Set assumption on symbolic object

`assume(`

states that
`condition`

)`condition`

is valid. `assume`

is not additive.
Instead, it automatically deletes all previous assumptions on the variables in
`condition`

.

Set an assumption using the associated syntax.

Assume ‘x’ is | Syntax |
---|---|

real | `assume(x,'real')` |

rational | `assume(x,'rational')` |

positive | `assume(x,'positive')` |

positive integer | `assume(x,{'positive','integer'})` |

less than -1 or greater than 1 | `assume(x<-1 | x>1)` |

an integer from 2 through 10 | `assume(in(x,'integer') & x>2 & x<10)` |

not an integer | `assume(~in(z,'integer'))` |

not equal to 0 | `assume(x ~= 0)` |

even | `assume(x/2,'integer')` |

odd | `assume((x-1)/2,'integer')` |

from 0 through 2π | `assume(x>0 & x<2*pi)` |

a multiple of π | `assume(x/pi,'integer')` |

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')`

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')

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))

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')

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')

Set assumption on the 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 *x*^{2} – 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')

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

Set assumptions on all elements of a matrix
using `sym`

.

Create the 2-by-2 symbolic matrix `A`

with auto-generated elements.
Specify the `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 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')

`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. Make 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'});

or more efficiently

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

`and`

| `assumeAlso`

| `assumptions`

| `in`

| `isAlways`

| `not`

| `or`

| `piecewise`

| `sym`

| `syms`