Classification of ternary quasicanonical number systems in imaginary quadratic fields and their application

In this paper all possible ternary quasicanonical number system in imaginary quadratic fields are considered. For representation of algebraic integers of imaginary quadratic fields in the specified number systems an algorithm based on the division with remainder is used. In addition, the algorithms of the basic arithmetic operations in ternary number systems in the ring of Eisenstain integers are synthesized. Method of fast error-free cyclic convolution computation is considered.