The twisted conjugacy problem for endomorphisms of polycyclic groups

An algorithm is constructed that, when given an explicit presentation of a polycyclic group G, decides for any endomorphism psi is an element of End(G) and any pair of elements u, v is an element of G, whether or not the equation (x psi)u = vx has a solution x is an element of G. Thus it is shown that the problem of the title is decidable. Also we present an algorithm that produces a finite set of generators of the subgroup Fix(psi)(G) <= G of all psi-invariant elements of G.