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MathGroup Archive 2005

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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


 filename="foo.nb"

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application, such as Mathematica, MathReader or Publicon. The data
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(*CacheID: 232*)


(*NotebookFileLineBreakTest
NotebookFileLineBreakTest*)
(*NotebookOptionsPosition[      2544,         85]*)
(*NotebookOutlinePosition[      3174,        107]*)
(*  CellTagsIndexPosition[      3130,        103]*)
(*WindowFrame->Normal*)



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  ]]
},
FrontEndVersion->"5.0 for X",
ScreenRectangle->{{0, 1280}, {0, 1024}},
WindowSize->{520, 600},
WindowMargins->{{Automatic, 24}, {69, Automatic}}
]

(*******************************************************************
Cached data follows.  If you edit this Notebook file directly, not
using Mathematica, you must remove the line containing CacheID at
the top of  the file.  The cache data will then be recreated when
you save this file from within Mathematica.
*******************************************************************)

(*CellTagsOutline
CellTagsIndex->{}
*)

(*CellTagsIndex
CellTagsIndex->{}
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(*NotebookFileOutline
Notebook[{
Cell[1754, 51, 123, 4, 52, "Text"],

Cell[CellGroupData[{
Cell[1902, 59, 119, 2, 51, "Input"],
Cell[2024, 63, 58, 1, 27, "Output"]
}, Open  ]],
Cell[2097, 67, 207, 5, 71, "Text"],

Cell[CellGroupData[{
Cell[2329, 76, 141, 3, 51, "Input"],
Cell[2473, 81, 55, 1, 27, "Output"]
}, Open  ]]
}
]
*)



(*******************************************************************
End of Mathematica Notebook file.
*******************************************************************)




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