A simple algorithm to compute comprehensive Gröbner bases using Gröbner bases

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A simple algorithm to compute comprehensive Gröbner bases using Gröbner bases

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 2006 international symposium on Symbolic and algebraic computation table of contents

Genoa, Italy

SESSION: Full papers table of contents

Pages: 326 - 331

Year of Publication: 2006

ISBN:1-59593-276-3

Authors

Akira Suzuki	Kobe University, Kobe, Japan
Yosuke Sato	Tokyo University of Science, Tokyo, Japan

Sponsors

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation
ACM: Association for Computing Machinery

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 6, Downloads (12 Months): 25, Citation Count: 11

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ABSTRACT

We introduce a simple algorithm to compute comprehensive Gröbner bases. It requires only computations of reduced Gröbner bases in polynomial rings over ground fields. It is so simple that we can easily implement it on any computer algebra system that has a routine to compute reduced Gröbner bases. Our implementations on several computer algebra systems show that it is also sufficiently fast comparing with other existing algorithms.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	Becker, T. (1994). On gröbner bases under specialization. Applicable Algebra in Engineering, Communication and Computing, 5, 1--8.
	2	Thomas Becker , Volker Weispfenning , Heinz Kredel, Gro¨bner bases: a computational approach to commutative algebra, Springer-Verlag, London, 1993
	3	Andreas Dolzmann , Thomas Sturn, REDLOG: computer algebra meets computer logic, ACM SIGSAM Bulletin, v.31 n.2, p.2-9, June 1997 [doi>10.1145/261320.261324]
	4	Michael Kalkbrener, On the stability of Groübner bases under specializations, Journal of Symbolic Computation, v.24 n.1, p.51-58, July 1997 [doi>10.1006/jsco.1997.0113]
	5	Antonio Montes, A new algorithm for discussing Gröbner bases with parameters, Journal of Symbolic Computation, v.33 n.2, p.183-208, February 2002 [doi>10.1006/jsco.2001.0504]
	6	Manubens, M. and Montes, A. (2005). Improving DISPGB Algorithm Using the Discriminant Ideal, J. Symb. Comp., A3L 2005 special issue, to appear.
	7	Masayuki Noro , Taku Takeshima, Risa/Asir—a computer algebra system, Papers from the international symposium on Symbolic and algebraic computation, p.387-396, July 27-29, 1992, Berkeley, California, United States [doi>10.1145/143242.143362]
	8	Akira Suzuki , Yosuke Sato, An alternative approach to comprehensive Gröbner bases, Proceedings of the 2002 international symposium on Symbolic and algebraic computation, p.255-261, July 07-10, 2002, Lille, France [doi>10.1145/780506.780539]
	9	Akira Suzuki , Yosuke Sato, An alternative approach to comprehensive Gröbner bases, Journal of Symbolic Computation, v.36 n.3-4, p.649-667, September 2003 [doi>10.1016/S0747-7171(03)00098-1]
	10	Volker Weispfenning, Comprehensive Gro¨bner bases, Journal of Symbolic Computation, v.14 n.1, p.1-29, July 1992 [doi>10.1016/0747-7171(92)90023-W]
	11	Volker Weispfenning, Canonical comprehensive Gröbner bases, Journal of Symbolic Computation, v.36 n.3-4, p.669-683, September 2003 [doi>10.1016/S0747-7171(03)00099-3]

CITED BY 11

	Shutaro Inoue , Kohei Mukaida , Akira Suzuki , Yosuke Sato, Computation of inverses in residue class rings with parameters, ACM Communications in Computer Algebra, v.42 n.3, September 2008
	Akira Suzuki , Yosuke Sato, Implementation of CGS and CGB on Risa/Asir and other computer algebra systems using Suzuki-Sato algorithm, ACM Communications in Computer Algebra, v.41 n.3, September 2007 issue 161
	Katsusuke Nabeshima, PGB: a package for computing parametric Gröbner and related objects, ACM Communications in Computer Algebra, v.41 n.3, September 2007 issue 161
	Shutaro Inoue , Yosuke Sato, On the parallel computation of comprehensive Gröbner systems, Proceedings of the 2007 international workshop on Parallel symbolic computation, July 27-28, 2007, London, Ontario, Canada
	Changbo Chen , Marc Moreno Maza , François Lemaire , Wei Pan , Liyun Li , Yuzhen Xie, The ConstructibleSetTools and ParametricSystemTools modules of the RegularChains library in Maple, ACM Communications in Computer Algebra, v.42 n.3, September 2008
	Montserrat Manubens , Antonio Montes, Minimal canonical comprehensive Gröbner systems, Journal of Symbolic Computation, v.44 n.5, p.463-478, May, 2009
	Katsusuke Nabeshima, A speed-up of the algorithm for computing comprehensive Gröbner systems, Proceedings of the 2007 international symposium on Symbolic and algebraic computation, July 29-August 01, 2007, Waterloo, Ontario, Canada
	Yosuke Kurata , Masayuki Noro, Computation of discrete comprehensive Gröbner bases using modular dynamic evaluation, Proceedings of the 2007 international symposium on Symbolic and algebraic computation, July 29-August 01, 2007, Waterloo, Ontario, Canada
	Masaaki Kanno , Kazuhiro Yokoyama , Hirokazu Anai , Shinji Hara, Parametric optimization in control using the sum of roots for parametric polynomial spectral factorization, Proceedings of the 2007 international symposium on Symbolic and algebraic computation, July 29-August 01, 2007, Waterloo, Ontario, Canada
	Michael Wibmer, Gröbner bases for families of affine or projective schemes, Journal of Symbolic Computation, v.42 n.8, p.803-834, August, 2007
	Masaaki Kanno , Kazuhiro Yokoyama , Hirokazu Anai , Shinji Hara, Symbolic optimization of algebraic functions, Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, July 20-23, 2008, Linz/Hagenberg, Austria