Clear Assumptions and Reset the Symbolic Engine

The symbolic engine workspace associated with the MATLAB^® workspace is usually empty. The MATLAB workspace tracks the values of symbolic variables, and passes them to the symbolic engine for evaluation as necessary. However, the symbolic engine workspace contains all assumptions you make about symbolic variables, such as whether a variable is real, positive, integer, greater or less than a certain value, and so on. These assumptions can affect solutions to equations, simplifications, and transformations, as explained in Effects of Assumptions on Computations.

For example, create a symbolic variable x and assume that it is positive.

syms x
assume(x > 0)

If you clear the variable x using the command clear x, the MATLAB workspace does not clear the assumption from the symbolic engine workspace.

clear x
assumptions

ans =
0 < x

To clear the assumption for the variable x, use the command assume(x,'clear').

syms x
assume(x > 0)
assume(x,'clear')
assumptions

ans =
Empty sym: 1-by-0

Alternatively, you can create a fresh symbolic variable without assumptions using syms.

syms x

If you want to clear a symbolic variable and also reset the symbolic engine, use the command clear all.

syms x positive
clear all
whos
assumptions

ans =
Empty sym: 1-by-0

The following shows how the MATLAB workspace and symbolic engine workspace differ in their responses to a sequence of commands.

Step	Command	MATLAB Workspace	Symbolic Engine Workspace
1	`syms x positive` or `syms x;` `assume(x > 0)`	`x`	`x > 0`
2	`clear x`	empty	`x > 0`
3	`syms x`	`x`	empty
4	`clear all`	empty	empty

Check Assumptions Set on Variables

To check whether a variable, say x, has any assumptions in the symbolic engine workspace associated with the MATLAB workspace, use the assumptions function in the MATLAB Live Editor:

assumptions(x)

If the function returns an empty symbolic object, there are no additional assumptions on the variable. The default assumption is that x represents any complex number. Otherwise, there are additional assumptions on the value that the variable represents.

For example, while declaring the symbolic variable x, make an assumption that the value of this variable is a real number.

syms x real
assumptions(x)

ans =
in(x, 'real')

Another way to set an assumption is to use the assume function.

syms z
assume(z ~= 0);
assumptions(z)

ans = 
z ~= 0

To see assumptions set on all variables in the MATLAB workspace, use assumptions without input arguments.

assumptions

ans =
[ in(x, 'real'), z ~= 0]

Clear assumptions set on x and z.

assume([x z],'clear')

assumptions

ans =
Empty sym: 1-by-0

Equivalently, the following command also clears assumptions from x and z.

syms x z

Effects of Assumptions on Computations

Assumptions can affect many computations, including results returned by the solve and simplify functions. For example, solve this equation without any additional assumptions on its variable.

syms x
solve(x^4 == 1, x)

ans =
 -1
  1
 -1i
  1i

Now assume that x is real and solve the same equation.

syms x real
solve(x^4 == 1, x)

ans =
 -1
  1

Use the assumeAlso function to add the assumption that x is also positive.

assumeAlso(x > 0)
solve(x^4 == 1, x)

ans =
  1

Clearing x does not change the underlying assumptions that x is real and positive.

clear x
x = sym('x');
assumptions(x)
solve(x^4 == 1, x)

ans =
[ in(x, 'real'), 0 < x]
ans =
1

Clearing x with assume(x,'clear') or syms x clears the assumptions.

syms x
assumptions(x)

ans =
Empty sym: 1-by-0