Zeros of slice functions and polynomials over dual quaternions

Graziano Gentili, Caterina Stoppato, Tomaso Trinci

Abstract:

This work studies the zeros of slice functions over the algebra of dual quaternions and
it comprises applications to the problem of factorizing motion polynomials. The class of
slice functions over a real alternative *-algebra A was defined by Ghiloni and Perotti in
2011, extending the class of slice regular functions introduced by Gentili and Struppa in
2006. Both classes strictly include the polynomials over A. We focus on the case when
A is the algebra of dual quaternions DH. The specific properties of this algebra allow a
full characterization of the zero sets, which is not available over general real alternative
*-algebras. This characterization sheds some light on the study of motion polynomials over
DH, introduced by Hegedus, Schicho, and Schrocker in 2013 for their relevance in mechanism
science.