高维关联射影几何的机械化，一种组合方法

Automated Deduction in Geometry Pub Date : 2021-12-29 DOI:10.4204/EPTCS.352.8

P. Schreck, Nicolas Magaud, David Braun

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摘要

已经开发了一些工具来增强二维平面上定理证明的自动化。然而，在3D中，只有少数方法被研究过，据我们所知，在更高的维度中还没有做过任何事情。本文给出了3、4、5维的关联几何定理的几个例子。然后，我们将矩阵理论应用于几何，利用组合证明法对它们进行了证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Mechanization of Incidence Projective Geometry in Higher Dimensions, a Combinatorial Approach

Several tools have been developed to enhance automation of theorem proving in the 2D plane. However, in 3D, only a few approaches have been studied, and to our knowledge, nothing has been done in higher dimensions. In this paper, we present a few examples of incidence geometry theorems in dimensions 3, 4, and 5. We then prove them with the help of a combinatorial prover based on matroid theory applied to geometry.

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Automated Deduction in Geometry

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