Campus Event Calendar
Event Entry
What and Who
The ‘doubly-exponential’ problem in equation/inequality solving
James Davenport
University of Bath
Talk
AG 1, AG 2, AG 3, AG 4, AG 5, SWS, RG1, MMCI
Public Audience
English
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Date, Time and Location
Monday, 23 January 2017
11:00
60 Minutes
E1 5
002
Saarbrücken
Abstract
It is well-known that the degrees of Gr\”obner Bases are doubly exponential in the number of variables [MayrMeyer1982]. Similarly, real quantifier elimination can be doubly exponential in the number of variables [DavenportHeintz1988]. Recent results show that Gr\”obner bases are only doubly exponential in the dimension, not the actual number of variables. In joint with with Matthew England, we have shown that the double exponent in real quantifier elimination can be reduced by the number of equations, provided that the equations (and their iterated resultants) are content-free. We will explain these results, and why the proviso is necessary. We will also introduce the algorithm LazyRealTriangularize [Chen et al., 2013a], which in practice seems to have good behaviour, though there is no theoretical analysis.
Contact
Jennifer Müller
2900
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Jennifer Müller, 01/20/2017 08:24 -- Created document.