Clifford algebras are at a crossing point in a variety of research areas, including abstract algebra, crystallography, projective geometry, quantum mechanics, differential geometry and analysis. For many researchers working in this field in ma- thematics and physics, computer algebra software systems have become indispensable tools in theory and applications. This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations, projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail, i.e., Maple, Mathematica, Axiom, etc. A key feature of the book is that it shows how scientific knowledge can advance with the use of computational tools and software.
1. Verifying and Falsifying Conjectures.- Counterexamples in Clifford algebras with CLICAL.- 2. Differential Geometry, Quantum Mechanics, Spinors and Conformal Group.- The use of computer algebra and Clifford algebra in teaching mathematical physics.- General Clifford algebra and related differential geometry calculations with MATHEMATICA.- Pauli-algebra calculations in MAPLE V.- The generative process of space-time and strong interaction quantum numbers of orientation.- On a new basis for a generalized Clifford algebra and its application to quantum mechanics.- Vector continued fraction algorithms.- LUCY: A Clifford algebra approach to spinor calculus.- Computer algebra in spinor calculations.- Vahlen matrices for non-definite metrics.- 3. Generalized Clifford Algebras and Number Systems, Projective Geometry and Crystallography.- On Clifford algebras of a bilinear form with an antisymmetric part.- A unipodal algebra package for MATHEMATICA.- Octonion X-product orbits.- A commutative hypercomplex algebra with associated function theory.- On generalized Clifford algebras - recent applications.- Oriented projective geometry with Clifford algebra.- The applications of Clifford algebras to crystallography using MATHEMATICA.- 4. Numerical Methods in Clifford Algebras.- Orthonormal basis sets in Clifford algebras.- Complex conjugation - relative to what?.- Object-oriented implementations of Clifford algebras in C++: a prototype.
