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Complex roots of quaternion polynomials. (English) Zbl 1393.30038
Kotsireas, Ilias S. (ed.) et al., Applications of computer algebra, Kalamata, Greece, July 20–23, 2015. Cham: Springer (ISBN 978-3-319-56930-7/hbk; 978-3-319-56932-1/ebook). Springer Proceedings in Mathematics & Statistics 198, 45-58 (2017).
Summary: In this paper, using hybrid Bézout matrices, we give necessary and sufficient conditions, for a quaternion polynomial to have a complex root, a spherical root, and a complex isolated root. These conditions can be easily checked since these matrices are implemented in the computational system MAPLE. Moreover, we compute upper bounds for the norm of the roots of a quaternion polynomial.
For the entire collection see [Zbl 1379.13001].

MSC:
30G35 Functions of hypercomplex variables and generalized variables
11R52 Quaternion and other division algebras: arithmetic, zeta functions
30-04 Software, source code, etc. for problems pertaining to functions of a complex variable
30C10 Polynomials and rational functions of one complex variable
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
68W30 Symbolic computation and algebraic computation
Software:
Maple
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References:
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