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Testing the 'type' of a root returned by Solve

• To: mathgroup at smc.vnet.net
• Subject: [mg54626] Testing the 'type' of a root returned by Solve
• From: Mike Witt <mwNOSPAM at mu.uoregon.edu>
• Date: Thu, 24 Feb 2005 03:21:30 -0500 (EST)
• Organization: University of Oregon
• Sender: owner-wri-mathgroup at wolfram.com

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


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Notebook[{
Cell["\<\
I want to be able to select the 'real' root using the 'Head' \
function, like this:\
\>", "Text",
  FontSize->14],

Cell[CellGroupData[{

Cell[BoxData[
    \(Head /@ \((r /. \ \((Solve[20 == \(4\ \[Pi]\ r\^3\)\/5, \ r] // 
              N)\))\)\)], "Input"],

Cell[BoxData[
    \({Complex, Complex, Real}\)], "Output"]
}, Open  ]],

Cell["\<\
But when I add a variable, then the 'type' of every root becomes \
'Times' because of the product of the variable and the number. Is 'Head' the \
wrong way to do this?\
\>", "Text",
  FontSize->14],

Cell[CellGroupData[{

Cell[BoxData[
    \(Head /@ \((r /. \((\ 
            Solve[20  Feet\^3 == \(4\ \[Pi]\ r\^3\)\/5, \ r] // 
              N)\))\)\)], "Input"],

Cell[BoxData[
    \({Times, Times, Times}\)], "Output"]
}, Open  ]]
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• Follow-Ups:
  • Re: Testing the 'type' of a root returned by Solve
    • From: Igor Antonio <igora@wolf-ram.com>