VEST: abstract vector calculus simplification in Mathematica

TL;DR

VEST is a Mathematica package that simplifies complex vector calculus expressions using index notation and Levi-Civita properties, enabling automation of high-order Lagrangian calculations in plasma physics.

Contribution

The paper introduces VEST, a new tool for abstract vector calculus computations that can handle large expressions and derive complex vector identities automatically.

Findings

Successfully simplifies large vector calculus expressions.

Automates high-order Lagrangian calculations in plasma physics.

Handles complex vector identities beyond standard reduction.

Abstract

We present a new package, VEST (Vector Einstein Summation Tools), that performs abstract vector calculus computations in Mathematica. Through the use of index notation, VEST is able to reduce three-dimensional scalar and vector expressions of a very general type to a well defined standard form. In addition, utilizing properties of the Levi-Civita symbol, the program can derive types of multi-term vector identities that are not recognized by reduction, subsequently applying these to simplify large expressions. In a companion paper (Burby et al., 2013), we employ VEST in the automation of the calculation of high-order Lagrangians for the single particle guiding center system in plasma physics, a computation which illustrates its ability to handle very large expressions. VEST has been designed to be simple and intuitive to use, both for basic checking of work and more involved computations.