Genre: Information/Explanation

Nature of problem : The analytical calculations using vector calculus that appear in plasma physics , fluid dynamics , and other fields sometimes can become extremely complex . The complexity usually originates from both the vector operations themselves and the underlying coordinate systems . Solution method : To implement automatic symbolic vector analysis in general coordinate systems , we need a simple and systematic mathematical framework . The modern viewpoint of 3D vector calculus , differential forms on 3-manifolds , is utilized for this purpose . On the other hand , a well - developed high level programming language with a symbolic computation capability is also necessary . To the end , we chose Mathematica by Wolfram Research Inc. Unusual features : Asymptotic capabilities , 2D vector analysis notation , and a simple interface for users to define their own coordinate systems . Running time : Running time is problem and machine dependent . Running Mathematica 3.0 on a Pentium II 150 MHz PC with 48M memory , is takes about 2 second CPU time to carry out a single vector differential operation to the second order of the inverse aspect ratio in the large aspect ratio circular concentric tokamak coordinate system .