Zeros and factorizations of quaternion polynomials: the algorithmic approach

Vladimir Bolotnikov

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arXiv · 1505.03573

Zeros and factorizations of quaternion polynomials: the algorithmic approach

Vladimir Bolotnikov

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Abstract

It is known that polynomials over quaternions may have spherical zeros and isolated left and right zeros. These zeros along with appropriately defined multiplicities form the zero structure of a polynomial. In this paper, we equivalently describe the zero structure of a polynomial in terms of its left and right spherical divisors as well as in terms of left and right indecomposable divisors. Several algorithms are proposed to find left/right zeros and left/right spherical divisors of a quaternion polynomial, to construct a polynomial with prescribed zero structure and more generally, to construct the least left/right common multiple of given polynomials. Similar questions are briefly discussed in the setting of quaternion formal power series.

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Vladimir Bolotnikov. 2015-05-13. Zeros and factorizations of quaternion polynomials: the algorithmic approach. https://arxiv.org/abs/1505.03573

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