Mechanical geometry theorem proving
Mechanical geometry theorem proving
A refutational approach to geometry theorem proving
Artificial Intelligence - Special issue on geometric reasoning
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
A Practical Program of Automated Proving for a Class of Geometric Inequalities
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
Elimination Practice: Software Tools and Applications
Elimination Practice: Software Tools and Applications
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
On Protocols for the Automated Discovery of Theorems in Elementary Geometry
Journal of Automated Reasoning
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The paper describes proving geometric inequalities in automated way without cell decomposition. Firstly an overview of known methods of proving inequalities is given including the method which is based on reduction of a conclusion polynomial to the canonical form modulo a hypotheses ideal. Then a parametrization method of proving geometric inequalities is introduced. Further a method of proving geometric inequalities which introduces an auxiliary polynomial is described.