Matrix equivalence grading

[jolyonb]

We should be able to check how many entries in a tensor expression are correct or not, and assign credit appropriately. At least, it should be an option. Another option that could be enabled is a message that returns which entries are incorrect.

[ChristopherChudzicki]

Sure. I think the way to do this would be to expand comparer_function to be like a normal customrespnse check function, returning either a boolean or a dict {'ok': ..., 'msg': ..., 'grade_decimal': ...}.

[jolyonb]

Hmm. I'll need to think on this one. I want to keep the comparer_function implementation as simple as possible, as it's intended for other people to be able to write these straightforwardly.

[ChristopherChudzicki]

Re comment in #94:

I think these last few changes have made implementing #74 much easier now, too. Yes, I think this would be easier now that comparer_function can return either True/False/'partial' or a dictionary with message and partial credit.

I think the biggest impediment is that currently FormulaGrader stops evaluating as soon as the first comparison fails (well, really, when n_failures exceeds n_failable_evals).

This would also really only be useful for matrix-entry problems. (Entering [1, 2, 3], etc) as opposed to problems where we only want matrices for non-commutative symbols.

[jolyonb]

Remember that the comparison function compares the entire matrix at once.

Also, agreed, this is only relevant for matrix-entry problems. If you're just manipulating expressions with array-like variables, this isn't a useful feature.

[jolyonb]

Resolved by #255