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 run-time 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.