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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