# New Ticket Created by Sam S.
# Please include the string: [perl #128785]
# in the subject line of all future correspondence about this issue.
# <URL: https://rt.perl.org/Ticket/Display.html?id=128785 >
Perl 6 agrees with pretty much all programming languages that 0**0 == 1, and
does so consistently for the Int, int, Rat, FatRat, and Num types.
Just the Complex type doesn't play along:
➜ say (0+0i) ** 0;
NaN+NaN\i
➜ say (0+0i) ** (0+0i);
0+0i
I think these should both of these print 1+0i.
------ Mathematical background: ------
The value of "Zero to the power of zero" seems to be a historically
controversial topic in mathematics:
https://en.wikipedia.org/wiki/Exponentiation#Zero_to_the_power_of_zero
>From that wiki article I gather that (0**0 == 1) is popular among those
>working with practical formulae and actual values, and (0**0 == undefined)
>popular among those focusing theoretical considerations about limits.
>Unsurprisingly, programming languages have sided with the former definition...
In any case, I don't see a reason to treat Complex differently from the other
numeric types.
In fact, isn't the whole idea of complex numbers, to be a generalization of
real numbers so that as long as the imaginary part is 0, you get the exact same
results as with real numbers?
Then again, I'm not a mathematician. Input from an expert would be appreciated.
------ Other programming languages: ------
The ones I checked, seem to agree with my line of thought:
Perl 5:
$ perl -E 'use Math::Complex; say cplx(0,0) ** 0;'
1
$ perl -E 'use Math::Complex; say cplx(0,0) ** cplx(0,0);'
1
Ruby:
$ ruby -e 'puts Complex(0,0) ** 0'
1+0i
$ ruby -e 'puts Complex(0,0) ** Complex(0,0)'
1+0i
Python:
$ python
>>> print((0+0j) ** 0)
(1+0j)
>>> print((0+0j) ** (0+0j))
(1+0j)
For more examples, see: http://rosettacode.org/wiki/Zero_to_the_zero_power
