@Kitonum Matrix is superfluous. The code `<|>`(v $ n) already makes a Matrix.

@MiguelJesus Yes, I see your point. There may be some extraneous and invalid solutions given by Kitonum's code. I can work on it in a few hours. Someone else may get to it first.

@Mac Dude I would have the processes communicate via Sockets rather than via files.

@MiguelJesus I see nothing new in your more-detailed description of the problem that wasn't already obvious. And I see nothing inaccurate with Kitonum's solutions. Can you be more specific about what you think is wrong with Kitonum's solutions?

By the way, Maple does allow subscripted variables: X[1] or X__1. But let's not go there, because for me it's much more readable with single-character variables.

@Kitonum GAP is a computer algebra system. See http://en.wikipedia.org/wiki/GAP_%28computer_algebra_system%29

@Joe Riel The name is unintentionally inappropriate. I should've named it HasNegative.

@micahdavid That's not the same thing. Maple can do (numerically) the same integral that you passed to WolframAlpha:

int(1/Li(x), x= 2..2.1);

Li(x) for x > 1 is defined as the Cauchy Principal Value of Int(1/ln(t), t= 0..x). The integral starts at 0, not 2. Your inner integral starts at 2. Your integral is int(1/int(1/ln(x[1]), x[1]= 2..x[2]), x[2]= 2..2.1). It definitely diverges at its left endpoint. Since the divergence is at an endpoint, it cannot be saved by using Cauchy Principal Value.

@k20057 5 You can only use two equations, not three.

@k20057 5 There are only two parameters, and hence only two equations.

f:= E-> exp(-E/kT)/A:
eq1:= f(0) = ...:
eq2:= f(1) = ...:
....

@k20057 5 The system of equations cannot be solved with independent solutions for A and B because B/A is essentially a single coefficient.

What version of Maple are you using? Maple 18 accepts your code, and the unapply changes x[2] to x_2, which shouldn't make any difference because it is a dummy variable.

The equations are missing from your Question. Try including them in plain text form, or try attaching a worksheet.

The worksheet attachment of your post is missing. Please try uploading and attaching again.

What exactly is in the Excel worksheet? Is it just a column of 200 or so numbers? Or does it have the variable name also? Is the issue that you want to match a list of 200 or so values with a list of 200 or so variables? That can be done fairly easily.

@lasseledet Give me the values of the parameters and I'll try to find something.

You said that the root that you want is close to -1+I. You can use RootFinding:-Analytic with the range being a box centered at -1+I.

You could let k = x+I*y, then use DirectSearch:-SolveEquations on Re(DispersionEq) and Im(DispersionEq).

@lasseledet Do you have numeric values for Omega, Zeta, lambda, nu, rho, and gamma__o? Without numeric values, I think that it is hopeless. With numeric values, I think that it will be easy with fsolve or another root finder.