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assume

Set assumption on symbolic object

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Syntax

assume(condition)
assume(expr,set)
assume(expr,"clear")

Description

assume(condition) sets mathematical assumptions or conditions on symbolic variables as defined by condition. assume is not additive. Instead, it automatically deletes all previous assumptions on the variables in condition.

example

assume(expr,set) states that expr belongs to set. assume deletes previous assumptions on the variables in expr.

example

assume(expr,"clear") clears all assumptions on all variables in expr.

example

Examples

Common Assumptions

Set an assumption using the associated syntax.

Assumption for Symbolic Variable xSyntax
realassume(x,"real")
rationalassume(x,"rational")
positiveassume(x,"positive")
positive integerassume(x,{'positive','integer'})
less than –1 or greater than 1assume(x<-1 | x>1)
an integer from 2 through 10assume(in(x,"integer") & x>2 & x<10)
not an integerassume(~in(z,"integer"))
not equal to 0assume(x ~= 0)
evenassume(x/2,"integer")
oddassume((x-1)/2,"integer")
from 0 through 2πassume(x>0 & x<2*pi)
a multiple of πassume(x/pi,"integer")

Assume Variable Is Even or Odd

Assume x is even by assuming that x/2 is an integer. Assume x is odd by assuming that (x-1)/2 is an integer.

Assume x is even.

syms x
assume(x/2,"integer")

Find all even numbers between 0 and 10 using solve.

solve(x>0,x<10,x)
ans =
 2
 4
 6
 8

Assume x is odd. assume is not additive, but instead automatically deletes the previous assumption in(x/2, "integer").

assume((x-1)/2,"integer")
solve(x>0,x<10,x)
ans =
 1
 3
 5
 7
 9

Clear the assumptions on x for further computations.

assume(x,"clear")

Multiple Assumptions

Successive assume commands do not set multiple assumptions. Instead, each assume command deletes previous assumptions and sets new assumptions. Set multiple assumptions by using assumeAlso or the & operator.

Assume x > 5 and then x < 10 by using assume. Use assumptions to check that only the second assumption exists because assume deleted the first assumption when setting the second.

syms x
assume(x > 5)
assume(x < 10)
assumptions
ans =
x < 10

Assume the first assumption in addition to the second by using assumeAlso. Check that both assumptions exist.

assumeAlso(x > 5)
assumptions
ans =
[ 5 < x, x < 10]

Clear the assumptions on x.

assume(x,"clear")

Assume both conditions using the & operator. Check that both assumptions exist.

assume(x>5 & x<10)
assumptions
ans =
[ 5 < x, x < 10]

Clear the assumptions on x for future calculations.

assume(x,"clear")

Assumptions on Integrand

Compute an indefinite integral with and without the assumption on the symbolic parameter a.

Use assume to set an assumption that a does not equal -1.

syms x a
assume(a ~= -1)

Compute this integral.

int(x^a,x)
ans =
x^(a + 1)/(a + 1)

Now, clear the assumption and compute the same integral. Without assumptions, int returns this piecewise result.

assume(a,"clear")
int(x^a, x)
ans =
piecewise(a == -1, log(x), a ~= -1, x^(a + 1)/(a + 1))

Assumptions on Parameters and Variables of Equation

Use assumptions to restrict the returned solutions of an equation to a particular interval.

Solve this equation.

syms x
eqn = x^5 - (565*x^4)/6 - (1159*x^3)/2 - (2311*x^2)/6 + (365*x)/2 + 250/3;
solve(eqn, x)
ans =
   -5
   -1
 -1/3
  1/2
  100

Use assume to restrict the solutions to the interval –1 <= x <= 1.

assume(-1 <= x <= 1)
solve(eqn, x)
ans =
   -1
 -1/3
  1/2

Set several assumptions simultaneously by using the logical operators and, or, xor, not, or their shortcuts. For example, all negative solutions less than -1 and all positive solutions greater than 1.

assume(x < -1 | x > 1)
solve(eqn, x)
ans =
  -5
 100

For further computations, clear the assumptions.

assume(x,"clear")

Use Assumptions for Simplification

Setting appropriate assumptions can result in simpler expressions.

Try to simplify the expression sin(2*pi*n) using simplify. The simplify function cannot simplify the input and returns the input as it is.

syms n
simplify(sin(2*n*pi))
ans =
sin(2*pi*n)

Assume n is an integer. simplify now simplifies the expression.

assume(n,"integer")
simplify(sin(2*n*pi))
ans =
0

For further computations, clear the assumption.

assume(n,"clear")

Assumptions on Expressions

Set an assumption on a symbolic expression.

You can set assumptions not only on variables, but also on expressions. For example, compute this integral.

syms x
f = 1/abs(x^2 - 1);
int(f,x)
ans =
-atanh(x)/sign(x^2 - 1)

Set the assumption x2 – 1 > 0 to produce a simpler result.

assume(x^2 - 1 > 0)
int(f,x)
ans =
-atanh(x)

For further computations, clear the assumption.

assume(x,"clear")

Assumptions to Prove Relations

Prove relations that hold under certain conditions by first assuming the conditions and then using isAlways.

Prove that sin(pi*x) is never equal to 0 when x is not an integer. The isAlways function returns logical 1 (true), which means the condition holds for all values of x under the set assumptions.

syms x
assume(~in(x,"integer"))
isAlways(sin(pi*x) ~= 0)
ans =
  logical
   1

Assumptions on Matrix Elements

Set assumptions on all elements of a matrix using sym.

Create the 2-by-2 symbolic matrix A with autogenerated elements. Specify set as rational.

A = sym("A",[2 2],"rational")
A =
[ A1_1, A1_2]
[ A2_1, A2_2]

Return the assumptions on the elements of A using assumptions.

assumptions(A)
ans =
[ in(A1_1, 'rational'), in(A1_2, 'rational'),...
  in(A2_1, 'rational'), in(A2_2, 'rational')]

You can also use assume to set assumptions on all elements of a matrix. Now, assume all elements of A have positive rational values. Set the assumptions as a cell array of character vectors {'positive','rational'}.

assume(A,{'positive','rational'})

Return the assumptions on the elements of A using assumptions.

assumptions(A)
ans =
[ 0 < A1_1, 0 < A1_2, 0 < A2_1, 0 < A2_2,...
  in(A1_1, 'rational'), in(A1_2, 'rational'),...
  in(A2_1, 'rational'), in(A2_2, 'rational')]

For further computations, clear the assumptions.

assume(A,"clear")

Input Arguments

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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, vector, or matrix. If expr is a vector or matrix, then assume(expr,set) sets an assumption that each element of expr belongs to set.

Set of assumptions, specified as a character vector, string scalar, 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

  • assume removes any assumptions previously set on the symbolic variables. To retain previous assumptions while adding an assumption, use assumeAlso.

  • 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 you later 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 delete all objects in the MATLAB workspace and close the Symbolic Math Toolbox™ engine associated with the MATLAB workspace clearing all 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. Set assumptions on symbolic variables and expressions instead.

  • When you create a new symbolic variable using sym and syms, you also can set an assumption that the variable is real, positive, integer, or rational.

    a = sym("a","real");
b = sym("b","rational");
c = sym("c","positive");
d = sym("d","positive");
e = sym("e",{'positive','integer'});

    Alternatively, you can use these commands, which are more efficient.

    syms a real
syms b rational
syms c d positive
syms e positive integer

Version History

Introduced in R2012a

See Also

Functions

Topics