Abstract
We show that any quaternionic polynomial with one variable can be represented in such a way that the number of its terms will be not larger than a certain number depending on the degree of the polynomial. We study also some particular cases where this number can be made even smaller. Then we use the above-mentioned representation to study how to check whether two given quaternionic polynomials with one variable are identically equal. We solve this problem for all linear polynomials and for some types of nonlinear polynomials.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Mierzejewski, D.A. On Reduction of Quaternionic Polynomials and Their Identical Equality. Adv. Appl. Clifford Algebras 22, 123–141 (2012). https://doi.org/10.1007/s00006-011-0296-2
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DOI: https://doi.org/10.1007/s00006-011-0296-2