Methods for mechanical geometry formula deriving

Authors:
S-C. Chou;X-S. Gao
Affiliations:
Department of Computer Sciences, The University of Texas at Austin, Austin, Texas;Department of Computer Sciences, The University of Texas at Austin, Austin, Texas and Institute of Systems Science, Academia, Sinica, Beijing
Venue:
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Year:
1990

Citing 7
Cited 10

A method for the mechanical derivation of formulas in elementary geometry

Journal of Automated Reasoning
Basic principles of mechanical theorem proving in elementary geometrics

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Mechanical geometry theorem proving

Mechanical geometry theorem proving
Gröbner bases and primary decomposition of polynomial ideals

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A Collection of 120 Computer Solved Geometry Problems in Mechanical FormulaDerivation

A Collection of 120 Computer Solved Geometry Problems in Mechanical FormulaDerivation
Mechanical Formula Derivation in Elementary Geometries

Mechanical Formula Derivation in Elementary Geometries
Ritt Wu''s Decomposition Algorithm and Geometry Theorem Proving

Ritt Wu''s Decomposition Algorithm and Geometry Theorem Proving

Automated reasoning in geometries using the characteristic set method and Gröbner basis method

ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Algebraic and geometric reasoning using Dixon resultants

ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Conditions for exact resultants using the Dixon formulation

ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Automatic Discovery of Theorems in Elementary Geometry

Journal of Automated Reasoning
A Deductive Database Approach to Automated Geometry Theorem Proving and Discovering

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Automated Geometry Diagram Construction and Engineering Geometry

ADG '98 Proceedings of the Second International Workshop on Automated Deduction in Geometry
Cited References

Computer algebra handbook
On Protocols for the Automated Discovery of Theorems in Elementary Geometry

Journal of Automated Reasoning
Automatic discovery of geometry theorems using minimal canonical comprehensive Gröbner systems

ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
Proving geometric theorems by partitioned-parametric gröbner bases

ADG'04 Proceedings of the 5th international conference on Automated Deduction in Geometry

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Abstract

A precise formulation for the relations among certain variables under a set of polynomial equations and a set of polynomial inequations (to exclude certain special cases which cannot be excluded by the selection of parameters alone) is given. Several methods are presented to find such relations. The methods have been implemented and used to find geometry formulas, to discover geometry theorems, and to find geometry locus equations. About 120 non-trivial problems have been solved using the methods.