Some Applications of Algebraic System Solving

Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact solve" commands (Grobner bases) is far more complex than the Gauss method, understanding and interpreting the output of the corresponding commands is not much more difficult than in the linear case, and can be introduced to non-specialists even at high-school level, if the computer is used as a black-box. Let us underline the case of statistical packages, which allow non-specialists to perform complex statistical studies. Similarly, computer algebra systems open a whole new world of exciting possibilities, covering a variety of fields. (Contains 4 figures.)