Grassmann Algebra. Exploring extended vector algebra with Mathematica

Three of the more important mathematical systems for representing the entities of contemporary engineering and physical science are the (three-dimensional) vector algebra, the more general tensor algebra, and geometric algebra. Grassmann algebra is more general than vector algebra, overlaps aspects of the tensor algebra, and underpins geometric algebra. It predates all three. In this book we will show that it is only via Grassmann algebra that many of the geometric and physical entities commonly used in the engineering and physical sciences may be represented mathematically in a way which correctly models their pertinent properties and leads straightforwardly to principal results.