Foundations of geometric algebra computing.
The author chooses to call Geometric Algebra what is often called Clifford Algebra, since he focuses on the geometric meaning of the algebraic expressions and operators. Within this framework, computing algorithms can be developed in a fast and intuitive way. Therefore the combination of applied Geometric Algebra and advanced computing platforms is called ``Geometric Algebra computing''. This book aims at introducing the foundations for Geometric Algebra as a new field of computing technology for all kind of engineering applications. The chosen style is tutorial-like since the author's purpose is to encourage readers to gain individual experience with relevant development tools such as CLUCalc and Gaalop. Actually, these software packages and some applications are available for free downloads. This book is divided into three parts. Both Part I and Part II introduce Geometric Algebra to the reader but they are almost independent of each other. Indeed, Part I is devoted to a theoretical introduction, while Part II focuses on the interactive handling of Geometric Algebra. The reader is encouraged to start with the introduction he prefers. Applications are provided by both parts. Part III deals with runtime performance. In particular, it describes a Gaalop compiler which, with its precompiler extension, allows Geometric Algebra to be integrated into a standard programming language such as C++. The matter is clear, well written and involving.
scientific article; zbMATH DE number 6092941