B. Buchberger
Abstract
We define a certain type of bases of polynomial ideals whose usefulness stems from the fact that a number of computability problems in the theory of polynomial ideals (e.g. the problem of constructing canonical forms for polynomials) is reducible to the construction of bases of this type. We prove a characterization theorem for these bases which immediately leads to an effective method for their construction.
- B. Buchberger, Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nuildimensionalen Polynomideal, Dissertation, Universität Innsbruck, 1965.Google Scholar
- B. Buchberger, Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems, Aequationes mathematicae, Vol. 4/3, S. 374--383, 1970.Google Scholar
- B. Buchberger, On Certain Bases of Polynomial ideals, Bericht Nr. 53, Institut für Mathematik, Universität Linz.Google Scholar
- W. Gröbner, Personal communication, Seminar d. institutes für Mathematik, Universität Innsbruck, 1964.Google Scholar
- M. Lauer, Canonical Representatives for Residue Classes of a Polynomial ideal, to appear in the Proceedings of the SIGSAM Conference 1976, ACM. Google ScholarDigital Library
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