Elementary Functions and Factorizations of Zeons

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.