MATLAB syms

Symbolic variables in MATLAB are variables that store a literal, such as x, $, as a symbol. This means that whatever a symbolic variable stores are not a value the computer can compute until it is assigned a numeric value. It is just a symbolic representation. To understand the same, see the following case.
If a user needs to display an equation like follows:

x = x + 1

This can be done with the usage of symbolic variables. One would make a symbolic variable, say x and assign them values x + 1. Then, typing the following will display the above equation.

x = x + 1

Now, we shall see how to create variables, functions, and matrix symbolic variables with an example of each.

Scalar Symbolic Variable:

To create a symbolic scalar variable, the syms keyword can be used. 

Syntax:

syms <variable list>

Example 1:

Matlab

% MATLAB Code
syms x z;
disp(x)
disp(z)

Every variable created will have a symbolic value, the same as its name.

Output:

Symbolic Functions:

Symbolic functions work upon symbolic variables and can be used for displaying and computing numeric calculations. 

Syntax:

syms <function name>(parameters)

This will create a symbolic function. See the following example for a better understanding.

In this example, we create two symbolic functions. The first one computes the square of a variable and the second one computes the whole square of the sum of two variables.

Example 2:

Matlab

% MATLAB Code
syms t(a) f(b,c);
t(a) = a^2;
f(b,c) = (b + c)^2;

% Getting function values for numeric data
t(5)
f(1, .5)

The output of the above code first displays the symbolic representation of the two functions and then computes the values of these functions for a given numeric data.

Output:

Symbolic Matrix:

A symbolic matrix will have representation like it is done in abstract algebra. To create such a matrix, the syms keyword takes the following form:

syms <matrix name> [size vector]

See the following example to understand the same. We will create a matrix named T of size 3×3.

Example 3:

Matlab

% MATLAB Code
syms T [3 3]
T

Output:

As can be seen, the elements in matrix T are represented in the following form.

T_{row number, column number} 

We can then change any element using the array indexing methods. 

Example 4:

Matlab

% MATLAB Code
syms T [3 3]
T(3,:) = [1 2 3]

In this example, we change the third row from symbolic to numeric data. The output of above code is:

Output:

Conclusion

In this article, we discussed how to create symbolic scalar variables, functions, and matrix variables in MATLAB with the help of syms function.