A few months ago, I posted my path integral functions, which are included in the MATH214 package. Recently, I came across something I’d been looking for: a Maxima utility for visualizing vector fields. Its in the Maxima/Share directory under drawutils.
Written in 2010 by Donald J Bindner, the commands plot_vector_field and plot_vector_field3d do almost everything I was looking for. The drawback is that I wanted to plot the vector fields along with the integration path. I modified those two commands slightly into versions called make_vector_field and make_vector_field3d to produce the lists of vectors for plugging into draw2d and draw3d, so that I could include the vector fields in bigger graphics calls. My modifications are available here. The package includes my home-baked help utility.
Here’s what the path integral command and the vector field generator look like on an example from chapter 13 of Stewart’s “Calculus Concepts and Contexts”