Abstract
This paper presents a completion technique for a set of polynomials in K[X 1,..., X n] which is closed under addition and under multiplication with symmetric polynomials as well as a solution for the corresponding membership problem. Our algorithmic approach is based on a generalization of a novel rewriting technique for the computation of bases for rings of permutation-invariant polynomials.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Becker, T., Weispfenning, V., in Cooperation with Kredel, H. (1993). Gröbner Bases: A Computational Approach to Commutative Algebra. Springer, New York
Buchberger, B. (1985). Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory. In: Bose, N. K. (ed.), Multidimensional Systems Theory. Reidel, Dordrecht, 184–232
Göbel, M. (1995). Computing Bases for Permutation-Invariant Polynomials. Journal of Symbolic Computation 19, 285–291
Göbel, M. (1996). Computing Bases for Permutation-Invariant Polynomials. Dissertation, Universität Tübingen. Shaker, Aachen
Knuth, D. E., Bendix, P. B. (1970). Simple Word Problems in Universal Algebras. In: Leech, J. (ed.), Computational Problems in Abstract Algebra. Pergamon Press, 263–297
Kredel, H. (1990). MAS: Modula-2 Algebra System. In: Gerdt, V. P., Rostovtsev, V. A., and Shirkov, D. V. (eds.), IV International Conference on Computer Algebra in Physical Research. World Scientific Publishing Co., Singapore, 31–34
Loos, R. (1981). Term Reduction Systems and Algebraic Algorithms. In: Siekmann, J. H. (ed.), GWAI-81, German Workshop on Artificial Intelligence, Bad Honnef. Informatik-Fachberichte, Herausgegeben von W. Brauer im Auftrag der Gesellschaft für Informatik (GI), 47. Springer, Berlin, 214–234
Sturmfels, B. (1993). Algorithms in Invariant Theory. Springer, Vienna
Weispfenning, V. (1987). Admissible Orders and Linear Forms. ACM SIGSAM Bulletin 21/2, 16–18
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Göbel, M. (1996). Symideal Gröbner bases. In: Ganzinger, H. (eds) Rewriting Techniques and Applications. RTA 1996. Lecture Notes in Computer Science, vol 1103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61464-8_42
Download citation
DOI: https://doi.org/10.1007/3-540-61464-8_42
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61464-7
Online ISBN: 978-3-540-68596-8
eBook Packages: Springer Book Archive