compute the smith normal form of a symbolic matrix in matlab

To compute the Smith normal form of a symbolic matrix in MATLAB, you can use the smithForm function from the Symbolic Math Toolbox. Here is an example implementation:

main.m
% Define a symbolic matrix
syms x y z
A = [x y z; x^2 y^2 z^2; x^3 y^3 z^3];

% Compute the Smith normal form
[B, J, K] = smithForm(A);
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In this example, the input matrix A is a symbolic matrix with variables x, y, and z. The smithForm function returns three matrices: B is the Smith normal form of A, J is the transformation matrix that converts A to B, and K is the transformation matrix that converts B back to A. The Smith normal form of a matrix is a diagonal matrix that represents the underlying structure of the matrix, and it can be useful for solving problems in linear algebra and other areas of mathematics.