A polynomial map ϕ_f, with f = (f_1, ..., f_n) element (K[X_1, ..., X_n])^m in a field K is called invertible if there exist g_1, ..., g_m element K[X_1, ..., x_n] such that g_i(f_1, ..., f_n) = X_i for 1<=n<=n so that ϕ_g °ϕ_f = id_k^n. Gröbner bases provide a means to decide for given f whether or not ϕ_f is invertible.

Gröbner basis | invertible polynomial | Jacobian conjecture | polynomial map