How to find the multiplicity of a rational function?

Finding the multiplicity of a rational function is not as easy as it looks! One of the biggest challenges is that there are two different ways you can interpret the multiplicity of a rational function. Let’s start with the first one. A rational function $f(x)$ is said to have a zero at a point $a$ if there exists a polynomial $g(x)$ such that $f(a)$ equals $0$, where $g(a)

How to find multiplicity of a rational function in Wolfram?

Use the WolframAlpha online calculator, paste your function in the input and press “Simplify”. The result will contain the multiplicity of the function.

How to find the multiplicity of a rational function in Mathematica?

There are two ways to access the multiplicity of a rational function. One is to use the function Simplify, which converts the function to an elementary one. For example, Simplify[Sin[x]] → Sin will convert the trigonometric function to just its sinusoidal part. You’ll get the same result if you use FullSimplify instead of Simplify.

How to find multiplicity of a rational function?

We will use the concept of isolated singularity for a rational function which is defined as follows. A singular point of a rational function is called isolated if the function is locally analytic at that point. A local analytic function at a singular point is a function which is analytic in a punctured neighbourhood of the point. A point is called an isolated singularity if it is an isolated singularity of the function. We will find the multiplicity of a rational function at a given isolated singularity which is defined

How to find the multiplicity of a rational function in

To find out the multiplicity of a rational function, you need to find the maximum exponent of the denominator involved. To do that, try to find the highest exponent that the function can have without being zero. If the function has a denominator with a zero at a given point, the function will be zero at that point. Once you have found the maximum exponent, add one to it to find the multiplicity.