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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
Online Help [2, 3]:
"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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