Abstract
The aim of this project is to illustrate how the framework of polynomial rings and computational methods designed for them can be of help in proving (plane) geometry theorems. The idea is not original and there are already, even for the beginner, excellent references concerning this topic. In coherence with the ‘tapas’ style of this book, we recall a few, tasty ones: for instance, the recent book by the founder of the modern approach to automatic geometry theorem proving, Wu Wen Tsun [5]; the textbook [2], which integrates one section on this material in a commutative algebra/algebraic geometry course, and the book by Chou [1], including an impressive collection of computed examples.
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References
S. C. Chou (1987): Mechanical Geometry Theorem Proving, D. Reidel.
D. Cox, J. Little, and D. O’Shea (1992): Ideals, Varieties, and Algorithms, Undergraduate Texts in Mathematics, Springer-Verlag, New York Berlin Heidelberg.
D. Kapur (1986): Geometry theorem proving using Hilberths Nullstellensatz, pp. 202–208, in: Proc. of the 1986 Symposium on Symbolic and Algebraic Computation, Ed. B.W. Char, ACM Press, Waterloo.
T. Recio and M. P. Vélez (1996): Automatic discovery of theorems in elementary geometry, submitted to Journal of Automated Reasoning.
W. T. Wu (1994): Mechanical Theorem Proving in Geometries, Texts and Monographs in Symbolic Computation, Springer-Verlag, Berlin Heidelberg New York.
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© 1999 Springer-Verlag Berlin Heidelberg
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Recio, T., Sterk, H., Vélez, M.P. (1999). Automatic Geometry Theorem Proving. In: Cohen, A.M., Cuypers, H., Sterk, H. (eds) Some Tapas of Computer Algebra. Algorithms and Computation in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03891-8_12
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DOI: https://doi.org/10.1007/978-3-662-03891-8_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08335-8
Online ISBN: 978-3-662-03891-8
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