Geometric algebra (GA) is a powerful language for formulating and solving problems in geometry, physics, engineering and graphics. SimpleGA is designed as a straightforward implementation of the most useful geometric algebras, with the key focus on performance. In this talk we use the library to explain some key properties of GA, and explain the motivation behind the design and how it utilises Julia's unique features.

Geometric algebra is a powerful mathematical language that unites many disparate concepts including complex numbers, quaternions, exterior algebra, spinors and projective geometry. The goal with this talk is to use a simple implementation of the algebra to explain the main features. No prior knowledge of geometric (aka Clifford) algebra will be assumed and by the end the audience should have a basic understanding of the properties of the geometric product - the key basis for the algebra. A novel implementation of this product in terms of binary operations will also be discussed. All of the SimpleGA source code is available, and there are many excellent free resources on geometric algebra for those interested in diving deaeper.