GA2015 – Lecture 8

Unification and Implementation

In this final lecture we complete the story of how conformal geometric algebra unifies many of the classical geometries, covering Euclidean, spherical, hyperbolic (non-Euclidean), projective and inversive geometries. Rotors are shown to generate rotations, translations and special conformal transformations in each of these geometries.

This leads onto a wider discussion of how geometric algebra provides a unifying language for many of the subjects traditionally taught with more specialised approaches.

We end by discussing various approaches to implementing geometric algebra in code. Many good libraries exist covering C++ and symbolic implementations, so instead we focus on an approach driven by functional programming in the language Haskell. Haskell’s┬áhas many features that make it an ideal language for expressing geometric algebra algorithms, from strong typing through to its class system it is arguably the clearest language for expressing concepts from geometric algebra.