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Manuscript Title: VECTOR33: a Reduce program for vector algebra and calculus in orthogonal curvilinear coordinates.
Authors: D. Harper
Program title: VECTOR33
Catalogue identifier: ABJC_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 54(1989)295
Programming language: Rlisp, Reduce.
Computer: IBM 3083.
Operating system: VM/CMS, VMS.
RAM: 1000K words
Word size: 32
Keywords: Computer algebra, Reduce, Vector algebra, Vector calculus, Coordinate systems, General purpose, Utility.
Classification: 4.14, 5.

Nature of problem:
Vector algebra and calculus is an important tool in the solution of many problems in physics and physical chemistry. However, vector calculus operations in orthogonal curvilinear coordinate systems often produce cumbersome expressions which are not easy to manipulate and simplify by hand.

Solution method:
This package enables the computer algebra system REDUCE to manipulate vector expressions and to perform vector calculus in orthogonal curvilinear coordinate systems.

Restrictions:
(i) This package only allows operations to be performed on 3-dimensional vectors. It is not suitable for calculations in higher dimensions.
(ii) The package is not compatible with releases of REDUCE earlier than version 3.3.

Unusual features:
This vector package is written mainly in RLISP which enables a new data type to be fully integrated into the REDUCE system. In contrast to similar packages, this package allows algebra and calculus operations to be applied to vectors using the same notation as for scalars and matrices. A complete set of vector differential operators are also defined for use in any orthogonal curvilinear coordinate system whose coordinate names and scale factors may be specified by the user.

Running time:
The accompanying test program takes 4.6 CPU seconds on the University of Liverpool IBM 3083 and 75.6 CPU seconds on a VAX 8350 at Nottingham University.