From: Rudolf Polzer <denshimeiru-sapmctacher@...>
Date: 2003-08-25T07:23:13+09:00
Subject: Re: POLS and names of mathematical functions

Scripsit ille �Daniel Carrera� <dcarrera@math.umd.edu>:
> On Mon, Aug 25, 2003 at 02:42:37AM +0900, Rudolf Polzer wrote:
> 
> > > As a mathematecian, I see no problem at all with atanh, asinh, etc.  
> > > Anyone who has used a scientific calculator will be familiar with the 
> > > shorter forms.
> > 
> > No, they use sin^-1 etc.
> 
> I've seen both in scientific claculators.  I didn't mention sin^-1 because 
> that's not in the discussion.
> 
> What do Maple and Mathematica use?  I can't remember, I haven't used those 
> in years.  Perhaps that's who Ruby should be copying.

The computer algebra system "maxima" uses the a-prefix method. BTW, it
also supports cot, acot, coth and acoth. Maple always uses the arc-prefix
and always has the cot family of functions.

> > But I think it's enough to have ONE form for them - one can get used to
> > it.
> 
> I think one is enough.  Just figure out which is least surprising.

The one which is already there.

  rpolzer@katsuragi ~ $ irb
  irb(main):001:0> Math.atan(17)
  => 1.51204050407917
  irb(main):002:0> Math.atanh(17)
  Errno::EDOM: Numerical argument out of domain - atanh
          from (irb):2:in `atanh'
          from (irb):2

Until now tan and tanh don't have much in common, mathematically.
But this makes them nearly the same functions:

  irb(main):003:0> require 'complex'
  => true
  irb(main):004:0> Math.atanh(17)
  => Complex(0.0588915178281917, 1.5707963267949)
  irb(main):005:0> Math.atanh(17 * Complex::I)
  => Complex(0.0, 1.51204050407917)

That makes it obvious that it would be good to use the same prefix for
the inverse functions.


-- 
|Is there any documentation of the O() notation for Array operations.
The source. ;-)  It answers everything (including bugs), except for
"why" part.
                                 [Yukihiro Matsumoto ("Matz") in comp.lang.ruby]