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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

Open Access
Online
ISSN
1898-9934
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Volume 24, Issue 4 (Dec 2016)

Issues

Homography in ℝℙ

Roland Coghetto
Published Online: 2017-02-23 | DOI: https://doi.org/10.1515/forma-2016-0020

Summary

The real projective plane has been formalized in Isabelle/HOL by Timothy Makarios [13] and in Coq by Nicolas Magaud, Julien Narboux and Pascal Schreck [12].

Some definitions on the real projective spaces were introduced early in the Mizar Mathematical Library by Wojciech Leonczuk [9], Krzysztof Prazmowski [10] and by Wojciech Skaba [18].

In this article, we check with the Mizar system [4], some properties on the determinants and the Grassmann-Plücker relation in rank 3 [2], [1], [7], [16], [17].

Then we show that the projective space induced (in the sense defined in [9]) by ℝ3 is a projective plane (in the sense defined in [10]).

Finally, in the real projective plane, we define the homography induced by a 3-by-3 invertible matrix and we show that the images of 3 collinear points are themselves collinear.

Keywords: projectivity; projective transformation; projective collineation; real projective plane; Grassmann-Plücker relation

MSC 2010: 51N15; 03B35

References

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About the article

Received: 2016-10-18

Published Online: 2017-02-23

Published in Print: 2016-12-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.1515/forma-2016-0020.

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© 2016 Roland Coghetto, published by De Gruyter Open. This work is licensed under version 3.0 of the Creative Commons Attribution–ShareAlike License. BY-SA 3.0

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Roland Coghetto
Formalized Mathematics, 2017, Volume 25, Number 2

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