On the computation of minimal polynomials (Q1080477)

The author describes an algorithm for computing the polynomial p(X,Y) of minimal degree such that \(p(f,g)=0\), where f and g are non-constant polynomials in one indeterminate with the coefficients in a field K with the property that char(K) does not divide the greatest common divisor of deg(f) and deg(g). He also obtains a new and nice proof of the epimorphism theorem of \textit{S. S. Abhyankar} and \textit{T.-t. Moh} [J. Reine Angew. Math. 276, 148-166 (1975; Zbl 0332.14004)] which avoids the appeal to the Newton-Puiseux expansion theorem.