10.4230/LIPICS.RTA.2012.1
Anai, Hirokazu
Hirokazu
Anai
Computational Real Algebraic Geometry in Practice (Invited Talk)
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
2012
Invited Talk
real algebraic geometry
quantifier elimination
cylindrical algebraic decomposition
symbolic optimization
Tiwari, Ashish
Ashish
Tiwari
2012
2012-05-29
2012-05-29
2012-05-29
en
urn:nbn:de:0030-drops-34784
10.4230/LIPIcs.RTA.2012
978-3-939897-38-5
1868-8969
10.4230/LIPIcs.RTA.2012
LIPIcs, Volume 15, RTA 2012
23rd International Conference on Rewriting Techniques and Applications (RTA'12)
2013
15
1
1
1
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Tiwari, Ashish
Ashish
Tiwari
1868-8969
Leibniz International Proceedings in Informatics (LIPIcs)
2012
15
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
1 pages
249359 bytes
application/pdf
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
info:eu-repo/semantics/openAccess
Real algebraic geometry deals with the solution set of (possibly quantified) systems of polynomial equations and/or inequalities over the real numbers, which arise frequently in science and engineering.
Main concern in real algebraic geometry is to determine the properties of the solution sets such as non-emptiness, dimension and quantifier free description as a semi-algebraic set. Such tasks are carried out by symbolic and algebraic algorithms:cylindrical algebraic decomposition (CAD) or quantifier elimination (QE).
Various algorithms and deep complexity results about CAD and QE have been studied during the last several decades. Moreover, practically efficient software systems of QE have been developed and also are applied to many nontrivial application problems. In this talk we explain several algorithms of CAD and QE together with their engineering applications.
LIPIcs, Vol. 15, 23rd International Conference on Rewriting Techniques and Applications (RTA'12), pages 1-1