VEST: Abstract vector calculus simplification in Mathematica

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)  [12], 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.Program summaryProgram title: VEST (Vector Einstein Summation Tools)Catalogue identifier: AEQN_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEQN_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 10469No. of bytes in distributed program, including test data, etc.: 72539Distribution format: tar.gzProgramming language: Mathematica.Computer: Any computer running Mathematica.Operating system: Linux, Unix, Windows, Mac OS X.RAM: Usually under 10 MbytesClassification: 5, 12, 19.Nature of problem:Large scale vector calculus computationsSolution method:Reduce expressions to standard form in index notation, automatic derivation of multi-term vector identities.Restrictions:Current version cannot derive vector identities without cross products or curlAdditional comments:Intuitive user input and output in a combination of vector and index notationRunning time:Reduction to standard form is usually less than one second. Simplification of very large expressions can take much longer.