Logo of Humboldt-Universität zu BerlinLogo of Humboldt-Universität zu Berlin
edoc-Server
Open-Access-Publikationsserver der Humboldt-Universität
de|en
Header image: facade of Humboldt-Universität zu Berlin
View Item 
  • edoc-Server Home
  • Schriftenreihen und Sammelbände
  • Fakultäten und Institute der HU
  • Institut für Mathematik
  • Preprints aus dem Institut für Mathematik
  • View Item
  • edoc-Server Home
  • Schriftenreihen und Sammelbände
  • Fakultäten und Institute der HU
  • Institut für Mathematik
  • Preprints aus dem Institut für Mathematik
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.
All of edoc-ServerCommunity & CollectionTitleAuthorSubjectThis CollectionTitleAuthorSubject
PublishLoginRegisterHelp
StatisticsView Usage Statistics
All of edoc-ServerCommunity & CollectionTitleAuthorSubjectThis CollectionTitleAuthorSubject
PublishLoginRegisterHelp
StatisticsView Usage Statistics
View Item 
  • edoc-Server Home
  • Schriftenreihen und Sammelbände
  • Fakultäten und Institute der HU
  • Institut für Mathematik
  • Preprints aus dem Institut für Mathematik
  • View Item
  • edoc-Server Home
  • Schriftenreihen und Sammelbände
  • Fakultäten und Institute der HU
  • Institut für Mathematik
  • Preprints aus dem Institut für Mathematik
  • View Item
1996-03-21Buch DOI: 10.18452/2538
Polar Varieties and Efficient Real Equation Solving
The Hypersurface Case
Bank, Bernd
Giusti, Marc
Heintz, Joos
Mandel, R.
Mbakop, G. M.
The objective of this paper is to show how the recently proposed method by Giusti, Heintz, Morais, Morgenstern, Pardo can be applied to a case of real polynomial equation solving. Our main result concerns the problem of finding one representative point for each connected component of a real bounded smooth hypersurface. The algorithm in yields a method for symbolically solving a zero-dimensional polynomial equation system in the affine (and toric) case. Its main feature is the use of adapted data structure: Arithmetical networks and straight-line programs. The algorithm solves any affine zero-dimensional equation system in non-uniform sequential time that is polynomial in the length of the input description and an adequately defined affine degree of the equation system. Replacing the affine degree of the equation system by a suitably defined real degree of certain polar varieties associated to the input equation, which describes the hypersurface under consideration, and using straight-line program codification of the input and intermediate results, we obtain a method for the problem introduced above that is polynomial in the input length and the real degree.
Files in this item
Thumbnail
10.pdf — Adobe PDF — 224.7 Kb
MD5: bb5faa0108ff5e7cb56dc5e2b5ed3468
Cite
BibTeX
EndNote
RIS
InCopyright
Details
DINI-Zertifikat 2019OpenAIRE validatedORCID Consortium
Imprint Policy Contact Data Privacy Statement
A service of University Library and Computer and Media Service
© Humboldt-Universität zu Berlin
 
DOI
10.18452/2538
Permanent URL
https://doi.org/10.18452/2538
HTML
<a href="https://doi.org/10.18452/2538">https://doi.org/10.18452/2538</a>