Pow operator precedence

[Manu]

On 13 January 2012 20:54, Stewart Gordon <smjg_1998 at yahoo.com> wrote:

> On 13/01/2012 13:47, Manu wrote:
> <snip>
>
>     Some people expect this:
>>    (-10 ^^ 2)
>>    To be 100 instead of -100
>>
> <snip>
>
>  I'm fairly amazed it's not the other way around... what's the logic
>> behind this?
>>
>
> It matches standard mathematical notation.  -x² means -(x²) not (-x)².
>
> This actually makes most sense when you consider that:
>
> (a) -2x² means -2(x²), because exponentiation beats multiplication.  With
> the precedence you're suggesting, removal of the 2 would completely change
> the expression.
>
> (b) 42 - x² means 42 - (x²).  With the precedence you're suggesting,
> removal of the 42 would completely change the expression.
>
> Both these rules play a significant part in how we write polynomial
> expressions.  Look at these:
>
> x³ - x² + 3
>   - x² + 3
>   -4x² + 3
>
> In all these, the coefficient of x² is negative.  It would be confusing if
> it were positive only in the second one.
>
> It might help to think of -Exp as syntactic sugar for 0-Exp.


I think there's one very important point to realise in all your examples
though...
We're NOT writing -4x² + 3. We write -4 * x ^^ 2 + 4. That's not a
polynomial expressions, it's source code.
I don't know about you, but the visual similarity is just not there for me.
I can't see C/D/Java/whatever code as a direct transcription of
mathematical notation no matter how hard I squint at it.
I personally have the presumption that unary operators have a higher
precedence than binary operators... period. I wouldn't give that a second
thought, and that trumps all other logic for me.
Secondary to that, when looking at that statement and deciding which of the
* or ^^ might have higher precedence, I would probably only then consider
that '^^' *may* have higher precedence than '*', but still not certain, and
I wouldn't be surprised (possibly assume) it had the same, ie. left to
right, as with * and /.
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