Re: Digest Number 594

From: Hubert HOLIN (Hubert.Holin_at_[hidden])
Date: 2001-05-25 18:09:21

Paris (U.E.), le 26/05/2001

--- In boost_at_y..., Kevin Lynch <krlynch_at_b...> wrote:
> boost_at_y... wrote:
> > 
> > 
> > Message: 13
> >    Date: Fri, 25 May 2001 14:39:33 +0200
> >    From: Peter Schmitteckert (boost) <boost_at_s...>
> > Subject: Comments on Special functions, Quaternions, Octonions
> > 
> > Salut,
> > 
> > first of all I would see the library in boost, but I suggest that problems
> > with accuracy/overflows  should be revised, or at least be mentioned.
> > 
> 
> I concur with this...I think this is a valuable library for boost, but I

        Thanks!

> would like to see the possibility of overflows addressed. 

        Will be addressed.

> but I haven't spent the time yet to analyze it in detail.  And I haven't
> figured out abs, sqrt, or any of the others that might be affected.  But
> I'm sure that your current implementation of abs has the problem.  And I
> didn't find a sqrt implementation (does sqrt even make sense for
> quaternions?  my ignorance is shining through....)

        Square roots do not behave very nicely with quaternions (they give 
full spheres of answers, and to illustrate, we see immediately that i, 
j and k are all square roots of -1). There might be some trick with 
continuation-like methods or Riemann surfaces, but I have had no time 
to investigate that properly yet. That's why I did not provide a square 
root function for quaternions or octonions, and that "pow" is severly 
limited when dealing with these entities. There's no undue ignorance 
here, as it is far from being well-known, and I found out about the 
problem by investigating it. I did have some doubts due to complex 
behaviour, after reading an article in "The Visual Computer" which 
atempted to use them (and which, IMHO was just gibberish, but since the 
method it described purportedly did work, I believe is some interesting 
investigation left yet :-)  ).

> > 
> > Best wishes,
> > Peter
> > 
> 
> -- 
> -------------------------------------------------------------------------------
> Kevin Lynch				voice:	 [phone]
> Physics Department			Fax: [phone]
> Boston University			office:	 PRB-565
> 590 Commonwealth Ave.			e-mail:	 krlynch_at_b...
> Boston, MA 02215 USA			http://physics.bu.edu/~krlynch
> -------------------------------------------------------------------------------

        Hubert Holin
        Hubert.Holin_at_[hidden]