12 citations · 29 across the 9 of their papers we have counts for
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Motion Polynomials Admitting a Factorization with Linear Factors
Zijia Li, Hans-Peter Schröcker, Mikhail Skopenkov +1
Motion polynomials (polynomials over the dual quaternions with nonzero real norm) describe rational motions. We present a necessary and sufficient condition for reduced bounded mot…
Factorization of Quaternionic Polynomials of Bi-Degree (n,1)
Johanna Lercher, Daniel F. Scharler, Hans-Peter Schröcker +1
We consider polynomials of bi-degree over the skew field of quaternions where the indeterminates commute with each other and with all coefficients. Polynomials of this type…
An Algorithm for the Factorization of Split Quaternion Polynomials
Daniel F. Scharler, Hans-Peter Schröcker
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…
Quadratic Split Quaternion Polynomials: Factorization and Geometry
Daniel F. Scharler, Johannes Siegele, Hans-Peter Schröcker
We investigate factorizability of a quadratic split quaternion polynomial. In addition to inequality conditions for existence of such factorization, we provide lucid geometric inte…
Rational Motions with Generic Trajectories of Low Degree
Johannes Siegele, Daniel F. Scharler, Hans-Peter Schröcker
The trajectories of a rational motion given by a polynomial of degree n in the dual quaternion model of rigid body displacements are generically of degree 2n. In this article we st…
Factorization Results for Left Polynomials in Some Associative Real Algebras: State of the Art, Applications, and Open Questions
Zijia Li, Daniel F. Scharler, Hans-Peter Schröcker
We discuss existence of factorizations with linear factors for (left) polynomials over certain associative real involutive algebras, most notably over Clifford algebras. Because of…