Employing C++ Templates in the Design of a Computer Algebra Library

We discuss design aspects of the open-source Basic Polynomial Algebra Subprograms (BPAS) library. We build on standard C++11 template mechanisms to improve ease of use and accessibility. The BPAS computer algebra library looks to enable end-users to do work more easily and efficiently through optimized C code wrapped in an object-oriented and user-friendly C++ interface. Two key aspects of this interface to be discussed are the encoding of the algebraic hierarchy as a class hierarchy and a mechanism to support the combination of algebraic types as a new type. Existing libraries, if encoding the algebraic hierarchy at all, use runtime value checks to determine if two elements belong to the same ring for an incorrect false sense of type safety in an otherwise statically-typed language. On the contrary, our template metaprogramming mechanism provides true compile-time type safety and compile-time code generation. The details of this mechanism are transparent to end-users, providing a very natural interface for an end-user mathematician.