HAL: hal-00657901, version 1

DOI: 10.1007/978-3-642-25070-5_3

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Automated Deduction in Geometry, ADG 2010, Munich : Allemagne (2010)

A Formalization of Grassmann-Cayley Algebra in COQ and Its Application to Theorem Proving in Projective Geometry

Laurent Fuchs (  Corresponding author ) 1, Laurent Thery 2

(2011)

This paper presents a formalization of Grassmann-Cayley algebra that has been done in the COQ proof assistant. The formalization is based on a data structure that represents elements of the algebra as complete binary trees. This allows to define the algebra products recursively. Using this formalization, published proofs of Pappus' and Desargues' theorem are interactively derived. A method that automatically proves projective geometric theorems is also translated successfully into the proposed formalization.

1:	XLIM (XLIM)
	CNRS : UMR6172 – Université de Limoges
2:	MARELLE (INRIA Sophia Antipolis)
	INRIA

Research team: SIC

Subject

:

Computer Science/Formal Languages and Automata Theory Computer Science/Computational Geometry Mathematics/Commutative Algebra

Keyword(s): Grassmann-Cayley algebra – COQ proof assistant – Automated theorem proving – projective geometry

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From: Laurent Fuchs <>

Submitted on: Monday, 9 January 2012 14:34:35

Updated on: Monday, 9 January 2012 15:11:36