Fix DecisionTreeFactor division

[varunagrawal]

Added a unit test that shows the number of keys is incorrect on division, and subsequently fixed it improves the understanding of discrete factor division.

Also added a Signature based constructor and updated the tests to use it.

[dellaert]

Hmmm, a signature-based constructor only makes sense to me for conditionals (or distributions). I think this mixes up the semantics

[dellaert]

I see why you did this, when looking at the tests, but there is a reason I left it in the tests: it is because signatures are a conditional thing. I think a better way is to create conditionals in the tests, which are derived from DTF anyway, so you can use them as factors in the tests

[varunagrawal]

I see why you did this, when looking at the tests, but there is a reason I left it in the tests: it is because signatures are a conditional thing. I think a better way is to create conditionals in the tests, which are derived from DTF anyway, so you can use them as factors in the tests

It doesn't really matter to be honest. I thought it was better to have Signature constructor since the create method was doing that indirectly, but I didn't have the full picture.

[dellaert]

CI fails now, maybe create was not re-instated?
Actually, I think my suggested change, creating conditionals to create the factors made sense, no?

[varunagrawal]

From the diff, it looks like create was added back. I'll look into this some more.

[varunagrawal]

On more thinking about this, I believe the mathematical structure should include all keys since we would have functional division $(\frac{f}{g})(x, y) = f(x, y) / g(x)$.

I'll update the unit test to showcase this and update the docstring.

[dellaert]

Cool!