[ruby-core:24730] About An Imaginary Number Literal (Translation)

This post is the summary of a recent discussion in [ruby-dev] about
imaginary numbers.

In [ruby-dev:38843] 複素数リテラルについて
http://blade.nagaokaut.ac.jp/cgi-bin/scat.rb/ruby/ruby-dev/38843 ,
Matz suggested introducing an imaginary number literal to ruby. After
his new patch is applied, we can use the following syntax:

  2i
  2.0i

He also showed some issues about:

* Backward compatibility
* Is i OK? (In python it's j)
* Is Numeric#i needed for imaginarization?
* If it is needed, what's the value of (an imaginary number).i or (a
complex number).i ?


The discussions about the topic are outlines below.

* Numeric#i should be equivalent to Complex(0, self)
* i is better because it's more popular than j
* It is confusing to introduce both i and j because of quatenion's i, j and k
* Numeric#i should be one of them: (1) 2.0i == 2.0.i (2) returns the
imaginary part (3) represents as a complex number like 2.0.i #=> 2.0 +
0i; (1) is the best
* Is Numeric#i really needed? We can write s.i as s * 1i
* The fact 1/3i in Ruby becomes (-1/3)i in Mathematics is confusing
* Actually once Numeric#i was proposed and reject on 1.9.1
* Is the literal really needed? What's the use case? Is it general enough?
* What about an "imaginariztion syntax" like 1+(2)i, 1+(n)i or 1+3#i
* Good literals matter
* Only in IRC is better or worse
* How about introducing Math::I (1 + n * Math::I)
  * Complex::I already exists
* Programming language J describes 1+3i as 1j3
* Matz supposes there must be someone who use complex numbers often
* Matz supposes this topic was for 2.0, but may make in on 1.9.2
* 1+2i is too dissimilar to Complex(1, n). "1+(2)i and 1+(n)i" is better.
  * "1+2i and 1+n.i" is better
  * "1+2.i and 1+n.i" is better for less rules
* How about introducing this syntactic sugar: 2xxx is equivalent to 2
* Math::XXX
* Imaginary numbers and Complex numbers are fundamentally different,
so 1+2i should be Complex(1, 2) rather than 1.+(Complex(0, 2))
* see also: C++0x current draft has User-defined literals
  * How about 2i #=> 2.literal_i, 3/2r #=> 3 / 2.literal_r, 5C3 #=>
5.literal_C(3)
  * It is useful to apply within a classbox

Although this discussion isn't concluded, there have been no new posts
for 11 days.

# Thanks Aaron Patterson for correcting my English!