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Re: algebraic solutions


  • To: mathgroup@smc.vnet.net
  • Subject: [mg11248] Re: algebraic solutions
  • From: Paul Abbott <paul@physics.uwa.edu.au>
  • Date: Wed, 4 Mar 1998 01:39:11 -0500
  • Organization: University of Western Australia
  • References: <6dfvus$29n@smc.vnet.net>

Daniel Teitelbaum wrote:

> I'm a fairly novice Mathematica user, and I'm having a problem.  I asked
> a more experienced user and he could solve it, either.  I hope there is
> a solution and that you all can help.
> 
> I want to find the roots of the following equation:
> 
>     z^5  + 2z^3 - p + 1 = 0
> 
> I want to solve for z in terms of p. 

In[1]:= Solve[z^5 + 2*z^3 - p + 1 == 0, z] Out[1]=
               5       3
{{z -> Root[-#1  - 2 #1  + p - 1 & , 1]}, 
 
                5       3
  {z -> Root[-#1  - 2 #1  + p - 1 & , 2]}, 
 
                5       3
  {z -> Root[-#1  - 2 #1  + p - 1 & , 3]}, 
 
                5       3
  {z -> Root[-#1  - 2 #1  + p - 1 & , 4]}, 
 
                5       3
  {z -> Root[-#1  - 2 #1  + p - 1 & , 5]}}

This is as good as it gets -- these algebraic roots cannot be expressed
in terms of radicals.
 
> Alternatively, I would like to be able to plot this
> function with p included as part of the vertical axis.

The roots are, in general, complex.  How about

In[2]:= Plot[Evaluate[Im[z /. %]], {p, -1, 1}]; 

Cheers,
	Paul 

____________________________________________________________________ 
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907       
mailto:paul@physics.uwa.edu.au  AUSTRALIA                            
http://www.pd.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
____________________________________________________________________



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