Re: square number

"Ioannis" <morpheus@xxxxxxxxxxxx> wrote in message
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<dcorbit@xxxxxxxxx> wrote in message
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[snip]

Here is the solution to a related problem:
Given a number, find what number raised to its own power is equal to
that number.
So given 4, the answer is 2 and given 27 the answer is 3. But what if
you are given 5 or 32.123?

This is known to have a solution via Lambert's W function. The equation
x^x=y
is solvable as:
x=log(y)/W(log(y)).

Of course, then one requires an algorithm for the principal branch of W
with
good precision, but such algorithms exist and can be found with Google.

My program attached also solves the problem. It uses Schroeder's
methods to
solve x^x-y = 0

If you don't have Maple or Mathematica, it is not likely that you have
an
implementation of Lambert's W function handy. The code I supplied
works for
any C compiler. I see that Lambert's W function is included in the
GSL. So
a shortened solution would be easy to produce.

--
Ioannis


.

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