Complex algebras on n-order polynomials and generalizations of trigonometry, oscillator model and Hamilton dynamics
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- Yamaleev, R.M. AACA (2005) 15: 123. doi:10.1007/s00006-005-0007-y
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A generator of the complex algebra within the framework of general formulation obeys the quadratic equation of the type e2 = a1e − a0. In this paper we construct the general complex algebras of the n-th order where the generators obey n-order polynomial equation of the type en = an - 1en - 1 − an - 2en - 2 + ... + (−)n + 1a0, with real coefficients ak, k = 0, 1, ... n − 1. This algebra induces a generalized trigonometry ((n + 1)-gonometry), subyacent to the n-th order oscillator model and to the n-th order Hamilton equations.