Estudio de transformaciones lineales de ℝ3 con Sistemas de Cómputo Algebraico

Abstract

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.