“Lambert Polynomials” vs Laurent Polynomials
$begingroup$
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.
polynomials
asked Jan 15 at 21:36
Gabriele ScarlattiGabriele Scarlatti
311112
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|
show 4 more comments
$begingroup$
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.
polynomials
asked Jan 15 at 21:36
Gabriele ScarlattiGabriele Scarlatti
311112
$endgroup$
$begingroup$
I don't understand your question.
$endgroup$
– Antonio Vargas
Jan 15 at 21:41
$begingroup$
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.
$endgroup$
– Gabriele Scarlatti
Jan 15 at 21:49
1
$begingroup$
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.
$endgroup$
– Rob Arthan
Jan 15 at 21:51
1
$begingroup$
"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)
$endgroup$
– Jean Marie
Jan 15 at 21:52
1
$begingroup$
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.
$endgroup$
– Steven Stadnicki
Jan 16 at 23:55
|
show 4 more comments
$begingroup$
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.
polynomials
asked Jan 15 at 21:36
Gabriele ScarlattiGabriele Scarlatti
311112
$endgroup$
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.
polynomials
polynomials
asked Jan 15 at 21:36
Gabriele ScarlattiGabriele Scarlatti
311112
asked Jan 15 at 21:36
Gabriele ScarlattiGabriele Scarlatti
311112
edited Jan 15 at 21:48
Gabriele Scarlatti
asked Jan 15 at 21:36
Gabriele ScarlattiGabriele Scarlatti
311112
asked Jan 15 at 21:36
Gabriele ScarlattiGabriele Scarlatti
311112
asked Jan 15 at 21:36
Gabriele ScarlattiGabriele Scarlatti
311112
311112
$begingroup$
I don't understand your question.
$endgroup$
– Antonio Vargas
Jan 15 at 21:41
$begingroup$
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.
$endgroup$
– Gabriele Scarlatti
Jan 15 at 21:49
1
$begingroup$
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.
$endgroup$
– Rob Arthan
Jan 15 at 21:51
1
$begingroup$
"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)
$endgroup$
– Jean Marie
Jan 15 at 21:52
1
$begingroup$
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.
$endgroup$
– Steven Stadnicki
Jan 16 at 23:55
|
show 4 more comments
$begingroup$
I don't understand your question.
$endgroup$
– Antonio Vargas
Jan 15 at 21:41
$begingroup$
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.
$endgroup$
– Gabriele Scarlatti
Jan 15 at 21:49
1
$begingroup$
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.
$endgroup$
– Rob Arthan
Jan 15 at 21:51
1
$begingroup$
"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)
$endgroup$
– Jean Marie
Jan 15 at 21:52
1
$begingroup$
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.
$endgroup$
– Steven Stadnicki
Jan 16 at 23:55
$begingroup$
I don't understand your question.
$endgroup$
– Antonio Vargas
Jan 15 at 21:41
$begingroup$
I don't understand your question.
$endgroup$
– Antonio Vargas
Jan 15 at 21:41
$begingroup$
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.
$endgroup$
– Gabriele Scarlatti
Jan 15 at 21:49
$begingroup$
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.
$endgroup$
– Gabriele Scarlatti
Jan 15 at 21:49
1
1
$begingroup$
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.
$endgroup$
– Rob Arthan
Jan 15 at 21:51
$begingroup$
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.
$endgroup$
– Rob Arthan
Jan 15 at 21:51
1
1
$begingroup$
"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)
$endgroup$
– Jean Marie
Jan 15 at 21:52
$begingroup$
"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)
$endgroup$
– Jean Marie
Jan 15 at 21:52
1
1
$begingroup$
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.
$endgroup$
– Steven Stadnicki
Jan 16 at 23:55
$begingroup$
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.
$endgroup$
– Steven Stadnicki
Jan 16 at 23:55
|
show 4 more comments
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$begingroup$
I don't understand your question.
$endgroup$
– Antonio Vargas
Jan 15 at 21:41
$begingroup$
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.
$endgroup$
– Gabriele Scarlatti
Jan 15 at 21:49
1
$begingroup$
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.
$endgroup$
– Rob Arthan
Jan 15 at 21:51
1
$begingroup$
"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)
$endgroup$
– Jean Marie
Jan 15 at 21:52
1
$begingroup$
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.
$endgroup$
– Steven Stadnicki
Jan 16 at 23:55