Why take a hint from Mapl (was re: simplification of atan2)

In the absence of strong objections from the Maple develop side, I think that the Maple design for complex number elementary function operations, and a bunch more of related material, was reviewed and revised in consultation with PRof. W. Kahan, my colleague and the principal designer of the IEEE floating point standard.  The major participant from the Maple side was Dave Hare.

While not everything can be resolved to perfect consistency in an imperfect (i.e. ambiguous) mathematical world view, it is plausible that the Maple design  (post version 9, I think) is going to be more useful as a model for CAS/ branch cuts/ etc, than something we make up incrementally, or perhaps some other model floating around.  Of which the obvious one is Mathematica (not my favorite) and DERIVE (which also benefited from Kahan's advice and has garnered quite a bit of praise.).
  So while I would be skeptical of a claim that we should do anything just because Maple does it,  I think in some areas it is more that possible that it would be a shortcut to an otherwise tedious design argument.

Kahan also contributed to the Common Lisp standard's arithmetic for complex elementary function branch cuts etc.

RJF


----- Original Message -----
From: sen1 at math.msu.edu
Date: Sunday, July 22, 2007 7:14 am
Subject: Re: [Maxima] simplification of atan2

> On Sat, 21 Jul 2007, Robert Dodier wrote:
> 
> 
> > if x > 0 then %pi/4 elseif x < 0 then 5*%pi/4 else 'atan2(x, x)
> 
> Why not conform to maple and use the principle value of the argument
> between %-pi and %pi as in
> 
> if x > 0 then %pi/4 elseif x < 0 then -3*%pi/4 else 'atan2(x, x)
> 
> -sen
> 
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