Spreads and Packings of PG(3,2), Formally!

Nicolas Magaud
(ICube UMR 7357 CNRS, Université de Strasbourg, France)

We study how to formalize in the Coq proof assistant the smallest projective space PG(3,2). We then describe formally the spreads and packings of PG(3,2), as well as some of their properties. The formalization is rather straightforward, however as the number of objects at stake increases rapidly, we need to exploit some symmetry arguments as well as smart proof techniques to make proof search and verification faster and thus tractable using the Coq proof assistant. This work can be viewed as a first step towards formalizing projective spaces of higher dimension, e.g. PG(4,2), or larger order, e.g. PG(3,3).

In Predrag Janičić and Zoltán Kovács: Proceedings of the 13th International Conference on Automated Deduction in Geometry (ADG 2021), Hagenberg, Austria/virtual, September 15-17, 2021, Electronic Proceedings in Theoretical Computer Science 352, pp. 107–115.
Published: 30th December 2021.

ArXived at: http://dx.doi.org/10.4204/EPTCS.352.12 bibtex PDF
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