  An efficient systematic procedure is provided for symbolic computation of Lie
groups of equivalence transformations and generalized equivalence
transformations of systems of differential equations that contain arbitrary
elements (arbitrary functions and/or arbitrary constant parameters), using the
software package GeM for Maple. Application of equivalence transformations to
the reduction of the number of arbitrary elements in a given system of
equations is discussed, and several examples are considered. First
computational example of a generalized equivalence transformation where the
transformation of the dependent variable involves the arbitrary constitutive
function is presented.
  As a detailed physical example, a three-parameter family of nonlinear wave
equations describing finite anti-plane shear displacements of an incompressible
hyperelasic fiber-reinforced medium is considered. Equivalence transformations
are computed and employed to radically simplify the model for an arbitrary
fiber direction, invertibly reducing the model to a simple form that
corresponds to a special fiber direction, and involves no arbitrary elements.
  The presented computation algorithm is applicable to wide classes of systems
of differential equations containing arbitrary elements.
