Create symbolic variables x and y.

syms x y
x

x = $$x$$

y

y = $$y$$

Create a 1-by-4 symbolic vector a with the automatically generated elements $$a_1,\dots ,a_4$$. This command also creates the symbolic variables a1, ..., a4 in the MATLAB workspace.

syms a [1 4]
a

a = $$\left(\begin{array}{cccc}{a}_1& a_2& a_3& a_4\end{array}\right)$$

whos

  Name      Size            Bytes  Class    Attributes

  a         1x4                 8  sym                
  a1        1x1                 8  sym                
  a2        1x1                 8  sym                
  a3        1x1                 8  sym                
  a4        1x1                 8  sym                

You can change the naming format of the generated elements by using a format character vector. Declare the symbolic variables by enclosing each variable name in single quotes. syms replaces %d in the format character vector with the index of the element to generate the element names.

syms 'p_a%d' 'p_b%d' [1 4]
p_a

p_a = $$\left(\begin{array}{cccc}{p}_{\mathrm{a1}}& p_{\mathrm{a2}}& p_{\mathrm{a3}}& p_{\mathrm{a4}}\end{array}\right)$$

p_b

p_b = $$\left(\begin{array}{cccc}{p}_{\mathrm{b1}}& p_{\mathrm{b2}}& p_{\mathrm{b3}}& p_{\mathrm{b4}}\end{array}\right)$$

Create a 3-by-4 symbolic matrix with automatically generated elements. The elements are of the form $$A_{i,j}$$, which generates the elements $$A_{1,1},\dots ,A_{3,4}$$.

syms A [3 4]
A

A = 
$$\left(\begin{array}{cccc}{A}_{1,1}& A_{1,2}& A_{1,3}& A_{1,4}\\ A_{2,1}& A_{2,2}& A_{2,3}& A_{2,4}\\ A_{3,1}& A_{3,2}& A_{3,3}& A_{3,4}\end{array}\right)$$

Create symbolic variables x and y, and assume that they are integers.

syms x y integer

Create another variable z, and assume that it has a positive rational value.

syms z positive rational

Check assumptions.

assumptions

ans = 

Alternatively, check assumptions on each variable. For example, check assumptions set on the variable x.

assumptions(x)

ans = $$x\in \mathbb{Z}$$

Clear assumptions on x, y, and z.

assume([x y z],'clear')
assumptions

 
ans =
 
Empty sym: 1-by-0
 

Create a 1-by-3 symbolic array a and assume that the array elements have real values.

syms a [1 3] real
assumptions

ans = $$\left(\begin{array}{ccc}{a}_1\in \mathbb{R}& a_2\in \mathbb{R}& a_3\in \mathbb{R}\end{array}\right)$$

Create symbolic functions with one and two arguments.

syms s(t) f(x,y)

Both s and f are abstract symbolic functions. They do not have symbolic expressions assigned to them, so the bodies of these functions are s(t) and f(x,y), respectively.

Specify the following formula for f.

f(x,y) = x + 2*y

f(x, y) = $$x+2\hspace{0.17em}y$$

Compute the function value at the point x = 1 and y = 2.

f(1,2)

ans = $$5$$

Create a symbolic function and specify its formula by using a symbolic matrix.

syms x
M = [x x^3; x^2 x^4];
f(x) = M

f(x) = 
$$\left(\begin{array}{cc}x& x^3\\ x^2& x^4\end{array}\right)$$

Compute the function value at the point x = 2:

f(2)

ans = 
$$\left(\begin{array}{cc}2& 8\\ 4& 16\end{array}\right)$$

Compute the value of this function for x = [1 2 3; 4 5 6]. The result is a cell array of symbolic matrices.

xVal = [1 2 3; 4 5 6];
y = f(xVal)

y=2×2 cell array
    {2x3 sym}    {2x3 sym}
    {2x3 sym}    {2x3 sym}

Access the contents of a cell in the cell array by using braces.

y{1}

ans = 
$$\left(\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\end{array}\right)$$

Create a 2-by-2 symbolic matrix with automatically generated symbolic functions as its elements.

syms f(x,y) 2
f

f(x, y) = 
$$\left(\begin{array}{cc}{f}_{1,1}\left(x,y\right)& f_{1,2}\left(x,y\right)\\ f_{2,1}\left(x,y\right)& f_{2,2}\left(x,y\right)\end{array}\right)$$

Assign symbolic expressions to the symbolic functions f1_1(x,y) and f2_2(x,y). These functions are displayed as $$f_{1,1}(x,y)$$ and $$f_{2,2}(x,y)$$ in the Live Editor. When you assign these expressions, the symbolic matrix f still contains the initial symbolic functions in its elements.

f1_1(x,y) = 2*x;
f2_2(x,y) = x - y;
f

f(x, y) = 
$$\left(\begin{array}{cc}{f}_{1,1}\left(x,y\right)& f_{1,2}\left(x,y\right)\\ f_{2,1}\left(x,y\right)& f_{2,2}\left(x,y\right)\end{array}\right)$$

Substitute the expressions assigned to f1_1(x,y) and f2_2(x,y) by using the subs function.

A = subs(f)

A(x, y) = 
$$\left(\begin{array}{cc}2\hspace{0.17em}x& f_{1,2}\left(x,y\right)\\ f_{2,1}\left(x,y\right)& x-y\end{array}\right)$$

Evaluate the value of the symbolic matrix A, which contains the substituted expressions at x = 2 and y = 3.

A(2,3)

ans = 
$$\left(\begin{array}{cc}4& f_{1,2}\left(2,3\right)\\ f_{2,1}\left(2,3\right)& -1\end{array}\right)$$

Certain functions, such as solve and symReadSSCVariables, can return a vector of symbolic variables or a cell array of symbolic variables and functions. These variables or functions do not automatically appear in the MATLAB workspace. Create these variables or functions from the vector or cell array by using syms.

Solve the equation sin(x) == 1 by using solve. The parameter k in the solution does not appear in the MATLAB workspace.

syms x
eqn = sin(x) == 1;
[sol, parameter, condition] = solve(eqn, x, 'ReturnConditions', true);
parameter

parameter = $$k$$

Create the parameter k by using syms. The parameter k now appears in the MATLAB workspace.

syms(parameter)

Similarly, use syms to create the symbolic objects contained in a vector or cell array. Examples of functions that return a cell array of symbolic objects are symReadSSCVariables and symReadSSCParameters.

Create some symbolic variables, functions, and arrays.

syms a f(x)
syms A [2 2]

Display a list of all symbolic objects that currently exist in the MATLAB workspace by using syms.

syms

Your symbolic variables are:

A     A1_1  A1_2  A2_1  A2_2  a     f     x                                   

Instead of displaying a list, return a cell array of all symbolic objects by providing an output to syms.

S = syms

S = 8x1 cell
    {'A'   }
    {'A1_1'}
    {'A1_2'}
    {'A2_1'}
    {'A2_2'}
    {'a'   }
    {'f'   }
    {'x'   }

Create several symbolic objects.

syms a b c f(x)

Return all symbolic objects as a cell array by using the syms function. Use the cellfun function to delete all symbolic objects in the cell array symObj.

symObj = syms;
cellfun(@clear,symObj)

Check that you deleted all symbolic objects by calling syms. The output is empty, meaning no symbolic objects exist in the MATLAB workspace.

syms