Building STEM Practice App - My Current Approach - Your Suggestions Please!

[Keith Young]

Hello,

I am making a Django App that is using Sympy.

Basically users need to be able to do calculations. I don't know how to give them access to shell type commands and it doesn't seem safe to do so.

So I've made a sort of markup language that I parse.

INTEGRATE( x ^ 2 + 2, x ) for example will be parsed. An Expression Tree is made where the node is basically just filled with the Sympy results.

I do NOT currently make an Expression Tree for what is inside a function such as INTEGRATE.

As I build out more and more Algebra, PreCalc, Calc 1 2 3, etc, type questions, I start finding edge cases.

• This needs to be intuitive to use, or I don't think people will use it
• There are many interesting curveballs that can be thrown, and I somehow need to handle them
• Maybe my whole approach is wrong to begin with

Currently the system can easily handle many things, including Double Definite Integrals as long as the bounds are like infinity, 0, 5, 2PI.

But once I have a bound such as SQRT(x + 2) things go bonkers. Sin Cos etc seem solid though.

Another problem is the system can properly solve things like Integrals that take and send e / EXP etc.

However when checking the student answer, it will mark the answer as incorrect when it is correct.

Finally, another I ran in to last night, is trying to get students to change LN(7/5) to LN(7) - LN(5). I don't yet have a good way to see if their answer is equal to the correct answer.

Then even things like "Change to a+bi form: (2+3i)(7-2i)", well in this case the student can literally copy the question mathy text, paste it in as the answer, and get it correct!

Background out of the way - Direct Questions - Please explain like I'm 5, I'm ME/AE not CS

1) What considerations do I need to make with Sympify and Eval?

    sympy.integrate( sympify( {user_input_string} ), {variable} )

The incoming string is manipulated to clean user mathy input. For example "the text" would be turned into "the*text". I know Eval in general is a security issue.

2) Good/safe way to create instances of Django models incorporating a sort of Sympy Shell in browser? I doubt it but worth asking just in case.

3) Good intuitive way to handle my SQRT problem? I've read real=True positive=True type arguments can help.

I don't know of a good way to get a user to straight up make a sympy.sqrt(), put in all needed arguments, etc, in a intuitive way.

4) Know what might be the issue with answers never coming out as correct when they involve things like (E - 1) * exp(-1) etc?

Thanks for any help!

Keith