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I teach vector calculus. I love both Math3D and Geogebra. But I have reached a limit in terms of what these programs can do. Some examples of features that I wish Math3D had:

  1. Draw vector fields with color or line weight representing magnitude, rather than length.
  2. Draw a slice of a vector field with vectors anchored just along a surface.
  3. Copy/paste objects with the same settings (e.g. making a new vector with all the same formatting of a vector I'm already using.)
  4. More robust operations (e.g. curl, div, etc.)
  5. Parameterize piecewise curves (or logic like "show point P if parameter T > 1, else suppress," etc.)

I could keep going! So I am just looking to upgrade to the next level of software sophistication. I've looked around some, but the lists of visualization software I've found are overwhelming and it's hard to know where to start. Any recommendations?

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    $\begingroup$ I'm guessing you'll need a programming environment instead of a graphing app. I wonder if sage can do these things... $\endgroup$
    – Sue VanHattum
    Dec 3 '21 at 15:17
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    $\begingroup$ As @SueVanHattum comments, Sage comes to mind, since you can program it in Python, and it does have lots of graphical capabilities. I don't attempt to "answer" since I've not personally verified the presence of the specific things you mention... $\endgroup$ Dec 3 '21 at 18:25
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    $\begingroup$ I spent several hours today messing with sage and it seems like it will do the job. I guess I was hoping for something "in between" sage/mathematica and geogebra/math3D. But having spent a few hours with sage, I've changed my mind and decided to just bite the bullet and learn sage. So thanks for the inspiration! $\endgroup$ Dec 4 '21 at 4:35
  • $\begingroup$ Sage ain't so bad. :D $\endgroup$ Dec 5 '21 at 0:13
  • $\begingroup$ Something to think about in terms of field lines... when divergence is nonzero the field lines (integral curves to vector fields) begin in such regions. The fields which arise from pointlike divergences are easier to understand in terms of field lines because the field lines begin and end at divergences. In contrast, for a field with nontrivial divergence over a finite region, the task of where to start field lines and how many to place requires more nuance. In that sense, the streamline plot features in various CASs are impressive. $\endgroup$ Dec 7 '21 at 1:40
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If you have familiarity with Python programming, you might want to consider the Manim library. It is frequently updated and, looking at your list of requirements, I believe Manim will check all of the boxes.

There are a lot of resources for learning and working with Manim; particularly on YouTube.

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  • $\begingroup$ That's an interesting suggestion. I am aware of Manim due to 3brown1blue being amazing. I was under the impression from 3brown1blue that his version of Manim is basically shoestrings and bubblegum and he essentially warns you against it. But I also know that a community of developers have got their hands on it and have been fleshing it out. Do you know: At this stage of development, is it more like a useful and well developed python library? Or still shoestrings and bubblegum, if that makes sense? $\endgroup$ Dec 7 '21 at 3:10
  • $\begingroup$ I use the Community Edition, which was just updated a couple of days ago and as such, has an active group of developers. $\endgroup$
    – SlyPuppy
    Dec 8 '21 at 10:52

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