Making a Sophisticated Symbolic Solver Available to Different Communities of Users

Triangular decompositions have become one of the major tools for solving systems of non-linear algebraic or differential equations symbolically. These decompositions display more geometrical information than other symbolic descriptions of polynomial systems. However, their specifications and the algorithms computing them are quite sophisticated. Their implementation in mathematical software, their accessibility, and ease of use for non-expert users are challenges that we discuss in this paper. We discuss our solutions and illustrate them with the implementation of an algorithm for triangular decompositions, called Triade, in three computer algebra systems: AXIOM, ALDOR, and MAPLE, targeting different communities of users. We believe that these implementations of the same sophisticated mathematical algorithm for different communities of experts, advanced users, and non-experts is a unique experience in the area of symbolic computations which could benefit other algorithms in this field.