Numerical Calculations in Clifford Algebra

1Introduction

The purpose of the suite of routines described here, the Clifford numerical suite (CNS), is to provide a platform for the implementation of applications which require numerical evaluation of the various mathematical operations offered within the context of Clifford algebra. The routines are designed to allow the user to ignore most of the internal details of data structures and memory management if so desired.

The suite is constructed using the ‘c’ computer programming language (Kernighan & Ritchie 1978, King 2008) so that it can be embedded into, compiled with, and invoked directly from the user's code. This avoids the overheads of copying data associated with the call mechanisms involved in implementations underneath interpretive meta‐languages¹ and consequently offers an overall higher speed of code execution. That in turn admits the possibility of solving problems which are more realistic and less trivial. The intention is to provide most users with a viable environment for the development of their own applications.

Providing the source code also allows the user to enhance and tailor it to best suit their own purposes. In cases where ultimate speed and memory efficiency is required, the suite can be used in the formative development phase, and substituted with the user's own hard‐coded replacements in the end application phase.

1.1 Operations

The basic mathematical operations which are supported by the CNS are listed in Table 1.1 and described with examples ...