Using Gröbner bases to reason about geometry problems
Journal of Symbolic Computation
Automated reasoning in geometries using the characteristic set method and Gröbner basis method
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Automated geometry theorem proving by vector calculation
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
Generalized homogeneous coordinates for computational geometry
Geometric computing with Clifford algebras
A Deductive Database Approach to Automated Geometry Theorem Proving and Discovering
Journal of Automated Reasoning
Symbolic computation in the homogeneous geometric model with clifford algebra
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
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The existing readable machine proving methods deal with geometry problems using some geometric quantities. In this paper, we focus on the mass point method which directly deals with the geometric points rather than the geometric quantities. We propose two algorithms, Mass Point Method and Complex Mass Point Method, which can deal with the Hilbert intersection point statements in affine geometry and the linear constructive geometry statements in metric geometry respectively. The two algorithms are implemented in Maple as provers. The results of hundreds of non-trivial geometry statements run by our provers show that the mass point method is efficient and the machine proofs are human-readable.