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MathGroup Archive 2005

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Re: Testing the 'type' of a root returned by Solve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54666] Re: Testing the 'type' of a root returned by Solve
  • From: Peter Pein <petsie at arcor.de>
  • Date: Fri, 25 Feb 2005 01:19:29 -0500 (EST)
  • References: <cvk4i5$dgq$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Mike Witt wrote:
> If I solve an equation in which the solutions turn out
> to be functions of some variable, I can't figure out how
> to pick out one of the roots based on whether the root is
> real or complex.
> 
> The problem is that Head[] reports that the roots are
> all "Times" because of the variable in them.
> 
> The following notebook demonstrates. Can someone tell me
> the right way to do this (or point me to the right place
> in the book or help pages?)
> 
> For private email remove the NOSPAM.
> 
> -Mike
> 
> <notebook snipped>

Hi Mike,

  hopefully you've got no imaginary feet ;-)

In[1]:=
Select[r /. N[Solve[20*Feet^3 == (4*Pi*r^3)/5, r]],
   Simplify[Im[Chop[#1]], Feet \[Element] Reals] == 0 & ]

Out[1]=
{1.99647 Feet}

is one possibility.

Or - if you prefer exact values:

In[2]:=
   Select[r /. Solve[20*Feet^3 == (4*Pi*r^3)/5, r],
     ComplexExpand[Im[#1]] == 0 & ]
Out[2]=
   {(5^(2/3)*Feet)/Pi^(1/3)}
-- 
Peter Pein
Berlin


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