Problem 7 and systems of algebraic equations

Abstract

In [1], Johnson and Graham considered the function[EQUATION]and asked for a method to find the minimal polynomial (of degree 10) of the value of the maximum of this function. They proposed such a method which needs the factorization of a polynomial of degree 40 into four irreductible tenth-degree factors and they set the following questions:1) "it would be of considerable interest if this problem could be solved by some other method which avoids the factorization".2) "it would be particularly interesting if there were an algebraic manipulation system which could do all the steps in an efficient and natural manner".