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An Algorithm for the Factorization of Split Quaternion Polynomials
- Source :
- Advances in Applied Clifford Algebras
- Publication Year :
- 2020
-
Abstract
- 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. Split quaternion polynomials describe rational motions in the hyperbolic plane. Factorization with linear factors corresponds to the decomposition of the rational motion into hyperbolic rotations. Since multiplication with a real polynomial does not change the motion, this decomposition is always possible. Some of our ideas can be transferred to the factorization theory of motion polynomials. These are polynomials over the dual quaternions with real norm polynomial and they describe rational motions in Euclidean kinematics. We transfer techniques developed for split quaternions to compute new factorizations of certain dual quaternion polynomials.
- Subjects :
- FOS: Computer and information sciences
Computer Science - Symbolic Computation
Skew polynomial ring
Polynomial
Quadric
Motion (geometry)
010103 numerical & computational mathematics
Symbolic Computation (cs.SC)
01 natural sciences
Article
Factorization
Mathematics - Metric Geometry
51M10
FOS: Mathematics
0101 mathematics
Zero divisor
Quaternion
Left/right ruling
Split-quaternion
Mathematics
51M09
Applied Mathematics
010102 general mathematics
12D05
Metric Geometry (math.MG)
Mathematics - Rings and Algebras
16S36
Null quadric
70B10
Clifford translation
Rings and Algebras (math.RA)
Rational motion
12D05, 16S36, 51M09, 51M10, 70B10
Hyperbolic kinematics
Dual quaternion
Algorithm
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Advances in Applied Clifford Algebras
- Accession number :
- edsair.doi.dedup.....1950c00b18aa15e46f36be096c208810