On the application of Buchberger's algorithm to automated geometry theorem proving
Journal of Symbolic Computation
On the application of Buchberger's algorithm to automated geometry theorem proving
Journal of Symbolic Computation
Careful algebraic translations of geometry theorems
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
On the synthetic factorization of projectively invariant polynomials
Journal of Symbolic Computation
Geometry theorem proving in vector spaces by means of Gröbner bases
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
A New Approach for Automatic Theorem Proving in Real Geometry
Journal of Automated Reasoning
Vectorial Equations Solving for Mechanical Geometry Theorem Proving
Journal of Automated Reasoning
Interactive versus Symbolic Approaches to Plane Loci Generation in Dynamic Geometry Environments
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Algebraic and Semialgebraic Proofs: Methods and Paradoxes
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
Randomized Zero Testing of Radical Expressions and Elementary Geometry Theorem Proving
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
Remarks on Geometric Theorem Proving
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
Computer algebra handbook
GRAMY: A Geometry Theorem Prover Capable of Construction
Journal of Automated Reasoning
On Wu's method for proving constructive geometric theorems
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 1
A web-based intelligent system for geometric discovery
ICCS'03 Proceedings of the 1st international conference on Computational science: PartI
Automatic discovery of geometry theorems using minimal canonical comprehensive Gröbner systems
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
Synthesizing geometry constructions
Proceedings of the 32nd ACM SIGPLAN conference on Programming language design and implementation
On the parametric representation of dynamic geometry constructions
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part IV
Computational origami construction of a regular heptagon with automated proof of its correctness
ADG'04 Proceedings of the 5th 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
Towards a geometric-object-oriented language
ADG'04 Proceedings of the 5th international conference on Automated Deduction in Geometry
Thousands of geometric problems for geometric theorem provers (TGTP)
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
A coherent logic based geometry theorem prover capable of producing formal and readable proofs
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
Journal of Automated Reasoning
A Combination of a Dynamic Geometry Software With a Proof Assistant for Interactive Formal Proofs
Electronic Notes in Theoretical Computer Science (ENTCS)
Automatic deduction in (dynamic) geometry: Loci computation
Computational Geometry: Theory and Applications
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The use of Grobner basis computation for reasoning about geometry problems is demonstrated. Two kinds of geometry problems are considered: (i) Given a finite set of geometry relations expressed as polynomial equations, in conjunction with a finite set of subsidiary conditions stated as negations of polynomial equations to rule out certain degenerate eases, check whether another geometry relation expressed as a polynomial equation and given as a conclusion, holds. (ii) Given a finite set of geometry relations expressed as polynomial equations, find a finite set of subsidiary conditions, if any, stated as negations of polynomial equations which rule out certain values of variables, such that another geometry relation expressed as a polynomial equation and given as a conclusion, holds under these conditions. Using a refutational approach for theorem proving, both kinds of problems are converted into reasoning about a finite set of polynomial equations. The first problem is shown to be equivalent to checking whether a set of polynomial equations does not have a solution; this can be decided by computing a Grobner basis of these polynomials and checking whether I is included in such a basis. In addition, it is shown that the second problem can also be solved by computing a Grobner basis and appropriately picking polynomials from it. A number of geometry problems of both kinds have been solved using this approach.