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DOI: 10.4230/LIPIcs.TYPES.2011.1

Non-constructive complex analysis in Coq

Authors: Aloïs Brunel

Published in: LIPIcs, Volume 19, 18th International Workshop on Types for Proofs and Programs (TYPES 2011)

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.

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Aloïs Brunel. Non-constructive complex analysis in Coq. In 18th International Workshop on Types for Proofs and Programs (TYPES 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 19, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{brunel:LIPIcs.TYPES.2011.1,
  author =	{Brunel, Alo\"{i}s},
  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 =	{Danielsson, Nils Anders and Nordstr\"{o}m, Bengt},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2011.1},
  URN =		{urn:nbn:de:0030-drops-38968},
  doi =		{10.4230/LIPIcs.TYPES.2011.1},
  annote =	{Keywords: Coq, winding number, complex analysis}
}

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Non-constructive complex analysis in Coq

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