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Representation and automated transformation of geometric statements


The emergence of a large quantity of digital resources in geometry, various geometric automated theorem proving systems, and kinds of dynamic geometry software systems has made geometric computation, reasoning, drawing, and knowledge management dynamic, automatic or interactive on computer. Integration of electronic contents and different systems is desired to enhance their accessibility and exploitability. This paper proposes an equivalent transformation framework for manipulating geometric statements available in the literature by using geometry software systems. Such a framework works based on a newly designed geometry description language (GDL), in which geometric statements can be represented naturally and easily. The author discusses and presents key procedures of automatically transforming GDL statements into target system-native representations for manipulation. The author also demonstrates the framework by illustrating equivalent transformation processes and interfaces for compiling the transformation results into executable formats that can be interpreted by the target geometry software systems for automated theorem proving and dynamic diagram drawing.

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Correspondence to Xiaoyu Chen.

Additional information

This work has been supported partially by the SKLSDE Open Fund (SKLSDE-2011KF-02), the Natural Science Foundation of China under Grant No. 61003139, and the MOE-Intel Joint Research Fund (MOE-INTEL-11-03).

This paper was recommended for publication by Editor LI Ziming.

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Chen, X. Representation and automated transformation of geometric statements. J Syst Sci Complex 27, 382–412 (2014).

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  • Automated diagram drawing
  • equivalent transformation
  • formalized geometric statements
  • geometric automated theorem proving