Formal Theory and Algorithmics of Noncommutative Gröbner Bases

Project Lead

Project Duration

01/10/2008 - 30/09/2011

Project URL

Go to Website

Publications

2017

Gröbner Bases Computation by Triangularizing Macaulay Matrices

Bruno Buchberger

Advanced Studies in Pure Mathematics (The 50th Anniversary of Gröbner Bases) 75, pp. 1-9. 2017. Mathematical Society of Japan, 0.
[bib]
@article{RISC5586,
author = {Bruno Buchberger},
title = {{Gröbner Bases Computation by Triangularizing Macaulay Matrices}},
language = {english},
journal = {Advanced Studies in Pure Mathematics (The 50th Anniversary of Gröbner Bases)},
volume = {75},
pages = {1--9},
publisher = {Mathematical Society of Japan},
isbn_issn = {0},
year = {2017},
refereed = {no},
length = {9}
}

Satisfiability Checking and Symbolic Computation

Abraham Erika , Abbott John , Becker Bernd , Bigatti Anna Maria , Brain Martin , Buchberger Bruno , Cimatti Alessandro , Davenport James , England Matthew , Fontaine Pascal , Forrest Stephen , Griggio Alberto , Kröning Daniel , Seiler Werner M. , Sturm

ACM Communications in Computer Algebra 50(4), pp. 145-147. 2017. 0.
[bib]
@article{RISC5587,
author = { Abraham Erika and Abbott John and Becker Bernd and Bigatti Anna Maria and Brain Martin and Buchberger Bruno and Cimatti Alessandro and Davenport James and England Matthew and Fontaine Pascal and Forrest Stephen and Griggio Alberto and Kröning Daniel and Seiler Werner M. and Sturm },
title = {{Satisfiability Checking and Symbolic Computation}},
language = {english},
journal = {ACM Communications in Computer Algebra},
volume = {50},
number = {4},
pages = {145--147},
isbn_issn = {0},
year = {2017},
refereed = {no},
length = {3}
}

2015

Efficient Computation of Multiplicity and Directional Multiplicity of an Isolated Point

Angelos Mantzaflaris, Hamid Rahkooy, Zafeirakis Zafeirakopoulos

Technical report no. 15-08 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 2015. [pdf]
[bib]
@techreport{RISC5152,
author = { Angelos Mantzaflaris and Hamid Rahkooy and Zafeirakis Zafeirakopoulos},
title = {{Efficient Computation of Multiplicity and Directional Multiplicity of an Isolated Point}},
language = {english},
number = {15-08},
year = {2015},
length = {25},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

Dual Space Algorithms for Computing Multiplicity Structure of Isolated Points

H. Rahkooy

RISC, JKU Linz. PhD Thesis. July 2015.
[bib]
@phdthesis{RISC5288,
author = {H. Rahkooy},
title = {{Dual Space Algorithms for Computing Multiplicity Structure of Isolated Points}},
language = {english},
year = {2015},
month = {July},
translation = {0},
school = {RISC, JKU Linz},
length = {69}
}

Gröbner Bases and Generalized Sylvester Matrices

Manuela Wiesinger-Widi

Johannes Kepler University Linz. PhD Thesis. 07 2015. [url]
[bib]
@phdthesis{RISC5170,
author = {Manuela Wiesinger-Widi},
title = {{Gröbner Bases and Generalized Sylvester Matrices}},
language = {english},
year = {2015},
month = {07},
translation = {0},
school = {Johannes Kepler University Linz},
length = {116},
url = {http://epub.jku.at/obvulihs/content/titleinfo/776913}
}

Gröbner Bases and Generalized Sylvester Matrices

Manuela Wiesinger-Widi

Technical report no. 15-15 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 2015. PhD Thesis.
[bib]
@techreport{RISC5171,
author = {Manuela Wiesinger-Widi},
title = {{Gröbner Bases and Generalized Sylvester Matrices}},
language = {english},
number = {15-15},
year = {2015},
note = {PhD Thesis},
length = {116},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

2014

Complexity Analysis of the Bivariate Buchberger Algorithm in Theorema

A. Maletzky, B. Buchberger

In: Mathematical Software - ICMS 2014, Hoon Hong and Chee Yap (ed.), Proceedings of The 4th International Congress on Mathematical Software (ICMS'2014), Seoul, Korea, August 5-9, 2014, Lecture Notes in Computer Science 8592, pp. 41-48. 2014. Springer Berlin Heidelberg, ISBN 978-3-662-44198-5. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-662-44199-2_8. [url] [pdf]
[bib]
@inproceedings{RISC4996,
author = {A. Maletzky and B. Buchberger},
title = {{Complexity Analysis of the Bivariate Buchberger Algorithm in Theorema}},
booktitle = {{Mathematical Software -- ICMS 2014}},
language = {english},
series = {Lecture Notes in Computer Science},
volume = {8592},
pages = {41--48},
publisher = {Springer Berlin Heidelberg},
isbn_issn = {ISBN 978-3-662-44198-5},
year = {2014},
annote = {2014-08-00-B},
note = {The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-662-44199-2_8},
editor = {Hoon Hong and Chee Yap},
refereed = {yes},
length = {8},
conferencename = {The 4th International Congress on Mathematical Software (ICMS'2014), Seoul, Korea, August 5-9, 2014},
url = {http://dx.doi.org/10.1007/978-3-662-44199-2_8}
}

Groebner Bases in Theorema

B. Buchberger, A. Maletzky

In: Mathematical Software - ICMS 2014, Hoon Hong and Chee Yap (ed.), Proceedings of The 4th International Congress on Mathematical Software (ICMS'2014), Seoul, Korea, August 5-9, 2014, Lecture Notes in Computer Science 8592, pp. 374-381. 2014. Springer Berlin Heidelberg, ISBN 978-3-662-44198-5. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-662-44199-2_58. [url] [pdf]
[bib]
@inproceedings{RISC4997,
author = {B. Buchberger and A. Maletzky},
title = {{Groebner Bases in Theorema}},
booktitle = {{Mathematical Software -- ICMS 2014}},
language = {english},
series = {Lecture Notes in Computer Science},
volume = {8592},
pages = {374--381},
publisher = {Springer Berlin Heidelberg},
isbn_issn = {ISBN 978-3-662-44198-5},
year = {2014},
annote = {2014-08-00-A},
note = {The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-662-44199-2_58},
editor = {Hoon Hong and Chee Yap},
refereed = {yes},
length = {8},
conferencename = {The 4th International Congress on Mathematical Software (ICMS'2014), Seoul, Korea, August 5-9, 2014},
url = {http://dx.doi.org/10.1007/978-3-662-44199-2_58}
}

Complexity Analysis of the Bivariate Buchberger Algorithm in Theorema

A. Maletzky, B. Buchberger

Technical report no. 14-10 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. October 2014. [zip]
[bib]
@techreport{RISC5063,
author = {A. Maletzky and B. Buchberger},
title = {{Complexity Analysis of the Bivariate Buchberger Algorithm in Theorema}},
language = {english},
number = {14-10},
year = {2014},
month = {October},
annote = {2014-10-00-A},
length = {0},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

2013

On Computing Elimination Ideals Using Resultants with Applications to Groebner Bases

Hamid Rahkooy, Zafeirakis Zafeirakopoulos

Research Institute for Symbolic Computations, Doctoral College Computational Mathematics. Technical report, 2013. [url]
[bib]
@techreport{RISC4731,
author = {Hamid Rahkooy and Zafeirakis Zafeirakopoulos},
title = {{On Computing Elimination Ideals Using Resultants with Applications to Groebner Bases}},
language = {english},
year = {2013},
institution = {Research Institute for Symbolic Computations, Doctoral College Computational Mathematics},
length = {23},
url = {https://www.dk-compmath.jku.at/publications/dk-reports/2013-05-21/view}
}

2011

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}
}

Buchberger's Algorithm

Bruno Buchberger, Manuel Kauers

Scholarpedia 6(10), pp. 7764-7764. October 2011. 1941-6016. [url]
[bib]
@article{RISC4394,
author = {Bruno Buchberger and Manuel Kauers},
title = {{Buchberger's Algorithm}},
language = {english},
journal = {Scholarpedia},
volume = {6},
number = {10},
pages = {7764--7764},
isbn_issn = {1941-6016},
year = {2011},
month = {October},
annote = {2011-10-00-A},
refereed = {yes},
length = {1},
url = {http://www.scholarpedia.org/article/Buchberger%27s_algorithm}
}

Groebner Bases and Generalized Sylvester Matrices

Manuela Wiesinger-Widi

ACM Communications in Computer Algebra 45(2), pp. -. June 2011. Accepted extended abstract from ISSAC 2011 poster presentation. [pdf]
[bib]
@article{RISC4333,
author = {Manuela Wiesinger-Widi},
title = {{Groebner Bases and Generalized Sylvester Matrices}},
language = {english},
journal = {ACM Communications in Computer Algebra},
volume = {45},
number = {2},
pages = {--},
isbn_issn = {?},
year = {2011},
month = {June},
note = {Accepted extended abstract from ISSAC 2011 poster presentation},
refereed = {yes},
length = {2}
}

Sylvester Matrix and GCD for Several Univariate Polynomials

Manuela Wiesinger-Widi

Technical report no. 11-07 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. May 2011. [pdf]
[bib]
@techreport{RISC4337,
author = {Manuela Wiesinger-Widi},
title = {{Sylvester Matrix and GCD for Several Univariate Polynomials}},
language = {english},
number = {11-07},
year = {2011},
month = {May},
length = {5},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

Towards Computing a Groebner Basis of a Polynomial Ideal over a Field by Using Matrix Triangularization

Manuela Wiesinger-Widi

Technical report no. 11-08 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. May 2011. [pdf]
[bib]
@techreport{RISC4338,
author = {Manuela Wiesinger-Widi},
title = {{Towards Computing a Groebner Basis of a Polynomial Ideal over a Field by Using Matrix Triangularization}},
language = {english},
number = {11-08},
year = {2011},
month = {May},
length = {10},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}

2010

A Purely Logical Approach to the Termination of Imperative Loops

M. Erascu, T. Jebelean

In: Proceedings of the 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, T. Ida, V. Negru, T. Jebelean, D. Petcu, S. M. Watt, D. Zaharie (ed.), pp. 142-149. September 2010. IEEE Computer Society, 978-0-7695-4324-6. [pdf]
[bib]
@inproceedings{RISC4181,
author = {M. Erascu and T. Jebelean},
title = {{A Purely Logical Approach to the Termination of Imperative Loops}},
booktitle = {{Proceedings of the 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing}},
language = {english},
pages = {142--149},
publisher = {IEEE Computer Society},
isbn_issn = { 978-0-7695-4324-6},
year = {2010},
month = {September},
editor = {T. Ida and V. Negru and T. Jebelean and D. Petcu and S. M. Watt and D. Zaharie},
refereed = {yes},
length = {8}
}

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