Alternating Roots of Polynomials over Cayley-Dickson Algebras

We introduce the notions of alternating roots of polynomials and alternatingpolynomials over a Cayley-Dickson algebra, and prove a connection between thealternating roots of a given polynomial and the roots of the correspondingalternating polynomial over the Cayley-Dickson doubling of the algebra. We alsoinclude a detailed Octave code for the computation of alternating roots overHamilton's quaternions