The equivalence of the paths in a quaternion vector spaces with respect to the action of the group $Sp(n)$

In the paper an explicit description of a finite generating system in a differential skew field of non-commutative differential rational functions invariant under the action of a group of symplectic transformations in a finite-dimensional quaternion space is given. Also, necessary and sufficient conditions are established for the equivalence of paths in an n-dimensional vector space over the skew field of the quaternion numbers.