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Title: VEST: Abstract Vector Calculus Simplification in Mathematica

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 scalar and vector expressions of a very general type using a systematic canonicalization procedure. In addition, utilizing properties of the Levi-Civita symbol, the program can derive types of multi-term vector identities that are not recognized by canonicalization, subsequently applying these to simplify large expressions. In a companion paper [1], we employ VEST in the automation of the calculation of 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. __________________________________________________

Authors:
Publication Date:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1073490
Report Number(s):
PPPL-4857
DOE Contract Number:  
DE-ACO2-09CH11466
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Guiding-center Approximations, Computational Physics, Computer Codes, Computer Algebra

Citation Formats

J. Squire, J. Burby and H. Qin. VEST: Abstract Vector Calculus Simplification in Mathematica. United States: N. p., 2013. Web. doi:10.2172/1073490.
J. Squire, J. Burby and H. Qin. VEST: Abstract Vector Calculus Simplification in Mathematica. United States. doi:10.2172/1073490.
J. Squire, J. Burby and H. Qin. Tue . "VEST: Abstract Vector Calculus Simplification in Mathematica". United States. doi:10.2172/1073490. https://www.osti.gov/servlets/purl/1073490.
@article{osti_1073490,
title = {VEST: Abstract Vector Calculus Simplification in Mathematica},
author = {J. Squire, J. Burby and H. Qin},
abstractNote = {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 scalar and vector expressions of a very general type using a systematic canonicalization procedure. In addition, utilizing properties of the Levi-Civita symbol, the program can derive types of multi-term vector identities that are not recognized by canonicalization, subsequently applying these to simplify large expressions. In a companion paper [1], we employ VEST in the automation of the calculation of 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. __________________________________________________},
doi = {10.2172/1073490},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue Mar 12 00:00:00 EDT 2013},
month = {Tue Mar 12 00:00:00 EDT 2013}
}

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