Open source math software competes in the classroom (Opensource.com)

Yes, symbolic, for my use anyway. Of course it can do numeric too. Yes, something quite like python, huge improvement over mathematica and maple. And again for my use, script, terminal, commandline, worksheet, based.

Haven't watched the video, who watches the videos in the articles?

It has similar symbolic capabilities.

> Or mostly numeric like Matlab or R?

It has similar numerical capabilities to Matlab and R. In fact, R is part of Sage, and you can use any R code in Sage; and SageMathCloud also includes numpy/scipy/pandas/octave, etc., so you get much of the functionality of Matlab as well.

> Do I write in python, or just something that's a lot like Python?

In Python. However, we do optionally have some minimal "preparsing" for a few edge cases where Python is annoying to mathematicians. For example, you can type 1/2 and get the rational number 1/2 instead of the Python2 int 0.

> Can I script it, or write complete GUI programs for analysis, or is it all notebook/CLI based?

Script it. Write GUI programs, etc. There is also a notebook and CLI.

Sage is basically much of open source math software all in one package with over 500K lines of code written by working mathematicians over the last decade to tie it all together and add missing functionality. See http://doc.sagemath.org/

It's neither, and from the language itself it's 99% and hence very close to R (imperative, object oriented, scripted, functions, similar type dispatching, etc.). R is included into SageMath as a component and exposed in Python via this excellent rpy2 library.

> Do I write in python, or just something that's a lot like Python?

You can write in Python or SageMath, which is 99% like Python. E.g. numbers are wrapped into "Integer" objects and the "^" has the meaning of the "power" operator, whereas in Python it's XOR. Beyond that there are two or three other preparsing magics going on, completely optional (turn it off via preparser(False)).

> Can I script it, or write complete GUI programs for analysis, or is it all notebook/CLI based?

You can do as good as everything you would expect from a Python program: you can script it, you can use it in a HTML template language for dynamic websites (e.g. www.lmfdb.org ), you can use it in a Jupyter Notebook, you can write a GUI, use it via dynamic websites (e.g. sagecell.sagemath.org ), the command-line (ipython console), or even skip all that and just call it from a normal Python program as an extension library. The last point implies, that you can easily mix it with other libraries, e.g. pandas, scikit learn, etc.