Re: In-reply-to: <199803040639.BAA09722@smc.vnet.net.>
- To: mathgroup@smc.vnet.net
- Subject: [mg11382] Re: In-reply-to: <199803040639.BAA09722@smc.vnet.net.>
- From: Allan Hayes <hay@haystack.demon.co.uk>
- Date: Sun, 8 Mar 1998 20:13:00 -0500
- References: <6dpgrb$3om$1@dragonfly.wolfram.com>
Fred Simons wrote:
>
> > Date: Wed, 4 Mar 1998 01:39:27 -0500
> > From: Daniel Lichtblau <danl@wolfram.com>
To: mathgroup@smc.vnet.net
> > To: mathgroup@smc.vnet.net
> > Subject: [mg11382] [mg11271] Re: [mg11193] algebraic solutions
>
> > Daniel Teitelbaum wrote:
> > >
> > > Hi all,
> > >
> > > 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. Now, if I pick some random number
> > > for p, I can get mathematica to solve for z, but I cant get a solution
> > > in terms of p. Alternatively, I would like to be able to plot this
> > > function with p included as part of the vertical axis.
> > >
> > > Thanks in advance for your help,
> > >
> > > Daniel
> >
> >
> > You have five functions of p, not one. Here is one way to plot one of
> > them. It relies on the fact that the first root of an odd-degree
> > algebraic function in Mathematica is always real-valued.
> >
> > In[3]:= algfuns = Solve[z^5 + 2z^3 - p + 1 == 0, z];
> >
> > In[4]:= zp = z /. %[[1]]
> > 3 5
> > Out[4]= Root[-1 + p - 2 #1 - #1 & , 1]
> >
> > (* I assume you want p to be the independent variable, that is, along
> > the horizontal axis. *)
> >
> > In[5]:= Plot[%, {p,0,3}]
> > Out[5]= -Graphics-
> >
> > Will only work for other root functions in ranges where they are
> > real-valued.
> >
> > Alternative methods using FindRoot or NSolve could also be coded without
> > too much trouble.
> >
> >
> > Daniel Lichtblau
> > Wolfram Research
> >
>
> A simpler approach for the graphs of the real-valued roots is to make a
> ContourPlot of z^5 + 2z^3 - p + 1 with level 0.
>
> Fred Simons
> Eindhoven University of Technology
> Fred Simons
> Eindhoven University of Technology
Or
In[1]:=
<<Graphics`ImplicitPlot`
In[2]:=
ImplicitPlot[z^5 + 2z^3 - p + 1==0, {p, 0, 3} ]
--
Allan Hayes
Mathematica Training and Consulting
Leicester, UK
hay@haystack.demon.co.uk
http://www.haystack.demon.co.uk
voice: +44 (0)116 271 4198
fax: +44 (0)116 271 8642