Re: algebraic solutions
- To: mathgroup@smc.vnet.net
- Subject: [mg11271] Re: [mg11193] algebraic solutions
- From: Daniel Lichtblau <danl@wolfram.com>
- Date: Wed, 4 Mar 1998 01:39:27 -0500
- References: <199803030410.XAA02144@smc.vnet.net.>
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
- References:
- algebraic solutions
- From: Daniel Teitelbaum <dt2m+@andrew.cmu.edu>
- algebraic solutions