Using Gröbner bases to reason about geometry problems
Journal of Symbolic Computation
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
Journal of Symbolic Computation
Mechanical theorem proving in geometries
Mechanical theorem proving in geometries
Realization of a geometry-theorem proving machine
Computers & thought
ACM SIGSAM Bulletin - Special issue of OpenMath
Journal of Symbolic Computation - Special issue on computer algebra and mechanized reasoning: selected St. Andrews' ISSAC/Calculemus 2000 contributions
A new algorithm for discussing Gröbner bases with parameters
Journal of Symbolic Computation
On the role of OpenMath in interactive mathematical documents
Journal of Symbolic Computation - Calculemus-99: integrating computation and deduction
Automatic Discovery of Theorems in Elementary Geometry
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
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
GEOTHER: A Geometry Theorem Prover
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
An alternative approach to comprehensive Gröbner bases
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
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
A simple algorithm to compute comprehensive Gröbner bases using Gröbner bases
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Solving parametric polynomial systems
Journal of Symbolic Computation
A Gröbner-based treatment of elimination theory for affine varieties
Journal of Symbolic Computation
Adding remote computational capabilities to Dynamic Geometry Systems
Mathematics and Computers in Simulation
Recognition of computationally constructed loci
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
Automatic discovery of geometry theorems using minimal canonical comprehensive Gröbner systems
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
Geometry expressions: a constraint based interactive symbolic geometry system
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
A new algorithm for computing comprehensive Gröbner systems
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Gröbner bases for polynomial systems with parameters
Journal of Symbolic Computation
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
Proving geometric theorems by partitioned-parametric gröbner bases
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
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A symbolic tool based on open source software that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction is presented. The prototype has been developed as two different worksheets for the open source computer algebra system Sage, corresponding to two different ways of coding a geometric construction, namely with the open source dynamic geometry system GeoGebra or using the common file format for dynamic geometry developed by the Intergeo project. Locus computation algorithms based on Automatic Deduction techniques are recalled and presented as basic for an efficient treatment of advanced methods in dynamic geometry. Moreover, an algorithm to eliminate extraneous parts in symbolically computed loci is discussed. The algorithm, based on a recent work on the Grobner cover of parametric systems, identifies degenerate components and extraneous adherence points in loci, both natural byproducts of general polynomial algebraic methods. Several examples are shown in detail.