DragginMath: Simplification

Some things are almost too simple, but we have to deal with them anyway. And some other things are not quite as simple as they appear.

Enter a+0 or 0+a. Drag 0 up onto +. The result is a.
Enter a∗1 or 1∗a. Drag 1 up onto ∗. The result is a.
Enter a−0. Drag 0 up onto −. The result is a.
Enter 0−a. Drag 0 up onto −. The result is -a.
Enter a÷1. Drag 1 up onto ÷. The result is a.
Enter 1÷a. Drag 1 up onto ÷. The result is ⅟a.
Enter a↑1. Drag 1 up onto ↑. The result is a.
Enter 1√a. Drag 1 up onto √. The result is a.
Enter 0∗a or a∗0. Drag 0 up onto ∗. The result is 0.
Enter 0÷a. Drag 0 up onto ÷. The result is 0.
Enter a↑0. Drag 0 up onto ↑. The result is 1.

DragginMath knows a lot of special cases like this, and it handles them directly, not by evaluation. But sometimes you must be careful. For example, enter 0÷x. Drag 0 up onto ÷. The result is 0. This may be obvious, but it is not always correct: what if x is zero? DragginMath doesn’t really object to dividing by zero because it knows about ∞ (Infinity) and ? (Not-a-Number). But to do the right thing in that rude case, DragginMath must know it is dividing by zero. It doesn’t know that here, and you don’t either. You must take note of this possibility as you solve a problem. If anything special must happen because of this, you must do it, and this is not the only such special case. This app is your assistant, not your replacement.