Divisors of integer or expression
Find all nonnegative divisors of these integers.
Find the divisors of integers. You can use double precision
numbers or numbers converted to symbolic objects. If you call divisors for
a double-precision number, then it returns a vector of double-precision
numbers.
divisors(42)
ans =
1 2 3 6 7 14 21 42Find the divisors of negative integers. divisors returns
nonnegative divisors for negative integers.
divisors(-42)
ans =
1 2 3 6 7 14 21 42If you call divisors for a symbolic number,
it returns a symbolic vector.
divisors(sym(42))
ans = [ 1, 2, 3, 6, 7, 14, 21, 42]
The only divisor of 0 is 0.
divisors(0)
ans =
0Find the divisors of univariate polynomial expressions.
Find the divisors of this univariate polynomial. You can specify the polynomial as a symbolic expression.
syms x divisors(x^4 - 1, x)
ans = [ 1, x - 1, x + 1, (x - 1)*(x + 1), x^2 + 1, (x^2 + 1)*(x - 1),... (x^2 + 1)*(x + 1), (x^2 + 1)*(x - 1)*(x + 1)]
You also can use a symbolic function to specify the polynomial.
syms f(t) f(t) = t^5; divisors(f,t)
ans(t) = [ 1, t, t^2, t^3, t^4, t^5]
When finding the divisors of a polynomial, divisors does
not return the divisors of the constant factor.
f(t) = 9*t^5; divisors(f,t)
ans(t) = [ 1, t, t^2, t^3, t^4, t^5]
Find the divisors of multivariate polynomial expressions.
Find the divisors of the multivariate polynomial expression.
Suppose that u and v are variables,
and a is a symbolic parameter. Specify the variables
as a symbolic vector.
syms a u v divisors(a*u^2*v^3, [u,v])
ans = [ 1, u, u^2, v, u*v, u^2*v, v^2, u*v^2, u^2*v^2, v^3, u*v^3, u^2*v^3]
Now, suppose that this expression contains only one variable
(for example, v), while a and u are
symbolic parameters. Here, divisors treats the
expression a*u^2 as a constant and ignores it,
returning only the divisors of v^3.
divisors(a*u^2*v^3, v)
ans = [ 1, v, v^2, v^3]
divisors(0) returns 0.
divisors(expr,vars) does not
return the divisors of the constant factor when finding the divisors
of a polynomial.
If you do not specify polynomial variables, divisors returns
as many divisors as it can find, including the divisors of constant
symbolic expressions. For example, divisors(sym(pi)^2*x^2) returns [
1, pi, pi^2, x, pi*x, pi^2*x, x^2, pi*x^2, pi^2*x^2] while divisors(sym(pi)^2*x^2,
x) returns [ 1, x, x^2].
For rational numbers, divisors returns
all divisors of the numerator divided by all divisors of the denominator.
For example, divisors(sym(9/8)) returns [
1, 3, 9, 1/2, 3/2, 9/2, 1/4, 3/4, 9/4, 1/8, 3/8, 9/8].