Titlebook: Automated Deduction in Geometry; 8th International Wo Pascal Schreck,Julien Narboux,Jürgen Richter-Geber Conference proceedings 2011 Spring

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https://doi.org/10.1007/3-540-33092-5e in a corner”). We wish to describe the locus of points covered by the midpoint of the triangle, as the vertices range over configurations allowed by the above constraint. This locus comprises a solid region. We use numerical and graphical methods, and also computational algebra, to find the boundary surface and visualize this locus.

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The Midpoint Locus of a Triangle in a Corner,e in a corner”). We wish to describe the locus of points covered by the midpoint of the triangle, as the vertices range over configurations allowed by the above constraint. This locus comprises a solid region. We use numerical and graphical methods, and also computational algebra, to find the boundary surface and visualize this locus.

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On One Method of Proving Inequalities in Automated Way,lities 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.

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A Formalization of Grassmann-Cayley Algebra in COQ and Its Application to Theorem Proving in Projec data structure that represents elements of the algebra as complete binary trees. This allows to define the algebra products recursively. Using this formalization, published proofs of Pappus’ and Desargues’ theorem?[7,1] are interactively derived. A method that automatically proves projective geomet

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,Automatic Calculation of Plane Loci Using Gr?bner Bases and Integration into a Dynamic Geometry Sysnamic geometry software JSXGraph. With our approach it is not only possible to determine loci depending on other loci but it is also possible to extend JSXGraph to deal with loci depending on arbitrary plane algebraic curves. For Gr?bner bases calculations we use CoCoa, a computer algebra system wit