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Adv Appl Clifford Algebr 2021 7;31(3):29. Epub 2021 Apr 7.

Department of Basic Sciences in Engineering Sciences, University of Innsbruck, Technikerstr. 13, 6020 Innsbruck, Austria.

We present an algorithm to compute all factorizations into linear factors of univariate polynomials over the split quaternions, provided such a factorization exists. Failure of the algorithm is equivalent to non-factorizability for which we present also geometric interpretations in terms of rulings on the quadric of non-invertible split quaternions. However, suitable real polynomial multiples of split quaternion polynomials can still be factorized and we describe how to find these real polynomials. Read More

Adv Appl Clifford Algebr 2021 5;31(2):22. Epub 2021 Mar 5.

Department of Basic Sciences in Engineering Sciences, University of Innsbruck, Techikerstr. 13, 6020 Innsbruck, Austria.

In this paper we investigate factorizations of polynomials over the ring of dual quaternions into linear factors. While earlier results assume that the norm polynomial is real ("motion polynomials"), we only require the absence of real polynomial factors in the primal part and factorizability of the norm polynomial over the dual numbers into monic quadratic factors. This obviously necessary condition is also sufficient for existence of factorizations. Read More

Adv Appl Clifford Algebr 2020 17;30(1):11. Epub 2019 Dec 17.

Department of Basic Sciences in Engineering Sciences, University of Innsbruck, Techikerstr. 13, 6020 Innsbruck, Austria.

We investigate factorizability of a quadratic split quaternion polynomial. In addition to inequality conditions for existence of such factorization, we provide lucid geometric interpretations in the projective space over the split quaternions. Read More