Why does -2^2 compute to -4 on my HP Prime?

[jte]

(02-09-2024 03:23 PM)KeithB Wrote:  As the "Elements of Programming Style" puts it:
"Parenthesize to avoid ambiguity"

But I am afraid I was wrong - on teh internet!

powers have higher precedence than unary negation:

Two items in that list of precedence don't properly describe the current behaviour of the HP Prime. I argued against those two during early development (and filed multiple bug reports etc.); it seems that a correct description of implemented precedence didn't quite make it out to the documentation writers in time.

(I did review the documentation involving the apps I implemented, but not the documentation in general. There is a third item in that list which I think should be a bit different, but... priorities... then & now. Oh, and none of these three I'm thinking of are negation — and there certainly are arguments towards different approaches that could be made there.)

[KeithB]

I guess what confuses me is that - and I am talking unary negation here - that these should be equivalent:

-2^2
and

x:= -2
x^2

But what I am seeing is that they aren't.

[KeithB]

The HP71 has pretty much the same precedence (including the unary minus! I have no idea how to enter that from the keyboard.)

When I do the A = -2: A^2 in calc mode, when I enter A it immediately puts parens around it. It does *not* put parens if I put A = 2!

[ijabbott]

(02-08-2024 09:12 PM)Albert Chan Wrote:  

(02-08-2024 05:59 PM)KeithB Wrote:  However, and I seem to be the one that always points this out:
Prime has *two* minus operators.

Are they (− vs -) really the same thing?

If Yes, why 2 minus operators?

To confound (human) operators.

[jte]

(02-09-2024 01:30 PM)Albert Chan Wrote:  ⋮
If we add MOD operator to the mix, zero make a difference.
Unary minus has higher precedence than binary minus, with MOD in-between.
⋮

It’s good for me to have read back a bit further in time. The “third item in that list” I was alluding to was MOD — how I personally view MOD depends on whether math mode is on in my brain. If it is, I like to see MOD as a declaration that we are doing modular arithmetic, so it would have much lower precedence — below equality tests, even (“(mod x)” would appear at the end of each line of mathematics). When I’m in programming mode, I can certainly appreciate % having the same precedence as /. Perhaps a hybrid approach would be to treat MOD as a declaration of arithmetic type, similar to how units are handled on the HP Prime. (Once applied, the modulus would carry through to results.)

[Joe Horn]

(02-11-2024 11:17 PM)jte Wrote:  Perhaps a hybrid approach would be to treat MOD as a declaration of arithmetic type, similar to how units are handled on the HP Prime. (Once applied, the modulus would carry through to results.)

Prime already does that, using %% syntax in CAS view. Example in CAS: (11111%%777)^22222 --> 100%%777. This is Prime's way of saying "11111^22222 ≡ 100 (mod 777)" as can be verified by performing powmod(11111,22222,777). Once %% notation is included in a calculation, the modulus carries through the calculation.

[jte]

(02-12-2024 01:57 PM)Joe Horn Wrote:  

(02-11-2024 11:17 PM)jte Wrote:  Perhaps a hybrid approach would be to treat MOD as a declaration of arithmetic type, similar to how units are handled on the HP Prime. (Once applied, the modulus would carry through to results.)

Prime already does that, using %% syntax in CAS view. Example in CAS: (11111%%777)^22222 --> 100%%777. This is Prime's way of saying "11111^22222 ≡ 100 (mod 777)" as can be verified by performing powmod(11111,22222,777). Once %% notation is included in a calculation, the modulus carries through the calculation.

Yes, although I was thinking (at least initially) of something a little different once you get into the details — my inclination would be to preserve the commutativity of + and x, for example. (Rather than prefer a modulus on the left over one on the right, combine them in a symmetric manner — for example, by taking the GCD [when left and right both have a modulus] and perhaps annotating discarded factors.) I'd also be inclined to preserve the modulus when a zero is produced (if we were to use %%% for this alternative operation, I mean that (1%%%2) + 1 would evaluate to 0%%%2, unlike how (1%%2) + 1 evaluates to 0 [not 0%%2]).

[Joe Horn]

(03-16-2024 11:57 PM)jte Wrote:  I'd also be inclined to preserve the modulus when a zero is produced (if we were to use %%% for this alternative operation, I mean that (1%%%2) + 1 would evaluate to 0%%%2, unlike how (1%%2) + 1 evaluates to 0 [not 0%%2]).

0%%2 is returned, as desired, when the CAS setting for Simplify is set to None or Minimum (default). 0 is returned only when the Simplify setting is Maximum.