License: Creative Commons Attribution-NoDerivs 3.0 Unported license (CC BY-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TYPES.2011.1
URN: urn:nbn:de:0030-drops-38968
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2013/3896/
Go to the corresponding LIPIcs Volume Portal

Brunel, Aloïs

Non-constructive complex analysis in Coq

pdf-format:
2.pdf (0.4 MB)

Abstract

Winding numbers are fundamental objects arising in algebraic topology, with many applications in non-constructive complex analysis. We present a formalization in Coq of the wind- ing numbers and their main properties. As an application of this development, we also give non-constructive proofs of the following theorems: the Fundamental Theorem of Algebra, the 2-dimensional Brouwer Fixed-Point theorem and the 2-dimensional Borsuk-Ulam theorem.

BibTeX - Entry

@InProceedings{brunel:LIPIcs:2013:3896,
  author =	{Alois Brunel},
  title =	{{Non-constructive complex analysis in Coq}},
  booktitle =	{18th International Workshop on Types for Proofs and Programs (TYPES 2011)},
  pages =	{1--15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-49-1},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{19},
  editor =	{Nils Anders Danielsson and Bengt Nordstr{\"o}m},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/3896},
  URN =		{urn:nbn:de:0030-drops-38968},
  doi =		{10.4230/LIPIcs.TYPES.2011.1},
  annote =	{Keywords: Coq, winding number, complex analysis}
}

Keywords: Coq, winding number, complex analysis
Collection: 18th International Workshop on Types for Proofs and Programs (TYPES 2011)
Issue Date: 2013
Date of publication: 21.01.2013

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI