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 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')
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 allMATLAB 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