assumeAlso

Description

example

assumeAlso(condition) states that condition is valid for all symbolic variables in condition. It retains all assumptions previously set on these symbolic variables.

example

assumeAlso(expr,set) states that expr belongs to set, in addition to all previously made assumptions.

Examples

Assumptions Specified as Relations

Set assumptions using assume. Then add more assumptions using assumeAlso.

Solve this equation assuming that both x and y are nonnegative.

syms x y
assume(x >= 0 & y >= 0)
s = solve(x^2 + y^2 == 1, y)
Warning: Solutions are valid under the following
conditions: x <= 1;
x == 1.
To include parameters and conditions in the
solution, specify the 'ReturnConditions' value as
'true'.
> In solve>warnIfParams (line 482)
In solve (line 357)
s =
(1 - x)^(1/2)*(x + 1)^(1/2)
-(1 - x)^(1/2)*(x + 1)^(1/2)

The solver warns that both solutions hold only under certain conditions.

Add the assumption that x < 1. To add a new assumption without removing the previous one, use assumeAlso.

assumeAlso(x < 1)

Solve the same equation under the expanded set of assumptions.

s = solve(x^2 + y^2 == 1, y)
s =
(1 - x)^(1/2)*(x + 1)^(1/2)

For further computations, clear the assumptions.

assume([x y],'clear')

Assumptions Specified as Sets

Set assumptions using syms. Then add more assumptions using assumeAlso.

When declaring the symbolic variable n, set an assumption that n is positive.

syms n positive

Using assumeAlso, add more assumptions on the same variable n. For example, assume also that n is an integer.

assumeAlso(n,'integer')

Return all assumptions affecting variable n using assumptions. In this case, n is a positive integer.

assumptions(n)
ans =
[ 0 < n, in(n, 'integer')]

For further computations, clear the assumptions.

assume(n,'clear')

Assumptions on Matrix Elements

Use the assumption on a matrix as a shortcut for setting the same assumption on each matrix element.

Create the 3-by-3 symbolic matrix A with auto-generated elements. To assume every element of A is rational, specify set as 'rational'.

A = sym('A',[3 3],'rational')
A =
[ A1_1, A1_2, A1_3]
[ A2_1, A2_2, A2_3]
[ A3_1, A3_2, A3_3]

Now, add the assumption that each element of A is greater than 1.

assumeAlso(A > 1)

Return assumptions affecting elements of A using assumptions:

assumptions(A)
ans =
[ 1 < A1_1, 1 < A1_2, 1 < A1_3, 1 < A2_1, 1 < A2_2, 1 < A2_3,...
1 < A3_1, 1 < A3_2, 1 < A3_3,...
in(A1_1, 'rational'), in(A1_2, 'rational'), in(A1_3, 'rational'),...
in(A2_1, 'rational'), in(A2_2, 'rational'), in(A2_3, 'rational'),...
in(A3_1, 'rational'), in(A3_2, 'rational'), in(A3_3, 'rational')]

For further computations, clear the assumptions.

assume(A,'clear')

When you add assumptions, ensure that the new assumptions do not contradict the previous assumptions. Contradicting assumptions can lead to inconsistent and unpredictable results. In some cases, assumeAlso detects conflicting assumptions and issues an error.

Try to set contradicting assumptions. assumeAlso returns an error.

syms y
assume(y,'real')
assumeAlso(y == i)
Inconsistent assumptions.
Error in sym/assumeAlso (line 627)
feval(symengine, 'assumeAlso', cond);

assumeAlso does not guarantee to detect contradicting assumptions. For example, assume that y is nonzero, and both y and y*i are real values.

syms y
assume(y ~= 0)
assumeAlso(y,'real')
assumeAlso(y*i,'real')

Return all assumptions affecting variable y using assumptions:

assumptions(y)
ans =
[ in(y, 'real'), in(y*1i, 'real'), y ~= 0]

For further computations, clear the assumptions.

assume(y,'clear')

Input Arguments

collapse all

Assumption statement, specified as a symbolic expression, equation, relation, or vector or matrix of symbolic expressions, equations, or relations. You also can combine several assumptions by using the logical operators and, or, xor, not, or their shortcuts.

Expression to set assumption on, specified as a symbolic variable, expression, or a vector or matrix of symbolic variables or expressions. If expr is a vector or matrix, then assumeAlso(expr,set) sets an assumption that each element of expr belongs to set.

Set of assumptions, specified as a character vector, string array, or cell array. The available assumptions are 'integer', 'rational', 'real', or 'positive'.

You can combine multiple assumptions by specifying a string array or cell array of character vectors. For example, assume a positive rational value by specifying set as ["positive" "rational"] or {'positive','rational'}.

Tips

• assumeAlso keeps all assumptions previously set on the symbolic variables. To replace previous assumptions with the new one, use assume.

• When adding assumptions, always check that a new assumption does not contradict the existing assumptions. To see existing assumptions, use assumptions. Symbolic Math Toolbox™ does not guarantee to detect conflicting assumptions. Conflicting assumptions can lead to unpredictable and inconsistent results.

• When you delete a symbolic variable from the MATLAB® workspace using clear, all assumptions that you set on that variable remain in the symbolic engine. If later you declare a new symbolic variable with the same name, it inherits these assumptions.

• To clear all assumptions set on a symbolic variable var use this command.

assume(var,'clear')
• To clear all objects in the MATLAB workspace and close the Symbolic Math Toolbox engine associated with the MATLAB workspace resetting all its assumptions, use this command.

clear all
• MATLAB projects complex numbers in inequalities to the real axis. If condition is an inequality, then both sides of the inequality must represent real values. Inequalities with complex numbers are invalid because the field of complex numbers is not an ordered field. (It is impossible to tell whether 5 + i is greater or less than 2 + 3*i.) For example, x > i becomes x > 0, and x <= 3 + 2*i becomes x <= 3.

• The toolbox does not support assumptions on symbolic functions. Make assumptions on symbolic variables and expressions instead.

• Instead of adding assumptions one by one, you can set several assumptions in one function call. To set several assumptions, use assume and combine these assumptions by using the logical operators and, or, xor, not, all, any, or their shortcuts.