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Re: Using results of "Solve"

• To: mathgroup at smc.vnet.net
• Subject: [mg25736] Re: [mg25693] Using results of "Solve"
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Sat, 21 Oct 2000 14:42:47 -0400 (EDT)
• References: <200010190835.EAA21602@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Helge Kreutzmann wrote:
> 
> Hello !
> I have a series of matrices which depend on several parameters. I can
> create those matrices fine and display them. They are called
> 
> S[k_,m_,b_,n_]
> 
> Now there is an unkown called "q" in the matrix which is evaluated by
> setting the determinant of the matrix zero and solving the resulting
> equation for q:
> 
> Solve[Det[S[2, m, b, 2]] == 0, q]
> 
> Now I want to use this function. The result is given in a form like:
> {{ q -> rhs1 },{ q -> rhs2}} and so on. I would like now to plot q.
> 
> A colleque gave me the following "hack":
> h =.;
> h[m_, b_] := Solve[Det[S[2, m, b, 2]] == 0, q];
> Plot3D[q  /. h[m, b] [[2]], {m, 0, 3}, {b, 0, 3}]
> 
> Is there a more straightforward way ? Especially I would like to create
> several functions this way and their sum is the resulting function I
> am interested in (actually it's a series).
> 
> Regards
> 
>          Helge

The way to get a list of solutions for q is simply

solns = q /. h[m,b]

You now have the solutions in a list and can plot any or all of them.

If you are working with algebraic functions (that is, the solution for q
is expressed in terms of Root[...] with ... dependent on parameters m
and b) then you might want to look into using RootSum. This is
frequently of use when one works with an ensemble of eigenvalues, say.


Daniel Lichtblau
Wolfram Research

• References:
  • Using results of "Solve"
    • From: Helge Kreutzmann <helgek@studserv.stud.uni-hannover.de>