Geometry Expert (GEX) and and Java Geometry Expert (JGEX)

Geometry Expert (GEX) and Java Geometry Expert (JGEX) are software systems for automated geometry theorem proving-discovering and geometric constraint solving.

GEX is a powerful computer program for geometric reasoning. Within its domain, it invites comparison with the best of human geometry provers. It implements most of the effective methods for geometric reasoning introduced in the past twenty years, including the deductive base method, Wu's method, the area method, the Groebner basis method, the vector method, and the full-angle method. With these methods, users may automated prove geometry theorems, to discover new properties of theorems, and to generate readable proofs for many geometry theorems.
A variant of GEX: MMP also implements several state of the art methods for geometric constraint solving, that is, the user can input the geometric properties satisfied by a geometric diagram, and the software will automatically generate a constructive way to draw the diagram. Geometric constraint solving is a key property of so-called intelligent computer-aided design (CAD).
GEX is also a dynamic geometry software, and can be used to build dynamic visual models to assist teaching and learning of various mathematical concepts. By dynamic visual models, we mean models built by computer softwares that can be changed dynamically. With GEX, we can build four classes of dynamic visual models: geometric transformations, loci generation, diagrams of functions, and loci generation.

Documents and Softwares

An introductory paper for GEX can be obtained here
An experimental Windows version of GEX, with a set of examples, can be obtained here

Java Geometry Exper (JGEX)t

Java GEX is an internet version of Geometry Expert, which is now an open source at the JGE Website. Introductions to JGEX can be found in the following papers.

Z. Ye, S.C. Chou, and X.S. Gao. An Introduction to Java Geometry Expert, In Automated Deduction in Geometry, LNAI 6301, 189-195, Springer, 2011.

Z. Ye, S.C. Chou, and X.S. Gao. Visually Dynamic Presentation of Proofs in Plane Geometry, Part 1. Basic Features and the Manual Input Method, Journal of Automated Reasoning, 45, 213-241, 2010.

Z. Ye, S.C. Chou, and X.S. Gao. Visually Dynamic Presentation of Proofs in Plane Geometry, Part 2. Automated Generation of Visually Dynamic Presentations with the Full-Angle Method and the Deductive Database Method, Journal of Automated Reasoning, 45, 243-266, 2010.

MMP/Geometer

MMP/Geometer is a new Chinese version of GEX with ability of automated geometric diagram construction.

X.S. Gao and Q. Lin, MMP/Geometer - A Software Package for Automated Geometry Reasoning, Automated Deduction in Geometry, 44-66, Springer, Berlin, 2004.

References for Automated Geometry Reasoning

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 of Automated Reasoning, 25(3), 219-246, 2000.
S.C. Chou, X.S. Gao, and J.Z. Zhang, Automated Generation of Readable Proofs with Geometric Invariants, I. Multiple and Shortest Proof Generation, Journal of of Automated Reasoning, 17, 325-347, 1996.
S.C. Chou, X.S. Gao, and J.Z. Zhang, Automated Generation of Readable Proofs with Geometric Invariants, II. Proving Theorems with Full-Angles, Journal of of Automated Reasoning, 17, 349-370, 1996.

References for Geometric Constraint Solving

X.S. Gao, Q. Lin, and G. Zhang, A C-tree Decomposition Algorithm for 2D and 3D Geometric Constraint Solving, Computer-Aided Design, 38(1), 1-13, 2006.
X.S. Gao, D. Lei, Q. Liao, and G. Zhang, Generalized Stewart Platforms and their Direct Kinematics, IEEE Trans. Robotics, vol 21, 141-151, 2005.
X.S. Gao, X. Hou, J. Tang and H. Chen, Complete Solution Classification for the Perspective-Three-Point Problem, IEEE Tran. on PAMI, 930-943, 25(8), 2003..
Here is the appendix to this paper
X.S. Gao, C.M. Hoffmann and W. Yang, Solving spatial basic geometric constraint configurations with locus intersection, Computer Aided Design, 111-122, 36(2), 2004.
J. Ge, S.C. Chou and X.S. Gao, Geometric Constraint Satisfaction Using Optimization Methods, Computer Aided Design, 31(14), 867-879, 2000.
X.S. Gao and S. C. Chou, Solving Geometric Constraint Systems, I. A Global Propagation Approach, Computer Aided Design, Vol. 30, No. 1, 47-54, 1998.
X.S. Gao and S. C. Chou, Solving Geometric Constraint Systems, II. A Symbolic Computational Approach, Computer Aided Design, Vol. 30, No.2, 115-122, 1998.

Using GEX for Mathematics Instruction

X.S. Gao, J.Z. Zhang, and S.C. Chou, Geometry Expert (in Chinese) , Nine Chapters, Taipei, 1998.
X. S. Gao, C.C. Zhu, and Y. Huang, Building Dynamic Mathematical Models with Geometry Expert, I. Geometric Transformations, Functions and Plane Curves, Proceedings of the Third Asian Technology Conference in Mathematics, eds W.C. Yang, pp. 216-224, Springer, 1998.
X.S. Gao, C.C. Zhu, and Y. Huang, Building Dynamic Mathematical Models with Geometry Expert, II. Linkages, Proc. of the Third Asian Symposium on Computer Mathematics, eds Z. B. Li, pp. 15-22, LanZhou University Press, 1998.
X.S. Gao, Building Dynamic Mathematical Models with Geometry Expert, III. A Geometry Deductive Database Proc. Of ATCM'99, 153-162, 1999, ATCM Inc., USA (Best paper Award of ATCM'99).