  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.
