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