Algebraic computation of resolvents without extraneous powers (Q444389)

A resolvent of a polynomial \(p\) is another polynomial whose roots are expressed as a function of the roots of \(p\). The resolvent is said to be absolute if it is invariant under permutations of the roots of \(p\) and it is called relative otherwise.NEWLINENEWLINEThe paper presents a symbolic method for computing relative resolvents. The method uses suitable resultant computations in a multivariate polynomial ring. The algorithm significantly improves on a previous version of the same authors, by controlling the swell of intermediate expressions. As a byproduct results a method, based on the Girard-Newton relations for symmetric functions, for determining an \(r\)-th root of a polynomial.NEWLINENEWLINEThe paper cites 17 references.