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SUMMARY:Parametric Groebner basis computations and elimination - Deepak Ka
 pur (University of New Mexico)
DTSTART:20170727T100000Z
DTEND:20170727T110000Z
UID:TALK74701@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Parametric Groebner basis and systems were proposed in 1990&#3
 9\;s independently by Weispfenning and Kapur to study solutions of paramet
 ric polynomials for various specializations of parameters. Kapur&#39\;s mo
 tivation for studying them arose from the application of geometry theorem 
 proving and model based image analysis.&nbsp\; Recently there is interest 
 in using these structures for developing heuristics that first consider eq
 ualities over the complex field in a formula expressed using ordering rela
 tion with an objective of developing an incomplete method for solving prob
 lems formulated in the theory of real closed field. It is hoped this incom
 plete approach can handle a larger class of problems in practice than the 
 cylinderical algebraic decomposition method by Collins and his collaborato
 rs.&nbsp\; We will give an overview of algorithms for computing parametric
  Groebner basis and system developed in collaboration with Profs. Sun and 
 Wang of the Academy of Mathematics and System Science of the Chinese Acade
 my of Sciences. An existence proof of a canonical comprehensive Groebner b
 asis associated a parametric ideal will be presented. However\, an algorit
 hm to compute this object is still elusive.&nbsp\; Some open problems in t
 his topic will be discussed.<br><br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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