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

[Eddie R. <er...@bm...>]

On Fri 22/08/08  5:34 PM , John Cowan co...@cc... sent:
> Eddie Rucker scripsit:
> 
> > The user must determine the domain they are
> going work in. No different> than working with OCaml.
> 
> A running joke was an acceptance test for nascent Common Lisp
> implementations developed by Guy Steele. It was in three
> parts. First you type T; if it responds T, it passes part
> 1. Second, you define the factorial function and then calculate
> (/ (factorial 1000) (factorial 999)).  If it responds 1000,
> it passes part 2. Third, you try (atanh -2). If it returns
> a complex number, it passes; extra credit if it returns the
> correct complex number. It was a long time before any Common
> Lisp implementation passed the third part.
> --Steele and Gabriel, "The Evolution of Lisp"

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)))))

> Common Lisp: The Language lays down explicitly that (expt -8 1/3) must
> not return -2, as -2 is not the *principal* cube root of -8; instead it
> should return #C(1.0 1.7320508).

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

I noticed in mzscheme,
  > (expt -8 1/3)
  1
  > (expt (expt -8 1/3) 2)
  -1.9999999999999991+3.4641016151377553i
  > (expt (expt -8 1/3) 3)
  -8.0+3.1086244689504383e-015i

Compare with 1 + i sqrt(3), -2 + 2 sqrt 3, and -8.

e.r.