Mathematica Tools for Coquaternions

Abstract

Coquaternions form a four dimensional real algebra generalizing complex numbers and were introduced by James Cockle at about the same time that Hamilton discovered the famous algebra of quaternions. Although not as popular as quaternions, in recent years one can observe an emerging interest among mathematicians and physicists on the study of these numbers. In this work we revisit a Mathematica package for implementing the algebra of coquaternions -Coquaternions -and discuss a set of Mathematica functions -CoqPolynomial -to deal with coquaternionic polynomials. These two sets of functions provide the basic tools necessary for manipulating coquaternions and unilateral coquaternionic polynomials, reflecting, in its present form, the recent interests of the authors in the area.

Fixed Points for Cubic Coquaternionic Maps

“…We now present some examples illustrating the theoretical results obtained in the previous section. In the determination of the zeros of the polynomials considered in the examples, we made use of a set of Mathematica functions -the package CoqPolynomial -which were specially designed to deal with coquaternionic polynomials [8]. The results of [7] show that the quadratic g b has z 1 , z 3 , L 3 and L 4 as fixed points and we would like to remark how the simple introduction of a new linear factor made us move form a (2, 2, 0) map to a (5, 4, 0) map.…”

Remarks on the Zeros of Quadratic Coquaternionic Polynomials

“…Assume first that C 1 contains a linear zero. From (10) we know that r 1 itself is a zero of P . Following Theorem 3 for the class C 2 , we obtain…”