Suppose that f,g,h are functions. What does f(g+h) mean?—f×(g+h) or f applied to g+h? (This assumes that f has an appropriately large domain.) As this illustrates, even knowing the types, you cannot unambiguously parse all expressions in mathematics.
I suspect that what users really want is for Maple to have a
mode. André Heck discusses something a little related in his Introduction to Maple
[2003: p.250]: evaluate
The answer given by Maple is too complicated and includes a limit; reevaluating with the assumption c
>0 gives the expected (simple) answer. Heck comments thus: “… you
may think of c
as a positive real constant, by Maple
does not start from this assumption!” Until the developers implement
mode, we will have issues.
I agree that having an unambiguous notation has strong advantages. Way back when, Ken Iverson
proposed revising mathematical notation, or at least a subset of it. Modern notation for floor/ceiling is due to him; previously, brackets were commonly used. Little else made it into the mainstream. (Some of his ideas were implemented as a computer language, APL; originally, though, his plan was for inter-human communication.)
I thought that Iverson's basic idea was really good—so good that I spent time working as a colleague of his on the plan. It is fair to say, then, that I am a really big supporter of unambiguous notation.
But mathematics has its conventional notation. Maple should support this on output. Given that and WYSIWYG
, then, as I said above, you have current Maple input, or something very similar.