Processing of the H-Holomorphic Functions

To automate cumbersome, error-prone and tedious manual procedures of calculations with quaternionic holomorphic (ℍ -holomorphic) functions we have developed and present here a special programmes pack in the Wolfram Mathematica® programming language. By using this pack a lot of examples of ℍ -holomorphic functions is processed. They give conclusive evidence that the so-called essentially adequate theory of quaternionic holomorphy is true. All considered ℍ -holomorphic functions are built from complex holomorphic ones in accordance with the general constructing rule defined earlier. At that combinations of ℍ -holomorphic functions are built from the simplest basis (irreducible) ℍ -holomorphic functions by using the usual rules of quaternionic algebraic operations.