Ya.А. Кalinovskiy 1, Yu.E. Boiarinova 1,2
1 Institute for Information Recording NAS of Ukraine
Shpaka str, 2, 03113 Kyiv, Ukraine
2 National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”
Peremogy pr., 37, 03113 Kyiv, Ukraine
The structure of method for constructing a representation of an exponential function in hypercomplex number systems (HNS) by the method of solving an associated system of linear differential equations is considered. Brief information about the hypercomplex computing software (HCS) is given. With the use of HCS, the necessary cumbersome operations on symbolic expressions were performed when constructing the representation of the exponent in the fifth-dimensional HNS. Fragments of programs in the environment of HCS and results of symbolic calculations are resulted.
hypercomplex number system, representation of functions, exponent, characteristic number, computer algebra systems, algebraic operation, Keli table.
- Hamilton, W.R. (1848), “Researches respecting quaternions: first series”, Transactions of the Royal Irish Academy, Vol. 21, no. 1, pp. 199–296.
- Brackx, F. (1979), “The exponential function of a quaternion variable”, Applicable Analysis, Vol. 8, pp. 265– 276.
- Scheicher, K., Tichy, R.F. and Tomantschger, K.W. (1997), “Elementary Inequalities in Hypercomplex Numbers”, Anzeiger, Vol. 2, no. 134, pp. 3–10.
- Kalinovskiy, Ya.A., Roenko, N.V. and Sinkov, M.V. (1996), “Methods for constructing nonlinearities in extensions of complex numbers”, Cybernetics and Systems Analysis, Vol. 4, 178–181.
- Kalinovskiy, Ya.A., Roenko, N.V. and Sinkov, M.V. (1994), “Building nonlinear functions in quaternion and other hypercomplex number systems for the solution of applied mecanics problem”, of the First Int. Conf. On parallel processing and appl. Math., Poland, pp. 170–177.
- Sinkov, M.V., Kalinovskiy, Ya.A., Boiarinova, Yu.E. and Fedorenko, A.F. (2006), “On differential equations defining functions of a hypercomplex variable”, Data Recording, Storage & Processing, Vol. 8, no. 3, pp. 20-24.
- Sinkov, M.V., Kalinovskiy, Ya.A., Boiarinova, Yu.E. and Fedorenko, A.F. (2008), “Imaging non-linearities in scanned-dynamic hypercomplex number systems”, Dopovidi NANU, Vol. 8, pp. 43-51.
- Sinkov, M.V., Boiarinova, Yu.E. and Kalinovskiy, Ya.A. (2010), Konechnomernyye giperkompleksnyye chislovyye sistemy. Osnovy teorii. Primeneniya [Finite-dimensional hypercomplex number systems. Foundations of the theory. Applications], Infodruk, Kyiv, Ukraine.
- Klimenko, V.P., Lyahov, A.L. and Gvozdik, D.N. (2011), “Modern features of the development of computer algebra systems”, Matematychni mashyny i systemy, Vol. 2, pp. 3-18.
- Тatarnikov, O. (2006), “Overview of Symbolic Mathematics Programs”, available at: https://compress.ru/article.aspx?id=16152.
- Kalinovskiy, Ya.A, Boiarinova, Yu.E. and Hitsko, Ya.V. (2020), Giperkompleksnyye vychisleniya v Maple [Hypercomplex calculates in Maple], IPRI NANU, Kyiv, Ukraine, ISBN 978-966-02-8879-9.
- Kostrikin, A.I. (1977), Vvedeniye v algebru [Introduction to algebra], Nauka, Moscow, USSR.
- Kalinovskiy, Ya.A. and Boiarinova, Yu.E. (2012), Vysokorazmernyye izomorfnyye giperkompleksnyye chislovyye sistemy i ikh primeneniya [High-dimensional isomorphic hypercomplex number systems and their applications], IPRI NANU, Kyiv, Ukraine.
- Korn, G. (1974), Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov [A guide to mathematics for scientists and engineers], Nauka, Moscow, USSR.