Homography in ℝℙ

Pole DC	Wartość	Język
dc.contributor.author	Coghetto, Roland	-
dc.date.accessioned	2017-06-02T11:55:28Z	-
dc.date.available	2017-06-02T11:55:28Z	-
dc.date.issued	2016	-
dc.identifier.citation	Formalized Mathematics, Volume 24, Issue 4, pp. 239-252	pl
dc.identifier.issn	1426-2630	pl
dc.identifier.issn	1898-9934	pl
dc.identifier.uri	http://hdl.handle.net/11320/5558	-
dc.description.abstract	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.	-
dc.language.iso	en	-
dc.publisher	De Gruyter Open	-
dc.subject	projectivity	-
dc.subject	projective transformation	-
dc.subject	projective collineation	-
dc.subject	real projective plane	-
dc.subject	Grassmann-Plücker relation	-
dc.title	Homography in ℝℙ	-
dc.type	Article	-
dc.identifier.doi	10.1515/forma-2016-0020	-
dc.description.Affiliation	Rue de la Brasserie 5, 7100 La Louvière, Belgium	-
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