A Method to Compute Minimal Polynomials
Peskin Barbara R, David R. Richman · SIAM Journal on Algebraic and Discrete Methods · 1985
Let $f ( X )$ and $g ( X )$ be polynomials with coefficients in an arbitrary field K. Assume that $f ( X )$ is irreducible and let r be a root of $f ( X )$. We describe a new algorithm for computing the minimal polynomial of $g ( r )$ over K. The novelty of our algorithm is that it begins by computing the polynomial $p ( X,Y )$ of smallest degree such that $p ( f,g ) = 0$.