Polynomial interpolation as detector of orbital equation equivalence

Equivalence between algebraic equations of motion may be detected by using a $p$-adic method, methods using factorization and linear algebra, or by systematic computer search of suitable Tschirnhausen transformations. Here, we show standard {\sl polynomial interpolation} to be a competitive alternative method for detecting orbital equivalences and field isomorphisms. Efficient algorithms for ascertaining equivalences are relevant for significantly minimizing computer searches in theoretical and practical applications.