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Elementary Functions and Factorizations of Zeons

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Abstract

Algebraic properties of zeons are considered, including the existence of elementary factorizations and homogeneous factorizations of invertible zeons. A “zeon division algorithm” is established, showing that every nontrivial invertible zeon can be written as a sum of homogeneously decomposable zeons. Elementary functions (exponential, logarithmic, hyperbolic, and trigonometric) are extended to zeons, and a number of properties and identities are revealed. Finally, fast computation of logarithms is discussed for homogeneously decomposable zeons.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL, 62026-1653, USA

    G. Stacey Staples & Alexander Weygandt

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  1. G. Stacey Staples
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  2. Alexander Weygandt
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Correspondence to G. Stacey Staples.

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Staples, G.S., Weygandt, A. Elementary Functions and Factorizations of Zeons. Adv. Appl. Clifford Algebras 28, 12 (2018). https://doi.org/10.1007/s00006-018-0836-0

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  • DOI: https://doi.org/10.1007/s00006-018-0836-0

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