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Equation solving in projective planes and planar ternary rings

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Algebraic and Logic Programming (ALP 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 850))

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Abstract

A geometrical approach to algebraic reasoning is presented. To every system of algebraic equations in the language of planar ternary rings is associated a system of equations in the language of a first order theory with equality equivalent to projective geometry. A narrowing-based mechanism computes the solutions of this geometrical system corresponding to the solutions of the original algebraic problem. As a corollary, unification in planar ternary rings is finitary and constitutes a decidable class of problems for which a type conformal algorithm exists.

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Authors and Affiliations

  1. Institut de recherche en informatique de Toulouse, France

    Philippe Balbiani

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  1. Philippe Balbiani
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Giorgio Levi Mario Rodríguez-Artalejo

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© 1994 Springer-Verlag

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Balbiani, P. (1994). Equation solving in projective planes and planar ternary rings. In: Levi, G., Rodríguez-Artalejo, M. (eds) Algebraic and Logic Programming. ALP 1994. Lecture Notes in Computer Science, vol 850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58431-5_9

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  • DOI: https://doi.org/10.1007/3-540-58431-5_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58431-5

  • Online ISBN: 978-3-540-48791-3

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