Mathographics
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Quantifier elimination for real algebra—the cubic case
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
A New Approach for Automatic Theorem Proving in Real Geometry
Journal of Automated Reasoning
Conic tangency equations and Apollonius problems in biochemistry and pharmacology
Mathematics and Computers in Simulation
Elimination Practice: Software Tools and Applications
Elimination Practice: Software Tools and Applications
Apollonius tenth problem via radius adjustment and Möbius transformations
Computer-Aided Design
Visually Dynamic Presentation of Proofs in Plane Geometry
Journal of Automated Reasoning
Solution formulas for cubic equations without or with constraints
Journal of Symbolic Computation
Solving dynamic geometric constraints involving inequalities
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
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The approach of solving geometric constraints involving inequalities proposed by Hong and others uses triangular decomposition, solution formulas, and quantifier elimination. We show that for generating dynamic diagrams automatically the performance of this approach can be enhanced, in terms of stability of numeric computation and quality of generated diagrams, when the used solution formulas of cubic and quartic equations are replaced by newly introduced real solution formulas with inequality constraints. Several examples are presented to illustrate the enhanced approach and to demonstrate the advantages and effectiveness of the new solution formulas. An implementation of the enhanced approach in Java with interface to Epsilon and QEPCAD for automated generation of dynamic diagrams is outlined and some experimental data are provided.