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

• To: mathgroup at smc.vnet.net
• Subject: [mg54671] Re: [mg54626] Testing the 'type' of a root returned by Solve
• From: "David Park" <djmp at earthlink.net>
• Date: Fri, 25 Feb 2005 01:19:41 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Mike,

sols=N[Solve[20*Feet^3 == (4*Pi*r^3)/5, r]]
(If[FreeQ[#1, Complex], Real, Complex] & ) /@ %
{Complex, Complex, Real}

The following is a little beyond the question. I am always a little dubious
about mixing data values and units into equations before they are solved. If
is often better to obtain a general and exact solution if possible. So for

sols = Solve[V == (4*Pi*r^3)/5, r]
{{r -> -(((-(5/Pi))^(1/3)*V^(1/3))/2^(2/3))},
{r -> ((5/Pi)^(1/3)*V^(1/3))/2^(2/3)},
{r -> ((-1)^(2/3)*(5/Pi)^(1/3)*V^(1/3))/2^(2/3)}}

Since V is positive we can test with...

If[FreeQ[#, Complex], Real, Complex] & /@ N[sols]
{Complex, Real, Complex}

Then we can substitute the 'data' into the the second real solution and

Simplify[sols[[2]] /. V -> 20*Foot^3, Foot > 0]
{r -> (5^(2/3)*Foot)/Pi^(1/3)}

David Park

From: Mike Witt [mailto:mwNOSPAM at mu.uoregon.edu]
To: mathgroup at smc.vnet.net

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

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

Cell[BoxData[
\({Complex, Complex, Real}\)], "Output"]
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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[
Solve[20  Feet\^3 == \(4\ \[Pi]\ r\^3\)\/5, \ r] //
N)\))\)\)], "Input"],

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```

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