OpenEuphoria

Re: Algebra problem

• Posted by "Juergen Luethje" <j.lue at gmx.de> Jul 07, 2005
• 997 views

Erik-Jan van Kampen wrote:

> Derek Parnell wrote:
>
>> My high school algebra has deserted me 
>>
>>  Given the formula
>>
>>    A^b + Cb = d
>>
>> how do I solve for 'b'?
>
>
> Hi Derek,
>
>  From the Matlab 6.5 Symbolic Toolbox:
>
>>> solve(A^b+C*b-d,b)
>
> ans =
>
> -(lambertw(log(A)/C*exp(d*log(A)/C))*C-d*log(A))/log(A)/C
>
>>> help lambertw
>
> LAMBERTW Lambert's W function.
>     W = LAMBERTW(X) is the solution to w*exp(w) = x.
>     W = LAMBERTW(K,X) is the K-th branch of this multi-valued function.
>     Reference: Robert M. Corless, G. H. Gonnet, D. E. G. Hare,
>     D. J. Jeffrey, and D. E. Knuth, "On the Lambert W Function",
>     Advances in Computational Mathematics, volume 5, 1996, pp. 329-359.
>     Also available from:
>     http://pineapple.apmaths.uwo.ca/~rmc/papers/LambertW/index.html

Interesting!
I just wrote a "brute force" lambertw() function in Euphoria, and
calculated the example that I gave in my other post:

constant
   E = 2.718281828459045235

type nonnegative_atom (object x)
   if atom(x) then
      return x >= 0
   end if
   return 0
end type

function lambertw (nonnegative_atom x)
   for w = 0 to x by 0.001 do
      if w*power(E,w) >= x then
         return w
      end if
   end for
   return 0
end function

atom A, C, d

A = 2
C = 3
d = 5
? -(lambertw(log(A)/C*power(E,d*log(A)/C))*C - d*log(A)) / log(A) / C

Prints 0.9986988627 -- the correct result is 1.

Regards,
   Juergen