Implementation of Geometric Algebra in Computer Algebra Systems

For describing specialized mathematical structures, it is preferable to use a special formalism rather than a general one. However, tradition often prevails in this case. For example, to describe rotations in the three-dimensional space or to describe motion in the Galilean or Minkowski spaces, vector (or tensor) formalism, rather than more specialized formalisms of Clifford algebra representations, is often used. This approach is historically justified. The application of specialized formalisms, such as spinors or quaternions, has not become a mainstream in science, but it has taken its place in solving practical and engineering problems. It should also be noted that all operations in theoretical problems are carried out precisely with symbolic data, and manipulations with multidimensional geometric objects require a large number of operations with the same objects. And it is in such problems that computer algebra is most powerful. In this paper, we want to draw attention to one of these specialized formalisms-the formalism of geometric algebra. Namely, it is proposed to consider options for the implementation of geometric algebra in the framework of the symbolic computation paradigm.