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

In: Clifford Algebras with Numeric and Symbolic Computations

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  • Arvind Raja

    (Helsinki University of Technology (HUT), Institute of Mathematics)

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 Cℓp,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 Cℓp,q can be performed. Routines for evaluating transcendental functions of Clifford elements, via matrix functions, are evolving.

Suggested Citation

  • Arvind Raja, 1996. "Object-Oriented Implementations of Clifford Algebras in C++: A Prototype," Springer Books, in: Rafał Abłamowicz & Josep M. Parra & Pertti Lounesto (ed.), Clifford Algebras with Numeric and Symbolic Computations, pages 295-315, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-8157-4_20
    DOI: 10.1007/978-1-4615-8157-4_20
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