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http://hdl.handle.net/11320/5558
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Pole DC | Wartość | Język |
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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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dc.description.references | Nicolas Magaud, Julien Narboux, and Pascal Schreck. Formalizing projective plane geometry in Coq. In Automated Deduction in Geometry, pages 141–162. Springer, 2008. | - |
dc.description.references | Timothy James McKenzie Makarios. A mechanical verification of the independence of Tarski’s Euclidean Axiom. Victoria University of Wellington, New Zealand, 2012. Master’s thesis. | - |
dc.description.references | Karol Pąk. Basic properties of the rank of matrices over a field. Formalized Mathematics, 15(4):199–211, 2007. doi:10.2478/v10037-007-0024-5. | - |
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dc.description.references | Jürgen Richter-Gebert. Mechanical theorem proving in projective geometry. Annals of Mathematics and Artificial Intelligence, 13(1-2):139–172, 1995. | - |
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Występuje w kolekcji(ach): | Formalized Mathematics, 2016, Volume 24, Issue 4 |
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