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I was reading this post on why polynomials can't have negative exponenents.
The most voted answer seems to bring out a difference between some objects called "Lambert Polynomials" and Laurent Polynomials.
These "Lambert polynomials" are cited as a counterexample to rational functions becasue they miss the property of being closed under division.
As reported in the original post "This property doesn't hold for your 'Lambert polynomials', because there's no finite expression in positive and/or negative powers of x that corresponds to the function $\displaystyle \frac{1}{1+x}$."

Then the author conludes explaining the notion of a Laurent Polynomial.
I didn't get the difference between the two notions as they were laid out in that post, but I'm very interested in the topic.
I hope someone can clarify the difference for me.

Gabriele Scarlatti
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  • I don't understand your question. – Antonio Vargas Jan 15 '19 at 21:41
  • I'm just asking what is the difference between a "Lambert polynomial" and a Laurent Polynomial. Both concepts are mentioned in the post I linked. – Gabriele Scarlatti Jan 15 '19 at 21:49
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    As far as I know, the term "Lambert polynomial" is meaningless. I suspect the MSE answer that is worrying you has a typo or is referring to something in a comment that has been deleted. – Rob Arthan Jan 15 '19 at 21:51
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    "Lambert polynomials" are almost unknown in mathematics under this name, whereas "Laurent polynomials" are essential in the study of (complex) analytical functions (complex function theory that you maybe haven't been presented yet) – Jean Marie Jan 15 '19 at 21:52
  • So Is the statement "This property doesn't hold for your 'Lambert polynomials' ( where property refer to closure under division) referred to Laurent Polynomials? – Gabriele Scarlatti Jan 15 '19 at 21:57
  • To be honest I'm not sure what Steven meant by "Lambert Polynomials". – Antonio Vargas Jan 15 '19 at 22:00
  • If you want to know what "Lambert polynomials" are, then write a comment on that answer and ask for an explanation. Nobody else knows what they are. – Somos Jan 15 '19 at 23:33
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    To be honest I'm also not sure what I meant by 'Lambert polynomials'; that was several years ago. I may look at revising the answer, but the short version is that Laurent Polynomial is the term that you want. – Steven Stadnicki Jan 16 '19 at 23:55

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