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
Mechanical geometry theorem proving
Mechanical geometry theorem proving
A refutational approach to geometry theorem proving
Artificial Intelligence - Special issue on geometric reasoning
Wu's method and its application to perspective viewing
Geometric reasoning
Methods for mechanical geometry formula deriving
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Mechanical theorem proving in geometries
Mechanical theorem proving in geometries
A Case of Automatic Theorem Proving in Euclidean Geometry: the Maclane 83Theorem
AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
A Deductive Database Approach to Automated Geometry Theorem Proving and Discovering
Journal of Automated Reasoning
A dynamic-symbolic interface for geometric theorem discovery
Computers & Education
A software tool for the investigation of plane loci
Mathematics and Computers in Simulation
Interactive versus Symbolic Approaches to Plane Loci Generation in Dynamic Geometry Environments
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Emphasizing Human Techniques in Automated Geometry Theorem Proving: A Practical Realization
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
The Kinds of Truth of Geometry Theorems
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
Automatic Determination of Geometric Loci. 3D-Extension of Simson-Steiner Theorem
AISC '00 Revised Papers from the International Conference on Artificial Intelligence and Symbolic Computation
Automatic determination of envelopes and other derived curves within a graphic environment
Mathematics and Computers in Simulation - Special issue: Applications of computer algebra in science, engineering, simulation and special software
On Protocols for the Automated Discovery of Theorems in Elementary Geometry
Journal of Automated Reasoning
A Groebner bases-based approach to backward reasoning in rule based expert systems
Annals of Mathematics and Artificial Intelligence
Connecting the 3D DGS Calques3D with the CAS Maple
Mathematics and Computers in Simulation
A web-based intelligent system for geometric discovery
ICCS'03 Proceedings of the 1st international conference on Computational science: PartI
Automatic determination of algebraic surfaces as loci of points
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
On the need of radical ideals in automatic proving: a theorem about regular polygons
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
A maple package for automatic theorem proving and discovery in 3D-geometry
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
Equal bisectors at a vertex of a triangle
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part IV
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
On equivalence of conditions for a quadrilateral to be cyclic
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part IV
A symbolic companion for interactive geometric systems
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
Towards solving the dynamic geometry bottleneck via a symbolic approach
ADG'04 Proceedings of the 5th international conference on Automated Deduction in Geometry
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
A bridge between dynamic geometry and computer algebra
Mathematical and Computer Modelling: An International Journal
Automatic deduction in (dynamic) geometry: Loci computation
Computational Geometry: Theory and Applications
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We present here a further development of the well-known approach to automatic theorem proving in elementary geometry via algorithmic commutative algebra and algebraic geometry. Rather than confirming/refuting geometric statements (automatic proving) or finding geometric formulae holding among prescribed geometric magnitudes (automatic derivation), in this paper we consider (following Kapur and Mundy) the problem of dealing automatically with arbitrary geometric statements (i.e., theses that do not follow, in general, from the given hypotheses) aiming to find complementary hypotheses for the statements to become true. First we introduce some standard algebraic geometry notions in automatic proving, both for self-containment and in order to focus our own contribution. Then we present a rather successful but noncomplete method for automatic discovery that, roughly, proceeds adding the given conjectural thesis to the collection of hypotheses and then derives some special consequences from this new set of conditions. Several examples are discussed in detail.