Re: Interpreting the solutions... better this time

• To: mathgroup at smc.vnet.net
• Subject: [mg75280] Re: Interpreting the solutions... better this time
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Mon, 23 Apr 2007 05:43:48 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <f0ejof\$pcq\$1@smc.vnet.net>

```Apostolos E. A. S. Evangelopoulos wrote:
> Right, here goes the whole thing again, since I didn't present it well last time...
>
> So, what I'm trying to solve is
>
> (8*Pi*R^3*S)/(3*h^2) + (2*h*Pi*(S + 3*\[Gamma]))/3 +
>  ((R^2*(-h + 2*R)^2*(-h/(2*R^2) - (2*R)/h^2))/
>     (Sqrt[3]*Sqrt[R^2*(-h^2/(4*R^2) + (2*R)/h)]) -
>    (4*(-h + 2*R)*Sqrt[R^2*(-h^2/(4*R^2) + (2*R)/h)])/
>     Sqrt[3] - (8*R*(-h + 2*R)*(-h/(2*R^2) - (2*R)/h^2)*
>      Sqrt[R^2*(-h^2/(4*R^2) + (2*R)/h)])/(3*Sqrt[3]) +
>    (16*(R^2*(-h^2/(4*R^2) + (2*R)/h))^(3/2))/
>     (9*Sqrt[3]*R) + (16*(-h/(2*R^2) - (2*R)/h^2)*
>      (R^2*(-h^2/(4*R^2) + (2*R)/h))^(3/2))/
>     (9*Sqrt[3]))*\[CapitalKappa] == 0
>
> with respect to h.
>
> What Mathematica returns is
[snip: ... root objects deleted...]

> I do not understand the # symbols and I do not know what I'm supposed to do with this, generally. How can I further evaluate these 'Root[blah]' forms?

What is returned is a list of *Root* objects [1]. According to the

"There are some equations, however, for which it is mathematically
impossible to find explicit formulas for the solutions. Mathematica uses
Root objects to represent the solutions in this case."

In[1]:=
Solve[2 - 4*x + x^5 == 0, x]

Out[1]=
{{x -> Root[2 - 4*#1 + #1^5 & , 1]},
{x -> Root[2 - 4*#1 + #1^5 & , 2]},
{x -> Root[2 - 4*#1 + #1^5 & , 3]},
{x -> Root[2 - 4*#1 + #1^5 & , 4]},
{x -> Root[2 - 4*#1 + #1^5 & , 5]}}

"Even though you cannot get explicit formulas, you can still find the
solutions numerically."

In[2]:=
N[%]

Out[2]=
{{x -> -1.51851}, {x -> 0.508499}, {x -> 1.2436},

{x -> -0.116792 - 1.43845 I},

{x -> -0.116792 + 1.43845 I}}

Regards
Jean-Marc

[1] "Built-in Functions / Numerical Computation / Number Representation
/ Root", http://documents.wolfram.com/mathematica/functions/Root

[2] _The Mathematica Book_, "1.5.7 Solving Equations",
http://documents.wolfram.com/mathematica/book/section-1.5.7

[3] _The Mathematica Book_, "3.4.2 Equations in One Variable",
http://documents.wolfram.com/mathematica/book/section-3.4.2

```

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