2000-01-06Buch DOI: 10.18452/2699
Equations for Polar Varieties and Efficient Real Elimination
 dc.contributor.author Bank, Bernd dc.contributor.author Giusti, Marc dc.contributor.author Heintz, Joos dc.contributor.author Mbakop, G. M. dc.date.accessioned 2017-06-15T18:01:01Z dc.date.available 2017-06-15T18:01:01Z dc.date.created 2005-11-16 dc.date.issued 2000-01-06 dc.identifier.issn 0863-0976 dc.identifier.uri http://edoc.hu-berlin.de/18452/3351 dc.description.abstract Let \$V_0\$ be a smooth and compact real variety given by a reduced regular sequence of polynomials \$f_1,..., f_p\$. This paper is devoted to the algorithmic problem of finding efficiently for each connected component of \$V_0\$ a representative point. For this purpose we exhibit explicit polynomial equations which describe for generic variables the polar varieties of \$V_0\$ of all dimensions. This leads to a procedure which solves our algorithmic problem in time that is polynomial in the (extrinsic) description length of the input equations \$f_1,...,f_p\$ and in a suitably introduced geometric (extrinsic) parameter, called the degree of the real interpretation of the given equation system \$f_1,...,f_p\$. eng dc.language.iso eng dc.publisher Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik dc.rights.uri http://rightsstatements.org/vocab/InC/1.0/ dc.subject polar variety eng dc.subject Real polynomial equation solving eng dc.subject complexity eng dc.subject geometric degree eng dc.subject arithmetic network eng dc.subject arithmetic circuit eng dc.subject.ddc 510 Mathematik dc.title Equations for Polar Varieties and Efficient Real Elimination dc.type book dc.identifier.urn urn:nbn:de:kobv:11-10053736 dc.identifier.doi http://dx.doi.org/10.18452/2699 local.edoc.pages 31 local.edoc.type-name Buch local.edoc.container-type series local.edoc.container-type-name Schriftenreihe local.edoc.container-year 1999 dc.identifier.zdb 2075199-0 bua.series.name Preprints aus dem Institut für Mathematik bua.series.issuenumber 1999,15