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[Dave Britten]

(12-30-2020 01:49 PM)ijabbott Wrote:  

(12-29-2020 06:31 PM)Dave Britten Wrote:  Between calculator models, there certainly seems to be.

The TI 84 Plus is worse than I thought: it's left-associative in classic mode, and right-associative in Math Print mode. The exact same key sequence will give you a different result depending on which of the two display modes you're in! I think Casio has the right idea of making it clearly right-associative, with a forced ( in line-I/O mode.

The Casio solution is a good technique. For the TI, you can understand why they would have made it left-associative in classic mode for consistency with other binary operators, and perhaps for consistency with earlier AOS models.

Back to HP Land, the HP-27S also has a left-associative exponentiation operator, but it displays partially evaluated results as it goes, so that [3] [x^y] [3] [x^y] [3] is finally displayed as 27^3.

Interestingly, the fx-CG500 (the calculator formerly known as ClassPad) will display the entry as 3^3^3 without any parentheses, but still evaluates it as right-associative (i.e. 7.63E12 rather than 19683). The fx-991MS 2nd Edition also does not include parentheses, but evaluates this as left-associative. The TI Voyage 200 - and presumably 92 and 89 - are right-associative, and will even automatically change your input to 3^(3^3) after entry if pretty print mode is turned off (if it's on you get a tower of superscripts).

Very strange to see so much inconsistency on this, even between calculators from a single manufacturer.