Joint differential resolvents for pseudopolynomials
Abstract
The existence of linear differential resolvents for zalpha for any root z of an ordinary polynomial with coefficients in a given ordinary differential field has been established, where alpha is an indeterminate constant with respect to the derivation of the given field. In this paper we consider several alphas. We will call a finite sum of indeterminate powers of a variable v a pseudopolynomial in v. We will generalize the definition of a differential resolvent of a single polynomial for a single monomial zalpha to the definition of a differential resolvent of several polynomials for a pseudopolynomial in the roots. We will also generalize the definition of a resolvent to have non-consecutive derivatives. We will show that the authors powersum formula may be used to compute this more general differential resolvent.