Representing Multivariate Rational Functions in Matlab

Hello,

I am interested in utilizing multivariate rational functions in MatLab. I would like to create a matrix of these rational functions and then apply common matrix operations to them (such as inverse and multiplication). I would like to avoid creating my own implementation and was hoping that Matlab has some sort of built-in implementation to accomplish this. I have searched through the documentation for this kind of structure, but I have been unable to find it. Does anyone know if Matlab has something built-in that would help me accomplish this?

Thank you.

Answer 1

[Ayush]

Hi Ian,

I understand that you want to create a multivariate matrix using the MATLAB based functions.

You can utilize MATLAB's Symbolic Math Toolbox to work with rational functions as symbolic expressions. The Symbolic Math Toolbox provides powerful tools for symbolic computation, including operations on rational functions.

Refer the example below of how you can work with multivariate rational functions using the Symbolic Math Toolbox:

% Define the variables
syms x y;

% Define the rational functions
f1 = (x^2 + y^2) / (x + y);
f2 = (x^3 + y^3) / (x^2 - y^2);

% Create a matrix of rational functions
R = [f1, f2; f2, f1];

% Perform matrix operations
R_inv = inv(R); % Inverse of the matrix
R_mult = R * R; % Matrix multiplication

% Display the results
disp(R_inv);

disp(R_mult);

For more information on “syms” function you can refer the link below:

https://www.mathworks.com/help/releases/R2021b/symbolic/syms.html

I hope this helps!

Regards,

Ayush