Make Egyptian fractions a little more robust.

Add checking for negative arguments, and arguments > 1

Don't know if this is actually needed; it does help avoid endless loops if you give an improper fraction to some of the algorithms.  Feel free to reject.
If you like.  It's a little inconsistent, being basically the Greedy algorithm up to a point and then switching to another.  And you can't just switch as soon as 0<r<1, because then you might wind up duplicating fractions.  You basically have to add up the divergent sequence until you can't use any more of it, and THEN switch over.  I've got code to do it, and I'll put it in if you like, just seems a little strange.  I'll try to document it as well as possible in the docstrings.

BTW, since I know this will come up: I intend to consider 1 as a unit fraction, and the divergent sequence starts 1/1 + 1/2 + 1/3 + ..., and thus the first element in the returned list may be a 1.