Resumen de Estudio de transformaciones lineales de ℝ3 con Sistemas de Cómputo Algebraico

Eugenio Roanes Macías , Eugenio Roanes Lozano

• The purpose of this article is to describe how Computer Algebra Systems can be excellent tools to study linear transformations (l.t.) in the 3-dimensional real affine space ( including isometries, similarities and affinities). In these systems it is possible to develop a package that: a) calculates images of points, lists of points and algebraic surfaces; b) obtains equations of l.t. defined in synthetic mode; c) classifies l.t.; d) calculates the product transformation of the previously executed I. t.; e) obtains the l. t. in which the second list of two lists of points is the image of the first one; f) produces the plots of the polygonal lines of a given list of points and its image. The development of the package is fully explained. Finally, the practical and didactic interest are also treated.