Automated Geometry Reasoning

Automated Geometry Reasoning: Area Method

• S.C. Chou, X.S. Gao, and J.Z. Zhang, Machine Proofs in Geometry, World Scientific, Singapore, 1994.
• S.C. Chou, X.S. Gao, and J.Z. Zhang, A Deductive Database Approach To Automated Geometry Theorem Proving and Discovering, Journal Automated Reasoning, 25(3), 219-246, 2000.
• S.C. Chou, X.S. Gao, and J.Z. Zhang, Automated Generation of of Readable Proofs with Geometric Invariants, I. Multiple and Shortest Proof Generation, Journal of Automated Reasoning, 17, 325-347, 1996.
• S.C. Chou, X.S. Gao, and J.Z. Zhang, Automated Generation of of Readable Proofs with Geometric Invariants, II. Proving Theorems with Full-Angles, Journal of Automated Reasoning, 17, 349-370, 1996.
• S.C. Chou, X.S. Gao, J.Z. Zhang, Automated Production of Traditional Proofs in Solid Geometry, Journal of Automated Reasoning, 14, p.257-291, 1995.
• S.C. Chou, X.S. Gao, and J. Z. Zhang, ``Automated Production of Traditional Proofs for Theorems in Euclidean Geometry, Part I. The Hilbert Intersection Point Theorems'', Annals of Mathematics and Artificial Intelligence, 13, (1995), p.109-137.
• L. Yang, X.S. Gao, S. C. Chou, and Z. J. Zhang, Automated Proving and Discovering of Theorems in Non-Euclidean Geometries, in: Automated Deduction in Geometry\/ (D.\ Wang, ed.), LNAI 1360, Springer-Verlag, Berlin Heidelberg, 1998, pp. 171--188.
• S.C. Chou, X.S. Gao, J.Z. Zhang, ``Automated Geometry Theorem Proving by Vector Calculation'', Proceedings of ISSAC-93, 284-291.

Automated Geometry Reasoning: Algebraic Method

• S.C. Chou and X.S. Gao, Ritt-Wu's Decomposition Algorithm and Geometry Theorem Proving in Proceedings of CADE--10, Lecture Notes in Artificial Intelligence 449, Springer--Verlag, 1990, 207--220.
• S.C. Chou and X.S. Gao, Methods for Mechanical Geometry Formula Deriving in Proceedings of ISSAC'90 , Japan, ACM Press, August 1990, 265--270.
• X.S. Gao and D.K. Wang, On the Automatic Derivation of a Set of Geometric Formulae, Journal of Geometry, vol. 53, p.79-88, 1995.
• S.C. Chou, X.S. Gao, N.M. Mcphee, and S. C. Chou, ``Mechanically Proving Geometry Theorems Using a Combination of Wu's Method and Collins' Method'', in Proceedings of CADE-12, Nancy, France, June 1994, 222--236.
• S.C. Chou, X.S. Gao, and D.S. Arnon, ``On the Mechanical Proof of Geometry Theorems Involving Inequalities'' Advances in Computing Research, 1992, Vol. 6, 139--181. An international journal.
• S.C. Chou and X.S. Gao, Proving Geometry Statements of Constructive Type, in Proceedings of CADE-11, Lecture Notes in Computer Science, Vol. 607, 20--34, Springer--Verlag, 1992.
• X.S. Gao, Transcendental Functions and Mechanical Theorem Proving in Elementary Geometries, Journal of Automated Reasoning, 6:403-417, 1990, Kluwer Academic Publishers.

Automated Geometry Reasoning: Differential Geometry

• S. C. Chou and X.S. Gao, Automated Reasoning in Differential Geometry and Mechanics: Part I. An Improved Version of Ritt--Wu's Decomposition Algorithm , Journal of Automated Reasoning, 10: 161--172, 1993.
• S. C. Chou and X.S. Gao, Automated Reasoning in Differential Geometry and Mechanics: Part II. Mechanical Theorem Proving, Journal of Automated Reasoning, 10: 173--189, 1993.
• SC Chou and XS Gao, Automated Reasoning in Differential Geometry and Mechanics Using the Characteristic Set Method; Part III Mechanical Formula Derivation, in Proceedings of the IFIP International Workshop on Automated Reasoning, Elsevier Science Publishers (North--Holland), Beijing, p1--12, 1992.
• S. C. Chou and X.S. Gao, Automated Reasoning in Differential Geometry and Mechanics: Part IV, Bertrand Curves , Journal of Sys. and Math., vol. 6, p.186-192, 1993.