MATLAB: Parametric solutions to system of equations inequations via solve()

Question

Given a square matrix A in n x n symbolic variables a_{i,j}, I want a parametric solutions for the a_{i,j} constrained to a system of equations and inequalities.

For instance, given

syms a, b, c, d, x

A = [[a, b]; [c, d]]

e(x) = charpoly(A, x)

I would like to find parametric solutions for all a, b, c, d that satisfy, for example

e(1)==0 and a >= 0, b >= 0, c >= 0, d >= 0.

Maple has functionality like this ("Solve semi-algebraic", or something) and I would like to be able to do this with Matlab.

I attempted to use solve() (see attached screenshot), but, even in this simpler case I consider there, I get the warning and the empty solution, so I'm guessing that I'm not understanding the solve() function correctly.

Thank you.

Answer 1

I see that you are using R2014a. Then your only option is to solve for one variable

solve(e(1) == 0, a)

and take this as a parameterization with which you can play by plugging in values for two variables, and solving result>=0 for the third.

If you upgrade to R2014b, just

 solve([e(1) == 0, a>=0, b>=0, c>=0, d>=0], [a, b, c, d])

works and gives you some solutions.