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>