
@article{RISC4889,
author = {G. Grasegger and G. Horváth and K.A. Kearnes},
title = {{Polynomial Equivalence of Finite Rings}},
language = {english},
journal = {Journal of the Australian Mathematical Society},
volume = {96},
number = {2},
pages = {244--257},
isbn_issn = {1446-8107},
year = {2014},
refereed = {yes},
length = {14},
url = {http://journals.cambridge.org/article_S1446788713000645}
}

Radical Solutions of First Order Autonomous Algebraic Ordinary Differential Equations

G. Grasegger

In: ISSAC '14: Proceedings of the 39th International Symposium on International Symposium on Symbolic and Algebraic Computation, Katsusuke Nabeshima (ed.), pp. 217-223. 2014. ACM, New York, ISBN 978-1-4503-2501-1. [pdf]
[bib]
@inproceedings{RISC4990,
author = {G. Grasegger},
title = {{Radical Solutions of First Order Autonomous Algebraic Ordinary Differential Equations}},
booktitle = {{ISSAC '14: Proceedings of the 39th International Symposium on International Symposium on Symbolic and Algebraic Computation}},
language = {english},
pages = {217--223},
publisher = {ACM},
address = {New York},
isbn_issn = {ISBN 978-1-4503-2501-1},
year = {2014},
editor = {Katsusuke Nabeshima},
refereed = {yes},
length = {7}
}

On Symbolic Solutions of Algebraic Partial Diff erential 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 Diff erential 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}
}

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