grouping an equation in quadratic/squared terms

Hi all,

I would like MATLAB to group my equation

(-a-b)*x1^2 + 0.2*b*x1*x2 - 0.2*c*x2^2

as all quadratic items like below:

-(b*x1-0.1*x2)^2 - (a+b-b^2)*x1^2 - (0.2*c-0.01)*x2^2

I had found a method once from Matlab answers but I can not remember it. This equation is OK but I would like to use MATLAB to make this arrangement (if it's algebraically possible) if my equation is updated in the future.

Answer 1

[T.Nikhil kumar]

Hello Berkin,

As per my understanding, you want to group all the items in your equation as quadratic or squared terms.

I recommend you leverage the symbolic variables and the symbolic algebra capabilities of MATLAB for this purpose. You can first create ‘x1’, ‘x2’,’a’ and ‘b’ as symbolic scalar variables of type ‘sym’. Then, you can define your equation in a separate variable after which you can use the ‘collect’ function to group the quadratic terms (x1^2 and x2^2) and squared terms. Refer to the following code snippet for an overview of the method.

%Creating the symbolic variables 

syms x1 x2 a b c 

 

%Defining the equation 

equation = (-a-b)*x1^2 + 0.2*b*x1*x2 - 0.2*c*x2^2; 

 

% Grouping the quadratic terms (This grouped_equation variable contains the 

% new equation) 

grouped_equation = collect(equation, [x1^2, x2^2]); 

By using symbolic variables, you can easily update your equation in the future and MATLAB will automatically group the quadratic terms for you.

Refer to the following documentation to understand more about ‘syms’ and ‘collect’ functions.

syms - https://www.mathworks.com/help/symbolic/syms.html

collect - https://www.mathworks.com/help/symbolic/sym.collect.html

Hope this helps!

[Berkin Birol]

Hello Nikhil,

Thank you for your answer. I just tried your suggestion, unfortunately, this is not what I was looking for. collect(equation, [x1^2, x2^2]) returns "(- a - b)*x1^2 + (b*x2*x1)/5 - (c*x2^2)/5", which is different what I asked: "-(b*x1-0.1*x2)^2 - (a+b-b^2)*x1^2 - (0.2*c-0.01)*x2^2"

I don't want to just group squared x1 or x2's. I want to group the equation with just squared terms, like I highlighted in bold in the previous paragraph; square of (b*x1-0.1*x2), square of x1 with some coefficient (a+b-b^2), and similar to x1, square of x2 with some coefficient (0.2*c-0.01). These should be returns of the function, separated by all squared/quadratic terms (with their coefficients).

By using this method, I could easily conclude if the equation is positive or not, depending on the variables. Or determine the positiveness conditions.

[T.Nikhil kumar]

you can try using the functions of the Symbolic Math Toolbox like simplify, collect, and expand that are useful for manipulating symbolic expressions. But, for grouping as required by, I think doing it manually is the best way

[Berkin Birol]

Thank you again, Nikhil.