Writing and solving systems of non-linear equation

Hi everybody!

I have learned how to use fsolve for systems of non-linear equations, but now I have a problem because the systems that I need to solve are very large ones (not very complicated though) so I would like to know if there is a way in MATLAB to write automatically the systems of equations from a general formula.

As an example, if I want to solve x + y - 4 = 0 & x*y - 4 = 0, I would just write:

function fcns = eqns(z)
fcns(1) = z(1) + z(2) - 4;
fcns(2) = z(1)*z(2) - 4;
end

However, if I want to solve a system whose equations are given by the formula, say, "z(k) = z(k)*z(k-p)" for k=1:100, I cannot write all equations explicitly in a short amount of time, so I would need some MATLAB functions to write them according to the formula. Is there a way to do it? Or, am I following the wrong approach for this kind of problem? Thank you very much!

[Andrew Newell]

Sure, MATLAB has powerful tools for handling equations that can be expressed in terms of vectors and matrices. If you can give a better description of the equations you need to solve, we can help you with setting them up.

[Lucio Milanese]

Thanks a lot! So, given an arbitrary N > 1, I would like to solve the system involving the unknowns a(1), a(2)... a(N), as given by the two equations in the attachment; the first equation is for p odd, and the second one for p even. p would go from 1 to N. Ideally I would like to be able to change just N on my final code and let MATLAB do the rest, i.d. create the equations according to the two formulas and solve them. Thanks again in advance!