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Some properties of Gröbner-bases for polynomial ideals
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Source ACM SIGSAM Bulletin archive
Volume 10 ,  Issue 4  (November 1976) table of contents
Pages: 19 - 24  
Year of Publication: 1976
ISSN:0163-5824
Author
B. Buchberger  Universität Linz, Austria
Publisher
ACM  New York, NY, USA
Bibliometrics
Downloads (6 Weeks): 2,   Downloads (12 Months): 13,   Citation Count: 8
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ABSTRACT

We give a uniqueness theorem for Gröbner-bases of polynomial ideals and show that it is effectively decidable whether a given basis is a (minimal normed) Gröbner-basis. Incidentally, we show how our methods may be applied to decide α ≤ β for given polynomial ideals α and β.


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
B. Buchberger, A theoretical basis for the reduction of polynomials to canonical forms, ACM SIGSAM Bulletin, v.10 n.3, p.19-29, August 1976  [doi>10.1145/1088216.1088219]

CITED BY  8
S. R. Czapor , K. O. Geddes, On implementing Buchberger's algorithm for Grobner bases, Proceedings of the fifth ACM symposium on Symbolic and algebraic computation, p.233-238, July 21-23, 1986, Waterloo, Ontario, Canada
Michael E. Pohst , David Y. Y. Yun, On solving systems of algebraic equations via ideal bases and elimination theory, Proceedings of the fourth ACM symposium on Symbolic and algebraic computation, p.206-211, August 05-07, 1981, Snowbird, Utah, United States
Armita Peymandoust , Giovanni De Micheli, Using symbolic algebra in algorithmic level DSP synthesis, Proceedings of the 38th conference on Design automation, p.277-282, June 2001, Las Vegas, Nevada, United States
G. L. Ebert, Some comments on the modular approach to Gröbner-bases, ACM SIGSAM Bulletin, v.17 n.2, p.28-32, May 1983
Armita Peymandoust , Giovanni De Micheli, Symbolic algebra and timing driven data-flow synthesis, Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design, November 04-08, 2001, San Jose, California
Sivaram Gopalakrishnan , Priyank Kalla , M. Brandon Meredith , Florian Enescu, Finding linear building-blocks for RTL synthesis of polynomial datapaths with fixed-size bit-vectors, Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design, November 05-08, 2007, San Jose, California
F. Winkler , B. Buchberger , F. Lichtenberger , H. Rolletschek, ALGORITHM 628: an algorithm for constructing canonical bases of polynomial ideals, ACM Transactions on Mathematical Software (TOMS), v.11 n.1, p.66-78, March 1985
Yuki Watanabe , Naofumi Homma , Takafumi Aoki , Tatsuo Higuchi, Arithmetic Circuit Verification Based on Symbolic Computer Algebra, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, v.E91-A n.10, p.3038-3046, October 2008
Collaborative Colleagues:
B. Buchberger: colleagues

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