New RPL: New Commands

[The Shadow]

I've been thinking of getting a spare 50g while they can still be had, and finding out about newRPL has pushed me over the edge. Thanks for your hard work and that of your team, Claudio!

That said, I do have a bit of a wishlist and a few suggested tweaks.

I love that you fixed the bizarre behavior of (sum)LIST and (product)LIST on lists of size 1. How about also adding the mathematical conventions for such operations on empty lists? By convention, the empty sum is 0 and the empty product is 1. This will save a bit of error handling, notably when dealing with lists produced by FACTORS.

Speaking of FACTORS... I know the CAS is a ways off, but you're going to have to do it differently than in RPL. On the 50g, the primes are integers and the exponents are reals, which gives you a handle for differentiating them using MAP and DOLIST. That won't be the case in newRPL. I suggest implementing it as a list of lists, so 24 would become { { 2 3 } { 3 1 } }. Or possibly a list of complex numbers, { (2,3) (3,1) }, or even 2x1 vectors. Then, rather than treating units like -1 or i as factors, they could simply be stuck in the list as numbers - the different type would be sufficient to tell them apart from the others. 0 could also be treated this way, to spare us the absurdity of treating it as a factor.

EDIT: I just realized that complex numbers would give the nice ability to do RE or IM on the list as a whole, rather than having to do << 1 GET >> MAP or the like.

EDIT2: Actually, you know what? The best thing would just be to return three items, the unit (or 0), one list of factors and one of their exponents.

I would also dearly love to see commands to find the Hermite and Smith normal forms of a matrix!

Aesthetically speaking, I'd like to see most commands given names short enough to be differentiated in the menus. (Also, shouldn't the help tell us the name of the function, so we can tell them apart?)