# How to simplify a rational function with floating point real coefficients (GCF)

How does one compute the simplified form of a rational function where the coefficients of the polynomial are floating point numbers (real, though I expect using complex numbers would be the same).

Wikipedia says it is possible using SVD, but I'm unsure about how to represent the polynomial so as to do use this.

• What do you mean by simplified form? Do you mean, dividing by common factors? Floating point is not suitable for this. Floating point is for representing approximate numbers, but for computing the greatest common factor, you need exact arithmetic. $p(x)$ might divide $q(x)$ but it won't divide $q(x)+\varepsilon$; and floating point numbers don't let you distinguish $q(x)$ from $q(x)+\varepsilon$. Basically, your question doesn't make sense. If you need to do this, you need to avoid using floating point. Where does Wikipedia say it is possible? Can you edit your question to link to it? – D.W. Sep 22 '15 at 16:23
• Sure, it's got to be approximation. Wikipedia mentions the existence of approximate methods. – Lucas Sep 24 '15 at 22:57
• I encourage you to edit your question to clarify these points. I suggest you clarify (a) what you mean by a simplified form, (b) what kind of approximation you're talking about and what amount of approximation is acceptance and what metric for approximation error you are using, (c) add links to the relevant part of Wikipedia that you refer to. – D.W. Sep 24 '15 at 23:03
• It sounds like you understand what I'm asking perfectly well, I don't know why you're acting like it doesn't make sense. – Lucas Sep 24 '15 at 23:13
• 1. Because it's not just about me; I also care about trying to ensure this question will be useful to others as well. Part of our mission on this site is to create an archive of high-quality questions and answers. For that reason, we want high-quality questions that stand on their own and provide all relevant information. Comments exist to help you identify ways to improve the question, but you shouldn't leave clarifications only in comments; people shouldn't have to read the comments to understand the question, and comments can disappear at any time. – D.W. Sep 24 '15 at 23:29