Abstract
This paper proposes a geometric-object-oriented language for symbolic geometric computation, reasoning, and visualization. In this language, geometric objects are constructed with indefinite parametric data. Modifications and basic operations on these objects are enabled. Degeneracy and uncertainty are handled effectively by means of imposing conditions and assumptions and geometric statements are formulated by declaring relations among different objects. A system implemented on the basis of this language will allow the user to perform geometric computation and reasoning rigorously and to prove geometric theorems and generate geometric diagrams and interactive documents automatically. We present the overall design of the language, explain the capabilities, features, main components of the proposed system, provide specifications for some of its functors, report our experiments with a preliminary implementation of the system, and discuss some encountered difficulties and research problems.
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References
Brown, C.: W., Hong, H.: QEPCAD — Quantifier elimination by partial cylindrical algebraic decomposition (2004), http://www.cs.usna.edu/~qepcad/B/QEPCAD.html
Chou, S.-C., Gao, X.-S., Liu, Z., Wang, D.-K., Wang, D.: Geometric theorem provers and algebraic equation solvers. In: Gao, X.-S., Wang, D. (eds.) Mathematics Mechanization and Applications, pp. 491–505. Academic Press, London (2000)
Hilbert, D.: Grundlagen der Geometrie. Teubner, Stuttgart (1899)
Jaffar, J., Maher, M.J.: J.: Constraint logic programming: A survey. J. Logic Program. 19/20, 503–581 (1994)
Kapur, D.: Using Gröbner bases to reason about geometry problems. J. Symb. Comput. 2, 399–408 (1986)
Kutzler, B.: Algebraic Approaches to Automated Geometry Theorem Proving. Ph.D. thesis, RISC-Linz, Johannes Kepler University, Austria (1988)
Kutzler, B., Stifter, S.: On the application of Buchberger’s algorithm to automated geometry theorem proving. J. Symb. Comput. 2, 389–397 (1986)
Wang, D.: Elimination procedures for mechanical theorem proving in geometry. Ann. Math. Artif. Intell. 13, 1–24 (1995)
Wang, D.: GEOTHER 1.1: Handling and proving geometric theorems automatically. In: Winkler, F. (ed.) ADG 2002. LNCS (LNAI), vol. 2930, pp. 194–215. Springer, Heidelberg (2004)
Wu, W.-t.: Mechanical Theorem Proving in Geometries: Basic Principles. Springer, Wien New York (1994) (translated from the Chinese by X. Jin and D. Wang)
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© 2006 Springer-Verlag Berlin Heidelberg
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Liang, T., Wang, D. (2006). Towards a Geometric-Object-Oriented Language. In: Hong, H., Wang, D. (eds) Automated Deduction in Geometry. ADG 2004. Lecture Notes in Computer Science(), vol 3763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11615798_9
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DOI: https://doi.org/10.1007/11615798_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31332-8
Online ISBN: 978-3-540-31363-2
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