Re: [pure-lang-users] math.pure

[Albert G. <Dr....@t-...>]

Eddie Rucker wrote:
> LOL! I noticed atanh is not defined in mzscheme so had to look it up.
> (define (atanh x) (* .5 (log (/ (+ 1.0 x) (- 1.0 x)))))

Beware, that definition gives you a +nan.0+nan.0i for x = 1.0+0.0i. Pure 
gets this right:

   > atanh 1, atanh (-1);
   inf,-inf
   > atanh (1+:0), atanh (-1+:0);
   inf+:0.0,-inf+:0.0

It will also compute the required complex result for atanh (-2), but of 
course in the latest revision you have to tell it that you want a 
complex result:

   > atanh (-2);
   nan
   > atanh (-2+:0);
   -0.549306144334055+:1.5707963267949

> Very good point! Hmmm... I guess this is another good reason for not duplicating the functionality of ^ and pow.
> (-8+0i)^(1%3) = 1.0000000000000002+:1.7320508075688772

Well, my definition of complex (^) of course computes all powers in 
polar representation (and then converts them back to rectangular if 
needed). As the polar representation is normalized to the (-pi,pi] phase 
range automagically (see the constructor equations for (<:) in 
math.pure), it will always give you the principal roots without any ado.

In fact, the definition I have does work pretty well, it's just a few 
corner cases with integer exponents that are causing me grief. Well, if 
nothing else helps I'll just have to add a few special case rules, but I 
thought it would be nice to put it all in a closed formula. ;-)

> pow (-8) (1%3) = -2

You must be running an old revision there, pow is only defined for 
integer exponents now.

> I noticed in mzscheme,
>   > (expt -8 1/3)
>   1

I don't get that here (mzscheme v372, running on 32 bit Linux), it gives 
me the proper result:

   > (expt -8 1/3)
   1.0000000000000002+1.7320508075688772i

Cheers,
Albert

-- 
Dr. Albert Gr"af
Dept. of Music-Informatics, University of Mainz, Germany
Email:  Dr....@t-..., ag...@mu...
WWW:    http://www.musikinformatik.uni-mainz.de/ag