@Preben Alsholm well done!

@Axel Vogt you are exactly right :)

@Axel Vogt Thanks for "analytic involution".  I had only ever seen the word "involution" used in a geometric construct, and that long ago.  Had no idea that the idea was in such wide use!  The Wikipedia entry on involution is quite informative.

You are also exactly right about the need to be careful with branches.  This particular computation would be easier if we had stuck with Dave Hare's original choice for the branch numbering; but the choices we made make things nicer both at zero and at infinity; and we saw no way to make them all work well.

-r 

Implicitly allowing a multiplication without a multiplication symbol has been a user desire for Maple for a very long time.  Donald Knuth wanted it in Maple, for instance.  That it's convenient I cannot deny: 2x versus 2*x.

But Maple's use of operators is simply too useful to throw away: f(x) means the application of the operator f to the argument x.  It is obvious that Maple must continue to allow that.  

But since the beginning, constants in Maple are constant *operators*.  Thus when we say 600(x) that means "six hundred applied to the argument x" we are asking to evaluate the constant operator at argument x.  The answer is 600.  This is an incredibly useful feature of the Maple language, and it is still present in Maple.  I remember writing a section of a chapter on this in my book (back before some of you were born, I think).  (Where's my cane?  You young whippersnappers.)

At some point, though, Maple bowed to the inevitable (they resisted Donald Knuth! But I suspect that lots of people wanted what he wanted) and so --- in 2D Math Input --- one can get 600*300 when one does 600(300) : Screenshot

Or, copying and pasting directly from the worksheet (which hides the 2D math formatting and really obscures the point)

600(300)
                              600

600*300;
                             180000

You will see when writing (x-600)(a + b) in 2D math input that when you open the "(" you get a pop-up window asking you if you really want to multiply instead of use the operator.  

I understand the need for the compromise and why implicit multiplication is needed, but I use operators nearly every week and when I say (x-600)(a+b) I always (what, always? Yes, always.  Always?  Well, almost always) want the operator form. So that message kind of annoys me.  But I see why it has to be there.

But having both really means that people who don't know about operators are going to stub their toes when what they type means something different to what they had intended.