Computing and Using Minimal Polynomials

Given a zero-dimensional ideal I in a polynomial ring, many computations start by finding univariate polynomials in I . Searching for a univariate polynomial in I is a particular case of considering the minimal polynomial of an element in P/I . It is well known that minimal polynomials may be computed via elimination, therefore this is considered to be a “resolved problem”. But being the key of so many computations, it is worth investigating its meaning, its optimization, its applications.