Priv.-Doz. Dr. Markus Rosenkranz

Research Area

Differential algebra; boundary problems

Software

Theorema

A Mathematical Assistant System implemented in Mathematica

The present prototype version of the Theorema software system is implemented in Mathematica . The system consists of a general higher-order predicate logic prover and a collection of special provers that call each other depending on the particular proof situations. ...

Authors: Alexander Maletzky, Bruno Buchberger, Markus Rosenkranz, Nikolaj Popov, Teimuraz Kutsia, Tudor Jebelean, Wolfgang Windsteiger

More Software Website

Publications

2011

[Rosenkranz]

Symbolic Analysis for Boundary Problems: From Rewriting to Parametrized Groebner Bases

Markus Rosenkranz, Georg Regensburger, Loredana Tec, Bruno Buchberger

In: Numerical and Symbolic Scientific Computing: Progress and Prospects, Ulrich Langer and Peter Paule (ed.), pp. 273-331. 2011. Springer, Wien, ISBN 978-3-7091-0793-5. Also available as RICAM Report 2010-05, September 2010. [pdf]

[bib]

@incollection{RISC4330,
author = {Markus Rosenkranz and Georg Regensburger and Loredana Tec and Bruno Buchberger},
title = {{Symbolic Analysis for Boundary Problems: From Rewriting to Parametrized Groebner Bases}},
booktitle = {{Numerical and Symbolic Scientific Computing: Progress and Prospects}},
language = {english},
pages = {273--331},
publisher = {Springer, Wien},
isbn_issn = {ISBN 978-3-7091-0793-5},
year = {2011},
annote = {2011-00-00-A},
note = {Also available as RICAM Report 2010-05, September 2010},
editor = {Ulrich Langer and Peter Paule},
refereed = {yes},
length = {54}
}

2009

[Rosenkranz]

A Symbolic Framework for Operations on Linear Boundary Problems

Markus Rosenkranz, Georg Regensburger, Loredana Tec, Bruno Buchberger

In: Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing , Gerdt, Vladimir P.; Mayr, Ernst W.; Vorozhtsov, Evgenii H. (ed.), Proceedings of CASC '09, Kobe, Japan, LNCS 5743, pp. 269-283. September 2009. Springer-Verlag, ISBN: 978-3-642-04102-0. Also available as RICAM Report 09-10, May 2009. [url]

[bib]

@inproceedings{RISC3843,
author = {Markus Rosenkranz and Georg Regensburger and Loredana Tec and Bruno Buchberger},
title = {{A Symbolic Framework for Operations on Linear Boundary Problems}},
booktitle = {{Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing }},
language = {english},
series = {LNCS},
volume = {5743},
pages = {269--283},
publisher = {Springer-Verlag},
isbn_issn = {ISBN: 978-3-642-04102-0},
year = {2009},
month = {September},
annote = {2009-05-00-A},
note = {Also available as RICAM Report 09-10, May 2009},
editor = {Gerdt and Vladimir P.; Mayr and Ernst W.; Vorozhtsov and Evgenii H. },
refereed = {yes},
length = {15},
conferencename = {CASC '09, Kobe, Japan},
url = {http://www.ricam.oeaw.ac.at/publications/reports/09/rep09-10.pdf}
}

[Rosenkranz]

A skew polynomial approach to integro-differential operators

Georg Regensburger, Markus Rosenkranz, Johannes Middeke

In: Proceedings of ISSAC 2009, Jeremy R. Johnson, Hyungju Park, Erich Kaltofen (ed.), Proceedings of Symbolic and Algebraic Computation, International Symposium, ISSAC 2009, pp. 287-294. 2009. ACM, 978-1-60558-609-0. [url] [pdf]

[bib]

@inproceedings{RISC4025,
author = {Georg Regensburger and Markus Rosenkranz and Johannes Middeke},
title = {{A skew polynomial approach to integro-differential operators}},
booktitle = {{Proceedings of ISSAC 2009}},
language = {english},
abstract = {We construct the algebra of integro-differential operators over anordinary integro-differential algebra directly in terms of normalforms. In the case of polynomial coefficients, we use skewpolynomials for defining the integro-differential Weyl algebra as anatural extension of the classical Weyl algebra in one variable. Its normal forms, algebraic properties and its relation to thelocalization of differential operators are studied. Fixing theintegration constant, we regain the integro-differential operatorswith polynomial coefficients.},
pages = {287--294},
publisher = {ACM},
isbn_issn = {978-1-60558-609-0},
year = {2009},
editor = {Jeremy R. Johnson and Hyungju Park and Erich Kaltofen},
refereed = {yes},
length = {8},
conferencename = {Symbolic and Algebraic Computation, International Symposium, ISSAC 2009},
url = {http://issac2009.kias.re.kr/}
}

2008

[Rosenkranz]

General Polynomial Reduction with Theorema Functors: Applications to Integro-Differential Operators and Polynomials

B. Buchberger, G. Regensburger, M. Rosenkranz, L. Tec

SIGSAM Bulletin 42(3), pp. 135-137. September 2008. ISSN 0163-5824. Extended abstract from ISSAC 2008 poster presentation. [url]

[bib]

@article{RISC3523,
author = {B. Buchberger and G. Regensburger and M. Rosenkranz and L. Tec},
title = {{General Polynomial Reduction with Theorema Functors: Applications to Integro-Differential Operators and Polynomials }},
language = {english},
journal = {SIGSAM Bulletin},
volume = {42},
number = {3},
pages = {135--137},
isbn_issn = {ISSN 0163-5824},
year = {2008},
month = {September},
annote = {2008-09-00-A},
note = {Extended abstract from ISSAC 2008 poster presentation},
refereed = {yes},
length = {3},
url = {http://delivery.acm.org/10.1145/1510000/1504355/p135-buchberger.pdf?key1=1504355&key2=4096815031&coll=DL&dl=ACM&ip=140.78.3.1&CFID=22482497&CFTOKEN=46546804}
}

2006

[Rosenkranz]

Theorema: Towards Computer-Aided Mathematical Theory Exploration

B. Buchberger, A. Craciun, T. Jebelean, L. Kovacs, T. Kutsia, K. Nakagawa, F. Piroi, N. Popov, J. Robu, M. Rosenkranz, W. Windsteiger

Journal of Applied Logic 4(4), pp. 470-504. 2006. ISSN 1570-8683. [doi] [pdf]

[bib]

@article{RISC2487,
author = {B. Buchberger and A. Craciun and T. Jebelean and L. Kovacs and T. Kutsia and K. Nakagawa and F. Piroi and N. Popov and J. Robu and M. Rosenkranz and W. Windsteiger},
title = {{Theorema: Towards Computer-Aided Mathematical Theory Exploration}},
language = {english},
journal = {Journal of Applied Logic},
volume = {4},
number = {4},
pages = { 470--504},
isbn_issn = {ISSN 1570-8683},
year = {2006},
annote = {2005-09-09-A},
refereed = {yes},
length = {35},
url = {http://dx.doi.org/10.1016/j.jal.2005.10.006}
}

[Rosenkranz]

Theorema

W. Windsteiger, B. Buchberger, M. Rosenkranz

In: The Seventeen Provers of the World, Freek Wiedijk (ed.), Lecture Notes in Artificial Intelligence (LNAI) 3600, pp. 96-107. 2006. Springer Berlin Heidelberg New York, ISBN 3-540-30704-4. [url] [pdf]

[bib]

@incollection{RISC2737,
author = {W. Windsteiger and B. Buchberger and M. Rosenkranz},
title = {{Theorema}},
booktitle = {{The Seventeen Provers of the World}},
language = {english},
series = {Lecture Notes in Artificial Intelligence (LNAI)},
volume = {3600},
pages = {96--107},
publisher = {Springer Berlin Heidelberg New York},
isbn_issn = {ISBN 3-540-30704-4},
year = {2006},
annote = {2006-03-16-A},
editor = {Freek Wiedijk},
refereed = {yes},
length = {12},
url = {http://link.springer.com/book/10.1007/11542384}
}

2004

[Rosenkranz]

New Symbolic Method for Solving Linear Two-Point Boundary Value Problems on the Level of Operators

M. Rosenkranz

Journal of Symbolic Computation 39(2), pp. 171-199. 2004. Elsevier, ISBN 0747-7171.

[bib]

@article{RISC2185,
author = {M. Rosenkranz},
title = {{New Symbolic Method for Solving Linear Two-Point Boundary Value Problems on the Level of Operators}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {39},
number = {2},
pages = {171--199},
publisher = {Elsevier},
isbn_issn = {ISBN 0747-7171},
year = {2004},
refereed = {yes},
length = {29}
}

[Rosenkranz]

The Algorithmization of Physics: Math Between Science and Engineering

M. Rosenkranz

In: Proceedings of AISC 2004, B. Buchberger, J.A. Campbell (ed.), Proceedings of Artificial Intelligence and Symbolic Computation: 7th International Conference, Linz, Austria, Lecture Notes in Artificial Intelligence (LNAI) 3249, pp. 1-7. September 2004. Springer, Castle of Hagenberg, Austria, ISBN 3-540-23212-5. Invited talk.

[bib]

@inproceedings{RISC2188,
author = {M. Rosenkranz},
title = {{The Algorithmization of Physics: Math Between Science and Engineering}},
booktitle = {{Proceedings of AISC 2004}},
language = {english},
series = {Lecture Notes in Artificial Intelligence (LNAI)},
volume = {3249},
pages = {1--7},
publisher = {Springer},
address = {Castle of Hagenberg, Austria},
isbn_issn = {ISBN 3-540-23212-5},
year = {2004},
month = {September},
note = {Invited talk},
editor = {B. Buchberger and J.A. Campbell},
refereed = {yes},
length = {7},
conferencename = {Artificial Intelligence and Symbolic Computation: 7th International Conference, Linz, Austria}
}

2003

[Rosenkranz]

The Green's Algebra: A Polynomial Approach to Boundary Value Problems

Markus Rosenkranz

Technical report no. 03-05 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). July 2003. PhD Thesis. [ps]

[bib]

@techreport{RISC1271,
author = {Markus Rosenkranz},
title = {{The Green's Algebra: A Polynomial Approach to Boundary Value Problems}},
number = {03-05},
year = {2003},
month = {July},
note = {PhD Thesis},
keywords = {symbolic ODE solution, noncommutative polynomials, Gr{\"o}bner bases},
sponsor = {FWF project F1302},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}
}

[Rosenkranz]

A Symbolic Algorithm for Solving Two-Point BVPs on the Operator Level

M. Rosenkranz, B. Buchberger, H. W. Engl

Johannes Kepler University Linz, Spezialforschungsbereich F013. Technical report no. 2003-41, SFB Report, October 2003. [pdf]

[bib]

@techreport{RISC2249,
author = {M. Rosenkranz and B. Buchberger and H. W. Engl},
title = {{A Symbolic Algorithm for Solving Two-Point BVPs on the Operator Level}},
language = {english},
number = {2003-41},
year = {2003},
month = {October},
annote = {2003-10-00-D},
howpublished = {SFB Report},
institution = {Johannes Kepler University Linz, Spezialforschungsbereich F013},
length = {29}
}

[Rosenkranz]

Solving Linear Boundary Value Problems Via Non–commutative Groebner Bases

M. Rosenkranz, B. Buchberger, H. W. Engl

Applicable Analysis 82(7), pp. 655-675. July 2003. Copyright: Taylor & Francis Ltd., ISSN 0003-6811, ISSN 1563-504X.

[bib]

@article{RISC2320,
author = {M. Rosenkranz and B. Buchberger and H. W. Engl},
title = {{Solving Linear Boundary Value Problems Via Non–commutative Groebner Bases}},
language = {english},
journal = {Applicable Analysis},
volume = {82},
number = {7},
pages = {655--675},
publisher = {Copyright: Taylor & Francis Ltd.},
isbn_issn = {ISSN 0003-6811, ISSN 1563-504X},
year = {2003},
month = {July},
annote = {2003-07-00-A},
refereed = {yes},
length = {20}
}

[Rosenkranz]

F 1302: THEOREMA: Proving, Solving, and Computing in the Theory of Hilbert Spaces

B. Buchberger, T. Jebelean, W. Windsteiger, T. Kutsia, K. Nakagawa, J. Robu, F. Piroi, A. Craciun, N. Popov, G. Kusper, M. Rosenkranz, L. Kovacs, C. Kocsis

In: Special Research Program (SFB) F 013, Numerical and Symbolic Scientific Computing, Proposal for Continuation, Part II: Proposal, P. Paule, U. Langer (ed.), pp. 58-73. October 2003. Johannes Kepler University Linz, Austria, -.

[bib]

@incollection{RISC2303,
author = {B. Buchberger and T. Jebelean and W. Windsteiger and T. Kutsia and K. Nakagawa and J. Robu and F. Piroi and A. Craciun and N. Popov and G. Kusper and M. Rosenkranz and L. Kovacs and C. Kocsis},
title = {{F 1302: THEOREMA: Proving, Solving, and Computing in the Theory of Hilbert Spaces}},
booktitle = {{Special Research Program (SFB) F 013, Numerical and Symbolic Scientific Computing, Proposal for Continuation, Part II: Proposal}},
language = {english},
pages = {58--73},
publisher = {Johannes Kepler University Linz, Austria},
isbn_issn = {-},
year = {2003},
month = {October},
annote = {2003-10-06-B},
editor = {P. Paule and U. Langer},
refereed = {no},
length = {25}
}

[Rosenkranz]

A Symbolic Algorithm for Generating Solutions of Boundary Value Problems

Markus Rosenkranz

RISC, Johannes Kepler University Linz. PhD Thesis. 2003.

[bib]

@phdthesis{RISC4114,
author = {Markus Rosenkranz},
title = {{A Symbolic Algorithm for Generating Solutions of Boundary Value Problems}},
language = {english},
year = {2003},
translation = {0},
school = {RISC, Johannes Kepler University Linz},
length = {0}
}

2002

[Rosenkranz]

F 1302: Solving and Proving in General Domains

B. Buchberger, T. Jebelean, W. Windsteiger, T. Kutsia, K. Nakagawa, J. Robu, F. Piroi, A. Craciun, N. Popov, G. Kusper, M. Rosenkranz

In: Special Research Program (SFB) F 013, Numerical and Symbolic Scientific Computing, Annual Report 2002, U. Langer, F. Winkler (ed.), pp. 4-5. February 2002. Johannes Kepler University Linz, Austria,

[bib]

@incollection{RISC2261,
author = {B. Buchberger and T. Jebelean and W. Windsteiger and T. Kutsia and K. Nakagawa and J. Robu and F. Piroi and A. Craciun and N. Popov and G. Kusper and M. Rosenkranz},
title = {{F 1302: Solving and Proving in General Domains}},
booktitle = {{Special Research Program (SFB) F 013, Numerical and Symbolic Scientific Computing, Annual Report 2002}},
language = {english},
pages = {4--5},
publisher = {Johannes Kepler University Linz, Austria},
year = {2002},
month = {February},
annote = {2002-02-00-A},
editor = {U. Langer and F. Winkler},
refereed = {no},
length = {2}
}

[Rosenkranz]

Solving Linear Boundary Value Problems Via Non–commutative Groebner Bases

M. Rosenkranz, B. Buchberger, H. W. Engl

In: Proceedings of SYNASC 2002, 4th International Workshop on Symbolic and Numeric Algorithms for Scientific Computing, D. Petcu, V. Negru, D. Zaharie, T. Jebelean (ed.), pp. 300-313. 9-12 October 2002. Mirton Publisher, Timisoara, Romania, ISBN 973-585-785-5.

[bib]

@inproceedings{RISC2324,
author = {M. Rosenkranz and B. Buchberger and H. W. Engl},
title = {{Solving Linear Boundary Value Problems Via Non–commutative Groebner Bases}},
booktitle = {{Proceedings of SYNASC 2002, 4th International Workshop on Symbolic and Numeric Algorithms for Scientific Computing}},
language = {english},
pages = {300--313},
publisher = { Mirton Publisher},
address = { Timisoara, Romania},
isbn_issn = {ISBN 973-585-785-5},
year = {2002},
month = {9-12 October},
annote = {2002-10-09-B},
editor = {D. Petcu and V. Negru and D. Zaharie and T. Jebelean},
refereed = {yes},
length = {13}
}

1997

[Rosenkranz]

Lagrange Inversion

M. Rosenkranz

RISC, J. Kepler University Linz. Diploma Thesis. 1997. [ps] [ps] [pdf]

[bib]

@mastersthesis{RISC2383,
author = {M. Rosenkranz},
title = {{Lagrange Inversion}},
language = {english},
year = {1997},
translation = {0},
school = {RISC, J. Kepler University Linz},
length = {95}
}