A condition for associativity of univariate resultants

Abstract

We provide a condition on the occurrences of variables in polynomials and show that it ensures associativity of univariate resultants in non-trivial cases. We give examples involving transformations and arithmetic with the zeros of polynomials. Associativity enables the composition of functions on the zeros of a polynomial by using resultants. The result is generalised to finite systems of polynomials.