Object-Oriented Implementations of Clifford Algebras in C++: A Prototype

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Abstract

This paper describes an evolving library of data types and algorithms for numerical Clifford algebra computations. C++ classes for representing elements of a Clifford algebra Cp,q are presented. Examples illustrating use of the library are included. These implementations will form the computation engine of a new interactive program, which is also under development. The library illustrates how “high level” mathematical descriptions can be implemented, elegantly and efficiently, in a “low level” programming language. This is achieved by using the object-oriented features supported by C++ (data abstraction, operator overloading and many others) At the time of writing, fundamental operations with elements of a Clifford algebra Cp,q can be performed. Routines for evaluating transcendental functions of Clifford elements, via matrix functions, are evolving.