2011 Apr 09 at 14:30
DC 1302
Christopher Brown, US Naval Academy
In symbolic computing, most of us are familiar with the basics of computing with polynomial systems over algebraically closed fields. We speak of systems of equations or, equivalently, the varieties they define; of elimination or projection. Most of the community is much less familiar with polynomial systems over the reals, where the fundamental questions and the kinds of solutions we get are very different. We speak of Tarski formulas and semi-algebraic sets, and problems from formal logic like quantifier elimination. This talk first looks at why the basic problem is different in the real case, and what solutions look like in the real case. It then looks at several algorithms, both recent and not so recent, that seem to be answering the same questions, and tries to understand them by their different perspectives of what the problem is and what constitutes a solution.
This talk is part of the East Coast Computer Algebra Day (ECCAD 2011). ECCAD is open to all and free to attend, but we encourage registration. See http://www.cs.uwaterloo.ca/conferences/eccad2011