Boyarinova Y. Development of methods of representation of the information by hypercomplex numbers and the decision of practical tasks

Traditional and nonconventional methods of data representation are considered in work. Each of these forms of data representation has the own features and the most effective scopes. The carried out work and the analysis of these systems allows to make a conclusion, that hypercomplex numerical systems are effective for use in practical problems of mechanics, electrodynamics, radio electronics and many others. The new section of toolkit is constructed in the field of position-independent methods in residual classes. Analytical expressions for executing of inverse nonlinear operations such, as logarithm, opposites to trigonometrical sine and cosine, to hyperbolic sine and cosine are received for the first time. For the first time it is offered to formulate a secret sharing problem in one of the big set of hypercomplex numerical systems. Essential complexity, which is consist in absence of analogue of Euler function for real numbers for considered hypercomplex numerical system has been overcome during practical realization of this new approach. The specified difficulty has been overcome in one of variants by using Euclid’s algorithm, and in the other – isomorphic transition to the real residues with the help of Gauss fundamental theorem.