[jhallenworld]

I think these old arguments are moot: all of these entry methods are from having to write equations linearly for the 1950s / 1960s teletype era (including "algebraic"). They all require you to keep a stack in your head.

Newer calculators have "natural textbook entry", where they show the equation in mathematical notation as you enter it, so no stack required in your head. The entry method (shown linearly) for division is: <divide> numerator <down> denominator <right>. The keystroke count is lower than it would appear because you can leave out all of the right-most cursor keystrokes.

The method could be further generalized to eliminate the need to know about precedence on entry. For example ab(c+d+e)*f could be: <mul> a <next> b <add> c <next> d <next> e <done> <next> f. Visually it could show the order of operations either with precedence, or in some new way (perhaps text size changes to indicate order).

It's interesting to think how programming languages could look in the post-teletype era.