From: Caleb Clausen <caleb@...>
Date: 2009-08-05T06:37:30+09:00
Subject: [ruby-core:24766] Re: About An Imaginary Number Literal (Translation)

ujihisa wrote:
> * 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

It isn't clear to me if the above encompassed this point or not. There
should be a separate Imaginary class, distinct from Complex. I can't
find anymore the article by a mathematician where he explains it in
detail, but part of the problem is that the wrong thing happens (in most
languages, not just ruby) when you do this:

Infinity=1.0/0
p Complex::I*Infinity
#should be Complex(0,Infinity), not Complex(NaN,Infinity)
#or really, should be Imaginary(Infinity)

I believe the c++ standard referenced above was informed by this article
that I can't find.

I'm intrigued by the possibility of having numeric literals like:

3/4r      #=>Rational
667.71d  #=>BigDecimal
3+4i      #=>Complex
2-1i      #=>Complex
42i       #=>Imaginary
1/3.0i  #=>Imaginary
1/3ri  #=>Imaginary Rational

Here's the best way I can see that will let that happen; allow the
characters + - and /  in numeric literals provided that they are
followed by a digit. Also allow any number of type characters to follow
the end of the numeric literal. If type characters are present, send the
method(s) with the same name to the numeric literal AS A STRING.

In other words, the following should hold:
3/4r      equivalent to "3/4".r
667.71d  equivalent to "667.71".d
3+4i      equivalent to "3+4".i
2-1i      equivalent to "2-1".i
42i       equivalent to "42".i
1/3ri    equivalent to "1/3".r.i
1/3.0i   equivalent to "1/3.0".i

It's important that the type character methods get the literal as a
string in order to avoid loss of information and prevent rounding errors
with BigDecimal or strange sign errors with 1/3ri. Also see that this
system allows more than one type character to be chained together.

+ - and / in a numeric literal without any type characters at the end
are treated as normal operators.