Create Symbolic Numbers, Variables, and Expressions
This page shows how to create symbolic numbers, variables, and expressions. To learn how to work with symbolic math, see Perform Symbolic Computations.
Create Symbolic Numbers
You can create symbolic numbers by using
sym. Symbolic numbers are exact
representations, unlike floating-point numbers.
Create a symbolic number by using
sym and compare it to the
same floating-point number.
ans = 1/3 ans = 0.3333
The symbolic number is represented in exact rational form, while the floating-point number is a decimal approximation. The symbolic result is not indented, while the standard MATLAB® result is indented.
Calculations on symbolic numbers are exact. Demonstrate this exactness by finding
sin(pi) symbolically and numerically. The symbolic result is
exact, while the numeric result is an approximation.
ans = 0 ans = 1.2246e-16
To learn more about symbolic representation of numbers, see Numeric to Symbolic Conversion.
Create Symbolic Variables
sym– Create numbered symbolic variables or create symbolic variables in MATLAB functions.
syms– Create fresh symbolic variables for interactive symbolic workflows, that is, for symbolic variable creation at the MATLAB command line or in MATLAB live scripts. A fresh symbolic variable does not have any assumptions.
syms command is shorthand for the
sym syntax, but the two functions handle assumptions
differently. For more details, see Reuse Names of Symbolic Objects.
Create the symbolic variables
syms x y = sym('y')
The first command creates a symbolic variable
x in the
MATLAB workspace with the value
x assigned to the variable
x. The second command creates a symbolic variable
y with the value
syms, you can create multiple variables in one command.
Create the variables
syms a b c
If you want to create a MATLAB array of numbered symbolic variables, the
syntax is inconvenient. Therefore, use
sym instead to create an
array of many numbered symbolic variables.
Clear the workspace. Create a row vector containing the symbolic variables
a1, ..., a20 and assign it to the MATLAB variable
A. Display the variable in the MATLAB workspace.
clear all A = sym('a', [1 20]) whos
A = [ a1, a2, a3, a4, a5, a6, a7, a8, a9, a10,... a11, a12, a13, a14, a15, a16, a17, a18, a19, a20] Name Size Bytes Class Attributes A 1x20 8 sym
A is a
20 array of
20 symbolic variables.
syms, you can
create many fresh symbolic variables with corresponding variables name in the
Clear the workspace. Create the fresh symbolic variables
a10 and assign them the MATLAB variable names
a1, ..., a10, respectively. Display
the variables in the MATLAB workspace.
clear all syms(sym('a', [1 10])) whos
Name Size Bytes Class Attributes a1 1x1 8 sym a10 1x1 8 sym a2 1x1 8 sym a3 1x1 8 sym a4 1x1 8 sym a5 1x1 8 sym a6 1x1 8 sym a7 1x1 8 sym a8 1x1 8 sym a9 1x1 8 sym
The MATLAB workspace contains 10 MATLAB variables that are symbolic variables.
syms command is a convenient shorthand for the
sym syntax, and its typical use is to create fresh symbolic
variables for interactive symbolic workflows. Use the
syntax to create the following:
Symbolic variables in MATLAB functions
Many numbered symbolic variables
Symbolic variable whose value differs from its name in the MATLAB workspace
Symbolic number, such as
Symbolic variable that inherits the assumptions from a previously used symbolic variable having the same name
Create Symbolic Expressions
Suppose you want to use a symbolic variable to represent the golden ratio
phi = (1 + sqrt(sym(5)))/2;
achieves this goal. Now you can perform various mathematical operations on
phi. For example,
f = phi^2 - phi - 1
f = (5^(1/2)/2 + 1/2)^2 - 5^(1/2)/2 - 3/2
Now suppose you want to study the quadratic function
c. First, create the symbolic variables
syms a b c x
Then, assign the expression to
f = a*x^2 + b*x + c;
To create a symbolic number, use the
sym command. Do not
syms function to create a symbolic expression that is
a constant. For example, to create the expression whose value is
f = sym(5). The command
f = 5 does not define
f as a symbolic expression.
Reuse Names of Symbolic Objects
If you set a variable equal to a symbolic expression, and then apply the
syms command to the variable, MATLAB software removes the previously defined expression from the variable.
syms a b f = a + b
f = a + b
If later you enter
syms f f
then MATLAB removes the value
a + b from the expression
f = f
You can use the
syms command to clear variables of definitions
that you previously assigned to them in your MATLAB session.
syms clears the assumptions of the
variables: complex, real, integer, and positive. These assumptions are stored
separately from the symbolic object. However, recreating a variable using
sym does not clear its assumptions. For more information, see
Delete Symbolic Objects and Their Assumptions.