MATLAB: How to parametrically solve a symbolic system of arbitrary size

Question

Hello,

I am trying to solve a symbolic system of equations that I automatically generate based on user data. The coefficients and the size of the system can change.

Here is an example of code for a 2×2 system :

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eps1 = 1;
eps2 = 1;
eps = [eps1;eps2];
sigma = 1;
k = ones(2,1);
h=[1;1];
Tw = sym(zeros(2, 1));
for i=1:2
 Tw(i) = sym(sprintf('Tw%d', i));
end
f = -sigma*eps.*Tw.^4;
Jacf = jacobian(f,Tw);
Tw0 = [293;293];
A = subs(Jacf,Tw,Tw0);
c = subs(f,Tw,Tw0)-A*Tw0;
T = sym(ones(2, 1));
T(1) = sym('To');
T(2) = sym('Ti');
S = sym(ones(2, 1));
for i=1:2
 S(i) = sym(sprintf('S%d', i));
end
G = S+h.*(T-Tw)+c+A*T;
solve(G,Tw);

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The system is obtained through linearisation of expression f. I would like to obtain Tw as an expression depending on T and S. But when I try to solve for G == 0, the solver solves in T and Tw instead of only Tw…

If I use solve(G,Tw(1),Tw(2)) then I get the good answer, but as the system is of arbitrary size in the general case, I don't know how to adapt this expression to get an answer.

Any idea how to fix this ?

Thanks,

Tomasz

Answer 1

Twcell = num2cell(Tw);
solve(G, Twcell{:})