Abstract
In /Bu65/, /Bu70/, /Bu76/ B. Buchberger presented an algorithm which, given a basis for an ideal in K[x1,...,xn] (the ring of polynomials in n indeterminates over the field K), constructs a so-called Gröbner-basis for the ideal. The importance of Gröbner-bases for effectively carrying out a large number of construction and decision problems in polynomial ideal theory has been investigated in /Bu65/, /Wi78/, /WB81/, /Bu83b/. For the case of two variables B. Buchberger /Bu79/, /Bu83a/ gave bounds for the degrees of the polynomials which are generated by the Gröbner-bases algorithm. However, no bound has been known until now for the case of more than two variables. In this paper we give such a bound for the case of three variables.
The results reported in this paper are part of the authors doctoral dissertation at the Johannes Kepler University, Linz, Austria.
The work for this paper was supported by the Austrian Research Fund under grant Nr. 4567.
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References
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Winkler, F. (1984). On the complexity of the Gröbner-bases algorithm over K[x,y,z]. In: Fitch, J. (eds) EUROSAM 84. EUROSAM 1984. Lecture Notes in Computer Science, vol 174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032841
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DOI: https://doi.org/10.1007/BFb0032841
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