Polynomial interpolation as detector of orbital equation equivalence

TL;DR

This paper presents polynomial interpolation as an effective and competitive method for detecting orbital equation equivalences and field isomorphisms, offering a practical alternative to existing algebraic and computational techniques.

Contribution

It introduces polynomial interpolation as a novel, efficient approach for identifying orbital equation equivalences, reducing computational effort in theoretical and practical contexts.

Findings

Polynomial interpolation effectively detects orbital equation equivalences.

The method reduces computational searches in applications.

It offers a competitive alternative to existing algebraic techniques.

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 {\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.