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 etal. (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 title: VEST (Vector Einstein Summation Tools) Catalogue identifier: AEQN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEQN_v1_0.html Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 10469 No. of bytes in distributed program, including test data, etc.: 72539 Distribution format: tar.gz Programming language: Mathematica. Computer: Any computer running Mathematica. Operating system: Linux, Unix, Windows, Mac OS X. RAM: Usually under 10 Mbytes Classification: 5, 12, 19. Nature of problem: Large scale vector calculus computations Solution 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 curl Additional comments: Intuitive user input and output in a combination of vector and index notation Running time: Reduction to standard form is usually less than one second. Simplification of very large expressions can take much longer.
vector calculus mathematica computer algebra tensors