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Automated proving and analysis of geometric theorems in coordinate-free form by using the anticommutative Gröbner basis method

Abstract

Some geometric theorems can be stated in coordinate-free form as polynomials in Grassman algebra and can be proven by the anticommutative Gröbner basis method. In this article, we analyze some properties of both sets of hypotheses and conclusions of the theorem.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 213–228, 2003.

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Tchoupaeva, I.J. Automated proving and analysis of geometric theorems in coordinate-free form by using the anticommutative Gröbner basis method. J Math Sci 135, 3409–3419 (2006). https://doi.org/10.1007/s10958-006-0170-2

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Keywords

  • Basis Method
  • Geometric Theorem
  • Automate Prove