An optimal algorithm for constructing the reduced Gröbner basis of binomial ideals

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An optimal algorithm for constructing the reduced Gröbner basis of binomial ideals

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1996 international symposium on Symbolic and algebraic computation table of contents

Zurich, Switzerland

Pages: 55 - 62

Year of Publication: 1996

ISBN:0-89791-796-0

Authors

Ulla Koppenhagen	Institut für Informatik, Technische Universität München, D-80290 München, Germany
Ernst W. Mayr	Institut für Informatik, Technische Universität München, D-80290 München, Germany

Sponsors

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation
SIGNUM: ACM Special Interest Group on Numerical Mathematics

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ACM New York, NY, USA

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Downloads (6 Weeks): 4, Downloads (12 Months): 11, Citation Count: 2

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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	David Allen Bayer, The division algorithm and the hilbert scheme, 1982
	2	BUCHBERGER, B. Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal. PhD thesis, Universit,it Innsbruck, 1965.
	3	Thomas W. Dubé, The structure of polynomial ideals and Grobner bases, SIAM Journal on Computing, v.19 n.4, p.750-773, Aug. 1990 [doi>10.1137/0219053]
	4	EISENBUD, D., AND STURMFELS, B. Binomial ideals. Preprint, 1994.
	5	Steven Fortune , James Wyllie, Parallelism in random access machines, Proceedings of the tenth annual ACM symposium on Theory of computing, p.114-118, May 01-03, 1978, San Diego, California, United States [doi>10.1145/800133.804339]
	6	HARDY, G., AND WRIGHT, E. An Introduction to the Theory of Numbers, 5th ed. Clarendon Press, 1985.
	7	HERMANN, G. Die Frage der endlich vielen Schritte in der Theorie der Polynomideale. Mathematische Annalen 95 (1926), 736-788.
	8	HIRONAKA, H. Resolution of singularities of an algebraic variety over a field of characteristic zero: I. Ann. of Math. 79(1) (1964), 109-203.
	9	Dung T Huynh, A superexponential lower bound for Gro¨bner bases and church-Rosser Commutative Thue systems, Information and Control, v.68 n.1-3, p.196-206, Jan/Feb/March 1986 [doi>10.1016/S0019-9958(86)80035-3]
	10	Richard M. Karp , Vijaya Ramachandran, Parallel algorithms for shared-memory machines, Handbook of theoretical computer science (vol. A): algorithms and complexity, MIT Press, Cambridge, MA, 1991
	11	KOPPENHAGEN, U., AND MAYR, E. W. The complexity of the equivalence problem for commutative semigroups. TUM-I 9603, Institut fiir Informatik, Technische Universiti~t Miinchen, 1996.
	12	Klaus Kühnle , Ernst W. Mayr, Exponential space computation of Gröbner bases, Proceedings of the 1996 international symposium on Symbolic and algebraic computation, p.63-71, July 24-26, 1996, Zurich, Switzerland [doi>10.1145/236869.236900]
	13	MAYR, E. W., AND MEYER, A. R. The complexity of the word problems for commutative semigroups and polynomial ideals. Advances in Mathematics 46, 3 (1982), 305-329.
	14	H. Michael Möller , Ferdinando Mora, Upper and Lower Bounds for the Degree of Groebner Bases, Proceedings of the International Symposium on Symbolic and Algebraic Computation, p.172-183, July 09-11, 1984
	15	Lorenzo Robbiano, Term Orderings on the Polynominal Ring, Research Contributions from the European Conference on Computer Algebra-Volume 2, p.513-517, April 01-03, 1985
	16	Walter J. Savitch, Deterministic simulation of non-deterministic turing machines (Detailed Abstract), Proceedings of the first annual ACM symposium on Theory of computing, p.247-248, May 05-07, 1969, Marina del Rey, California, United States [doi>10.1145/800169.805439]

CITED BY 2

	Klaus Kühnle , Ernst W. Mayr, Exponential space computation of Gröbner bases, Proceedings of the 1996 international symposium on Symbolic and algebraic computation, p.63-71, July 24-26, 1996, Zurich, Switzerland
	Leo Bachmair , Ashish Tiwari , Laurent Vigneron, Abstract Congruence Closure, Journal of Automated Reasoning, v.31 n.2, p.129-168, 2003