The Essentials of Clifford Algebras with Maple Programming

Abstract

Clifford algebra (geometric algebra) which has many applications in physics, robotics, CAD (Computer-Aided Design) /CAM (Computer-Aided Manufacture), computer graphics, image processing, etc. is one of the important subjects in mathematics. In this paper, after we give the definition of Clifford algebras, introduce their subspaces. Firstly, we develop an algorithm which obtain some concepts of Clifford algebras using by Maple programming. Secondly, another algorithm calculates the norm of the multivector obtained by finding the Clifford product of any two vectors of the same finite dimension.