Convert symbolic inequality to matrix form

Let's say I have a symbolic inequality:

2*x + 3*y <= 5

Is there a way to elegantly extract the matrices A, b for the equivalent inequality A*[x;y] <= b?

I know the function equationsToMatrix but that only works for equalities.

Thanks!

[Torsten]

equationsToMatrix works for equalities ...

So imagine at last you have a "<=" instead of a "=" between A*[x;y] and b.

[Nathan Hardenberg]

My thought was the same as the one from @Torsten (I think). But I would not consider it an elegant way

syms x y
eq = 2*x + 3*y <= 5;
eq1 = lhs(eq) == rhs(eq)  % convert to equality

eq1 = 

[A, b] = equationsToMatrix(eq1, [x y])

A = 

b = 

[Cedric Kotitschke]

I would surely call that elegant, thanks!

Answer 1

[Gandham Heamanth]

Yes, in MATLAB, you can use the symbolic math toolbox to extract the matrices A and b from a symbolic inequality. Here's how you can do it:

syms x y;

% Define the symbolic inequality

inequality = 2*x + 3*y <= 5;

% Extract the coefficients of x and y

coefficients = coeffs(inequality, [x, y]);

% Extract the matrix A and vector b

A = [coefficients(1), coefficients(2)];

b = coefficients(3);

% Display the matrices A and b

disp('Matrix A:');

disp(A);

disp('Vector b:');

disp(b);

Note that this code assumes you have the Symbolic Math Toolbox installed in MATLAB.

[Nathan Hardenberg]

The coeffs functions does not seem to work.

syms x y;
% Define the symbolic inequality
inequality = 2*x + 3*y <= 5;
% Extract the coefficients of x and y
coefficients = coeffs(inequality, [x, y])

coefficients = 

% Extract the matrix A and vector b
A = [coefficients(1), coefficients(2)];

Index exceeds the number of array elements. Index must not exceed 1.

Error in indexing (line 936)
R_tilde = builtin('subsref',L_tilde,Idx);

b = coefficients(3);
% Display the matrices A and b
disp('Matrix A:');
disp(A);
disp('Vector b:');
disp(b);

As an advice: you can past your code and mark it as code. Then you can run it in the browser and it is easier to read

[Cedric Kotitschke]

But this assumes a very specific structure of the inequality. I also want to be able to deal with those structurs:

syms x y
ineq1 = 2*x <= 2-y;
ineq2 = 0 >= 4*x + 6*y;
ineq3 = 3 >= 5*y;

etc.

Answer 2

[Nathan Hardenberg]

Moved my comment to an answer (to be accepted only if satisfied):

syms x y
eq = 2*x + 3*y <= 5;      % inequality
eq1 = lhs(eq) == rhs(eq)  % convert to equality

eq1 = 

[A, b] = equationsToMatrix(eq1, [x y])  % use equationsToMatrix-function

A = 

b =