Learn more about Symbolic Math Toolbox

Assumptions for Symbolic Objects

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Default Assumption Setting Assumptions for Symbolic Variables Deleting Symbolic Objects and Their Assumptions

Default Assumption

In Symbolic Math Toolbox, symbolic variables are single complex variables by default. For example, if you declare z as a symbolic variable:

syms z

MATLAB assumes z is a complex variable. You can always check if a symbolic variable is assumed to be complex or real by entering conj command. If conj(x) == x returns 1, x is a real variable:

z == conj(z)

ans =
     0

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Setting Assumptions for Symbolic Variables

The sym and syms commands allow you to set up assumptions for symbolic variables. For example, create the real symbolic variables x and y and the positive symbolic variable z:

x = sym('x', 'real');
y = sym('y', 'real');
z = sym('z', 'positive');

or more efficiently

syms x y real;
syms z positive;

There are two assumptions you can assign to a symbolic object within the sym command: real and positive. Together with the default complex property of a symbolic variable, it gives you three choices for an assumption for a symbolic variable: complex, real, and positive.

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Deleting Symbolic Objects and Their Assumptions

When you declare x to be real with the command

syms x real

you create a symbolic object x and the assumption that the object is real. Symbolic objects and their assumptions are stored separately. When you delete a symbolic object from the MATLAB workspace

clear x

the assumption that x is real stays in symbolic engine. If you declare a new symbolic variable x later, it inherits the assumption that x is real instead of getting a default assumption. If later you solve an equation and simplify an expression with the symbolic variable x, you could get incomplete results. For example, the assumption that x is real causes the polynomial x²+1 to have no roots:

syms x real;
clear x;
syms x;
solve(x^2+1)

Warning: Explicit solution could not be found. 
> In solve at 81
 
ans =
[ empty sym ]

The complex roots of this polynomial disappear because the symbolic variable x still has the assumption that x is real stored in the symbolic engine. To clear the assumption, enter

syms x clear

After you clear the assumption, the symbolic object stays in the MATLAB workspace. If you want to remove both the symbolic object and its assumption, use two subsequent commands:

1. To clear the assumption, enter

   syms x clear

2. To delete the symbolic object, enter

   clear x

For more information on clearing symbolic variables, see Clearing Assumptions and Resetting the Symbolic Engine.

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Performing Symbolic Computations

Examples

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