use yalmip to find if equation is sum of squares in matlab

To use YALMIP to determine if an equation can be expressed as a sum-of-squares (SOS) decomposition, you need to set up a semidefinite optimization problem. First, define the variables in the problem and create the desired polynomial expression. Next, use the "sos" function in YALMIP to obtain the SOS constraint. Finally, solve the optimization problem and check if the SOS constraint has been satisfied.

Here's an example code snippet of this process:

main.m
% Define variables and polynomial expression
x = sdpvar(n,1);
p = x(1)^4 + 2*x(1)^2*x(2)^2 + x(2)^4;

% Obtain SOS constraint
[s1,c1] = polynomial(x,2);
F = [sos(p - s1), sos(s1)];

% Solve optimization problem with the SOS constraint
optimize(F,[],[]);

% Check if the SOS constraint is satisfied
if double(c1) > 0
    disp('The expression is a sum-of-squares');
else
    disp('The expression is not a sum-of-squares');
end
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In the above code, n is the number of variables in the expression. The polyomial function is used to create a polynomial with the specified degree and variables. sos is used to enforce the SOS constraint. The optimize function solves the SDP, while double(c1) returns the value of the variable corresponding to s1. If c1 is positive, then the polynomial p is indeed a sum-of-squares.