Cylindrical algebraic decomposition II: an adjacency algorithm for the plane
SIAM Journal on Computing
Automated reasoning in geometry theorem proving with Prolog
Journal of Automated Reasoning
Geometry theorem proving using Hilbert's Nullstellensatz
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
Automated geometry theorem proving using Buchberger's algorithm
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
Basic principles of mechanical theorem proving in elementary geometrics
Journal of Automated Reasoning
Proving geometry theorems with rewrite rules
Journal of Automated Reasoning
Mechanical geometry theorem proving
Mechanical geometry theorem proving
Wu's method and its application to perspective viewing
Artificial Intelligence - Special issue on geometric reasoning
A refutational approach to geometry theorem proving
Artificial Intelligence - Special issue on geometric reasoning
Artificial Intelligence - Special issue on geometric reasoning
Ritt-Wu's decomposition algorithm and geometry theorem proving
CADE-10 Proceedings of the tenth international conference on Automated deduction
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
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
Design of an intelligent system for the automatic demonstration of geometry theorems
TELE-INFO'10 Proceedings of the 9th WSEAS international conference on Telecommunications and informatics
WSEAS Transactions on Computers
Characteristic set algorithms for equation solving in finite fields
Journal of Symbolic Computation
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A refutational approach to geometry theorem proving using Ritt-Wu's algorithm for computing a characteristic set is discussed. A geometry problem is specified as a quantifier-free formula consisting of a finite set of hypotheses implying a conclusion, where each hypothesis is either a geometry relation or a subsidiary condition ruling out degenerate cases, and the conclusion is another geometry relation. The conclusion is negated, and each of the hypotheses (including the subsidiary conditions) and the negated conclusion is converted to a polynomial equation. Characteristic set computation is used for checking the inconsistency of a finite set of polynomial equations over an algebraic closed field. The method is contrasted with a related refutational method that used Buchberger's Gröbner basis algorithm for the inconsistency check.