Deterministically Computing Reduction Numbers of Polynomial Ideals
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Co-author(s): Amir Hashemi and Michael Schweinfurter |
Reference: Computer Algebra in Scientific Computing - CASC 2014,
V.P. Gerdt, W. Koepf, W.M. Seiler, E.V. Vorozhtsov (eds.), Springer-Verlag,
Berlin 2014, Lecture Notes in Computer Science 8660, pp. 186-201 |
Description: We study how to compute the absolute and the big reduction number of a
polynomial ideal and the set of all possible reduction numbers. The emphasis
is on deterministic approaches that do not apply probabilistic methods (for
example to compute the generic initial ideal). For the absolute reduction
number, we add sufficiently generic linear forms and then compute the
regularity of the obtained reduction with Pommaret bases. For computing the
reduction number set (and thus also the big reduction number), we use
Gröbner systems. While computationally rather expensive, we believe that
this approach is still much more efficient than alternative approaches
proposed in the literature. |
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