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An Example of the Use of Mathematica

The task was to carry out an analysis of the most general type of pencils of conic sections in the isotropic plane and to classify its subtypes, using methods of analytical geometry and linear algebra. The classification of conic pencils in I_2 can be made with respect to the reality and multiplicity of fundamental points and regarding their position, as well as the position of fundamental lines according to the absolute figure {; ; f, F}; ; . Once the analytical part of the classification of conic pencils was over, the question of their illustration naturally cropped up. The application of the software system Mathematica has been shown to be very useful. Thereby all 16 various subclasses of the most general type of conic sections were carried out and illustrated.

pencil of conic sections; isotropic plane; classification

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