Polynomial interpolation as detector of orbital equation equivalence

Abstract

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 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.