  Equivalence transformations play one of the important roles in continuum
mechanics. These transformations reduce the original equations to simpler
forms. One of the classes of nonlocal equivalence transformations is the class
of reciprocal transformations. Despite the long history of applications of such
transformations in continuum mechanics, there is no method of obtaining them.
Recently such a method was proposed by the second author of the present paper.
The method uses group analysis approach and it consists of similar steps as for
finding an equivalence group of transformations. The new method provides a
systematic tool for finding classes of reciprocal transformations (group of
reciprocal transformations). As an illustration, the method was applied to the
one-dimensional gas dynamics equations, and new reciprocal transformations were
found. Similar to the classical group analysis this approach can be also
applied for finding all reciprocal transformations (not only composing a group)
of studied equations. The present paper provides this algorithm. As an
illustration the method is applied to the two-dimensional stationary gas
dynamics equations. Equivalence group, reciprocal equivalence group and
completeness of all discrete reciprocal transformations are presented in the
paper.
