Tame and wild coordinates of Z[x,y]

AbstractAlgorithms to decide whether a polynomial is a coordinates (tame coordinate, respectively) of Z[x,y] are given. Moreover, if a polynomial p∈Z[x,y] is a coordinate (tame coordinate, respectively), the algorithms effectively construct a concrete automorphism of Z[x,y] that sends x to p. The algorithm to determine tame coordinate is applicable to R[x,y] where R is an Euclidean domain; while the algorithm to determine coordinate is applicable to D[x.y] where D is a unique factorization domain