This article presents a design philosophy for computations using operations on a number field. This philosophy primarily allows for the solution of fundamental problems involving operations not defined in classical computer architectures. As a case study, the TRIAD algorithm will be analyzed, based on its fundamental operations and converted into operations defined in a number field, which in turn will exponentially facilitate implementation, for example, on flexible architectures such as FPGAs. The philosophy is basically to construct equivalent functions that only include additions, shifts, and multiplications. For the specific case of TRIAD, the continued fractions and Newton-Raphson methods will be used to find equivalent functions. Finally, through this philosophy, we obtain a systematization for the general implementation of any algorithm with nonlinear computations on any numerical architecture if it is desired to implement it on embedded devices, regardless of their internal architecture.