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Mathematical vectors, operations on vectors and vectorized programming.

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Plotting vectors using derivatives

If you are only interested to calculate the vector field from a given density distribution \[Rho], then I would suggest you use his method and calculate the vector field directly (of course, if [\Rho] … You could even think about parallelization of the computation as each vector is independent from the other ones. …
Christoph Groß's user avatar