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On the complexity of multivariate polynomial division. (English) Zbl 1383.68039
Kotsireas, Ilias S. (ed.) et al., Applications of computer algebra, Kalamata, Greece, July 20–23, 2015. Cham: Springer (ISBN 978-3-319-56930-7/hbk; 978-3-319-56932-1/ebook). Springer Proceedings in Mathematics & Statistics 198, 447-458 (2017).
Summary: In this paper, we present a new algorithm for reducing a multivariate polynomial with respect to an autoreduced tuple of other polynomials. In a suitable sparse complexity model, it is shown that the execution time is essentially the same (up to a logarithmic factor) as the time needed to verify that the result is correct.
For the entire collection see [Zbl 1379.13001].
MSC:
68Q25 Analysis of algorithms and problem complexity
12Y05 Computational aspects of field theory and polynomials (MSC2010)
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
13P05 Polynomials, factorization in commutative rings
68W30 Symbolic computation and algebraic computation
68W40 Analysis of algorithms
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