More advanced (free) alternatives to Math3D or Geogebra [closed]

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?

Solution 1:

Sagemath is free, has roughly the same capabilities of Mathematica, is based on Python, and can be used and shared in the browser: https://sagecell.sagemath.org/

You can see some of the vector calculus tools here: https://doc.sagemath.org/html/en/thematic_tutorials/vector_calculus/vector_calc_cartesian.html