Geometric algebra - the mathematical language for computational engineering?

This work reviews some current engineering applications of geometric algebra and observes the potential of this mathematical language to become a basis for a wide range of computational engineering applications. Geometric algebra unifies many other mathematical concepts like quaternions and projective geometry and is able to easily deal with geometric objects, operations and transformations. For computational engineering, not only these nice properties are important, but also the computational point-of-view. We describe the big potential of geometric algebra for optimizations leading to highly efficient implementations.