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Re: FindRoots?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112201] Re: FindRoots?
  • From: Mark Adler <madler at alumni.caltech.edu>
  • Date: Sat, 4 Sep 2010 04:01:51 -0400 (EDT)
  • References: <i5d01u$bsv$1@smc.vnet.net> <i5qhi6$plh$1@smc.vnet.net>

On 2010-09-03 03:10:14 -0700, Gianluca Gorni said:
> Still, Reduce does not see it (as of version 7.0.1):
>
> Reduce[2 x + Log[-((-1 + 2 x)/(-1 + 2 x^2))] ==== 0 && -2 <
>    x < -1/Sqrt[2], x, Reals]
> False

I don't know what's with the quadruple equals, but if I put in a double
equals I get:

Reduce[2 x + Log[-((-1 + 2 x)/(-1 + 2 x^2))] == 0 && -2 < x <
-1/Sqrt[2], x, Reals]

x == Root[{Log[-((-1 + 2 #1)/(-1 + 2 #1^2))] + 2 #1 &,
-0.86193624643066461860}]

Which seems like a quite reasonable answer to an exact equation without
a closed form solution.  The -0.8619... is the location of the root.

$Version
"7.0 for Mac OS X x86 (64-bit) (February 19, 2009)"

> Next, Reduce has problems with inexact input,

Indeed, Reduce will often complain when given numerical problems and say:

"Reduce was unable to solve the system with inexact coefficients or the
system obtained by direct rationalization of inexact numbers present in
the system.  Since many of the methods used by Reduce require exact
input, providing Reduce with an exact version of the system may help."

Clearly Reduce was not designed to be a numerical equation solver, at
least so far.  So the recommendations to use it as such are, I think, a
little off base.

Mark


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