Complexity of Membership Problems of Different Types of Polynomial Ideals

Ernst W. Mayr () and Stefan Toman ()
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Ernst W. Mayr: TU München, Institut für Informatik
Stefan Toman: TU München, Institut für Informatik

A chapter in Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, 2017, pp 481-493 from Springer

Abstract: Abstract We survey degree bounds and complexity classes of the word problem for polynomial ideals and related problems. The word problem for general polynomial ideals is known to be exponential space-complete, but there are several interesting subclasses of polynomial ideals that allow for better bounds. We review complexity results for polynomial ideals with low degree, toric ideals, binomial ideals, and radical ideals. Previously known results as well as recent findings in our project “Degree Bounds for Gröbner Bases of Important Classes of Polynomial Ideals and Efficient Algorithms” are presented.

Keywords: Polynomial ideal; Binomial ideal; Gröbner basis; Degree bound; Radical; Thue system; Cellular decomposition; Computational complexity; 13P10; 14Q20; 03D40; 08A50; 03D03; 06B10 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-70566-8_20

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DOI: 10.1007/978-3-319-70566-8_20

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