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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Parametric Groebner basis computations and elimina
tion - Deepak Kapur (University of New Mexico)
DTSTART;TZID=Europe/London:20170727T110000
DTEND;TZID=Europe/London:20170727T120000
UID:TALK74701AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/74701
DESCRIPTION:Parametric Groebner basis and systems were propose
d in 1990'\;s independently by Weispfenning and
Kapur to study solutions of parametric polynomial
s for various specializations of parameters. Kapur
'\;s motivation for studying them arose from th
e application of geometry theorem proving and mode
l based image analysis. \; Recently there is i
nterest in using these structures for developing h
euristics that first consider equalities over the
complex field in a formula expressed using orderin
g relation with an objective of developing an inco
mplete method for solving problems formulated in t
he theory of real closed field. It is hoped this i
ncomplete approach can handle a larger class of pr
oblems in practice than the cylinderical algebraic
decomposition method by Collins and his collabora
tors. \; We will give an overview of algorithm
s for computing parametric Groebner basis and syst
em developed in collaboration with Profs. Sun and
Wang of the Academy of Mathematics and System Scie
nce of the Chinese Academy of Sciences. An existen
ce proof of a canonical comprehensive Groebner bas
is associated a parametric ideal will be presented
. However\, an algorithm to compute this object is
still elusive. \; Some open problems in this
topic will be discussed.

LOCATION:Seminar Room 2\, Newton Institute
CONTACT:INI IT
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