Abstract
We introduce a software package, MMP/Geometer, developed by us to automate some of the basic geometric activities including geometric theorem proving, geometric theorem discovering, and geometric diagram generation. As a theorem prover, MMP/Geometer implements Wu’s method for Euclidean and differential geometries, the area method and the geometric deductive database method. With these methods, we can not only prove difficult geometric theorems but also discover new theorems and generate short and readable proofs. As a geometric diagram editor, MMP/Geometer is an intelligent dynamic geometric software tool which may be used to input and manipulate geometric diagrams conveniently and interactively by combining the idea of dynamic geometry and methods of automated diagram generation.
This work was supported by a National Key Basic Research Project (NO. G19980306) and by a USA NSF grant CCR-0201253.
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Aubry, P., Lazard, D., Moreno Maza, M.: On the Theories of Triangular Sets. J. of Symbolic Computation 28, 45–124 (1999)
Chou, S.C.: Mechanical Geometry Theorem Proving. D.Reidel Publishing Company, Dordrecht (1988)
Chou, S.C., Gao, X.S.: Ritt-Wu’s Decomposition Algorithm and Geometry Theorem Proving. In: Stickel, M.E. (ed.) CADE 1990. LNCS, vol. 449, pp. 207–220. Springer, Heidelberg (1990)
Chou, S.C., Gao, X.S.: Mechanical Formula Derivation in Elementary Geometries. In: Proc. ISSAC 1990, pp. 265–270. ACM Press, New York (1990)
Chou, S.C., Gao, X.S.: Proving Constructive Geometry Statements. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 20–34. Springer, Heidelberg (1992)
Chou, S.C., Gao, X.S.: Automated Reasoning in Differential Geometry and Mechanics: Part II. Mechanical Theorem Proving. J. of Automated Reasoning 10, 173–189 (1993)
Chou, S.C., Gao, X.S.: Automated Reasoning in Geometry. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 709–749. Elsevier, Amsterdam (2001)
Chou, S.C., Gao, X.S., Zhang, J.Z.: Machine Proofs in Geometry. World Scientific, Singapore (1994)
Chou, S.C., Gao, X.S., Zhang, J.Z.: A Deductive Database Approach To Automated Geometry Theorem Proving and Discovering. J. Automated Reasoning 25, 219–246 (2000)
Davis, P.J.: The Rise, Fall, and Possible Transfiguration of Triangle Geometry: A Mini-history. The American Mathematical Monthly 102, 204–214 (1993)
Gao, X.S., Huang, L., Jiang, K.: A Hybrid Method for Solving Geometric Constraint Problems. In: Richter-Gebert, J., Wang, D. (eds.) ADG 2000. LNCS (LNAI), vol. 2061, pp. 16–25. Springer, Heidelberg (2001)
Gao, X.S., Wang, D.K., Qiu, Z., Yang, H., Lin, D.: MMP: A Mathematics- Mechanization Platform - a Progress Report, Preprints, MMRC, Academ, ia Sinica (April 2002), http://www.mmrc.iss.ac.cn/~mmsoft/
Gao, X.S., Zhang, J.Z., Chou, S.C.: Geometry Expert. Nine Chapter Pub., Taipai (1998) (in Chinese)
Gao, X.S., Zhang, G.: Geometric Constraint Solving via C-tree Decomposition. In: Proc. of ACM SM 2003, Seattle, June 2003. ACM Press, New York (2003)
Gao, X.S., Hoffmann, C.M., Yang, W.: Solving Basic Gometric Constraint Configurations with Locus Intersection. In: Proc. ACM SM 2002, Saarbruecken Germany, pp. 95–104. ACM Press, New York (2002)
Gao, X.-S., Zhu, C., Chou, S.-C., Ge, J.-X.: Automated Generation of Kempe Linkages for Algebraic Curves and Surfaces. Mechanism and Machine Theory 36(9), 1019–1033 (2002)
Ge, J., Chou, S.C., Gao, X.S.: Geometric Constraint Satisfaction Using Optimization Methods. Computer Aided Design 31(14), 867–879 (2000)
Gelernter, H.: Realization of a Geometry-theorem Proving Machine. In: Feigenbaum, E.A., Feldman, J. (eds.) Comput. and Thought, pp. 134–152. Mcgraw Hill, New York (1963)
Heydon, A., Nelson, G.: The Juno-2 Constraint-Based Drawing Editor. SRC Research Report 131a (1994)
Hoffmann, C.: Geometric Constraint Solving in R2 and R3. In: Du, Z., Huang, F. (eds.) Computing in Euclidean Geometry, pp. 266–298. World Scientific, Singapore (1995)
Hong, H., Wang, D., Winkler, F.: Short Description of Existing Provers. Ann. Math. Artif. Intell. 13, 195–202 (1995)
Jakiw, N.: Geometer’s Sketchpad, User Guide and Reference Manual. Key Curriculum Press, Berkeley (1994)
Laborde, J.M.: GABRI Geometry II, Texas Instruments, Dallas (1994)
Latheam, R.S., Middleditch, A.E.: Connectivity Analysis: a Tool for Processing Geometric Constraints. Computer Aided Design 28(11), 917–928 (1994)
Lazard, D.: A New method for Solving Algebraic Systems of Positive Dimension. Discrete Appl. Math. 33, 147–160 (1991)
Kalkbrener, M.: A Generalized Euclidean Algorithm for Computing Triangular Representations of Algebraic Varieties. J. Symb. Comput. 15, 143–167 (1993)
Kapur, D., Wan, H.K.: Refutational Proofs of Geometry Theorems via Characteristic Set Computation. In: Proc. of ISSAC 1990, pp. 277–284. ACM Press, New York (1990)
Richter-Gebert, J., Kortenkamp, U.H.: The Interactive Geometry Software Cinderalla. Springer, Berlin (1999)
Owen, J.: Algebraic Solution for Geometry from Dimensional Constraints. In: ACM Symp. Found of Solid Modeling, pp. 397–407. ACM Press, Austin (1991)
Wang, D.: Elimination Methods. Springer, Berlin (2000)
Wang, D.: Geother: A Geometry Theorem Prover. In: McRobbie, M.A., Slaney, J.K. (eds.) CADE 1996. Lecture Notes in Computer Science(LNAI), vol. 1104, pp. 166–170. Springer, Heidelberg (1996)
Wang, D.K.: Polynomial Equations Solving and Mechanical Geometric Theorem Proving. Ph.D Thesis, Inst. of Sys. Sci., Academia Sinica (1993)
Wu, W.T.: Basic Principles of Mechanical Theorem Proving in Geometries. Science Press, Beijing (1984) (in chinese); English Version, Springer-Verlag, Berlin (1994)
Wu, W.T.: A Mechanization Method of Geometry and its Applications I. Distances, Areas, and Volumes. J. Sys. Sci. and Math. Scis. 6, 204–216 (1986)
Wu, W.T.: A Constructive Theory of Differential Algebraic Geometry. In: LNM, vol. 1255, pp. 173–189. Springer, Berlin (1987)
Wu, W.T.: Mathematics Mechanization. Science Press/Kluwer, Beijing (2000)
Yang, L., Zhang, J., Hou, X.R.: Nonlinear Algebraic Equation System and Automated Theorem Proving. Shanghai Sci. and Tech. Education Publ. House, Shanghai (1996) [in Chinese]
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Gao, XS., Lin, Q. (2004). MMP/Geometer – A Software Package for Automated Geometric Reasoning. In: Winkler, F. (eds) Automated Deduction in Geometry. ADG 2002. Lecture Notes in Computer Science(), vol 2930. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24616-9_4
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DOI: https://doi.org/10.1007/978-3-540-24616-9_4
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