The Grobner basis of a module over KUX1,...,Xne and polynomial solutions of a system of linear equations

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The Grobner basis of a module over KUX1,...,Xne and polynomial solutions of a system of linear equations

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Symposium on Symbolic and Algebraic Manipulation archive
Proceedings of the fifth ACM symposium on Symbolic and algebraic computation table of contents

Waterloo, Ontario, Canada

Pages: 222 - 224

Year of Publication: 1986

ISBN:0-89791-199-7

Authors

A. Furukawa	Tokyo Metropolitan Univ., Tokyo, Japan
T. Sasaki	The Institute of Physical and Chemical Research, Saitama, Japan
H. Kobayashi	Nihon Univ., Tokyo, Japan

Sponsor

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 2, Downloads (12 Months): 10, Citation Count: 3

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ABSTRACT

Many computations relating polynomial ideals are reduced to calculating polynomial solutions of a system of linear equations with polynomial coefficients[1]. Zacharias[2] pointed out that Buchberger's algorithm[3] for Gröbner basis can be applied to solving such a linear equation. From the computational viewpoint, Zacharias' method seems to be much better than the previous methods. Hence, we have generalized his method to solve a system of equations directly. After completing the paper, we knew that similar works had been done by several authors[4,5]. This paper describes our method briefly.

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	A, Seidenberg, "Constructions in algebra", Trans. Amer. Math. Soc. 197, pp.273-313, 1974.
	2	G. Zacharias, "Generalized GrSbner basis in commutative polynomial rings", Bachelor Thesis, M.I.T., Dept. of Comp. Scie., 1978.
	3	Bruno Buchberger, Basic features and development of the critical-pair/completion procedure, Proc. of the first international conference on Rewriting techniques and applications, p.1-45, December 1985, Dijon, France
	4	H. M. M~iller and F. Mora, "New constructive methods in classical ideal theory" Journ. Algebra, 99, 1986.
	5	D. Bayer, F. Mora, H. M. M611er, private comrnuni cation.

CITED BY 3

	B. Wall, On the computation of syzygies, ACM SIGSAM Bulletin, v.23 n.4, p.5-14, Oct. 1989
	N. Takayama, Gröbner basis, integration and transcendental functions, Proceedings of the international symposium on Symbolic and algebraic computation, p.152-156, August 20-24, 1990, Tokyo, Japan
	Franz Baader, Unification in commutative theories, Hilbert's basis theorem, and Gröbner bases, Journal of the ACM (JACM), v.40 n.3, p.477-503, July 1993