`poles`

Poles of a rational expression and their multiplicities.

Category: Mathematics > Equation Solving

Syntax

p = poles(f)

Returns the poles of f in its default variable.

[p, n] = poles(f, x)

Returns the poles in x and the order of each.

Description

A pole is a point where the denominator vanishes and is not cancelled by the numerator. poles cancels common factors first, so (x+1)/(x^2-1) has the single pole 1, not -1. The multiplicity tells how fast the function blows up near the pole.

Input arguments

f: Symbolic rational expression or function.
x: Variable in which the poles are sought.

Output arguments

p: Column vector of the poles, each listed once.
n: Column vector with the multiplicity (order) of each pole.

Example

Poles with multiplicity

syms x
[p, n] = poles(1/((x-1)*(x+2)^2), x)

Output

p = 
-2
 1
n = 
2
1

Notes

In MatLivre poles handles rational functions only, not poles of functions such as tan(x).

poles