Negation of a number to the power

[Konrad-Franz]

Calculations of the form -x^y take place in AutoIt contrary to the mathematical standard (https://en.wikipedia.org/wiki/Order_of_operations#Unary_minus_sign). According to this standard, the power calculation is first, followed by the negation. This is what happens in the computer algebra system Maxima, as well as in Javascript.

AutoIt handles this the other way round, first the negation, then the power calculation. The list 'operator precedence' ('From highest precedence to lowest') reflects this misleadingly by placing the '^' sign above the '-' sign, thus suggesting a precedence of power calculation over negation.

It is not acceptable to have to convert expressions of the form -x^y in mathematically correct formulas to -(x^y) just because AutoIt does not adhere to the mathematical standard.

Edited October 27, 2021 by Konrad-Franz

[Nine]

Based on your own link :

Unary minus sign
There are differing conventions concerning the unary operator − (usually read "minus"). In written or printed mathematics, the expression −32 is interpreted to mean −(32) = − 9.[1][19]

In some applications and programming languages, notably Microsoft Excel, PlanMaker (and other spreadsheet applications) and the programming language bc, unary operators have a higher priority than binary operators, that is, the unary minus has higher precedence than exponentiation, so in those languages −32 will be interpreted as (−3)2 = 9.[20] This does not apply to the binary minus operator −; for example in Microsoft Excel while the formulas =−2^2, =-(2)^2 and =0+−2^2 return 4, the formula =0−2^2 and =−(2^2) return −4.

There are different conventions.  If we change it to your preference, someone else will complain that it does not follow Excel and other languages.

It is a "dam if you do, dam if you don't" dilemma. 

[Melba23]

Konrad-Franz,

Welcome to the AutoIt forum.

As a programmer of some 50+ years experience I would never rely on operator precedence in any mathematical expression and would always use parentheses to make the order explicit. While this may make the original formulation of the expression slightly more onerous, the advantages of not having to rely on the arbitrary operator precedence (amply shown in the post above) of the various programming languages that might be used to evaluate it far outweigh this minor inconvenience.

M23

Edited October 26, 2021 by Melba23
Older than I thought!

[jchd]

@Konrad-Franz there are indeed differing conventions among applications and programming languages.

For instance Wolfram Mathematica also handles -2^3 as (-2)^3 = -8

Would you go as far as say that Mathematica isn't mathematically sound and call Stephen Wolfram an impostor?

Edited October 26, 2021 by jchd
Thinkos!

[Konrad-Franz]

Hello Nine. If you calculate like AutoIt -3^2 = 9 and 3^2 = 9 then the minus sign is obviously meaningless. Do you consider this logical? If 'spreadsheet applications' and 'other languages' (which? relevant?) ignore the mathematical (and logical!) standard, they should change their behaviour and not AutoIt also take this erroneous path.

Melba23, hello to you too. If you would get from a mathematical programme like Maxima endless formulas which you have to transfer to AutoIt, you would not consider to add hundreds of (mostly unnecessary) parantheses. No, you would long for a consistent standard to which AutoIt adheres too.

 

[Konrad-Franz]

Hello jchd. WolframAlpha is calculating -3^2 = -9. This is the mathematical standard! Any further questions?

[jchd]

I said "Wolfram Mathematica", not "Wolfram Alpha".

Edited October 26, 2021 by jchd

[Melba23]

Konrad-Franz,

I would argue that the author of Maxima is at fault for not offering the ability to produce precedence-explicit expressions given the known differences between the various platforms on which they might be used. 

But then I would say that, wouldn't I!

M23

[jchd]

The question made me wonder and look twice since the discrepancy was blatant: if fact I'm by default using an overloaded version of Minus I need for special purposes.

Living my specific environment, indeed:
FullForm[-a^b]
Times[-1,Power[a,b]]

Sorry for noise.

[Konrad-Franz]

OK jchd. And what is 'Wolfram Mathematica" saying to -3^2? The same same like AutoIt (9) or the mathematical solution (-9).

By the way: Your example -2^3 is not helpful, because in case of an exponentiation with a negative base and an odd exponent the result will be negative regardless of whether you write the expression (-2)^3 = -8 or -(2^3) = -8. However, it becomes problematic with even exponents.

Edited October 27, 2021 by Konrad-Franz

[jchd]

Yes I answered a bit hastily! Yet I prefer typing defensively with potentially ambiguous constructs.

At least in Mma, we have the possibility to decide precedence, associativity, distributivity, ... of every user function.

Edited October 26, 2021 by jchd

[JockoDundee]

Proof that Google stole Microsoft source code:

 

[JockoDundee]

22 hours ago, Konrad-Franz said:

It is not acceptable to have to convert expressions of the form -x^y in mathematically correct formulas to -(x^y) just because AutoIt does not adhere to the mathematical standard.

Totally unacceptable…

I can’t even imagine the horror of having to convert expressions just because you decided to use a language written by some guy who negated before he expontiated.

It’s an outrage and you should ask for a full refund.

Edited October 27, 2021 by JockoDundee

[mikell]

... or at least a tiny update of the corresponding page in the helpfile, to mention as said Melba "don't rely on operator precedence" - btw in this case such a thread would never have existed 

[CoffeeJoe]

6 minutes ago, mikell said:

in this case such a thread would never have existed

Where's the fun in that?

[mikell]

No fun, just an ascertainment - please read post #1 again

[Exit]

How to encrypt the digit 1 ?

Spoiler

ConsoleWrite(-3^-3^-0& @CRLF)

[mikell]

ConsoleWrite("Exit is crazy"^0 & @CRLF)