Multi-algebra Fluency	

Chris Doran --	Cambridge University	

When proving results `by hand' in geometric algebra it is frequently helpful to move between different algebras, most commonly versions of Euclidean, projective and conformal algebras. This flexibility is harder to achieve in code without a sufficiently powerful type system. In this talk I describe a solution to the problem in the language of Julia, though many of the lessons hold for other languages. Julia is dynamically typed and its type system contains two powerful features: parametric polymorphism and multiple dispatch. Utilising these we can develop code that can move between algebras with minimal overhead. We illustrate how this operates with a simple ray-tracing engine constructed entirely from GA primitives, with all source code available on GitHub.