[Tutor] a puzzle about -3**2 vs (-3)**2

[Todd]

On Fri, Jul 31, 2015 at 2:58 AM, D Wyatt <fiberfolly at gmail.com> wrote:

> I just read in a book a little while ago that ** trumps a negative
> sign?  I am struggling with the audacity of that as -1 is negative 1,
> NOT minus 1.  How can an arithmetic operation trump an attribute of a
> negative integer?  It truly makes no sense to me.  Thank you for any
> enlightenment you can provide.
>
> Python 3.4.3 (v3.4.3:9b73f1c3e601, Feb 24 2015, 22:43:06) [MSC v.1600 32
> bit (In
> tel)] on win32
> Type "help", "copyright", "credits" or "license" for more information.
> >>> 3**2
> 9
> >>> (-3)**2
> 9
> >>> -3**2
> -9
> >>>
>
>
It is a matter of operator precedence.  Certain operators are carried out
before others.  See here:
https://docs.python.org/3/reference/expressions.html#operator-precedence

Negation has lower precedence than exponentiation.  That means that the
exponentiation is carried out first, and negation is carried out second.
So "-3**2" is equivalent to "-(3**2)".

This matches the precedence rules for written mathematics, where negation
has a lower precedence than exponentiation as well.  So python is doing the
correct thing here mathematically.  See, for example,
http://mathforum.org/library/drmath/view/53194.html