VEST

1. Code Name: VEST (Vector Einstein Summation Tools)
2. Code Category: Algebraic code for vector calculus
3. Primary Developer: J. Squire
4. Other Developers and Users: J. Burby, H. Qin
5. Short description: VEST is a collection of tools for carrying out abstract vector calculus computations in Mathematica.
6. Computer Language and approx # of lines: Mathematica (requires v9.0 or later) - approx. 3000 lines.
7. Type of input required. Code is interactive. Input can be either standard vector notation, index notation or a mix of both.
8. Type of output produced: Algebraic vector expressions (not in co-ordinates) in either vector or index notation.
9. Describe any postprocessors which read the output files:
10. Status and location of code input/output documentation: VEST includes a comprehensive tutorial.
11. Code web site?
12. Is code under version control? What system? Is automated regression testing performed? no.
13. One to two paragraph description of equations solved and functionality:
VEST performs abstract vector calculus computations in Mathematica, simplifying expressions involving dot products, cross produces, gradients etc.. 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. VEST has been applied to automate of the calculation of Lagrangians for the single particle guiding center system, 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. 14. What modes of operation of code are there (eg: linear, nonlinear, reduced models, etc ): 15. Journal references describing code:
Submitted to Computer Physics Communications (2013).
16. Codes it is similar to and differences: Similar in some ways to various differential geometry packages (e.g., xAct, MathTensor), but with a very different focus and functionality. While there are many previous vector simplification codes, almost all focus on the expansion of expressions into a given co-ordinate system.
17. Results of code verification studies: many long calculations have been checked against each other to verify correct code operation.
18. Present and recent applications and validation exercises: N/A
19. Limitations of code parameter regime: VEST cannot handle expressions with more than 1 free index.
20. What third party software is used? Mathematica
21. Description of scalability: VEST operates on a single processor at the current time, although this could be upgraded.
22. Major serial and parallel bottlenecks: Vector identity generation can be rather slow. This will hopefully be upgraded in the future by storing lists of identities rather than calculating in real time.
23. Are there smaller codes contained in the larger code? Describe: No.
24. Supported platforms and portability: Any computer running Mathematica 9.0 or later.
25. Illustrations of time-to-solution on different platforms and for different complexity of physics, if applicable: Most calculations take less than a second.