The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) On the equivalence of k curves in \({\mathbb{C}}^ n\) and reconstruction of k curves up to G-equivalence with respect to their differential invariants under the action of the groups SL(n,\({\mathbb{C}})\) and GL(n,\({\mathbb{C}})\) 